M   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/sysimg.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

Core.include(Main, "Base.jl")

using .Base

# Set up Main module
using Base.MainInclude # ans, err, and sometimes Out
import Base.MainInclude: eval, include

# Ensure this file is also tracked
pushfirst!(Base._included_files, (@__MODULE__, abspath(@__FILE__)))

# set up depot & load paths to be able to find stdlib packages
Base.init_depot_path()
Base.init_load_path()

if Base.is_primary_base_module
# load some stdlib packages but don't put their names in Main
let
    # Loading here does not call __init__(). This leads to uninitialized RNG
    # state which causes rand(::UnitRange{Int}) to hang. This is a workaround:
    task = current_task()
    task.rngState0 = 0x5156087469e170ab
    task.rngState1 = 0x7431eaead385992c
    task.rngState2 = 0x503e1d32781c2608
    task.rngState3 = 0x3a77f7189200c20b
    task.rngState4 = 0x5502376d099035ae

    # Stdlibs sorted in dependency, then alphabetical, order by contrib/print_sorted_stdlibs.jl
    # Run with the `--exclude-jlls` option to filter out all JLL packages
    stdlibs = [
        # No dependencies
        :ArgTools,
        :Artifacts,
        :Base64,
        :CRC32c,
        :FileWatching,
        :Libdl,
        :Logging,
        :Mmap,
        :NetworkOptions,
        :SHA,
        :Serialization,
        :Sockets,
        :Unicode,

        # 1-depth packages
        :LinearAlgebra,
        :Markdown,
        :Printf,
        :Random,
        :Tar,

        # 2-depth packages
        :Dates,
        :Future,
        :InteractiveUtils,
        :LibGit2,
        :UUIDs,

        # 3-depth packages
        :REPL,
        :TOML,

        # 4-depth packages
        :LibCURL,

        # 5-depth packages
        :Downloads,

        # 6-depth packages
        :Pkg,
    ]
    # PackageCompiler can filter out stdlibs so it can be empty
    maxlen = maximum(textwidth.(string.(stdlibs)); init=0)

    tot_time_stdlib = 0.0
    # use a temp module to avoid leaving the type of this closure in Main
    m = Module()
    GC.@preserve m begin
        print_time = @eval m (mod, t) -> (print(rpad(string(mod) * "  ", $maxlen + 3, "─"));
                                          Base.time_print(stdout, t * 10^9); println())
        print_time(Base, (Base.end_base_include - Base.start_base_include) * 10^(-9))

        Base._track_dependencies[] = true
        tot_time_stdlib = @elapsed for stdlib in stdlibs
            tt = @elapsed Base.require(Base, stdlib)
            print_time(stdlib, tt)
        end
        for dep in Base._require_dependencies
            dep[3] == 0.0 && continue
            push!(Base._included_files, dep[1:2])
        end
        empty!(Base._require_dependencies)
        Base._track_dependencies[] = false

        print_time("Stdlibs total", tot_time_stdlib)
    end

    # Clear global state
    empty!(Core.ARGS)
    empty!(Base.ARGS)
    empty!(LOAD_PATH)
    Base.init_load_path() # want to be able to find external packages in userimg.jl

    ccall(:jl_clear_implicit_imports, Cvoid, (Any,), Main)
    tot_time_userimg = @elapsed (isfile("userimg.jl") && Base.include(Main, "userimg.jl"))

    tot_time_base = (Base.end_base_include - Base.start_base_include) * 10.0^(-9)
    tot_time = tot_time_base + tot_time_stdlib + tot_time_userimg

    println("Sysimage built. Summary:")
    print("Base ──────── "); Base.time_print(stdout, tot_time_base    * 10^9); print(" "); show(IOContext(stdout, :compact=>true), (tot_time_base    / tot_time) * 100); println("%")
    print("Stdlibs ───── "); Base.time_print(stdout, tot_time_stdlib  * 10^9); print(" "); show(IOContext(stdout, :compact=>true), (tot_time_stdlib  / tot_time) * 100); println("%")
    if isfile("userimg.jl")
    print("Userimg ───── "); Base.time_print(stdout, tot_time_userimg * 10^9); print(" "); show(IOContext(stdout, :compact=>true), (tot_time_userimg / tot_time) * 100); println("%")
    end
    print("Total ─────── "); Base.time_print(stdout, tot_time         * 10^9); println();

    empty!(LOAD_PATH)
    empty!(DEPOT_PATH)
end

empty!(Base.TOML_CACHE.d)
Base.TOML.reinit!(Base.TOML_CACHE.p, "")
@eval Sys begin
    BINDIR = ""
    STDLIB = ""
end
end
K   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/Base.jl�K      # This file is a part of Julia. License is MIT: https://julialang.org/license

baremodule Base

using Core.Intrinsics, Core.IR

# to start, we're going to use a very simple definition of `include`
# that doesn't require any function (except what we can get from the `Core` top-module)
const _included_files = Array{Tuple{Module,String},1}(Core.undef, 1)
function include(mod::Module, path::String)
    ccall(:jl_array_grow_end, Cvoid, (Any, UInt), _included_files, UInt(1))
    Core.arrayset(true, _included_files, (mod, ccall(:jl_prepend_cwd, Any, (Any,), path)), arraylen(_included_files))
    Core.println(path)
    ccall(:jl_uv_flush, Nothing, (Ptr{Nothing},), Core.io_pointer(Core.stdout))
    Core.include(mod, path)
end
include(path::String) = include(Base, path)

# from now on, this is now a top-module for resolving syntax
const is_primary_base_module = ccall(:jl_module_parent, Ref{Module}, (Any,), Base) === Core.Main
ccall(:jl_set_istopmod, Cvoid, (Any, Bool), Base, is_primary_base_module)

# The @inline/@noinline macros that can be applied to a function declaration are not available
# until after array.jl, and so we will mark them within a function body instead.
macro inline()   Expr(:meta, :inline)   end
macro noinline() Expr(:meta, :noinline) end

# Try to help prevent users from shooting them-selves in the foot
# with ambiguities by defining a few common and critical operations
# (and these don't need the extra convert code)
getproperty(x::Module, f::Symbol) = (@inline; getglobal(x, f))
getproperty(x::Type, f::Symbol) = (@inline; getfield(x, f))
setproperty!(x::Type, f::Symbol, v) = error("setfield! fields of Types should not be changed")
getproperty(x::Tuple, f::Int) = (@inline; getfield(x, f))
setproperty!(x::Tuple, f::Int, v) = setfield!(x, f, v) # to get a decent error

getproperty(x, f::Symbol) = (@inline; getfield(x, f))
function setproperty!(x, f::Symbol, v)
    ty = fieldtype(typeof(x), f)
    val = v isa ty ? v : convert(ty, v)
    return setfield!(x, f, val)
end

dotgetproperty(x, f) = getproperty(x, f)

getproperty(x::Module, f::Symbol, order::Symbol) = (@inline; getglobal(x, f, order))
function setproperty!(x::Module, f::Symbol, v, order::Symbol=:monotonic)
    @inline
    ty = Core.get_binding_type(x, f)
    val = v isa ty ? v : convert(ty, v)
    return setglobal!(x, f, val, order)
end
getproperty(x::Type, f::Symbol, order::Symbol) = (@inline; getfield(x, f, order))
setproperty!(x::Type, f::Symbol, v, order::Symbol) = error("setfield! fields of Types should not be changed")
getproperty(x::Tuple, f::Int, order::Symbol) = (@inline; getfield(x, f, order))
setproperty!(x::Tuple, f::Int, v, order::Symbol) = setfield!(x, f, v, order) # to get a decent error

getproperty(x, f::Symbol, order::Symbol) = (@inline; getfield(x, f, order))
function setproperty!(x, f::Symbol, v, order::Symbol)
    @inline
    ty = fieldtype(typeof(x), f)
    val = v isa ty ? v : convert(ty, v)
    return setfield!(x, f, val, order)
end

function swapproperty!(x, f::Symbol, v, order::Symbol=:not_atomic)
    @inline
    ty = fieldtype(typeof(x), f)
    val = v isa ty ? v : convert(ty, v)
    return Core.swapfield!(x, f, val, order)
end
function modifyproperty!(x, f::Symbol, op, v, order::Symbol=:not_atomic)
    @inline
    return Core.modifyfield!(x, f, op, v, order)
end
function replaceproperty!(x, f::Symbol, expected, desired, success_order::Symbol=:not_atomic, fail_order::Symbol=success_order)
    @inline
    ty = fieldtype(typeof(x), f)
    val = desired isa ty ? desired : convert(ty, desired)
    return Core.replacefield!(x, f, expected, val, success_order, fail_order)
end

convert(::Type{Any}, Core.@nospecialize x) = x
convert(::Type{T}, x::T) where {T} = x
include("coreio.jl")

eval(x) = Core.eval(Base, x)
eval(m::Module, x) = Core.eval(m, x)

# init core docsystem
import Core: @doc, @__doc__, WrappedException, @int128_str, @uint128_str, @big_str, @cmd
if isdefined(Core, :Compiler)
    import Core.Compiler.CoreDocs
    Core.atdoc!(CoreDocs.docm)
end

include("exports.jl")

if false
    # simple print definitions for debugging. enable these if something
    # goes wrong during bootstrap before printing code is available.
    # otherwise, they just just eventually get (noisily) overwritten later
    global show, print, println
    show(io::IO, x) = Core.show(io, x)
    print(io::IO, a...) = Core.print(io, a...)
    println(io::IO, x...) = Core.println(io, x...)
end

"""
    time_ns() -> UInt64

Get the time in nanoseconds. The time corresponding to 0 is undefined, and wraps every 5.8 years.
"""
time_ns() = ccall(:jl_hrtime, UInt64, ())

start_base_include = time_ns()

# A warning to be interpolated in the docstring of every dangerous mutating function in Base, see PR #50824
const _DOCS_ALIASING_WARNING = """
!!! warning
    Behavior can be unexpected when any mutated argument shares memory with any other argument.
"""

## Load essential files and libraries
include("essentials.jl")
include("ctypes.jl")
include("gcutils.jl")
include("generator.jl")
include("reflection.jl")
include("options.jl")

# define invoke(f, T, args...; kwargs...), without kwargs wrapping
# to forward to invoke
function Core.kwcall(kwargs::NamedTuple, ::typeof(invoke), f, T, args...)
    @inline
    # prepend kwargs and f to the invoked from the user
    T = rewrap_unionall(Tuple{Core.Typeof(kwargs), Core.Typeof(f), (unwrap_unionall(T)::DataType).parameters...}, T)
    return invoke(Core.kwcall, T, kwargs, f, args...)
end
# invoke does not have its own call cache, but kwcall for invoke does
setfield!(typeof(invoke).name.mt, :max_args, 3, :monotonic) # invoke, f, T, args...

# define applicable(f, T, args...; kwargs...), without kwargs wrapping
# to forward to applicable
function Core.kwcall(kwargs::NamedTuple, ::typeof(applicable), @nospecialize(args...))
    @inline
    return applicable(Core.kwcall, kwargs, args...)
end
function Core._hasmethod(@nospecialize(f), @nospecialize(t)) # this function has a special tfunc (TODO: make this a Builtin instead like applicable)
    tt = rewrap_unionall(Tuple{Core.Typeof(f), (unwrap_unionall(t)::DataType).parameters...}, t)
    return Core._hasmethod(tt)
end


# core operations & types
include("promotion.jl")
include("tuple.jl")
include("expr.jl")
include("pair.jl")
include("traits.jl")
include("range.jl")
include("error.jl")

# core numeric operations & types
==(x, y) = x === y
include("bool.jl")
include("number.jl")
include("int.jl")
include("operators.jl")
include("pointer.jl")
include("refvalue.jl")
include("cmem.jl")
include("refpointer.jl")

# now replace the Pair constructor (relevant for NamedTuples) with one that calls our Base.convert
delete_method(which(Pair{Any,Any}, (Any, Any)))
@eval function (P::Type{Pair{A, B}})(@nospecialize(a), @nospecialize(b)) where {A, B}
    @inline
    return $(Expr(:new, :P, :(a isa A ? a : convert(A, a)), :(b isa B ? b : convert(B, b))))
end

# The REPL stdlib hooks into Base using this Ref
const REPL_MODULE_REF = Ref{Module}()

include("checked.jl")
using .Checked
function cld end
function fld end

# Lazy strings
include("strings/lazy.jl")

# array structures
include("indices.jl")
include("array.jl")
include("abstractarray.jl")
include("subarray.jl")
include("views.jl")
include("baseext.jl")

include("ntuple.jl")

include("abstractdict.jl")
include("iddict.jl")
include("idset.jl")

include("iterators.jl")
using .Iterators: zip, enumerate, only
using .Iterators: Flatten, Filter, product  # for generators
using .Iterators: Stateful    # compat (was formerly used in reinterpretarray.jl)

include("namedtuple.jl")

# For OS specific stuff
# We need to strcat things here, before strings are really defined
function strcat(x::String, y::String)
    out = ccall(:jl_alloc_string, Ref{String}, (Csize_t,), Core.sizeof(x) + Core.sizeof(y))
    GC.@preserve x y out begin
        out_ptr = unsafe_convert(Ptr{UInt8}, out)
        unsafe_copyto!(out_ptr, unsafe_convert(Ptr{UInt8}, x), Core.sizeof(x))
        unsafe_copyto!(out_ptr + Core.sizeof(x), unsafe_convert(Ptr{UInt8}, y), Core.sizeof(y))
    end
    return out
end
include(strcat((length(Core.ARGS)>=2 ? Core.ARGS[2] : ""), "build_h.jl"))     # include($BUILDROOT/base/build_h.jl)
include(strcat((length(Core.ARGS)>=2 ? Core.ARGS[2] : ""), "version_git.jl")) # include($BUILDROOT/base/version_git.jl)

# numeric operations
include("hashing.jl")
include("rounding.jl")
using .Rounding
include("div.jl")
include("float.jl")
include("twiceprecision.jl")
include("complex.jl")
include("rational.jl")
include("multinverses.jl")
using .MultiplicativeInverses
include("abstractarraymath.jl")
include("arraymath.jl")
include("slicearray.jl")

# SIMD loops
sizeof(s::String) = Core.sizeof(s)  # needed by gensym as called from simdloop
include("simdloop.jl")
using .SimdLoop

# map-reduce operators
include("reduce.jl")

## core structures
include("reshapedarray.jl")
include("reinterpretarray.jl")
include("bitarray.jl")
include("bitset.jl")

if !isdefined(Core, :Compiler)
    include("docs/core.jl")
    Core.atdoc!(CoreDocs.docm)
end

include("multimedia.jl")
using .Multimedia

# Some type
include("some.jl")

include("dict.jl")
include("abstractset.jl")
include("set.jl")

# Strings
include("char.jl")
include("strings/basic.jl")
include("strings/string.jl")
include("strings/substring.jl")

# Initialize DL_LOAD_PATH as early as possible.  We are defining things here in
# a slightly more verbose fashion than usual, because we're running so early.
const DL_LOAD_PATH = String[]
let os = ccall(:jl_get_UNAME, Any, ())
    if os === :Darwin || os === :Apple
        if Base.DARWIN_FRAMEWORK
            push!(DL_LOAD_PATH, "@loader_path/Frameworks")
        end
        push!(DL_LOAD_PATH, "@loader_path")
    end
end

include("osutils.jl")
include("c.jl")

# Core I/O
include("io.jl")
include("iobuffer.jl")

# strings & printing
include("intfuncs.jl")
include("strings/strings.jl")
include("regex.jl")
include("parse.jl")
include("shell.jl")
include("show.jl")
include("arrayshow.jl")
include("methodshow.jl")

# multidimensional arrays
include("cartesian.jl")
using .Cartesian
include("multidimensional.jl")

include("broadcast.jl")
using .Broadcast
using .Broadcast: broadcasted, broadcasted_kwsyntax, materialize, materialize!,
                  broadcast_preserving_zero_d, andand, oror

# missing values
include("missing.jl")

# version
include("version.jl")

# system & environment
include("sysinfo.jl")
include("libc.jl")
using .Libc: getpid, gethostname, time, memcpy, memset, memmove, memcmp

# These used to be in build_h.jl and are retained for backwards compatibility.
# NOTE: keep in sync with `libblastrampoline_jll.libblastrampoline`.
const libblas_name = "libblastrampoline" * (Sys.iswindows() ? "-5" : "")
const liblapack_name = libblas_name

# Logging
include("logging.jl")
using .CoreLogging

# Concurrency
include("linked_list.jl")
include("condition.jl")
include("threads.jl")
include("lock.jl")
include("channels.jl")
include("partr.jl")
include("task.jl")
include("threads_overloads.jl")
include("weakkeydict.jl")

include("env.jl")

# functions defined in Random
function rand end
function randn end

# I/O
include("libuv.jl")
include("asyncevent.jl")
include("iostream.jl")
include("stream.jl")
include("filesystem.jl")
using .Filesystem
include("cmd.jl")
include("process.jl")
include("ttyhascolor.jl")
include("secretbuffer.jl")

# core math functions
include("floatfuncs.jl")
include("math.jl")
using .Math
const (√)=sqrt
const (∛)=cbrt
const (∜)=fourthroot

# now switch to a simple, race-y TLS, relative include for the rest of Base
delete_method(which(include, (Module, String)))
let SOURCE_PATH = ""
    global function include(mod::Module, path::String)
        prev = SOURCE_PATH::String
        path = normpath(joinpath(dirname(prev), path))
        Core.println(path)
        ccall(:jl_uv_flush, Nothing, (Ptr{Nothing},), Core.io_pointer(Core.stdout))
        push!(_included_files, (mod, abspath(path)))
        SOURCE_PATH = path
        result = Core.include(mod, path)
        SOURCE_PATH = prev
        return result
    end
end

# reduction along dims
include("reducedim.jl")  # macros in this file rely on string.jl
include("accumulate.jl")

include("permuteddimsarray.jl")
using .PermutedDimsArrays

# basic data structures
include("ordering.jl")
using .Order

# Combinatorics
include("sort.jl")
using .Sort

# BinaryPlatforms, used by Artifacts.  Needs `Sort`.
include("binaryplatforms.jl")

# Fast math
include("fastmath.jl")
using .FastMath

function deepcopy_internal end

# enums
include("Enums.jl")
using .Enums

# BigInts
include("gmp.jl")
using .GMP

# float printing: requires BigInt
include("ryu/Ryu.jl")
using .Ryu

# BigFloats
include("mpfr.jl")
using .MPFR

include("combinatorics.jl")

# irrational mathematical constants
include("irrationals.jl")
include("mathconstants.jl")
using .MathConstants: ℯ, π, pi

# metaprogramming
include("meta.jl")

# Stack frames and traces
include("stacktraces.jl")
using .StackTraces

# experimental API's
include("experimental.jl")

# utilities
include("deepcopy.jl")
include("download.jl")
include("summarysize.jl")
include("errorshow.jl")

include("initdefs.jl")

# worker threads
include("threadcall.jl")

# code loading
include("uuid.jl")
include("pkgid.jl")
include("toml_parser.jl")
include("linking.jl")
include("loading.jl")

# misc useful functions & macros
include("timing.jl")
include("util.jl")
include("client.jl")
include("asyncmap.jl")

# deprecated functions
include("deprecated.jl")
#
# Some additional basic documentation
include("docs/basedocs.jl")

# Documentation -- should always be included last in sysimg.
include("docs/Docs.jl")
using .Docs
if isdefined(Core, :Compiler) && is_primary_base_module
    Docs.loaddocs(Core.Compiler.CoreDocs.DOCS)
end

# finally, now make `include` point to the full version
for m in methods(include)
    delete_method(m)
end

# This method is here only to be overwritten during the test suite to test
# various sysimg related invalidation scenarios.
a_method_to_overwrite_in_test() = inferencebarrier(1)

# These functions are duplicated in client.jl/include(::String) for
# nicer stacktraces. Modifications here have to be backported there
include(mod::Module, _path::AbstractString) = _include(identity, mod, _path)
include(mapexpr::Function, mod::Module, _path::AbstractString) = _include(mapexpr, mod, _path)

# External libraries vendored into Base
Core.println("JuliaSyntax/src/JuliaSyntax.jl")
include(@__MODULE__, "JuliaSyntax/src/JuliaSyntax.jl")

end_base_include = time_ns()

const _sysimage_modules = PkgId[]
in_sysimage(pkgid::PkgId) = pkgid in _sysimage_modules

# Precompiles for Revise and other packages
# TODO: move these to contrib/generate_precompile.jl
# The problem is they don't work there
for match = _methods(+, (Int, Int), -1, get_world_counter())
    m = match.method
    delete!(push!(Set{Method}(), m), m)
    copy(Core.Compiler.retrieve_code_info(Core.Compiler.specialize_method(match), typemax(UInt)))

    empty!(Set())
    push!(push!(Set{Union{GlobalRef,Symbol}}(), :two), GlobalRef(Base, :two))
    (setindex!(Dict{String,Base.PkgId}(), Base.PkgId(Base), "file.jl"))["file.jl"]
    (setindex!(Dict{Symbol,Vector{Int}}(), [1], :two))[:two]
    (setindex!(Dict{Base.PkgId,String}(), "file.jl", Base.PkgId(Base)))[Base.PkgId(Base)]
    (setindex!(Dict{Union{GlobalRef,Symbol}, Vector{Int}}(), [1], :two))[:two]
    (setindex!(IdDict{Type, Union{Missing, Vector{Tuple{LineNumberNode, Expr}}}}(), missing, Int))[Int]
    Dict{Symbol, Union{Nothing, Bool, Symbol}}(:one => false)[:one]
    Dict(Base => [:(1+1)])[Base]
    Dict(:one => [1])[:one]
    Dict("abc" => Set())["abc"]
    pushfirst!([], sum)
    get(Base.pkgorigins, Base.PkgId(Base), nothing)
    sort!([1,2,3])
    unique!([1,2,3])
    cumsum([1,2,3])
    append!(Int[], BitSet())
    isempty(BitSet())
    delete!(BitSet([1,2]), 3)
    deleteat!(Int32[1,2,3], [1,3])
    deleteat!(Any[1,2,3], [1,3])
    Core.svec(1, 2) == Core.svec(3, 4)
    any(t->t[1].line > 1, [(LineNumberNode(2,:none), :(1+1))])

    # Code loading uses this
    sortperm(mtime.(readdir(".")), rev=true)
    # JLLWrappers uses these
    Dict{UUID,Set{String}}()[UUID("692b3bcd-3c85-4b1f-b108-f13ce0eb3210")] = Set{String}()
    get!(Set{String}, Dict{UUID,Set{String}}(), UUID("692b3bcd-3c85-4b1f-b108-f13ce0eb3210"))
    eachindex(IndexLinear(), Expr[])
    push!(Expr[], Expr(:return, false))
    vcat(String[], String[])
    k, v = (:hello => nothing)
    precompile(indexed_iterate, (Pair{Symbol, Union{Nothing, String}}, Int))
    precompile(indexed_iterate, (Pair{Symbol, Union{Nothing, String}}, Int, Int))
    # Preferences uses these
    precompile(get_preferences, (UUID,))
    precompile(record_compiletime_preference, (UUID, String))
    get(Dict{String,Any}(), "missing", nothing)
    delete!(Dict{String,Any}(), "missing")
    for (k, v) in Dict{String,Any}()
        println(k)
    end

    break   # only actually need to do this once
end

if is_primary_base_module

# Profiling helper
# triggers printing the report and (optionally) saving a heap snapshot after a SIGINFO/SIGUSR1 profile request
# Needs to be in Base because Profile is no longer loaded on boot
const PROFILE_PRINT_COND = Ref{Base.AsyncCondition}()
function profile_printing_listener()
    profile = nothing
    try
        while true
            wait(PROFILE_PRINT_COND[])
            profile = @something(profile, require(PkgId(UUID("9abbd945-dff8-562f-b5e8-e1ebf5ef1b79"), "Profile")))

            invokelatest(profile.peek_report[])
            if Base.get_bool_env("JULIA_PROFILE_PEEK_HEAP_SNAPSHOT", false) === true
                println(stderr, "Saving heap snapshot...")
                fname = invokelatest(profile.take_heap_snapshot)
                println(stderr, "Heap snapshot saved to `$(fname)`")
            end
        end
    catch ex
        if !isa(ex, InterruptException)
            @error "Profile printing listener crashed" exception=ex,catch_backtrace()
        end
    end
end

function __init__()
    # Base library init
    reinit_stdio()
    Multimedia.reinit_displays() # since Multimedia.displays uses stdout as fallback
    # initialize loading
    init_depot_path()
    init_load_path()
    init_active_project()
    append!(empty!(_sysimage_modules), keys(loaded_modules))
    if haskey(ENV, "JULIA_MAX_NUM_PRECOMPILE_FILES")
        MAX_NUM_PRECOMPILE_FILES[] = parse(Int, ENV["JULIA_MAX_NUM_PRECOMPILE_FILES"])
    end
    # Profiling helper
    @static if !Sys.iswindows()
        # triggering a profile via signals is not implemented on windows
        cond = Base.AsyncCondition()
        Base.uv_unref(cond.handle)
        PROFILE_PRINT_COND[] = cond
        ccall(:jl_set_peek_cond, Cvoid, (Ptr{Cvoid},), PROFILE_PRINT_COND[].handle)
        errormonitor(Threads.@spawn(profile_printing_listener()))
    end
    _require_world_age[] = get_world_counter()
    # Prevent spawned Julia process from getting stuck waiting on Tracy to connect.
    delete!(ENV, "JULIA_WAIT_FOR_TRACY")
    if get_bool_env("JULIA_USE_FLISP_PARSER", false) === false
        JuliaSyntax.enable_in_core!()
    end
    nothing
end

# enable threads support
@eval PCRE PCRE_COMPILE_LOCK = Threads.SpinLock()

end

# Ensure this file is also tracked
@assert !isassigned(_included_files, 1)
_included_files[1] = (parentmodule(Base), abspath(@__FILE__))

end # baremodule Base
M   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/coreio.jl-      # This file is a part of Julia. License is MIT: https://julialang.org/license

print(xs...)   = print(stdout, xs...)
println(xs...) = println(stdout, xs...)
println(io::IO) = print(io, '\n')

function show end
function repr end

struct DevNull <: IO end
const devnull = DevNull()
write(::DevNull, ::UInt8) = 1
unsafe_write(::DevNull, ::Ptr{UInt8}, n::UInt)::Int = n
close(::DevNull) = nothing
wait_close(::DevNull) = wait()
bytesavailable(io::DevNull) = 0

let CoreIO = Union{Core.CoreSTDOUT, Core.CoreSTDERR}
    global write(io::CoreIO, x::UInt8) = Core.write(io, x)
    global unsafe_write(io::CoreIO, x::Ptr{UInt8}, nb::UInt) = Core.unsafe_write(io, x, nb)

    CoreIO = Union{CoreIO, DevNull}
    global read(::CoreIO, ::Type{UInt8}) = throw(EOFError())
    global isopen(::CoreIO) = true
    global isreadable(::CoreIO) = false
    global iswritable(::CoreIO) = true
    global flush(::CoreIO) = nothing
    global eof(::CoreIO) = true
    global wait_readnb(::CoreIO, nb::Int) = nothing
end

stdin::IO = devnull
stdout::IO = Core.stdout
stderr::IO = Core.stderr
N   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/exports.jlx7      # This file is a part of Julia. License is MIT: https://julialang.org/license

export
# Modules
    Meta,
    StackTraces,
    Sys,
    Libc,
    Docs,
    Threads,
    Iterators,
    Broadcast,
    MathConstants,

# Types
    AbstractChannel,
    AbstractIrrational,
    AbstractMatrix,
    AbstractRange,
    AbstractSet,
    AbstractSlices,
    AbstractUnitRange,
    AbstractVector,
    AbstractVecOrMat,
    Array,
    AbstractMatch,
    AbstractPattern,
    AbstractDict,
    BigFloat,
    BigInt,
    BitArray,
    BitMatrix,
    BitVector,
    CartesianIndex,
    CartesianIndices,
    LinearIndices,
    Channel,
    Cmd,
    Colon,
    Complex,
    ComplexF64,
    ComplexF32,
    ComplexF16,
    ComposedFunction,
    ColumnSlices,
    DenseMatrix,
    DenseVecOrMat,
    DenseVector,
    Dict,
    Dims,
    Enum,
    ExponentialBackOff,
    IndexCartesian,
    IndexLinear,
    IndexStyle,
    InsertionSort,
    BitSet,
    IOBuffer,
    IOStream,
    LinRange,
    Irrational,
    LazyString,
    Matrix,
    MergeSort,
    Missing,
    NTuple,
    IdDict,
    OrdinalRange,
    Pair,
    PartialQuickSort,
    PermutedDimsArray,
    QuickSort,
    Rational,
    Regex,
    RegexMatch,
    Returns,
    RoundFromZero,
    RoundDown,
    RoundingMode,
    RoundNearest,
    RoundNearestTiesAway,
    RoundNearestTiesUp,
    RoundToZero,
    RoundUp,
    RowSlices,
    Set,
    Some,
    Slices,
    StepRange,
    StepRangeLen,
    StridedArray,
    StridedMatrix,
    StridedVecOrMat,
    StridedVector,
    SubArray,
    SubString,
    SubstitutionString,
    Timer,
    UnitRange,
    Val,
    VecOrMat,
    Vector,
    VersionNumber,
    WeakKeyDict,

# Ccall types
    Cchar,
    Cdouble,
    Cfloat,
    Cint,
    Cintmax_t,
    Clong,
    Clonglong,
    Cptrdiff_t,
    Cshort,
    Csize_t,
    Cssize_t,
    Cuchar,
    Cuint,
    Cuintmax_t,
    Culong,
    Culonglong,
    Cushort,
    Cwchar_t,
    Cstring,
    Cwstring,

# Exceptions
    CanonicalIndexError,
    CapturedException,
    CompositeException,
    DimensionMismatch,
    EOFError,
    InvalidStateException,
    KeyError,
    MissingException,
    ProcessFailedException,
    TaskFailedException,
    SystemError,
    StringIndexError,

# Global constants and variables
    ARGS,
    C_NULL,
    DEPOT_PATH,
    ENDIAN_BOM,
    ENV,
    LOAD_PATH,
    PROGRAM_FILE,
    stderr,
    stdin,
    stdout,
    VERSION,
    devnull,

# Mathematical constants
    Inf,
    Inf16,
    Inf32,
    Inf64,
    NaN,
    NaN16,
    NaN32,
    NaN64,
    im,
    π, pi,
    ℯ,

# Operators
    !,
    !=,
    ≠,
    !==,
    ≡,
    ≢,
    xor,
    ⊻,
    nand,
    nor,
    ⊼,
    ⊽,
    %,
    ÷,
    &,
    *,
    +,
    -,
    /,
    //,
    <,
    <:,
    <<,
    <=,
    ≤,
    ==,
    >,
    >:,
    >=,
    ≥,
    >>,
    >>>,
    \,
    ^,
    |,
    |>,
    ~,
    :,
    =>,
    ∘,

# scalar math
    @evalpoly,
    evalpoly,
    abs,
    abs2,
    acos,
    acosd,
    acosh,
    acot,
    acotd,
    acoth,
    acsc,
    acscd,
    acsch,
    angle,
    asec,
    asecd,
    asech,
    asin,
    asind,
    asinh,
    atan,
    atand,
    atanh,
    big,
    binomial,
    bitreverse,
    bitrotate,
    bswap,
    cbrt,
    fourthroot,
    ceil,
    cis,
    cispi,
    clamp,
    cld,
    cmp,
    complex,
    conj,
    copysign,
    cos,
    cosc,
    cosd,
    cosh,
    cospi,
    cot,
    cotd,
    coth,
    count_ones,
    count_zeros,
    csc,
    cscd,
    csch,
    deg2rad,
    denominator,
    div,
    divrem,
    eps,
    exp,
    exp10,
    exp2,
    expm1,
    exponent,
    factorial,
    fld,
    fld1,
    fldmod,
    fldmod1,
    flipsign,
    float,
    tryparse,
    floor,
    fma,
    frexp,
    gcd,
    gcdx,
    hypot,
    imag,
    inv,
    invmod,
    isapprox,
    iseven,
    isfinite,
    isinf,
    isinteger,
    isnan,
    isodd,
    ispow2,
    isqrt,
    isreal,
    issubnormal,
    iszero,
    isone,
    lcm,
    ldexp,
    leading_ones,
    leading_zeros,
    log,
    log10,
    log1p,
    log2,
    maxintfloat,
    mod,
    mod1,
    modf,
    mod2pi,
    muladd,
    nextfloat,
    nextpow,
    nextprod,
    numerator,
    one,
    oneunit,
    powermod,
    prevfloat,
    prevpow,
    rad2deg,
    rationalize,
    real,
    floatmax,
    floatmin,
    reim,
    reinterpret,
    rem,
    rem2pi,
    round,
    sec,
    secd,
    sech,
    sign,
    signbit,
    signed,
    significand,
    sin,
    sinc,
    sincos,
    sincosd,
    sincospi,
    sind,
    sinh,
    sinpi,
    sqrt,
    tan,
    tand,
    tanh,
    tanpi,
    trailing_ones,
    trailing_zeros,
    trunc,
    unsafe_trunc,
    typemax,
    typemin,
    unsigned,
    widemul,
    zero,
    √,
    ∛,
    ∜,
    ≈,
    ≉,

# arrays
    axes,
    broadcast!,
    broadcast,
    cat,
    checkbounds,
    checkindex,
    circcopy!,
    circshift,
    circshift!,
    clamp!,
    conj!,
    copy!,
    copyto!,
    diff,
    cumprod,
    cumprod!,
    cumsum,
    cumsum!,
    accumulate,
    accumulate!,
    eachcol,
    eachindex,
    eachrow,
    eachslice,
    extrema!,
    extrema,
    fill!,
    fill,
    first,
    hcat,
    hvcat,
    hvncat,
    indexin,
    argmax,
    argmin,
    invperm,
    invpermute!,
    isassigned,
    isperm,
    issorted,
    last,
    mapslices,
    max,
    maximum!,
    maximum,
    min,
    minimum!,
    minimum,
    minmax,
    ndims,
    ones,
    parent,
    parentindices,
    partialsort,
    partialsort!,
    partialsortperm,
    partialsortperm!,
    permute!,
    permutedims,
    permutedims!,
    prod!,
    prod,
    promote_shape,
    range,
    reshape,
    reverse!,
    reverse,
    rot180,
    rotl90,
    rotr90,
    size,
    selectdim,
    sort!,
    sort,
    sortperm,
    sortperm!,
    sortslices,
    dropdims,
    stack,
    step,
    stride,
    strides,
    sum!,
    sum,
    to_indices,
    vcat,
    vec,
    view,
    zeros,

# search, find, match and related functions
    contains,
    eachmatch,
    endswith,
    findall,
    findfirst,
    findlast,
    findmax,
    findmin,
    findmin!,
    findmax!,
    findnext,
    findprev,
    match,
    occursin,
    searchsorted,
    searchsortedfirst,
    searchsortedlast,
    insorted,
    startswith,

# linear algebra
    var"'", # to enable syntax a' for adjoint
    adjoint,
    transpose,
    kron,
    kron!,

# bitarrays
    falses,
    trues,

# dequeues
    append!,
    insert!,
    pop!,
    popat!,
    prepend!,
    push!,
    resize!,
    popfirst!,
    pushfirst!,

# collections
    all!,
    all,
    allequal,
    allunique,
    any!,
    any,
    firstindex,
    collect,
    count!,
    count,
    delete!,
    deleteat!,
    keepat!,
    eltype,
    empty!,
    empty,
    lastindex,
    filter!,
    filter,
    foldl,
    foldr,
    foreach,
    get,
    get!,
    getindex,
    getkey,
    haskey,
    in,
    intersect!,
    intersect,
    isdisjoint,
    isempty,
    issubset,
    issetequal,
    keys,
    keytype,
    length,
    map!,
    map,
    mapfoldl,
    mapfoldr,
    mapreduce,
    merge!,
    mergewith!,
    merge,
    mergewith,
    pairs,
    reduce,
    setdiff!,
    setdiff,
    setindex!,
    similar,
    sizehint!,
    splice!,
    symdiff!,
    symdiff,
    union!,
    union,
    unique!,
    unique,
    values,
    valtype,
    ∈,
    ∉,
    ∋,
    ∌,
    ⊆,
    ⊈,
    ⊊,
    ⊇,
    ⊉,
    ⊋,
    ∩,
    ∪,

# strings
    ascii,
    bitstring,
    bytes2hex,
    chomp,
    chop,
    chopprefix,
    chopsuffix,
    codepoint,
    codeunit,
    codeunits,
    digits,
    digits!,
    eachsplit,
    escape_string,
    hex2bytes,
    hex2bytes!,
    isascii,
    iscntrl,
    isdigit,
    isletter,
    islowercase,
    isnumeric,
    isprint,
    ispunct,
    isspace,
    isuppercase,
    isxdigit,
    lowercase,
    lowercasefirst,
    isvalid,
    join,
    lpad,
    lstrip,
    ncodeunits,
    ndigits,
    nextind,
    prevind,
    repeat,
    replace,
    replace!,
    repr,
    reverseind,
    rpad,
    rsplit,
    rstrip,
    split,
    string,
    strip,
    textwidth,
    thisind,
    titlecase,
    transcode,
    unescape_string,
    uppercase,
    uppercasefirst,

# text output
    IOContext,
    displaysize,
    dump,
    print,
    println,
    printstyled,
    show,
    showerror,
    sprint,
    summary,

# logging
    @debug,
    @info,
    @warn,
    @error,

# bigfloat & precision
    precision,
    rounding,
    setprecision,
    setrounding,
    get_zero_subnormals,
    set_zero_subnormals,

# iteration
    iterate,
    enumerate,  # re-exported from Iterators
    zip,
    only,

# object identity and equality
    copy,
    deepcopy,
    hash,
    identity,
    isbits,
    isequal,
    ismutable,
    ismutabletype,
    isless,
    isunordered,
    ifelse,
    objectid,
    sizeof,

# tasks and conditions
    Condition,
    current_task,
    islocked,
    istaskdone,
    istaskstarted,
    istaskfailed,
    lock,
    @lock,
    notify,
    ReentrantLock,
    schedule,
    task_local_storage,
    trylock,
    unlock,
    yield,
    yieldto,
    wait,
    timedwait,
    asyncmap,
    asyncmap!,
    errormonitor,

# channels
    take!,
    put!,
    isready,
    fetch,
    bind,

# missing values
    coalesce,
    @coalesce,
    ismissing,
    missing,
    skipmissing,
    @something,
    something,
    isnothing,
    nonmissingtype,

# time
    sleep,
    time,
    time_ns,

# errors
    backtrace,
    catch_backtrace,
    current_exceptions,
    error,
    rethrow,
    retry,
    systemerror,

# stack traces
    stacktrace,

# types
    convert,
    getproperty,
    setproperty!,
    swapproperty!,
    modifyproperty!,
    replaceproperty!,
    fieldoffset,
    fieldname,
    fieldnames,
    fieldcount,
    fieldtypes,
    hasfield,
    propertynames,
    hasproperty,
    isabstracttype,
    isbitstype,
    isprimitivetype,
    isstructtype,
    isconcretetype,
    isdispatchtuple,
    oftype,
    promote,
    promote_rule,
    promote_type,
    instances,
    supertype,
    typeintersect,
    typejoin,
    widen,

# syntax
    esc,
    gensym,
    @kwdef,
    macroexpand,
    @macroexpand1,
    @macroexpand,
    parse,

# help and reflection
    code_typed,
    code_lowered,
    fullname,
    functionloc,
    isconst,
    isinteractive,
    hasmethod,
    methods,
    nameof,
    parentmodule,
    pathof,
    pkgdir,
    pkgversion,
    names,
    which,
    @isdefined,
    @invoke,
    invokelatest,
    @invokelatest,

# loading source files
    __precompile__,
    evalfile,
    include_string,
    include_dependency,

# RTS internals
    GC,
    finalizer,
    finalize,
    precompile,

# misc
    atexit,
    atreplinit,
    exit,
    ntuple,
    splat,

# I/O and events
    close,
    closewrite,
    countlines,
    eachline,
    readeach,
    eof,
    fd,
    fdio,
    flush,
    gethostname,
    htol,
    hton,
    ismarked,
    isopen,
    isreadonly,
    ltoh,
    mark,
    bytesavailable,
    ntoh,
    open,
    peek,
    pipeline,
    Pipe,
    PipeBuffer,
    position,
    RawFD,
    read,
    read!,
    readavailable,
    readbytes!,
    readchomp,
    readdir,
    readline,
    readlines,
    readuntil,
    redirect_stdio,
    redirect_stderr,
    redirect_stdin,
    redirect_stdout,
    reset,
    seek,
    seekend,
    seekstart,
    skip,
    skipchars,
    take!,
    truncate,
    unmark,
    unsafe_read,
    unsafe_write,
    write,

# multimedia I/O
    AbstractDisplay,
    display,
    displayable,
    TextDisplay,
    istextmime,
    MIME,
    @MIME_str,
    popdisplay,
    pushdisplay,
    redisplay,
    showable,
    HTML,
    Text,

# paths and file names
    abspath,
    basename,
    dirname,
    expanduser,
    contractuser,
    homedir,
    isabspath,
    isdirpath,
    joinpath,
    normpath,
    realpath,
    relpath,
    splitdir,
    splitdrive,
    splitext,
    splitpath,

# filesystem operations
    cd,
    chmod,
    chown,
    cp,
    ctime,
    diskstat,
    download,
    filemode,
    filesize,
    gperm,
    hardlink,
    isblockdev,
    ischardev,
    isdir,
    isfifo,
    isfile,
    islink,
    ismount,
    ispath,
    isreadable,
    issetgid,
    issetuid,
    issocket,
    issticky,
    iswritable,
    lstat,
    mkdir,
    mkpath,
    mktemp,
    mktempdir,
    mtime,
    mv,
    operm,
    pwd,
    readlink,
    rm,
    samefile,
    stat,
    symlink,
    tempdir,
    tempname,
    touch,
    uperm,
    walkdir,

# external processes
    detach,
    getpid,
    ignorestatus,
    kill,
    process_exited,
    process_running,
    run,
    setenv,
    addenv,
    setcpuaffinity,
    success,
    withenv,

# C interface
    @cfunction,
    @ccall,
    cglobal,
    disable_sigint,
    pointer,
    pointer_from_objref,
    unsafe_wrap,
    unsafe_string,
    reenable_sigint,
    unsafe_copyto!,
    unsafe_load,
    unsafe_modify!,
    unsafe_pointer_to_objref,
    unsafe_replace!,
    unsafe_store!,
    unsafe_swap!,

# implemented in Random module
    rand,
    randn,

# Macros
    # parser internal
    @__FILE__,
    @__DIR__,
    @__LINE__,
    @__MODULE__,
    @int128_str,
    @uint128_str,
    @big_str,
    @cmd,    # `commands`

    # notation for certain types
    @b_str,    # byte vector
    @r_str,    # regex
    @s_str,    # regex substitution string
    @v_str,    # version number
    @raw_str,  # raw string with no interpolation/unescaping
    @NamedTuple,
    @Kwargs,
    @lazy_str, # lazy string

    # documentation
    @text_str,
    @html_str,
    @doc,

    # output
    @show,

    # profiling
    @time,
    @showtime,
    @timed,
    @timev,
    @elapsed,
    @allocated,
    @allocations,

    # tasks
    @sync,
    @async,
    @task,
    @threadcall,

    # metaprogramming utilities
    @generated,
    @gensym,
    @eval,
    @deprecate,

    # performance annotations
    @boundscheck,
    @inbounds,
    @fastmath,
    @simd,
    @inline,
    @noinline,
    @nospecialize,
    @specialize,
    @polly,

    @assert,
    @atomic,
    @atomicswap,
    @atomicreplace,
    @__dot__,
    @enum,
    @label,
    @goto,
    @view,
    @views,
    @static
Q   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/essentials.jl�~      # This file is a part of Julia. License is MIT: https://julialang.org/license

import Core: CodeInfo, SimpleVector, donotdelete, compilerbarrier, arrayref

const Callable = Union{Function,Type}

const Bottom = Union{}

# Define minimal array interface here to help code used in macros:
length(a::Array) = arraylen(a)

# This is more complicated than it needs to be in order to get Win64 through bootstrap
eval(:(getindex(A::Array, i1::Int) = arrayref($(Expr(:boundscheck)), A, i1)))
eval(:(getindex(A::Array, i1::Int, i2::Int, I::Int...) = (@inline; arrayref($(Expr(:boundscheck)), A, i1, i2, I...))))

==(a::GlobalRef, b::GlobalRef) = a.mod === b.mod && a.name === b.name

"""
    AbstractSet{T}

Supertype for set-like types whose elements are of type `T`.
[`Set`](@ref), [`BitSet`](@ref) and other types are subtypes of this.
"""
abstract type AbstractSet{T} end

"""
    AbstractDict{K, V}

Supertype for dictionary-like types with keys of type `K` and values of type `V`.
[`Dict`](@ref), [`IdDict`](@ref) and other types are subtypes of this.
An `AbstractDict{K, V}` should be an iterator of `Pair{K, V}`.
"""
abstract type AbstractDict{K,V} end

## optional pretty printer:
#const NamedTuplePair{N, V, names, T<:NTuple{N, Any}} = Pairs{Symbol, V, NTuple{N, Symbol}, NamedTuple{names, T}}
#export NamedTuplePair

macro _gc_preserve_begin(arg1)
    Expr(:gc_preserve_begin, esc(arg1))
end

macro _gc_preserve_end(token)
    Expr(:gc_preserve_end, esc(token))
end

"""
    @nospecialize

Applied to a function argument name, hints to the compiler that the method
implementation should not be specialized for different types of that argument,
but instead use the declared type for that argument.
It can be applied to an argument within a formal argument list,
or in the function body.
When applied to an argument, the macro must wrap the entire argument expression, e.g.,
`@nospecialize(x::Real)` or `@nospecialize(i::Integer...)` rather than wrapping just the argument name.
When used in a function body, the macro must occur in statement position and
before any code.

When used without arguments, it applies to all arguments of the parent scope.
In local scope, this means all arguments of the containing function.
In global (top-level) scope, this means all methods subsequently defined in the current module.

Specialization can reset back to the default by using [`@specialize`](@ref).

```julia
function example_function(@nospecialize x)
    ...
end

function example_function(x, @nospecialize(y = 1))
    ...
end

function example_function(x, y, z)
    @nospecialize x y
    ...
end

@nospecialize
f(y) = [x for x in y]
@specialize
```

!!! note
    `@nospecialize` affects code generation but not inference: it limits the diversity
    of the resulting native code, but it does not impose any limitations (beyond the
    standard ones) on type-inference. Use [`Base.@nospecializeinfer`](@ref) together with
    `@nospecialize` to additionally suppress inference.

# Example

```julia
julia> f(A::AbstractArray) = g(A)
f (generic function with 1 method)

julia> @noinline g(@nospecialize(A::AbstractArray)) = A[1]
g (generic function with 1 method)

julia> @code_typed f([1.0])
CodeInfo(
1 ─ %1 = invoke Main.g(_2::AbstractArray)::Float64
└──      return %1
) => Float64
```

Here, the `@nospecialize` annotation results in the equivalent of

```julia
f(A::AbstractArray) = invoke(g, Tuple{AbstractArray}, A)
```

ensuring that only one version of native code will be generated for `g`,
one that is generic for any `AbstractArray`.
However, the specific return type is still inferred for both `g` and `f`,
and this is still used in optimizing the callers of `f` and `g`.
"""
macro nospecialize(vars...)
    if nfields(vars) === 1
        # in argument position, need to fix `@nospecialize x=v` to `@nospecialize (kw x v)`
        var = getfield(vars, 1)
        if isa(var, Expr) && var.head === :(=)
            var.head = :kw
        end
    end
    return Expr(:meta, :nospecialize, vars...)
end

"""
    @specialize

Reset the specialization hint for an argument back to the default.
For details, see [`@nospecialize`](@ref).
"""
macro specialize(vars...)
    if nfields(vars) === 1
        # in argument position, need to fix `@specialize x=v` to `@specialize (kw x v)`
        var = getfield(vars, 1)
        if isa(var, Expr) && var.head === :(=)
            var.head = :kw
        end
    end
    return Expr(:meta, :specialize, vars...)
end

"""
    @isdefined s -> Bool

Tests whether variable `s` is defined in the current scope.

See also [`isdefined`](@ref) for field properties and [`isassigned`](@ref) for
array indexes or [`haskey`](@ref) for other mappings.

# Examples
```jldoctest
julia> @isdefined newvar
false

julia> newvar = 1
1

julia> @isdefined newvar
true

julia> function f()
           println(@isdefined x)
           x = 3
           println(@isdefined x)
       end
f (generic function with 1 method)

julia> f()
false
true
```
"""
macro isdefined(s::Symbol)
    return Expr(:escape, Expr(:isdefined, s))
end

"""
    nameof(m::Module) -> Symbol

Get the name of a `Module` as a [`Symbol`](@ref).

# Examples
```jldoctest
julia> nameof(Base.Broadcast)
:Broadcast
```
"""
nameof(m::Module) = ccall(:jl_module_name, Ref{Symbol}, (Any,), m)

function _is_internal(__module__)
    if ccall(:jl_base_relative_to, Any, (Any,), __module__)::Module === Core.Compiler ||
       nameof(__module__) === :Base
        return true
    end
    return false
end

# can be used in place of `@assume_effects :total` (supposed to be used for bootstrapping)
macro _total_meta()
    return _is_internal(__module__) && Expr(:meta, Expr(:purity,
        #=:consistent=#true,
        #=:effect_free=#true,
        #=:nothrow=#true,
        #=:terminates_globally=#true,
        #=:terminates_locally=#false,
        #=:notaskstate=#true,
        #=:inaccessiblememonly=#true))
end
# can be used in place of `@assume_effects :foldable` (supposed to be used for bootstrapping)
macro _foldable_meta()
    return _is_internal(__module__) && Expr(:meta, Expr(:purity,
        #=:consistent=#true,
        #=:effect_free=#true,
        #=:nothrow=#false,
        #=:terminates_globally=#true,
        #=:terminates_locally=#false,
        #=:notaskstate=#false,
        #=:inaccessiblememonly=#true))
end
# can be used in place of `@assume_effects :nothrow` (supposed to be used for bootstrapping)
macro _nothrow_meta()
    return _is_internal(__module__) && Expr(:meta, Expr(:purity,
        #=:consistent=#false,
        #=:effect_free=#false,
        #=:nothrow=#true,
        #=:terminates_globally=#false,
        #=:terminates_locally=#false,
        #=:notaskstate=#false,
        #=:inaccessiblememonly=#false))
end
# can be used in place of `@assume_effects :terminates_locally` (supposed to be used for bootstrapping)
macro _terminates_locally_meta()
    return _is_internal(__module__) && Expr(:meta, Expr(:purity,
        #=:consistent=#false,
        #=:effect_free=#false,
        #=:nothrow=#false,
        #=:terminates_globally=#false,
        #=:terminates_locally=#true,
        #=:notaskstate=#false,
        #=:inaccessiblememonly=#false))
end
# can be used in place of `@assume_effects :effect_free :terminates_locally` (supposed to be used for bootstrapping)
macro _effect_free_terminates_locally_meta()
    return _is_internal(__module__) && Expr(:meta, Expr(:purity,
        #=:consistent=#false,
        #=:effect_free=#true,
        #=:nothrow=#false,
        #=:terminates_globally=#false,
        #=:terminates_locally=#true,
        #=:notaskstate=#false,
        #=:inaccessiblememonly=#false))
end

# another version of inlining that propagates an inbounds context
macro _propagate_inbounds_meta()
    return Expr(:meta, :inline, :propagate_inbounds)
end

function iterate end

"""
    convert(T, x)

Convert `x` to a value of type `T`.

If `T` is an [`Integer`](@ref) type, an [`InexactError`](@ref) will be raised if `x`
is not representable by `T`, for example if `x` is not integer-valued, or is outside the
range supported by `T`.

# Examples
```jldoctest
julia> convert(Int, 3.0)
3

julia> convert(Int, 3.5)
ERROR: InexactError: Int64(3.5)
Stacktrace:
[...]
```

If `T` is a [`AbstractFloat`](@ref) type,
then it will return the closest value to `x` representable by `T`.

```jldoctest
julia> x = 1/3
0.3333333333333333

julia> convert(Float32, x)
0.33333334f0

julia> convert(BigFloat, x)
0.333333333333333314829616256247390992939472198486328125
```

If `T` is a collection type and `x` a collection, the result of
`convert(T, x)` may alias all or part of `x`.
```jldoctest
julia> x = Int[1, 2, 3];

julia> y = convert(Vector{Int}, x);

julia> y === x
true
```

See also: [`round`](@ref), [`trunc`](@ref), [`oftype`](@ref), [`reinterpret`](@ref).
"""
function convert end

# ensure this is never ambiguous, and therefore fast for lookup
convert(T::Type{Union{}}, x...) = throw(ArgumentError("cannot convert a value to Union{} for assignment"))

convert(::Type{Type}, x::Type) = x # the ssair optimizer is strongly dependent on this method existing to avoid over-specialization
                                   # in the absence of inlining-enabled
                                   # (due to fields typed as `Type`, which is generally a bad idea)
# These end up being called during bootstrap and then would be invalidated if not for the following:
convert(::Type{String}, x::String) = x

"""
    @eval [mod,] ex

Evaluate an expression with values interpolated into it using `eval`.
If two arguments are provided, the first is the module to evaluate in.
"""
macro eval(ex)
    return Expr(:escape, Expr(:call, GlobalRef(Core, :eval), __module__, Expr(:quote, ex)))
end
macro eval(mod, ex)
    return Expr(:escape, Expr(:call, GlobalRef(Core, :eval), mod, Expr(:quote, ex)))
end

# use `@eval` here to directly form `:new` expressions avoid implicit `convert`s
# in order to achieve better effects inference
@eval struct Pairs{K, V, I, A} <: AbstractDict{K, V}
    data::A
    itr::I
    Pairs{K, V, I, A}(data, itr) where {K, V, I, A} = $(Expr(:new, :(Pairs{K, V, I, A}), :(data isa A ? data : convert(A, data)), :(itr isa I ? itr : convert(I, itr))))
    Pairs{K, V}(data::A, itr::I) where {K, V, I, A} = $(Expr(:new, :(Pairs{K, V, I, A}), :data, :itr))
    Pairs{K}(data::A, itr::I) where {K, I, A} = $(Expr(:new, :(Pairs{K, eltype(A), I, A}), :data, :itr))
    Pairs(data::A, itr::I) where  {I, A} = $(Expr(:new, :(Pairs{eltype(I), eltype(A), I, A}), :data, :itr))
end
pairs(::Type{NamedTuple}) = Pairs{Symbol, V, NTuple{N, Symbol}, NamedTuple{names, T}} where {V, N, names, T<:NTuple{N, Any}}

"""
    Iterators.Pairs(values, keys) <: AbstractDict{eltype(keys), eltype(values)}

Transforms an indexable container into a Dictionary-view of the same data.
Modifying the key-space of the underlying data may invalidate this object.
"""
Pairs

argtail(x, rest...) = rest

"""
    tail(x::Tuple)::Tuple

Return a `Tuple` consisting of all but the first component of `x`.

See also: [`front`](@ref Base.front), [`rest`](@ref Base.rest), [`first`](@ref), [`Iterators.peel`](@ref).

# Examples
```jldoctest
julia> Base.tail((1,2,3))
(2, 3)

julia> Base.tail(())
ERROR: ArgumentError: Cannot call tail on an empty tuple.
```
"""
tail(x::Tuple) = argtail(x...)
tail(::Tuple{}) = throw(ArgumentError("Cannot call tail on an empty tuple."))

function unwrap_unionall(@nospecialize(a))
    while isa(a,UnionAll)
        a = a.body
    end
    return a
end

function rewrap_unionall(@nospecialize(t), @nospecialize(u))
    if !isa(u, UnionAll)
        return t
    end
    return UnionAll(u.var, rewrap_unionall(t, u.body))
end

function rewrap_unionall(t::Core.TypeofVararg, @nospecialize(u))
    isdefined(t, :T) || return t
    if !isa(u, UnionAll)
        return t
    end
    T = rewrap_unionall(t.T, u)
    if !isdefined(t, :N) || t.N === u.var
        return Vararg{T}
    end
    return Vararg{T, t.N}
end

# replace TypeVars in all enclosing UnionAlls with fresh TypeVars
function rename_unionall(@nospecialize(u))
    if !isa(u, UnionAll)
        return u
    end
    var = u.var::TypeVar
    body = UnionAll(var, rename_unionall(u.body))
    nv = TypeVar(var.name, var.lb, var.ub)
    return UnionAll(nv, body{nv})
end

# remove concrete constraint on diagonal TypeVar if it comes from troot
function widen_diagonal(@nospecialize(t), troot::UnionAll)
    body = ccall(:jl_widen_diagonal, Any, (Any, Any), t, troot)
end

function isvarargtype(@nospecialize(t))
    return isa(t, Core.TypeofVararg)
end

function isvatuple(@nospecialize(t))
    t = unwrap_unionall(t)
    if isa(t, DataType)
        n = length(t.parameters)
        return n > 0 && isvarargtype(t.parameters[n])
    end
    return false
end

function unwrapva(@nospecialize(t))
    isa(t, Core.TypeofVararg) || return t
    return isdefined(t, :T) ? t.T : Any
end

function unconstrain_vararg_length(va::Core.TypeofVararg)
    # construct a new Vararg type where its length is unconstrained,
    # but its element type still captures any dependencies the input
    # element type may have had on the input length
    return Vararg{unwrapva(va)}
end

typename(a) = error("typename does not apply to this type")
typename(a::DataType) = a.name
function typename(a::Union)
    ta = typename(a.a)
    tb = typename(a.b)
    ta === tb || error("typename does not apply to unions whose components have different typenames")
    return tb
end
typename(union::UnionAll) = typename(union.body)

_tuple_error(T::Type, x) = (@noinline; throw(MethodError(convert, (T, x))))

convert(::Type{T}, x::T) where {T<:Tuple} = x
function convert(::Type{T}, x::NTuple{N,Any}) where {N, T<:Tuple}
    # First see if there could be any conversion of the input type that'd be a subtype of the output.
    # If not, we'll throw an explicit MethodError (otherwise, it might throw a typeassert).
    if typeintersect(NTuple{N,Any}, T) === Union{}
        _tuple_error(T, x)
    end
    function cvt1(n)
        @inline
        Tn = fieldtype(T, n)
        xn = getfield(x, n, #=boundscheck=#false)
        xn isa Tn && return xn
        return convert(Tn, xn)
    end
    return ntuple(cvt1, Val(N))::NTuple{N,Any}
end

# optimizations?
# converting to tuple types of fixed length
#convert(::Type{T}, x::T) where {N, T<:NTuple{N,Any}} = x
#convert(::Type{T}, x::NTuple{N,Any}) where {N, T<:NTuple{N,Any}} =
#    ntuple(n -> convert(fieldtype(T, n), x[n]), Val(N))
#convert(::Type{T}, x::Tuple{Vararg{Any}}) where {N, T<:NTuple{N,Any}} =
#    throw(MethodError(convert, (T, x)))
# converting to tuple types of indefinite length
#convert(::Type{Tuple{Vararg{V}}}, x::Tuple{Vararg{V}}) where {V} = x
#convert(::Type{NTuple{N, V}}, x::NTuple{N, V}) where {N, V} = x
#function convert(T::Type{Tuple{Vararg{V}}}, x::Tuple) where {V}
#    @isdefined(V) || (V = fieldtype(T, 1))
#    return map(t -> convert(V, t), x)
#end
#function convert(T::Type{NTuple{N, V}}, x::NTuple{N, Any}) where {N, V}
#    @isdefined(V) || (V = fieldtype(T, 1))
#    return map(t -> convert(V, t), x)
#end
# short tuples
#convert(::Type{Tuple{}}, ::Tuple{}) = ()
#convert(::Type{Tuple{S}}, x::Tuple{S}) where {S} = x
#convert(::Type{Tuple{S, T}}, x::Tuple{S, T}) where {S, T} = x
#convert(::Type{Tuple{S, T, U}}, x::Tuple{S, T, U}) where {S, T, U} = x
#convert(::Type{Tuple{S}}, x::Tuple{Any}) where {S} = (convert(S, x[1]),)
#convert(::Type{Tuple{S, T}}, x::Tuple{Any, Any}) where {S, T} = (convert(S, x[1]), convert(T, x[2]),)
#convert(::Type{Tuple{S, T, U}}, x::Tuple{Any, Any, Any}) where {S, T, U} = (convert(S, x[1]), convert(T, x[2]), convert(U, x[3]))
#convert(::Type{Tuple{}}, x::Tuple) = _tuple_error(Tuple{}, x)
#convert(::Type{Tuple{S}}, x::Tuple) = _tuple_error(Tuple{S}, x)
#convert(::Type{Tuple{S, T}}, x::Tuple{Any, Any}) where {S, T} =_tuple_error(Tuple{S, T}, x)
#convert(::Type{Tuple{S, T, U}}, x::Tuple{Any, Any, Any}) where {S, T, U} = _tuple_error(Tuple{S, T, U}, x)

"""
    oftype(x, y)

Convert `y` to the type of `x` i.e. `convert(typeof(x), y)`.

# Examples
```jldoctest
julia> x = 4;

julia> y = 3.;

julia> oftype(x, y)
3

julia> oftype(y, x)
4.0
```
"""
oftype(x, y) = y isa typeof(x) ? y : convert(typeof(x), y)::typeof(x)

unsigned(x::Int) = reinterpret(UInt, x)
signed(x::UInt) = reinterpret(Int, x)

"""
    cconvert(T,x)

Convert `x` to a value to be passed to C code as type `T`, typically by calling `convert(T, x)`.

In cases where `x` cannot be safely converted to `T`, unlike [`convert`](@ref), `cconvert` may
return an object of a type different from `T`, which however is suitable for
[`unsafe_convert`](@ref) to handle. The result of this function should be kept valid (for the GC)
until the result of [`unsafe_convert`](@ref) is not needed anymore.
This can be used to allocate memory that will be accessed by the `ccall`.
If multiple objects need to be allocated, a tuple of the objects can be used as return value.

Neither `convert` nor `cconvert` should take a Julia object and turn it into a `Ptr`.
"""
function cconvert end

cconvert(T::Type, x) = x isa T ? x : convert(T, x) # do the conversion eagerly in most cases
cconvert(::Type{Union{}}, x...) = convert(Union{}, x...)
cconvert(::Type{<:Ptr}, x) = x # but defer the conversion to Ptr to unsafe_convert
unsafe_convert(::Type{T}, x::T) where {T} = x # unsafe_convert (like convert) defaults to assuming the convert occurred
unsafe_convert(::Type{T}, x::T) where {T<:Ptr} = x  # to resolve ambiguity with the next method
unsafe_convert(::Type{P}, x::Ptr) where {P<:Ptr} = convert(P, x)

"""
    reinterpret(::Type{Out}, x::In)

Change the type-interpretation of the binary data in the isbits value `x`
to that of the isbits type `Out`.
The size (ignoring padding) of `Out` has to be the same as that of the type of `x`.
For example, `reinterpret(Float32, UInt32(7))` interprets the 4 bytes corresponding to `UInt32(7)` as a
[`Float32`](@ref).

```jldoctest
julia> reinterpret(Float32, UInt32(7))
1.0f-44

julia> reinterpret(NTuple{2, UInt8}, 0x1234)
(0x34, 0x12)

julia> reinterpret(UInt16, (0x34, 0x12))
0x1234

julia> reinterpret(Tuple{UInt16, UInt8}, (0x01, 0x0203))
(0x0301, 0x02)
```

!!! warning

    Use caution if some combinations of bits in `Out` are not considered valid and would
    otherwise be prevented by the type's constructors and methods. Unexpected behavior
    may result without additional validation.
"""
function reinterpret(::Type{Out}, x) where {Out}
    if isprimitivetype(Out) && isprimitivetype(typeof(x))
        return bitcast(Out, x)
    end
    # only available when Base is fully loaded.
    return _reinterpret(Out, x)
end

"""
    sizeof(T::DataType)
    sizeof(obj)

Size, in bytes, of the canonical binary representation of the given `DataType` `T`, if any.
Or the size, in bytes, of object `obj` if it is not a `DataType`.

See also [`Base.summarysize`](@ref).

# Examples
```jldoctest
julia> sizeof(Float32)
4

julia> sizeof(ComplexF64)
16

julia> sizeof(1.0)
8

julia> sizeof(collect(1.0:10.0))
80

julia> struct StructWithPadding
           x::Int64
           flag::Bool
       end

julia> sizeof(StructWithPadding) # not the sum of `sizeof` of fields due to padding
16

julia> sizeof(Int64) + sizeof(Bool) # different from above
9
```

If `DataType` `T` does not have a specific size, an error is thrown.

```jldoctest
julia> sizeof(AbstractArray)
ERROR: Abstract type AbstractArray does not have a definite size.
Stacktrace:
[...]
```
"""
sizeof(x) = Core.sizeof(x)

"""
    ifelse(condition::Bool, x, y)

Return `x` if `condition` is `true`, otherwise return `y`. This differs from `?` or `if` in
that it is an ordinary function, so all the arguments are evaluated first. In some cases,
using `ifelse` instead of an `if` statement can eliminate the branch in generated code and
provide higher performance in tight loops.

# Examples
```jldoctest
julia> ifelse(1 > 2, 1, 2)
2
```
"""
ifelse(condition::Bool, x, y) = Core.ifelse(condition, x, y)

# simple Array{Any} operations needed for bootstrap
@eval setindex!(A::Array{Any}, @nospecialize(x), i::Int) = arrayset($(Expr(:boundscheck)), A, x, i)

"""
    esc(e)

Only valid in the context of an [`Expr`](@ref) returned from a macro. Prevents the macro hygiene
pass from turning embedded variables into gensym variables. See the [Macros](@ref man-macros)
section of the Metaprogramming chapter of the manual for more details and examples.
"""
esc(@nospecialize(e)) = Expr(:escape, e)

"""
    @boundscheck(blk)

Annotates the expression `blk` as a bounds checking block, allowing it to be elided by [`@inbounds`](@ref).

!!! note
    The function in which `@boundscheck` is written must be inlined into
    its caller in order for `@inbounds` to have effect.

# Examples
```jldoctest; filter = r"Stacktrace:(\\n \\[[0-9]+\\].*)*"
julia> @inline function g(A, i)
           @boundscheck checkbounds(A, i)
           return "accessing (\$A)[\$i]"
       end;

julia> f1() = return g(1:2, -1);

julia> f2() = @inbounds return g(1:2, -1);

julia> f1()
ERROR: BoundsError: attempt to access 2-element UnitRange{Int64} at index [-1]
Stacktrace:
 [1] throw_boundserror(::UnitRange{Int64}, ::Tuple{Int64}) at ./abstractarray.jl:455
 [2] checkbounds at ./abstractarray.jl:420 [inlined]
 [3] g at ./none:2 [inlined]
 [4] f1() at ./none:1
 [5] top-level scope

julia> f2()
"accessing (1:2)[-1]"
```

!!! warning

    The `@boundscheck` annotation allows you, as a library writer, to opt-in to
    allowing *other code* to remove your bounds checks with [`@inbounds`](@ref).
    As noted there, the caller must verify—using information they can access—that
    their accesses are valid before using `@inbounds`. For indexing into your
    [`AbstractArray`](@ref) subclasses, for example, this involves checking the
    indices against its [`axes`](@ref). Therefore, `@boundscheck` annotations
    should only be added to a [`getindex`](@ref) or [`setindex!`](@ref)
    implementation after you are certain its behavior is correct.
"""
macro boundscheck(blk)
    return Expr(:if, Expr(:boundscheck), esc(blk))
end

"""
    @inbounds(blk)

Eliminates array bounds checking within expressions.

In the example below the in-range check for referencing
element `i` of array `A` is skipped to improve performance.

```julia
function sum(A::AbstractArray)
    r = zero(eltype(A))
    for i in eachindex(A)
        @inbounds r += A[i]
    end
    return r
end
```

!!! warning

    Using `@inbounds` may return incorrect results/crashes/corruption
    for out-of-bounds indices. The user is responsible for checking it manually.
    Only use `@inbounds` when it is certain from the information locally available
    that all accesses are in bounds. In particular, using `1:length(A)` instead of
    `eachindex(A)` in a function like the one above is _not_ safely inbounds because
    the first index of `A` may not be `1` for all user defined types that subtype
    `AbstractArray`.
"""
macro inbounds(blk)
    return Expr(:block,
        Expr(:inbounds, true),
        Expr(:local, Expr(:(=), :val, esc(blk))),
        Expr(:inbounds, :pop),
        :val)
end

"""
    @label name

Labels a statement with the symbolic label `name`. The label marks the end-point
of an unconditional jump with [`@goto name`](@ref).
"""
macro label(name::Symbol)
    return esc(Expr(:symboliclabel, name))
end

"""
    @goto name

`@goto name` unconditionally jumps to the statement at the location [`@label name`](@ref).

`@label` and `@goto` cannot create jumps to different top-level statements. Attempts cause an
error. To still use `@goto`, enclose the `@label` and `@goto` in a block.
"""
macro goto(name::Symbol)
    return esc(Expr(:symbolicgoto, name))
end

# SimpleVector

getindex(v::SimpleVector, i::Int) = (@_foldable_meta; Core._svec_ref(v, i))
function length(v::SimpleVector)
    @_total_meta
    t = @_gc_preserve_begin v
    len = unsafe_load(Ptr{Int}(pointer_from_objref(v)))
    @_gc_preserve_end t
    return len
end
firstindex(v::SimpleVector) = 1
lastindex(v::SimpleVector) = length(v)
iterate(v::SimpleVector, i=1) = (length(v) < i ? nothing : (v[i], i + 1))
eltype(::Type{SimpleVector}) = Any
keys(v::SimpleVector) = OneTo(length(v))
isempty(v::SimpleVector) = (length(v) == 0)
axes(v::SimpleVector) = (OneTo(length(v)),)
axes(v::SimpleVector, d::Integer) = d <= 1 ? axes(v)[d] : OneTo(1)

function ==(v1::SimpleVector, v2::SimpleVector)
    length(v1)==length(v2) || return false
    for i = 1:length(v1)
        v1[i] == v2[i] || return false
    end
    return true
end

map(f, v::SimpleVector) = Any[ f(v[i]) for i = 1:length(v) ]

getindex(v::SimpleVector, I::AbstractArray) = Core.svec(Any[ v[i] for i in I ]...)

unsafe_convert(::Type{Ptr{Any}}, sv::SimpleVector) = convert(Ptr{Any},pointer_from_objref(sv)) + sizeof(Ptr)

"""
    isassigned(array, i) -> Bool

Test whether the given array has a value associated with index `i`. Return `false`
if the index is out of bounds, or has an undefined reference.

# Examples
```jldoctest
julia> isassigned(rand(3, 3), 5)
true

julia> isassigned(rand(3, 3), 3 * 3 + 1)
false

julia> mutable struct Foo end

julia> v = similar(rand(3), Foo)
3-element Vector{Foo}:
 #undef
 #undef
 #undef

julia> isassigned(v, 1)
false
```
"""
function isassigned end

function isassigned(v::SimpleVector, i::Int)
    @boundscheck 1 <= i <= length(v) || return false
    return true
end


"""
    Colon()

Colons (:) are used to signify indexing entire objects or dimensions at once.

Very few operations are defined on Colons directly; instead they are converted
by [`to_indices`](@ref) to an internal vector type (`Base.Slice`) to represent the
collection of indices they span before being used.

The singleton instance of `Colon` is also a function used to construct ranges;
see [`:`](@ref).
"""
struct Colon <: Function
end
const (:) = Colon()


"""
    Val(c)

Return `Val{c}()`, which contains no run-time data. Types like this can be used to
pass the information between functions through the value `c`, which must be an `isbits`
value or a `Symbol`. The intent of this construct is to be able to dispatch on constants
directly (at compile time) without having to test the value of the constant at run time.

# Examples
```jldoctest
julia> f(::Val{true}) = "Good"
f (generic function with 1 method)

julia> f(::Val{false}) = "Bad"
f (generic function with 2 methods)

julia> f(Val(true))
"Good"
```
"""
struct Val{x}
end

Val(x) = Val{x}()

"""
    invokelatest(f, args...; kwargs...)

Calls `f(args...; kwargs...)`, but guarantees that the most recent method of `f`
will be executed.   This is useful in specialized circumstances,
e.g. long-running event loops or callback functions that may
call obsolete versions of a function `f`.
(The drawback is that `invokelatest` is somewhat slower than calling
`f` directly, and the type of the result cannot be inferred by the compiler.)

!!! compat "Julia 1.9"
    Prior to Julia 1.9, this function was not exported, and was called as `Base.invokelatest`.
"""
function invokelatest(@nospecialize(f), @nospecialize args...; kwargs...)
    kwargs = merge(NamedTuple(), kwargs)
    if isempty(kwargs)
        return Core._call_latest(f, args...)
    end
    return Core._call_latest(Core.kwcall, kwargs, f, args...)
end

"""
    invoke_in_world(world, f, args...; kwargs...)

Call `f(args...; kwargs...)` in a fixed world age, `world`.

This is useful for infrastructure running in the user's Julia session which is
not part of the user's program. For example, things related to the REPL, editor
support libraries, etc. In these cases it can be useful to prevent unwanted
method invalidation and recompilation latency, and to prevent the user from
breaking supporting infrastructure by mistake.

The current world age can be queried using [`Base.get_world_counter()`](@ref)
and stored for later use within the lifetime of the current Julia session, or
when serializing and reloading the system image.

Technically, `invoke_in_world` will prevent any function called by `f` from
being extended by the user during their Julia session. That is, generic
function method tables seen by `f` (and any functions it calls) will be frozen
as they existed at the given `world` age. In a sense, this is like the opposite
of [`invokelatest`](@ref).

!!! note
    It is not valid to store world ages obtained in precompilation for later use.
    This is because precompilation generates a "parallel universe" where the
    world age refers to system state unrelated to the main Julia session.
"""
function invoke_in_world(world::UInt, @nospecialize(f), @nospecialize args...; kwargs...)
    kwargs = Base.merge(NamedTuple(), kwargs)
    if isempty(kwargs)
        return Core._call_in_world(world, f, args...)
    end
    return Core._call_in_world(world, Core.kwcall, kwargs, f, args...)
end

inferencebarrier(@nospecialize(x)) = compilerbarrier(:type, x)

"""
    isempty(collection) -> Bool

Determine whether a collection is empty (has no elements).

!!! warning

    `isempty(itr)` may consume the next element of a stateful iterator `itr`
    unless an appropriate `Base.isdone(itr)` or `isempty` method is defined.
    Use of `isempty` should therefore be avoided when writing generic
    code which should support any iterator type.

# Examples
```jldoctest
julia> isempty([])
true

julia> isempty([1 2 3])
false
```
"""
function isempty(itr)
    d = isdone(itr)
    d !== missing && return d
    iterate(itr) === nothing
end

"""
    values(iterator)

For an iterator or collection that has keys and values, return an iterator
over the values.
This function simply returns its argument by default, since the elements
of a general iterator are normally considered its "values".

# Examples
```jldoctest
julia> d = Dict("a"=>1, "b"=>2);

julia> values(d)
ValueIterator for a Dict{String, Int64} with 2 entries. Values:
  2
  1

julia> values([2])
1-element Vector{Int64}:
 2
```
"""
values(itr) = itr

"""
    Missing

A type with no fields whose singleton instance [`missing`](@ref) is used
to represent missing values.

See also: [`skipmissing`](@ref), [`nonmissingtype`](@ref), [`Nothing`](@ref).
"""
struct Missing end

"""
    missing

The singleton instance of type [`Missing`](@ref) representing a missing value.

See also: [`NaN`](@ref), [`skipmissing`](@ref), [`nonmissingtype`](@ref).
"""
const missing = Missing()

"""
    ismissing(x)

Indicate whether `x` is [`missing`](@ref).

See also: [`skipmissing`](@ref), [`isnothing`](@ref), [`isnan`](@ref).
"""
ismissing(x) = x === missing

function popfirst! end

"""
    peek(stream[, T=UInt8])

Read and return a value of type `T` from a stream without advancing the current position
in the stream.   See also [`startswith(stream, char_or_string)`](@ref).

# Examples

```jldoctest
julia> b = IOBuffer("julia");

julia> peek(b)
0x6a

julia> position(b)
0

julia> peek(b, Char)
'j': ASCII/Unicode U+006A (category Ll: Letter, lowercase)
```

!!! compat "Julia 1.5"
    The method which accepts a type requires Julia 1.5 or later.
"""
function peek end

"""
    @__LINE__ -> Int

Expand to the line number of the location of the macrocall.
Return `0` if the line number could not be determined.
"""
macro __LINE__()
    return __source__.line
end

# Iteration
"""
    isdone(itr, state...) -> Union{Bool, Missing}

This function provides a fast-path hint for iterator completion.
This is useful for mutable iterators that want to avoid having elements
consumed, if they are not going to be exposed to the user (e.g. to check
for done-ness in `isempty` or `zip`). Mutable iterators that want to
opt into this feature should define an isdone method that returns
true/false depending on whether the iterator is done or not. Stateless
iterators need not implement this function. If the result is `missing`,
callers may go ahead and compute `iterate(x, state...) === nothing` to
compute a definite answer.
"""
isdone(itr, state...) = missing

"""
    iterate(iter [, state]) -> Union{Nothing, Tuple{Any, Any}}

Advance the iterator to obtain the next element. If no elements
remain, `nothing` should be returned. Otherwise, a 2-tuple of the
next element and the new iteration state should be returned.
"""
function iterate end

"""
    isiterable(T) -> Bool

Test if type `T` is an iterable collection type or not,
that is whether it has an `iterate` method or not.
"""
function isiterable(T)::Bool
    return hasmethod(iterate, Tuple{T})
end
M   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/ctypes.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

# essential type definitions for interacting with C code
# (platform- or OS-dependent types are defined in c.jl)

"""
    Cuchar

Equivalent to the native `unsigned char` c-type ([`UInt8`](@ref)).
"""
const Cuchar = UInt8


"""
    Cshort

Equivalent to the native `signed short` c-type ([`Int16`](@ref)).
"""
const Cshort = Int16


"""
    Cushort

Equivalent to the native `unsigned short` c-type ([`UInt16`](@ref)).
"""
const Cushort = UInt16


"""
    Cint

Equivalent to the native `signed int` c-type ([`Int32`](@ref)).
"""
const Cint = Int32


"""
    Cuint

Equivalent to the native `unsigned int` c-type ([`UInt32`](@ref)).
"""
const Cuint = UInt32


"""
    Cptrdiff_t

Equivalent to the native `ptrdiff_t` c-type (`Int`).
"""
const Cptrdiff_t = Int


"""
    Csize_t

Equivalent to the native `size_t` c-type (`UInt`).
"""
const Csize_t = UInt


"""
    Cssize_t

Equivalent to the native `ssize_t` c-type.
"""
const Cssize_t = Int


"""
    Cintmax_t

Equivalent to the native `intmax_t` c-type ([`Int64`](@ref)).
"""
const Cintmax_t = Int64


"""
    Cuintmax_t

Equivalent to the native `uintmax_t` c-type ([`UInt64`](@ref)).
"""
const Cuintmax_t = UInt64


"""
    Clonglong

Equivalent to the native `signed long long` c-type ([`Int64`](@ref)).
"""
const Clonglong = Int64


"""
    Culonglong

Equivalent to the native `unsigned long long` c-type ([`UInt64`](@ref)).
"""
const Culonglong = UInt64


"""
    Cfloat

Equivalent to the native `float` c-type ([`Float32`](@ref)).
"""
const Cfloat = Float32


"""
    Cdouble

Equivalent to the native `double` c-type ([`Float64`](@ref)).
"""
const Cdouble = Float64
N   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/gcutils.jlv      # This file is a part of Julia. License is MIT: https://julialang.org/license


"""
    WeakRef(x)

`w = WeakRef(x)` constructs a [weak reference](https://en.wikipedia.org/wiki/Weak_reference)
to the Julia value `x`: although `w` contains a reference to `x`, it does not prevent `x` from being
garbage collected. `w.value` is either `x` (if `x` has not been garbage-collected yet) or `nothing`
(if `x` has been garbage-collected).

```jldoctest
julia> x = "a string"
"a string"

julia> w = WeakRef(x)
WeakRef("a string")

julia> GC.gc()

julia> w           # a reference is maintained via `x`
WeakRef("a string")

julia> x = nothing # clear reference

julia> GC.gc()

julia> w
WeakRef(nothing)
```
"""
WeakRef

==(w::WeakRef, v::WeakRef) = isequal(w.value, v.value)
==(w::WeakRef, v) = isequal(w.value, v)
==(w, v::WeakRef) = isequal(w, v.value)

# Used by `Base.finalizer` to validate mutability of an object being finalized.
function _check_mutable(@nospecialize(o)) @noinline
    if !ismutable(o)
        error("objects of type ", typeof(o), " cannot be finalized")
    end
end

"""
    finalizer(f, x)

Register a function `f(x)` to be called when there are no program-accessible references to
`x`, and return `x`. The type of `x` must be a `mutable struct`, otherwise the function
will throw.

`f` must not cause a task switch, which excludes most I/O operations such as `println`.
Using the `@async` macro (to defer context switching to outside of the finalizer) or
`ccall` to directly invoke IO functions in C may be helpful for debugging purposes.

Note that there is no guaranteed world age for the execution of `f`. It may be
called in the world age in which the finalizer was registered or any later world age.

# Examples
```julia
finalizer(my_mutable_struct) do x
    @async println("Finalizing \$x.")
end

finalizer(my_mutable_struct) do x
    ccall(:jl_safe_printf, Cvoid, (Cstring, Cstring), "Finalizing %s.", repr(x))
end
```

A finalizer may be registered at object construction. In the following example note that
we implicitly rely on the finalizer returning the newly created mutable struct `x`.

# Example
```julia
mutable struct MyMutableStruct
    bar
    function MyMutableStruct(bar)
        x = new(bar)
        f(t) = @async println("Finalizing \$t.")
        finalizer(f, x)
    end
end
```
"""
function finalizer(@nospecialize(f), @nospecialize(o))
    _check_mutable(o)
    Core.finalizer(f, o)
    return o
end

function finalizer(f::Ptr{Cvoid}, o::T) where T @inline
    _check_mutable(o)
    ccall(:jl_gc_add_ptr_finalizer, Cvoid, (Ptr{Cvoid}, Any, Ptr{Cvoid}),
          Core.getptls(), o, f)
    return o
end

"""
    finalize(x)

Immediately run finalizers registered for object `x`.
"""
finalize(@nospecialize(o)) = ccall(:jl_finalize_th, Cvoid, (Any, Any,),
                                   current_task(), o)

"""
    Base.GC

Module with garbage collection utilities.
"""
module GC

# mirrored from julia.h
const GC_AUTO = 0
const GC_FULL = 1
const GC_INCREMENTAL = 2

"""
    GC.gc([full=true])

Perform garbage collection. The argument `full` determines the kind of
collection: A full collection (default) sweeps all objects, which makes the
next GC scan much slower, while an incremental collection may only sweep
so-called young objects.

!!! warning
    Excessive use will likely lead to poor performance.
"""
gc(full::Bool=true) =
    ccall(:jl_gc_collect, Cvoid, (Cint,), full ? GC_FULL : GC_INCREMENTAL)

"""
    GC.enable(on::Bool)

Control whether garbage collection is enabled using a boolean argument (`true` for enabled,
`false` for disabled). Return previous GC state.

!!! warning
    Disabling garbage collection should be used only with caution, as it can cause memory
    use to grow without bound.
"""
enable(on::Bool) = ccall(:jl_gc_enable, Int32, (Int32,), on) != 0

"""
    GC.enable_finalizers(on::Bool)

Increment or decrement the counter that controls the running of finalizers on
the current Task. Finalizers will only run when the counter is at zero. (Set
`true` for enabling, `false` for disabling). They may still run concurrently on
another Task or thread.
"""
enable_finalizers(on::Bool) = on ? enable_finalizers() : disable_finalizers()

function enable_finalizers() @inline
    ccall(:jl_gc_enable_finalizers_internal, Cvoid, ())
    if Core.Intrinsics.atomic_pointerref(cglobal(:jl_gc_have_pending_finalizers, Cint), :monotonic) != 0
        ccall(:jl_gc_run_pending_finalizers, Cvoid, (Ptr{Cvoid},), C_NULL)
    end
end

function disable_finalizers() @inline
    ccall(:jl_gc_disable_finalizers_internal, Cvoid, ())
end

"""
    GC.in_finalizer()::Bool

Returns `true` if the current task is running a finalizer, returns `false`
otherwise. Will also return `false` within a finalizer which was inlined by the
compiler's eager finalization optimization, or if `finalize` is called on the
finalizer directly.

The result of this function may be useful, for example, when a finalizer must
wait on a resource to become available; instead of polling the resource in a
`yield` loop (which is not legal to execute within a task running finalizers),
busy polling or an `@async` continuation could be used instead.
"""
function in_finalizer() @inline
    ccall(:jl_gc_is_in_finalizer, Int8, ()) > 0
end

"""
    GC.@preserve x1 x2 ... xn expr

Mark the objects `x1, x2, ...` as being *in use* during the evaluation of the
expression `expr`. This is only required in unsafe code where `expr`
*implicitly uses* memory or other resources owned by one of the `x`s.

*Implicit use* of `x` covers any indirect use of resources logically owned by
`x` which the compiler cannot see. Some examples:
* Accessing memory of an object directly via a `Ptr`
* Passing a pointer to `x` to `ccall`
* Using resources of `x` which would be cleaned up in the finalizer.

`@preserve` should generally not have any performance impact in typical use
cases where it briefly extends object lifetime. In implementation, `@preserve`
has effects such as protecting dynamically allocated objects from garbage
collection.

# Examples

When loading from a pointer with `unsafe_load`, the underlying object is
implicitly used, for example `x` is implicitly used by `unsafe_load(p)` in the
following:

```jldoctest
julia> let
           x = Ref{Int}(101)
           p = Base.unsafe_convert(Ptr{Int}, x)
           GC.@preserve x unsafe_load(p)
       end
101
```

When passing pointers to `ccall`, the pointed-to object is implicitly used and
should be preserved. (Note however that you should normally just pass `x`
directly to `ccall` which counts as an explicit use.)

```jldoctest
julia> let
           x = "Hello"
           p = pointer(x)
           Int(GC.@preserve x @ccall strlen(p::Cstring)::Csize_t)
           # Preferred alternative
           Int(@ccall strlen(x::Cstring)::Csize_t)
       end
5
```
"""
macro preserve(args...)
    syms = args[1:end-1]
    for x in syms
        isa(x, Symbol) || error("Preserved variable must be a symbol")
    end
    esc(Expr(:gc_preserve, args[end], syms...))
end

"""
    GC.safepoint()

Inserts a point in the program where garbage collection may run.
This can be useful in rare cases in multi-threaded programs where some threads
are allocating memory (and hence may need to run GC) but other threads are doing
only simple operations (no allocation, task switches, or I/O).
Calling this function periodically in non-allocating threads allows garbage
collection to run.

!!! compat "Julia 1.4"
    This function is available as of Julia 1.4.
"""
safepoint() = ccall(:jl_gc_safepoint, Cvoid, ())

"""
    GC.enable_logging(on::Bool)

When turned on, print statistics about each GC to stderr.
"""
function enable_logging(on::Bool=true)
    ccall(:jl_enable_gc_logging, Cvoid, (Cint,), on)
end

end # module GC
P   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/generator.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
    Generator(f, iter)

Given a function `f` and an iterator `iter`, construct an iterator that yields
the values of `f` applied to the elements of `iter`.
The syntax for constructing an instance of this type is `f(x) for x in iter [if cond(x)::Bool] `.
The `[if cond(x)::Bool]` expression is optional and acts as a "guard", effectively
filtering out values where the condition is false.

```jldoctest
julia> g = (abs2(x) for x in 1:5 if x != 3);

julia> for x in g
           println(x)
       end
1
4
16
25

julia> collect(g)
4-element Vector{Int64}:
  1
  4
 16
 25
```
"""
struct Generator{I,F}
    f::F
    iter::I
end

Generator(f, I1, I2, Is...) = Generator(a->f(a...), zip(I1, I2, Is...))

Generator(::Type{T}, iter::I) where {T,I} = Generator{I,Type{T}}(T, iter)

Generator(::Type{T}, I1, I2, Is...) where {T} = Generator(a->T(a...), zip(I1, I2, Is...))

function iterate(g::Generator, s...)
    @inline
    y = iterate(g.iter, s...)
    y === nothing && return nothing
    y = y::Tuple{Any, Any} # try to give inference some idea of what to expect about the behavior of the next line
    return (g.f(y[1]), y[2])
end

length(g::Generator) = length(g.iter)
size(g::Generator) = size(g.iter)
axes(g::Generator) = axes(g.iter)
ndims(g::Generator) = ndims(g.iter)
keys(g::Generator) = keys(g.iter)
last(g::Generator) = g.f(last(g.iter))
isempty(g::Generator) = isempty(g.iter)
isdone(g::Generator, state...) = isdone(g.iter, state...)

## iterator traits

abstract type IteratorSize end
struct SizeUnknown <: IteratorSize end
struct HasLength <: IteratorSize end
struct HasShape{N} <: IteratorSize end
struct IsInfinite <: IteratorSize end

"""
    IteratorSize(itertype::Type) -> IteratorSize

Given the type of an iterator, return one of the following values:

* `SizeUnknown()` if the length (number of elements) cannot be determined in advance.
* `HasLength()` if there is a fixed, finite length.
* `HasShape{N}()` if there is a known length plus a notion of multidimensional shape (as for an array).
   In this case `N` should give the number of dimensions, and the [`axes`](@ref) function is valid
   for the iterator.
* `IsInfinite()` if the iterator yields values forever.

The default value (for iterators that do not define this function) is `HasLength()`.
This means that most iterators are assumed to implement [`length`](@ref).

This trait is generally used to select between algorithms that pre-allocate space for their
result, and algorithms that resize their result incrementally.

```jldoctest
julia> Base.IteratorSize(1:5)
Base.HasShape{1}()

julia> Base.IteratorSize((2,3))
Base.HasLength()
```
"""
IteratorSize(x) = IteratorSize(typeof(x))
IteratorSize(::Type) = HasLength()  # HasLength is the default
IteratorSize(::Type{Union{}}, slurp...) = throw(ArgumentError("Union{} does not have elements"))
IteratorSize(::Type{Any}) = SizeUnknown()

IteratorSize(::Type{<:Tuple}) = HasLength()
IteratorSize(::Type{<:AbstractArray{<:Any,N}})  where {N} = HasShape{N}()
IteratorSize(::Type{Generator{I,F}}) where {I,F} = IteratorSize(I)

haslength(iter) = IteratorSize(iter) isa Union{HasShape, HasLength}

abstract type IteratorEltype end
struct EltypeUnknown <: IteratorEltype end
struct HasEltype <: IteratorEltype end

"""
    IteratorEltype(itertype::Type) -> IteratorEltype

Given the type of an iterator, return one of the following values:

* `EltypeUnknown()` if the type of elements yielded by the iterator is not known in advance.
* `HasEltype()` if the element type is known, and [`eltype`](@ref) would return a meaningful value.

`HasEltype()` is the default, since iterators are assumed to implement [`eltype`](@ref).

This trait is generally used to select between algorithms that pre-allocate a specific
type of result, and algorithms that pick a result type based on the types of yielded
values.

```jldoctest
julia> Base.IteratorEltype(1:5)
Base.HasEltype()
```
"""
IteratorEltype(x) = IteratorEltype(typeof(x))
IteratorEltype(::Type) = HasEltype()  # HasEltype is the default
IteratorEltype(::Type{Union{}}, slurp...) = throw(ArgumentError("Union{} does not have elements"))
IteratorEltype(::Type{Any}) = EltypeUnknown()

IteratorEltype(::Type{Generator{I,T}}) where {I,T} = EltypeUnknown()
Q   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/reflection.jl�"     # This file is a part of Julia. License is MIT: https://julialang.org/license

# name and module reflection

"""
    parentmodule(m::Module) -> Module

Get a module's enclosing `Module`. `Main` is its own parent.

See also: [`names`](@ref), [`nameof`](@ref), [`fullname`](@ref), [`@__MODULE__`](@ref).

# Examples
```jldoctest
julia> parentmodule(Main)
Main

julia> parentmodule(Base.Broadcast)
Base
```
"""
parentmodule(m::Module) = ccall(:jl_module_parent, Ref{Module}, (Any,), m)

"""
    moduleroot(m::Module) -> Module

Find the root module of a given module. This is the first module in the chain of
parent modules of `m` which is either a registered root module or which is its
own parent module.
"""
function moduleroot(m::Module)
    while true
        is_root_module(m) && return m
        p = parentmodule(m)
        p === m && return m
        m = p
    end
end

"""
    @__MODULE__ -> Module

Get the `Module` of the toplevel eval,
which is the `Module` code is currently being read from.
"""
macro __MODULE__()
    return __module__
end

"""
    fullname(m::Module)

Get the fully-qualified name of a module as a tuple of symbols. For example,

# Examples
```jldoctest
julia> fullname(Base.Iterators)
(:Base, :Iterators)

julia> fullname(Main)
(:Main,)
```
"""
function fullname(m::Module)
    mn = nameof(m)
    if m === Main || m === Base || m === Core
        return (mn,)
    end
    mp = parentmodule(m)
    if mp === m
        return (mn,)
    end
    return (fullname(mp)..., mn)
end

"""
    names(x::Module; all::Bool = false, imported::Bool = false)

Get an array of the names exported by a `Module`, excluding deprecated names.
If `all` is true, then the list also includes non-exported names defined in the module,
deprecated names, and compiler-generated names.
If `imported` is true, then names explicitly imported from other modules
are also included.

As a special case, all names defined in `Main` are considered \"exported\",
since it is not idiomatic to explicitly export names from `Main`.

See also: [`@locals`](@ref Base.@locals), [`@__MODULE__`](@ref).
"""
names(m::Module; all::Bool = false, imported::Bool = false) =
    sort!(unsorted_names(m; all, imported))
unsorted_names(m::Module; all::Bool = false, imported::Bool = false) =
    ccall(:jl_module_names, Array{Symbol,1}, (Any, Cint, Cint), m, all, imported)

isexported(m::Module, s::Symbol) = ccall(:jl_module_exports_p, Cint, (Any, Any), m, s) != 0
isdeprecated(m::Module, s::Symbol) = ccall(:jl_is_binding_deprecated, Cint, (Any, Any), m, s) != 0
isbindingresolved(m::Module, var::Symbol) = ccall(:jl_binding_resolved_p, Cint, (Any, Any), m, var) != 0

function binding_module(m::Module, s::Symbol)
    p = ccall(:jl_get_module_of_binding, Ptr{Cvoid}, (Any, Any), m, s)
    p == C_NULL && return m
    return unsafe_pointer_to_objref(p)::Module
end

const _NAMEDTUPLE_NAME = NamedTuple.body.body.name

function _fieldnames(@nospecialize t)
    if t.name === _NAMEDTUPLE_NAME
        if t.parameters[1] isa Tuple
            return t.parameters[1]
        else
            throw(ArgumentError("type does not have definite field names"))
        end
    end
    return t.name.names
end

"""
    fieldname(x::DataType, i::Integer)

Get the name of field `i` of a `DataType`.

# Examples
```jldoctest
julia> fieldname(Rational, 1)
:num

julia> fieldname(Rational, 2)
:den
```
"""
function fieldname(t::DataType, i::Integer)
    throw_not_def_field() = throw(ArgumentError("type does not have definite field names"))
    function throw_field_access(t, i, n_fields)
        field_label = n_fields == 1 ? "field" : "fields"
        throw(ArgumentError("Cannot access field $i since type $t only has $n_fields $field_label."))
    end
    throw_need_pos_int(i) = throw(ArgumentError("Field numbers must be positive integers. $i is invalid."))

    isabstracttype(t) && throw_not_def_field()
    names = _fieldnames(t)
    n_fields = length(names)::Int
    i > n_fields && throw_field_access(t, i, n_fields)
    i < 1 && throw_need_pos_int(i)
    return @inbounds names[i]::Symbol
end

fieldname(t::UnionAll, i::Integer) = fieldname(unwrap_unionall(t), i)
fieldname(t::Type{<:Tuple}, i::Integer) =
    i < 1 || i > fieldcount(t) ? throw(BoundsError(t, i)) : Int(i)

"""
    fieldnames(x::DataType)

Get a tuple with the names of the fields of a `DataType`.

See also [`propertynames`](@ref), [`hasfield`](@ref).

# Examples
```jldoctest
julia> fieldnames(Rational)
(:num, :den)

julia> fieldnames(typeof(1+im))
(:re, :im)
```
"""
fieldnames(t::DataType) = (fieldcount(t); # error check to make sure type is specific enough
                           (_fieldnames(t)...,))::Tuple{Vararg{Symbol}}
fieldnames(t::UnionAll) = fieldnames(unwrap_unionall(t))
fieldnames(::Core.TypeofBottom) =
    throw(ArgumentError("The empty type does not have field names since it does not have instances."))
fieldnames(t::Type{<:Tuple}) = ntuple(identity, fieldcount(t))

"""
    hasfield(T::Type, name::Symbol)

Return a boolean indicating whether `T` has `name` as one of its own fields.

See also [`fieldnames`](@ref), [`fieldcount`](@ref), [`hasproperty`](@ref).

!!! compat "Julia 1.2"
     This function requires at least Julia 1.2.

# Examples
```jldoctest
julia> struct Foo
            bar::Int
       end

julia> hasfield(Foo, :bar)
true

julia> hasfield(Foo, :x)
false
```
"""
hasfield(T::Type, name::Symbol) = fieldindex(T, name, false) > 0

"""
    nameof(t::DataType) -> Symbol

Get the name of a (potentially `UnionAll`-wrapped) `DataType` (without its parent module)
as a symbol.

# Examples
```jldoctest
julia> module Foo
           struct S{T}
           end
       end
Foo

julia> nameof(Foo.S{T} where T)
:S
```
"""
nameof(t::DataType) = t.name.name
nameof(t::UnionAll) = nameof(unwrap_unionall(t))::Symbol

"""
    parentmodule(t::DataType) -> Module

Determine the module containing the definition of a (potentially `UnionAll`-wrapped) `DataType`.

# Examples
```jldoctest
julia> module Foo
           struct Int end
       end
Foo

julia> parentmodule(Int)
Core

julia> parentmodule(Foo.Int)
Foo
```
"""
parentmodule(t::DataType) = t.name.module
parentmodule(t::UnionAll) = parentmodule(unwrap_unionall(t))

"""
    isconst(m::Module, s::Symbol) -> Bool

Determine whether a global is declared `const` in a given module `m`.
"""
isconst(m::Module, s::Symbol) =
    ccall(:jl_is_const, Cint, (Any, Any), m, s) != 0

function isconst(g::GlobalRef)
    return ccall(:jl_globalref_is_const, Cint, (Any,), g) != 0
end

"""
    isconst(t::DataType, s::Union{Int,Symbol}) -> Bool

Determine whether a field `s` is declared `const` in a given type `t`.
"""
function isconst(@nospecialize(t::Type), s::Symbol)
    t = unwrap_unionall(t)
    isa(t, DataType) || return false
    return isconst(t, fieldindex(t, s, false))
end
function isconst(@nospecialize(t::Type), s::Int)
    t = unwrap_unionall(t)
    # TODO: what to do for `Union`?
    isa(t, DataType) || return false # uncertain
    ismutabletype(t) || return true # immutable structs are always const
    1 <= s <= length(t.name.names) || return true # OOB reads are "const" since they always throw
    constfields = t.name.constfields
    constfields === C_NULL && return false
    s -= 1
    return unsafe_load(Ptr{UInt32}(constfields), 1 + s÷32) & (1 << (s%32)) != 0
end

"""
    isfieldatomic(t::DataType, s::Union{Int,Symbol}) -> Bool

Determine whether a field `s` is declared `@atomic` in a given type `t`.
"""
function isfieldatomic(@nospecialize(t::Type), s::Symbol)
    t = unwrap_unionall(t)
    isa(t, DataType) || return false
    return isfieldatomic(t, fieldindex(t, s, false))
end
function isfieldatomic(@nospecialize(t::Type), s::Int)
    t = unwrap_unionall(t)
    # TODO: what to do for `Union`?
    isa(t, DataType) || return false # uncertain
    ismutabletype(t) || return false # immutable structs are never atomic
    1 <= s <= length(t.name.names) || return false # OOB reads are not atomic (they always throw)
    atomicfields = t.name.atomicfields
    atomicfields === C_NULL && return false
    s -= 1
    return unsafe_load(Ptr{UInt32}(atomicfields), 1 + s÷32) & (1 << (s%32)) != 0
end

"""
    @locals()

Construct a dictionary of the names (as symbols) and values of all local
variables defined as of the call site.

!!! compat "Julia 1.1"
    This macro requires at least Julia 1.1.

# Examples
```jldoctest
julia> let x = 1, y = 2
           Base.@locals
       end
Dict{Symbol, Any} with 2 entries:
  :y => 2
  :x => 1

julia> function f(x)
           local y
           show(Base.@locals); println()
           for i = 1:1
               show(Base.@locals); println()
           end
           y = 2
           show(Base.@locals); println()
           nothing
       end;

julia> f(42)
Dict{Symbol, Any}(:x => 42)
Dict{Symbol, Any}(:i => 1, :x => 42)
Dict{Symbol, Any}(:y => 2, :x => 42)
```
"""
macro locals()
    return Expr(:locals)
end

# concrete datatype predicates

datatype_fieldtypes(x::DataType) = ccall(:jl_get_fieldtypes, Core.SimpleVector, (Any,), x)

struct DataTypeLayout
    size::UInt32
    nfields::UInt32
    npointers::UInt32
    firstptr::Int32
    alignment::UInt16
    flags::UInt16
    # haspadding : 1;
    # fielddesc_type : 2;
end

"""
    Base.datatype_alignment(dt::DataType) -> Int

Memory allocation minimum alignment for instances of this type.
Can be called on any `isconcretetype`.
"""
function datatype_alignment(dt::DataType)
    @_foldable_meta
    dt.layout == C_NULL && throw(UndefRefError())
    alignment = unsafe_load(convert(Ptr{DataTypeLayout}, dt.layout)).alignment
    return Int(alignment)
end

function uniontype_layout(@nospecialize T::Type)
    sz = RefValue{Csize_t}(0)
    algn = RefValue{Csize_t}(0)
    isinline = ccall(:jl_islayout_inline, Cint, (Any, Ptr{Csize_t}, Ptr{Csize_t}), T, sz, algn) != 0
    (isinline, Int(sz[]), Int(algn[]))
end

LLT_ALIGN(x, sz) = (x + sz - 1) & -sz

# amount of total space taken by T when stored in a container
function aligned_sizeof(@nospecialize T::Type)
    @_foldable_meta
    if isa(T, Union)
        if allocatedinline(T)
            # NOTE this check is equivalent to `isbitsunion(T)`, we can improve type
            # inference in the second branch with the outer `isa(T, Union)` check
            _, sz, al = uniontype_layout(T)
            return LLT_ALIGN(sz, al)
        end
    elseif allocatedinline(T)
        al = datatype_alignment(T)
        return LLT_ALIGN(Core.sizeof(T), al)
    end
    return Core.sizeof(Ptr{Cvoid})
end

gc_alignment(sz::Integer) = Int(ccall(:jl_alignment, Cint, (Csize_t,), sz))
gc_alignment(T::Type) = gc_alignment(Core.sizeof(T))

"""
    Base.datatype_haspadding(dt::DataType) -> Bool

Return whether the fields of instances of this type are packed in memory,
with no intervening padding bytes.
Can be called on any `isconcretetype`.
"""
function datatype_haspadding(dt::DataType)
    @_foldable_meta
    dt.layout == C_NULL && throw(UndefRefError())
    flags = unsafe_load(convert(Ptr{DataTypeLayout}, dt.layout)).flags
    return flags & 1 == 1
end

"""
    Base.datatype_nfields(dt::DataType) -> Bool

Return the number of fields known to this datatype's layout.
Can be called on any `isconcretetype`.
"""
function datatype_nfields(dt::DataType)
    @_foldable_meta
    dt.layout == C_NULL && throw(UndefRefError())
    return unsafe_load(convert(Ptr{DataTypeLayout}, dt.layout)).nfields
end

"""
    Base.datatype_pointerfree(dt::DataType) -> Bool

Return whether instances of this type can contain references to gc-managed memory.
Can be called on any `isconcretetype`.
"""
function datatype_pointerfree(dt::DataType)
    @_foldable_meta
    dt.layout == C_NULL && throw(UndefRefError())
    npointers = unsafe_load(convert(Ptr{DataTypeLayout}, dt.layout)).npointers
    return npointers == 0
end

"""
    Base.datatype_fielddesc_type(dt::DataType) -> Int

Return the size in bytes of each field-description entry in the layout array,
located at `(dt.layout + sizeof(DataTypeLayout))`.
Can be called on any `isconcretetype`.

See also [`fieldoffset`](@ref).
"""
function datatype_fielddesc_type(dt::DataType)
    @_foldable_meta
    dt.layout == C_NULL && throw(UndefRefError())
    flags = unsafe_load(convert(Ptr{DataTypeLayout}, dt.layout)).flags
    return (flags >> 1) & 3
end

# For type stability, we only expose a single struct that describes everything
struct FieldDesc
    isforeign::Bool
    isptr::Bool
    size::UInt32
    offset::UInt32
end

struct FieldDescStorage{T}
    ptrsize::T
    offset::T
end
FieldDesc(fd::FieldDescStorage{T}) where {T} =
    FieldDesc(false, fd.ptrsize & 1 != 0,
              fd.ptrsize >> 1, fd.offset)

struct DataTypeFieldDesc
    dt::DataType
    function DataTypeFieldDesc(dt::DataType)
        dt.layout == C_NULL && throw(UndefRefError())
        new(dt)
    end
end

function getindex(dtfd::DataTypeFieldDesc, i::Int)
    layout_ptr = convert(Ptr{DataTypeLayout}, dtfd.dt.layout)
    fd_ptr = layout_ptr + sizeof(DataTypeLayout)
    layout = unsafe_load(layout_ptr)
    fielddesc_type = (layout.flags >> 1) & 3
    nfields = layout.nfields
    @boundscheck ((1 <= i <= nfields) || throw(BoundsError(dtfd, i)))
    if fielddesc_type == 0
        return FieldDesc(unsafe_load(Ptr{FieldDescStorage{UInt8}}(fd_ptr), i))
    elseif fielddesc_type == 1
        return FieldDesc(unsafe_load(Ptr{FieldDescStorage{UInt16}}(fd_ptr), i))
    elseif fielddesc_type == 2
        return FieldDesc(unsafe_load(Ptr{FieldDescStorage{UInt32}}(fd_ptr), i))
    else
        # fielddesc_type == 3
        return FieldDesc(true, true, 0, 0)
    end
end

"""
    ismutable(v) -> Bool

Return `true` if and only if value `v` is mutable.  See [Mutable Composite Types](@ref)
for a discussion of immutability. Note that this function works on values, so if you
give it a `DataType`, it will tell you that a value of the type is mutable.

!!! note
    For technical reasons, `ismutable` returns `true` for values of certain special types
    (for example `String` and `Symbol`) even though they cannot be mutated in a permissible way.

See also [`isbits`](@ref), [`isstructtype`](@ref).

# Examples
```jldoctest
julia> ismutable(1)
false

julia> ismutable([1,2])
true
```

!!! compat "Julia 1.5"
    This function requires at least Julia 1.5.
"""
ismutable(@nospecialize(x)) = (@_total_meta; (typeof(x).name::Core.TypeName).flags & 0x2 == 0x2)
# The type assertion above is required to fix some invalidations.
# See also https://github.com/JuliaLang/julia/issues/52134

"""
    ismutabletype(T) -> Bool

Determine whether type `T` was declared as a mutable type
(i.e. using `mutable struct` keyword).

!!! compat "Julia 1.7"
    This function requires at least Julia 1.7.
"""
function ismutabletype(@nospecialize t)
    @_total_meta
    t = unwrap_unionall(t)
    # TODO: what to do for `Union`?
    return isa(t, DataType) && t.name.flags & 0x2 == 0x2
end

"""
    isstructtype(T) -> Bool

Determine whether type `T` was declared as a struct type
(i.e. using the `struct` or `mutable struct` keyword).
"""
function isstructtype(@nospecialize t)
    @_total_meta
    t = unwrap_unionall(t)
    # TODO: what to do for `Union`?
    isa(t, DataType) || return false
    return !isprimitivetype(t) && !isabstracttype(t)
end

"""
    isprimitivetype(T) -> Bool

Determine whether type `T` was declared as a primitive type
(i.e. using the `primitive type` syntax).
"""
function isprimitivetype(@nospecialize t)
    @_total_meta
    t = unwrap_unionall(t)
    # TODO: what to do for `Union`?
    isa(t, DataType) || return false
    return (t.flags & 0x0080) == 0x0080
end

"""
    isbitstype(T)

Return `true` if type `T` is a "plain data" type,
meaning it is immutable and contains no references to other values,
only `primitive` types and other `isbitstype` types.
Typical examples are numeric types such as [`UInt8`](@ref),
[`Float64`](@ref), and [`Complex{Float64}`](@ref).
This category of types is significant since they are valid as type parameters,
may not track [`isdefined`](@ref) / [`isassigned`](@ref) status,
and have a defined layout that is compatible with C.

See also [`isbits`](@ref), [`isprimitivetype`](@ref), [`ismutable`](@ref).

# Examples
```jldoctest
julia> isbitstype(Complex{Float64})
true

julia> isbitstype(Complex)
false
```
"""
isbitstype(@nospecialize t) = (@_total_meta; isa(t, DataType) && (t.flags & 0x0008) == 0x0008)

"""
    isbits(x)

Return `true` if `x` is an instance of an [`isbitstype`](@ref) type.
"""
isbits(@nospecialize x) = isbitstype(typeof(x))

"""
    objectid(x) -> UInt

Get a hash value for `x` based on object identity.

If `x === y` then `objectid(x) == objectid(y)`, and usually when `x !== y`, `objectid(x) != objectid(y)`.

See also [`hash`](@ref), [`IdDict`](@ref).
"""
function objectid(x)
    # objectid is foldable iff it isn't a pointer.
    if isidentityfree(typeof(x))
        return _foldable_objectid(x)
    end
    return _objectid(x)
end
function _foldable_objectid(@nospecialize(x))
    @_foldable_meta
    _objectid(x)
end
_objectid(@nospecialize(x)) = ccall(:jl_object_id, UInt, (Any,), x)

"""
    isdispatchtuple(T)

Determine whether type `T` is a tuple "leaf type",
meaning it could appear as a type signature in dispatch
and has no subtypes (or supertypes) which could appear in a call.
"""
isdispatchtuple(@nospecialize(t)) = (@_total_meta; isa(t, DataType) && (t.flags & 0x0004) == 0x0004)

datatype_ismutationfree(dt::DataType) = (@_total_meta; (dt.flags & 0x0100) == 0x0100)

"""
    ismutationfree(T)

Determine whether type `T` is mutation free in the sense that no mutable memory
is reachable from this type (either in the type itself) or through any fields.
Note that the type itself need not be immutable. For example, an empty mutable
type is `ismutabletype`, but also `ismutationfree`.
"""
function ismutationfree(@nospecialize(t))
    t = unwrap_unionall(t)
    if isa(t, DataType)
        return datatype_ismutationfree(t)
    elseif isa(t, Union)
        return ismutationfree(t.a) && ismutationfree(t.b)
    end
    # TypeVar, etc.
    return false
end

datatype_isidentityfree(dt::DataType) = (@_total_meta; (dt.flags & 0x0200) == 0x0200)

"""
    isidentityfree(T)

Determine whether type `T` is identity free in the sense that this type or any
reachable through its fields has non-content-based identity.
"""
function isidentityfree(@nospecialize(t))
    t = unwrap_unionall(t)
    if isa(t, DataType)
        return datatype_isidentityfree(t)
    elseif isa(t, Union)
        return isidentityfree(t.a) && isidentityfree(t.b)
    end
    # TypeVar, etc.
    return false
end

iskindtype(@nospecialize t) = (t === DataType || t === UnionAll || t === Union || t === typeof(Bottom))
isconcretedispatch(@nospecialize t) = isconcretetype(t) && !iskindtype(t)
has_free_typevars(@nospecialize(t)) = ccall(:jl_has_free_typevars, Cint, (Any,), t) != 0

# equivalent to isa(v, Type) && isdispatchtuple(Tuple{v}) || v === Union{}
# and is thus perhaps most similar to the old (pre-1.0) `isleaftype` query
function isdispatchelem(@nospecialize v)
    return (v === Bottom) || (v === typeof(Bottom)) || isconcretedispatch(v) ||
        (isType(v) && !has_free_typevars(v))
end

const _TYPE_NAME = Type.body.name
isType(@nospecialize t) = isa(t, DataType) && t.name === _TYPE_NAME

"""
    isconcretetype(T)

Determine whether type `T` is a concrete type, meaning it could have direct instances
(values `x` such that `typeof(x) === T`).

See also: [`isbits`](@ref), [`isabstracttype`](@ref), [`issingletontype`](@ref).

# Examples
```jldoctest
julia> isconcretetype(Complex)
false

julia> isconcretetype(Complex{Float32})
true

julia> isconcretetype(Vector{Complex})
true

julia> isconcretetype(Vector{Complex{Float32}})
true

julia> isconcretetype(Union{})
false

julia> isconcretetype(Union{Int,String})
false
```
"""
isconcretetype(@nospecialize(t)) = (@_total_meta; isa(t, DataType) && (t.flags & 0x0002) == 0x0002)

"""
    isabstracttype(T)

Determine whether type `T` was declared as an abstract type
(i.e. using the `abstract type` syntax).

# Examples
```jldoctest
julia> isabstracttype(AbstractArray)
true

julia> isabstracttype(Vector)
false
```
"""
function isabstracttype(@nospecialize(t))
    @_total_meta
    t = unwrap_unionall(t)
    # TODO: what to do for `Union`?
    return isa(t, DataType) && (t.name.flags & 0x1) == 0x1
end

"""
    Base.issingletontype(T)

Determine whether type `T` has exactly one possible instance; for example, a
struct type with no fields.
"""
issingletontype(@nospecialize(t)) = (@_total_meta; isa(t, DataType) && isdefined(t, :instance))

"""
    typeintersect(T::Type, S::Type)

Compute a type that contains the intersection of `T` and `S`. Usually this will be the
smallest such type or one close to it.
"""
typeintersect(@nospecialize(a), @nospecialize(b)) = (@_total_meta; ccall(:jl_type_intersection, Any, (Any, Any), a::Type, b::Type))

morespecific(@nospecialize(a), @nospecialize(b)) = (@_total_meta; ccall(:jl_type_morespecific, Cint, (Any, Any), a::Type, b::Type) != 0)

"""
    fieldoffset(type, i)

The byte offset of field `i` of a type relative to the data start. For example, we could
use it in the following manner to summarize information about a struct:

```jldoctest
julia> structinfo(T) = [(fieldoffset(T,i), fieldname(T,i), fieldtype(T,i)) for i = 1:fieldcount(T)];

julia> structinfo(Base.Filesystem.StatStruct)
13-element Vector{Tuple{UInt64, Symbol, Type}}:
 (0x0000000000000000, :desc, Union{RawFD, String})
 (0x0000000000000008, :device, UInt64)
 (0x0000000000000010, :inode, UInt64)
 (0x0000000000000018, :mode, UInt64)
 (0x0000000000000020, :nlink, Int64)
 (0x0000000000000028, :uid, UInt64)
 (0x0000000000000030, :gid, UInt64)
 (0x0000000000000038, :rdev, UInt64)
 (0x0000000000000040, :size, Int64)
 (0x0000000000000048, :blksize, Int64)
 (0x0000000000000050, :blocks, Int64)
 (0x0000000000000058, :mtime, Float64)
 (0x0000000000000060, :ctime, Float64)
```
"""
fieldoffset(x::DataType, idx::Integer) = (@_foldable_meta; ccall(:jl_get_field_offset, Csize_t, (Any, Cint), x, idx))

"""
    fieldtype(T, name::Symbol | index::Int)

Determine the declared type of a field (specified by name or index) in a composite DataType `T`.

# Examples
```jldoctest
julia> struct Foo
           x::Int64
           y::String
       end

julia> fieldtype(Foo, :x)
Int64

julia> fieldtype(Foo, 2)
String
```
"""
fieldtype

"""
    Base.fieldindex(T, name::Symbol, err:Bool=true)

Get the index of a named field, throwing an error if the field does not exist (when err==true)
or returning 0 (when err==false).

# Examples
```jldoctest
julia> struct Foo
           x::Int64
           y::String
       end

julia> Base.fieldindex(Foo, :z)
ERROR: type Foo has no field z
Stacktrace:
[...]

julia> Base.fieldindex(Foo, :z, false)
0
```
"""
function fieldindex(T::DataType, name::Symbol, err::Bool=true)
    return err ? _fieldindex_maythrow(T, name) : _fieldindex_nothrow(T, name)
end

function _fieldindex_maythrow(T::DataType, name::Symbol)
    @_foldable_meta
    @noinline
    return Int(ccall(:jl_field_index, Cint, (Any, Any, Cint), T, name, true)+1)
end

function _fieldindex_nothrow(T::DataType, name::Symbol)
    @_total_meta
    @noinline
    return Int(ccall(:jl_field_index, Cint, (Any, Any, Cint), T, name, false)+1)
end

function fieldindex(t::UnionAll, name::Symbol, err::Bool=true)
    t = argument_datatype(t)
    if t === nothing
        err && throw(ArgumentError("type does not have definite fields"))
        return 0
    end
    return fieldindex(t, name, err)
end

function argument_datatype(@nospecialize t)
    @_total_meta
    @noinline
    return ccall(:jl_argument_datatype, Any, (Any,), t)::Union{Nothing,DataType}
end

function datatype_fieldcount(t::DataType)
    if t.name === _NAMEDTUPLE_NAME
        names, types = t.parameters[1], t.parameters[2]
        if names isa Tuple
            return length(names)
        end
        if types isa DataType && types <: Tuple
            return fieldcount(types)
        end
        return nothing
    elseif isabstracttype(t) || (t.name === Tuple.name && isvatuple(t))
        return nothing
    end
    if isdefined(t, :types)
        return length(t.types)
    end
    return length(t.name.names)
end

"""
    fieldcount(t::Type)

Get the number of fields that an instance of the given type would have.
An error is thrown if the type is too abstract to determine this.
"""
function fieldcount(@nospecialize t)
    @_foldable_meta
    if t isa UnionAll || t isa Union
        t = argument_datatype(t)
        if t === nothing
            throw(ArgumentError("type does not have a definite number of fields"))
        end
    elseif t === Union{}
        throw(ArgumentError("The empty type does not have a well-defined number of fields since it does not have instances."))
    end
    if !(t isa DataType)
        throw(TypeError(:fieldcount, DataType, t))
    end
    fcount = datatype_fieldcount(t)
    if fcount === nothing
        throw(ArgumentError("type does not have a definite number of fields"))
    end
    return fcount
end

"""
    fieldtypes(T::Type)

The declared types of all fields in a composite DataType `T` as a tuple.

!!! compat "Julia 1.1"
    This function requires at least Julia 1.1.

# Examples
```jldoctest
julia> struct Foo
           x::Int64
           y::String
       end

julia> fieldtypes(Foo)
(Int64, String)
```
"""
fieldtypes(T::Type) = (@_foldable_meta; ntupleany(i -> fieldtype(T, i), fieldcount(T)))

# return all instances, for types that can be enumerated

"""
    instances(T::Type)

Return a collection of all instances of the given type, if applicable. Mostly used for
enumerated types (see `@enum`).

# Example
```jldoctest
julia> @enum Color red blue green

julia> instances(Color)
(red, blue, green)
```
"""
function instances end

function to_tuple_type(@nospecialize(t))
    if isa(t, Tuple) || isa(t, AbstractArray) || isa(t, SimpleVector)
        t = Tuple{t...}
    end
    if isa(t, Type) && t <: Tuple
        for p in (unwrap_unionall(t)::DataType).parameters
            if isa(p, Core.TypeofVararg)
                p = unwrapva(p)
            end
            if !(isa(p, Type) || isa(p, TypeVar))
                error("argument tuple type must contain only types")
            end
        end
    else
        error("expected tuple type")
    end
    t
end

function signature_type(@nospecialize(f), @nospecialize(argtypes))
    argtypes = to_tuple_type(argtypes)
    ft = Core.Typeof(f)
    u = unwrap_unionall(argtypes)::DataType
    return rewrap_unionall(Tuple{ft, u.parameters...}, argtypes)
end

"""
    code_lowered(f, types; generated=true, debuginfo=:default)

Return an array of the lowered forms (IR) for the methods matching the given generic function
and type signature.

If `generated` is `false`, the returned `CodeInfo` instances will correspond to fallback
implementations. An error is thrown if no fallback implementation exists.
If `generated` is `true`, these `CodeInfo` instances will correspond to the method bodies
yielded by expanding the generators.

The keyword `debuginfo` controls the amount of code metadata present in the output.

Note that an error will be thrown if `types` are not leaf types when `generated` is
`true` and any of the corresponding methods are an `@generated` method.
"""
function code_lowered(@nospecialize(f), @nospecialize(t=Tuple); generated::Bool=true, debuginfo::Symbol=:default)
    if @isdefined(IRShow)
        debuginfo = IRShow.debuginfo(debuginfo)
    elseif debuginfo === :default
        debuginfo = :source
    end
    if debuginfo !== :source && debuginfo !== :none
        throw(ArgumentError("'debuginfo' must be either :source or :none"))
    end
    world = get_world_counter()
    return map(method_instances(f, t, world)) do m
        if generated && hasgenerator(m)
            if may_invoke_generator(m)
                return ccall(:jl_code_for_staged, Any, (Any, UInt), m, world)::CodeInfo
            else
                error("Could not expand generator for `@generated` method ", m, ". ",
                      "This can happen if the provided argument types (", t, ") are ",
                      "not leaf types, but the `generated` argument is `true`.")
            end
        end
        code = uncompressed_ir(m.def::Method)
        debuginfo === :none && remove_linenums!(code)
        return code
    end
end

hasgenerator(m::Method) = isdefined(m, :generator)
hasgenerator(m::Core.MethodInstance) = hasgenerator(m.def::Method)

# low-level method lookup functions used by the compiler

unionlen(x::Union) = unionlen(x.a) + unionlen(x.b)
unionlen(@nospecialize(x)) = 1

_uniontypes(x::Union, ts) = (_uniontypes(x.a,ts); _uniontypes(x.b,ts); ts)
_uniontypes(@nospecialize(x), ts) = (push!(ts, x); ts)
uniontypes(@nospecialize(x)) = _uniontypes(x, Any[])

function _methods(@nospecialize(f), @nospecialize(t), lim::Int, world::UInt)
    tt = signature_type(f, t)
    return _methods_by_ftype(tt, lim, world)
end

function _methods_by_ftype(@nospecialize(t), lim::Int, world::UInt)
    return _methods_by_ftype(t, nothing, lim, world)
end
function _methods_by_ftype(@nospecialize(t), mt::Union{Core.MethodTable, Nothing}, lim::Int, world::UInt)
    return _methods_by_ftype(t, mt, lim, world, false, RefValue{UInt}(typemin(UInt)), RefValue{UInt}(typemax(UInt)), Ptr{Int32}(C_NULL))
end
function _methods_by_ftype(@nospecialize(t), mt::Union{Core.MethodTable, Nothing}, lim::Int, world::UInt, ambig::Bool, min::Ref{UInt}, max::Ref{UInt}, has_ambig::Ref{Int32})
    return ccall(:jl_matching_methods, Any, (Any, Any, Cint, Cint, UInt, Ptr{UInt}, Ptr{UInt}, Ptr{Int32}), t, mt, lim, ambig, world, min, max, has_ambig)::Union{Vector{Any},Nothing}
end

# high-level, more convenient method lookup functions

# type for reflecting and pretty-printing a subset of methods
mutable struct MethodList <: AbstractArray{Method,1}
    ms::Array{Method,1}
    mt::Core.MethodTable
end

size(m::MethodList) = size(m.ms)
getindex(m::MethodList, i::Integer) = m.ms[i]

function MethodList(mt::Core.MethodTable)
    ms = Method[]
    visit(mt) do m
        push!(ms, m)
    end
    return MethodList(ms, mt)
end

"""
    methods(f, [types], [module])

Return the method table for `f`.

If `types` is specified, return an array of methods whose types match.
If `module` is specified, return an array of methods defined in that module.
A list of modules can also be specified as an array.

!!! compat "Julia 1.4"
    At least Julia 1.4 is required for specifying a module.

See also: [`which`](@ref) and `@which`.
"""
function methods(@nospecialize(f), @nospecialize(t),
                 mod::Union{Tuple{Module},AbstractArray{Module},Nothing}=nothing)
    world = get_world_counter()
    # Lack of specialization => a comprehension triggers too many invalidations via _collect, so collect the methods manually
    ms = Method[]
    for m in _methods(f, t, -1, world)::Vector
        m = m::Core.MethodMatch
        (mod === nothing || parentmodule(m.method) ∈ mod) && push!(ms, m.method)
    end
    MethodList(ms, typeof(f).name.mt)
end
methods(@nospecialize(f), @nospecialize(t), mod::Module) = methods(f, t, (mod,))

function methods_including_ambiguous(@nospecialize(f), @nospecialize(t))
    tt = signature_type(f, t)
    world = get_world_counter()
    (ccall(:jl_is_in_pure_context, Bool, ()) || world == typemax(UInt)) &&
        error("code reflection cannot be used from generated functions")
    min = RefValue{UInt}(typemin(UInt))
    max = RefValue{UInt}(typemax(UInt))
    ms = _methods_by_ftype(tt, nothing, -1, world, true, min, max, Ptr{Int32}(C_NULL))::Vector
    return MethodList(Method[(m::Core.MethodMatch).method for m in ms], typeof(f).name.mt)
end

function methods(@nospecialize(f),
                 mod::Union{Module,AbstractArray{Module},Nothing}=nothing)
    # return all matches
    return methods(f, Tuple{Vararg{Any}}, mod)
end

function visit(f, mt::Core.MethodTable)
    mt.defs !== nothing && visit(f, mt.defs)
    nothing
end
function visit(f, mc::Core.TypeMapLevel)
    function avisit(f, e::Array{Any,1})
        for i in 2:2:length(e)
            isassigned(e, i) || continue
            ei = e[i]
            if ei isa Vector{Any}
                for j in 2:2:length(ei)
                    isassigned(ei, j) || continue
                    visit(f, ei[j])
                end
            else
                visit(f, ei)
            end
        end
    end
    if mc.targ !== nothing
        avisit(f, mc.targ::Vector{Any})
    end
    if mc.arg1 !== nothing
        avisit(f, mc.arg1::Vector{Any})
    end
    if mc.tname !== nothing
        avisit(f, mc.tname::Vector{Any})
    end
    if mc.name1 !== nothing
        avisit(f, mc.name1::Vector{Any})
    end
    mc.list !== nothing && visit(f, mc.list)
    mc.any !== nothing && visit(f, mc.any)
    nothing
end
function visit(f, d::Core.TypeMapEntry)
    while d !== nothing
        f(d.func)
        d = d.next
    end
    nothing
end
struct MethodSpecializations
    specializations::Union{Nothing, Core.MethodInstance, Core.SimpleVector}
end
"""
    specializations(m::Method) → itr

Return an iterator `itr` of all compiler-generated specializations of `m`.
"""
specializations(m::Method) = MethodSpecializations(isdefined(m, :specializations) ? m.specializations : nothing)
function iterate(specs::MethodSpecializations)
    s = specs.specializations
    s === nothing && return nothing
    isa(s, Core.MethodInstance) && return (s, nothing)
    return iterate(specs, 0)
end
iterate(specs::MethodSpecializations, ::Nothing) = nothing
function iterate(specs::MethodSpecializations, i::Int)
    s = specs.specializations::Core.SimpleVector
    n = length(s)
    i >= n && return nothing
    item = nothing
    while i < n && item === nothing
        item = s[i+=1]
    end
    item === nothing && return nothing
    return (item, i)
end
length(specs::MethodSpecializations) = count(Returns(true), specs)

function length(mt::Core.MethodTable)
    n = 0
    visit(mt) do m
        n += 1
    end
    return n::Int
end
isempty(mt::Core.MethodTable) = (mt.defs === nothing)

uncompressed_ir(m::Method) = isdefined(m, :source) ? _uncompressed_ir(m, m.source) :
                             isdefined(m, :generator) ? error("Method is @generated; try `code_lowered` instead.") :
                             error("Code for this Method is not available.")
_uncompressed_ir(m::Method, s::CodeInfo) = copy(s)
_uncompressed_ir(m::Method, s::String) = ccall(:jl_uncompress_ir, Any, (Any, Ptr{Cvoid}, Any), m, C_NULL, s)::CodeInfo
_uncompressed_ir(ci::Core.CodeInstance, s::String) = ccall(:jl_uncompress_ir, Any, (Any, Any, Any), ci.def.def::Method, ci, s)::CodeInfo
# for backwards compat
const uncompressed_ast = uncompressed_ir
const _uncompressed_ast = _uncompressed_ir

function method_instances(@nospecialize(f), @nospecialize(t), world::UInt)
    tt = signature_type(f, t)
    results = Core.MethodInstance[]
    # this make a better error message than the typeassert that follows
    world == typemax(UInt) && error("code reflection cannot be used from generated functions")
    for match in _methods_by_ftype(tt, -1, world)::Vector
        instance = Core.Compiler.specialize_method(match)
        push!(results, instance)
    end
    return results
end

default_debug_info_kind() = unsafe_load(cglobal(:jl_default_debug_info_kind, Cint))

# this type mirrors jl_cgparams_t (documented in julia.h)
struct CodegenParams
    track_allocations::Cint
    code_coverage::Cint
    prefer_specsig::Cint
    gnu_pubnames::Cint
    debug_info_kind::Cint
    safepoint_on_entry::Cint
    gcstack_arg::Cint

    lookup::Ptr{Cvoid}

    generic_context::Any

    function CodegenParams(; track_allocations::Bool=true, code_coverage::Bool=true,
                   prefer_specsig::Bool=false,
                   gnu_pubnames=true, debug_info_kind::Cint = default_debug_info_kind(),
                   safepoint_on_entry::Bool=true,
                   gcstack_arg::Bool=true,
                   lookup::Ptr{Cvoid}=unsafe_load(cglobal(:jl_rettype_inferred_addr, Ptr{Cvoid})),
                   generic_context = nothing)
        return new(
            Cint(track_allocations), Cint(code_coverage),
            Cint(prefer_specsig),
            Cint(gnu_pubnames), debug_info_kind,
            Cint(safepoint_on_entry),
            Cint(gcstack_arg),
            lookup, generic_context)
    end
end

const SLOT_USED = 0x8
ast_slotflag(@nospecialize(code), i) = ccall(:jl_ir_slotflag, UInt8, (Any, Csize_t), code, i - 1)

"""
    may_invoke_generator(method, atype, sparams) -> Bool

Computes whether or not we may invoke the generator for the given `method` on
the given `atype` and `sparams`. For correctness, all generated function are
required to return monotonic answers. However, since we don't expect users to
be able to successfully implement this criterion, we only call generated
functions on concrete types. The one exception to this is that we allow calling
generators with abstract types if the generator does not use said abstract type
(and thus cannot incorrectly use it to break monotonicity). This function
computes whether we are in either of these cases.

Unlike normal functions, the compilation heuristics still can't generate good dispatch
in some cases, but this may still allow inference not to fall over in some limited cases.
"""
function may_invoke_generator(mi::MethodInstance)
    return may_invoke_generator(mi.def::Method, mi.specTypes, mi.sparam_vals)
end
function may_invoke_generator(method::Method, @nospecialize(atype), sparams::SimpleVector)
    # If we have complete information, we may always call the generator
    isdispatchtuple(atype) && return true

    # We don't have complete information, but it is possible that the generator
    # syntactically doesn't make use of the information we don't have. Check
    # for that.

    # For now, only handle the (common, generated by the frontend case) that the
    # generator only has one method
    generator = method.generator
    isa(generator, Core.GeneratedFunctionStub) || return false
    tt = Tuple{typeof(generator.gen), Vararg{Any}}
    gen_mthds = _methods_by_ftype(tt, #=lim=#1, method.primary_world)
    gen_mthds isa Vector || return false
    length(gen_mthds) == 1 || return false

    generator_method = first(gen_mthds).method
    nsparams = length(sparams)
    isdefined(generator_method, :source) || return false
    code = generator_method.source
    nslots = ccall(:jl_ir_nslots, Int, (Any,), code)
    at = unwrap_unionall(atype)
    at isa DataType || return false
    (nslots >= 1 + length(sparams) + length(at.parameters)) || return false

    firstarg = 1
    for i = 1:nsparams
        if isa(sparams[i], TypeVar)
            if (ast_slotflag(code, firstarg + i) & SLOT_USED) != 0
                return false
            end
        end
    end
    nargs = Int(method.nargs)
    non_va_args = method.isva ? nargs - 1 : nargs
    for i = 1:non_va_args
        if !isdispatchelem(at.parameters[i])
            if (ast_slotflag(code, firstarg + i + nsparams) & SLOT_USED) != 0
                return false
            end
        end
    end
    if method.isva
        # If the va argument is used, we need to ensure that all arguments that
        # contribute to the va tuple are dispatchelemes
        if (ast_slotflag(code, firstarg + nargs + nsparams) & SLOT_USED) != 0
            for i = (non_va_args+1):length(at.parameters)
                if !isdispatchelem(at.parameters[i])
                    return false
                end
            end
        end
    end
    return true
end

# give a decent error message if we try to instantiate a staged function on non-leaf types
function func_for_method_checked(m::Method, @nospecialize(types), sparams::SimpleVector)
    if isdefined(m, :generator) && !may_invoke_generator(m, types, sparams)
        error("cannot call @generated function `", m, "` ",
              "with abstract argument types: ", types)
    end
    return m
end

"""
    code_typed(f, types; kw...)

Returns an array of type-inferred lowered form (IR) for the methods matching the given
generic function and type signature.

# Keyword Arguments

- `optimize::Bool = true`: optional, controls whether additional optimizations,
  such as inlining, are also applied.
- `debuginfo::Symbol = :default`: optional, controls the amount of code metadata present
  in the output, possible options are `:source` or `:none`.

# Internal Keyword Arguments

This section should be considered internal, and is only for who understands Julia compiler
internals.

- `world::UInt = Base.get_world_counter()`: optional, controls the world age to use
  when looking up methods, use current world age if not specified.
- `interp::Core.Compiler.AbstractInterpreter = Core.Compiler.NativeInterpreter(world)`:
  optional, controls the abstract interpreter to use, use the native interpreter if not specified.

# Example

One can put the argument types in a tuple to get the corresponding `code_typed`.

```julia
julia> code_typed(+, (Float64, Float64))
1-element Vector{Any}:
 CodeInfo(
1 ─ %1 = Base.add_float(x, y)::Float64
└──      return %1
) => Float64
```
"""
function code_typed(@nospecialize(f), @nospecialize(types=default_tt(f)); kwargs...)
    if isa(f, Core.OpaqueClosure)
        return code_typed_opaque_closure(f; kwargs...)
    end
    tt = signature_type(f, types)
    return code_typed_by_type(tt; kwargs...)
end

# returns argument tuple type which is supposed to be used for `code_typed` and its family;
# if there is a single method this functions returns the method argument signature,
# otherwise returns `Tuple` that doesn't match with any signature
function default_tt(@nospecialize(f))
    ms = methods(f)
    if length(ms) == 1
        return tuple_type_tail(only(ms).sig)
    else
        return Tuple
    end
end

"""
    code_typed_by_type(types::Type{<:Tuple}; ...)

Similar to [`code_typed`](@ref), except the argument is a tuple type describing
a full signature to query.
"""
function code_typed_by_type(@nospecialize(tt::Type);
                            optimize::Bool=true,
                            debuginfo::Symbol=:default,
                            world::UInt=get_world_counter(),
                            interp::Core.Compiler.AbstractInterpreter=Core.Compiler.NativeInterpreter(world))
    (ccall(:jl_is_in_pure_context, Bool, ()) || world == typemax(UInt)) &&
        error("code reflection cannot be used from generated functions")
    if @isdefined(IRShow)
        debuginfo = IRShow.debuginfo(debuginfo)
    elseif debuginfo === :default
        debuginfo = :source
    end
    if debuginfo !== :source && debuginfo !== :none
        throw(ArgumentError("'debuginfo' must be either :source or :none"))
    end
    tt = to_tuple_type(tt)
    matches = _methods_by_ftype(tt, #=lim=#-1, world)::Vector
    asts = []
    for match in matches
        match = match::Core.MethodMatch
        meth = func_for_method_checked(match.method, tt, match.sparams)
        (code, ty) = Core.Compiler.typeinf_code(interp, meth, match.spec_types, match.sparams, optimize)
        if code === nothing
            push!(asts, meth => Any)
        else
            debuginfo === :none && remove_linenums!(code)
            push!(asts, code => ty)
        end
    end
    return asts
end

function code_typed_opaque_closure(@nospecialize(oc::Core.OpaqueClosure);
                                   debuginfo::Symbol=:default, _...)
    ccall(:jl_is_in_pure_context, Bool, ()) && error("code reflection cannot be used from generated functions")
    m = oc.source
    if isa(m, Method)
        code = _uncompressed_ir(m, m.source)
        debuginfo === :none && remove_linenums!(code)
        # intersect the declared return type and the inferred return type (if available)
        rt = typeintersect(code.rettype, typeof(oc).parameters[2])
        return Any[code => rt]
    else
        error("encountered invalid Core.OpaqueClosure object")
    end
end

"""
    code_ircode(f, [types])

Return an array of pairs of `IRCode` and inferred return type if type inference succeeds.
The `Method` is included instead of `IRCode` otherwise.

See also: [`code_typed`](@ref)

# Internal Keyword Arguments

This section should be considered internal, and is only for who understands Julia compiler
internals.

- `world::UInt = Base.get_world_counter()`: optional, controls the world age to use
  when looking up methods, use current world age if not specified.
- `interp::Core.Compiler.AbstractInterpreter = Core.Compiler.NativeInterpreter(world)`:
  optional, controls the abstract interpreter to use, use the native interpreter if not specified.
- `optimize_until::Union{Integer,AbstractString,Nothing} = nothing`: optional,
  controls the optimization passes to run.
  If it is a string, it specifies the name of the pass up to which the optimizer is run.
  If it is an integer, it specifies the number of passes to run.
  If it is `nothing` (default), all passes are run.

# Example

One can put the argument types in a tuple to get the corresponding `code_ircode`.

```julia
julia> Base.code_ircode(+, (Float64, Int64))
1-element Vector{Any}:
 388 1 ─ %1 = Base.sitofp(Float64, _3)::Float64
    │   %2 = Base.add_float(_2, %1)::Float64
    └──      return %2
     => Float64

julia> Base.code_ircode(+, (Float64, Int64); optimize_until = "compact 1")
1-element Vector{Any}:
 388 1 ─ %1 = Base.promote(_2, _3)::Tuple{Float64, Float64}
    │   %2 = Core._apply_iterate(Base.iterate, Base.:+, %1)::Float64
    └──      return %2
     => Float64
```
"""
function code_ircode(@nospecialize(f), @nospecialize(types = default_tt(f)); kwargs...)
    if isa(f, Core.OpaqueClosure)
        error("OpaqueClosure not supported")
    end
    tt = signature_type(f, types)
    return code_ircode_by_type(tt; kwargs...)
end

"""
    code_ircode_by_type(types::Type{<:Tuple}; ...)

Similar to [`code_ircode`](@ref), except the argument is a tuple type describing
a full signature to query.
"""
function code_ircode_by_type(
    @nospecialize(tt::Type);
    world::UInt=get_world_counter(),
    interp::Core.Compiler.AbstractInterpreter=Core.Compiler.NativeInterpreter(world),
    optimize_until::Union{Integer,AbstractString,Nothing}=nothing,
)
    (ccall(:jl_is_in_pure_context, Bool, ()) || world == typemax(UInt)) &&
        error("code reflection cannot be used from generated functions")
    tt = to_tuple_type(tt)
    matches = _methods_by_ftype(tt, #=lim=#-1, world)::Vector
    asts = []
    for match in matches
        match = match::Core.MethodMatch
        meth = func_for_method_checked(match.method, tt, match.sparams)
        (code, ty) = Core.Compiler.typeinf_ircode(
            interp,
            meth,
            match.spec_types,
            match.sparams,
            optimize_until,
        )
        if code === nothing
            push!(asts, meth => Any)
        else
            push!(asts, code => ty)
        end
    end
    return asts
end


"""
    Base.return_types(f::Function, types::DataType=default_tt(f);
                      world::UInt=get_world_counter(), interp::NativeInterpreter=Core.Compiler.NativeInterpreter(world))

Return a list of possible return types for a given function `f` and argument types `types`.
The list corresponds to the results of type inference on all the possible method match
candidates for `f` and `types` (see also [`methods(f, types)`](@ref methods).

# Example

```julia
julia> Base.return_types(sum, Tuple{Vector{Int}})
1-element Vector{Any}:
 Int64

julia> methods(sum, (Union{Vector{Int},UnitRange{Int}},))
# 2 methods for generic function "sum" from Base:
 [1] sum(r::AbstractRange{<:Real})
     @ range.jl:1396
 [2] sum(a::AbstractArray; dims, kw...)
     @ reducedim.jl:996

julia> Base.return_types(sum, (Union{Vector{Int},UnitRange{Int}},))
2-element Vector{Any}:
 Int64 # the result of inference on sum(r::AbstractRange{<:Real})
 Int64 # the result of inference on sum(a::AbstractArray; dims, kw...)
```

!!! warning
    The `return_types` function should not be used from generated functions;
    doing so will result in an error.
"""
function return_types(@nospecialize(f), @nospecialize(types=default_tt(f));
                      world::UInt=get_world_counter(),
                      interp::Core.Compiler.AbstractInterpreter=Core.Compiler.NativeInterpreter(world))
    (ccall(:jl_is_in_pure_context, Bool, ()) || world == typemax(UInt)) &&
        error("code reflection cannot be used from generated functions")
    if isa(f, Core.OpaqueClosure)
        _, rt = only(code_typed_opaque_closure(f))
        return Any[rt]
    end

    if isa(f, Core.Builtin)
        argtypes = Any[to_tuple_type(types).parameters...]
        rt = Core.Compiler.builtin_tfunction(interp, f, argtypes, nothing)
        return Any[Core.Compiler.widenconst(rt)]
    end
    rts = []
    tt = signature_type(f, types)
    matches = _methods_by_ftype(tt, #=lim=#-1, world)::Vector
    for match in matches
        match = match::Core.MethodMatch
        meth = func_for_method_checked(match.method, types, match.sparams)
        ty = Core.Compiler.typeinf_type(interp, meth, match.spec_types, match.sparams)
        push!(rts, something(ty, Any))
    end
    return rts
end

"""
    infer_effects(f, types=default_tt(f); world=get_world_counter(), interp=Core.Compiler.NativeInterpreter(world))

Compute the `Effects` of a function `f` with argument types `types`. The `Effects` represents the computational effects of the function call, such as whether it is free of side effects, guaranteed not to throw an exception, guaranteed to terminate, etc. The `world` and `interp` arguments specify the world counter and the native interpreter to use for the analysis.

# Arguments
- `f`: The function to analyze.
- `types` (optional): The argument types of the function. Defaults to the default tuple type of `f`.
- `world` (optional): The world counter to use for the analysis. Defaults to the current world counter.
- `interp` (optional): The native interpreter to use for the analysis. Defaults to a new `Core.Compiler.NativeInterpreter` with the specified `world`.

# Returns
- `effects::Effects`: The computed effects of the function call.

# Example

```julia
julia> function foo(x)
           y = x * 2
           return y
       end;

julia> effects = Base.infer_effects(foo, (Int,))
(+c,+e,+n,+t,+s,+m,+i)
```

This function will return an `Effects` object with information about the computational effects of the function `foo` when called with an `Int` argument. See the documentation for `Effects` for more information on the various effect properties.

!!! warning
    The `infer_effects` function should not be used from generated functions;
    doing so will result in an error.

# See Also
- [`Core.Compiler.Effects`](@ref): A type representing the computational effects of a method call.
- [`Base.@assume_effects`](@ref): A macro for making assumptions about the effects of a method.
"""
function infer_effects(@nospecialize(f), @nospecialize(types=default_tt(f));
                       world = get_world_counter(),
                       interp = Core.Compiler.NativeInterpreter(world))
    (ccall(:jl_is_in_pure_context, Bool, ()) || world == typemax(UInt)) &&
        error("code reflection cannot be used from generated functions")
    if isa(f, Core.Builtin)
        types = to_tuple_type(types)
        argtypes = Any[Core.Compiler.Const(f), types.parameters...]
        rt = Core.Compiler.builtin_tfunction(interp, f, argtypes[2:end], nothing)
        return Core.Compiler.builtin_effects(Core.Compiler.typeinf_lattice(interp), f,
            Core.Compiler.ArgInfo(nothing, argtypes), rt)
    end
    tt = signature_type(f, types)
    result = Core.Compiler.findall(tt, Core.Compiler.method_table(interp))
    if result === missing
        # unanalyzable call, return the unknown effects
        return Core.Compiler.Effects()
    end
    (; matches) = result
    effects = Core.Compiler.EFFECTS_TOTAL
    if matches.ambig || !any(match::Core.MethodMatch->match.fully_covers, matches.matches)
        # account for the fact that we may encounter a MethodError with a non-covered or ambiguous signature.
        effects = Core.Compiler.Effects(effects; nothrow=false)
    end
    for match in matches.matches
        match = match::Core.MethodMatch
        frame = Core.Compiler.typeinf_frame(interp,
            match.method, match.spec_types, match.sparams, #=run_optimizer=#false)
        frame === nothing && return Core.Compiler.Effects()
        effects = Core.Compiler.merge_effects(effects, frame.ipo_effects)
    end
    return effects
end

"""
    print_statement_costs(io::IO, f, types)

Print type-inferred and optimized code for `f` given argument types `types`,
prepending each line with its cost as estimated by the compiler's inlining engine.
"""
function print_statement_costs(io::IO, @nospecialize(f), @nospecialize(t); kwargs...)
    tt = signature_type(f, t)
    print_statement_costs(io, tt; kwargs...)
end

function print_statement_costs(io::IO, @nospecialize(tt::Type);
                               world::UInt=get_world_counter(),
                               interp::Core.Compiler.AbstractInterpreter=Core.Compiler.NativeInterpreter(world))
    tt = to_tuple_type(tt)
    matches = _methods_by_ftype(tt, #=lim=#-1, world)::Vector
    params = Core.Compiler.OptimizationParams(interp)
    cst = Int[]
    for match in matches
        match = match::Core.MethodMatch
        meth = func_for_method_checked(match.method, tt, match.sparams)
        println(io, meth)
        (code, ty) = Core.Compiler.typeinf_code(interp, meth, match.spec_types, match.sparams, true)
        if code === nothing
            println(io, "  inference not successful")
        else
            empty!(cst)
            resize!(cst, length(code.code))
            sptypes = Core.Compiler.VarState[Core.Compiler.VarState(sp, false) for sp in match.sparams]
            maxcost = Core.Compiler.statement_costs!(cst, code.code, code, sptypes, false, params)
            nd = ndigits(maxcost)
            irshow_config = IRShow.IRShowConfig() do io, linestart, idx
                print(io, idx > 0 ? lpad(cst[idx], nd+1) : " "^(nd+1), " ")
                return ""
            end
            IRShow.show_ir(io, code, irshow_config)
        end
        println(io)
    end
end

print_statement_costs(args...; kwargs...) = print_statement_costs(stdout, args...; kwargs...)

function _which(@nospecialize(tt::Type);
    method_table::Union{Nothing,Core.MethodTable,Core.Compiler.MethodTableView}=nothing,
    world::UInt=get_world_counter(),
    raise::Bool=true)
    world == typemax(UInt) && error("code reflection cannot be used from generated functions")
    if method_table === nothing
        table = Core.Compiler.InternalMethodTable(world)
    elseif method_table isa Core.MethodTable
        table = Core.Compiler.OverlayMethodTable(world, method_table)
    else
        table = method_table
    end
    match, = Core.Compiler.findsup(tt, table)
    if match === nothing
        raise && error("no unique matching method found for the specified argument types")
        return nothing
    end
    return match
end

"""
    which(f, types)

Returns the method of `f` (a `Method` object) that would be called for arguments of the given `types`.

If `types` is an abstract type, then the method that would be called by `invoke` is returned.

See also: [`parentmodule`](@ref), and `@which` and `@edit` in [`InteractiveUtils`](@ref man-interactive-utils).
"""
function which(@nospecialize(f), @nospecialize(t))
    tt = signature_type(f, t)
    return which(tt)
end

"""
    which(types::Type{<:Tuple})

Returns the method that would be called by the given type signature (as a tuple type).
"""
function which(@nospecialize(tt#=::Type=#))
    return _which(tt).method
end

"""
    which(module, symbol)

Return the module in which the binding for the variable referenced by `symbol` in `module` was created.
"""
function which(m::Module, s::Symbol)
    if !isdefined(m, s)
        error("\"$s\" is not defined in module $m")
    end
    return binding_module(m, s)
end

# function reflection

"""
    nameof(f::Function) -> Symbol

Get the name of a generic `Function` as a symbol. For anonymous functions,
this is a compiler-generated name. For explicitly-declared subtypes of
`Function`, it is the name of the function's type.
"""
function nameof(f::Function)
    t = typeof(f)
    mt = t.name.mt
    if mt === Symbol.name.mt
        # uses shared method table, so name is not unique to this function type
        return nameof(t)
    end
    return mt.name
end

function nameof(f::Core.IntrinsicFunction)
    name = ccall(:jl_intrinsic_name, Ptr{UInt8}, (Core.IntrinsicFunction,), f)
    return ccall(:jl_symbol, Ref{Symbol}, (Ptr{UInt8},), name)
end

"""
    parentmodule(f::Function) -> Module

Determine the module containing the (first) definition of a generic
function.
"""
parentmodule(f::Function) = parentmodule(typeof(f))

"""
    parentmodule(f::Function, types) -> Module

Determine the module containing the first method of a generic function `f` matching
the specified `types`.
"""
function parentmodule(@nospecialize(f), @nospecialize(types))
    m = methods(f, types)
    if isempty(m)
        error("no matching methods")
    end
    return parentmodule(first(m))
end

"""
    parentmodule(m::Method) -> Module

Return the module in which the given method `m` is defined.

!!! compat "Julia 1.9"
    Passing a `Method` as an argument requires Julia 1.9 or later.
"""
parentmodule(m::Method) = m.module

"""
    hasmethod(f, t::Type{<:Tuple}[, kwnames]; world=get_world_counter()) -> Bool

Determine whether the given generic function has a method matching the given
`Tuple` of argument types with the upper bound of world age given by `world`.

If a tuple of keyword argument names `kwnames` is provided, this also checks
whether the method of `f` matching `t` has the given keyword argument names.
If the matching method accepts a variable number of keyword arguments, e.g.
with `kwargs...`, any names given in `kwnames` are considered valid. Otherwise
the provided names must be a subset of the method's keyword arguments.

See also [`applicable`](@ref).

!!! compat "Julia 1.2"
    Providing keyword argument names requires Julia 1.2 or later.

# Examples
```jldoctest
julia> hasmethod(length, Tuple{Array})
true

julia> f(; oranges=0) = oranges;

julia> hasmethod(f, Tuple{}, (:oranges,))
true

julia> hasmethod(f, Tuple{}, (:apples, :bananas))
false

julia> g(; xs...) = 4;

julia> hasmethod(g, Tuple{}, (:a, :b, :c, :d))  # g accepts arbitrary kwargs
true
```
"""
function hasmethod(@nospecialize(f), @nospecialize(t))
    return Core._hasmethod(f, t isa Type ? t : to_tuple_type(t))
end

function Core.kwcall(kwargs::NamedTuple, ::typeof(hasmethod), @nospecialize(f), @nospecialize(t))
    world = kwargs.world::UInt # make sure this is the only local, to avoid confusing kwarg_decl()
    return ccall(:jl_gf_invoke_lookup, Any, (Any, Any, UInt), signature_type(f, t), nothing, world) !== nothing
end

function hasmethod(f, t, kwnames::Tuple{Vararg{Symbol}}; world::UInt=get_world_counter())
    @nospecialize
    isempty(kwnames) && return hasmethod(f, t; world)
    t = to_tuple_type(t)
    ft = Core.Typeof(f)
    u = unwrap_unionall(t)::DataType
    tt = rewrap_unionall(Tuple{typeof(Core.kwcall), NamedTuple, ft, u.parameters...}, t)
    match = ccall(:jl_gf_invoke_lookup, Any, (Any, Any, UInt), tt, nothing, world)
    match === nothing && return false
    kws = ccall(:jl_uncompress_argnames, Array{Symbol,1}, (Any,), (match::Method).slot_syms)
    isempty(kws) && return true # some kwfuncs simply forward everything directly
    for kw in kws
        endswith(String(kw), "...") && return true
    end
    kwnames = Symbol[kwnames[i] for i in 1:length(kwnames)]
    return issubset(kwnames, kws)
end

"""
    fbody = bodyfunction(basemethod::Method)

Find the keyword "body function" (the function that contains the body of the method
as written, called after all missing keyword-arguments have been assigned default values).
`basemethod` is the method you obtain via [`which`](@ref) or [`methods`](@ref).
"""
function bodyfunction(basemethod::Method)
    fmod = parentmodule(basemethod)
    # The lowered code for `basemethod` should look like
    #   %1 = mkw(kwvalues..., #self#, args...)
    #        return %1
    # where `mkw` is the name of the "active" keyword body-function.
    ast = uncompressed_ast(basemethod)
    if isa(ast, Core.CodeInfo) && length(ast.code) >= 2
        callexpr = ast.code[end-1]
        if isa(callexpr, Expr) && callexpr.head === :call
            fsym = callexpr.args[1]
            while true
                if isa(fsym, Symbol)
                    return getfield(fmod, fsym)
                elseif isa(fsym, GlobalRef)
                    if fsym.mod === Core && fsym.name === :_apply
                        fsym = callexpr.args[2]
                    elseif fsym.mod === Core && fsym.name === :_apply_iterate
                        fsym = callexpr.args[3]
                    end
                    if isa(fsym, Symbol)
                        return getfield(fmod, fsym)::Function
                    elseif isa(fsym, GlobalRef)
                        return getfield(fsym.mod, fsym.name)::Function
                    elseif isa(fsym, Core.SSAValue)
                        fsym = ast.code[fsym.id]
                    else
                        return nothing
                    end
                else
                    return nothing
                end
            end
        end
    end
    return nothing
end

"""
    Base.isambiguous(m1, m2; ambiguous_bottom=false) -> Bool

Determine whether two methods `m1` and `m2` may be ambiguous for some call
signature. This test is performed in the context of other methods of the same
function; in isolation, `m1` and `m2` might be ambiguous, but if a third method
resolving the ambiguity has been defined, this returns `false`.
Alternatively, in isolation `m1` and `m2` might be ordered, but if a third
method cannot be sorted with them, they may cause an ambiguity together.

For parametric types, the `ambiguous_bottom` keyword argument controls whether
`Union{}` counts as an ambiguous intersection of type parameters – when `true`,
it is considered ambiguous, when `false` it is not.

# Examples
```jldoctest
julia> foo(x::Complex{<:Integer}) = 1
foo (generic function with 1 method)

julia> foo(x::Complex{<:Rational}) = 2
foo (generic function with 2 methods)

julia> m1, m2 = collect(methods(foo));

julia> typeintersect(m1.sig, m2.sig)
Tuple{typeof(foo), Complex{Union{}}}

julia> Base.isambiguous(m1, m2, ambiguous_bottom=true)
true

julia> Base.isambiguous(m1, m2, ambiguous_bottom=false)
false
```
"""
function isambiguous(m1::Method, m2::Method; ambiguous_bottom::Bool=false)
    m1 === m2 && return false
    ti = typeintersect(m1.sig, m2.sig)
    ti === Bottom && return false
    function inner(ti)
        ti === Bottom && return false
        if !ambiguous_bottom
            has_bottom_parameter(ti) && return false
        end
        world = get_world_counter()
        min = Ref{UInt}(typemin(UInt))
        max = Ref{UInt}(typemax(UInt))
        has_ambig = Ref{Int32}(0)
        ms = _methods_by_ftype(ti, nothing, -1, world, true, min, max, has_ambig)::Vector
        has_ambig[] == 0 && return false
        if !ambiguous_bottom
            filter!(ms) do m::Core.MethodMatch
                return !has_bottom_parameter(m.spec_types)
            end
        end
        # if ml-matches reported the existence of an ambiguity over their
        # intersection, see if both m1 and m2 seem to be involved in it
        # (if one was fully dominated by a different method, we want to will
        # report the other ambiguous pair)
        have_m1 = have_m2 = false
        for match in ms
            match = match::Core.MethodMatch
            m = match.method
            m === m1 && (have_m1 = true)
            m === m2 && (have_m2 = true)
        end
        if !have_m1 || !have_m2
            # ml-matches did not need both methods to expose the reported ambiguity
            return false
        end
        if !ambiguous_bottom
            # since we're intentionally ignoring certain ambiguities (via the
            # filter call above), see if we can now declare the intersection fully
            # covered even though it is partially ambiguous over Union{} as a type
            # parameter somewhere
            minmax = nothing
            for match in ms
                m = match.method
                match.fully_covers || continue
                if minmax === nothing || morespecific(m.sig, minmax.sig)
                    minmax = m
                end
            end
            if minmax === nothing || minmax == m1 || minmax == m2
                return true
            end
            for match in ms
                m = match.method
                m === minmax && continue
                if !morespecific(minmax.sig, m.sig)
                    if match.fully_covers || !morespecific(m.sig, minmax.sig)
                        return true
                    end
                end
            end
            return false
        end
        return true
    end
    if !(ti <: m1.sig && ti <: m2.sig)
        # When type-intersection fails, it's often also not commutative. Thus
        # checking the reverse may allow detecting ambiguity solutions
        # correctly in more cases (and faster).
        ti2 = typeintersect(m2.sig, m1.sig)
        if ti2 <: m1.sig && ti2 <: m2.sig
            ti = ti2
        elseif ti != ti2
            # TODO: this would be the more correct way to handle this case, but
            #       people complained so we don't do it
            #inner(ti2) || return false # report that the type system failed to decide if it was ambiguous by saying they definitely are
            return false # report that the type system failed to decide if it was ambiguous by saying they definitely are not
        else
            return false # report that the type system failed to decide if it was ambiguous by saying they definitely are not
        end
    end
    inner(ti) || return false
    # otherwise type-intersection reported an ambiguity we couldn't solve
    return true
end

"""
    delete_method(m::Method)

Make method `m` uncallable and force recompilation of any methods that use(d) it.
"""
function delete_method(m::Method)
    ccall(:jl_method_table_disable, Cvoid, (Any, Any), get_methodtable(m), m)
end

function get_methodtable(m::Method)
    mt = ccall(:jl_method_get_table, Any, (Any,), m)
    if mt === nothing
        return nothing
    end
    return mt::Core.MethodTable
end

"""
    has_bottom_parameter(t) -> Bool

Determine whether `t` is a Type for which one or more of its parameters is `Union{}`.
"""
function has_bottom_parameter(t::DataType)
    for p in t.parameters
        has_bottom_parameter(p) && return true
    end
    return false
end
has_bottom_parameter(t::typeof(Bottom)) = true
has_bottom_parameter(t::UnionAll) = has_bottom_parameter(unwrap_unionall(t))
has_bottom_parameter(t::Union) = has_bottom_parameter(t.a) & has_bottom_parameter(t.b)
has_bottom_parameter(t::TypeVar) = has_bottom_parameter(t.ub)
has_bottom_parameter(::Any) = false

min_world(m::Core.CodeInstance) = m.min_world
max_world(m::Core.CodeInstance) = m.max_world
min_world(m::Core.CodeInfo) = m.min_world
max_world(m::Core.CodeInfo) = m.max_world
get_world_counter() = ccall(:jl_get_world_counter, UInt, ())

"""
    propertynames(x, private=false)

Get a tuple or a vector of the properties (`x.property`) of an object `x`.
This is typically the same as [`fieldnames(typeof(x))`](@ref), but types
that overload [`getproperty`](@ref) should generally overload `propertynames`
as well to get the properties of an instance of the type.

`propertynames(x)` may return only "public" property names that are part
of the documented interface of `x`.   If you want it to also return "private"
property names intended for internal use, pass `true` for the optional second argument.
REPL tab completion on `x.` shows only the `private=false` properties.

See also: [`hasproperty`](@ref), [`hasfield`](@ref).
"""
propertynames(x) = fieldnames(typeof(x))
propertynames(m::Module) = names(m)
propertynames(x, private::Bool) = propertynames(x) # ignore private flag by default

"""
    hasproperty(x, s::Symbol)

Return a boolean indicating whether the object `x` has `s` as one of its own properties.

!!! compat "Julia 1.2"
     This function requires at least Julia 1.2.

See also: [`propertynames`](@ref), [`hasfield`](@ref).
"""
hasproperty(x, s::Symbol) = s in propertynames(x)

"""
    @invoke f(arg::T, ...; kwargs...)

Provides a convenient way to call [`invoke`](@ref) by expanding
`@invoke f(arg1::T1, arg2::T2; kwargs...)` to `invoke(f, Tuple{T1,T2}, arg1, arg2; kwargs...)`.
When an argument's type annotation is omitted, it's replaced with `Core.Typeof` that argument.
To invoke a method where an argument is untyped or explicitly typed as `Any`, annotate the
argument with `::Any`.

It also supports the following syntax:
- `@invoke (x::X).f` expands to `invoke(getproperty, Tuple{X,Symbol}, x, :f)`
- `@invoke (x::X).f = v::V` expands to `invoke(setproperty!, Tuple{X,Symbol,V}, x, :f, v)`
- `@invoke (xs::Xs)[i::I]` expands to `invoke(getindex, Tuple{Xs,I}, xs, i)`
- `@invoke (xs::Xs)[i::I] = v::V` expands to `invoke(setindex!, Tuple{Xs,V,I}, xs, v, i)`

# Examples

```jldoctest
julia> @macroexpand @invoke f(x::T, y)
:(Core.invoke(f, Tuple{T, Core.Typeof(y)}, x, y))

julia> @invoke 420::Integer % Unsigned
0x00000000000001a4

julia> @macroexpand @invoke (x::X).f
:(Core.invoke(Base.getproperty, Tuple{X, Core.Typeof(:f)}, x, :f))

julia> @macroexpand @invoke (x::X).f = v::V
:(Core.invoke(Base.setproperty!, Tuple{X, Core.Typeof(:f), V}, x, :f, v))

julia> @macroexpand @invoke (xs::Xs)[i::I]
:(Core.invoke(Base.getindex, Tuple{Xs, I}, xs, i))

julia> @macroexpand @invoke (xs::Xs)[i::I] = v::V
:(Core.invoke(Base.setindex!, Tuple{Xs, V, I}, xs, v, i))
```

!!! compat "Julia 1.7"
    This macro requires Julia 1.7 or later.

!!! compat "Julia 1.9"
    This macro is exported as of Julia 1.9.

!!! compat "Julia 1.10"
    The additional syntax is supported as of Julia 1.10.
"""
macro invoke(ex)
    topmod = Core.Compiler._topmod(__module__) # well, except, do not get it via CC but define it locally
    f, args, kwargs = destructure_callex(topmod, ex)
    types = Expr(:curly, :Tuple)
    out = Expr(:call, GlobalRef(Core, :invoke))
    isempty(kwargs) || push!(out.args, Expr(:parameters, kwargs...))
    push!(out.args, f)
    push!(out.args, types)
    for arg in args
        if isexpr(arg, :(::))
            push!(out.args, arg.args[1])
            push!(types.args, arg.args[2])
        else
            push!(out.args, arg)
            push!(types.args, Expr(:call, GlobalRef(Core, :Typeof), arg))
        end
    end
    return esc(out)
end

"""
    @invokelatest f(args...; kwargs...)

Provides a convenient way to call [`invokelatest`](@ref).
`@invokelatest f(args...; kwargs...)` will simply be expanded into
`Base.invokelatest(f, args...; kwargs...)`.

It also supports the following syntax:
- `@invokelatest x.f` expands to `Base.invokelatest(getproperty, x, :f)`
- `@invokelatest x.f = v` expands to `Base.invokelatest(setproperty!, x, :f, v)`
- `@invokelatest xs[i]` expands to `Base.invokelatest(getindex, xs, i)`
- `@invokelatest xs[i] = v` expands to `Base.invokelatest(setindex!, xs, v, i)`

```jldoctest
julia> @macroexpand @invokelatest f(x; kw=kwv)
:(Base.invokelatest(f, x; kw = kwv))

julia> @macroexpand @invokelatest x.f
:(Base.invokelatest(Base.getproperty, x, :f))

julia> @macroexpand @invokelatest x.f = v
:(Base.invokelatest(Base.setproperty!, x, :f, v))

julia> @macroexpand @invokelatest xs[i]
:(Base.invokelatest(Base.getindex, xs, i))

julia> @macroexpand @invokelatest xs[i] = v
:(Base.invokelatest(Base.setindex!, xs, v, i))
```

!!! compat "Julia 1.7"
    This macro requires Julia 1.7 or later.

!!! compat "Julia 1.9"
    Prior to Julia 1.9, this macro was not exported, and was called as `Base.@invokelatest`.

!!! compat "Julia 1.10"
    The additional `x.f` and `xs[i]` syntax requires Julia 1.10.
"""
macro invokelatest(ex)
    topmod = Core.Compiler._topmod(__module__) # well, except, do not get it via CC but define it locally
    f, args, kwargs = destructure_callex(topmod, ex)
    out = Expr(:call, GlobalRef(Base, :invokelatest))
    isempty(kwargs) || push!(out.args, Expr(:parameters, kwargs...))
    push!(out.args, f)
    append!(out.args, args)
    return esc(out)
end

function destructure_callex(topmod::Module, @nospecialize(ex))
    function flatten(xs)
        out = Any[]
        for x in xs
            if isexpr(x, :tuple)
                append!(out, x.args)
            else
                push!(out, x)
            end
        end
        return out
    end

    kwargs = Any[]
    if isexpr(ex, :call) # `f(args...)`
        f = first(ex.args)
        args = Any[]
        for x in ex.args[2:end]
            if isexpr(x, :parameters)
                append!(kwargs, x.args)
            elseif isexpr(x, :kw)
                push!(kwargs, x)
            else
                push!(args, x)
            end
        end
    elseif isexpr(ex, :.)   # `x.f`
        f = GlobalRef(topmod, :getproperty)
        args = flatten(ex.args)
    elseif isexpr(ex, :ref) # `x[i]`
        f = GlobalRef(topmod, :getindex)
        args = flatten(ex.args)
    elseif isexpr(ex, :(=)) # `x.f = v` or `x[i] = v`
        lhs, rhs = ex.args
        if isexpr(lhs, :.)
            f = GlobalRef(topmod, :setproperty!)
            args = flatten(Any[lhs.args..., rhs])
        elseif isexpr(lhs, :ref)
            f = GlobalRef(topmod, :setindex!)
            args = flatten(Any[lhs.args[1], rhs, lhs.args[2]])
        else
            throw(ArgumentError("expected a `setproperty!` expression `x.f = v` or `setindex!` expression `x[i] = v`"))
        end
    else
        throw(ArgumentError("expected a `:call` expression `f(args...; kwargs...)`"))
    end
    return f, args, kwargs
end
N   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/options.jl~
      # This file is a part of Julia. License is MIT: https://julialang.org/license

# NOTE: This type needs to be kept in sync with jl_options in src/jloptions.h
struct JLOptions
    quiet::Int8
    banner::Int8
    julia_bindir::Ptr{UInt8}
    julia_bin::Ptr{UInt8}
    commands::Ptr{Ptr{UInt8}} # (e)eval, (E)print, (L)load
    image_file::Ptr{UInt8}
    cpu_target::Ptr{UInt8}
    nthreadpools::Int16
    nthreads::Int16
    nmarkthreads::Int16
    nsweepthreads::Int8
    nthreads_per_pool::Ptr{Int16}
    nprocs::Int32
    machine_file::Ptr{UInt8}
    project::Ptr{UInt8}
    isinteractive::Int8
    color::Int8
    historyfile::Int8
    startupfile::Int8
    compile_enabled::Int8
    code_coverage::Int8
    malloc_log::Int8
    tracked_path::Ptr{UInt8}
    opt_level::Int8
    opt_level_min::Int8
    debug_level::Int8
    check_bounds::Int8
    depwarn::Int8
    warn_overwrite::Int8
    can_inline::Int8
    polly::Int8
    trace_compile::Ptr{UInt8}
    fast_math::Int8
    worker::Int8
    cookie::Ptr{UInt8}
    handle_signals::Int8
    use_sysimage_native_code::Int8
    use_compiled_modules::Int8
    use_pkgimages::Int8
    bindto::Ptr{UInt8}
    outputbc::Ptr{UInt8}
    outputunoptbc::Ptr{UInt8}
    outputo::Ptr{UInt8}
    outputasm::Ptr{UInt8}
    outputji::Ptr{UInt8}
    output_code_coverage::Ptr{UInt8}
    incremental::Int8
    image_file_specified::Int8
    warn_scope::Int8
    image_codegen::Int8
    rr_detach::Int8
    strip_metadata::Int8
    strip_ir::Int8
    permalloc_pkgimg::Int8
    heap_size_hint::UInt64
end

# This runs early in the sysimage != is not defined yet
if sizeof(JLOptions) === ccall(:jl_sizeof_jl_options, Int, ())
else
    ccall(:jl_throw, Cvoid, (Any,), "Option structure mismatch")
end

JLOptions() = unsafe_load(cglobal(:jl_options, JLOptions))

function show(io::IO, opt::JLOptions)
    print(io, "JLOptions(")
    fields = fieldnames(JLOptions)
    nfields = length(fields)
    for (i, f) in enumerate(fields)
        v = getfield(opt, i)
        if isa(v, Ptr{UInt8})
            v = (v != C_NULL) ? unsafe_string(v) : ""
        elseif isa(v, Ptr{Ptr{UInt8}})
            v = unsafe_load_commands(v)
        end
        print(io, f, " = ", repr(v), i < nfields ? ", " : "")
    end
    print(io, ")")
end

function unsafe_load_commands(v::Ptr{Ptr{UInt8}})
    cmds = Pair{Char, String}[]
    v == C_NULL && return cmds
    i = 1
    while true
        s = unsafe_load(v, i)
        s == C_NULL && break
        e = Char(unsafe_load(s))
        push!(cmds, e => unsafe_string(s + 1))
        i += 1
    end
    return cmds
end

function is_file_tracked(file::Symbol)
    return ccall(:jl_is_file_tracked, Cint, (Any,), file) == 1
end
P   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/promotion.jl@      # This file is a part of Julia. License is MIT: https://julialang.org/license

## type join (closest common ancestor, or least upper bound) ##

"""
    typejoin(T, S, ...)

Return the closest common ancestor of types `T` and `S`, i.e. the narrowest type from which
they both inherit. Recurses on additional varargs.

# Examples
```jldoctest
julia> typejoin(Int, Float64)
Real

julia> typejoin(Int, Float64, ComplexF32)
Number
```
"""
typejoin() = Bottom
typejoin(@nospecialize(t)) = t
typejoin(@nospecialize(t), ts...) = (@_foldable_meta; typejoin(t, typejoin(ts...)))
function typejoin(@nospecialize(a), @nospecialize(b))
    @_foldable_meta
    if isa(a, TypeVar)
        return typejoin(a.ub, b)
    elseif isa(b, TypeVar)
        return typejoin(a, b.ub)
    elseif a <: b
        return b
    elseif b <: a
        return a
    elseif isa(a, UnionAll)
        return UnionAll(a.var, typejoin(a.body, b))
    elseif isa(b, UnionAll)
        return UnionAll(b.var, typejoin(a, b.body))
    elseif isa(a, Union)
        return typejoin(typejoin(a.a, a.b), b)
    elseif isa(b, Union)
        return typejoin(a, typejoin(b.a, b.b))
    end
    # a and b are DataTypes
    # We have to hide Constant info from inference, see #44390
    a, b = inferencebarrier(a)::DataType, inferencebarrier(b)::DataType
    if a <: Tuple
        if !(b <: Tuple)
            return Any
        end
        ap, bp = a.parameters, b.parameters
        lar = length(ap)
        lbr = length(bp)
        if lar == 0
            return Tuple{Vararg{tailjoin(bp, 1)}}
        end
        if lbr == 0
            return Tuple{Vararg{tailjoin(ap, 1)}}
        end
        laf, afixed = full_va_len(ap)
        lbf, bfixed = full_va_len(bp)
        if laf < lbf
            if isvarargtype(ap[lar]) && !afixed
                c = Vector{Any}(undef, laf)
                c[laf] = Vararg{typejoin(unwrapva(ap[lar]), tailjoin(bp, laf))}
                n = laf-1
            else
                c = Vector{Any}(undef, laf+1)
                c[laf+1] = Vararg{tailjoin(bp, laf+1)}
                n = laf
            end
        elseif lbf < laf
            if isvarargtype(bp[lbr]) && !bfixed
                c = Vector{Any}(undef, lbf)
                c[lbf] = Vararg{typejoin(unwrapva(bp[lbr]), tailjoin(ap, lbf))}
                n = lbf-1
            else
                c = Vector{Any}(undef, lbf+1)
                c[lbf+1] = Vararg{tailjoin(ap, lbf+1)}
                n = lbf
            end
        else
            c = Vector{Any}(undef, laf)
            n = laf
        end
        for i = 1:n
            ai = ap[min(i,lar)]; bi = bp[min(i,lbr)]
            ci = typejoin(unwrapva(ai), unwrapva(bi))
            c[i] = i == length(c) && (isvarargtype(ai) || isvarargtype(bi)) ? Vararg{ci} : ci
        end
        return Tuple{c...}
    elseif b <: Tuple
        return Any
    end
    while b !== Any
        if a <: b.name.wrapper
            while a.name !== b.name
                a = supertype(a)::DataType
            end
            if a.name === Type.body.name
                ap = a.parameters[1]
                bp = b.parameters[1]
                if ((isa(ap,TypeVar) && ap.lb === Bottom && ap.ub === Any) ||
                    (isa(bp,TypeVar) && bp.lb === Bottom && bp.ub === Any))
                    # handle special Type{T} supertype
                    return Type
                end
            end
            aprimary = a.name.wrapper
            # join on parameters
            n = length(a.parameters)
            if n == 0
                return aprimary
            end
            vars = []
            for i = 1:n
                ai, bi = a.parameters[i], b.parameters[i]
                if ai === bi || (isa(ai,Type) && isa(bi,Type) && ai <: bi && bi <: ai)
                    aprimary = aprimary{ai}
                else
                    aprimary = aprimary::UnionAll
                    # pushfirst!(vars, aprimary.var)
                    _growbeg!(vars, 1)
                    arrayset(false, vars, aprimary.var, 1)
                    aprimary = aprimary.body
                end
            end
            for v in vars
                aprimary = UnionAll(v, aprimary)
            end
            return aprimary
        end
        b = supertype(b)::DataType
    end
    return Any
end

# return an upper-bound on type `a` with type `b` removed
# such that `return <: a` && `Union{return, b} == Union{a, b}`
# WARNING: this is wrong for some objects for which subtyping is broken
#          (Core.Compiler.isnotbrokensubtype), use only simple types for `b`
function typesplit(@nospecialize(a), @nospecialize(b))
    @_foldable_meta
    if a <: b
        return Bottom
    end
    if isa(a, Union)
        return Union{typesplit(a.a, b),
                     typesplit(a.b, b)}
    end
    return a
end


"""
    promote_typejoin(T, S)

Compute a type that contains both `T` and `S`, which could be
either a parent of both types, or a `Union` if appropriate.
Falls back to [`typejoin`](@ref).

See instead [`promote`](@ref), [`promote_type`](@ref).

# Examples
```jldoctest
julia> Base.promote_typejoin(Int, Float64)
Real

julia> Base.promote_type(Int, Float64)
Float64
```
"""
function promote_typejoin(@nospecialize(a), @nospecialize(b))
    c = typejoin(_promote_typesubtract(a), _promote_typesubtract(b))
    return Union{a, b, c}::Type
end
_promote_typesubtract(@nospecialize(a)) =
    a === Any ? a :
    a >: Union{Nothing, Missing} ? typesplit(a, Union{Nothing, Missing}) :
    a >: Nothing ? typesplit(a, Nothing) :
    a >: Missing ? typesplit(a, Missing) :
    a

function promote_typejoin_union(::Type{T}) where T
    if T === Union{}
        return Union{}
    elseif T isa UnionAll
        return Any # TODO: compute more precise bounds
    elseif T isa Union
        return promote_typejoin(promote_typejoin_union(T.a), promote_typejoin_union(T.b))
    elseif T isa DataType
        T <: Tuple && return typejoin_union_tuple(T)
        return T
    else
        error("unreachable") # not a type??
    end
end

function typejoin_union_tuple(T::DataType)
    @_foldable_meta
    u = Base.unwrap_unionall(T)
    p = (u::DataType).parameters
    lr = length(p)::Int
    if lr == 0
        return Tuple{}
    end
    c = Vector{Any}(undef, lr)
    for i = 1:lr
        pi = p[i]
        U = Core.Compiler.unwrapva(pi)
        if U === Union{}
            ci = Union{}
        elseif U isa Union
            ci = typejoin(U.a, U.b)
        elseif U isa UnionAll
            return Any # TODO: compute more precise bounds
        else
            ci = promote_typejoin_union(U)
        end
        if i == lr && Core.Compiler.isvarargtype(pi)
            c[i] = isdefined(pi, :N) ? Vararg{ci, pi.N} : Vararg{ci}
        else
            c[i] = ci
        end
    end
    return Base.rewrap_unionall(Tuple{c...}, T)
end

# Returns length, isfixed
function full_va_len(p::Core.SimpleVector)
    isempty(p) && return 0, true
    last = p[end]
    if isvarargtype(last)
        if isdefined(last, :N)
            N = last.N
            isa(N, Int) && return length(p) + N - 1, true
        end
        return length(p), false
    end
    return length(p), true
end

# reduce typejoin over A[i:end]
function tailjoin(A, i)
    if i > length(A)
        return unwrapva(A[end])
    end
    t = Bottom
    for j = i:length(A)
        t = typejoin(t, unwrapva(A[j]))
    end
    return t
end

## promotion mechanism ##

"""
    promote_type(type1, type2, ...)

Promotion refers to converting values of mixed types to a single common type.
`promote_type` represents the default promotion behavior in Julia when
operators (usually mathematical) are given arguments of differing types.
`promote_type` generally tries to return a type which can at least approximate
most values of either input type without excessively widening.  Some loss is
tolerated; for example, `promote_type(Int64, Float64)` returns
[`Float64`](@ref) even though strictly, not all [`Int64`](@ref) values can be
represented exactly as `Float64` values.

See also: [`promote`](@ref), [`promote_typejoin`](@ref), [`promote_rule`](@ref).

# Examples
```jldoctest
julia> promote_type(Int64, Float64)
Float64

julia> promote_type(Int32, Int64)
Int64

julia> promote_type(Float32, BigInt)
BigFloat

julia> promote_type(Int16, Float16)
Float16

julia> promote_type(Int64, Float16)
Float16

julia> promote_type(Int8, UInt16)
UInt16
```

!!! warning "Don't overload this directly"
    To overload promotion for your own types you should overload [`promote_rule`](@ref).
    `promote_type` calls `promote_rule` internally to determine the type.
    Overloading `promote_type` directly can cause ambiguity errors.
"""
function promote_type end

promote_type()  = Bottom
promote_type(T) = T
promote_type(T, S, U, V...) = (@inline; promote_type(T, promote_type(S, U, V...)))

promote_type(::Type{Bottom}, ::Type{Bottom}) = Bottom
promote_type(::Type{T}, ::Type{T}) where {T} = T
promote_type(::Type{T}, ::Type{Bottom}) where {T} = T
promote_type(::Type{Bottom}, ::Type{T}) where {T} = T

function promote_type(::Type{T}, ::Type{S}) where {T,S}
    @inline
    # Try promote_rule in both orders. Typically only one is defined,
    # and there is a fallback returning Bottom below, so the common case is
    #   promote_type(T, S) =>
    #   promote_result(T, S, result, Bottom) =>
    #   typejoin(result, Bottom) => result
    promote_result(T, S, promote_rule(T,S), promote_rule(S,T))
end

"""
    promote_rule(type1, type2)

Specifies what type should be used by [`promote`](@ref) when given values of types `type1` and
`type2`. This function should not be called directly, but should have definitions added to
it for new types as appropriate.
"""
function promote_rule end

promote_rule(::Type, ::Type) = Bottom
# Define some methods to avoid needing to enumerate unrelated possibilities when presented
# with Type{<:T}, and return a value in general accordance with the result given by promote_type
promote_rule(::Type{Bottom}, slurp...) = Bottom
promote_rule(::Type{Bottom}, ::Type{Bottom}, slurp...) = Bottom # not strictly necessary, since the next method would match unambiguously anyways
promote_rule(::Type{Bottom}, ::Type{T}, slurp...) where {T} = T
promote_rule(::Type{T}, ::Type{Bottom}, slurp...) where {T} = T

promote_result(::Type,::Type,::Type{T},::Type{S}) where {T,S} = (@inline; promote_type(T,S))
# If no promote_rule is defined, both directions give Bottom. In that
# case use typejoin on the original types instead.
promote_result(::Type{T},::Type{S},::Type{Bottom},::Type{Bottom}) where {T,S} = (@inline; typejoin(T, S))

"""
    promote(xs...)

Convert all arguments to a common type, and return them all (as a tuple).
If no arguments can be converted, an error is raised.

See also: [`promote_type`](@ref), [`promote_rule`](@ref).

# Examples
```jldoctest
julia> promote(Int8(1), Float16(4.5), Float32(4.1))
(1.0f0, 4.5f0, 4.1f0)

julia> promote_type(Int8, Float16, Float32)
Float32

julia> reduce(Base.promote_typejoin, (Int8, Float16, Float32))
Real

julia> promote(1, "x")
ERROR: promotion of types Int64 and String failed to change any arguments
[...]

julia> promote_type(Int, String)
Any
```
"""
function promote end

function _promote(x::T, y::S) where {T,S}
    @inline
    R = promote_type(T, S)
    return (convert(R, x), convert(R, y))
end
promote_typeof(x) = typeof(x)
promote_typeof(x, xs...) = (@inline; promote_type(typeof(x), promote_typeof(xs...)))
function _promote(x, y, z)
    @inline
    R = promote_typeof(x, y, z)
    return (convert(R, x), convert(R, y), convert(R, z))
end
function _promote(x, y, zs...)
    @inline
    R = promote_typeof(x, y, zs...)
    return (convert(R, x), convert(R, y), convert(Tuple{Vararg{R}}, zs)...)
end
# TODO: promote(x::T, ys::T...) where {T} here to catch all circularities?

## promotions in arithmetic, etc. ##

promote() = ()
promote(x) = (x,)

function promote(x, y)
    @inline
    px, py = _promote(x, y)
    not_sametype((x,y), (px,py))
    px, py
end
function promote(x, y, z)
    @inline
    px, py, pz = _promote(x, y, z)
    not_sametype((x,y,z), (px,py,pz))
    px, py, pz
end
function promote(x, y, z, a...)
    p = _promote(x, y, z, a...)
    not_sametype((x, y, z, a...), p)
    p
end

promote(x::T, y::T, zs::T...) where {T} = (x, y, zs...)

not_sametype(x::T, y::T) where {T} = sametype_error(x)

not_sametype(x, y) = nothing

function sametype_error(input)
    @noinline
    error("promotion of types ",
          join(map(x->string(typeof(x)), input), ", ", " and "),
          " failed to change any arguments")
end

+(x::Number, y::Number) = +(promote(x,y)...)
*(x::Number, y::Number) = *(promote(x,y)...)
-(x::Number, y::Number) = -(promote(x,y)...)
/(x::Number, y::Number) = /(promote(x,y)...)

"""
    ^(x, y)

Exponentiation operator. If `x` is a matrix, computes matrix exponentiation.

If `y` is an `Int` literal (e.g. `2` in `x^2` or `-3` in `x^-3`), the Julia code
`x^y` is transformed by the compiler to `Base.literal_pow(^, x, Val(y))`, to
enable compile-time specialization on the value of the exponent.
(As a default fallback we have `Base.literal_pow(^, x, Val(y)) = ^(x,y)`,
where usually `^ == Base.^` unless `^` has been defined in the calling
namespace.) If `y` is a negative integer literal, then `Base.literal_pow`
transforms the operation to `inv(x)^-y` by default, where `-y` is positive.

# Examples
```jldoctest
julia> 3^5
243

julia> A = [1 2; 3 4]
2×2 Matrix{Int64}:
 1  2
 3  4

julia> A^3
2×2 Matrix{Int64}:
 37   54
 81  118
```
"""
^(x::Number, y::Number) = ^(promote(x,y)...)

fma(x::Number, y::Number, z::Number) = fma(promote(x,y,z)...)
muladd(x::Number, y::Number, z::Number) = muladd(promote(x,y,z)...)

==(x::Number, y::Number) = (==)(promote(x,y)...)
<( x::Real, y::Real)     = (< )(promote(x,y)...)
<=(x::Real, y::Real)     = (<=)(promote(x,y)...)

rem(x::Real, y::Real) = rem(promote(x,y)...)
mod(x::Real, y::Real) = mod(promote(x,y)...)

mod1(x::Real, y::Real) = mod1(promote(x,y)...)
fld1(x::Real, y::Real) = fld1(promote(x,y)...)

max(x::Real, y::Real) = max(promote(x,y)...)
min(x::Real, y::Real) = min(promote(x,y)...)
minmax(x::Real, y::Real) = minmax(promote(x, y)...)

if isdefined(Core, :Compiler)
    const _return_type = Core.Compiler.return_type
else
    _return_type(@nospecialize(f), @nospecialize(t)) = Any
end

function TupleOrBottom(tt...)
    any(p -> p === Union{}, tt) && return Union{}
    return Tuple{tt...}
end

"""
    promote_op(f, argtypes...)

Guess what an appropriate container eltype would be for storing results of
`f(::argtypes...)`. The guess is in part based on type inference, so can change any time.

!!! warning
    Due to its fragility, use of `promote_op` should be avoided. It is preferable to base
    the container eltype on the type of the actual elements. Only in the absence of any
    elements (for an empty result container), it may be unavoidable to call `promote_op`.
"""
function promote_op(f, S::Type...)
    argT = TupleOrBottom(S...)
    argT === Union{} && return Union{}
    return _return_type(f, argT)
end


## catch-alls to prevent infinite recursion when definitions are missing ##

no_op_err(name, T) = error(name," not defined for ",T)
(+)(x::T, y::T) where {T<:Number} = no_op_err("+", T)
(*)(x::T, y::T) where {T<:Number} = no_op_err("*", T)
(-)(x::T, y::T) where {T<:Number} = no_op_err("-", T)
(/)(x::T, y::T) where {T<:Number} = no_op_err("/", T)
(^)(x::T, y::T) where {T<:Number} = no_op_err("^", T)

fma(x::T, y::T, z::T) where {T<:Number} = no_op_err("fma", T)
fma(x::Integer, y::Integer, z::Integer) = x*y+z
muladd(x::T, y::T, z::T) where {T<:Number} = x*y+z

(&)(x::T, y::T) where {T<:Integer} = no_op_err("&", T)
(|)(x::T, y::T) where {T<:Integer} = no_op_err("|", T)
xor(x::T, y::T) where {T<:Integer} = no_op_err("xor", T)

(==)(x::T, y::T) where {T<:Number} = x === y
(< )(x::T, y::T) where {T<:Real} = no_op_err("<" , T)
(<=)(x::T, y::T) where {T<:Real} = (x == y) | (x < y)

rem(x::T, y::T) where {T<:Real} = no_op_err("rem", T)
mod(x::T, y::T) where {T<:Real} = no_op_err("mod", T)

min(x::Real) = x
max(x::Real) = x
minmax(x::Real) = (x, x)

max(x::T, y::T) where {T<:Real} = ifelse(y < x, x, y)
min(x::T, y::T) where {T<:Real} = ifelse(y < x, y, x)
minmax(x::T, y::T) where {T<:Real} = y < x ? (y, x) : (x, y)

flipsign(x::T, y::T) where {T<:Signed} = no_op_err("flipsign", T)
L   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/tuple.jl2K      # This file is a part of Julia. License is MIT: https://julialang.org/license

# Document NTuple here where we have everything needed for the doc system
"""
    NTuple{N, T}

A compact way of representing the type for a tuple of length `N` where all elements are of type `T`.

# Examples
```jldoctest
julia> isa((1, 2, 3, 4, 5, 6), NTuple{6, Int})
true
```

See also [`ntuple`](@ref).
"""
NTuple

# convenience function for extracting N from a Tuple (if defined)
# else return `nothing` for anything else given (such as Vararg or other non-sized Union)
_counttuple(::Type{<:NTuple{N,Any}}) where {N} = N
_counttuple(::Type) = nothing

## indexing ##

length(@nospecialize t::Tuple) = nfields(t)
firstindex(@nospecialize t::Tuple) = 1
lastindex(@nospecialize t::Tuple) = length(t)
size(@nospecialize(t::Tuple), d::Integer) = (d == 1) ? length(t) : throw(ArgumentError("invalid tuple dimension $d"))
axes(@nospecialize t::Tuple) = (OneTo(length(t)),)
@eval getindex(@nospecialize(t::Tuple), i::Int) = getfield(t, i, $(Expr(:boundscheck)))
@eval getindex(@nospecialize(t::Tuple), i::Integer) = getfield(t, convert(Int, i), $(Expr(:boundscheck)))
__inbounds_getindex(@nospecialize(t::Tuple), i::Int) = getfield(t, i, false)
__inbounds_getindex(@nospecialize(t::Tuple), i::Integer) = getfield(t, convert(Int, i), false)
getindex(t::Tuple, r::AbstractArray{<:Any,1}) = (eltype(t)[t[ri] for ri in r]...,)
getindex(t::Tuple, b::AbstractArray{Bool,1}) = length(b) == length(t) ? getindex(t, findall(b)) : throw(BoundsError(t, b))
getindex(t::Tuple, c::Colon) = t

get(t::Tuple, i::Integer, default) = i in 1:length(t) ? getindex(t, i) : default
get(f::Callable, t::Tuple, i::Integer) = i in 1:length(t) ? getindex(t, i) : f()

# returns new tuple; N.B.: becomes no-op if `i` is out-of-bounds

"""
    setindex(c::Tuple, v, i::Integer)

Creates a new tuple similar to `x` with the value at index `i` set to `v`.
Throws a `BoundsError` when out of bounds.

# Examples
```jldoctest
julia> Base.setindex((1, 2, 6), 2, 3) == (1, 2, 2)
true
```
"""
function setindex(x::Tuple, v, i::Integer)
    @boundscheck 1 <= i <= length(x) || throw(BoundsError(x, i))
    @inline
    _setindex(v, i, x...)
end

function _setindex(v, i::Integer, args::Vararg{Any,N}) where {N}
    @inline
    return ntuple(j -> ifelse(j == i, v, args[j]), Val{N}())
end


## iterating ##

function iterate(@nospecialize(t::Tuple), i::Int=1)
    @inline
    return (1 <= i <= length(t)) ? (t[i], i + 1) : nothing
end

keys(@nospecialize t::Tuple) = OneTo(length(t))

prevind(@nospecialize(t::Tuple), i::Integer) = Int(i)-1
nextind(@nospecialize(t::Tuple), i::Integer) = Int(i)+1

function keys(t::Tuple, t2::Tuple...)
    @inline
    OneTo(_maxlength(t, t2...))
end
_maxlength(t::Tuple) = length(t)
function _maxlength(t::Tuple, t2::Tuple, t3::Tuple...)
    @inline
    max(length(t), _maxlength(t2, t3...))
end

# this allows partial evaluation of bounded sequences of next() calls on tuples,
# while reducing to plain next() for arbitrary iterables.
indexed_iterate(t::Tuple, i::Int, state=1) = (@inline; (getfield(t, i), i+1))
indexed_iterate(a::Array, i::Int, state=1) = (@inline; (a[i], i+1))
function indexed_iterate(I, i)
    x = iterate(I)
    x === nothing && throw(BoundsError(I, i))
    x
end
function indexed_iterate(I, i, state)
    x = iterate(I, state)
    x === nothing && throw(BoundsError(I, i))
    x
end

"""
    Base.rest(collection[, itr_state])

Generic function for taking the tail of `collection`, starting from a specific iteration
state `itr_state`. Return a `Tuple`, if `collection` itself is a `Tuple`, a subtype of
`AbstractVector`, if `collection` is an `AbstractArray`, a subtype of `AbstractString`
if `collection` is an `AbstractString`, and an arbitrary iterator, falling back to
`Iterators.rest(collection[, itr_state])`, otherwise.

Can be overloaded for user-defined collection types to customize the behavior of [slurping
in assignments](@ref destructuring-assignment) in final position, like `a, b... = collection`.

!!! compat "Julia 1.6"
    `Base.rest` requires at least Julia 1.6.

See also: [`first`](@ref first), [`Iterators.rest`](@ref), [`Base.split_rest`](@ref).

# Examples
```jldoctest
julia> a = [1 2; 3 4]
2×2 Matrix{Int64}:
 1  2
 3  4

julia> first, state = iterate(a)
(1, 2)

julia> first, Base.rest(a, state)
(1, [3, 2, 4])
```
"""
function rest end
rest(t::Tuple) = t
rest(t::Tuple, i::Int) = ntuple(x -> getfield(t, x+i-1), length(t)-i+1)
rest(a::Array, i::Int=1) = a[i:end]
rest(a::Core.SimpleVector, i::Int=1) = a[i:end]
rest(itr, state...) = Iterators.rest(itr, state...)

"""
    Base.split_rest(collection, n::Int[, itr_state]) -> (rest_but_n, last_n)

Generic function for splitting the tail of `collection`, starting from a specific iteration
state `itr_state`. Returns a tuple of two new collections. The first one contains all
elements of the tail but the `n` last ones, which make up the second collection.

The type of the first collection generally follows that of [`Base.rest`](@ref), except that
the fallback case is not lazy, but is collected eagerly into a vector.

Can be overloaded for user-defined collection types to customize the behavior of [slurping
in assignments](@ref destructuring-assignment) in non-final position, like `a, b..., c = collection`.

!!! compat "Julia 1.9"
    `Base.split_rest` requires at least Julia 1.9.

See also: [`Base.rest`](@ref).

# Examples
```jldoctest
julia> a = [1 2; 3 4]
2×2 Matrix{Int64}:
 1  2
 3  4

julia> first, state = iterate(a)
(1, 2)

julia> first, Base.split_rest(a, 1, state)
(1, ([3, 2], [4]))
```
"""
function split_rest end
function split_rest(itr, n::Int, state...)
    if IteratorSize(itr) == IsInfinite()
        throw(ArgumentError("Cannot split an infinite iterator in the middle."))
    end
    return _split_rest(rest(itr, state...), n)
end
_split_rest(itr, n::Int) = _split_rest(collect(itr), n)
function _check_length_split_rest(len, n)
    len < n && throw(ArgumentError(
        "The iterator only contains $len elements, but at least $n were requested."
    ))
end
function _split_rest(a::Union{AbstractArray, Core.SimpleVector}, n::Int)
    _check_length_split_rest(length(a), n)
    return a[begin:end-n], a[end-n+1:end]
end

@eval split_rest(t::Tuple, n::Int, i=1) = ($(Expr(:meta, :aggressive_constprop)); (t[i:end-n], t[end-n+1:end]))

# Use dispatch to avoid a branch in first
first(::Tuple{}) = throw(ArgumentError("tuple must be non-empty"))
first(t::Tuple) = t[1]

# eltype

eltype(::Type{Tuple{}}) = Bottom
function eltype(t::Type{<:Tuple{Vararg{E}}}) where {E}
    if @isdefined(E)
        return E
    else
        # TODO: need to guard against E being miscomputed by subtyping (ref #23017)
        # and compute the result manually in this case
        return _compute_eltype(t)
    end
end
eltype(t::Type{<:Tuple}) = _compute_eltype(t)
function _tuple_unique_fieldtypes(@nospecialize t)
    @_total_meta
    types = IdSet()
    t´ = unwrap_unionall(t)
    # Given t = Tuple{Vararg{S}} where S<:Real, the various
    # unwrapping/wrapping/va-handling here will return Real
    if t´ isa Union
        union!(types, _tuple_unique_fieldtypes(rewrap_unionall(t´.a, t)))
        union!(types, _tuple_unique_fieldtypes(rewrap_unionall(t´.b, t)))
    else
        for ti in (t´::DataType).parameters
            push!(types, rewrap_unionall(unwrapva(ti), t))
        end
    end
    return Core.svec(types...)
end
function _compute_eltype(@nospecialize t)
    @_total_meta # TODO: the compiler shouldn't need this
    types = _tuple_unique_fieldtypes(t)
    return afoldl(types...) do a, b
        # if we've already reached Any, it can't widen any more
        a === Any && return Any
        b === Any && return Any
        return promote_typejoin(a, b)
    end
end

# We'd like to be able to infer eltype(::Tuple), which needs to be able to
# look at these four methods:
#
# julia> methods(Base.eltype, Tuple{Type{<:Tuple}})
# 4 methods for generic function "eltype" from Base:
# [1] eltype(::Type{Union{}})
#  @ abstractarray.jl:234
# [2] eltype(::Type{Tuple{}})
#  @ tuple.jl:199
# [3] eltype(t::Type{<:Tuple{Vararg{E}}}) where E
#  @ tuple.jl:200
# [4] eltype(t::Type{<:Tuple})
#  @ tuple.jl:209
typeof(function eltype end).name.max_methods = UInt8(4)

# version of tail that doesn't throw on empty tuples (used in array indexing)
safe_tail(t::Tuple) = tail(t)
safe_tail(t::Tuple{}) = ()

# front (the converse of tail: it skips the last entry)

"""
    front(x::Tuple)::Tuple

Return a `Tuple` consisting of all but the last component of `x`.

See also: [`first`](@ref), [`tail`](@ref Base.tail).

# Examples
```jldoctest
julia> Base.front((1,2,3))
(1, 2)

julia> Base.front(())
ERROR: ArgumentError: Cannot call front on an empty tuple.
```
"""
function front(t::Tuple)
    @inline
    _front(t...)
end
_front() = throw(ArgumentError("Cannot call front on an empty tuple."))
_front(v) = ()
function _front(v, t...)
    @inline
    (v, _front(t...)...)
end

## mapping ##

# 1 argument function
map(f, t::Tuple{})              = ()
map(f, t::Tuple{Any,})          = (@inline; (f(t[1]),))
map(f, t::Tuple{Any, Any})      = (@inline; (f(t[1]), f(t[2])))
map(f, t::Tuple{Any, Any, Any}) = (@inline; (f(t[1]), f(t[2]), f(t[3])))
map(f, t::Tuple)                = (@inline; (f(t[1]), map(f,tail(t))...))
# stop inlining after some number of arguments to avoid code blowup
const Any32{N} = Tuple{Any,Any,Any,Any,Any,Any,Any,Any,
                       Any,Any,Any,Any,Any,Any,Any,Any,
                       Any,Any,Any,Any,Any,Any,Any,Any,
                       Any,Any,Any,Any,Any,Any,Any,Any,
                       Vararg{Any,N}}
const All32{T,N} = Tuple{T,T,T,T,T,T,T,T,
                         T,T,T,T,T,T,T,T,
                         T,T,T,T,T,T,T,T,
                         T,T,T,T,T,T,T,T,
                         Vararg{T,N}}
function map(f, t::Any32)
    n = length(t)
    A = Vector{Any}(undef, n)
    for i=1:n
        A[i] = f(t[i])
    end
    (A...,)
end
# 2 argument function
map(f, t::Tuple{},        s::Tuple{})        = ()
map(f, t::Tuple,          s::Tuple{})        = ()
map(f, t::Tuple{},        s::Tuple)          = ()
map(f, t::Tuple{Any,},    s::Tuple{Any,})    = (@inline; (f(t[1],s[1]),))
map(f, t::Tuple{Any,Any}, s::Tuple{Any,Any}) = (@inline; (f(t[1],s[1]), f(t[2],s[2])))
function map(f, t::Tuple, s::Tuple)
    @inline
    (f(t[1],s[1]), map(f, tail(t), tail(s))...)
end
function map(f, t::Any32, s::Any32)
    n = min(length(t), length(s))
    A = Vector{Any}(undef, n)
    for i = 1:n
        A[i] = f(t[i], s[i])
    end
    (A...,)
end
# n argument function
heads(ts::Tuple...) = map(t -> t[1], ts)
tails(ts::Tuple...) = map(tail, ts)
map(f, ::Tuple{}...) = ()
anyempty(x::Tuple{}, xs...) = true
anyempty(x::Tuple, xs...) = anyempty(xs...)
anyempty() = false
function map(f, t1::Tuple, t2::Tuple, ts::Tuple...)
    @inline
    anyempty(t1, t2, ts...) && return ()
    (f(heads(t1, t2, ts...)...), map(f, tails(t1, t2, ts...)...)...)
end
function map(f, t1::Any32, t2::Any32, ts::Any32...)
    n = min(length(t1), length(t2), minimum(length, ts))
    A = Vector{Any}(undef, n)
    for i = 1:n
        A[i] = f(t1[i], t2[i], map(t -> t[i], ts)...)
    end
    (A...,)
end

# type-stable padding
fill_to_length(t::NTuple{N,Any}, val, ::Val{N}) where {N} = t
fill_to_length(t::Tuple{}, val, ::Val{1}) = (val,)
fill_to_length(t::Tuple{Any}, val, ::Val{2}) = (t..., val)
fill_to_length(t::Tuple{}, val, ::Val{2}) = (val, val)
#function fill_to_length(t::Tuple, val, ::Val{N}) where {N}
#    @inline
#    return (t..., ntuple(i -> val, N - length(t))...)
#end

# constructing from an iterator

# only define these in Base, to avoid overwriting the constructors
# NOTE: this means this constructor must be avoided in Core.Compiler!
if nameof(@__MODULE__) === :Base

function tuple_type_tail(T::Type)
    @_foldable_meta # TODO: this method is wrong (and not :foldable)
    if isa(T, UnionAll)
        return UnionAll(T.var, tuple_type_tail(T.body))
    elseif isa(T, Union)
        return Union{tuple_type_tail(T.a), tuple_type_tail(T.b)}
    else
        T.name === Tuple.name || throw(MethodError(tuple_type_tail, (T,)))
        if isvatuple(T) && length(T.parameters) == 1
            va = unwrap_unionall(T.parameters[1])::Core.TypeofVararg
            (isdefined(va, :N) && isa(va.N, Int)) || return T
            return Tuple{Vararg{va.T, va.N-1}}
        end
        return Tuple{argtail(T.parameters...)...}
    end
end

(::Type{T})(x::Tuple) where {T<:Tuple} = x isa T ? x : convert(T, x)  # still use `convert` for tuples

Tuple(x::Ref) = tuple(getindex(x))  # faster than iterator for one element
Tuple(x::Array{T,0}) where {T} = tuple(getindex(x))

(::Type{T})(itr) where {T<:Tuple} = _totuple(T, itr)

_totuple(::Type{Tuple{}}, itr, s...) = ()

function _totuple_err(@nospecialize T)
    @noinline
    throw(ArgumentError("too few elements for tuple type $T"))
end

function _totuple(::Type{T}, itr, s::Vararg{Any,N}) where {T,N}
    @inline
    y = iterate(itr, s...)
    y === nothing && _totuple_err(T)
    T1 = fieldtype(T, 1)
    y1 = y[1]
    t1 = y1 isa T1 ? y1 : convert(T1, y1)::T1
    # inference may give up in recursive calls, so annotate here to force accurate return type to be propagated
    rT = tuple_type_tail(T)
    ts = _totuple(rT, itr, y[2])::rT
    return (t1, ts...)::T
end

# use iterative algorithm for long tuples
function _totuple(T::Type{All32{E,N}}, itr) where {E,N}
    len = N+32
    elts = collect(E, Iterators.take(itr,len))
    if length(elts) != len
        _totuple_err(T)
    end
    (elts...,)
end

_totuple(::Type{Tuple{Vararg{E}}}, itr, s...) where {E} = (collect(E, Iterators.rest(itr,s...))...,)

_totuple(::Type{Tuple}, itr, s...) = (collect(Iterators.rest(itr,s...))...,)

# for types that `apply` knows about, just splatting is faster than collecting first
_totuple(::Type{Tuple}, itr::Array) = (itr...,)
_totuple(::Type{Tuple}, itr::SimpleVector) = (itr...,)
_totuple(::Type{Tuple}, itr::NamedTuple) = (itr...,)
_totuple(::Type{Tuple}, x::Number) = (x,) # to make Tuple(x) inferable

end

## find ##

_findfirst_rec(f, i::Int, ::Tuple{}) = nothing
_findfirst_rec(f, i::Int, t::Tuple) = (@inline; f(first(t)) ? i : _findfirst_rec(f, i+1, tail(t)))
function _findfirst_loop(f::Function, t)
    for i in 1:length(t)
        f(t[i]) && return i
    end
    return nothing
end
findfirst(f::Function, t::Tuple) = length(t) < 32 ? _findfirst_rec(f, 1, t) : _findfirst_loop(f, t)

findlast(f::Function, t::Tuple) = length(t) < 32 ? _findlast_rec(f, t) : _findlast_loop(f, t)
function _findlast_rec(f::Function, x::Tuple)
    r = findfirst(f, reverse(x))
    return isnothing(r) ? r : length(x) - r + 1
end
function _findlast_loop(f::Function, t)
    for i in reverse(1:length(t))
        f(t[i]) && return i
    end
    return nothing
end

## filter ##

filter_rec(f, xs::Tuple) = afoldl((ys, x) -> f(x) ? (ys..., x) : ys, (), xs...)

# use Array for long tuples
filter(f, t::Tuple) = length(t) < 32 ? filter_rec(f, t) : Tuple(filter(f, collect(t)))

## comparison ##

isequal(t1::Tuple, t2::Tuple) = length(t1) == length(t2) && _isequal(t1, t2)
_isequal(::Tuple{}, ::Tuple{}) = true
function _isequal(t1::Tuple{Any,Vararg{Any}}, t2::Tuple{Any,Vararg{Any}})
    return isequal(t1[1], t2[1]) && _isequal(tail(t1), tail(t2))
end
function _isequal(t1::Any32, t2::Any32)
    for i = 1:length(t1)
        if !isequal(t1[i], t2[i])
            return false
        end
    end
    return true
end

==(t1::Tuple, t2::Tuple) = (length(t1) == length(t2)) && _eq(t1, t2)
_eq(t1::Tuple{}, t2::Tuple{}) = true
_eq_missing(t1::Tuple{}, t2::Tuple{}) = missing
function _eq(t1::Tuple, t2::Tuple)
    eq = t1[1] == t2[1]
    if eq === false
        return false
    elseif ismissing(eq)
        return _eq_missing(tail(t1), tail(t2))
    else
        return _eq(tail(t1), tail(t2))
    end
end
function _eq_missing(t1::Tuple, t2::Tuple)
    eq = t1[1] == t2[1]
    if eq === false
        return false
    else
        return _eq_missing(tail(t1), tail(t2))
    end
end
function _eq(t1::Any32, t2::Any32)
    anymissing = false
    for i = 1:length(t1)
        eq = (t1[i] == t2[i])
        if ismissing(eq)
            anymissing = true
        elseif !eq
           return false
       end
    end
    return anymissing ? missing : true
end

const tuplehash_seed = UInt === UInt64 ? 0x77cfa1eef01bca90 : 0xf01bca90
hash(::Tuple{}, h::UInt) = h + tuplehash_seed
hash(t::Tuple, h::UInt) = hash(t[1], hash(tail(t), h))
function hash(t::Any32, h::UInt)
    out = h + tuplehash_seed
    for i = length(t):-1:1
        out = hash(t[i], out)
    end
    return out
end

<(::Tuple{}, ::Tuple{}) = false
<(::Tuple{}, ::Tuple) = true
<(::Tuple, ::Tuple{}) = false
function <(t1::Tuple, t2::Tuple)
    a, b = t1[1], t2[1]
    eq = (a == b)
    if ismissing(eq)
        return missing
    elseif !eq
        return a < b
    end
    return tail(t1) < tail(t2)
end
function <(t1::Any32, t2::Any32)
    n1, n2 = length(t1), length(t2)
    for i = 1:min(n1, n2)
        a, b = t1[i], t2[i]
        eq = (a == b)
        if ismissing(eq)
            return missing
        elseif !eq
           return a < b
        end
    end
    return n1 < n2
end

isless(::Tuple{}, ::Tuple{}) = false
isless(::Tuple{}, ::Tuple) = true
isless(::Tuple, ::Tuple{}) = false

"""
    isless(t1::Tuple, t2::Tuple)

Return `true` when `t1` is less than `t2` in lexicographic order.
"""
function isless(t1::Tuple, t2::Tuple)
    a, b = t1[1], t2[1]
    isless(a, b) || (isequal(a, b) && isless(tail(t1), tail(t2)))
end
function isless(t1::Any32, t2::Any32)
    n1, n2 = length(t1), length(t2)
    for i = 1:min(n1, n2)
        a, b = t1[i], t2[i]
        if !isequal(a, b)
            return isless(a, b)
        end
    end
    return n1 < n2
end

## functions ##

isempty(x::Tuple{}) = true
isempty(@nospecialize x::Tuple) = false

revargs() = ()
revargs(x, r...) = (revargs(r...)..., x)

reverse(t::Tuple) = revargs(t...)

## specialized reduction ##

prod(x::Tuple{}) = 1
# This is consistent with the regular prod because there is no need for size promotion
# if all elements in the tuple are of system size.
# It is defined here separately in order to support bootstrap, because it's needed earlier
# than the general prod definition is available.
prod(x::Tuple{Int, Vararg{Int}}) = *(x...)

all(x::Tuple{}) = true
all(x::Tuple{Bool}) = x[1]
all(x::Tuple{Bool, Bool}) = x[1]&x[2]
all(x::Tuple{Bool, Bool, Bool}) = x[1]&x[2]&x[3]
# use generic reductions for the rest

any(x::Tuple{}) = false
any(x::Tuple{Bool}) = x[1]
any(x::Tuple{Bool, Bool}) = x[1]|x[2]
any(x::Tuple{Bool, Bool, Bool}) = x[1]|x[2]|x[3]

# a version of `in` esp. for NamedTuple, to make it pure, and not compiled for each tuple length
function sym_in(x::Symbol, itr::Tuple{Vararg{Symbol}})
    @noinline
    @_total_meta
    for y in itr
        y === x && return true
    end
    return false
end
in(x::Symbol, itr::Tuple{Vararg{Symbol}}) = sym_in(x, itr)


"""
    empty(x::Tuple)

Return an empty tuple, `()`.
"""
empty(@nospecialize x::Tuple) = ()

foreach(f, itr::Tuple) = foldl((_, x) -> (f(x); nothing), itr, init=nothing)
foreach(f, itrs::Tuple...) = foldl((_, xs) -> (f(xs...); nothing), zip(itrs...), init=nothing)
K   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/expr.jl��      # This file is a part of Julia. License is MIT: https://julialang.org/license

isexpr(@nospecialize(ex), heads) = isa(ex, Expr) && in(ex.head, heads)
isexpr(@nospecialize(ex), heads, n::Int) = isa(ex, Expr) && in(ex.head, heads) && length(ex.args) == n
const is_expr = isexpr

## symbols ##

"""
    gensym([tag])

Generates a symbol which will not conflict with other variable names (in the same module).
"""
gensym() = ccall(:jl_gensym, Ref{Symbol}, ())

gensym(s::String) = ccall(:jl_tagged_gensym, Ref{Symbol}, (Ptr{UInt8}, Csize_t), s, sizeof(s))

gensym(ss::String...) = map(gensym, ss)
gensym(s::Symbol) = ccall(:jl_tagged_gensym, Ref{Symbol}, (Ptr{UInt8}, Csize_t), s, -1 % Csize_t)

"""
    @gensym

Generates a gensym symbol for a variable. For example, `@gensym x y` is transformed into
`x = gensym("x"); y = gensym("y")`.
"""
macro gensym(names...)
    blk = Expr(:block)
    for name in names
        push!(blk.args, :($(esc(name)) = gensym($(string(name)))))
    end
    push!(blk.args, :nothing)
    return blk
end

## expressions ##

isexpr(@nospecialize(ex), head::Symbol) = isa(ex, Expr) && ex.head === head
isexpr(@nospecialize(ex), head::Symbol, n::Int) = isa(ex, Expr) && ex.head === head && length(ex.args) == n

copy(e::Expr) = exprarray(e.head, copy_exprargs(e.args))

# copy parts of an AST that the compiler mutates
function copy_exprs(@nospecialize(x))
    if isa(x, Expr)
        return copy(x)
    elseif isa(x, PhiNode)
        values = x.values
        nvalues = length(values)
        new_values = Vector{Any}(undef, nvalues)
        @inbounds for i = 1:nvalues
            isassigned(values, i) || continue
            new_values[i] = copy_exprs(values[i])
        end
        return PhiNode(copy(x.edges), new_values)
    elseif isa(x, PhiCNode)
        values = x.values
        nvalues = length(values)
        new_values = Vector{Any}(undef, nvalues)
        @inbounds for i = 1:nvalues
            isassigned(values, i) || continue
            new_values[i] = copy_exprs(values[i])
        end
        return PhiCNode(new_values)
    end
    return x
end
copy_exprargs(x::Array{Any,1}) = Any[copy_exprs(@inbounds x[i]) for i in 1:length(x)]

@eval exprarray(head::Symbol, arg::Array{Any,1}) = $(Expr(:new, :Expr, :head, :arg))

# create copies of the CodeInfo definition, and any mutable fields
function copy(c::CodeInfo)
    cnew = ccall(:jl_copy_code_info, Ref{CodeInfo}, (Any,), c)
    cnew.code = copy_exprargs(cnew.code)
    cnew.slotnames = copy(cnew.slotnames)
    cnew.slotflags = copy(cnew.slotflags)
    if cnew.slottypes !== nothing
        cnew.slottypes = copy(cnew.slottypes)
    end
    cnew.codelocs  = copy(cnew.codelocs)
    cnew.linetable = copy(cnew.linetable::Union{Vector{Any},Vector{Core.LineInfoNode}})
    cnew.ssaflags  = copy(cnew.ssaflags)
    cnew.edges     = cnew.edges === nothing ? nothing : copy(cnew.edges::Vector)
    ssavaluetypes  = cnew.ssavaluetypes
    ssavaluetypes isa Vector{Any} && (cnew.ssavaluetypes = copy(ssavaluetypes))
    return cnew
end


==(x::Expr, y::Expr) = x.head === y.head && isequal(x.args, y.args)
==(x::QuoteNode, y::QuoteNode) = isequal(x.value, y.value)
==(stmt1::Core.PhiNode, stmt2::Core.PhiNode) = stmt1.edges == stmt2.edges && stmt1.values == stmt2.values

"""
    macroexpand(m::Module, x; recursive=true)

Take the expression `x` and return an equivalent expression with all macros removed (expanded)
for executing in module `m`.
The `recursive` keyword controls whether deeper levels of nested macros are also expanded.
This is demonstrated in the example below:
```julia-repl
julia> module M
           macro m1()
               42
           end
           macro m2()
               :(@m1())
           end
       end
M

julia> macroexpand(M, :(@m2()), recursive=true)
42

julia> macroexpand(M, :(@m2()), recursive=false)
:(#= REPL[16]:6 =# M.@m1)
```
"""
function macroexpand(m::Module, @nospecialize(x); recursive=true)
    if recursive
        ccall(:jl_macroexpand, Any, (Any, Any), x, m)
    else
        ccall(:jl_macroexpand1, Any, (Any, Any), x, m)
    end
end

"""
    @macroexpand

Return equivalent expression with all macros removed (expanded).

There are differences between `@macroexpand` and [`macroexpand`](@ref).

* While [`macroexpand`](@ref) takes a keyword argument `recursive`, `@macroexpand`
  is always recursive. For a non recursive macro version, see [`@macroexpand1`](@ref).

* While [`macroexpand`](@ref) has an explicit `module` argument, `@macroexpand` always
  expands with respect to the module in which it is called.

This is best seen in the following example:
```julia-repl
julia> module M
           macro m()
               1
           end
           function f()
               (@macroexpand(@m),
                macroexpand(M, :(@m)),
                macroexpand(Main, :(@m))
               )
           end
       end
M

julia> macro m()
           2
       end
@m (macro with 1 method)

julia> M.f()
(1, 1, 2)
```
With `@macroexpand` the expression expands where `@macroexpand` appears in the code (module `M` in the example).
With `macroexpand` the expression expands in the module given as the first argument.
"""
macro macroexpand(code)
    return :(macroexpand($__module__, $(QuoteNode(code)), recursive=true))
end


"""
    @macroexpand1

Non recursive version of [`@macroexpand`](@ref).
"""
macro macroexpand1(code)
    return :(macroexpand($__module__, $(QuoteNode(code)), recursive=false))
end

## misc syntax ##

"""
    Core.eval(m::Module, expr)

Evaluate an expression in the given module and return the result.
"""
Core.eval

"""
    @inline

Give a hint to the compiler that this function is worth inlining.

Small functions typically do not need the `@inline` annotation,
as the compiler does it automatically. By using `@inline` on bigger functions,
an extra nudge can be given to the compiler to inline it.

`@inline` can be applied immediately before a function definition or within a function body.

```julia
# annotate long-form definition
@inline function longdef(x)
    ...
end

# annotate short-form definition
@inline shortdef(x) = ...

# annotate anonymous function that a `do` block creates
f() do
    @inline
    ...
end
```

!!! compat "Julia 1.8"
    The usage within a function body requires at least Julia 1.8.

---
    @inline block

Give a hint to the compiler that calls within `block` are worth inlining.

```julia
# The compiler will try to inline `f`
@inline f(...)

# The compiler will try to inline `f`, `g` and `+`
@inline f(...) + g(...)
```

!!! note
    A callsite annotation always has the precedence over the annotation applied to the
    definition of the called function:
    ```julia
    @noinline function explicit_noinline(args...)
        # body
    end

    let
        @inline explicit_noinline(args...) # will be inlined
    end
    ```

!!! note
    When there are nested callsite annotations, the innermost annotation has the precedence:
    ```julia
    @noinline let a0, b0 = ...
        a = @inline f(a0)  # the compiler will try to inline this call
        b = f(b0)          # the compiler will NOT try to inline this call
        return a, b
    end
    ```

!!! warning
    Although a callsite annotation will try to force inlining in regardless of the cost model,
    there are still chances it can't succeed in it. Especially, recursive calls can not be
    inlined even if they are annotated as `@inline`d.

!!! compat "Julia 1.8"
    The callsite annotation requires at least Julia 1.8.
"""
macro inline(x)
    return annotate_meta_def_or_block(x, :inline)
end

"""
    @noinline

Give a hint to the compiler that it should not inline a function.

Small functions are typically inlined automatically.
By using `@noinline` on small functions, auto-inlining can be
prevented.

`@noinline` can be applied immediately before a function definition or within a function body.

```julia
# annotate long-form definition
@noinline function longdef(x)
    ...
end

# annotate short-form definition
@noinline shortdef(x) = ...

# annotate anonymous function that a `do` block creates
f() do
    @noinline
    ...
end
```

!!! compat "Julia 1.8"
    The usage within a function body requires at least Julia 1.8.

---
    @noinline block

Give a hint to the compiler that it should not inline the calls within `block`.

```julia
# The compiler will try to not inline `f`
@noinline f(...)

# The compiler will try to not inline `f`, `g` and `+`
@noinline f(...) + g(...)
```

!!! note
    A callsite annotation always has the precedence over the annotation applied to the
    definition of the called function:
    ```julia
    @inline function explicit_inline(args...)
        # body
    end

    let
        @noinline explicit_inline(args...) # will not be inlined
    end
    ```

!!! note
    When there are nested callsite annotations, the innermost annotation has the precedence:
    ```julia
    @inline let a0, b0 = ...
        a = @noinline f(a0)  # the compiler will NOT try to inline this call
        b = f(b0)            # the compiler will try to inline this call
        return a, b
    end
    ```

!!! compat "Julia 1.8"
    The callsite annotation requires at least Julia 1.8.

---
!!! note
    If the function is trivial (for example returning a constant) it might get inlined anyway.
"""
macro noinline(x)
    return annotate_meta_def_or_block(x, :noinline)
end

"""
    @constprop setting [ex]

Control the mode of interprocedural constant propagation for the annotated function.

Two `setting`s are supported:

- `@constprop :aggressive [ex]`: apply constant propagation aggressively.
  For a method where the return type depends on the value of the arguments,
  this can yield improved inference results at the cost of additional compile time.
- `@constprop :none [ex]`: disable constant propagation. This can reduce compile
  times for functions that Julia might otherwise deem worthy of constant-propagation.
  Common cases are for functions with `Bool`- or `Symbol`-valued arguments or keyword arguments.

`@constprop` can be applied immediately before a function definition or within a function body.

```julia
# annotate long-form definition
@constprop :aggressive function longdef(x)
  ...
end

# annotate short-form definition
@constprop :aggressive shortdef(x) = ...

# annotate anonymous function that a `do` block creates
f() do
    @constprop :aggressive
    ...
end
```

!!! compat "Julia 1.10"
  The usage within a function body requires at least Julia 1.10.
"""
macro constprop(setting, ex)
    sym = constprop_setting(setting)
    isa(ex, Expr) && return esc(pushmeta!(ex, sym))
    throw(ArgumentError(LazyString("Bad expression `", ex, "` in `@constprop settings ex`")))
end
macro constprop(setting)
    sym = constprop_setting(setting)
    return Expr(:meta, sym)
end

function constprop_setting(@nospecialize setting)
    isa(setting, QuoteNode) && (setting = setting.value)
    if setting === :aggressive
        return :aggressive_constprop
    elseif setting === :none
        return :no_constprop
    end
    throw(ArgumentError(LazyString("@constprop "), setting, "not supported"))
end

"""
    @assume_effects setting... [ex]

Override the compiler's effect modeling for the given method or foreign call.
`@assume_effects` can be applied immediately before a function definition or within a function body.
It can also be applied immediately before a `@ccall` expression.

!!! compat "Julia 1.8"
    Using `Base.@assume_effects` requires Julia version 1.8.

# Examples
```jldoctest
julia> Base.@assume_effects :terminates_locally function pow(x)
           # this :terminates_locally allows `pow` to be constant-folded
           res = 1
           1 < x < 20 || error("bad pow")
           while x > 1
               res *= x
               x -= 1
           end
           return res
       end
pow (generic function with 1 method)

julia> code_typed() do
           pow(12)
       end
1-element Vector{Any}:
 CodeInfo(
1 ─     return 479001600
) => Int64

julia> code_typed() do
           map((2,3,4)) do x
               # this :terminates_locally allows this anonymous function to be constant-folded
               Base.@assume_effects :terminates_locally
               res = 1
               1 < x < 20 || error("bad pow")
               while x > 1
                   res *= x
                   x -= 1
               end
               return res
           end
       end
1-element Vector{Any}:
 CodeInfo(
1 ─     return (2, 6, 24)
) => Tuple{Int64, Int64, Int64}

julia> Base.@assume_effects :total !:nothrow @ccall jl_type_intersection(Vector{Int}::Any, Vector{<:Integer}::Any)::Any
Vector{Int64} (alias for Array{Int64, 1})
```

!!! compat "Julia 1.10"
  The usage within a function body requires at least Julia 1.10.

!!! warning
    Improper use of this macro causes undefined behavior (including crashes,
    incorrect answers, or other hard to track bugs). Use with care and only as a
    last resort if absolutely required. Even in such a case, you SHOULD take all
    possible steps to minimize the strength of the effect assertion (e.g.,
    do not use `:total` if `:nothrow` would have been sufficient).

In general, each `setting` value makes an assertion about the behavior of the
function, without requiring the compiler to prove that this behavior is indeed
true. These assertions are made for all world ages. It is thus advisable to limit
the use of generic functions that may later be extended to invalidate the
assumption (which would cause undefined behavior).

The following `setting`s are supported.
- `:consistent`
- `:effect_free`
- `:nothrow`
- `:terminates_globally`
- `:terminates_locally`
- `:notaskstate`
- `:inaccessiblememonly`
- `:foldable`
- `:removable`
- `:total`

# Extended help

---
## `:consistent`

The `:consistent` setting asserts that for egal (`===`) inputs:
- The manner of termination (return value, exception, non-termination) will always be the same.
- If the method returns, the results will always be egal.

!!! note
    This in particular implies that the method must not return a freshly allocated
    mutable object. Multiple allocations of mutable objects (even with identical
    contents) are not egal.

!!! note
    The `:consistent`-cy assertion is made world-age wise. More formally, write
    ``fᵢ`` for the evaluation of ``f`` in world-age ``i``, then we require:
    ```math
    ∀ i, x, y: x ≡ y → fᵢ(x) ≡ fᵢ(y)
    ```
    However, for two world ages ``i``, ``j`` s.t. ``i ≠ j``, we may have ``fᵢ(x) ≢ fⱼ(y)``.

    A further implication is that `:consistent` functions may not make their
    return value dependent on the state of the heap or any other global state
    that is not constant for a given world age.

!!! note
    The `:consistent`-cy includes all legal rewrites performed by the optimizer.
    For example, floating-point fastmath operations are not considered `:consistent`,
    because the optimizer may rewrite them causing the output to not be `:consistent`,
    even for the same world age (e.g. because one ran in the interpreter, while
    the other was optimized).

!!! note
    The `:consistent`-cy assertion currrently includes the assertion that the function
    will not execute any undefined behavior (for any input). Note that undefined behavior
    may technically cause the function to violate other effect assertions (such as
    `:nothrow` or `:effect_free`) as well, but we do not model this, and all effects
    except `:consistent` assume the absence of undefined behavior.

!!! note
    If `:consistent` functions terminate by throwing an exception, that exception
    itself is not required to meet the egality requirement specified above.

---
## `:effect_free`

The `:effect_free` setting asserts that the method is free of externally semantically
visible side effects. The following is an incomplete list of externally semantically
visible side effects:
- Changing the value of a global variable.
- Mutating the heap (e.g. an array or mutable value), except as noted below
- Changing the method table (e.g. through calls to eval)
- File/Network/etc. I/O
- Task switching

However, the following are explicitly not semantically visible, even if they
may be observable:
- Memory allocations (both mutable and immutable)
- Elapsed time
- Garbage collection
- Heap mutations of objects whose lifetime does not exceed the method (i.e.
  were allocated in the method and do not escape).
- The returned value (which is externally visible, but not a side effect)

The rule of thumb here is that an externally visible side effect is anything
that would affect the execution of the remainder of the program if the function
were not executed.

!!! note
    The `:effect_free` assertion is made both for the method itself and any code
    that is executed by the method. Keep in mind that the assertion must be
    valid for all world ages and limit use of this assertion accordingly.

---
## `:nothrow`

The `:nothrow` settings asserts that this method does not terminate abnormally
(i.e. will either always return a value or never return).

!!! note
    It is permissible for `:nothrow` annotated methods to make use of exception
    handling internally as long as the exception is not rethrown out of the
    method itself.

!!! note
    `MethodErrors` and similar exceptions count as abnormal termination.

---
## `:terminates_globally`

The `:terminates_globally` settings asserts that this method will eventually terminate
(either normally or abnormally), i.e. does not loop indefinitely.

!!! note
    This `:terminates_globally` assertion covers any other methods called by the annotated method.

!!! note
    The compiler will consider this a strong indication that the method will
    terminate relatively *quickly* and may (if otherwise legal), call this
    method at compile time. I.e. it is a bad idea to annotate this setting
    on a method that *technically*, but not *practically*, terminates.

---
## `:terminates_locally`

The `:terminates_locally` setting is like `:terminates_globally`, except that it only
applies to syntactic control flow *within* the annotated method. It is thus
a much weaker (and thus safer) assertion that allows for the possibility of
non-termination if the method calls some other method that does not terminate.

!!! note
    `:terminates_globally` implies `:terminates_locally`.

---
## `:notaskstate`

The `:notaskstate` setting asserts that the method does not use or modify the
local task state (task local storage, RNG state, etc.) and may thus be safely
moved between tasks without observable results.

!!! note
    The implementation of exception handling makes use of state stored in the
    task object. However, this state is currently not considered to be within
    the scope of `:notaskstate` and is tracked separately using the `:nothrow`
    effect.

!!! note
    The `:notaskstate` assertion concerns the state of the *currently running task*.
    If a reference to a `Task` object is obtained by some other means that
    does not consider which task is *currently* running, the `:notaskstate`
    effect need not be tainted. This is true, even if said task object happens
    to be `===` to the currently running task.

!!! note
    Access to task state usually also results in the tainting of other effects,
    such as `:effect_free` (if task state is modified) or `:consistent` (if
    task state is used in the computation of the result). In particular,
    code that is not `:notaskstate`, but is `:effect_free` and `:consistent`
    may still be dead-code-eliminated and thus promoted to `:total`.

---
## `:inaccessiblememonly`

The `:inaccessiblememonly` setting asserts that the method does not access or modify
externally accessible mutable memory. This means the method can access or modify mutable
memory for newly allocated objects that is not accessible by other methods or top-level
execution before return from the method, but it can not access or modify any mutable
global state or mutable memory pointed to by its arguments.

!!! note
    Below is an incomplete list of examples that invalidate this assumption:
    - a global reference or `getglobal` call to access a mutable global variable
    - a global assignment or `setglobal!` call to perform assignment to a non-constant global variable
    - `setfield!` call that changes a field of a global mutable variable

!!! note
    This `:inaccessiblememonly` assertion covers any other methods called by the annotated method.

---
## `:foldable`

This setting is a convenient shortcut for the set of effects that the compiler
requires to be guaranteed to constant fold a call at compile time. It is
currently equivalent to the following `setting`s:
- `:consistent`
- `:effect_free`
- `:terminates_globally`

!!! note
    This list in particular does not include `:nothrow`. The compiler will still
    attempt constant propagation and note any thrown error at compile time. Note
    however, that by the `:consistent`-cy requirements, any such annotated call
    must consistently throw given the same argument values.

!!! note
    An explicit `@inbounds` annotation inside the function will also disable
    constant folding and not be overriden by `:foldable`.

---
## `:removable`

This setting is a convenient shortcut for the set of effects that the compiler
requires to be guaranteed to delete a call whose result is unused at compile time.
It is currently equivalent to the following `setting`s:
- `:effect_free`
- `:nothrow`
- `:terminates_globally`

---
## `:total`

This `setting` is the maximum possible set of effects. It currently implies
the following other `setting`s:
- `:consistent`
- `:effect_free`
- `:nothrow`
- `:terminates_globally`
- `:notaskstate`
- `:inaccessiblememonly`

!!! warning
    `:total` is a very strong assertion and will likely gain additional semantics
    in future versions of Julia (e.g. if additional effects are added and included
    in the definition of `:total`). As a result, it should be used with care.
    Whenever possible, prefer to use the minimum possible set of specific effect
    assertions required for a particular application. In cases where a large
    number of effect overrides apply to a set of functions, a custom macro is
    recommended over the use of `:total`.

---
## Negated effects

Effect names may be prefixed by `!` to indicate that the effect should be removed
from an earlier meta effect. For example, `:total !:nothrow` indicates that while
the call is generally total, it may however throw.
"""
macro assume_effects(args...)
    lastex = args[end]
    inner = unwrap_macrocalls(lastex)
    if is_function_def(inner)
        ex = lastex
        idx = length(args)-1
    elseif isexpr(lastex, :macrocall) && lastex.args[1] === Symbol("@ccall")
        ex = lastex
        idx = length(args)-1
    else # anonymous function case
        ex = nothing
        idx = length(args)
    end
    (consistent, effect_free, nothrow, terminates_globally, terminates_locally, notaskstate, inaccessiblememonly) =
        (false, false, false, false, false, false, false, false)
    for org_setting in args[1:idx]
        (setting, val) = compute_assumed_setting(org_setting)
        if setting === :consistent
            consistent = val
        elseif setting === :effect_free
            effect_free = val
        elseif setting === :nothrow
            nothrow = val
        elseif setting === :terminates_globally
            terminates_globally = val
        elseif setting === :terminates_locally
            terminates_locally = val
        elseif setting === :notaskstate
            notaskstate = val
        elseif setting === :inaccessiblememonly
            inaccessiblememonly = val
        elseif setting === :foldable
            consistent = effect_free = terminates_globally = val
        elseif setting === :removable
            effect_free = nothrow = terminates_globally = val
        elseif setting === :total
            consistent = effect_free = nothrow = terminates_globally = notaskstate = inaccessiblememonly = val
        else
            throw(ArgumentError("@assume_effects $org_setting not supported"))
        end
    end
    if is_function_def(inner)
        return esc(pushmeta!(ex, :purity,
            consistent, effect_free, nothrow, terminates_globally, terminates_locally, notaskstate, inaccessiblememonly))
    elseif isexpr(ex, :macrocall) && ex.args[1] === Symbol("@ccall")
        ex.args[1] = GlobalRef(Base, Symbol("@ccall_effects"))
        insert!(ex.args, 3, Core.Compiler.encode_effects_override(Core.Compiler.EffectsOverride(
            consistent, effect_free, nothrow, terminates_globally, terminates_locally, notaskstate, inaccessiblememonly,
        )))
        return esc(ex)
    else # anonymous function case
        return Expr(:meta, Expr(:purity,
            consistent, effect_free, nothrow, terminates_globally, terminates_locally, notaskstate, inaccessiblememonly))
    end
end

function compute_assumed_setting(@nospecialize(setting), val::Bool=true)
    if isexpr(setting, :call) && setting.args[1] === :(!)
        return compute_assumed_setting(setting.args[2], !val)
    elseif isa(setting, QuoteNode)
        return compute_assumed_setting(setting.value, val)
    else
        return (setting, val)
    end
end

"""
    Base.@nospecializeinfer function f(args...)
        @nospecialize ...
        ...
    end
    Base.@nospecializeinfer f(@nospecialize args...) = ...

Tells the compiler to infer `f` using the declared types of `@nospecialize`d arguments.
This can be used to limit the number of compiler-generated specializations during inference.

# Example

```julia
julia> f(A::AbstractArray) = g(A)
f (generic function with 1 method)

julia> @noinline Base.@nospecializeinfer g(@nospecialize(A::AbstractArray)) = A[1]
g (generic function with 1 method)

julia> @code_typed f([1.0])
CodeInfo(
1 ─ %1 = invoke Main.g(_2::AbstractArray)::Any
└──      return %1
) => Any
```

In this example, `f` will be inferred for each specific type of `A`,
but `g` will only be inferred once with the declared argument type `A::AbstractArray`,
meaning that the compiler will not likely see the excessive inference time on it
while it can not infer the concrete return type of it.
Without the `@nospecializeinfer`, `f([1.0])` would infer the return type of `g` as `Float64`,
indicating that inference ran for `g(::Vector{Float64})` despite the prohibition on
specialized code generation.
"""
macro nospecializeinfer(ex)
    esc(isa(ex, Expr) ? pushmeta!(ex, :nospecializeinfer) : ex)
end

"""
    @propagate_inbounds

Tells the compiler to inline a function while retaining the caller's inbounds context.
"""
macro propagate_inbounds(ex)
    if isa(ex, Expr)
        pushmeta!(ex, :inline)
        pushmeta!(ex, :propagate_inbounds)
    end
    esc(ex)
end

"""
    @polly

Tells the compiler to apply the polyhedral optimizer Polly to a function.
"""
macro polly(ex)
    esc(isa(ex, Expr) ? pushmeta!(ex, :polly) : ex)
end

## some macro utilities ##

unwrap_macrocalls(@nospecialize(x)) = x
function unwrap_macrocalls(ex::Expr)
    inner = ex
    while inner.head === :macrocall
        inner = inner.args[end]::Expr
    end
    return inner
end

function pushmeta!(ex::Expr, sym::Symbol, args::Any...)
    if isempty(args)
        tag = sym
    else
        tag = Expr(sym, args...)::Expr
    end

    inner = unwrap_macrocalls(ex)

    idx, exargs = findmeta(inner)
    if idx != 0
        push!(exargs[idx].args, tag)
    else
        body = inner.args[2]::Expr
        pushfirst!(body.args, Expr(:meta, tag))
    end
    ex
end

popmeta!(body, sym) = _getmeta(body, sym, true)
peekmeta(body, sym) = _getmeta(body, sym, false)

function _getmeta(body::Expr, sym::Symbol, delete::Bool)
    body.head === :block || return false, []
    _getmeta(body.args, sym, delete)
end
_getmeta(arg, sym, delete::Bool) = (false, [])
function _getmeta(body::Array{Any,1}, sym::Symbol, delete::Bool)
    idx, blockargs = findmeta_block(body, args -> findmetaarg(args,sym)!=0)
    if idx == 0
        return false, []
    end
    metaargs = blockargs[idx].args
    i = findmetaarg(blockargs[idx].args, sym)
    if i == 0
        return false, []
    end
    ret = isa(metaargs[i], Expr) ? (metaargs[i]::Expr).args : []
    if delete
        deleteat!(metaargs, i)
        isempty(metaargs) && deleteat!(blockargs, idx)
    end
    true, ret
end

# Find index of `sym` in a meta expression argument list, or 0.
function findmetaarg(metaargs, sym)
    for i = 1:length(metaargs)
        arg = metaargs[i]
        if (isa(arg, Symbol) && (arg::Symbol)    == sym) ||
           (isa(arg, Expr)   && (arg::Expr).head == sym)
            return i
        end
    end
    return 0
end

function annotate_meta_def_or_block(@nospecialize(ex), meta::Symbol)
    inner = unwrap_macrocalls(ex)
    if is_function_def(inner)
        # annotation on a definition
        return esc(pushmeta!(ex, meta))
    else
        # annotation on a block
        return Expr(:block,
                    Expr(meta, true),
                    Expr(:local, Expr(:(=), :val, esc(ex))),
                    Expr(meta, false),
                    :val)
    end
end

function is_short_function_def(@nospecialize(ex))
    isexpr(ex, :(=)) || return false
    while length(ex.args) >= 1 && isa(ex.args[1], Expr)
        (ex.args[1].head === :call) && return true
        (ex.args[1].head === :where || ex.args[1].head === :(::)) || return false
        ex = ex.args[1]
    end
    return false
end
is_function_def(@nospecialize(ex)) =
    return isexpr(ex, :function) || is_short_function_def(ex) || isexpr(ex, :->)

function findmeta(ex::Expr)
    if is_function_def(ex)
        body = ex.args[2]::Expr
        body.head === :block || error(body, " is not a block expression")
        return findmeta_block(ex.args)
    end
    error(ex, " is not a function expression")
end

findmeta(ex::Array{Any,1}) = findmeta_block(ex)

function findmeta_block(exargs, argsmatch=args->true)
    for i = 1:length(exargs)
        a = exargs[i]
        if isa(a, Expr)
            if a.head === :meta && argsmatch(a.args)
                return i, exargs
            elseif a.head === :block
                idx, exa = findmeta_block(a.args, argsmatch)
                if idx != 0
                    return idx, exa
                end
            end
        end
    end
    return 0, []
end

remove_linenums!(ex) = ex
function remove_linenums!(ex::Expr)
    if ex.head === :block || ex.head === :quote
        # remove line number expressions from metadata (not argument literal or inert) position
        filter!(ex.args) do x
            isa(x, Expr) && x.head === :line && return false
            isa(x, LineNumberNode) && return false
            return true
        end
    end
    for subex in ex.args
        subex isa Expr && remove_linenums!(subex)
    end
    return ex
end
function remove_linenums!(src::CodeInfo)
    src.codelocs .= 0
    length(src.linetable) > 1 && resize!(src.linetable, 1)
    return src
end

replace_linenums!(ex, ln::LineNumberNode) = ex
function replace_linenums!(ex::Expr, ln::LineNumberNode)
    if ex.head === :block || ex.head === :quote
        # replace line number expressions from metadata (not argument literal or inert) position
        map!(ex.args, ex.args) do @nospecialize(x)
            isa(x, Expr) && x.head === :line && length(x.args) == 1 && return Expr(:line, ln.line)
            isa(x, Expr) && x.head === :line && length(x.args) == 2 && return Expr(:line, ln.line, ln.file)
            isa(x, LineNumberNode) && return ln
            return x
        end
    end
    # preserve any linenums inside `esc(...)` guards
    if ex.head !== :escape
        for subex in ex.args
            subex isa Expr && replace_linenums!(subex, ln)
        end
    end
    return ex
end

macro generated()
    return Expr(:generated)
end

"""
    @generated f

`@generated` is used to annotate a function which will be generated.
In the body of the generated function, only types of arguments can be read
(not the values). The function returns a quoted expression evaluated when the
function is called. The `@generated` macro should not be used on functions mutating
the global scope or depending on mutable elements.

See [Metaprogramming](@ref) for further details.

# Examples
```jldoctest
julia> @generated function bar(x)
           if x <: Integer
               return :(x ^ 2)
           else
               return :(x)
           end
       end
bar (generic function with 1 method)

julia> bar(4)
16

julia> bar("baz")
"baz"
```
"""
macro generated(f)
    if isa(f, Expr) && (f.head === :function || is_short_function_def(f))
        body = f.args[2]
        lno = body.args[1]
        tmp = gensym("tmp")
        return Expr(:escape,
                    Expr(f.head, f.args[1],
                         Expr(:block,
                              lno,
                              Expr(:if, Expr(:generated),
                                   body,
                                   Expr(:block,
                                        Expr(:meta, :generated_only),
                                        Expr(:return, nothing))))))
    else
        error("invalid syntax; @generated must be used with a function definition")
    end
end


"""
    @atomic var
    @atomic order ex

Mark `var` or `ex` as being performed atomically, if `ex` is a supported expression.
If no `order` is specified it defaults to :sequentially_consistent.

    @atomic a.b.x = new
    @atomic a.b.x += addend
    @atomic :release a.b.x = new
    @atomic :acquire_release a.b.x += addend

Perform the store operation expressed on the right atomically and return the
new value.

With `=`, this operation translates to a `setproperty!(a.b, :x, new)` call.
With any operator also, this operation translates to a `modifyproperty!(a.b,
:x, +, addend)[2]` call.

    @atomic a.b.x max arg2
    @atomic a.b.x + arg2
    @atomic max(a.b.x, arg2)
    @atomic :acquire_release max(a.b.x, arg2)
    @atomic :acquire_release a.b.x + arg2
    @atomic :acquire_release a.b.x max arg2

Perform the binary operation expressed on the right atomically. Store the
result into the field in the first argument and return the values `(old, new)`.

This operation translates to a `modifyproperty!(a.b, :x, func, arg2)` call.


See [Per-field atomics](@ref man-atomics) section in the manual for more details.

# Examples
```jldoctest
julia> mutable struct Atomic{T}; @atomic x::T; end

julia> a = Atomic(1)
Atomic{Int64}(1)

julia> @atomic a.x # fetch field x of a, with sequential consistency
1

julia> @atomic :sequentially_consistent a.x = 2 # set field x of a, with sequential consistency
2

julia> @atomic a.x += 1 # increment field x of a, with sequential consistency
3

julia> @atomic a.x + 1 # increment field x of a, with sequential consistency
3 => 4

julia> @atomic a.x # fetch field x of a, with sequential consistency
4

julia> @atomic max(a.x, 10) # change field x of a to the max value, with sequential consistency
4 => 10

julia> @atomic a.x max 5 # again change field x of a to the max value, with sequential consistency
10 => 10
```

!!! compat "Julia 1.7"
    This functionality requires at least Julia 1.7.
"""
macro atomic(ex)
    if !isa(ex, Symbol) && !is_expr(ex, :(::))
        return make_atomic(QuoteNode(:sequentially_consistent), ex)
    end
    return esc(Expr(:atomic, ex))
end
macro atomic(order, ex)
    order isa QuoteNode || (order = esc(order))
    return make_atomic(order, ex)
end
macro atomic(a1, op, a2)
    return make_atomic(QuoteNode(:sequentially_consistent), a1, op, a2)
end
macro atomic(order, a1, op, a2)
    order isa QuoteNode || (order = esc(order))
    return make_atomic(order, a1, op, a2)
end
function make_atomic(order, ex)
    @nospecialize
    if ex isa Expr
        if isexpr(ex, :., 2)
            l, r = esc(ex.args[1]), esc(ex.args[2])
            return :(getproperty($l, $r, $order))
        elseif isexpr(ex, :call, 3)
            return make_atomic(order, ex.args[2], ex.args[1], ex.args[3])
        elseif ex.head === :(=)
            l, r = ex.args[1], esc(ex.args[2])
            if is_expr(l, :., 2)
                ll, lr = esc(l.args[1]), esc(l.args[2])
                return :(setproperty!($ll, $lr, $r, $order))
            end
        end
        if length(ex.args) == 2
            if ex.head === :(+=)
                op = :+
            elseif ex.head === :(-=)
                op = :-
            elseif @isdefined string
                shead = string(ex.head)
                if endswith(shead, '=')
                    op = Symbol(shead[1:prevind(shead, end)])
                end
            end
            if @isdefined(op)
                return Expr(:ref, make_atomic(order, ex.args[1], op, ex.args[2]), 2)
            end
        end
    end
    error("could not parse @atomic expression $ex")
end
function make_atomic(order, a1, op, a2)
    @nospecialize
    is_expr(a1, :., 2) || error("@atomic modify expression missing field access")
    a1l, a1r, op, a2 = esc(a1.args[1]), esc(a1.args[2]), esc(op), esc(a2)
    return :(modifyproperty!($a1l, $a1r, $op, $a2, $order))
end


"""
    @atomicswap a.b.x = new
    @atomicswap :sequentially_consistent a.b.x = new

Stores `new` into `a.b.x` and returns the old value of `a.b.x`.

This operation translates to a `swapproperty!(a.b, :x, new)` call.

See [Per-field atomics](@ref man-atomics) section in the manual for more details.

# Examples
```jldoctest
julia> mutable struct Atomic{T}; @atomic x::T; end

julia> a = Atomic(1)
Atomic{Int64}(1)

julia> @atomicswap a.x = 2+2 # replace field x of a with 4, with sequential consistency
1

julia> @atomic a.x # fetch field x of a, with sequential consistency
4
```

!!! compat "Julia 1.7"
    This functionality requires at least Julia 1.7.
"""
macro atomicswap(order, ex)
    order isa QuoteNode || (order = esc(order))
    return make_atomicswap(order, ex)
end
macro atomicswap(ex)
    return make_atomicswap(QuoteNode(:sequentially_consistent), ex)
end
function make_atomicswap(order, ex)
    @nospecialize
    is_expr(ex, :(=), 2) || error("@atomicswap expression missing assignment")
    l, val = ex.args[1], esc(ex.args[2])
    is_expr(l, :., 2) || error("@atomicswap expression missing field access")
    ll, lr = esc(l.args[1]), esc(l.args[2])
    return :(swapproperty!($ll, $lr, $val, $order))
end


"""
    @atomicreplace a.b.x expected => desired
    @atomicreplace :sequentially_consistent a.b.x expected => desired
    @atomicreplace :sequentially_consistent :monotonic a.b.x expected => desired

Perform the conditional replacement expressed by the pair atomically, returning
the values `(old, success::Bool)`. Where `success` indicates whether the
replacement was completed.

This operation translates to a `replaceproperty!(a.b, :x, expected, desired)` call.

See [Per-field atomics](@ref man-atomics) section in the manual for more details.

# Examples
```jldoctest
julia> mutable struct Atomic{T}; @atomic x::T; end

julia> a = Atomic(1)
Atomic{Int64}(1)

julia> @atomicreplace a.x 1 => 2 # replace field x of a with 2 if it was 1, with sequential consistency
(old = 1, success = true)

julia> @atomic a.x # fetch field x of a, with sequential consistency
2

julia> @atomicreplace a.x 1 => 2 # replace field x of a with 2 if it was 1, with sequential consistency
(old = 2, success = false)

julia> xchg = 2 => 0; # replace field x of a with 0 if it was 2, with sequential consistency

julia> @atomicreplace a.x xchg
(old = 2, success = true)

julia> @atomic a.x # fetch field x of a, with sequential consistency
0
```

!!! compat "Julia 1.7"
    This functionality requires at least Julia 1.7.
"""
macro atomicreplace(success_order, fail_order, ex, old_new)
    fail_order isa QuoteNode || (fail_order = esc(fail_order))
    success_order isa QuoteNode || (success_order = esc(success_order))
    return make_atomicreplace(success_order, fail_order, ex, old_new)
end
macro atomicreplace(order, ex, old_new)
    order isa QuoteNode || (order = esc(order))
    return make_atomicreplace(order, order, ex, old_new)
end
macro atomicreplace(ex, old_new)
    return make_atomicreplace(QuoteNode(:sequentially_consistent), QuoteNode(:sequentially_consistent), ex, old_new)
end
function make_atomicreplace(success_order, fail_order, ex, old_new)
    @nospecialize
    is_expr(ex, :., 2) || error("@atomicreplace expression missing field access")
    ll, lr = esc(ex.args[1]), esc(ex.args[2])
    if is_expr(old_new, :call, 3) && old_new.args[1] === :(=>)
        exp, rep = esc(old_new.args[2]), esc(old_new.args[3])
        return :(replaceproperty!($ll, $lr, $exp, $rep, $success_order, $fail_order))
    else
        old_new = esc(old_new)
        return :(replaceproperty!($ll, $lr, $old_new::Pair..., $success_order, $fail_order))
    end
end
K   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/pair.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

const => = Pair

"""
    Pair(x, y)
    x => y

Construct a `Pair` object with type `Pair{typeof(x), typeof(y)}`. The elements
are stored in the fields `first` and `second`. They can also be accessed via
iteration (but a `Pair` is treated as a single "scalar" for broadcasting operations).

See also [`Dict`](@ref).

# Examples
```jldoctest
julia> p = "foo" => 7
"foo" => 7

julia> typeof(p)
Pair{String, Int64}

julia> p.first
"foo"

julia> for x in p
           println(x)
       end
foo
7

julia> replace.(["xops", "oxps"], "x" => "o")
2-element Vector{String}:
 "oops"
 "oops"
```
"""
Pair, =>

eltype(p::Type{Pair{A, B}}) where {A, B} = Union{A, B}
iterate(p::Pair, i=1) = i > 2 ? nothing : (getfield(p, i), i + 1)
indexed_iterate(p::Pair, i::Int, state=1) = (getfield(p, i), i + 1)

hash(p::Pair, h::UInt) = hash(p.second, hash(p.first, h))

==(p::Pair, q::Pair) = (p.first==q.first) & (p.second==q.second)
isequal(p::Pair, q::Pair) = isequal(p.first,q.first)::Bool & isequal(p.second,q.second)::Bool

isless(p::Pair, q::Pair) = ifelse(!isequal(p.first,q.first), isless(p.first,q.first),
                                                             isless(p.second,q.second))
getindex(p::Pair,i::Int) = getfield(p,i)
getindex(p::Pair,i::Real) = getfield(p, convert(Int, i))
reverse(p::Pair{A,B}) where {A,B} = Pair{B,A}(p.second, p.first)

firstindex(p::Pair) = 1
lastindex(p::Pair) = 2
length(p::Pair) = 2
first(p::Pair) = p.first
last(p::Pair) = p.second

convert(::Type{Pair{A,B}}, x::Pair{A,B}) where {A,B} = x
function convert(::Type{Pair{A,B}}, x::Pair) where {A,B}
    a = getfield(x, :first)
    a isa A || (a = convert(A, a))
    b = getfield(x, :second)
    b isa B || (b = convert(B, b))
    return Pair{A,B}(a, b)::Pair{A,B}
end

promote_rule(::Type{Pair{A1,B1}}, ::Type{Pair{A2,B2}}) where {A1,B1,A2,B2} =
    Pair{promote_type(A1, A2), promote_type(B1, B2)}
M   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/traits.jlB
      # This file is a part of Julia. License is MIT: https://julialang.org/license

## numeric/object traits
# trait for objects that have an ordering
abstract type OrderStyle end
struct Ordered <: OrderStyle end
struct Unordered <: OrderStyle end

OrderStyle(instance) = OrderStyle(typeof(instance))
OrderStyle(::Type{<:Real}) = Ordered()
OrderStyle(::Type{<:AbstractString}) = Ordered()
OrderStyle(::Type{Symbol}) = Ordered()
OrderStyle(::Type{<:Any}) = Unordered()
OrderStyle(::Type{Union{}}, slurp...) = Ordered()

# trait for objects that support arithmetic
abstract type ArithmeticStyle end
struct ArithmeticRounds <: ArithmeticStyle end     # least significant bits can be lost
struct ArithmeticWraps <: ArithmeticStyle end      #  most significant bits can be lost
struct ArithmeticUnknown <: ArithmeticStyle end

ArithmeticStyle(instance) = ArithmeticStyle(typeof(instance))
ArithmeticStyle(::Type{<:AbstractFloat}) = ArithmeticRounds()
ArithmeticStyle(::Type{<:Integer}) = ArithmeticWraps()
ArithmeticStyle(::Type{<:Any}) = ArithmeticUnknown()
ArithmeticStyle(::Type{Union{}}, slurp...) = ArithmeticUnknown()

# trait for objects that support ranges with regular step
"""
    RangeStepStyle(instance)
    RangeStepStyle(T::Type)

Indicate whether an instance or a type supports constructing a range with
a perfectly regular step or not. A regular step means that
[`step`](@ref) will always be exactly equal to the difference between two
subsequent elements in a range, i.e. for a range `r::AbstractRange{T}`:
```julia
all(diff(r) .== step(r))
```

When a type `T` always leads to ranges with regular steps, it should
define the following method:
```julia
Base.RangeStepStyle(::Type{<:AbstractRange{<:T}}) = Base.RangeStepRegular()
```
This will allow [`hash`](@ref) to use an O(1) algorithm for `AbstractRange{T}`
objects instead of the default O(N) algorithm (with N the length of the range).

In some cases, whether the step will be regular depends not only on the
element type `T`, but also on the type of the step `S`. In that case, more
specific methods should be defined:
```julia
Base.RangeStepStyle(::Type{<:OrdinalRange{<:T, <:S}}) = Base.RangeStepRegular()
```

By default, all range types are assumed to be `RangeStepIrregular`, except
ranges with an element type which is a subtype of `Integer`.
"""
abstract type RangeStepStyle end
struct RangeStepRegular   <: RangeStepStyle end # range with regular step
struct RangeStepIrregular <: RangeStepStyle end # range with rounding error
RangeStepStyle(::Type{Union{}}, slurp...) = RangeStepIrregular()

RangeStepStyle(instance) = RangeStepStyle(typeof(instance))
L   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/range.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

(:)(a::Real, b::Real) = (:)(promote(a, b)...)

(:)(start::T, stop::T) where {T<:Real} = UnitRange{T}(start, stop)

(:)(start::T, stop::T) where {T} = (:)(start, oftype(stop >= start ? stop - start : start - stop, 1), stop)

# promote start and stop, leaving step alone
(:)(start::A, step, stop::C) where {A<:Real, C<:Real} =
    (:)(convert(promote_type(A, C), start), step, convert(promote_type(A, C), stop))

# AbstractFloat specializations
(:)(a::T, b::T) where {T<:AbstractFloat} = (:)(a, T(1), b)

(:)(a::T, b::AbstractFloat, c::T) where {T<:Real} = (:)(promote(a, b, c)...)
(:)(a::T, b::AbstractFloat, c::T) where {T<:AbstractFloat} = (:)(promote(a, b, c)...)
(:)(a::T, b::Real, c::T) where {T<:AbstractFloat} = (:)(promote(a, b, c)...)

(:)(start::T, step::T, stop::T) where {T<:AbstractFloat} =
    _colon(OrderStyle(T), ArithmeticStyle(T), start, step, stop)
(:)(start::T, step::T, stop::T) where {T<:Real} =
    _colon(OrderStyle(T), ArithmeticStyle(T), start, step, stop)
_colon(::Ordered, ::Any, start::T, step, stop::T) where {T} = StepRange(start, step, stop)
# for T<:Union{Float16,Float32,Float64} see twiceprecision.jl
_colon(::Ordered, ::ArithmeticRounds, start::T, step, stop::T) where {T} =
    StepRangeLen(start, step, convert(Integer, fld(stop - start, step)) + 1)
_colon(::Any, ::Any, start::T, step, stop::T) where {T} =
    StepRangeLen(start, step, convert(Integer, fld(stop - start, step)) + 1)

"""
    (:)(start, [step], stop)

Range operator. `a:b` constructs a range from `a` to `b` with a step size
equal to 1, which produces:

* a [`UnitRange`](@ref) when `a` and `b` are integers, or
* a [`StepRange`](@ref) when `a` and `b` are characters, or
* a [`StepRangeLen`](@ref) when `a` and/or `b` are floating-point.

`a:s:b` is similar but uses a step size of `s` (a [`StepRange`](@ref) or
[`StepRangeLen`](@ref)). See also [`range`](@ref) for more control.

The operator `:` is also used in indexing to select whole dimensions, e.g. in `A[:, 1]`.

`:` is also used to [`quote`](@ref) code, e.g. `:(x + y) isa Expr` and `:x isa Symbol`.
Since `:2 isa Int`, it does *not* create a range in indexing: `v[:2] == v[2] != v[begin:2]`.
"""
(:)(start::T, step, stop::T) where {T} = _colon(start, step, stop)
(:)(start::T, step, stop::T) where {T<:Real} = _colon(start, step, stop)
# without the second method above, the first method above is ambiguous with
# (:)(start::A, step, stop::C) where {A<:Real,C<:Real}
function _colon(start::T, step, stop::T) where T
    T′ = typeof(start+zero(step))
    StepRange(convert(T′,start), step, convert(T′,stop))
end

"""
    range(start, stop, length)
    range(start, stop; length, step)
    range(start; length, stop, step)
    range(;start, length, stop, step)

Construct a specialized array with evenly spaced elements and optimized storage (an [`AbstractRange`](@ref)) from the arguments.
Mathematically a range is uniquely determined by any three of `start`, `step`, `stop` and `length`.
Valid invocations of range are:
* Call `range` with any three of `start`, `step`, `stop`, `length`.
* Call `range` with two of `start`, `stop`, `length`. In this case `step` will be assumed
  to be one. If both arguments are Integers, a [`UnitRange`](@ref) will be returned.
* Call `range` with one of `stop` or `length`. `start` and `step` will be assumed to be one.

See Extended Help for additional details on the returned type.

# Examples
```jldoctest
julia> range(1, length=100)
1:100

julia> range(1, stop=100)
1:100

julia> range(1, step=5, length=100)
1:5:496

julia> range(1, step=5, stop=100)
1:5:96

julia> range(1, 10, length=101)
1.0:0.09:10.0

julia> range(1, 100, step=5)
1:5:96

julia> range(stop=10, length=5)
6:10

julia> range(stop=10, step=1, length=5)
6:1:10

julia> range(start=1, step=1, stop=10)
1:1:10

julia> range(; length = 10)
Base.OneTo(10)

julia> range(; stop = 6)
Base.OneTo(6)

julia> range(; stop = 6.5)
1.0:1.0:6.0
```
If `length` is not specified and `stop - start` is not an integer multiple of `step`, a range that ends before `stop` will be produced.
```jldoctest
julia> range(1, 3.5, step=2)
1.0:2.0:3.0
```

Special care is taken to ensure intermediate values are computed rationally.
To avoid this induced overhead, see the [`LinRange`](@ref) constructor.

!!! compat "Julia 1.1"
    `stop` as a positional argument requires at least Julia 1.1.

!!! compat "Julia 1.7"
    The versions without keyword arguments and `start` as a keyword argument
    require at least Julia 1.7.

!!! compat "Julia 1.8"
    The versions with `stop` as a sole keyword argument,
    or `length` as a sole keyword argument require at least Julia 1.8.


# Extended Help

`range` will produce a `Base.OneTo` when the arguments are Integers and
* Only `length` is provided
* Only `stop` is provided

`range` will produce a `UnitRange` when the arguments are Integers and
* Only `start`  and `stop` are provided
* Only `length` and `stop` are provided

A `UnitRange` is not produced if `step` is provided even if specified as one.
"""
function range end

range(start; stop=nothing, length::Union{Integer,Nothing}=nothing, step=nothing) =
    _range(start, step, stop, length)
range(start, stop; length::Union{Integer,Nothing}=nothing, step=nothing) = _range(start, step, stop, length)
range(start, stop, length::Integer) = _range(start, nothing, stop, length)

range(;start=nothing, stop=nothing, length::Union{Integer, Nothing}=nothing, step=nothing) =
    _range(start, step, stop, length)

_range(start::Nothing, step::Nothing, stop::Nothing, len::Nothing) = range_error(start, step, stop, len)
_range(start::Nothing, step::Nothing, stop::Nothing, len::Any    ) = range_length(len)
_range(start::Nothing, step::Nothing, stop::Any    , len::Nothing) = range_stop(stop)
_range(start::Nothing, step::Nothing, stop::Any    , len::Any    ) = range_stop_length(stop, len)
_range(start::Nothing, step::Any    , stop::Nothing, len::Nothing) = range_error(start, step, stop, len)
_range(start::Nothing, step::Any    , stop::Nothing, len::Any    ) = range_error(start, step, stop, len)
_range(start::Nothing, step::Any    , stop::Any    , len::Nothing) = range_error(start, step, stop, len)
_range(start::Nothing, step::Any    , stop::Any    , len::Any    ) = range_step_stop_length(step, stop, len)
_range(start::Any    , step::Nothing, stop::Nothing, len::Nothing) = range_error(start, step, stop, len)
_range(start::Any    , step::Nothing, stop::Nothing, len::Any    ) = range_start_length(start, len)
_range(start::Any    , step::Nothing, stop::Any    , len::Nothing) = range_start_stop(start, stop)
_range(start::Any    , step::Nothing, stop::Any    , len::Any    ) = range_start_stop_length(start, stop, len)
_range(start::Any    , step::Any    , stop::Nothing, len::Nothing) = range_error(start, step, stop, len)
_range(start::Any    , step::Any    , stop::Nothing, len::Any    ) = range_start_step_length(start, step, len)
_range(start::Any    , step::Any    , stop::Any    , len::Nothing) = range_start_step_stop(start, step, stop)
_range(start::Any    , step::Any    , stop::Any    , len::Any    ) = range_error(start, step, stop, len)

# Length as the only argument
range_length(len::Integer) = OneTo(len)

# Stop as the only argument
range_stop(stop) = range_start_stop(oftype(stop, 1), stop)
range_stop(stop::Integer) = range_length(stop)

function range_step_stop_length(step, a, len::Integer)
    start = a - step * (len - oneunit(len))
    if start isa Signed
        # overflow in recomputing length from stop is okay
        return StepRange{typeof(start),typeof(step)}(start, step, convert(typeof(start), a))
    end
    return StepRangeLen{typeof(start),typeof(start),typeof(step)}(start, step, len)
end

# Stop and length as the only argument
function range_stop_length(a, len::Integer)
    step = oftype(a - a, 1) # assert that step is representable
    start = a - (len - oneunit(len))
    if start isa Signed
        # overflow in recomputing length from stop is okay
        return UnitRange(start, oftype(start, a))
    end
    return StepRangeLen{typeof(start),typeof(start),typeof(step)}(start, step, len)
end

# Start and length as the only argument
function range_start_length(a, len::Integer)
    step = oftype(a - a, 1) # assert that step is representable
    stop = a + (len - oneunit(len))
    if stop isa Signed
        # overflow in recomputing length from stop is okay
        return UnitRange(oftype(stop, a), stop)
    end
    return StepRangeLen{typeof(stop),typeof(a),typeof(step)}(a, step, len)
end

range_start_stop(start, stop) = start:stop

function range_start_step_length(a, step, len::Integer)
    stop = a + step * (len - oneunit(len))
    if stop isa Signed
        # overflow in recomputing length from stop is okay
        return StepRange{typeof(stop),typeof(step)}(convert(typeof(stop), a), step, stop)
    end
    return StepRangeLen{typeof(stop),typeof(a),typeof(step)}(a, step, len)
end

range_start_step_stop(start, step, stop) = start:step:stop

function range_error(start, step, stop, length)
    hasstart  = start !== nothing
    hasstep   = step  !== nothing
    hasstop   = stop  !== nothing
    haslength = start !== nothing

    hint = if hasstart && hasstep && hasstop && haslength
        "Try specifying only three arguments"
    elseif !hasstop && !haslength
        "At least one of `length` or `stop` must be specified."
    elseif !hasstep && !haslength
        "At least one of `length` or `step` must be specified."
    elseif !hasstart && !hasstop
        "At least one of `start` or `stop` must be specified."
    else
        "Try specifying more arguments."
    end

    msg = """
    Cannot construct range from arguments:
    start = $start
    step = $step
    stop = $stop
    length = $length
    $hint
    """
    throw(ArgumentError(msg))
end

## 1-dimensional ranges ##

"""
    AbstractRange{T}

Supertype for ranges with elements of type `T`.
[`UnitRange`](@ref) and other types are subtypes of this.
"""
abstract type AbstractRange{T} <: AbstractArray{T,1} end

RangeStepStyle(::Type{<:AbstractRange}) = RangeStepIrregular()
RangeStepStyle(::Type{<:AbstractRange{<:Integer}}) = RangeStepRegular()

convert(::Type{T}, r::AbstractRange) where {T<:AbstractRange} = r isa T ? r : T(r)::T

## ordinal ranges

"""
    OrdinalRange{T, S} <: AbstractRange{T}

Supertype for ordinal ranges with elements of type `T` with
spacing(s) of type `S`. The steps should be always-exact
multiples of [`oneunit`](@ref), and `T` should be a "discrete"
type, which cannot have values smaller than `oneunit`. For example,
`Integer` or `Date` types would qualify, whereas `Float64` would not (since this
type can represent values smaller than `oneunit(Float64)`.
[`UnitRange`](@ref), [`StepRange`](@ref), and other types are subtypes of this.
"""
abstract type OrdinalRange{T,S} <: AbstractRange{T} end

"""
    AbstractUnitRange{T} <: OrdinalRange{T, T}

Supertype for ranges with a step size of [`oneunit(T)`](@ref) with elements of type `T`.
[`UnitRange`](@ref) and other types are subtypes of this.
"""
abstract type AbstractUnitRange{T} <: OrdinalRange{T,T} end

"""
    StepRange{T, S} <: OrdinalRange{T, S}

Ranges with elements of type `T` with spacing of type `S`. The step
between each element is constant, and the range is defined in terms
of a `start` and `stop` of type `T` and a `step` of type `S`. Neither
`T` nor `S` should be floating point types. The syntax `a:b:c` with `b != 0`
and `a`, `b`, and `c` all integers creates a `StepRange`.

# Examples
```jldoctest
julia> collect(StepRange(1, Int8(2), 10))
5-element Vector{Int64}:
 1
 3
 5
 7
 9

julia> typeof(StepRange(1, Int8(2), 10))
StepRange{Int64, Int8}

julia> typeof(1:3:6)
StepRange{Int64, Int64}
```
"""
struct StepRange{T,S} <: OrdinalRange{T,S}
    start::T
    step::S
    stop::T

    function StepRange{T,S}(start, step, stop) where {T,S}
        start = convert(T, start)
        step = convert(S, step)
        stop = convert(T, stop)
        return new(start, step, steprange_last(start, step, stop))
    end
end

# to make StepRange constructor inlineable, so optimizer can see `step` value
function steprange_last(start, step, stop)::typeof(stop)
    if isa(start, AbstractFloat) || isa(step, AbstractFloat)
        throw(ArgumentError("StepRange should not be used with floating point"))
    end
    if isa(start, Integer) && !isinteger(start + step)
        throw(ArgumentError("StepRange{<:Integer} cannot have non-integer step"))
    end
    z = zero(step)
    step == z && throw(ArgumentError("step cannot be zero"))

    if stop == start
        last = stop
    else
        if (step > z) != (stop > start)
            last = steprange_last_empty(start, step, stop)
        else
            # Compute absolute value of difference between `start` and `stop`
            # (to simplify handling both signed and unsigned T and checking for signed overflow):
            absdiff, absstep = stop > start ? (stop - start, step) : (start - stop, -step)

            # Compute remainder as a nonnegative number:
            if absdiff isa Signed && absdiff < zero(absdiff)
                # unlikely, but handle the signed overflow case with unsigned rem
                overflow_case(absdiff, absstep) = (@noinline; convert(typeof(absdiff), unsigned(absdiff) % absstep))
                remain = overflow_case(absdiff, absstep)
            else
                remain = convert(typeof(absdiff), absdiff % absstep)
            end
            # Move `stop` closer to `start` if there is a remainder:
            last = stop > start ? stop - remain : stop + remain
        end
    end
    return last
end

function steprange_last_empty(start::Integer, step, stop)::typeof(stop)
    # empty range has a special representation where stop = start-1,
    # which simplifies arithmetic for Signed numbers
    if step > zero(step)
        last = start - oneunit(step)
    else
        last = start + oneunit(step)
    end
    return last
end
# For types where x+oneunit(x) may not be well-defined use the user-given value for stop
steprange_last_empty(start, step, stop) = stop

StepRange{T}(start, step::S, stop) where {T,S} = StepRange{T,S}(start, step, stop)
StepRange(start::T, step::S, stop::T) where {T,S} = StepRange{T,S}(start, step, stop)

"""
    UnitRange{T<:Real}

A range parameterized by a `start` and `stop` of type `T`, filled
with elements spaced by `1` from `start` until `stop` is exceeded.
The syntax `a:b` with `a` and `b` both `Integer`s creates a `UnitRange`.

# Examples
```jldoctest
julia> collect(UnitRange(2.3, 5.2))
3-element Vector{Float64}:
 2.3
 3.3
 4.3

julia> typeof(1:10)
UnitRange{Int64}
```
"""
struct UnitRange{T<:Real} <: AbstractUnitRange{T}
    start::T
    stop::T
    UnitRange{T}(start::T, stop::T) where {T<:Real} = new(start, unitrange_last(start, stop))
end
UnitRange{T}(start, stop) where {T<:Real} = UnitRange{T}(convert(T, start), convert(T, stop))
UnitRange(start::T, stop::T) where {T<:Real} = UnitRange{T}(start, stop)
function UnitRange(start, stop)
    startstop_promoted = promote(start, stop)
    not_sametype((start, stop), startstop_promoted)
    UnitRange(startstop_promoted...)
end

# if stop and start are integral, we know that their difference is a multiple of 1
unitrange_last(start::Integer, stop::Integer) =
    stop >= start ? stop : convert(typeof(stop), start - oneunit(start - stop))
# otherwise, use `floor` as a more efficient way to compute modulus with step=1
unitrange_last(start, stop) =
    stop >= start ? convert(typeof(stop), start + floor(stop - start)) :
                    convert(typeof(stop), start - oneunit(start - stop))

unitrange(x::AbstractUnitRange) = UnitRange(x) # convenience conversion for promoting the range type

if isdefined(Main, :Base)
    # Constant-fold-able indexing into tuples to functionally expose Base.tail and Base.front
    function getindex(@nospecialize(t::Tuple), r::AbstractUnitRange)
        @inline
        require_one_based_indexing(r)
        if length(r) <= 10
            return ntuple(i -> t[i + first(r) - 1], length(r))
        elseif first(r) == 1
            last(r) == length(t)   && return t
            last(r) == length(t)-1 && return front(t)
            last(r) == length(t)-2 && return front(front(t))
        elseif last(r) == length(t)
            first(r) == 2 && return tail(t)
            first(r) == 3 && return tail(tail(t))
        end
        return (eltype(t)[t[ri] for ri in r]...,)
    end
end

"""
    Base.OneTo(n)

Define an `AbstractUnitRange` that behaves like `1:n`, with the added
distinction that the lower limit is guaranteed (by the type system) to
be 1.
"""
struct OneTo{T<:Integer} <: AbstractUnitRange{T}
    stop::T
    function OneTo{T}(stop) where {T<:Integer}
        throwbool(r)  = (@noinline; throw(ArgumentError("invalid index: $r of type Bool")))
        T === Bool && throwbool(stop)
        return new(max(zero(T), stop))
    end

    function OneTo{T}(r::AbstractRange) where {T<:Integer}
        throwstart(r) = (@noinline; throw(ArgumentError("first element must be 1, got $(first(r))")))
        throwstep(r)  = (@noinline; throw(ArgumentError("step must be 1, got $(step(r))")))
        throwbool(r)  = (@noinline; throw(ArgumentError("invalid index: $r of type Bool")))
        first(r) == 1 || throwstart(r)
        step(r)  == 1 || throwstep(r)
        T === Bool && throwbool(r)
        return new(max(zero(T), last(r)))
    end
end
OneTo(stop::T) where {T<:Integer} = OneTo{T}(stop)
OneTo(r::AbstractRange{T}) where {T<:Integer} = OneTo{T}(r)
oneto(r) = OneTo(r)

## Step ranges parameterized by length

"""
    StepRangeLen(         ref::R, step::S, len, [offset=1]) where {  R,S}
    StepRangeLen{T,R,S}(  ref::R, step::S, len, [offset=1]) where {T,R,S}
    StepRangeLen{T,R,S,L}(ref::R, step::S, len, [offset=1]) where {T,R,S,L}

A range `r` where `r[i]` produces values of type `T` (in the first
form, `T` is deduced automatically), parameterized by a `ref`erence
value, a `step`, and the `len`gth. By default `ref` is the starting
value `r[1]`, but alternatively you can supply it as the value of
`r[offset]` for some other index `1 <= offset <= len`. The syntax `a:b`
or `a:b:c`, where any of `a`, `b`, or `c` are floating-point numbers, creates a
`StepRangeLen`.

!!! compat "Julia 1.7"
    The 4th type parameter `L` requires at least Julia 1.7.
"""
struct StepRangeLen{T,R,S,L<:Integer} <: AbstractRange{T}
    ref::R       # reference value (might be smallest-magnitude value in the range)
    step::S      # step value
    len::L       # length of the range
    offset::L    # the index of ref

    function StepRangeLen{T,R,S,L}(ref::R, step::S, len::Integer, offset::Integer = 1) where {T,R,S,L}
        if T <: Integer && !isinteger(ref + step)
            throw(ArgumentError("StepRangeLen{<:Integer} cannot have non-integer step"))
        end
        len = convert(L, len)
        len >= zero(len) || throw(ArgumentError("length cannot be negative, got $len"))
        offset = convert(L, offset)
        L1 = oneunit(typeof(len))
        L1 <= offset <= max(L1, len) || throw(ArgumentError("StepRangeLen: offset must be in [1,$len], got $offset"))
        return new(ref, step, len, offset)
    end
end

StepRangeLen{T,R,S}(ref::R, step::S, len::Integer, offset::Integer = 1) where {T,R,S} =
    StepRangeLen{T,R,S,promote_type(Int,typeof(len))}(ref, step, len, offset)
StepRangeLen(ref::R, step::S, len::Integer, offset::Integer = 1) where {R,S} =
    StepRangeLen{typeof(ref+zero(step)),R,S,promote_type(Int,typeof(len))}(ref, step, len, offset)
StepRangeLen{T}(ref::R, step::S, len::Integer, offset::Integer = 1) where {T,R,S} =
    StepRangeLen{T,R,S,promote_type(Int,typeof(len))}(ref, step, len, offset)

## range with computed step

"""
    LinRange{T,L}

A range with `len` linearly spaced elements between its `start` and `stop`.
The size of the spacing is controlled by `len`, which must
be an `Integer`.

# Examples
```jldoctest
julia> LinRange(1.5, 5.5, 9)
9-element LinRange{Float64, Int64}:
 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5
```

Compared to using [`range`](@ref), directly constructing a `LinRange` should
have less overhead but won't try to correct for floating point errors:
```jldoctest
julia> collect(range(-0.1, 0.3, length=5))
5-element Vector{Float64}:
 -0.1
  0.0
  0.1
  0.2
  0.3

julia> collect(LinRange(-0.1, 0.3, 5))
5-element Vector{Float64}:
 -0.1
 -1.3877787807814457e-17
  0.09999999999999999
  0.19999999999999998
  0.3
```
"""
struct LinRange{T,L<:Integer} <: AbstractRange{T}
    start::T
    stop::T
    len::L
    lendiv::L

    function LinRange{T,L}(start::T, stop::T, len::L) where {T,L<:Integer}
        len >= 0 || throw(ArgumentError("range($start, stop=$stop, length=$len): negative length"))
        onelen = oneunit(typeof(len))
        if len == onelen
            start == stop || throw(ArgumentError("range($start, stop=$stop, length=$len): endpoints differ"))
            return new(start, stop, len, len)
        end
        lendiv = max(len - onelen, onelen)
        if T <: Integer && !iszero(mod(stop-start, lendiv))
            throw(ArgumentError("LinRange{<:Integer} cannot have non-integer step"))
        end
        return new(start, stop, len, lendiv)
    end
end

function LinRange{T,L}(start, stop, len::Integer) where {T,L}
    LinRange{T,L}(convert(T, start), convert(T, stop), convert(L, len))
end

function LinRange{T}(start, stop, len::Integer) where T
    LinRange{T,promote_type(Int,typeof(len))}(start, stop, len)
end

function LinRange(start, stop, len::Integer)
    T = typeof((zero(stop) - zero(start)) / oneunit(len))
    LinRange{T}(start, stop, len)
end

range_start_stop_length(start, stop, len::Integer) =
    range_start_stop_length(promote(start, stop)..., len)
range_start_stop_length(start::T, stop::T, len::Integer) where {T} = LinRange(start, stop, len)
range_start_stop_length(start::T, stop::T, len::Integer) where {T<:Integer} =
    _linspace(float(T), start, stop, len)
## for Float16, Float32, and Float64 we hit twiceprecision.jl to lift to higher precision StepRangeLen
# for all other types we fall back to a plain old LinRange
_linspace(::Type{T}, start::Integer, stop::Integer, len::Integer) where T = LinRange{T}(start, stop, len)

function show(io::IO, r::LinRange{T}) where {T}
    print(io, "LinRange{")
    show(io, T)
    print(io, "}(")
    ioc = IOContext(io, :typeinfo=>T)
    show(ioc, first(r))
    print(io, ", ")
    show(ioc, last(r))
    print(io, ", ")
    show(io, length(r))
    print(io, ')')
end

"""
`print_range(io, r)` prints out a nice looking range r in terms of its elements
as if it were `collect(r)`, dependent on the size of the
terminal, and taking into account whether compact numbers should be shown.
It figures out the width in characters of each element, and if they
end up too wide, it shows the first and last elements separated by a
horizontal ellipsis. Typical output will look like `1.0, 2.0, …, 5.0, 6.0`.

`print_range(io, r, pre, sep, post, hdots)` uses optional
parameters `pre` and `post` characters for each printed row,
`sep` separator string between printed elements,
`hdots` string for the horizontal ellipsis.
"""
function print_range(io::IO, r::AbstractRange,
                     pre::AbstractString = " ",
                     sep::AbstractString = ", ",
                     post::AbstractString = "",
                     hdots::AbstractString = ", \u2026, ") # horiz ellipsis
    # This function borrows from print_matrix() in show.jl
    # and should be called by show and display
    sz = displaysize(io)
    if !haskey(io, :compact)
        io = IOContext(io, :compact => true)
    end
    screenheight, screenwidth = sz[1] - 4, sz[2]
    screenwidth -= length(pre) + length(post)
    postsp = ""
    sepsize = length(sep)
    m = 1 # treat the range as a one-row matrix
    n = length(r)
    # Figure out spacing alignments for r, but only need to examine the
    # left and right edge columns, as many as could conceivably fit on the
    # screen, with the middle columns summarized by horz, vert, or diag ellipsis
    maxpossiblecols = div(screenwidth, 1+sepsize) # assume each element is at least 1 char + 1 separator
    colsr = n <= maxpossiblecols ? (1:n) : [1:div(maxpossiblecols,2)+1; (n-div(maxpossiblecols,2)):n]
    rowmatrix = reshape(r[colsr], 1, length(colsr)) # treat the range as a one-row matrix for print_matrix_row
    nrow, idxlast = size(rowmatrix, 2), last(axes(rowmatrix, 2))
    A = alignment(io, rowmatrix, 1:m, 1:length(rowmatrix), screenwidth, screenwidth, sepsize, nrow) # how much space range takes
    if n <= length(A) # cols fit screen, so print out all elements
        print(io, pre) # put in pre chars
        print_matrix_row(io,rowmatrix,A,1,1:n,sep,idxlast) # the entire range
        print(io, post) # add the post characters
    else # cols don't fit so put horiz ellipsis in the middle
        # how many chars left after dividing width of screen in half
        # and accounting for the horiz ellipsis
        c = div(screenwidth-length(hdots)+1,2)+1 # chars remaining for each side of rowmatrix
        alignR = reverse(alignment(io, rowmatrix, 1:m, length(rowmatrix):-1:1, c, c, sepsize, nrow)) # which cols of rowmatrix to put on the right
        c = screenwidth - sum(map(sum,alignR)) - (length(alignR)-1)*sepsize - length(hdots)
        alignL = alignment(io, rowmatrix, 1:m, 1:length(rowmatrix), c, c, sepsize, nrow) # which cols of rowmatrix to put on the left
        print(io, pre)   # put in pre chars
        print_matrix_row(io, rowmatrix,alignL,1,1:length(alignL),sep,idxlast) # left part of range
        print(io, hdots) # horizontal ellipsis
        print_matrix_row(io, rowmatrix,alignR,1,length(rowmatrix)-length(alignR)+1:length(rowmatrix),sep,idxlast) # right part of range
        print(io, post)  # post chars
    end
end

## interface implementations

length(r::AbstractRange) = error("length implementation missing") # catch mistakes
size(r::AbstractRange) = (length(r),)

isempty(r::StepRange) =
    # steprange_last(r.start, r.step, r.stop) == r.stop
    (r.start != r.stop) & ((r.step > zero(r.step)) != (r.stop > r.start))
isempty(r::AbstractUnitRange) = first(r) > last(r)
isempty(r::StepRangeLen) = length(r) == 0
isempty(r::LinRange) = length(r) == 0

"""
    step(r)

Get the step size of an [`AbstractRange`](@ref) object.

# Examples
```jldoctest
julia> step(1:10)
1

julia> step(1:2:10)
2

julia> step(2.5:0.3:10.9)
0.3

julia> step(range(2.5, stop=10.9, length=85))
0.1
```
"""
step(r::StepRange) = r.step
step(r::AbstractUnitRange{T}) where {T} = oneunit(T) - zero(T)
step(r::StepRangeLen) = r.step
step(r::StepRangeLen{T}) where {T<:AbstractFloat} = T(r.step)
step(r::LinRange) = (last(r)-first(r))/r.lendiv

# high-precision step
step_hp(r::StepRangeLen) = r.step
step_hp(r::AbstractRange) = step(r)

axes(r::AbstractRange) = (oneto(length(r)),)

# Needed to ensure `has_offset_axes` can constant-fold.
has_offset_axes(::StepRange) = false

# n.b. checked_length for these is defined iff checked_add and checked_sub are
# defined between the relevant types
function checked_length(r::OrdinalRange{T}) where T
    s = step(r)
    start = first(r)
    if isempty(r)
        return Integer(div(start - start, oneunit(s)))
    end
    stop = last(r)
    if isless(s, zero(s))
        diff = checked_sub(start, stop)
        s = -s
    else
        diff = checked_sub(stop, start)
    end
    a = div(diff, s)
    return Integer(checked_add(a, oneunit(a)))
end

function checked_length(r::AbstractUnitRange{T}) where T
    # compiler optimization: remove dead cases from above
    if isempty(r)
        return Integer(first(r) - first(r))
    end
    a = checked_sub(last(r), first(r))
    return Integer(checked_add(a, oneunit(a)))
end

function length(r::OrdinalRange{T}) where T
    s = step(r)
    start = first(r)
    if isempty(r)
        return Integer(div(start - start, oneunit(s)))
    end
    stop = last(r)
    if isless(s, zero(s))
        diff = start - stop
        s = -s
    else
        diff = stop - start
    end
    a = div(diff, s)
    return Integer(a + oneunit(a))
end

function length(r::AbstractUnitRange{T}) where T
    @inline
    start, stop = first(r), last(r)
    a = oneunit(zero(stop) - zero(start))
    if a isa Signed || stop >= start
        a += stop - start # Signed are allowed to go negative
    else
        a = zero(a) # Unsigned don't necessarily underflow
    end
    return Integer(a)
end

length(r::OneTo) = Integer(r.stop - zero(r.stop))
length(r::StepRangeLen) = r.len
length(r::LinRange) = r.len

let bigints = Union{Int, UInt, Int64, UInt64, Int128, UInt128},
    smallints = (Int === Int64 ?
                Union{Int8, UInt8, Int16, UInt16, Int32, UInt32} :
                Union{Int8, UInt8, Int16, UInt16}),
    bitints = Union{bigints, smallints}
    global length, checked_length, firstindex
    # compile optimization for which promote_type(T, Int) == T
    length(r::OneTo{T}) where {T<:bigints} = r.stop
    # slightly more accurate length and checked_length in extreme cases
    # (near typemax) for types with known `unsigned` functions
    function length(r::OrdinalRange{T}) where T<:bigints
        s = step(r)
        diff = last(r) - first(r)
        isempty(r) && return zero(diff)
        # if |s| > 1, diff might have overflowed, but unsigned(diff)÷s should
        # therefore still be valid (if the result is representable at all)
        # n.b. !(s isa T)
        if s isa Unsigned || -1 <= s <= 1 || s == -s
            a = div(diff, s) % typeof(diff)
        elseif s < 0
            a = div(unsigned(-diff), -s) % typeof(diff)
        else
            a = div(unsigned(diff), s) % typeof(diff)
        end
        return a + oneunit(a)
    end
    function checked_length(r::OrdinalRange{T}) where T<:bigints
        s = step(r)
        stop, start = last(r), first(r)
        ET = promote_type(typeof(stop), typeof(start))
        isempty(r) && return zero(ET)
        # n.b. !(s isa T)
        if s > 1
            diff = stop - start
            a = convert(ET, div(unsigned(diff), s))
        elseif s < -1
            diff = start - stop
            a = convert(ET, div(unsigned(diff), -s))
        elseif s > 0
            a = convert(ET, div(checked_sub(stop, start), s))
        else
            a = convert(ET, div(checked_sub(start, stop), -s))
        end
        return checked_add(a, oneunit(a))
    end
    firstindex(r::StepRange{<:bigints,<:bitints}) = one(last(r)-first(r))

    # some special cases to favor default Int type
    function length(r::OrdinalRange{<:smallints})
        s = step(r)
        isempty(r) && return 0
        # n.b. !(step isa T)
        return Int(div(Int(last(r)) - Int(first(r)), s)) + 1
    end
    length(r::AbstractUnitRange{<:smallints}) = Int(last(r)) - Int(first(r)) + 1
    length(r::OneTo{<:smallints}) = Int(r.stop)
    checked_length(r::OrdinalRange{<:smallints}) = length(r)
    checked_length(r::AbstractUnitRange{<:smallints}) = length(r)
    checked_length(r::OneTo{<:smallints}) = length(r)
    firstindex(::StepRange{<:smallints,<:bitints}) = 1
end

first(r::OrdinalRange{T}) where {T} = convert(T, r.start)
first(r::OneTo{T}) where {T} = oneunit(T)
first(r::StepRangeLen) = unsafe_getindex(r, 1)
first(r::LinRange) = r.start

last(r::OrdinalRange{T}) where {T} = convert(T, r.stop) # via steprange_last
last(r::StepRangeLen) = unsafe_getindex(r, length(r))
last(r::LinRange) = r.stop

minimum(r::AbstractUnitRange) = isempty(r) ? throw(ArgumentError("range must be non-empty")) : first(r)
maximum(r::AbstractUnitRange) = isempty(r) ? throw(ArgumentError("range must be non-empty")) : last(r)
minimum(r::AbstractRange)  = isempty(r) ? throw(ArgumentError("range must be non-empty")) : min(first(r), last(r))
maximum(r::AbstractRange)  = isempty(r) ? throw(ArgumentError("range must be non-empty")) : max(first(r), last(r))

"""
    argmin(r::AbstractRange)

Ranges can have multiple minimal elements. In that case
`argmin` will return a minimal index, but not necessarily the
first one.
"""
function argmin(r::AbstractRange)
    if isempty(r)
        throw(ArgumentError("range must be non-empty"))
    elseif step(r) > 0
        firstindex(r)
    else
        lastindex(r)
    end
end

"""
    argmax(r::AbstractRange)

Ranges can have multiple maximal elements. In that case
`argmax` will return a maximal index, but not necessarily the
first one.
"""
function argmax(r::AbstractRange)
    if isempty(r)
        throw(ArgumentError("range must be non-empty"))
    elseif step(r) > 0
        lastindex(r)
    else
        firstindex(r)
    end
end

extrema(r::AbstractRange) = (minimum(r), maximum(r))

# Ranges are immutable
copy(r::AbstractRange) = r


## iteration

function iterate(r::Union{StepRangeLen,LinRange}, i::Integer=zero(length(r)))
    @inline
    i += oneunit(i)
    length(r) < i && return nothing
    unsafe_getindex(r, i), i
end

iterate(r::OrdinalRange) = isempty(r) ? nothing : (first(r), first(r))

function iterate(r::OrdinalRange{T}, i) where {T}
    @inline
    i == last(r) && return nothing
    next = convert(T, i + step(r))
    (next, next)
end

## indexing

function isassigned(r::AbstractRange, i::Integer)
    i isa Bool && throw(ArgumentError("invalid index: $i of type Bool"))
    firstindex(r) <= i <= lastindex(r)
end

_in_unit_range(v::UnitRange, val, i::Integer) = i > 0 && val <= v.stop && val >= v.start

function getindex(v::UnitRange{T}, i::Integer) where T
    @inline
    i isa Bool && throw(ArgumentError("invalid index: $i of type Bool"))
    val = convert(T, v.start + (i - oneunit(i)))
    @boundscheck _in_unit_range(v, val, i) || throw_boundserror(v, i)
    val
end

const OverflowSafe = Union{Bool,Int8,Int16,Int32,Int64,Int128,
                           UInt8,UInt16,UInt32,UInt64,UInt128}

function getindex(v::UnitRange{T}, i::Integer) where {T<:OverflowSafe}
    @inline
    i isa Bool && throw(ArgumentError("invalid index: $i of type Bool"))
    val = v.start + (i - oneunit(i))
    @boundscheck _in_unit_range(v, val, i) || throw_boundserror(v, i)
    val % T
end

function getindex(v::OneTo{T}, i::Integer) where T
    @inline
    i isa Bool && throw(ArgumentError("invalid index: $i of type Bool"))
    @boundscheck ((i > 0) & (i <= v.stop)) || throw_boundserror(v, i)
    convert(T, i)
end

function getindex(v::AbstractRange{T}, i::Integer) where T
    @inline
    i isa Bool && throw(ArgumentError("invalid index: $i of type Bool"))
    ret = convert(T, first(v) + (i - oneunit(i))*step_hp(v))
    ok = ifelse(step(v) > zero(step(v)),
                (ret <= last(v)) & (ret >= first(v)),
                (ret <= first(v)) & (ret >= last(v)))
    @boundscheck ((i > 0) & ok) || throw_boundserror(v, i)
    ret
end

function getindex(r::Union{StepRangeLen,LinRange}, i::Integer)
    @inline
    i isa Bool && throw(ArgumentError("invalid index: $i of type Bool"))
    @boundscheck checkbounds(r, i)
    unsafe_getindex(r, i)
end

# This is separate to make it useful even when running with --check-bounds=yes
function unsafe_getindex(r::StepRangeLen{T}, i::Integer) where T
    i isa Bool && throw(ArgumentError("invalid index: $i of type Bool"))
    u = oftype(r.offset, i) - r.offset
    T(r.ref + u*r.step)
end

function _getindex_hiprec(r::StepRangeLen, i::Integer)  # without rounding by T
    i isa Bool && throw(ArgumentError("invalid index: $i of type Bool"))
    u = oftype(r.offset, i) - r.offset
    r.ref + u*r.step
end

function unsafe_getindex(r::LinRange, i::Integer)
    i isa Bool && throw(ArgumentError("invalid index: $i of type Bool"))
    lerpi(i-oneunit(i), r.lendiv, r.start, r.stop)
end

function lerpi(j::Integer, d::Integer, a::T, b::T) where T
    @inline
    t = j/d # ∈ [0,1]
    # compute approximately fma(t, b, -fma(t, a, a))
    return T((1-t)*a + t*b)
end

getindex(r::AbstractRange, ::Colon) = copy(r)

function getindex(r::AbstractUnitRange, s::AbstractUnitRange{T}) where {T<:Integer}
    @inline
    @boundscheck checkbounds(r, s)

    if T === Bool
        return range(first(s) ? first(r) : last(r), length = last(s))
    else
        f = first(r)
        start = oftype(f, f + first(s) - firstindex(r))
        len = length(s)
        stop = oftype(f, start + (len - oneunit(len)))
        return range(start, stop)
    end
end

function getindex(r::OneTo{T}, s::OneTo) where T
    @inline
    @boundscheck checkbounds(r, s)
    return OneTo(T(s.stop))
end

function getindex(r::AbstractUnitRange, s::StepRange{T}) where {T<:Integer}
    @inline
    @boundscheck checkbounds(r, s)

    if T === Bool
        return range(first(s) ? first(r) : last(r), step=oneunit(eltype(r)), length=last(s))
    else
        f = first(r)
        start = oftype(f, f + s.start - firstindex(r))
        st = step(s)
        len = length(s)
        stop = oftype(f, start + (len - oneunit(len)) * st)
        return range(start, stop; step=st)
    end
end

function getindex(r::StepRange, s::AbstractRange{T}) where {T<:Integer}
    @inline
    @boundscheck checkbounds(r, s)

    if T === Bool
        if length(s) == 0
            start, len = first(r), 0
        elseif length(s) == 1
            if first(s)
                start, len = first(r), 1
            else
                start, len = first(r), 0
            end
        else # length(s) == 2
            start, len = last(r), 1
        end
        return range(start, step=step(r); length=len)
    else
        f = r.start
        fs = first(s)
        st = r.step
        start = oftype(f, f + (fs - oneunit(fs)) * st)
        st = st * step(s)
        len = length(s)
        stop = oftype(f, start + (len - oneunit(len)) * st)
        return range(start, stop; step=st)
    end
end

function getindex(r::StepRangeLen{T}, s::OrdinalRange{S}) where {T, S<:Integer}
    @inline
    @boundscheck checkbounds(r, s)

    len = length(s)
    sstep = step_hp(s)
    rstep = step_hp(r)
    L = typeof(len)
    if S === Bool
        rstep *= one(sstep)
        if len == 0
            return StepRangeLen{T}(first(r), rstep, zero(L), oneunit(L))
        elseif len == 1
            if first(s)
                return StepRangeLen{T}(first(r), rstep, oneunit(L), oneunit(L))
            else
                return StepRangeLen{T}(first(r), rstep, zero(L), oneunit(L))
            end
        else # len == 2
            return StepRangeLen{T}(last(r), rstep, oneunit(L), oneunit(L))
        end
    else
        # Find closest approach to offset by s
        ind = LinearIndices(s)
        offset = L(max(min(1 + round(L, (r.offset - first(s))/sstep), last(ind)), first(ind)))
        ref = _getindex_hiprec(r, first(s) + (offset - oneunit(offset)) * sstep)
        return StepRangeLen{T}(ref, rstep*sstep, len, offset)
    end
end

function getindex(r::LinRange{T}, s::OrdinalRange{S}) where {T, S<:Integer}
    @inline
    @boundscheck checkbounds(r, s)

    len = length(s)
    L = typeof(len)
    if S === Bool
        if len == 0
            return LinRange{T}(first(r), first(r), len)
        elseif len == 1
            if first(s)
                return LinRange{T}(first(r), first(r), len)
            else
                return LinRange{T}(first(r), first(r), zero(L))
            end
        else # length(s) == 2
            return LinRange{T}(last(r), last(r), oneunit(L))
        end
    else
        vfirst = unsafe_getindex(r, first(s))
        vlast  = unsafe_getindex(r, last(s))
        return LinRange{T}(vfirst, vlast, len)
    end
end

show(io::IO, r::AbstractRange) = print(io, repr(first(r)), ':', repr(step(r)), ':', repr(last(r)))
show(io::IO, r::UnitRange) = print(io, repr(first(r)), ':', repr(last(r)))
show(io::IO, r::OneTo) = print(io, "Base.OneTo(", r.stop, ")")
function show(io::IO, r::StepRangeLen)
    if !iszero(step(r))
        print(io, repr(first(r)), ':', repr(step(r)), ':', repr(last(r)))
    else
        # ugly temporary printing, to avoid 0:0:0 etc.
        print(io, "StepRangeLen(", repr(first(r)), ", ", repr(step(r)), ", ", repr(length(r)), ")")
    end
end

function ==(r::T, s::T) where {T<:AbstractRange}
    isempty(r) && return isempty(s)
    _has_length_one(r) && return _has_length_one(s) & (first(r) == first(s))
    (first(r) == first(s)) & (step(r) == step(s)) & (last(r) == last(s))
end

function ==(r::OrdinalRange, s::OrdinalRange)
    isempty(r) && return isempty(s)
    _has_length_one(r) && return _has_length_one(s) & (first(r) == first(s))
    (first(r) == first(s)) & (step(r) == step(s)) & (last(r) == last(s))
end

==(r::AbstractUnitRange, s::AbstractUnitRange) =
    (isempty(r) & isempty(s)) | ((first(r) == first(s)) & (last(r) == last(s)))

==(r::OneTo, s::OneTo) = last(r) == last(s)

==(r::T, s::T) where {T<:Union{StepRangeLen,LinRange}} =
    (isempty(r) & isempty(s)) | ((first(r) == first(s)) & (length(r) == length(s)) & (last(r) == last(s)))

function ==(r::Union{StepRange{T},StepRangeLen{T,T}}, s::Union{StepRange{T},StepRangeLen{T,T}}) where {T}
    isempty(r) && return isempty(s)
    _has_length_one(r) && return _has_length_one(s) & (first(r) == first(s))
    (first(r) == first(s)) & (step(r) == step(s)) & (last(r) == last(s))
end

_has_length_one(r::OrdinalRange) = first(r) == last(r)
_has_length_one(r::AbstractRange) = isone(length(r))

function ==(r::AbstractRange, s::AbstractRange)
    lr = length(r)
    if lr != length(s)
        return false
    elseif iszero(lr)
        return true
    end
    yr, ys = iterate(r), iterate(s)
    while yr !== nothing
        yr[1] == ys[1] || return false
        yr, ys = iterate(r, yr[2]), iterate(s, ys[2])
    end
    return true
end

intersect(r::OneTo, s::OneTo) = OneTo(min(r.stop,s.stop))
union(r::OneTo, s::OneTo) = OneTo(max(r.stop,s.stop))

intersect(r::AbstractUnitRange{<:Integer}, s::AbstractUnitRange{<:Integer}) = max(first(r),first(s)):min(last(r),last(s))

intersect(i::Integer, r::AbstractUnitRange{<:Integer}) = range(max(i, first(r)), length=in(i, r))

intersect(r::AbstractUnitRange{<:Integer}, i::Integer) = intersect(i, r)

function intersect(r::AbstractUnitRange{<:Integer}, s::StepRange{<:Integer})
    T = promote_type(eltype(r), eltype(s))
    if isempty(s)
        StepRange{T}(first(r), +step(s), first(r)-step(s))
    else
        sta, ste, sto = first_step_last_ascending(s)
        lo = first(r)
        hi = last(r)
        i0 = max(sta, lo + mod(sta - lo, ste))
        i1 = min(sto, hi - mod(hi - sta, ste))
        StepRange{T}(i0, ste, i1)
    end
end

function first_step_last_ascending(r::StepRange)
    if step(r) < zero(step(r))
        last(r), -step(r), first(r)
    else
        first(r), +step(r), last(r)
    end
end

function intersect(r::StepRange{<:Integer}, s::AbstractUnitRange{<:Integer})
    if step(r) < 0
        reverse(intersect(s, reverse(r)))
    else
        intersect(s, r)
    end
end

function intersect(r::StepRange, s::StepRange)
    T = promote_type(eltype(r), eltype(s))
    S = promote_type(typeof(step(r)), typeof(step(s)))
    if isempty(r) || isempty(s)
        return StepRange{T,S}(first(r), step(r), first(r)-step(r))
    end

    start1, step1, stop1 = first_step_last_ascending(r)
    start2, step2, stop2 = first_step_last_ascending(s)
    a = lcm(step1, step2)

    g, x, y = gcdx(step1, step2)

    if !iszero(rem(start1 - start2, g))
        # Unaligned, no overlap possible.
        if  step(r) < zero(step(r))
            return StepRange{T,S}(stop1, -a, stop1+a)
        else
            return StepRange{T,S}(start1, a, start1-a)
        end
    end

    z = div(start1 - start2, g)
    b = start1 - x * z * step1
    # Possible points of the intersection of r and s are
    # ..., b-2a, b-a, b, b+a, b+2a, ...
    # Determine where in the sequence to start and stop.
    m = max(start1 + mod(b - start1, a), start2 + mod(b - start2, a))
    n = min(stop1 - mod(stop1 - b, a), stop2 - mod(stop2 - b, a))
    step(r) < zero(step(r)) ? StepRange{T,S}(n, -a, m) : StepRange{T,S}(m, a, n)
end

function intersect(r1::AbstractRange, r2::AbstractRange)
    # To iterate over the shorter range
    length(r1) > length(r2) && return intersect(r2, r1)

    r1 = unique(r1)
    T = promote_eltype(r1, r2)

    return T[x for x in r1 if x ∈ r2]
end

function intersect(r1::AbstractRange, r2::AbstractRange, r3::AbstractRange, r::AbstractRange...)
    i = intersect(intersect(r1, r2), r3)
    for t in r
        i = intersect(i, t)
    end
    i
end

# _findin (the index of intersection)
function _findin(r::AbstractRange{<:Integer}, span::AbstractUnitRange{<:Integer})
    fspan = first(span)
    lspan = last(span)
    fr = first(r)
    lr = last(r)
    sr = step(r)
    if sr > 0
        ifirst = fr >= fspan ? 1 : cld(fspan-fr, sr)+1
        ilast = lr <= lspan ? length(r) : length(r) - cld(lr-lspan, sr)
    elseif sr < 0
        ifirst = fr <= lspan ? 1 : cld(lspan-fr, sr)+1
        ilast = lr >= fspan ? length(r) : length(r) - cld(lr-fspan, sr)
    else
        ifirst = fr >= fspan ? 1 : length(r)+1
        ilast = fr <= lspan ? length(r) : 0
    end
    r isa AbstractUnitRange ? (ifirst:ilast) : (ifirst:1:ilast)
end

issubset(r::OneTo, s::OneTo) = r.stop <= s.stop

issubset(r::AbstractUnitRange{<:Integer}, s::AbstractUnitRange{<:Integer}) =
    isempty(r) || (first(r) >= first(s) && last(r) <= last(s))

## linear operations on ranges ##

-(r::OrdinalRange) = range(-first(r), step=negate(step(r)), length=length(r))
-(r::StepRangeLen{T,R,S,L}) where {T,R,S,L} =
    StepRangeLen{T,R,S,L}(-r.ref, -r.step, r.len, r.offset)
function -(r::LinRange)
    start = -r.start
    LinRange{typeof(start)}(start, -r.stop, length(r))
end

# promote eltype if at least one container wouldn't change, otherwise join container types.
el_same(::Type{T}, a::Type{<:AbstractArray{T,n}}, b::Type{<:AbstractArray{T,n}}) where {T,n}   = a # we assume a === b
el_same(::Type{T}, a::Type{<:AbstractArray{T,n}}, b::Type{<:AbstractArray{S,n}}) where {T,S,n} = a
el_same(::Type{T}, a::Type{<:AbstractArray{S,n}}, b::Type{<:AbstractArray{T,n}}) where {T,S,n} = b
el_same(::Type, a, b) = promote_typejoin(a, b)

promote_rule(a::Type{UnitRange{T1}}, b::Type{UnitRange{T2}}) where {T1,T2} =
    el_same(promote_type(T1, T2), a, b)
UnitRange{T}(r::UnitRange{T}) where {T<:Real} = r
UnitRange{T}(r::UnitRange) where {T<:Real} = UnitRange{T}(r.start, r.stop)

promote_rule(a::Type{OneTo{T1}}, b::Type{OneTo{T2}}) where {T1,T2} =
    el_same(promote_type(T1, T2), a, b)
OneTo{T}(r::OneTo{T}) where {T<:Integer} = r
OneTo{T}(r::OneTo) where {T<:Integer} = OneTo{T}(r.stop)

promote_rule(a::Type{UnitRange{T1}}, ::Type{UR}) where {T1,UR<:AbstractUnitRange} =
    promote_rule(a, UnitRange{eltype(UR)})
UnitRange{T}(r::AbstractUnitRange) where {T<:Real} = UnitRange{T}(first(r), last(r))
UnitRange(r::AbstractUnitRange) = UnitRange(first(r), last(r))

AbstractUnitRange{T}(r::AbstractUnitRange{T}) where {T} = r
AbstractUnitRange{T}(r::UnitRange) where {T} = UnitRange{T}(r)
AbstractUnitRange{T}(r::OneTo) where {T} = OneTo{T}(r)

OrdinalRange{T, S}(r::OrdinalRange) where {T, S} = StepRange{T, S}(r)
OrdinalRange{T, T}(r::AbstractUnitRange) where {T} = AbstractUnitRange{T}(r)

function promote_rule(::Type{StepRange{T1a,T1b}}, ::Type{StepRange{T2a,T2b}}) where {T1a,T1b,T2a,T2b}
    Tb = promote_type(T1b, T2b)
    # el_same only operates on array element type, so just promote second type parameter
    el_same(promote_type(T1a, T2a), StepRange{T1a,Tb}, StepRange{T2a,Tb})
end
StepRange{T1,T2}(r::StepRange{T1,T2}) where {T1,T2} = r

promote_rule(a::Type{StepRange{T1a,T1b}}, ::Type{UR}) where {T1a,T1b,UR<:AbstractUnitRange} =
    promote_rule(a, StepRange{eltype(UR), eltype(UR)})
StepRange{T1,T2}(r::AbstractRange) where {T1,T2} =
    StepRange{T1,T2}(convert(T1, first(r)), convert(T2, step(r)), convert(T1, last(r)))
StepRange(r::AbstractUnitRange{T}) where {T} =
    StepRange{T,T}(first(r), step(r), last(r))
(StepRange{T1,T2} where T1)(r::AbstractRange) where {T2} = StepRange{eltype(r),T2}(r)

function promote_rule(::Type{StepRangeLen{T1,R1,S1,L1}},::Type{StepRangeLen{T2,R2,S2,L2}}) where {T1,T2,R1,R2,S1,S2,L1,L2}
    R, S, L = promote_type(R1, R2), promote_type(S1, S2), promote_type(L1, L2)
    el_same(promote_type(T1, T2), StepRangeLen{T1,R,S,L}, StepRangeLen{T2,R,S,L})
end
StepRangeLen{T,R,S,L}(r::StepRangeLen{T,R,S,L}) where {T,R,S,L} = r
StepRangeLen{T,R,S,L}(r::StepRangeLen) where {T,R,S,L} =
    StepRangeLen{T,R,S,L}(convert(R, r.ref), convert(S, r.step), convert(L, r.len), convert(L, r.offset))
StepRangeLen{T}(r::StepRangeLen) where {T} =
    StepRangeLen(convert(T, r.ref), convert(T, r.step), r.len, r.offset)

promote_rule(a::Type{StepRangeLen{T,R,S,L}}, ::Type{OR}) where {T,R,S,L,OR<:AbstractRange} =
    promote_rule(a, StepRangeLen{eltype(OR), eltype(OR), eltype(OR), Int})
StepRangeLen{T,R,S,L}(r::AbstractRange) where {T,R,S,L} =
    StepRangeLen{T,R,S,L}(R(first(r)), S(step(r)), length(r))
StepRangeLen{T}(r::AbstractRange) where {T} =
    StepRangeLen(T(first(r)), T(step(r)), length(r))
StepRangeLen(r::AbstractRange) = StepRangeLen{eltype(r)}(r)

function promote_rule(a::Type{LinRange{T1,L1}}, b::Type{LinRange{T2,L2}}) where {T1,T2,L1,L2}
    L = promote_type(L1, L2)
    el_same(promote_type(T1, T2), LinRange{T1,L}, LinRange{T2,L})
end
LinRange{T,L}(r::LinRange{T,L}) where {T,L} = r
LinRange{T,L}(r::AbstractRange) where {T,L} = LinRange{T,L}(first(r), last(r), length(r))
LinRange{T}(r::AbstractRange) where {T} = LinRange{T,typeof(length(r))}(first(r), last(r), length(r))
LinRange(r::AbstractRange{T}) where {T} = LinRange{T}(r)

promote_rule(a::Type{LinRange{T,L}}, ::Type{OR}) where {T,L,OR<:OrdinalRange} =
    promote_rule(a, LinRange{eltype(OR),L})

promote_rule(::Type{LinRange{A,L}}, b::Type{StepRangeLen{T2,R2,S2,L2}}) where {A,L,T2,R2,S2,L2} =
    promote_rule(StepRangeLen{A,A,A,L}, b)

## concatenation ##

function vcat(rs::AbstractRange{T}...) where T
    n::Int = 0
    for ra in rs
        n += length(ra)
    end
    a = Vector{T}(undef, n)
    i = 1
    for ra in rs, x in ra
        @inbounds a[i] = x
        i += 1
    end
    return a
end

# This method differs from that for AbstractArrays as it
# use iteration instead of indexing. This works even if certain
# non-standard ranges don't support indexing.
# See https://github.com/JuliaLang/julia/pull/27302
# Similarly, collect(r::AbstractRange) uses iteration
function Array{T,1}(r::AbstractRange{T}) where {T}
    a = Vector{T}(undef, length(r))
    i = 1
    for x in r
        @inbounds a[i] = x
        i += 1
    end
    return a
end
collect(r::AbstractRange) = Array(r)

_reverse(r::OrdinalRange, ::Colon) = (:)(last(r), negate(step(r)), first(r))
function _reverse(r::StepRangeLen, ::Colon)
    # If `r` is empty, `length(r) - r.offset + 1 will be nonpositive hence
    # invalid. As `reverse(r)` is also empty, any offset would work so we keep
    # `r.offset`
    offset = isempty(r) ? r.offset : length(r)-r.offset+1
    return typeof(r)(r.ref, negate(r.step), length(r), offset)
end
_reverse(r::LinRange{T}, ::Colon) where {T} = typeof(r)(r.stop, r.start, length(r))

## sorting ##

issorted(r::AbstractUnitRange) = true
issorted(r::AbstractRange) = length(r) <= 1 || step(r) >= zero(step(r))

sort(r::AbstractUnitRange) = r
sort!(r::AbstractUnitRange) = r

sort(r::AbstractRange) = issorted(r) ? r : reverse(r)

sortperm(r::AbstractUnitRange) = 1:length(r)
sortperm(r::AbstractRange) = issorted(r) ? (1:1:length(r)) : (length(r):-1:1)

function sum(r::AbstractRange{<:Real})
    l = length(r)
    # note that a little care is required to avoid overflow in l*(l-1)/2
    return l * first(r) + (iseven(l) ? (step(r) * (l-1)) * (l>>1)
                                     : (step(r) * l) * ((l-1)>>1))
end

function _in_range(x, r::AbstractRange)
    isempty(r) && return false
    f, l = first(r), last(r)
    # check for NaN, Inf, and large x that may overflow in the next calculation
    f <= x <= l || l <= x <= f || return false
    iszero(step(r)) && return true
    n = round(Integer, (x - f) / step(r)) + 1
    n >= 1 && n <= length(r) && r[n] == x
end
in(x::Real, r::AbstractRange{<:Real}) = _in_range(x, r)
# This method needs to be defined separately since -(::T, ::T) can be implemented
# even if -(::T, ::Real) is not
in(x::T, r::AbstractRange{T}) where {T} = _in_range(x, r)

in(x::Integer, r::AbstractUnitRange{<:Integer}) = (first(r) <= x) & (x <= last(r))

in(x::Real, r::AbstractRange{T}) where {T<:Integer} =
    isinteger(x) && !isempty(r) &&
    (iszero(step(r)) ? x == first(r) : (x >= minimum(r) && x <= maximum(r) &&
        (mod(convert(T,x),step(r))-mod(first(r),step(r)) == 0)))
in(x::AbstractChar, r::AbstractRange{<:AbstractChar}) =
    !isempty(r) &&
    (iszero(step(r)) ? x == first(r) : (x >= minimum(r) && x <= maximum(r) &&
        (mod(Int(x) - Int(first(r)), step(r)) == 0)))

# Addition/subtraction of ranges

function _define_range_op(@nospecialize f)
    @eval begin
        function $f(r1::OrdinalRange, r2::OrdinalRange)
            r1l = length(r1)
            (r1l == length(r2) ||
             throw(DimensionMismatch("argument dimensions must match: length of r1 is $r1l, length of r2 is $(length(r2))")))
            StepRangeLen($f(first(r1), first(r2)), $f(step(r1), step(r2)), r1l)
        end

        function $f(r1::LinRange{T}, r2::LinRange{T}) where T
            len = r1.len
            (len == r2.len ||
             throw(DimensionMismatch("argument dimensions must match: length of r1 is $len, length of r2 is $(r2.len)")))
            LinRange{T}(convert(T, $f(first(r1), first(r2))),
                        convert(T, $f(last(r1), last(r2))), len)
        end

        $f(r1::Union{StepRangeLen, OrdinalRange, LinRange},
           r2::Union{StepRangeLen, OrdinalRange, LinRange}) =
               $f(promote(r1, r2)...)
    end
end
_define_range_op(:+)
_define_range_op(:-)

function +(r1::StepRangeLen{T,S}, r2::StepRangeLen{T,S}) where {T,S}
    len = length(r1)
    (len == length(r2) ||
     throw(DimensionMismatch("argument dimensions must match: length of r1 is $len, length of r2 is $(length(r2))")))
    StepRangeLen(first(r1)+first(r2), step(r1)+step(r2), len)
end

-(r1::StepRangeLen, r2::StepRangeLen) = +(r1, -r2)

# Modular arithmetic on ranges

"""
    mod(x::Integer, r::AbstractUnitRange)

Find `y` in the range `r` such that ``x ≡ y (mod n)``, where `n = length(r)`,
i.e. `y = mod(x - first(r), n) + first(r)`.

See also [`mod1`](@ref).

# Examples
```jldoctest
julia> mod(0, Base.OneTo(3))  # mod1(0, 3)
3

julia> mod(3, 0:2)  # mod(3, 3)
0
```

!!! compat "Julia 1.3"
     This method requires at least Julia 1.3.
"""
mod(i::Integer, r::OneTo) = mod1(i, last(r))
mod(i::Integer, r::AbstractUnitRange{<:Integer}) = mod(i-first(r), length(r)) + first(r)
L   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/error.jl9)      # This file is a part of Julia. License is MIT: https://julialang.org/license

# pseudo-definitions to show how everything behaves
#
# throw(label, val) = # throw a value to a dynamically enclosing block
#
# function rethrow(val)
#     global current_exception = val
#     throw(current_handler(), current_exception)
# end
#
# rethrow() = rethrow(current_exception)
#
# function throw(val)
#     global catch_backtrace = backtrace()
#     rethrow(val)
# end

"""
    throw(e)

Throw an object as an exception.

See also: [`rethrow`](@ref), [`error`](@ref).
"""
throw

## native julia error handling ##

"""
    error(message::AbstractString)

Raise an `ErrorException` with the given message.
"""
error(s::AbstractString) = throw(ErrorException(s))

"""
    error(msg...)

Raise an `ErrorException` with the given message.
"""
function error(s::Vararg{Any,N}) where {N}
    @noinline
    throw(ErrorException(Main.Base.string(s...)))
end

"""
    rethrow()

Rethrow the current exception from within a `catch` block. The rethrown
exception will continue propagation as if it had not been caught.

!!! note
    The alternative form `rethrow(e)` allows you to associate an alternative
    exception object `e` with the current backtrace. However this misrepresents
    the program state at the time of the error so you're encouraged to instead
    throw a new exception using `throw(e)`. In Julia 1.1 and above, using
    `throw(e)` will preserve the root cause exception on the stack, as
    described in [`current_exceptions`](@ref).
"""
rethrow() = ccall(:jl_rethrow, Bottom, ())
rethrow(@nospecialize(e)) = ccall(:jl_rethrow_other, Bottom, (Any,), e)

struct InterpreterIP
    code::Union{CodeInfo,Core.MethodInstance,Nothing}
    stmt::Csize_t
    mod::Union{Module,Nothing}
end

# convert dual arrays (raw bt buffer, array of GC managed values) to a single
# array of locations
function _reformat_bt(bt::Array{Ptr{Cvoid},1}, bt2::Array{Any,1})
    ret = Vector{Union{InterpreterIP,Ptr{Cvoid}}}()
    i, j = 1, 1
    while i <= length(bt)
        ip = bt[i]::Ptr{Cvoid}
        if UInt(ip) != (-1 % UInt) # See also jl_bt_is_native
            # native frame
            push!(ret, ip)
            i += 1
            continue
        end
        # Extended backtrace entry
        entry_metadata = reinterpret(UInt, bt[i+1])::UInt
        njlvalues =  entry_metadata & 0x7
        nuintvals = (entry_metadata >> 3) & 0x7
        tag       = (entry_metadata >> 6) & 0xf
        header    =  entry_metadata >> 10
        if tag == 1 # JL_BT_INTERP_FRAME_TAG
            code = bt2[j]::Union{CodeInfo,Core.MethodInstance,Nothing}
            mod = njlvalues == 2 ? bt2[j+1]::Union{Module,Nothing} : nothing
            push!(ret, InterpreterIP(code, header, mod))
        else
            # Tags we don't know about are an error
            throw(ArgumentError("Unexpected extended backtrace entry tag $tag at bt[$i]"))
        end
        # See jl_bt_entry_size
        j += Int(njlvalues)
        i += 2 + Int(njlvalues + nuintvals)
    end
    ret
end

"""
    backtrace()

Get a backtrace object for the current program point.
"""
function backtrace()
    @noinline
    # skip frame for backtrace(). Note that for this to work properly,
    # backtrace() itself must not be interpreted nor inlined.
    skip = 1
    bt1, bt2 = ccall(:jl_backtrace_from_here, Ref{SimpleVector}, (Cint, Cint), false, skip)
    return _reformat_bt(bt1::Vector{Ptr{Cvoid}}, bt2::Vector{Any})
end

"""
    catch_backtrace()

Get the backtrace of the current exception, for use within `catch` blocks.
"""
function catch_backtrace()
    bt, bt2 = ccall(:jl_get_backtrace, Ref{SimpleVector}, ())
    return _reformat_bt(bt::Vector{Ptr{Cvoid}}, bt2::Vector{Any})
end

struct ExceptionStack <: AbstractArray{Any,1}
    stack::Array{Any,1}
end

"""
    current_exceptions(task::Task=current_task(); [backtrace::Bool=true])

Get the stack of exceptions currently being handled. For nested catch blocks
there may be more than one current exception in which case the most recently
thrown exception is last in the stack. The stack is returned as an
`ExceptionStack` which is an AbstractVector of named tuples
`(exception,backtrace)`. If `backtrace` is false, the backtrace in each pair
will be set to `nothing`.

Explicitly passing `task` will return the current exception stack on an
arbitrary task. This is useful for inspecting tasks which have failed due to
uncaught exceptions.

!!! compat "Julia 1.7"
    This function went by the experimental name `catch_stack()` in Julia
    1.1–1.6, and had a plain Vector-of-tuples as a return type.
"""
function current_exceptions(task::Task=current_task(); backtrace::Bool=true)
    raw = ccall(:jl_get_excstack, Any, (Any,Cint,Cint), task, backtrace, typemax(Cint))::Vector{Any}
    formatted = Any[]
    stride = backtrace ? 3 : 1
    for i = reverse(1:stride:length(raw))
        exc = raw[i]
        bt = backtrace ? Base._reformat_bt(raw[i+1],raw[i+2]) : nothing
        push!(formatted, (exception=exc,backtrace=bt))
    end
    ExceptionStack(formatted)
end

## keyword arg lowering generates calls to this ##
function kwerr(kw, args::Vararg{Any,N}) where {N}
    @noinline
    throw(MethodError(Core.kwcall, (kw, args...)))
end

## system error handling ##
"""
    systemerror(sysfunc[, errno::Cint=Libc.errno()])
    systemerror(sysfunc, iftrue::Bool)

Raises a `SystemError` for `errno` with the descriptive string `sysfunc` if `iftrue` is `true`
"""
systemerror(p, b::Bool; extrainfo=nothing) = b ? systemerror(p, extrainfo=extrainfo) : nothing
systemerror(p, errno::Cint=Libc.errno(); extrainfo=nothing) = throw(Main.Base.SystemError(string(p), errno, extrainfo))

## system errors from Windows API functions
struct WindowsErrorInfo
    errnum::UInt32
    extrainfo
end
"""
    windowserror(sysfunc[, code::UInt32=Libc.GetLastError()])
    windowserror(sysfunc, iftrue::Bool)

Like [`systemerror`](@ref), but for Windows API functions that use [`GetLastError`](@ref Base.Libc.GetLastError) to
return an error code instead of setting [`errno`](@ref Base.Libc.errno).
"""
windowserror(p, b::Bool; extrainfo=nothing) = b ? windowserror(p, extrainfo=extrainfo) : nothing
windowserror(p, code::UInt32=Libc.GetLastError(); extrainfo=nothing) = throw(Main.Base.SystemError(string(p), 0, WindowsErrorInfo(code, extrainfo)))


## assertion macro ##


"""
    @assert cond [text]

Throw an [`AssertionError`](@ref) if `cond` is `false`. Preferred syntax for writing assertions.
Message `text` is optionally displayed upon assertion failure.

!!! warning
    An assert might be disabled at various optimization levels.
    Assert should therefore only be used as a debugging tool
    and not used for authentication verification (e.g., verifying passwords),
    nor should side effects needed for the function to work correctly
    be used inside of asserts.

# Examples
```jldoctest
julia> @assert iseven(3) "3 is an odd number!"
ERROR: AssertionError: 3 is an odd number!

julia> @assert isodd(3) "What even are numbers?"
```
"""
macro assert(ex, msgs...)
    msg = isempty(msgs) ? ex : msgs[1]
    if isa(msg, AbstractString)
        msg = msg # pass-through
    elseif !isempty(msgs) && (isa(msg, Expr) || isa(msg, Symbol))
        # message is an expression needing evaluating
        msg = :(Main.Base.string($(esc(msg))))
    elseif isdefined(Main, :Base) && isdefined(Main.Base, :string) && applicable(Main.Base.string, msg)
        msg = Main.Base.string(msg)
    else
        # string() might not be defined during bootstrap
        msg = quote
            msg = $(Expr(:quote,msg))
            isdefined(Main, :Base) ? Main.Base.string(msg) :
                (Core.println(msg); "Error during bootstrap. See stdout.")
        end
    end
    return :($(esc(ex)) ? $(nothing) : throw(AssertionError($msg)))
end

struct ExponentialBackOff
    n::Int
    first_delay::Float64
    max_delay::Float64
    factor::Float64
    jitter::Float64

    function ExponentialBackOff(n, first_delay, max_delay, factor, jitter)
        all(x->x>=0, (n, first_delay, max_delay, factor, jitter)) || error("all inputs must be non-negative")
        new(n, first_delay, max_delay, factor, jitter)
    end
end

"""
    ExponentialBackOff(; n=1, first_delay=0.05, max_delay=10.0, factor=5.0, jitter=0.1)

A [`Float64`](@ref) iterator of length `n` whose elements exponentially increase at a
rate in the interval `factor` * (1 ± `jitter`).  The first element is
`first_delay` and all elements are clamped to `max_delay`.
"""
ExponentialBackOff(; n=1, first_delay=0.05, max_delay=10.0, factor=5.0, jitter=0.1) =
    ExponentialBackOff(n, first_delay, max_delay, factor, jitter)
function iterate(ebo::ExponentialBackOff, state= (ebo.n, min(ebo.first_delay, ebo.max_delay)))
    state[1] < 1 && return nothing
    next_n = state[1]-1
    curr_delay = state[2]
    next_delay = min(ebo.max_delay, state[2] * ebo.factor * (1.0 - ebo.jitter + (Libc.rand(Float64) * 2.0 * ebo.jitter)))
    (curr_delay, (next_n, next_delay))
end
length(ebo::ExponentialBackOff) = ebo.n
eltype(::Type{ExponentialBackOff}) = Float64

"""
    retry(f;  delays=ExponentialBackOff(), check=nothing) -> Function

Return an anonymous function that calls function `f`.  If an exception arises,
`f` is repeatedly called again, each time `check` returns `true`, after waiting the
number of seconds specified in `delays`.  `check` should input `delays`'s
current state and the `Exception`.

!!! compat "Julia 1.2"
    Before Julia 1.2 this signature was restricted to `f::Function`.

# Examples
```julia
retry(f, delays=fill(5.0, 3))
retry(f, delays=rand(5:10, 2))
retry(f, delays=Base.ExponentialBackOff(n=3, first_delay=5, max_delay=1000))
retry(http_get, check=(s,e)->e.status == "503")(url)
retry(read, check=(s,e)->isa(e, IOError))(io, 128; all=false)
```
"""
function retry(f;  delays=ExponentialBackOff(), check=nothing)
    (args...; kwargs...) -> begin
        y = iterate(delays)
        while y !== nothing
            (delay, state) = y
            try
                return f(args...; kwargs...)
            catch e
                if check !== nothing
                    result = check(state, e)
                    state, retry_or_not = length(result) == 2 ? result : (state, result)
                    retry_or_not || rethrow()
                end
            end
            sleep(delay)
            y = iterate(delays, state)
        end
        # When delays is out, just run the function without try/catch
        return f(args...; kwargs...)
    end
end
K   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/bool.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

# promote Bool to any other numeric type
promote_rule(::Type{Bool}, ::Type{T}) where {T<:Number} = T

typemin(::Type{Bool}) = false
typemax(::Type{Bool}) = true

## boolean operations ##

"""
    !(x)

Boolean not. Implements [three-valued logic](https://en.wikipedia.org/wiki/Three-valued_logic),
returning [`missing`](@ref) if `x` is `missing`.

See also [`~`](@ref) for bitwise not.

# Examples
```jldoctest
julia> !true
false

julia> !false
true

julia> !missing
missing

julia> .![true false true]
1×3 BitMatrix:
 0  1  0
```
"""
!(x::Bool) = not_int(x)

(~)(x::Bool) = !x
(&)(x::Bool, y::Bool) = and_int(x, y)
(|)(x::Bool, y::Bool) = or_int(x, y)

"""
    xor(x, y)
    ⊻(x, y)

Bitwise exclusive or of `x` and `y`. Implements
[three-valued logic](https://en.wikipedia.org/wiki/Three-valued_logic),
returning [`missing`](@ref) if one of the arguments is `missing`.

The infix operation `a ⊻ b` is a synonym for `xor(a,b)`, and
`⊻` can be typed by tab-completing `\\xor` or `\\veebar` in the Julia REPL.

# Examples
```jldoctest
julia> xor(true, false)
true

julia> xor(true, true)
false

julia> xor(true, missing)
missing

julia> false ⊻ false
false

julia> [true; true; false] .⊻ [true; false; false]
3-element BitVector:
 0
 1
 0
```
"""
xor(x::Bool, y::Bool) = (x != y)

"""
    nand(x, y)
    ⊼(x, y)

Bitwise nand (not and) of `x` and `y`. Implements
[three-valued logic](https://en.wikipedia.org/wiki/Three-valued_logic),
returning [`missing`](@ref) if one of the arguments is `missing`.

The infix operation `a ⊼ b` is a synonym for `nand(a,b)`, and
`⊼` can be typed by tab-completing `\\nand` or `\\barwedge` in the Julia REPL.

# Examples
```jldoctest
julia> nand(true, false)
true

julia> nand(true, true)
false

julia> nand(true, missing)
missing

julia> false ⊼ false
true

julia> [true; true; false] .⊼ [true; false; false]
3-element BitVector:
 0
 1
 1
```
"""
nand(x...) = ~(&)(x...)

"""
    nor(x, y)
    ⊽(x, y)

Bitwise nor (not or) of `x` and `y`. Implements
[three-valued logic](https://en.wikipedia.org/wiki/Three-valued_logic),
returning [`missing`](@ref) if one of the arguments is `missing` and the
other is not `true`.

The infix operation `a ⊽ b` is a synonym for `nor(a,b)`, and
`⊽` can be typed by tab-completing `\\nor` or `\\barvee` in the Julia REPL.

# Examples
```jldoctest
julia> nor(true, false)
false

julia> nor(true, true)
false

julia> nor(true, missing)
false

julia> false ⊽ false
true

julia> false ⊽ missing
missing

julia> [true; true; false] .⊽ [true; false; false]
3-element BitVector:
 0
 0
 1
```
"""
nor(x...) = ~(|)(x...)

>>(x::Bool, c::UInt) = Int(x) >> c
<<(x::Bool, c::UInt) = Int(x) << c
>>>(x::Bool, c::UInt) = Int(x) >>> c

signbit(x::Bool) = false
sign(x::Bool) = x
abs(x::Bool) = x
abs2(x::Bool) = x
iszero(x::Bool) = !x
isone(x::Bool) = x

<(x::Bool, y::Bool) = y&!x
<=(x::Bool, y::Bool) = y|!x

## do arithmetic as Int ##

+(x::Bool) =  Int(x)
-(x::Bool) = -Int(x)

+(x::Bool, y::Bool) = Int(x) + Int(y)
-(x::Bool, y::Bool) = Int(x) - Int(y)
*(x::Bool, y::Bool) = x & y
^(x::Bool, y::Bool) = x | !y
^(x::Integer, y::Bool) = ifelse(y, x, one(x))

# preserve -0.0 in `false + -0.0`
function +(x::Bool, y::T)::promote_type(Bool,T) where T<:AbstractFloat
    return ifelse(x, oneunit(y) + y, y)
end
+(y::AbstractFloat, x::Bool) = x + y

# make `false` a "strong zero": false*NaN == 0.0
function *(x::Bool, y::T)::promote_type(Bool,T) where T<:AbstractFloat
    return ifelse(x, y, copysign(zero(y), y))
end
*(y::AbstractFloat, x::Bool) = x * y

div(x::Bool, y::Bool) = y ? x : throw(DivideError())
rem(x::Bool, y::Bool) = y ? false : throw(DivideError())
mod(x::Bool, y::Bool) = rem(x,y)
M   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/number.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

## generic operations on numbers ##

# Numbers are convertible
convert(::Type{T}, x::T)      where {T<:Number} = x
convert(::Type{T}, x::Number) where {T<:Number} = T(x)::T

"""
    isinteger(x) -> Bool

Test whether `x` is numerically equal to some integer.

# Examples
```jldoctest
julia> isinteger(4.0)
true
```
"""
isinteger(x::Integer) = true

"""
    iszero(x)

Return `true` if `x == zero(x)`; if `x` is an array, this checks whether
all of the elements of `x` are zero.

See also: [`isone`](@ref), [`isinteger`](@ref), [`isfinite`](@ref), [`isnan`](@ref).

# Examples
```jldoctest
julia> iszero(0.0)
true

julia> iszero([1, 9, 0])
false

julia> iszero([false, 0, 0])
true
```
"""
iszero(x) = x == zero(x) # fallback method

"""
    isone(x)

Return `true` if `x == one(x)`; if `x` is an array, this checks whether
`x` is an identity matrix.

# Examples
```jldoctest
julia> isone(1.0)
true

julia> isone([1 0; 0 2])
false

julia> isone([1 0; 0 true])
true
```
"""
isone(x) = x == one(x) # fallback method

"""
    isfinite(f) -> Bool

Test whether a number is finite.

# Examples
```jldoctest
julia> isfinite(5)
true

julia> isfinite(NaN32)
false
```
"""
isfinite(x::Number) = iszero(x - x)

size(x::Number) = ()
size(x::Number, d::Integer) = d < 1 ? throw(BoundsError()) : 1
axes(x::Number) = ()
axes(x::Number, d::Integer) = d < 1 ? throw(BoundsError()) : OneTo(1)
eltype(::Type{T}) where {T<:Number} = T
ndims(x::Number) = 0
ndims(::Type{<:Number}) = 0
length(x::Number) = 1
firstindex(x::Number) = 1
firstindex(x::Number, d::Int) = d < 1 ? throw(BoundsError()) : 1
lastindex(x::Number) = 1
lastindex(x::Number, d::Int) = d < 1 ? throw(BoundsError()) : 1
IteratorSize(::Type{<:Number}) = HasShape{0}()
keys(::Number) = OneTo(1)

getindex(x::Number) = x
function getindex(x::Number, i::Integer)
    @inline
    @boundscheck i == 1 || throw(BoundsError(x, i))
    x
end
function getindex(x::Number, I::Integer...)
    @inline
    @boundscheck all(isone, I) || throw(BoundsError(x, I))
    x
end
get(x::Number, i::Integer, default) = isone(i) ? x : default
get(x::Number, ind::Tuple, default) = all(isone, ind) ? x : default
get(f::Callable, x::Number, i::Integer) = isone(i) ? x : f()
get(f::Callable, x::Number, ind::Tuple) = all(isone, ind) ? x : f()

first(x::Number) = x
last(x::Number) = x
copy(x::Number) = x # some code treats numbers as collection-like

"""
    signbit(x)

Return `true` if the value of the sign of `x` is negative, otherwise `false`.

See also [`sign`](@ref) and [`copysign`](@ref).

# Examples
```jldoctest
julia> signbit(-4)
true

julia> signbit(5)
false

julia> signbit(5.5)
false

julia> signbit(-4.1)
true
```
"""
signbit(x::Real) = x < 0

"""
    sign(x)

Return zero if `x==0` and ``x/|x|`` otherwise (i.e., ±1 for real `x`).

See also [`signbit`](@ref), [`zero`](@ref), [`copysign`](@ref), [`flipsign`](@ref).

# Examples
```jldoctest
julia> sign(-4.0)
-1.0

julia> sign(99)
1

julia> sign(-0.0)
-0.0

julia> sign(0 + im)
0.0 + 1.0im
```
"""
sign(x::Number) = iszero(x) ? x/abs(oneunit(x)) : x/abs(x)
sign(x::Real) = ifelse(x < zero(x), oftype(one(x),-1), ifelse(x > zero(x), one(x), typeof(one(x))(x)))
sign(x::Unsigned) = ifelse(x > zero(x), one(x), oftype(one(x),0))
abs(x::Real) = ifelse(signbit(x), -x, x)

"""
    abs2(x)

Squared absolute value of `x`.

This can be faster than `abs(x)^2`, especially for complex
numbers where `abs(x)` requires a square root via [`hypot`](@ref).

See also [`abs`](@ref), [`conj`](@ref), [`real`](@ref).

# Examples
```jldoctest
julia> abs2(-3)
9

julia> abs2(3.0 + 4.0im)
25.0

julia> sum(abs2, [1+2im, 3+4im])  # LinearAlgebra.norm(x)^2
30
```
"""
abs2(x::Number) = abs(x)^2
abs2(x::Real) = x*x

"""
    flipsign(x, y)

Return `x` with its sign flipped if `y` is negative. For example `abs(x) = flipsign(x,x)`.

# Examples
```jldoctest
julia> flipsign(5, 3)
5

julia> flipsign(5, -3)
-5
```
"""
flipsign(x::Real, y::Real) = ifelse(signbit(y), -x, +x) # the + is for type-stability on Bool

"""
    copysign(x, y) -> z

Return `z` which has the magnitude of `x` and the same sign as `y`.

# Examples
```jldoctest
julia> copysign(1, -2)
-1

julia> copysign(-1, 2)
1
```
"""
copysign(x::Real, y::Real) = ifelse(signbit(x)!=signbit(y), -x, +x)

conj(x::Real) = x
transpose(x::Number) = x
adjoint(x::Number) = conj(x)
angle(z::Real) = atan(zero(z), z)

"""
    inv(x)

Return the multiplicative inverse of `x`, such that `x*inv(x)` or `inv(x)*x`
yields [`one(x)`](@ref) (the multiplicative identity) up to roundoff errors.

If `x` is a number, this is essentially the same as `one(x)/x`, but for
some types `inv(x)` may be slightly more efficient.

# Examples
```jldoctest
julia> inv(2)
0.5

julia> inv(1 + 2im)
0.2 - 0.4im

julia> inv(1 + 2im) * (1 + 2im)
1.0 + 0.0im

julia> inv(2//3)
3//2
```

!!! compat "Julia 1.2"
    `inv(::Missing)` requires at least Julia 1.2.
"""
inv(x::Number) = one(x)/x


"""
    widemul(x, y)

Multiply `x` and `y`, giving the result as a larger type.

See also [`promote`](@ref), [`Base.add_sum`](@ref).

# Examples
```jldoctest
julia> widemul(Float32(3.0), 4.0) isa BigFloat
true

julia> typemax(Int8) * typemax(Int8)
1

julia> widemul(typemax(Int8), typemax(Int8))  # == 127^2
16129
```
"""
widemul(x::Number, y::Number) = widen(x)*widen(y)

iterate(x::Number) = (x, nothing)
iterate(x::Number, ::Any) = nothing
isempty(x::Number) = false
in(x::Number, y::Number) = x == y

map(f, x::Number, ys::Number...) = f(x, ys...)

"""
    zero(x)
    zero(::Type)

Get the additive identity element for the type of `x` (`x` can also specify the type itself).

See also [`iszero`](@ref), [`one`](@ref), [`oneunit`](@ref), [`oftype`](@ref).

# Examples
```jldoctest
julia> zero(1)
0

julia> zero(big"2.0")
0.0

julia> zero(rand(2,2))
2×2 Matrix{Float64}:
 0.0  0.0
 0.0  0.0
```
"""
zero(x::Number) = oftype(x,0)
zero(::Type{T}) where {T<:Number} = convert(T,0)
zero(::Type{Union{}}, slurp...) = Union{}(0)

"""
    one(x)
    one(T::type)

Return a multiplicative identity for `x`: a value such that
`one(x)*x == x*one(x) == x`.  Alternatively `one(T)` can
take a type `T`, in which case `one` returns a multiplicative
identity for any `x` of type `T`.

If possible, `one(x)` returns a value of the same type as `x`,
and `one(T)` returns a value of type `T`.  However, this may
not be the case for types representing dimensionful quantities
(e.g. time in days), since the multiplicative
identity must be dimensionless.  In that case, `one(x)`
should return an identity value of the same precision
(and shape, for matrices) as `x`.

If you want a quantity that is of the same type as `x`, or of type `T`,
even if `x` is dimensionful, use [`oneunit`](@ref) instead.

See also the [`identity`](@ref) function,
and `I` in [`LinearAlgebra`](@ref man-linalg) for the identity matrix.

# Examples
```jldoctest
julia> one(3.7)
1.0

julia> one(Int)
1

julia> import Dates; one(Dates.Day(1))
1
```
"""
one(::Type{T}) where {T<:Number} = convert(T,1)
one(x::T) where {T<:Number} = one(T)
one(::Type{Union{}}, slurp...) = Union{}(1)
# note that convert(T, 1) should throw an error if T is dimensionful,
# so this fallback definition should be okay.

"""
    oneunit(x::T)
    oneunit(T::Type)

Return `T(one(x))`, where `T` is either the type of the argument or
(if a type is passed) the argument.  This differs from [`one`](@ref) for
dimensionful quantities: `one` is dimensionless (a multiplicative identity)
while `oneunit` is dimensionful (of the same type as `x`, or of type `T`).

# Examples
```jldoctest
julia> oneunit(3.7)
1.0

julia> import Dates; oneunit(Dates.Day)
1 day
```
"""
oneunit(x::T) where {T} = T(one(x))
oneunit(::Type{T}) where {T} = T(one(T))
oneunit(::Type{Union{}}, slurp...) = Union{}(1)

"""
    big(T::Type)

Compute the type that represents the numeric type `T` with arbitrary precision.
Equivalent to `typeof(big(zero(T)))`.

# Examples
```jldoctest
julia> big(Rational)
Rational{BigInt}

julia> big(Float64)
BigFloat

julia> big(Complex{Int})
Complex{BigInt}
```
"""
big(::Type{T}) where {T<:Number} = typeof(big(zero(T)))
big(::Type{Union{}}, slurp...) = Union{}(0)
J   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/int.jl+x      # This file is a part of Julia. License is MIT: https://julialang.org/license

## integer arithmetic ##

# The tuples and types that do not include 128 bit sizes are necessary to handle
# certain issues on 32-bit machines, and also to simplify promotion rules, as
# they are also used elsewhere where Int128/UInt128 support is separated out,
# such as in hashing2.jl

const BitSigned32_types      = (Int8, Int16, Int32)
const BitUnsigned32_types    = (UInt8, UInt16, UInt32)
const BitInteger32_types     = (BitSigned32_types..., BitUnsigned32_types...)

const BitSigned64_types      = (BitSigned32_types..., Int64)
const BitUnsigned64_types    = (BitUnsigned32_types..., UInt64)
const BitInteger64_types     = (BitSigned64_types..., BitUnsigned64_types...)

const BitSigned_types        = (BitSigned64_types..., Int128)
const BitUnsigned_types      = (BitUnsigned64_types..., UInt128)
const BitInteger_types       = (BitSigned_types..., BitUnsigned_types...)

const BitSignedSmall_types   = Int === Int64 ? ( Int8,  Int16,  Int32) : ( Int8,  Int16)
const BitUnsignedSmall_types = Int === Int64 ? (UInt8, UInt16, UInt32) : (UInt8, UInt16)
const BitIntegerSmall_types  = (BitSignedSmall_types..., BitUnsignedSmall_types...)

const BitSigned32      = Union{BitSigned32_types...}
const BitUnsigned32    = Union{BitUnsigned32_types...}
const BitInteger32     = Union{BitInteger32_types...}

const BitSigned64      = Union{BitSigned64_types...}
const BitUnsigned64    = Union{BitUnsigned64_types...}
const BitInteger64     = Union{BitInteger64_types...}

const BitSigned        = Union{BitSigned_types...}
const BitUnsigned      = Union{BitUnsigned_types...}
const BitInteger       = Union{BitInteger_types...}

const BitSignedSmall   = Union{BitSignedSmall_types...}
const BitUnsignedSmall = Union{BitUnsignedSmall_types...}
const BitIntegerSmall  = Union{BitIntegerSmall_types...}

const BitSigned64T     = Union{Type{Int8}, Type{Int16}, Type{Int32}, Type{Int64}}
const BitUnsigned64T   = Union{Type{UInt8}, Type{UInt16}, Type{UInt32}, Type{UInt64}}

const BitIntegerType = Union{map(T->Type{T}, BitInteger_types)...}

# >> this use of `unsigned` is defined somewhere else << the docstring should migrate there
"""
    unsigned(T::Integer)

Convert an integer bitstype to the unsigned type of the same size.
# Examples
```jldoctest
julia> unsigned(Int16)
UInt16
julia> unsigned(UInt64)
UInt64
```
""" unsigned

"""
    signed(T::Integer)

Convert an integer bitstype to the signed type of the same size.
# Examples
```jldoctest
julia> signed(UInt16)
Int16
julia> signed(UInt64)
Int64
```
"""
signed(::Type{Bool}) = Int
signed(::Type{UInt8}) = Int8
signed(::Type{UInt16}) = Int16
signed(::Type{UInt32}) = Int32
signed(::Type{UInt64}) = Int64
signed(::Type{UInt128}) = Int128
signed(::Type{T}) where {T<:Signed} = T

## integer comparisons ##

(<)(x::T, y::T) where {T<:BitSigned}  = slt_int(x, y)

(-)(x::BitInteger)                    = neg_int(x)
(-)(x::T, y::T) where {T<:BitInteger} = sub_int(x, y)
(+)(x::T, y::T) where {T<:BitInteger} = add_int(x, y)
(*)(x::T, y::T) where {T<:BitInteger} = mul_int(x, y)

negate(x) = -x
negate(x::Unsigned) = -convert(Signed, x)
#widenegate(x) = -convert(widen(signed(typeof(x))), x)

inv(x::Integer) = float(one(x)) / float(x)
(/)(x::T, y::T) where {T<:Integer} = float(x) / float(y)
# skip promotion for system integer types
(/)(x::BitInteger, y::BitInteger) = float(x) / float(y)

"""
    isodd(x::Number) -> Bool

Return `true` if `x` is an odd integer (that is, an integer not divisible by 2), and `false` otherwise.

!!! compat "Julia 1.7"
    Non-`Integer` arguments require Julia 1.7 or later.

# Examples
```jldoctest
julia> isodd(9)
true

julia> isodd(10)
false
```
"""
isodd(n::Number) = isreal(n) && isodd(real(n))
isodd(n::Real) = isinteger(n) && !iszero(rem(Integer(n), 2))

"""
    iseven(x::Number) -> Bool

Return `true` if `x` is an even integer (that is, an integer divisible by 2), and `false` otherwise.

!!! compat "Julia 1.7"
    Non-`Integer` arguments require Julia 1.7 or later.

# Examples
```jldoctest
julia> iseven(9)
false

julia> iseven(10)
true
```
"""
iseven(n::Number) = isreal(n) && iseven(real(n))
iseven(n::Real) = isinteger(n) && iszero(rem(Integer(n), 2))

signbit(x::Integer) = x < 0
signbit(x::Unsigned) = false

flipsign(x::T, y::T) where {T<:BitSigned} = flipsign_int(x, y)
flipsign(x::BitSigned, y::BitSigned) = flipsign_int(promote(x, y)...) % typeof(x)

flipsign(x::Signed, y::Float16) = flipsign(x, bitcast(Int16, y))
flipsign(x::Signed, y::Float32) = flipsign(x, bitcast(Int32, y))
flipsign(x::Signed, y::Float64) = flipsign(x, bitcast(Int64, y))
flipsign(x::Signed, y::Real)    = flipsign(x, -oftype(x, signbit(y)))

copysign(x::Signed, y::Signed)  = flipsign(x, x ⊻ y)
copysign(x::Signed, y::Float16) = copysign(x, bitcast(Int16, y))
copysign(x::Signed, y::Float32) = copysign(x, bitcast(Int32, y))
copysign(x::Signed, y::Float64) = copysign(x, bitcast(Int64, y))
copysign(x::Signed, y::Real)    = copysign(x, -oftype(x, signbit(y)))

"""
    abs(x)

The absolute value of `x`.

When `abs` is applied to signed integers, overflow may occur,
resulting in the return of a negative value. This overflow occurs only
when `abs` is applied to the minimum representable value of a signed
integer. That is, when `x == typemin(typeof(x))`, `abs(x) == x < 0`,
not `-x` as might be expected.

See also: [`abs2`](@ref), [`unsigned`](@ref), [`sign`](@ref).

# Examples
```jldoctest
julia> abs(-3)
3

julia> abs(1 + im)
1.4142135623730951

julia> abs.(Int8[-128 -127 -126 0 126 127])  # overflow at typemin(Int8)
1×6 Matrix{Int8}:
 -128  127  126  0  126  127

julia> maximum(abs, [1, -2, 3, -4])
4
```
"""
function abs end

abs(x::Unsigned) = x
abs(x::Signed) = flipsign(x,x)

~(n::Integer) = -n-1

"""
    unsigned(x)

Convert a number to an unsigned integer. If the argument is signed, it is reinterpreted as
unsigned without checking for negative values.

See also: [`signed`](@ref), [`sign`](@ref), [`signbit`](@ref).

# Examples
```jldoctest
julia> unsigned(-2)
0xfffffffffffffffe

julia> unsigned(Int8(2))
0x02

julia> typeof(ans)
UInt8

julia> signed(unsigned(-2))
-2
```
"""
unsigned(x) = x % typeof(convert(Unsigned, zero(x)))
unsigned(x::BitSigned) = reinterpret(typeof(convert(Unsigned, zero(x))), x)

"""
    signed(x)

Convert a number to a signed integer. If the argument is unsigned, it is reinterpreted as
signed without checking for overflow.

See also: [`unsigned`](@ref), [`sign`](@ref), [`signbit`](@ref).
"""
signed(x) = x % typeof(convert(Signed, zero(x)))
signed(x::BitUnsigned) = reinterpret(typeof(convert(Signed, zero(x))), x)

div(x::BitSigned, y::Unsigned) = flipsign(signed(div(unsigned(abs(x)), y)), x)
div(x::Unsigned, y::BitSigned) = unsigned(flipsign(signed(div(x, unsigned(abs(y)))), y))

rem(x::BitSigned, y::Unsigned) = flipsign(signed(rem(unsigned(abs(x)), y)), x)
rem(x::Unsigned, y::BitSigned) = rem(x, unsigned(abs(y)))

function divrem(x::BitSigned, y::Unsigned)
    q, r = divrem(unsigned(abs(x)), y)
    flipsign(signed(q), x), flipsign(signed(r), x)
end

function divrem(x::Unsigned, y::BitSigned)
    q, r = divrem(x, unsigned(abs(y)))
    unsigned(flipsign(signed(q), y)), r
end


"""
    mod(x, y)
    rem(x, y, RoundDown)

The reduction of `x` modulo `y`, or equivalently, the remainder of `x` after floored
division by `y`, i.e. `x - y*fld(x,y)` if computed without intermediate rounding.

The result will have the same sign as `y`, and magnitude less than `abs(y)` (with some
exceptions, see note below).

!!! note

    When used with floating point values, the exact result may not be representable by the
    type, and so rounding error may occur. In particular, if the exact result is very
    close to `y`, then it may be rounded to `y`.

See also: [`rem`](@ref), [`div`](@ref), [`fld`](@ref), [`mod1`](@ref), [`invmod`](@ref).

```jldoctest
julia> mod(8, 3)
2

julia> mod(9, 3)
0

julia> mod(8.9, 3)
2.9000000000000004

julia> mod(eps(), 3)
2.220446049250313e-16

julia> mod(-eps(), 3)
3.0

julia> mod.(-5:5, 3)'
1×11 adjoint(::Vector{Int64}) with eltype Int64:
 1  2  0  1  2  0  1  2  0  1  2
```
"""
function mod(x::T, y::T) where T<:Integer
    y == -1 && return T(0)   # avoid potential overflow in fld
    return x - fld(x, y) * y
end
mod(x::BitSigned, y::Unsigned) = rem(y + unsigned(rem(x, y)), y)
mod(x::Unsigned, y::Signed) = rem(y + signed(rem(x, y)), y)
mod(x::T, y::T) where {T<:Unsigned} = rem(x, y)

# Don't promote integers for div/rem/mod since there is no danger of overflow,
# while there is a substantial performance penalty to 64-bit promotion.
div(x::T, y::T) where {T<:BitSigned64} = checked_sdiv_int(x, y)
rem(x::T, y::T) where {T<:BitSigned64} = checked_srem_int(x, y)
div(x::T, y::T) where {T<:BitUnsigned64} = checked_udiv_int(x, y)
rem(x::T, y::T) where {T<:BitUnsigned64} = checked_urem_int(x, y)

## integer bitwise operations ##

"""
    ~(x)

Bitwise not.

See also: [`!`](@ref), [`&`](@ref), [`|`](@ref).

# Examples
```jldoctest
julia> ~4
-5

julia> ~10
-11

julia> ~true
false
```
"""
(~)(x::BitInteger)             = not_int(x)

"""
    x & y

Bitwise and. Implements [three-valued logic](https://en.wikipedia.org/wiki/Three-valued_logic),
returning [`missing`](@ref) if one operand is `missing` and the other is `true`. Add parentheses for
function application form: `(&)(x, y)`.

See also: [`|`](@ref), [`xor`](@ref), [`&&`](@ref).

# Examples
```jldoctest
julia> 4 & 10
0

julia> 4 & 12
4

julia> true & missing
missing

julia> false & missing
false
```
"""
(&)(x::T, y::T) where {T<:BitInteger} = and_int(x, y)

"""
    x | y

Bitwise or. Implements [three-valued logic](https://en.wikipedia.org/wiki/Three-valued_logic),
returning [`missing`](@ref) if one operand is `missing` and the other is `false`.

See also: [`&`](@ref), [`xor`](@ref), [`||`](@ref).

# Examples
```jldoctest
julia> 4 | 10
14

julia> 4 | 1
5

julia> true | missing
true

julia> false | missing
missing
```
"""
(|)(x::T, y::T) where {T<:BitInteger} = or_int(x, y)
xor(x::T, y::T) where {T<:BitInteger} = xor_int(x, y)

"""
    bswap(n)

Reverse the byte order of `n`.

(See also [`ntoh`](@ref) and [`hton`](@ref) to convert between the current native byte order and big-endian order.)

# Examples
```jldoctest
julia> a = bswap(0x10203040)
0x40302010

julia> bswap(a)
0x10203040

julia> string(1, base = 2)
"1"

julia> string(bswap(1), base = 2)
"100000000000000000000000000000000000000000000000000000000"
```
"""
bswap(x::Union{Int8, UInt8, Bool}) = x
bswap(x::Union{Int16, UInt16, Int32, UInt32, Int64, UInt64, Int128, UInt128}) =
    bswap_int(x)

"""
    count_ones(x::Integer) -> Integer

Number of ones in the binary representation of `x`.

# Examples
```jldoctest
julia> count_ones(7)
3

julia> count_ones(Int32(-1))
32
```
"""
count_ones(x::BitInteger) = (ctpop_int(x) % Int)::Int

"""
    leading_zeros(x::Integer) -> Integer

Number of zeros leading the binary representation of `x`.

# Examples
```jldoctest
julia> leading_zeros(Int32(1))
31
```
"""
leading_zeros(x::BitInteger) = (ctlz_int(x) % Int)::Int

"""
    trailing_zeros(x::Integer) -> Integer

Number of zeros trailing the binary representation of `x`.

# Examples
```jldoctest
julia> trailing_zeros(2)
1
```
"""
trailing_zeros(x::BitInteger) = (cttz_int(x) % Int)::Int

"""
    count_zeros(x::Integer) -> Integer

Number of zeros in the binary representation of `x`.

# Examples
```jldoctest
julia> count_zeros(Int32(2 ^ 16 - 1))
16

julia> count_zeros(-1)
0
```
"""
count_zeros(x::Integer) = count_ones(~x)

"""
    leading_ones(x::Integer) -> Integer

Number of ones leading the binary representation of `x`.

# Examples
```jldoctest
julia> leading_ones(UInt32(2 ^ 32 - 2))
31
```
"""
leading_ones(x::Integer) = leading_zeros(~x)

"""
    trailing_ones(x::Integer) -> Integer

Number of ones trailing the binary representation of `x`.

# Examples
```jldoctest
julia> trailing_ones(3)
2
```
"""
trailing_ones(x::Integer) = trailing_zeros(~x)

"""
    top_set_bit(x::Integer) -> Integer

The number of bits in `x`'s binary representation, excluding leading zeros.

Equivalently, the position of the most significant set bit in `x`'s binary
representation, measured from the least significant side.

Negative `x` are only supported when `x::BitSigned`.

See also: [`ndigits0z`](@ref), [`ndigits`](@ref).

# Examples
```jldoctest
julia> Base.top_set_bit(4)
3

julia> Base.top_set_bit(0)
0

julia> Base.top_set_bit(-1)
64
```
"""
top_set_bit(x::BitInteger) = 8sizeof(x) - leading_zeros(x)

## integer comparisons ##

(< )(x::T, y::T) where {T<:BitUnsigned} = ult_int(x, y)
(<=)(x::T, y::T) where {T<:BitSigned}   = sle_int(x, y)
(<=)(x::T, y::T) where {T<:BitUnsigned} = ule_int(x, y)

==(x::BitSigned,   y::BitUnsigned) = (x >= 0) & (unsigned(x) == y)
==(x::BitUnsigned, y::BitSigned  ) = (y >= 0) & (x == unsigned(y))
<( x::BitSigned,   y::BitUnsigned) = (x <  0) | (unsigned(x) <  y)
<( x::BitUnsigned, y::BitSigned  ) = (y >= 0) & (x <  unsigned(y))
<=(x::BitSigned,   y::BitUnsigned) = (x <  0) | (unsigned(x) <= y)
<=(x::BitUnsigned, y::BitSigned  ) = (y >= 0) & (x <= unsigned(y))

## integer shifts ##

# unsigned shift counts always shift in the same direction
>>(x::BitSigned,   y::BitUnsigned) = ashr_int(x, y)
>>(x::BitUnsigned, y::BitUnsigned) = lshr_int(x, y)
<<(x::BitInteger,  y::BitUnsigned) = shl_int(x, y)
>>>(x::BitInteger, y::BitUnsigned) = lshr_int(x, y)
# signed shift counts can shift in either direction
# note: this early during bootstrap, `>=` is not yet available
# note: we only define Int shift counts here; the generic case is handled later
>>(x::BitInteger, y::Int) =
    ifelse(0 <= y, x >> unsigned(y), x << unsigned(-y))
<<(x::BitInteger, y::Int) =
    ifelse(0 <= y, x << unsigned(y), x >> unsigned(-y))
>>>(x::BitInteger, y::Int) =
    ifelse(0 <= y, x >>> unsigned(y), x << unsigned(-y))

for to in BitInteger_types, from in (BitInteger_types..., Bool)
    if !(to === from)
        if Core.sizeof(to) < Core.sizeof(from)
            @eval rem(x::($from), ::Type{$to}) = trunc_int($to, x)
        elseif from === Bool
            @eval rem(x::($from), ::Type{$to}) = convert($to, x)
        elseif Core.sizeof(from) < Core.sizeof(to)
            if from <: Signed
                @eval rem(x::($from), ::Type{$to}) = sext_int($to, x)
            else
                @eval rem(x::($from), ::Type{$to}) = convert($to, x)
            end
        else
            @eval rem(x::($from), ::Type{$to}) = bitcast($to, x)
        end
    end
end

## integer bitwise rotations ##

"""
    bitrotate(x::Base.BitInteger, k::Integer)

`bitrotate(x, k)` implements bitwise rotation.
It returns the value of `x` with its bits rotated left `k` times.
A negative value of `k` will rotate to the right instead.

!!! compat "Julia 1.5"
    This function requires Julia 1.5 or later.

See also: [`<<`](@ref), [`circshift`](@ref), [`BitArray`](@ref).

```jldoctest
julia> bitrotate(UInt8(114), 2)
0xc9

julia> bitstring(bitrotate(0b01110010, 2))
"11001001"

julia> bitstring(bitrotate(0b01110010, -2))
"10011100"

julia> bitstring(bitrotate(0b01110010, 8))
"01110010"
```
"""
bitrotate(x::T, k::Integer) where {T <: BitInteger} =
    (x << ((sizeof(T) << 3 - 1) & k)) | (x >>> ((sizeof(T) << 3 - 1) & -k))

# @doc isn't available when running in Core at this point.
# Tuple syntax for documentation two function signatures at the same time
# doesn't work either at this point.
if nameof(@__MODULE__) === :Base
    for fname in (:mod, :rem)
        @eval @doc """
            rem(x::Integer, T::Type{<:Integer}) -> T
            mod(x::Integer, T::Type{<:Integer}) -> T
            %(x::Integer, T::Type{<:Integer}) -> T

        Find `y::T` such that `x` ≡ `y` (mod n), where n is the number of integers representable
        in `T`, and `y` is an integer in `[typemin(T),typemax(T)]`.
        If `T` can represent any integer (e.g. `T == BigInt`), then this operation corresponds to
        a conversion to `T`.

        # Examples
        ```jldoctest
        julia> x = 129 % Int8
        -127

        julia> typeof(x)
        Int8

        julia> x = 129 % BigInt
        129

        julia> typeof(x)
        BigInt
        ```
        """ $fname(x::Integer, T::Type{<:Integer})
    end
end

rem(x::T, ::Type{T}) where {T<:Integer} = x
rem(x::Signed, ::Type{Unsigned}) = x % unsigned(typeof(x))
rem(x::Unsigned, ::Type{Signed}) = x % signed(typeof(x))
rem(x::Integer, T::Type{<:Integer}) = convert(T, x)  # `x % T` falls back to `convert`
rem(x::Integer, ::Type{Bool}) = ((x & 1) != 0)
mod(x::Integer, ::Type{T}) where {T<:Integer} = rem(x, T)

unsafe_trunc(::Type{T}, x::Integer) where {T<:Integer} = rem(x, T)

"""
    trunc([T,] x)
    trunc(x; digits::Integer= [, base = 10])
    trunc(x; sigdigits::Integer= [, base = 10])

`trunc(x)` returns the nearest integral value of the same type as `x` whose absolute value
is less than or equal to the absolute value of `x`.

`trunc(T, x)` converts the result to type `T`, throwing an `InexactError` if the value is
not representable.

Keywords `digits`, `sigdigits` and `base` work as for [`round`](@ref).

See also: [`%`](@ref rem), [`floor`](@ref), [`unsigned`](@ref), [`unsafe_trunc`](@ref).

# Examples
```jldoctest
julia> trunc(2.22)
2.0

julia> trunc(-2.22, digits=1)
-2.2

julia> trunc(Int, -2.22)
-2
```
"""
function trunc end

"""
    floor([T,] x)
    floor(x; digits::Integer= [, base = 10])
    floor(x; sigdigits::Integer= [, base = 10])

`floor(x)` returns the nearest integral value of the same type as `x` that is less than or
equal to `x`.

`floor(T, x)` converts the result to type `T`, throwing an `InexactError` if the value is
not representable.

Keywords `digits`, `sigdigits` and `base` work as for [`round`](@ref).
"""
function floor end

"""
    ceil([T,] x)
    ceil(x; digits::Integer= [, base = 10])
    ceil(x; sigdigits::Integer= [, base = 10])

`ceil(x)` returns the nearest integral value of the same type as `x` that is greater than or
equal to `x`.

`ceil(T, x)` converts the result to type `T`, throwing an `InexactError` if the value is not
representable.

Keywords `digits`, `sigdigits` and `base` work as for [`round`](@ref).
"""
function ceil end

round(::Type{T}, x::Integer) where {T<:Integer} = convert(T, x)
trunc(::Type{T}, x::Integer) where {T<:Integer} = convert(T, x)
floor(::Type{T}, x::Integer) where {T<:Integer} = convert(T, x)
 ceil(::Type{T}, x::Integer) where {T<:Integer} = convert(T, x)

## integer construction ##

"""
    @int128_str str

Parse `str` as an [`Int128`](@ref).
Throw an `ArgumentError` if the string is not a valid integer.

# Examples
```jldoctest
julia> int128"123456789123"
123456789123

julia> int128"123456789123.4"
ERROR: LoadError: ArgumentError: invalid base 10 digit '.' in "123456789123.4"
[...]
```
"""
macro int128_str(s)
    return parse(Int128, s)
end

"""
    @uint128_str str

Parse `str` as an [`UInt128`](@ref).
Throw an `ArgumentError` if the string is not a valid integer.

# Examples
```
julia> uint128"123456789123"
0x00000000000000000000001cbe991a83

julia> uint128"-123456789123"
ERROR: LoadError: ArgumentError: invalid base 10 digit '-' in "-123456789123"
[...]
```
"""
macro uint128_str(s)
    return parse(UInt128, s)
end

"""
    @big_str str

Parse a string into a [`BigInt`](@ref) or [`BigFloat`](@ref),
and throw an `ArgumentError` if the string is not a valid number.
For integers `_` is allowed in the string as a separator.

# Examples
```jldoctest
julia> big"123_456"
123456

julia> big"7891.5"
7891.5

julia> big"_"
ERROR: ArgumentError: invalid number format _ for BigInt or BigFloat
[...]
```
"""
macro big_str(s)
    message = "invalid number format $s for BigInt or BigFloat"
    throw_error =  :(throw(ArgumentError($message)))
    if '_' in s
        # remove _ in s[2:end-1]
        bf = IOBuffer(maxsize=lastindex(s))
        c = s[1]
        print(bf, c)
        is_prev_underscore = (c == '_')
        is_prev_dot = (c == '.')
        for c in SubString(s, 2, lastindex(s)-1)
            c != '_' && print(bf, c)
            c == '_' && is_prev_dot && return throw_error
            c == '.' && is_prev_underscore && return throw_error
            is_prev_underscore = (c == '_')
            is_prev_dot = (c == '.')
        end
        print(bf, s[end])
        s = String(take!(bf))
    end
    n = tryparse(BigInt, s)
    n === nothing || return n
    n = tryparse(BigFloat, s)
    n === nothing || return n
    return throw_error
end

## integer promotions ##

# with different sizes, promote to larger type
promote_rule(::Type{Int16}, ::Union{Type{Int8}, Type{UInt8}}) = Int16
promote_rule(::Type{Int32}, ::Union{Type{Int16}, Type{Int8}, Type{UInt16}, Type{UInt8}}) = Int32
promote_rule(::Type{Int64}, ::Union{Type{Int16}, Type{Int32}, Type{Int8}, Type{UInt16}, Type{UInt32}, Type{UInt8}}) = Int64
promote_rule(::Type{Int128}, ::Union{Type{Int16}, Type{Int32}, Type{Int64}, Type{Int8}, Type{UInt16}, Type{UInt32}, Type{UInt64}, Type{UInt8}}) = Int128
promote_rule(::Type{UInt16}, ::Union{Type{Int8}, Type{UInt8}}) = UInt16
promote_rule(::Type{UInt32}, ::Union{Type{Int16}, Type{Int8}, Type{UInt16}, Type{UInt8}}) = UInt32
promote_rule(::Type{UInt64}, ::Union{Type{Int16}, Type{Int32}, Type{Int8}, Type{UInt16}, Type{UInt32}, Type{UInt8}}) = UInt64
promote_rule(::Type{UInt128}, ::Union{Type{Int16}, Type{Int32}, Type{Int64}, Type{Int8}, Type{UInt16}, Type{UInt32}, Type{UInt64}, Type{UInt8}}) = UInt128
# with mixed signedness and same size, Unsigned wins
promote_rule(::Type{UInt8},   ::Type{Int8}  ) = UInt8
promote_rule(::Type{UInt16},  ::Type{Int16} ) = UInt16
promote_rule(::Type{UInt32},  ::Type{Int32} ) = UInt32
promote_rule(::Type{UInt64},  ::Type{Int64} ) = UInt64
promote_rule(::Type{UInt128}, ::Type{Int128}) = UInt128

## traits ##

"""
    typemin(T)

The lowest value representable by the given (real) numeric DataType `T`.

See also: [`floatmin`](@ref), [`typemax`](@ref), [`eps`](@ref).

# Examples
```jldoctest
julia> typemin(Int8)
-128

julia> typemin(UInt32)
0x00000000

julia> typemin(Float16)
-Inf16

julia> typemin(Float32)
-Inf32

julia> nextfloat(-Inf32)  # smallest finite Float32 floating point number
-3.4028235f38
```
"""
function typemin end

"""
    typemax(T)

The highest value representable by the given (real) numeric `DataType`.

See also: [`floatmax`](@ref), [`typemin`](@ref), [`eps`](@ref).

# Examples
```jldoctest
julia> typemax(Int8)
127

julia> typemax(UInt32)
0xffffffff

julia> typemax(Float64)
Inf

julia> typemax(Float32)
Inf32

julia> floatmax(Float32)  # largest finite Float32 floating point number
3.4028235f38
```
"""
function typemax end

typemin(::Type{Int8  }) = Int8(-128)
typemax(::Type{Int8  }) = Int8(127)
typemin(::Type{UInt8 }) = UInt8(0)
typemax(::Type{UInt8 }) = UInt8(255)
typemin(::Type{Int16 }) = Int16(-32768)
typemax(::Type{Int16 }) = Int16(32767)
typemin(::Type{UInt16}) = UInt16(0)
typemax(::Type{UInt16}) = UInt16(65535)
typemin(::Type{Int32 }) = Int32(-2147483648)
typemax(::Type{Int32 }) = Int32(2147483647)
typemin(::Type{UInt32}) = UInt32(0)
typemax(::Type{UInt32}) = UInt32(4294967295)
typemin(::Type{Int64 }) = -9223372036854775808
typemax(::Type{Int64 }) = 9223372036854775807
typemin(::Type{UInt64}) = UInt64(0)
typemax(::Type{UInt64}) = 0xffffffffffffffff
@eval typemin(::Type{UInt128}) = $(convert(UInt128, 0))
@eval typemax(::Type{UInt128}) = $(bitcast(UInt128, convert(Int128, -1)))
@eval typemin(::Type{Int128} ) = $(convert(Int128, 1) << 127)
@eval typemax(::Type{Int128} ) = $(bitcast(Int128, typemax(UInt128) >> 1))


widen(::Type{Int8}) = Int16
widen(::Type{Int16}) = Int32
widen(::Type{Int32}) = Int64
widen(::Type{Int64}) = Int128
widen(::Type{UInt8}) = UInt16
widen(::Type{UInt16}) = UInt32
widen(::Type{UInt32}) = UInt64
widen(::Type{UInt64}) = UInt128

# a few special cases,
# Int64*UInt64 => Int128
# |x|<=2^(k-1), |y|<=2^k-1   =>   |x*y|<=2^(2k-1)-1
widemul(x::Signed,y::Unsigned) = widen(x) * signed(widen(y))
widemul(x::Unsigned,y::Signed) = signed(widen(x)) * widen(y)
# multplication by Bool doesn't require widening
widemul(x::Bool,y::Bool) = x * y
widemul(x::Bool,y::Number) = x * y
widemul(x::Number,y::Bool) = x * y


## wide multiplication, Int128 multiply and divide ##

if Core.sizeof(Int) == 4
    function widemul(u::Int64, v::Int64)
        local u0::UInt64, v0::UInt64, w0::UInt64
        local u1::Int64, v1::Int64, w1::UInt64, w2::Int64, t::UInt64

        u0 = u & 0xffffffff; u1 = u >> 32
        v0 = v & 0xffffffff; v1 = v >> 32
        w0 = u0 * v0
        t = reinterpret(UInt64, u1) * v0 + (w0 >>> 32)
        w2 = reinterpret(Int64, t) >> 32
        w1 = u0 * reinterpret(UInt64, v1) + (t & 0xffffffff)
        hi = u1 * v1 + w2 + (reinterpret(Int64, w1) >> 32)
        lo = w0 & 0xffffffff + (w1 << 32)
        return Int128(hi) << 64 + Int128(lo)
    end

    function widemul(u::UInt64, v::UInt64)
        local u0::UInt64, v0::UInt64, w0::UInt64
        local u1::UInt64, v1::UInt64, w1::UInt64, w2::UInt64, t::UInt64

        u0 = u & 0xffffffff; u1 = u >>> 32
        v0 = v & 0xffffffff; v1 = v >>> 32
        w0 = u0 * v0
        t = u1 * v0 + (w0 >>> 32)
        w2 = t >>> 32
        w1 = u0 * v1 + (t & 0xffffffff)
        hi = u1 * v1 + w2 + (w1 >>> 32)
        lo = w0 & 0xffffffff + (w1 << 32)
        return UInt128(hi) << 64 + UInt128(lo)
    end

    function *(u::Int128, v::Int128)
        u0 = u % UInt64; u1 = Int64(u >> 64)
        v0 = v % UInt64; v1 = Int64(v >> 64)
        lolo = widemul(u0, v0)
        lohi = widemul(reinterpret(Int64, u0), v1)
        hilo = widemul(u1, reinterpret(Int64, v0))
        t = reinterpret(UInt128, hilo) + (lolo >>> 64)
        w1 = reinterpret(UInt128, lohi) + (t & 0xffffffffffffffff)
        return Int128(lolo & 0xffffffffffffffff) + reinterpret(Int128, w1) << 64
    end

    function *(u::UInt128, v::UInt128)
        u0 = u % UInt64; u1 = UInt64(u>>>64)
        v0 = v % UInt64; v1 = UInt64(v>>>64)
        lolo = widemul(u0, v0)
        lohi = widemul(u0, v1)
        hilo = widemul(u1, v0)
        t = hilo + (lolo >>> 64)
        w1 = lohi + (t & 0xffffffffffffffff)
        return (lolo & 0xffffffffffffffff) + UInt128(w1) << 64
    end

    function _setbit(x::UInt128, i)
        # faster version of `return x | (UInt128(1) << i)`
        j = i >> 5
        y = UInt128(one(UInt32) << (i & 0x1f))
        if j == 0
            return x | y
        elseif j == 1
            return x | (y << 32)
        elseif j == 2
            return x | (y << 64)
        elseif j == 3
            return x | (y << 96)
        end
        return x
    end

    function divrem(x::UInt128, y::UInt128)
        iszero(y) && throw(DivideError())
        if (x >> 64) % UInt64 == 0
            if (y >> 64) % UInt64 == 0
                # fast path: upper 64 bits are zero, so we can fallback to UInt64 division
                q64, x64 = divrem(x % UInt64, y % UInt64)
                return UInt128(q64), UInt128(x64)
            else
                # this implies y>x, so
                return zero(UInt128), x
            end
        end
        n = leading_zeros(y) - leading_zeros(x)
        q = zero(UInt128)
        ys = y << n
        while n >= 0
            # ys == y * 2^n
            if ys <= x
                x -= ys
                q = _setbit(q, n)
                if (x >> 64) % UInt64 == 0
                    # exit early, similar to above fast path
                    if (y >> 64) % UInt64 == 0
                        q64, x64 = divrem(x % UInt64, y % UInt64)
                        q |= q64
                        x = UInt128(x64)
                    end
                    return q, x
                end
            end
            ys >>>= 1
            n -= 1
        end
        return q, x
    end

    function div(x::Int128, y::Int128)
        (x == typemin(Int128)) & (y == -1) && throw(DivideError())
        return Int128(div(BigInt(x), BigInt(y)))::Int128
    end
    div(x::UInt128, y::UInt128) = divrem(x, y)[1]

    function rem(x::Int128, y::Int128)
        return Int128(rem(BigInt(x), BigInt(y)))::Int128
    end

    function rem(x::UInt128, y::UInt128)
        iszero(y) && throw(DivideError())
        if (x >> 64) % UInt64 == 0
            if (y >> 64) % UInt64 == 0
                # fast path: upper 64 bits are zero, so we can fallback to UInt64 division
                return UInt128(rem(x % UInt64, y % UInt64))
            else
                # this implies y>x, so
                return x
            end
        end
        n = leading_zeros(y) - leading_zeros(x)
        ys = y << n
        while n >= 0
            # ys == y * 2^n
            if ys <= x
                x -= ys
                if (x >> 64) % UInt64 == 0
                    # exit early, similar to above fast path
                    if (y >> 64) % UInt64 == 0
                        x = UInt128(rem(x % UInt64, y % UInt64))
                    end
                    return x
                end
            end
            ys >>>= 1
            n -= 1
        end
        return x
    end

    function mod(x::Int128, y::Int128)
        return Int128(mod(BigInt(x), BigInt(y)))::Int128
    end
else
    *(x::T, y::T) where {T<:Union{Int128,UInt128}}  = mul_int(x, y)

    div(x::Int128,  y::Int128)  = checked_sdiv_int(x, y)
    div(x::UInt128, y::UInt128) = checked_udiv_int(x, y)

    rem(x::Int128,  y::Int128)  = checked_srem_int(x, y)
    rem(x::UInt128, y::UInt128) = checked_urem_int(x, y)
end

# issue #15489: since integer ops are unchecked, they shouldn't check promotion
for op in (:+, :-, :*, :&, :|, :xor)
    @eval function $op(a::Integer, b::Integer)
        T = promote_typeof(a, b)
        aT, bT = a % T, b % T
        not_sametype((a, b), (aT, bT))
        return $op(aT, bT)
    end
end

const _mask1_uint128 = (UInt128(0x5555555555555555) << 64) | UInt128(0x5555555555555555)
const _mask2_uint128 = (UInt128(0x3333333333333333) << 64) | UInt128(0x3333333333333333)
const _mask4_uint128 = (UInt128(0x0f0f0f0f0f0f0f0f) << 64) | UInt128(0x0f0f0f0f0f0f0f0f)

"""
    bitreverse(x)

Reverse the order of bits in integer `x`. `x` must have a fixed bit width,
e.g. be an `Int16` or `Int32`.

!!! compat "Julia 1.5"
    This function requires Julia 1.5 or later.

# Examples
```jldoctest
julia> bitreverse(0x8080808080808080)
0x0101010101010101

julia> reverse(bitstring(0xa06e)) == bitstring(bitreverse(0xa06e))
true
```
"""
function bitreverse(x::BitInteger)
    # TODO: consider using llvm.bitreverse intrinsic
    z = unsigned(x)
    mask1 = _mask1_uint128 % typeof(z)
    mask2 = _mask2_uint128 % typeof(z)
    mask4 = _mask4_uint128 % typeof(z)
    z = ((z & mask1) << 1) | ((z >> 1) & mask1)
    z = ((z & mask2) << 2) | ((z >> 2) & mask2)
    z = ((z & mask4) << 4) | ((z >> 4) & mask4)
    return bswap(z) % typeof(x)
end
P   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/operators.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

## types ##

"""
    <:(T1, T2)

Subtype operator: returns `true` if and only if all values of type `T1` are
also of type `T2`.

# Examples
```jldoctest
julia> Float64 <: AbstractFloat
true

julia> Vector{Int} <: AbstractArray
true

julia> Matrix{Float64} <: Matrix{AbstractFloat}
false
```
"""
(<:)

"""
    >:(T1, T2)

Supertype operator, equivalent to `T2 <: T1`.
"""
(>:)(@nospecialize(a), @nospecialize(b)) = (b <: a)

"""
    supertype(T::DataType)

Return the supertype of DataType `T`.

# Examples
```jldoctest
julia> supertype(Int32)
Signed
```
"""
supertype(T::DataType) = (@_total_meta; T.super)
supertype(T::UnionAll) = (@_total_meta; UnionAll(T.var, supertype(T.body)))

## generic comparison ##

"""
    ==(x, y)

Generic equality operator. Falls back to [`===`](@ref).
Should be implemented for all types with a notion of equality, based on the abstract value
that an instance represents. For example, all numeric types are compared by numeric value,
ignoring type. Strings are compared as sequences of characters, ignoring encoding.
For collections, `==` is generally called recursively on all contents,
though other properties (like the shape for arrays) may also be taken into account.

This operator follows IEEE semantics for floating-point numbers: `0.0 == -0.0` and
`NaN != NaN`.

The result is of type `Bool`, except when one of the operands is [`missing`](@ref),
in which case `missing` is returned
([three-valued logic](https://en.wikipedia.org/wiki/Three-valued_logic)).
For collections, `missing` is returned if at least one of the operands contains
a `missing` value and all non-missing values are equal.
Use [`isequal`](@ref) or [`===`](@ref) to always get a `Bool` result.

# Implementation
New numeric types should implement this function for two arguments of the new type, and
handle comparison to other types via promotion rules where possible.

[`isequal`](@ref) falls back to `==`, so new methods of `==` will be used by the
[`Dict`](@ref) type to compare keys. If your type will be used as a dictionary key, it
should therefore also implement [`hash`](@ref).

If some type defines `==`, [`isequal`](@ref), and [`isless`](@ref) then it should
also implement [`<`](@ref) to ensure consistency of comparisons.
"""
==

"""
    isequal(x, y) -> Bool

Similar to [`==`](@ref), except for the treatment of floating point numbers
and of missing values. `isequal` treats all floating-point `NaN` values as equal
to each other, treats `-0.0` as unequal to `0.0`, and [`missing`](@ref) as equal
to `missing`. Always returns a `Bool` value.

`isequal` is an equivalence relation - it is reflexive (`===` implies `isequal`), symmetric
(`isequal(a, b)` implies `isequal(b, a)`) and transitive (`isequal(a, b)` and
`isequal(b, c)` implies `isequal(a, c)`).

# Implementation
The default implementation of `isequal` calls `==`, so a type that does not involve
floating-point values generally only needs to define `==`.

`isequal` is the comparison function used by hash tables (`Dict`). `isequal(x,y)` must imply
that `hash(x) == hash(y)`.

This typically means that types for which a custom `==` or `isequal` method exists must
implement a corresponding [`hash`](@ref) method (and vice versa). Collections typically
implement `isequal` by calling `isequal` recursively on all contents.

Furthermore, `isequal` is linked with [`isless`](@ref), and they work together to
define a fixed total ordering, where exactly one of `isequal(x, y)`, `isless(x, y)`, or
`isless(y, x)` must be `true` (and the other two `false`).

Scalar types generally do not need to implement `isequal` separate from `==`, unless they
represent floating-point numbers amenable to a more efficient implementation than that
provided as a generic fallback (based on `isnan`, `signbit`, and `==`).

# Examples
```jldoctest
julia> isequal([1., NaN], [1., NaN])
true

julia> [1., NaN] == [1., NaN]
false

julia> 0.0 == -0.0
true

julia> isequal(0.0, -0.0)
false

julia> missing == missing
missing

julia> isequal(missing, missing)
true
```
"""
isequal(x, y) = (x == y)::Bool # all `missing` cases are handled in missing.jl

signequal(x, y) = signbit(x)::Bool == signbit(y)::Bool
signless(x, y) = signbit(x)::Bool & !signbit(y)::Bool

isequal(x::AbstractFloat, y::AbstractFloat) = (isnan(x) & isnan(y)) | signequal(x, y) & (x == y)::Bool
isequal(x::Real,          y::AbstractFloat) = (isnan(x) & isnan(y)) | signequal(x, y) & (x == y)::Bool
isequal(x::AbstractFloat, y::Real         ) = (isnan(x) & isnan(y)) | signequal(x, y) & (x == y)::Bool

"""
    isless(x, y)

Test whether `x` is less than `y`, according to a fixed total order (defined together with
[`isequal`](@ref)). `isless` is not defined for pairs `(x, y)` of all types. However, if it
is defined, it is expected to satisfy the following:
- If `isless(x, y)` is defined, then so is `isless(y, x)` and `isequal(x, y)`,
  and exactly one of those three yields `true`.
- The relation defined by `isless` is transitive, i.e.,
  `isless(x, y) && isless(y, z)` implies `isless(x, z)`.

Values that are normally unordered, such as `NaN`,
are ordered after regular values.
[`missing`](@ref) values are ordered last.

This is the default comparison used by [`sort!`](@ref).

# Implementation
Non-numeric types with a total order should implement this function.
Numeric types only need to implement it if they have special values such as `NaN`.
Types with a partial order should implement [`<`](@ref).
See the documentation on [Alternate Orderings](@ref) for how to define alternate
ordering methods that can be used in sorting and related functions.

# Examples
```jldoctest
julia> isless(1, 3)
true

julia> isless("Red", "Blue")
false
```
"""
function isless end

isless(x::AbstractFloat, y::AbstractFloat) = (!isnan(x) & (isnan(y) | signless(x, y))) | (x < y)
isless(x::Real,          y::AbstractFloat) = (!isnan(x) & (isnan(y) | signless(x, y))) | (x < y)
isless(x::AbstractFloat, y::Real         ) = (!isnan(x) & (isnan(y) | signless(x, y))) | (x < y)

# Performance optimization to reduce branching
# This is useful for sorting tuples of integers
# TODO: remove this when the compiler can optimize the generic version better
# See #48724 and #48753
isless(a::Tuple{BitInteger, BitInteger}, b::Tuple{BitInteger, BitInteger}) =
    isless(a[1], b[1]) | (isequal(a[1], b[1]) & isless(a[2], b[2]))

"""
    isgreater(x, y)

Not the inverse of `isless`! Test whether `x` is greater than `y`, according to
a fixed total order compatible with `min`.

Defined with `isless`, this function is usually `isless(y, x)`, but `NaN` and
[`missing`](@ref) are ordered as smaller than any regular value with `missing`
smaller than `NaN`.

So `isless` defines an ascending total order with `NaN` and `missing` as the
largest values and `isgreater` defines a descending total order with `NaN` and
`missing` as the smallest values.

!!! note

    Like `min`, `isgreater` orders containers (tuples, vectors, etc)
    lexicographically with `isless(y, x)` rather than recursively with itself:

    ```jldoctest
    julia> Base.isgreater(1, NaN) # 1 is greater than NaN
    true

    julia> Base.isgreater((1,), (NaN,)) # But (1,) is not greater than (NaN,)
    false

    julia> sort([1, 2, 3, NaN]; lt=Base.isgreater)
    4-element Vector{Float64}:
       3.0
       2.0
       1.0
     NaN

    julia> sort(tuple.([1, 2, 3, NaN]); lt=Base.isgreater)
    4-element Vector{Tuple{Float64}}:
     (NaN,)
     (3.0,)
     (2.0,)
     (1.0,)
    ```

# Implementation
This is unexported. Types should not usually implement this function. Instead, implement `isless`.
"""
isgreater(x, y) = isunordered(x) || isunordered(y) ? isless(x, y) : isless(y, x)

"""
    isunordered(x)

Return `true` if `x` is a value that is not orderable according to [`<`](@ref), such as `NaN`
or `missing`.

The values that evaluate to `true` with this predicate may be orderable with respect to other
orderings such as [`isless`](@ref).

!!! compat "Julia 1.7"
    This function requires Julia 1.7 or later.
"""
isunordered(x) = false
isunordered(x::AbstractFloat) = isnan(x)
isunordered(x::Missing) = true

==(T::Type, S::Type) = (@_total_meta; ccall(:jl_types_equal, Cint, (Any, Any), T, S) != 0)
!=(T::Type, S::Type) = (@_total_meta; !(T == S))
==(T::TypeVar, S::Type) = false
==(T::Type, S::TypeVar) = false

## comparison fallbacks ##

"""
    !=(x, y)
    ≠(x,y)

Not-equals comparison operator. Always gives the opposite answer as [`==`](@ref).

# Implementation
New types should generally not implement this, and rely on the fallback definition
`!=(x,y) = !(x==y)` instead.

# Examples
```jldoctest
julia> 3 != 2
true

julia> "foo" ≠ "foo"
false
```
"""
!=(x, y) = !(x == y)
const ≠ = !=

"""
    ===(x,y) -> Bool
    ≡(x,y) -> Bool

Determine whether `x` and `y` are identical, in the sense that no program could distinguish
them. First the types of `x` and `y` are compared. If those are identical, mutable objects
are compared by address in memory and immutable objects (such as numbers) are compared by
contents at the bit level. This function is sometimes called "egal".
It always returns a `Bool` value.

# Examples
```jldoctest
julia> a = [1, 2]; b = [1, 2];

julia> a == b
true

julia> a === b
false

julia> a === a
true
```
"""
===
const ≡ = ===

"""
    !==(x, y)
    ≢(x,y)

Always gives the opposite answer as [`===`](@ref).

# Examples
```jldoctest
julia> a = [1, 2]; b = [1, 2];

julia> a ≢ b
true

julia> a ≢ a
false
```
"""
!==(@nospecialize(x), @nospecialize(y)) = !(x === y)
const ≢ = !==

"""
    <(x, y)

Less-than comparison operator. Falls back to [`isless`](@ref).
Because of the behavior of floating-point NaN values, this operator implements
a partial order.

# Implementation
New types with a canonical partial order should implement this function for
two arguments of the new type.
Types with a canonical total order should implement [`isless`](@ref) instead.

See also [`isunordered`](@ref).

# Examples
```jldoctest
julia> 'a' < 'b'
true

julia> "abc" < "abd"
true

julia> 5 < 3
false
```
"""
<(x, y) = isless(x, y)

"""
    >(x, y)

Greater-than comparison operator. Falls back to `y < x`.

# Implementation
Generally, new types should implement [`<`](@ref) instead of this function,
and rely on the fallback definition `>(x, y) = y < x`.

# Examples
```jldoctest
julia> 'a' > 'b'
false

julia> 7 > 3 > 1
true

julia> "abc" > "abd"
false

julia> 5 > 3
true
```
"""
>(x, y) = y < x

"""
    <=(x, y)
    ≤(x,y)

Less-than-or-equals comparison operator. Falls back to `(x < y) | (x == y)`.

# Examples
```jldoctest
julia> 'a' <= 'b'
true

julia> 7 ≤ 7 ≤ 9
true

julia> "abc" ≤ "abc"
true

julia> 5 <= 3
false
```
"""
<=(x, y) = (x < y) | (x == y)
const ≤ = <=

"""
    >=(x, y)
    ≥(x,y)

Greater-than-or-equals comparison operator. Falls back to `y <= x`.

# Examples
```jldoctest
julia> 'a' >= 'b'
false

julia> 7 ≥ 7 ≥ 3
true

julia> "abc" ≥ "abc"
true

julia> 5 >= 3
true
```
"""
>=(x, y) = (y <= x)
const ≥ = >=

# this definition allows Number types to implement < instead of isless,
# which is more idiomatic:
isless(x::Real, y::Real) = x<y

"""
    cmp(x,y)

Return -1, 0, or 1 depending on whether `x` is less than, equal to, or greater than `y`,
respectively. Uses the total order implemented by `isless`.

# Examples
```jldoctest
julia> cmp(1, 2)
-1

julia> cmp(2, 1)
1

julia> cmp(2+im, 3-im)
ERROR: MethodError: no method matching isless(::Complex{Int64}, ::Complex{Int64})
[...]
```
"""
cmp(x, y) = isless(x, y) ? -1 : ifelse(isless(y, x), 1, 0)

"""
    cmp(<, x, y)

Return -1, 0, or 1 depending on whether `x` is less than, equal to, or greater than `y`,
respectively. The first argument specifies a less-than comparison function to use.
"""
cmp(<, x, y) = (x < y) ? -1 : ifelse(y < x, 1, 0)

# cmp returns -1, 0, +1 indicating ordering
cmp(x::Integer, y::Integer) = ifelse(isless(x, y), -1, ifelse(isless(y, x), 1, 0))

"""
    max(x, y, ...)

Return the maximum of the arguments (with respect to [`isless`](@ref)). See also the [`maximum`](@ref) function
to take the maximum element from a collection.

# Examples
```jldoctest
julia> max(2, 5, 1)
5
```
"""
max(x, y) = ifelse(isless(y, x), x, y)

"""
    min(x, y, ...)

Return the minimum of the arguments (with respect to [`isless`](@ref)). See also the [`minimum`](@ref) function
to take the minimum element from a collection.

# Examples
```jldoctest
julia> min(2, 5, 1)
1
```
"""
min(x,y) = ifelse(isless(y, x), y, x)

"""
    minmax(x, y)

Return `(min(x,y), max(x,y))`.

See also [`extrema`](@ref) that returns `(minimum(x), maximum(x))`.

# Examples
```jldoctest
julia> minmax('c','b')
('b', 'c')
```
"""
minmax(x,y) = isless(y, x) ? (y, x) : (x, y)

## definitions providing basic traits of arithmetic operators ##

"""
    identity(x)

The identity function. Returns its argument.

See also: [`one`](@ref), [`oneunit`](@ref), and [`LinearAlgebra`](@ref man-linalg)'s `I`.

# Examples
```jldoctest
julia> identity("Well, what did you expect?")
"Well, what did you expect?"
```
"""
identity(@nospecialize x) = x

+(x::Number) = x
*(x::Number) = x
(&)(x::Integer) = x
(|)(x::Integer) = x
xor(x::Integer) = x

const ⊻ = xor
const ⊼ = nand
const ⊽ = nor

# foldl for argument lists. expand fully up to a point, then
# switch to a loop. this allows small cases like `a+b+c+d` to be managed
# efficiently, without a major slowdown for `+(x...)` when `x` is big.
# n.b.: keep this method count small, so it can be inferred without hitting the
# method count limit in inference
afoldl(op, a) = a
function afoldl(op, a, bs...)
    l = length(bs)
    i =  0; y = a;            l == i && return y
    #@nexprs 31 i -> (y = op(y, bs[i]); l == i && return y)
    i =  1; y = op(y, bs[i]); l == i && return y
    i =  2; y = op(y, bs[i]); l == i && return y
    i =  3; y = op(y, bs[i]); l == i && return y
    i =  4; y = op(y, bs[i]); l == i && return y
    i =  5; y = op(y, bs[i]); l == i && return y
    i =  6; y = op(y, bs[i]); l == i && return y
    i =  7; y = op(y, bs[i]); l == i && return y
    i =  8; y = op(y, bs[i]); l == i && return y
    i =  9; y = op(y, bs[i]); l == i && return y
    i = 10; y = op(y, bs[i]); l == i && return y
    i = 11; y = op(y, bs[i]); l == i && return y
    i = 12; y = op(y, bs[i]); l == i && return y
    i = 13; y = op(y, bs[i]); l == i && return y
    i = 14; y = op(y, bs[i]); l == i && return y
    i = 15; y = op(y, bs[i]); l == i && return y
    i = 16; y = op(y, bs[i]); l == i && return y
    i = 17; y = op(y, bs[i]); l == i && return y
    i = 18; y = op(y, bs[i]); l == i && return y
    i = 19; y = op(y, bs[i]); l == i && return y
    i = 20; y = op(y, bs[i]); l == i && return y
    i = 21; y = op(y, bs[i]); l == i && return y
    i = 22; y = op(y, bs[i]); l == i && return y
    i = 23; y = op(y, bs[i]); l == i && return y
    i = 24; y = op(y, bs[i]); l == i && return y
    i = 25; y = op(y, bs[i]); l == i && return y
    i = 26; y = op(y, bs[i]); l == i && return y
    i = 27; y = op(y, bs[i]); l == i && return y
    i = 28; y = op(y, bs[i]); l == i && return y
    i = 29; y = op(y, bs[i]); l == i && return y
    i = 30; y = op(y, bs[i]); l == i && return y
    i = 31; y = op(y, bs[i]); l == i && return y
    for i in (i + 1):l
        y = op(y, bs[i])
    end
    return y
end
setfield!(typeof(afoldl).name.mt, :max_args, 34, :monotonic)

for op in (:+, :*, :&, :|, :xor, :min, :max, :kron)
    @eval begin
        # note: these definitions must not cause a dispatch loop when +(a,b) is
        # not defined, and must only try to call 2-argument definitions, so
        # that defining +(a,b) is sufficient for full functionality.
        ($op)(a, b, c, xs...) = (@inline; afoldl($op, ($op)(($op)(a,b),c), xs...))
        # a further concern is that it's easy for a type like (Int,Int...)
        # to match many definitions, so we need to keep the number of
        # definitions down to avoid losing type information.
    end
end

function kron! end

const var"'" = adjoint

"""
    \\(x, y)

Left division operator: multiplication of `y` by the inverse of `x` on the left. Gives
floating-point results for integer arguments.

# Examples
```jldoctest
julia> 3 \\ 6
2.0

julia> inv(3) * 6
2.0

julia> A = [4 3; 2 1]; x = [5, 6];

julia> A \\ x
2-element Vector{Float64}:
  6.5
 -7.0

julia> inv(A) * x
2-element Vector{Float64}:
  6.5
 -7.0
```
"""
\(x,y) = adjoint(adjoint(y)/adjoint(x))

# Core <<, >>, and >>> take either Int or UInt as second arg. Signed shift
# counts can shift in either direction, and are translated here to unsigned
# counts. Integer datatypes only need to implement the unsigned version.

"""
    <<(x, n)

Left bit shift operator, `x << n`. For `n >= 0`, the result is `x` shifted left
by `n` bits, filling with `0`s. This is equivalent to `x * 2^n`. For `n < 0`,
this is equivalent to `x >> -n`.

# Examples
```jldoctest
julia> Int8(3) << 2
12

julia> bitstring(Int8(3))
"00000011"

julia> bitstring(Int8(12))
"00001100"
```
See also [`>>`](@ref), [`>>>`](@ref), [`exp2`](@ref), [`ldexp`](@ref).
"""
function <<(x::Integer, c::Integer)
    @inline
    typemin(Int) <= c <= typemax(Int) && return x << (c % Int)
    (x >= 0 || c >= 0) && return zero(x) << 0  # for type stability
    oftype(x, -1)
end
function <<(x::Integer, c::Unsigned)
    @inline
    if c isa UInt
        throw(MethodError(<<, (x, c)))
    end
    c <= typemax(UInt) ? x << (c % UInt) : zero(x) << UInt(0)
end
<<(x::Integer, c::Int) = c >= 0 ? x << unsigned(c) : x >> unsigned(-c)

"""
    >>(x, n)

Right bit shift operator, `x >> n`. For `n >= 0`, the result is `x` shifted
right by `n` bits, filling with `0`s if `x >= 0`, `1`s if `x < 0`, preserving
the sign of `x`. This is equivalent to `fld(x, 2^n)`. For `n < 0`, this is
equivalent to `x << -n`.

# Examples
```jldoctest
julia> Int8(13) >> 2
3

julia> bitstring(Int8(13))
"00001101"

julia> bitstring(Int8(3))
"00000011"

julia> Int8(-14) >> 2
-4

julia> bitstring(Int8(-14))
"11110010"

julia> bitstring(Int8(-4))
"11111100"
```
See also [`>>>`](@ref), [`<<`](@ref).
"""
function >>(x::Integer, c::Integer)
    @inline
    if c isa UInt
        throw(MethodError(>>, (x, c)))
    end
    typemin(Int) <= c <= typemax(Int) && return x >> (c % Int)
    (x >= 0 || c < 0) && return zero(x) >> 0
    oftype(x, -1)
end
>>(x::Integer, c::Int) = c >= 0 ? x >> unsigned(c) : x << unsigned(-c)

"""
    >>>(x, n)

Unsigned right bit shift operator, `x >>> n`. For `n >= 0`, the result is `x`
shifted right by `n` bits, filling with `0`s. For `n < 0`, this is equivalent
to `x << -n`.

For [`Unsigned`](@ref) integer types, this is equivalent to [`>>`](@ref). For
[`Signed`](@ref) integer types, this is equivalent to `signed(unsigned(x) >> n)`.

# Examples
```jldoctest
julia> Int8(-14) >>> 2
60

julia> bitstring(Int8(-14))
"11110010"

julia> bitstring(Int8(60))
"00111100"
```

[`BigInt`](@ref)s are treated as if having infinite size, so no filling is required and this
is equivalent to [`>>`](@ref).

See also [`>>`](@ref), [`<<`](@ref).
"""
function >>>(x::Integer, c::Integer)
    @inline
    typemin(Int) <= c <= typemax(Int) ? x >>> (c % Int) : zero(x) >>> 0
end
function >>>(x::Integer, c::Unsigned)
    @inline
    if c isa UInt
        throw(MethodError(>>>, (x, c)))
    end
    c <= typemax(UInt) ? x >>> (c % UInt) : zero(x) >>> 0
end
>>>(x::Integer, c::Int) = c >= 0 ? x >>> unsigned(c) : x << unsigned(-c)

# operator alias

"""
    rem(x, y)
    %(x, y)

Remainder from Euclidean division, returning a value of the same sign as `x`, and smaller in
magnitude than `y`. This value is always exact.

See also: [`div`](@ref), [`mod`](@ref), [`mod1`](@ref), [`divrem`](@ref).

# Examples
```jldoctest
julia> x = 15; y = 4;

julia> x % y
3

julia> x == div(x, y) * y + rem(x, y)
true

julia> rem.(-5:5, 3)'
1×11 adjoint(::Vector{Int64}) with eltype Int64:
 -2  -1  0  -2  -1  0  1  2  0  1  2
```
"""
rem
const % = rem

"""
    div(x, y)
    ÷(x, y)

The quotient from Euclidean (integer) division. Generally equivalent
to a mathematical operation x/y without a fractional part.

See also: [`cld`](@ref), [`fld`](@ref), [`rem`](@ref), [`divrem`](@ref).

# Examples
```jldoctest
julia> 9 ÷ 4
2

julia> -5 ÷ 3
-1

julia> 5.0 ÷ 2
2.0

julia> div.(-5:5, 3)'
1×11 adjoint(::Vector{Int64}) with eltype Int64:
 -1  -1  -1  0  0  0  0  0  1  1  1
```
"""
div
const ÷ = div

"""
    mod1(x, y)

Modulus after flooring division, returning a value `r` such that `mod(r, y) == mod(x, y)`
in the range ``(0, y]`` for positive `y` and in the range ``[y,0)`` for negative `y`.

With integer arguments and positive `y`, this is equal to `mod(x, 1:y)`, and hence natural
for 1-based indexing. By comparison, `mod(x, y) == mod(x, 0:y-1)` is natural for computations with
offsets or strides.

See also [`mod`](@ref), [`fld1`](@ref), [`fldmod1`](@ref).

# Examples
```jldoctest
julia> mod1(4, 2)
2

julia> mod1.(-5:5, 3)'
1×11 adjoint(::Vector{Int64}) with eltype Int64:
 1  2  3  1  2  3  1  2  3  1  2

julia> mod1.([-0.1, 0, 0.1, 1, 2, 2.9, 3, 3.1]', 3)
1×8 Matrix{Float64}:
 2.9  3.0  0.1  1.0  2.0  2.9  3.0  0.1
```
"""
mod1(x::T, y::T) where {T<:Real} = (m = mod(x, y); ifelse(m == 0, y, m))


"""
    fld1(x, y)

Flooring division, returning a value consistent with `mod1(x,y)`

See also [`mod1`](@ref), [`fldmod1`](@ref).

# Examples
```jldoctest
julia> x = 15; y = 4;

julia> fld1(x, y)
4

julia> x == fld(x, y) * y + mod(x, y)
true

julia> x == (fld1(x, y) - 1) * y + mod1(x, y)
true
```
"""
fld1(x::T, y::T) where {T<:Real} = (m = mod1(x, y); fld((x - m) + y, y))
function fld1(x::T, y::T) where T<:Integer
    d = div(x, y)
    return d + (!signbit(x ⊻ y) & (d * y != x))
end

"""
    fldmod1(x, y)

Return `(fld1(x,y), mod1(x,y))`.

See also [`fld1`](@ref), [`mod1`](@ref).
"""
fldmod1(x, y) = (fld1(x, y), mod1(x, y))


"""
    widen(x)

If `x` is a type, return a "larger" type, defined so that arithmetic operations
`+` and `-` are guaranteed not to overflow nor lose precision for any combination
of values that type `x` can hold.

For fixed-size integer types less than 128 bits, `widen` will return a type with
twice the number of bits.

If `x` is a value, it is converted to `widen(typeof(x))`.

# Examples
```jldoctest
julia> widen(Int32)
Int64

julia> widen(1.5f0)
1.5
```
"""
widen(x::T) where {T} = convert(widen(T), x)
widen(x::Type{T}) where {T} = throw(MethodError(widen, (T,)))
widen(x::Type{Union{}}, slurp...) = throw(MethodError(widen, (Union{},)))

# function pipelining

"""
    |>(x, f)

Infix operator which applies function `f` to the argument `x`.
This allows `f(g(x))` to be written `x |> g |> f`.
When used with anonymous functions, parentheses are typically required around
the definition to get the intended chain.

# Examples
```jldoctest
julia> 4 |> inv
0.25

julia> [2, 3, 5] |> sum |> inv
0.1

julia> [0 1; 2 3] .|> (x -> x^2) |> sum
14
```
"""
|>(x, f) = f(x)

_stable_typeof(x) = typeof(x)
_stable_typeof(::Type{T}) where {T} = @isdefined(T) ? Type{T} : DataType

"""
    f = Returns(value)

Create a callable `f` such that `f(args...; kw...) === value` holds.

# Examples

```jldoctest
julia> f = Returns(42);

julia> f(1)
42

julia> f("hello", x=32)
42

julia> f.value
42
```

!!! compat "Julia 1.7"
    `Returns` requires at least Julia 1.7.
"""
struct Returns{V} <: Function
    value::V
    Returns{V}(value) where {V} = new{V}(value)
    Returns(value) = new{_stable_typeof(value)}(value)
end

(obj::Returns)(@nospecialize(args...); @nospecialize(kw...)) = obj.value

# function composition

"""
    f ∘ g

Compose functions: i.e. `(f ∘ g)(args...; kwargs...)` means `f(g(args...; kwargs...))`. The `∘` symbol can be
entered in the Julia REPL (and most editors, appropriately configured) by typing `\\circ<tab>`.

Function composition also works in prefix form: `∘(f, g)` is the same as `f ∘ g`.
The prefix form supports composition of multiple functions: `∘(f, g, h) = f ∘ g ∘ h`
and splatting `∘(fs...)` for composing an iterable collection of functions.
The last argument to `∘` execute first.

!!! compat "Julia 1.4"
    Multiple function composition requires at least Julia 1.4.

!!! compat "Julia 1.5"
    Composition of one function ∘(f) requires at least Julia 1.5.

!!! compat "Julia 1.7"
    Using keyword arguments requires at least Julia 1.7.

# Examples
```jldoctest
julia> map(uppercase∘first, ["apple", "banana", "carrot"])
3-element Vector{Char}:
 'A': ASCII/Unicode U+0041 (category Lu: Letter, uppercase)
 'B': ASCII/Unicode U+0042 (category Lu: Letter, uppercase)
 'C': ASCII/Unicode U+0043 (category Lu: Letter, uppercase)

julia> (==(6)∘length).(["apple", "banana", "carrot"])
3-element BitVector:
 0
 1
 1

julia> fs = [
           x -> 2x
           x -> x-1
           x -> x/2
           x -> x+1
       ];

julia> ∘(fs...)(3)
2.0
```
See also [`ComposedFunction`](@ref), [`!f::Function`](@ref).
"""
function ∘ end

"""
    ComposedFunction{Outer,Inner} <: Function

Represents the composition of two callable objects `outer::Outer` and `inner::Inner`. That is
```julia
ComposedFunction(outer, inner)(args...; kw...) === outer(inner(args...; kw...))
```
The preferred way to construct an instance of `ComposedFunction` is to use the composition operator [`∘`](@ref):
```jldoctest
julia> sin ∘ cos === ComposedFunction(sin, cos)
true

julia> typeof(sin∘cos)
ComposedFunction{typeof(sin), typeof(cos)}
```
The composed pieces are stored in the fields of `ComposedFunction` and can be retrieved as follows:
```jldoctest
julia> composition = sin ∘ cos
sin ∘ cos

julia> composition.outer === sin
true

julia> composition.inner === cos
true
```
!!! compat "Julia 1.6"
    ComposedFunction requires at least Julia 1.6. In earlier versions `∘` returns an anonymous function instead.

See also [`∘`](@ref).
"""
struct ComposedFunction{O,I} <: Function
    outer::O
    inner::I
    ComposedFunction{O, I}(outer, inner) where {O, I} = new{O, I}(outer, inner)
    ComposedFunction(outer, inner) = new{Core.Typeof(outer),Core.Typeof(inner)}(outer, inner)
end

(c::ComposedFunction)(x...; kw...) = call_composed(unwrap_composed(c), x, kw)
unwrap_composed(c::ComposedFunction) = (unwrap_composed(c.outer)..., unwrap_composed(c.inner)...)
unwrap_composed(c) = (maybeconstructor(c),)
call_composed(fs, x, kw) = (@inline; fs[1](call_composed(tail(fs), x, kw)))
call_composed(fs::Tuple{Any}, x, kw) = fs[1](x...; kw...)

struct Constructor{F} <: Function end
(::Constructor{F})(args...; kw...) where {F} = (@inline; F(args...; kw...))
maybeconstructor(::Type{F}) where {F} = Constructor{F}()
maybeconstructor(f) = f

∘(f) = f
∘(f, g) = ComposedFunction(f, g)
∘(f, g, h...) = ∘(f ∘ g, h...)

function show(io::IO, c::ComposedFunction)
    c.outer isa ComposedFunction ? show(io, c.outer) : _showcomposed(io, c.outer)
    print(io, " ∘ ")
    _showcomposed(io, c.inner)
end

#shows !f instead of (!) ∘ f when ! is the outermost function
function show(io::IO, c::ComposedFunction{typeof(!)})
    print(io, '!')
    _showcomposed(io, c.inner)
end

_showcomposed(io::IO, x) = show(io, x)
#display operators like + and - inside parens
_showcomposed(io::IO, f::Function) = isoperator(Symbol(f)) ? (print(io, '('); show(io, f); print(io, ')')) : show(io, f)
#nesting for chained composition
_showcomposed(io::IO, f::ComposedFunction) = (print(io, '('); show(io, f); print(io, ')'))
#no nesting when ! is the outer function in a composition chain
_showcomposed(io::IO, f::ComposedFunction{typeof(!)}) = show(io, f)

"""
    !f::Function

Predicate function negation: when the argument of `!` is a function, it returns a composed function which computes the boolean negation of `f`.

See also [`∘`](@ref).

# Examples
```jldoctest
julia> str = "∀ ε > 0, ∃ δ > 0: |x-y| < δ ⇒ |f(x)-f(y)| < ε"
"∀ ε > 0, ∃ δ > 0: |x-y| < δ ⇒ |f(x)-f(y)| < ε"

julia> filter(isletter, str)
"εδxyδfxfyε"

julia> filter(!isletter, str)
"∀  > 0, ∃  > 0: |-| <  ⇒ |()-()| < "
```

!!! compat "Julia 1.9"
    Starting with Julia 1.9, `!f` returns a [`ComposedFunction`](@ref) instead of an anonymous function.
"""
!(f::Function) = (!) ∘ f
!(f::ComposedFunction{typeof(!)}) = f.inner #allows !!f === f

"""
    Fix1(f, x)

A type representing a partially-applied version of the two-argument function
`f`, with the first argument fixed to the value "x". In other words,
`Fix1(f, x)` behaves similarly to `y->f(x, y)`.

See also [`Fix2`](@ref Base.Fix2).
"""
struct Fix1{F,T} <: Function
    f::F
    x::T

    Fix1(f::F, x) where {F} = new{F,_stable_typeof(x)}(f, x)
    Fix1(f::Type{F}, x) where {F} = new{Type{F},_stable_typeof(x)}(f, x)
end

(f::Fix1)(y) = f.f(f.x, y)

"""
    Fix2(f, x)

A type representing a partially-applied version of the two-argument function
`f`, with the second argument fixed to the value "x". In other words,
`Fix2(f, x)` behaves similarly to `y->f(y, x)`.
"""
struct Fix2{F,T} <: Function
    f::F
    x::T

    Fix2(f::F, x) where {F} = new{F,_stable_typeof(x)}(f, x)
    Fix2(f::Type{F}, x) where {F} = new{Type{F},_stable_typeof(x)}(f, x)
end

(f::Fix2)(y) = f.f(y, f.x)

"""
    isequal(x)

Create a function that compares its argument to `x` using [`isequal`](@ref), i.e.
a function equivalent to `y -> isequal(y, x)`.

The returned function is of type `Base.Fix2{typeof(isequal)}`, which can be
used to implement specialized methods.
"""
isequal(x) = Fix2(isequal, x)

"""
    ==(x)

Create a function that compares its argument to `x` using [`==`](@ref), i.e.
a function equivalent to `y -> y == x`.

The returned function is of type `Base.Fix2{typeof(==)}`, which can be
used to implement specialized methods.
"""
==(x) = Fix2(==, x)

"""
    !=(x)

Create a function that compares its argument to `x` using [`!=`](@ref), i.e.
a function equivalent to `y -> y != x`.
The returned function is of type `Base.Fix2{typeof(!=)}`, which can be
used to implement specialized methods.

!!! compat "Julia 1.2"
    This functionality requires at least Julia 1.2.
"""
!=(x) = Fix2(!=, x)

"""
    >=(x)

Create a function that compares its argument to `x` using [`>=`](@ref), i.e.
a function equivalent to `y -> y >= x`.
The returned function is of type `Base.Fix2{typeof(>=)}`, which can be
used to implement specialized methods.

!!! compat "Julia 1.2"
    This functionality requires at least Julia 1.2.
"""
>=(x) = Fix2(>=, x)

"""
    <=(x)

Create a function that compares its argument to `x` using [`<=`](@ref), i.e.
a function equivalent to `y -> y <= x`.
The returned function is of type `Base.Fix2{typeof(<=)}`, which can be
used to implement specialized methods.

!!! compat "Julia 1.2"
    This functionality requires at least Julia 1.2.
"""
<=(x) = Fix2(<=, x)

"""
    >(x)

Create a function that compares its argument to `x` using [`>`](@ref), i.e.
a function equivalent to `y -> y > x`.
The returned function is of type `Base.Fix2{typeof(>)}`, which can be
used to implement specialized methods.

!!! compat "Julia 1.2"
    This functionality requires at least Julia 1.2.
"""
>(x) = Fix2(>, x)

"""
    <(x)

Create a function that compares its argument to `x` using [`<`](@ref), i.e.
a function equivalent to `y -> y < x`.
The returned function is of type `Base.Fix2{typeof(<)}`, which can be
used to implement specialized methods.

!!! compat "Julia 1.2"
    This functionality requires at least Julia 1.2.
"""
<(x) = Fix2(<, x)

"""
    splat(f)

Equivalent to
```julia
    my_splat(f) = args->f(args...)
```
i.e. given a function returns a new function that takes one argument and splats
it into the original function. This is useful as an adaptor to pass a
multi-argument function in a context that expects a single argument, but passes
a tuple as that single argument.

# Example usage:
```jldoctest
julia> map(splat(+), zip(1:3,4:6))
3-element Vector{Int64}:
 5
 7
 9

julia> my_add = splat(+)
splat(+)

julia> my_add((1,2,3))
6
```
"""
splat(f) = Splat(f)

"""
    Base.Splat{F} <: Function

Represents a splatted function. That is
```julia
Base.Splat(f)(args) === f(args...)
```
The preferred way to construct an instance of `Base.Splat` is to use the [`splat`](@ref) function.

!!! compat "Julia 1.9"
    Splat requires at least Julia 1.9. In earlier versions `splat` returns an anonymous function instead.

See also [`splat`](@ref).
"""
struct Splat{F} <: Function
    f::F
    Splat(f) = new{Core.Typeof(f)}(f)
end
(s::Splat)(args) = s.f(args...)
print(io::IO, s::Splat) = print(io, "splat(", s.f, ')')
show(io::IO, s::Splat) = print(io, s)

## in and related operators

"""
    in(collection)
    ∈(collection)

Create a function that checks whether its argument is [`in`](@ref) `collection`, i.e.
a function equivalent to `y -> y in collection`. See also [`insorted`](@ref) for use
with sorted collections.

The returned function is of type `Base.Fix2{typeof(in)}`, which can be
used to implement specialized methods.
"""
in(x) = Fix2(in, x)

function in(x, itr)
    anymissing = false
    for y in itr
        v = (y == x)
        if ismissing(v)
            anymissing = true
        elseif v
            return true
        end
    end
    return anymissing ? missing : false
end

const ∈ = in
∉(x, itr) = !∈(x, itr)
∉(itr) = Fix2(∉, itr)

"""
    ∋(collection, item) -> Bool

Like [`in`](@ref), but with arguments in reverse order.
Avoid adding methods to this function; define `in` instead.
"""
∋(itr, x) = in(x, itr)

"""
    ∋(item)

Create a function that checks whether its argument contains the given `item`, i.e.
a function equivalent to `y -> item in y`.

!!! compat "Julia 1.6"
    This method requires Julia 1.6 or later.
"""
∋(x) = Fix2(∋, x)

∌(itr, x) = !∋(itr, x)
∌(x) = Fix2(∌, x)

"""
    in(item, collection) -> Bool
    ∈(item, collection) -> Bool

Determine whether an item is in the given collection, in the sense that it is
[`==`](@ref) to one of the values generated by iterating over the collection.
Return a `Bool` value, except if `item` is [`missing`](@ref) or `collection`
contains `missing` but not `item`, in which case `missing` is returned
([three-valued logic](https://en.wikipedia.org/wiki/Three-valued_logic),
matching the behavior of [`any`](@ref) and [`==`](@ref)).

Some collections follow a slightly different definition. For example,
[`Set`](@ref)s check whether the item [`isequal`](@ref) to one of the elements;
[`Dict`](@ref)s look for `key=>value` pairs, and the `key` is compared using
[`isequal`](@ref).

To test for the presence of a key in a dictionary, use [`haskey`](@ref)
or `k in keys(dict)`. For the collections mentioned above,
the result is always a `Bool`.

When broadcasting with `in.(items, collection)` or `items .∈ collection`, both
`item` and `collection` are broadcasted over, which is often not what is intended.
For example, if both arguments are vectors (and the dimensions match), the result is
a vector indicating whether each value in collection `items` is `in` the value at the
corresponding position in `collection`. To get a vector indicating whether each value
in `items` is in `collection`, wrap `collection` in a tuple or a `Ref` like this:
`in.(items, Ref(collection))` or `items .∈ Ref(collection)`.

See also: [`∉`](@ref), [`insorted`](@ref), [`contains`](@ref), [`occursin`](@ref), [`issubset`](@ref).

# Examples
```jldoctest
julia> a = 1:3:20
1:3:19

julia> 4 in a
true

julia> 5 in a
false

julia> missing in [1, 2]
missing

julia> 1 in [2, missing]
missing

julia> 1 in [1, missing]
true

julia> missing in Set([1, 2])
false

julia> (1=>missing) in Dict(1=>10, 2=>20)
missing

julia> [1, 2] .∈ [2, 3]
2-element BitVector:
 0
 0

julia> [1, 2] .∈ ([2, 3],)
2-element BitVector:
 0
 1
```
"""
in

"""
    ∉(item, collection) -> Bool
    ∌(collection, item) -> Bool

Negation of `∈` and `∋`, i.e. checks that `item` is not in `collection`.

When broadcasting with `items .∉ collection`, both `item` and `collection` are
broadcasted over, which is often not what is intended. For example, if both arguments
are vectors (and the dimensions match), the result is a vector indicating whether
each value in collection `items` is not in the value at the corresponding position
in `collection`. To get a vector indicating whether each value in `items` is not in
`collection`, wrap `collection` in a tuple or a `Ref` like this:
`items .∉ Ref(collection)`.

# Examples
```jldoctest
julia> 1 ∉ 2:4
true

julia> 1 ∉ 1:3
false

julia> [1, 2] .∉ [2, 3]
2-element BitVector:
 1
 1

julia> [1, 2] .∉ ([2, 3],)
2-element BitVector:
 1
 0
```
"""
∉, ∌
N   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/pointer.jl�.      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
    Ptr{T}

A memory address referring to data of type `T`.  However, there is no guarantee that the
memory is actually valid, or that it actually represents data of the specified type.
"""
Ptr

## converting pointers to an appropriate unsigned ##

"""
    C_NULL

The C null pointer constant, sometimes used when calling external code.
"""
const C_NULL = bitcast(Ptr{Cvoid}, 0)

# TODO: deprecate these conversions. C doesn't even allow them.

# pointer to integer
convert(::Type{T}, x::Ptr) where {T<:Integer} = T(UInt(x))::T

# integer to pointer
convert(::Type{Ptr{T}}, x::Union{Int,UInt}) where {T} = Ptr{T}(x)

# pointer to pointer
convert(::Type{Ptr{T}}, p::Ptr{T}) where {T} = p
convert(::Type{Ptr{T}}, p::Ptr) where {T} = bitcast(Ptr{T}, p)::Ptr{T}

# object to pointer (when used with ccall)

"""
    unsafe_convert(T, x)

Convert `x` to a C argument of type `T`
where the input `x` must be the return value of `cconvert(T, ...)`.

In cases where [`convert`](@ref) would need to take a Julia object
and turn it into a `Ptr`, this function should be used to define and perform
that conversion.

Be careful to ensure that a Julia reference to `x` exists as long as the result of this
function will be used. Accordingly, the argument `x` to this function should never be an
expression, only a variable name or field reference. For example, `x=a.b.c` is acceptable,
but `x=[a,b,c]` is not.

The `unsafe` prefix on this function indicates that using the result of this function after
the `x` argument to this function is no longer accessible to the program may cause undefined
behavior, including program corruption or segfaults, at any later time.

See also [`cconvert`](@ref)
"""
function unsafe_convert end

unsafe_convert(::Type{Ptr{UInt8}}, x::Symbol) = ccall(:jl_symbol_name, Ptr{UInt8}, (Any,), x)
unsafe_convert(::Type{Ptr{Int8}}, x::Symbol) = ccall(:jl_symbol_name, Ptr{Int8}, (Any,), x)
unsafe_convert(::Type{Ptr{UInt8}}, s::String) = ccall(:jl_string_ptr, Ptr{UInt8}, (Any,), s)
unsafe_convert(::Type{Ptr{Int8}}, s::String) = ccall(:jl_string_ptr, Ptr{Int8}, (Any,), s)
# convert strings to String etc. to pass as pointers
cconvert(::Type{Ptr{UInt8}}, s::AbstractString) = String(s)
cconvert(::Type{Ptr{Int8}}, s::AbstractString) = String(s)

unsafe_convert(::Type{Ptr{T}}, a::Array{T}) where {T} = ccall(:jl_array_ptr, Ptr{T}, (Any,), a)
unsafe_convert(::Type{Ptr{S}}, a::AbstractArray{T}) where {S,T} = convert(Ptr{S}, unsafe_convert(Ptr{T}, a))
unsafe_convert(::Type{Ptr{T}}, a::AbstractArray{T}) where {T} = error("conversion to pointer not defined for $(typeof(a))")

# unsafe pointer to array conversions
"""
    unsafe_wrap(Array, pointer::Ptr{T}, dims; own = false)

Wrap a Julia `Array` object around the data at the address given by `pointer`,
without making a copy.  The pointer element type `T` determines the array
element type. `dims` is either an integer (for a 1d array) or a tuple of the array dimensions.
`own` optionally specifies whether Julia should take ownership of the memory,
calling `free` on the pointer when the array is no longer referenced.

This function is labeled "unsafe" because it will crash if `pointer` is not
a valid memory address to data of the requested length. Unlike [`unsafe_load`](@ref)
and [`unsafe_store!`](@ref), the programmer is responsible also for ensuring that the
underlying data is not accessed through two arrays of different element type, similar
to the strict aliasing rule in C.
"""
function unsafe_wrap(::Union{Type{Array},Type{Array{T}},Type{Array{T,N}}},
                     p::Ptr{T}, dims::NTuple{N,Int}; own::Bool = false) where {T,N}
    ccall(:jl_ptr_to_array, Array{T,N}, (Any, Ptr{Cvoid}, Any, Int32),
          Array{T,N}, p, dims, own)
end
function unsafe_wrap(::Union{Type{Array},Type{Array{T}},Type{Array{T,1}}},
                     p::Ptr{T}, d::Integer; own::Bool = false) where {T}
    ccall(:jl_ptr_to_array_1d, Array{T,1},
          (Any, Ptr{Cvoid}, Csize_t, Cint), Array{T,1}, p, d, own)
end
unsafe_wrap(Atype::Union{Type{Array},Type{Array{T}},Type{Array{T,N}}},
            p::Ptr{T}, dims::NTuple{N,<:Integer}; own::Bool = false) where {T,N} =
    unsafe_wrap(Atype, p, convert(Tuple{Vararg{Int}}, dims), own = own)

"""
    unsafe_load(p::Ptr{T}, i::Integer=1)
    unsafe_load(p::Ptr{T}, order::Symbol)
    unsafe_load(p::Ptr{T}, i::Integer, order::Symbol)

Load a value of type `T` from the address of the `i`th element (1-indexed) starting at `p`.
This is equivalent to the C expression `p[i-1]`. Optionally, an atomic memory ordering can
be provided.

The `unsafe` prefix on this function indicates that no validation is performed on the
pointer `p` to ensure that it is valid. Like C, the programmer is responsible for ensuring
that referenced memory is not freed or garbage collected while invoking this function.
Incorrect usage may segfault your program or return garbage answers. Unlike C, dereferencing
memory region allocated as different type may be valid provided that the types are compatible.

!!! compat "Julia 1.10"
     The `order` argument is available as of Julia 1.10.

See also: [`atomic`](@ref)
"""
unsafe_load(p::Ptr, i::Integer=1) = pointerref(p, Int(i), 1)
unsafe_load(p::Ptr, order::Symbol) = atomic_pointerref(p, order)
function unsafe_load(p::Ptr, i::Integer, order::Symbol)
    unsafe_load(p + (elsize(typeof(p)) * (Int(i) - 1)), order)
end

"""
    unsafe_store!(p::Ptr{T}, x, i::Integer=1)
    unsafe_store!(p::Ptr{T}, x, order::Symbol)
    unsafe_store!(p::Ptr{T}, x, i::Integer, order::Symbol)

Store a value of type `T` to the address of the `i`th element (1-indexed) starting at `p`.
This is equivalent to the C expression `p[i-1] = x`. Optionally, an atomic memory ordering
can be provided.

The `unsafe` prefix on this function indicates that no validation is performed on the
pointer `p` to ensure that it is valid. Like C, the programmer is responsible for ensuring
that referenced memory is not freed or garbage collected while invoking this function.
Incorrect usage may segfault your program. Unlike C, storing memory region allocated as
different type may be valid provided that that the types are compatible.

!!! compat "Julia 1.10"
     The `order` argument is available as of Julia 1.10.

See also: [`atomic`](@ref)
"""
unsafe_store!(p::Ptr{Any}, @nospecialize(x), i::Integer=1) = pointerset(p, x, Int(i), 1)
unsafe_store!(p::Ptr{T}, x, i::Integer=1) where {T} = pointerset(p, convert(T,x), Int(i), 1)
unsafe_store!(p::Ptr{T}, x, order::Symbol) where {T} = atomic_pointerset(p, x isa T ? x : convert(T,x), order)
function unsafe_store!(p::Ptr, x, i::Integer, order::Symbol)
    unsafe_store!(p + (elsize(typeof(p)) * (Int(i) - 1)), x, order)
end

"""
    unsafe_modify!(p::Ptr{T}, op, x, [order::Symbol]) -> Pair

These atomically perform the operations to get and set a memory address after applying
the function `op`. If supported by the hardware (for example, atomic increment), this may be
optimized to the appropriate hardware instruction, otherwise its execution will be
similar to:

    y = unsafe_load(p)
    z = op(y, x)
    unsafe_store!(p, z)
    return y => z

The `unsafe` prefix on this function indicates that no validation is performed on the
pointer `p` to ensure that it is valid. Like C, the programmer is responsible for ensuring
that referenced memory is not freed or garbage collected while invoking this function.
Incorrect usage may segfault your program.

!!! compat "Julia 1.10"
     This function requires at least Julia 1.10.

See also: [`modifyproperty!`](@ref Base.modifyproperty!), [`atomic`](@ref)
"""
function unsafe_modify!(p::Ptr, op, x, order::Symbol=:not_atomic)
    return atomic_pointermodify(p, op, x, order)
end

"""
    unsafe_replace!(p::Ptr{T}, expected, desired,
                   [success_order::Symbol[, fail_order::Symbol=success_order]]) -> (; old, success::Bool)

These atomically perform the operations to get and conditionally set a memory address to
a given value. If supported by the hardware, this may be optimized to the appropriate
hardware instruction, otherwise its execution will be similar to:

    y = unsafe_load(p, fail_order)
    ok = y === expected
    if ok
        unsafe_store!(p, desired, success_order)
    end
    return (; old = y, success = ok)

The `unsafe` prefix on this function indicates that no validation is performed on the
pointer `p` to ensure that it is valid. Like C, the programmer is responsible for ensuring
that referenced memory is not freed or garbage collected while invoking this function.
Incorrect usage may segfault your program.

!!! compat "Julia 1.10"
     This function requires at least Julia 1.10.

See also: [`replaceproperty!`](@ref Base.replaceproperty!), [`atomic`](@ref)
"""
function unsafe_replace!(p::Ptr{T}, expected, desired, success_order::Symbol=:not_atomic, fail_order::Symbol=success_order) where {T}
    @inline
    xT = desired isa T ? desired : convert(T, desired)
    return atomic_pointerreplace(p, expected, xT, success_order, fail_order)
end
function unsafe_replace!(p::Ptr{Any}, @nospecialize(expected), @nospecialize(desired), success_order::Symbol=:not_atomic, fail_order::Symbol=success_order)
    return atomic_pointerreplace(p, expected, desired, success_order, fail_order)
end

"""
    unsafe_swap!(p::Ptr{T}, x, [order::Symbol])

These atomically perform the operations to simultaneously get and set a memory address.
If supported by the hardware, this may be optimized to the appropriate hardware
instruction, otherwise its execution will be similar to:

    y = unsafe_load(p)
    unsafe_store!(p, x)
    return y

The `unsafe` prefix on this function indicates that no validation is performed on the
pointer `p` to ensure that it is valid. Like C, the programmer is responsible for ensuring
that referenced memory is not freed or garbage collected while invoking this function.
Incorrect usage may segfault your program.

!!! compat "Julia 1.10"
     This function requires at least Julia 1.10.

See also: [`swapproperty!`](@ref Base.swapproperty!), [`atomic`](@ref)
"""
function unsafe_swap!(p::Ptr{Any}, x, order::Symbol=:not_atomic)
    return atomic_pointerswap(p, x, order)
end
function unsafe_swap!(p::Ptr{T}, x, order::Symbol=:not_atomic) where {T}
    @inline
    xT = x isa T ? x : convert(T, x)
    return atomic_pointerswap(p, xT, order)
end

# convert a raw Ptr to an object reference, and vice-versa
"""
    unsafe_pointer_to_objref(p::Ptr)

Convert a `Ptr` to an object reference. Assumes the pointer refers to a valid heap-allocated
Julia object. If this is not the case, undefined behavior results, hence this function is
considered "unsafe" and should be used with care.

See also [`pointer_from_objref`](@ref).
"""
unsafe_pointer_to_objref(x::Ptr) = ccall(:jl_value_ptr, Any, (Ptr{Cvoid},), x)

"""
    pointer_from_objref(x)

Get the memory address of a Julia object as a `Ptr`. The existence of the resulting `Ptr`
will not protect the object from garbage collection, so you must ensure that the object
remains referenced for the whole time that the `Ptr` will be used.

This function may not be called on immutable objects, since they do not have
stable memory addresses.

See also [`unsafe_pointer_to_objref`](@ref).
"""
function pointer_from_objref(@nospecialize(x))
    @inline
    ismutable(x) || error("pointer_from_objref cannot be used on immutable objects")
    ccall(:jl_value_ptr, Ptr{Cvoid}, (Any,), x)
end

## limited pointer arithmetic & comparison ##

isequal(x::Ptr, y::Ptr) = (x === y)
isless(x::Ptr{T}, y::Ptr{T}) where {T} = x < y

==(x::Ptr, y::Ptr) = UInt(x) == UInt(y)
<(x::Ptr,  y::Ptr) = UInt(x) < UInt(y)
-(x::Ptr,  y::Ptr) = UInt(x) - UInt(y)

+(x::Ptr, y::Integer) = oftype(x, add_ptr(UInt(x), (y % UInt) % UInt))
-(x::Ptr, y::Integer) = oftype(x, sub_ptr(UInt(x), (y % UInt) % UInt))
+(x::Integer, y::Ptr) = y + x

unsigned(x::Ptr) = UInt(x)
signed(x::Ptr) = Int(x)
O   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/refvalue.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

### Methods for a Ref object that can store a single value of any type

mutable struct RefValue{T} <: Ref{T}
    x::T
    RefValue{T}() where {T} = new()
    RefValue{T}(x) where {T} = new(x)
end
RefValue(x::T) where {T} = RefValue{T}(x)
"""
    isassigned(ref::RefValue) -> Bool

Test whether the given [`Ref`](@ref) is associated with a value.
This is always true for a [`Ref`](@ref) of a bitstype object.
Return `false` if the reference is undefined.

# Examples
```jldoctest
julia> ref = Ref{Function}()
Base.RefValue{Function}(#undef)

julia> isassigned(ref)
false

julia> ref[] = (foobar(x) = x)
foobar (generic function with 1 method)

julia> isassigned(ref)
true

julia> isassigned(Ref{Int}())
true
```
"""
isassigned(x::RefValue) = isdefined(x, :x)

function unsafe_convert(P::Union{Type{Ptr{T}},Type{Ptr{Cvoid}}}, b::RefValue{T})::P where T
    if allocatedinline(T)
        p = pointer_from_objref(b)
    elseif isconcretetype(T) && ismutabletype(T)
        p = pointer_from_objref(b.x)
    else
        # If the slot is not leaf type, it could be either immutable or not.
        # If it is actually an immutable, then we can't take it's pointer directly
        # Instead, explicitly load the pointer from the `RefValue`,
        # which also ensures this returns same pointer as the one rooted in the `RefValue` object.
        p = atomic_pointerref(Ptr{Ptr{Cvoid}}(pointer_from_objref(b)), :monotonic)
    end
    if p == C_NULL
        throw(UndefRefError())
    end
    return p
end
function unsafe_convert(::Type{Ptr{Any}}, b::RefValue{Any})::Ptr{Any}
    return pointer_from_objref(b)
end

getindex(b::RefValue) = b.x
setindex!(b::RefValue, x) = (b.x = x; b)
K   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/cmem.jl=      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
    memcpy(dst::Ptr, src::Ptr, n::Integer) -> Ptr{Cvoid}

Call `memcpy` from the C standard library.

!!! compat "Julia 1.10"
    Support for `memcpy` requires at least Julia 1.10.

"""
function memcpy(dst::Ptr, src::Ptr, n::Integer)
    ccall(:memcpy, Ptr{Cvoid}, (Ptr{Cvoid}, Ptr{Cvoid}, Csize_t), dst, src, n)
end

"""
    memmove(dst::Ptr, src::Ptr, n::Integer) -> Ptr{Cvoid}

Call `memmove` from the C standard library.

!!! compat "Julia 1.10"
    Support for `memmove` requires at least Julia 1.10.

"""
function memmove(dst::Ptr, src::Ptr, n::Integer)
    ccall(:memmove, Ptr{Cvoid}, (Ptr{Cvoid}, Ptr{Cvoid}, Csize_t), dst, src, n)
end

"""
    memset(dst::Ptr, val, n::Integer) -> Ptr{Cvoid}

Call `memset` from the C standard library.

!!! compat "Julia 1.10"
    Support for `memset` requires at least Julia 1.10.

"""
function memset(p::Ptr, val, n::Integer)
    ccall(:memset, Ptr{Cvoid}, (Ptr{Cvoid}, Cint, Csize_t), p, val, n)
end

"""
    memcmp(a::Ptr, b::Ptr, n::Integer) -> Int

Call `memcmp` from the C standard library.

!!! compat "Julia 1.10"
    Support for `memcmp` requires at least Julia 1.9.

"""
function memcmp(a::Ptr, b::Ptr, n::Integer)
    ccall(:memcmp, Cint, (Ptr{Cvoid}, Ptr{Cvoid}, Csize_t), a, b, n % Csize_t) % Int
end
Q   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/refpointer.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
    Ref{T}

An object that safely references data of type `T`. This type is guaranteed to point to
valid, Julia-allocated memory of the correct type. The underlying data is protected from
freeing by the garbage collector as long as the `Ref` itself is referenced.

In Julia, `Ref` objects are dereferenced (loaded or stored) with `[]`.

Creation of a `Ref` to a value `x` of type `T` is usually written `Ref(x)`.
Additionally, for creating interior pointers to containers (such as Array or Ptr),
it can be written `Ref(a, i)` for creating a reference to the `i`-th element of `a`.

`Ref{T}()` creates a reference to a value of type `T` without initialization.
For a bitstype `T`, the value will be whatever currently resides in the memory
allocated. For a non-bitstype `T`, the reference will be undefined and attempting to
dereference it will result in an error, "UndefRefError: access to undefined reference".

To check if a `Ref` is an undefined reference, use [`isassigned(ref::RefValue)`](@ref).
For example, `isassigned(Ref{T}())` is `false` if `T` is not a bitstype.
If `T` is a bitstype, `isassigned(Ref{T}())` will always be true.

When passed as a `ccall` argument (either as a `Ptr` or `Ref` type), a `Ref`
object will be converted to a native pointer to the data it references.
For most `T`, or when converted to a `Ptr{Cvoid}`, this is a pointer to the
object data. When `T` is an `isbits` type, this value may be safely mutated,
otherwise mutation is strictly undefined behavior.

As a special case, setting `T = Any` will instead cause the creation of a
pointer to the reference itself when converted to a `Ptr{Any}`
(a `jl_value_t const* const*` if T is immutable, else a `jl_value_t *const *`).
When converted to a `Ptr{Cvoid}`, it will still return a pointer to the data
region as for any other `T`.

A `C_NULL` instance of `Ptr` can be passed to a `ccall` `Ref` argument to initialize it.

# Use in broadcasting
`Ref` is sometimes used in broadcasting in order to treat the referenced values as a scalar.

# Examples

```jldoctest
julia> Ref(5)
Base.RefValue{Int64}(5)

julia> isa.(Ref([1,2,3]), [Array, Dict, Int]) # Treat reference values as scalar during broadcasting
3-element BitVector:
 1
 0
 0

julia> Ref{Function}()  # Undefined reference to a non-bitstype, Function
Base.RefValue{Function}(#undef)

julia> try
           Ref{Function}()[] # Dereferencing an undefined reference will result in an error
       catch e
           println(e)
       end
UndefRefError()

julia> Ref{Int64}()[]; # A reference to a bitstype refers to an undetermined value if not given

julia> isassigned(Ref{Int64}()) # A reference to a bitstype is always assigned
true

julia> Ref{Int64}(0)[] == 0 # Explicitly give a value for a bitstype reference
true
```
"""
Ref

# C NUL-terminated string pointers; these can be used in ccall
# instead of Ptr{Cchar} and Ptr{Cwchar_t}, respectively, to enforce
# a check for embedded NUL chars in the string (to avoid silent truncation).
if Int === Int64
    primitive type Cstring  64 end
    primitive type Cwstring 64 end
else
    primitive type Cstring  32 end
    primitive type Cwstring 32 end
end


### General Methods for Ref{T} type

eltype(x::Type{<:Ref{T}}) where {T} = @isdefined(T) ? T : Any
convert(::Type{Ref{T}}, x::Ref{T}) where {T} = x
size(x::Ref) = ()
axes(x::Ref) = ()
length(x::Ref) = 1
isempty(x::Ref) = false
ndims(x::Ref) = 0
ndims(::Type{<:Ref}) = 0
iterate(r::Ref) = (r[], nothing)
iterate(r::Ref, s) = nothing
IteratorSize(::Type{<:Ref}) = HasShape{0}()

# create Ref objects for general object conversion
unsafe_convert(::Type{Ref{T}}, x::Ref{T}) where {T} = unsafe_convert(Ptr{T}, x)
unsafe_convert(::Type{Ref{T}}, x) where {T} = unsafe_convert(Ptr{T}, x)

convert(::Type{Ref{T}}, x) where {T} = RefValue{T}(x)::RefValue{T}

### Methods for a Ref object that is backed by an array at index i
struct RefArray{T,A<:AbstractArray{T},R} <: Ref{T}
    x::A
    i::Int
    roots::R # should be either ::Nothing or ::Any
    RefArray{T,A,R}(x,i,roots=nothing) where {T,A<:AbstractArray{T},R} = new(x,i,roots)
end
RefArray(x::AbstractArray{T}, i::Int, roots::Any) where {T} = RefArray{T,typeof(x),Any}(x, i, roots)
RefArray(x::AbstractArray{T}, i::Int=1, roots::Nothing=nothing) where {T} = RefArray{T,typeof(x),Nothing}(x, i, nothing)
RefArray(x::AbstractArray{T}, i::Integer, roots::Any) where {T} = RefArray{T,typeof(x),Any}(x, Int(i), roots)
RefArray(x::AbstractArray{T}, i::Integer, roots::Nothing=nothing) where {T} = RefArray{T,typeof(x),Nothing}(x, Int(i), nothing)
convert(::Type{Ref{T}}, x::AbstractArray{T}) where {T} = RefArray(x, 1)

function unsafe_convert(P::Union{Type{Ptr{T}},Type{Ptr{Cvoid}}}, b::RefArray{T})::P where T
    if allocatedinline(T)
        p = pointer(b.x, b.i)
    elseif isconcretetype(T) && ismutabletype(T)
        p = pointer_from_objref(b.x[b.i])
    else
        # see comment on equivalent branch for RefValue
        p = pointerref(Ptr{Ptr{Cvoid}}(pointer(b.x, b.i)), 1, Core.sizeof(Ptr{Cvoid}))
    end
    return p
end
function unsafe_convert(::Type{Ptr{Any}}, b::RefArray{Any})::Ptr{Any}
    return pointer(b.x, b.i)
end

###
if is_primary_base_module
    Ref(x::Any) = RefValue(x)
    Ref{T}() where {T} = RefValue{T}() # Ref{T}()
    Ref{T}(x) where {T} = RefValue{T}(x) # Ref{T}(x)

    Ref(x::Ref, i::Integer) = (i != 1 && error("Ref only has one element"); x)
    Ref(x::Ptr{T}, i::Integer) where {T} = x + (i - 1) * Core.sizeof(T)

    # convert Arrays to pointer arrays for ccall
    function Ref{P}(a::Array{<:Union{Ptr,Cwstring,Cstring}}) where P<:Union{Ptr,Cwstring,Cstring}
        return RefArray(a) # effectively a no-op
    end
    function Ref{P}(a::Array{T}) where P<:Union{Ptr,Cwstring,Cstring} where T
        if (!isbitstype(T) && T <: eltype(P))
            # this Array already has the right memory layout for the requested Ref
            return RefArray(a,1,false) # root something, so that this function is type-stable
        else
            ptrs = Vector{P}(undef, length(a)+1)
            roots = Vector{Any}(undef, length(a))
            for i = 1:length(a)
                root = cconvert(P, a[i])
                ptrs[i] = unsafe_convert(P, root)::P
                roots[i] = root
            end
            ptrs[length(a)+1] = C_NULL
            return RefArray(ptrs,1,roots)
        end
    end
    Ref(x::AbstractArray, i::Integer) = RefArray(x, i)
end

cconvert(::Type{Ptr{P}}, a::Array{<:Ptr}) where {P<:Ptr} = a
cconvert(::Type{Ref{P}}, a::Array{<:Ptr}) where {P<:Ptr} = a
cconvert(::Type{Ptr{P}}, a::Array) where {P<:Union{Ptr,Cwstring,Cstring}} = Ref{P}(a)
cconvert(::Type{Ref{P}}, a::Array) where {P<:Union{Ptr,Cwstring,Cstring}} = Ref{P}(a)

# pass NTuple{N,T} as Ptr{T}/Ref{T}
cconvert(::Type{Ref{T}}, t::NTuple{N,T}) where {N,T} = Ref{NTuple{N,T}}(t)
cconvert(::Type{Ref{T}}, r::Ref{NTuple{N,T}}) where {N,T} = r
unsafe_convert(::Type{Ref{T}}, r::Ref{NTuple{N,T}}) where {N,T} =
    convert(Ptr{T}, unsafe_convert(Ptr{NTuple{N,T}}, r))
unsafe_convert(::Type{Ptr{T}}, r::Ref{NTuple{N,T}}) where {N,T} =
    convert(Ptr{T}, unsafe_convert(Ptr{NTuple{N,T}}, r))
unsafe_convert(::Type{Ptr{T}}, r::Ptr{NTuple{N,T}}) where {N,T} =
    convert(Ptr{T}, r)

###

getindex(b::RefArray) = b.x[b.i]
setindex!(b::RefArray, x) = (b.x[b.i] = x; b)

###

"""
    LLVMPtr{T, AS}

A pointer type that more closely resembles LLVM semantics: It includes the pointer address
space, and will be passed as an actual pointer instead of an integer.

This type is mainly used to interface with code that has strict requirements about pointers,
e.g., intrinsics that are selected based on the address space, or back-ends that require
pointers to be identifiable by their types.
"""
Core.LLVMPtr
N   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/checked.jl0      # This file is a part of Julia. License is MIT: https://julialang.org/license

# Support for checked integer arithmetic

"""
    Checked

The Checked module provides arithmetic functions for the built-in signed and unsigned
Integer types which throw an error when an overflow occurs. They are named like `checked_sub`,
`checked_div`, etc. In addition, `add_with_overflow`, `sub_with_overflow`, `mul_with_overflow`
return both the unchecked results and a boolean value denoting the presence of an overflow.
"""
module Checked

export checked_neg, checked_abs, checked_add, checked_sub, checked_mul,
       checked_div, checked_rem, checked_fld, checked_mod, checked_cld,
       checked_length, add_with_overflow, sub_with_overflow, mul_with_overflow

import Core.Intrinsics:
       checked_sadd_int, checked_ssub_int, checked_smul_int, checked_sdiv_int,
       checked_srem_int,
       checked_uadd_int, checked_usub_int, checked_umul_int, checked_udiv_int,
       checked_urem_int
import ..no_op_err, ..@inline, ..@noinline, ..checked_length

# define promotion behavior for checked operations
checked_add(x::Integer, y::Integer) = checked_add(promote(x,y)...)
checked_sub(x::Integer, y::Integer) = checked_sub(promote(x,y)...)
checked_mul(x::Integer, y::Integer) = checked_mul(promote(x,y)...)
checked_div(x::Integer, y::Integer) = checked_div(promote(x,y)...)
checked_rem(x::Integer, y::Integer) = checked_rem(promote(x,y)...)
checked_fld(x::Integer, y::Integer) = checked_fld(promote(x,y)...)
checked_mod(x::Integer, y::Integer) = checked_mod(promote(x,y)...)
checked_cld(x::Integer, y::Integer) = checked_cld(promote(x,y)...)

# fallback catchall rules to prevent infinite recursion if promotion succeeds,
# but no method exists to handle those types
checked_abs(x::T) where {T<:Integer} = no_op_err("checked_abs", T)

const SignedInt = Union{Int8,Int16,Int32,Int64,Int128}
const UnsignedInt = Union{UInt8,UInt16,UInt32,UInt64,UInt128}

# LLVM has several code generation bugs for checked integer arithmetic (see e.g.
# #4905). We thus distinguish between operations that can be implemented via
# intrinsics, and operations for which we have to provide workarounds.

# Note: As far as this code has been tested, most checked_* functions are
# working fine in LLVM. (Note that division is still handled via `base/int.jl`,
# which always checks for overflow, and which provides its own sets of
# workarounds for LLVM codegen bugs.) However, the comments in `base/int.jl`
# and in issue #4905 are more pessimistic. For the time being, we thus retain
# the ability to handle codegen bugs in LLVM, until the code here has been
# tested on more systems and architectures. It also seems that things depend on
# which compiler that was used to build LLVM (i.e. either gcc or clang).

# These unions are used for most checked functions:
#     BrokenSignedInt
#     BrokenUnsignedInt
# These unions are used for checked_{mul,div,rem}:
#     BrokenSignedIntMul
#     BrokenUnsignedIntMul

# This code runs early during bootstrap, and we can't use Julia's version
# strings yet
const llvm_version = Int(ccall(:jl_get_LLVM_VERSION, UInt32, ()))

brokenSignedInt = Union{}
brokenUnsignedInt = Union{}
brokenSignedIntMul = Int128
brokenUnsignedIntMul = UInt128
if Core.sizeof(Ptr{Cvoid}) == 4
    brokenSignedIntMul = Union{brokenSignedIntMul, Int64}
    brokenUnsignedIntMul = Union{brokenUnsignedIntMul, UInt64}
end
const BrokenSignedInt = brokenSignedInt
const BrokenUnsignedInt = brokenUnsignedInt
const BrokenSignedIntMul = brokenSignedIntMul
const BrokenUnsignedIntMul = brokenUnsignedIntMul
# Use these definitions to test the non-LLVM implementations
# const BrokenSignedInt = SignedInt
# const BrokenUnsignedInt = UnsignedInt
# const BrokenSignedIntMul = SignedInt
# const BrokenUnsignedIntMul = UnsignedInt

"""
    Base.checked_neg(x)

Calculates `-x`, checking for overflow errors where applicable. For
example, standard two's complement signed integers (e.g. `Int`) cannot
represent `-typemin(Int)`, thus leading to an overflow.

The overflow protection may impose a perceptible performance penalty.
"""
function checked_neg(x::T) where T<:Integer
    checked_sub(T(0), x)
end
throw_overflowerr_negation(x) = (@noinline;
    throw(OverflowError(Base.invokelatest(string, "checked arithmetic: cannot compute -x for x = ", x, "::", typeof(x)))))
if BrokenSignedInt != Union{}
function checked_neg(x::BrokenSignedInt)
    r = -x
    (x<0) & (r<0) && throw_overflowerr_negation(x)
    r
end
end
if BrokenUnsignedInt != Union{}
function checked_neg(x::T) where T<:BrokenUnsignedInt
    x != 0 && throw_overflowerr_negation(x)
    T(0)
end
end

"""
    Base.checked_abs(x)

Calculates `abs(x)`, checking for overflow errors where applicable.
For example, standard two's complement signed integers (e.g. `Int`)
cannot represent `abs(typemin(Int))`, thus leading to an overflow.

The overflow protection may impose a perceptible performance penalty.
"""
function checked_abs end

function checked_abs(x::SignedInt)
    r = ifelse(x<0, -x, x)
    r<0 || return r
    msg = LazyString("checked arithmetic: cannot compute |x| for x = ", x, "::", typeof(x))
    throw(OverflowError(msg))
end
checked_abs(x::UnsignedInt) = x
checked_abs(x::Bool) = x


"""
    Base.add_with_overflow(x, y) -> (r, f)

Calculates `r = x+y`, with the flag `f` indicating whether overflow has occurred.
"""
function add_with_overflow end
add_with_overflow(x::T, y::T) where {T<:SignedInt}   = checked_sadd_int(x, y)
add_with_overflow(x::T, y::T) where {T<:UnsignedInt} = checked_uadd_int(x, y)
add_with_overflow(x::Bool, y::Bool) = (x+y, false)

if BrokenSignedInt != Union{}
function add_with_overflow(x::T, y::T) where T<:BrokenSignedInt
    r = x + y
    # x and y have the same sign, and the result has a different sign
    f = (x<0) == (y<0) != (r<0)
    r, f
end
end
if BrokenUnsignedInt != Union{}
function add_with_overflow(x::T, y::T) where T<:BrokenUnsignedInt
    # x + y > typemax(T)
    # Note: ~y == -y-1
    x + y, x > ~y
end
end


throw_overflowerr_binaryop(op, x, y) = (@noinline;
    throw(OverflowError(LazyString(x, " ", op, " ", y, " overflowed for type ", typeof(x)))))

"""
    Base.checked_add(x, y)

Calculates `x+y`, checking for overflow errors where applicable.

The overflow protection may impose a perceptible performance penalty.
"""
function checked_add(x::T, y::T) where T<:Integer
    @inline
    z, b = add_with_overflow(x, y)
    b && throw_overflowerr_binaryop(:+, x, y)
    z
end

# Handle multiple arguments
checked_add(x) = x
checked_add(x::Bool) = +x

checked_add(x1::T, x2::T, x3::T) where {T} =
    checked_add(checked_add(x1, x2), x3)
checked_add(x1::T, x2::T, x3::T, x4::T) where {T} =
    checked_add(checked_add(x1, x2), x3, x4)
checked_add(x1::T, x2::T, x3::T, x4::T, x5::T) where {T} =
    checked_add(checked_add(x1, x2), x3, x4, x5)
checked_add(x1::T, x2::T, x3::T, x4::T, x5::T, x6::T) where {T} =
    checked_add(checked_add(x1, x2), x3, x4, x5, x6)
checked_add(x1::T, x2::T, x3::T, x4::T, x5::T, x6::T, x7::T) where {T} =
    checked_add(checked_add(x1, x2), x3, x4, x5, x6, x7)
checked_add(x1::T, x2::T, x3::T, x4::T, x5::T, x6::T, x7::T, x8::T) where {T} =
    checked_add(checked_add(x1, x2), x3, x4, x5, x6, x7, x8)


"""
    Base.sub_with_overflow(x, y) -> (r, f)

Calculates `r = x-y`, with the flag `f` indicating whether overflow has occurred.
"""
function sub_with_overflow end
sub_with_overflow(x::T, y::T) where {T<:SignedInt}   = checked_ssub_int(x, y)
sub_with_overflow(x::T, y::T) where {T<:UnsignedInt} = checked_usub_int(x, y)
sub_with_overflow(x::Bool, y::Bool) = (x-y, false)

if BrokenSignedInt != Union{}
function sub_with_overflow(x::T, y::T) where T<:BrokenSignedInt
    r = x - y
    # x and y have different signs, and the result has a different sign than x
    f = (x<0) != (y<0) == (r<0)
    r, f
end
end
if BrokenUnsignedInt != Union{}
function sub_with_overflow(x::T, y::T) where T<:BrokenUnsignedInt
    # x - y < 0
    x - y, x < y
end
end

"""
    Base.checked_sub(x, y)

Calculates `x-y`, checking for overflow errors where applicable.

The overflow protection may impose a perceptible performance penalty.
"""
function checked_sub(x::T, y::T) where T<:Integer
    @inline
    z, b = sub_with_overflow(x, y)
    b && throw_overflowerr_binaryop(:-, x, y)
    z
end


"""
    Base.mul_with_overflow(x, y) -> (r, f)

Calculates `r = x*y`, with the flag `f` indicating whether overflow has occurred.
"""
function mul_with_overflow end
mul_with_overflow(x::T, y::T) where {T<:SignedInt}   = checked_smul_int(x, y)
mul_with_overflow(x::T, y::T) where {T<:UnsignedInt} = checked_umul_int(x, y)
mul_with_overflow(x::Bool, y::Bool) = (x*y, false)

if BrokenSignedIntMul != Union{} && BrokenSignedIntMul != Int128
function mul_with_overflow(x::T, y::T) where T<:BrokenSignedIntMul
    r = widemul(x, y)
    f = r % T != r
    r % T, f
end
end
if BrokenUnsignedIntMul != Union{} && BrokenUnsignedIntMul != UInt128
function mul_with_overflow(x::T, y::T) where T<:BrokenUnsignedIntMul
    r = widemul(x, y)
    f = r % T != r
    r % T, f
end
end
if Int128 <: BrokenSignedIntMul
    # Avoid BigInt
    function mul_with_overflow(x::T, y::T) where T<:Int128
        f = if y > 0
            # x * y > typemax(T)
            # x * y < typemin(T)
            x > fld(typemax(T), y) || x < cld(typemin(T), y)
        elseif y < 0
            # x * y > typemax(T)
            # x * y < typemin(T)
            # y == -1 can overflow fld
            x < cld(typemax(T), y) || y != -1 && x > fld(typemin(T), y)
        else
            false
        end
        x*y, f
    end
end
if UInt128 <: BrokenUnsignedIntMul
    # Avoid BigInt
    function mul_with_overflow(x::T, y::T) where T<:UInt128
        # x * y > typemax(T)
        x * y, y > 0 && x > fld(typemax(T), y)
    end
end

"""
    Base.checked_mul(x, y)

Calculates `x*y`, checking for overflow errors where applicable.

The overflow protection may impose a perceptible performance penalty.
"""
function checked_mul(x::T, y::T) where T<:Integer
    @inline
    z, b = mul_with_overflow(x, y)
    b && throw_overflowerr_binaryop(:*, x, y)
    z
end

# Handle multiple arguments
checked_mul(x) = x
checked_mul(x1::T, x2::T, x3::T) where {T} =
    checked_mul(checked_mul(x1, x2), x3)
checked_mul(x1::T, x2::T, x3::T, x4::T) where {T} =
    checked_mul(checked_mul(x1, x2), x3, x4)
checked_mul(x1::T, x2::T, x3::T, x4::T, x5::T) where {T} =
    checked_mul(checked_mul(x1, x2), x3, x4, x5)
checked_mul(x1::T, x2::T, x3::T, x4::T, x5::T, x6::T) where {T} =
    checked_mul(checked_mul(x1, x2), x3, x4, x5, x6)
checked_mul(x1::T, x2::T, x3::T, x4::T, x5::T, x6::T, x7::T) where {T} =
    checked_mul(checked_mul(x1, x2), x3, x4, x5, x6, x7)
checked_mul(x1::T, x2::T, x3::T, x4::T, x5::T, x6::T, x7::T, x8::T) where {T} =
    checked_mul(checked_mul(x1, x2), x3, x4, x5, x6, x7, x8)

"""
    Base.checked_div(x, y)

Calculates `div(x,y)`, checking for overflow errors where applicable.

The overflow protection may impose a perceptible performance penalty.
"""
checked_div(x::T, y::T) where {T<:Integer} = div(x, y) # Base.div already checks

"""
    Base.checked_rem(x, y)

Calculates `x%y`, checking for overflow errors where applicable.

The overflow protection may impose a perceptible performance penalty.
"""
checked_rem(x::T, y::T) where {T<:Integer} = rem(x, y) # Base.rem already checks

"""
    Base.checked_fld(x, y)

Calculates `fld(x,y)`, checking for overflow errors where applicable.

The overflow protection may impose a perceptible performance penalty.
"""
checked_fld(x::T, y::T) where {T<:Integer} = fld(x, y) # Base.fld already checks

"""
    Base.checked_mod(x, y)

Calculates `mod(x,y)`, checking for overflow errors where applicable.

The overflow protection may impose a perceptible performance penalty.
"""
checked_mod(x::T, y::T) where {T<:Integer} = mod(x, y) # Base.mod already checks

"""
    Base.checked_cld(x, y)

Calculates `cld(x,y)`, checking for overflow errors where applicable.

The overflow protection may impose a perceptible performance penalty.
"""
checked_cld(x::T, y::T) where {T<:Integer} = cld(x, y) # Base.cld already checks

"""
    Base.checked_length(r)

Calculates `length(r)`, but may check for overflow errors where applicable when
the result doesn't fit into `Union{Integer(eltype(r)),Int}`.
"""
checked_length(r) = length(r) # for most things, length doesn't error

end
S   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/strings/lazy.jl�      """
    LazyString <: AbstractString

A lazy representation of string interpolation. This is useful when a string
needs to be constructed in a context where performing the actual interpolation
and string construction is unnecessary or undesirable (e.g. in error paths
of functions).

This type is designed to be cheap to construct at runtime, trying to offload
as much work as possible to either the macro or later printing operations.

# Examples

```jldoctest
julia> n = 5; str = LazyString("n is ", n)
"n is 5"
```

See also [`@lazy_str`](@ref).

!!! compat "Julia 1.8"
    `LazyString` requires Julia 1.8 or later.

# Extended help
## Safety properties for concurrent programs

A lazy string itself does not introduce any concurrency problems even if it is printed in
multiple Julia tasks.  However, if `print` methods on a captured value can have a
concurrency issue when invoked without synchronizations, printing the lazy string may cause
an issue.  Furthermore, the `print` methods on the captured values may be invoked multiple
times, though only exactly one result will be returned.

!!! compat "Julia 1.9"
    `LazyString` is safe in the above sense in Julia 1.9 and later.
"""
mutable struct LazyString <: AbstractString
    const parts::Tuple
    # Created on first access
    @atomic str::Union{String,Nothing}
    global _LazyString(parts, str) = new(parts, str)
    LazyString(args...) = new(args, nothing)
end

"""
    lazy"str"

Create a [`LazyString`](@ref) using regular string interpolation syntax.
Note that interpolations are *evaluated* at LazyString construction time,
but *printing* is delayed until the first access to the string.

See [`LazyString`](@ref) documentation for the safety properties for concurrent programs.

# Examples

```
julia> n = 5; str = lazy"n is \$n"
"n is 5"

julia> typeof(str)
LazyString
```

!!! compat "Julia 1.8"
    `lazy"str"` requires Julia 1.8 or later.
"""
macro lazy_str(text)
    parts = Any[]
    lastidx = idx = 1
    while (idx = findnext('$', text, idx)) !== nothing
        lastidx < idx && push!(parts, text[lastidx:prevind(text, idx)])
        idx += 1
        expr, idx = Meta.parseatom(text, idx; filename=string(__source__.file))
        push!(parts, esc(expr))
        lastidx = idx
    end
    lastidx <= lastindex(text) && push!(parts, text[lastidx:end])
    :(LazyString($(parts...)))
end

function String(l::LazyString)
    old = @atomic :acquire l.str
    old === nothing || return old
    str = sprint() do io
        for p in l.parts
            print(io, p)
        end
    end
    old, ok = @atomicreplace :acquire_release :acquire l.str nothing => str
    return ok ? str : (old::String)
end

hash(s::LazyString, h::UInt64) = hash(String(s), h)
lastindex(s::LazyString) = lastindex(String(s))
iterate(s::LazyString) = iterate(String(s))
iterate(s::LazyString, i::Integer) = iterate(String(s), i)
isequal(a::LazyString, b::LazyString) = isequal(String(a), String(b))
==(a::LazyString, b::LazyString) = (String(a) == String(b))
ncodeunits(s::LazyString) = ncodeunits(String(s))
codeunit(s::LazyString) = codeunit(String(s))
codeunit(s::LazyString, i::Integer) = codeunit(String(s), i)
isvalid(s::LazyString, i::Integer) = isvalid(String(s), i)
N   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/indices.jl�M      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
    Dims{N}

An `NTuple` of `N` `Int`s used to represent the dimensions
of an [`AbstractArray`](@ref).
"""
Dims{N} = NTuple{N,Int}
DimsInteger{N} = NTuple{N,Integer}
Indices{N} = NTuple{N,AbstractUnitRange}

## Traits for array types ##

abstract type IndexStyle end
"""
    IndexLinear()

Subtype of [`IndexStyle`](@ref) used to describe arrays which
are optimally indexed by one linear index.

A linear indexing style uses one integer index to describe the position in the array
(even if it's a multidimensional array) and column-major
ordering is used to efficiently access the elements. This means that
requesting [`eachindex`](@ref) from an array that is `IndexLinear` will return
a simple one-dimensional range, even if it is multidimensional.

A custom array that reports its `IndexStyle` as `IndexLinear` only needs
to implement indexing (and indexed assignment) with a single `Int` index;
all other indexing expressions — including multidimensional accesses — will
be recomputed to the linear index.  For example, if `A` were a `2×3` custom
matrix with linear indexing, and we referenced `A[1, 3]`, this would be
recomputed to the equivalent linear index and call `A[5]` since `1 + 2*(3 - 1) = 5`.

See also [`IndexCartesian`](@ref).
"""
struct IndexLinear <: IndexStyle end

"""
    IndexCartesian()

Subtype of [`IndexStyle`](@ref) used to describe arrays which
are optimally indexed by a Cartesian index. This is the default
for new custom [`AbstractArray`](@ref) subtypes.

A Cartesian indexing style uses multiple integer indices to describe the position in
a multidimensional array, with exactly one index per dimension. This means that
requesting [`eachindex`](@ref) from an array that is `IndexCartesian` will return
a range of [`CartesianIndices`](@ref).

A `N`-dimensional custom array that reports its `IndexStyle` as `IndexCartesian` needs
to implement indexing (and indexed assignment) with exactly `N` `Int` indices;
all other indexing expressions — including linear indexing — will
be recomputed to the equivalent Cartesian location.  For example, if `A` were a `2×3` custom
matrix with cartesian indexing, and we referenced `A[5]`, this would be
recomputed to the equivalent Cartesian index and call `A[1, 3]` since `5 = 1 + 2*(3 - 1)`.

It is significantly more expensive to compute Cartesian indices from a linear index than it is
to go the other way.  The former operation requires division — a very costly operation — whereas
the latter only uses multiplication and addition and is essentially free. This asymmetry means it
is far more costly to use linear indexing with an `IndexCartesian` array than it is to use
Cartesian indexing with an `IndexLinear` array.

See also [`IndexLinear`](@ref).
"""
struct IndexCartesian <: IndexStyle end

"""
    IndexStyle(A)
    IndexStyle(typeof(A))

`IndexStyle` specifies the "native indexing style" for array `A`. When
you define a new [`AbstractArray`](@ref) type, you can choose to implement
either linear indexing (with [`IndexLinear`](@ref)) or cartesian indexing.
If you decide to only implement linear indexing, then you must set this trait for your array
type:

    Base.IndexStyle(::Type{<:MyArray}) = IndexLinear()

The default is [`IndexCartesian()`](@ref).

Julia's internal indexing machinery will automatically (and invisibly)
recompute all indexing operations into the preferred style. This allows users
to access elements of your array using any indexing style, even when explicit
methods have not been provided.

If you define both styles of indexing for your `AbstractArray`, this
trait can be used to select the most performant indexing style. Some
methods check this trait on their inputs, and dispatch to different
algorithms depending on the most efficient access pattern. In
particular, [`eachindex`](@ref) creates an iterator whose type depends
on the setting of this trait.
"""
IndexStyle(A::AbstractArray) = IndexStyle(typeof(A))
IndexStyle(::Type{Union{}}, slurp...) = IndexLinear()
IndexStyle(::Type{<:AbstractArray}) = IndexCartesian()
IndexStyle(::Type{<:Array}) = IndexLinear()
IndexStyle(::Type{<:AbstractRange}) = IndexLinear()

IndexStyle(A::AbstractArray, B::AbstractArray) = IndexStyle(IndexStyle(A), IndexStyle(B))
IndexStyle(A::AbstractArray, B::AbstractArray...) = IndexStyle(IndexStyle(A), IndexStyle(B...))
IndexStyle(::IndexLinear, ::IndexLinear) = IndexLinear()
IndexStyle(::IndexStyle, ::IndexStyle) = IndexCartesian()

# array shape rules

promote_shape(::Tuple{}, ::Tuple{}) = ()

function promote_shape(a::Tuple{Int,}, b::Tuple{Int,})
    if a[1] != b[1]
        throw(DimensionMismatch("dimensions must match: a has dims $a, b has dims $b"))
    end
    return a
end

function promote_shape(a::Tuple{Int,Int}, b::Tuple{Int,})
    if a[1] != b[1] || a[2] != 1
        throw(DimensionMismatch("dimensions must match: a has dims $a, b has dims $b"))
    end
    return a
end

promote_shape(a::Tuple{Int,}, b::Tuple{Int,Int}) = promote_shape(b, a)

function promote_shape(a::Tuple{Int, Int}, b::Tuple{Int, Int})
    if a[1] != b[1] || a[2] != b[2]
        throw(DimensionMismatch("dimensions must match: a has dims $a, b has dims $b"))
    end
    return a
end

"""
    promote_shape(s1, s2)

Check two array shapes for compatibility, allowing trailing singleton dimensions, and return
whichever shape has more dimensions.

# Examples
```jldoctest
julia> a = fill(1, (3,4,1,1,1));

julia> b = fill(1, (3,4));

julia> promote_shape(a,b)
(Base.OneTo(3), Base.OneTo(4), Base.OneTo(1), Base.OneTo(1), Base.OneTo(1))

julia> promote_shape((2,3,1,4), (2, 3, 1, 4, 1))
(2, 3, 1, 4, 1)
```
"""
function promote_shape(a::Dims, b::Dims)
    if length(a) < length(b)
        return promote_shape(b, a)
    end
    for i=1:length(b)
        if a[i] != b[i]
            throw(DimensionMismatch("dimensions must match: a has dims $a, b has dims $b, mismatch at $i"))
        end
    end
    for i=length(b)+1:length(a)
        if a[i] != 1
            throw(DimensionMismatch("dimensions must match: a has dims $a, must have singleton at dim $i"))
        end
    end
    return a
end

function promote_shape(a::AbstractArray, b::AbstractArray)
    promote_shape(axes(a), axes(b))
end

function promote_shape(a::Indices, b::Indices)
    if length(a) < length(b)
        return promote_shape(b, a)
    end
    for i=1:length(b)
        if a[i] != b[i]
            throw(DimensionMismatch("dimensions must match: a has dims $a, b has dims $b, mismatch at $i"))
        end
    end
    for i=length(b)+1:length(a)
        if a[i] != 1:1
            throw(DimensionMismatch("dimensions must match: a has dims $a, must have singleton at dim $i"))
        end
    end
    return a
end

function throw_setindex_mismatch(X, I)
    if length(I) == 1
        throw(DimensionMismatch("tried to assign $(length(X)) elements to $(I[1]) destinations"))
    else
        throw(DimensionMismatch("tried to assign $(dims2string(size(X))) array to $(dims2string(I)) destination"))
    end
end

# check for valid sizes in A[I...] = X where X <: AbstractArray
# we want to allow dimensions that are equal up to permutation, but only
# for permutations that leave array elements in the same linear order.
# those are the permutations that preserve the order of the non-singleton
# dimensions.
function setindex_shape_check(X::AbstractArray, I::Integer...)
    li = ndims(X)
    lj = length(I)
    i = j = 1
    while true
        ii = length(axes(X,i))
        jj = I[j]
        if i == li || j == lj
            while i < li
                i += 1
                ii *= length(axes(X,i))
            end
            while j < lj
                j += 1
                jj *= I[j]
            end
            if ii != jj
                throw_setindex_mismatch(X, I)
            end
            return
        end
        if ii == jj
            i += 1
            j += 1
        elseif ii == 1
            i += 1
        elseif jj == 1
            j += 1
        else
            throw_setindex_mismatch(X, I)
        end
    end
end

setindex_shape_check(X::AbstractArray) =
    (length(X)==1 || throw_setindex_mismatch(X,()))

setindex_shape_check(X::AbstractArray, i::Integer) =
    (length(X)==i || throw_setindex_mismatch(X, (i,)))

setindex_shape_check(X::AbstractArray{<:Any, 0}, i::Integer...) =
    (length(X) == prod(i) || throw_setindex_mismatch(X, i))

setindex_shape_check(X::AbstractArray{<:Any,1}, i::Integer) =
    (length(X)==i || throw_setindex_mismatch(X, (i,)))

setindex_shape_check(X::AbstractArray{<:Any,1}, i::Integer, j::Integer) =
    (length(X)==i*j || throw_setindex_mismatch(X, (i,j)))

function setindex_shape_check(X::AbstractArray{<:Any,2}, i::Integer, j::Integer)
    if length(X) != i*j
        throw_setindex_mismatch(X, (i,j))
    end
    sx1 = length(axes(X,1))
    if !(i == 1 || i == sx1 || sx1 == 1)
        throw_setindex_mismatch(X, (i,j))
    end
end

setindex_shape_check(::Any...) =
    throw(ArgumentError("indexed assignment with a single value to possibly many locations is not supported; perhaps use broadcasting `.=` instead?"))

# convert to a supported index type (array or Int)
"""
    to_index(A, i)

Convert index `i` to an `Int` or array of indices to be used as an index into array `A`.

Custom array types may specialize `to_index(::CustomArray, i)` to provide
special indexing behaviors. Note that some index types (like `Colon`) require
more context in order to transform them into an array of indices; those get
converted in the more complicated `to_indices` function. By default, this
simply calls the generic `to_index(i)`. This must return either an `Int` or an
`AbstractArray` of scalar indices that are supported by `A`.
"""
to_index(A, i) = to_index(i)

# This is ok for Array because values larger than
# typemax(Int) will BoundsError anyway
to_index(A::Array, i::UInt) = reinterpret(Int, i)

"""
    to_index(i)

Convert index `i` to an `Int` or array of `Int`s to be used as an index for all arrays.

Custom index types may specialize `to_index(::CustomIndex)` to provide special
indexing behaviors. This must return either an `Int` or an `AbstractArray` of
`Int`s.
"""
to_index(i::Integer) = convert(Int,i)::Int
to_index(i::Bool) = throw(ArgumentError("invalid index: $i of type Bool"))
to_index(I::AbstractArray{Bool}) = LogicalIndex(I)
to_index(I::AbstractArray) = I
to_index(I::AbstractArray{Union{}}) = I
to_index(I::AbstractArray{<:Union{AbstractArray, Colon}}) =
    throw(ArgumentError("invalid index: $(limitrepr(I)) of type $(typeof(I))"))
to_index(::Colon) = throw(ArgumentError("colons must be converted by to_indices(...)"))
to_index(i) = throw(ArgumentError("invalid index: $(limitrepr(i)) of type $(typeof(i))"))

# The general to_indices is mostly defined in multidimensional.jl, but this
# definition is required for bootstrap:
"""
    to_indices(A, I::Tuple)

Convert the tuple `I` to a tuple of indices for use in indexing into array `A`.

The returned tuple must only contain either `Int`s or `AbstractArray`s of
scalar indices that are supported by array `A`. It will error upon encountering
a novel index type that it does not know how to process.

For simple index types, it defers to the unexported `Base.to_index(A, i)` to
process each index `i`. While this internal function is not intended to be
called directly, `Base.to_index` may be extended by custom array or index types
to provide custom indexing behaviors.

More complicated index types may require more context about the dimension into
which they index. To support those cases, `to_indices(A, I)` calls
`to_indices(A, axes(A), I)`, which then recursively walks through both the
given tuple of indices and the dimensional indices of `A` in tandem. As such,
not all index types are guaranteed to propagate to `Base.to_index`.

# Examples
```jldoctest
julia> A = zeros(1,2,3,4);

julia> to_indices(A, (1,1,2,2))
(1, 1, 2, 2)

julia> to_indices(A, (1,1,2,20)) # no bounds checking
(1, 1, 2, 20)

julia> to_indices(A, (CartesianIndex((1,)), 2, CartesianIndex((3,4)))) # exotic index
(1, 2, 3, 4)

julia> to_indices(A, ([1,1], 1:2, 3, 4))
([1, 1], 1:2, 3, 4)

julia> to_indices(A, (1,2)) # no shape checking
(1, 2)
```
"""
to_indices(A, I::Tuple) = (@inline; to_indices(A, axes(A), I))
to_indices(A, I::Tuple{Any}) = (@inline; to_indices(A, (eachindex(IndexLinear(), A),), I))
# In simple cases, we know that we don't need to use axes(A), optimize those.
# Having this here avoids invalidations from multidimensional.jl: to_indices(A, I::Tuple{Vararg{Union{Integer, CartesianIndex}}})
to_indices(A, I::Tuple{}) = ()
to_indices(A, I::Tuple{Vararg{Int}}) = I
to_indices(A, I::Tuple{Vararg{Integer}}) = (@inline; to_indices(A, (), I))
to_indices(A, inds, ::Tuple{}) = ()
function to_indices(A, inds, I::Tuple{Any, Vararg{Any}})
    @inline
    head = _to_indices1(A, inds, I[1])
    rest = to_indices(A, _cutdim(inds, I[1]), tail(I))
    (head..., rest...)
end

_to_indices1(A, inds, I1) = (to_index(A, I1),)
_cutdim(inds, I1) = safe_tail(inds)

"""
    Slice(indices)

Represent an AbstractUnitRange of indices as a vector of the indices themselves,
with special handling to signal they represent a complete slice of a dimension (:).

Upon calling `to_indices`, Colons are converted to Slice objects to represent
the indices over which the Colon spans. Slice objects are themselves unit
ranges with the same indices as those they wrap. This means that indexing into
Slice objects with an integer always returns that exact integer, and they
iterate over all the wrapped indices, even supporting offset indices.
"""
struct Slice{T<:AbstractUnitRange} <: AbstractUnitRange{Int}
    indices::T
end
Slice(S::Slice) = S
Slice{T}(S::Slice) where {T<:AbstractUnitRange} = Slice{T}(T(S.indices))

axes(S::Slice) = (IdentityUnitRange(S.indices),)
axes1(S::Slice) = IdentityUnitRange(S.indices)
axes(S::Slice{<:OneTo}) = (S.indices,)
axes1(S::Slice{<:OneTo}) = S.indices

first(S::Slice) = first(S.indices)
last(S::Slice) = last(S.indices)
size(S::Slice) = (length(S.indices),)
length(S::Slice) = length(S.indices)
getindex(S::Slice, i::Int) = (@inline; @boundscheck checkbounds(S, i); i)
getindex(S::Slice, i::AbstractUnitRange{<:Integer}) = (@inline; @boundscheck checkbounds(S, i); i)
getindex(S::Slice, i::StepRange{<:Integer}) = (@inline; @boundscheck checkbounds(S, i); i)
show(io::IO, r::Slice) = print(io, "Base.Slice(", r.indices, ")")
iterate(S::Slice, s...) = iterate(S.indices, s...)

"""
    IdentityUnitRange(range::AbstractUnitRange)

Represent an AbstractUnitRange `range` as an offset vector such that `range[i] == i`.

`IdentityUnitRange`s are frequently used as axes for offset arrays.
"""
struct IdentityUnitRange{T<:AbstractUnitRange} <: AbstractUnitRange{Int}
    indices::T
end
IdentityUnitRange(S::IdentityUnitRange) = S
IdentityUnitRange{T}(S::IdentityUnitRange) where {T<:AbstractUnitRange} = IdentityUnitRange{T}(T(S.indices))

# IdentityUnitRanges are offset and thus have offset axes, so they are their own axes
axes(S::IdentityUnitRange) = (S,)
axes1(S::IdentityUnitRange) = S
axes(S::IdentityUnitRange{<:OneTo}) = (S.indices,)
axes1(S::IdentityUnitRange{<:OneTo}) = S.indices

first(S::IdentityUnitRange) = first(S.indices)
last(S::IdentityUnitRange) = last(S.indices)
size(S::IdentityUnitRange) = (length(S.indices),)
length(S::IdentityUnitRange) = length(S.indices)
getindex(S::IdentityUnitRange, i::Int) = (@inline; @boundscheck checkbounds(S, i); i)
getindex(S::IdentityUnitRange, i::AbstractUnitRange{<:Integer}) = (@inline; @boundscheck checkbounds(S, i); i)
getindex(S::IdentityUnitRange, i::StepRange{<:Integer}) = (@inline; @boundscheck checkbounds(S, i); i)
show(io::IO, r::IdentityUnitRange) = print(io, "Base.IdentityUnitRange(", r.indices, ")")
iterate(S::IdentityUnitRange, s...) = iterate(S.indices, s...)

# For OneTo, the values and indices of the values are identical, so this may be defined in Base.
# In general such an indexing operation would produce offset ranges
getindex(S::OneTo, I::IdentityUnitRange{<:AbstractUnitRange{<:Integer}}) = (@inline; @boundscheck checkbounds(S, I); I)

"""
    LinearIndices(A::AbstractArray)

Return a `LinearIndices` array with the same shape and [`axes`](@ref) as `A`,
holding the linear index of each entry in `A`. Indexing this array with
cartesian indices allows mapping them to linear indices.

For arrays with conventional indexing (indices start at 1), or any multidimensional
array, linear indices range from 1 to `length(A)`. However, for `AbstractVector`s
linear indices are `axes(A, 1)`, and therefore do not start at 1 for vectors with
unconventional indexing.

Calling this function is the "safe" way to write algorithms that
exploit linear indexing.

# Examples
```jldoctest
julia> A = fill(1, (5,6,7));

julia> b = LinearIndices(A);

julia> extrema(b)
(1, 210)
```

    LinearIndices(inds::CartesianIndices) -> R
    LinearIndices(sz::Dims) -> R
    LinearIndices((istart:istop, jstart:jstop, ...)) -> R

Return a `LinearIndices` array with the specified shape or [`axes`](@ref).

# Example

The main purpose of this constructor is intuitive conversion
from cartesian to linear indexing:

```jldoctest
julia> linear = LinearIndices((1:3, 1:2))
3×2 LinearIndices{2, Tuple{UnitRange{Int64}, UnitRange{Int64}}}:
 1  4
 2  5
 3  6

julia> linear[1,2]
4
```
"""
struct LinearIndices{N,R<:NTuple{N,AbstractUnitRange{Int}}} <: AbstractArray{Int,N}
    indices::R
end
convert(::Type{LinearIndices{N,R}}, inds::LinearIndices{N}) where {N,R<:NTuple{N,AbstractUnitRange{Int}}} =
    LinearIndices{N,R}(convert(R, inds.indices))::LinearIndices{N,R}

LinearIndices(::Tuple{}) = LinearIndices{0,typeof(())}(())
LinearIndices(inds::NTuple{N,AbstractUnitRange{<:Integer}}) where {N} =
    LinearIndices(map(r->convert(AbstractUnitRange{Int}, r), inds))
LinearIndices(inds::NTuple{N,Union{<:Integer,AbstractUnitRange{<:Integer}}}) where {N} =
    LinearIndices(map(_convert2ind, inds))
LinearIndices(A::Union{AbstractArray,SimpleVector}) = LinearIndices(axes(A))

_convert2ind(i::Integer) = Base.OneTo(i)
_convert2ind(ind::AbstractUnitRange) = first(ind):last(ind)

function indices_promote_type(::Type{Tuple{R1,Vararg{R1,N}}}, ::Type{Tuple{R2,Vararg{R2,N}}}) where {R1,R2,N}
    R = promote_type(R1, R2)
    return Tuple{R, Vararg{R, N}}
end

promote_rule(::Type{LinearIndices{N,R1}}, ::Type{LinearIndices{N,R2}}) where {N,R1,R2} =
    LinearIndices{N,indices_promote_type(R1,R2)}
promote_rule(a::Type{Slice{T1}}, b::Type{Slice{T2}}) where {T1,T2} =
    el_same(promote_type(T1, T2), a, b)
promote_rule(a::Type{IdentityUnitRange{T1}}, b::Type{IdentityUnitRange{T2}}) where {T1,T2} =
    el_same(promote_type(T1, T2), a, b)

# AbstractArray implementation
IndexStyle(::Type{<:LinearIndices}) = IndexLinear()
axes(iter::LinearIndices) = map(axes1, iter.indices)
size(iter::LinearIndices) = map(length, iter.indices)
isassigned(iter::LinearIndices, i::Int) = checkbounds(Bool, iter, i)
function getindex(iter::LinearIndices, i::Int)
    @inline
    @boundscheck checkbounds(iter, i)
    i
end
function getindex(iter::LinearIndices, i::AbstractRange{<:Integer})
    @inline
    @boundscheck checkbounds(iter, i)
    @inbounds isa(iter, LinearIndices{1}) ? iter.indices[1][i] : (first(iter):last(iter))[i]
end
# More efficient iteration — predominantly for non-vector LinearIndices
# but one-dimensional LinearIndices must be special-cased to support OffsetArrays
iterate(iter::LinearIndices{1}, s...) = iterate(axes1(iter.indices[1]), s...)
iterate(iter::LinearIndices, i=1) = i > length(iter) ? nothing : (i, i+1)

# Needed since firstindex and lastindex are defined in terms of LinearIndices
first(iter::LinearIndices) = 1
first(iter::LinearIndices{1}) = (@inline; first(axes1(iter.indices[1])))
last(iter::LinearIndices) = (@inline; length(iter))
last(iter::LinearIndices{1}) = (@inline; last(axes1(iter.indices[1])))
L   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/array.jl�     # This file is a part of Julia. License is MIT: https://julialang.org/license

## array.jl: Dense arrays

"""
    DimensionMismatch([msg])

The objects called do not have matching dimensionality. Optional argument `msg` is a
descriptive error string.
"""
struct DimensionMismatch <: Exception
    msg::AbstractString
end
DimensionMismatch() = DimensionMismatch("")

## Type aliases for convenience ##
"""
    AbstractVector{T}

Supertype for one-dimensional arrays (or array-like types) with
elements of type `T`. Alias for [`AbstractArray{T,1}`](@ref).
"""
const AbstractVector{T} = AbstractArray{T,1}

"""
    AbstractMatrix{T}

Supertype for two-dimensional arrays (or array-like types) with
elements of type `T`. Alias for [`AbstractArray{T,2}`](@ref).
"""
const AbstractMatrix{T} = AbstractArray{T,2}

"""
    AbstractVecOrMat{T}

Union type of [`AbstractVector{T}`](@ref) and [`AbstractMatrix{T}`](@ref).
"""
const AbstractVecOrMat{T} = Union{AbstractVector{T}, AbstractMatrix{T}}
const RangeIndex = Union{<:BitInteger, AbstractRange{<:BitInteger}}
const DimOrInd = Union{Integer, AbstractUnitRange}
const IntOrInd = Union{Int, AbstractUnitRange}
const DimsOrInds{N} = NTuple{N,DimOrInd}
const NeedsShaping = Union{Tuple{Integer,Vararg{Integer}}, Tuple{OneTo,Vararg{OneTo}}}

"""
    Array{T,N} <: AbstractArray{T,N}

`N`-dimensional dense array with elements of type `T`.
"""
Array

"""
    Vector{T} <: AbstractVector{T}

One-dimensional dense array with elements of type `T`, often used to represent
a mathematical vector. Alias for [`Array{T,1}`](@ref).

See also [`empty`](@ref), [`similar`](@ref) and [`zero`](@ref) for creating vectors.
"""
const Vector{T} = Array{T,1}

"""
    Matrix{T} <: AbstractMatrix{T}

Two-dimensional dense array with elements of type `T`, often used to represent
a mathematical matrix. Alias for [`Array{T,2}`](@ref).

See also [`fill`](@ref), [`zeros`](@ref), [`undef`](@ref) and [`similar`](@ref)
for creating matrices.
"""
const Matrix{T} = Array{T,2}

"""
    VecOrMat{T}

Union type of [`Vector{T}`](@ref) and [`Matrix{T}`](@ref) which allows functions to accept either a Matrix or a Vector.

# Examples
```jldoctest
julia> Vector{Float64} <: VecOrMat{Float64}
true

julia> Matrix{Float64} <: VecOrMat{Float64}
true

julia> Array{Float64, 3} <: VecOrMat{Float64}
false
```
"""
const VecOrMat{T} = Union{Vector{T}, Matrix{T}}

"""
    DenseArray{T, N} <: AbstractArray{T,N}

`N`-dimensional dense array with elements of type `T`.
The elements of a dense array are stored contiguously in memory.
"""
DenseArray

"""
    DenseVector{T}

One-dimensional [`DenseArray`](@ref) with elements of type `T`. Alias for `DenseArray{T,1}`.
"""
const DenseVector{T} = DenseArray{T,1}

"""
    DenseMatrix{T}

Two-dimensional [`DenseArray`](@ref) with elements of type `T`. Alias for `DenseArray{T,2}`.
"""
const DenseMatrix{T} = DenseArray{T,2}

"""
    DenseVecOrMat{T}

Union type of [`DenseVector{T}`](@ref) and [`DenseMatrix{T}`](@ref).
"""
const DenseVecOrMat{T} = Union{DenseVector{T}, DenseMatrix{T}}

## Basic functions ##

using Core: arraysize, arrayset, const_arrayref

"""
    @_safeindex

This internal macro converts:
- `getindex(xs::Tuple, )` -> `__inbounds_getindex(args...)`
- `setindex!(xs::Vector, args...)` -> `__inbounds_setindex!(xs, args...)`
to tell the compiler that indexing operations within the applied expression are always
inbounds and do not need to taint `:consistent` and `:nothrow`.
"""
macro _safeindex(ex)
    return esc(_safeindex(__module__, ex))
end
function _safeindex(__module__, ex)
    isa(ex, Expr) || return ex
    if ex.head === :(=)
        lhs = arrayref(true, ex.args, 1)
        if isa(lhs, Expr) && lhs.head === :ref # xs[i] = x
            rhs = arrayref(true, ex.args, 2)
            xs = arrayref(true, lhs.args, 1)
            args = Vector{Any}(undef, length(lhs.args)-1)
            for i = 2:length(lhs.args)
                arrayset(true, args, _safeindex(__module__, arrayref(true, lhs.args, i)), i-1)
            end
            return Expr(:call, GlobalRef(__module__, :__inbounds_setindex!), xs, _safeindex(__module__, rhs), args...)
        end
    elseif ex.head === :ref # xs[i]
        return Expr(:call, GlobalRef(__module__, :__inbounds_getindex), ex.args...)
    end
    args = Vector{Any}(undef, length(ex.args))
    for i = 1:length(ex.args)
        arrayset(true, args, _safeindex(__module__, arrayref(true, ex.args, i)), i)
    end
    return Expr(ex.head, args...)
end

vect() = Vector{Any}()
function vect(X::T...) where T
    @_terminates_locally_meta
    vec = Vector{T}(undef, length(X))
    @_safeindex for i = 1:length(X)
        vec[i] = X[i]
    end
    return vec
end

"""
    vect(X...)

Create a [`Vector`](@ref) with element type computed from the `promote_typeof` of the argument,
containing the argument list.

# Examples
```jldoctest
julia> a = Base.vect(UInt8(1), 2.5, 1//2)
3-element Vector{Float64}:
 1.0
 2.5
 0.5
```
"""
function vect(X...)
    T = promote_typeof(X...)
    return T[X...]
end

size(a::Array, d::Integer) = arraysize(a, d isa Int ? d : convert(Int, d))
size(a::Vector) = (arraysize(a,1),)
size(a::Matrix) = (arraysize(a,1), arraysize(a,2))
size(a::Array{<:Any,N}) where {N} = (@inline; ntuple(M -> size(a, M), Val(N))::Dims)

asize_from(a::Array, n) = n > ndims(a) ? () : (arraysize(a,n), asize_from(a, n+1)...)

allocatedinline(@nospecialize T::Type) = (@_total_meta; ccall(:jl_stored_inline, Cint, (Any,), T) != Cint(0))

"""
    Base.isbitsunion(::Type{T})

Return whether a type is an "is-bits" Union type, meaning each type included in a Union is [`isbitstype`](@ref).

# Examples
```jldoctest
julia> Base.isbitsunion(Union{Float64, UInt8})
true

julia> Base.isbitsunion(Union{Float64, String})
false
```
"""
isbitsunion(u::Union) = allocatedinline(u)
isbitsunion(x) = false

function _unsetindex!(A::Array{T}, i::Int) where {T}
    @inline
    @boundscheck checkbounds(A, i)
    t = @_gc_preserve_begin A
    p = Ptr{Ptr{Cvoid}}(pointer(A, i))
    if !allocatedinline(T)
        Intrinsics.atomic_pointerset(p, C_NULL, :monotonic)
    elseif T isa DataType
        if !datatype_pointerfree(T)
            for j = 1:Core.sizeof(Ptr{Cvoid}):Core.sizeof(T)
                Intrinsics.atomic_pointerset(p + j - 1, C_NULL, :monotonic)
            end
        end
    end
    @_gc_preserve_end t
    return A
end


"""
    Base.bitsunionsize(U::Union) -> Int

For a `Union` of [`isbitstype`](@ref) types, return the size of the largest type; assumes `Base.isbitsunion(U) == true`.

# Examples
```jldoctest
julia> Base.bitsunionsize(Union{Float64, UInt8})
8

julia> Base.bitsunionsize(Union{Float64, UInt8, Int128})
16
```
"""
function bitsunionsize(u::Union)
    isinline, sz, _ = uniontype_layout(u)
    @assert isinline
    return sz
end

elsize(@nospecialize _::Type{A}) where {T,A<:Array{T}} = aligned_sizeof(T)
function elsize(::Type{Ptr{T}}) where T
    # this only must return something valid for values which satisfy is_valid_intrinsic_elptr(T),
    # which includes Any and most concrete datatypes
    T === Any && return sizeof(Ptr{Any})
    T isa DataType || sizeof(Any) # throws
    return LLT_ALIGN(Core.sizeof(T), datatype_alignment(T))
end
elsize(::Type{Union{}}, slurp...) = 0
sizeof(a::Array) = Core.sizeof(a)

function isassigned(a::Array, i::Int...)
    @inline
    @boundscheck checkbounds(Bool, a, i...) || return false
    ii = (_sub2ind(size(a), i...) % UInt) - 1
    ccall(:jl_array_isassigned, Cint, (Any, UInt), a, ii) == 1
end

## copy ##

"""
    unsafe_copyto!(dest::Ptr{T}, src::Ptr{T}, N)

Copy `N` elements from a source pointer to a destination, with no checking. The size of an
element is determined by the type of the pointers.

The `unsafe` prefix on this function indicates that no validation is performed on the
pointers `dest` and `src` to ensure that they are valid. Incorrect usage may corrupt or
segfault your program, in the same manner as C.
"""
function unsafe_copyto!(dest::Ptr{T}, src::Ptr{T}, n) where T
    # Do not use this to copy data between pointer arrays.
    # It can't be made safe no matter how carefully you checked.
    memmove(dest, src, n * aligned_sizeof(T))
    return dest
end


function _unsafe_copyto!(dest, doffs, src, soffs, n)
    destp = pointer(dest, doffs)
    srcp = pointer(src, soffs)
    @inbounds if destp < srcp || destp > srcp + n
        for i = 1:n
            if isassigned(src, soffs + i - 1)
                dest[doffs + i - 1] = src[soffs + i - 1]
            else
                _unsetindex!(dest, doffs + i - 1)
            end
        end
    else
        for i = n:-1:1
            if isassigned(src, soffs + i - 1)
                dest[doffs + i - 1] = src[soffs + i - 1]
            else
                _unsetindex!(dest, doffs + i - 1)
            end
        end
    end
    return dest
end

"""
    unsafe_copyto!(dest::Array, do, src::Array, so, N)

Copy `N` elements from a source array to a destination, starting at the linear index `so` in the
source and `do` in the destination (1-indexed).

The `unsafe` prefix on this function indicates that no validation is performed to ensure
that N is inbounds on either array. Incorrect usage may corrupt or segfault your program, in
the same manner as C.

$(_DOCS_ALIASING_WARNING)
"""
function unsafe_copyto!(dest::Array{T}, doffs, src::Array{T}, soffs, n) where T
    t1 = @_gc_preserve_begin dest
    t2 = @_gc_preserve_begin src
    destp = pointer(dest, doffs)
    srcp = pointer(src, soffs)
    if !allocatedinline(T)
        ccall(:jl_array_ptr_copy, Cvoid, (Any, Ptr{Cvoid}, Any, Ptr{Cvoid}, Int),
              dest, destp, src, srcp, n)
    elseif isbitstype(T)
        memmove(destp, srcp, n * aligned_sizeof(T))
    elseif isbitsunion(T)
        memmove(destp, srcp, n * aligned_sizeof(T))
        # copy selector bytes
        memmove(
              ccall(:jl_array_typetagdata, Ptr{UInt8}, (Any,), dest) + doffs - 1,
              ccall(:jl_array_typetagdata, Ptr{UInt8}, (Any,), src) + soffs - 1,
              n)
    else
        _unsafe_copyto!(dest, doffs, src, soffs, n)
    end
    @_gc_preserve_end t2
    @_gc_preserve_end t1
    return dest
end

unsafe_copyto!(dest::Array, doffs, src::Array, soffs, n) =
    _unsafe_copyto!(dest, doffs, src, soffs, n)

"""
    copyto!(dest, do, src, so, N)

Copy `N` elements from collection `src` starting at the linear index `so`, to array `dest` starting at
the index `do`. Return `dest`.
"""
function copyto!(dest::Array, doffs::Integer, src::Array, soffs::Integer, n::Integer)
    return _copyto_impl!(dest, doffs, src, soffs, n)
end

# this is only needed to avoid possible ambiguities with methods added in some packages
function copyto!(dest::Array{T}, doffs::Integer, src::Array{T}, soffs::Integer, n::Integer) where T
    return _copyto_impl!(dest, doffs, src, soffs, n)
end

function _copyto_impl!(dest::Array, doffs::Integer, src::Array, soffs::Integer, n::Integer)
    n == 0 && return dest
    n > 0 || _throw_argerror("Number of elements to copy must be nonnegative.")
    @boundscheck checkbounds(dest, doffs:doffs+n-1)
    @boundscheck checkbounds(src, soffs:soffs+n-1)
    unsafe_copyto!(dest, doffs, src, soffs, n)
    return dest
end

# Outlining this because otherwise a catastrophic inference slowdown
# occurs, see discussion in #27874.
# It is also mitigated by using a constant string.
_throw_argerror(s) = (@noinline; throw(ArgumentError(s)))

copyto!(dest::Array, src::Array) = copyto!(dest, 1, src, 1, length(src))

# also to avoid ambiguities in packages
copyto!(dest::Array{T}, src::Array{T}) where {T} = copyto!(dest, 1, src, 1, length(src))

# N.B: The generic definition in multidimensional.jl covers, this, this is just here
# for bootstrapping purposes.
function fill!(dest::Array{T}, x) where T
    xT = x isa T ? x : convert(T, x)::T
    for i in eachindex(dest)
        @inbounds dest[i] = xT
    end
    return dest
end

"""
    copy(x)

Create a shallow copy of `x`: the outer structure is copied, but not all internal values.
For example, copying an array produces a new array with identically-same elements as the
original.

See also [`copy!`](@ref Base.copy!), [`copyto!`](@ref), [`deepcopy`](@ref).
"""
copy

copy(a::T) where {T<:Array} = ccall(:jl_array_copy, Ref{T}, (Any,), a)

## Constructors ##

similar(a::Array{T,1}) where {T}                    = Vector{T}(undef, size(a,1))
similar(a::Array{T,2}) where {T}                    = Matrix{T}(undef, size(a,1), size(a,2))
similar(a::Array{T,1}, S::Type) where {T}           = Vector{S}(undef, size(a,1))
similar(a::Array{T,2}, S::Type) where {T}           = Matrix{S}(undef, size(a,1), size(a,2))
similar(a::Array{T}, m::Int) where {T}              = Vector{T}(undef, m)
similar(a::Array, T::Type, dims::Dims{N}) where {N} = Array{T,N}(undef, dims)
similar(a::Array{T}, dims::Dims{N}) where {T,N}     = Array{T,N}(undef, dims)

# T[x...] constructs Array{T,1}
"""
    getindex(type[, elements...])

Construct a 1-d array of the specified type. This is usually called with the syntax
`Type[]`. Element values can be specified using `Type[a,b,c,...]`.

# Examples
```jldoctest
julia> Int8[1, 2, 3]
3-element Vector{Int8}:
 1
 2
 3

julia> getindex(Int8, 1, 2, 3)
3-element Vector{Int8}:
 1
 2
 3
```
"""
function getindex(::Type{T}, vals...) where T
    @inline
    @_effect_free_terminates_locally_meta
    a = Vector{T}(undef, length(vals))
    if vals isa NTuple
        @_safeindex for i in 1:length(vals)
            a[i] = vals[i]
        end
    else
        # use afoldl to avoid type instability inside loop
        afoldl(1, vals...) do i, v
            @inbounds a[i] = v
            return i + 1
        end
    end
    return a
end

function getindex(::Type{Any}, @nospecialize vals...)
    @_effect_free_terminates_locally_meta
    a = Vector{Any}(undef, length(vals))
    @_safeindex for i = 1:length(vals)
        a[i] = vals[i]
    end
    return a
end
getindex(::Type{Any}) = Vector{Any}()

function fill!(a::Union{Array{UInt8}, Array{Int8}}, x::Integer)
    t = @_gc_preserve_begin a
    p = unsafe_convert(Ptr{Cvoid}, a)
    memset(p, x isa eltype(a) ? x : convert(eltype(a), x), length(a))
    @_gc_preserve_end t
    return a
end

to_dim(d::Integer) = d
to_dim(d::OneTo) = last(d)

"""
    fill(value, dims::Tuple)
    fill(value, dims...)

Create an array of size `dims` with every location set to `value`.

For example, `fill(1.0, (5,5))` returns a 5×5 array of floats,
with `1.0` in every location of the array.

The dimension lengths `dims` may be specified as either a tuple or a sequence of arguments.
An `N`-length tuple or `N` arguments following the `value` specify an `N`-dimensional
array. Thus, a common idiom for creating a zero-dimensional array with its only location
set to `x` is `fill(x)`.

Every location of the returned array is set to (and is thus [`===`](@ref) to)
the `value` that was passed; this means that if the `value` is itself modified,
all elements of the `fill`ed array will reflect that modification because they're
_still_ that very `value`. This is of no concern with `fill(1.0, (5,5))` as the
`value` `1.0` is immutable and cannot itself be modified, but can be unexpected
with mutable values like — most commonly — arrays.  For example, `fill([], 3)`
places _the very same_ empty array in all three locations of the returned vector:

```jldoctest
julia> v = fill([], 3)
3-element Vector{Vector{Any}}:
 []
 []
 []

julia> v[1] === v[2] === v[3]
true

julia> value = v[1]
Any[]

julia> push!(value, 867_5309)
1-element Vector{Any}:
 8675309

julia> v
3-element Vector{Vector{Any}}:
 [8675309]
 [8675309]
 [8675309]
```

To create an array of many independent inner arrays, use a [comprehension](@ref man-comprehensions) instead.
This creates a new and distinct array on each iteration of the loop:

```jldoctest
julia> v2 = [[] for _ in 1:3]
3-element Vector{Vector{Any}}:
 []
 []
 []

julia> v2[1] === v2[2] === v2[3]
false

julia> push!(v2[1], 8675309)
1-element Vector{Any}:
 8675309

julia> v2
3-element Vector{Vector{Any}}:
 [8675309]
 []
 []
```

See also: [`fill!`](@ref), [`zeros`](@ref), [`ones`](@ref), [`similar`](@ref).

# Examples
```jldoctest
julia> fill(1.0, (2,3))
2×3 Matrix{Float64}:
 1.0  1.0  1.0
 1.0  1.0  1.0

julia> fill(42)
0-dimensional Array{Int64, 0}:
42

julia> A = fill(zeros(2), 2) # sets both elements to the same [0.0, 0.0] vector
2-element Vector{Vector{Float64}}:
 [0.0, 0.0]
 [0.0, 0.0]

julia> A[1][1] = 42; # modifies the filled value to be [42.0, 0.0]

julia> A # both A[1] and A[2] are the very same vector
2-element Vector{Vector{Float64}}:
 [42.0, 0.0]
 [42.0, 0.0]
```
"""
function fill end

fill(v, dims::DimOrInd...) = fill(v, dims)
fill(v, dims::NTuple{N, Union{Integer, OneTo}}) where {N} = fill(v, map(to_dim, dims))
fill(v, dims::NTuple{N, Integer}) where {N} = (a=Array{typeof(v),N}(undef, dims); fill!(a, v); a)
fill(v, dims::Tuple{}) = (a=Array{typeof(v),0}(undef, dims); fill!(a, v); a)

"""
    zeros([T=Float64,] dims::Tuple)
    zeros([T=Float64,] dims...)

Create an `Array`, with element type `T`, of all zeros with size specified by `dims`.
See also [`fill`](@ref), [`ones`](@ref), [`zero`](@ref).

# Examples
```jldoctest
julia> zeros(1)
1-element Vector{Float64}:
 0.0

julia> zeros(Int8, 2, 3)
2×3 Matrix{Int8}:
 0  0  0
 0  0  0
```
"""
function zeros end

"""
    ones([T=Float64,] dims::Tuple)
    ones([T=Float64,] dims...)

Create an `Array`, with element type `T`, of all ones with size specified by `dims`.
See also [`fill`](@ref), [`zeros`](@ref).

# Examples
```jldoctest
julia> ones(1,2)
1×2 Matrix{Float64}:
 1.0  1.0

julia> ones(ComplexF64, 2, 3)
2×3 Matrix{ComplexF64}:
 1.0+0.0im  1.0+0.0im  1.0+0.0im
 1.0+0.0im  1.0+0.0im  1.0+0.0im
```
"""
function ones end

for (fname, felt) in ((:zeros, :zero), (:ones, :one))
    @eval begin
        $fname(dims::DimOrInd...) = $fname(dims)
        $fname(::Type{T}, dims::DimOrInd...) where {T} = $fname(T, dims)
        $fname(dims::Tuple{Vararg{DimOrInd}}) = $fname(Float64, dims)
        $fname(::Type{T}, dims::NTuple{N, Union{Integer, OneTo}}) where {T,N} = $fname(T, map(to_dim, dims))
        function $fname(::Type{T}, dims::NTuple{N, Integer}) where {T,N}
            a = Array{T,N}(undef, dims)
            fill!(a, $felt(T))
            return a
        end
        function $fname(::Type{T}, dims::Tuple{}) where {T}
            a = Array{T}(undef)
            fill!(a, $felt(T))
            return a
        end
    end
end

function _one(unit::T, x::AbstractMatrix) where T
    require_one_based_indexing(x)
    m,n = size(x)
    m==n || throw(DimensionMismatch("multiplicative identity defined only for square matrices"))
    # Matrix{T}(I, m, m)
    I = zeros(T, m, m)
    for i in 1:m
        I[i,i] = unit
    end
    I
end

one(x::AbstractMatrix{T}) where {T} = _one(one(T), x)
oneunit(x::AbstractMatrix{T}) where {T} = _one(oneunit(T), x)

## Conversions ##

convert(::Type{T}, a::AbstractArray) where {T<:Array} = a isa T ? a : T(a)::T

promote_rule(a::Type{Array{T,n}}, b::Type{Array{S,n}}) where {T,n,S} = el_same(promote_type(T,S), a, b)

## Constructors ##

if nameof(@__MODULE__) === :Base  # avoid method overwrite
# constructors should make copies
Array{T,N}(x::AbstractArray{S,N})         where {T,N,S} = copyto_axcheck!(Array{T,N}(undef, size(x)), x)
AbstractArray{T,N}(A::AbstractArray{S,N}) where {T,N,S} = copyto_axcheck!(similar(A,T), A)
end

## copying iterators to containers

"""
    collect(element_type, collection)

Return an `Array` with the given element type of all items in a collection or iterable.
The result has the same shape and number of dimensions as `collection`.

# Examples
```jldoctest
julia> collect(Float64, 1:2:5)
3-element Vector{Float64}:
 1.0
 3.0
 5.0
```
"""
collect(::Type{T}, itr) where {T} = _collect(T, itr, IteratorSize(itr))

_collect(::Type{T}, itr, isz::Union{HasLength,HasShape}) where {T} =
    copyto!(_array_for(T, isz, _similar_shape(itr, isz)), itr)
function _collect(::Type{T}, itr, isz::SizeUnknown) where T
    a = Vector{T}()
    for x in itr
        push!(a, x)
    end
    return a
end

# make a collection similar to `c` and appropriate for collecting `itr`
_similar_for(c, ::Type{T}, itr, isz, shp) where {T} = similar(c, T)

_similar_shape(itr, ::SizeUnknown) = nothing
_similar_shape(itr, ::HasLength) = length(itr)::Integer
_similar_shape(itr, ::HasShape) = axes(itr)

_similar_for(c::AbstractArray, ::Type{T}, itr, ::SizeUnknown, ::Nothing) where {T} =
    similar(c, T, 0)
_similar_for(c::AbstractArray, ::Type{T}, itr, ::HasLength, len::Integer) where {T} =
    similar(c, T, len)
_similar_for(c::AbstractArray, ::Type{T}, itr, ::HasShape, axs) where {T} =
    similar(c, T, axs)

# make a collection appropriate for collecting `itr::Generator`
_array_for(::Type{T}, ::SizeUnknown, ::Nothing) where {T} = Vector{T}(undef, 0)
_array_for(::Type{T}, ::HasLength, len::Integer) where {T} = Vector{T}(undef, Int(len))
_array_for(::Type{T}, ::HasShape{N}, axs) where {T,N} = similar(Array{T,N}, axs)

# used by syntax lowering for simple typed comprehensions
_array_for(::Type{T}, itr, isz) where {T} = _array_for(T, isz, _similar_shape(itr, isz))


"""
    collect(collection)

Return an `Array` of all items in a collection or iterator. For dictionaries, returns
`Vector{Pair{KeyType, ValType}}`. If the argument is array-like or is an iterator with the
[`HasShape`](@ref IteratorSize) trait, the result will have the same shape
and number of dimensions as the argument.

Used by comprehensions to turn a generator into an `Array`.

# Examples
```jldoctest
julia> collect(1:2:13)
7-element Vector{Int64}:
  1
  3
  5
  7
  9
 11
 13

julia> [x^2 for x in 1:8 if isodd(x)]
4-element Vector{Int64}:
  1
  9
 25
 49
```
"""
collect(itr) = _collect(1:1 #= Array =#, itr, IteratorEltype(itr), IteratorSize(itr))

collect(A::AbstractArray) = _collect_indices(axes(A), A)

collect_similar(cont, itr) = _collect(cont, itr, IteratorEltype(itr), IteratorSize(itr))

_collect(cont, itr, ::HasEltype, isz::Union{HasLength,HasShape}) =
    copyto!(_similar_for(cont, eltype(itr), itr, isz, _similar_shape(itr, isz)), itr)

function _collect(cont, itr, ::HasEltype, isz::SizeUnknown)
    a = _similar_for(cont, eltype(itr), itr, isz, nothing)
    for x in itr
        push!(a,x)
    end
    return a
end

_collect_indices(::Tuple{}, A) = copyto!(Array{eltype(A),0}(undef), A)
_collect_indices(indsA::Tuple{Vararg{OneTo}}, A) =
    copyto!(Array{eltype(A)}(undef, length.(indsA)), A)
function _collect_indices(indsA, A)
    B = Array{eltype(A)}(undef, length.(indsA))
    copyto!(B, CartesianIndices(axes(B)), A, CartesianIndices(indsA))
end

# NOTE: this function is not meant to be called, only inferred, for the
# purpose of bounding the types of values generated by an iterator.
function _iterator_upper_bound(itr)
    x = iterate(itr)
    while x !== nothing
        val = getfield(x, 1)
        if inferencebarrier(nothing)
            return val
        end
        x = iterate(itr, getfield(x, 2))
    end
    throw(nothing)
end

# define this as a macro so that the call to Core.Compiler
# gets inlined into the caller before recursion detection
# gets a chance to see it, so that recursive calls to the caller
# don't trigger the inference limiter
if isdefined(Core, :Compiler)
    macro default_eltype(itr)
        I = esc(itr)
        return quote
            if $I isa Generator && ($I).f isa Type
                T = ($I).f
            else
                T = Core.Compiler.return_type(_iterator_upper_bound, Tuple{typeof($I)})
            end
            promote_typejoin_union(T)
        end
    end
else
    macro default_eltype(itr)
        I = esc(itr)
        return quote
            if $I isa Generator && ($I).f isa Type
                promote_typejoin_union($I.f)
            else
                Any
            end
        end
    end
end

function collect(itr::Generator)
    isz = IteratorSize(itr.iter)
    et = @default_eltype(itr)
    if isa(isz, SizeUnknown)
        return grow_to!(Vector{et}(), itr)
    else
        shp = _similar_shape(itr, isz)
        y = iterate(itr)
        if y === nothing
            return _array_for(et, isz, shp)
        end
        v1, st = y
        dest = _array_for(typeof(v1), isz, shp)
        # The typeassert gives inference a helping hand on the element type and dimensionality
        # (work-around for #28382)
        et′ = et <: Type ? Type : et
        RT = dest isa AbstractArray ? AbstractArray{<:et′, ndims(dest)} : Any
        collect_to_with_first!(dest, v1, itr, st)::RT
    end
end

_collect(c, itr, ::EltypeUnknown, isz::SizeUnknown) =
    grow_to!(_similar_for(c, @default_eltype(itr), itr, isz, nothing), itr)

function _collect(c, itr, ::EltypeUnknown, isz::Union{HasLength,HasShape})
    et = @default_eltype(itr)
    shp = _similar_shape(itr, isz)
    y = iterate(itr)
    if y === nothing
        return _similar_for(c, et, itr, isz, shp)
    end
    v1, st = y
    dest = _similar_for(c, typeof(v1), itr, isz, shp)
    # The typeassert gives inference a helping hand on the element type and dimensionality
    # (work-around for #28382)
    et′ = et <: Type ? Type : et
    RT = dest isa AbstractArray ? AbstractArray{<:et′, ndims(dest)} : Any
    collect_to_with_first!(dest, v1, itr, st)::RT
end

function collect_to_with_first!(dest::AbstractArray, v1, itr, st)
    i1 = first(LinearIndices(dest))
    dest[i1] = v1
    return collect_to!(dest, itr, i1+1, st)
end

function collect_to_with_first!(dest, v1, itr, st)
    push!(dest, v1)
    return grow_to!(dest, itr, st)
end

function setindex_widen_up_to(dest::AbstractArray{T}, el, i) where T
    @inline
    new = similar(dest, promote_typejoin(T, typeof(el)))
    f = first(LinearIndices(dest))
    copyto!(new, first(LinearIndices(new)), dest, f, i-f)
    @inbounds new[i] = el
    return new
end

function collect_to!(dest::AbstractArray{T}, itr, offs, st) where T
    # collect to dest array, checking the type of each result. if a result does not
    # match, widen the result type and re-dispatch.
    i = offs
    while true
        y = iterate(itr, st)
        y === nothing && break
        el, st = y
        if el isa T
            @inbounds dest[i] = el
            i += 1
        else
            new = setindex_widen_up_to(dest, el, i)
            return collect_to!(new, itr, i+1, st)
        end
    end
    return dest
end

function grow_to!(dest, itr)
    y = iterate(itr)
    y === nothing && return dest
    dest2 = empty(dest, typeof(y[1]))
    push!(dest2, y[1])
    grow_to!(dest2, itr, y[2])
end

function push_widen(dest, el)
    @inline
    new = sizehint!(empty(dest, promote_typejoin(eltype(dest), typeof(el))), length(dest))
    if new isa AbstractSet
        # TODO: merge back these two branches when copy! is re-enabled for sets/vectors
        union!(new, dest)
    else
        append!(new, dest)
    end
    push!(new, el)
    return new
end

function grow_to!(dest, itr, st)
    T = eltype(dest)
    y = iterate(itr, st)
    while y !== nothing
        el, st = y
        if el isa T
            push!(dest, el)
        else
            new = push_widen(dest, el)
            return grow_to!(new, itr, st)
        end
        y = iterate(itr, st)
    end
    return dest
end

## Iteration ##

iterate(A::Array, i=1) = (@inline; (i % UInt) - 1 < length(A) ? (@inbounds A[i], i + 1) : nothing)

## Indexing: getindex ##

"""
    getindex(collection, key...)

Retrieve the value(s) stored at the given key or index within a collection. The syntax
`a[i,j,...]` is converted by the compiler to `getindex(a, i, j, ...)`.

See also [`get`](@ref), [`keys`](@ref), [`eachindex`](@ref).

# Examples
```jldoctest
julia> A = Dict("a" => 1, "b" => 2)
Dict{String, Int64} with 2 entries:
  "b" => 2
  "a" => 1

julia> getindex(A, "a")
1
```
"""
function getindex end

# Faster contiguous indexing using copyto! for AbstractUnitRange and Colon
function getindex(A::Array, I::AbstractUnitRange{<:Integer})
    @inline
    @boundscheck checkbounds(A, I)
    lI = length(I)
    X = similar(A, axes(I))
    if lI > 0
        copyto!(X, firstindex(X), A, first(I), lI)
    end
    return X
end

# getindex for carrying out logical indexing for AbstractUnitRange{Bool} as Bool <: Integer
getindex(a::Array, r::AbstractUnitRange{Bool}) = getindex(a, to_index(r))

function getindex(A::Array, c::Colon)
    lI = length(A)
    X = similar(A, lI)
    if lI > 0
        unsafe_copyto!(X, 1, A, 1, lI)
    end
    return X
end

# This is redundant with the abstract fallbacks, but needed for bootstrap
function getindex(A::Array{S}, I::AbstractRange{Int}) where S
    return S[ A[i] for i in I ]
end

## Indexing: setindex! ##

"""
    setindex!(collection, value, key...)

Store the given value at the given key or index within a collection. The syntax `a[i,j,...] =
x` is converted by the compiler to `(setindex!(a, x, i, j, ...); x)`.

# Examples
```jldoctest
julia> a = Dict("a"=>1)
Dict{String, Int64} with 1 entry:
  "a" => 1

julia> setindex!(a, 2, "b")
Dict{String, Int64} with 2 entries:
  "b" => 2
  "a" => 1
```
"""
function setindex! end

@eval setindex!(A::Array{T}, x, i1::Int) where {T} =
    arrayset($(Expr(:boundscheck)), A, x isa T ? x : convert(T,x)::T, i1)
@eval setindex!(A::Array{T}, x, i1::Int, i2::Int, I::Int...) where {T} =
    (@inline; arrayset($(Expr(:boundscheck)), A, x isa T ? x : convert(T,x)::T, i1, i2, I...))

__inbounds_setindex!(A::Array{T}, x, i1::Int) where {T} =
    arrayset(false, A, convert(T,x)::T, i1)
__inbounds_setindex!(A::Array{T}, x, i1::Int, i2::Int, I::Int...) where {T} =
    (@inline; arrayset(false, A, convert(T,x)::T, i1, i2, I...))

# This is redundant with the abstract fallbacks but needed and helpful for bootstrap
function setindex!(A::Array, X::AbstractArray, I::AbstractVector{Int})
    @_propagate_inbounds_meta
    @boundscheck setindex_shape_check(X, length(I))
    require_one_based_indexing(X)
    X′ = unalias(A, X)
    I′ = unalias(A, I)
    count = 1
    for i in I′
        @inbounds x = X′[count]
        A[i] = x
        count += 1
    end
    return A
end

# Faster contiguous setindex! with copyto!
function setindex!(A::Array{T}, X::Array{T}, I::AbstractUnitRange{Int}) where T
    @inline
    @boundscheck checkbounds(A, I)
    lI = length(I)
    @boundscheck setindex_shape_check(X, lI)
    if lI > 0
        unsafe_copyto!(A, first(I), X, 1, lI)
    end
    return A
end
function setindex!(A::Array{T}, X::Array{T}, c::Colon) where T
    @inline
    lI = length(A)
    @boundscheck setindex_shape_check(X, lI)
    if lI > 0
        unsafe_copyto!(A, 1, X, 1, lI)
    end
    return A
end

# efficiently grow an array

_growbeg!(a::Vector, delta::Integer) =
    ccall(:jl_array_grow_beg, Cvoid, (Any, UInt), a, delta)
_growend!(a::Vector, delta::Integer) =
    ccall(:jl_array_grow_end, Cvoid, (Any, UInt), a, delta)
_growat!(a::Vector, i::Integer, delta::Integer) =
    ccall(:jl_array_grow_at, Cvoid, (Any, Int, UInt), a, i - 1, delta)

# efficiently delete part of an array

_deletebeg!(a::Vector, delta::Integer) =
    ccall(:jl_array_del_beg, Cvoid, (Any, UInt), a, delta)
_deleteend!(a::Vector, delta::Integer) =
    ccall(:jl_array_del_end, Cvoid, (Any, UInt), a, delta)
_deleteat!(a::Vector, i::Integer, delta::Integer) =
    ccall(:jl_array_del_at, Cvoid, (Any, Int, UInt), a, i - 1, delta)

## Dequeue functionality ##

"""
    push!(collection, items...) -> collection

Insert one or more `items` in `collection`. If `collection` is an ordered container,
the items are inserted at the end (in the given order).

# Examples
```jldoctest
julia> push!([1, 2, 3], 4, 5, 6)
6-element Vector{Int64}:
 1
 2
 3
 4
 5
 6
```

If `collection` is ordered, use [`append!`](@ref) to add all the elements of another
collection to it. The result of the preceding example is equivalent to `append!([1, 2, 3], [4,
5, 6])`. For `AbstractSet` objects, [`union!`](@ref) can be used instead.

See [`sizehint!`](@ref) for notes about the performance model.

See also [`pushfirst!`](@ref).
"""
function push! end

function push!(a::Vector{T}, item) where T
    # convert first so we don't grow the array if the assignment won't work
    itemT = item isa T ? item : convert(T, item)::T
    _growend!(a, 1)
    @_safeindex a[length(a)] = itemT
    return a
end

# specialize and optimize the single argument case
function push!(a::Vector{Any}, @nospecialize x)
    _growend!(a, 1)
    @_safeindex a[length(a)] = x
    return a
end
function push!(a::Vector{Any}, @nospecialize x...)
    @_terminates_locally_meta
    na = length(a)
    nx = length(x)
    _growend!(a, nx)
    @_safeindex for i = 1:nx
        a[na+i] = x[i]
    end
    return a
end

"""
    append!(collection, collections...) -> collection.

For an ordered container `collection`, add the elements of each `collections`
to the end of it.

!!! compat "Julia 1.6"
    Specifying multiple collections to be appended requires at least Julia 1.6.

# Examples
```jldoctest
julia> append!([1], [2, 3])
3-element Vector{Int64}:
 1
 2
 3

julia> append!([1, 2, 3], [4, 5], [6])
6-element Vector{Int64}:
 1
 2
 3
 4
 5
 6
```

Use [`push!`](@ref) to add individual items to `collection` which are not already
themselves in another collection. The result of the preceding example is equivalent to
`push!([1, 2, 3], 4, 5, 6)`.

See [`sizehint!`](@ref) for notes about the performance model.

See also [`vcat`](@ref) for vectors, [`union!`](@ref) for sets,
and [`prepend!`](@ref) and [`pushfirst!`](@ref) for the opposite order.
"""
function append! end

function append!(a::Vector, items::AbstractVector)
    itemindices = eachindex(items)
    n = length(itemindices)
    _growend!(a, n)
    copyto!(a, length(a)-n+1, items, first(itemindices), n)
    return a
end

append!(a::AbstractVector, iter) = _append!(a, IteratorSize(iter), iter)
push!(a::AbstractVector, iter...) = append!(a, iter)

append!(a::AbstractVector, iter...) = foldl(append!, iter, init=a)

function _append!(a::AbstractVector, ::Union{HasLength,HasShape}, iter)
    @_terminates_locally_meta
    n = length(a)
    i = lastindex(a)
    resize!(a, n+Int(length(iter))::Int)
    for (i, item) in zip(i+1:lastindex(a), iter)
        if isa(a, Vector) # give better effects for builtin vectors
            @_safeindex a[i] = item
        else
            a[i] = item
        end
    end
    a
end
function _append!(a::AbstractVector, ::IteratorSize, iter)
    for item in iter
        push!(a, item)
    end
    a
end

"""
    prepend!(a::Vector, collections...) -> collection

Insert the elements of each `collections` to the beginning of `a`.

When `collections` specifies multiple collections, order is maintained:
elements of `collections[1]` will appear leftmost in `a`, and so on.

!!! compat "Julia 1.6"
    Specifying multiple collections to be prepended requires at least Julia 1.6.

# Examples
```jldoctest
julia> prepend!([3], [1, 2])
3-element Vector{Int64}:
 1
 2
 3

julia> prepend!([6], [1, 2], [3, 4, 5])
6-element Vector{Int64}:
 1
 2
 3
 4
 5
 6
```
"""
function prepend! end

function prepend!(a::Vector, items::AbstractVector)
    itemindices = eachindex(items)
    n = length(itemindices)
    _growbeg!(a, n)
    if a === items
        copyto!(a, 1, items, n+1, n)
    else
        copyto!(a, 1, items, first(itemindices), n)
    end
    return a
end

prepend!(a::Vector, iter) = _prepend!(a, IteratorSize(iter), iter)
pushfirst!(a::Vector, iter...) = prepend!(a, iter)

prepend!(a::AbstractVector, iter...) = foldr((v, a) -> prepend!(a, v), iter, init=a)

function _prepend!(a::Vector, ::Union{HasLength,HasShape}, iter)
    @_terminates_locally_meta
    require_one_based_indexing(a)
    n = length(iter)
    _growbeg!(a, n)
    i = 0
    for item in iter
        @_safeindex a[i += 1] = item
    end
    a
end
function _prepend!(a::Vector, ::IteratorSize, iter)
    n = 0
    for item in iter
        n += 1
        pushfirst!(a, item)
    end
    reverse!(a, 1, n)
    a
end

"""
    resize!(a::Vector, n::Integer) -> Vector

Resize `a` to contain `n` elements. If `n` is smaller than the current collection
length, the first `n` elements will be retained. If `n` is larger, the new elements are not
guaranteed to be initialized.

# Examples
```jldoctest
julia> resize!([6, 5, 4, 3, 2, 1], 3)
3-element Vector{Int64}:
 6
 5
 4

julia> a = resize!([6, 5, 4, 3, 2, 1], 8);

julia> length(a)
8

julia> a[1:6]
6-element Vector{Int64}:
 6
 5
 4
 3
 2
 1
```
"""
function resize!(a::Vector, nl::Integer)
    l = length(a)
    if nl > l
        _growend!(a, nl-l)
    elseif nl != l
        if nl < 0
            _throw_argerror("new length must be ≥ 0")
        end
        _deleteend!(a, l-nl)
    end
    return a
end

"""
    sizehint!(s, n) -> s

Suggest that collection `s` reserve capacity for at least `n` elements. That is, if
you expect that you're going to have to push a lot of values onto `s`, you can avoid
the cost of incremental reallocation by doing it once up front; this can improve
performance.

See also [`resize!`](@ref).

# Notes on the performance model

For types that support `sizehint!`,

1. `push!` and `append!` methods generally may (but are not required to) preallocate extra
   storage. For types implemented in `Base`, they typically do, using a heuristic optimized for
   a general use case.

2. `sizehint!` may control this preallocation. Again, it typically does this for types in
   `Base`.

3. `empty!` is nearly costless (and O(1)) for types that support this kind of preallocation.
"""
function sizehint! end

function sizehint!(a::Vector, sz::Integer)
    ccall(:jl_array_sizehint, Cvoid, (Any, UInt), a, sz)
    a
end

"""
    pop!(collection) -> item

Remove an item in `collection` and return it. If `collection` is an
ordered container, the last item is returned; for unordered containers,
an arbitrary element is returned.

See also: [`popfirst!`](@ref), [`popat!`](@ref), [`delete!`](@ref), [`deleteat!`](@ref), [`splice!`](@ref), and [`push!`](@ref).

# Examples
```jldoctest
julia> A=[1, 2, 3]
3-element Vector{Int64}:
 1
 2
 3

julia> pop!(A)
3

julia> A
2-element Vector{Int64}:
 1
 2

julia> S = Set([1, 2])
Set{Int64} with 2 elements:
  2
  1

julia> pop!(S)
2

julia> S
Set{Int64} with 1 element:
  1

julia> pop!(Dict(1=>2))
1 => 2
```
"""
function pop!(a::Vector)
    if isempty(a)
        _throw_argerror("array must be non-empty")
    end
    item = a[end]
    _deleteend!(a, 1)
    return item
end

"""
    popat!(a::Vector, i::Integer, [default])

Remove the item at the given `i` and return it. Subsequent items
are shifted to fill the resulting gap.
When `i` is not a valid index for `a`, return `default`, or throw an error if
`default` is not specified.

See also: [`pop!`](@ref), [`popfirst!`](@ref), [`deleteat!`](@ref), [`splice!`](@ref).

!!! compat "Julia 1.5"
    This function is available as of Julia 1.5.

# Examples
```jldoctest
julia> a = [4, 3, 2, 1]; popat!(a, 2)
3

julia> a
3-element Vector{Int64}:
 4
 2
 1

julia> popat!(a, 4, missing)
missing

julia> popat!(a, 4)
ERROR: BoundsError: attempt to access 3-element Vector{Int64} at index [4]
[...]
```
"""
function popat!(a::Vector, i::Integer)
    x = a[i]
    _deleteat!(a, i, 1)
    x
end

function popat!(a::Vector, i::Integer, default)
    if 1 <= i <= length(a)
        x = @inbounds a[i]
        _deleteat!(a, i, 1)
        x
    else
        default
    end
end

"""
    pushfirst!(collection, items...) -> collection

Insert one or more `items` at the beginning of `collection`.

This function is called `unshift` in many other programming languages.

# Examples
```jldoctest
julia> pushfirst!([1, 2, 3, 4], 5, 6)
6-element Vector{Int64}:
 5
 6
 1
 2
 3
 4
```
"""
function pushfirst!(a::Vector{T}, item) where T
    item = item isa T ? item : convert(T, item)::T
    _growbeg!(a, 1)
    @_safeindex a[1] = item
    return a
end

# specialize and optimize the single argument case
function pushfirst!(a::Vector{Any}, @nospecialize x)
    _growbeg!(a, 1)
    @_safeindex a[1] = x
    return a
end
function pushfirst!(a::Vector{Any}, @nospecialize x...)
    @_terminates_locally_meta
    na = length(a)
    nx = length(x)
    _growbeg!(a, nx)
    @_safeindex for i = 1:nx
        a[i] = x[i]
    end
    return a
end

"""
    popfirst!(collection) -> item

Remove the first `item` from `collection`.

This function is called `shift` in many other programming languages.

See also: [`pop!`](@ref), [`popat!`](@ref), [`delete!`](@ref).

# Examples
```jldoctest
julia> A = [1, 2, 3, 4, 5, 6]
6-element Vector{Int64}:
 1
 2
 3
 4
 5
 6

julia> popfirst!(A)
1

julia> A
5-element Vector{Int64}:
 2
 3
 4
 5
 6
```
"""
function popfirst!(a::Vector)
    if isempty(a)
        _throw_argerror("array must be non-empty")
    end
    item = a[1]
    _deletebeg!(a, 1)
    return item
end

"""
    insert!(a::Vector, index::Integer, item)

Insert an `item` into `a` at the given `index`. `index` is the index of `item` in
the resulting `a`.

See also: [`push!`](@ref), [`replace`](@ref), [`popat!`](@ref), [`splice!`](@ref).

# Examples
```jldoctest
julia> insert!(Any[1:6;], 3, "here")
7-element Vector{Any}:
 1
 2
  "here"
 3
 4
 5
 6
```
"""
function insert!(a::Array{T,1}, i::Integer, item) where T
    # Throw convert error before changing the shape of the array
    _item = item isa T ? item : convert(T, item)::T
    _growat!(a, i, 1)
    # _growat! already did bound check
    @inbounds a[i] = _item
    return a
end

"""
    deleteat!(a::Vector, i::Integer)

Remove the item at the given `i` and return the modified `a`. Subsequent items
are shifted to fill the resulting gap.

See also: [`keepat!`](@ref), [`delete!`](@ref), [`popat!`](@ref), [`splice!`](@ref).

# Examples
```jldoctest
julia> deleteat!([6, 5, 4, 3, 2, 1], 2)
5-element Vector{Int64}:
 6
 4
 3
 2
 1
```
"""
function deleteat!(a::Vector, i::Integer)
    i isa Bool && depwarn("passing Bool as an index is deprecated", :deleteat!)
    _deleteat!(a, i, 1)
    return a
end

function deleteat!(a::Vector, r::AbstractUnitRange{<:Integer})
    if eltype(r) === Bool
        return invoke(deleteat!, Tuple{Vector, AbstractVector{Bool}}, a, r)
    else
        n = length(a)
        f = first(r)
        f isa Bool && depwarn("passing Bool as an index is deprecated", :deleteat!)
        isempty(r) || _deleteat!(a, f, length(r))
        return a
    end
end

"""
    deleteat!(a::Vector, inds)

Remove the items at the indices given by `inds`, and return the modified `a`.
Subsequent items are shifted to fill the resulting gap.

`inds` can be either an iterator or a collection of sorted and unique integer indices,
or a boolean vector of the same length as `a` with `true` indicating entries to delete.

# Examples
```jldoctest
julia> deleteat!([6, 5, 4, 3, 2, 1], 1:2:5)
3-element Vector{Int64}:
 5
 3
 1

julia> deleteat!([6, 5, 4, 3, 2, 1], [true, false, true, false, true, false])
3-element Vector{Int64}:
 5
 3
 1

julia> deleteat!([6, 5, 4, 3, 2, 1], (2, 2))
ERROR: ArgumentError: indices must be unique and sorted
Stacktrace:
[...]
```
"""
deleteat!(a::Vector, inds) = _deleteat!(a, inds)
deleteat!(a::Vector, inds::AbstractVector) = _deleteat!(a, to_indices(a, (inds,))[1])

struct Nowhere; end
push!(::Nowhere, _) = nothing
_growend!(::Nowhere, _) = nothing

@inline function _push_deleted!(dltd, a::Vector, ind)
    if @inbounds isassigned(a, ind)
        push!(dltd, @inbounds a[ind])
    else
        _growend!(dltd, 1)
    end
end

@inline function _copy_item!(a::Vector, p, q)
    if @inbounds isassigned(a, q)
        @inbounds a[p] = a[q]
    else
        _unsetindex!(a, p)
    end
end

function _deleteat!(a::Vector, inds, dltd=Nowhere())
    n = length(a)
    y = iterate(inds)
    y === nothing && return a
    (p, s) = y
    checkbounds(a, p)
    _push_deleted!(dltd, a, p)
    q = p+1
    while true
        y = iterate(inds, s)
        y === nothing && break
        (i,s) = y
        if !(q <= i <= n)
            if i < q
                _throw_argerror("indices must be unique and sorted")
            else
                throw(BoundsError())
            end
        end
        while q < i
            _copy_item!(a, p, q)
            p += 1; q += 1
        end
        _push_deleted!(dltd, a, i)
        q = i+1
    end
    while q <= n
        _copy_item!(a, p, q)
        p += 1; q += 1
    end
    _deleteend!(a, n-p+1)
    return a
end

# Simpler and more efficient version for logical indexing
function deleteat!(a::Vector, inds::AbstractVector{Bool})
    n = length(a)
    length(inds) == n || throw(BoundsError(a, inds))
    p = 1
    for (q, i) in enumerate(inds)
        _copy_item!(a, p, q)
        p += !i
    end
    _deleteend!(a, n-p+1)
    return a
end

const _default_splice = []

"""
    splice!(a::Vector, index::Integer, [replacement]) -> item

Remove the item at the given index, and return the removed item.
Subsequent items are shifted left to fill the resulting gap.
If specified, replacement values from an ordered
collection will be spliced in place of the removed item.

See also: [`replace`](@ref), [`delete!`](@ref), [`deleteat!`](@ref), [`pop!`](@ref), [`popat!`](@ref).

# Examples
```jldoctest
julia> A = [6, 5, 4, 3, 2, 1]; splice!(A, 5)
2

julia> A
5-element Vector{Int64}:
 6
 5
 4
 3
 1

julia> splice!(A, 5, -1)
1

julia> A
5-element Vector{Int64}:
  6
  5
  4
  3
 -1

julia> splice!(A, 1, [-1, -2, -3])
6

julia> A
7-element Vector{Int64}:
 -1
 -2
 -3
  5
  4
  3
 -1
```

To insert `replacement` before an index `n` without removing any items, use
`splice!(collection, n:n-1, replacement)`.
"""
function splice!(a::Vector, i::Integer, ins=_default_splice)
    v = a[i]
    m = length(ins)
    if m == 0
        _deleteat!(a, i, 1)
    elseif m == 1
        a[i] = ins[1]
    else
        _growat!(a, i, m-1)
        k = 1
        for x in ins
            a[i+k-1] = x
            k += 1
        end
    end
    return v
end

"""
    splice!(a::Vector, indices, [replacement]) -> items

Remove items at specified indices, and return a collection containing
the removed items.
Subsequent items are shifted left to fill the resulting gaps.
If specified, replacement values from an ordered collection will be spliced in
place of the removed items; in this case, `indices` must be a `AbstractUnitRange`.

To insert `replacement` before an index `n` without removing any items, use
`splice!(collection, n:n-1, replacement)`.

$(_DOCS_ALIASING_WARNING)

!!! compat "Julia 1.5"
    Prior to Julia 1.5, `indices` must always be a `UnitRange`.

!!! compat "Julia 1.8"
    Prior to Julia 1.8, `indices` must be a `UnitRange` if splicing in replacement values.

# Examples
```jldoctest
julia> A = [-1, -2, -3, 5, 4, 3, -1]; splice!(A, 4:3, 2)
Int64[]

julia> A
8-element Vector{Int64}:
 -1
 -2
 -3
  2
  5
  4
  3
 -1
```
"""
function splice!(a::Vector, r::AbstractUnitRange{<:Integer}, ins=_default_splice)
    v = a[r]
    m = length(ins)
    if m == 0
        deleteat!(a, r)
        return v
    end

    n = length(a)
    f = first(r)
    l = last(r)
    d = length(r)

    if m < d
        delta = d - m
        _deleteat!(a, (f - 1 < n - l) ? f : (l - delta + 1), delta)
    elseif m > d
        _growat!(a, (f - 1 < n - l) ? f : (l + 1), m - d)
    end

    k = 1
    for x in ins
        a[f+k-1] = x
        k += 1
    end
    return v
end

splice!(a::Vector, inds) = (dltds = eltype(a)[]; _deleteat!(a, inds, dltds); dltds)

function empty!(a::Vector)
    _deleteend!(a, length(a))
    return a
end

# use memcmp for cmp on byte arrays
function cmp(a::Array{UInt8,1}, b::Array{UInt8,1})
    ta = @_gc_preserve_begin a
    tb = @_gc_preserve_begin b
    pa = unsafe_convert(Ptr{Cvoid}, a)
    pb = unsafe_convert(Ptr{Cvoid}, b)
    c = memcmp(pa, pb, min(length(a),length(b)))
    @_gc_preserve_end ta
    @_gc_preserve_end tb
    return c < 0 ? -1 : c > 0 ? +1 : cmp(length(a),length(b))
end

const BitIntegerArray{N} = Union{map(T->Array{T,N}, BitInteger_types)...} where N
# use memcmp for == on bit integer types
function ==(a::Arr, b::Arr) where {Arr <: BitIntegerArray}
    if size(a) == size(b)
        ta = @_gc_preserve_begin a
        tb = @_gc_preserve_begin b
        pa = unsafe_convert(Ptr{Cvoid}, a)
        pb = unsafe_convert(Ptr{Cvoid}, b)
        c = memcmp(pa, pb, sizeof(eltype(Arr)) * length(a))
        @_gc_preserve_end ta
        @_gc_preserve_end tb
        return c == 0
    else
        return false
    end
end

function ==(a::Arr, b::Arr) where Arr <: BitIntegerArray{1}
    len = length(a)
    if len == length(b)
        ta = @_gc_preserve_begin a
        tb = @_gc_preserve_begin b
        T = eltype(Arr)
        pa = unsafe_convert(Ptr{T}, a)
        pb = unsafe_convert(Ptr{T}, b)
        c = memcmp(pa, pb, sizeof(T) * len)
        @_gc_preserve_end ta
        @_gc_preserve_end tb
        return c == 0
    else
        return false
    end
end

"""
    reverse(v [, start=firstindex(v) [, stop=lastindex(v) ]] )

Return a copy of `v` reversed from start to stop.  See also [`Iterators.reverse`](@ref)
for reverse-order iteration without making a copy, and in-place [`reverse!`](@ref).

# Examples
```jldoctest
julia> A = Vector(1:5)
5-element Vector{Int64}:
 1
 2
 3
 4
 5

julia> reverse(A)
5-element Vector{Int64}:
 5
 4
 3
 2
 1

julia> reverse(A, 1, 4)
5-element Vector{Int64}:
 4
 3
 2
 1
 5

julia> reverse(A, 3, 5)
5-element Vector{Int64}:
 1
 2
 5
 4
 3
```
"""
function reverse(A::AbstractVector, start::Integer, stop::Integer=lastindex(A))
    s, n = Int(start), Int(stop)
    B = similar(A)
    for i = firstindex(A):s-1
        B[i] = A[i]
    end
    for i = s:n
        B[i] = A[n+s-i]
    end
    for i = n+1:lastindex(A)
        B[i] = A[i]
    end
    return B
end

# 1d special cases of reverse(A; dims) and reverse!(A; dims):
for (f,_f) in ((:reverse,:_reverse), (:reverse!,:_reverse!))
    @eval begin
        $f(A::AbstractVector; dims=:) = $_f(A, dims)
        $_f(A::AbstractVector, ::Colon) = $f(A, firstindex(A), lastindex(A))
        $_f(A::AbstractVector, dim::Tuple{Integer}) = $_f(A, first(dim))
        function $_f(A::AbstractVector, dim::Integer)
            dim == 1 || _throw_argerror(LazyString("invalid dimension ", dim, " ≠ 1"))
            return $_f(A, :)
        end
    end
end

function reverseind(a::AbstractVector, i::Integer)
    li = LinearIndices(a)
    first(li) + last(li) - i
end

# This implementation of `midpoint` is performance-optimized but safe
# only if `lo <= hi`.
midpoint(lo::T, hi::T) where T<:Integer = lo + ((hi - lo) >>> 0x01)
midpoint(lo::Integer, hi::Integer) = midpoint(promote(lo, hi)...)

"""
    reverse!(v [, start=firstindex(v) [, stop=lastindex(v) ]]) -> v

In-place version of [`reverse`](@ref).

# Examples
```jldoctest
julia> A = Vector(1:5)
5-element Vector{Int64}:
 1
 2
 3
 4
 5

julia> reverse!(A);

julia> A
5-element Vector{Int64}:
 5
 4
 3
 2
 1
```
"""
function reverse!(v::AbstractVector, start::Integer, stop::Integer=lastindex(v))
    s, n = Int(start), Int(stop)
    if n > s # non-empty and non-trivial
        liv = LinearIndices(v)
        if !(first(liv) ≤ s ≤ last(liv))
            throw(BoundsError(v, s))
        elseif !(first(liv) ≤ n ≤ last(liv))
            throw(BoundsError(v, n))
        end
        r = n
        @inbounds for i in s:midpoint(s, n-1)
            v[i], v[r] = v[r], v[i]
            r -= 1
        end
    end
    return v
end

# concatenations of (in)homogeneous combinations of vectors, horizontal and vertical

vcat() = Vector{Any}()
hcat() = Vector{Any}()

function hcat(V::Vector{T}...) where T
    height = length(V[1])
    for j = 2:length(V)
        if length(V[j]) != height
            throw(DimensionMismatch("vectors must have same lengths"))
        end
    end
    return [ V[j][i]::T for i=1:length(V[1]), j=1:length(V) ]
end
hcat(A::Vector...) = cat(A...; dims=Val(2)) # more special than SparseArrays's hcat

function vcat(arrays::Vector{T}...) where T
    n = 0
    for a in arrays
        n += length(a)
    end
    arr = Vector{T}(undef, n)
    nd = 1
    for a in arrays
        na = length(a)
        @assert nd + na <= 1 + length(arr) # Concurrent modification of arrays?
        unsafe_copyto!(arr, nd, a, 1, na)
        nd += na
    end
    return arr
end
vcat(A::Vector...) = cat(A...; dims=Val(1)) # more special than SparseArrays's vcat

_cat(n::Integer, x::Integer...) = reshape([x...], (ntuple(Returns(1), n-1)..., length(x)))

## find ##

"""
    findnext(A, i)

Find the next index after or including `i` of a `true` element of `A`,
or `nothing` if not found.

Indices are of the same type as those returned by [`keys(A)`](@ref)
and [`pairs(A)`](@ref).

# Examples
```jldoctest
julia> A = [false, false, true, false]
4-element Vector{Bool}:
 0
 0
 1
 0

julia> findnext(A, 1)
3

julia> findnext(A, 4) # returns nothing, but not printed in the REPL

julia> A = [false false; true false]
2×2 Matrix{Bool}:
 0  0
 1  0

julia> findnext(A, CartesianIndex(1, 1))
CartesianIndex(2, 1)
```
"""
findnext(A, start) = findnext(identity, A, start)

"""
    findfirst(A)

Return the index or key of the first `true` value in `A`.
Return `nothing` if no such value is found.
To search for other kinds of values, pass a predicate as the first argument.

Indices or keys are of the same type as those returned by [`keys(A)`](@ref)
and [`pairs(A)`](@ref).

See also: [`findall`](@ref), [`findnext`](@ref), [`findlast`](@ref), [`searchsortedfirst`](@ref).

# Examples
```jldoctest
julia> A = [false, false, true, false]
4-element Vector{Bool}:
 0
 0
 1
 0

julia> findfirst(A)
3

julia> findfirst(falses(3)) # returns nothing, but not printed in the REPL

julia> A = [false false; true false]
2×2 Matrix{Bool}:
 0  0
 1  0

julia> findfirst(A)
CartesianIndex(2, 1)
```
"""
findfirst(A) = findfirst(identity, A)

# Needed for bootstrap, and allows defining only an optimized findnext method
findfirst(A::AbstractArray) = findnext(A, first(keys(A)))

"""
    findnext(predicate::Function, A, i)

Find the next index after or including `i` of an element of `A`
for which `predicate` returns `true`, or `nothing` if not found.

Indices are of the same type as those returned by [`keys(A)`](@ref)
and [`pairs(A)`](@ref).

# Examples
```jldoctest
julia> A = [1, 4, 2, 2];

julia> findnext(isodd, A, 1)
1

julia> findnext(isodd, A, 2) # returns nothing, but not printed in the REPL

julia> A = [1 4; 2 2];

julia> findnext(isodd, A, CartesianIndex(1, 1))
CartesianIndex(1, 1)
```
"""
function findnext(testf::Function, A, start)
    i = oftype(first(keys(A)), start)
    l = last(keys(A))
    i > l && return nothing
    while true
        testf(A[i]) && return i
        i == l && break
        # nextind(A, l) can throw/overflow
        i = nextind(A, i)
    end
    return nothing
end

"""
    findfirst(predicate::Function, A)

Return the index or key of the first element of `A` for which `predicate` returns `true`.
Return `nothing` if there is no such element.

Indices or keys are of the same type as those returned by [`keys(A)`](@ref)
and [`pairs(A)`](@ref).

# Examples
```jldoctest
julia> A = [1, 4, 2, 2]
4-element Vector{Int64}:
 1
 4
 2
 2

julia> findfirst(iseven, A)
2

julia> findfirst(x -> x>10, A) # returns nothing, but not printed in the REPL

julia> findfirst(isequal(4), A)
2

julia> A = [1 4; 2 2]
2×2 Matrix{Int64}:
 1  4
 2  2

julia> findfirst(iseven, A)
CartesianIndex(2, 1)
```
"""
function findfirst(testf::Function, A)
    for (i, a) in pairs(A)
        testf(a) && return i
    end
    return nothing
end

# Needed for bootstrap, and allows defining only an optimized findnext method
findfirst(testf::Function, A::Union{AbstractArray, AbstractString}) =
    findnext(testf, A, first(keys(A)))

findfirst(p::Union{Fix2{typeof(isequal),Int},Fix2{typeof(==),Int}}, r::OneTo{Int}) =
    1 <= p.x <= r.stop ? p.x : nothing

findfirst(p::Union{Fix2{typeof(isequal),T},Fix2{typeof(==),T}}, r::AbstractUnitRange) where {T<:Integer} =
    first(r) <= p.x <= last(r) ? firstindex(r) + Int(p.x - first(r)) : nothing

function findfirst(p::Union{Fix2{typeof(isequal),T},Fix2{typeof(==),T}}, r::StepRange{T,S}) where {T,S}
    isempty(r) && return nothing
    minimum(r) <= p.x <= maximum(r) || return nothing
    d = convert(S, p.x - first(r))::S
    iszero(d % step(r)) || return nothing
    return d ÷ step(r) + 1
end

"""
    findprev(A, i)

Find the previous index before or including `i` of a `true` element of `A`,
or `nothing` if not found.

Indices are of the same type as those returned by [`keys(A)`](@ref)
and [`pairs(A)`](@ref).

See also: [`findnext`](@ref), [`findfirst`](@ref), [`findall`](@ref).

# Examples
```jldoctest
julia> A = [false, false, true, true]
4-element Vector{Bool}:
 0
 0
 1
 1

julia> findprev(A, 3)
3

julia> findprev(A, 1) # returns nothing, but not printed in the REPL

julia> A = [false false; true true]
2×2 Matrix{Bool}:
 0  0
 1  1

julia> findprev(A, CartesianIndex(2, 1))
CartesianIndex(2, 1)
```
"""
findprev(A, start) = findprev(identity, A, start)

"""
    findlast(A)

Return the index or key of the last `true` value in `A`.
Return `nothing` if there is no `true` value in `A`.

Indices or keys are of the same type as those returned by [`keys(A)`](@ref)
and [`pairs(A)`](@ref).

See also: [`findfirst`](@ref), [`findprev`](@ref), [`findall`](@ref).

# Examples
```jldoctest
julia> A = [true, false, true, false]
4-element Vector{Bool}:
 1
 0
 1
 0

julia> findlast(A)
3

julia> A = falses(2,2);

julia> findlast(A) # returns nothing, but not printed in the REPL

julia> A = [true false; true false]
2×2 Matrix{Bool}:
 1  0
 1  0

julia> findlast(A)
CartesianIndex(2, 1)
```
"""
findlast(A) = findlast(identity, A)

# Needed for bootstrap, and allows defining only an optimized findprev method
findlast(A::AbstractArray) = findprev(A, last(keys(A)))

"""
    findprev(predicate::Function, A, i)

Find the previous index before or including `i` of an element of `A`
for which `predicate` returns `true`, or `nothing` if not found.

Indices are of the same type as those returned by [`keys(A)`](@ref)
and [`pairs(A)`](@ref).

# Examples
```jldoctest
julia> A = [4, 6, 1, 2]
4-element Vector{Int64}:
 4
 6
 1
 2

julia> findprev(isodd, A, 1) # returns nothing, but not printed in the REPL

julia> findprev(isodd, A, 3)
3

julia> A = [4 6; 1 2]
2×2 Matrix{Int64}:
 4  6
 1  2

julia> findprev(isodd, A, CartesianIndex(1, 2))
CartesianIndex(2, 1)
```
"""
function findprev(testf::Function, A, start)
    f = first(keys(A))
    i = oftype(f, start)
    i < f && return nothing
    while true
        testf(A[i]) && return i
        i == f && break
        # prevind(A, f) can throw/underflow
        i = prevind(A, i)
    end
    return nothing
end

"""
    findlast(predicate::Function, A)

Return the index or key of the last element of `A` for which `predicate` returns `true`.
Return `nothing` if there is no such element.

Indices or keys are of the same type as those returned by [`keys(A)`](@ref)
and [`pairs(A)`](@ref).

# Examples
```jldoctest
julia> A = [1, 2, 3, 4]
4-element Vector{Int64}:
 1
 2
 3
 4

julia> findlast(isodd, A)
3

julia> findlast(x -> x > 5, A) # returns nothing, but not printed in the REPL

julia> A = [1 2; 3 4]
2×2 Matrix{Int64}:
 1  2
 3  4

julia> findlast(isodd, A)
CartesianIndex(2, 1)
```
"""
function findlast(testf::Function, A)
    for (i, a) in Iterators.reverse(pairs(A))
        testf(a) && return i
    end
    return nothing
end

# Needed for bootstrap, and allows defining only an optimized findprev method
findlast(testf::Function, A::Union{AbstractArray, AbstractString}) =
    findprev(testf, A, last(keys(A)))

"""
    findall(f::Function, A)

Return a vector `I` of the indices or keys of `A` where `f(A[I])` returns `true`.
If there are no such elements of `A`, return an empty array.

Indices or keys are of the same type as those returned by [`keys(A)`](@ref)
and [`pairs(A)`](@ref).

# Examples
```jldoctest
julia> x = [1, 3, 4]
3-element Vector{Int64}:
 1
 3
 4

julia> findall(isodd, x)
2-element Vector{Int64}:
 1
 2

julia> A = [1 2 0; 3 4 0]
2×3 Matrix{Int64}:
 1  2  0
 3  4  0
julia> findall(isodd, A)
2-element Vector{CartesianIndex{2}}:
 CartesianIndex(1, 1)
 CartesianIndex(2, 1)

julia> findall(!iszero, A)
4-element Vector{CartesianIndex{2}}:
 CartesianIndex(1, 1)
 CartesianIndex(2, 1)
 CartesianIndex(1, 2)
 CartesianIndex(2, 2)

julia> d = Dict(:A => 10, :B => -1, :C => 0)
Dict{Symbol, Int64} with 3 entries:
  :A => 10
  :B => -1
  :C => 0

julia> findall(x -> x >= 0, d)
2-element Vector{Symbol}:
 :A
 :C

```
"""
function findall(testf::Function, A)
    T = eltype(keys(A))
    gen = (first(p) for p in pairs(A) if testf(last(p)))
    isconcretetype(T) ? collect(T, gen) : collect(gen)
end

# Broadcasting is much faster for small testf, and computing
# integer indices from logical index using findall has a negligible cost
findall(testf::F, A::AbstractArray) where {F<:Function} = findall(testf.(A))

"""
    findall(A)

Return a vector `I` of the `true` indices or keys of `A`.
If there are no such elements of `A`, return an empty array.
To search for other kinds of values, pass a predicate as the first argument.

Indices or keys are of the same type as those returned by [`keys(A)`](@ref)
and [`pairs(A)`](@ref).

See also: [`findfirst`](@ref), [`searchsorted`](@ref).

# Examples
```jldoctest
julia> A = [true, false, false, true]
4-element Vector{Bool}:
 1
 0
 0
 1

julia> findall(A)
2-element Vector{Int64}:
 1
 4

julia> A = [true false; false true]
2×2 Matrix{Bool}:
 1  0
 0  1

julia> findall(A)
2-element Vector{CartesianIndex{2}}:
 CartesianIndex(1, 1)
 CartesianIndex(2, 2)

julia> findall(falses(3))
Int64[]
```
"""
function findall(A)
    collect(first(p) for p in pairs(A) if last(p))
end

# Allocating result upfront is faster (possible only when collection can be iterated twice)
function findall(A::AbstractArray{Bool})
    n = count(A)
    I = Vector{eltype(keys(A))}(undef, n)
    cnt = 1
    for (i,a) in pairs(A)
        if a
            I[cnt] = i
            cnt += 1
        end
    end
    I
end

findall(x::Bool) = x ? [1] : Vector{Int}()
findall(testf::Function, x::Number) = testf(x) ? [1] : Vector{Int}()
findall(p::Fix2{typeof(in)}, x::Number) = x in p.x ? [1] : Vector{Int}()

# similar to Matlab's ismember
"""
    indexin(a, b)

Return an array containing the first index in `b` for
each value in `a` that is a member of `b`. The output
array contains `nothing` wherever `a` is not a member of `b`.

See also: [`sortperm`](@ref), [`findfirst`](@ref).

# Examples
```jldoctest
julia> a = ['a', 'b', 'c', 'b', 'd', 'a'];

julia> b = ['a', 'b', 'c'];

julia> indexin(a, b)
6-element Vector{Union{Nothing, Int64}}:
 1
 2
 3
 2
  nothing
 1

julia> indexin(b, a)
3-element Vector{Union{Nothing, Int64}}:
 1
 2
 3
```
"""
function indexin(a, b::AbstractArray)
    inds = keys(b)
    bdict = Dict{eltype(b),eltype(inds)}()
    for (val, ind) in zip(b, inds)
        get!(bdict, val, ind)
    end
    return Union{eltype(inds), Nothing}[
        get(bdict, i, nothing) for i in a
    ]
end

function _findin(a::Union{AbstractArray, Tuple}, b)
    ind  = Vector{eltype(keys(a))}()
    bset = Set(b)
    @inbounds for (i,ai) in pairs(a)
        ai in bset && push!(ind, i)
    end
    ind
end

# If two collections are already sorted, _findin can be computed with
# a single traversal of the two collections. This is much faster than
# using a hash table (although it has the same complexity).
function _sortedfindin(v::Union{AbstractArray, Tuple}, w)
    viter, witer = keys(v), eachindex(w)
    out  = eltype(viter)[]
    vy, wy = iterate(viter), iterate(witer)
    if vy === nothing || wy === nothing
        return out
    end
    viteri, i = vy
    witerj, j = wy
    @inbounds begin
        vi, wj = v[viteri], w[witerj]
        while true
            if isless(vi, wj)
                vy = iterate(viter, i)
                if vy === nothing
                    break
                end
                viteri, i = vy
                vi        = v[viteri]
            elseif isless(wj, vi)
                wy = iterate(witer, j)
                if wy === nothing
                    break
                end
                witerj, j = wy
                wj        = w[witerj]
            else
                push!(out, viteri)
                vy = iterate(viter, i)
                if vy === nothing
                    break
                end
                # We only increment the v iterator because v can have
                # repeated matches to a single value in w
                viteri, i = vy
                vi        = v[viteri]
            end
        end
    end
    return out
end

function findall(pred::Fix2{typeof(in),<:Union{Array{<:Real},Real}}, x::Array{<:Real})
    if issorted(x, Sort.Forward) && issorted(pred.x, Sort.Forward)
        return _sortedfindin(x, pred.x)
    else
        return _findin(x, pred.x)
    end
end
# issorted fails for some element types so the method above has to be restricted
# to element with isless/< defined.
findall(pred::Fix2{typeof(in)}, x::AbstractArray) = _findin(x, pred.x)
findall(pred::Fix2{typeof(in)}, x::Tuple) = _findin(x, pred.x)

# Copying subregions
function indcopy(sz::Dims, I::Vector)
    n = length(I)
    s = sz[n]
    for i = n+1:length(sz)
        s *= sz[i]
    end
    dst = eltype(I)[_findin(I[i], i < n ? (1:sz[i]) : (1:s)) for i = 1:n]
    src = eltype(I)[I[i][_findin(I[i], i < n ? (1:sz[i]) : (1:s))] for i = 1:n]
    dst, src
end

function indcopy(sz::Dims, I::Tuple{Vararg{RangeIndex}})
    n = length(I)
    s = sz[n]
    for i = n+1:length(sz)
        s *= sz[i]
    end
    dst::typeof(I) = ntuple(i-> _findin(I[i], i < n ? (1:sz[i]) : (1:s)), n)::typeof(I)
    src::typeof(I) = ntuple(i-> I[i][_findin(I[i], i < n ? (1:sz[i]) : (1:s))], n)::typeof(I)
    dst, src
end

## Filter ##

"""
    filter(f, a)

Return a copy of collection `a`, removing elements for which `f` is `false`.
The function `f` is passed one argument.

!!! compat "Julia 1.4"
    Support for `a` as a tuple requires at least Julia 1.4.

See also: [`filter!`](@ref), [`Iterators.filter`](@ref).

# Examples
```jldoctest
julia> a = 1:10
1:10

julia> filter(isodd, a)
5-element Vector{Int64}:
 1
 3
 5
 7
 9
```
"""
function filter(f, a::Array{T, N}) where {T, N}
    j = 1
    b = Vector{T}(undef, length(a))
    for ai in a
        @inbounds b[j] = ai
        j = ifelse(f(ai)::Bool, j+1, j)
    end
    resize!(b, j-1)
    sizehint!(b, length(b))
    b
end

function filter(f, a::AbstractArray)
    (IndexStyle(a) != IndexLinear()) && return a[map(f, a)::AbstractArray{Bool}]

    j = 1
    idxs = Vector{Int}(undef, length(a))
    for idx in eachindex(a)
        @inbounds idxs[j] = idx
        ai = @inbounds a[idx]
        j = ifelse(f(ai)::Bool, j+1, j)
    end
    resize!(idxs, j-1)
    res = a[idxs]
    empty!(idxs)
    sizehint!(idxs, 0)
    return res
end

"""
    filter!(f, a)

Update collection `a`, removing elements for which `f` is `false`.
The function `f` is passed one argument.

# Examples
```jldoctest
julia> filter!(isodd, Vector(1:10))
5-element Vector{Int64}:
 1
 3
 5
 7
 9
```
"""
function filter!(f, a::AbstractVector)
    j = firstindex(a)
    for ai in a
        @inbounds a[j] = ai
        j = ifelse(f(ai)::Bool, nextind(a, j), j)
    end
    j > lastindex(a) && return a
    if a isa Vector
        resize!(a, j-1)
        sizehint!(a, j-1)
    else
        deleteat!(a, j:lastindex(a))
    end
    return a
end

"""
    filter(f)

Create a function that filters its arguments with function `f` using [`filter`](@ref), i.e.
a function equivalent to `x -> filter(f, x)`.

The returned function is of type `Base.Fix1{typeof(filter)}`, which can be
used to implement specialized methods.

# Examples
```jldoctest
julia> (1, 2, Inf, 4, NaN, 6) |> filter(isfinite)
(1, 2, 4, 6)

julia> map(filter(iseven), [1:3, 2:4, 3:5])
3-element Vector{Vector{Int64}}:
 [2]
 [2, 4]
 [4]
```
!!! compat "Julia 1.9"
    This method requires at least Julia 1.9.
"""
function filter(f)
    Fix1(filter, f)
end

"""
    keepat!(a::Vector, inds)
    keepat!(a::BitVector, inds)

Remove the items at all the indices which are not given by `inds`,
and return the modified `a`.
Items which are kept are shifted to fill the resulting gaps.

$(_DOCS_ALIASING_WARNING)

`inds` must be an iterator of sorted and unique integer indices.
See also [`deleteat!`](@ref).

!!! compat "Julia 1.7"
    This function is available as of Julia 1.7.

# Examples
```jldoctest
julia> keepat!([6, 5, 4, 3, 2, 1], 1:2:5)
3-element Vector{Int64}:
 6
 4
 2
```
"""
keepat!(a::Vector, inds) = _keepat!(a, inds)

"""
    keepat!(a::Vector, m::AbstractVector{Bool})
    keepat!(a::BitVector, m::AbstractVector{Bool})

The in-place version of logical indexing `a = a[m]`. That is, `keepat!(a, m)` on
vectors of equal length `a` and `m` will remove all elements from `a` for which
`m` at the corresponding index is `false`.

# Examples
```jldoctest
julia> a = [:a, :b, :c];

julia> keepat!(a, [true, false, true])
2-element Vector{Symbol}:
 :a
 :c

julia> a
2-element Vector{Symbol}:
 :a
 :c
```
"""
keepat!(a::Vector, m::AbstractVector{Bool}) = _keepat!(a, m)

# set-like operators for vectors
# These are moderately efficient, preserve order, and remove dupes.

_unique_filter!(pred::P, update!::U, state) where {P,U} = function (x)
    # P, U force specialization
    if pred(x, state)
        update!(state, x)
        true
    else
        false
    end
end

_grow_filter!(seen) = _unique_filter!(∉, push!, seen)
_shrink_filter!(keep) = _unique_filter!(∈, pop!, keep)

function _grow!(pred!, v::AbstractVector, itrs)
    filter!(pred!, v) # uniquify v
    for itr in itrs
        mapfilter(pred!, push!, itr, v)
    end
    return v
end

union!(v::AbstractVector{T}, itrs...) where {T} =
    _grow!(_grow_filter!(sizehint!(Set{T}(), length(v))), v, itrs)

symdiff!(v::AbstractVector{T}, itrs...) where {T} =
    _grow!(_shrink_filter!(symdiff!(Set{T}(), v, itrs...)), v, itrs)

function _shrink!(shrinker!::F, v::AbstractVector, itrs) where F
    seen = Set{eltype(v)}()
    filter!(_grow_filter!(seen), v)
    shrinker!(seen, itrs...)
    filter!(in(seen), v)
end

intersect!(v::AbstractVector, itrs...) = _shrink!(intersect!, v, itrs)
setdiff!(  v::AbstractVector, itrs...) = _shrink!(setdiff!, v, itrs)

vectorfilter(T::Type, f, v) = T[x for x in v if f(x)]

function _shrink(shrinker!::F, itr, itrs) where F
    T = promote_eltype(itr, itrs...)
    keep = shrinker!(Set{T}(itr), itrs...)
    vectorfilter(T, _shrink_filter!(keep), itr)
end

intersect(itr, itrs...) = _shrink(intersect!, itr, itrs)
setdiff(  itr, itrs...) = _shrink(setdiff!, itr, itrs)

function intersect(v::AbstractVector, r::AbstractRange)
    T = promote_eltype(v, r)
    common = Iterators.filter(in(r), v)
    seen = Set{T}(common)
    return vectorfilter(T, _shrink_filter!(seen), common)
end
intersect(r::AbstractRange, v::AbstractVector) = intersect(v, r)
T   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/abstractarray.jl��     # This file is a part of Julia. License is MIT: https://julialang.org/license

## Basic functions ##

"""
    AbstractArray{T,N}

Supertype for `N`-dimensional arrays (or array-like types) with elements of type `T`.
[`Array`](@ref) and other types are subtypes of this. See the manual section on the
[`AbstractArray` interface](@ref man-interface-array).

See also: [`AbstractVector`](@ref), [`AbstractMatrix`](@ref), [`eltype`](@ref), [`ndims`](@ref).
"""
AbstractArray

convert(::Type{T}, a::T) where {T<:AbstractArray} = a
convert(::Type{AbstractArray{T}}, a::AbstractArray) where {T} = AbstractArray{T}(a)::AbstractArray{T}
convert(::Type{AbstractArray{T,N}}, a::AbstractArray{<:Any,N}) where {T,N} = AbstractArray{T,N}(a)::AbstractArray{T,N}

"""
    size(A::AbstractArray, [dim])

Return a tuple containing the dimensions of `A`. Optionally you can specify a
dimension to just get the length of that dimension.

Note that `size` may not be defined for arrays with non-standard indices, in which case [`axes`](@ref)
may be useful. See the manual chapter on [arrays with custom indices](@ref man-custom-indices).

See also: [`length`](@ref), [`ndims`](@ref), [`eachindex`](@ref), [`sizeof`](@ref).

# Examples
```jldoctest
julia> A = fill(1, (2,3,4));

julia> size(A)
(2, 3, 4)

julia> size(A, 2)
3
```
"""
size(t::AbstractArray{T,N}, d) where {T,N} = d::Integer <= N ? size(t)[d] : 1

"""
    axes(A, d)

Return the valid range of indices for array `A` along dimension `d`.

See also [`size`](@ref), and the manual chapter on [arrays with custom indices](@ref man-custom-indices).

# Examples

```jldoctest
julia> A = fill(1, (5,6,7));

julia> axes(A, 2)
Base.OneTo(6)

julia> axes(A, 4) == 1:1  # all dimensions d > ndims(A) have size 1
true
```

# Usage note

Each of the indices has to be an `AbstractUnitRange{<:Integer}`, but at the same time can be
a type that uses custom indices. So, for example, if you need a subset, use generalized
indexing constructs like `begin`/`end` or [`firstindex`](@ref)/[`lastindex`](@ref):

```julia
ix = axes(v, 1)
ix[2:end]          # will work for eg Vector, but may fail in general
ix[(begin+1):end]  # works for generalized indexes
```
"""
function axes(A::AbstractArray{T,N}, d) where {T,N}
    @inline
    d::Integer <= N ? axes(A)[d] : OneTo(1)
end

"""
    axes(A)

Return the tuple of valid indices for array `A`.

See also: [`size`](@ref), [`keys`](@ref), [`eachindex`](@ref).

# Examples

```jldoctest
julia> A = fill(1, (5,6,7));

julia> axes(A)
(Base.OneTo(5), Base.OneTo(6), Base.OneTo(7))
```
"""
function axes(A)
    @inline
    map(oneto, size(A))
end

"""
    has_offset_axes(A)
    has_offset_axes(A, B, ...)

Return `true` if the indices of `A` start with something other than 1 along any axis.
If multiple arguments are passed, equivalent to `has_offset_axes(A) || has_offset_axes(B) || ...`.

See also [`require_one_based_indexing`](@ref).
"""
has_offset_axes() = false
has_offset_axes(A) = _any_tuple(x->Int(first(x))::Int != 1, false, axes(A)...)
has_offset_axes(A::AbstractVector) = Int(firstindex(A))::Int != 1 # improve performance of a common case (ranges)
has_offset_axes(::Colon) = false
has_offset_axes(::Array) = false
# note: this could call `any` directly if the compiler can infer it. We don't use _any_tuple
# here because it stops full elision in some cases (#49332) and we don't need handling of
# `missing` (has_offset_axes(A) always returns a Bool)
has_offset_axes(A, As...) = has_offset_axes(A) || has_offset_axes(As...)


"""
    require_one_based_indexing(A::AbstractArray)
    require_one_based_indexing(A,B...)

Throw an `ArgumentError` if the indices of any argument start with something other than `1` along any axis.
See also [`has_offset_axes`](@ref).

!!! compat "Julia 1.2"
     This function requires at least Julia 1.2.
"""
require_one_based_indexing(A...) = !has_offset_axes(A...) || throw(ArgumentError("offset arrays are not supported but got an array with index other than 1"))

# Performance optimization: get rid of a branch on `d` in `axes(A, d)`
# for d=1. 1d arrays are heavily used, and the first dimension comes up
# in other applications.
axes1(A::AbstractArray{<:Any,0}) = OneTo(1)
axes1(A::AbstractArray) = (@inline; axes(A)[1])
axes1(iter) = oneto(length(iter))

"""
    keys(a::AbstractArray)

Return an efficient array describing all valid indices for `a` arranged in the shape of `a` itself.

The keys of 1-dimensional arrays (vectors) are integers, whereas all other N-dimensional
arrays use [`CartesianIndex`](@ref) to describe their locations.  Often the special array
types [`LinearIndices`](@ref) and [`CartesianIndices`](@ref) are used to efficiently
represent these arrays of integers and `CartesianIndex`es, respectively.

Note that the `keys` of an array might not be the most efficient index type; for maximum
performance use  [`eachindex`](@ref) instead.

# Examples
```jldoctest
julia> keys([4, 5, 6])
3-element LinearIndices{1, Tuple{Base.OneTo{Int64}}}:
 1
 2
 3

julia> keys([4 5; 6 7])
CartesianIndices((2, 2))
```
"""
keys(a::AbstractArray) = CartesianIndices(axes(a))
keys(a::AbstractVector) = LinearIndices(a)

"""
    keytype(T::Type{<:AbstractArray})
    keytype(A::AbstractArray)

Return the key type of an array. This is equal to the
[`eltype`](@ref) of the result of `keys(...)`, and is provided
mainly for compatibility with the dictionary interface.

# Examples
```jldoctest
julia> keytype([1, 2, 3]) == Int
true

julia> keytype([1 2; 3 4])
CartesianIndex{2}
```

!!! compat "Julia 1.2"
     For arrays, this function requires at least Julia 1.2.
"""
keytype(a::AbstractArray) = keytype(typeof(a))
keytype(::Type{Union{}}, slurp...) = eltype(Union{})

keytype(A::Type{<:AbstractArray}) = CartesianIndex{ndims(A)}
keytype(A::Type{<:AbstractVector}) = Int

valtype(a::AbstractArray) = valtype(typeof(a))
valtype(::Type{Union{}}, slurp...) = eltype(Union{})

"""
    valtype(T::Type{<:AbstractArray})
    valtype(A::AbstractArray)

Return the value type of an array. This is identical to [`eltype`](@ref) and is
provided mainly for compatibility with the dictionary interface.

# Examples
```jldoctest
julia> valtype(["one", "two", "three"])
String
```

!!! compat "Julia 1.2"
     For arrays, this function requires at least Julia 1.2.
"""
valtype(A::Type{<:AbstractArray}) = eltype(A)

prevind(::AbstractArray, i::Integer) = Int(i)-1
nextind(::AbstractArray, i::Integer) = Int(i)+1


"""
    eltype(type)

Determine the type of the elements generated by iterating a collection of the given `type`.
For dictionary types, this will be a `Pair{KeyType,ValType}`. The definition
`eltype(x) = eltype(typeof(x))` is provided for convenience so that instances can be passed
instead of types. However the form that accepts a type argument should be defined for new
types.

See also: [`keytype`](@ref), [`typeof`](@ref).

# Examples
```jldoctest
julia> eltype(fill(1f0, (2,2)))
Float32

julia> eltype(fill(0x1, (2,2)))
UInt8
```
"""
eltype(::Type) = Any
eltype(::Type{Bottom}, slurp...) = throw(ArgumentError("Union{} does not have elements"))
eltype(x) = eltype(typeof(x))
eltype(::Type{<:AbstractArray{E}}) where {E} = @isdefined(E) ? E : Any

"""
    elsize(type)

Compute the memory stride in bytes between consecutive elements of [`eltype`](@ref)
stored inside the given `type`, if the array elements are stored densely with a
uniform linear stride.

# Examples
```jldoctest
julia> Base.elsize(rand(Float32, 10))
4
```
"""
elsize(A::AbstractArray) = elsize(typeof(A))

"""
    ndims(A::AbstractArray) -> Integer

Return the number of dimensions of `A`.

See also: [`size`](@ref), [`axes`](@ref).

# Examples
```jldoctest
julia> A = fill(1, (3,4,5));

julia> ndims(A)
3
```
"""
ndims(::AbstractArray{T,N}) where {T,N} = N
ndims(::Type{<:AbstractArray{<:Any,N}}) where {N} = N
ndims(::Type{Union{}}, slurp...) = throw(ArgumentError("Union{} does not have elements"))

"""
    length(collection) -> Integer

Return the number of elements in the collection.

Use [`lastindex`](@ref) to get the last valid index of an indexable collection.

See also: [`size`](@ref), [`ndims`](@ref), [`eachindex`](@ref).

# Examples
```jldoctest
julia> length(1:5)
5

julia> length([1, 2, 3, 4])
4

julia> length([1 2; 3 4])
4
```
"""
length

"""
    length(A::AbstractArray)

Return the number of elements in the array, defaults to `prod(size(A))`.

# Examples
```jldoctest
julia> length([1, 2, 3, 4])
4

julia> length([1 2; 3 4])
4
```
"""
length(t::AbstractArray) = (@inline; prod(size(t)))

# `eachindex` is mostly an optimization of `keys`
eachindex(itrs...) = keys(itrs...)

# eachindex iterates over all indices. IndexCartesian definitions are later.
eachindex(A::AbstractVector) = (@inline(); axes1(A))


@noinline function throw_eachindex_mismatch_indices(::IndexLinear, inds...)
    throw(DimensionMismatch("all inputs to eachindex must have the same indices, got $(join(inds, ", ", " and "))"))
end
@noinline function throw_eachindex_mismatch_indices(::IndexCartesian, inds...)
    throw(DimensionMismatch("all inputs to eachindex must have the same axes, got $(join(inds, ", ", " and "))"))
end

"""
    eachindex(A...)
    eachindex(::IndexStyle, A::AbstractArray...)

Create an iterable object for visiting each index of an `AbstractArray` `A` in an efficient
manner. For array types that have opted into fast linear indexing (like `Array`), this is
simply the range `1:length(A)` if they use 1-based indexing.
For array types that have not opted into fast linear indexing, a specialized Cartesian
range is typically returned to efficiently index into the array with indices specified
for every dimension.

In general `eachindex` accepts arbitrary iterables, including strings and dictionaries, and returns
an iterator object supporting arbitrary index types (e.g. unevenly spaced or non-integer indices).

If `A` is `AbstractArray` it is possible to explicitly specify the style of the indices that
should be returned by `eachindex` by passing a value having `IndexStyle` type as its first argument
(typically `IndexLinear()` if linear indices are required or `IndexCartesian()` if Cartesian
range is wanted).

If you supply more than one `AbstractArray` argument, `eachindex` will create an
iterable object that is fast for all arguments (typically a [`UnitRange`](@ref)
if all inputs have fast linear indexing, a [`CartesianIndices`](@ref) otherwise).
If the arrays have different sizes and/or dimensionalities, a `DimensionMismatch` exception
will be thrown.

See also [`pairs`](@ref)`(A)` to iterate over indices and values together,
and [`axes`](@ref)`(A, 2)` for valid indices along one dimension.

# Examples
```jldoctest
julia> A = [10 20; 30 40];

julia> for i in eachindex(A) # linear indexing
           println("A[", i, "] == ", A[i])
       end
A[1] == 10
A[2] == 30
A[3] == 20
A[4] == 40

julia> for i in eachindex(view(A, 1:2, 1:1)) # Cartesian indexing
           println(i)
       end
CartesianIndex(1, 1)
CartesianIndex(2, 1)
```
"""
eachindex(A::AbstractArray) = (@inline(); eachindex(IndexStyle(A), A))

function eachindex(A::AbstractArray, B::AbstractArray)
    @inline
    eachindex(IndexStyle(A,B), A, B)
end
function eachindex(A::AbstractArray, B::AbstractArray...)
    @inline
    eachindex(IndexStyle(A,B...), A, B...)
end
eachindex(::IndexLinear, A::AbstractArray) = (@inline; oneto(length(A)))
eachindex(::IndexLinear, A::AbstractVector) = (@inline; axes1(A))
function eachindex(::IndexLinear, A::AbstractArray, B::AbstractArray...)
    @inline
    indsA = eachindex(IndexLinear(), A)
    _all_match_first(X->eachindex(IndexLinear(), X), indsA, B...) ||
        throw_eachindex_mismatch_indices(IndexLinear(), eachindex(A), eachindex.(B)...)
    indsA
end
function _all_match_first(f::F, inds, A, B...) where F<:Function
    @inline
    (inds == f(A)) & _all_match_first(f, inds, B...)
end
_all_match_first(f::F, inds) where F<:Function = true

# keys with an IndexStyle
keys(s::IndexStyle, A::AbstractArray, B::AbstractArray...) = eachindex(s, A, B...)

"""
    lastindex(collection) -> Integer
    lastindex(collection, d) -> Integer

Return the last index of `collection`. If `d` is given, return the last index of `collection` along dimension `d`.

The syntaxes `A[end]` and `A[end, end]` lower to `A[lastindex(A)]` and
`A[lastindex(A, 1), lastindex(A, 2)]`, respectively.

See also: [`axes`](@ref), [`firstindex`](@ref), [`eachindex`](@ref), [`prevind`](@ref).

# Examples
```jldoctest
julia> lastindex([1,2,4])
3

julia> lastindex(rand(3,4,5), 2)
4
```
"""
lastindex(a::AbstractArray) = (@inline; last(eachindex(IndexLinear(), a)))
lastindex(a, d) = (@inline; last(axes(a, d)))

"""
    firstindex(collection) -> Integer
    firstindex(collection, d) -> Integer

Return the first index of `collection`. If `d` is given, return the first index of `collection` along dimension `d`.

The syntaxes `A[begin]` and `A[1, begin]` lower to `A[firstindex(A)]` and
`A[1, firstindex(A, 2)]`, respectively.

See also: [`first`](@ref), [`axes`](@ref), [`lastindex`](@ref), [`nextind`](@ref).

# Examples
```jldoctest
julia> firstindex([1,2,4])
1

julia> firstindex(rand(3,4,5), 2)
1
```
"""
firstindex(a::AbstractArray) = (@inline; first(eachindex(IndexLinear(), a)))
firstindex(a, d) = (@inline; first(axes(a, d)))

first(a::AbstractArray) = a[first(eachindex(a))]

"""
    first(coll)

Get the first element of an iterable collection. Return the start point of an
[`AbstractRange`](@ref) even if it is empty.

See also: [`only`](@ref), [`firstindex`](@ref), [`last`](@ref).

# Examples
```jldoctest
julia> first(2:2:10)
2

julia> first([1; 2; 3; 4])
1
```
"""
function first(itr)
    x = iterate(itr)
    x === nothing && throw(ArgumentError("collection must be non-empty"))
    x[1]
end

"""
    first(itr, n::Integer)

Get the first `n` elements of the iterable collection `itr`, or fewer elements if `itr` is not
long enough.

See also: [`startswith`](@ref), [`Iterators.take`](@ref).

!!! compat "Julia 1.6"
    This method requires at least Julia 1.6.

# Examples
```jldoctest
julia> first(["foo", "bar", "qux"], 2)
2-element Vector{String}:
 "foo"
 "bar"

julia> first(1:6, 10)
1:6

julia> first(Bool[], 1)
Bool[]
```
"""
first(itr, n::Integer) = collect(Iterators.take(itr, n))
# Faster method for vectors
function first(v::AbstractVector, n::Integer)
    n < 0 && throw(ArgumentError("Number of elements must be nonnegative"))
    v[range(begin, length=min(n, checked_length(v)))]
end

"""
    last(coll)

Get the last element of an ordered collection, if it can be computed in O(1) time. This is
accomplished by calling [`lastindex`](@ref) to get the last index. Return the end
point of an [`AbstractRange`](@ref) even if it is empty.

See also [`first`](@ref), [`endswith`](@ref).

# Examples
```jldoctest
julia> last(1:2:10)
9

julia> last([1; 2; 3; 4])
4
```
"""
last(a) = a[end]

"""
    last(itr, n::Integer)

Get the last `n` elements of the iterable collection `itr`, or fewer elements if `itr` is not
long enough.

!!! compat "Julia 1.6"
    This method requires at least Julia 1.6.

# Examples
```jldoctest
julia> last(["foo", "bar", "qux"], 2)
2-element Vector{String}:
 "bar"
 "qux"

julia> last(1:6, 10)
1:6

julia> last(Float64[], 1)
Float64[]
```
"""
last(itr, n::Integer) = reverse!(collect(Iterators.take(Iterators.reverse(itr), n)))
# Faster method for arrays
function last(v::AbstractVector, n::Integer)
    n < 0 && throw(ArgumentError("Number of elements must be nonnegative"))
    v[range(stop=lastindex(v), length=min(n, checked_length(v)))]
end

"""
    strides(A)

Return a tuple of the memory strides in each dimension.

See also: [`stride`](@ref).

# Examples
```jldoctest
julia> A = fill(1, (3,4,5));

julia> strides(A)
(1, 3, 12)
```
"""
function strides end

"""
    stride(A, k::Integer)

Return the distance in memory (in number of elements) between adjacent elements in dimension `k`.

See also: [`strides`](@ref).

# Examples
```jldoctest
julia> A = fill(1, (3,4,5));

julia> stride(A,2)
3

julia> stride(A,3)
12
```
"""
function stride(A::AbstractArray, k::Integer)
    st = strides(A)
    k ≤ ndims(A) && return st[k]
    ndims(A) == 0 && return 1
    sz = size(A)
    s = st[1] * sz[1]
    for i in 2:ndims(A)
        s += st[i] * sz[i]
    end
    return s
end

@inline size_to_strides(s, d, sz...) = (s, size_to_strides(s * d, sz...)...)
size_to_strides(s, d) = (s,)
size_to_strides(s) = ()

function isstored(A::AbstractArray{<:Any,N}, I::Vararg{Integer,N}) where {N}
    @boundscheck checkbounds(A, I...)
    return true
end

# used to compute "end" for last index
function trailingsize(A, n)
    s = 1
    for i=n:ndims(A)
        s *= size(A,i)
    end
    return s
end
function trailingsize(inds::Indices, n)
    s = 1
    for i=n:length(inds)
        s *= length(inds[i])
    end
    return s
end
# This version is type-stable even if inds is heterogeneous
function trailingsize(inds::Indices)
    @inline
    prod(map(length, inds))
end

## Bounds checking ##

# The overall hierarchy is
#     `checkbounds(A, I...)` ->
#         `checkbounds(Bool, A, I...)` ->
#             `checkbounds_indices(Bool, IA, I)`, which recursively calls
#                 `checkindex` for each dimension
#
# See the "boundscheck" devdocs for more information.
#
# Note this hierarchy has been designed to reduce the likelihood of
# method ambiguities.  We try to make `checkbounds` the place to
# specialize on array type, and try to avoid specializations on index
# types; conversely, `checkindex` is intended to be specialized only
# on index type (especially, its last argument).

"""
    checkbounds(Bool, A, I...)

Return `true` if the specified indices `I` are in bounds for the given
array `A`. Subtypes of `AbstractArray` should specialize this method
if they need to provide custom bounds checking behaviors; however, in
many cases one can rely on `A`'s indices and [`checkindex`](@ref).

See also [`checkindex`](@ref).

# Examples
```jldoctest
julia> A = rand(3, 3);

julia> checkbounds(Bool, A, 2)
true

julia> checkbounds(Bool, A, 3, 4)
false

julia> checkbounds(Bool, A, 1:3)
true

julia> checkbounds(Bool, A, 1:3, 2:4)
false
```
"""
function checkbounds(::Type{Bool}, A::AbstractArray, I...)
    @inline
    checkbounds_indices(Bool, axes(A), I)
end

# Linear indexing is explicitly allowed when there is only one (non-cartesian) index
function checkbounds(::Type{Bool}, A::AbstractArray, i)
    @inline
    checkindex(Bool, eachindex(IndexLinear(), A), i)
end
# As a special extension, allow using logical arrays that match the source array exactly
function checkbounds(::Type{Bool}, A::AbstractArray{<:Any,N}, I::AbstractArray{Bool,N}) where N
    @inline
    axes(A) == axes(I)
end

"""
    checkbounds(A, I...)

Throw an error if the specified indices `I` are not in bounds for the given array `A`.
"""
function checkbounds(A::AbstractArray, I...)
    @inline
    checkbounds(Bool, A, I...) || throw_boundserror(A, I)
    nothing
end

"""
    checkbounds_indices(Bool, IA, I)

Return `true` if the "requested" indices in the tuple `I` fall within
the bounds of the "permitted" indices specified by the tuple
`IA`. This function recursively consumes elements of these tuples,
usually in a 1-for-1 fashion,

    checkbounds_indices(Bool, (IA1, IA...), (I1, I...)) = checkindex(Bool, IA1, I1) &
                                                          checkbounds_indices(Bool, IA, I)

Note that [`checkindex`](@ref) is being used to perform the actual
bounds-check for a single dimension of the array.

There are two important exceptions to the 1-1 rule: linear indexing and
CartesianIndex{N}, both of which may "consume" more than one element
of `IA`.

See also [`checkbounds`](@ref).
"""
function checkbounds_indices(::Type{Bool}, IA::Tuple, I::Tuple)
    @inline
    checkindex(Bool, IA[1], I[1])::Bool & checkbounds_indices(Bool, tail(IA), tail(I))
end
function checkbounds_indices(::Type{Bool}, ::Tuple{}, I::Tuple)
    @inline
    checkindex(Bool, OneTo(1), I[1])::Bool & checkbounds_indices(Bool, (), tail(I))
end
checkbounds_indices(::Type{Bool}, IA::Tuple, ::Tuple{}) = (@inline; all(x->length(x)==1, IA))
checkbounds_indices(::Type{Bool}, ::Tuple{}, ::Tuple{}) = true

throw_boundserror(A, I) = (@noinline; throw(BoundsError(A, I)))

# check along a single dimension
"""
    checkindex(Bool, inds::AbstractUnitRange, index)

Return `true` if the given `index` is within the bounds of
`inds`. Custom types that would like to behave as indices for all
arrays can extend this method in order to provide a specialized bounds
checking implementation.

See also [`checkbounds`](@ref).

# Examples
```jldoctest
julia> checkindex(Bool, 1:20, 8)
true

julia> checkindex(Bool, 1:20, 21)
false
```
"""
checkindex(::Type{Bool}, inds::AbstractUnitRange, i) =
    throw(ArgumentError("unable to check bounds for indices of type $(typeof(i))"))
checkindex(::Type{Bool}, inds::AbstractUnitRange, i::Real) = (first(inds) <= i) & (i <= last(inds))
checkindex(::Type{Bool}, inds::IdentityUnitRange, i::Real) = checkindex(Bool, inds.indices, i)
checkindex(::Type{Bool}, inds::OneTo{T}, i::T) where {T<:BitInteger} = unsigned(i - one(i)) < unsigned(last(inds))
checkindex(::Type{Bool}, inds::AbstractUnitRange, ::Colon) = true
checkindex(::Type{Bool}, inds::AbstractUnitRange, ::Slice) = true
function checkindex(::Type{Bool}, inds::AbstractUnitRange, r::AbstractRange)
    @_propagate_inbounds_meta
    isempty(r) | (checkindex(Bool, inds, first(r)) & checkindex(Bool, inds, last(r)))
end
checkindex(::Type{Bool}, indx::AbstractUnitRange, I::AbstractVector{Bool}) = indx == axes1(I)
checkindex(::Type{Bool}, indx::AbstractUnitRange, I::AbstractArray{Bool}) = false
function checkindex(::Type{Bool}, inds::AbstractUnitRange, I::AbstractArray)
    @inline
    b = true
    for i in I
        b &= checkindex(Bool, inds, i)
    end
    b
end

# See also specializations in multidimensional

## Constructors ##

# default arguments to similar()
"""
    similar(array, [element_type=eltype(array)], [dims=size(array)])

Create an uninitialized mutable array with the given element type and size, based upon the
given source array. The second and third arguments are both optional, defaulting to the
given array's `eltype` and `size`. The dimensions may be specified either as a single tuple
argument or as a series of integer arguments.

Custom AbstractArray subtypes may choose which specific array type is best-suited to return
for the given element type and dimensionality. If they do not specialize this method, the
default is an `Array{element_type}(undef, dims...)`.

For example, `similar(1:10, 1, 4)` returns an uninitialized `Array{Int,2}` since ranges are
neither mutable nor support 2 dimensions:

```julia-repl
julia> similar(1:10, 1, 4)
1×4 Matrix{Int64}:
 4419743872  4374413872  4419743888  0
```

Conversely, `similar(trues(10,10), 2)` returns an uninitialized `BitVector` with two
elements since `BitArray`s are both mutable and can support 1-dimensional arrays:

```julia-repl
julia> similar(trues(10,10), 2)
2-element BitVector:
 0
 0
```

Since `BitArray`s can only store elements of type [`Bool`](@ref), however, if you request a
different element type it will create a regular `Array` instead:

```julia-repl
julia> similar(falses(10), Float64, 2, 4)
2×4 Matrix{Float64}:
 2.18425e-314  2.18425e-314  2.18425e-314  2.18425e-314
 2.18425e-314  2.18425e-314  2.18425e-314  2.18425e-314
```

See also: [`undef`](@ref), [`isassigned`](@ref).
"""
similar(a::AbstractArray{T}) where {T}                             = similar(a, T)
similar(a::AbstractArray, ::Type{T}) where {T}                     = similar(a, T, to_shape(axes(a)))
similar(a::AbstractArray{T}, dims::Tuple) where {T}                = similar(a, T, to_shape(dims))
similar(a::AbstractArray{T}, dims::DimOrInd...) where {T}          = similar(a, T, to_shape(dims))
similar(a::AbstractArray, ::Type{T}, dims::DimOrInd...) where {T}  = similar(a, T, to_shape(dims))
# Similar supports specifying dims as either Integers or AbstractUnitRanges or any mixed combination
# thereof. Ideally, we'd just convert Integers to OneTos and then call a canonical method with the axes,
# but we don't want to require all AbstractArray subtypes to dispatch on Base.OneTo. So instead we
# define this method to convert supported axes to Ints, with the expectation that an offset array
# package will define a method with dims::Tuple{Union{Integer, UnitRange}, Vararg{Union{Integer, UnitRange}}}
similar(a::AbstractArray, ::Type{T}, dims::Tuple{Union{Integer, OneTo}, Vararg{Union{Integer, OneTo}}}) where {T} = similar(a, T, to_shape(dims))
similar(a::AbstractArray, ::Type{T}, dims::Tuple{Integer, Vararg{Integer}}) where {T} = similar(a, T, to_shape(dims))
# similar creates an Array by default
similar(a::AbstractArray, ::Type{T}, dims::Dims{N}) where {T,N}    = Array{T,N}(undef, dims)

to_shape(::Tuple{}) = ()
to_shape(dims::Dims) = dims
to_shape(dims::DimsOrInds) = map(to_shape, dims)::DimsOrInds
# each dimension
to_shape(i::Int) = i
to_shape(i::Integer) = Int(i)
to_shape(r::OneTo) = Int(last(r))
to_shape(r::AbstractUnitRange) = r

"""
    similar(storagetype, axes)

Create an uninitialized mutable array analogous to that specified by
`storagetype`, but with `axes` specified by the last
argument.

**Examples**:

    similar(Array{Int}, axes(A))

creates an array that "acts like" an `Array{Int}` (and might indeed be
backed by one), but which is indexed identically to `A`. If `A` has
conventional indexing, this will be identical to
`Array{Int}(undef, size(A))`, but if `A` has unconventional indexing then the
indices of the result will match `A`.

    similar(BitArray, (axes(A, 2),))

would create a 1-dimensional logical array whose indices match those
of the columns of `A`.
"""
similar(::Type{T}, dims::DimOrInd...) where {T<:AbstractArray} = similar(T, dims)
similar(::Type{T}, shape::Tuple{Union{Integer, OneTo}, Vararg{Union{Integer, OneTo}}}) where {T<:AbstractArray} = similar(T, to_shape(shape))
similar(::Type{T}, dims::Dims) where {T<:AbstractArray} = T(undef, dims)

"""
    empty(v::AbstractVector, [eltype])

Create an empty vector similar to `v`, optionally changing the `eltype`.

See also: [`empty!`](@ref), [`isempty`](@ref), [`isassigned`](@ref).

# Examples

```jldoctest
julia> empty([1.0, 2.0, 3.0])
Float64[]

julia> empty([1.0, 2.0, 3.0], String)
String[]
```
"""
empty(a::AbstractVector{T}, ::Type{U}=T) where {T,U} = Vector{U}()

# like empty, but should return a mutable collection, a Vector by default
emptymutable(a::AbstractVector{T}, ::Type{U}=T) where {T,U} = Vector{U}()
emptymutable(itr, ::Type{U}) where {U} = Vector{U}()

"""
    copy!(dst, src) -> dst

In-place [`copy`](@ref) of `src` into `dst`, discarding any pre-existing
elements in `dst`.
If `dst` and `src` are of the same type, `dst == src` should hold after
the call. If `dst` and `src` are multidimensional arrays, they must have
equal [`axes`](@ref).

$(_DOCS_ALIASING_WARNING)

See also [`copyto!`](@ref).

!!! compat "Julia 1.1"
    This method requires at least Julia 1.1. In Julia 1.0 this method
    is available from the `Future` standard library as `Future.copy!`.
"""
function copy!(dst::AbstractVector, src::AbstractVector)
    firstindex(dst) == firstindex(src) || throw(ArgumentError(
        "vectors must have the same offset for copy! (consider using `copyto!`)"))
    if length(dst) != length(src)
        resize!(dst, length(src))
    end
    copyto!(dst, src)
end

function copy!(dst::AbstractArray, src::AbstractArray)
    axes(dst) == axes(src) || throw(ArgumentError(
        "arrays must have the same axes for copy! (consider using `copyto!`)"))
    copyto!(dst, src)
end

## from general iterable to any array

# This is `Experimental.@max_methods 1 function copyto! end`, which is not
# defined at this point in bootstrap.
typeof(function copyto! end).name.max_methods = UInt8(1)

function copyto!(dest::AbstractArray, src)
    destiter = eachindex(dest)
    y = iterate(destiter)
    for x in src
        y === nothing &&
            throw(ArgumentError("destination has fewer elements than required"))
        dest[y[1]] = x
        y = iterate(destiter, y[2])
    end
    return dest
end

function copyto!(dest::AbstractArray, dstart::Integer, src)
    i = Int(dstart)
    if haslength(src) && length(dest) > 0
        @boundscheck checkbounds(dest, i:(i + length(src) - 1))
        for x in src
            @inbounds dest[i] = x
            i += 1
        end
    else
        for x in src
            dest[i] = x
            i += 1
        end
    end
    return dest
end

# copy from an some iterable object into an AbstractArray
function copyto!(dest::AbstractArray, dstart::Integer, src, sstart::Integer)
    if (sstart < 1)
        throw(ArgumentError(LazyString("source start offset (",sstart,") is < 1")))
    end
    y = iterate(src)
    for j = 1:(sstart-1)
        if y === nothing
            throw(ArgumentError(LazyString(
                "source has fewer elements than required, ",
                "expected at least ", sstart,", got ", j-1)))
        end
        y = iterate(src, y[2])
    end
    if y === nothing
        throw(ArgumentError(LazyString(
            "source has fewer elements than required, ",
            "expected at least ",sstart," got ", sstart-1)))
    end
    i = Int(dstart)
    while y !== nothing
        val, st = y
        dest[i] = val
        i += 1
        y = iterate(src, st)
    end
    return dest
end

# this method must be separate from the above since src might not have a length
function copyto!(dest::AbstractArray, dstart::Integer, src, sstart::Integer, n::Integer)
    n < 0 && throw(ArgumentError(LazyString("tried to copy n=",n,
        ", elements, but n should be nonnegative")))
    n == 0 && return dest
    dmax = dstart + n - 1
    inds = LinearIndices(dest)
    if (dstart ∉ inds || dmax ∉ inds) | (sstart < 1)
        sstart < 1 && throw(ArgumentError(LazyString("source start offset (",
            sstart,") is < 1")))
        throw(BoundsError(dest, dstart:dmax))
    end
    y = iterate(src)
    for j = 1:(sstart-1)
        if y === nothing
            throw(ArgumentError(LazyString(
                "source has fewer elements than required, ",
                "expected at least ",sstart,", got ",j-1)))
        end
        y = iterate(src, y[2])
    end
    i = Int(dstart)
    while i <= dmax && y !== nothing
        val, st = y
        @inbounds dest[i] = val
        y = iterate(src, st)
        i += 1
    end
    i <= dmax && throw(BoundsError(dest, i))
    return dest
end

## copy between abstract arrays - generally more efficient
## since a single index variable can be used.

"""
    copyto!(dest::AbstractArray, src) -> dest

Copy all elements from collection `src` to array `dest`, whose length must be greater than
or equal to the length `n` of `src`. The first `n` elements of `dest` are overwritten,
the other elements are left untouched.

See also [`copy!`](@ref Base.copy!), [`copy`](@ref).

# Examples
```jldoctest
julia> x = [1., 0., 3., 0., 5.];

julia> y = zeros(7);

julia> copyto!(y, x);

julia> y
7-element Vector{Float64}:
 1.0
 0.0
 3.0
 0.0
 5.0
 0.0
 0.0
```
"""
function copyto!(dest::AbstractArray, src::AbstractArray)
    isempty(src) && return dest
    if dest isa BitArray
        # avoid ambiguities with other copyto!(::AbstractArray, ::SourceArray) methods
        return _copyto_bitarray!(dest, src)
    end
    src′ = unalias(dest, src)
    copyto_unaliased!(IndexStyle(dest), dest, IndexStyle(src′), src′)
end

function copyto!(deststyle::IndexStyle, dest::AbstractArray, srcstyle::IndexStyle, src::AbstractArray)
    isempty(src) && return dest
    src′ = unalias(dest, src)
    copyto_unaliased!(deststyle, dest, srcstyle, src′)
end

function copyto_unaliased!(deststyle::IndexStyle, dest::AbstractArray, srcstyle::IndexStyle, src::AbstractArray)
    isempty(src) && return dest
    destinds, srcinds = LinearIndices(dest), LinearIndices(src)
    idf, isf = first(destinds), first(srcinds)
    Δi = idf - isf
    (checkbounds(Bool, destinds, isf+Δi) & checkbounds(Bool, destinds, last(srcinds)+Δi)) ||
        throw(BoundsError(dest, srcinds))
    if deststyle isa IndexLinear
        if srcstyle isa IndexLinear
            # Single-index implementation
            @inbounds for i in srcinds
                dest[i + Δi] = src[i]
            end
        else
            # Dual-index implementation
            i = idf - 1
            @inbounds for a in src
                dest[i+=1] = a
            end
        end
    else
        iterdest, itersrc = eachindex(dest), eachindex(src)
        if iterdest == itersrc
            # Shared-iterator implementation
            for I in iterdest
                @inbounds dest[I] = src[I]
            end
        else
            # Dual-iterator implementation
            ret = iterate(iterdest)
            @inbounds for a in src
                idx, state = ret::NTuple{2,Any}
                dest[idx] = a
                ret = iterate(iterdest, state)
            end
        end
    end
    return dest
end

function copyto!(dest::AbstractArray, dstart::Integer, src::AbstractArray)
    copyto!(dest, dstart, src, first(LinearIndices(src)), length(src))
end

function copyto!(dest::AbstractArray, dstart::Integer, src::AbstractArray, sstart::Integer)
    srcinds = LinearIndices(src)
    checkbounds(Bool, srcinds, sstart) || throw(BoundsError(src, sstart))
    copyto!(dest, dstart, src, sstart, last(srcinds)-sstart+1)
end

function copyto!(dest::AbstractArray, dstart::Integer,
               src::AbstractArray, sstart::Integer,
               n::Integer)
    n == 0 && return dest
    n < 0 && throw(ArgumentError(LazyString("tried to copy n=",
        n," elements, but n should be nonnegative")))
    destinds, srcinds = LinearIndices(dest), LinearIndices(src)
    (checkbounds(Bool, destinds, dstart) && checkbounds(Bool, destinds, dstart+n-1)) || throw(BoundsError(dest, dstart:dstart+n-1))
    (checkbounds(Bool, srcinds, sstart)  && checkbounds(Bool, srcinds, sstart+n-1))  || throw(BoundsError(src,  sstart:sstart+n-1))
    src′ = unalias(dest, src)
    @inbounds for i = 0:n-1
        dest[dstart+i] = src′[sstart+i]
    end
    return dest
end

function copy(a::AbstractArray)
    @_propagate_inbounds_meta
    copymutable(a)
end

function copyto!(B::AbstractVecOrMat{R}, ir_dest::AbstractRange{Int}, jr_dest::AbstractRange{Int},
               A::AbstractVecOrMat{S}, ir_src::AbstractRange{Int}, jr_src::AbstractRange{Int}) where {R,S}
    if length(ir_dest) != length(ir_src)
        throw(ArgumentError(LazyString("source and destination must have same size (got ",
            length(ir_src)," and ",length(ir_dest),")")))
    end
    if length(jr_dest) != length(jr_src)
        throw(ArgumentError(LazyString("source and destination must have same size (got ",
            length(jr_src)," and ",length(jr_dest),")")))
    end
    @boundscheck checkbounds(B, ir_dest, jr_dest)
    @boundscheck checkbounds(A, ir_src, jr_src)
    A′ = unalias(B, A)
    jdest = first(jr_dest)
    for jsrc in jr_src
        idest = first(ir_dest)
        for isrc in ir_src
            @inbounds B[idest,jdest] = A′[isrc,jsrc]
            idest += step(ir_dest)
        end
        jdest += step(jr_dest)
    end
    return B
end

@noinline _checkaxs(axd, axs) = axd == axs || throw(DimensionMismatch("axes must agree, got $axd and $axs"))

function copyto_axcheck!(dest, src)
    _checkaxs(axes(dest), axes(src))
    copyto!(dest, src)
end

"""
    copymutable(a)

Make a mutable copy of an array or iterable `a`.  For `a::Array`,
this is equivalent to `copy(a)`, but for other array types it may
differ depending on the type of `similar(a)`.  For generic iterables
this is equivalent to `collect(a)`.

# Examples
```jldoctest
julia> tup = (1, 2, 3)
(1, 2, 3)

julia> Base.copymutable(tup)
3-element Vector{Int64}:
 1
 2
 3
```
"""
function copymutable(a::AbstractArray)
    @_propagate_inbounds_meta
    copyto!(similar(a), a)
end
copymutable(itr) = collect(itr)

zero(x::AbstractArray{T}) where {T} = fill!(similar(x, typeof(zero(T))), zero(T))

## iteration support for arrays by iterating over `eachindex` in the array ##
# Allows fast iteration by default for both IndexLinear and IndexCartesian arrays

# While the definitions for IndexLinear are all simple enough to inline on their
# own, IndexCartesian's CartesianIndices is more complicated and requires explicit
# inlining.
function iterate(A::AbstractArray, state=(eachindex(A),))
    y = iterate(state...)
    y === nothing && return nothing
    A[y[1]], (state[1], tail(y)...)
end

isempty(a::AbstractArray) = (length(a) == 0)


## range conversions ##

map(::Type{T}, r::StepRange) where {T<:Real} = T(r.start):T(r.step):T(last(r))
map(::Type{T}, r::UnitRange) where {T<:Real} = T(r.start):T(last(r))
map(::Type{T}, r::StepRangeLen) where {T<:AbstractFloat} = convert(StepRangeLen{T}, r)
function map(::Type{T}, r::LinRange) where T<:AbstractFloat
    LinRange(T(r.start), T(r.stop), length(r))
end

## unsafe/pointer conversions ##

# note: the following type definitions don't mean any AbstractArray is convertible to
# a data Ref. they just map the array element type to the pointer type for
# convenience in cases that work.
pointer(x::AbstractArray{T}) where {T} = unsafe_convert(Ptr{T}, x)
function pointer(x::AbstractArray{T}, i::Integer) where T
    @inline
    unsafe_convert(Ptr{T}, x) + Int(_memory_offset(x, i))::Int
end

# The distance from pointer(x) to the element at x[I...] in bytes
_memory_offset(x::DenseArray, I::Vararg{Any,N}) where {N} = (_to_linear_index(x, I...) - first(LinearIndices(x)))*elsize(x)
function _memory_offset(x::AbstractArray, I::Vararg{Any,N}) where {N}
    J = _to_subscript_indices(x, I...)
    return sum(map((i, s, o)->s*(i-o), J, strides(x), Tuple(first(CartesianIndices(x)))))*elsize(x)
end

## Approach:
# We only define one fallback method on getindex for all argument types.
# That dispatches to an (inlined) internal _getindex function, where the goal is
# to transform the indices such that we can call the only getindex method that
# we require the type A{T,N} <: AbstractArray{T,N} to define; either:
#       getindex(::A, ::Int) # if IndexStyle(A) == IndexLinear() OR
#       getindex(::A{T,N}, ::Vararg{Int, N}) where {T,N} # if IndexCartesian()
# If the subtype hasn't defined the required method, it falls back to the
# _getindex function again where an error is thrown to prevent stack overflows.
"""
    getindex(A, inds...)

Return a subset of array `A` as specified by `inds`, where each `ind` may be,
for example, an `Int`, an [`AbstractRange`](@ref), or a [`Vector`](@ref).
See the manual section on [array indexing](@ref man-array-indexing) for details.

# Examples
```jldoctest
julia> A = [1 2; 3 4]
2×2 Matrix{Int64}:
 1  2
 3  4

julia> getindex(A, 1)
1

julia> getindex(A, [2, 1])
2-element Vector{Int64}:
 3
 1

julia> getindex(A, 2:4)
3-element Vector{Int64}:
 3
 2
 4
```
"""
function getindex(A::AbstractArray, I...)
    @_propagate_inbounds_meta
    error_if_canonical_getindex(IndexStyle(A), A, I...)
    _getindex(IndexStyle(A), A, to_indices(A, I)...)
end
# To avoid invalidations from multidimensional.jl: getindex(A::Array, i1::Union{Integer, CartesianIndex}, I::Union{Integer, CartesianIndex}...)
@propagate_inbounds getindex(A::Array, i1::Integer, I::Integer...) = A[to_indices(A, (i1, I...))...]

function unsafe_getindex(A::AbstractArray, I...)
    @inline
    @inbounds r = getindex(A, I...)
    r
end

struct CanonicalIndexError <: Exception
    func::String
    type::Any
    CanonicalIndexError(func::String, @nospecialize(type)) = new(func, type)
end

error_if_canonical_getindex(::IndexLinear, A::AbstractArray, ::Int) =
    throw(CanonicalIndexError("getindex", typeof(A)))
error_if_canonical_getindex(::IndexCartesian, A::AbstractArray{T,N}, ::Vararg{Int,N}) where {T,N} =
    throw(CanonicalIndexError("getindex", typeof(A)))
error_if_canonical_getindex(::IndexStyle, ::AbstractArray, ::Any...) = nothing

## Internal definitions
_getindex(::IndexStyle, A::AbstractArray, I...) =
    error("getindex for $(typeof(A)) with types $(typeof(I)) is not supported")

## IndexLinear Scalar indexing: canonical method is one Int
_getindex(::IndexLinear, A::AbstractVector, i::Int) = (@_propagate_inbounds_meta; getindex(A, i))  # ambiguity resolution in case packages specialize this (to be avoided if at all possible, but see Interpolations.jl)
_getindex(::IndexLinear, A::AbstractArray, i::Int) = (@_propagate_inbounds_meta; getindex(A, i))
function _getindex(::IndexLinear, A::AbstractArray, I::Vararg{Int,M}) where M
    @inline
    @boundscheck checkbounds(A, I...) # generally _to_linear_index requires bounds checking
    @inbounds r = getindex(A, _to_linear_index(A, I...))
    r
end
_to_linear_index(A::AbstractArray, i::Integer) = i
_to_linear_index(A::AbstractVector, i::Integer, I::Integer...) = i
_to_linear_index(A::AbstractArray) = first(LinearIndices(A))
_to_linear_index(A::AbstractArray, I::Integer...) = (@inline; _sub2ind(A, I...))

## IndexCartesian Scalar indexing: Canonical method is full dimensionality of Ints
function _getindex(::IndexCartesian, A::AbstractArray, I::Vararg{Int,M}) where M
    @inline
    @boundscheck checkbounds(A, I...) # generally _to_subscript_indices requires bounds checking
    @inbounds r = getindex(A, _to_subscript_indices(A, I...)...)
    r
end
function _getindex(::IndexCartesian, A::AbstractArray{T,N}, I::Vararg{Int, N}) where {T,N}
    @_propagate_inbounds_meta
    getindex(A, I...)
end
_to_subscript_indices(A::AbstractArray, i::Integer) = (@inline; _unsafe_ind2sub(A, i))
_to_subscript_indices(A::AbstractArray{T,N}) where {T,N} = (@inline; fill_to_length((), 1, Val(N)))
_to_subscript_indices(A::AbstractArray{T,0}) where {T} = ()
_to_subscript_indices(A::AbstractArray{T,0}, i::Integer) where {T} = ()
_to_subscript_indices(A::AbstractArray{T,0}, I::Integer...) where {T} = ()
function _to_subscript_indices(A::AbstractArray{T,N}, I::Integer...) where {T,N}
    @inline
    J, Jrem = IteratorsMD.split(I, Val(N))
    _to_subscript_indices(A, J, Jrem)
end
_to_subscript_indices(A::AbstractArray, J::Tuple, Jrem::Tuple{}) =
    __to_subscript_indices(A, axes(A), J, Jrem)
function __to_subscript_indices(A::AbstractArray,
        ::Tuple{AbstractUnitRange,Vararg{AbstractUnitRange}}, J::Tuple, Jrem::Tuple{})
    @inline
    (J..., map(first, tail(_remaining_size(J, axes(A))))...)
end
_to_subscript_indices(A, J::Tuple, Jrem::Tuple) = J # already bounds-checked, safe to drop
_to_subscript_indices(A::AbstractArray{T,N}, I::Vararg{Int,N}) where {T,N} = I
_remaining_size(::Tuple{Any}, t::Tuple) = t
_remaining_size(h::Tuple, t::Tuple) = (@inline; _remaining_size(tail(h), tail(t)))
_unsafe_ind2sub(::Tuple{}, i) = () # _ind2sub may throw(BoundsError()) in this case
_unsafe_ind2sub(sz, i) = (@inline; _ind2sub(sz, i))

## Setindex! is defined similarly. We first dispatch to an internal _setindex!
# function that allows dispatch on array storage

"""
    setindex!(A, X, inds...)
    A[inds...] = X

Store values from array `X` within some subset of `A` as specified by `inds`.
The syntax `A[inds...] = X` is equivalent to `(setindex!(A, X, inds...); X)`.

$(_DOCS_ALIASING_WARNING)

# Examples
```jldoctest
julia> A = zeros(2,2);

julia> setindex!(A, [10, 20], [1, 2]);

julia> A[[3, 4]] = [30, 40];

julia> A
2×2 Matrix{Float64}:
 10.0  30.0
 20.0  40.0
```
"""
function setindex!(A::AbstractArray, v, I...)
    @_propagate_inbounds_meta
    error_if_canonical_setindex(IndexStyle(A), A, I...)
    _setindex!(IndexStyle(A), A, v, to_indices(A, I)...)
end
function unsafe_setindex!(A::AbstractArray, v, I...)
    @inline
    @inbounds r = setindex!(A, v, I...)
    r
end

error_if_canonical_setindex(::IndexLinear, A::AbstractArray, ::Int) =
    throw(CanonicalIndexError("setindex!", typeof(A)))
error_if_canonical_setindex(::IndexCartesian, A::AbstractArray{T,N}, ::Vararg{Int,N}) where {T,N} =
    throw(CanonicalIndexError("setindex!", typeof(A)))
error_if_canonical_setindex(::IndexStyle, ::AbstractArray, ::Any...) = nothing

## Internal definitions
_setindex!(::IndexStyle, A::AbstractArray, v, I...) =
    error("setindex! for $(typeof(A)) with types $(typeof(I)) is not supported")

## IndexLinear Scalar indexing
_setindex!(::IndexLinear, A::AbstractArray, v, i::Int) = (@_propagate_inbounds_meta; setindex!(A, v, i))
function _setindex!(::IndexLinear, A::AbstractArray, v, I::Vararg{Int,M}) where M
    @inline
    @boundscheck checkbounds(A, I...)
    @inbounds r = setindex!(A, v, _to_linear_index(A, I...))
    r
end

# IndexCartesian Scalar indexing
function _setindex!(::IndexCartesian, A::AbstractArray{T,N}, v, I::Vararg{Int, N}) where {T,N}
    @_propagate_inbounds_meta
    setindex!(A, v, I...)
end
function _setindex!(::IndexCartesian, A::AbstractArray, v, I::Vararg{Int,M}) where M
    @inline
    @boundscheck checkbounds(A, I...)
    @inbounds r = setindex!(A, v, _to_subscript_indices(A, I...)...)
    r
end

"""
    parent(A)

Return the underlying parent object of the view. This parent of objects of types `SubArray`, `SubString`, `ReshapedArray`
or `LinearAlgebra.Transpose` is what was passed as an argument to `view`, `reshape`, `transpose`, etc.
during object creation. If the input is not a wrapped object, return the input itself. If the input is
wrapped multiple times, only the outermost wrapper will be removed.

# Examples
```jldoctest
julia> A = [1 2; 3 4]
2×2 Matrix{Int64}:
 1  2
 3  4

julia> V = view(A, 1:2, :)
2×2 view(::Matrix{Int64}, 1:2, :) with eltype Int64:
 1  2
 3  4

julia> parent(V)
2×2 Matrix{Int64}:
 1  2
 3  4
```
"""
function parent end

parent(a::AbstractArray) = a

## rudimentary aliasing detection ##
"""
    Base.unalias(dest, A)

Return either `A` or a copy of `A` in a rough effort to prevent modifications to `dest` from
affecting the returned object. No guarantees are provided.

Custom arrays that wrap or use fields containing arrays that might alias against other
external objects should provide a [`Base.dataids`](@ref) implementation.

This function must return an object of exactly the same type as `A` for performance and type
stability. Mutable custom arrays for which [`copy(A)`](@ref) is not `typeof(A)` should
provide a [`Base.unaliascopy`](@ref) implementation.

See also [`Base.mightalias`](@ref).
"""
unalias(dest, A::AbstractArray) = mightalias(dest, A) ? unaliascopy(A) : A
unalias(dest, A::AbstractRange) = A
unalias(dest, A) = A

"""
    Base.unaliascopy(A)

Make a preventative copy of `A` in an operation where `A` [`Base.mightalias`](@ref) against
another array in order to preserve consistent semantics as that other array is mutated.

This must return an object of the same type as `A` to preserve optimal performance in the
much more common case where aliasing does not occur. By default,
`unaliascopy(A::AbstractArray)` will attempt to use [`copy(A)`](@ref), but in cases where
`copy(A)` is not a `typeof(A)`, then the array should provide a custom implementation of
`Base.unaliascopy(A)`.
"""
unaliascopy(A::Array) = copy(A)
unaliascopy(A::AbstractArray)::typeof(A) = (@noinline; _unaliascopy(A, copy(A)))
_unaliascopy(A::T, C::T) where {T} = C
_unaliascopy(A, C) = throw(ArgumentError("""
    an array of type `$(typename(typeof(A)).wrapper)` shares memory with another argument
    and must make a preventative copy of itself in order to maintain consistent semantics,
    but `copy(::$(typeof(A)))` returns a new array of type `$(typeof(C))`.
    To fix, implement:
        `Base.unaliascopy(A::$(typename(typeof(A)).wrapper))::typeof(A)`"""))
unaliascopy(A) = A

"""
    Base.mightalias(A::AbstractArray, B::AbstractArray)

Perform a conservative test to check if arrays `A` and `B` might share the same memory.

By default, this simply checks if either of the arrays reference the same memory
regions, as identified by their [`Base.dataids`](@ref).
"""
mightalias(A::AbstractArray, B::AbstractArray) = !isbits(A) && !isbits(B) && !_isdisjoint(dataids(A), dataids(B))
mightalias(x, y) = false

_isdisjoint(as::Tuple{}, bs::Tuple{}) = true
_isdisjoint(as::Tuple{}, bs::Tuple{UInt}) = true
_isdisjoint(as::Tuple{}, bs::Tuple) = true
_isdisjoint(as::Tuple{UInt}, bs::Tuple{}) = true
_isdisjoint(as::Tuple{UInt}, bs::Tuple{UInt}) = as[1] != bs[1]
_isdisjoint(as::Tuple{UInt}, bs::Tuple) = !(as[1] in bs)
_isdisjoint(as::Tuple, bs::Tuple{}) = true
_isdisjoint(as::Tuple, bs::Tuple{UInt}) = !(bs[1] in as)
_isdisjoint(as::Tuple, bs::Tuple) = !(as[1] in bs) && _isdisjoint(tail(as), bs)

"""
    Base.dataids(A::AbstractArray)

Return a tuple of `UInt`s that represent the mutable data segments of an array.

Custom arrays that would like to opt-in to aliasing detection of their component
parts can specialize this method to return the concatenation of the `dataids` of
their component parts.  A typical definition for an array that wraps a parent is
`Base.dataids(C::CustomArray) = dataids(C.parent)`.
"""
dataids(A::AbstractArray) = (UInt(objectid(A)),)
dataids(A::Array) = (UInt(pointer(A)),)
dataids(::AbstractRange) = ()
dataids(x) = ()

## get (getindex with a default value) ##

RangeVecIntList{A<:AbstractVector{Int}} = Union{Tuple{Vararg{Union{AbstractRange, AbstractVector{Int}}}},
    AbstractVector{UnitRange{Int}}, AbstractVector{AbstractRange{Int}}, AbstractVector{A}}

get(A::AbstractArray, i::Integer, default) = checkbounds(Bool, A, i) ? A[i] : default
get(A::AbstractArray, I::Tuple{}, default) = checkbounds(Bool, A) ? A[] : default
get(A::AbstractArray, I::Dims, default) = checkbounds(Bool, A, I...) ? A[I...] : default
get(f::Callable, A::AbstractArray, i::Integer) = checkbounds(Bool, A, i) ? A[i] : f()
get(f::Callable, A::AbstractArray, I::Tuple{}) = checkbounds(Bool, A) ? A[] : f()
get(f::Callable, A::AbstractArray, I::Dims) = checkbounds(Bool, A, I...) ? A[I...] : f()

function get!(X::AbstractVector{T}, A::AbstractVector, I::Union{AbstractRange,AbstractVector{Int}}, default::T) where T
    # 1d is not linear indexing
    ind = findall(in(axes1(A)), I)
    X[ind] = A[I[ind]]
    Xind = axes1(X)
    X[first(Xind):first(ind)-1] = default
    X[last(ind)+1:last(Xind)] = default
    X
end
function get!(X::AbstractArray{T}, A::AbstractArray, I::Union{AbstractRange,AbstractVector{Int}}, default::T) where T
    # Linear indexing
    ind = findall(in(1:length(A)), I)
    X[ind] = A[I[ind]]
    fill!(view(X, 1:first(ind)-1), default)
    fill!(view(X, last(ind)+1:length(X)), default)
    X
end

get(A::AbstractArray, I::AbstractRange, default) = get!(similar(A, typeof(default), index_shape(I)), A, I, default)

function get!(X::AbstractArray{T}, A::AbstractArray, I::RangeVecIntList, default::T) where T
    fill!(X, default)
    dst, src = indcopy(size(A), I)
    X[dst...] = A[src...]
    X
end

get(A::AbstractArray, I::RangeVecIntList, default) =
    get!(similar(A, typeof(default), index_shape(I...)), A, I, default)

## structured matrix methods ##
replace_in_print_matrix(A::AbstractMatrix,i::Integer,j::Integer,s::AbstractString) = s
replace_in_print_matrix(A::AbstractVector,i::Integer,j::Integer,s::AbstractString) = s

## Concatenation ##
eltypeof(x) = typeof(x)
eltypeof(x::AbstractArray) = eltype(x)

promote_eltypeof() = error()
promote_eltypeof(v1) = eltypeof(v1)
promote_eltypeof(v1, vs...) = promote_type(eltypeof(v1), promote_eltypeof(vs...))
promote_eltypeof(v1::T, vs::T...) where {T} = eltypeof(v1)
promote_eltypeof(v1::AbstractArray{T}, vs::AbstractArray{T}...) where {T} = T

promote_eltype() = error()
promote_eltype(v1) = eltype(v1)
promote_eltype(v1, vs...) = promote_type(eltype(v1), promote_eltype(vs...))
promote_eltype(v1::T, vs::T...) where {T} = eltype(T)
promote_eltype(v1::AbstractArray{T}, vs::AbstractArray{T}...) where {T} = T

#TODO: ERROR CHECK
_cat(catdim::Int) = Vector{Any}()

typed_vcat(::Type{T}) where {T} = Vector{T}()
typed_hcat(::Type{T}) where {T} = Vector{T}()

## cat: special cases
vcat(X::T...) where {T}         = T[ X[i] for i=1:length(X) ]
vcat(X::T...) where {T<:Number} = T[ X[i] for i=1:length(X) ]
hcat(X::T...) where {T}         = T[ X[j] for i=1:1, j=1:length(X) ]
hcat(X::T...) where {T<:Number} = T[ X[j] for i=1:1, j=1:length(X) ]

vcat(X::Number...) = hvcat_fill!(Vector{promote_typeof(X...)}(undef, length(X)), X)
hcat(X::Number...) = hvcat_fill!(Matrix{promote_typeof(X...)}(undef, 1,length(X)), X)
typed_vcat(::Type{T}, X::Number...) where {T} = hvcat_fill!(Vector{T}(undef, length(X)), X)
typed_hcat(::Type{T}, X::Number...) where {T} = hvcat_fill!(Matrix{T}(undef, 1,length(X)), X)

vcat(V::AbstractVector...) = typed_vcat(promote_eltype(V...), V...)
vcat(V::AbstractVector{T}...) where {T} = typed_vcat(T, V...)

# FIXME: this alias would better be Union{AbstractVector{T}, Tuple{Vararg{T}}}
# and method signatures should do AbstractVecOrTuple{<:T} when they want covariance,
# but that solution currently fails (see #27188 and #27224)
AbstractVecOrTuple{T} = Union{AbstractVector{<:T}, Tuple{Vararg{T}}}

_typed_vcat_similar(V, ::Type{T}, n) where T = similar(V[1], T, n)
_typed_vcat(::Type{T}, V::AbstractVecOrTuple{AbstractVector}) where T =
    _typed_vcat!(_typed_vcat_similar(V, T, sum(map(length, V))), V)

function _typed_vcat!(a::AbstractVector{T}, V::AbstractVecOrTuple{AbstractVector}) where T
    pos = 1
    for k=1:Int(length(V))::Int
        Vk = V[k]
        p1 = pos + Int(length(Vk))::Int - 1
        a[pos:p1] = Vk
        pos = p1+1
    end
    a
end

typed_hcat(::Type{T}, A::AbstractVecOrMat...) where {T} = _typed_hcat(T, A)

# Catch indexing errors like v[i +1] (instead of v[i+1] or v[i + 1]), where indexing is
# interpreted as a typed concatenation. (issue #49676)
typed_hcat(::AbstractArray, other...) = throw(ArgumentError("It is unclear whether you \
    intend to perform an indexing operation or typed concatenation. If you intend to \
    perform indexing (v[1 + 2]), adjust spacing or insert missing operator to clarify. \
    If you intend to perform typed concatenation (T[1 2]), ensure that T is a type."))


hcat(A::AbstractVecOrMat...) = typed_hcat(promote_eltype(A...), A...)
hcat(A::AbstractVecOrMat{T}...) where {T} = typed_hcat(T, A...)

function _typed_hcat(::Type{T}, A::AbstractVecOrTuple{AbstractVecOrMat}) where T
    nargs = length(A)
    nrows = size(A[1], 1)
    ncols = 0
    dense = true
    for j = 1:nargs
        Aj = A[j]
        if size(Aj, 1) != nrows
            throw(DimensionMismatch("number of rows of each array must match (got $(map(x->size(x,1), A)))"))
        end
        dense &= isa(Aj,Array)
        nd = ndims(Aj)
        ncols += (nd==2 ? size(Aj,2) : 1)
    end
    B = similar(A[1], T, nrows, ncols)
    pos = 1
    if dense
        for k=1:nargs
            Ak = A[k]
            n = length(Ak)
            copyto!(B, pos, Ak, 1, n)
            pos += n
        end
    else
        for k=1:nargs
            Ak = A[k]
            p1 = pos+(isa(Ak,AbstractMatrix) ? size(Ak, 2) : 1)-1
            B[:, pos:p1] = Ak
            pos = p1+1
        end
    end
    return B
end

vcat(A::AbstractVecOrMat...) = typed_vcat(promote_eltype(A...), A...)
vcat(A::AbstractVecOrMat{T}...) where {T} = typed_vcat(T, A...)

function _typed_vcat(::Type{T}, A::AbstractVecOrTuple{AbstractVecOrMat}) where T
    nargs = length(A)
    nrows = sum(a->size(a, 1), A)::Int
    ncols = size(A[1], 2)
    for j = 2:nargs
        if size(A[j], 2) != ncols
            throw(DimensionMismatch("number of columns of each array must match (got $(map(x->size(x,2), A)))"))
        end
    end
    B = similar(A[1], T, nrows, ncols)
    pos = 1
    for k=1:nargs
        Ak = A[k]
        p1 = pos+size(Ak,1)::Int-1
        B[pos:p1, :] = Ak
        pos = p1+1
    end
    return B
end

typed_vcat(::Type{T}, A::AbstractVecOrMat...) where {T} = _typed_vcat(T, A)

reduce(::typeof(vcat), A::AbstractVector{<:AbstractVecOrMat}) =
    _typed_vcat(mapreduce(eltype, promote_type, A), A)

reduce(::typeof(hcat), A::AbstractVector{<:AbstractVecOrMat}) =
    _typed_hcat(mapreduce(eltype, promote_type, A), A)

## cat: general case

# helper functions
cat_size(A) = (1,)
cat_size(A::AbstractArray) = size(A)
cat_size(A, d) = 1
cat_size(A::AbstractArray, d) = size(A, d)

cat_length(::Any) = 1
cat_length(a::AbstractArray) = length(a)

cat_ndims(a) = 0
cat_ndims(a::AbstractArray) = ndims(a)

cat_indices(A, d) = OneTo(1)
cat_indices(A::AbstractArray, d) = axes(A, d)

cat_similar(A, ::Type{T}, shape::Tuple) where T = Array{T}(undef, shape)
cat_similar(A, ::Type{T}, shape::Vector) where T = Array{T}(undef, shape...)
cat_similar(A::Array, ::Type{T}, shape::Tuple) where T = Array{T}(undef, shape)
cat_similar(A::Array, ::Type{T}, shape::Vector) where T = Array{T}(undef, shape...)
cat_similar(A::AbstractArray, T::Type, shape::Tuple) = similar(A, T, shape)
cat_similar(A::AbstractArray, T::Type, shape::Vector) = similar(A, T, shape...)

# These are for backwards compatibility (even though internal)
cat_shape(dims, shape::Tuple{Vararg{Int}}) = shape
function cat_shape(dims, shapes::Tuple)
    out_shape = ()
    for s in shapes
        out_shape = _cshp(1, dims, out_shape, s)
    end
    return out_shape
end
# The new way to compute the shape (more inferable than combining cat_size & cat_shape, due to Varargs + issue#36454)
cat_size_shape(dims) = ntuple(zero, Val(length(dims)))
@inline cat_size_shape(dims, X, tail...) = _cat_size_shape(dims, _cshp(1, dims, (), cat_size(X)), tail...)
_cat_size_shape(dims, shape) = shape
@inline _cat_size_shape(dims, shape, X, tail...) = _cat_size_shape(dims, _cshp(1, dims, shape, cat_size(X)), tail...)

_cshp(ndim::Int, ::Tuple{}, ::Tuple{}, ::Tuple{}) = ()
_cshp(ndim::Int, ::Tuple{}, ::Tuple{}, nshape) = nshape
_cshp(ndim::Int, dims, ::Tuple{}, ::Tuple{}) = ntuple(Returns(1), Val(length(dims)))
@inline _cshp(ndim::Int, dims, shape, ::Tuple{}) =
    (shape[1] + dims[1], _cshp(ndim + 1, tail(dims), tail(shape), ())...)
@inline _cshp(ndim::Int, dims, ::Tuple{}, nshape) =
    (nshape[1], _cshp(ndim + 1, tail(dims), (), tail(nshape))...)
@inline function _cshp(ndim::Int, ::Tuple{}, shape, ::Tuple{})
    _cs(ndim, shape[1], 1)
    (1, _cshp(ndim + 1, (), tail(shape), ())...)
end
@inline function _cshp(ndim::Int, ::Tuple{}, shape, nshape)
    next = _cs(ndim, shape[1], nshape[1])
    (next, _cshp(ndim + 1, (), tail(shape), tail(nshape))...)
end
@inline function _cshp(ndim::Int, dims, shape, nshape)
    a = shape[1]
    b = nshape[1]
    next = dims[1] ? a + b : _cs(ndim, a, b)
    (next, _cshp(ndim + 1, tail(dims), tail(shape), tail(nshape))...)
end

_cs(d, a, b) = (a == b ? a : throw(DimensionMismatch(
    "mismatch in dimension $d (expected $a got $b)")))

dims2cat(::Val{dims}) where dims = dims2cat(dims)
function dims2cat(dims)
    if any(≤(0), dims)
        throw(ArgumentError("All cat dimensions must be positive integers, but got $dims"))
    end
    ntuple(in(dims), maximum(dims))
end

_cat(dims, X...) = _cat_t(dims, promote_eltypeof(X...), X...)

@inline function _cat_t(dims, ::Type{T}, X...) where {T}
    catdims = dims2cat(dims)
    shape = cat_size_shape(catdims, X...)
    A = cat_similar(X[1], T, shape)
    if count(!iszero, catdims)::Int > 1
        fill!(A, zero(T))
    end
    return __cat(A, shape, catdims, X...)
end
# this version of `cat_t` is not very kind for inference and so its usage should be avoided,
# nevertheless it is here just for compat after https://github.com/JuliaLang/julia/pull/45028
@inline cat_t(::Type{T}, X...; dims) where {T} = _cat_t(dims, T, X...)

# Why isn't this called `__cat!`?
__cat(A, shape, catdims, X...) = __cat_offset!(A, shape, catdims, ntuple(zero, length(shape)), X...)

function __cat_offset!(A, shape, catdims, offsets, x, X...)
    # splitting the "work" on x from X... may reduce latency (fewer costly specializations)
    newoffsets = __cat_offset1!(A, shape, catdims, offsets, x)
    return __cat_offset!(A, shape, catdims, newoffsets, X...)
end
__cat_offset!(A, shape, catdims, offsets) = A

function __cat_offset1!(A, shape, catdims, offsets, x)
    inds = ntuple(length(offsets)) do i
        (i <= length(catdims) && catdims[i]) ? offsets[i] .+ cat_indices(x, i) : 1:shape[i]
    end
    _copy_or_fill!(A, inds, x)
    newoffsets = ntuple(length(offsets)) do i
        (i <= length(catdims) && catdims[i]) ? offsets[i] + cat_size(x, i) : offsets[i]
    end
    return newoffsets
end

_copy_or_fill!(A, inds, x) = fill!(view(A, inds...), x)
_copy_or_fill!(A, inds, x::AbstractArray) = (A[inds...] = x)

"""
    vcat(A...)

Concatenate arrays or numbers vertically. Equivalent to [`cat`](@ref)`(A...; dims=1)`,
and to the syntax `[a; b; c]`.

To concatenate a large vector of arrays, `reduce(vcat, A)` calls an efficient method
when `A isa AbstractVector{<:AbstractVecOrMat}`, rather than working pairwise.

See also [`hcat`](@ref), [`Iterators.flatten`](@ref), [`stack`](@ref).

# Examples
```jldoctest
julia> v = vcat([1,2], [3,4])
4-element Vector{Int64}:
 1
 2
 3
 4

julia> v == vcat(1, 2, [3,4])  # accepts numbers
true

julia> v == [1; 2; [3,4]]  # syntax for the same operation
true

julia> summary(ComplexF64[1; 2; [3,4]])  # syntax for supplying the element type
"4-element Vector{ComplexF64}"

julia> vcat(range(1, 2, length=3))  # collects lazy ranges
3-element Vector{Float64}:
 1.0
 1.5
 2.0

julia> two = ([10, 20, 30]', Float64[4 5 6; 7 8 9])  # row vector and a matrix
([10 20 30], [4.0 5.0 6.0; 7.0 8.0 9.0])

julia> vcat(two...)
3×3 Matrix{Float64}:
 10.0  20.0  30.0
  4.0   5.0   6.0
  7.0   8.0   9.0

julia> vs = [[1, 2], [3, 4], [5, 6]];

julia> reduce(vcat, vs)  # more efficient than vcat(vs...)
6-element Vector{Int64}:
 1
 2
 3
 4
 5
 6

julia> ans == collect(Iterators.flatten(vs))
true
```
"""
vcat(X...) = cat(X...; dims=Val(1))
"""
    hcat(A...)

Concatenate arrays or numbers horizontally. Equivalent to [`cat`](@ref)`(A...; dims=2)`,
and to the syntax `[a b c]` or `[a;; b;; c]`.

For a large vector of arrays, `reduce(hcat, A)` calls an efficient method
when `A isa AbstractVector{<:AbstractVecOrMat}`.
For a vector of vectors, this can also be written [`stack`](@ref)`(A)`.

See also [`vcat`](@ref), [`hvcat`](@ref).

# Examples
```jldoctest
julia> hcat([1,2], [3,4], [5,6])
2×3 Matrix{Int64}:
 1  3  5
 2  4  6

julia> hcat(1, 2, [30 40], [5, 6, 7]')  # accepts numbers
1×7 Matrix{Int64}:
 1  2  30  40  5  6  7

julia> ans == [1 2 [30 40] [5, 6, 7]']  # syntax for the same operation
true

julia> Float32[1 2 [30 40] [5, 6, 7]']  # syntax for supplying the eltype
1×7 Matrix{Float32}:
 1.0  2.0  30.0  40.0  5.0  6.0  7.0

julia> ms = [zeros(2,2), [1 2; 3 4], [50 60; 70 80]];

julia> reduce(hcat, ms)  # more efficient than hcat(ms...)
2×6 Matrix{Float64}:
 0.0  0.0  1.0  2.0  50.0  60.0
 0.0  0.0  3.0  4.0  70.0  80.0

julia> stack(ms) |> summary  # disagrees on a vector of matrices
"2×2×3 Array{Float64, 3}"

julia> hcat(Int[], Int[], Int[])  # empty vectors, each of size (0,)
0×3 Matrix{Int64}

julia> hcat([1.1, 9.9], Matrix(undef, 2, 0))  # hcat with empty 2×0 Matrix
2×1 Matrix{Any}:
 1.1
 9.9
```
"""
hcat(X...) = cat(X...; dims=Val(2))

typed_vcat(::Type{T}, X...) where T = _cat_t(Val(1), T, X...)
typed_hcat(::Type{T}, X...) where T = _cat_t(Val(2), T, X...)

"""
    cat(A...; dims)

Concatenate the input arrays along the dimensions specified in `dims`.

Along a dimension `d in dims`, the size of the output array is `sum(size(a,d) for
a in A)`.
Along other dimensions, all input arrays should have the same size,
which will also be the size of the output array along those dimensions.

If `dims` is a single number, the different arrays are tightly packed along that dimension.
If `dims` is an iterable containing several dimensions, the positions along these dimensions
are increased simultaneously for each input array, filling with zero elsewhere.
This allows one to construct block-diagonal matrices as `cat(matrices...; dims=(1,2))`,
and their higher-dimensional analogues.

The special case `dims=1` is [`vcat`](@ref), and `dims=2` is [`hcat`](@ref).
See also [`hvcat`](@ref), [`hvncat`](@ref), [`stack`](@ref), [`repeat`](@ref).

The keyword also accepts `Val(dims)`.

!!! compat "Julia 1.8"
    For multiple dimensions `dims = Val(::Tuple)` was added in Julia 1.8.

# Examples
```jldoctest
julia> cat([1 2; 3 4], [pi, pi], fill(10, 2,3,1); dims=2)  # same as hcat
2×6×1 Array{Float64, 3}:
[:, :, 1] =
 1.0  2.0  3.14159  10.0  10.0  10.0
 3.0  4.0  3.14159  10.0  10.0  10.0

julia> cat(true, trues(2,2), trues(4)', dims=(1,2))  # block-diagonal
4×7 Matrix{Bool}:
 1  0  0  0  0  0  0
 0  1  1  0  0  0  0
 0  1  1  0  0  0  0
 0  0  0  1  1  1  1

julia> cat(1, [2], [3;;]; dims=Val(2))
1×3 Matrix{Int64}:
 1  2  3
```
"""
@inline cat(A...; dims) = _cat(dims, A...)
# `@constprop :aggressive` allows `catdims` to be propagated as constant improving return type inference
@constprop :aggressive _cat(catdims, A::AbstractArray{T}...) where {T} = _cat_t(catdims, T, A...)

# The specializations for 1 and 2 inputs are important
# especially when running with --inline=no, see #11158
vcat(A::AbstractArray) = cat(A; dims=Val(1))
vcat(A::AbstractArray, B::AbstractArray) = cat(A, B; dims=Val(1))
vcat(A::AbstractArray...) = cat(A...; dims=Val(1))
vcat(A::Union{AbstractArray,Number}...) = cat(A...; dims=Val(1))
hcat(A::AbstractArray) = cat(A; dims=Val(2))
hcat(A::AbstractArray, B::AbstractArray) = cat(A, B; dims=Val(2))
hcat(A::AbstractArray...) = cat(A...; dims=Val(2))
hcat(A::Union{AbstractArray,Number}...) = cat(A...; dims=Val(2))

typed_vcat(T::Type, A::AbstractArray) = _cat_t(Val(1), T, A)
typed_vcat(T::Type, A::AbstractArray, B::AbstractArray) = _cat_t(Val(1), T, A, B)
typed_vcat(T::Type, A::AbstractArray...) = _cat_t(Val(1), T, A...)
typed_hcat(T::Type, A::AbstractArray) = _cat_t(Val(2), T, A)
typed_hcat(T::Type, A::AbstractArray, B::AbstractArray) = _cat_t(Val(2), T, A, B)
typed_hcat(T::Type, A::AbstractArray...) = _cat_t(Val(2), T, A...)

# 2d horizontal and vertical concatenation

# these are produced in lowering if splatting occurs inside hvcat
hvcat_rows(rows::Tuple...) = hvcat(map(length, rows), (rows...)...)
typed_hvcat_rows(T::Type, rows::Tuple...) = typed_hvcat(T, map(length, rows), (rows...)...)

function hvcat(nbc::Int, as...)
    # nbc = # of block columns
    n = length(as)
    mod(n,nbc) != 0 &&
        throw(ArgumentError("number of arrays $n is not a multiple of the requested number of block columns $nbc"))
    nbr = div(n,nbc)
    hvcat(ntuple(Returns(nbc), nbr), as...)
end

"""
    hvcat(blocks_per_row::Union{Tuple{Vararg{Int}}, Int}, values...)

Horizontal and vertical concatenation in one call. This function is called for block matrix
syntax. The first argument specifies the number of arguments to concatenate in each block
row. If the first argument is a single integer `n`, then all block rows are assumed to have `n`
block columns.

# Examples
```jldoctest
julia> a, b, c, d, e, f = 1, 2, 3, 4, 5, 6
(1, 2, 3, 4, 5, 6)

julia> [a b c; d e f]
2×3 Matrix{Int64}:
 1  2  3
 4  5  6

julia> hvcat((3,3), a,b,c,d,e,f)
2×3 Matrix{Int64}:
 1  2  3
 4  5  6

julia> [a b; c d; e f]
3×2 Matrix{Int64}:
 1  2
 3  4
 5  6

julia> hvcat((2,2,2), a,b,c,d,e,f)
3×2 Matrix{Int64}:
 1  2
 3  4
 5  6
julia> hvcat((2,2,2), a,b,c,d,e,f) == hvcat(2, a,b,c,d,e,f)
true
```
"""
hvcat(rows::Tuple{Vararg{Int}}, xs::AbstractArray...) = typed_hvcat(promote_eltype(xs...), rows, xs...)
hvcat(rows::Tuple{Vararg{Int}}, xs::AbstractArray{T}...) where {T} = typed_hvcat(T, rows, xs...)

function typed_hvcat(::Type{T}, rows::Tuple{Vararg{Int}}, as::AbstractVecOrMat...) where T
    nbr = length(rows)  # number of block rows

    nc = 0
    for i=1:rows[1]
        nc += size(as[i],2)
    end

    nr = 0
    a = 1
    for i = 1:nbr
        nr += size(as[a],1)
        a += rows[i]
    end

    out = similar(as[1], T, nr, nc)

    a = 1
    r = 1
    for i = 1:nbr
        c = 1
        szi = size(as[a],1)
        for j = 1:rows[i]
            Aj = as[a+j-1]
            szj = size(Aj,2)
            if size(Aj,1) != szi
                throw(DimensionMismatch("mismatched height in block row $(i) (expected $szi, got $(size(Aj,1)))"))
            end
            if c-1+szj > nc
                throw(DimensionMismatch("block row $(i) has mismatched number of columns (expected $nc, got $(c-1+szj))"))
            end
            out[r:r-1+szi, c:c-1+szj] = Aj
            c += szj
        end
        if c != nc+1
            throw(DimensionMismatch("block row $(i) has mismatched number of columns (expected $nc, got $(c-1))"))
        end
        r += szi
        a += rows[i]
    end
    out
end

hvcat(rows::Tuple{Vararg{Int}}) = []
typed_hvcat(::Type{T}, rows::Tuple{Vararg{Int}}) where {T} = Vector{T}()

function hvcat(rows::Tuple{Vararg{Int}}, xs::T...) where T<:Number
    nr = length(rows)
    nc = rows[1]

    a = Matrix{T}(undef, nr, nc)
    if length(a) != length(xs)
        throw(ArgumentError("argument count does not match specified shape (expected $(length(a)), got $(length(xs)))"))
    end
    k = 1
    @inbounds for i=1:nr
        if nc != rows[i]
            throw(DimensionMismatch("row $(i) has mismatched number of columns (expected $nc, got $(rows[i]))"))
        end
        for j=1:nc
            a[i,j] = xs[k]
            k += 1
        end
    end
    a
end

function hvcat_fill!(a::Array, xs::Tuple)
    nr, nc = size(a,1), size(a,2)
    len = length(xs)
    if nr*nc != len
        throw(ArgumentError("argument count $(len) does not match specified shape $((nr,nc))"))
    end
    k = 1
    for i=1:nr
        @inbounds for j=1:nc
            a[i,j] = xs[k]
            k += 1
        end
    end
    a
end

hvcat(rows::Tuple{Vararg{Int}}, xs::Number...) = typed_hvcat(promote_typeof(xs...), rows, xs...)
hvcat(rows::Tuple{Vararg{Int}}, xs...) = typed_hvcat(promote_eltypeof(xs...), rows, xs...)
# the following method is needed to provide a more specific one compared to LinearAlgebra/uniformscaling.jl
hvcat(rows::Tuple{Vararg{Int}}, xs::Union{AbstractArray,Number}...) = typed_hvcat(promote_eltypeof(xs...), rows, xs...)

function typed_hvcat(::Type{T}, rows::Tuple{Vararg{Int}}, xs::Number...) where T
    nr = length(rows)
    nc = rows[1]
    for i = 2:nr
        if nc != rows[i]
            throw(DimensionMismatch("row $(i) has mismatched number of columns (expected $nc, got $(rows[i]))"))
        end
    end
    hvcat_fill!(Matrix{T}(undef, nr, nc), xs)
end

function typed_hvcat(::Type{T}, rows::Tuple{Vararg{Int}}, as...) where T
    nbr = length(rows)  # number of block rows
    rs = Vector{Any}(undef, nbr)
    a = 1
    for i = 1:nbr
        rs[i] = typed_hcat(T, as[a:a-1+rows[i]]...)
        a += rows[i]
    end
    T[rs...;]
end

## N-dimensional concatenation ##

"""
    hvncat(dim::Int, row_first, values...)
    hvncat(dims::Tuple{Vararg{Int}}, row_first, values...)
    hvncat(shape::Tuple{Vararg{Tuple}}, row_first, values...)

Horizontal, vertical, and n-dimensional concatenation of many `values` in one call.

This function is called for block matrix syntax. The first argument either specifies the
shape of the concatenation, similar to `hvcat`, as a tuple of tuples, or the dimensions that
specify the key number of elements along each axis, and is used to determine the output
dimensions. The `dims` form is more performant, and is used by default when the concatenation
operation has the same number of elements along each axis (e.g., [a b; c d;;; e f ; g h]).
The `shape` form is used when the number of elements along each axis is unbalanced
(e.g., [a b ; c]). Unbalanced syntax needs additional validation overhead. The `dim` form
is an optimization for concatenation along just one dimension. `row_first` indicates how
`values` are ordered. The meaning of the first and second elements of `shape` are also
swapped based on `row_first`.

# Examples
```jldoctest
julia> a, b, c, d, e, f = 1, 2, 3, 4, 5, 6
(1, 2, 3, 4, 5, 6)

julia> [a b c;;; d e f]
1×3×2 Array{Int64, 3}:
[:, :, 1] =
 1  2  3

[:, :, 2] =
 4  5  6

julia> hvncat((2,1,3), false, a,b,c,d,e,f)
2×1×3 Array{Int64, 3}:
[:, :, 1] =
 1
 2

[:, :, 2] =
 3
 4

[:, :, 3] =
 5
 6

julia> [a b;;; c d;;; e f]
1×2×3 Array{Int64, 3}:
[:, :, 1] =
 1  2

[:, :, 2] =
 3  4

[:, :, 3] =
 5  6

julia> hvncat(((3, 3), (3, 3), (6,)), true, a, b, c, d, e, f)
1×3×2 Array{Int64, 3}:
[:, :, 1] =
 1  2  3

[:, :, 2] =
 4  5  6
```

# Examples for construction of the arguments
```
[a b c ; d e f ;;;
 g h i ; j k l ;;;
 m n o ; p q r ;;;
 s t u ; v w x]
⇒ dims = (2, 3, 4)

[a b ; c ;;; d ;;;;]
 ___   _     _
 2     1     1 = elements in each row (2, 1, 1)
 _______     _
 3           1 = elements in each column (3, 1)
 _____________
 4             = elements in each 3d slice (4,)
 _____________
 4             = elements in each 4d slice (4,)
⇒ shape = ((2, 1, 1), (3, 1), (4,), (4,)) with `row_first` = true
```
"""
hvncat(dimsshape::Tuple, row_first::Bool, xs...) = _hvncat(dimsshape, row_first, xs...)
hvncat(dim::Int, xs...) = _hvncat(dim, true, xs...)

_hvncat(dimsshape::Union{Tuple, Int}, row_first::Bool) = _typed_hvncat(Any, dimsshape, row_first)
_hvncat(dimsshape::Union{Tuple, Int}, row_first::Bool, xs...) = _typed_hvncat(promote_eltypeof(xs...), dimsshape, row_first, xs...)
_hvncat(dimsshape::Union{Tuple, Int}, row_first::Bool, xs::T...) where T<:Number = _typed_hvncat(T, dimsshape, row_first, xs...)
_hvncat(dimsshape::Union{Tuple, Int}, row_first::Bool, xs::Number...) = _typed_hvncat(promote_typeof(xs...), dimsshape, row_first, xs...)
_hvncat(dimsshape::Union{Tuple, Int}, row_first::Bool, xs::AbstractArray...) = _typed_hvncat(promote_eltype(xs...), dimsshape, row_first, xs...)
_hvncat(dimsshape::Union{Tuple, Int}, row_first::Bool, xs::AbstractArray{T}...) where T = _typed_hvncat(T, dimsshape, row_first, xs...)


typed_hvncat(T::Type, dimsshape::Tuple, row_first::Bool, xs...) = _typed_hvncat(T, dimsshape, row_first, xs...)
typed_hvncat(T::Type, dim::Int, xs...) = _typed_hvncat(T, Val(dim), xs...)

# 1-dimensional hvncat methods

_typed_hvncat(::Type, ::Val{0}) = _typed_hvncat_0d_only_one()
_typed_hvncat(T::Type, ::Val{0}, x) = fill(convert(T, x))
_typed_hvncat(T::Type, ::Val{0}, x::Number) = fill(convert(T, x))
_typed_hvncat(T::Type, ::Val{0}, x::AbstractArray) = convert.(T, x)
_typed_hvncat(::Type, ::Val{0}, ::Any...) = _typed_hvncat_0d_only_one()
_typed_hvncat(::Type, ::Val{0}, ::Number...) = _typed_hvncat_0d_only_one()
_typed_hvncat(::Type, ::Val{0}, ::AbstractArray...) = _typed_hvncat_0d_only_one()

_typed_hvncat_0d_only_one() =
    throw(ArgumentError("a 0-dimensional array may only contain exactly one element"))

# `@constprop :aggressive` here to form constant `Val(dim)` type to get type stability
@constprop :aggressive _typed_hvncat(T::Type, dim::Int, ::Bool, xs...) = _typed_hvncat(T, Val(dim), xs...) # catches from _hvncat type promoters

function _typed_hvncat(::Type{T}, ::Val{N}) where {T, N}
    N < 0 &&
        throw(ArgumentError("concatenation dimension must be nonnegative"))
    return Array{T, N}(undef, ntuple(x -> 0, Val(N)))
end

function _typed_hvncat(T::Type, ::Val{N}, xs::Number...) where N
    N < 0 &&
        throw(ArgumentError("concatenation dimension must be nonnegative"))
    A = cat_similar(xs[1], T, (ntuple(x -> 1, Val(N - 1))..., length(xs)))
    hvncat_fill!(A, false, xs)
    return A
end

function _typed_hvncat(::Type{T}, ::Val{N}, as::AbstractArray...) where {T, N}
    # optimization for arrays that can be concatenated by copying them linearly into the destination
    # conditions: the elements must all have 1-length dimensions above N
    length(as) > 0 ||
        throw(ArgumentError("must have at least one element"))
    N < 0 &&
        throw(ArgumentError("concatenation dimension must be nonnegative"))
    for a ∈ as
        ndims(a) <= N || all(x -> size(a, x) == 1, (N + 1):ndims(a)) ||
            return _typed_hvncat(T, (ntuple(x -> 1, Val(N - 1))..., length(as), 1), false, as...)
            # the extra 1 is to avoid an infinite cycle
    end

    nd = N

    Ndim = 0
    for i ∈ eachindex(as)
        Ndim += cat_size(as[i], N)
        nd = max(nd, cat_ndims(as[i]))
        for d ∈ 1:N - 1
            cat_size(as[1], d) == cat_size(as[i], d) || throw(DimensionMismatch("mismatched size along axis $d in element $i"))
        end
    end

    A = cat_similar(as[1], T, (ntuple(d -> size(as[1], d), N - 1)..., Ndim, ntuple(x -> 1, nd - N)...))
    k = 1
    for a ∈ as
        for i ∈ eachindex(a)
            A[k] = a[i]
            k += 1
        end
    end
    return A
end

function _typed_hvncat(::Type{T}, ::Val{N}, as...) where {T, N}
    length(as) > 0 ||
        throw(ArgumentError("must have at least one element"))
    N < 0 &&
        throw(ArgumentError("concatenation dimension must be nonnegative"))
    nd = N
    Ndim = 0
    for i ∈ eachindex(as)
        Ndim += cat_size(as[i], N)
        nd = max(nd, cat_ndims(as[i]))
        for d ∈ 1:N-1
            cat_size(as[i], d) == 1 ||
                throw(DimensionMismatch("all dimensions of element $i other than $N must be of length 1"))
        end
    end

    A = Array{T, nd}(undef, ntuple(x -> 1, Val(N - 1))..., Ndim, ntuple(x -> 1, nd - N)...)

    k = 1
    for a ∈ as
        if a isa AbstractArray
            lena = length(a)
            copyto!(A, k, a, 1, lena)
            k += lena
        else
            A[k] = a
            k += 1
        end
    end
    return A
end

# 0-dimensional cases for balanced and unbalanced hvncat method

_typed_hvncat(T::Type, ::Tuple{}, ::Bool, x...) = _typed_hvncat(T, Val(0), x...)
_typed_hvncat(T::Type, ::Tuple{}, ::Bool, x::Number...) = _typed_hvncat(T, Val(0), x...)


# balanced dimensions hvncat methods

_typed_hvncat(T::Type, dims::Tuple{Int}, ::Bool, as...) = _typed_hvncat_1d(T, dims[1], Val(false), as...)
_typed_hvncat(T::Type, dims::Tuple{Int}, ::Bool, as::Number...) = _typed_hvncat_1d(T, dims[1], Val(false), as...)

function _typed_hvncat_1d(::Type{T}, ds::Int, ::Val{row_first}, as...) where {T, row_first}
    lengthas = length(as)
    ds > 0 ||
        throw(ArgumentError("`dimsshape` argument must consist of positive integers"))
    lengthas == ds ||
        throw(ArgumentError("number of elements does not match `dimshape` argument; expected $ds, got $lengthas"))
    if row_first
        return _typed_hvncat(T, Val(2), as...)
    else
        return _typed_hvncat(T, Val(1), as...)
    end
end

function _typed_hvncat(::Type{T}, dims::NTuple{N, Int}, row_first::Bool, xs::Number...) where {T, N}
    all(>(0), dims) ||
        throw(ArgumentError("`dims` argument must contain positive integers"))
    A = Array{T, N}(undef, dims...)
    lengtha = length(A)  # Necessary to store result because throw blocks are being deoptimized right now, which leads to excessive allocations
    lengthx = length(xs) # Cuts from 3 allocations to 1.
    if lengtha != lengthx
       throw(ArgumentError("argument count does not match specified shape (expected $lengtha, got $lengthx)"))
    end
    hvncat_fill!(A, row_first, xs)
    return A
end

function hvncat_fill!(A::Array, row_first::Bool, xs::Tuple)
    nr, nc = size(A, 1), size(A, 2)
    na = prod(size(A)[3:end])
    len = length(xs)
    nrc = nr * nc
    if nrc * na != len
        throw(ArgumentError("argument count $(len) does not match specified shape $(size(A))"))
    end
    # putting these in separate functions leads to unnecessary allocations
    if row_first
        k = 1
        for d ∈ 1:na
            dd = nrc * (d - 1)
            for i ∈ 1:nr
                Ai = dd + i
                for j ∈ 1:nc
                    @inbounds A[Ai] = xs[k]
                    k += 1
                    Ai += nr
                end
            end
        end
    else
        for k ∈ eachindex(xs)
            @inbounds A[k] = xs[k]
        end
    end
end

function _typed_hvncat(T::Type, dims::NTuple{N, Int}, row_first::Bool, as...) where {N}
    # function barrier after calculating the max is necessary for high performance
    nd = max(maximum(cat_ndims(a) for a ∈ as), N)
    return _typed_hvncat_dims(T, (dims..., ntuple(x -> 1, nd - N)...), row_first, as)
end

function _typed_hvncat_dims(::Type{T}, dims::NTuple{N, Int}, row_first::Bool, as::Tuple) where {T, N}
    length(as) > 0 ||
        throw(ArgumentError("must have at least one element"))
    all(>(0), dims) ||
        throw(ArgumentError("`dims` argument must contain positive integers"))

    d1 = row_first ? 2 : 1
    d2 = row_first ? 1 : 2

    outdims = zeros(Int, N)

    # validate shapes for lowest level of concatenation
    d = findfirst(>(1), dims)
    if d !== nothing # all dims are 1
        if row_first && d < 3
            d = d == 1 ? 2 : 1
        end
        nblocks = length(as) ÷ dims[d]
        for b ∈ 1:nblocks
            offset = ((b - 1) * dims[d])
            startelementi = offset + 1
            for i ∈ offset .+ (2:dims[d])
                for dd ∈ 1:N
                    dd == d && continue
                    if cat_size(as[startelementi], dd) != cat_size(as[i], dd)
                        throw(DimensionMismatch("incompatible shape in element $i"))
                    end
                end
            end
        end
    end

    # discover number of rows or columns
    for i ∈ 1:dims[d1]
        outdims[d1] += cat_size(as[i], d1)
    end

    currentdims = zeros(Int, N)
    blockcount = 0
    elementcount = 0
    for i ∈ eachindex(as)
        elementcount += cat_length(as[i])
        currentdims[d1] += cat_size(as[i], d1)
        if currentdims[d1] == outdims[d1]
            currentdims[d1] = 0
            for d ∈ (d2, 3:N...)
                currentdims[d] += cat_size(as[i], d)
                if outdims[d] == 0 # unfixed dimension
                    blockcount += 1
                    if blockcount == dims[d]
                        outdims[d] = currentdims[d]
                        currentdims[d] = 0
                        blockcount = 0
                    else
                        break
                    end
                else # fixed dimension
                    if currentdims[d] == outdims[d] # end of dimension
                        currentdims[d] = 0
                    elseif currentdims[d] < outdims[d] # dimension in progress
                        break
                    else # exceeded dimension
                        throw(DimensionMismatch("argument $i has too many elements along axis $d"))
                    end
                end
            end
        elseif currentdims[d1] > outdims[d1] # exceeded dimension
            throw(DimensionMismatch("argument $i has too many elements along axis $d1"))
        end
    end

    outlen = prod(outdims)
    elementcount == outlen ||
        throw(DimensionMismatch("mismatched number of elements; expected $(outlen), got $(elementcount)"))

    # copy into final array
    A = cat_similar(as[1], T, outdims)
    # @assert all(==(0), currentdims)
    outdims .= 0
    hvncat_fill!(A, currentdims, outdims, d1, d2, as)
    return A
end


# unbalanced dimensions hvncat methods

function _typed_hvncat(T::Type, shape::Tuple{Tuple}, row_first::Bool, xs...)
    length(shape[1]) > 0 ||
        throw(ArgumentError("each level of `shape` argument must have at least one value"))
    return _typed_hvncat_1d(T, shape[1][1], Val(row_first), xs...)
end

function _typed_hvncat(T::Type, shape::NTuple{N, Tuple}, row_first::Bool, as...) where {N}
    # function barrier after calculating the max is necessary for high performance
    nd = max(maximum(cat_ndims(a) for a ∈ as), N)
    return _typed_hvncat_shape(T, (shape..., ntuple(x -> shape[end], nd - N)...), row_first, as)
end

function _typed_hvncat_shape(::Type{T}, shape::NTuple{N, Tuple}, row_first, as::Tuple) where {T, N}
    length(as) > 0 ||
        throw(ArgumentError("must have at least one element"))
    all(>(0), tuple((shape...)...)) ||
        throw(ArgumentError("`shape` argument must consist of positive integers"))

    d1 = row_first ? 2 : 1
    d2 = row_first ? 1 : 2

    shapev = collect(shape) # saves allocations later
    all(!isempty, shapev) ||
        throw(ArgumentError("each level of `shape` argument must have at least one value"))
    length(shapev[end]) == 1 ||
        throw(ArgumentError("last level of shape must contain only one integer"))
    shapelength = shapev[end][1]
    lengthas = length(as)
    shapelength == lengthas || throw(ArgumentError("number of elements does not match shape; expected $(shapelength), got $lengthas)"))
    # discover dimensions
    nd = max(N, cat_ndims(as[1]))
    outdims = fill(-1, nd)
    currentdims = zeros(Int, nd)
    blockcounts = zeros(Int, nd)
    shapepos = ones(Int, nd)

    elementcount = 0
    for i ∈ eachindex(as)
        elementcount += cat_length(as[i])
        wasstartblock = false
        for d ∈ 1:N
            ad = (d < 3 && row_first) ? (d == 1 ? 2 : 1) : d
            dsize = cat_size(as[i], ad)
            blockcounts[d] += 1

            if d == 1 || i == 1 || wasstartblock
                currentdims[d] += dsize
            elseif dsize != cat_size(as[i - 1], ad)
                throw(DimensionMismatch("argument $i has a mismatched number of elements along axis $ad; \
                                         expected $(cat_size(as[i - 1], ad)), got $dsize"))
            end

            wasstartblock = blockcounts[d] == 1 # remember for next dimension

            isendblock = blockcounts[d] == shapev[d][shapepos[d]]
            if isendblock
                if outdims[d] == -1
                    outdims[d] = currentdims[d]
                elseif outdims[d] != currentdims[d]
                    throw(DimensionMismatch("argument $i has a mismatched number of elements along axis $ad; \
                                             expected $(abs(outdims[d] - (currentdims[d] - dsize))), got $dsize"))
                end
                currentdims[d] = 0
                blockcounts[d] = 0
                shapepos[d] += 1
                d > 1 && (blockcounts[d - 1] == 0 ||
                    throw(DimensionMismatch("shape in level $d is inconsistent; level counts must nest \
                                             evenly into each other")))
            end
        end
    end

    outlen = prod(outdims)
    elementcount == outlen ||
        throw(ArgumentError("mismatched number of elements; expected $(outlen), got $(elementcount)"))

    if row_first
        outdims[1], outdims[2] = outdims[2], outdims[1]
    end

    # @assert all(==(0), currentdims)
    # @assert all(==(0), blockcounts)

    # copy into final array
    A = cat_similar(as[1], T, outdims)
    hvncat_fill!(A, currentdims, blockcounts, d1, d2, as)
    return A
end

function hvncat_fill!(A::AbstractArray{T, N}, scratch1::Vector{Int}, scratch2::Vector{Int},
                              d1::Int, d2::Int, as::Tuple) where {T, N}
    N > 1 || throw(ArgumentError("dimensions of the destination array must be at least 2"))
    length(scratch1) == length(scratch2) == N ||
        throw(ArgumentError("scratch vectors must have as many elements as the destination array has dimensions"))
    0 < d1 < 3 &&
    0 < d2 < 3 &&
    d1 != d2 ||
        throw(ArgumentError("d1 and d2 must be either 1 or 2, exclusive."))
    outdims = size(A)
    offsets = scratch1
    inneroffsets = scratch2
    for a ∈ as
        if isa(a, AbstractArray)
            for ai ∈ a
                @inbounds Ai = hvncat_calcindex(offsets, inneroffsets, outdims, N)
                A[Ai] = ai

                @inbounds for j ∈ 1:N
                    inneroffsets[j] += 1
                    inneroffsets[j] < cat_size(a, j) && break
                    inneroffsets[j] = 0
                end
            end
        else
            @inbounds Ai = hvncat_calcindex(offsets, inneroffsets, outdims, N)
            A[Ai] = a
        end

        @inbounds for j ∈ (d1, d2, 3:N...)
            offsets[j] += cat_size(a, j)
            offsets[j] < outdims[j] && break
            offsets[j] = 0
        end
    end
end

@propagate_inbounds function hvncat_calcindex(offsets::Vector{Int}, inneroffsets::Vector{Int},
                                              outdims::Tuple{Vararg{Int}}, nd::Int)
    Ai = inneroffsets[1] + offsets[1] + 1
    for j ∈ 2:nd
        increment = inneroffsets[j] + offsets[j]
        for k ∈ 1:j-1
            increment *= outdims[k]
        end
        Ai += increment
    end
    Ai
end

"""
    stack(iter; [dims])

Combine a collection of arrays (or other iterable objects) of equal size
into one larger array, by arranging them along one or more new dimensions.

By default the axes of the elements are placed first,
giving `size(result) = (size(first(iter))..., size(iter)...)`.
This has the same order of elements as [`Iterators.flatten`](@ref)`(iter)`.

With keyword `dims::Integer`, instead the `i`th element of `iter` becomes the slice
[`selectdim`](@ref)`(result, dims, i)`, so that `size(result, dims) == length(iter)`.
In this case `stack` reverses the action of [`eachslice`](@ref) with the same `dims`.

The various [`cat`](@ref) functions also combine arrays. However, these all
extend the arrays' existing (possibly trivial) dimensions, rather than placing
the arrays along new dimensions.
They also accept arrays as separate arguments, rather than a single collection.

!!! compat "Julia 1.9"
    This function requires at least Julia 1.9.

# Examples
```jldoctest
julia> vecs = (1:2, [30, 40], Float32[500, 600]);

julia> mat = stack(vecs)
2×3 Matrix{Float32}:
 1.0  30.0  500.0
 2.0  40.0  600.0

julia> mat == hcat(vecs...) == reduce(hcat, collect(vecs))
true

julia> vec(mat) == vcat(vecs...) == reduce(vcat, collect(vecs))
true

julia> stack(zip(1:4, 10:99))  # accepts any iterators of iterators
2×4 Matrix{Int64}:
  1   2   3   4
 10  11  12  13

julia> vec(ans) == collect(Iterators.flatten(zip(1:4, 10:99)))
true

julia> stack(vecs; dims=1)  # unlike any cat function, 1st axis of vecs[1] is 2nd axis of result
3×2 Matrix{Float32}:
   1.0    2.0
  30.0   40.0
 500.0  600.0

julia> x = rand(3,4);

julia> x == stack(eachcol(x)) == stack(eachrow(x), dims=1)  # inverse of eachslice
true
```

Higher-dimensional examples:

```jldoctest
julia> A = rand(5, 7, 11);

julia> E = eachslice(A, dims=2);  # a vector of matrices

julia> (element = size(first(E)), container = size(E))
(element = (5, 11), container = (7,))

julia> stack(E) |> size
(5, 11, 7)

julia> stack(E) == stack(E; dims=3) == cat(E...; dims=3)
true

julia> A == stack(E; dims=2)
true

julia> M = (fill(10i+j, 2, 3) for i in 1:5, j in 1:7);

julia> (element = size(first(M)), container = size(M))
(element = (2, 3), container = (5, 7))

julia> stack(M) |> size  # keeps all dimensions
(2, 3, 5, 7)

julia> stack(M; dims=1) |> size  # vec(container) along dims=1
(35, 2, 3)

julia> hvcat(5, M...) |> size  # hvcat puts matrices next to each other
(14, 15)
```
"""
stack(iter; dims=:) = _stack(dims, iter)

"""
    stack(f, args...; [dims])

Apply a function to each element of a collection, and `stack` the result.
Or to several collections, [`zip`](@ref)ped together.

The function should return arrays (or tuples, or other iterators) all of the same size.
These become slices of the result, each separated along `dims` (if given) or by default
along the last dimensions.

See also [`mapslices`](@ref), [`eachcol`](@ref).

# Examples
```jldoctest
julia> stack(c -> (c, c-32), "julia")
2×5 Matrix{Char}:
 'j'  'u'  'l'  'i'  'a'
 'J'  'U'  'L'  'I'  'A'

julia> stack(eachrow([1 2 3; 4 5 6]), (10, 100); dims=1) do row, n
         vcat(row, row .* n, row ./ n)
       end
2×9 Matrix{Float64}:
 1.0  2.0  3.0   10.0   20.0   30.0  0.1   0.2   0.3
 4.0  5.0  6.0  400.0  500.0  600.0  0.04  0.05  0.06
```
"""
stack(f, iter; dims=:) = _stack(dims, f(x) for x in iter)
stack(f, xs, yzs...; dims=:) = _stack(dims, f(xy...) for xy in zip(xs, yzs...))

_stack(dims::Union{Integer, Colon}, iter) = _stack(dims, IteratorSize(iter), iter)

_stack(dims, ::IteratorSize, iter) = _stack(dims, collect(iter))

function _stack(dims, ::Union{HasShape, HasLength}, iter)
    S = @default_eltype iter
    T = S != Union{} ? eltype(S) : Any  # Union{} occurs for e.g. stack(1,2), postpone the error
    if isconcretetype(T)
        _typed_stack(dims, T, S, iter)
    else  # Need to look inside, but shouldn't run an expensive iterator twice:
        array = iter isa Union{Tuple, AbstractArray} ? iter : collect(iter)
        isempty(array) && return _empty_stack(dims, T, S, iter)
        T2 = mapreduce(eltype, promote_type, array)
        _typed_stack(dims, T2, eltype(array), array)
    end
end

function _typed_stack(::Colon, ::Type{T}, ::Type{S}, A, Aax=_iterator_axes(A)) where {T, S}
    xit = iterate(A)
    nothing === xit && return _empty_stack(:, T, S, A)
    x1, _ = xit
    ax1 = _iterator_axes(x1)
    B = similar(_ensure_array(x1), T, ax1..., Aax...)
    off = firstindex(B)
    len = length(x1)
    while xit !== nothing
        x, state = xit
        _stack_size_check(x, ax1)
        copyto!(B, off, x)
        off += len
        xit = iterate(A, state)
    end
    B
end

_iterator_axes(x) = _iterator_axes(x, IteratorSize(x))
_iterator_axes(x, ::HasLength) = (OneTo(length(x)),)
_iterator_axes(x, ::IteratorSize) = axes(x)

# For some dims values, stack(A; dims) == stack(vec(A)), and the : path will be faster
_typed_stack(dims::Integer, ::Type{T}, ::Type{S}, A) where {T,S} =
    _typed_stack(dims, T, S, IteratorSize(S), A)
_typed_stack(dims::Integer, ::Type{T}, ::Type{S}, ::HasLength, A) where {T,S} =
    _typed_stack(dims, T, S, HasShape{1}(), A)
function _typed_stack(dims::Integer, ::Type{T}, ::Type{S}, ::HasShape{N}, A) where {T,S,N}
    if dims == N+1
        _typed_stack(:, T, S, A, (_vec_axis(A),))
    else
        _dim_stack(dims, T, S, A)
    end
end
_typed_stack(dims::Integer, ::Type{T}, ::Type{S}, ::IteratorSize, A) where {T,S} =
    _dim_stack(dims, T, S, A)

_vec_axis(A, ax=_iterator_axes(A)) = length(ax) == 1 ? only(ax) : OneTo(prod(length, ax; init=1))

@constprop :aggressive function _dim_stack(dims::Integer, ::Type{T}, ::Type{S}, A) where {T,S}
    xit = Iterators.peel(A)
    nothing === xit && return _empty_stack(dims, T, S, A)
    x1, xrest = xit
    ax1 = _iterator_axes(x1)
    N1 = length(ax1)+1
    dims in 1:N1 || throw(ArgumentError(LazyString("cannot stack slices ndims(x) = ", N1-1, " along dims = ", dims)))

    newaxis = _vec_axis(A)
    outax = ntuple(d -> d==dims ? newaxis : ax1[d - (d>dims)], N1)
    B = similar(_ensure_array(x1), T, outax...)

    if dims == 1
        _dim_stack!(Val(1), B, x1, xrest)
    elseif dims == 2
        _dim_stack!(Val(2), B, x1, xrest)
    else
        _dim_stack!(Val(dims), B, x1, xrest)
    end
    B
end

function _dim_stack!(::Val{dims}, B::AbstractArray, x1, xrest) where {dims}
    before = ntuple(d -> Colon(), dims - 1)
    after = ntuple(d -> Colon(), ndims(B) - dims)

    i = firstindex(B, dims)
    copyto!(view(B, before..., i, after...), x1)

    for x in xrest
        _stack_size_check(x, _iterator_axes(x1))
        i += 1
        @inbounds copyto!(view(B, before..., i, after...), x)
    end
end

@inline function _stack_size_check(x, ax1::Tuple)
    if _iterator_axes(x) != ax1
        uax1 = map(UnitRange, ax1)
        uaxN = map(UnitRange, axes(x))
        throw(DimensionMismatch(
            LazyString("stack expects uniform slices, got axes(x) == ", uaxN, " while first had ", uax1)))
    end
end

_ensure_array(x::AbstractArray) = x
_ensure_array(x) = 1:0  # passed to similar, makes stack's output an Array

_empty_stack(_...) = throw(ArgumentError("`stack` on an empty collection is not allowed"))


## Reductions and accumulates ##

function isequal(A::AbstractArray, B::AbstractArray)
    if A === B return true end
    if axes(A) != axes(B)
        return false
    end
    for (a, b) in zip(A, B)
        if !isequal(a, b)
            return false
        end
    end
    return true
end

function cmp(A::AbstractVector, B::AbstractVector)
    for (a, b) in zip(A, B)
        if !isequal(a, b)
            return isless(a, b) ? -1 : 1
        end
    end
    return cmp(length(A), length(B))
end

"""
    isless(A::AbstractVector, B::AbstractVector)

Return `true` when `A` is less than `B` in lexicographic order.
"""
isless(A::AbstractVector, B::AbstractVector) = cmp(A, B) < 0

function (==)(A::AbstractArray, B::AbstractArray)
    if axes(A) != axes(B)
        return false
    end
    anymissing = false
    for (a, b) in zip(A, B)
        eq = (a == b)
        if ismissing(eq)
            anymissing = true
        elseif !eq
            return false
        end
    end
    return anymissing ? missing : true
end

# _sub2ind and _ind2sub
# fallbacks
function _sub2ind(A::AbstractArray, I...)
    @inline
    _sub2ind(axes(A), I...)
end

function _ind2sub(A::AbstractArray, ind)
    @inline
    _ind2sub(axes(A), ind)
end

# 0-dimensional arrays and indexing with []
_sub2ind(::Tuple{}) = 1
_sub2ind(::DimsInteger) = 1
_sub2ind(::Indices) = 1
_sub2ind(::Tuple{}, I::Integer...) = (@inline; _sub2ind_recurse((), 1, 1, I...))

# Generic cases
_sub2ind(dims::DimsInteger, I::Integer...) = (@inline; _sub2ind_recurse(dims, 1, 1, I...))
_sub2ind(inds::Indices, I::Integer...) = (@inline; _sub2ind_recurse(inds, 1, 1, I...))
# In 1d, there's a question of whether we're doing cartesian indexing
# or linear indexing. Support only the former.
_sub2ind(inds::Indices{1}, I::Integer...) =
    throw(ArgumentError("Linear indexing is not defined for one-dimensional arrays"))
_sub2ind(inds::Tuple{OneTo}, I::Integer...) = (@inline; _sub2ind_recurse(inds, 1, 1, I...)) # only OneTo is safe
_sub2ind(inds::Tuple{OneTo}, i::Integer)    = i

_sub2ind_recurse(::Any, L, ind) = ind
function _sub2ind_recurse(::Tuple{}, L, ind, i::Integer, I::Integer...)
    @inline
    _sub2ind_recurse((), L, ind+(i-1)*L, I...)
end
function _sub2ind_recurse(inds, L, ind, i::Integer, I::Integer...)
    @inline
    r1 = inds[1]
    _sub2ind_recurse(tail(inds), nextL(L, r1), ind+offsetin(i, r1)*L, I...)
end

nextL(L, l::Integer) = L*l
nextL(L, r::AbstractUnitRange) = L*length(r)
nextL(L, r::Slice) = L*length(r.indices)
offsetin(i, l::Integer) = i-1
offsetin(i, r::AbstractUnitRange) = i-first(r)

_ind2sub(::Tuple{}, ind::Integer) = (@inline; ind == 1 ? () : throw(BoundsError()))
_ind2sub(dims::DimsInteger, ind::Integer) = (@inline; _ind2sub_recurse(dims, ind-1))
_ind2sub(inds::Indices, ind::Integer)     = (@inline; _ind2sub_recurse(inds, ind-1))
_ind2sub(inds::Indices{1}, ind::Integer) =
    throw(ArgumentError("Linear indexing is not defined for one-dimensional arrays"))
_ind2sub(inds::Tuple{OneTo}, ind::Integer) = (ind,)

_ind2sub_recurse(::Tuple{}, ind) = (ind+1,)
function _ind2sub_recurse(indslast::NTuple{1}, ind)
    @inline
    (_lookup(ind, indslast[1]),)
end
function _ind2sub_recurse(inds, ind)
    @inline
    r1 = inds[1]
    indnext, f, l = _div(ind, r1)
    (ind-l*indnext+f, _ind2sub_recurse(tail(inds), indnext)...)
end

_lookup(ind, d::Integer) = ind+1
_lookup(ind, r::AbstractUnitRange) = ind+first(r)
_div(ind, d::Integer) = div(ind, d), 1, d
_div(ind, r::AbstractUnitRange) = (d = length(r); (div(ind, d), first(r), d))

# Vectorized forms
function _sub2ind(inds::Indices{1}, I1::AbstractVector{T}, I::AbstractVector{T}...) where T<:Integer
    throw(ArgumentError("Linear indexing is not defined for one-dimensional arrays"))
end
_sub2ind(inds::Tuple{OneTo}, I1::AbstractVector{T}, I::AbstractVector{T}...) where {T<:Integer} =
    _sub2ind_vecs(inds, I1, I...)
_sub2ind(inds::Union{DimsInteger,Indices}, I1::AbstractVector{T}, I::AbstractVector{T}...) where {T<:Integer} =
    _sub2ind_vecs(inds, I1, I...)
function _sub2ind_vecs(inds, I::AbstractVector...)
    I1 = I[1]
    Iinds = axes1(I1)
    for j = 2:length(I)
        axes1(I[j]) == Iinds || throw(DimensionMismatch("indices of I[1] ($(Iinds)) does not match indices of I[$j] ($(axes1(I[j])))"))
    end
    Iout = similar(I1)
    _sub2ind!(Iout, inds, Iinds, I)
    Iout
end

function _sub2ind!(Iout, inds, Iinds, I)
    @noinline
    for i in Iinds
        # Iout[i] = _sub2ind(inds, map(Ij -> Ij[i], I)...)
        Iout[i] = sub2ind_vec(inds, i, I)
    end
    Iout
end

sub2ind_vec(inds, i, I) = (@inline; _sub2ind(inds, _sub2ind_vec(i, I...)...))
_sub2ind_vec(i, I1, I...) = (@inline; (I1[i], _sub2ind_vec(i, I...)...))
_sub2ind_vec(i) = ()

function _ind2sub(inds::Union{DimsInteger{N},Indices{N}}, ind::AbstractVector{<:Integer}) where N
    M = length(ind)
    t = ntuple(n->similar(ind),Val(N))
    for (i,idx) in pairs(IndexLinear(), ind)
        sub = _ind2sub(inds, idx)
        for j = 1:N
            t[j][i] = sub[j]
        end
    end
    t
end

## iteration utilities ##

"""
    foreach(f, c...) -> Nothing

Call function `f` on each element of iterable `c`.
For multiple iterable arguments, `f` is called elementwise, and iteration stops when
any iterator is finished.

`foreach` should be used instead of [`map`](@ref) when the results of `f` are not
needed, for example in `foreach(println, array)`.

# Examples
```jldoctest
julia> tri = 1:3:7; res = Int[];

julia> foreach(x -> push!(res, x^2), tri)

julia> res
3-element Vector{$(Int)}:
  1
 16
 49

julia> foreach((x, y) -> println(x, " with ", y), tri, 'a':'z')
1 with a
4 with b
7 with c
```
"""
foreach(f) = (f(); nothing)
foreach(f, itr) = (for x in itr; f(x); end; nothing)
foreach(f, itrs...) = (for z in zip(itrs...); f(z...); end; nothing)

## map over arrays ##

## transform any set of dimensions
## dims specifies which dimensions will be transformed. for example
## dims==1:2 will call f on all slices A[:,:,...]
"""
    mapslices(f, A; dims)

Transform the given dimensions of array `A` by applying a function `f` on each slice
of the form `A[..., :, ..., :, ...]`, with a colon at each `d` in `dims`. The results are
concatenated along the remaining dimensions.

For example, if `dims = [1,2]` and `A` is 4-dimensional, then `f` is called on `x = A[:,:,i,j]`
for all `i` and `j`, and `f(x)` becomes `R[:,:,i,j]` in the result `R`.

See also [`eachcol`](@ref) or [`eachslice`](@ref), used with [`map`](@ref) or [`stack`](@ref).

# Examples
```jldoctest
julia> A = reshape(1:30,(2,5,3))
2×5×3 reshape(::UnitRange{$Int}, 2, 5, 3) with eltype $Int:
[:, :, 1] =
 1  3  5  7   9
 2  4  6  8  10

[:, :, 2] =
 11  13  15  17  19
 12  14  16  18  20

[:, :, 3] =
 21  23  25  27  29
 22  24  26  28  30

julia> f(x::Matrix) = fill(x[1,1], 1,4);  # returns a 1×4 matrix

julia> B = mapslices(f, A, dims=(1,2))
1×4×3 Array{$Int, 3}:
[:, :, 1] =
 1  1  1  1

[:, :, 2] =
 11  11  11  11

[:, :, 3] =
 21  21  21  21

julia> f2(x::AbstractMatrix) = fill(x[1,1], 1,4);

julia> B == stack(f2, eachslice(A, dims=3))
true

julia> g(x) = x[begin] // x[end-1];  # returns a number

julia> mapslices(g, A, dims=[1,3])
1×5×1 Array{Rational{$Int}, 3}:
[:, :, 1] =
 1//21  3//23  1//5  7//27  9//29

julia> map(g, eachslice(A, dims=2))
5-element Vector{Rational{$Int}}:
 1//21
 3//23
 1//5
 7//27
 9//29

julia> mapslices(sum, A; dims=(1,3)) == sum(A; dims=(1,3))
true
```

Notice that in `eachslice(A; dims=2)`, the specified dimension is the
one *without* a colon in the slice. This is `view(A,:,i,:)`, whereas
`mapslices(f, A; dims=(1,3))` uses `A[:,i,:]`. The function `f` may mutate
values in the slice without affecting `A`.
"""
function mapslices(f, A::AbstractArray; dims)
    isempty(dims) && return map(f, A)

    for d in dims
        d isa Integer || throw(ArgumentError("mapslices: dimension must be an integer, got $d"))
        d >= 1 || throw(ArgumentError("mapslices: dimension must be ≥ 1, got $d"))
        # Indexing a matrix M[:,1,:] produces a 1-column matrix, but dims=(1,3) here
        # would otherwise ignore 3, and slice M[:,i]. Previously this gave error:
        # BoundsError: attempt to access 2-element Vector{Any} at index [3]
        d > ndims(A) && throw(ArgumentError("mapslices does not accept dimensions > ndims(A) = $(ndims(A)), got $d"))
    end
    dim_mask = ntuple(d -> d in dims, ndims(A))

    # Apply the function to the first slice in order to determine the next steps
    idx1 = ntuple(d -> d in dims ? (:) : firstindex(A,d), ndims(A))
    Aslice = A[idx1...]
    r1 = f(Aslice)

    res1 = if r1 isa AbstractArray && ndims(r1) > 0
        n = sum(dim_mask)
        if ndims(r1) > n && any(ntuple(d -> size(r1,d+n)>1, ndims(r1)-n))
            s = size(r1)[1:n]
            throw(DimensionMismatch("mapslices cannot assign slice f(x) of size $(size(r1)) into output of size $s"))
        end
        r1
    else
        # If the result of f on a single slice is a scalar then we add singleton
        # dimensions. When adding the dimensions, we have to respect the
        # index type of the input array (e.g. in the case of OffsetArrays)
        _res1 = similar(Aslice, typeof(r1), reduced_indices(Aslice, 1:ndims(Aslice)))
        _res1[begin] = r1
        _res1
    end

    # Determine result size and allocate. We always pad ndims(res1) out to length(dims):
    din = Ref(0)
    Rsize = ntuple(ndims(A)) do d
        if d in dims
            axes(res1, din[] += 1)
        else
            axes(A,d)
        end
    end
    R = similar(res1, Rsize)

    # Determine iteration space. It will be convenient in the loop to mask N-dimensional
    # CartesianIndices, with some trivial dimensions:
    itershape = ntuple(d -> d in dims ? Base.OneTo(1) : axes(A,d), ndims(A))
    indices = Iterators.drop(CartesianIndices(itershape), 1)

    # That skips the first element, which we already have:
    ridx = ntuple(d -> d in dims ? Slice(axes(R,d)) : firstindex(A,d), ndims(A))
    concatenate_setindex!(R, res1, ridx...)

    # In some cases, we can re-use the first slice for a dramatic performance
    # increase. The slice itself must be mutable and the result cannot contain
    # any mutable containers. The following errs on the side of being overly
    # strict (#18570 & #21123).
    safe_for_reuse = isa(Aslice, StridedArray) &&
                     (isa(r1, Number) || (isa(r1, AbstractArray) && eltype(r1) <: Number))

    _inner_mapslices!(R, indices, f, A, dim_mask, Aslice, safe_for_reuse)
    return R
end

@noinline function _inner_mapslices!(R, indices, f, A, dim_mask, Aslice, safe_for_reuse)
    must_extend = any(dim_mask .& size(R) .> 1)
    if safe_for_reuse
        # when f returns an array, R[ridx...] = f(Aslice) line copies elements,
        # so we can reuse Aslice
        for I in indices
            idx = ifelse.(dim_mask, Slice.(axes(A)), Tuple(I))
            _unsafe_getindex!(Aslice, A, idx...)
            r = f(Aslice)
            if r isa AbstractArray || must_extend
                ridx = ifelse.(dim_mask, Slice.(axes(R)), Tuple(I))
                R[ridx...] = r
            else
                ridx = ifelse.(dim_mask, first.(axes(R)), Tuple(I))
                R[ridx...] = r
            end
        end
    else
        # we can't guarantee safety (#18524), so allocate new storage for each slice
        for I in indices
            idx = ifelse.(dim_mask, Slice.(axes(A)), Tuple(I))
            ridx = ifelse.(dim_mask, Slice.(axes(R)), Tuple(I))
            concatenate_setindex!(R, f(A[idx...]), ridx...)
        end
    end
end

concatenate_setindex!(R, v, I...) = (R[I...] .= (v,); R)
concatenate_setindex!(R, X::AbstractArray, I...) = (R[I...] = X)

## 0 arguments

map(f) = f()

## 1 argument

function map!(f::F, dest::AbstractArray, A::AbstractArray) where F
    for (i,j) in zip(eachindex(dest),eachindex(A))
        val = f(@inbounds A[j])
        @inbounds dest[i] = val
    end
    return dest
end

# map on collections
map(f, A::AbstractArray) = collect_similar(A, Generator(f,A))

mapany(f, A::AbstractArray) = map!(f, Vector{Any}(undef, length(A)), A)
mapany(f, itr) = Any[f(x) for x in itr]

"""
    map(f, c...) -> collection

Transform collection `c` by applying `f` to each element. For multiple collection arguments,
apply `f` elementwise, and stop when any of them is exhausted.

See also [`map!`](@ref), [`foreach`](@ref), [`mapreduce`](@ref), [`mapslices`](@ref), [`zip`](@ref), [`Iterators.map`](@ref).

# Examples
```jldoctest
julia> map(x -> x * 2, [1, 2, 3])
3-element Vector{Int64}:
 2
 4
 6

julia> map(+, [1, 2, 3], [10, 20, 30, 400, 5000])
3-element Vector{Int64}:
 11
 22
 33
```
"""
map(f, A) = collect(Generator(f,A)) # default to returning an Array for `map` on general iterators

map(f, ::AbstractDict) = error("map is not defined on dictionaries")
map(f, ::AbstractSet) = error("map is not defined on sets")

## 2 argument
function map!(f::F, dest::AbstractArray, A::AbstractArray, B::AbstractArray) where F
    for (i, j, k) in zip(eachindex(dest), eachindex(A), eachindex(B))
        @inbounds a, b = A[j], B[k]
        val = f(a, b)
        @inbounds dest[i] = val
    end
    return dest
end

## N argument

@inline ith_all(i, ::Tuple{}) = ()
function ith_all(i, as)
    @_propagate_inbounds_meta
    return (as[1][i], ith_all(i, tail(as))...)
end

function map_n!(f::F, dest::AbstractArray, As) where F
    idxs1 = LinearIndices(As[1])
    @boundscheck LinearIndices(dest) == idxs1 && all(x -> LinearIndices(x) == idxs1, As)
    for i = idxs1
        @inbounds I = ith_all(i, As)
        val = f(I...)
        @inbounds dest[i] = val
    end
    return dest
end

"""
    map!(function, destination, collection...)

Like [`map`](@ref), but stores the result in `destination` rather than a new
collection. `destination` must be at least as large as the smallest collection.

$(_DOCS_ALIASING_WARNING)

See also: [`map`](@ref), [`foreach`](@ref), [`zip`](@ref), [`copyto!`](@ref).

# Examples
```jldoctest
julia> a = zeros(3);

julia> map!(x -> x * 2, a, [1, 2, 3]);

julia> a
3-element Vector{Float64}:
 2.0
 4.0
 6.0

julia> map!(+, zeros(Int, 5), 100:999, 1:3)
5-element Vector{$(Int)}:
 101
 103
 105
   0
   0
```
"""
function map!(f::F, dest::AbstractArray, As::AbstractArray...) where {F}
    isempty(As) && throw(ArgumentError(
        """map! requires at least one "source" argument"""))
    map_n!(f, dest, As)
end

"""
    map(f, A::AbstractArray...) -> N-array

When acting on multi-dimensional arrays of the same [`ndims`](@ref),
they must all have the same [`axes`](@ref), and the answer will too.

See also [`broadcast`](@ref), which allows mismatched sizes.

# Examples
```
julia> map(//, [1 2; 3 4], [4 3; 2 1])
2×2 Matrix{Rational{$Int}}:
 1//4  2//3
 3//2  4//1

julia> map(+, [1 2; 3 4], zeros(2,1))
ERROR: DimensionMismatch

julia> map(+, [1 2; 3 4], [1,10,100,1000], zeros(3,1))  # iterates until 3rd is exhausted
3-element Vector{Float64}:
   2.0
  13.0
 102.0
```
"""
map(f, iters...) = collect(Generator(f, iters...))

# multi-item push!, pushfirst! (built on top of type-specific 1-item version)
# (note: must not cause a dispatch loop when 1-item case is not defined)
push!(A, a, b) = push!(push!(A, a), b)
push!(A, a, b, c...) = push!(push!(A, a, b), c...)
pushfirst!(A, a, b) = pushfirst!(pushfirst!(A, b), a)
pushfirst!(A, a, b, c...) = pushfirst!(pushfirst!(A, c...), a, b)

## hashing AbstractArray ##

const hash_abstractarray_seed = UInt === UInt64 ? 0x7e2d6fb6448beb77 : 0xd4514ce5
function hash(A::AbstractArray, h::UInt)
    h += hash_abstractarray_seed
    # Axes are themselves AbstractArrays, so hashing them directly would stack overflow
    # Instead hash the tuple of firsts and lasts along each dimension
    h = hash(map(first, axes(A)), h)
    h = hash(map(last, axes(A)), h)

    # For short arrays, it's not worth doing anything complicated
    if length(A) < 8192
        for x in A
            h = hash(x, h)
        end
        return h
    end

    # Goal: Hash approximately log(N) entries with a higher density of hashed elements
    # weighted towards the end and special consideration for repeated values. Colliding
    # hashes will often subsequently be compared by equality -- and equality between arrays
    # works elementwise forwards and is short-circuiting. This means that a collision
    # between arrays that differ by elements at the beginning is cheaper than one where the
    # difference is towards the end. Furthermore, choosing `log(N)` arbitrary entries from a
    # sparse array will likely only choose the same element repeatedly (zero in this case).

    # To achieve this, we work backwards, starting by hashing the last element of the
    # array. After hashing each element, we skip `fibskip` elements, where `fibskip`
    # is pulled from the Fibonacci sequence -- Fibonacci was chosen as a simple
    # ~O(log(N)) algorithm that ensures we don't hit a common divisor of a dimension
    # and only end up hashing one slice of the array (as might happen with powers of
    # two). Finally, we find the next distinct value from the one we just hashed.

    # This is a little tricky since skipping an integer number of values inherently works
    # with linear indices, but `findprev` uses `keys`. Hoist out the conversion "maps":
    ks = keys(A)
    key_to_linear = LinearIndices(ks) # Index into this map to compute the linear index
    linear_to_key = vec(ks)           # And vice-versa

    # Start at the last index
    keyidx = last(ks)
    linidx = key_to_linear[keyidx]
    fibskip = prevfibskip = oneunit(linidx)
    first_linear = first(LinearIndices(linear_to_key))
    n = 0
    while true
        n += 1
        # Hash the element
        elt = A[keyidx]
        h = hash(keyidx=>elt, h)

        # Skip backwards a Fibonacci number of indices -- this is a linear index operation
        linidx = key_to_linear[keyidx]
        linidx < fibskip + first_linear && break
        linidx -= fibskip
        keyidx = linear_to_key[linidx]

        # Only increase the Fibonacci skip once every N iterations. This was chosen
        # to be big enough that all elements of small arrays get hashed while
        # obscenely large arrays are still tractable. With a choice of N=4096, an
        # entirely-distinct 8000-element array will have ~75% of its elements hashed,
        # with every other element hashed in the first half of the array. At the same
        # time, hashing a `typemax(Int64)`-length Float64 range takes about a second.
        if rem(n, 4096) == 0
            fibskip, prevfibskip = fibskip + prevfibskip, fibskip
        end

        # Find a key index with a value distinct from `elt` -- might be `keyidx` itself
        keyidx = findprev(!isequal(elt), A, keyidx)
        keyidx === nothing && break
    end

    return h
end

# The semantics of `collect` are weird. Better to write our own
function rest(a::AbstractArray{T}, state...) where {T}
    v = Vector{T}(undef, 0)
    # assume only very few items are taken from the front
    sizehint!(v, length(a))
    return foldl(push!, Iterators.rest(a, state...), init=v)
end


## keepat! ##

# NOTE: since these use `@inbounds`, they are actually only intended for Vector and BitVector

function _keepat!(a::AbstractVector, inds)
    local prev
    i = firstindex(a)
    for k in inds
        if @isdefined(prev)
            prev < k || throw(ArgumentError("indices must be unique and sorted"))
        end
        ak = a[k] # must happen even when i==k for bounds checking
        if i != k
            @inbounds a[i] = ak # k > i, so a[i] is inbounds
        end
        prev = k
        i = nextind(a, i)
    end
    deleteat!(a, i:lastindex(a))
    return a
end

function _keepat!(a::AbstractVector, m::AbstractVector{Bool})
    length(m) == length(a) || throw(BoundsError(a, m))
    j = firstindex(a)
    for i in eachindex(a, m)
        @inbounds begin
            if m[i]
                i == j || (a[j] = a[i])
                j = nextind(a, j)
            end
        end
    end
    deleteat!(a, j:lastindex(a))
end

## 1-d circshift ##
function circshift!(a::AbstractVector, shift::Integer)
    n = length(a)
    n == 0 && return
    shift = mod(shift, n)
    shift == 0 && return
    l = lastindex(a)
    reverse!(a, firstindex(a), l-shift)
    reverse!(a, l-shift+1, lastindex(a))
    reverse!(a)
    return a
end
O   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/subarray.jlRR      # This file is a part of Julia. License is MIT: https://julialang.org/license

abstract type AbstractCartesianIndex{N} end # This is a hacky forward declaration for CartesianIndex
const ViewIndex = Union{Real, AbstractArray}
const ScalarIndex = Real

"""
    SubArray{T,N,P,I,L} <: AbstractArray{T,N}

`N`-dimensional view into a parent array (of type `P`) with an element type `T`, restricted by a tuple of indices (of type `I`). `L` is true for types that support fast linear indexing, and `false` otherwise.

Construct `SubArray`s using the [`view`](@ref) function.
"""
struct SubArray{T,N,P,I,L} <: AbstractArray{T,N}
    parent::P
    indices::I
    offset1::Int       # for linear indexing and pointer, only valid when L==true
    stride1::Int       # used only for linear indexing
    function SubArray{T,N,P,I,L}(parent, indices, offset1, stride1) where {T,N,P,I,L}
        @inline
        check_parent_index_match(parent, indices)
        new(parent, indices, offset1, stride1)
    end
end
# Compute the linear indexability of the indices, and combine it with the linear indexing of the parent
function SubArray(parent::AbstractArray, indices::Tuple)
    @inline
    SubArray(IndexStyle(viewindexing(indices), IndexStyle(parent)), parent, ensure_indexable(indices), index_dimsum(indices...))
end
function SubArray(::IndexCartesian, parent::P, indices::I, ::NTuple{N,Any}) where {P,I,N}
    @inline
    SubArray{eltype(P), N, P, I, false}(parent, indices, 0, 0)
end
function SubArray(::IndexLinear, parent::P, indices::I, ::NTuple{N,Any}) where {P,I,N}
    @inline
    # Compute the stride and offset
    stride1 = compute_stride1(parent, indices)
    SubArray{eltype(P), N, P, I, true}(parent, indices, compute_offset1(parent, stride1, indices), stride1)
end

check_parent_index_match(parent, indices) = check_parent_index_match(parent, index_ndims(indices...))
check_parent_index_match(parent::AbstractArray{T,N}, ::NTuple{N, Bool}) where {T,N} = nothing
check_parent_index_match(parent, ::NTuple{N, Bool}) where {N} =
    throw(ArgumentError("number of indices ($N) must match the parent dimensionality ($(ndims(parent)))"))

# This computes the linear indexing compatibility for a given tuple of indices
viewindexing(I::Tuple{}) = IndexLinear()
# Leading scalar indices simply increase the stride
viewindexing(I::Tuple{ScalarIndex, Vararg{Any}}) = (@inline; viewindexing(tail(I)))
# Slices may begin a section which may be followed by any number of Slices
viewindexing(I::Tuple{Slice, Slice, Vararg{Any}}) = (@inline; viewindexing(tail(I)))
# A UnitRange can follow Slices, but only if all other indices are scalar
viewindexing(I::Tuple{Slice, AbstractUnitRange, Vararg{ScalarIndex}}) = IndexLinear()
viewindexing(I::Tuple{Slice, Slice, Vararg{ScalarIndex}}) = IndexLinear() # disambiguate
# In general, ranges are only fast if all other indices are scalar
viewindexing(I::Tuple{AbstractRange, Vararg{ScalarIndex}}) = IndexLinear()
# All other index combinations are slow
viewindexing(I::Tuple{Vararg{Any}}) = IndexCartesian()
# Of course, all other array types are slow
viewindexing(I::Tuple{AbstractArray, Vararg{Any}}) = IndexCartesian()

# Simple utilities
size(V::SubArray) = (@inline; map(length, axes(V)))

similar(V::SubArray, T::Type, dims::Dims) = similar(V.parent, T, dims)

sizeof(V::SubArray) = length(V) * sizeof(eltype(V))
sizeof(V::SubArray{<:Any,<:Any,<:Array}) = length(V) * elsize(V.parent)

function Base.copy(V::SubArray)
    v = V.parent[V.indices...]
    ndims(V) == 0 || return v
    x = similar(V) # ensure proper type of x
    x[] = v
    return x
end

parent(V::SubArray) = V.parent
parentindices(V::SubArray) = V.indices

"""
    parentindices(A)

Return the indices in the [`parent`](@ref) which correspond to the view `A`.

# Examples
```jldoctest
julia> A = [1 2; 3 4];

julia> V = view(A, 1, :)
2-element view(::Matrix{Int64}, 1, :) with eltype Int64:
 1
 2

julia> parentindices(V)
(1, Base.Slice(Base.OneTo(2)))
```
"""
function parentindices end

parentindices(a::AbstractArray) = map(oneto, size(a))

## Aliasing detection
dataids(A::SubArray) = (dataids(A.parent)..., _splatmap(dataids, A.indices)...)
_splatmap(f, ::Tuple{}) = ()
_splatmap(f, t::Tuple) = (f(t[1])..., _splatmap(f, tail(t))...)
unaliascopy(A::SubArray) = typeof(A)(unaliascopy(A.parent), map(unaliascopy, A.indices), A.offset1, A.stride1)

# When the parent is an Array we can trim the size down a bit. In the future this
# could possibly be extended to any mutable array.
function unaliascopy(V::SubArray{T,N,A,I,LD}) where {T,N,A<:Array,I<:Tuple{Vararg{Union{Real,AbstractRange,Array}}},LD}
    dest = Array{T}(undef, index_lengths(V.indices...))
    copyto!(dest, V)
    SubArray{T,N,A,I,LD}(dest, map(_trimmedindex, V.indices), 0, Int(LD))
end
# Transform indices to be "dense"
_trimmedindex(i::Real) = oftype(i, 1)
_trimmedindex(i::AbstractUnitRange) = oftype(i, oneto(length(i)))
_trimmedindex(i::AbstractArray) = oftype(i, reshape(eachindex(IndexLinear(), i), axes(i)))

## SubArray creation
# We always assume that the dimensionality of the parent matches the number of
# indices that end up getting passed to it, so we store the parent as a
# ReshapedArray view if necessary. The trouble is that arrays of `CartesianIndex`
# can make the number of effective indices not equal to length(I).
_maybe_reshape_parent(A::AbstractArray, ::NTuple{1, Bool}) = reshape(A, Val(1))
_maybe_reshape_parent(A::AbstractArray{<:Any,1}, ::NTuple{1, Bool}) = reshape(A, Val(1))
_maybe_reshape_parent(A::AbstractArray{<:Any,N}, ::NTuple{N, Bool}) where {N} = A
_maybe_reshape_parent(A::AbstractArray, ::NTuple{N, Bool}) where {N} = reshape(A, Val(N))
# The trailing singleton indices could be eliminated after bounds checking.
rm_singleton_indices(ndims::Tuple, J1, Js...) = (J1, rm_singleton_indices(IteratorsMD._splitrest(ndims, index_ndims(J1)), Js...)...)
rm_singleton_indices(::Tuple{}, ::ScalarIndex, Js...) = rm_singleton_indices((), Js...)
rm_singleton_indices(::Tuple) = ()

"""
    view(A, inds...)

Like [`getindex`](@ref), but returns a lightweight array that lazily references
(or is effectively a _view_ into) the parent array `A` at the given index or indices
`inds` instead of eagerly extracting elements or constructing a copied subset.
Calling [`getindex`](@ref) or [`setindex!`](@ref) on the returned value
(often a [`SubArray`](@ref)) computes the indices to access or modify the
parent array on the fly.  The behavior is undefined if the shape of the parent array is
changed after `view` is called because there is no bound check for the parent array; e.g.,
it may cause a segmentation fault.

Some immutable parent arrays (like ranges) may choose to simply
recompute a new array in some circumstances instead of returning
a `SubArray` if doing so is efficient and provides compatible semantics.

!!! compat "Julia 1.6"
    In Julia 1.6 or later, `view` can be called on an `AbstractString`, returning a
    `SubString`.

# Examples
```jldoctest
julia> A = [1 2; 3 4]
2×2 Matrix{Int64}:
 1  2
 3  4

julia> b = view(A, :, 1)
2-element view(::Matrix{Int64}, :, 1) with eltype Int64:
 1
 3

julia> fill!(b, 0)
2-element view(::Matrix{Int64}, :, 1) with eltype Int64:
 0
 0

julia> A # Note A has changed even though we modified b
2×2 Matrix{Int64}:
 0  2
 0  4

julia> view(2:5, 2:3) # returns a range as type is immutable
3:4
```
"""
function view(A::AbstractArray, I::Vararg{Any,M}) where {M}
    @inline
    J = map(i->unalias(A,i), to_indices(A, I))
    @boundscheck checkbounds(A, J...)
    J′ = rm_singleton_indices(ntuple(Returns(true), Val(ndims(A))), J...)
    unsafe_view(_maybe_reshape_parent(A, index_ndims(J′...)), J′...)
end

# Ranges implement getindex to return recomputed ranges; use that for views, too (when possible)
function view(r1::OneTo, r2::OneTo)
    @_propagate_inbounds_meta
    getindex(r1, r2)
end
function view(r1::AbstractUnitRange, r2::AbstractUnitRange{<:Integer})
    @_propagate_inbounds_meta
    getindex(r1, r2)
end
function view(r1::AbstractUnitRange, r2::StepRange{<:Integer})
    @_propagate_inbounds_meta
    getindex(r1, r2)
end
function view(r1::StepRange, r2::AbstractRange{<:Integer})
    @_propagate_inbounds_meta
    getindex(r1, r2)
end
function view(r1::StepRangeLen, r2::OrdinalRange{<:Integer})
    @_propagate_inbounds_meta
    getindex(r1, r2)
end
function view(r1::LinRange, r2::OrdinalRange{<:Integer})
    @_propagate_inbounds_meta
    getindex(r1, r2)
end

# getindex(r::AbstractRange, ::Colon) returns a copy of the range, and we may do the same for a view
function view(r1::AbstractRange, c::Colon)
    @_propagate_inbounds_meta
    getindex(r1, c)
end

function unsafe_view(A::AbstractArray, I::Vararg{ViewIndex,N}) where {N}
    @inline
    SubArray(A, I)
end
# When we take the view of a view, it's often possible to "reindex" the parent
# view's indices such that we can "pop" the parent view and keep just one layer
# of indirection. But we can't always do this because arrays of `CartesianIndex`
# might span multiple parent indices, making the reindex calculation very hard.
# So we use _maybe_reindex to figure out if there are any arrays of
# `CartesianIndex`, and if so, we punt and keep two layers of indirection.
unsafe_view(V::SubArray, I::Vararg{ViewIndex,N}) where {N} =
    (@inline; _maybe_reindex(V, I))
_maybe_reindex(V, I) = (@inline; _maybe_reindex(V, I, I))
_maybe_reindex(V, I, ::Tuple{AbstractArray{<:AbstractCartesianIndex}, Vararg{Any}}) =
    (@inline; SubArray(V, I))
# But allow arrays of CartesianIndex{1}; they behave just like arrays of Ints
_maybe_reindex(V, I, A::Tuple{AbstractArray{<:AbstractCartesianIndex{1}}, Vararg{Any}}) =
    (@inline; _maybe_reindex(V, I, tail(A)))
_maybe_reindex(V, I, A::Tuple{Any, Vararg{Any}}) = (@inline; _maybe_reindex(V, I, tail(A)))
function _maybe_reindex(V, I, ::Tuple{})
    @inline
    @inbounds idxs = to_indices(V.parent, reindex(V.indices, I))
    SubArray(V.parent, idxs)
end

## Re-indexing is the heart of a view, transforming A[i, j][x, y] to A[i[x], j[y]]
#
# Recursively look through the heads of the parent- and sub-indices, considering
# the following cases:
# * Parent index is array  -> re-index that with one or more sub-indices (one per dimension)
# * Parent index is Colon  -> just use the sub-index as provided
# * Parent index is scalar -> that dimension was dropped, so skip the sub-index and use the index as is

AbstractZeroDimArray{T} = AbstractArray{T, 0}

reindex(::Tuple{}, ::Tuple{}) = ()

# Skip dropped scalars, so simply peel them off the parent indices and continue
reindex(idxs::Tuple{ScalarIndex, Vararg{Any}}, subidxs::Tuple{Vararg{Any}}) =
    (@_propagate_inbounds_meta; (idxs[1], reindex(tail(idxs), subidxs)...))

# Slices simply pass their subindices straight through
reindex(idxs::Tuple{Slice, Vararg{Any}}, subidxs::Tuple{Any, Vararg{Any}}) =
    (@_propagate_inbounds_meta; (subidxs[1], reindex(tail(idxs), tail(subidxs))...))

# Re-index into parent vectors with one subindex
reindex(idxs::Tuple{AbstractVector, Vararg{Any}}, subidxs::Tuple{Any, Vararg{Any}}) =
    (@_propagate_inbounds_meta; (idxs[1][subidxs[1]], reindex(tail(idxs), tail(subidxs))...))

# Parent matrices are re-indexed with two sub-indices
reindex(idxs::Tuple{AbstractMatrix, Vararg{Any}}, subidxs::Tuple{Any, Any, Vararg{Any}}) =
    (@_propagate_inbounds_meta; (idxs[1][subidxs[1], subidxs[2]], reindex(tail(idxs), tail(tail(subidxs)))...))

# In general, we index N-dimensional parent arrays with N indices
@generated function reindex(idxs::Tuple{AbstractArray{T,N}, Vararg{Any}}, subidxs::Tuple{Vararg{Any}}) where {T,N}
    if length(subidxs.parameters) >= N
        subs = [:(subidxs[$d]) for d in 1:N]
        tail = [:(subidxs[$d]) for d in N+1:length(subidxs.parameters)]
        :(@_propagate_inbounds_meta; (idxs[1][$(subs...)], reindex(tail(idxs), ($(tail...),))...))
    else
        :(throw(ArgumentError("cannot re-index SubArray with fewer indices than dimensions\nThis should not occur; please submit a bug report.")))
    end
end

# In general, we simply re-index the parent indices by the provided ones
SlowSubArray{T,N,P,I} = SubArray{T,N,P,I,false}
function getindex(V::SubArray{T,N}, I::Vararg{Int,N}) where {T,N}
    @inline
    @boundscheck checkbounds(V, I...)
    @inbounds r = V.parent[reindex(V.indices, I)...]
    r
end

# But SubArrays with fast linear indexing pre-compute a stride and offset
FastSubArray{T,N,P,I} = SubArray{T,N,P,I,true}
function getindex(V::FastSubArray, i::Int)
    @inline
    @boundscheck checkbounds(V, i)
    @inbounds r = V.parent[V.offset1 + V.stride1*i]
    r
end
# We can avoid a multiplication if the first parent index is a Colon or AbstractUnitRange,
# or if all the indices are scalars, i.e. the view is for a single value only
FastContiguousSubArray{T,N,P,I<:Union{Tuple{Union{Slice, AbstractUnitRange}, Vararg{Any}},
                                      Tuple{Vararg{ScalarIndex}}}} = SubArray{T,N,P,I,true}
function getindex(V::FastContiguousSubArray, i::Int)
    @inline
    @boundscheck checkbounds(V, i)
    @inbounds r = V.parent[V.offset1 + i]
    r
end
# For vector views with linear indexing, we disambiguate to favor the stride/offset
# computation as that'll generally be faster than (or just as fast as) re-indexing into a range.
function getindex(V::FastSubArray{<:Any, 1}, i::Int)
    @inline
    @boundscheck checkbounds(V, i)
    @inbounds r = V.parent[V.offset1 + V.stride1*i]
    r
end
function getindex(V::FastContiguousSubArray{<:Any, 1}, i::Int)
    @inline
    @boundscheck checkbounds(V, i)
    @inbounds r = V.parent[V.offset1 + i]
    r
end

# Indexed assignment follows the same pattern as `getindex` above
function setindex!(V::SubArray{T,N}, x, I::Vararg{Int,N}) where {T,N}
    @inline
    @boundscheck checkbounds(V, I...)
    @inbounds V.parent[reindex(V.indices, I)...] = x
    V
end
function setindex!(V::FastSubArray, x, i::Int)
    @inline
    @boundscheck checkbounds(V, i)
    @inbounds V.parent[V.offset1 + V.stride1*i] = x
    V
end
function setindex!(V::FastContiguousSubArray, x, i::Int)
    @inline
    @boundscheck checkbounds(V, i)
    @inbounds V.parent[V.offset1 + i] = x
    V
end
function setindex!(V::FastSubArray{<:Any, 1}, x, i::Int)
    @inline
    @boundscheck checkbounds(V, i)
    @inbounds V.parent[V.offset1 + V.stride1*i] = x
    V
end
function setindex!(V::FastContiguousSubArray{<:Any, 1}, x, i::Int)
    @inline
    @boundscheck checkbounds(V, i)
    @inbounds V.parent[V.offset1 + i] = x
    V
end

function isassigned(V::SubArray{T,N}, I::Vararg{Int,N}) where {T,N}
    @inline
    @boundscheck checkbounds(Bool, V, I...) || return false
    @inbounds r = isassigned(V.parent, reindex(V.indices, I)...)
    r
end
function isassigned(V::FastSubArray, i::Int)
    @inline
    @boundscheck checkbounds(Bool, V, i) || return false
    @inbounds r = isassigned(V.parent, V.offset1 + V.stride1*i)
    r
end
function isassigned(V::FastContiguousSubArray, i::Int)
    @inline
    @boundscheck checkbounds(Bool, V, i) || return false
    @inbounds r = isassigned(V.parent, V.offset1 + i)
    r
end
function isassigned(V::FastSubArray{<:Any, 1}, i::Int)
    @inline
    @boundscheck checkbounds(Bool, V, i) || return false
    @inbounds r = isassigned(V.parent, V.offset1 + V.stride1*i)
    r
end
function isassigned(V::FastContiguousSubArray{<:Any, 1}, i::Int)
    @inline
    @boundscheck checkbounds(Bool, V, i) || return false
    @inbounds r = isassigned(V.parent, V.offset1 + i)
    r
end

IndexStyle(::Type{<:FastSubArray}) = IndexLinear()
IndexStyle(::Type{<:SubArray}) = IndexCartesian()

# Strides are the distance in memory between adjacent elements in a given dimension
# which we determine from the strides of the parent
strides(V::SubArray) = substrides(strides(V.parent), V.indices)

substrides(strds::Tuple{}, ::Tuple{}) = ()
substrides(strds::NTuple{N,Int}, I::Tuple{ScalarIndex, Vararg{Any}}) where N = (substrides(tail(strds), tail(I))...,)
substrides(strds::NTuple{N,Int}, I::Tuple{Slice, Vararg{Any}}) where N = (first(strds), substrides(tail(strds), tail(I))...)
substrides(strds::NTuple{N,Int}, I::Tuple{AbstractRange, Vararg{Any}}) where N = (first(strds)*step(I[1]), substrides(tail(strds), tail(I))...)
substrides(strds, I::Tuple{Any, Vararg{Any}}) = throw(ArgumentError("strides is invalid for SubArrays with indices of type $(typeof(I[1]))"))

stride(V::SubArray, d::Integer) = d <= ndims(V) ? strides(V)[d] : strides(V)[end] * size(V)[end]

compute_stride1(parent::AbstractArray, I::NTuple{N,Any}) where {N} =
    (@inline; compute_stride1(1, fill_to_length(axes(parent), OneTo(1), Val(N)), I))
compute_stride1(s, inds, I::Tuple{}) = s
compute_stride1(s, inds, I::Tuple{Vararg{ScalarIndex}}) = s
compute_stride1(s, inds, I::Tuple{ScalarIndex, Vararg{Any}}) =
    (@inline; compute_stride1(s*length(inds[1]), tail(inds), tail(I)))
compute_stride1(s, inds, I::Tuple{AbstractRange, Vararg{Any}}) = s*step(I[1])
compute_stride1(s, inds, I::Tuple{Slice, Vararg{Any}}) = s
compute_stride1(s, inds, I::Tuple{Any, Vararg{Any}}) = throw(ArgumentError("invalid strided index type $(typeof(I[1]))"))

elsize(::Type{<:SubArray{<:Any,<:Any,P}}) where {P} = elsize(P)

iscontiguous(A::SubArray) = iscontiguous(typeof(A))
iscontiguous(::Type{<:SubArray}) = false
iscontiguous(::Type{<:FastContiguousSubArray}) = true

first_index(V::FastSubArray) = V.offset1 + V.stride1 # cached for fast linear SubArrays
function first_index(V::SubArray)
    P, I = parent(V), V.indices
    s1 = compute_stride1(P, I)
    s1 + compute_offset1(P, s1, I)
end

# Computing the first index simply steps through the indices, accumulating the
# sum of index each multiplied by the parent's stride.
# The running sum is `f`; the cumulative stride product is `s`.
# If the parent is a vector, then we offset the parent's own indices with parameters of I
compute_offset1(parent::AbstractVector, stride1::Integer, I::Tuple{AbstractRange}) =
    (@inline; first(I[1]) - stride1*first(axes1(I[1])))
# If the result is one-dimensional and it's a Colon, then linear
# indexing uses the indices along the given dimension.
# If the result is one-dimensional and it's a range, then linear
# indexing might be offset if the index itself is offset
# Otherwise linear indexing always matches the parent.
compute_offset1(parent, stride1::Integer, I::Tuple) =
    (@inline; compute_offset1(parent, stride1, find_extended_dims(1, I...), find_extended_inds(I...), I))
compute_offset1(parent, stride1::Integer, dims::Tuple{Int}, inds::Tuple{Slice}, I::Tuple) =
    (@inline; compute_linindex(parent, I) - stride1*first(axes(parent, dims[1])))  # index-preserving case
compute_offset1(parent, stride1::Integer, dims, inds::Tuple{AbstractRange}, I::Tuple) =
    (@inline; compute_linindex(parent, I) - stride1*first(axes1(inds[1]))) # potentially index-offsetting case
compute_offset1(parent, stride1::Integer, dims, inds, I::Tuple) =
    (@inline; compute_linindex(parent, I) - stride1)
function compute_linindex(parent, I::NTuple{N,Any}) where N
    @inline
    IP = fill_to_length(axes(parent), OneTo(1), Val(N))
    compute_linindex(first(LinearIndices(parent)), 1, IP, I)
end
function compute_linindex(f, s, IP::Tuple, I::Tuple{ScalarIndex, Vararg{Any}})
    @inline
    Δi = I[1]-first(IP[1])
    compute_linindex(f + Δi*s, s*length(IP[1]), tail(IP), tail(I))
end
function compute_linindex(f, s, IP::Tuple, I::Tuple{Any, Vararg{Any}})
    @inline
    Δi = first(I[1])-first(IP[1])
    compute_linindex(f + Δi*s, s*length(IP[1]), tail(IP), tail(I))
end
compute_linindex(f, s, IP::Tuple, I::Tuple{}) = f

find_extended_dims(dim, ::ScalarIndex, I...) = (@inline; find_extended_dims(dim + 1, I...))
find_extended_dims(dim, i1, I...) = (@inline; (dim, find_extended_dims(dim + 1, I...)...))
find_extended_dims(dim) = ()
find_extended_inds(::ScalarIndex, I...) = (@inline; find_extended_inds(I...))
find_extended_inds(i1, I...) = (@inline; (i1, find_extended_inds(I...)...))
find_extended_inds() = ()

function unsafe_convert(::Type{Ptr{T}}, V::SubArray{T,N,P,<:Tuple{Vararg{RangeIndex}}}) where {T,N,P}
    return unsafe_convert(Ptr{T}, V.parent) + _memory_offset(V.parent, map(first, V.indices)...)
end

pointer(V::FastSubArray, i::Int) = pointer(V.parent, V.offset1 + V.stride1*i)
pointer(V::FastContiguousSubArray, i::Int) = pointer(V.parent, V.offset1 + i)

function pointer(V::SubArray{<:Any,<:Any,<:Array,<:Tuple{Vararg{RangeIndex}}}, is::AbstractCartesianIndex{N}) where {N}
    index = first_index(V)
    strds = strides(V)
    for d = 1:N
        index += (is[d]-1)*strds[d]
    end
    return pointer(V.parent, index)
end

# indices are taken from the range/vector
# Since bounds-checking is performance-critical and uses
# indices, it's worth optimizing these implementations thoroughly
axes(S::SubArray) = (@inline; _indices_sub(S.indices...))
_indices_sub(::Real, I...) = (@inline; _indices_sub(I...))
_indices_sub() = ()
function _indices_sub(i1::AbstractArray, I...)
    @inline
    (axes(i1)..., _indices_sub(I...)...)
end

has_offset_axes(S::SubArray) = has_offset_axes(S.indices...)
L   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/views.jl�!      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
    replace_ref_begin_end!(ex)

Recursively replace occurrences of the symbols `:begin` and `:end` in a "ref" expression
(i.e. `A[...]`) `ex` with the appropriate function calls (`firstindex` or `lastindex`).
Replacement uses the closest enclosing ref, so

    A[B[end]]

should transform to

    A[B[lastindex(B)]]

"""
replace_ref_begin_end!(ex) = replace_ref_begin_end_!(ex, nothing)[1]
# replace_ref_begin_end_!(ex,withex) returns (new ex, whether withex was used)
function replace_ref_begin_end_!(ex, withex)
    used_withex = false
    if isa(ex,Symbol)
        if ex === :begin
            withex === nothing && error("Invalid use of begin")
            return withex[1], true
        elseif ex === :end
            withex === nothing && error("Invalid use of end")
            return withex[2], true
        end
    elseif isa(ex,Expr)
        if ex.head === :ref
            ex.args[1], used_withex = replace_ref_begin_end_!(ex.args[1], withex)
            S = isa(ex.args[1],Symbol) ? ex.args[1]::Symbol : gensym(:S) # temp var to cache ex.args[1] if needed
            used_S = false # whether we actually need S
            # new :ref, so redefine withex
            nargs = length(ex.args)-1
            if nargs == 0
                return ex, used_withex
            elseif nargs == 1
                # replace with lastindex(S)
                ex.args[2], used_S = replace_ref_begin_end_!(ex.args[2], (:($firstindex($S)),:($lastindex($S))))
            else
                n = 1
                J = lastindex(ex.args)
                for j = 2:J
                    exj, used = replace_ref_begin_end_!(ex.args[j], (:($firstindex($S,$n)),:($lastindex($S,$n))))
                    used_S |= used
                    ex.args[j] = exj
                    if isa(exj,Expr) && exj.head === :...
                        # splatted object
                        exjs = exj.args[1]
                        n = :($n + length($exjs))
                    elseif isa(n, Expr)
                        # previous expression splatted
                        n = :($n + 1)
                    else
                        # an integer
                        n += 1
                    end
                end
            end
            if used_S && S !== ex.args[1]
                S0 = ex.args[1]
                ex.args[1] = S
                ex = Expr(:let, :($S = $S0), ex)
            end
        else
            # recursive search
            for i = eachindex(ex.args)
                ex.args[i], used = replace_ref_begin_end_!(ex.args[i], withex)
                used_withex |= used
            end
        end
    end
    ex, used_withex
end

"""
    @view A[inds...]

Transform the indexing expression `A[inds...]` into the equivalent [`view`](@ref) call.

This can only be applied directly to a single indexing expression and is particularly
helpful for expressions that include the special `begin` or `end` indexing syntaxes
like `A[begin, 2:end-1]` (as those are not supported by the normal [`view`](@ref)
function).

Note that `@view` cannot be used as the target of a regular assignment (e.g.,
`@view(A[1, 2:end]) = ...`), nor would the un-decorated
[indexed assignment](@ref man-indexed-assignment) (`A[1, 2:end] = ...`)
or broadcasted indexed assignment (`A[1, 2:end] .= ...`) make a copy.  It can be useful,
however, for _updating_ broadcasted assignments like `@view(A[1, 2:end]) .+= 1`
because this is a simple syntax for `@view(A[1, 2:end]) .= @view(A[1, 2:end]) + 1`,
and the indexing expression on the right-hand side would otherwise make a
copy without the `@view`.

See also [`@views`](@ref) to switch an entire block of code to use views for non-scalar indexing.

!!! compat "Julia 1.5"
    Using `begin` in an indexing expression to refer to the first index requires at least
    Julia 1.5.

# Examples
```jldoctest
julia> A = [1 2; 3 4]
2×2 Matrix{Int64}:
 1  2
 3  4

julia> b = @view A[:, 1]
2-element view(::Matrix{Int64}, :, 1) with eltype Int64:
 1
 3

julia> fill!(b, 0)
2-element view(::Matrix{Int64}, :, 1) with eltype Int64:
 0
 0

julia> A
2×2 Matrix{Int64}:
 0  2
 0  4
```
"""
macro view(ex)
    if Meta.isexpr(ex, :ref)
        ex = replace_ref_begin_end!(ex)
        if Meta.isexpr(ex, :ref)
            ex = Expr(:call, view, ex.args...)
        else # ex replaced by let ...; foo[...]; end
            if !(Meta.isexpr(ex, :let) && Meta.isexpr(ex.args[2], :ref))
                error("invalid expression")
            end
            ex.args[2] = Expr(:call, view, ex.args[2].args...)
        end
        Expr(:&&, true, esc(ex))
    else
        throw(ArgumentError("Invalid use of @view macro: argument must be a reference expression A[...]."))
    end
end

############################################################################
# @views macro code:

# maybeview is like getindex, but returns a view for slicing operations
# (while remaining equivalent to getindex for scalar indices and non-array types)
@propagate_inbounds maybeview(A, args...) = getindex(A, args...)
@propagate_inbounds maybeview(A::AbstractArray, args...) = view(A, args...)
@propagate_inbounds maybeview(A::AbstractArray, args::Union{Number,AbstractCartesianIndex}...) = getindex(A, args...)
@propagate_inbounds maybeview(A) = getindex(A)
@propagate_inbounds maybeview(A::AbstractArray) = getindex(A)

# _views implements the transformation for the @views macro.
# @views calls esc(_views(...)) to work around #20241,
# so any function calls we insert (to maybeview, or to
# firstindex and lastindex in replace_ref_begin_end!) must be interpolated
# as values rather than as symbols to ensure that they are called
# from Base rather than from the caller's scope.
_views(x) = x
function _views(ex::Expr)
    if ex.head in (:(=), :(.=))
        # don't use view for ref on the lhs of an assignment,
        # but still use views for the args of the ref:
        arg1 = ex.args[1]
        Expr(ex.head, Meta.isexpr(arg1, :ref) ?
                        Expr(:ref, mapany(_views, (arg1::Expr).args)...) : _views(arg1),
                _views(ex.args[2]))
    elseif ex.head === :ref
        Expr(:call, maybeview, mapany(_views, ex.args)...)::Expr
    else
        h = string(ex.head)
        # don't use view on the lhs of an op-assignment a[i...] += ...
        if last(h) == '=' && Meta.isexpr(ex.args[1], :ref)
            lhs = ex.args[1]::Expr

            # temp vars to avoid recomputing a and i,
            # which will be assigned in a let block:
            a = gensym(:a)
            i = let lhs=lhs     # #15276
                [gensym(:i) for k = 1:length(lhs.args)-1]
            end

            # for splatted indices like a[i, j...], we need to
            # splat the corresponding temp var.
            I = similar(i, Any)
            for k = 1:length(i)
                argk1 = lhs.args[k+1]
                if Meta.isexpr(argk1, :...)
                    I[k] = Expr(:..., i[k])
                    lhs.args[k+1] = (argk1::Expr).args[1] # unsplat
                else
                    I[k] = i[k]
                end
            end

            Expr(:let,
                 Expr(:block,
                      :($a = $(_views(lhs.args[1]))),
                      Any[:($(i[k]) = $(_views(lhs.args[k+1]))) for k=1:length(i)]...),
                 Expr(first(h) == '.' ? :(.=) : :(=), :($a[$(I...)]),
                      Expr(:call, Symbol(h[1:end-1]),
                           :($maybeview($a, $(I...))),
                           mapany(_views, ex.args[2:end])...)))
        else
            exprarray(ex.head, mapany(_views, ex.args))
        end
    end
end

"""
    @views expression

Convert every array-slicing operation in the given expression
(which may be a `begin`/`end` block, loop, function, etc.)
to return a view. Scalar indices, non-array types, and
explicit [`getindex`](@ref) calls (as opposed to `array[...]`) are
unaffected.

Similarly, `@views` converts string slices into [`SubString`](@ref) views.

!!! note
    The `@views` macro only affects `array[...]` expressions
    that appear explicitly in the given `expression`, not array slicing that
    occurs in functions called by that code.

!!! compat "Julia 1.5"
    Using `begin` in an indexing expression to refer to the first index requires at least
    Julia 1.5.

# Examples
```jldoctest
julia> A = zeros(3, 3);

julia> @views for row in 1:3
           b = A[row, :]
           b[:] .= row
       end

julia> A
3×3 Matrix{Float64}:
 1.0  1.0  1.0
 2.0  2.0  2.0
 3.0  3.0  3.0
```
"""
macro views(x)
    esc(_views(replace_ref_begin_end!(x)))
end
N   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/baseext.jlz
      # This file is a part of Julia. License is MIT: https://julialang.org/license

# extensions to Core types to add features in Base

"""
    VecElement{T}

A wrapper type that holds a single value of type `T`. When used in the context of an
`NTuple{N, VecElement{T}} where {T, N}` object, it provides a hint to the runtime
system to align that struct to be more amenable to vectorization optimization
opportunities. In `ccall`, such an NTuple in the type signature will also use the
vector register ABI, rather than the usual struct ABI.
"""
VecElement

# hook up VecElement constructor to Base.convert
VecElement{T}(arg) where {T} = VecElement{T}(convert(T, arg))
convert(::Type{T}, arg::T) where {T<:VecElement} = arg
convert(::Type{T}, arg)  where {T<:VecElement} = T(arg)::T

# ## dims-type-converting Array constructors for convenience
# type and dimensionality specified, accepting dims as series of Integers
Vector{T}(::UndefInitializer, m::Integer) where {T} = Vector{T}(undef, Int(m))
Matrix{T}(::UndefInitializer, m::Integer, n::Integer) where {T} = Matrix{T}(undef, Int(m), Int(n))
Array{T,N}(::UndefInitializer, d::Vararg{Integer,N}) where {T,N} = Array{T,N}(undef, convert(Tuple{Vararg{Int}}, d))
# type but not dimensionality specified, accepting dims as series of Integers
Array{T}(::UndefInitializer, m::Integer) where {T} = Array{T,1}(undef, Int(m))
Array{T}(::UndefInitializer, m::Integer, n::Integer) where {T} = Array{T,2}(undef, Int(m), Int(n))
Array{T}(::UndefInitializer, m::Integer, n::Integer, o::Integer) where {T} = Array{T,3}(undef, Int(m), Int(n), Int(o))
Array{T}(::UndefInitializer, d::Integer...) where {T} = Array{T}(undef, convert(Tuple{Vararg{Int}}, d))
# dimensionality but not type specified, accepting dims as series of Integers
Vector(::UndefInitializer, m::Integer) = Vector{Any}(undef, Int(m))
Matrix(::UndefInitializer, m::Integer, n::Integer) = Matrix{Any}(undef, Int(m), Int(n))
# Dimensions as a single tuple
Array{T}(::UndefInitializer, d::NTuple{N,Integer}) where {T,N} = Array{T,N}(undef, convert(Tuple{Vararg{Int}}, d))
Array{T,N}(::UndefInitializer, d::NTuple{N,Integer}) where {T,N} = Array{T,N}(undef, convert(Tuple{Vararg{Int}}, d))
# empty vector constructor
Vector() = Vector{Any}(undef, 0)

# Array constructors for nothing and missing
# type and dimensionality specified
Array{T,N}(::Nothing, d...) where {T,N} = fill!(Array{T,N}(undef, d...), nothing)
Array{T,N}(::Missing, d...) where {T,N} = fill!(Array{T,N}(undef, d...), missing)
# type but not dimensionality specified
Array{T}(::Nothing, d...) where {T} = fill!(Array{T}(undef, d...), nothing)
Array{T}(::Missing, d...) where {T} = fill!(Array{T}(undef, d...), missing)
M   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/ntuple.jl�
      # This file is a part of Julia. License is MIT: https://julialang.org/license

# `ntuple`, for constructing tuples of a given length

"""
    ntuple(f::Function, n::Integer)

Create a tuple of length `n`, computing each element as `f(i)`,
where `i` is the index of the element.

# Examples
```jldoctest
julia> ntuple(i -> 2*i, 4)
(2, 4, 6, 8)
```
"""
@inline function ntuple(f::F, n::Integer) where F
    # marked inline since this benefits from constant propagation of `n`
    t = n == 0  ? () :
        n == 1  ? (f(1),) :
        n == 2  ? (f(1), f(2)) :
        n == 3  ? (f(1), f(2), f(3)) :
        n == 4  ? (f(1), f(2), f(3), f(4)) :
        n == 5  ? (f(1), f(2), f(3), f(4), f(5)) :
        n == 6  ? (f(1), f(2), f(3), f(4), f(5), f(6)) :
        n == 7  ? (f(1), f(2), f(3), f(4), f(5), f(6), f(7)) :
        n == 8  ? (f(1), f(2), f(3), f(4), f(5), f(6), f(7), f(8)) :
        n == 9  ? (f(1), f(2), f(3), f(4), f(5), f(6), f(7), f(8), f(9)) :
        n == 10 ? (f(1), f(2), f(3), f(4), f(5), f(6), f(7), f(8), f(9), f(10)) :
        _ntuple(f, n)
    return t
end

function _ntuple(f::F, n) where F
    @noinline
    (n >= 0) || throw(ArgumentError(LazyString("tuple length should be ≥ 0, got ", n)))
    ([f(i) for i = 1:n]...,)
end

function ntupleany(f, n)
    @noinline
    (n >= 0) || throw(ArgumentError(LazyString("tuple length should be ≥ 0, got ", n)))
    (Any[f(i) for i = 1:n]...,)
end

# inferable ntuple (enough for bootstrapping)
ntuple(f, ::Val{0}) = ()
ntuple(f, ::Val{1}) = (@inline; (f(1),))
ntuple(f, ::Val{2}) = (@inline; (f(1), f(2)))
ntuple(f, ::Val{3}) = (@inline; (f(1), f(2), f(3)))

"""
    ntuple(f, ::Val{N})

Create a tuple of length `N`, computing each element as `f(i)`,
where `i` is the index of the element. By taking a `Val(N)`
argument, it is possible that this version of ntuple may
generate more efficient code than the version taking the
length as an integer. But `ntuple(f, N)` is preferable to
`ntuple(f, Val(N))` in cases where `N` cannot be determined
at compile time.

# Examples
```jldoctest
julia> ntuple(i -> 2*i, Val(4))
(2, 4, 6, 8)
```
"""
@inline function ntuple(f::F, ::Val{N}) where {F,N}
    N::Int
    (N >= 0) || throw(ArgumentError(LazyString("tuple length should be ≥ 0, got ", N)))
    if @generated
        :(@ntuple $N i -> f(i))
    else
        Tuple(f(i) for i = 1:N)
    end
end

@inline function fill_to_length(t::Tuple, val, ::Val{_N}) where {_N}
    M = length(t)
    N = _N::Int
    M > N && throw(ArgumentError(LazyString("input tuple of length ", M, ", requested ", N)))
    if @generated
        quote
            (t..., $(fill(:val, (_N::Int) - length(t.parameters))...))
        end
    else
        (t..., fill(val, N-M)...)
    end
end
S   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/abstractdict.jl�?      # This file is a part of Julia. License is MIT: https://julialang.org/license

# generic operations on dictionaries

"""
    KeyError(key)

An indexing operation into an `AbstractDict` (`Dict`) or `Set` like object tried to access or
delete a non-existent element.
"""
struct KeyError <: Exception
    key
end

const secret_table_token = :__c782dbf1cf4d6a2e5e3865d7e95634f2e09b5902__

haskey(d::AbstractDict, k) = in(k, keys(d))

function in(p::Pair, a::AbstractDict, valcmp=(==))
    v = get(a, p.first, secret_table_token)
    if v !== secret_table_token
        return valcmp(v, p.second)
    end
    return false
end

function in(p, a::AbstractDict)
    error("""AbstractDict collections only contain Pairs;
             Either look for e.g. A=>B instead, or use the `keys` or `values`
             function if you are looking for a key or value respectively.""")
end

function summary(io::IO, t::AbstractDict)
    showarg(io, t, true)
    if Base.IteratorSize(t) isa HasLength
        n = length(t)
        print(io, " with ", n, (n==1 ? " entry" : " entries"))
    else
        print(io, "(...)")
    end
end

struct KeySet{K, T <: AbstractDict{K}} <: AbstractSet{K}
    dict::T
end

struct ValueIterator{T<:AbstractDict}
    dict::T
end

function summary(io::IO, iter::T) where {T<:Union{KeySet,ValueIterator}}
    print(io, T.name.name, " for a ")
    summary(io, iter.dict)
end

show(io::IO, iter::Union{KeySet,ValueIterator}) = show_vector(io, iter)

length(v::Union{KeySet,ValueIterator}) = length(v.dict)
isempty(v::Union{KeySet,ValueIterator}) = isempty(v.dict)
_tt2(::Type{Pair{A,B}}) where {A,B} = B
eltype(::Type{ValueIterator{D}}) where {D} = _tt2(eltype(D))

function iterate(v::Union{KeySet,ValueIterator}, state...)
    y = iterate(v.dict, state...)
    y === nothing && return nothing
    return (y[1][isa(v, KeySet) ? 1 : 2], y[2])
end

copy(v::KeySet) = copymutable(v)

in(k, v::KeySet) = get(v.dict, k, secret_table_token) !== secret_table_token

"""
    keys(iterator)

For an iterator or collection that has keys and values (e.g. arrays and dictionaries),
return an iterator over the keys.
"""
function keys end

"""
    keys(a::AbstractDict)

Return an iterator over all keys in a dictionary.
`collect(keys(a))` returns an array of keys.
When the keys are stored internally in a hash table,
as is the case for `Dict`,
the order in which they are returned may vary.
But `keys(a)` and `values(a)` both iterate `a` and
return the elements in the same order.

# Examples
```jldoctest
julia> D = Dict('a'=>2, 'b'=>3)
Dict{Char, Int64} with 2 entries:
  'a' => 2
  'b' => 3

julia> collect(keys(D))
2-element Vector{Char}:
 'a': ASCII/Unicode U+0061 (category Ll: Letter, lowercase)
 'b': ASCII/Unicode U+0062 (category Ll: Letter, lowercase)
```
"""
keys(a::AbstractDict) = KeySet(a)

"""
    values(a::AbstractDict)

Return an iterator over all values in a collection.
`collect(values(a))` returns an array of values.
When the values are stored internally in a hash table,
as is the case for `Dict`,
the order in which they are returned may vary.
But `keys(a)` and `values(a)` both iterate `a` and
return the elements in the same order.

# Examples
```jldoctest
julia> D = Dict('a'=>2, 'b'=>3)
Dict{Char, Int64} with 2 entries:
  'a' => 2
  'b' => 3

julia> collect(values(D))
2-element Vector{Int64}:
 2
 3
```
"""
values(a::AbstractDict) = ValueIterator(a)

"""
    pairs(collection)

Return an iterator over `key => value` pairs for any
collection that maps a set of keys to a set of values.
This includes arrays, where the keys are the array indices.

# Examples
```jldoctest
julia> a = Dict(zip(["a", "b", "c"], [1, 2, 3]))
Dict{String, Int64} with 3 entries:
  "c" => 3
  "b" => 2
  "a" => 1

julia> pairs(a)
Dict{String, Int64} with 3 entries:
  "c" => 3
  "b" => 2
  "a" => 1

julia> foreach(println, pairs(["a", "b", "c"]))
1 => "a"
2 => "b"
3 => "c"

julia> (;a=1, b=2, c=3) |> pairs |> collect
3-element Vector{Pair{Symbol, Int64}}:
 :a => 1
 :b => 2
 :c => 3

julia> (;a=1, b=2, c=3) |> collect
3-element Vector{Int64}:
 1
 2
 3
```
"""
pairs(collection) = Generator(=>, keys(collection), values(collection))

pairs(a::AbstractDict) = a

"""
    empty(a::AbstractDict, [index_type=keytype(a)], [value_type=valtype(a)])

Create an empty `AbstractDict` container which can accept indices of type `index_type` and
values of type `value_type`. The second and third arguments are optional and default to the
input's `keytype` and `valtype`, respectively. (If only one of the two types is specified,
it is assumed to be the `value_type`, and the `index_type` we default to `keytype(a)`).

Custom `AbstractDict` subtypes may choose which specific dictionary type is best suited to
return for the given index and value types, by specializing on the three-argument signature.
The default is to return an empty `Dict`.
"""
empty(a::AbstractDict) = empty(a, keytype(a), valtype(a))
empty(a::AbstractDict, ::Type{V}) where {V} = empty(a, keytype(a), V) # Note: this is the form which makes sense for `Vector`.

copy(a::AbstractDict) = merge!(empty(a), a)
function copy!(dst::AbstractDict, src::AbstractDict)
    dst === src && return dst
    merge!(empty!(dst), src)
end

"""
    merge!(d::AbstractDict, others::AbstractDict...)

Update collection with pairs from the other collections.
See also [`merge`](@ref).

# Examples
```jldoctest
julia> d1 = Dict(1 => 2, 3 => 4);

julia> d2 = Dict(1 => 4, 4 => 5);

julia> merge!(d1, d2);

julia> d1
Dict{Int64, Int64} with 3 entries:
  4 => 5
  3 => 4
  1 => 4
```
"""
function merge!(d::AbstractDict, others::AbstractDict...)
    for other in others
        if haslength(d) && haslength(other)
            sizehint!(d, length(d) + length(other))
        end
        for (k,v) in other
            d[k] = v
        end
    end
    return d
end

"""
    mergewith!(combine, d::AbstractDict, others::AbstractDict...) -> d
    mergewith!(combine)
    merge!(combine, d::AbstractDict, others::AbstractDict...) -> d

Update collection with pairs from the other collections.
Values with the same key will be combined using the
combiner function.  The curried form `mergewith!(combine)` returns the
function `(args...) -> mergewith!(combine, args...)`.

Method `merge!(combine::Union{Function,Type}, args...)` as an alias of
`mergewith!(combine, args...)` is still available for backward
compatibility.

!!! compat "Julia 1.5"
    `mergewith!` requires Julia 1.5 or later.

# Examples
```jldoctest
julia> d1 = Dict(1 => 2, 3 => 4);

julia> d2 = Dict(1 => 4, 4 => 5);

julia> mergewith!(+, d1, d2);

julia> d1
Dict{Int64, Int64} with 3 entries:
  4 => 5
  3 => 4
  1 => 6

julia> mergewith!(-, d1, d1);

julia> d1
Dict{Int64, Int64} with 3 entries:
  4 => 0
  3 => 0
  1 => 0

julia> foldl(mergewith!(+), [d1, d2]; init=Dict{Int64, Int64}())
Dict{Int64, Int64} with 3 entries:
  4 => 5
  3 => 0
  1 => 4
```
"""
function mergewith!(combine, d::AbstractDict, others::AbstractDict...)
    foldl(mergewith!(combine), others; init = d)
end

function mergewith!(combine, d1::AbstractDict, d2::AbstractDict)
    for (k, v) in d2
        d1[k] = haskey(d1, k) ? combine(d1[k], v) : v
    end
    return d1
end

mergewith!(combine) = (args...) -> mergewith!(combine, args...)

merge!(combine::Callable, args...) = mergewith!(combine, args...)

"""
    keytype(type)

Get the key type of a dictionary type. Behaves similarly to [`eltype`](@ref).

# Examples
```jldoctest
julia> keytype(Dict(Int32(1) => "foo"))
Int32
```
"""
keytype(::Type{<:AbstractDict{K,V}}) where {K,V} = K
keytype(a::AbstractDict) = keytype(typeof(a))

"""
    valtype(type)

Get the value type of a dictionary type. Behaves similarly to [`eltype`](@ref).

# Examples
```jldoctest
julia> valtype(Dict(Int32(1) => "foo"))
String
```
"""
valtype(::Type{<:AbstractDict{K,V}}) where {K,V} = V
valtype(a::AbstractDict) = valtype(typeof(a))

"""
    merge(d::AbstractDict, others::AbstractDict...)

Construct a merged collection from the given collections. If necessary, the
types of the resulting collection will be promoted to accommodate the types of
the merged collections. If the same key is present in another collection, the
value for that key will be the value it has in the last collection listed.
See also [`mergewith`](@ref) for custom handling of values with the same key.

# Examples
```jldoctest
julia> a = Dict("foo" => 0.0, "bar" => 42.0)
Dict{String, Float64} with 2 entries:
  "bar" => 42.0
  "foo" => 0.0

julia> b = Dict("baz" => 17, "bar" => 4711)
Dict{String, Int64} with 2 entries:
  "bar" => 4711
  "baz" => 17

julia> merge(a, b)
Dict{String, Float64} with 3 entries:
  "bar" => 4711.0
  "baz" => 17.0
  "foo" => 0.0

julia> merge(b, a)
Dict{String, Float64} with 3 entries:
  "bar" => 42.0
  "baz" => 17.0
  "foo" => 0.0
```
"""
merge(d::AbstractDict, others::AbstractDict...) =
    merge!(_typeddict(d, others...), others...)

"""
    mergewith(combine, d::AbstractDict, others::AbstractDict...)
    mergewith(combine)
    merge(combine, d::AbstractDict, others::AbstractDict...)

Construct a merged collection from the given collections. If necessary, the
types of the resulting collection will be promoted to accommodate the types of
the merged collections. Values with the same key will be combined using the
combiner function.  The curried form `mergewith(combine)` returns the function
`(args...) -> mergewith(combine, args...)`.

Method `merge(combine::Union{Function,Type}, args...)` as an alias of
`mergewith(combine, args...)` is still available for backward compatibility.

!!! compat "Julia 1.5"
    `mergewith` requires Julia 1.5 or later.

# Examples
```jldoctest
julia> a = Dict("foo" => 0.0, "bar" => 42.0)
Dict{String, Float64} with 2 entries:
  "bar" => 42.0
  "foo" => 0.0

julia> b = Dict("baz" => 17, "bar" => 4711)
Dict{String, Int64} with 2 entries:
  "bar" => 4711
  "baz" => 17

julia> mergewith(+, a, b)
Dict{String, Float64} with 3 entries:
  "bar" => 4753.0
  "baz" => 17.0
  "foo" => 0.0

julia> ans == mergewith(+)(a, b)
true
```
"""
mergewith(combine, d::AbstractDict, others::AbstractDict...) =
    mergewith!(combine, _typeddict(d, others...), others...)
mergewith(combine) = (args...) -> mergewith(combine, args...)
merge(combine::Callable, d::AbstractDict, others::AbstractDict...) =
    merge!(combine, _typeddict(d, others...), others...)

promoteK(K) = K
promoteV(V) = V
promoteK(K, d, ds...) = promoteK(promote_type(K, keytype(d)), ds...)
promoteV(V, d, ds...) = promoteV(promote_type(V, valtype(d)), ds...)
function _typeddict(d::AbstractDict, others::AbstractDict...)
    K = promoteK(keytype(d), others...)
    V = promoteV(valtype(d), others...)
    Dict{K,V}(d)
end

"""
    filter!(f, d::AbstractDict)

Update `d`, removing elements for which `f` is `false`.
The function `f` is passed `key=>value` pairs.

# Example
```jldoctest
julia> d = Dict(1=>"a", 2=>"b", 3=>"c")
Dict{Int64, String} with 3 entries:
  2 => "b"
  3 => "c"
  1 => "a"

julia> filter!(p->isodd(p.first), d)
Dict{Int64, String} with 2 entries:
  3 => "c"
  1 => "a"
```
"""
function filter!(f, d::AbstractDict)
    badkeys = Vector{keytype(d)}()
    for pair in d
        # don't delete!(d, k) here, since dictionary types
        # may not support mutation during iteration
        f(pair) || push!(badkeys, pair.first)
    end
    for k in badkeys
        delete!(d, k)
    end
    return d
end

function filter_in_one_pass!(f, d::AbstractDict)
    for pair in d
        if !f(pair)
            delete!(d, pair.first)
        end
    end
    return d
end

"""
    filter(f, d::AbstractDict)

Return a copy of `d`, removing elements for which `f` is `false`.
The function `f` is passed `key=>value` pairs.

# Examples
```jldoctest
julia> d = Dict(1=>"a", 2=>"b")
Dict{Int64, String} with 2 entries:
  2 => "b"
  1 => "a"

julia> filter(p->isodd(p.first), d)
Dict{Int64, String} with 1 entry:
  1 => "a"
```
"""
function filter(f, d::AbstractDict)
    # don't just do filter!(f, copy(d)): avoid making a whole copy of d
    df = empty(d)
    for pair in d
        if f(pair)
            df[pair.first] = pair.second
        end
    end
    return df
end

function eltype(::Type{<:AbstractDict{K,V}}) where {K,V}
    if @isdefined(K)
        if @isdefined(V)
            return Pair{K,V}
        else
            return Pair{K}
        end
    elseif @isdefined(V)
        return Pair{k,V} where k
    else
        return Pair
    end
end

function isequal(l::AbstractDict, r::AbstractDict)
    l === r && return true
    if isa(l,IdDict) != isa(r,IdDict)
        return false
    end
    if length(l) != length(r) return false end
    for pair in l
        if !in(pair, r, isequal)
            return false
        end
    end
    true
end

function ==(l::AbstractDict, r::AbstractDict)
    if isa(l,IdDict) != isa(r,IdDict)
        return false
    end
    length(l) != length(r) && return false
    anymissing = false
    for pair in l
        isin = in(pair, r)
        if ismissing(isin)
            anymissing = true
        elseif !isin
            return false
        end
    end
    return anymissing ? missing : true
end

# Fallback implementation
sizehint!(d::AbstractDict, n) = d

const hasha_seed = UInt === UInt64 ? 0x6d35bb51952d5539 : 0x952d5539
function hash(a::AbstractDict, h::UInt)
    hv = hasha_seed
    for (k,v) in a
        hv ⊻= hash(k, hash(v))
    end
    hash(hv, h)
end

function getindex(t::AbstractDict{<:Any,V}, key) where V
    v = get(t, key, secret_table_token)
    if v === secret_table_token
        throw(KeyError(key))
    end
    return v::V
end

# t[k1,k2,ks...] is syntactic sugar for t[(k1,k2,ks...)].  (Note
# that we need to avoid dispatch loops if setindex!(t,v,k) is not defined.)
getindex(t::AbstractDict, k1, k2, ks...) = getindex(t, tuple(k1,k2,ks...))
setindex!(t::AbstractDict, v, k1, k2, ks...) = setindex!(t, v, tuple(k1,k2,ks...))

get!(t::AbstractDict, key, default) = get!(() -> default, t, key)
function get!(default::Callable, t::AbstractDict{K,V}, key) where K where V
    key = convert(K, key)
    if haskey(t, key)
        return t[key]
    else
        return t[key] = convert(V, default())
    end
end

push!(t::AbstractDict, p::Pair) = setindex!(t, p.second, p.first)

# AbstractDicts are convertible
convert(::Type{T}, x::T) where {T<:AbstractDict} = x

function convert(::Type{T}, x::AbstractDict) where T<:AbstractDict
    h = T(x)::T
    if length(h) != length(x)
        error("key collision during dictionary conversion")
    end
    return h
end

# hashing objects by identity
_tablesz(x::T) where T <: Integer = x < 16 ? T(16) : one(T)<<(top_set_bit(x-one(T)))

TP{K,V} = Union{Type{Tuple{K,V}},Type{Pair{K,V}}}

dict_with_eltype(DT_apply, kv, ::TP{K,V}) where {K,V} = DT_apply(K, V)(kv)
dict_with_eltype(DT_apply, kv::Generator, ::TP{K,V}) where {K,V} = DT_apply(K, V)(kv)
dict_with_eltype(DT_apply, ::Type{Pair{K,V}}) where {K,V} = DT_apply(K, V)()
dict_with_eltype(DT_apply, ::Type) = DT_apply(Any, Any)()
dict_with_eltype(DT_apply::F, kv, t) where {F} = grow_to!(dict_with_eltype(DT_apply, @default_eltype(typeof(kv))), kv)
function dict_with_eltype(DT_apply::F, kv::Generator, t) where F
    T = @default_eltype(kv)
    if T <: Union{Pair, Tuple{Any, Any}} && isconcretetype(T)
        return dict_with_eltype(DT_apply, kv, T)
    end
    return grow_to!(dict_with_eltype(DT_apply, T), kv)
end

"""
    map!(f, values(dict::AbstractDict))

Modifies `dict` by transforming each value from `val` to `f(val)`.
Note that the type of `dict` cannot be changed: if `f(val)` is not an instance of the value type
of `dict` then it will be converted to the value type if possible and otherwise raise an error.

!!! compat "Julia 1.2"
    `map!(f, values(dict::AbstractDict))` requires Julia 1.2 or later.

# Examples
```jldoctest
julia> d = Dict(:a => 1, :b => 2)
Dict{Symbol, Int64} with 2 entries:
  :a => 1
  :b => 2

julia> map!(v -> v-1, values(d))
ValueIterator for a Dict{Symbol, Int64} with 2 entries. Values:
  0
  1
```
"""
function map!(f, iter::ValueIterator)
    # This is the naive fallback which requires hash evaluations
    # Contrary to the example Dict has an implementation which does not require hash evaluations
    dict = iter.dict
    for (key, val) in pairs(dict)
        dict[key] = f(val)
    end
    return iter
end
M   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/iddict.jlA      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
    IdDict([itr])

`IdDict{K,V}()` constructs a hash table using [`objectid`](@ref) as hash and
`===` as equality with keys of type `K` and values of type `V`.

See [`Dict`](@ref) for further help. In the example below, The `Dict`
keys are all `isequal` and therefore get hashed the same, so they get overwritten.
The `IdDict` hashes by object-id, and thus preserves the 3 different keys.

# Examples
```julia-repl
julia> Dict(true => "yes", 1 => "no", 1.0 => "maybe")
Dict{Real, String} with 1 entry:
  1.0 => "maybe"

julia> IdDict(true => "yes", 1 => "no", 1.0 => "maybe")
IdDict{Any, String} with 3 entries:
  true => "yes"
  1.0  => "maybe"
  1    => "no"
```
"""
mutable struct IdDict{K,V} <: AbstractDict{K,V}
    ht::Vector{Any}
    count::Int
    ndel::Int
    IdDict{K,V}() where {K, V} = new{K,V}(Vector{Any}(undef, 32), 0, 0)

    function IdDict{K,V}(itr) where {K, V}
        d = IdDict{K,V}()
        for (k,v) in itr; d[k] = v; end
        d
    end

    function IdDict{K,V}(pairs::Pair...) where {K, V}
        d = IdDict{K,V}()
        sizehint!(d, length(pairs))
        for (k,v) in pairs; d[k] = v; end
        d
    end

    IdDict{K,V}(d::IdDict{K,V}) where {K, V} = new{K,V}(copy(d.ht), d.count, d.ndel)
end

IdDict() = IdDict{Any,Any}()
IdDict(kv::Tuple{}) = IdDict()

IdDict(ps::Pair{K,V}...)           where {K,V} = IdDict{K,V}(ps)
IdDict(ps::Pair{K}...)             where {K}   = IdDict{K,Any}(ps)
IdDict(ps::(Pair{K,V} where K)...) where {V}   = IdDict{Any,V}(ps)
IdDict(ps::Pair...)                            = IdDict{Any,Any}(ps)

function IdDict(kv)
    try
        dict_with_eltype((K, V) -> IdDict{K, V}, kv, eltype(kv))
    catch
        if !applicable(iterate, kv) || !all(x->isa(x,Union{Tuple,Pair}),kv)
            throw(ArgumentError(
                "IdDict(kv): kv needs to be an iterator of tuples or pairs"))
        else
            rethrow()
        end
    end
end

empty(d::IdDict, ::Type{K}, ::Type{V}) where {K, V} = IdDict{K,V}()

function rehash!(d::IdDict, newsz = length(d.ht)%UInt)
    d.ht = ccall(:jl_idtable_rehash, Vector{Any}, (Any, Csize_t), d.ht, newsz)
    d
end

function sizehint!(d::IdDict, newsz)
    newsz = _tablesz(newsz*2)  # *2 for keys and values in same array
    oldsz = length(d.ht)
    # grow at least 25%
    if newsz < (oldsz*5)>>2
        return d
    end
    rehash!(d, newsz)
end

function setindex!(d::IdDict{K,V}, @nospecialize(val), @nospecialize(key)) where {K, V}
    !isa(key, K) && throw(ArgumentError("$(limitrepr(key)) is not a valid key for type $K"))
    if !(val isa V) # avoid a dynamic call
        val = convert(V, val)::V
    end
    if d.ndel >= ((3*length(d.ht))>>2)
        rehash!(d, max((length(d.ht)%UInt)>>1, 32))
        d.ndel = 0
    end
    inserted = RefValue{Cint}(0)
    d.ht = ccall(:jl_eqtable_put, Array{Any,1}, (Any, Any, Any, Ptr{Cint}), d.ht, key, val, inserted)
    d.count += inserted[]
    return d
end

function get(d::IdDict{K,V}, @nospecialize(key), @nospecialize(default)) where {K, V}
    val = ccall(:jl_eqtable_get, Any, (Any, Any, Any), d.ht, key, default)
    val === default ? default : val::V
end

function getindex(d::IdDict{K,V}, @nospecialize(key)) where {K, V}
    val = ccall(:jl_eqtable_get, Any, (Any, Any, Any), d.ht, key, secret_table_token)
    val === secret_table_token && throw(KeyError(key))
    return val::V
end

function pop!(d::IdDict{K,V}, @nospecialize(key), @nospecialize(default)) where {K, V}
    found = RefValue{Cint}(0)
    val = ccall(:jl_eqtable_pop, Any, (Any, Any, Any, Ptr{Cint}), d.ht, key, default, found)
    if found[] === Cint(0)
        return default
    else
        d.count -= 1
        d.ndel += 1
        return val::V
    end
end

function pop!(d::IdDict{K,V}, @nospecialize(key)) where {K, V}
    val = pop!(d, key, secret_table_token)
    val === secret_table_token && throw(KeyError(key))
    return val::V
end

function delete!(d::IdDict{K}, @nospecialize(key)) where K
    pop!(d, key, secret_table_token)
    d
end

function empty!(d::IdDict)
    resize!(d.ht, 32)
    ht = d.ht
    t = @_gc_preserve_begin ht
    memset(unsafe_convert(Ptr{Cvoid}, ht), 0, sizeof(ht))
    @_gc_preserve_end t
    d.ndel = 0
    d.count = 0
    return d
end

_oidd_nextind(a, i) = reinterpret(Int, ccall(:jl_eqtable_nextind, Csize_t, (Any, Csize_t), a, i))

function iterate(d::IdDict{K,V}, idx=0) where {K, V}
    idx = _oidd_nextind(d.ht, idx%UInt)
    idx == -1 && return nothing
    return (Pair{K, V}(d.ht[idx + 1]::K, d.ht[idx + 2]::V), idx + 2)
end

length(d::IdDict) = d.count

copy(d::IdDict) = typeof(d)(d)

function get!(d::IdDict{K,V}, @nospecialize(key), @nospecialize(default)) where {K, V}
    val = ccall(:jl_eqtable_get, Any, (Any, Any, Any), d.ht, key, secret_table_token)
    if val === secret_table_token
        val = isa(default, V) ? default : convert(V, default)::V
        setindex!(d, val, key)
        return val
    else
        return val::V
    end
end

function get(default::Callable, d::IdDict{K,V}, @nospecialize(key)) where {K, V}
    val = ccall(:jl_eqtable_get, Any, (Any, Any, Any), d.ht, key, secret_table_token)
    if val === secret_table_token
        return default()
    else
        return val::V
    end
end

function get!(default::Callable, d::IdDict{K,V}, @nospecialize(key)) where {K, V}
    val = ccall(:jl_eqtable_get, Any, (Any, Any, Any), d.ht, key, secret_table_token)
    if val === secret_table_token
        val = default()
        if !isa(val, V)
            val = convert(V, val)::V
        end
        setindex!(d, val, key)
        return val
    else
        return val::V
    end
end

in(@nospecialize(k), v::KeySet{<:Any,<:IdDict}) = get(v.dict, k, secret_table_token) !== secret_table_token

# For some AbstractDict types, it is safe to implement filter!
# by deleting keys during iteration.
filter!(f, d::IdDict) = filter_in_one_pass!(f, d)
L   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/idset.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

# Like Set, but using IdDict
mutable struct IdSet{T} <: AbstractSet{T}
    dict::IdDict{T,Nothing}

    IdSet{T}() where {T} = new(IdDict{T,Nothing}())
    IdSet{T}(s::IdSet{T}) where {T} = new(copy(s.dict))
end

IdSet{T}(itr) where {T} = union!(IdSet{T}(), itr)
IdSet() = IdSet{Any}()

copymutable(s::IdSet) = typeof(s)(s)
emptymutable(s::IdSet{T}, ::Type{U}=T) where {T,U} = IdSet{U}()
copy(s::IdSet) = typeof(s)(s)

isempty(s::IdSet) = isempty(s.dict)
length(s::IdSet)  = length(s.dict)
in(@nospecialize(x), s::IdSet) = haskey(s.dict, x)
push!(s::IdSet, @nospecialize(x)) = (s.dict[x] = nothing; s)
pop!(s::IdSet, @nospecialize(x)) = (pop!(s.dict, x); x)
pop!(s::IdSet, @nospecialize(x), @nospecialize(default)) = (x in s ? pop!(s, x) : default)
delete!(s::IdSet, @nospecialize(x)) = (delete!(s.dict, x); s)

sizehint!(s::IdSet, newsz) = (sizehint!(s.dict, newsz); s)
empty!(s::IdSet) = (empty!(s.dict); s)

filter!(f, d::IdSet) = unsafe_filter!(f, d)

function iterate(s::IdSet, state...)
    y = iterate(s.dict, state...)
    y === nothing && return nothing
    ((k, _), i) = y
    return (k, i)
end
P   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/iterators.jlŰ      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
Methods for working with Iterators.
"""
baremodule Iterators

# small dance to make this work from Base or Intrinsics
import ..@__MODULE__, ..parentmodule
const Base = parentmodule(@__MODULE__)
using .Base:
    @inline, Pair, Pairs, AbstractDict, IndexLinear, IndexStyle, AbstractVector, Vector,
    SizeUnknown, HasLength, HasShape, IsInfinite, EltypeUnknown, HasEltype, OneTo,
    @propagate_inbounds, @isdefined, @boundscheck, @inbounds, Generator,
    AbstractRange, AbstractUnitRange, UnitRange, LinearIndices, TupleOrBottom,
    (:), |, +, -, *, !==, !, ==, !=, <=, <, >, >=, missing,
    any, _counttuple, eachindex, ntuple, zero, prod, reduce, in, firstindex, lastindex,
    tail, fieldtypes, min, max, minimum, zero, oneunit, promote, promote_shape
using Core: @doc

if Base !== Core.Compiler
using .Base:
    cld, fld, SubArray, view, resize!, IndexCartesian
using .Base.Checked: checked_mul
else
    # Checked.checked_mul is not available during bootstrapping:
    const checked_mul = *
end

import .Base:
    first, last,
    isempty, length, size, axes, ndims,
    eltype, IteratorSize, IteratorEltype,
    haskey, keys, values, pairs,
    getindex, setindex!, get, iterate,
    popfirst!, isdone, peek, intersect

export enumerate, zip, rest, countfrom, take, drop, takewhile, dropwhile, cycle, repeated, product, flatten, flatmap

if Base !== Core.Compiler
export partition
end

"""
    Iterators.map(f, iterators...)

Create a lazy mapping.  This is another syntax for writing
`(f(args...) for args in zip(iterators...))`.

!!! compat "Julia 1.6"
    This function requires at least Julia 1.6.

# Examples
```jldoctest
julia> collect(Iterators.map(x -> x^2, 1:3))
3-element Vector{Int64}:
 1
 4
 9
```
"""
map(f, args...) = Base.Generator(f, args...)

tail_if_any(::Tuple{}) = ()
tail_if_any(x::Tuple) = tail(x)

_min_length(a, b, ::IsInfinite, ::IsInfinite) = min(length(a),length(b)) # inherit behaviour, error
_min_length(a, b, A, ::IsInfinite) = length(a)
_min_length(a, b, ::IsInfinite, B) = length(b)
_min_length(a, b, A, B) = min(length(a),length(b))

_diff_length(a, b, A, ::IsInfinite) = 0
_diff_length(a, b, ::IsInfinite, ::IsInfinite) = 0
_diff_length(a, b, ::IsInfinite, B) = length(a) # inherit behaviour, error
function _diff_length(a, b, A, B)
    m, n = length(a), length(b)
    return m > n ? m - n : zero(n - m)
end

and_iteratorsize(isz::T, ::T) where {T} = isz
and_iteratorsize(::HasLength, ::HasShape) = HasLength()
and_iteratorsize(::HasShape, ::HasLength) = HasLength()
and_iteratorsize(a, b) = SizeUnknown()

and_iteratoreltype(iel::T, ::T) where {T} = iel
and_iteratoreltype(a, b) = EltypeUnknown()

## Reverse-order iteration for arrays and other collections.  Collections
## should implement iterate etcetera if possible/practical.
"""
    Iterators.reverse(itr)

Given an iterator `itr`, then `reverse(itr)` is an iterator over the
same collection but in the reverse order.
This iterator is "lazy" in that it does not make a copy of the collection in
order to reverse it; see [`Base.reverse`](@ref) for an eager implementation.

(By default, this returns
an `Iterators.Reverse` object wrapping `itr`, which is iterable
if the corresponding [`iterate`](@ref) methods are defined, but some `itr` types
may implement more specialized `Iterators.reverse` behaviors.)

Not all iterator types `T` support reverse-order iteration.  If `T`
doesn't, then iterating over `Iterators.reverse(itr::T)` will throw a [`MethodError`](@ref)
because of the missing `iterate` methods for `Iterators.Reverse{T}`.
(To implement these methods, the original iterator
`itr::T` can be obtained from an `r::Iterators.Reverse{T}` object by `r.itr`;
more generally, one can use `Iterators.reverse(r)`.)

# Examples
```jldoctest
julia> foreach(println, Iterators.reverse(1:5))
5
4
3
2
1
```
"""
reverse(itr) = Reverse(itr)

struct Reverse{T}
    itr::T
end
eltype(::Type{Reverse{T}}) where {T} = eltype(T)
length(r::Reverse) = length(r.itr)
size(r::Reverse) = size(r.itr)
IteratorSize(::Type{Reverse{T}}) where {T} = IteratorSize(T)
IteratorEltype(::Type{Reverse{T}}) where {T} = IteratorEltype(T)
last(r::Reverse) = first(r.itr) # the first shall be last

# reverse-order array iterators: assumes more-specialized Reverse for eachindex
@propagate_inbounds function iterate(A::Reverse{<:AbstractArray}, state=(reverse(eachindex(A.itr)),))
    y = iterate(state...)
    y === nothing && return y
    idx, itrs = y
    (A.itr[idx], (state[1], itrs))
end

# Fallback method of `iterate(::Reverse{T})` which assumes the collection has `getindex(::T) and `reverse(eachindex(::T))`
# don't propagate inbounds for this just in case
function iterate(A::Reverse, state=(reverse(eachindex(A.itr)),))
    y = iterate(state...)
    y === nothing && return y
    idx, itrs = y
    (A.itr[idx], (state[1], itrs))
end

reverse(R::AbstractRange) = Base.reverse(R) # copying ranges is cheap
reverse(G::Generator) = Generator(G.f, reverse(G.iter))
reverse(r::Reverse) = r.itr
reverse(x::Union{Number,AbstractChar}) = x
reverse(p::Pair) = Base.reverse(p) # copying pairs is cheap

iterate(r::Reverse{<:Union{Tuple, NamedTuple}}, i::Int = length(r.itr)) = i < 1 ? nothing : (r.itr[i], i-1)

# enumerate

struct Enumerate{I}
    itr::I
end

"""
    enumerate(iter)

An iterator that yields `(i, x)` where `i` is a counter starting at 1,
and `x` is the `i`th value from the given iterator. It's useful when
you need not only the values `x` over which you are iterating, but
also the number of iterations so far.

Note that `i` may not be valid for indexing `iter`, or may index a
different element. This will happen if `iter` has indices that do not
start at 1, and may happen for strings, dictionaries, etc.
See the `pairs(IndexLinear(), iter)` method if you want to ensure that `i` is an index.

# Examples
```jldoctest
julia> a = ["a", "b", "c"];

julia> for (index, value) in enumerate(a)
           println("\$index \$value")
       end
1 a
2 b
3 c

julia> str = "naïve";

julia> for (i, val) in enumerate(str)
           print("i = ", i, ", val = ", val, ", ")
           try @show(str[i]) catch e println(e) end
       end
i = 1, val = n, str[i] = 'n'
i = 2, val = a, str[i] = 'a'
i = 3, val = ï, str[i] = 'ï'
i = 4, val = v, StringIndexError("naïve", 4)
i = 5, val = e, str[i] = 'v'
```
"""
enumerate(iter) = Enumerate(iter)

length(e::Enumerate) = length(e.itr)
size(e::Enumerate) = size(e.itr)
@propagate_inbounds function iterate(e::Enumerate, state=(1,))
    i, rest = state[1], tail(state)
    n = iterate(e.itr, rest...)
    n === nothing && return n
    (i, n[1]), (i+1, n[2])
end
last(e::Enumerate) = (length(e.itr), e.itr[end])

eltype(::Type{Enumerate{I}}) where {I} = TupleOrBottom(Int, eltype(I))

IteratorSize(::Type{Enumerate{I}}) where {I} = IteratorSize(I)
IteratorEltype(::Type{Enumerate{I}}) where {I} = IteratorEltype(I)

@inline function iterate(r::Reverse{<:Enumerate})
    ri = reverse(r.itr.itr)
    iterate(r, (length(ri), ri))
end
@inline function iterate(r::Reverse{<:Enumerate}, state)
    i, ri, rest = state[1], state[2], tail(tail(state))
    n = iterate(ri, rest...)
    n === nothing && return n
    (i, n[1]), (i-1, ri, n[2])
end

"""
    pairs(IndexLinear(), A)
    pairs(IndexCartesian(), A)
    pairs(IndexStyle(A), A)

An iterator that accesses each element of the array `A`, returning
`i => x`, where `i` is the index for the element and `x = A[i]`.
Identical to `pairs(A)`, except that the style of index can be selected.
Also similar to `enumerate(A)`, except `i` will be a valid index
for `A`, while `enumerate` always counts from 1 regardless of the indices
of `A`.

Specifying [`IndexLinear()`](@ref) ensures that `i` will be an integer;
specifying [`IndexCartesian()`](@ref) ensures that `i` will be a
[`Base.CartesianIndex`](@ref); specifying `IndexStyle(A)` chooses whichever has
been defined as the native indexing style for array `A`.

Mutation of the bounds of the underlying array will invalidate this iterator.

# Examples
```jldoctest
julia> A = ["a" "d"; "b" "e"; "c" "f"];

julia> for (index, value) in pairs(IndexStyle(A), A)
           println("\$index \$value")
       end
1 a
2 b
3 c
4 d
5 e
6 f

julia> S = view(A, 1:2, :);

julia> for (index, value) in pairs(IndexStyle(S), S)
           println("\$index \$value")
       end
CartesianIndex(1, 1) a
CartesianIndex(2, 1) b
CartesianIndex(1, 2) d
CartesianIndex(2, 2) e
```

See also [`IndexStyle`](@ref), [`axes`](@ref).
"""
pairs(::IndexLinear,    A::AbstractArray) = Pairs(A, LinearIndices(A))

# preserve indexing capabilities for known indexable types
# faster than zip(keys(a), values(a)) for arrays
pairs(tuple::Tuple) = Pairs{Int}(tuple, keys(tuple))
pairs(nt::NamedTuple) = Pairs{Symbol}(nt, keys(nt))
pairs(v::Core.SimpleVector) = Pairs(v, LinearIndices(v))
pairs(A::AbstractVector) = pairs(IndexLinear(), A)
# pairs(v::Pairs) = v # listed for reference, but already defined from being an AbstractDict

if Base !== Core.Compiler
pairs(::IndexCartesian, A::AbstractArray) = Pairs(A, Base.CartesianIndices(axes(A)))
pairs(A::AbstractArray)  = pairs(IndexCartesian(), A)
end

length(v::Pairs) = length(getfield(v, :itr))
axes(v::Pairs) = axes(getfield(v, :itr))
size(v::Pairs) = size(getfield(v, :itr))

Base.@eval @propagate_inbounds function _pairs_elt(p::Pairs{K, V}, idx) where {K, V}
    return $(Expr(:new, :(Pair{K, V}), :idx, :(getfield(p, :data)[idx])))
end

@propagate_inbounds function iterate(p::Pairs{K, V}, state...) where {K, V}
    x = iterate(getfield(p, :itr), state...)
    x === nothing && return x
    idx, next = x
    return (_pairs_elt(p, idx), next)
end

@propagate_inbounds function iterate(r::Reverse{<:Pairs}, state=(reverse(getfield(r.itr, :itr)),))
    x = iterate(state...)
    x === nothing && return x
    idx, next = x
    return (_pairs_elt(r.itr, idx), (state[1], next))
end

@inline isdone(v::Pairs, state...) = isdone(getfield(v, :itr), state...)

IteratorSize(::Type{<:Pairs{<:Any, <:Any, I}}) where {I} = IteratorSize(I)
IteratorSize(::Type{<:Pairs{<:Any, <:Any, <:AbstractUnitRange, <:Tuple}}) = HasLength()

function last(v::Pairs{K, V}) where {K, V}
    idx = last(getfield(v, :itr))
    return Pair{K, V}(idx, v[idx])
end

haskey(v::Pairs, key) = (key in getfield(v, :itr))
keys(v::Pairs) = getfield(v, :itr)
values(v::Pairs) = getfield(v, :data) # TODO: this should be a view of data subset by itr
getindex(v::Pairs, key) = getfield(v, :data)[key]
setindex!(v::Pairs, value, key) = (getfield(v, :data)[key] = value; v)
get(v::Pairs, key, default) = get(getfield(v, :data), key, default)
get(f::Base.Callable, v::Pairs, key) = get(f, getfield(v, :data), key)

# zip

struct Zip{Is<:Tuple}
    is::Is
end

"""
    zip(iters...)

Run multiple iterators at the same time, until any of them is exhausted. The value type of
the `zip` iterator is a tuple of values of its subiterators.

!!! note
    `zip` orders the calls to its subiterators in such a way that stateful iterators will
    not advance when another iterator finishes in the current iteration.

!!! note

    `zip()` with no arguments yields an infinite iterator of empty tuples.

See also: [`enumerate`](@ref), [`Base.splat`](@ref).

# Examples
```jldoctest
julia> a = 1:5
1:5

julia> b = ["e","d","b","c","a"]
5-element Vector{String}:
 "e"
 "d"
 "b"
 "c"
 "a"

julia> c = zip(a,b)
zip(1:5, ["e", "d", "b", "c", "a"])

julia> length(c)
5

julia> first(c)
(1, "e")
```
"""
zip(a...) = Zip(a)
function length(z::Zip)
    n = _zip_min_length(z.is)
    n === nothing && throw(ArgumentError("iterator is of undefined length"))
    return n
end
function _zip_min_length(is)
    i = is[1]
    n = _zip_min_length(tail(is))
    if IteratorSize(i) isa IsInfinite
        return n
    else
        return n === nothing ? length(i) : min(n, length(i))
    end
end
_zip_min_length(is::Tuple{}) = nothing
size(z::Zip) = _promote_tuple_shape(Base.map(size, z.is)...)
axes(z::Zip) = _promote_tuple_shape(Base.map(axes, z.is)...)
_promote_tuple_shape((a,)::Tuple{OneTo}, (b,)::Tuple{OneTo}) = (intersect(a, b),)
_promote_tuple_shape((m,)::Tuple{Integer}, (n,)::Tuple{Integer}) = (min(m, n),)
_promote_tuple_shape(a, b) = promote_shape(a, b)
_promote_tuple_shape(a, b...) = _promote_tuple_shape(a, _promote_tuple_shape(b...))
_promote_tuple_shape(a) = a
eltype(::Type{Zip{Is}}) where {Is<:Tuple} = TupleOrBottom(map(eltype, fieldtypes(Is))...)
#eltype(::Type{Zip{Tuple{}}}) = Tuple{}
#eltype(::Type{Zip{Tuple{A}}}) where {A} = Tuple{eltype(A)}
#eltype(::Type{Zip{Tuple{A, B}}}) where {A, B} = Tuple{eltype(A), eltype(B)}
@inline isdone(z::Zip) = _zip_any_isdone(z.is, Base.map(_ -> (), z.is))
@inline isdone(z::Zip, ss) = _zip_any_isdone(z.is, Base.map(tuple, ss))
@inline function _zip_any_isdone(is, ss)
    d1 = isdone(is[1], ss[1]...)
    d1 === true && return true
    return d1 | _zip_any_isdone(tail(is), tail(ss))
end
@inline _zip_any_isdone(::Tuple{}, ::Tuple{}) = false

@propagate_inbounds iterate(z::Zip) = _zip_iterate_all(z.is, Base.map(_ -> (), z.is))
@propagate_inbounds iterate(z::Zip, ss) = _zip_iterate_all(z.is, Base.map(tuple, ss))

# This first queries isdone from every iterator. If any gives true, it immediately returns
# nothing. It then iterates all those where isdone returned missing, afterwards all those
# it returned false, again terminating immediately if any iterator is exhausted. Finally,
# the results are interleaved appropriately.
@propagate_inbounds function _zip_iterate_all(is, ss)
    d, ds = _zip_isdone(is, ss)
    d && return nothing
    xs1 = _zip_iterate_some(is, ss, ds, missing)
    xs1 === nothing && return nothing
    xs2 = _zip_iterate_some(is, ss, ds, false)
    xs2 === nothing && return nothing
    return _zip_iterate_interleave(xs1, xs2, ds)
end

@propagate_inbounds function _zip_iterate_some(is, ss, ds::Tuple{T,Vararg{Any}}, f::T) where T
    x = iterate(is[1], ss[1]...)
    x === nothing && return nothing
    y = _zip_iterate_some(tail(is), tail(ss), tail(ds), f)
    y === nothing && return nothing
    return (x, y...)
end
@propagate_inbounds _zip_iterate_some(is, ss, ds::Tuple{Any,Vararg{Any}}, f) =
    _zip_iterate_some(tail(is), tail(ss), tail(ds), f)
_zip_iterate_some(::Tuple{}, ::Tuple{}, ::Tuple{}, ::Any) = ()

function _zip_iterate_interleave(xs1, xs2, ds)
    t = _zip_iterate_interleave(tail(xs1), xs2, tail(ds))
    ((xs1[1][1], t[1]...), (xs1[1][2], t[2]...))
end
function _zip_iterate_interleave(xs1, xs2, ds::Tuple{Bool,Vararg{Any}})
    t = _zip_iterate_interleave(xs1, tail(xs2), tail(ds))
    ((xs2[1][1], t[1]...), (xs2[1][2], t[2]...))
end
_zip_iterate_interleave(::Tuple{}, ::Tuple{}, ::Tuple{}) = ((), ())

function _zip_isdone(is, ss)
    d = isdone(is[1], ss[1]...)
    d´, ds = _zip_isdone(tail(is), tail(ss))
    return (d === true || d´, (d, ds...))
end
_zip_isdone(::Tuple{}, ::Tuple{}) = (false, ())

IteratorSize(::Type{Zip{Is}}) where {Is<:Tuple} = zip_iteratorsize(ntuple(n -> IteratorSize(fieldtype(Is, n)), _counttuple(Is)::Int)...)
IteratorEltype(::Type{Zip{Is}}) where {Is<:Tuple} = zip_iteratoreltype(ntuple(n -> IteratorEltype(fieldtype(Is, n)), _counttuple(Is)::Int)...)

zip_iteratorsize() = IsInfinite()
zip_iteratorsize(I) = I
zip_iteratorsize(a, b) = and_iteratorsize(a,b) # as `and_iteratorsize` but inherit `Union{HasLength,IsInfinite}` of the shorter iterator
zip_iteratorsize(::HasLength, ::IsInfinite) = HasLength()
zip_iteratorsize(::HasShape, ::IsInfinite) = HasLength()
zip_iteratorsize(a::IsInfinite, b) = zip_iteratorsize(b,a)
zip_iteratorsize(a::IsInfinite, b::IsInfinite) = IsInfinite()
zip_iteratorsize(a, b, tail...) = zip_iteratorsize(a, zip_iteratorsize(b, tail...))

zip_iteratoreltype() = HasEltype()
zip_iteratoreltype(a) = a
zip_iteratoreltype(a, tail...) = and_iteratoreltype(a, zip_iteratoreltype(tail...))

reverse(z::Zip) = Zip(Base.map(reverse, z.is)) # n.b. we assume all iterators are the same length
last(z::Zip) = getindex.(z.is, minimum(Base.map(lastindex, z.is)))

# filter

struct Filter{F,I}
    flt::F
    itr::I
end

"""
    Iterators.filter(flt, itr)

Given a predicate function `flt` and an iterable object `itr`, return an
iterable object which upon iteration yields the elements `x` of `itr` that
satisfy `flt(x)`. The order of the original iterator is preserved.

This function is *lazy*; that is, it is guaranteed to return in ``Θ(1)`` time
and use ``Θ(1)`` additional space, and `flt` will not be called by an
invocation of `filter`. Calls to `flt` will be made when iterating over the
returned iterable object. These calls are not cached and repeated calls will be
made when reiterating.

See [`Base.filter`](@ref) for an eager implementation of filtering for arrays.

# Examples
```jldoctest
julia> f = Iterators.filter(isodd, [1, 2, 3, 4, 5])
Base.Iterators.Filter{typeof(isodd), Vector{Int64}}(isodd, [1, 2, 3, 4, 5])

julia> foreach(println, f)
1
3
5

julia> [x for x in [1, 2, 3, 4, 5] if isodd(x)]  # collects a generator over Iterators.filter
3-element Vector{Int64}:
 1
 3
 5
```
"""
filter(flt, itr) = Filter(flt, itr)

function iterate(f::Filter, state...)
    y = iterate(f.itr, state...)
    while y !== nothing
        if f.flt(y[1])
            return y
        end
        y = iterate(f.itr, y[2])
    end
    nothing
end

eltype(::Type{Filter{F,I}}) where {F,I} = eltype(I)
IteratorEltype(::Type{Filter{F,I}}) where {F,I} = IteratorEltype(I)
IteratorSize(::Type{<:Filter}) = SizeUnknown()

reverse(f::Filter) = Filter(f.flt, reverse(f.itr))
last(f::Filter) = first(reverse(f))

# Accumulate -- partial reductions of a function over an iterator

struct Accumulate{F,I,T}
    f::F
    itr::I
    init::T
end

"""
    Iterators.accumulate(f, itr; [init])

Given a 2-argument function `f` and an iterator `itr`, return a new
iterator that successively applies `f` to the previous value and the
next element of `itr`.

This is effectively a lazy version of [`Base.accumulate`](@ref).

!!! compat "Julia 1.5"
    Keyword argument `init` is added in Julia 1.5.

# Examples
```jldoctest
julia> a = Iterators.accumulate(+, [1,2,3,4]);

julia> foreach(println, a)
1
3
6
10

julia> b = Iterators.accumulate(/, (2, 5, 2, 5); init = 100);

julia> collect(b)
4-element Vector{Float64}:
 50.0
 10.0
  5.0
  1.0
```
"""
accumulate(f, itr; init = Base._InitialValue()) = Accumulate(f, itr, init)

function iterate(itr::Accumulate)
    state = iterate(itr.itr)
    if state === nothing
        return nothing
    end
    val = Base.BottomRF(itr.f)(itr.init, state[1])
    return (val, (val, state[2]))
end

function iterate(itr::Accumulate, state)
    nxt = iterate(itr.itr, state[2])
    if nxt === nothing
        return nothing
    end
    val = itr.f(state[1], nxt[1])
    return (val, (val, nxt[2]))
end

length(itr::Accumulate) = length(itr.itr)
size(itr::Accumulate) = size(itr.itr)

IteratorSize(::Type{<:Accumulate{<:Any,I}}) where {I} = IteratorSize(I)
IteratorEltype(::Type{<:Accumulate}) = EltypeUnknown()

# Rest -- iterate starting at the given state

struct Rest{I,S}
    itr::I
    st::S
end

"""
    rest(iter, state)

An iterator that yields the same elements as `iter`, but starting at the given `state`.

See also: [`Iterators.drop`](@ref), [`Iterators.peel`](@ref), [`Base.rest`](@ref).

# Examples
```jldoctest
julia> collect(Iterators.rest([1,2,3,4], 2))
3-element Vector{Int64}:
 2
 3
 4
```
"""
rest(itr,state) = Rest(itr,state)
rest(itr::Rest,state) = Rest(itr.itr,state)
rest(itr) = itr

"""
    peel(iter)

Returns the first element and an iterator over the remaining elements.

If the iterator is empty return `nothing` (like `iterate`).

!!! compat "Julia 1.7"
    Prior versions throw a BoundsError if the iterator is empty.

See also: [`Iterators.drop`](@ref), [`Iterators.take`](@ref).

# Examples
```jldoctest
julia> (a, rest) = Iterators.peel("abc");

julia> a
'a': ASCII/Unicode U+0061 (category Ll: Letter, lowercase)

julia> collect(rest)
2-element Vector{Char}:
 'b': ASCII/Unicode U+0062 (category Ll: Letter, lowercase)
 'c': ASCII/Unicode U+0063 (category Ll: Letter, lowercase)
```
"""
function peel(itr)
    y = iterate(itr)
    y === nothing && return y
    val, s = y
    val, rest(itr, s)
end

@propagate_inbounds iterate(i::Rest, st=i.st) = iterate(i.itr, st)
isdone(i::Rest, st...) = isdone(i.itr, st...)

eltype(::Type{<:Rest{I}}) where {I} = eltype(I)
IteratorEltype(::Type{<:Rest{I}}) where {I} = IteratorEltype(I)
rest_iteratorsize(a) = SizeUnknown()
rest_iteratorsize(::IsInfinite) = IsInfinite()
IteratorSize(::Type{<:Rest{I}}) where {I} = rest_iteratorsize(IteratorSize(I))

# Count -- infinite counting

struct Count{T,S}
    start::T
    step::S
end

"""
    countfrom(start=1, step=1)

An iterator that counts forever, starting at `start` and incrementing by `step`.

# Examples
```jldoctest
julia> for v in Iterators.countfrom(5, 2)
           v > 10 && break
           println(v)
       end
5
7
9
```
"""
countfrom(start::T, step::S) where {T,S} = Count{typeof(start+step),S}(start, step)
countfrom(start::Number, step::Number)   = Count(promote(start, step)...)
countfrom(start)                         = Count(start, oneunit(start))
countfrom()                              = Count(1, 1)


eltype(::Type{<:Count{T}}) where {T} = T

iterate(it::Count, state=it.start) = (state, state + it.step)

IteratorSize(::Type{<:Count}) = IsInfinite()

# Take -- iterate through the first n elements

struct Take{I}
    xs::I
    n::Int
    function Take(xs::I, n::Integer) where {I}
        n < 0 && throw(ArgumentError("Take length must be nonnegative"))
        return new{I}(xs, n)
    end
end

"""
    take(iter, n)

An iterator that generates at most the first `n` elements of `iter`.

See also: [`drop`](@ref Iterators.drop), [`peel`](@ref Iterators.peel), [`first`](@ref), [`Base.take!`](@ref).

# Examples
```jldoctest
julia> a = 1:2:11
1:2:11

julia> collect(a)
6-element Vector{Int64}:
  1
  3
  5
  7
  9
 11

julia> collect(Iterators.take(a,3))
3-element Vector{Int64}:
 1
 3
 5
```
"""
take(xs, n::Integer) = Take(xs, Int(n))
take(xs::Take, n::Integer) = Take(xs.xs, min(Int(n), xs.n))

eltype(::Type{Take{I}}) where {I} = eltype(I)
IteratorEltype(::Type{Take{I}}) where {I} = IteratorEltype(I)
take_iteratorsize(a) = HasLength()
take_iteratorsize(::SizeUnknown) = SizeUnknown()
IteratorSize(::Type{Take{I}}) where {I} = take_iteratorsize(IteratorSize(I))
length(t::Take) = _min_length(t.xs, 1:t.n, IteratorSize(t.xs), HasLength())
isdone(t::Take) = isdone(t.xs)
isdone(t::Take, state) = (state[1] <= 0) | isdone(t.xs, tail(state))

@propagate_inbounds function iterate(it::Take, state=(it.n,))
    n, rest = state[1], tail(state)
    n <= 0 && return nothing
    y = iterate(it.xs, rest...)
    y === nothing && return nothing
    return y[1], (n - 1, y[2])
end

# Drop -- iterator through all but the first n elements

struct Drop{I}
    xs::I
    n::Int
    function Drop(xs::I, n::Integer) where {I}
        n < 0 && throw(ArgumentError("Drop length must be nonnegative"))
        return new{I}(xs, n)
    end
end

"""
    drop(iter, n)

An iterator that generates all but the first `n` elements of `iter`.

# Examples
```jldoctest
julia> a = 1:2:11
1:2:11

julia> collect(a)
6-element Vector{Int64}:
  1
  3
  5
  7
  9
 11

julia> collect(Iterators.drop(a,4))
2-element Vector{Int64}:
  9
 11
```
"""
drop(xs, n::Integer) = Drop(xs, Int(n))
drop(xs::Take, n::Integer) = Take(drop(xs.xs, Int(n)), max(0, xs.n - Int(n)))
drop(xs::Drop, n::Integer) = Drop(xs.xs, Int(n) + xs.n)

eltype(::Type{Drop{I}}) where {I} = eltype(I)
IteratorEltype(::Type{Drop{I}}) where {I} = IteratorEltype(I)
drop_iteratorsize(::SizeUnknown) = SizeUnknown()
drop_iteratorsize(::Union{HasShape, HasLength}) = HasLength()
drop_iteratorsize(::IsInfinite) = IsInfinite()
IteratorSize(::Type{Drop{I}}) where {I} = drop_iteratorsize(IteratorSize(I))
length(d::Drop) = _diff_length(d.xs, 1:d.n, IteratorSize(d.xs), HasLength())

function iterate(it::Drop)
    y = iterate(it.xs)
    for i in 1:it.n
        y === nothing && return y
        y = iterate(it.xs, y[2])
    end
    y
end
iterate(it::Drop, state) = iterate(it.xs, state)
isdone(it::Drop, state) = isdone(it.xs, state)


# takewhile

struct TakeWhile{I,P<:Function}
    pred::P
    xs::I
end

"""
    takewhile(pred, iter)

An iterator that generates element from `iter` as long as predicate `pred` is true,
afterwards, drops every element.

!!! compat "Julia 1.4"
    This function requires at least Julia 1.4.

# Examples

```jldoctest
julia> s = collect(1:5)
5-element Vector{Int64}:
 1
 2
 3
 4
 5

julia> collect(Iterators.takewhile(<(3),s))
2-element Vector{Int64}:
 1
 2
```
"""
takewhile(pred,xs) = TakeWhile(pred,xs)

function iterate(ibl::TakeWhile, itr...)
    y = iterate(ibl.xs,itr...)
    y === nothing && return nothing
    ibl.pred(y[1]) || return nothing
    y
end

IteratorSize(::Type{<:TakeWhile}) = SizeUnknown()
eltype(::Type{TakeWhile{I,P}} where P) where {I} = eltype(I)
IteratorEltype(::Type{TakeWhile{I, P}} where P) where {I} = IteratorEltype(I)


# dropwhile

struct DropWhile{I,P<:Function}
    pred::P
    xs::I
end

"""
    dropwhile(pred, iter)

An iterator that drops element from `iter` as long as predicate `pred` is true,
afterwards, returns every element.

!!! compat "Julia 1.4"
    This function requires at least Julia 1.4.

# Examples

```jldoctest
julia> s = collect(1:5)
5-element Vector{Int64}:
 1
 2
 3
 4
 5

julia> collect(Iterators.dropwhile(<(3),s))
3-element Vector{Int64}:
 3
 4
 5
```
"""
dropwhile(pred,itr) = DropWhile(pred,itr)

iterate(ibl::DropWhile,itr) = iterate(ibl.xs, itr)
function iterate(ibl::DropWhile)
    y = iterate(ibl.xs)
    while y !== nothing
        ibl.pred(y[1]) || break
        y = iterate(ibl.xs,y[2])
    end
    y
end

IteratorSize(::Type{<:DropWhile}) = SizeUnknown()
eltype(::Type{DropWhile{I,P}}) where {I,P} = eltype(I)
IteratorEltype(::Type{DropWhile{I,P}}) where {I,P} = IteratorEltype(I)


# Cycle an iterator forever

struct Cycle{I}
    xs::I
end

"""
    cycle(iter)

An iterator that cycles through `iter` forever.
If `iter` is empty, so is `cycle(iter)`.

See also: [`Iterators.repeated`](@ref), [`Base.repeat`](@ref).

# Examples
```jldoctest
julia> for (i, v) in enumerate(Iterators.cycle("hello"))
           print(v)
           i > 10 && break
       end
hellohelloh
```
"""
cycle(xs) = Cycle(xs)

eltype(::Type{Cycle{I}}) where {I} = eltype(I)
IteratorEltype(::Type{Cycle{I}}) where {I} = IteratorEltype(I)
IteratorSize(::Type{Cycle{I}}) where {I} = IsInfinite()

iterate(it::Cycle) = iterate(it.xs)
isdone(it::Cycle) = isdone(it.xs)
isdone(it::Cycle, state) = false
function iterate(it::Cycle, state)
    y = iterate(it.xs, state)
    y === nothing && return iterate(it)
    y
end

reverse(it::Cycle) = Cycle(reverse(it.xs))
last(it::Cycle) = last(it.xs)

# Repeated - repeat an object infinitely many times

struct Repeated{O}
    x::O
end
repeated(x) = Repeated(x)

"""
    repeated(x[, n::Int])

An iterator that generates the value `x` forever. If `n` is specified, generates `x` that
many times (equivalent to `take(repeated(x), n)`).

See also: [`Iterators.cycle`](@ref), [`Base.repeat`](@ref).

# Examples
```jldoctest
julia> a = Iterators.repeated([1 2], 4);

julia> collect(a)
4-element Vector{Matrix{Int64}}:
 [1 2]
 [1 2]
 [1 2]
 [1 2]
```
"""
repeated(x, n::Integer) = take(repeated(x), Int(n))

eltype(::Type{Repeated{O}}) where {O} = O

iterate(it::Repeated, state...) = (it.x, nothing)

IteratorSize(::Type{<:Repeated}) = IsInfinite()
IteratorEltype(::Type{<:Repeated}) = HasEltype()

reverse(it::Union{Repeated,Take{<:Repeated}}) = it
last(it::Union{Repeated,Take{<:Repeated}}) = first(it)

# Product -- cartesian product of iterators
struct ProductIterator{T<:Tuple}
    iterators::T
end

"""
    product(iters...)

Return an iterator over the product of several iterators. Each generated element is
a tuple whose `i`th element comes from the `i`th argument iterator. The first iterator
changes the fastest.

See also: [`zip`](@ref), [`Iterators.flatten`](@ref).

# Examples
```jldoctest
julia> collect(Iterators.product(1:2, 3:5))
2×3 Matrix{Tuple{Int64, Int64}}:
 (1, 3)  (1, 4)  (1, 5)
 (2, 3)  (2, 4)  (2, 5)

julia> ans == [(x,y) for x in 1:2, y in 3:5]  # collects a generator involving Iterators.product
true
```
"""
product(iters...) = ProductIterator(iters)

IteratorSize(::Type{ProductIterator{Tuple{}}}) = HasShape{0}()
IteratorSize(::Type{ProductIterator{T}}) where {T<:Tuple} =
    prod_iteratorsize(ntuple(n -> IteratorSize(fieldtype(T, n)), _counttuple(T)::Int)..., HasShape{0}())

prod_iteratorsize() = HasShape{0}()
prod_iteratorsize(I) = I

prod_iteratorsize(::HasLength, ::HasLength) = HasShape{2}()
prod_iteratorsize(::HasLength, ::HasShape{N}) where {N} = HasShape{N+1}()
prod_iteratorsize(::HasShape{N}, ::HasLength) where {N} = HasShape{N+1}()
prod_iteratorsize(::HasShape{M}, ::HasShape{N}) where {M,N} = HasShape{M+N}()

# products can have an infinite iterator
prod_iteratorsize(::IsInfinite, ::IsInfinite) = IsInfinite()
prod_iteratorsize(a, ::IsInfinite) = IsInfinite()
prod_iteratorsize(::IsInfinite, b) = IsInfinite()
prod_iteratorsize(a, b) = SizeUnknown()
prod_iteratorsize(a, b, tail...) = prod_iteratorsize(a, prod_iteratorsize(b, tail...))

size(P::ProductIterator) = _prod_size(P.iterators)
_prod_size(::Tuple{}) = ()
_prod_size(t::Tuple) = (_prod_size1(t[1], IteratorSize(t[1]))..., _prod_size(tail(t))...)
_prod_size1(a, ::HasShape)  = size(a)
_prod_size1(a, ::HasLength) = (length(a),)
_prod_size1(a, A) =
    throw(ArgumentError("Cannot compute size for object of type $(typeof(a))"))

axes(P::ProductIterator) = _prod_indices(P.iterators)
_prod_indices(::Tuple{}) = ()
_prod_indices(t::Tuple) = (_prod_axes1(t[1], IteratorSize(t[1]))..., _prod_indices(tail(t))...)
_prod_axes1(a, ::HasShape)  = axes(a)
_prod_axes1(a, ::HasLength) = (OneTo(length(a)),)
_prod_axes1(a, A) =
    throw(ArgumentError("Cannot compute indices for object of type $(typeof(a))"))

ndims(p::ProductIterator) = length(axes(p))
length(P::ProductIterator) = reduce(checked_mul, size(P); init=1)

IteratorEltype(::Type{ProductIterator{Tuple{}}}) = HasEltype()
IteratorEltype(::Type{ProductIterator{Tuple{I}}}) where {I} = IteratorEltype(I)

function IteratorEltype(::Type{ProductIterator{T}}) where {T<:Tuple}
    E = ntuple(n -> IteratorEltype(fieldtype(T, n)), _counttuple(T)::Int)
    any(I -> I == EltypeUnknown(), E) && return EltypeUnknown()
    return E[end]
end

eltype(::Type{ProductIterator{I}}) where {I} = _prod_eltype(I)
_prod_eltype(::Type{Tuple{}}) = Tuple{}
_prod_eltype(::Type{I}) where {I<:Tuple} = TupleOrBottom(ntuple(n -> eltype(fieldtype(I, n)), _counttuple(I)::Int)...)

iterate(::ProductIterator{Tuple{}}) = (), true
iterate(::ProductIterator{Tuple{}}, state) = nothing

@inline isdone(P::ProductIterator) = any(isdone, P.iterators)
@inline function _pisdone(iters, states)
    iter1 = first(iters)
    done1 = isdone(iter1, first(states)[2]) # check step
    done1 === true || return done1 # false or missing
    done1 = isdone(iter1) # check restart
    done1 === true || return done1 # false or missing
    return _pisdone(tail(iters), tail(states)) # check tail
end
@inline isdone(::ProductIterator{Tuple{}}, states) = true
@inline isdone(P::ProductIterator, states) = _pisdone(P.iterators, states)

@inline _piterate() = ()
@inline function _piterate(iter1, rest...)
    next = iterate(iter1)
    next === nothing && return nothing
    restnext = _piterate(rest...)
    restnext === nothing && return nothing
    return (next, restnext...)
end
@inline function iterate(P::ProductIterator)
    isdone(P) === true && return nothing
    next = _piterate(P.iterators...)
    next === nothing && return nothing
    return (Base.map(x -> x[1], next), next)
end

@inline _piterate1(::Tuple{}, ::Tuple{}) = nothing
@inline function _piterate1(iters, states)
    iter1 = first(iters)
    next = iterate(iter1, first(states)[2])
    restnext = tail(states)
    if next === nothing
        isdone(iter1) === true && return nothing
        restnext = _piterate1(tail(iters), restnext)
        restnext === nothing && return nothing
        next = iterate(iter1)
        next === nothing && return nothing
    end
    return (next, restnext...)
end
@inline function iterate(P::ProductIterator, states)
    isdone(P, states) === true && return nothing
    next = _piterate1(P.iterators, states)
    next === nothing && return nothing
    return (Base.map(x -> x[1], next), next)
end

reverse(p::ProductIterator) = ProductIterator(Base.map(reverse, p.iterators))
last(p::ProductIterator) = Base.map(last, p.iterators)
intersect(a::ProductIterator, b::ProductIterator) = ProductIterator(intersect.(a.iterators, b.iterators))

# flatten an iterator of iterators

struct Flatten{I}
    it::I
end

"""
    flatten(iter)

Given an iterator that yields iterators, return an iterator that yields the
elements of those iterators.
Put differently, the elements of the argument iterator are concatenated.

# Examples
```jldoctest
julia> collect(Iterators.flatten((1:2, 8:9)))
4-element Vector{Int64}:
 1
 2
 8
 9

julia> [(x,y) for x in 0:1 for y in 'a':'c']  # collects generators involving Iterators.flatten
6-element Vector{Tuple{Int64, Char}}:
 (0, 'a')
 (0, 'b')
 (0, 'c')
 (1, 'a')
 (1, 'b')
 (1, 'c')
```
"""
flatten(itr) = Flatten(itr)

eltype(::Type{Flatten{I}}) where {I} = eltype(eltype(I))
eltype(::Type{Flatten{Tuple{}}}) = eltype(Tuple{})
IteratorEltype(::Type{Flatten{I}}) where {I} = _flatteneltype(I, IteratorEltype(I))
IteratorEltype(::Type{Flatten{Tuple{}}}) = IteratorEltype(Tuple{})
_flatteneltype(I, ::HasEltype) = IteratorEltype(eltype(I))
_flatteneltype(I, et) = EltypeUnknown()

flatten_iteratorsize(::Union{HasShape, HasLength}, ::Type{Union{}}, slurp...) = HasLength() # length==0
flatten_iteratorsize(::Union{HasShape, HasLength}, ::Type{<:NTuple{N,Any}}) where {N} = HasLength()
flatten_iteratorsize(::Union{HasShape, HasLength}, ::Type{<:Tuple}) = SizeUnknown()
flatten_iteratorsize(::Union{HasShape, HasLength}, ::Type{<:Number}) = HasLength()
flatten_iteratorsize(a, b) = SizeUnknown()

_flatten_iteratorsize(sz, ::EltypeUnknown, I) = SizeUnknown()
_flatten_iteratorsize(sz, ::HasEltype, I) = flatten_iteratorsize(sz, eltype(I))
_flatten_iteratorsize(sz, ::HasEltype, ::Type{Tuple{}}) = HasLength()

IteratorSize(::Type{Flatten{I}}) where {I} = _flatten_iteratorsize(IteratorSize(I), IteratorEltype(I), I)

flatten_length(f, T::Type{Union{}}, slurp...) = 0
function flatten_length(f, T::Type{<:NTuple{N,Any}}) where {N}
    return N * length(f.it)
end
flatten_length(f, ::Type{<:Number}) = length(f.it)
flatten_length(f, T) = throw(ArgumentError(
    "Iterates of the argument to Flatten are not known to have constant length"))
length(f::Flatten{I}) where {I} = flatten_length(f, eltype(I))
length(f::Flatten{Tuple{}}) = 0

@propagate_inbounds function iterate(f::Flatten, state=())
    if state !== ()
        y = iterate(tail(state)...)
        y !== nothing && return (y[1], (state[1], state[2], y[2]))
    end
    x = (state === () ? iterate(f.it) : iterate(f.it, state[1]))
    x === nothing && return nothing
    y = iterate(x[1])
    while y === nothing
         x = iterate(f.it, x[2])
         x === nothing && return nothing
         y = iterate(x[1])
    end
    return y[1], (x[2], x[1], y[2])
end

reverse(f::Flatten) = Flatten(reverse(itr) for itr in reverse(f.it))
last(f::Flatten) = last(last(f.it))

"""
    Iterators.flatmap(f, iterators...)

Equivalent to `flatten(map(f, iterators...))`.

See also [`Iterators.flatten`](@ref), [`Iterators.map`](@ref).

!!! compat "Julia 1.9"
    This function was added in Julia 1.9.

# Examples
```jldoctest
julia> Iterators.flatmap(n -> -n:2:n, 1:3) |> collect
9-element Vector{Int64}:
 -1
  1
 -2
  0
  2
 -3
 -1
  1
  3

julia> stack(n -> -n:2:n, 1:3)
ERROR: DimensionMismatch: stack expects uniform slices, got axes(x) == (1:3,) while first had (1:2,)
[...]

julia> Iterators.flatmap(n -> (-n, 10n), 1:2) |> collect
4-element Vector{Int64}:
 -1
 10
 -2
 20

julia> ans == vec(stack(n -> (-n, 10n), 1:2))
true
```
"""
flatmap(f, c...) = flatten(map(f, c...))

if Base !== Core.Compiler # views are not defined
@doc """
    partition(collection, n)

Iterate over a collection `n` elements at a time.

# Examples
```jldoctest
julia> collect(Iterators.partition([1,2,3,4,5], 2))
3-element Vector{SubArray{Int64, 1, Vector{Int64}, Tuple{UnitRange{Int64}}, true}}:
 [1, 2]
 [3, 4]
 [5]
```
""" function partition(c, n::Integer)
    n < 1 && throw(ArgumentError("cannot create partitions of length $n"))
    return PartitionIterator(c, Int(n))
end

struct PartitionIterator{T}
    c::T
    n::Int
end
# Partitions are explicitly a linear indexing operation, so reshape to 1-d immediately
PartitionIterator(A::AbstractArray, n::Int) = PartitionIterator(Base.vec(A), n)
PartitionIterator(v::AbstractVector, n::Int) = PartitionIterator{typeof(v)}(v, n)

eltype(::Type{PartitionIterator{T}}) where {T} = Vector{eltype(T)}
# Arrays use a generic `view`-of-a-`vec`, so we cannot exactly predict what we'll get back
eltype(::Type{PartitionIterator{T}}) where {T<:AbstractArray} = AbstractVector{eltype(T)}
# But for some common implementations in Base we know the answer exactly
eltype(::Type{PartitionIterator{T}}) where {T<:Vector} = SubArray{eltype(T), 1, T, Tuple{UnitRange{Int}}, true}

IteratorEltype(::Type{PartitionIterator{T}}) where {T} = IteratorEltype(T)
IteratorEltype(::Type{PartitionIterator{T}}) where {T<:AbstractArray} = EltypeUnknown()
IteratorEltype(::Type{PartitionIterator{T}}) where {T<:Vector} = IteratorEltype(T)

partition_iteratorsize(::HasShape) = HasLength()
partition_iteratorsize(isz) = isz
function IteratorSize(::Type{PartitionIterator{T}}) where {T}
    partition_iteratorsize(IteratorSize(T))
end

function length(itr::PartitionIterator)
    l = length(itr.c)
    return cld(l, itr.n)
end

function iterate(itr::PartitionIterator{<:AbstractRange}, state = firstindex(itr.c))
    state > lastindex(itr.c) && return nothing
    r = min(state + itr.n - 1, lastindex(itr.c))
    return @inbounds itr.c[state:r], r + 1
end

function iterate(itr::PartitionIterator{<:AbstractArray}, state = firstindex(itr.c))
    state > lastindex(itr.c) && return nothing
    r = min(state + itr.n - 1, lastindex(itr.c))
    return @inbounds view(itr.c, state:r), r + 1
end

struct IterationCutShort; end

function iterate(itr::PartitionIterator, state...)
    # This is necessary to remember whether we cut the
    # last element short. In such cases, we do return that
    # element, but not the next one
    state === (IterationCutShort(),) && return nothing
    v = Vector{eltype(itr.c)}(undef, itr.n)
    i = 0
    y = iterate(itr.c, state...)
    while y !== nothing
        i += 1
        v[i] = y[1]
        if i >= itr.n
            break
        end
        y = iterate(itr.c, y[2])
    end
    i === 0 && return nothing
    return resize!(v, i), y === nothing ? IterationCutShort() : y[2]
end

@doc """
    Stateful(itr)

There are several different ways to think about this iterator wrapper:

1. It provides a mutable wrapper around an iterator and
   its iteration state.
2. It turns an iterator-like abstraction into a `Channel`-like
   abstraction.
3. It's an iterator that mutates to become its own rest iterator
   whenever an item is produced.

`Stateful` provides the regular iterator interface. Like other mutable iterators
(e.g. [`Base.Channel`](@ref)), if iteration is stopped early (e.g. by a [`break`](@ref) in a [`for`](@ref) loop),
iteration can be resumed from the same spot by continuing to iterate over the
same iterator object (in contrast, an immutable iterator would restart from the
beginning).

# Examples
```jldoctest
julia> a = Iterators.Stateful("abcdef");

julia> isempty(a)
false

julia> popfirst!(a)
'a': ASCII/Unicode U+0061 (category Ll: Letter, lowercase)

julia> collect(Iterators.take(a, 3))
3-element Vector{Char}:
 'b': ASCII/Unicode U+0062 (category Ll: Letter, lowercase)
 'c': ASCII/Unicode U+0063 (category Ll: Letter, lowercase)
 'd': ASCII/Unicode U+0064 (category Ll: Letter, lowercase)

julia> collect(a)
2-element Vector{Char}:
 'e': ASCII/Unicode U+0065 (category Ll: Letter, lowercase)
 'f': ASCII/Unicode U+0066 (category Ll: Letter, lowercase)

julia> Iterators.reset!(a); popfirst!(a)
'a': ASCII/Unicode U+0061 (category Ll: Letter, lowercase)

julia> Iterators.reset!(a, "hello"); popfirst!(a)
'h': ASCII/Unicode U+0068 (category Ll: Letter, lowercase)
```

```jldoctest
julia> a = Iterators.Stateful([1,1,1,2,3,4]);

julia> for x in a; x == 1 || break; end

julia> peek(a)
3

julia> sum(a) # Sum the remaining elements
7
```
"""
mutable struct Stateful{T, VS, N<:Integer}
    itr::T
    # A bit awkward right now, but adapted to the new iteration protocol
    nextvalstate::Union{VS, Nothing}

    # Number of remaining elements, if itr is HasLength or HasShape.
    # if not, store -1 - number_of_consumed_elements.
    # This allows us to defer calculating length until asked for.
    # See PR #45924
    remaining::N
    @inline function Stateful{<:Any, Any}(itr::T) where {T}
        itl = iterlength(itr)
        new{T, Any, typeof(itl)}(itr, iterate(itr), itl)
    end
    @inline function Stateful(itr::T) where {T}
        VS = approx_iter_type(T)
        itl = iterlength(itr)
        return new{T, VS, typeof(itl)}(itr, iterate(itr)::VS, itl)
    end
end

function iterlength(it)::Signed
    if IteratorSize(it) isa Union{HasShape, HasLength}
       return length(it)
    else
        -1
    end
end

function reset!(s::Stateful{T,VS}, itr::T=s.itr) where {T,VS}
    s.itr = itr
    itl = iterlength(itr)
    setfield!(s, :nextvalstate, iterate(itr))
    s.remaining = itl
    s
end

# Try to find an appropriate type for the (value, state tuple),
# by doing a recursive unrolling of the iteration protocol up to
# fixpoint.
approx_iter_type(itrT::Type) = _approx_iter_type(itrT, Base._return_type(iterate, Tuple{itrT}))
# Not actually called, just passed to return type to avoid
# having to typesplit on Nothing
function doiterate(itr, valstate::Union{Nothing, Tuple{Any, Any}})
    valstate === nothing && return nothing
    val, st = valstate
    return iterate(itr, st)
end
function _approx_iter_type(itrT::Type, vstate::Type)
    vstate <: Union{Nothing, Tuple{Any, Any}} || return Any
    vstate <: Union{} && return Union{}
    itrT <: Union{} && return Union{}
    nextvstate = Base._return_type(doiterate, Tuple{itrT, vstate})
    return (nextvstate <: vstate ? vstate : Any)
end

Stateful(x::Stateful) = x
convert(::Type{Stateful}, itr) = Stateful(itr)

@inline isdone(s::Stateful, st=nothing) = s.nextvalstate === nothing

@inline function popfirst!(s::Stateful)
    vs = s.nextvalstate
    if vs === nothing
        throw(Base.EOFError())
    else
        val, state = vs
        Core.setfield!(s, :nextvalstate, iterate(s.itr, state))
        rem = s.remaining
        s.remaining = rem - typeof(rem)(1)
        return val
    end
end

@inline function peek(s::Stateful, sentinel=nothing)
    ns = s.nextvalstate
    return ns !== nothing ? ns[1] : sentinel
end
@inline iterate(s::Stateful, state=nothing) = s.nextvalstate === nothing ? nothing : (popfirst!(s), nothing)
IteratorSize(::Type{<:Stateful{T}}) where {T} = IteratorSize(T) isa HasShape ? HasLength() : IteratorSize(T)
eltype(::Type{<:Stateful{T}}) where {T} = eltype(T)
IteratorEltype(::Type{<:Stateful{T}}) where {T} = IteratorEltype(T)

function length(s::Stateful)
    rem = s.remaining
    # If rem is actually remaining length, return it.
    # else, rem is number of consumed elements.
    if rem >= 0
        rem
    else
        length(s.itr) - (typeof(rem)(1) - rem)
    end
end
end # if statement several hundred lines above

"""
    only(x)

Return the one and only element of collection `x`, or throw an [`ArgumentError`](@ref) if the
collection has zero or multiple elements.

See also [`first`](@ref), [`last`](@ref).

!!! compat "Julia 1.4"
    This method requires at least Julia 1.4.

# Examples
```jldoctest
julia> only(["a"])
"a"

julia> only("a")
'a': ASCII/Unicode U+0061 (category Ll: Letter, lowercase)

julia> only(())
ERROR: ArgumentError: Tuple contains 0 elements, must contain exactly 1 element
Stacktrace:
[...]

julia> only(('a', 'b'))
ERROR: ArgumentError: Tuple contains 2 elements, must contain exactly 1 element
Stacktrace:
[...]
```
"""
@propagate_inbounds function only(x)
    i = iterate(x)
    @boundscheck if i === nothing
        throw(ArgumentError("Collection is empty, must contain exactly 1 element"))
    end
    (ret, state) = i::NTuple{2,Any}
    @boundscheck if iterate(x, state) !== nothing
        throw(ArgumentError("Collection has multiple elements, must contain exactly 1 element"))
    end
    return ret
end

# Collections of known size
only(x::Ref) = x[]
only(x::Number) = x
only(x::Char) = x
only(x::Tuple{Any}) = x[1]
only(x::Tuple) = throw(
    ArgumentError("Tuple contains $(length(x)) elements, must contain exactly 1 element")
)
only(a::AbstractArray{<:Any, 0}) = @inbounds return a[]
only(x::NamedTuple{<:Any, <:Tuple{Any}}) = first(x)
only(x::NamedTuple) = throw(
    ArgumentError("NamedTuple contains $(length(x)) elements, must contain exactly 1 element")
)

end
Q   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/namedtuple.jlNK      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
    NamedTuple

`NamedTuple`s are, as their name suggests, named [`Tuple`](@ref)s. That is, they're a
tuple-like collection of values, where each entry has a unique name, represented as a
[`Symbol`](@ref). Like `Tuple`s, `NamedTuple`s are immutable; neither the names nor the values
can be modified in place after construction.

A named tuple can be created as a tuple literal with keys, e.g. `(a=1, b=2)`,
or as a tuple literal with semicolon after the opening parenthesis, e.g. `(;
a=1, b=2)` (this form also accepts programmatically generated names as
described below), or using a `NamedTuple` type as constructor, e.g.
`NamedTuple{(:a, :b)}((1,2))`.

Accessing the value associated with a name in a named tuple can be done using field
access syntax, e.g. `x.a`, or using [`getindex`](@ref), e.g. `x[:a]` or `x[(:a, :b)]`.
A tuple of the names can be obtained using [`keys`](@ref), and a tuple of the values
can be obtained using [`values`](@ref).

!!! note
    Iteration over `NamedTuple`s produces the *values* without the names. (See example
    below.) To iterate over the name-value pairs, use the [`pairs`](@ref) function.

The [`@NamedTuple`](@ref) macro can be used for conveniently declaring `NamedTuple` types.

# Examples
```jldoctest
julia> x = (a=1, b=2)
(a = 1, b = 2)

julia> x.a
1

julia> x[:a]
1

julia> x[(:a,)]
(a = 1,)

julia> keys(x)
(:a, :b)

julia> values(x)
(1, 2)

julia> collect(x)
2-element Vector{Int64}:
 1
 2

julia> collect(pairs(x))
2-element Vector{Pair{Symbol, Int64}}:
 :a => 1
 :b => 2
```

In a similar fashion as to how one can define keyword arguments programmatically,
a named tuple can be created by giving pairs `name::Symbol => value` after a
semicolon inside a tuple literal. This and the `name=value` syntax can be mixed:

```jldoctest
julia> (; :a => 1, :b => 2, c=3)
(a = 1, b = 2, c = 3)
```

The name-value pairs can also be provided by splatting a named tuple or any
iterator that yields two-value collections holding each a symbol as first
value:

```jldoctest
julia> keys = (:a, :b, :c); values = (1, 2, 3);

julia> NamedTuple{keys}(values)
(a = 1, b = 2, c = 3)

julia> (; (keys .=> values)...)
(a = 1, b = 2, c = 3)

julia> nt1 = (a=1, b=2);

julia> nt2 = (c=3, d=4);

julia> (; nt1..., nt2..., b=20) # the final b overwrites the value from nt1
(a = 1, b = 20, c = 3, d = 4)

julia> (; zip(keys, values)...) # zip yields tuples such as (:a, 1)
(a = 1, b = 2, c = 3)
```

As in keyword arguments, identifiers and dot expressions imply names:

```jldoctest
julia> x = 0
0

julia> t = (; x)
(x = 0,)

julia> (; t.x)
(x = 0,)
```

!!! compat "Julia 1.5"
    Implicit names from identifiers and dot expressions are available as of Julia 1.5.

!!! compat "Julia 1.7"
    Use of `getindex` methods with multiple `Symbol`s is available as of Julia 1.7.
"""
Core.NamedTuple

if nameof(@__MODULE__) === :Base

@eval function (NT::Type{NamedTuple{names,T}})(args::Tuple) where {names, T <: Tuple}
    if length(args) != length(names::Tuple)
        throw(ArgumentError("Wrong number of arguments to named tuple constructor."))
    end
    # Note T(args) might not return something of type T; e.g.
    # Tuple{Type{Float64}}((Float64,)) returns a Tuple{DataType}
    $(Expr(:splatnew, :NT, :(T(args))))
end

function (NT::Type{NamedTuple{names, T}})(nt::NamedTuple) where {names, T <: Tuple}
    if @generated
        Expr(:new, :NT,
             Any[ :(let Tn = fieldtype(NT, $n),
                      ntn = getfield(nt, $(QuoteNode(names[n])))
                      ntn isa Tn ? ntn : convert(Tn, ntn)
                  end) for n in 1:length(names) ]...)
    else
        NT(map(Fix1(getfield, nt), names))
    end
end

function NamedTuple{names}(nt::NamedTuple) where {names}
    if @generated
        idx = Int[ fieldindex(nt, names[n]) for n in 1:length(names) ]
        types = Tuple{(fieldtype(nt, idx[n]) for n in 1:length(idx))...}
        Expr(:new, :(NamedTuple{names, $types}), Any[ :(getfield(nt, $(idx[n]))) for n in 1:length(idx) ]...)
    else
        length_names = length(names::Tuple)
        types = Tuple{(fieldtype(typeof(nt), names[n]) for n in 1:length_names)...}
        _new_NamedTuple(NamedTuple{names, types}, map(Fix1(getfield, nt), names))
    end
end

(NT::Type{NamedTuple{names, T}})(itr) where {names, T <: Tuple} = NT(T(itr))
(NT::Type{NamedTuple{names}})(itr) where {names} = NT(Tuple(itr))

NamedTuple(itr) = (; itr...)

end # if Base

# Like NamedTuple{names, T} as a constructor, but omits the additional
# `convert` call, when the types are known to match the fields
@eval function _new_NamedTuple(T::Type{NamedTuple{NTN, NTT}} where {NTN, NTT}, args::Tuple)
    $(Expr(:splatnew, :T, :args))
end

length(t::NamedTuple) = nfields(t)
iterate(t::NamedTuple, iter=1) = iter > nfields(t) ? nothing : (getfield(t, iter), iter + 1)
rest(t::NamedTuple) = t
@inline rest(t::NamedTuple{names}, i::Int) where {names} = NamedTuple{rest(names,i)}(t)
firstindex(t::NamedTuple) = 1
lastindex(t::NamedTuple) = nfields(t)
getindex(t::NamedTuple, i::Int) = getfield(t, i)
getindex(t::NamedTuple, i::Symbol) = getfield(t, i)
getindex(t::NamedTuple, ::Colon) = t
@inline getindex(t::NamedTuple, idxs::Tuple{Vararg{Symbol}}) = NamedTuple{idxs}(t)
@inline getindex(t::NamedTuple, idxs::AbstractVector{Symbol}) = NamedTuple{Tuple(idxs)}(t)
indexed_iterate(t::NamedTuple, i::Int, state=1) = (getfield(t, i), i+1)
isempty(::NamedTuple{()}) = true
isempty(::NamedTuple) = false
empty(::NamedTuple) = NamedTuple()

prevind(@nospecialize(t::NamedTuple), i::Integer) = Int(i)-1
nextind(@nospecialize(t::NamedTuple), i::Integer) = Int(i)+1

convert(::Type{NT}, nt::NT) where {names, NT<:NamedTuple{names}} = nt
convert(::Type{NT}, nt::NT) where {names, T<:Tuple, NT<:NamedTuple{names,T}} = nt

function convert(::Type{NT}, nt::NamedTuple{names}) where {names, T<:Tuple, NT<:NamedTuple{names,T}}
    if !@isdefined T
        # converting abstract NT to an abstract Tuple type, to a concrete NT1, is not straightforward, so this could just be an error, but we define it anyways
        # _tuple_error(NT, nt)
        T1 = Tuple{ntuple(i -> fieldtype(NT, i), Val(length(names)))...}
        NT1 = NamedTuple{names, T1}
    else
        T1 = T
        NT1 = NT
    end
    return NT1(T1(nt))::NT1::NT
end

if nameof(@__MODULE__) === :Base
    Tuple(nt::NamedTuple) = (nt...,)
    (::Type{T})(nt::NamedTuple) where {T <: Tuple} = (t = Tuple(nt); t isa T ? t : convert(T, t)::T)
end

function show(io::IO, t::NamedTuple)
    n = nfields(t)
    for i = 1:n
        # if field types aren't concrete, show full type
        if typeof(getfield(t, i)) !== fieldtype(typeof(t), i)
            show(io, typeof(t))
            print(io, "(")
            show(io, Tuple(t))
            print(io, ")")
            return
        end
    end
    if n == 0
        print(io, "NamedTuple()")
    else
        typeinfo = get(io, :typeinfo, Any)
        print(io, "(")
        for i = 1:n
            show_sym(io, fieldname(typeof(t), i))
            print(io, " = ")
            show(IOContext(io, :typeinfo =>
                           t isa typeinfo <: NamedTuple ? fieldtype(typeinfo, i) : Any),
                 getfield(t, i))
            if n == 1
                print(io, ",")
            elseif i < n
                print(io, ", ")
            end
        end
        print(io, ")")
    end
end

eltype(::Type{T}) where T<:NamedTuple = nteltype(T)
nteltype(::Type) = Any
nteltype(::Type{NamedTuple{names,T}} where names) where {T} = eltype(T)

keytype(@nospecialize nt::NamedTuple) = keytype(typeof(nt))
keytype(@nospecialize T::Type{<:NamedTuple}) = Symbol

valtype(@nospecialize nt::NamedTuple) = valtype(typeof(nt))
valtype(@nospecialize T::Type{<:NamedTuple}) = eltype(T)

==(a::NamedTuple{n}, b::NamedTuple{n}) where {n} = Tuple(a) == Tuple(b)
==(a::NamedTuple, b::NamedTuple) = false

isequal(a::NamedTuple{n}, b::NamedTuple{n}) where {n} = isequal(Tuple(a), Tuple(b))
isequal(a::NamedTuple, b::NamedTuple) = false

_nt_names(::NamedTuple{names}) where {names} = names
_nt_names(::Type{T}) where {names,T<:NamedTuple{names}} = names

hash(x::NamedTuple, h::UInt) = xor(objectid(_nt_names(x)), hash(Tuple(x), h))

(<)(a::NamedTuple{n}, b::NamedTuple{n}) where {n} = Tuple(a) < Tuple(b)
isless(a::NamedTuple{n}, b::NamedTuple{n}) where {n} = isless(Tuple(a), Tuple(b))

same_names(::NamedTuple{names}...) where {names} = true
same_names(::NamedTuple...) = false

# NOTE: this method signature makes sure we don't define map(f)
function map(f, nt::NamedTuple{names}, nts::NamedTuple...) where names
    if !same_names(nt, nts...)
        throw(ArgumentError("Named tuple names do not match."))
    end
    NamedTuple{names}(map(f, map(Tuple, (nt, nts...))...))
end

@assume_effects :total function merge_names(an::Tuple{Vararg{Symbol}}, bn::Tuple{Vararg{Symbol}})
    @nospecialize an bn
    names = Symbol[an...]
    for n in bn
        if !sym_in(n, an)
            push!(names, n)
        end
    end
    (names...,)
end

@assume_effects :total function merge_types(names::Tuple{Vararg{Symbol}}, a::Type{<:NamedTuple}, b::Type{<:NamedTuple})
    @nospecialize names a b
    bn = _nt_names(b)
    return Tuple{Any[ fieldtype(sym_in(names[n], bn) ? b : a, names[n]) for n in 1:length(names) ]...}
end

@assume_effects :foldable function merge_fallback(@nospecialize(a::NamedTuple), @nospecialize(b::NamedTuple),
        @nospecialize(an::Tuple{Vararg{Symbol}}), @nospecialize(bn::Tuple{Vararg{Symbol}}))
    names = merge_names(an, bn)
    types = merge_types(names, typeof(a), typeof(b))
    n = length(names)
    A = Vector{Any}(undef, n)
    for i=1:n
        n = names[i]
        A[i] = getfield(sym_in(n, bn) ? b : a, n)
    end
    _new_NamedTuple(NamedTuple{names, types}, (A...,))
end

"""
    merge(a::NamedTuple, bs::NamedTuple...)

Construct a new named tuple by merging two or more existing ones, in a left-associative
manner. Merging proceeds left-to-right, between pairs of named tuples, and so the order of fields
present in both the leftmost and rightmost named tuples take the same position as they are found in the
leftmost named tuple. However, values are taken from matching fields in the rightmost named tuple that
contains that field. Fields present in only the rightmost named tuple of a pair are appended at the end.
A fallback is implemented for when only a single named tuple is supplied,
with signature `merge(a::NamedTuple)`.

!!! compat "Julia 1.1"
    Merging 3 or more `NamedTuple` requires at least Julia 1.1.

# Examples
```jldoctest
julia> merge((a=1, b=2, c=3), (b=4, d=5))
(a = 1, b = 4, c = 3, d = 5)
```

```jldoctest
julia> merge((a=1, b=2), (b=3, c=(d=1,)), (c=(d=2,),))
(a = 1, b = 3, c = (d = 2,))
```
"""
function merge(a::NamedTuple{an}, b::NamedTuple{bn}) where {an, bn}
    if @generated
        names = merge_names(an, bn)
        types = merge_types(names, a, b)
        vals = Any[ :(getfield($(sym_in(names[n], bn) ? :b : :a), $(QuoteNode(names[n])))) for n in 1:length(names) ]
        :( _new_NamedTuple(NamedTuple{$names,$types}, ($(vals...),)) )
    else
        merge_fallback(a, b, an, bn)
    end
end

merge(a::NamedTuple,     b::NamedTuple{()}) = a
merge(a::NamedTuple{()}, b::NamedTuple{()}) = a
merge(a::NamedTuple{()}, b::NamedTuple)     = b

merge(a::NamedTuple, b::Iterators.Pairs{<:Any,<:Any,<:Any,<:NamedTuple}) = merge(a, getfield(b, :data))

merge(a::NamedTuple, b::Iterators.Zip{<:Tuple{Any,Any}}) = merge(a, NamedTuple{Tuple(b.is[1])}(b.is[2]))

merge(a::NamedTuple, b::NamedTuple, cs::NamedTuple...) = merge(merge(a, b), cs...)

merge(a::NamedTuple) = a

"""
    merge(a::NamedTuple, iterable)

Interpret an iterable of key-value pairs as a named tuple, and perform a merge.

```jldoctest
julia> merge((a=1, b=2, c=3), [:b=>4, :d=>5])
(a = 1, b = 4, c = 3, d = 5)
```
"""
function merge(a::NamedTuple, itr)
    names = Symbol[]
    vals = Any[]
    inds = IdDict{Symbol,Int}()
    for (k, v) in itr
        k = k::Symbol
        oldind = get(inds, k, 0)
        if oldind > 0
            vals[oldind] = v
        else
            push!(names, k)
            push!(vals, v)
            inds[k] = length(names)
        end
    end
    merge(a, NamedTuple{(names...,)}((vals...,)))
end

keys(nt::NamedTuple{names}) where {names} = names::Tuple{Vararg{Symbol}}
values(nt::NamedTuple) = Tuple(nt)
haskey(nt::NamedTuple, key::Union{Integer, Symbol}) = isdefined(nt, key)
get(nt::NamedTuple, key::Union{Integer, Symbol}, default) = isdefined(nt, key) ? getfield(nt, key) : default
get(f::Callable, nt::NamedTuple, key::Union{Integer, Symbol}) = isdefined(nt, key) ? getfield(nt, key) : f()
tail(t::NamedTuple{names}) where names = NamedTuple{tail(names::Tuple)}(t)
front(t::NamedTuple{names}) where names = NamedTuple{front(names::Tuple)}(t)
reverse(nt::NamedTuple) = NamedTuple{reverse(keys(nt))}(reverse(values(nt)))

@assume_effects :total function diff_names(an::Tuple{Vararg{Symbol}}, bn::Tuple{Vararg{Symbol}})
    @nospecialize an bn
    names = Symbol[]
    for n in an
        if !sym_in(n, bn)
            push!(names, n)
        end
    end
    (names...,)
end

@assume_effects :foldable function diff_types(@nospecialize(a::NamedTuple), @nospecialize(names::Tuple{Vararg{Symbol}}))
    return Tuple{Any[ fieldtype(typeof(a), names[n]) for n in 1:length(names) ]...}
end

@assume_effects :foldable function diff_fallback(@nospecialize(a::NamedTuple), @nospecialize(an::Tuple{Vararg{Symbol}}), @nospecialize(bn::Tuple{Vararg{Symbol}}))
    names = diff_names(an, bn)
    isempty(names) && return (;)
    types = diff_types(a, names)
    n = length(names)
    A = Vector{Any}(undef, n)
    for i=1:n
        n = names[i]
        A[i] = getfield(a, n)
    end
    _new_NamedTuple(NamedTuple{names, types}, (A...,))
end

"""
    structdiff(a::NamedTuple, b::Union{NamedTuple,Type{NamedTuple}})

Construct a copy of named tuple `a`, except with fields that exist in `b` removed.
`b` can be a named tuple, or a type of the form `NamedTuple{field_names}`.
"""
function structdiff(a::NamedTuple{an}, b::Union{NamedTuple{bn}, Type{NamedTuple{bn}}}) where {an, bn}
    if @generated
        names = diff_names(an, bn)
        isempty(names) && return (;) # just a fast pass
        idx = Int[ fieldindex(a, names[n]) for n in 1:length(names) ]
        types = Tuple{Any[ fieldtype(a, idx[n]) for n in 1:length(idx) ]...}
        vals = Any[ :(getfield(a, $(idx[n]))) for n in 1:length(idx) ]
        return :( _new_NamedTuple(NamedTuple{$names,$types}, ($(vals...),)) )
    else
        return diff_fallback(a, an, bn)
    end
end

structdiff(a::NamedTuple{an}, b::Union{NamedTuple{an}, Type{NamedTuple{an}}}) where {an} = (;)

"""
    setindex(nt::NamedTuple, val, key::Symbol)

Constructs a new `NamedTuple` with the key `key` set to `val`.
If `key` is already in the keys of `nt`, `val` replaces the old value.

```jldoctest
julia> nt = (a = 3,)
(a = 3,)

julia> Base.setindex(nt, 33, :b)
(a = 3, b = 33)

julia> Base.setindex(nt, 4, :a)
(a = 4,)

julia> Base.setindex(nt, "a", :a)
(a = "a",)
```
"""
function setindex(nt::NamedTuple, v, idx::Symbol)
    merge(nt, (; idx => v))
end

"""
    @NamedTuple{key1::Type1, key2::Type2, ...}
    @NamedTuple begin key1::Type1; key2::Type2; ...; end

This macro gives a more convenient syntax for declaring `NamedTuple` types. It returns a `NamedTuple`
type with the given keys and types, equivalent to `NamedTuple{(:key1, :key2, ...), Tuple{Type1,Type2,...}}`.
If the `::Type` declaration is omitted, it is taken to be `Any`.   The `begin ... end` form allows the
declarations to be split across multiple lines (similar to a `struct` declaration), but is otherwise
equivalent. The `NamedTuple` macro is used when printing `NamedTuple` types to e.g. the REPL.

For example, the tuple `(a=3.1, b="hello")` has a type `NamedTuple{(:a, :b), Tuple{Float64, String}}`, which
can also be declared via `@NamedTuple` as:

```jldoctest
julia> @NamedTuple{a::Float64, b::String}
@NamedTuple{a::Float64, b::String}

julia> @NamedTuple begin
           a::Float64
           b::String
       end
@NamedTuple{a::Float64, b::String}
```

!!! compat "Julia 1.5"
    This macro is available as of Julia 1.5.
"""
macro NamedTuple(ex)
    Meta.isexpr(ex, :braces) || Meta.isexpr(ex, :block) ||
        throw(ArgumentError("@NamedTuple expects {...} or begin...end"))
    decls = filter(e -> !(e isa LineNumberNode), ex.args)
    all(e -> e isa Symbol || Meta.isexpr(e, :(::)), decls) ||
        throw(ArgumentError("@NamedTuple must contain a sequence of name or name::type expressions"))
    vars = [QuoteNode(e isa Symbol ? e : e.args[1]) for e in decls]
    types = [esc(e isa Symbol ? :Any : e.args[2]) for e in decls]
    return :(NamedTuple{($(vars...),), Tuple{$(types...)}})
end

"""
    @Kwargs{key1::Type1, key2::Type2, ...}

This macro gives a convenient way to construct the type representation of keyword arguments
from the same syntax as [`@NamedTuple`](@ref).
For example, when we have a function call like `func([positional arguments]; kw1=1.0, kw2="2")`,
we can use this macro to construct the internal type representation of the keyword arguments
as `@Kwargs{kw1::Float64, kw2::String}`.
The macro syntax is specifically designed to simplify the signature type of a keyword method
when it is printed in the stack trace view.

```julia
julia> @Kwargs{init::Int} # the internal representation of keyword arguments
Base.Pairs{Symbol, Int64, Tuple{Symbol}, @NamedTuple{init::Int64}}

julia> sum("julia"; init=1)
ERROR: MethodError: no method matching +(::Char, ::Char)

Closest candidates are:
  +(::Any, ::Any, ::Any, ::Any...)
   @ Base operators.jl:585
  +(::Integer, ::AbstractChar)
   @ Base char.jl:247
  +(::T, ::Integer) where T<:AbstractChar
   @ Base char.jl:237

Stacktrace:
  [1] add_sum(x::Char, y::Char)
    @ Base ./reduce.jl:24
  [2] BottomRF
    @ Base ./reduce.jl:86 [inlined]
  [3] _foldl_impl(op::Base.BottomRF{typeof(Base.add_sum)}, init::Int64, itr::String)
    @ Base ./reduce.jl:62
  [4] foldl_impl(op::Base.BottomRF{typeof(Base.add_sum)}, nt::Int64, itr::String)
    @ Base ./reduce.jl:48 [inlined]
  [5] mapfoldl_impl(f::typeof(identity), op::typeof(Base.add_sum), nt::Int64, itr::String)
    @ Base ./reduce.jl:44 [inlined]
  [6] mapfoldl(f::typeof(identity), op::typeof(Base.add_sum), itr::String; init::Int64)
    @ Base ./reduce.jl:175 [inlined]
  [7] mapreduce(f::typeof(identity), op::typeof(Base.add_sum), itr::String; kw::@Kwargs{init::Int64})
    @ Base ./reduce.jl:307 [inlined]
  [8] sum(f::typeof(identity), a::String; kw::@Kwargs{init::Int64})
    @ Base ./reduce.jl:535 [inlined]
  [9] sum(a::String; kw::@Kwargs{init::Int64})
    @ Base ./reduce.jl:564 [inlined]
 [10] top-level scope
    @ REPL[12]:1
```

!!! compat "Julia 1.10"
    This macro is available as of Julia 1.10.
"""
macro Kwargs(ex)
    return :(let
        NT = @NamedTuple $ex
        Base.Pairs{keytype(NT),eltype(NT),typeof(NT.parameters[1]),NT}
    end)
end

@constprop :aggressive function split_rest(t::NamedTuple{names}, n::Int, st...) where {names}
    _check_length_split_rest(length(t), n)
    names_front, names_last_n = split_rest(names, n, st...)
    return NamedTuple{names_front}(t), NamedTuple{names_last_n}(t)
end
P   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/./build_h.jl�      # This file is automatically generated in base/Makefile
const MACHINE = "x86_64-linux-gnu"
const libm_name = "libopenlibm"
const USE_BLAS64 = true
const USE_GPL_LIBS = true
const libllvm_version_string = "15.0.7jl"
const libllvm_name = "libLLVM-15jl"
const VERSION_STRING = "1.10.3"
const TAGGED_RELEASE_BANNER = "Official https://julialang.org/ release"
const SYSCONFDIR = "../etc"
const DATAROOTDIR = "../share"
const DOCDIR = "../share/doc/julia"
const LIBDIR = "../lib"
const LIBEXECDIR = "../libexec"
const PRIVATE_LIBDIR = "../lib/julia"
const PRIVATE_LIBEXECDIR = "../libexec/julia"
const INCLUDEDIR = "../include"
const DARWIN_FRAMEWORK = false
const BUILD_TRIPLET = "x86_64-linux-gnu-libgfortran5-cxx11"
T   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/./version_git.jl`      # This file was autogenerated by base/version_git.sh
struct GitVersionInfo
    commit::String
    commit_short::String
    branch::String
    build_number::Int
    date_string::String
    tagged_commit::Bool
    fork_master_distance::Int
    fork_master_timestamp::Float64
    build_system_commit::String
    build_system_commit_short::String
end

const GIT_VERSION_INFO = GitVersionInfo(
    "0b4590a5507d3f3046e5bafc007cacbbfc9b310b",
    "0b4590a5507",
    "v1.10.3",
    0,
    "2024-04-30 10:59 UTC",
    true,
    353,
    1688376058.0,
    "ea50eb719242bc3e844227a2ebf54a49d308bafc",
    "ea50eb7",
)
N   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/hashing.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

## hashing a single value ##

"""
    hash(x[, h::UInt]) -> UInt

Compute an integer hash code such that `isequal(x,y)` implies `hash(x)==hash(y)`. The
optional second argument `h` is another hash code to be mixed with the result.

New types should implement the 2-argument form, typically by calling the 2-argument `hash`
method recursively in order to mix hashes of the contents with each other (and with `h`).
Typically, any type that implements `hash` should also implement its own [`==`](@ref) (hence
[`isequal`](@ref)) to guarantee the property mentioned above. Types supporting subtraction
(operator `-`) should also implement [`widen`](@ref), which is required to hash
values inside heterogeneous arrays.

The hash value may change when a new Julia process is started.

```jldoctest
julia> a = hash(10)
0x95ea2955abd45275

julia> hash(10, a) # only use the output of another hash function as the second argument
0xd42bad54a8575b16
```

See also: [`objectid`](@ref), [`Dict`](@ref), [`Set`](@ref).
"""
hash(x::Any) = hash(x, zero(UInt))
hash(w::WeakRef, h::UInt) = hash(w.value, h)
hash(T::Type, h::UInt) = hash_uint(3h - ccall(:jl_type_hash, UInt, (Any,), T))

## hashing general objects ##

hash(@nospecialize(x), h::UInt) = hash_uint(3h - objectid(x))

hash(x::Symbol) = objectid(x)

## core data hashing functions ##

function hash_64_64(n::UInt64)
    a::UInt64 = n
    a = ~a + a << 21
    a =  a ⊻ a >> 24
    a =  a + a << 3 + a << 8
    a =  a ⊻ a >> 14
    a =  a + a << 2 + a << 4
    a =  a ⊻ a >> 28
    a =  a + a << 31
    return a
end

function hash_64_32(n::UInt64)
    a::UInt64 = n
    a = ~a + a << 18
    a =  a ⊻ a >> 31
    a =  a * 21
    a =  a ⊻ a >> 11
    a =  a + a << 6
    a =  a ⊻ a >> 22
    return a % UInt32
end

function hash_32_32(n::UInt32)
    a::UInt32 = n
    a = a + 0x7ed55d16 + a << 12
    a = a ⊻ 0xc761c23c ⊻ a >> 19
    a = a + 0x165667b1 + a << 5
    a = a + 0xd3a2646c ⊻ a << 9
    a = a + 0xfd7046c5 + a << 3
    a = a ⊻ 0xb55a4f09 ⊻ a >> 16
    return a
end

if UInt === UInt64
    hash_uint64(x::UInt64) = hash_64_64(x)
    hash_uint(x::UInt)     = hash_64_64(x)
else
    hash_uint64(x::UInt64) = hash_64_32(x)
    hash_uint(x::UInt)     = hash_32_32(x)
end

## efficient value-based hashing of integers ##

hash(x::Int64,  h::UInt) = hash_uint64(bitcast(UInt64, x)) - 3h
hash(x::UInt64, h::UInt) = hash_uint64(x) - 3h
hash(x::Union{Bool,Int8,UInt8,Int16,UInt16,Int32,UInt32}, h::UInt) = hash(Int64(x), h)

function hash_integer(n::Integer, h::UInt)
    h ⊻= hash_uint((n % UInt) ⊻ h)
    n = abs(n)
    n >>>= sizeof(UInt) << 3
    while n != 0
        h ⊻= hash_uint((n % UInt) ⊻ h)
        n >>>= sizeof(UInt) << 3
    end
    return h
end

## symbol & expression hashing ##

if UInt === UInt64
    hash(x::Expr, h::UInt) = hash(x.args, hash(x.head, h + 0x83c7900696d26dc6))
    hash(x::QuoteNode, h::UInt) = hash(x.value, h + 0x2c97bf8b3de87020)
else
    hash(x::Expr, h::UInt) = hash(x.args, hash(x.head, h + 0x96d26dc6))
    hash(x::QuoteNode, h::UInt) = hash(x.value, h + 0x469d72af)
end

## hashing strings ##

const memhash = UInt === UInt64 ? :memhash_seed : :memhash32_seed
const memhash_seed = UInt === UInt64 ? 0x71e729fd56419c81 : 0x56419c81

@assume_effects :total function hash(s::String, h::UInt)
    h += memhash_seed
    ccall(memhash, UInt, (Ptr{UInt8}, Csize_t, UInt32), s, sizeof(s), h % UInt32) + h
end
O   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/rounding.jl      # This file is a part of Julia. License is MIT: https://julialang.org/license

module Rounding

let fenv_consts = Vector{Cint}(undef, 9)
    ccall(:jl_get_fenv_consts, Cvoid, (Ptr{Cint},), fenv_consts)
    global const JL_FE_INEXACT = fenv_consts[1]
    global const JL_FE_UNDERFLOW = fenv_consts[2]
    global const JL_FE_OVERFLOW = fenv_consts[3]
    global const JL_FE_DIVBYZERO = fenv_consts[4]
    global const JL_FE_INVALID = fenv_consts[5]

    global const JL_FE_TONEAREST = fenv_consts[6]
    global const JL_FE_UPWARD = fenv_consts[7]
    global const JL_FE_DOWNWARD = fenv_consts[8]
    global const JL_FE_TOWARDZERO = fenv_consts[9]
end

export
    RoundingMode, RoundNearest, RoundToZero, RoundUp, RoundDown, RoundFromZero,
    RoundNearestTiesAway, RoundNearestTiesUp,
    rounding, setrounding,
    get_zero_subnormals, set_zero_subnormals

## rounding modes ##
"""
    RoundingMode

A type used for controlling the rounding mode of floating point operations (via
[`rounding`](@ref)/[`setrounding`](@ref) functions), or as
optional arguments for rounding to the nearest integer (via the [`round`](@ref)
function).

Currently supported rounding modes are:

- [`RoundNearest`](@ref) (default)
- [`RoundNearestTiesAway`](@ref)
- [`RoundNearestTiesUp`](@ref)
- [`RoundToZero`](@ref)
- [`RoundFromZero`](@ref)
- [`RoundUp`](@ref)
- [`RoundDown`](@ref)

!!! compat "Julia 1.9"
    `RoundFromZero` requires at least Julia 1.9. Prior versions support
    `RoundFromZero` for `BigFloat`s only.
"""
struct RoundingMode{T} end

"""
    RoundNearest

The default rounding mode. Rounds to the nearest integer, with ties (fractional values of
0.5) being rounded to the nearest even integer.
"""
const RoundNearest = RoundingMode{:Nearest}()

"""
    RoundToZero

[`round`](@ref) using this rounding mode is an alias for [`trunc`](@ref).
"""
const RoundToZero = RoundingMode{:ToZero}()

"""
    RoundUp

[`round`](@ref) using this rounding mode is an alias for [`ceil`](@ref).
"""
const RoundUp = RoundingMode{:Up}()

"""
    RoundDown

[`round`](@ref) using this rounding mode is an alias for [`floor`](@ref).
"""
const RoundDown = RoundingMode{:Down}()

"""
    RoundFromZero

Rounds away from zero.

!!! compat "Julia 1.9"
    `RoundFromZero` requires at least Julia 1.9. Prior versions support
    `RoundFromZero` for `BigFloat`s only.

# Examples
```jldoctest
julia> BigFloat("1.0000000000000001", 5, RoundFromZero)
1.06
```
"""
const RoundFromZero = RoundingMode{:FromZero}()

"""
    RoundNearestTiesAway

Rounds to nearest integer, with ties rounded away from zero (C/C++
[`round`](@ref) behaviour).
"""
const RoundNearestTiesAway = RoundingMode{:NearestTiesAway}()

"""
    RoundNearestTiesUp

Rounds to nearest integer, with ties rounded toward positive infinity (Java/JavaScript
[`round`](@ref) behaviour).
"""
const RoundNearestTiesUp = RoundingMode{:NearestTiesUp}()

to_fenv(::RoundingMode{:Nearest}) = JL_FE_TONEAREST
to_fenv(::RoundingMode{:ToZero}) = JL_FE_TOWARDZERO
to_fenv(::RoundingMode{:Up}) = JL_FE_UPWARD
to_fenv(::RoundingMode{:Down}) = JL_FE_DOWNWARD

function from_fenv(r::Integer)
    if r == JL_FE_TONEAREST
        return RoundNearest
    elseif r == JL_FE_DOWNWARD
        return RoundDown
    elseif r == JL_FE_UPWARD
        return RoundUp
    elseif r == JL_FE_TOWARDZERO
        return RoundToZero
    else
        throw(ArgumentError("invalid rounding mode code: $r"))
    end
end

"""
    setrounding(T, mode)

Set the rounding mode of floating point type `T`, controlling the rounding of basic
arithmetic functions ([`+`](@ref), [`-`](@ref), [`*`](@ref),
[`/`](@ref) and [`sqrt`](@ref)) and type conversion. Other numerical
functions may give incorrect or invalid values when using rounding modes other than the
default [`RoundNearest`](@ref).

Note that this is currently only supported for `T == BigFloat`.

!!! warning

    This function is not thread-safe. It will affect code running on all threads, but
    its behavior is undefined if called concurrently with computations that use the
    setting.
"""
setrounding(T::Type, mode)

"""
    rounding(T)

Get the current floating point rounding mode for type `T`, controlling the rounding of basic
arithmetic functions ([`+`](@ref), [`-`](@ref), [`*`](@ref), [`/`](@ref)
and [`sqrt`](@ref)) and type conversion.

See [`RoundingMode`](@ref) for available modes.
"""
:rounding

setrounding_raw(::Type{<:Union{Float32,Float64}}, i::Integer) = ccall(:jl_set_fenv_rounding, Int32, (Int32,), i)
rounding_raw(::Type{<:Union{Float32,Float64}}) = ccall(:jl_get_fenv_rounding, Int32, ())

rounding(::Type{T}) where {T<:Union{Float32,Float64}} = from_fenv(rounding_raw(T))

"""
    setrounding(f::Function, T, mode)

Change the rounding mode of floating point type `T` for the duration of `f`. It is logically
equivalent to:

    old = rounding(T)
    setrounding(T, mode)
    f()
    setrounding(T, old)

See [`RoundingMode`](@ref) for available rounding modes.
"""
function setrounding(f::Function, ::Type{T}, rounding::RoundingMode) where T
    old_rounding_raw = rounding_raw(T)
    setrounding(T,rounding)
    try
        return f()
    finally
        setrounding_raw(T,old_rounding_raw)
    end
end
function setrounding_raw(f::Function, ::Type{T}, rounding) where T
    old_rounding_raw = rounding_raw(T)
    setrounding_raw(T,rounding)
    try
        return f()
    finally
        setrounding_raw(T,old_rounding_raw)
    end
end


# Should be equivalent to:
#   setrounding(Float64,r) do
#       convert(T,x)
#   end
# but explicit checks are currently quicker (~20x).
# Assumes conversion is performed by rounding to nearest value.

# To avoid ambiguous dispatch with methods in mpfr.jl:
(::Type{T})(x::Real, r::RoundingMode) where {T<:AbstractFloat} = _convert_rounding(T,x,r)::T

_convert_rounding(::Type{T}, x::Real, r::RoundingMode{:Nearest}) where {T<:AbstractFloat} = convert(T,x)::T
function _convert_rounding(::Type{T}, x::Real, r::RoundingMode{:Down}) where T<:AbstractFloat
    y = convert(T,x)::T
    y > x ? prevfloat(y) : y
end
function _convert_rounding(::Type{T}, x::Real, r::RoundingMode{:Up}) where T<:AbstractFloat
    y = convert(T,x)::T
    y < x ? nextfloat(y) : y
end
function _convert_rounding(::Type{T}, x::Real, r::RoundingMode{:ToZero}) where T<:AbstractFloat
    y = convert(T,x)::T
    if x > 0.0
        y > x ? prevfloat(y) : y
    else
        y < x ? nextfloat(y) : y
    end
end

"""
    set_zero_subnormals(yes::Bool) -> Bool

If `yes` is `false`, subsequent floating-point operations follow rules for IEEE arithmetic
on subnormal values ("denormals"). Otherwise, floating-point operations are permitted (but
not required) to convert subnormal inputs or outputs to zero. Returns `true` unless
`yes==true` but the hardware does not support zeroing of subnormal numbers.

`set_zero_subnormals(true)` can speed up some computations on some hardware. However, it can
break identities such as `(x-y==0) == (x==y)`.

!!! warning

    This function only affects the current thread.
"""
set_zero_subnormals(yes::Bool) = ccall(:jl_set_zero_subnormals,Int32,(Int8,),yes)==0

"""
    get_zero_subnormals() -> Bool

Return `false` if operations on subnormal floating-point values ("denormals") obey rules
for IEEE arithmetic, and `true` if they might be converted to zeros.

!!! warning

    This function only affects the current thread.
"""
get_zero_subnormals() = ccall(:jl_get_zero_subnormals,Int32,())!=0

end #module
J   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/div.jl�-      # This file is a part of Julia. License is MIT: https://julialang.org/license

# Div is truncating by default

"""
    div(x, y, r::RoundingMode=RoundToZero)

The quotient from Euclidean (integer) division. Computes `x / y`, rounded to
an integer according to the rounding mode `r`. In other words, the quantity

    round(x / y, r)

without any intermediate rounding.

!!! compat "Julia 1.4"
    The three-argument method taking a `RoundingMode` requires Julia 1.4 or later.

See also [`fld`](@ref) and [`cld`](@ref), which are special cases of this function.

!!! compat "Julia 1.9"
    `RoundFromZero` requires at least Julia 1.9.

# Examples:
```jldoctest
julia> div(4, 3, RoundDown) # Matches fld(4, 3)
1
julia> div(4, 3, RoundUp) # Matches cld(4, 3)
2
julia> div(5, 2, RoundNearest)
2
julia> div(5, 2, RoundNearestTiesAway)
3
julia> div(-5, 2, RoundNearest)
-2
julia> div(-5, 2, RoundNearestTiesAway)
-3
julia> div(-5, 2, RoundNearestTiesUp)
-2
julia> div(4, 3, RoundFromZero)
2
julia> div(-4, 3, RoundFromZero)
-2
```
"""
div(x, y, r::RoundingMode)

div(a, b) = div(a, b, RoundToZero)

"""
    rem(x, y, r::RoundingMode=RoundToZero)

Compute the remainder of `x` after integer division by `y`, with the quotient rounded
according to the rounding mode `r`. In other words, the quantity

    x - y * round(x / y, r)

without any intermediate rounding.

- if `r == RoundNearest`, then the result is exact, and in the interval
  ``[-|y| / 2, |y| / 2]``. See also [`RoundNearest`](@ref).

- if `r == RoundToZero` (default), then the result is exact, and in the interval
  ``[0, |y|)`` if `x` is positive, or ``(-|y|, 0]`` otherwise. See also [`RoundToZero`](@ref).

- if `r == RoundDown`, then the result is in the interval ``[0, y)`` if `y` is positive, or
  ``(y, 0]`` otherwise. The result may not be exact if `x` and `y` have different signs, and
  `abs(x) < abs(y)`. See also [`RoundDown`](@ref).

- if `r == RoundUp`, then the result is in the interval ``(-y, 0]`` if `y` is positive, or
  ``[0, -y)`` otherwise. The result may not be exact if `x` and `y` have the same sign, and
  `abs(x) < abs(y)`. See also [`RoundUp`](@ref).

- if `r == RoundFromZero`, then the result is in the interval ``(-y, 0]`` if `y` is positive, or
  ``[0, -y)`` otherwise. The result may not be exact if `x` and `y` have the same sign, and
  `abs(x) < abs(y)`. See also [`RoundFromZero`](@ref).

!!! compat "Julia 1.9"
    `RoundFromZero` requires at least Julia 1.9.

# Examples:
```jldoctest
julia> x = 9; y = 4;

julia> x % y  # same as rem(x, y)
1

julia> x ÷ y  # same as div(x, y)
2

julia> x == div(x, y) * y + rem(x, y)
true
```
"""
rem(x, y, r::RoundingMode)

# TODO: Make these primitive and have the two-argument version call these
rem(x, y, ::RoundingMode{:ToZero}) = rem(x, y)
rem(x, y, ::RoundingMode{:Down}) = mod(x, y)
rem(x, y, ::RoundingMode{:Up}) = mod(x, -y)
rem(x, y, r::RoundingMode{:Nearest}) = x - y * div(x, y, r)
rem(x::Integer, y::Integer, r::RoundingMode{:Nearest}) = divrem(x, y, r)[2]

function rem(x, y, ::typeof(RoundFromZero))
    signbit(x) == signbit(y) ? rem(x, y, RoundUp) : rem(x, y, RoundDown)
end

"""
    fld(x, y)

Largest integer less than or equal to `x / y`. Equivalent to `div(x, y, RoundDown)`.

See also [`div`](@ref), [`cld`](@ref), [`fld1`](@ref).

# Examples
```jldoctest
julia> fld(7.3, 5.5)
1.0

julia> fld.(-5:5, 3)'
1×11 adjoint(::Vector{Int64}) with eltype Int64:
 -2  -2  -1  -1  -1  0  0  0  1  1  1
```
Because `fld(x, y)` implements strictly correct floored rounding based on the true
value of floating-point numbers, unintuitive situations can arise. For example:
```jldoctest
julia> fld(6.0, 0.1)
59.0
julia> 6.0 / 0.1
60.0
julia> 6.0 / big(0.1)
59.99999999999999666933092612453056361837965690217069245739573412231113406246995
```
What is happening here is that the true value of the floating-point number written
as `0.1` is slightly larger than the numerical value 1/10 while `6.0` represents
the number 6 precisely. Therefore the true value of `6.0 / 0.1` is slightly less
than 60. When doing division, this is rounded to precisely `60.0`, but
`fld(6.0, 0.1)` always takes the floor of the true value, so the result is `59.0`.
"""
fld(a, b) = div(a, b, RoundDown)

"""
    cld(x, y)

Smallest integer larger than or equal to `x / y`. Equivalent to `div(x, y, RoundUp)`.

See also [`div`](@ref), [`fld`](@ref).

# Examples
```jldoctest
julia> cld(5.5, 2.2)
3.0

julia> cld.(-5:5, 3)'
1×11 adjoint(::Vector{Int64}) with eltype Int64:
 -1  -1  -1  0  0  0  1  1  1  2  2
```
"""
cld(a, b) = div(a, b, RoundUp)

# divrem
"""
    divrem(x, y, r::RoundingMode=RoundToZero)

The quotient and remainder from Euclidean division.
Equivalent to `(div(x, y, r), rem(x, y, r))`. Equivalently, with the default
value of `r`, this call is equivalent to `(x ÷ y, x % y)`.

See also: [`fldmod`](@ref), [`cld`](@ref).

# Examples
```jldoctest
julia> divrem(3, 7)
(0, 3)

julia> divrem(7, 3)
(2, 1)
```
"""
divrem(x, y) = divrem(x, y, RoundToZero)


function divrem(a, b, r::RoundingMode)
    if r === RoundToZero
        # For compat. Remove in 2.0.
        (div(a, b), rem(a, b))
    elseif r === RoundDown
        # For compat. Remove in 2.0.
        (fld(a, b), mod(a, b))
    else
        (div(a, b, r), rem(a, b, r))
    end
end
# avoids calling rem for Integers-Integers (all modes),
# a - d * b not precise for Floats - AbstractFloat, AbstractIrrational.
# Rationals are still slower
function divrem(a::Integer, b::Integer, r::Union{typeof(RoundUp),
                                                typeof(RoundDown),
                                                typeof(RoundToZero)})
    if r === RoundToZero
        # For compat. Remove in 2.0.
        d = div(a, b)
        (d, a - d * b)
    elseif r === RoundDown
        # For compat. Remove in 2.0.
        d = fld(a, b)
        (d, a - d * b)
    elseif r === RoundUp
        # For compat. Remove in 2.0.
        d = div(a, b, r)
        (d, a - d * b)
    end
end
function divrem(x::Integer, y::Integer, rnd::typeof(RoundNearest))
    (q, r) = divrem(x, y)
    if x >= 0
        if y >= 0
            r >=        (y÷2) + (isodd(y) | iseven(q)) ? (q+true, r-y) : (q, r)
        else
            r >=       -(y÷2) + (isodd(y) | iseven(q)) ? (q-true, r+y) : (q, r)
        end
    else
        if y >= 0
            r <= -signed(y÷2) - (isodd(y) | iseven(q)) ? (q-true, r+y) : (q, r)
        else
            r <=        (y÷2) - (isodd(y) | iseven(q)) ? (q+true, r-y) : (q, r)
        end
    end
end
function divrem(x::Integer, y::Integer, rnd:: typeof(RoundNearestTiesAway))
    (q, r) = divrem(x, y)
    if x >= 0
        if y >= 0
            r >=        (y÷2) + isodd(y) ? (q+true, r-y) : (q, r)
        else
            r >=       -(y÷2) + isodd(y) ? (q-true, r+y) : (q, r)
        end
    else
        if y >= 0
            r <= -signed(y÷2) - isodd(y) ? (q-true, r+y) : (q, r)
        else
            r <=        (y÷2) - isodd(y) ? (q+true, r-y) : (q, r)
        end
    end
end
function divrem(x::Integer, y::Integer, rnd::typeof(RoundNearestTiesUp))
    (q, r) = divrem(x, y)
    if x >= 0
        if y >= 0
            r >=        (y÷2) + isodd(y) ? (q+true, r-y) : (q, r)
        else
            r >=       -(y÷2) + true     ? (q-true, r+y) : (q, r)
        end
    else
        if y >= 0
            r <= -signed(y÷2) - true     ? (q-true, r+y) : (q, r)
        else
            r <=        (y÷2) - isodd(y) ? (q+true, r-y) : (q, r)
        end
    end
end

function divrem(x, y, ::typeof(RoundFromZero))
    signbit(x) == signbit(y) ? divrem(x, y, RoundUp) : divrem(x, y, RoundDown)
end

"""
    fldmod(x, y)

The floored quotient and modulus after division. A convenience wrapper for
`divrem(x, y, RoundDown)`. Equivalent to `(fld(x, y), mod(x, y))`.

See also: [`fld`](@ref), [`cld`](@ref), [`fldmod1`](@ref).
"""
fldmod(x, y) = divrem(x, y, RoundDown)

# We definite generic rounding methods for other rounding modes in terms of
# RoundToZero.
function div(x::Signed, y::Unsigned, ::typeof(RoundDown))
    (q, r) = divrem(x, y)
    q - (signbit(x) & (r != 0))
end
function div(x::Unsigned, y::Signed, ::typeof(RoundDown))
    (q, r) = divrem(x, y)
    q - (signbit(y) & (r != 0))
end

function div(x::Signed, y::Unsigned, ::typeof(RoundUp))
    (q, r) = divrem(x, y)
    q + (!signbit(x) & (r != 0))
end
function div(x::Unsigned, y::Signed, ::typeof(RoundUp))
    (q, r) = divrem(x, y)
    q + (!signbit(y) & (r != 0))
end

function div(x::Integer, y::Integer, rnd::Union{typeof(RoundNearest),
                                              typeof(RoundNearestTiesAway),
                                              typeof(RoundNearestTiesUp)})
    divrem(x, y, rnd)[1]
end

function div(x::Integer, y::Integer, ::typeof(RoundFromZero))
    signbit(x) == signbit(y) ? div(x, y, RoundUp) : div(x, y, RoundDown)
end

# For bootstrapping purposes, we define div for integers directly. Provide the
# generic signature also
div(a::T, b::T, ::typeof(RoundToZero)) where {T<:Union{BitSigned, BitUnsigned64}} = div(a, b)
div(a::Bool, b::Bool, r::RoundingMode) = div(a, b)
# Prevent ambiguities
for rm in (RoundUp, RoundDown, RoundToZero, RoundFromZero)
    @eval div(a::Bool, b::Bool, r::$(typeof(rm))) = div(a, b)
end
function div(x::Bool, y::Bool, rnd::Union{typeof(RoundNearest),
                                        typeof(RoundNearestTiesAway),
                                        typeof(RoundNearestTiesUp)})
    div(x, y)
end
fld(a::T, b::T) where {T<:Union{Integer,AbstractFloat}} = div(a, b, RoundDown)
cld(a::T, b::T) where {T<:Union{Integer,AbstractFloat}} = div(a, b, RoundUp)
div(a::Int128, b::Int128, ::typeof(RoundToZero)) = div(a, b)
div(a::UInt128, b::UInt128, ::typeof(RoundToZero)) = div(a, b)
rem(a::Int128, b::Int128, ::typeof(RoundToZero)) = rem(a, b)
rem(a::UInt128, b::UInt128, ::typeof(RoundToZero)) = rem(a, b)

# These are kept for compatibility with external packages overriding fld / cld.
# In 2.0, packages should extend div(a, b, r) instead, in which case, these can
# be removed.
fld(x::Real, y::Real) = div(promote(x, y)..., RoundDown)
cld(x::Real, y::Real) = div(promote(x, y)..., RoundUp)
fld(x::Signed, y::Unsigned) = div(x, y, RoundDown)
fld(x::Unsigned, y::Signed) = div(x, y, RoundDown)
cld(x::Signed, y::Unsigned) = div(x, y, RoundUp)
cld(x::Unsigned, y::Signed) = div(x, y, RoundUp)
fld(x::T, y::T) where {T<:Real} = throw(MethodError(div, (x, y, RoundDown)))
cld(x::T, y::T) where {T<:Real} = throw(MethodError(div, (x, y, RoundUp)))

# Promotion
function div(x::Real, y::Real, r::RoundingMode)
    typeof(x) === typeof(y) && throw(MethodError(div, (x, y, r)))
    if r === RoundToZero
        # For compat. Remove in 2.0.
        div(promote(x, y)...)
    else
        div(promote(x, y)..., r)
    end
end

# Integers
# fld(x, y) == div(x, y) - ((x >= 0) != (y >= 0) && rem(x, y) != 0 ? 1 : 0)
div(x::T, y::T, ::typeof(RoundDown)) where {T<:Unsigned} = div(x, y)
function div(x::T, y::T, ::typeof(RoundDown)) where T<:Integer
    d = div(x, y, RoundToZero)
    return d - (signbit(x ⊻ y) & (d * y != x))
end

# cld(x, y) = div(x, y) + ((x > 0) == (y > 0) && rem(x, y) != 0 ? 1 : 0)
function div(x::T, y::T, ::typeof(RoundUp)) where T<:Unsigned
    d = div(x, y, RoundToZero)
    return d + (d * y != x)
end
function div(x::T, y::T, ::typeof(RoundUp)) where T<:Integer
    d = div(x, y, RoundToZero)
    return d + (((x > 0) == (y > 0)) & (d * y != x))
end

# Real
# NOTE: C89 fmod() and x87 FPREM implicitly provide truncating float division,
# so it is used here as the basis of float div().
div(x::T, y::T, r::RoundingMode) where {T<:AbstractFloat} = convert(T, round((x - rem(x, y, r)) / y))
L   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/float.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

const IEEEFloat = Union{Float16, Float32, Float64}

## floating point traits ##

"""
    Inf16

Positive infinity of type [`Float16`](@ref).
"""
const Inf16 = bitcast(Float16, 0x7c00)
"""
    NaN16

A not-a-number value of type [`Float16`](@ref).
"""
const NaN16 = bitcast(Float16, 0x7e00)
"""
    Inf32

Positive infinity of type [`Float32`](@ref).
"""
const Inf32 = bitcast(Float32, 0x7f800000)
"""
    NaN32

A not-a-number value of type [`Float32`](@ref).
"""
const NaN32 = bitcast(Float32, 0x7fc00000)
const Inf64 = bitcast(Float64, 0x7ff0000000000000)
const NaN64 = bitcast(Float64, 0x7ff8000000000000)

const Inf = Inf64
"""
    Inf, Inf64

Positive infinity of type [`Float64`](@ref).

See also: [`isfinite`](@ref), [`typemax`](@ref), [`NaN`](@ref), [`Inf32`](@ref).

# Examples
```jldoctest
julia> π/0
Inf

julia> +1.0 / -0.0
-Inf

julia> ℯ^-Inf
0.0
```
"""
Inf, Inf64

const NaN = NaN64
"""
    NaN, NaN64

A not-a-number value of type [`Float64`](@ref).

See also: [`isnan`](@ref), [`missing`](@ref), [`NaN32`](@ref), [`Inf`](@ref).

# Examples
```jldoctest
julia> 0/0
NaN

julia> Inf - Inf
NaN

julia> NaN == NaN, isequal(NaN, NaN), NaN === NaN
(false, true, true)
```
"""
NaN, NaN64

# bit patterns
reinterpret(::Type{Unsigned}, x::Float64) = reinterpret(UInt64, x)
reinterpret(::Type{Unsigned}, x::Float32) = reinterpret(UInt32, x)
reinterpret(::Type{Unsigned}, x::Float16) = reinterpret(UInt16, x)
reinterpret(::Type{Signed}, x::Float64) = reinterpret(Int64, x)
reinterpret(::Type{Signed}, x::Float32) = reinterpret(Int32, x)
reinterpret(::Type{Signed}, x::Float16) = reinterpret(Int16, x)

sign_mask(::Type{Float64}) =        0x8000_0000_0000_0000
exponent_mask(::Type{Float64}) =    0x7ff0_0000_0000_0000
exponent_one(::Type{Float64}) =     0x3ff0_0000_0000_0000
exponent_half(::Type{Float64}) =    0x3fe0_0000_0000_0000
significand_mask(::Type{Float64}) = 0x000f_ffff_ffff_ffff

sign_mask(::Type{Float32}) =        0x8000_0000
exponent_mask(::Type{Float32}) =    0x7f80_0000
exponent_one(::Type{Float32}) =     0x3f80_0000
exponent_half(::Type{Float32}) =    0x3f00_0000
significand_mask(::Type{Float32}) = 0x007f_ffff

sign_mask(::Type{Float16}) =        0x8000
exponent_mask(::Type{Float16}) =    0x7c00
exponent_one(::Type{Float16}) =     0x3c00
exponent_half(::Type{Float16}) =    0x3800
significand_mask(::Type{Float16}) = 0x03ff

mantissa(x::T) where {T} = reinterpret(Unsigned, x) & significand_mask(T)

for T in (Float16, Float32, Float64)
    @eval significand_bits(::Type{$T}) = $(trailing_ones(significand_mask(T)))
    @eval exponent_bits(::Type{$T}) = $(sizeof(T)*8 - significand_bits(T) - 1)
    @eval exponent_bias(::Type{$T}) = $(Int(exponent_one(T) >> significand_bits(T)))
    # maximum float exponent
    @eval exponent_max(::Type{$T}) = $(Int(exponent_mask(T) >> significand_bits(T)) - exponent_bias(T) - 1)
    # maximum float exponent without bias
    @eval exponent_raw_max(::Type{$T}) = $(Int(exponent_mask(T) >> significand_bits(T)))
end

"""
    exponent_max(T)

Maximum [`exponent`](@ref) value for a floating point number of type `T`.

# Examples
```jldoctest
julia> Base.exponent_max(Float64)
1023
```

Note, `exponent_max(T) + 1` is a possible value of the exponent field
with bias, which might be used as sentinel value for `Inf` or `NaN`.
"""
function exponent_max end

"""
    exponent_raw_max(T)

Maximum value of the [`exponent`](@ref) field for a floating point number of type `T` without bias,
i.e. the maximum integer value representable by [`exponent_bits(T)`](@ref) bits.
"""
function exponent_raw_max end

"""
    uabs(x::Integer)

Return the absolute value of `x`, possibly returning a different type should the
operation be susceptible to overflow. This typically arises when `x` is a two's complement
signed integer, so that `abs(typemin(x)) == typemin(x) < 0`, in which case the result of
`uabs(x)` will be an unsigned integer of the same size.
"""
uabs(x::Integer) = abs(x)
uabs(x::BitSigned) = unsigned(abs(x))

## conversions to floating-point ##

# TODO: deprecate in 2.0
Float16(x::Integer) = convert(Float16, convert(Float32, x)::Float32)

for t1 in (Float16, Float32, Float64)
    for st in (Int8, Int16, Int32, Int64)
        @eval begin
            (::Type{$t1})(x::($st)) = sitofp($t1, x)
            promote_rule(::Type{$t1}, ::Type{$st}) = $t1
        end
    end
    for ut in (Bool, UInt8, UInt16, UInt32, UInt64)
        @eval begin
            (::Type{$t1})(x::($ut)) = uitofp($t1, x)
            promote_rule(::Type{$t1}, ::Type{$ut}) = $t1
        end
    end
end

Bool(x::Real) = x==0 ? false : x==1 ? true : throw(InexactError(:Bool, Bool, x))

promote_rule(::Type{Float64}, ::Type{UInt128}) = Float64
promote_rule(::Type{Float64}, ::Type{Int128}) = Float64
promote_rule(::Type{Float32}, ::Type{UInt128}) = Float32
promote_rule(::Type{Float32}, ::Type{Int128}) = Float32
promote_rule(::Type{Float16}, ::Type{UInt128}) = Float16
promote_rule(::Type{Float16}, ::Type{Int128}) = Float16

function Float64(x::UInt128)
    if x < UInt128(1) << 104 # Can fit it in two 52 bits mantissas
        low_exp = 0x1p52
        high_exp = 0x1p104
        low_bits = (x % UInt64) & Base.significand_mask(Float64)
        low_value = reinterpret(Float64, reinterpret(UInt64, low_exp) | low_bits) - low_exp
        high_bits = ((x >> 52) % UInt64)
        high_value = reinterpret(Float64, reinterpret(UInt64, high_exp) | high_bits) - high_exp
        low_value + high_value
    else # Large enough that low bits only affect rounding, pack low bits
        low_exp = 0x1p76
        high_exp = 0x1p128
        low_bits = ((x >> 12) % UInt64) >> 12 | (x % UInt64) & 0xFFFFFF
        low_value = reinterpret(Float64, reinterpret(UInt64, low_exp) | low_bits) - low_exp
        high_bits = ((x >> 76) % UInt64)
        high_value = reinterpret(Float64, reinterpret(UInt64, high_exp) | high_bits) - high_exp
        low_value + high_value
    end
end

function Float64(x::Int128)
    sign_bit = ((x >> 127) % UInt64) << 63
    ux = uabs(x)
    if ux < UInt128(1) << 104 # Can fit it in two 52 bits mantissas
        low_exp = 0x1p52
        high_exp = 0x1p104
        low_bits = (ux % UInt64) & Base.significand_mask(Float64)
        low_value = reinterpret(Float64, reinterpret(UInt64, low_exp) | low_bits) - low_exp
        high_bits = ((ux >> 52) % UInt64)
        high_value = reinterpret(Float64, reinterpret(UInt64, high_exp) | high_bits) - high_exp
        reinterpret(Float64, sign_bit | reinterpret(UInt64, low_value + high_value))
    else # Large enough that low bits only affect rounding, pack low bits
        low_exp = 0x1p76
        high_exp = 0x1p128
        low_bits = ((ux >> 12) % UInt64) >> 12 | (ux % UInt64) & 0xFFFFFF
        low_value = reinterpret(Float64, reinterpret(UInt64, low_exp) | low_bits) - low_exp
        high_bits = ((ux >> 76) % UInt64)
        high_value = reinterpret(Float64, reinterpret(UInt64, high_exp) | high_bits) - high_exp
        reinterpret(Float64, sign_bit | reinterpret(UInt64, low_value + high_value))
    end
end

function Float32(x::UInt128)
    x == 0 && return 0f0
    n = top_set_bit(x) # ndigits0z(x,2)
    if n <= 24
        y = ((x % UInt32) << (24-n)) & 0x007f_ffff
    else
        y = ((x >> (n-25)) % UInt32) & 0x00ff_ffff # keep 1 extra bit
        y = (y+one(UInt32))>>1 # round, ties up (extra leading bit in case of next exponent)
        y &= ~UInt32(trailing_zeros(x) == (n-25)) # fix last bit to round to even
    end
    d = ((n+126) % UInt32) << 23
    reinterpret(Float32, d + y)
end

function Float32(x::Int128)
    x == 0 && return 0f0
    s = ((x >>> 96) % UInt32) & 0x8000_0000 # sign bit
    x = abs(x) % UInt128
    n = top_set_bit(x) # ndigits0z(x,2)
    if n <= 24
        y = ((x % UInt32) << (24-n)) & 0x007f_ffff
    else
        y = ((x >> (n-25)) % UInt32) & 0x00ff_ffff # keep 1 extra bit
        y = (y+one(UInt32))>>1 # round, ties up (extra leading bit in case of next exponent)
        y &= ~UInt32(trailing_zeros(x) == (n-25)) # fix last bit to round to even
    end
    d = ((n+126) % UInt32) << 23
    reinterpret(Float32, s | d + y)
end

# TODO: optimize
Float16(x::UInt128) = convert(Float16, Float64(x))
Float16(x::Int128)  = convert(Float16, Float64(x))

Float16(x::Float32) = fptrunc(Float16, x)
Float16(x::Float64) = fptrunc(Float16, x)
Float32(x::Float64) = fptrunc(Float32, x)

Float32(x::Float16) = fpext(Float32, x)
Float64(x::Float32) = fpext(Float64, x)
Float64(x::Float16) = fpext(Float64, x)

AbstractFloat(x::Bool)    = Float64(x)
AbstractFloat(x::Int8)    = Float64(x)
AbstractFloat(x::Int16)   = Float64(x)
AbstractFloat(x::Int32)   = Float64(x)
AbstractFloat(x::Int64)   = Float64(x) # LOSSY
AbstractFloat(x::Int128)  = Float64(x) # LOSSY
AbstractFloat(x::UInt8)   = Float64(x)
AbstractFloat(x::UInt16)  = Float64(x)
AbstractFloat(x::UInt32)  = Float64(x)
AbstractFloat(x::UInt64)  = Float64(x) # LOSSY
AbstractFloat(x::UInt128) = Float64(x) # LOSSY

Bool(x::Float16) = x==0 ? false : x==1 ? true : throw(InexactError(:Bool, Bool, x))

"""
    float(x)

Convert a number or array to a floating point data type.

See also: [`complex`](@ref), [`oftype`](@ref), [`convert`](@ref).

# Examples
```jldoctest
julia> float(1:1000)
1.0:1.0:1000.0

julia> float(typemax(Int32))
2.147483647e9
```
"""
float(x) = AbstractFloat(x)

"""
    float(T::Type)

Return an appropriate type to represent a value of type `T` as a floating point value.
Equivalent to `typeof(float(zero(T)))`.

# Examples
```jldoctest
julia> float(Complex{Int})
ComplexF64 (alias for Complex{Float64})

julia> float(Int)
Float64
```
"""
float(::Type{T}) where {T<:Number} = typeof(float(zero(T)))
float(::Type{T}) where {T<:AbstractFloat} = T
float(::Type{Union{}}, slurp...) = Union{}(0.0)

"""
    unsafe_trunc(T, x)

Return the nearest integral value of type `T` whose absolute value is
less than or equal to the absolute value of `x`. If the value is not representable by `T`,
an arbitrary value will be returned.
See also [`trunc`](@ref).

# Examples
```jldoctest
julia> unsafe_trunc(Int, -2.2)
-2

julia> unsafe_trunc(Int, NaN)
-9223372036854775808
```
"""
function unsafe_trunc end

for Ti in (Int8, Int16, Int32, Int64)
    @eval begin
        unsafe_trunc(::Type{$Ti}, x::IEEEFloat) = fptosi($Ti, x)
    end
end
for Ti in (UInt8, UInt16, UInt32, UInt64)
    @eval begin
        unsafe_trunc(::Type{$Ti}, x::IEEEFloat) = fptoui($Ti, x)
    end
end

function unsafe_trunc(::Type{UInt128}, x::Float64)
    xu = reinterpret(UInt64,x)
    k = Int(xu >> 52) & 0x07ff - 1075
    xu = (xu & 0x000f_ffff_ffff_ffff) | 0x0010_0000_0000_0000
    if k <= 0
        UInt128(xu >> -k)
    else
        UInt128(xu) << k
    end
end
function unsafe_trunc(::Type{Int128}, x::Float64)
    copysign(unsafe_trunc(UInt128,x) % Int128, x)
end

function unsafe_trunc(::Type{UInt128}, x::Float32)
    xu = reinterpret(UInt32,x)
    k = Int(xu >> 23) & 0x00ff - 150
    xu = (xu & 0x007f_ffff) | 0x0080_0000
    if k <= 0
        UInt128(xu >> -k)
    else
        UInt128(xu) << k
    end
end
function unsafe_trunc(::Type{Int128}, x::Float32)
    copysign(unsafe_trunc(UInt128,x) % Int128, x)
end

unsafe_trunc(::Type{UInt128}, x::Float16) = unsafe_trunc(UInt128, Float32(x))
unsafe_trunc(::Type{Int128}, x::Float16) = unsafe_trunc(Int128, Float32(x))

# matches convert methods
# also determines floor, ceil, round
trunc(::Type{Signed}, x::IEEEFloat) = trunc(Int,x)
trunc(::Type{Unsigned}, x::IEEEFloat) = trunc(UInt,x)
trunc(::Type{Integer}, x::IEEEFloat) = trunc(Int,x)

# fallbacks
floor(::Type{T}, x::AbstractFloat) where {T<:Integer} = trunc(T,round(x, RoundDown))
ceil(::Type{T}, x::AbstractFloat) where {T<:Integer} = trunc(T,round(x, RoundUp))
round(::Type{T}, x::AbstractFloat) where {T<:Integer} = trunc(T,round(x, RoundNearest))

# Bool
trunc(::Type{Bool}, x::AbstractFloat) = (-1 < x < 2) ? 1 <= x : throw(InexactError(:trunc, Bool, x))
floor(::Type{Bool}, x::AbstractFloat) = (0 <= x < 2) ? 1 <= x : throw(InexactError(:floor, Bool, x))
ceil(::Type{Bool}, x::AbstractFloat)  = (-1 < x <= 1) ? 0 < x : throw(InexactError(:ceil, Bool, x))
round(::Type{Bool}, x::AbstractFloat) = (-0.5 <= x < 1.5) ? 0.5 < x : throw(InexactError(:round, Bool, x))

round(x::IEEEFloat, r::RoundingMode{:ToZero})  = trunc_llvm(x)
round(x::IEEEFloat, r::RoundingMode{:Down})    = floor_llvm(x)
round(x::IEEEFloat, r::RoundingMode{:Up})      = ceil_llvm(x)
round(x::IEEEFloat, r::RoundingMode{:Nearest}) = rint_llvm(x)

## floating point promotions ##
promote_rule(::Type{Float32}, ::Type{Float16}) = Float32
promote_rule(::Type{Float64}, ::Type{Float16}) = Float64
promote_rule(::Type{Float64}, ::Type{Float32}) = Float64

widen(::Type{Float16}) = Float32
widen(::Type{Float32}) = Float64

## floating point arithmetic ##
-(x::IEEEFloat) = neg_float(x)

+(x::T, y::T) where {T<:IEEEFloat} = add_float(x, y)
-(x::T, y::T) where {T<:IEEEFloat} = sub_float(x, y)
*(x::T, y::T) where {T<:IEEEFloat} = mul_float(x, y)
/(x::T, y::T) where {T<:IEEEFloat} = div_float(x, y)

muladd(x::T, y::T, z::T) where {T<:IEEEFloat} = muladd_float(x, y, z)

# TODO: faster floating point div?
# TODO: faster floating point fld?
# TODO: faster floating point mod?

function unbiased_exponent(x::T) where {T<:IEEEFloat}
    return (reinterpret(Unsigned, x) & exponent_mask(T)) >> significand_bits(T)
end

function explicit_mantissa_noinfnan(x::T) where {T<:IEEEFloat}
    m = mantissa(x)
    issubnormal(x) || (m |= significand_mask(T) + uinttype(T)(1))
    return m
end

function _to_float(number::U, ep) where {U<:Unsigned}
    F = floattype(U)
    S = signed(U)
    epint = unsafe_trunc(S,ep)
    lz::signed(U) = unsafe_trunc(S, Core.Intrinsics.ctlz_int(number) - U(exponent_bits(F)))
    number <<= lz
    epint -= lz
    bits = U(0)
    if epint >= 0
        bits = number & significand_mask(F)
        bits |= ((epint + S(1)) << significand_bits(F)) & exponent_mask(F)
    else
        bits = (number >> -epint) & significand_mask(F)
    end
    return reinterpret(F, bits)
end

@assume_effects :terminates_locally :nothrow function rem_internal(x::T, y::T) where {T<:IEEEFloat}
    xuint = reinterpret(Unsigned, x)
    yuint = reinterpret(Unsigned, y)
    if xuint <= yuint
        if xuint < yuint
            return x
        end
        return zero(T)
    end

    e_x = unbiased_exponent(x)
    e_y = unbiased_exponent(y)
    # Most common case where |y| is "very normal" and |x/y| < 2^EXPONENT_WIDTH
    if e_y > (significand_bits(T)) && (e_x - e_y) <= (exponent_bits(T))
        m_x = explicit_mantissa_noinfnan(x)
        m_y = explicit_mantissa_noinfnan(y)
        d = urem_int((m_x << (e_x - e_y)),  m_y)
        iszero(d) && return zero(T)
        return _to_float(d, e_y - uinttype(T)(1))
    end
    # Both are subnormals
    if e_x == 0 && e_y == 0
        return reinterpret(T, urem_int(xuint, yuint) & significand_mask(T))
    end

    m_x = explicit_mantissa_noinfnan(x)
    e_x -= uinttype(T)(1)
    m_y = explicit_mantissa_noinfnan(y)
    lz_m_y = uinttype(T)(exponent_bits(T))
    if e_y > 0
        e_y -= uinttype(T)(1)
    else
        m_y = mantissa(y)
        lz_m_y = Core.Intrinsics.ctlz_int(m_y)
    end

    tz_m_y = Core.Intrinsics.cttz_int(m_y)
    sides_zeroes_cnt = lz_m_y + tz_m_y

    # n>0
    exp_diff = e_x - e_y
    # Shift hy right until the end or n = 0
    right_shift = min(exp_diff, tz_m_y)
    m_y >>= right_shift
    exp_diff -= right_shift
    e_y += right_shift
    # Shift hx left until the end or n = 0
    left_shift = min(exp_diff, uinttype(T)(exponent_bits(T)))
    m_x <<= left_shift
    exp_diff -= left_shift

    m_x = urem_int(m_x, m_y)
    iszero(m_x) && return zero(T)
    iszero(exp_diff) && return _to_float(m_x, e_y)

    while exp_diff > sides_zeroes_cnt
        exp_diff -= sides_zeroes_cnt
        m_x <<= sides_zeroes_cnt
        m_x = urem_int(m_x, m_y)
    end
    m_x <<= exp_diff
    m_x = urem_int(m_x, m_y)
    return _to_float(m_x, e_y)
end

function rem(x::T, y::T) where {T<:IEEEFloat}
    if isfinite(x) && !iszero(x) && isfinite(y) && !iszero(y)
        return copysign(rem_internal(abs(x), abs(y)), x)
    elseif isinf(x) || isnan(y) || iszero(y)  # y can still be Inf
        return T(NaN)
    else
        return x
    end
end

function mod(x::T, y::T) where {T<:AbstractFloat}
    r = rem(x,y)
    if r == 0
        copysign(r,y)
    elseif (r > 0) ⊻ (y > 0)
        r+y
    else
        r
    end
end

## floating point comparisons ##
==(x::T, y::T) where {T<:IEEEFloat} = eq_float(x, y)
!=(x::T, y::T) where {T<:IEEEFloat} = ne_float(x, y)
<( x::T, y::T) where {T<:IEEEFloat} = lt_float(x, y)
<=(x::T, y::T) where {T<:IEEEFloat} = le_float(x, y)

isequal(x::T, y::T) where {T<:IEEEFloat} = fpiseq(x, y)

# interpret as sign-magnitude integer
@inline function _fpint(x)
    IntT = inttype(typeof(x))
    ix = reinterpret(IntT, x)
    return ifelse(ix < zero(IntT), ix ⊻ typemax(IntT), ix)
end

@inline function isless(a::T, b::T) where T<:IEEEFloat
    (isnan(a) || isnan(b)) && return !isnan(a)

    return _fpint(a) < _fpint(b)
end

# Exact Float (Tf) vs Integer (Ti) comparisons
# Assumes:
# - typemax(Ti) == 2^n-1
# - typemax(Ti) can't be exactly represented by Tf:
#   => Tf(typemax(Ti)) == 2^n or Inf
# - typemin(Ti) can be exactly represented by Tf
#
# 1. convert y::Ti to float fy::Tf
# 2. perform Tf comparison x vs fy
# 3. if x == fy, check if (1) resulted in rounding:
#  a. convert fy back to Ti and compare with original y
#  b. unsafe_convert undefined behaviour if fy == Tf(typemax(Ti))
#     (but consequently x == fy > y)
for Ti in (Int64,UInt64,Int128,UInt128)
    for Tf in (Float32,Float64)
        @eval begin
            function ==(x::$Tf, y::$Ti)
                fy = ($Tf)(y)
                (x == fy) & (fy != $(Tf(typemax(Ti)))) & (y == unsafe_trunc($Ti,fy))
            end
            ==(y::$Ti, x::$Tf) = x==y

            function <(x::$Ti, y::$Tf)
                fx = ($Tf)(x)
                (fx < y) | ((fx == y) & ((fx == $(Tf(typemax(Ti)))) | (x < unsafe_trunc($Ti,fx)) ))
            end
            function <=(x::$Ti, y::$Tf)
                fx = ($Tf)(x)
                (fx < y) | ((fx == y) & ((fx == $(Tf(typemax(Ti)))) | (x <= unsafe_trunc($Ti,fx)) ))
            end

            function <(x::$Tf, y::$Ti)
                fy = ($Tf)(y)
                (x < fy) | ((x == fy) & (fy < $(Tf(typemax(Ti)))) & (unsafe_trunc($Ti,fy) < y))
            end
            function <=(x::$Tf, y::$Ti)
                fy = ($Tf)(y)
                (x < fy) | ((x == fy) & (fy < $(Tf(typemax(Ti)))) & (unsafe_trunc($Ti,fy) <= y))
            end
        end
    end
end
for op in (:(==), :<, :<=)
    @eval begin
        ($op)(x::Float16, y::Union{Int128,UInt128,Int64,UInt64}) = ($op)(Float64(x), Float64(y))
        ($op)(x::Union{Int128,UInt128,Int64,UInt64}, y::Float16) = ($op)(Float64(x), Float64(y))

        ($op)(x::Union{Float16,Float32}, y::Union{Int32,UInt32}) = ($op)(Float64(x), Float64(y))
        ($op)(x::Union{Int32,UInt32}, y::Union{Float16,Float32}) = ($op)(Float64(x), Float64(y))

        ($op)(x::Float16, y::Union{Int16,UInt16}) = ($op)(Float32(x), Float32(y))
        ($op)(x::Union{Int16,UInt16}, y::Float16) = ($op)(Float32(x), Float32(y))
    end
end


abs(x::IEEEFloat) = abs_float(x)

"""
    isnan(f) -> Bool

Test whether a number value is a NaN, an indeterminate value which is neither an infinity
nor a finite number ("not a number").

See also: [`iszero`](@ref), [`isone`](@ref), [`isinf`](@ref), [`ismissing`](@ref).
"""
isnan(x::AbstractFloat) = (x != x)::Bool
isnan(x::Number) = false

isfinite(x::AbstractFloat) = !isnan(x - x)
isfinite(x::Real) = decompose(x)[3] != 0
isfinite(x::Integer) = true

"""
    isinf(f) -> Bool

Test whether a number is infinite.

See also: [`Inf`](@ref), [`iszero`](@ref), [`isfinite`](@ref), [`isnan`](@ref).
"""
isinf(x::Real) = !isnan(x) & !isfinite(x)
isinf(x::IEEEFloat) = abs(x) === oftype(x, Inf)

const hx_NaN = hash_uint64(reinterpret(UInt64, NaN))
function hash(x::Float64, h::UInt)
    # see comments on trunc and hash(Real, UInt)
    if typemin(Int64) <= x < typemax(Int64)
        xi = fptosi(Int64, x)
        if isequal(xi, x)
            return hash(xi, h)
        end
    elseif typemin(UInt64) <= x < typemax(UInt64)
        xu = fptoui(UInt64, x)
        if isequal(xu, x)
            return hash(xu, h)
        end
    elseif isnan(x)
        return hx_NaN ⊻ h # NaN does not have a stable bit pattern
    end
    return hash_uint64(bitcast(UInt64, x)) - 3h
end

hash(x::Float32, h::UInt) = hash(Float64(x), h)

function hash(x::Float16, h::UInt)
    # see comments on trunc and hash(Real, UInt)
    if isfinite(x) # all finite Float16 fit in Int64
        xi = fptosi(Int64, x)
        if isequal(xi, x)
            return hash(xi, h)
        end
    elseif isnan(x)
        return hx_NaN ⊻ h # NaN does not have a stable bit pattern
    end
    return hash_uint64(bitcast(UInt64, Float64(x))) - 3h
end

## generic hashing for rational values ##
function hash(x::Real, h::UInt)
    # decompose x as num*2^pow/den
    num, pow, den = decompose(x)

    # handle special values
    num == 0 && den == 0 && return hash(NaN, h)
    num == 0 && return hash(ifelse(den > 0, 0.0, -0.0), h)
    den == 0 && return hash(ifelse(num > 0, Inf, -Inf), h)

    # normalize decomposition
    if den < 0
        num = -num
        den = -den
    end
    num_z = trailing_zeros(num)
    num >>= num_z
    den_z = trailing_zeros(den)
    den >>= den_z
    pow += num_z - den_z
    # If the real can be represented as an Int64, UInt64, or Float64, hash as those types.
    # To be an Integer the denominator must be 1 and the power must be non-negative.
    if den == 1
        # left = ceil(log2(num*2^pow))
        left = top_set_bit(abs(num)) + pow
        # 2^-1074 is the minimum Float64 so if the power is smaller, not a Float64
        if -1074 <= pow
            if 0 <= pow # if pow is non-negative, it is an integer
                left <= 63 && return hash(Int64(num) << Int(pow), h)
                left <= 64 && !signbit(num) && return hash(UInt64(num) << Int(pow), h)
            end # typemin(Int64) handled by Float64 case
            # 2^1024 is the maximum Float64 so if the power is greater, not a Float64
            # Float64s only have 53 mantisa bits (including implicit bit)
            left <= 1024 && left - pow <= 53 && return hash(ldexp(Float64(num), pow), h)
        end
    else
        h = hash_integer(den, h)
    end
    # handle generic rational values
    h = hash_integer(pow, h)
    h = hash_integer(num, h)
    return h
end

#=
`decompose(x)`: non-canonical decomposition of rational values as `num*2^pow/den`.

The decompose function is the point where rational-valued numeric types that support
hashing hook into the hashing protocol. `decompose(x)` should return three integer
values `num, pow, den`, such that the value of `x` is mathematically equal to

    num*2^pow/den

The decomposition need not be canonical in the sense that it just needs to be *some*
way to express `x` in this form, not any particular way – with the restriction that
`num` and `den` may not share any odd common factors. They may, however, have powers
of two in common – the generic hashing code will normalize those as necessary.

Special values:

 - `x` is zero: `num` should be zero and `den` should have the same sign as `x`
 - `x` is infinite: `den` should be zero and `num` should have the same sign as `x`
 - `x` is not a number: `num` and `den` should both be zero
=#

decompose(x::Integer) = x, 0, 1

function decompose(x::Float16)::NTuple{3,Int}
    isnan(x) && return 0, 0, 0
    isinf(x) && return ifelse(x < 0, -1, 1), 0, 0
    n = reinterpret(UInt16, x)
    s = (n & 0x03ff) % Int16
    e = ((n & 0x7c00) >> 10) % Int
    s |= Int16(e != 0) << 10
    d = ifelse(signbit(x), -1, 1)
    s, e - 25 + (e == 0), d
end

function decompose(x::Float32)::NTuple{3,Int}
    isnan(x) && return 0, 0, 0
    isinf(x) && return ifelse(x < 0, -1, 1), 0, 0
    n = reinterpret(UInt32, x)
    s = (n & 0x007fffff) % Int32
    e = ((n & 0x7f800000) >> 23) % Int
    s |= Int32(e != 0) << 23
    d = ifelse(signbit(x), -1, 1)
    s, e - 150 + (e == 0), d
end

function decompose(x::Float64)::Tuple{Int64, Int, Int}
    isnan(x) && return 0, 0, 0
    isinf(x) && return ifelse(x < 0, -1, 1), 0, 0
    n = reinterpret(UInt64, x)
    s = (n & 0x000fffffffffffff) % Int64
    e = ((n & 0x7ff0000000000000) >> 52) % Int
    s |= Int64(e != 0) << 52
    d = ifelse(signbit(x), -1, 1)
    s, e - 1075 + (e == 0), d
end


"""
    precision(num::AbstractFloat; base::Integer=2)
    precision(T::Type; base::Integer=2)

Get the precision of a floating point number, as defined by the effective number of bits in
the significand, or the precision of a floating-point type `T` (its current default, if
`T` is a variable-precision type like [`BigFloat`](@ref)).

If `base` is specified, then it returns the maximum corresponding
number of significand digits in that base.

!!! compat "Julia 1.8"
    The `base` keyword requires at least Julia 1.8.
"""
function precision end

_precision(::Type{Float16}) = 11
_precision(::Type{Float32}) = 24
_precision(::Type{Float64}) = 53
function _precision(x, base::Integer=2)
    base > 1 || throw(DomainError(base, "`base` cannot be less than 2."))
    p = _precision(x)
    return base == 2 ? Int(p) : floor(Int, p / log2(base))
end
precision(::Type{T}; base::Integer=2) where {T<:AbstractFloat} = _precision(T, base)
precision(::T; base::Integer=2) where {T<:AbstractFloat} = precision(T; base)


"""
    nextfloat(x::AbstractFloat, n::Integer)

The result of `n` iterative applications of `nextfloat` to `x` if `n >= 0`, or `-n`
applications of [`prevfloat`](@ref) if `n < 0`.
"""
function nextfloat(f::IEEEFloat, d::Integer)
    F = typeof(f)
    fumax = reinterpret(Unsigned, F(Inf))
    U = typeof(fumax)

    isnan(f) && return f
    fi = reinterpret(Signed, f)
    fneg = fi < 0
    fu = unsigned(fi & typemax(fi))

    dneg = d < 0
    da = uabs(d)
    if da > typemax(U)
        fneg = dneg
        fu = fumax
    else
        du = da % U
        if fneg ⊻ dneg
            if du > fu
                fu = min(fumax, du - fu)
                fneg = !fneg
            else
                fu = fu - du
            end
        else
            if fumax - fu < du
                fu = fumax
            else
                fu = fu + du
            end
        end
    end
    if fneg
        fu |= sign_mask(F)
    end
    reinterpret(F, fu)
end

"""
    nextfloat(x::AbstractFloat)

Return the smallest floating point number `y` of the same type as `x` such `x < y`. If no
such `y` exists (e.g. if `x` is `Inf` or `NaN`), then return `x`.

See also: [`prevfloat`](@ref), [`eps`](@ref), [`issubnormal`](@ref).
"""
nextfloat(x::AbstractFloat) = nextfloat(x,1)

"""
    prevfloat(x::AbstractFloat, n::Integer)

The result of `n` iterative applications of `prevfloat` to `x` if `n >= 0`, or `-n`
applications of [`nextfloat`](@ref) if `n < 0`.
"""
prevfloat(x::AbstractFloat, d::Integer) = nextfloat(x, -d)

"""
    prevfloat(x::AbstractFloat)

Return the largest floating point number `y` of the same type as `x` such `y < x`. If no
such `y` exists (e.g. if `x` is `-Inf` or `NaN`), then return `x`.
"""
prevfloat(x::AbstractFloat) = nextfloat(x,-1)

for Ti in (Int8, Int16, Int32, Int64, Int128, UInt8, UInt16, UInt32, UInt64, UInt128)
    for Tf in (Float16, Float32, Float64)
        if Ti <: Unsigned || sizeof(Ti) < sizeof(Tf)
            # Here `Tf(typemin(Ti))-1` is exact, so we can compare the lower-bound
            # directly. `Tf(typemax(Ti))+1` is either always exactly representable, or
            # rounded to `Inf` (e.g. when `Ti==UInt128 && Tf==Float32`).
            @eval begin
                function trunc(::Type{$Ti},x::$Tf)
                    if $(Tf(typemin(Ti))-one(Tf)) < x < $(Tf(typemax(Ti))+one(Tf))
                        return unsafe_trunc($Ti,x)
                    else
                        throw(InexactError(:trunc, $Ti, x))
                    end
                end
                function (::Type{$Ti})(x::$Tf)
                    # When typemax(Ti) is not representable by Tf but typemax(Ti) + 1 is,
                    # then < Tf(typemax(Ti) + 1) is stricter than <= Tf(typemax(Ti)). Using
                    # the former causes us to throw on UInt64(Float64(typemax(UInt64))+1)
                    if ($(Tf(typemin(Ti))) <= x < $(Tf(typemax(Ti))+one(Tf))) && isinteger(x)
                        return unsafe_trunc($Ti,x)
                    else
                        throw(InexactError($(Expr(:quote,Ti.name.name)), $Ti, x))
                    end
                end
            end
        else
            # Here `eps(Tf(typemin(Ti))) > 1`, so the only value which can be truncated to
            # `Tf(typemin(Ti)` is itself. Similarly, `Tf(typemax(Ti))` is inexact and will
            # be rounded up. This assumes that `Tf(typemin(Ti)) > -Inf`, which is true for
            # these types, but not for `Float16` or larger integer types.
            @eval begin
                function trunc(::Type{$Ti},x::$Tf)
                    if $(Tf(typemin(Ti))) <= x < $(Tf(typemax(Ti)))
                        return unsafe_trunc($Ti,x)
                    else
                        throw(InexactError(:trunc, $Ti, x))
                    end
                end
                function (::Type{$Ti})(x::$Tf)
                    if ($(Tf(typemin(Ti))) <= x < $(Tf(typemax(Ti)))) && isinteger(x)
                        return unsafe_trunc($Ti,x)
                    else
                        throw(InexactError($(Expr(:quote,Ti.name.name)), $Ti, x))
                    end
                end
            end
        end
    end
end

"""
    issubnormal(f) -> Bool

Test whether a floating point number is subnormal.

An IEEE floating point number is [subnormal](https://en.wikipedia.org/wiki/Subnormal_number)
when its exponent bits are zero and its significand is not zero.

# Examples
```jldoctest
julia> floatmin(Float32)
1.1754944f-38

julia> issubnormal(1.0f-37)
false

julia> issubnormal(1.0f-38)
true
```
"""
function issubnormal(x::T) where {T<:IEEEFloat}
    y = reinterpret(Unsigned, x)
    (y & exponent_mask(T) == 0) & (y & significand_mask(T) != 0)
end

ispow2(x::AbstractFloat) = !iszero(x) && frexp(x)[1] == 0.5
iseven(x::AbstractFloat) = isinteger(x) && (abs(x) > maxintfloat(x) || iseven(Integer(x)))
isodd(x::AbstractFloat) = isinteger(x) && abs(x) ≤ maxintfloat(x) && isodd(Integer(x))

@eval begin
    typemin(::Type{Float16}) = $(bitcast(Float16, 0xfc00))
    typemax(::Type{Float16}) = $(Inf16)
    typemin(::Type{Float32}) = $(-Inf32)
    typemax(::Type{Float32}) = $(Inf32)
    typemin(::Type{Float64}) = $(-Inf64)
    typemax(::Type{Float64}) = $(Inf64)
    typemin(x::T) where {T<:Real} = typemin(T)
    typemax(x::T) where {T<:Real} = typemax(T)

    floatmin(::Type{Float16}) = $(bitcast(Float16, 0x0400))
    floatmin(::Type{Float32}) = $(bitcast(Float32, 0x00800000))
    floatmin(::Type{Float64}) = $(bitcast(Float64, 0x0010000000000000))
    floatmax(::Type{Float16}) = $(bitcast(Float16, 0x7bff))
    floatmax(::Type{Float32}) = $(bitcast(Float32, 0x7f7fffff))
    floatmax(::Type{Float64}) = $(bitcast(Float64, 0x7fefffffffffffff))

    eps(x::AbstractFloat) = isfinite(x) ? abs(x) >= floatmin(x) ? ldexp(eps(typeof(x)), exponent(x)) : nextfloat(zero(x)) : oftype(x, NaN)
    eps(::Type{Float16}) = $(bitcast(Float16, 0x1400))
    eps(::Type{Float32}) = $(bitcast(Float32, 0x34000000))
    eps(::Type{Float64}) = $(bitcast(Float64, 0x3cb0000000000000))
    eps() = eps(Float64)
end

"""
    floatmin(T = Float64)

Return the smallest positive normal number representable by the floating-point
type `T`.

# Examples
```jldoctest
julia> floatmin(Float16)
Float16(6.104e-5)

julia> floatmin(Float32)
1.1754944f-38

julia> floatmin()
2.2250738585072014e-308
```
"""
floatmin(x::T) where {T<:AbstractFloat} = floatmin(T)

"""
    floatmax(T = Float64)

Return the largest finite number representable by the floating-point type `T`.

See also: [`typemax`](@ref), [`floatmin`](@ref), [`eps`](@ref).

# Examples
```jldoctest
julia> floatmax(Float16)
Float16(6.55e4)

julia> floatmax(Float32)
3.4028235f38

julia> floatmax()
1.7976931348623157e308

julia> typemax(Float64)
Inf
```
"""
floatmax(x::T) where {T<:AbstractFloat} = floatmax(T)

floatmin() = floatmin(Float64)
floatmax() = floatmax(Float64)

"""
    eps(::Type{T}) where T<:AbstractFloat
    eps()

Return the *machine epsilon* of the floating point type `T` (`T = Float64` by
default). This is defined as the gap between 1 and the next largest value representable by
`typeof(one(T))`, and is equivalent to `eps(one(T))`.  (Since `eps(T)` is a
bound on the *relative error* of `T`, it is a "dimensionless" quantity like [`one`](@ref).)

# Examples
```jldoctest
julia> eps()
2.220446049250313e-16

julia> eps(Float32)
1.1920929f-7

julia> 1.0 + eps()
1.0000000000000002

julia> 1.0 + eps()/2
1.0
```
"""
eps(::Type{<:AbstractFloat})

"""
    eps(x::AbstractFloat)

Return the *unit in last place* (ulp) of `x`. This is the distance between consecutive
representable floating point values at `x`. In most cases, if the distance on either side
of `x` is different, then the larger of the two is taken, that is

    eps(x) == max(x-prevfloat(x), nextfloat(x)-x)

The exceptions to this rule are the smallest and largest finite values
(e.g. `nextfloat(-Inf)` and `prevfloat(Inf)` for [`Float64`](@ref)), which round to the
smaller of the values.

The rationale for this behavior is that `eps` bounds the floating point rounding
error. Under the default `RoundNearest` rounding mode, if ``y`` is a real number and ``x``
is the nearest floating point number to ``y``, then

```math
|y-x| \\leq \\operatorname{eps}(x)/2.
```

See also: [`nextfloat`](@ref), [`issubnormal`](@ref), [`floatmax`](@ref).

# Examples
```jldoctest
julia> eps(1.0)
2.220446049250313e-16

julia> eps(prevfloat(2.0))
2.220446049250313e-16

julia> eps(2.0)
4.440892098500626e-16

julia> x = prevfloat(Inf)      # largest finite Float64
1.7976931348623157e308

julia> x + eps(x)/2            # rounds up
Inf

julia> x + prevfloat(eps(x)/2) # rounds down
1.7976931348623157e308
```
"""
eps(::AbstractFloat)


## byte order swaps for arbitrary-endianness serialization/deserialization ##
bswap(x::IEEEFloat) = bswap_int(x)

# integer size of float
uinttype(::Type{Float64}) = UInt64
uinttype(::Type{Float32}) = UInt32
uinttype(::Type{Float16}) = UInt16
inttype(::Type{Float64}) = Int64
inttype(::Type{Float32}) = Int32
inttype(::Type{Float16}) = Int16
# float size of integer
floattype(::Type{UInt64}) = Float64
floattype(::Type{UInt32}) = Float32
floattype(::Type{UInt16}) = Float16
floattype(::Type{Int64}) = Float64
floattype(::Type{Int32}) = Float32
floattype(::Type{Int16}) = Float16


## Array operations on floating point numbers ##

float(A::AbstractArray{<:AbstractFloat}) = A

function float(A::AbstractArray{T}) where T
    if !isconcretetype(T)
        error("`float` not defined on abstractly-typed arrays; please convert to a more specific type")
    end
    convert(AbstractArray{typeof(float(zero(T)))}, A)
end

float(r::StepRange) = float(r.start):float(r.step):float(last(r))
float(r::UnitRange) = float(r.start):float(last(r))
float(r::StepRangeLen{T}) where {T} =
    StepRangeLen{typeof(float(T(r.ref)))}(float(r.ref), float(r.step), length(r), r.offset)
function float(r::LinRange)
    LinRange(float(r.start), float(r.stop), length(r))
end
U   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/twiceprecision.jlRs      # This file is a part of Julia. License is MIT: https://julialang.org/license

# Twice-precision arithmetic.

# Necessary for creating nicely-behaved ranges like r = 0.1:0.1:0.3
# that return r[3] == 0.3.  Otherwise, we have roundoff error due to
#     0.1 + 2*0.1 = 0.30000000000000004

"""
    hi, lo = splitprec(F::Type{<:AbstractFloat}, i::Integer)

Represent an integer `i` as a pair of floating-point numbers `hi` and
`lo` (of type `F`) such that:
- `widen(hi) + widen(lo) ≈ i`. It is exact if 1.5 * (number of precision bits in `F`) is greater than the number of bits in `i`.
- all bits in `hi` are more significant than any of the bits in `lo`
- `hi` can be exactly multiplied by the `hi` component of another call to `splitprec`.

In particular, while `convert(Float64, i)` can be lossy since Float64
has only 53 bits of precision, `splitprec(Float64, i)` is exact for
any Int64/UInt64.
"""
function splitprec(::Type{F}, i::Integer) where {F<:AbstractFloat}
    hi = truncbits(F(i), cld(precision(F), 2))
    ihi = oftype(i, hi)
    hi, F(i - ihi)
end

function truncmask(x::F, mask) where {F<:IEEEFloat}
    reinterpret(F, mask & reinterpret(uinttype(F), x))
end
truncmask(x, mask) = x

function truncbits(x::F, nb) where {F<:IEEEFloat}
    truncmask(x, typemax(uinttype(F)) << nb)
end
truncbits(x, nb) = x


## Dekker arithmetic

"""
    hi, lo = canonicalize2(big, little)

Generate a representation where all the nonzero bits in `hi` are more
significant than any of the nonzero bits in `lo`. `big` must be larger
in absolute value than `little`.
"""
function canonicalize2(big, little)
    h = big+little
    h, (big - h) + little
end

"""
    zhi, zlo = add12(x, y)

A high-precision representation of `x + y` for floating-point
numbers. Mathematically, `zhi + zlo = x + y`, where `zhi` contains the
most significant bits and `zlo` the least significant.

Because of the way floating-point numbers are printed, `lo` may not
look the way you might expect from the standpoint of decimal
representation, even though it is exact from the standpoint of binary
representation.

Example:
```julia-repl
julia> 1.0 + 1.0001e-15
1.000000000000001

julia> big(1.0) + big(1.0001e-15)
1.000000000000001000100000000000020165767380775934141445417482375879192346701529

julia> hi, lo = Base.add12(1.0, 1.0001e-15)
(1.000000000000001, -1.1012302462515652e-16)

julia> big(hi) + big(lo)
1.000000000000001000100000000000020165767380775934141445417482375879192346701529
```

`lo` differs from 1.0e-19 because `hi` is not exactly equal to
the first 16 decimal digits of the answer.
"""
function add12(x::T, y::T) where {T}
    x, y = ifelse(abs(y) > abs(x), (y, x), (x, y))
    canonicalize2(x, y)
end
add12(x, y) = add12(promote(x, y)...)

"""
    zhi, zlo = mul12(x, y)

A high-precision representation of `x * y` for floating-point
numbers. Mathematically, `zhi + zlo = x * y`, where `zhi` contains the
most significant bits and `zlo` the least significant.

Example:
```julia-repl
julia> x = Float32(π)
3.1415927f0

julia> x * x
9.869605f0

julia> Float64(x) * Float64(x)
9.869604950382893

julia> hi, lo = Base.mul12(x, x)
(9.869605f0, -1.140092f-7)

julia> Float64(hi) + Float64(lo)
9.869604950382893
```
"""
function mul12(x::T, y::T) where {T<:AbstractFloat}
    (h, l) = Math.two_mul(x, y)
    ifelse(!isfinite(h), (h, h), (h, l))
end
mul12(x::T, y::T) where {T} = (p = x * y; (p, zero(p)))
mul12(x, y) = mul12(promote(x, y)...)

"""
    zhi, zlo = div12(x, y)

A high-precision representation of `x / y` for floating-point
numbers. Mathematically, `zhi + zlo ≈ x / y`, where `zhi` contains the
most significant bits and `zlo` the least significant.

Example:
```julia-repl
julia> x, y = Float32(π), 3.1f0
(3.1415927f0, 3.1f0)

julia> x / y
1.013417f0

julia> Float64(x) / Float64(y)
1.0134170444063078

julia> hi, lo = Base.div12(x, y)
(1.013417f0, 3.8867366f-8)

julia> Float64(hi) + Float64(lo)
1.0134170444063066
```
"""
function div12(x::T, y::T) where {T<:AbstractFloat}
    # We lose precision if any intermediate calculation results in a subnormal.
    # To prevent this from happening, standardize the values.
    xs, xe = frexp(x)
    ys, ye = frexp(y)
    r = xs / ys
    rh, rl = canonicalize2(r, -fma(r, ys, -xs)/ys)
    ifelse(iszero(r) | !isfinite(r), (r, r), (ldexp(rh, xe-ye), ldexp(rl, xe-ye)))
end
div12(x::T, y::T) where {T} = (p = x / y; (p, zero(p)))
div12(x, y) = div12(promote(x, y)...)


## TwicePrecision

"""
    TwicePrecision{T}(hi::T, lo::T)
    TwicePrecision{T}((num, denom))

A number with twice the precision of `T`, e.g., quad-precision if `T =
Float64`.

!!! warning
    `TwicePrecision` is an internal type used to increase the
    precision of floating-point ranges, and not intended for external use.
    If you encounter them in real code, the most likely explanation is
    that you are directly accessing the fields of a range. Use
    the function interface instead, `step(r)` rather than `r.step`

# Extended help

`hi` represents the high bits (most significant bits) and
`lo` the low bits (least significant bits). Rational values
`num//denom` can be approximated conveniently using the syntax
`TwicePrecision{T}((num, denom))`.

When used with `T<:Union{Float16,Float32,Float64}` to construct an "exact"
`StepRangeLen`, `ref` should be the range element with smallest
magnitude and `offset` set to the corresponding index.  For
efficiency, multiplication of `step` by the index is not performed at
twice precision: `step.hi` should have enough trailing zeros in its
`bits` representation that `(0:len-1)*step.hi` is exact (has no
roundoff error).  If `step` has an exact rational representation
`num//denom`, then you can construct `step` using

    step = TwicePrecision{T}((num, denom), nb)

where `nb` is the number of trailing zero bits of `step.hi`.  For
ranges, you can set `nb = ceil(Int, log2(len-1))`.
"""
struct TwicePrecision{T}
    hi::T    # most significant bits
    lo::T    # least significant bits
end

TwicePrecision{T}(x::T) where {T} = TwicePrecision{T}(x, zero(T))

TwicePrecision{T}(x::TwicePrecision{T}) where {T} = x

function TwicePrecision{T}(x) where {T}
    xT = T(x)
    Δx = x - xT
    TwicePrecision{T}(xT, T(Δx))
end

TwicePrecision{T}(i::Integer) where {T<:AbstractFloat} =
    TwicePrecision{T}(canonicalize2(splitprec(T, i)...)...)

TwicePrecision(x) = TwicePrecision{typeof(x)}(x)

# Numerator/Denominator constructors
function TwicePrecision{T}(nd::Tuple{Integer,Integer}) where {T<:Union{Float16,Float32}}
    n, d = nd
    TwicePrecision{T}(n/d)
end

function TwicePrecision{T}(nd::Tuple{Any,Any}) where {T}
    n, d = nd
    TwicePrecision{T}(TwicePrecision{T}(n) / d)
end

function TwicePrecision{T}(nd::Tuple{I,I}, nb::Integer) where {T,I}
    twiceprecision(TwicePrecision{T}(nd), nb)
end

# Fix #39798
# See steprangelen_hp(::Type{Float64}, ref::Tuple{Integer,Integer},
#                         step::Tuple{Integer,Integer}, nb::Integer,
#                         len::Integer, offset::Integer)
function TwicePrecision{T}(nd::Tuple{Integer,Integer}, nb::Integer) where T
    twiceprecision(TwicePrecision{T}(nd), nb)
end

# Truncating constructors. Useful for generating values that can be
# exactly multiplied by small integers.
function twiceprecision(val::T, nb::Integer) where {T<:IEEEFloat}
    hi = truncbits(val, nb)
    TwicePrecision{T}(hi, val - hi)
end

function twiceprecision(val::TwicePrecision{T}, nb::Integer) where {T<:IEEEFloat}
    hi = truncbits(val.hi, nb)
    TwicePrecision{T}(hi, (val.hi - hi) + val.lo)
end

nbitslen(r::StepRangeLen) = nbitslen(eltype(r), length(r), r.offset)
nbitslen(::Type{T}, len, offset) where {T<:IEEEFloat} =
    min(cld(precision(T), 2), nbitslen(len, offset))
# The +1 here is for safety, because the precision of the significand
# is 1 bit higher than the number that are explicitly stored.
nbitslen(len, offset) = len < 2 ? 0 : top_set_bit(max(offset-1, len-offset) - 1) + 1

eltype(::Type{TwicePrecision{T}}) where {T} = T

promote_rule(::Type{TwicePrecision{R}}, ::Type{TwicePrecision{S}}) where {R,S} =
    TwicePrecision{promote_type(R,S)}
promote_rule(::Type{TwicePrecision{R}}, ::Type{S}) where {R,S<:Number} =
    TwicePrecision{promote_type(R,S)}

(::Type{T})(x::TwicePrecision) where {T<:Number} = (T(x.hi) + T(x.lo))::T

convert(::Type{TwicePrecision{T}}, x::TwicePrecision{T}) where {T} = x
convert(::Type{TwicePrecision{T}}, x::TwicePrecision) where {T} =
    TwicePrecision{T}(convert(T, x.hi), convert(T, x.lo))::TwicePrecision{T}

convert(::Type{T}, x::TwicePrecision) where {T<:Number} = T(x)::T
convert(::Type{TwicePrecision{T}}, x::Number) where {T} = TwicePrecision{T}(x)::TwicePrecision{T}

float(x::TwicePrecision{<:AbstractFloat}) = x
float(x::TwicePrecision) = TwicePrecision(float(x.hi), float(x.lo))

big(x::TwicePrecision) = big(x.hi) + big(x.lo)

-(x::TwicePrecision) = TwicePrecision(-x.hi, -x.lo)

function zero(::Type{TwicePrecision{T}}) where {T}
    z = zero(T)
    TwicePrecision{T}(z, z)
end

# Arithmetic

function +(x::TwicePrecision, y::Number)
    s_hi, s_lo = add12(x.hi, y)
    TwicePrecision(canonicalize2(s_hi, s_lo+x.lo)...)
end
+(x::Number, y::TwicePrecision) = y+x

function +(x::TwicePrecision{T}, y::TwicePrecision{T}) where T
    r = x.hi + y.hi
    s = abs(x.hi) > abs(y.hi) ? (((x.hi - r) + y.hi) + y.lo) + x.lo : (((y.hi - r) + x.hi) + x.lo) + y.lo
    TwicePrecision(canonicalize2(r, s)...)
end
+(x::TwicePrecision, y::TwicePrecision) = +(promote(x, y)...)

-(x::TwicePrecision, y::TwicePrecision) = x + (-y)
-(x::TwicePrecision, y::Number) = x + (-y)
-(x::Number, y::TwicePrecision) = x + (-y)

function *(x::TwicePrecision, v::Number)
    v == 0 && return TwicePrecision(x.hi*v, x.lo*v)
    x * TwicePrecision(oftype(x.hi*v, v))
end
function *(x::TwicePrecision{<:IEEEFloat}, v::Integer)
    v == 0 && return TwicePrecision(x.hi*v, x.lo*v)
    nb = top_set_bit(abs(v)-1)
    u = truncbits(x.hi, nb)
    TwicePrecision(canonicalize2(u*v, ((x.hi-u) + x.lo)*v)...)
end
*(v::Number, x::TwicePrecision) = x*v

function *(x::TwicePrecision{T}, y::TwicePrecision{T}) where {T}
    zh, zl = mul12(x.hi, y.hi)
    ret = TwicePrecision{T}(canonicalize2(zh, (x.hi * y.lo + x.lo * y.hi) + zl)...)
    ifelse(iszero(zh) | !isfinite(zh), TwicePrecision{T}(zh, zh), ret)
end
*(x::TwicePrecision, y::TwicePrecision) = *(promote(x, y)...)

function /(x::TwicePrecision, v::Number)
    x / TwicePrecision(oftype(x.hi/v, v))
end

function /(x::TwicePrecision, y::TwicePrecision)
    hi = x.hi / y.hi
    uh, ul = mul12(hi, y.hi)
    lo = ((((x.hi - uh) - ul) + x.lo) - hi*y.lo)/y.hi
    ret = TwicePrecision(canonicalize2(hi, lo)...)
    ifelse(iszero(hi) | !isfinite(hi), TwicePrecision(hi, hi), ret)
end

## StepRangeLen

# Use TwicePrecision only for Float64; use Float64 for T<:Union{Float16,Float32}
# See also _linspace1
# Ratio-of-integers constructors
function steprangelen_hp(::Type{Float64}, ref::Tuple{Integer,Integer},
                         step::Tuple{Integer,Integer}, nb::Integer,
                         len::Integer, offset::Integer)
    StepRangeLen(TwicePrecision{Float64}(ref),
                 TwicePrecision{Float64}(step, nb), len, offset)
end

function steprangelen_hp(::Type{T}, ref::Tuple{Integer,Integer},
                         step::Tuple{Integer,Integer}, nb::Integer,
                         len::Integer, offset::Integer) where {T<:IEEEFloat}
    StepRangeLen{T}(ref[1]/ref[2], step[1]/step[2], len, offset)
end

# AbstractFloat constructors (can supply a single number or a 2-tuple
const F_or_FF = Union{AbstractFloat, Tuple{AbstractFloat,AbstractFloat}}
asF64(x::AbstractFloat) = Float64(x)
asF64(x::Tuple{AbstractFloat,AbstractFloat}) = Float64(x[1]) + Float64(x[2])

function steprangelen_hp(::Type{Float64}, ref::F_or_FF,
                         step::F_or_FF, nb::Integer,
                         len::Integer, offset::Integer)
    StepRangeLen(TwicePrecision{Float64}(ref...),
                 twiceprecision(TwicePrecision{Float64}(step...), nb), len, offset)
end

function steprangelen_hp(::Type{T}, ref::F_or_FF,
                         step::F_or_FF, nb::Integer,
                         len::Integer, offset::Integer) where {T<:IEEEFloat}
    StepRangeLen{T}(asF64(ref), asF64(step), len, offset)
end


StepRangeLen(ref::TwicePrecision{T}, step::TwicePrecision{T},
             len::Integer, offset::Integer=1) where {T} =
    StepRangeLen{T,TwicePrecision{T},TwicePrecision{T}}(ref, step, len, offset)

# Construct range for rational start=start_n/den, step=step_n/den
function floatrange(::Type{T}, start_n::Integer, step_n::Integer, len::Integer, den::Integer) where T
    len = len + 0 # promote with Int
    if len < 2 || step_n == 0
        return steprangelen_hp(T, (start_n, den), (step_n, den), 0, len, oneunit(len))
    end
    # index of smallest-magnitude value
    L = typeof(len)
    imin = clamp(round(typeof(len), -start_n/step_n+1), oneunit(L), len)
    # Compute smallest-magnitude element to 2x precision
    ref_n = start_n+(imin-1)*step_n  # this shouldn't overflow, so don't check
    nb = nbitslen(T, len, imin)
    steprangelen_hp(T, (ref_n, den), (step_n, den), nb, len, imin)
end

function (:)(start::T, step::T, stop::T) where T<:IEEEFloat
    step == 0 && throw(ArgumentError("range step cannot be zero"))
    # see if the inputs have exact rational approximations (and if so,
    # perform all computations in terms of the rationals)
    step_n, step_d = rat(step)
    if step_d != 0 && T(step_n/step_d) == step
        start_n, start_d = rat(start)
        stop_n, stop_d = rat(stop)
        if start_d != 0 && stop_d != 0 &&
                T(start_n/start_d) == start && T(stop_n/stop_d) == stop
            den = lcm_unchecked(start_d, step_d) # use same denominator for start and step
            m = maxintfloat(T, Int)
            if den != 0 && abs(start*den) <= m && abs(step*den) <= m &&  # will round succeed?
                    rem(den, start_d) == 0 && rem(den, step_d) == 0      # check lcm overflow
                start_n = round(Int, start*den)
                step_n = round(Int, step*den)
                len = max(0, Int(div(den*stop_n - stop_d*start_n + step_n*stop_d, step_n*stop_d)))
                # Integer ops could overflow, so check that this makes sense
                if isbetween(start, start + (len-1)*step, stop + step/2) &&
                        !isbetween(start, start + len*step, stop)
                    # Return a 2x precision range
                    return floatrange(T, start_n, step_n, len, den)
                end
            end
        end
    end
    # Fallback, taking start and step literally
    # n.b. we use Int as the default length type for IEEEFloats
    lf = (stop-start)/step
    if lf < 0
        len = 0
    elseif lf == 0
        len = 1
    else
        len = round(Int, lf) + 1
        stop′ = start + (len-1)*step
        # if we've overshot the end, subtract one:
        len -= (start < stop < stop′) + (start > stop > stop′)
    end
    steprangelen_hp(T, start, step, 0, len, 1)
end

step(r::StepRangeLen{T,TwicePrecision{T},TwicePrecision{T}}) where {T<:AbstractFloat} = T(r.step)
step(r::StepRangeLen{T,TwicePrecision{T},TwicePrecision{T}}) where {T} = T(r.step)

range_start_step_length(a::Real, st::IEEEFloat, len::Integer) =
    range_start_step_length(promote(a, st)..., len)

range_start_step_length(a::IEEEFloat, st::Real, len::Integer) =
    range_start_step_length(promote(a, st)..., len)

range_start_step_length(a::IEEEFloat, st::IEEEFloat, len::Integer) =
    range_start_step_length(promote(a, st)..., len)

function range_start_step_length(a::T, st::T, len::Integer) where T<:IEEEFloat
    len = len + 0 # promote with Int
    start_n, start_d = rat(a)
    step_n, step_d = rat(st)
    if start_d != 0 && step_d != 0 &&
            T(start_n/start_d) == a && T(step_n/step_d) == st
        den = lcm_unchecked(start_d, step_d)
        m = maxintfloat(T, Int)
        if abs(den*a) <= m && abs(den*st) <= m &&
                rem(den, start_d) == 0 && rem(den, step_d) == 0
            start_n = round(Int, den*a)
            step_n = round(Int, den*st)
            return floatrange(T, start_n, step_n, len, den)
        end
    end
    steprangelen_hp(T, a, st, 0, len, 1)
end

range_step_stop_length(step::Real, stop::IEEEFloat, len::Integer) =
    range_step_stop_length(promote(step, stop)..., len)

range_step_stop_length(step::IEEEFloat, stop::Real, len::Integer) =
    range_step_stop_length(promote(step, stop)..., len)

function range_step_stop_length(step::IEEEFloat, stop::IEEEFloat, len::Integer)
    r = range_start_step_length(stop, negate(step), len)
    reverse(r)
end

# This assumes that r.step has already been split so that (0:len-1)*r.step.hi is exact
function unsafe_getindex(r::StepRangeLen{T,<:TwicePrecision,<:TwicePrecision}, i::Integer) where T
    # Very similar to _getindex_hiprec, but optimized to avoid a 2nd call to add12
    @inline
    i isa Bool && throw(ArgumentError("invalid index: $i of type Bool"))
    u = oftype(r.offset, i) - r.offset
    shift_hi, shift_lo = u*r.step.hi, u*r.step.lo
    x_hi, x_lo = add12(r.ref.hi, shift_hi)
    T(x_hi + (x_lo + (shift_lo + r.ref.lo)))
end

function _getindex_hiprec(r::StepRangeLen{<:Any,<:TwicePrecision,<:TwicePrecision}, i::Integer)
    i isa Bool && throw(ArgumentError("invalid index: $i of type Bool"))
    u = oftype(r.offset, i) - r.offset
    shift_hi, shift_lo = u*r.step.hi, u*r.step.lo
    x_hi, x_lo = add12(r.ref.hi, shift_hi)
    x_hi, x_lo = add12(x_hi, x_lo + (shift_lo + r.ref.lo))
    TwicePrecision(x_hi, x_lo)
end

function getindex(r::StepRangeLen{T,<:TwicePrecision,<:TwicePrecision}, s::OrdinalRange{S}) where {T, S<:Integer}
    @boundscheck checkbounds(r, s)
    len = length(s)
    L = typeof(len)
    sstep = step_hp(s)
    rstep = step_hp(r)
    if S === Bool
        #rstep *= one(sstep)
        if len == 0
            return StepRangeLen{T}(first(r), rstep, zero(L), oneunit(L))
        elseif len == 1
            if first(s)
                return StepRangeLen{T}(first(r), rstep, oneunit(L), oneunit(L))
            else
                return StepRangeLen{T}(first(r), rstep, zero(L), oneunit(L))
            end
        else # len == 2
            return StepRangeLen{T}(last(r), step(r), oneunit(L), oneunit(L))
        end
    else
        soffset = round(L, (r.offset - first(s))/sstep + 1)
        soffset = clamp(soffset, oneunit(L), len)
        ioffset = L(first(s) + (soffset - oneunit(L)) * sstep)
        if sstep == 1 || len < 2
            newstep = rstep #* one(sstep)
        else
            newstep = rstep * sstep
            newstep = twiceprecision(newstep, nbitslen(T, len, soffset))
        end
        soffset = max(oneunit(L), soffset)
        if ioffset == r.offset
            return StepRangeLen{T}(r.ref, newstep, len, soffset)
        else
            return StepRangeLen{T}(r.ref + (ioffset-r.offset)*rstep, newstep, len, soffset)
        end
    end
end

*(x::Real, r::StepRangeLen{<:Real,<:TwicePrecision}) =
    StepRangeLen(x*r.ref, twiceprecision(x*r.step, nbitslen(r)), length(r), r.offset)
*(r::StepRangeLen{<:Real,<:TwicePrecision}, x::Real) = x*r
/(r::StepRangeLen{<:Real,<:TwicePrecision}, x::Real) =
    StepRangeLen(r.ref/x, twiceprecision(r.step/x, nbitslen(r)), length(r), r.offset)

StepRangeLen{T,R,S,L}(r::StepRangeLen{T,R,S,L}) where {T<:AbstractFloat,R<:TwicePrecision,S<:TwicePrecision,L} = r

StepRangeLen{T,R,S,L}(r::StepRangeLen) where {T<:AbstractFloat,R<:TwicePrecision,S<:TwicePrecision,L} =
    _convertSRL(StepRangeLen{T,R,S,L}, r)

StepRangeLen{Float64}(r::StepRangeLen) =
    _convertSRL(StepRangeLen{Float64,TwicePrecision{Float64},TwicePrecision{Float64},Int}, r)
StepRangeLen{T}(r::StepRangeLen) where {T<:IEEEFloat} =
    _convertSRL(StepRangeLen{T,Float64,Float64,Int}, r)

StepRangeLen{Float64}(r::AbstractRange) =
    _convertSRL(StepRangeLen{Float64,TwicePrecision{Float64},TwicePrecision{Float64},Int}, r)
StepRangeLen{T}(r::AbstractRange) where {T<:IEEEFloat} =
    _convertSRL(StepRangeLen{T,Float64,Float64,Int}, r)

function _convertSRL(::Type{StepRangeLen{T,R,S,L}}, r::StepRangeLen{<:Integer}) where {T,R,S,L}
    StepRangeLen{T,R,S,L}(R(r.ref), S(r.step), L(length(r)), L(r.offset))
end

function _convertSRL(::Type{StepRangeLen{T,R,S,L}}, r::AbstractRange{<:Integer}) where {T,R,S,L}
    StepRangeLen{T,R,S,L}(R(first(r)), S(step(r)), L(length(r)))
end

function _convertSRL(::Type{StepRangeLen{T,R,S,L}}, r::AbstractRange{U}) where {T,R,S,L,U}
    # if start and step have a rational approximation in the old type,
    # then we transfer that rational approximation to the new type
    f, s = first(r), step(r)
    start_n, start_d = rat(f)
    step_n, step_d = rat(s)
    if start_d != 0 && step_d != 0 &&
            U(start_n/start_d) == f && U(step_n/step_d) == s
        den = lcm_unchecked(start_d, step_d)
        m = maxintfloat(T, Int)
        if den != 0 && abs(f*den) <= m && abs(s*den) <= m &&
                rem(den, start_d) == 0 && rem(den, step_d) == 0
            start_n = round(Int, f*den)
            step_n = round(Int, s*den)
            return floatrange(T, start_n, step_n, L(length(r)), den)
        end
    end
    return __convertSRL(StepRangeLen{T,R,S,L}, r)
end

function __convertSRL(::Type{StepRangeLen{T,R,S,L}}, r::StepRangeLen{U}) where {T,R,S,L,U}
    StepRangeLen{T,R,S,L}(R(r.ref), S(r.step), L(length(r)), L(r.offset))
end
function __convertSRL(::Type{StepRangeLen{T,R,S,L}}, r::AbstractRange{U}) where {T,R,S,L,U}
    StepRangeLen{T,R,S,L}(R(first(r)), S(step(r)), L(length(r)))
end

function sum(r::StepRangeLen)
    l = length(r)
    # Compute the contribution of step over all indices.
    # Indexes on opposite side of r.offset contribute with opposite sign,
    #    r.step * (sum(1:np) - sum(1:nn))
    np, nn = l - r.offset, r.offset - 1  # positive, negative
    # To prevent overflow in sum(1:n), multiply its factors by the step
    sp, sn = sumpair(np), sumpair(nn)
    W = widen(typeof(l))
    Δn = W(sp[1]) * W(sp[2]) - W(sn[1]) * W(sn[2])
    s = r.step * Δn
    # Add in contributions of ref
    ref = r.ref * l
    convert(eltype(r), s + ref)
end
function sum(r::StepRangeLen{<:Any,<:TwicePrecision,<:TwicePrecision})
    l = length(r)
    # Compute the contribution of step over all indices.
    # Indexes on opposite side of r.offset contribute with opposite sign,
    #    r.step * (sum(1:np) - sum(1:nn))
    np, nn = l - r.offset, r.offset - 1  # positive, negative
    # To prevent overflow in sum(1:n), multiply its factors by the step
    sp, sn = sumpair(np), sumpair(nn)
    tp = _tp_prod(r.step, sp[1], sp[2])
    tn = _tp_prod(r.step, sn[1], sn[2])
    s_hi, s_lo = add12(tp.hi, -tn.hi)
    s_lo += tp.lo - tn.lo
    # Add in contributions of ref
    ref = r.ref * l
    sm_hi, sm_lo = add12(s_hi, ref.hi)
    add12(sm_hi, sm_lo + ref.lo)[1]
end

# sum(1:n) as a product of two integers
sumpair(n::Integer) = iseven(n) ? (n+1, n>>1) : (n, (n+1)>>1)

function +(r1::StepRangeLen{T,R}, r2::StepRangeLen{T,R}) where T where R<:TwicePrecision
    len = length(r1)
    (len == length(r2) ||
        throw(DimensionMismatch("argument dimensions must match")))
    if r1.offset == r2.offset
        imid = r1.offset
        ref = r1.ref + r2.ref
    else
        imid = round(typeof(len), (r1.offset+r2.offset)/2)
        ref1mid = _getindex_hiprec(r1, imid)
        ref2mid = _getindex_hiprec(r2, imid)
        ref = ref1mid + ref2mid
    end
    step = twiceprecision(r1.step + r2.step, nbitslen(T, len, imid))
    StepRangeLen{T,typeof(ref),typeof(step),typeof(len)}(ref, step, len, imid)
end

## LinRange

# For Float16, Float32, and Float64, this returns a StepRangeLen
function range_start_stop_length(start::T, stop::T, len::Integer) where {T<:IEEEFloat}
    len = len + 0 # promote with Int
    len < 2 && return _linspace1(T, start, stop, len)
    if start == stop
        return steprangelen_hp(T, start, zero(T), 0, len, 1)
    end
    # Attempt to find exact rational approximations
    start_n, start_d = rat(start)
    stop_n, stop_d = rat(stop)
    if start_d != 0 && stop_d != 0
        den = lcm_unchecked(start_d, stop_d)
        m = maxintfloat(T, Int)
        if den != 0 && abs(den*start) <= m && abs(den*stop) <= m
            start_n = round(Int, den*start)
            stop_n = round(Int, den*stop)
            if T(start_n/den) == start && T(stop_n/den) == stop
                return _linspace(T, start_n, stop_n, len, den)
            end
        end
    end
    _linspace(start, stop, len)
end

function _linspace(start::T, stop::T, len::Integer) where {T<:IEEEFloat}
    len = len + 0 # promote with Int
    (isfinite(start) && isfinite(stop)) || throw(ArgumentError("start and stop must be finite, got $start and $stop"))
    # Find the index that returns the smallest-magnitude element
    Δ, Δfac = stop-start, 1
    if !isfinite(Δ)   # handle overflow for large endpoints
        Δ, Δfac = stop/len - start/len, len
    end
    tmin = -(start/Δ)/Δfac            # t such that (1-t)*start + t*stop == 0
    L = typeof(len)
    lenn1 = len - oneunit(L)
    imin = round(L, tmin*lenn1 + 1) # index approximately corresponding to t
    if 1 < imin < len
        # The smallest-magnitude element is in the interior
        t = (imin - 1)/lenn1
        ref = T((1-t)*start + t*stop)
        step = imin-1 < len-imin ? (ref-start)/(imin-1) : (stop-ref)/(len-imin)
    elseif imin <= 1
        imin = oneunit(L)
        ref = start
        step = (Δ/(lenn1))*Δfac
    else
        imin = len
        ref = stop
        step = (Δ/(lenn1))*Δfac
    end
    if len == 2 && !isfinite(step)
        # For very large endpoints where step overflows, exploit the
        # split-representation to handle the overflow
        return steprangelen_hp(T, start, (-start, stop), 0, len, oneunit(L))
    end
    # 2x calculations to get high precision endpoint matching while also
    # preventing overflow in ref_hi+(i-offset)*step_hi
    m, k = prevfloat(floatmax(T)), max(imin-1, len-imin)
    step_hi_pre = clamp(step, max(-(m+ref)/k, (-m+ref)/k), min((m-ref)/k, (m+ref)/k))
    nb = nbitslen(T, len, imin)
    step_hi = truncbits(step_hi_pre, nb)
    x1_hi, x1_lo = add12((1-imin)*step_hi, ref)
    x2_hi, x2_lo = add12((len-imin)*step_hi, ref)
    a, b = (start - x1_hi) - x1_lo, (stop - x2_hi) - x2_lo
    step_lo = (b - a)/(len - 1)
    ref_lo = a - (1 - imin)*step_lo
    steprangelen_hp(T, (ref, ref_lo), (step_hi, step_lo), 0, len, imin)
end

# range for rational numbers, start = start_n/den, stop = stop_n/den
# Note this returns a StepRangeLen
_linspace(::Type{T}, start::Integer, stop::Integer, len::Integer) where {T<:IEEEFloat} = _linspace(T, start, stop, len, one(start))
function _linspace(::Type{T}, start_n::Integer, stop_n::Integer, len::Integer, den::Integer) where T<:IEEEFloat
    len = len + 0 # promote with Int
    len < 2 && return _linspace1(T, start_n/den, stop_n/den, len)
    L = typeof(len)
    start_n == stop_n && return steprangelen_hp(T, (start_n, den), (zero(start_n), den), 0, len, oneunit(L))
    tmin = -start_n/(Float64(stop_n) - Float64(start_n))
    imin = round(typeof(len), tmin*(len-1)+1)
    imin = clamp(imin, oneunit(L), len)
    W = widen(L)
    start_n = W(start_n)
    stop_n = W(stop_n)
    ref_num = W(len-imin) * start_n + W(imin-1) * stop_n
    ref_denom = W(len-1) * den
    ref = (ref_num, ref_denom)
    step_full = (stop_n - start_n, ref_denom)
    steprangelen_hp(T, ref, step_full, nbitslen(T, len, imin), len, imin)
end

# For len < 2
function _linspace1(::Type{T}, start, stop, len::Integer) where T<:IEEEFloat
    len >= 0 || throw(ArgumentError("range($start, stop=$stop, length=$len): negative length"))
    if len <= 1
        len == 1 && (start == stop || throw(ArgumentError("range($start, stop=$stop, length=$len): endpoints differ")))
        # Ensure that first(r)==start and last(r)==stop even for len==0
        # The output type must be consistent with steprangelen_hp
        if T<:Union{Float32,Float16}
            return StepRangeLen{T}(Float64(start), Float64(start) - Float64(stop), len, 1)
        else # T == Float64
            return StepRangeLen(TwicePrecision(start, zero(T)), TwicePrecision(start, -stop), len, 1)
        end
    end
    throw(ArgumentError("should only be called for len < 2, got $len"))
end

### Numeric utilities

# Approximate x with a rational representation as a pair of Int values.
# Guaranteed to return, but not guaranteed to return a precise answer.
# https://en.wikipedia.org/wiki/Continued_fraction#Best_rational_approximations
function rat(x)
    y = x
    a = d = 1
    b = c = 0
    m = maxintfloat(narrow(typeof(x)), Int)
    while abs(y) <= m
        f = trunc(Int, y)
        y -= f
        a, c = f*a + c, a
        b, d = f*b + d, b
        max(abs(a), abs(b)) <= convert(Int,m) || return c, d
        oftype(x,a)/oftype(x,b) == x && break
        y = inv(y)
    end
    return a, b
end

# This version of lcm does not check for overflows
lcm_unchecked(a::T, b::T) where T<:Integer = a * div(b, gcd(a, b))

narrow(::Type{T}) where {T<:AbstractFloat} = Float64
narrow(::Type{Float64}) = Float32
narrow(::Type{Float32}) = Float16
narrow(::Type{Float16}) = Float16

function _tp_prod(t::TwicePrecision, x, y...)
    @inline
    _tp_prod(t * x, y...)
end
_tp_prod(t::TwicePrecision) = t
<(x::TwicePrecision{T}, y::TwicePrecision{T}) where {T} =
    x.hi < y.hi || ((x.hi == y.hi) & (x.lo < y.lo))

isbetween(a, x, b) = a <= x <= b || b <= x <= a
N   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/complex.jl�{      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
    Complex{T<:Real} <: Number

Complex number type with real and imaginary part of type `T`.

`ComplexF16`, `ComplexF32` and `ComplexF64` are aliases for
`Complex{Float16}`, `Complex{Float32}` and `Complex{Float64}` respectively.

See also: [`Real`](@ref), [`complex`](@ref), [`real`](@ref).
"""
struct Complex{T<:Real} <: Number
    re::T
    im::T
end
Complex(x::Real, y::Real) = Complex(promote(x,y)...)
Complex(x::Real) = Complex(x, zero(x))

"""
    im

The imaginary unit.

See also: [`imag`](@ref), [`angle`](@ref), [`complex`](@ref).

# Examples
```jldoctest
julia> im * im
-1 + 0im

julia> (2.0 + 3im)^2
-5.0 + 12.0im
```
"""
const im = Complex(false, true)

const ComplexF64  = Complex{Float64}
const ComplexF32  = Complex{Float32}
const ComplexF16  = Complex{Float16}

Complex{T}(x::Real) where {T<:Real} = Complex{T}(x,0)
Complex{T}(z::Complex) where {T<:Real} = Complex{T}(real(z),imag(z))
(::Type{T})(z::Complex) where {T<:Real} =
    isreal(z) ? T(real(z))::T : throw(InexactError(nameof(T), T, z))

Complex(z::Complex) = z

promote_rule(::Type{Complex{T}}, ::Type{S}) where {T<:Real,S<:Real} =
    Complex{promote_type(T,S)}
promote_rule(::Type{Complex{T}}, ::Type{Complex{S}}) where {T<:Real,S<:Real} =
    Complex{promote_type(T,S)}

widen(::Type{Complex{T}}) where {T} = Complex{widen(T)}

float(::Type{Complex{T}}) where {T<:AbstractFloat} = Complex{T}
float(::Type{Complex{T}}) where {T} = Complex{float(T)}

"""
    real(z)

Return the real part of the complex number `z`.

See also: [`imag`](@ref), [`reim`](@ref), [`complex`](@ref), [`isreal`](@ref), [`Real`](@ref).

# Examples
```jldoctest
julia> real(1 + 3im)
1
```
"""
real(z::Complex) = z.re

"""
    imag(z)

Return the imaginary part of the complex number `z`.

See also: [`conj`](@ref), [`reim`](@ref), [`adjoint`](@ref), [`angle`](@ref).

# Examples
```jldoctest
julia> imag(1 + 3im)
3
```
"""
imag(z::Complex) = z.im
real(x::Real) = x
imag(x::Real) = zero(x)

"""
    reim(z)

Return a tuple of the real and imaginary parts of the complex number `z`.

# Examples
```jldoctest
julia> reim(1 + 3im)
(1, 3)
```
"""
reim(z) = (real(z), imag(z))

"""
    real(T::Type)

Return the type that represents the real part of a value of type `T`.
e.g: for `T == Complex{R}`, returns `R`.
Equivalent to `typeof(real(zero(T)))`.

# Examples
```jldoctest
julia> real(Complex{Int})
Int64

julia> real(Float64)
Float64
```
"""
real(T::Type) = typeof(real(zero(T)))
real(::Type{T}) where {T<:Real} = T
real(C::Type{<:Complex}) = fieldtype(C, 1)
real(::Type{Union{}}, slurp...) = Union{}(im)

"""
    isreal(x) -> Bool

Test whether `x` or all its elements are numerically equal to some real number
including infinities and NaNs. `isreal(x)` is true if `isequal(x, real(x))`
is true.

# Examples
```jldoctest
julia> isreal(5.)
true

julia> isreal(1 - 3im)
false

julia> isreal(Inf + 0im)
true

julia> isreal([4.; complex(0,1)])
false
```
"""
isreal(x::Real) = true
isreal(z::Complex) = iszero(imag(z))
isinteger(z::Complex) = isreal(z) & isinteger(real(z))
isfinite(z::Complex) = isfinite(real(z)) & isfinite(imag(z))
isnan(z::Complex) = isnan(real(z)) | isnan(imag(z))
isinf(z::Complex) = isinf(real(z)) | isinf(imag(z))
iszero(z::Complex) = iszero(real(z)) & iszero(imag(z))
isone(z::Complex) = isone(real(z)) & iszero(imag(z))

"""
    complex(r, [i])

Convert real numbers or arrays to complex. `i` defaults to zero.

# Examples
```jldoctest
julia> complex(7)
7 + 0im

julia> complex([1, 2, 3])
3-element Vector{Complex{Int64}}:
 1 + 0im
 2 + 0im
 3 + 0im
```
"""
complex(z::Complex) = z
complex(x::Real) = Complex(x)
complex(x::Real, y::Real) = Complex(x, y)

"""
    complex(T::Type)

Return an appropriate type which can represent a value of type `T` as a complex number.
Equivalent to `typeof(complex(zero(T)))`.

# Examples
```jldoctest
julia> complex(Complex{Int})
Complex{Int64}

julia> complex(Int)
Complex{Int64}
```
"""
complex(::Type{T}) where {T<:Real} = Complex{T}
complex(::Type{Complex{T}}) where {T<:Real} = Complex{T}

flipsign(x::Complex, y::Real) = ifelse(signbit(y), -x, x)

function show(io::IO, z::Complex)
    r, i = reim(z)
    compact = get(io, :compact, false)::Bool
    show(io, r)
    if signbit(i) && !isnan(i)
        print(io, compact ? "-" : " - ")
        if isa(i,Signed) && !isa(i,BigInt) && i == typemin(typeof(i))
            show(io, -widen(i))
        else
            show(io, -i)
        end
    else
        print(io, compact ? "+" : " + ")
        show(io, i)
    end
    if !(isa(i,Integer) && !isa(i,Bool) || isa(i,AbstractFloat) && isfinite(i))
        print(io, "*")
    end
    print(io, "im")
end
show(io::IO, z::Complex{Bool}) =
    print(io, z == im ? "im" : "Complex($(z.re),$(z.im))")

function show_unquoted(io::IO, z::Complex, ::Int, prec::Int)
    if operator_precedence(:+) <= prec
        print(io, "(")
        show(io, z)
        print(io, ")")
    else
        show(io, z)
    end
end

function read(s::IO, ::Type{Complex{T}}) where T<:Real
    r = read(s,T)
    i = read(s,T)
    Complex{T}(r,i)
end
function write(s::IO, z::Complex)
    write(s,real(z),imag(z))
end

## byte order swaps: real and imaginary part are swapped individually
bswap(z::Complex) = Complex(bswap(real(z)), bswap(imag(z)))

## equality and hashing of complex numbers ##

==(z::Complex, w::Complex) = (real(z) == real(w)) & (imag(z) == imag(w))
==(z::Complex, x::Real) = isreal(z) && real(z) == x
==(x::Real, z::Complex) = isreal(z) && real(z) == x

isequal(z::Complex, w::Complex) = isequal(real(z),real(w))::Bool & isequal(imag(z),imag(w))::Bool
isequal(z::Complex, w::Real) = isequal(real(z),w)::Bool & isequal(imag(z),zero(w))::Bool
isequal(z::Real, w::Complex) = isequal(z,real(w))::Bool & isequal(zero(z),imag(w))::Bool

in(x::Complex, r::AbstractRange{<:Real}) = isreal(x) && real(x) in r

if UInt === UInt64
    const h_imag = 0x32a7a07f3e7cd1f9
else
    const h_imag = 0x3e7cd1f9
end
const hash_0_imag = hash(0, h_imag)

function hash(z::Complex, h::UInt)
    # TODO: with default argument specialization, this would be better:
    # hash(real(z), h ⊻ hash(imag(z), h ⊻ h_imag) ⊻ hash(0, h ⊻ h_imag))
    hash(real(z), h ⊻ hash(imag(z), h_imag) ⊻ hash_0_imag)
end

## generic functions of complex numbers ##

"""
    conj(z)

Compute the complex conjugate of a complex number `z`.

See also: [`angle`](@ref), [`adjoint`](@ref).

# Examples
```jldoctest
julia> conj(1 + 3im)
1 - 3im
```
"""
conj(z::Complex) = Complex(real(z),-imag(z))
abs(z::Complex)  = hypot(real(z), imag(z))
abs2(z::Complex) = real(z)*real(z) + imag(z)*imag(z)
function inv(z::Complex)
    c, d = reim(z)
    (isinf(c) | isinf(d)) && return complex(copysign(zero(c), c), flipsign(-zero(d), d))
    complex(c, -d)/(c * c + d * d)
end
inv(z::Complex{<:Integer}) = inv(float(z))

+(z::Complex) = Complex(+real(z), +imag(z))
-(z::Complex) = Complex(-real(z), -imag(z))
+(z::Complex, w::Complex) = Complex(real(z) + real(w), imag(z) + imag(w))
-(z::Complex, w::Complex) = Complex(real(z) - real(w), imag(z) - imag(w))
*(z::Complex, w::Complex) = Complex(real(z) * real(w) - imag(z) * imag(w),
                                    real(z) * imag(w) + imag(z) * real(w))

muladd(z::Complex, w::Complex, x::Complex) =
    Complex(muladd(real(z), real(w), -muladd(imag(z), imag(w), -real(x))),
            muladd(real(z), imag(w),  muladd(imag(z), real(w),  imag(x))))

# handle Bool and Complex{Bool}
# avoid type signature ambiguity warnings
+(x::Bool, z::Complex{Bool}) = Complex(x + real(z), imag(z))
+(z::Complex{Bool}, x::Bool) = Complex(real(z) + x, imag(z))
-(x::Bool, z::Complex{Bool}) = Complex(x - real(z), - imag(z))
-(z::Complex{Bool}, x::Bool) = Complex(real(z) - x, imag(z))
*(x::Bool, z::Complex{Bool}) = Complex(x * real(z), x * imag(z))
*(z::Complex{Bool}, x::Bool) = Complex(real(z) * x, imag(z) * x)

+(x::Bool, z::Complex) = Complex(x + real(z), imag(z))
+(z::Complex, x::Bool) = Complex(real(z) + x, imag(z))
-(x::Bool, z::Complex) = Complex(x - real(z), - imag(z))
-(z::Complex, x::Bool) = Complex(real(z) - x, imag(z))
*(x::Bool, z::Complex) = Complex(x * real(z), x * imag(z))
*(z::Complex, x::Bool) = Complex(real(z) * x, imag(z) * x)

+(x::Real, z::Complex{Bool}) = Complex(x + real(z), imag(z))
+(z::Complex{Bool}, x::Real) = Complex(real(z) + x, imag(z))
function -(x::Real, z::Complex{Bool})
    # we don't want the default type for -(Bool)
    re = x-real(z)
    Complex(re, - oftype(re, imag(z)))
end
-(z::Complex{Bool}, x::Real) = Complex(real(z) - x, imag(z))
*(x::Real, z::Complex{Bool}) = Complex(x * real(z), x * imag(z))
*(z::Complex{Bool}, x::Real) = Complex(real(z) * x, imag(z) * x)

# adding or multiplying real & complex is common
+(x::Real, z::Complex) = Complex(x + real(z), imag(z))
+(z::Complex, x::Real) = Complex(x + real(z), imag(z))
function -(x::Real, z::Complex)
    # we don't want the default type for -(Bool)
    re = x - real(z)
    Complex(re, - oftype(re, imag(z)))
end
-(z::Complex, x::Real) = Complex(real(z) - x, imag(z))
*(x::Real, z::Complex) = Complex(x * real(z), x * imag(z))
*(z::Complex, x::Real) = Complex(x * real(z), x * imag(z))

muladd(x::Real, z::Complex, y::Number) = muladd(z, x, y)
muladd(z::Complex, x::Real, y::Real) = Complex(muladd(real(z),x,y), imag(z)*x)
muladd(z::Complex, x::Real, w::Complex) =
    Complex(muladd(real(z),x,real(w)), muladd(imag(z),x,imag(w)))
muladd(x::Real, y::Real, z::Complex) = Complex(muladd(x,y,real(z)), imag(z))
muladd(z::Complex, w::Complex, x::Real) =
    Complex(muladd(real(z), real(w), -muladd(imag(z), imag(w), -x)),
            muladd(real(z), imag(w), imag(z) * real(w)))

/(a::R, z::S) where {R<:Real,S<:Complex} = (T = promote_type(R,S); a*inv(T(z)))
/(z::Complex, x::Real) = Complex(real(z)/x, imag(z)/x)

function /(a::Complex{T}, b::Complex{T}) where T<:Real
    are = real(a); aim = imag(a); bre = real(b); bim = imag(b)
    if (isinf(bre) | isinf(bim))
        if isfinite(a)
            return complex(zero(T)*sign(are)*sign(bre), -zero(T)*sign(aim)*sign(bim))
        end
        return T(NaN)+T(NaN)*im
    end
    if abs(bre) <= abs(bim)
        r = bre / bim
        den = bim + r*bre
        Complex((are*r + aim)/den, (aim*r - are)/den)
    else
        r = bim / bre
        den = bre + r*bim
        Complex((are + aim*r)/den, (aim - are*r)/den)
    end
end

function /(z::Complex{T}, w::Complex{T}) where {T<:Union{Float16,Float32}}
    c, d = reim(widen(w))
    a, b = reim(widen(z))
    if (isinf(c) | isinf(d))
        if isfinite(z)
            return complex(zero(T)*sign(real(z))*sign(real(w)), -zero(T)*sign(imag(z))*sign(imag(w)))
        end
        return T(NaN)+T(NaN)*im
    end
    mag = inv(muladd(c, c, d^2))
    re_part = muladd(a, c, b*d)
    im_part = muladd(b, c, -a*d)
    return oftype(z, Complex(re_part*mag, im_part*mag))
end

# robust complex division for double precision
# variables are scaled & unscaled to avoid over/underflow, if necessary
# based on arxiv.1210.4539
#             a + i*b
#  p + i*q = ---------
#             c + i*d
function /(z::ComplexF64, w::ComplexF64)
    a, b = reim(z); c, d = reim(w)
    absa = abs(a); absb = abs(b);  ab = absa >= absb ? absa : absb # equiv. to max(abs(a),abs(b)) but without NaN-handling (faster)
    absc = abs(c); absd = abs(d);  cd = absc >= absd ? absc : absd
    if (isinf(c) | isinf(d))
        if isfinite(z)
            return complex(0.0*sign(a)*sign(c), -0.0*sign(b)*sign(d))
        end
        return NaN+NaN*im
    end
    halfov = 0.5*floatmax(Float64)              # overflow threshold
    twounϵ = floatmin(Float64)*2.0/eps(Float64) # underflow threshold

    # actual division operations
    if  ab>=halfov || ab<=twounϵ || cd>=halfov || cd<=twounϵ # over/underflow case
        p,q = scaling_cdiv(a,b,c,d,ab,cd) # scales a,b,c,d before division (unscales after)
    else
        p,q = cdiv(a,b,c,d)
    end

    return ComplexF64(p,q)
end

# sub-functionality for /(z::ComplexF64, w::ComplexF64)
@inline function cdiv(a::Float64, b::Float64, c::Float64, d::Float64)
    if abs(d)<=abs(c)
        p,q = robust_cdiv1(a,b,c,d)
    else
        p,q = robust_cdiv1(b,a,d,c)
        q = -q
    end
    return p,q
end
@noinline function scaling_cdiv(a::Float64, b::Float64, c::Float64, d::Float64, ab::Float64, cd::Float64)
    # this over/underflow functionality is outlined for performance, cf. #29688
    a,b,c,d,s = scaleargs_cdiv(a,b,c,d,ab,cd)
    p,q = cdiv(a,b,c,d)
    return p*s,q*s
end
function scaleargs_cdiv(a::Float64, b::Float64, c::Float64, d::Float64, ab::Float64, cd::Float64)
    ϵ      = eps(Float64)
    halfov = 0.5*floatmax(Float64)
    twounϵ = floatmin(Float64)*2.0/ϵ
    bs     = 2.0/(ϵ*ϵ)

    # scaling
    s = 1.0
    if ab >= halfov
        a*=0.5; b*=0.5; s*=2.0  # scale down a,b
    elseif ab <= twounϵ
        a*=bs;  b*=bs;  s/=bs   # scale up a,b
    end
    if cd >= halfov
        c*=0.5; d*=0.5; s*=0.5  # scale down c,d
    elseif cd <= twounϵ
        c*=bs;  d*=bs;  s*=bs   # scale up c,d
    end

    return a,b,c,d,s
end
@inline function robust_cdiv1(a::Float64, b::Float64, c::Float64, d::Float64)
    r = d/c
    t = 1.0/(c+d*r)
    p = robust_cdiv2(a,b,c,d,r,t)
    q = robust_cdiv2(b,-a,c,d,r,t)
    return p,q
end
function robust_cdiv2(a::Float64, b::Float64, c::Float64, d::Float64, r::Float64, t::Float64)
    if r != 0
        br = b*r
        return (br != 0 ? (a+br)*t : a*t + (b*t)*r)
    else
        return (a + d*(b/c)) * t
    end
end

function inv(z::Complex{T}) where T<:Union{Float16,Float32}
    c, d = reim(widen(z))
    (isinf(c) | isinf(d)) && return complex(copysign(zero(T), c), flipsign(-zero(T), d))
    mag = inv(muladd(c, c, d^2))
    return oftype(z, Complex(c*mag, -d*mag))
end
function inv(w::ComplexF64)
    c, d = reim(w)
    absc, absd = abs(c), abs(d)
    cd, dc = ifelse(absc>absd, (absc, absd), (absd, absc))
    # no overflow from abs2
    if sqrt(floatmin(Float64)/2) <= cd <= sqrt(floatmax(Float64)/2)
        return conj(w) / muladd(cd, cd, dc*dc)
    end
    (isinf(c) | isinf(d)) && return complex(copysign(0.0, c), flipsign(-0.0, d))

    ϵ  = eps(Float64)
    bs = 2/(ϵ*ϵ)

    # scaling
    s = 1.0
    if cd >= floatmax(Float64)/2
        c *= 0.5; d *= 0.5; s = 0.5 # scale down c, d
    elseif cd <= 2floatmin(Float64)/ϵ
        c *= bs;  d *= bs;  s = bs  # scale up c, d
    end

    # inversion operations
    if absd <= absc
        p, q = robust_cinv(c, d)
    else
        q, p = robust_cinv(-d, -c)
    end
    return ComplexF64(p*s, q*s)
end
function robust_cinv(c::Float64, d::Float64)
    r = d/c
    z = muladd(d, r, c)
    p = 1.0/z
    q = -r/z
    return p, q
end

function ssqs(x::T, y::T) where T<:Real
    k::Int = 0
    ρ = x*x + y*y
    if !isfinite(ρ) && (isinf(x) || isinf(y))
        ρ = convert(T, Inf)
    elseif isinf(ρ) || (ρ==0 && (x!=0 || y!=0)) || ρ<nextfloat(zero(T))/(2*eps(T)^2)
        m::T = max(abs(x), abs(y))
        k = m==0 ? m : exponent(m)
        xk, yk = ldexp(x,-k), ldexp(y,-k)
        ρ = xk*xk + yk*yk
    end
    ρ, k
end

function sqrt(z::Complex)
    z = float(z)
    x, y = reim(z)
    if x==y==0
        return Complex(zero(x),y)
    end
    ρ, k::Int = ssqs(x, y)
    if isfinite(x) ρ=ldexp(abs(x),-k)+sqrt(ρ) end
    if isodd(k)
        k = div(k-1,2)
    else
        k = div(k,2)-1
        ρ += ρ
    end
    ρ = ldexp(sqrt(ρ),k) #sqrt((abs(z)+abs(x))/2) without over/underflow
    ξ = ρ
    η = y
    if ρ != 0
        if isfinite(η) η=(η/ρ)/2 end
        if x<0
            ξ = abs(η)
            η = copysign(ρ,y)
        end
    end
    Complex(ξ,η)
end

# function sqrt(z::Complex)
#     rz = float(real(z))
#     iz = float(imag(z))
#     r = sqrt((hypot(rz,iz)+abs(rz))/2)
#     if r == 0
#         return Complex(zero(iz), iz)
#     end
#     if rz >= 0
#         return Complex(r, iz/r/2)
#     end
#     return Complex(abs(iz)/r/2, copysign(r,iz))
# end

"""
    cis(x)

More efficient method for `exp(im*x)` by using Euler's formula: ``cos(x) + i sin(x) = \\exp(i x)``.

See also [`cispi`](@ref), [`sincos`](@ref), [`exp`](@ref), [`angle`](@ref).

# Examples
```jldoctest
julia> cis(π) ≈ -1
true
```
"""
function cis end
function cis(theta::Real)
    s, c = sincos(theta)
    Complex(c, s)
end

function cis(z::Complex)
    v = exp(-imag(z))
    s, c = sincos(real(z))
    Complex(v * c, v * s)
end

"""
    cispi(x)

More accurate method for `cis(pi*x)` (especially for large `x`).

See also [`cis`](@ref), [`sincospi`](@ref), [`exp`](@ref), [`angle`](@ref).

# Examples
```jldoctest
julia> cispi(10000)
1.0 + 0.0im

julia> cispi(0.25 + 1im)
0.030556854645954562 + 0.03055685464595456im
```

!!! compat "Julia 1.6"
    This function requires Julia 1.6 or later.
"""
function cispi end
cispi(theta::Real) = Complex(reverse(sincospi(theta))...)

function cispi(z::Complex)
    v = exp(-(pi*imag(z)))
    s, c = sincospi(real(z))
    Complex(v * c, v * s)
end

"""
    angle(z)

Compute the phase angle in radians of a complex number `z`.

See also: [`atan`](@ref), [`cis`](@ref).

# Examples
```jldoctest
julia> rad2deg(angle(1 + im))
45.0

julia> rad2deg(angle(1 - im))
-45.0

julia> rad2deg(angle(-1 - im))
-135.0
```
"""
angle(z::Complex) = atan(imag(z), real(z))

function log(z::Complex)
    z = float(z)
    T = typeof(real(z))
    T1  = convert(T,5)/convert(T,4)
    T2  = convert(T,3)
    ln2 = log(convert(T,2))  #0.6931471805599453
    x, y = reim(z)
    ρ, k = ssqs(x,y)
    ax = abs(x)
    ay = abs(y)
    if ax < ay
        θ, β = ax, ay
    else
        θ, β = ay, ax
    end
    if k==0 && (0.5 < β*β) && (β <= T1 || ρ < T2)
        ρρ = log1p((β-1)*(β+1)+θ*θ)/2
    else
        ρρ = log(ρ)/2 + k*ln2
    end
    Complex(ρρ, angle(z))
end

# function log(z::Complex)
#     ar = abs(real(z))
#     ai = abs(imag(z))
#     if ar < ai
#         r = ar/ai
#         re = log(ai) + log1p(r*r)/2
#     else
#         if ar == 0
#             re = isnan(ai) ? ai : -inv(ar)
#         elseif isinf(ai)
#             re = oftype(ar,Inf)
#         else
#             r = ai/ar
#             re = log(ar) + log1p(r*r)/2
#         end
#     end
#     Complex(re, angle(z))
# end

function log10(z::Complex)
    a = log(z)
    a/log(oftype(real(a),10))
end
function log2(z::Complex)
    a = log(z)
    a/log(oftype(real(a),2))
end

function exp(z::Complex)
    zr, zi = reim(z)
    if isnan(zr)
        Complex(zr, zi==0 ? zi : zr)
    elseif !isfinite(zi)
        if zr == Inf
            Complex(-zr, oftype(zr,NaN))
        elseif zr == -Inf
            Complex(-zero(zr), copysign(zero(zi), zi))
        else
            Complex(oftype(zr,NaN), oftype(zi,NaN))
        end
    else
        er = exp(zr)
        if iszero(zi)
            Complex(er, zi)
        else
            s, c = sincos(zi)
            Complex(er * c, er * s)
        end
    end
end

function expm1(z::Complex{T}) where T<:Real
    Tf = float(T)
    zr,zi = reim(z)
    if isnan(zr)
        Complex(zr, zi==0 ? zi : zr)
    elseif !isfinite(zi)
        if zr == Inf
            Complex(-zr, oftype(zr,NaN))
        elseif zr == -Inf
            Complex(-one(zr), copysign(zero(zi), zi))
        else
            Complex(oftype(zr,NaN), oftype(zi,NaN))
        end
    else
        erm1 = expm1(zr)
        if zi == 0
            Complex(erm1, zi)
        else
            er = erm1+one(erm1)
            if isfinite(er)
                wr = erm1 - 2 * er * (sin(convert(Tf, 0.5) * zi))^2
                return Complex(wr, er * sin(zi))
            else
                s, c = sincos(zi)
                return Complex(er * c, er * s)
            end
        end
    end
end

function log1p(z::Complex{T}) where T
    zr,zi = reim(z)
    if isfinite(zr)
        isinf(zi) && return log(z)
        # This is based on a well-known trick for log1p of real z,
        # allegedly due to Kahan, only modified to handle real(u) <= 0
        # differently to avoid inaccuracy near z==-2 and for correct branch cut
        u = one(float(T)) + z
        u == 1 ? convert(typeof(u), z) : real(u) <= 0 ? log(u) : log(u)*z/(u-1)
    elseif isnan(zr)
        Complex(zr, zr)
    elseif isfinite(zi)
        Complex(T(Inf), copysign(zr > 0 ? zero(T) : convert(T, pi), zi))
    else
        Complex(T(Inf), T(NaN))
    end
end

function exp2(z::Complex{T}) where T
    z = float(z)
    er = exp2(real(z))
    theta = imag(z) * log(convert(float(T), 2))
    s, c = sincos(theta)
    Complex(er * c, er * s)
end

function exp10(z::Complex{T}) where T
    z = float(z)
    er = exp10(real(z))
    theta = imag(z) * log(convert(float(T), 10))
    s, c = sincos(theta)
    Complex(er * c, er * s)
end

# _cpow helper function to avoid method ambiguity with ^(::Complex,::Real)
function _cpow(z::Union{T,Complex{T}}, p::Union{T,Complex{T}}) where T
    z = float(z)
    p = float(p)
    Tf = float(T)
    if isreal(p)
        pᵣ = real(p)
        if isinteger(pᵣ) && abs(pᵣ) < typemax(Int32)
            # |p| < typemax(Int32) serves two purposes: it prevents overflow
            # when converting p to Int, and it also turns out to be roughly
            # the crossover point for exp(p*log(z)) or similar to be faster.
            if iszero(pᵣ) # fix signs of imaginary part for z^0
                zer = flipsign(copysign(zero(Tf),pᵣ), imag(z))
                return Complex(one(Tf), zer)
            end
            ip = convert(Int, pᵣ)
            if isreal(z)
                zᵣ = real(z)
                if ip < 0
                    iszero(z) && return Complex(Tf(NaN),Tf(NaN))
                    re = power_by_squaring(inv(zᵣ), -ip)
                    im = -imag(z)
                else
                    re = power_by_squaring(zᵣ, ip)
                    im = imag(z)
                end
                # slightly tricky to get the correct sign of zero imag. part
                return Complex(re, ifelse(iseven(ip) & signbit(zᵣ), -im, im))
            else
                return ip < 0 ? power_by_squaring(inv(z), -ip) : power_by_squaring(z, ip)
            end
        elseif isreal(z)
            # (note: if both z and p are complex with ±0.0 imaginary parts,
            #  the sign of the ±0.0 imaginary part of the result is ambiguous)
            if iszero(real(z))
                return pᵣ > 0 ? complex(z) : Complex(Tf(NaN),Tf(NaN)) # 0 or NaN+NaN*im
            elseif real(z) > 0
                return Complex(real(z)^pᵣ, z isa Real ? ifelse(real(z) < 1, -imag(p), imag(p)) : flipsign(imag(z), pᵣ))
            else
                zᵣ = real(z)
                rᵖ = (-zᵣ)^pᵣ
                if isfinite(pᵣ)
                    # figuring out the sign of 0.0 when p is a complex number
                    # with zero imaginary part and integer/2 real part could be
                    # improved here, but it's not clear if it's worth it…
                    return rᵖ * complex(cospi(pᵣ), flipsign(sinpi(pᵣ),imag(z)))
                else
                    iszero(rᵖ) && return zero(Complex{Tf}) # no way to get correct signs of 0.0
                    return Complex(Tf(NaN),Tf(NaN)) # non-finite phase angle or NaN input
                end
            end
        else
            rᵖ = abs(z)^pᵣ
            ϕ = pᵣ*angle(z)
        end
    elseif isreal(z)
        iszero(z) && return real(p) > 0 ? complex(z) : Complex(Tf(NaN),Tf(NaN)) # 0 or NaN+NaN*im
        zᵣ = real(z)
        pᵣ, pᵢ = reim(p)
        if zᵣ > 0
            rᵖ = zᵣ^pᵣ
            ϕ = pᵢ*log(zᵣ)
        else
            r = -zᵣ
            θ = copysign(Tf(π),imag(z))
            rᵖ = r^pᵣ * exp(-pᵢ*θ)
            ϕ = pᵣ*θ + pᵢ*log(r)
        end
    else
        pᵣ, pᵢ = reim(p)
        r = abs(z)
        θ = angle(z)
        rᵖ = r^pᵣ * exp(-pᵢ*θ)
        ϕ = pᵣ*θ + pᵢ*log(r)
    end

    if isfinite(ϕ)
        return rᵖ * cis(ϕ)
    else
        iszero(rᵖ) && return zero(Complex{Tf}) # no way to get correct signs of 0.0
        return Complex(Tf(NaN),Tf(NaN)) # non-finite phase angle or NaN input
    end
end
^(z::Complex{T}, p::Complex{T}) where T<:Real = _cpow(z, p)
^(z::Complex{T}, p::T) where T<:Real = _cpow(z, p)
^(z::T, p::Complex{T}) where T<:Real = _cpow(z, p)

^(z::Complex, n::Bool) = n ? z : one(z)
^(z::Complex, n::Integer) = z^Complex(n)

^(z::Complex{<:AbstractFloat}, n::Bool) = n ? z : one(z)  # to resolve ambiguity
^(z::Complex{<:Integer}, n::Bool) = n ? z : one(z)        # to resolve ambiguity

^(z::Complex{<:AbstractFloat}, n::Integer) =
    n>=0 ? power_by_squaring(z,n) : power_by_squaring(inv(z),-n)
^(z::Complex{<:Integer}, n::Integer) = power_by_squaring(z,n) # DomainError for n<0

function ^(z::Complex{T}, p::S) where {T<:Real,S<:Real}
    P = promote_type(T,S)
    return Complex{P}(z) ^ P(p)
end
function ^(z::T, p::Complex{S}) where {T<:Real,S<:Real}
    P = promote_type(T,S)
    return P(z) ^ Complex{P}(p)
end

function sin(z::Complex{T}) where T
    F = float(T)
    zr, zi = reim(z)
    if zr == 0
        Complex(F(zr), sinh(zi))
    elseif !isfinite(zr)
        if zi == 0 || isinf(zi)
            Complex(F(NaN), F(zi))
        else
            Complex(F(NaN), F(NaN))
        end
    else
        s, c = sincos(zr)
        Complex(s * cosh(zi), c * sinh(zi))
    end
end


function cos(z::Complex{T}) where T
    F = float(T)
    zr, zi = reim(z)
    if zr == 0
        Complex(cosh(zi), isnan(zi) ? F(zr) : -flipsign(F(zr),zi))
    elseif !isfinite(zr)
        if zi == 0
            Complex(F(NaN), isnan(zr) ? zero(F) : -flipsign(F(zi),zr))
        elseif isinf(zi)
            Complex(F(Inf), F(NaN))
        else
            Complex(F(NaN), F(NaN))
        end
    else
        s, c = sincos(zr)
        Complex(c * cosh(zi), -s * sinh(zi))
    end
end


function tan(z::Complex)
    zr, zi = reim(z)
    w = tanh(Complex(-zi, zr))
    Complex(imag(w), -real(w))
end

function asin(z::Complex)
    zr, zi = reim(z)
    if isinf(zr) && isinf(zi)
        return Complex(copysign(oftype(zr,pi)/4, zr),zi)
    elseif isnan(zi) && isinf(zr)
        return Complex(zi, oftype(zr, Inf))
    end
    ξ = zr == 0       ? zr :
        !isfinite(zr) ? oftype(zr,pi)/2 * sign(zr) :
        atan(zr, real(sqrt(1-z)*sqrt(1+z)))
    η = asinh(copysign(imag(sqrt(conj(1-z))*sqrt(1+z)), imag(z)))
    Complex(ξ,η)
end

function acos(z::Complex)
    z = float(z)
    zr, zi = reim(z)
    if isnan(zr)
        if isinf(zi) return Complex(zr, -zi)
        else         return Complex(zr, zr) end
    elseif isnan(zi)
        if isinf(zr) return Complex(zi, abs(zr))
        elseif zr==0 return Complex(oftype(zr,pi)/2, zi)
        else         return Complex(zi, zi) end
    elseif zr==zi==0
        return Complex(oftype(zr,pi)/2, -zi)
    elseif zr==Inf && zi===0.0
        return Complex(zi, -zr)
    elseif zr==-Inf && zi===-0.0
        return Complex(oftype(zi,pi), -zr)
    end
    ξ = 2*atan(real(sqrt(1-z)), real(sqrt(1+z)))
    η = asinh(imag(sqrt(conj(1+z))*sqrt(1-z)))
    if isinf(zr) && isinf(zi) ξ -= oftype(η,pi)/4 * sign(zr) end
    Complex(ξ,η)
end

function atan(z::Complex)
    w = atanh(Complex(-imag(z),real(z)))
    Complex(imag(w),-real(w))
end

function sinh(z::Complex)
    zr, zi = reim(z)
    w = sin(Complex(zi, zr))
    Complex(imag(w),real(w))
end

function cosh(z::Complex)
    zr, zi = reim(z)
    cos(Complex(zi,-zr))
end

function tanh(z::Complex{T}) where T
    z = float(z)
    Tf = float(T)
    Ω = prevfloat(typemax(Tf))
    ξ, η = reim(z)
    if isnan(ξ) && η==0 return Complex(ξ, η) end
    if 4*abs(ξ) > asinh(Ω) #Overflow?
        Complex(copysign(one(Tf),ξ),
                copysign(zero(Tf),η*(isfinite(η) ? sin(2*abs(η)) : one(η))))
    else
        t = tan(η)
        β = 1+t*t #sec(η)^2
        s = sinh(ξ)
        ρ = sqrt(1 + s*s) #cosh(ξ)
        if isinf(t)
            Complex(ρ/s,1/t)
        else
            Complex(β*ρ*s,t)/(1+β*s*s)
        end
    end
end

function asinh(z::Complex)
    w = asin(Complex(-imag(z),real(z)))
    Complex(imag(w),-real(w))
end

function acosh(z::Complex)
    zr, zi = reim(z)
    if isnan(zr) || isnan(zi)
        if isinf(zr) || isinf(zi)
            return Complex(oftype(zr, Inf), oftype(zi, NaN))
        else
            return Complex(oftype(zr, NaN), oftype(zi, NaN))
        end
    elseif zr==-Inf && zi===-0.0 #Edge case is wrong - WHY?
        return Complex(oftype(zr,Inf), oftype(zi, -pi))
    end
    ξ = asinh(real(sqrt(conj(z-1))*sqrt(z+1)))
    η = 2*atan(imag(sqrt(z-1)),real(sqrt(z+1)))
    if isinf(zr) && isinf(zi)
        η -= oftype(η,pi)/4 * sign(zi) * sign(zr)
    end
    Complex(ξ, η)
end

function atanh(z::Complex{T}) where T
    z = float(z)
    Tf = float(T)
    Ω = prevfloat(typemax(Tf))
    θ = sqrt(Ω)/4
    ρ = 1/θ
    x, y = reim(z)
    ax = abs(x)
    ay = abs(y)
    if ax > θ || ay > θ #Prevent overflow
        if isnan(y)
            if isinf(x)
                return Complex(copysign(zero(x),x), y)
            else
                return Complex(real(1/z), y)
            end
        end
        if isinf(y)
            return Complex(copysign(zero(x),x), copysign(oftype(y,pi)/2, y))
        end
        return Complex(real(1/z), copysign(oftype(y,pi)/2, y))
    end
    β = copysign(one(Tf), x)
    z *= β
    x, y = reim(z)
    if x == 1
        if y == 0
            ξ = oftype(x, Inf)
            η = y
        else
            ym = ay+ρ
            ξ = log(sqrt(sqrt(4+y*y))/sqrt(ym))
            η = copysign(oftype(y,pi)/2 + atan(ym/2), y)/2
        end
    else #Normal case
        ysq = (ay+ρ)^2
        if x == 0
            ξ = x
        else
            ξ = log1p(4x/((1-x)^2 + ysq))/4
        end
        η = angle(Complex((1-x)*(1+x)-ysq, 2y))/2
    end
    β * Complex(ξ, η)
end

#Rounding complex numbers
#Requires two different RoundingModes for the real and imaginary components
"""
    round(z::Complex[, RoundingModeReal, [RoundingModeImaginary]])
    round(z::Complex[, RoundingModeReal, [RoundingModeImaginary]]; digits=0, base=10)
    round(z::Complex[, RoundingModeReal, [RoundingModeImaginary]]; sigdigits, base=10)

Return the nearest integral value of the same type as the complex-valued `z` to `z`,
breaking ties using the specified [`RoundingMode`](@ref)s. The first
[`RoundingMode`](@ref) is used for rounding the real components while the
second is used for rounding the imaginary components.


`RoundingModeReal` and `RoundingModeImaginary` default to [`RoundNearest`](@ref),
which rounds to the nearest integer, with ties (fractional values of 0.5)
being rounded to the nearest even integer.

# Example
```jldoctest
julia> round(3.14 + 4.5im)
3.0 + 4.0im

julia> round(3.14 + 4.5im, RoundUp, RoundNearestTiesUp)
4.0 + 5.0im

julia> round(3.14159 + 4.512im; digits = 1)
3.1 + 4.5im

julia> round(3.14159 + 4.512im; sigdigits = 3)
3.14 + 4.51im
```
"""
function round(z::Complex, rr::RoundingMode=RoundNearest, ri::RoundingMode=rr; kwargs...)
    Complex(round(real(z), rr; kwargs...),
            round(imag(z), ri; kwargs...))
end


float(z::Complex{<:AbstractFloat}) = z
float(z::Complex) = Complex(float(real(z)), float(imag(z)))

big(::Type{Complex{T}}) where {T<:Real} = Complex{big(T)}
big(z::Complex{T}) where {T<:Real} = Complex{big(T)}(z)

## Array operations on complex numbers ##

complex(A::AbstractArray{<:Complex}) = A

function complex(A::AbstractArray{T}) where T
    if !isconcretetype(T)
        error("`complex` not defined on abstractly-typed arrays; please convert to a more specific type")
    end
    convert(AbstractArray{typeof(complex(zero(T)))}, A)
end
O   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/rational.jlH      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
    Rational{T<:Integer} <: Real

Rational number type, with numerator and denominator of type `T`.
Rationals are checked for overflow.
"""
struct Rational{T<:Integer} <: Real
    num::T
    den::T

    # Unexported inner constructor of Rational that bypasses all checks
    global unsafe_rational(::Type{T}, num, den) where {T} = new{T}(num, den)
end

unsafe_rational(num::T, den::T) where {T<:Integer} = unsafe_rational(T, num, den)
unsafe_rational(num::Integer, den::Integer) = unsafe_rational(promote(num, den)...)

@noinline __throw_rational_argerror_typemin(T) = throw(ArgumentError("invalid rational: denominator can't be typemin($T)"))
function checked_den(::Type{T}, num::T, den::T) where T<:Integer
    if signbit(den)
        den = -den
        signbit(den) && __throw_rational_argerror_typemin(typeof(den))
        num = -num
    end
    return unsafe_rational(T, num, den)
end
checked_den(num::T, den::T) where T<:Integer = checked_den(T, num, den)
checked_den(num::Integer, den::Integer) = checked_den(promote(num, den)...)

@noinline __throw_rational_argerror_zero(T) = throw(ArgumentError("invalid rational: zero($T)//zero($T)"))
function Rational{T}(num::Integer, den::Integer) where T<:Integer
    iszero(den) && iszero(num) && __throw_rational_argerror_zero(T)
    num, den = divgcd(num, den)
    return checked_den(T, T(num), T(den))
end

Rational(n::T, d::T) where {T<:Integer} = Rational{T}(n, d)
Rational(n::Integer, d::Integer) = Rational(promote(n, d)...)
Rational(n::Integer) = unsafe_rational(n, one(n))

function divgcd(x::Integer,y::Integer)
    g = gcd(x,y)
    div(x,g), div(y,g)
end

"""
    //(num, den)

Divide two integers or rational numbers, giving a [`Rational`](@ref) result.

# Examples
```jldoctest
julia> 3 // 5
3//5

julia> (3 // 5) // (2 // 1)
3//10
```
"""
//(n::Integer,  d::Integer) = Rational(n,d)

function //(x::Rational, y::Integer)
    xn, yn = divgcd(promote(x.num, y)...)
    checked_den(xn, checked_mul(x.den, yn))
end
function //(x::Integer,  y::Rational)
    xn, yn = divgcd(promote(x, y.num)...)
    checked_den(checked_mul(xn, y.den), yn)
end
function //(x::Rational, y::Rational)
    xn,yn = divgcd(promote(x.num, y.num)...)
    xd,yd = divgcd(promote(x.den, y.den)...)
    checked_den(checked_mul(xn, yd), checked_mul(xd, yn))
end

//(x::Complex, y::Real) = complex(real(x)//y, imag(x)//y)
//(x::Number, y::Complex) = x*conj(y)//abs2(y)


//(X::AbstractArray, y::Number) = X .// y

function show(io::IO, x::Rational)
    show(io, numerator(x))

    if isone(denominator(x)) && get(io, :typeinfo, Any) <: Rational
        return
    end

    print(io, "//")
    show(io, denominator(x))
end

function read(s::IO, ::Type{Rational{T}}) where T<:Integer
    r = read(s,T)
    i = read(s,T)
    r//i
end
function write(s::IO, z::Rational)
    write(s,numerator(z),denominator(z))
end
function parse(::Type{Rational{T}}, s::AbstractString) where T<:Integer
    ss = split(s, '/'; limit = 2)
    if isone(length(ss))
        return Rational{T}(parse(T, s))
    end
    @inbounds ns, ds = ss[1], ss[2]
    if startswith(ds, '/')
        ds = chop(ds; head = 1, tail = 0)
    end
    n = parse(T, ns)
    d = parse(T, ds)
    return n//d
end


function Rational{T}(x::Rational) where T<:Integer
    unsafe_rational(T, convert(T, x.num), convert(T, x.den))
end
function Rational{T}(x::Integer) where T<:Integer
    unsafe_rational(T, convert(T, x), one(T))
end

Rational(x::Rational) = x

Bool(x::Rational) = x==0 ? false : x==1 ? true :
    throw(InexactError(:Bool, Bool, x)) # to resolve ambiguity
(::Type{T})(x::Rational) where {T<:Integer} = (isinteger(x) ? convert(T, x.num)::T :
    throw(InexactError(nameof(T), T, x)))

AbstractFloat(x::Rational) = (float(x.num)/float(x.den))::AbstractFloat
function (::Type{T})(x::Rational{S}) where T<:AbstractFloat where S
    P = promote_type(T,S)
    convert(T, convert(P,x.num)/convert(P,x.den))::T
end

function Rational{T}(x::AbstractFloat) where T<:Integer
    r = rationalize(T, x, tol=0)
    x == convert(typeof(x), r) || throw(InexactError(:Rational, Rational{T}, x))
    r
end
Rational(x::Float64) = Rational{Int64}(x)
Rational(x::Float32) = Rational{Int}(x)

big(q::Rational) = unsafe_rational(big(numerator(q)), big(denominator(q)))

big(z::Complex{<:Rational{<:Integer}}) = Complex{Rational{BigInt}}(z)

promote_rule(::Type{Rational{T}}, ::Type{S}) where {T<:Integer,S<:Integer} = Rational{promote_type(T,S)}
promote_rule(::Type{Rational{T}}, ::Type{Rational{S}}) where {T<:Integer,S<:Integer} = Rational{promote_type(T,S)}
promote_rule(::Type{Rational{T}}, ::Type{S}) where {T<:Integer,S<:AbstractFloat} = promote_type(T,S)

widen(::Type{Rational{T}}) where {T} = Rational{widen(T)}

@noinline __throw_negate_unsigned() = throw(OverflowError("cannot negate unsigned number"))

"""
    rationalize([T<:Integer=Int,] x; tol::Real=eps(x))

Approximate floating point number `x` as a [`Rational`](@ref) number with components
of the given integer type. The result will differ from `x` by no more than `tol`.

# Examples
```jldoctest
julia> rationalize(5.6)
28//5

julia> a = rationalize(BigInt, 10.3)
103//10

julia> typeof(numerator(a))
BigInt
```
"""
function rationalize(::Type{T}, x::Union{AbstractFloat, Rational}, tol::Real) where T<:Integer
    if tol < 0
        throw(ArgumentError("negative tolerance $tol"))
    end

    T<:Unsigned && x < 0 && __throw_negate_unsigned()
    isnan(x) && return T(x)//one(T)
    isinf(x) && return unsafe_rational(x < 0 ? -one(T) : one(T), zero(T))

    p,  q  = (x < 0 ? -one(T) : one(T)), zero(T)
    pp, qq = zero(T), one(T)

    x = abs(x)
    a = trunc(x)
    r = x-a
    y = one(x)
    tolx = oftype(x, tol)
    nt, t, tt = tolx, zero(tolx), tolx
    ia = np = nq = zero(T)

    # compute the successive convergents of the continued fraction
    #  np // nq = (p*a + pp) // (q*a + qq)
    while r > nt
        try
            ia = convert(T,a)

            np = checked_add(checked_mul(ia,p),pp)
            nq = checked_add(checked_mul(ia,q),qq)
            p, pp = np, p
            q, qq = nq, q
        catch e
            isa(e,InexactError) || isa(e,OverflowError) || rethrow()
            return p // q
        end

        # naive approach of using
        #   x = 1/r; a = trunc(x); r = x - a
        # is inexact, so we store x as x/y
        x, y = y, r
        a, r = divrem(x,y)

        # maintain
        # x0 = (p + (-1)^i * r) / q
        t, tt = nt, t
        nt = a*t+tt
    end

    # find optimal semiconvergent
    # smallest a such that x-a*y < a*t+tt
    a = cld(x-tt,y+t)
    try
        ia = convert(T,a)
        np = checked_add(checked_mul(ia,p),pp)
        nq = checked_add(checked_mul(ia,q),qq)
        return np // nq
    catch e
        isa(e,InexactError) || isa(e,OverflowError) || rethrow()
        return p // q
    end
end
rationalize(::Type{T}, x::AbstractFloat; tol::Real = eps(x)) where {T<:Integer} = rationalize(T, x, tol)
rationalize(x::AbstractFloat; kvs...) = rationalize(Int, x; kvs...)
rationalize(::Type{T}, x::Complex; kvs...) where {T<:Integer} = Complex(rationalize(T, x.re; kvs...), rationalize(T, x.im; kvs...))
rationalize(x::Complex; kvs...) = Complex(rationalize(Int, x.re; kvs...), rationalize(Int, x.im; kvs...))
rationalize(::Type{T}, x::Rational; tol::Real = 0) where {T<:Integer} = rationalize(T, x, tol)
rationalize(x::Rational; kvs...) = x
rationalize(x::Integer; kvs...) = Rational(x)
function rationalize(::Type{T}, x::Integer; kvs...) where {T<:Integer}
    if Base.hastypemax(T) # BigInt doesn't
        x < typemin(T) && return unsafe_rational(-one(T), zero(T))
        x > typemax(T) && return unsafe_rational(one(T), zero(T))
    end
    return Rational{T}(x)
end


"""
    numerator(x)

Numerator of the rational representation of `x`.

# Examples
```jldoctest
julia> numerator(2//3)
2

julia> numerator(4)
4
```
"""
numerator(x::Integer) = x
numerator(x::Rational) = x.num

"""
    denominator(x)

Denominator of the rational representation of `x`.

# Examples
```jldoctest
julia> denominator(2//3)
3

julia> denominator(4)
1
```
"""
denominator(x::Integer) = one(x)
denominator(x::Rational) = x.den

sign(x::Rational) = oftype(x, sign(x.num))
signbit(x::Rational) = signbit(x.num)
copysign(x::Rational, y::Real) = unsafe_rational(copysign(x.num, y), x.den)
copysign(x::Rational, y::Rational) = unsafe_rational(copysign(x.num, y.num), x.den)

abs(x::Rational) = unsafe_rational(checked_abs(x.num), x.den)

typemin(::Type{Rational{T}}) where {T<:Signed} = unsafe_rational(T, -one(T), zero(T))
typemin(::Type{Rational{T}}) where {T<:Integer} = unsafe_rational(T, zero(T), one(T))
typemax(::Type{Rational{T}}) where {T<:Integer} = unsafe_rational(T, one(T), zero(T))

isinteger(x::Rational) = x.den == 1
ispow2(x::Rational) = ispow2(x.num) & ispow2(x.den)

+(x::Rational) = unsafe_rational(+x.num, x.den)
-(x::Rational) = unsafe_rational(-x.num, x.den)

function -(x::Rational{T}) where T<:BitSigned
    x.num == typemin(T) && __throw_rational_numerator_typemin(T)
    unsafe_rational(-x.num, x.den)
end
@noinline __throw_rational_numerator_typemin(T) = throw(OverflowError("rational numerator is typemin($T)"))

function -(x::Rational{T}) where T<:Unsigned
    x.num != zero(T) && __throw_negate_unsigned()
    x
end

function +(x::Rational, y::Rational)
    xp, yp = promote(x, y)::NTuple{2,Rational}
    if isinf(x) && x == y
        return xp
    end
    xd, yd = divgcd(promote(x.den, y.den)...)
    Rational(checked_add(checked_mul(x.num,yd), checked_mul(y.num,xd)), checked_mul(x.den,yd))
end

function -(x::Rational, y::Rational)
    xp, yp = promote(x, y)::NTuple{2,Rational}
    if isinf(x) && x == -y
        return xp
    end
    xd, yd = divgcd(promote(x.den, y.den)...)
    Rational(checked_sub(checked_mul(x.num,yd), checked_mul(y.num,xd)), checked_mul(x.den,yd))
end

for (op,chop) in ((:rem,:rem), (:mod,:mod))
    @eval begin
        function ($op)(x::Rational, y::Rational)
            xd, yd = divgcd(promote(x.den, y.den)...)
            Rational(($chop)(checked_mul(x.num,yd), checked_mul(y.num,xd)), checked_mul(x.den,yd))
        end
    end
end

for (op,chop) in ((:+,:checked_add), (:-,:checked_sub), (:rem,:rem), (:mod,:mod))
    @eval begin
        function ($op)(x::Rational, y::Integer)
            unsafe_rational(($chop)(x.num, checked_mul(x.den, y)), x.den)
        end
    end
end
for (op,chop) in ((:+,:checked_add), (:-,:checked_sub))
    @eval begin
        function ($op)(y::Integer, x::Rational)
            unsafe_rational(($chop)(checked_mul(x.den, y), x.num), x.den)
        end
    end
end
for (op,chop) in ((:rem,:rem), (:mod,:mod))
    @eval begin
        function ($op)(y::Integer, x::Rational)
            Rational(($chop)(checked_mul(x.den, y), x.num), x.den)
        end
    end
end

function *(x::Rational, y::Rational)
    xn, yd = divgcd(promote(x.num, y.den)...)
    xd, yn = divgcd(promote(x.den, y.num)...)
    unsafe_rational(checked_mul(xn, yn), checked_mul(xd, yd))
end
function *(x::Rational, y::Integer)
    xd, yn = divgcd(promote(x.den, y)...)
    unsafe_rational(checked_mul(x.num, yn), xd)
end
function *(y::Integer, x::Rational)
    yn, xd = divgcd(promote(y, x.den)...)
    unsafe_rational(checked_mul(yn, x.num), xd)
end
/(x::Rational, y::Union{Rational, Integer, Complex{<:Union{Integer,Rational}}}) = x//y
/(x::Union{Integer, Complex{<:Union{Integer,Rational}}}, y::Rational) = x//y
inv(x::Rational{T}) where {T} = checked_den(x.den, x.num)

fma(x::Rational, y::Rational, z::Rational) = x*y+z

==(x::Rational, y::Rational) = (x.den == y.den) & (x.num == y.num)
<( x::Rational, y::Rational) = x.den == y.den ? x.num < y.num :
                               widemul(x.num,y.den) < widemul(x.den,y.num)
<=(x::Rational, y::Rational) = x.den == y.den ? x.num <= y.num :
                               widemul(x.num,y.den) <= widemul(x.den,y.num)


==(x::Rational, y::Integer ) = (x.den == 1) & (x.num == y)
==(x::Integer , y::Rational) = y == x
<( x::Rational, y::Integer ) = x.num < widemul(x.den,y)
<( x::Integer , y::Rational) = widemul(x,y.den) < y.num
<=(x::Rational, y::Integer ) = x.num <= widemul(x.den,y)
<=(x::Integer , y::Rational) = widemul(x,y.den) <= y.num

function ==(x::AbstractFloat, q::Rational)
    if isfinite(x)
        (count_ones(q.den) == 1) & (x*q.den == q.num)
    else
        x == q.num/q.den
    end
end

==(q::Rational, x::AbstractFloat) = x == q

for rel in (:<,:<=,:cmp)
    for (Tx,Ty) in ((Rational,AbstractFloat), (AbstractFloat,Rational))
        @eval function ($rel)(x::$Tx, y::$Ty)
            if isnan(x)
                $(rel === :cmp ? :(return isnan(y) ? 0 : 1) :
                                :(return false))
            end
            if isnan(y)
                $(rel === :cmp ? :(return -1) :
                                :(return false))
            end

            xn, xp, xd = decompose(x)
            yn, yp, yd = decompose(y)

            if xd < 0
                xn = -xn
                xd = -xd
            end
            if yd < 0
                yn = -yn
                yd = -yd
            end

            xc, yc = widemul(xn,yd), widemul(yn,xd)
            xs, ys = sign(xc), sign(yc)

            if xs != ys
                return ($rel)(xs,ys)
            elseif xs == 0
                # both are zero or ±Inf
                return ($rel)(xn,yn)
            end

            xb, yb = ndigits0z(xc,2) + xp, ndigits0z(yc,2) + yp

            if xb == yb
                xc, yc = promote(xc,yc)
                if xp > yp
                    xc = (xc<<(xp-yp))
                else
                    yc = (yc<<(yp-xp))
                end
                return ($rel)(xc,yc)
            else
                return xc > 0 ? ($rel)(xb,yb) : ($rel)(yb,xb)
            end
        end
    end
end

# needed to avoid ambiguity between ==(x::Real, z::Complex) and ==(x::Rational, y::Number)
==(z::Complex , x::Rational) = isreal(z) & (real(z) == x)
==(x::Rational, z::Complex ) = isreal(z) & (real(z) == x)

function div(x::Rational, y::Integer, r::RoundingMode)
    xn,yn = divgcd(x.num,y)
    div(xn, checked_mul(x.den,yn), r)
end
function div(x::Integer, y::Rational, r::RoundingMode)
    xn,yn = divgcd(x,y.num)
    div(checked_mul(xn,y.den), yn, r)
end
function div(x::Rational, y::Rational, r::RoundingMode)
    xn,yn = divgcd(x.num,y.num)
    xd,yd = divgcd(x.den,y.den)
    div(checked_mul(xn,yd), checked_mul(xd,yn), r)
end

# For compatibility - to be removed in 2.0 when the generic fallbacks
# are removed from div.jl
div(x::T, y::T, r::RoundingMode) where {T<:Rational} =
    invoke(div, Tuple{Rational, Rational, RoundingMode}, x, y, r)
for (S, T) in ((Rational, Integer), (Integer, Rational), (Rational, Rational))
    @eval begin
        div(x::$S, y::$T) = div(x, y, RoundToZero)
        fld(x::$S, y::$T) = div(x, y, RoundDown)
        cld(x::$S, y::$T) = div(x, y, RoundUp)
    end
end

trunc(::Type{T}, x::Rational) where {T} = round(T, x, RoundToZero)
floor(::Type{T}, x::Rational) where {T} = round(T, x, RoundDown)
ceil(::Type{T}, x::Rational) where {T} = round(T, x, RoundUp)

round(x::Rational, r::RoundingMode=RoundNearest) = round(typeof(x), x, r)

function round(::Type{T}, x::Rational{Tr}, r::RoundingMode=RoundNearest) where {T,Tr}
    if iszero(denominator(x)) && !(T <: Integer)
        return convert(T, copysign(unsafe_rational(one(Tr), zero(Tr)), numerator(x)))
    end
    convert(T, div(numerator(x), denominator(x), r))
end

function round(::Type{T}, x::Rational{Bool}, ::RoundingMode=RoundNearest) where T
    if denominator(x) == false && (T <: Integer)
        throw(DivideError())
    end
    convert(T, x)
end

function ^(x::Rational, n::Integer)
    n >= 0 ? power_by_squaring(x,n) : power_by_squaring(inv(x),-n)
end

^(x::Number, y::Rational) = x^(y.num/y.den)
^(x::T, y::Rational) where {T<:AbstractFloat} = x^convert(T,y)
^(z::Complex{T}, p::Rational) where {T<:Real} = z^convert(typeof(one(T)^p), p)

^(z::Complex{<:Rational}, n::Bool) = n ? z : one(z) # to resolve ambiguity
function ^(z::Complex{<:Rational}, n::Integer)
    n >= 0 ? power_by_squaring(z,n) : power_by_squaring(inv(z),-n)
end

iszero(x::Rational) = iszero(numerator(x))
isone(x::Rational) = isone(numerator(x)) & isone(denominator(x))

function lerpi(j::Integer, d::Integer, a::Rational, b::Rational)
    ((d-j)*a)/d + (j*b)/d
end

float(::Type{Rational{T}}) where {T<:Integer} = float(T)

gcd(x::Rational, y::Rational) = unsafe_rational(gcd(x.num, y.num), lcm(x.den, y.den))
lcm(x::Rational, y::Rational) = unsafe_rational(lcm(x.num, y.num), gcd(x.den, y.den))
function gcdx(x::Rational, y::Rational)
    c = gcd(x, y)
    if iszero(c.num)
        a, b = one(c.num), c.num
    elseif iszero(c.den)
        a = ifelse(iszero(x.den), one(c.den), c.den)
        b = ifelse(iszero(y.den), one(c.den), c.den)
    else
        idiv(x, c) = div(x.num, c.num) * div(c.den, x.den)
        _, a, b = gcdx(idiv(x, c), idiv(y, c))
    end
    c, a, b
end

## streamlined hashing for smallish rational types ##

decompose(x::Rational) = numerator(x), 0, denominator(x)
function hash(x::Rational{<:BitInteger64}, h::UInt)
    num, den = Base.numerator(x), Base.denominator(x)
    den == 1 && return hash(num, h)
    den == 0 && return hash(ifelse(num > 0, Inf, -Inf), h)
    if isodd(den) # since den != 1, this rational can't be a Float64
        pow = trailing_zeros(num)
        num >>= pow
        h = hash_integer(den, h)
    else
        pow = trailing_zeros(den)
        den >>= pow
        pow = -pow
        if den == 1
            if uabs(num) < UInt64(maxintfloat(Float64))
                return hash(ldexp(Float64(num),pow),h)
            end
        else
            h = hash_integer(den, h)
        end
    end
    h = hash_integer(pow, h)
    h = hash_integer(num, h)
    return h
end

# These methods are only needed for performance. Since `first(r)` and `last(r)` have the
# same denominator (because their difference is an integer), `length(r)` can be calculated
# without calling `gcd`.
function length(r::AbstractUnitRange{T}) where T<:Rational
    @inline
    f = first(r)
    l = last(r)
    return div(l.num - f.num + f.den, f.den)
end
function checked_length(r::AbstractUnitRange{T}) where T<:Rational
    f = first(r)
    l = last(r)
    if isempty(r)
        return f.num - f.num
    end
    return div(checked_add(checked_sub(l.num, f.num), f.den), f.den)
end
S   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/multinverses.jl&      # This file is a part of Julia. License is MIT: https://julialang.org/license

module MultiplicativeInverses

import Base: div, divrem, rem, unsigned
using  Base: IndexLinear, IndexCartesian, tail
export multiplicativeinverse

unsigned(::Type{Bool}) = UInt
unsigned(::Type{Int8}) = UInt8
unsigned(::Type{Int16}) = UInt16
unsigned(::Type{Int32}) = UInt32
unsigned(::Type{Int64}) = UInt64
unsigned(::Type{Int128}) = UInt128
unsigned(::Type{T}) where {T<:Unsigned} = T

abstract type  MultiplicativeInverse{T} <: Number end

# Computes integer division by a constant using multiply, add, and bitshift.

# The idea here is to compute floor(n/d) as floor(m*n/2^p) and then
# implement division by 2^p as a right bitshift.  The trick is finding
# m (the "magic number") and p. Roughly speaking, one can think of this as
#        floor(n/d) = floor((n/2^p) * (2^p/d))
# so that m is effectively 2^p/d.
#
# A few examples are illustrative:
# Division of Int32 by 3:
#   floor((2^32+2)/3 * n/2^32) = floor(n/3 + 2n/(3*2^32))
# The correction term, 2n/(3*2^32), is strictly less than 1/3 for any
# nonnegative n::Int32, so this divides any nonnegative Int32 by 3.
# (When n < 0, we add 1, and one can show that this computes
# ceil(n/d) = -floor(abs(n)/d).)
#
# Division of Int32 by 5 uses a magic number (2^33+3)/5 and then
# right-shifts by 33 rather than 32. Consequently, the size of the
# shift depends on the specific denominator.
#
# Division of Int32 by 7 would be problematic, because a viable magic
# number of (2^34+5)/7 is too big to represent as an Int32 (the
# unsigned representation needs 32 bits). We can exploit wrap-around
# and use (2^34+5)/7 - 2^32 (an Int32 < 0), and then correct the
# 64-bit product with an add (the `addmul` field below).
#
# Further details can be found in Hacker's Delight, Chapter 10.

struct SignedMultiplicativeInverse{T<:Signed} <: MultiplicativeInverse{T}
    divisor::T
    multiplier::T
    addmul::Int8
    shift::UInt8

    function SignedMultiplicativeInverse{T}(d::T) where T<:Signed
        d == 0 && throw(ArgumentError("cannot compute magic for d == $d"))
        signedmin = unsigned(typemin(T))
        UT = unsigned(T)

        # Algorithm from Hacker's Delight, section 10-4
        ad = unsigned(abs(d))
        t = signedmin + signbit(d)
        anc = t - one(UT) - rem(t, ad)   # absolute value of nc
        p = sizeof(d)*8 - 1
        q1, r1 = divrem(signedmin, anc)
        q2, r2 = divrem(signedmin, ad)
        while true
            p += 1                       # loop until we find a satisfactory p
            # update q1, r1 = divrem(2^p, abs(nc))
            q1 = q1<<1
            r1 = r1<<1
            if r1 >= anc                 # must be unsigned comparison
                q1 += one(UT)
                r1 -= anc
            end
            # update q2, r2 = divrem(2^p, abs(d))
            q2 = q2<<1
            r2 = r2<<1
            if r2 >= ad
                q2 += one(UT)
                r2 -= ad
            end
            delta = ad - r2
            (q1 < delta || (q1 == delta && r1 == 0)) || break
        end

        m = flipsign((q2 + one(UT)) % T, d)  # resulting magic number
        s = p - sizeof(d)*8                  # resulting shift
        new(d, m, d > 0 && m < 0 ? Int8(1) : d < 0 && m > 0 ? Int8(-1) : Int8(0), UInt8(s))
    end
end
SignedMultiplicativeInverse(x::Signed) = SignedMultiplicativeInverse{typeof(x)}(x)

struct UnsignedMultiplicativeInverse{T<:Unsigned} <: MultiplicativeInverse{T}
    divisor::T
    multiplier::T
    add::Bool
    shift::UInt8

    function UnsignedMultiplicativeInverse{T}(d::T) where T<:Unsigned
        d == 0 && throw(ArgumentError("cannot compute magic for d == $d"))
        add = false
        signedmin = one(d) << (sizeof(d)*8-1)
        signedmax = signedmin - one(T)
        allones = (zero(d) - 1) % T

        nc = allones - rem(convert(T, allones - d), d)
        p = 8*sizeof(d) - 1
        q1, r1 = divrem(signedmin, nc)
        q2, r2 = divrem(signedmax, d)
        while true
            p += 1
            if r1 >= convert(T, nc - r1)
                q1 = q1 + q1 + one(T)
                r1 = r1 + r1 - nc
            else
                q1 = q1 + q1
                r1 = r1 + r1
            end
            if convert(T, r2 + one(T)) >= convert(T, d - r2)
                add |= q2 >= signedmax
                q2 = q2 + q2 + one(T)
                r2 = r2 + r2 + one(T) - d
            else
                add |= q2 >= signedmin
                q2 = q2 + q2
                r2 = r2 + r2 + one(T)
            end
            delta = d - one(T) - r2
            (p < sizeof(d)*16 && (q1 < delta || (q1 == delta && r1 == 0))) || break
        end
        m = q2 + one(T)              # resulting magic number
        s = p - sizeof(d)*8 - add    # resulting shift
        new(d, m, add, s % UInt8)
    end
end
UnsignedMultiplicativeInverse(x::Unsigned) = UnsignedMultiplicativeInverse{typeof(x)}(x)

# Returns the higher half of the product a*b
function _mul_high(a::T, b::T) where {T<:Union{Signed, Unsigned}}
    ((widen(a)*b) >>> (sizeof(a)*8)) % T
end

function _mul_high(a::UInt128, b::UInt128)
    shift = sizeof(a)*4
    mask = typemax(UInt128) >> shift
    a1, a2 = a >>> shift, a & mask
    b1, b2 = b >>> shift, b & mask
    a1b1, a1b2, a2b1, a2b2 = a1*b1, a1*b2, a2*b1, a2*b2
    carry = ((a1b2 & mask) + (a2b1 & mask) + (a2b2 >>> shift)) >>> shift
    a1b1 + (a1b2 >>> shift) + (a2b1 >>> shift) + carry
end
function _mul_high(a::Int128, b::Int128)
    shift = sizeof(a)*8 - 1
    t1, t2 = (a >> shift) & b % UInt128, (b >> shift) & a % UInt128
    (_mul_high(a % UInt128, b % UInt128) - t1 - t2) % Int128
end

function div(a::T, b::SignedMultiplicativeInverse{T}) where T
    x = _mul_high(a, b.multiplier)
    x += (a*b.addmul) % T
    ifelse(abs(b.divisor) == 1, a*b.divisor, (signbit(x) + (x >> b.shift)) % T)
end
function div(a::T, b::UnsignedMultiplicativeInverse{T}) where T
    x = _mul_high(a, b.multiplier)
    x = ifelse(b.add, convert(T, convert(T, (convert(T, a - x) >>> 1)) + x), x)
    ifelse(b.divisor == 1, a, x >>> b.shift)
end

rem(a::T, b::MultiplicativeInverse{T}) where {T} =
    a - div(a, b)*b.divisor

function divrem(a::T, b::MultiplicativeInverse{T}) where T
    d = div(a, b)
    (d, a - d*b.divisor)
end

multiplicativeinverse(x::Signed) = SignedMultiplicativeInverse(x)
multiplicativeinverse(x::Unsigned) = UnsignedMultiplicativeInverse(x)

end
X   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/abstractarraymath.jl�1      # This file is a part of Julia. License is MIT: https://julialang.org/license

 ## Basic functions ##

isreal(x::AbstractArray) = all(isreal,x)
iszero(x::AbstractArray) = all(iszero,x)
isreal(x::AbstractArray{<:Real}) = true

## Constructors ##

"""
    vec(a::AbstractArray) -> AbstractVector

Reshape the array `a` as a one-dimensional column vector. Return `a` if it is
already an `AbstractVector`. The resulting array
shares the same underlying data as `a`, so it will only be mutable if `a` is
mutable, in which case modifying one will also modify the other.

# Examples
```jldoctest
julia> a = [1 2 3; 4 5 6]
2×3 Matrix{Int64}:
 1  2  3
 4  5  6

julia> vec(a)
6-element Vector{Int64}:
 1
 4
 2
 5
 3
 6

julia> vec(1:3)
1:3
```

See also [`reshape`](@ref), [`dropdims`](@ref).
"""
vec(a::AbstractArray) = reshape(a,length(a))
vec(a::AbstractVector) = a

_sub(::Tuple{}, ::Tuple{}) = ()
_sub(t::Tuple, ::Tuple{}) = t
_sub(t::Tuple, s::Tuple) = _sub(tail(t), tail(s))

"""
    dropdims(A; dims)

Return an array with the same data as `A`, but with the dimensions specified by
`dims` removed. `size(A,d)` must equal 1 for every `d` in `dims`,
and repeated dimensions or numbers outside `1:ndims(A)` are forbidden.

The result shares the same underlying data as `A`, such that the
result is mutable if and only if `A` is mutable, and setting elements of one
alters the values of the other.

See also: [`reshape`](@ref), [`vec`](@ref).

# Examples
```jldoctest
julia> a = reshape(Vector(1:4),(2,2,1,1))
2×2×1×1 Array{Int64, 4}:
[:, :, 1, 1] =
 1  3
 2  4

julia> b = dropdims(a; dims=3)
2×2×1 Array{Int64, 3}:
[:, :, 1] =
 1  3
 2  4

julia> b[1,1,1] = 5; a
2×2×1×1 Array{Int64, 4}:
[:, :, 1, 1] =
 5  3
 2  4
```
"""
dropdims(A; dims) = _dropdims(A, dims)
function _dropdims(A::AbstractArray, dims::Dims)
    for i in eachindex(dims)
        1 <= dims[i] <= ndims(A) || throw(ArgumentError("dropped dims must be in range 1:ndims(A)"))
        length(axes(A, dims[i])) == 1 || throw(ArgumentError("dropped dims must all be size 1"))
        for j = 1:i-1
            dims[j] == dims[i] && throw(ArgumentError("dropped dims must be unique"))
        end
    end
    ax = _foldoneto((ds, d) -> d in dims ? ds : (ds..., axes(A,d)), (), Val(ndims(A)))
    reshape(A, ax::typeof(_sub(axes(A), dims)))
end
_dropdims(A::AbstractArray, dim::Integer) = _dropdims(A, (Int(dim),))

## Unary operators ##

"""
    conj!(A)

Transform an array to its complex conjugate in-place.

See also [`conj`](@ref).

# Examples
```jldoctest
julia> A = [1+im 2-im; 2+2im 3+im]
2×2 Matrix{Complex{Int64}}:
 1+1im  2-1im
 2+2im  3+1im

julia> conj!(A);

julia> A
2×2 Matrix{Complex{Int64}}:
 1-1im  2+1im
 2-2im  3-1im
```
"""
conj!(A::AbstractArray{<:Number}) = (@inbounds broadcast!(conj, A, A); A)
conj!(x::AbstractArray{<:Real}) = x

"""
    conj(A::AbstractArray)

Return an array containing the complex conjugate of each entry in array `A`.

Equivalent to `conj.(A)`, except that when `eltype(A) <: Real`
`A` is returned without copying, and that when `A` has zero dimensions,
a 0-dimensional array is returned (rather than a scalar).

# Examples
```jldoctest
julia> conj([1, 2im, 3 + 4im])
3-element Vector{Complex{Int64}}:
 1 + 0im
 0 - 2im
 3 - 4im

julia> conj(fill(2 - im))
0-dimensional Array{Complex{Int64}, 0}:
2 + 1im
```
"""
conj(A::AbstractArray) = broadcast_preserving_zero_d(conj, A)
conj(A::AbstractArray{<:Real}) = A

"""
    real(A::AbstractArray)

Return an array containing the real part of each entry in array `A`.

Equivalent to `real.(A)`, except that when `eltype(A) <: Real`
`A` is returned without copying, and that when `A` has zero dimensions,
a 0-dimensional array is returned (rather than a scalar).

# Examples
```jldoctest
julia> real([1, 2im, 3 + 4im])
3-element Vector{Int64}:
 1
 0
 3

julia> real(fill(2 - im))
0-dimensional Array{Int64, 0}:
2
```
"""
real(A::AbstractArray) = broadcast_preserving_zero_d(real, A)
real(A::AbstractArray{<:Real}) = A

"""
    imag(A::AbstractArray)

Return an array containing the imaginary part of each entry in array `A`.

Equivalent to `imag.(A)`, except that when `A` has zero dimensions,
a 0-dimensional array is returned (rather than a scalar).

# Examples
```jldoctest
julia> imag([1, 2im, 3 + 4im])
3-element Vector{Int64}:
 0
 2
 4

julia> imag(fill(2 - im))
0-dimensional Array{Int64, 0}:
-1
```
"""
imag(A::AbstractArray) = broadcast_preserving_zero_d(imag, A)
imag(A::AbstractArray{<:Real}) = zero(A)

"""
    reim(A::AbstractArray)

Return a tuple of two arrays containing respectively the real and the imaginary
part of each entry in `A`.

Equivalent to `(real.(A), imag.(A))`, except that when `eltype(A) <: Real`
`A` is returned without copying to represent the real part, and that when `A` has
zero dimensions, a 0-dimensional array is returned (rather than a scalar).

# Examples
```jldoctest
julia> reim([1, 2im, 3 + 4im])
([1, 0, 3], [0, 2, 4])

julia> reim(fill(2 - im))
(fill(2), fill(-1))
```
"""
reim(A::AbstractArray)

-(A::AbstractArray) = broadcast_preserving_zero_d(-, A)

+(x::AbstractArray{<:Number}) = x
*(x::AbstractArray{<:Number,2}) = x

# index A[:,:,...,i,:,:,...] where "i" is in dimension "d"

"""
    selectdim(A, d::Integer, i)

Return a view of all the data of `A` where the index for dimension `d` equals `i`.

Equivalent to `view(A,:,:,...,i,:,:,...)` where `i` is in position `d`.

See also: [`eachslice`](@ref).

# Examples
```jldoctest
julia> A = [1 2 3 4; 5 6 7 8]
2×4 Matrix{Int64}:
 1  2  3  4
 5  6  7  8

julia> selectdim(A, 2, 3)
2-element view(::Matrix{Int64}, :, 3) with eltype Int64:
 3
 7

julia> selectdim(A, 2, 3:4)
2×2 view(::Matrix{Int64}, :, 3:4) with eltype Int64:
 3  4
 7  8
```
"""
@inline selectdim(A::AbstractArray, d::Integer, i) = _selectdim(A, d, i, _setindex(i, d, map(Slice, axes(A))...))
@noinline function _selectdim(A, d, i, idxs)
    d >= 1 || throw(ArgumentError("dimension must be ≥ 1, got $d"))
    nd = ndims(A)
    d > nd && (i == 1 || throw(BoundsError(A, (ntuple(Returns(Colon()),d-1)..., i))))
    return view(A, idxs...)
end

function circshift(a::AbstractArray, shiftamt::Real)
    circshift!(similar(a), a, (Integer(shiftamt),))
end
circshift(a::AbstractArray, shiftamt::DimsInteger) = circshift!(similar(a), a, shiftamt)
"""
    circshift(A, shifts)

Circularly shift, i.e. rotate, the data in an array. The second argument is a tuple or
vector giving the amount to shift in each dimension, or an integer to shift only in the
first dimension.

See also: [`circshift!`](@ref), [`circcopy!`](@ref), [`bitrotate`](@ref), [`<<`](@ref).

# Examples
```jldoctest
julia> b = reshape(Vector(1:16), (4,4))
4×4 Matrix{Int64}:
 1  5   9  13
 2  6  10  14
 3  7  11  15
 4  8  12  16

julia> circshift(b, (0,2))
4×4 Matrix{Int64}:
  9  13  1  5
 10  14  2  6
 11  15  3  7
 12  16  4  8

julia> circshift(b, (-1,0))
4×4 Matrix{Int64}:
 2  6  10  14
 3  7  11  15
 4  8  12  16
 1  5   9  13

julia> a = BitArray([true, true, false, false, true])
5-element BitVector:
 1
 1
 0
 0
 1

julia> circshift(a, 1)
5-element BitVector:
 1
 1
 1
 0
 0

julia> circshift(a, -1)
5-element BitVector:
 1
 0
 0
 1
 1
```
"""
function circshift(a::AbstractArray, shiftamt)
    circshift!(similar(a), a, map(Integer, (shiftamt...,)))
end

## Other array functions ##

"""
    repeat(A::AbstractArray, counts::Integer...)

Construct an array by repeating array `A` a given number of times in each dimension, specified by `counts`.

See also: [`fill`](@ref), [`Iterators.repeated`](@ref), [`Iterators.cycle`](@ref).

# Examples
```jldoctest
julia> repeat([1, 2, 3], 2)
6-element Vector{Int64}:
 1
 2
 3
 1
 2
 3

julia> repeat([1, 2, 3], 2, 3)
6×3 Matrix{Int64}:
 1  1  1
 2  2  2
 3  3  3
 1  1  1
 2  2  2
 3  3  3
```
"""
function repeat(A::AbstractArray, counts...)
    return _RepeatInnerOuter.repeat(A, outer=counts)
end

"""
    repeat(A::AbstractArray; inner=ntuple(Returns(1), ndims(A)), outer=ntuple(Returns(1), ndims(A)))

Construct an array by repeating the entries of `A`. The i-th element of `inner` specifies
the number of times that the individual entries of the i-th dimension of `A` should be
repeated. The i-th element of `outer` specifies the number of times that a slice along the
i-th dimension of `A` should be repeated. If `inner` or `outer` are omitted, no repetition
is performed.

# Examples
```jldoctest
julia> repeat(1:2, inner=2)
4-element Vector{Int64}:
 1
 1
 2
 2

julia> repeat(1:2, outer=2)
4-element Vector{Int64}:
 1
 2
 1
 2

julia> repeat([1 2; 3 4], inner=(2, 1), outer=(1, 3))
4×6 Matrix{Int64}:
 1  2  1  2  1  2
 1  2  1  2  1  2
 3  4  3  4  3  4
 3  4  3  4  3  4
```
"""
function repeat(A::AbstractArray; inner = nothing, outer = nothing)
    return _RepeatInnerOuter.repeat(A, inner=inner, outer=outer)
end

module _RepeatInnerOuter

function repeat(arr; inner=nothing, outer=nothing)
    check(arr, inner, outer)
    arr, inner, outer = resolve(arr, inner, outer)
    repeat_inner_outer(arr, inner, outer)
end

to_tuple(t::Tuple) = t
to_tuple(x::Integer) = (x,)
to_tuple(itr) = tuple(itr...)

function pad(a, b)
    N = max(length(a), length(b))
    Base.fill_to_length(a, 1, Val(N)), Base.fill_to_length(b, 1, Val(N))
end
function pad(a, b, c)
    N = max(max(length(a), length(b)), length(c))
    Base.fill_to_length(a, 1, Val(N)), Base.fill_to_length(b, 1, Val(N)), Base.fill_to_length(c, 1, Val(N))
end

function resolve(arr::AbstractArray{<:Any, N}, inner::NTuple{N, Any}, outer::NTuple{N,Any}) where {N}
    arr, inner, outer
end
function resolve(arr, inner, outer)
    dims, inner, outer = pad(size(arr), to_tuple(inner), to_tuple(outer))
    reshape(arr, dims), inner, outer
end
function resolve(arr, inner::Nothing, outer::Nothing)
    return arr, inner, outer
end
function resolve(arr, inner::Nothing, outer)
    dims, outer = pad(size(arr), to_tuple(outer))
    reshape(arr, dims), inner, outer
end
function resolve(arr, inner, outer::Nothing)
    dims, inner = pad(size(arr), to_tuple(inner))
    reshape(arr, dims), inner, outer
end

function check(arr, inner, outer)
    if inner !== nothing
        # TODO: Currently one based indexing is demanded for inner !== nothing,
        # but not for outer !== nothing. Decide for something consistent.
        Base.require_one_based_indexing(arr)
        if any(<(0), inner)
            throw(ArgumentError("no inner repetition count may be negative; got $inner"))
        end
        if length(inner) < ndims(arr)
            throw(ArgumentError("number of inner repetitions ($(length(inner))) cannot be less than number of dimensions of input array ($(ndims(arr)))"))
        end
    end
    if outer !== nothing
        if any(<(0), outer)
            throw(ArgumentError("no outer repetition count may be negative; got $outer"))
        end
        if (length(outer) < ndims(arr)) && (inner !== nothing)
            throw(ArgumentError("number of outer repetitions ($(length(outer))) cannot be less than number of dimensions of input array ($(ndims(arr)))"))
        end
    end
end

repeat_inner_outer(arr, inner::Nothing, outer::Nothing) = arr
repeat_inner_outer(arr, ::Nothing, outer) = repeat_outer(arr, outer)
repeat_inner_outer(arr, inner, ::Nothing) = repeat_inner(arr, inner)
repeat_inner_outer(arr, inner, outer) = repeat_outer(repeat_inner(arr, inner), outer)

function repeat_outer(a::AbstractMatrix, (m,n)::NTuple{2, Any})
    o, p = size(a,1), size(a,2)
    b = similar(a, o*m, p*n)
    for j=1:n
        d = (j-1)*p+1
        R = d:d+p-1
        for i=1:m
            c = (i-1)*o+1
            @inbounds b[c:c+o-1, R] = a
        end
    end
    return b
end

function repeat_outer(a::AbstractVector, (m,)::Tuple{Any})
    o = length(a)
    b = similar(a, o*m)
    for i=1:m
        c = (i-1)*o+1
        @inbounds b[c:c+o-1] = a
    end
    return b
end

function repeat_outer(arr::AbstractArray{<:Any,N}, dims::NTuple{N,Any}) where {N}
    insize  = size(arr)
    outsize = map(*, insize, dims)
    out = similar(arr, outsize)
    for I in CartesianIndices(arr)
        for J in CartesianIndices(dims)
            TIJ = map(Tuple(I), Tuple(J), insize) do i, j, d
                i + d * (j-1)
            end
            IJ = CartesianIndex(TIJ)
            @inbounds out[IJ] = arr[I]
        end
    end
    return out
end

function repeat_inner(arr, inner)
    outsize = map(*, size(arr), inner)
    out = similar(arr, outsize)
    for I in CartesianIndices(arr)
        for J in CartesianIndices(inner)
            TIJ = map(Tuple(I), Tuple(J), inner) do i, j, d
                (i-1) * d + j
            end
            IJ = CartesianIndex(TIJ)
            @inbounds out[IJ] = arr[I]
        end
    end
    return out
end

end#module
P   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/arraymath.jl      # This file is a part of Julia. License is MIT: https://julialang.org/license

## Binary arithmetic operators ##

for f in (:+, :-)
    @eval function ($f)(A::AbstractArray, B::AbstractArray)
        promote_shape(A, B) # check size compatibility
        broadcast_preserving_zero_d($f, A, B)
    end
end

function +(A::Array, Bs::Array...)
    for B in Bs
        promote_shape(A, B) # check size compatibility
    end
    broadcast_preserving_zero_d(+, A, Bs...)
end

for f in (:/, :\, :*)
    if f !== :/
        @eval ($f)(A::Number, B::AbstractArray) = broadcast_preserving_zero_d($f, A, B)
    end
    if f !== :\
        @eval ($f)(A::AbstractArray, B::Number) = broadcast_preserving_zero_d($f, A, B)
    end
end

## data movement ##

"""
    reverse(A; dims=:)

Reverse `A` along dimension `dims`, which can be an integer (a
single dimension), a tuple of integers (a tuple of dimensions)
or `:` (reverse along all the dimensions, the default).  See
also [`reverse!`](@ref) for in-place reversal.

# Examples
```jldoctest
julia> b = Int64[1 2; 3 4]
2×2 Matrix{Int64}:
 1  2
 3  4

julia> reverse(b, dims=2)
2×2 Matrix{Int64}:
 2  1
 4  3

julia> reverse(b)
2×2 Matrix{Int64}:
 4  3
 2  1
```

!!! compat "Julia 1.6"
    Prior to Julia 1.6, only single-integer `dims` are supported in `reverse`.
"""
reverse(A::AbstractArray; dims=:) = _reverse(A, dims)
_reverse(A, dims) = reverse!(copymutable(A); dims)

"""
    reverse!(A; dims=:)

Like [`reverse`](@ref), but operates in-place in `A`.

!!! compat "Julia 1.6"
    Multidimensional `reverse!` requires Julia 1.6.
"""
reverse!(A::AbstractArray; dims=:) = _reverse!(A, dims)
_reverse!(A::AbstractArray{<:Any,N}, ::Colon) where {N} = _reverse!(A, ntuple(identity, Val{N}()))
_reverse!(A, dim::Integer) = _reverse!(A, (Int(dim),))
_reverse!(A, dims::NTuple{M,Integer}) where {M} = _reverse!(A, Int.(dims))
function _reverse!(A::AbstractArray{<:Any,N}, dims::NTuple{M,Int}) where {N,M}
    dimrev = ntuple(k -> k in dims, Val{N}()) # boolean tuple indicating reversed dims

    if N < M || M != sum(dimrev)
        throw(ArgumentError("invalid dimensions $dims in reverse!"))
    end
    M == 0 && return A # nothing to reverse

    # swapping loop only needs to traverse ≈half of the array
    halfsz = ntuple(k -> k == dims[1] ? size(A,k) ÷ 2 : size(A,k), Val{N}())

    last1 = ntuple(k -> lastindex(A,k)+firstindex(A,k), Val{N}()) # offset for reversed index
    for i in CartesianIndices(ntuple(k -> firstindex(A,k):firstindex(A,k)-1+@inbounds(halfsz[k]), Val{N}()))
        iₜ = Tuple(i)
        iᵣ = CartesianIndex(ifelse.(dimrev, last1 .- iₜ, iₜ))
        @inbounds A[iᵣ], A[i] = A[i], A[iᵣ]
    end
    if M > 1 && isodd(size(A, dims[1]))
        # middle slice for odd dimensions must be recursively flipped
        mid = firstindex(A, dims[1]) + (size(A, dims[1]) ÷ 2)
        midslice = CartesianIndices(ntuple(k -> k == dims[1] ? (mid:mid) : (firstindex(A,k):lastindex(A,k)), Val{N}()))
        _reverse!(view(A, midslice), dims[2:end])
    end
    return A
end
# fix ambiguity with array.jl:
_reverse!(A::AbstractVector, dim::Tuple{Int}) = _reverse!(A, first(dim))


"""
    rotl90(A)

Rotate matrix `A` left 90 degrees.

# Examples
```jldoctest
julia> a = [1 2; 3 4]
2×2 Matrix{Int64}:
 1  2
 3  4

julia> rotl90(a)
2×2 Matrix{Int64}:
 2  4
 1  3
```
"""
function rotl90(A::AbstractMatrix)
    ind1, ind2 = axes(A)
    B = similar(A, (ind2,ind1))
    n = first(ind2)+last(ind2)
    for i=axes(A,1), j=ind2
        B[n-j,i] = A[i,j]
    end
    return B
end

"""
    rotr90(A)

Rotate matrix `A` right 90 degrees.

# Examples
```jldoctest
julia> a = [1 2; 3 4]
2×2 Matrix{Int64}:
 1  2
 3  4

julia> rotr90(a)
2×2 Matrix{Int64}:
 3  1
 4  2
```
"""
function rotr90(A::AbstractMatrix)
    ind1, ind2 = axes(A)
    B = similar(A, (ind2,ind1))
    m = first(ind1)+last(ind1)
    for i=ind1, j=axes(A,2)
        B[j,m-i] = A[i,j]
    end
    return B
end
"""
    rot180(A)

Rotate matrix `A` 180 degrees.

# Examples
```jldoctest
julia> a = [1 2; 3 4]
2×2 Matrix{Int64}:
 1  2
 3  4

julia> rot180(a)
2×2 Matrix{Int64}:
 4  3
 2  1
```
"""
function rot180(A::AbstractMatrix)
    B = similar(A)
    ind1, ind2 = axes(A,1), axes(A,2)
    m, n = first(ind1)+last(ind1), first(ind2)+last(ind2)
    for j=ind2, i=ind1
        B[m-i,n-j] = A[i,j]
    end
    return B
end
"""
    rotl90(A, k)

Left-rotate matrix `A` 90 degrees counterclockwise an integer `k` number of times.
If `k` is a multiple of four (including zero), this is equivalent to a `copy`.

# Examples
```jldoctest
julia> a = [1 2; 3 4]
2×2 Matrix{Int64}:
 1  2
 3  4

julia> rotl90(a,1)
2×2 Matrix{Int64}:
 2  4
 1  3

julia> rotl90(a,2)
2×2 Matrix{Int64}:
 4  3
 2  1

julia> rotl90(a,3)
2×2 Matrix{Int64}:
 3  1
 4  2

julia> rotl90(a,4)
2×2 Matrix{Int64}:
 1  2
 3  4
```
"""
function rotl90(A::AbstractMatrix, k::Integer)
    k = mod(k, 4)
    k == 1 ? rotl90(A) :
    k == 2 ? rot180(A) :
    k == 3 ? rotr90(A) : copy(A)
end
"""
    rotr90(A, k)

Right-rotate matrix `A` 90 degrees clockwise an integer `k` number of times.
If `k` is a multiple of four (including zero), this is equivalent to a `copy`.

# Examples
```jldoctest
julia> a = [1 2; 3 4]
2×2 Matrix{Int64}:
 1  2
 3  4

julia> rotr90(a,1)
2×2 Matrix{Int64}:
 3  1
 4  2

julia> rotr90(a,2)
2×2 Matrix{Int64}:
 4  3
 2  1

julia> rotr90(a,3)
2×2 Matrix{Int64}:
 2  4
 1  3

julia> rotr90(a,4)
2×2 Matrix{Int64}:
 1  2
 3  4
```
"""
rotr90(A::AbstractMatrix, k::Integer) = rotl90(A,-k)
"""
    rot180(A, k)

Rotate matrix `A` 180 degrees an integer `k` number of times.
If `k` is even, this is equivalent to a `copy`.

# Examples
```jldoctest
julia> a = [1 2; 3 4]
2×2 Matrix{Int64}:
 1  2
 3  4

julia> rot180(a,1)
2×2 Matrix{Int64}:
 4  3
 2  1

julia> rot180(a,2)
2×2 Matrix{Int64}:
 1  2
 3  4
```
"""
rot180(A::AbstractMatrix, k::Integer) = mod(k, 2) == 1 ? rot180(A) : copy(A)
Q   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/slicearray.jl�      """
    AbstractSlices{S,N} <: AbstractArray{S,N}

Supertype for arrays of slices into a parent array over some dimension(s),
returning views that select all the data from the other dimensions.

`parent` will return the parent array.
"""
abstract type AbstractSlices{T,N} <: AbstractArray{T,N} end

"""
    Slices{P,SM,AX,S,N} <: AbstractSlices{S,N}

An `AbstractArray` of slices into a parent array over specified dimension(s),
returning views that select all the data from the other dimension(s).

These should typically be constructed by [`eachslice`](@ref), [`eachcol`](@ref) or
[`eachrow`](@ref).

[`parent(s::Slices)`](@ref) will return the parent array.
"""
struct Slices{P,SM,AX,S,N} <: AbstractSlices{S,N}
    """
    Parent array
    """
    parent::P
    """
    A tuple of length `ndims(parent)`, denoting how each dimension should be handled:
      - an integer `i`: this is the `i`th dimension of the outer `Slices` object.
      - `:`: an "inner" dimension
    """
    slicemap::SM
    """
    A tuple of length `N` containing the [`axes`](@ref) of the `Slices` object.
    """
    axes::AX
end

unitaxis(::AbstractArray) = Base.OneTo(1)

function Slices(A::P, slicemap::SM, ax::AX) where {P,SM,AX}
    N = length(ax)
    argT = map((a,l) -> l === (:) ? Colon : eltype(a), axes(A), slicemap)
    S = Base.promote_op(view, P, argT...)
    Slices{P,SM,AX,S,N}(A, slicemap, ax)
end

_slice_check_dims(N) = nothing
function _slice_check_dims(N, dim, dims...)
    1 <= dim <= N || throw(DimensionMismatch("Invalid dimension $dim"))
    dim in dims && throw(DimensionMismatch("Dimensions $dims are not unique"))
    _slice_check_dims(N,dims...)
end

@constprop :aggressive function _eachslice(A::AbstractArray{T,N}, dims::NTuple{M,Integer}, drop::Bool) where {T,N,M}
    _slice_check_dims(N,dims...)
    if drop
        # if N = 4, dims = (3,1) then
        # axes = (axes(A,3), axes(A,1))
        # slicemap = (2, :, 1, :)
        ax = map(dim -> axes(A,dim), dims)
        slicemap = ntuple(dim -> something(findfirst(isequal(dim), dims), (:)), N)
        return Slices(A, slicemap, ax)
    else
        # if N = 4, dims = (3,1) then
        # axes = (axes(A,1), OneTo(1), axes(A,3), OneTo(1))
        # slicemap = (1, :, 3, :)
        ax = ntuple(dim -> dim in dims ? axes(A,dim) : unitaxis(A), N)
        slicemap = ntuple(dim -> dim in dims ? dim : (:), N)
        return Slices(A, slicemap, ax)
    end
end
@inline function _eachslice(A::AbstractArray, dim::Integer, drop::Bool)
    _eachslice(A, (dim,), drop)
end

"""
    eachslice(A::AbstractArray; dims, drop=true)

Create a [`Slices`](@ref) object that is an array of slices over dimensions `dims` of `A`, returning
views that select all the data from the other dimensions in `A`. `dims` can either by an
integer or a tuple of integers.

If `drop = true` (the default), the outer `Slices` will drop the inner dimensions, and
the ordering of the dimensions will match those in `dims`. If `drop = false`, then the
`Slices` will have the same dimensionality as the underlying array, with inner
dimensions having size 1.

See [`stack`](@ref)`(slices; dims)` for the inverse of `eachslice(A; dims::Integer)`.

See also [`eachrow`](@ref), [`eachcol`](@ref), [`mapslices`](@ref) and [`selectdim`](@ref).

!!! compat "Julia 1.1"
     This function requires at least Julia 1.1.

!!! compat "Julia 1.9"
     Prior to Julia 1.9, this returned an iterator, and only a single dimension `dims` was supported.

# Example

```jldoctest
julia> m = [1 2 3; 4 5 6; 7 8 9]
3×3 Matrix{Int64}:
 1  2  3
 4  5  6
 7  8  9

julia> s = eachslice(m, dims=1)
3-element RowSlices{Matrix{Int64}, Tuple{Base.OneTo{Int64}}, SubArray{Int64, 1, Matrix{Int64}, Tuple{Int64, Base.Slice{Base.OneTo{Int64}}}, true}}:
 [1, 2, 3]
 [4, 5, 6]
 [7, 8, 9]

julia> s[1]
3-element view(::Matrix{Int64}, 1, :) with eltype Int64:
 1
 2
 3

julia> eachslice(m, dims=1, drop=false)
3×1 Slices{Matrix{Int64}, Tuple{Int64, Colon}, Tuple{Base.OneTo{Int64}, Base.OneTo{Int64}}, SubArray{Int64, 1, Matrix{Int64}, Tuple{Int64, Base.Slice{Base.OneTo{Int64}}}, true}, 2}:
 [1, 2, 3]
 [4, 5, 6]
 [7, 8, 9]
```
"""
@inline function eachslice(A; dims, drop=true)
    _eachslice(A, dims, drop)
end

"""
    eachrow(A::AbstractVecOrMat) <: AbstractVector

Create a [`RowSlices`](@ref) object that is a vector of rows of matrix or vector `A`.
Row slices are returned as `AbstractVector` views of `A`.

For the inverse, see [`stack`](@ref)`(rows; dims=1)`.

See also [`eachcol`](@ref), [`eachslice`](@ref) and [`mapslices`](@ref).

!!! compat "Julia 1.1"
     This function requires at least Julia 1.1.

!!! compat "Julia 1.9"
     Prior to Julia 1.9, this returned an iterator.

# Example

```jldoctest
julia> a = [1 2; 3 4]
2×2 Matrix{Int64}:
 1  2
 3  4

julia> s = eachrow(a)
2-element RowSlices{Matrix{Int64}, Tuple{Base.OneTo{Int64}}, SubArray{Int64, 1, Matrix{Int64}, Tuple{Int64, Base.Slice{Base.OneTo{Int64}}}, true}}:
 [1, 2]
 [3, 4]

julia> s[1]
2-element view(::Matrix{Int64}, 1, :) with eltype Int64:
 1
 2
```
"""
eachrow(A::AbstractMatrix) = _eachslice(A, (1,), true)
eachrow(A::AbstractVector) = eachrow(reshape(A, size(A,1), 1))

"""
    eachcol(A::AbstractVecOrMat) <: AbstractVector

Create a [`ColumnSlices`](@ref) object that is a vector of columns of matrix or vector `A`.
Column slices are returned as `AbstractVector` views of `A`.

For the inverse, see [`stack`](@ref)`(cols)` or `reduce(`[`hcat`](@ref)`, cols)`.

See also [`eachrow`](@ref), [`eachslice`](@ref) and [`mapslices`](@ref).

!!! compat "Julia 1.1"
     This function requires at least Julia 1.1.

!!! compat "Julia 1.9"
     Prior to Julia 1.9, this returned an iterator.

# Example

```jldoctest
julia> a = [1 2; 3 4]
2×2 Matrix{Int64}:
 1  2
 3  4

julia> s = eachcol(a)
2-element ColumnSlices{Matrix{Int64}, Tuple{Base.OneTo{Int64}}, SubArray{Int64, 1, Matrix{Int64}, Tuple{Base.Slice{Base.OneTo{Int64}}, Int64}, true}}:
 [1, 3]
 [2, 4]

julia> s[1]
2-element view(::Matrix{Int64}, :, 1) with eltype Int64:
 1
 3
```
"""
eachcol(A::AbstractMatrix) = _eachslice(A, (2,), true)
eachcol(A::AbstractVector) = eachcol(reshape(A, size(A, 1), 1))

"""
    RowSlices{M,AX,S}

A special case of [`Slices`](@ref) that is a vector of row slices of a matrix, as
constructed by [`eachrow`](@ref).

[`parent`](@ref) can be used to get the underlying matrix.
"""
const RowSlices{P<:AbstractMatrix,AX,S<:AbstractVector} = Slices{P,Tuple{Int,Colon},AX,S,1}

"""
    ColumnSlices{M,AX,S}

A special case of [`Slices`](@ref) that is a vector of column slices of a matrix, as
constructed by [`eachcol`](@ref).

[`parent`](@ref) can be used to get the underlying matrix.
"""
const ColumnSlices{P<:AbstractMatrix,AX,S<:AbstractVector} = Slices{P,Tuple{Colon,Int},AX,S,1}


IteratorSize(::Type{Slices{P,SM,AX,S,N}}) where {P,SM,AX,S,N} = HasShape{N}()
axes(s::Slices) = s.axes
size(s::Slices) = map(length, s.axes)

@inline function _slice_index(s::Slices, c...)
    return map(l -> l === (:) ? (:) : c[l], s.slicemap)
end

@inline function getindex(s::Slices{P,SM,AX,S,N}, I::Vararg{Int,N}) where {P,SM,AX,S,N}
    @boundscheck checkbounds(s, I...)
    @inbounds view(s.parent, _slice_index(s, I...)...)
end
@inline function setindex!(s::Slices{P,SM,AX,S,N}, val, I::Vararg{Int,N}) where {P,SM,AX,S,N}
    @boundscheck checkbounds(s, I...)
    @inbounds s.parent[_slice_index(s, I...)...] = val
end

parent(s::Slices) = s.parent
O   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/simdloop.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

# Support for @simd for

module SimdLoop

export @simd, simd_outer_range, simd_inner_length, simd_index

# Error thrown from ill-formed uses of @simd
struct SimdError <: Exception
    msg::String
end

# Parse iteration space expression
#       symbol '=' range
#       symbol 'in' range
function parse_iteration_space(x)
    (isa(x, Expr) && (x.head === :(=) || x.head === :in)) || throw(SimdError("= or in expected"))
    length(x.args) == 2 || throw(SimdError("simd range syntax is wrong"))
    isa(x.args[1], Symbol) || throw(SimdError("simd loop index must be a symbol"))
    x.args # symbol, range
end

# reject invalid control flow statements in @simd loop body
function check_body!(x::Expr)
    if x.head === :break || x.head === :continue
        throw(SimdError("$(x.head) is not allowed inside a @simd loop body"))
    elseif x.head === :macrocall && x.args[1] === Symbol("@goto")
        throw(SimdError("@goto is not allowed inside a @simd loop body"))
    end
    for arg in x.args
        check_body!(arg)
    end
    return true
end
check_body!(x::QuoteNode) = check_body!(x.value)
check_body!(x) = true

# @simd splits a for loop into two loops: an outer scalar loop and
# an inner loop marked with :loopinfo. The simd_... functions define
# the splitting.
# Custom iterators that do not support random access cannot support
# vectorization. In order to be compatible with `@simd` annotated loops,
#they should override `simd_inner_length(v::MyIter, j) = 1`,
#`simd_outer_range(v::MyIter) = v`, and `simd_index(v::MyIter, j, i) = j`.

# Get range for outer loop.
simd_outer_range(r) = 0:0

# Get trip count for inner loop.
@inline simd_inner_length(r, j) = Base.length(r)

# Construct user-level element from original range, outer loop index j, and inner loop index i.
@inline simd_index(r, j, i) = (@inbounds ret = r[i+firstindex(r)]; ret)

# Compile Expr x in context of @simd.
function compile(x, ivdep)
    (isa(x, Expr) && x.head === :for) || throw(SimdError("for loop expected"))
    length(x.args) == 2 || throw(SimdError("1D for loop expected"))
    check_body!(x)

    var,range = parse_iteration_space(x.args[1])
    r = gensym("r") # Range value
    j = gensym("i") # Iteration variable for outer loop
    n = gensym("n") # Trip count for inner loop
    i = gensym("i") # Trip index for inner loop
    quote
        # Evaluate range value once, to enhance type and data flow analysis by optimizers.
        let $r = $range
            for $j in Base.simd_outer_range($r)
                let $n = Base.simd_inner_length($r,$j)
                    if zero($n) < $n
                        # Lower loop in way that seems to work best for LLVM 3.3 vectorizer.
                        let $i = zero($n)
                            while $i < $n
                                local $var = Base.simd_index($r,$j,$i)
                                $(x.args[2])        # Body of loop
                                $i += 1
                                $(Expr(:loopinfo, Symbol("julia.simdloop"), ivdep))  # Mark loop as SIMD loop
                            end
                        end
                    end
                end
            end
        end
        nothing
    end
end

"""
    @simd

Annotate a `for` loop to allow the compiler to take extra liberties to allow loop re-ordering

!!! warning
    This feature is experimental and could change or disappear in future versions of Julia.
    Incorrect use of the `@simd` macro may cause unexpected results.

The object iterated over in a `@simd for` loop should be a one-dimensional range.
By using `@simd`, you are asserting several properties of the loop:

* It is safe to execute iterations in arbitrary or overlapping order, with special consideration for reduction variables.
* Floating-point operations on reduction variables can be reordered or contracted, possibly causing different results than without `@simd`.

In many cases, Julia is able to automatically vectorize inner for loops without the use of `@simd`.
Using `@simd` gives the compiler a little extra leeway to make it possible in more situations. In
either case, your inner loop should have the following properties to allow vectorization:

* The loop must be an innermost loop
* The loop body must be straight-line code. Therefore, [`@inbounds`](@ref) is
    currently needed for all array accesses. The compiler can sometimes turn
    short `&&`, `||`, and `?:` expressions into straight-line code if it is safe
    to evaluate all operands unconditionally. Consider using the [`ifelse`](@ref)
    function instead of `?:` in the loop if it is safe to do so.
* Accesses must have a stride pattern and cannot be "gathers" (random-index
    reads) or "scatters" (random-index writes).
* The stride should be unit stride.

!!! note
    The `@simd` does not assert by default that the loop is completely free of loop-carried
    memory dependencies, which is an assumption that can easily be violated in generic code.
    If you are writing non-generic code, you can use `@simd ivdep for ... end` to also assert that:

* There exists no loop-carried memory dependencies
* No iteration ever waits on a previous iteration to make forward progress.
"""
macro simd(forloop)
    esc(compile(forloop, nothing))
end

macro simd(ivdep, forloop)
    if ivdep === :ivdep
        esc(compile(forloop, Symbol("julia.ivdep")))
    else
        throw(SimdError("Only ivdep is valid as the first argument to @simd"))
    end
end

end # module SimdLoop
M   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/reduce.jlT�      # This file is a part of Julia. License is MIT: https://julialang.org/license

## reductions ##

###### Generic (map)reduce functions ######

if Int === Int32
    const SmallSigned = Union{Int8,Int16}
    const SmallUnsigned = Union{UInt8,UInt16}
else
    const SmallSigned = Union{Int8,Int16,Int32}
    const SmallUnsigned = Union{UInt8,UInt16,UInt32}
end

abstract type AbstractBroadcasted end
const AbstractArrayOrBroadcasted = Union{AbstractArray, AbstractBroadcasted}

"""
    Base.add_sum(x, y)

The reduction operator used in `sum`. The main difference from [`+`](@ref) is that small
integers are promoted to `Int`/`UInt`.
"""
add_sum(x, y) = x + y
add_sum(x::SmallSigned, y::SmallSigned) = Int(x) + Int(y)
add_sum(x::SmallUnsigned, y::SmallUnsigned) = UInt(x) + UInt(y)
add_sum(x::Real, y::Real)::Real = x + y

"""
    Base.mul_prod(x, y)

The reduction operator used in `prod`. The main difference from [`*`](@ref) is that small
integers are promoted to `Int`/`UInt`.
"""
mul_prod(x, y) = x * y
mul_prod(x::SmallSigned, y::SmallSigned) = Int(x) * Int(y)
mul_prod(x::SmallUnsigned, y::SmallUnsigned) = UInt(x) * UInt(y)
mul_prod(x::Real, y::Real)::Real = x * y

## foldl && mapfoldl

function mapfoldl_impl(f::F, op::OP, nt, itr) where {F,OP}
    op′, itr′ = _xfadjoint(BottomRF(op), Generator(f, itr))
    return foldl_impl(op′, nt, itr′)
end

function foldl_impl(op::OP, nt, itr) where {OP}
    v = _foldl_impl(op, nt, itr)
    v isa _InitialValue && return reduce_empty_iter(op, itr)
    return v
end

function _foldl_impl(op::OP, init, itr) where {OP}
    # Unroll the while loop once; if init is known, the call to op may
    # be evaluated at compile time
    y = iterate(itr)
    y === nothing && return init
    v = op(init, y[1])
    while true
        y = iterate(itr, y[2])
        y === nothing && break
        v = op(v, y[1])
    end
    return v
end

function _foldl_impl(op, init, itr::Union{Tuple,NamedTuple})
    length(itr) <= 32 && return afoldl(op, init, itr...)
    @invoke _foldl_impl(op, init, itr::Any)
end

struct _InitialValue end

"""
    BottomRF(rf) -> rf′

"Bottom" reducing function.  This is a thin wrapper around the `op` argument
passed to `foldl`-like functions for handling the initial invocation to call
[`reduce_first`](@ref).
"""
struct BottomRF{T}
    rf::T
end

@inline (op::BottomRF)(::_InitialValue, x) = reduce_first(op.rf, x)
@inline (op::BottomRF)(acc, x) = op.rf(acc, x)

"""
    MappingRF(f, rf) -> rf′

Create a mapping reducing function `rf′(acc, x) = rf(acc, f(x))`.
"""
struct MappingRF{F, T}
    f::F
    rf::T
    MappingRF(f::F, rf::T) where {F,T} = new{F,T}(f, rf)
    MappingRF(::Type{f}, rf::T) where {f,T} = new{Type{f},T}(f, rf)
end

@inline (op::MappingRF)(acc, x) = op.rf(acc, op.f(x))

"""
    FilteringRF(f, rf) -> rf′

Create a filtering reducing function `rf′(acc, x) = f(x) ? rf(acc, x) : acc`.
"""
struct FilteringRF{F, T}
    f::F
    rf::T
end

@inline (op::FilteringRF)(acc, x) = op.f(x) ? op.rf(acc, x) : acc

"""
    FlatteningRF(rf) -> rf′

Create a flattening reducing function that is roughly equivalent to
`rf′(acc, x) = foldl(rf, x; init=acc)`.
"""
struct FlatteningRF{T}
    rf::T
end

@inline function (op::FlatteningRF)(acc, x)
    op′, itr′ = _xfadjoint(op.rf, x)
    return _foldl_impl(op′, acc, itr′)
end

"""
    _xfadjoint(op, itr) -> op′, itr′

Given a pair of reducing function `op` and an iterator `itr`, return a pair
`(op′, itr′)` of similar types.  If the iterator `itr` is transformed by an
iterator transform `ixf` whose adjoint transducer `xf` is known, `op′ = xf(op)`
and `itr′ = ixf⁻¹(itr)` is returned.  Otherwise, `op` and `itr` are returned
as-is.  For example, transducer `rf -> MappingRF(f, rf)` is the adjoint of
iterator transform `itr -> Generator(f, itr)`.

Nested iterator transforms are converted recursively.  That is to say,
given `op` and

    itr = (ixf₁ ∘ ixf₂ ∘ ... ∘ ixfₙ)(itr′)

what is returned is `itr′` and

    op′ = (xfₙ ∘ ... ∘ xf₂ ∘ xf₁)(op)
"""
function _xfadjoint(op, itr)
    itr′, wrap = _xfadjoint_unwrap(itr)
    wrap(op), itr′
end

_xfadjoint_unwrap(itr) = itr, identity
function _xfadjoint_unwrap(itr::Generator)
    itr′, wrap = _xfadjoint_unwrap(itr.iter)
    itr.f === identity && return itr′, wrap
    return itr′, wrap ∘ Fix1(MappingRF, itr.f)
end
function _xfadjoint_unwrap(itr::Filter)
    itr′, wrap = _xfadjoint_unwrap(itr.itr)
    return itr′, wrap ∘ Fix1(FilteringRF, itr.flt)
end
function _xfadjoint_unwrap(itr::Flatten)
    itr′, wrap = _xfadjoint_unwrap(itr.it)
    return itr′, wrap ∘ FlatteningRF
end

"""
    mapfoldl(f, op, itr; [init])

Like [`mapreduce`](@ref), but with guaranteed left associativity, as in [`foldl`](@ref).
If provided, the keyword argument `init` will be used exactly once. In general, it will be
necessary to provide `init` to work with empty collections.
"""
mapfoldl(f, op, itr; init=_InitialValue()) = mapfoldl_impl(f, op, init, itr)

"""
    foldl(op, itr; [init])

Like [`reduce`](@ref), but with guaranteed left associativity. If provided, the keyword
argument `init` will be used exactly once. In general, it will be necessary to provide
`init` to work with empty collections.

See also [`mapfoldl`](@ref), [`foldr`](@ref), [`accumulate`](@ref).

# Examples
```jldoctest
julia> foldl(=>, 1:4)
((1 => 2) => 3) => 4

julia> foldl(=>, 1:4; init=0)
(((0 => 1) => 2) => 3) => 4

julia> accumulate(=>, (1,2,3,4))
(1, 1 => 2, (1 => 2) => 3, ((1 => 2) => 3) => 4)
```
"""
foldl(op, itr; kw...) = mapfoldl(identity, op, itr; kw...)

## foldr & mapfoldr

function mapfoldr_impl(f, op, nt, itr)
    op′, itr′ = _xfadjoint(BottomRF(FlipArgs(op)), Generator(f, itr))
    return foldl_impl(op′, nt, _reverse_iter(itr′))
end

_reverse_iter(itr) = Iterators.reverse(itr)
_reverse_iter(itr::Union{Tuple,NamedTuple}) = length(itr) <= 32 ? reverse(itr) : Iterators.reverse(itr) #33235

struct FlipArgs{F}
    f::F
end

@inline (f::FlipArgs)(x, y) = f.f(y, x)

"""
    mapfoldr(f, op, itr; [init])

Like [`mapreduce`](@ref), but with guaranteed right associativity, as in [`foldr`](@ref). If
provided, the keyword argument `init` will be used exactly once. In general, it will be
necessary to provide `init` to work with empty collections.
"""
mapfoldr(f, op, itr; init=_InitialValue()) = mapfoldr_impl(f, op, init, itr)


"""
    foldr(op, itr; [init])

Like [`reduce`](@ref), but with guaranteed right associativity. If provided, the keyword
argument `init` will be used exactly once. In general, it will be necessary to provide
`init` to work with empty collections.

# Examples
```jldoctest
julia> foldr(=>, 1:4)
1 => (2 => (3 => 4))

julia> foldr(=>, 1:4; init=0)
1 => (2 => (3 => (4 => 0)))
```
"""
foldr(op, itr; kw...) = mapfoldr(identity, op, itr; kw...)

## reduce & mapreduce

# `mapreduce_impl()` is called by `mapreduce()` (via `_mapreduce()`, when `A`
# supports linear indexing) and does actual calculations (for `A[ifirst:ilast]` subset).
# For efficiency, no parameter validity checks are done, it's the caller's responsibility.
# `ifirst:ilast` range is assumed to be a valid non-empty subset of `A` indices.

# This is a generic implementation of `mapreduce_impl()`,
# certain `op` (e.g. `min` and `max`) may have their own specialized versions.
@noinline function mapreduce_impl(f, op, A::AbstractArrayOrBroadcasted,
                                  ifirst::Integer, ilast::Integer, blksize::Int)
    if ifirst == ilast
        @inbounds a1 = A[ifirst]
        return mapreduce_first(f, op, a1)
    elseif ilast - ifirst < blksize
        # sequential portion
        @inbounds a1 = A[ifirst]
        @inbounds a2 = A[ifirst+1]
        v = op(f(a1), f(a2))
        @simd for i = ifirst + 2 : ilast
            @inbounds ai = A[i]
            v = op(v, f(ai))
        end
        return v
    else
        # pairwise portion
        imid = ifirst + (ilast - ifirst) >> 1
        v1 = mapreduce_impl(f, op, A, ifirst, imid, blksize)
        v2 = mapreduce_impl(f, op, A, imid+1, ilast, blksize)
        return op(v1, v2)
    end
end

mapreduce_impl(f, op, A::AbstractArrayOrBroadcasted, ifirst::Integer, ilast::Integer) =
    mapreduce_impl(f, op, A, ifirst, ilast, pairwise_blocksize(f, op))

"""
    mapreduce(f, op, itrs...; [init])

Apply function `f` to each element(s) in `itrs`, and then reduce the result using the binary
function `op`. If provided, `init` must be a neutral element for `op` that will be returned
for empty collections. It is unspecified whether `init` is used for non-empty collections.
In general, it will be necessary to provide `init` to work with empty collections.

[`mapreduce`](@ref) is functionally equivalent to calling
`reduce(op, map(f, itr); init=init)`, but will in general execute faster since no
intermediate collection needs to be created. See documentation for [`reduce`](@ref) and
[`map`](@ref).

!!! compat "Julia 1.2"
    `mapreduce` with multiple iterators requires Julia 1.2 or later.

# Examples
```jldoctest
julia> mapreduce(x->x^2, +, [1:3;]) # == 1 + 4 + 9
14
```

The associativity of the reduction is implementation-dependent. Additionally, some
implementations may reuse the return value of `f` for elements that appear multiple times in
`itr`. Use [`mapfoldl`](@ref) or [`mapfoldr`](@ref) instead for
guaranteed left or right associativity and invocation of `f` for every value.
"""
mapreduce(f, op, itr; kw...) = mapfoldl(f, op, itr; kw...)
mapreduce(f, op, itrs...; kw...) = reduce(op, Generator(f, itrs...); kw...)

# Note: sum_seq usually uses four or more accumulators after partial
# unrolling, so each accumulator gets at most 256 numbers
pairwise_blocksize(f, op) = 1024

# This combination appears to show a benefit from a larger block size
pairwise_blocksize(::typeof(abs2), ::typeof(+)) = 4096


# handling empty arrays
_empty_reduce_error() = throw(ArgumentError("reducing over an empty collection is not allowed"))
_empty_reduce_error(@nospecialize(f), @nospecialize(T::Type)) = throw(ArgumentError("""
    reducing with $f over an empty collection of element type $T is not allowed.
    You may be able to prevent this error by supplying an `init` value to the reducer."""))

"""
    Base.reduce_empty(op, T)

The value to be returned when calling [`reduce`](@ref), [`foldl`](@ref) or [`foldr`](@ref)
with reduction `op` over an empty array with element type of `T`.

This should only be defined in unambiguous cases; for example,

```julia
Base.reduce_empty(::typeof(+), ::Type{T}) where T = zero(T)
```

is justified (the sum of zero elements is zero), whereas
`reduce_empty(::typeof(max), ::Type{Any})` is not (the maximum value of an empty collection
is generally ambiguous, and especially so when the element type is unknown).

As an alternative, consider supplying an `init` value to the reducer.
"""
reduce_empty(::typeof(+), ::Type{Union{}}) = _empty_reduce_error(+, Union{})
reduce_empty(::typeof(+), ::Type{T}) where {T} = zero(T)
reduce_empty(::typeof(+), ::Type{Bool}) = zero(Int)
reduce_empty(::typeof(*), ::Type{Union{}}) = _empty_reduce_error(*, Union{})
reduce_empty(::typeof(*), ::Type{T}) where {T} = one(T)
reduce_empty(::typeof(*), ::Type{<:AbstractChar}) = ""
reduce_empty(::typeof(&), ::Type{Bool}) = true
reduce_empty(::typeof(|), ::Type{Bool}) = false

reduce_empty(::typeof(add_sum), ::Type{Union{}}) = _empty_reduce_error(add_sum, Union{})
reduce_empty(::typeof(add_sum), ::Type{T}) where {T} = reduce_empty(+, T)
reduce_empty(::typeof(add_sum), ::Type{T}) where {T<:SmallSigned}  = zero(Int)
reduce_empty(::typeof(add_sum), ::Type{T}) where {T<:SmallUnsigned} = zero(UInt)
reduce_empty(::typeof(mul_prod), ::Type{Union{}}) = _empty_reduce_error(mul_prod, Union{})
reduce_empty(::typeof(mul_prod), ::Type{T}) where {T} = reduce_empty(*, T)
reduce_empty(::typeof(mul_prod), ::Type{T}) where {T<:SmallSigned}  = one(Int)
reduce_empty(::typeof(mul_prod), ::Type{T}) where {T<:SmallUnsigned} = one(UInt)

reduce_empty(op::BottomRF, ::Type{T}) where {T} = reduce_empty(op.rf, T)
reduce_empty(op::MappingRF, ::Type{T}) where {T} = mapreduce_empty(op.f, op.rf, T)
reduce_empty(op::FilteringRF, ::Type{T}) where {T} = reduce_empty(op.rf, T)
reduce_empty(op::FlipArgs, ::Type{T}) where {T} = reduce_empty(op.f, T)

"""
    Base.mapreduce_empty(f, op, T)

The value to be returned when calling [`mapreduce`](@ref), [`mapfoldl`](@ref`) or
[`mapfoldr`](@ref) with map `f` and reduction `op` over an empty array with element type
of `T`. See [`Base.reduce_empty`](@ref) for more information.
"""
mapreduce_empty(::typeof(identity), op, T) = reduce_empty(op, T)
mapreduce_empty(::typeof(abs), op, T)      = abs(reduce_empty(op, T))
mapreduce_empty(::typeof(abs2), op, T)     = abs2(reduce_empty(op, T))

mapreduce_empty(f::typeof(abs),  ::typeof(max), T) = abs(zero(T))
mapreduce_empty(f::typeof(abs2), ::typeof(max), T) = abs2(zero(T))

# For backward compatibility:
mapreduce_empty_iter(f, op, itr, ItrEltype) =
    reduce_empty_iter(MappingRF(f, op), itr, ItrEltype)

@inline reduce_empty_iter(op, itr) = reduce_empty_iter(op, itr, IteratorEltype(itr))
@inline reduce_empty_iter(op, itr, ::HasEltype) = reduce_empty(op, eltype(itr))
reduce_empty_iter(op, itr, ::EltypeUnknown) = throw(ArgumentError("""
    reducing over an empty collection of unknown element type is not allowed.
    You may be able to prevent this error by supplying an `init` value to the reducer."""))


# handling of single-element iterators
"""
    Base.reduce_first(op, x)

The value to be returned when calling [`reduce`](@ref), [`foldl`](@ref`) or
[`foldr`](@ref) with reduction `op` over an iterator which contains a single element
`x`. This value may also be used to initialise the recursion, so that `reduce(op, [x, y])`
may call `op(reduce_first(op, x), y)`.

The default is `x` for most types. The main purpose is to ensure type stability, so
additional methods should only be defined for cases where `op` gives a result with
different types than its inputs.
"""
reduce_first(op, x) = x
reduce_first(::typeof(+), x::Bool) = Int(x)
reduce_first(::typeof(*), x::AbstractChar) = string(x)

reduce_first(::typeof(add_sum), x) = reduce_first(+, x)
reduce_first(::typeof(add_sum), x::SmallSigned)   = Int(x)
reduce_first(::typeof(add_sum), x::SmallUnsigned) = UInt(x)
reduce_first(::typeof(mul_prod), x) = reduce_first(*, x)
reduce_first(::typeof(mul_prod), x::SmallSigned)   = Int(x)
reduce_first(::typeof(mul_prod), x::SmallUnsigned) = UInt(x)

"""
    Base.mapreduce_first(f, op, x)

The value to be returned when calling [`mapreduce`](@ref), [`mapfoldl`](@ref`) or
[`mapfoldr`](@ref) with map `f` and reduction `op` over an iterator which contains a
single element `x`. This value may also be used to initialise the recursion, so that
`mapreduce(f, op, [x, y])` may call `op(mapreduce_first(f, op, x), f(y))`.

The default is `reduce_first(op, f(x))`.
"""
mapreduce_first(f, op, x) = reduce_first(op, f(x))

_mapreduce(f, op, A::AbstractArrayOrBroadcasted) = _mapreduce(f, op, IndexStyle(A), A)

function _mapreduce(f, op, ::IndexLinear, A::AbstractArrayOrBroadcasted)
    inds = LinearIndices(A)
    n = length(inds)
    if n == 0
        return mapreduce_empty_iter(f, op, A, IteratorEltype(A))
    elseif n == 1
        @inbounds a1 = A[first(inds)]
        return mapreduce_first(f, op, a1)
    elseif n < 16 # process short array here, avoid mapreduce_impl() compilation
        @inbounds i = first(inds)
        @inbounds a1 = A[i]
        @inbounds a2 = A[i+=1]
        s = op(f(a1), f(a2))
        while i < last(inds)
            @inbounds Ai = A[i+=1]
            s = op(s, f(Ai))
        end
        return s
    else
        return mapreduce_impl(f, op, A, first(inds), last(inds))
    end
end

mapreduce(f, op, a::Number) = mapreduce_first(f, op, a)

_mapreduce(f, op, ::IndexCartesian, A::AbstractArrayOrBroadcasted) = mapfoldl(f, op, A)

"""
    reduce(op, itr; [init])

Reduce the given collection `itr` with the given binary operator `op`. If provided, the
initial value `init` must be a neutral element for `op` that will be returned for empty
collections. It is unspecified whether `init` is used for non-empty collections.

For empty collections, providing `init` will be necessary, except for some special cases
(e.g. when `op` is one of `+`, `*`, `max`, `min`, `&`, `|`) when Julia can determine the
neutral element of `op`.

Reductions for certain commonly-used operators may have special implementations, and
should be used instead: [`maximum`](@ref)`(itr)`, [`minimum`](@ref)`(itr)`, [`sum`](@ref)`(itr)`,
[`prod`](@ref)`(itr)`, [`any`](@ref)`(itr)`, [`all`](@ref)`(itr)`.
There are efficient methods for concatenating certain arrays of arrays
by calling `reduce(`[`vcat`](@ref)`, arr)` or `reduce(`[`hcat`](@ref)`, arr)`.

The associativity of the reduction is implementation dependent. This means that you can't
use non-associative operations like `-` because it is undefined whether `reduce(-,[1,2,3])`
should be evaluated as `(1-2)-3` or `1-(2-3)`. Use [`foldl`](@ref) or
[`foldr`](@ref) instead for guaranteed left or right associativity.

Some operations accumulate error. Parallelism will be easier if the reduction can be
executed in groups. Future versions of Julia might change the algorithm. Note that the
elements are not reordered if you use an ordered collection.

# Examples
```jldoctest
julia> reduce(*, [2; 3; 4])
24

julia> reduce(*, [2; 3; 4]; init=-1)
-24
```
"""
reduce(op, itr; kw...) = mapreduce(identity, op, itr; kw...)

reduce(op, a::Number) = a  # Do we want this?

###### Specific reduction functions ######

## sum

"""
    sum(f, itr; [init])

Sum the results of calling function `f` on each element of `itr`.

The return type is `Int` for signed integers of less than system word size, and
`UInt` for unsigned integers of less than system word size.  For all other
arguments, a common return type is found to which all arguments are promoted.

The value returned for empty `itr` can be specified by `init`. It must be
the additive identity (i.e. zero) as it is unspecified whether `init` is used
for non-empty collections.

!!! compat "Julia 1.6"
    Keyword argument `init` requires Julia 1.6 or later.

# Examples
```jldoctest
julia> sum(abs2, [2; 3; 4])
29
```

Note the important difference between `sum(A)` and `reduce(+, A)` for arrays
with small integer eltype:

```jldoctest
julia> sum(Int8[100, 28])
128

julia> reduce(+, Int8[100, 28])
-128
```

In the former case, the integers are widened to system word size and therefore
the result is 128. In the latter case, no such widening happens and integer
overflow results in -128.
"""
sum(f, a; kw...) = mapreduce(f, add_sum, a; kw...)

"""
    sum(itr; [init])

Return the sum of all elements in a collection.

The return type is `Int` for signed integers of less than system word size, and
`UInt` for unsigned integers of less than system word size.  For all other
arguments, a common return type is found to which all arguments are promoted.

The value returned for empty `itr` can be specified by `init`. It must be
the additive identity (i.e. zero) as it is unspecified whether `init` is used
for non-empty collections.

!!! compat "Julia 1.6"
    Keyword argument `init` requires Julia 1.6 or later.

See also: [`reduce`](@ref), [`mapreduce`](@ref), [`count`](@ref), [`union`](@ref).

# Examples
```jldoctest
julia> sum(1:20)
210

julia> sum(1:20; init = 0.0)
210.0
```
"""
sum(a; kw...) = sum(identity, a; kw...)
sum(a::AbstractArray{Bool}; kw...) =
    isempty(kw) ? count(a) : reduce(add_sum, a; kw...)

## prod
"""
    prod(f, itr; [init])

Return the product of `f` applied to each element of `itr`.

The return type is `Int` for signed integers of less than system word size, and
`UInt` for unsigned integers of less than system word size.  For all other
arguments, a common return type is found to which all arguments are promoted.

The value returned for empty `itr` can be specified by `init`. It must be the
multiplicative identity (i.e. one) as it is unspecified whether `init` is used
for non-empty collections.

!!! compat "Julia 1.6"
    Keyword argument `init` requires Julia 1.6 or later.

# Examples
```jldoctest
julia> prod(abs2, [2; 3; 4])
576
```
"""
prod(f, a; kw...) = mapreduce(f, mul_prod, a; kw...)

"""
    prod(itr; [init])

Return the product of all elements of a collection.

The return type is `Int` for signed integers of less than system word size, and
`UInt` for unsigned integers of less than system word size.  For all other
arguments, a common return type is found to which all arguments are promoted.

The value returned for empty `itr` can be specified by `init`. It must be the
multiplicative identity (i.e. one) as it is unspecified whether `init` is used
for non-empty collections.

!!! compat "Julia 1.6"
    Keyword argument `init` requires Julia 1.6 or later.

See also: [`reduce`](@ref), [`cumprod`](@ref), [`any`](@ref).

# Examples
```jldoctest
julia> prod(1:5)
120

julia> prod(1:5; init = 1.0)
120.0
```
"""
prod(a; kw...) = mapreduce(identity, mul_prod, a; kw...)

## maximum, minimum, & extrema
_fast(::typeof(min),x,y) = min(x,y)
_fast(::typeof(max),x,y) = max(x,y)
function _fast(::typeof(max), x::AbstractFloat, y::AbstractFloat)
    ifelse(isnan(x),
        x,
        ifelse(x > y, x, y))
end

function _fast(::typeof(min),x::AbstractFloat, y::AbstractFloat)
    ifelse(isnan(x),
        x,
        ifelse(x < y, x, y))
end

isbadzero(::typeof(max), x::AbstractFloat) = (x == zero(x)) & signbit(x)
isbadzero(::typeof(min), x::AbstractFloat) = (x == zero(x)) & !signbit(x)
isbadzero(op, x) = false
isgoodzero(::typeof(max), x) = isbadzero(min, x)
isgoodzero(::typeof(min), x) = isbadzero(max, x)

function mapreduce_impl(f, op::Union{typeof(max), typeof(min)},
                        A::AbstractArrayOrBroadcasted, first::Int, last::Int)
    a1 = @inbounds A[first]
    v1 = mapreduce_first(f, op, a1)
    v2 = v3 = v4 = v1
    chunk_len = 256
    start = first + 1
    simdstop  = start + chunk_len - 4
    while simdstop <= last - 3
        @inbounds for i in start:4:simdstop
            v1 = _fast(op, v1, f(A[i+0]))
            v2 = _fast(op, v2, f(A[i+1]))
            v3 = _fast(op, v3, f(A[i+2]))
            v4 = _fast(op, v4, f(A[i+3]))
        end
        checkbounds(A, simdstop+3)
        start += chunk_len
        simdstop += chunk_len
    end
    v = op(op(v1,v2),op(v3,v4))
    for i in start:last
        @inbounds ai = A[i]
        v = op(v, f(ai))
    end

    # enforce correct order of 0.0 and -0.0
    # e.g. maximum([0.0, -0.0]) === 0.0
    # should hold
    if isbadzero(op, v)
        for i in first:last
            x = @inbounds A[i]
            isgoodzero(op,x) && return x
        end
    end
    return v
end

"""
    maximum(f, itr; [init])

Return the largest result of calling function `f` on each element of `itr`.

The value returned for empty `itr` can be specified by `init`. It must be
a neutral element for `max` (i.e. which is less than or equal to any
other element) as it is unspecified whether `init` is used
for non-empty collections.

!!! compat "Julia 1.6"
    Keyword argument `init` requires Julia 1.6 or later.

# Examples
```jldoctest
julia> maximum(length, ["Julion", "Julia", "Jule"])
6

julia> maximum(length, []; init=-1)
-1

julia> maximum(sin, Real[]; init=-1.0)  # good, since output of sin is >= -1
-1.0
```
"""
maximum(f, a; kw...) = mapreduce(f, max, a; kw...)

"""
    minimum(f, itr; [init])

Return the smallest result of calling function `f` on each element of `itr`.

The value returned for empty `itr` can be specified by `init`. It must be
a neutral element for `min` (i.e. which is greater than or equal to any
other element) as it is unspecified whether `init` is used
for non-empty collections.

!!! compat "Julia 1.6"
    Keyword argument `init` requires Julia 1.6 or later.

# Examples
```jldoctest
julia> minimum(length, ["Julion", "Julia", "Jule"])
4

julia> minimum(length, []; init=typemax(Int64))
9223372036854775807

julia> minimum(sin, Real[]; init=1.0)  # good, since output of sin is <= 1
1.0
```
"""
minimum(f, a; kw...) = mapreduce(f, min, a; kw...)

"""
    maximum(itr; [init])

Return the largest element in a collection.

The value returned for empty `itr` can be specified by `init`. It must be
a neutral element for `max` (i.e. which is less than or equal to any
other element) as it is unspecified whether `init` is used
for non-empty collections.

!!! compat "Julia 1.6"
    Keyword argument `init` requires Julia 1.6 or later.

# Examples
```jldoctest
julia> maximum(-20.5:10)
9.5

julia> maximum([1,2,3])
3

julia> maximum(())
ERROR: MethodError: reducing over an empty collection is not allowed; consider supplying `init` to the reducer
Stacktrace:
[...]

julia> maximum((); init=-Inf)
-Inf
```
"""
maximum(a; kw...) = mapreduce(identity, max, a; kw...)

"""
    minimum(itr; [init])

Return the smallest element in a collection.

The value returned for empty `itr` can be specified by `init`. It must be
a neutral element for `min` (i.e. which is greater than or equal to any
other element) as it is unspecified whether `init` is used
for non-empty collections.

!!! compat "Julia 1.6"
    Keyword argument `init` requires Julia 1.6 or later.

# Examples
```jldoctest
julia> minimum(-20.5:10)
-20.5

julia> minimum([1,2,3])
1

julia> minimum([])
ERROR: MethodError: reducing over an empty collection is not allowed; consider supplying `init` to the reducer
Stacktrace:
[...]

julia> minimum([]; init=Inf)
Inf
```
"""
minimum(a; kw...) = mapreduce(identity, min, a; kw...)

"""
    extrema(itr; [init]) -> (mn, mx)

Compute both the minimum `mn` and maximum `mx` element in a single pass, and return them
as a 2-tuple.

The value returned for empty `itr` can be specified by `init`. It must be a 2-tuple whose
first and second elements are neutral elements for `min` and `max` respectively
(i.e. which are greater/less than or equal to any other element). As a consequence, when
`itr` is empty the returned `(mn, mx)` tuple will satisfy `mn ≥ mx`. When `init` is
specified it may be used even for non-empty `itr`.

!!! compat "Julia 1.8"
    Keyword argument `init` requires Julia 1.8 or later.

# Examples
```jldoctest
julia> extrema(2:10)
(2, 10)

julia> extrema([9,pi,4.5])
(3.141592653589793, 9.0)

julia> extrema([]; init = (Inf, -Inf))
(Inf, -Inf)
```
"""
extrema(itr; kw...) = extrema(identity, itr; kw...)

"""
    extrema(f, itr; [init]) -> (mn, mx)

Compute both the minimum `mn` and maximum `mx` of `f` applied to each element in `itr` and
return them as a 2-tuple. Only one pass is made over `itr`.

The value returned for empty `itr` can be specified by `init`. It must be a 2-tuple whose
first and second elements are neutral elements for `min` and `max` respectively
(i.e. which are greater/less than or equal to any other element). It is used for non-empty
collections. Note: it implies that, for empty `itr`, the returned value `(mn, mx)` satisfies
`mn ≥ mx` even though for non-empty `itr` it  satisfies `mn ≤ mx`.  This is a "paradoxical"
but yet expected result.

!!! compat "Julia 1.2"
    This method requires Julia 1.2 or later.

!!! compat "Julia 1.8"
    Keyword argument `init` requires Julia 1.8 or later.

# Examples
```jldoctest
julia> extrema(sin, 0:π)
(0.0, 0.9092974268256817)

julia> extrema(sin, Real[]; init = (1.0, -1.0))  # good, since -1 ≤ sin(::Real) ≤ 1
(1.0, -1.0)
```
"""
extrema(f, itr; kw...) = mapreduce(ExtremaMap(f), _extrema_rf, itr; kw...)

# Not using closure since `extrema(type, itr)` is a very likely use-case and it's better
# to avoid type-instability (#23618).
struct ExtremaMap{F} <: Function
    f::F
end
ExtremaMap(::Type{T}) where {T} = ExtremaMap{Type{T}}(T)
@inline (f::ExtremaMap)(x) = (y = f.f(x); (y, y))

@inline _extrema_rf((min1, max1), (min2, max2)) = (min(min1, min2), max(max1, max2))
# optimization for IEEEFloat
function _extrema_rf(x::NTuple{2,T}, y::NTuple{2,T}) where {T<:IEEEFloat}
    (x1, x2), (y1, y2) = x, y
    anynan = isnan(x1)|isnan(y1)
    z1 = ifelse(anynan, x1-y1, ifelse(signbit(x1-y1), x1, y1))
    z2 = ifelse(anynan, x1-y1, ifelse(signbit(x2-y2), y2, x2))
    z1, z2
end

## findmax, findmin, argmax & argmin

"""
    findmax(f, domain) -> (f(x), index)

Return a pair of a value in the codomain (outputs of `f`) and the index of
the corresponding value in the `domain` (inputs to `f`) such that `f(x)` is maximised.
If there are multiple maximal points, then the first one will be returned.

`domain` must be a non-empty iterable.

Values are compared with `isless`.

!!! compat "Julia 1.7"
    This method requires Julia 1.7 or later.

# Examples

```jldoctest
julia> findmax(identity, 5:9)
(9, 5)

julia> findmax(-, 1:10)
(-1, 1)

julia> findmax(first, [(1, :a), (3, :b), (3, :c)])
(3, 2)

julia> findmax(cos, 0:π/2:2π)
(1.0, 1)
```
"""
findmax(f, domain) = _findmax(f, domain, :)
_findmax(f, domain, ::Colon) = mapfoldl( ((k, v),) -> (f(v), k), _rf_findmax, pairs(domain) )
_rf_findmax((fm, im), (fx, ix)) = isless(fm, fx) ? (fx, ix) : (fm, im)

"""
    findmax(itr) -> (x, index)

Return the maximal element of the collection `itr` and its index or key.
If there are multiple maximal elements, then the first one will be returned.
Values are compared with `isless`.

See also: [`findmin`](@ref), [`argmax`](@ref), [`maximum`](@ref).

# Examples

```jldoctest
julia> findmax([8, 0.1, -9, pi])
(8.0, 1)

julia> findmax([1, 7, 7, 6])
(7, 2)

julia> findmax([1, 7, 7, NaN])
(NaN, 4)
```
"""
findmax(itr) = _findmax(itr, :)
_findmax(a, ::Colon) = findmax(identity, a)

"""
    findmin(f, domain) -> (f(x), index)

Return a pair of a value in the codomain (outputs of `f`) and the index of
the corresponding value in the `domain` (inputs to `f`) such that `f(x)` is minimised.
If there are multiple minimal points, then the first one will be returned.

`domain` must be a non-empty iterable.

`NaN` is treated as less than all other values except `missing`.

!!! compat "Julia 1.7"
    This method requires Julia 1.7 or later.

# Examples

```jldoctest
julia> findmin(identity, 5:9)
(5, 1)

julia> findmin(-, 1:10)
(-10, 10)

julia> findmin(first, [(2, :a), (2, :b), (3, :c)])
(2, 1)

julia> findmin(cos, 0:π/2:2π)
(-1.0, 3)
```

"""
findmin(f, domain) = _findmin(f, domain, :)
_findmin(f, domain, ::Colon) = mapfoldl( ((k, v),) -> (f(v), k), _rf_findmin, pairs(domain) )
_rf_findmin((fm, im), (fx, ix)) = isgreater(fm, fx) ? (fx, ix) : (fm, im)

"""
    findmin(itr) -> (x, index)

Return the minimal element of the collection `itr` and its index or key.
If there are multiple minimal elements, then the first one will be returned.
`NaN` is treated as less than all other values except `missing`.

See also: [`findmax`](@ref), [`argmin`](@ref), [`minimum`](@ref).

# Examples

```jldoctest
julia> findmin([8, 0.1, -9, pi])
(-9.0, 3)

julia> findmin([1, 7, 7, 6])
(1, 1)

julia> findmin([1, 7, 7, NaN])
(NaN, 4)
```
"""
findmin(itr) = _findmin(itr, :)
_findmin(a, ::Colon) = findmin(identity, a)

"""
    argmax(f, domain)

Return a value `x` from `domain` for which `f(x)` is maximised.
If there are multiple maximal values for `f(x)` then the first one will be found.

`domain` must be a non-empty iterable.

Values are compared with `isless`.

!!! compat "Julia 1.7"
    This method requires Julia 1.7 or later.

See also [`argmin`](@ref), [`findmax`](@ref).

# Examples
```jldoctest
julia> argmax(abs, -10:5)
-10

julia> argmax(cos, 0:π/2:2π)
0.0
```
"""
argmax(f, domain) = mapfoldl(x -> (f(x), x), _rf_findmax, domain)[2]

"""
    argmax(itr)

Return the index or key of the maximal element in a collection.
If there are multiple maximal elements, then the first one will be returned.

The collection must not be empty.

Values are compared with `isless`.

See also: [`argmin`](@ref), [`findmax`](@ref).

# Examples
```jldoctest
julia> argmax([8, 0.1, -9, pi])
1

julia> argmax([1, 7, 7, 6])
2

julia> argmax([1, 7, 7, NaN])
4
```
"""
argmax(itr) = findmax(itr)[2]

"""
    argmin(f, domain)

Return a value `x` from `domain` for which `f(x)` is minimised.
If there are multiple minimal values for `f(x)` then the first one will be found.

`domain` must be a non-empty iterable.

`NaN` is treated as less than all other values except `missing`.

!!! compat "Julia 1.7"
    This method requires Julia 1.7 or later.

See also [`argmax`](@ref), [`findmin`](@ref).

# Examples
```jldoctest
julia> argmin(sign, -10:5)
-10

julia> argmin(x -> -x^3 + x^2 - 10, -5:5)
5

julia> argmin(acos, 0:0.1:1)
1.0
```
"""
argmin(f, domain) = mapfoldl(x -> (f(x), x), _rf_findmin, domain)[2]

"""
    argmin(itr)

Return the index or key of the minimal element in a collection.
If there are multiple minimal elements, then the first one will be returned.

The collection must not be empty.

`NaN` is treated as less than all other values except `missing`.

See also: [`argmax`](@ref), [`findmin`](@ref).

# Examples
```jldoctest
julia> argmin([8, 0.1, -9, pi])
3

julia> argmin([7, 1, 1, 6])
2

julia> argmin([7, 1, 1, NaN])
4
```
"""
argmin(itr) = findmin(itr)[2]

## all & any

"""
    any(itr) -> Bool

Test whether any elements of a boolean collection are `true`, returning `true` as
soon as the first `true` value in `itr` is encountered (short-circuiting). To
short-circuit on `false`, use [`all`](@ref).

If the input contains [`missing`](@ref) values, return `missing` if all non-missing
values are `false` (or equivalently, if the input contains no `true` value), following
[three-valued logic](https://en.wikipedia.org/wiki/Three-valued_logic).

See also: [`all`](@ref), [`count`](@ref), [`sum`](@ref), [`|`](@ref), , [`||`](@ref).

# Examples
```jldoctest
julia> a = [true,false,false,true]
4-element Vector{Bool}:
 1
 0
 0
 1

julia> any(a)
true

julia> any((println(i); v) for (i, v) in enumerate(a))
1
true

julia> any([missing, true])
true

julia> any([false, missing])
missing
```
"""
any(itr) = any(identity, itr)

"""
    all(itr) -> Bool

Test whether all elements of a boolean collection are `true`, returning `false` as
soon as the first `false` value in `itr` is encountered (short-circuiting). To
short-circuit on `true`, use [`any`](@ref).

If the input contains [`missing`](@ref) values, return `missing` if all non-missing
values are `true` (or equivalently, if the input contains no `false` value), following
[three-valued logic](https://en.wikipedia.org/wiki/Three-valued_logic).

See also: [`all!`](@ref), [`any`](@ref), [`count`](@ref), [`&`](@ref), , [`&&`](@ref), [`allunique`](@ref).

# Examples
```jldoctest
julia> a = [true,false,false,true]
4-element Vector{Bool}:
 1
 0
 0
 1

julia> all(a)
false

julia> all((println(i); v) for (i, v) in enumerate(a))
1
2
false

julia> all([missing, false])
false

julia> all([true, missing])
missing
```
"""
all(itr) = all(identity, itr)

"""
    any(p, itr) -> Bool

Determine whether predicate `p` returns `true` for any elements of `itr`, returning
`true` as soon as the first item in `itr` for which `p` returns `true` is encountered
(short-circuiting). To short-circuit on `false`, use [`all`](@ref).

If the input contains [`missing`](@ref) values, return `missing` if all non-missing
values are `false` (or equivalently, if the input contains no `true` value), following
[three-valued logic](https://en.wikipedia.org/wiki/Three-valued_logic).

# Examples
```jldoctest
julia> any(i->(4<=i<=6), [3,5,7])
true

julia> any(i -> (println(i); i > 3), 1:10)
1
2
3
4
true

julia> any(i -> i > 0, [1, missing])
true

julia> any(i -> i > 0, [-1, missing])
missing

julia> any(i -> i > 0, [-1, 0])
false
```
"""
any(f, itr) = _any(f, itr, :)

function _any(f, itr, ::Colon)
    anymissing = false
    for x in itr
        v = f(x)
        if ismissing(v)
            anymissing = true
        elseif v
            return true
        end
    end
    return anymissing ? missing : false
end

# Specialized versions of any(f, ::Tuple)
# We fall back to the for loop implementation all elements have the same type or
# if the tuple is too large.
function any(f, itr::Tuple)
    if itr isa NTuple || length(itr) > 32
        return _any(f, itr, :)
    end
    _any_tuple(f, false, itr...)
end

@inline function _any_tuple(f, anymissing, x, rest...)
    v = f(x)
    if ismissing(v)
        anymissing = true
    elseif v
        return true
    end
    return _any_tuple(f, anymissing, rest...)
end
@inline _any_tuple(f, anymissing) = anymissing ? missing : false

"""
    all(p, itr) -> Bool

Determine whether predicate `p` returns `true` for all elements of `itr`, returning
`false` as soon as the first item in `itr` for which `p` returns `false` is encountered
(short-circuiting). To short-circuit on `true`, use [`any`](@ref).

If the input contains [`missing`](@ref) values, return `missing` if all non-missing
values are `true` (or equivalently, if the input contains no `false` value), following
[three-valued logic](https://en.wikipedia.org/wiki/Three-valued_logic).

# Examples
```jldoctest
julia> all(i->(4<=i<=6), [4,5,6])
true

julia> all(i -> (println(i); i < 3), 1:10)
1
2
3
false

julia> all(i -> i > 0, [1, missing])
missing

julia> all(i -> i > 0, [-1, missing])
false

julia> all(i -> i > 0, [1, 2])
true
```
"""
all(f, itr) = _all(f, itr, :)

function _all(f, itr, ::Colon)
    anymissing = false
    for x in itr
        v = f(x)
        if ismissing(v)
            anymissing = true
        # this syntax allows throwing a TypeError for non-Bool, for consistency with any
        elseif v
            continue
        else
            return false
        end
    end
    return anymissing ? missing : true
end

# Specialized versions of all(f, ::Tuple),
# This is similar to any(f, ::Tuple) defined above.
function all(f, itr::Tuple)
    if itr isa NTuple || length(itr) > 32
        return _all(f, itr, :)
    end
    _all_tuple(f, false, itr...)
end

@inline function _all_tuple(f, anymissing, x, rest...)
    v = f(x)
    if ismissing(v)
        anymissing = true
    # this syntax allows throwing a TypeError for non-Bool, for consistency with any
    elseif v
        nothing
    else
        return false
    end
    return _all_tuple(f, anymissing, rest...)
end
@inline _all_tuple(f, anymissing) = anymissing ? missing : true

## count

_bool(f) = x->f(x)::Bool

"""
    count([f=identity,] itr; init=0) -> Integer

Count the number of elements in `itr` for which the function `f` returns `true`.
If `f` is omitted, count the number of `true` elements in `itr` (which
should be a collection of boolean values). `init` optionally specifies the value
to start counting from and therefore also determines the output type.

!!! compat "Julia 1.6"
    `init` keyword was added in Julia 1.6.

See also: [`any`](@ref), [`sum`](@ref).

# Examples
```jldoctest
julia> count(i->(4<=i<=6), [2,3,4,5,6])
3

julia> count([true, false, true, true])
3

julia> count(>(3), 1:7, init=0x03)
0x07
```
"""
count(itr; init=0) = count(identity, itr; init)

count(f, itr; init=0) = _simple_count(f, itr, init)

_simple_count(pred, itr, init) = sum(_bool(pred), itr; init)

function _simple_count(::typeof(identity), x::Array{Bool}, init::T=0) where {T}
    n::T = init
    chunks = length(x) ÷ sizeof(UInt)
    mask = 0x0101010101010101 % UInt
    GC.@preserve x begin
        ptr = Ptr{UInt}(pointer(x))
        for i in 1:chunks
            n = (n + count_ones(unsafe_load(ptr, i) & mask)) % T
        end
    end
    for i in sizeof(UInt)*chunks+1:length(x)
        n = (n + x[i]) % T
    end
    return n
end
T   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/reshapedarray.jlb8      # This file is a part of Julia. License is MIT: https://julialang.org/license

using  Base.MultiplicativeInverses: SignedMultiplicativeInverse

struct ReshapedArray{T,N,P<:AbstractArray,MI<:Tuple{Vararg{SignedMultiplicativeInverse{Int}}}} <: AbstractArray{T,N}
    parent::P
    dims::NTuple{N,Int}
    mi::MI
end
ReshapedArray(parent::AbstractArray{T}, dims::NTuple{N,Int}, mi) where {T,N} = ReshapedArray{T,N,typeof(parent),typeof(mi)}(parent, dims, mi)

# IndexLinear ReshapedArray
const ReshapedArrayLF{T,N,P<:AbstractArray} = ReshapedArray{T,N,P,Tuple{}}

# Fast iteration on ReshapedArrays: use the parent iterator
struct ReshapedArrayIterator{I,M}
    iter::I
    mi::NTuple{M,SignedMultiplicativeInverse{Int}}
end
ReshapedArrayIterator(A::ReshapedArray) = _rs_iterator(parent(A), A.mi)
function _rs_iterator(P, mi::NTuple{M}) where M
    iter = eachindex(P)
    ReshapedArrayIterator{typeof(iter),M}(iter, mi)
end

struct ReshapedIndex{T}
    parentindex::T
end

# eachindex(A::ReshapedArray) = ReshapedArrayIterator(A)  # TODO: uncomment this line
@inline function iterate(R::ReshapedArrayIterator, i...)
    item, inext = iterate(R.iter, i...)
    ReshapedIndex(item), inext
end
length(R::ReshapedArrayIterator) = length(R.iter)
eltype(::Type{<:ReshapedArrayIterator{I}}) where {I} = @isdefined(I) ? ReshapedIndex{eltype(I)} : Any

## reshape(::Array, ::Dims) returns an Array, except for isbitsunion eltypes (issue #28611)
# reshaping to same # of dimensions
function reshape(a::Array{T,M}, dims::NTuple{N,Int}) where {T,N,M}
    throw_dmrsa(dims, len) =
        throw(DimensionMismatch("new dimensions $(dims) must be consistent with array size $len"))

    if prod(dims) != length(a)
        throw_dmrsa(dims, length(a))
    end
    isbitsunion(T) && return ReshapedArray(a, dims, ())
    if N == M && dims == size(a)
        return a
    end
    ccall(:jl_reshape_array, Array{T,N}, (Any, Any, Any), Array{T,N}, a, dims)
end

"""
    reshape(A, dims...) -> AbstractArray
    reshape(A, dims) -> AbstractArray

Return an array with the same data as `A`, but with different
dimension sizes or number of dimensions. The two arrays share the same
underlying data, so that the result is mutable if and only if `A` is
mutable, and setting elements of one alters the values of the other.

The new dimensions may be specified either as a list of arguments or
as a shape tuple. At most one dimension may be specified with a `:`,
in which case its length is computed such that its product with all
the specified dimensions is equal to the length of the original array
`A`. The total number of elements must not change.

# Examples
```jldoctest
julia> A = Vector(1:16)
16-element Vector{Int64}:
  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16

julia> reshape(A, (4, 4))
4×4 Matrix{Int64}:
 1  5   9  13
 2  6  10  14
 3  7  11  15
 4  8  12  16

julia> reshape(A, 2, :)
2×8 Matrix{Int64}:
 1  3  5  7   9  11  13  15
 2  4  6  8  10  12  14  16

julia> reshape(1:6, 2, 3)
2×3 reshape(::UnitRange{Int64}, 2, 3) with eltype Int64:
 1  3  5
 2  4  6
```
"""
reshape

reshape(parent::AbstractArray, dims::IntOrInd...) = reshape(parent, dims)
reshape(parent::AbstractArray, shp::Tuple{Union{Integer,OneTo}, Vararg{Union{Integer,OneTo}}}) = reshape(parent, to_shape(shp))
reshape(parent::AbstractArray, dims::Dims)        = _reshape(parent, dims)

# Allow missing dimensions with Colon():
reshape(parent::AbstractVector, ::Colon) = parent
reshape(parent::AbstractVector, ::Tuple{Colon}) = parent
reshape(parent::AbstractArray, dims::Int...) = reshape(parent, dims)
reshape(parent::AbstractArray, dims::Union{Int,Colon}...) = reshape(parent, dims)
reshape(parent::AbstractArray, dims::Tuple{Vararg{Union{Int,Colon}}}) = reshape(parent, _reshape_uncolon(parent, dims))
@inline function _reshape_uncolon(A, dims)
    @noinline throw1(dims) = throw(DimensionMismatch(string("new dimensions $(dims) ",
        "may have at most one omitted dimension specified by `Colon()`")))
    @noinline throw2(A, dims) = throw(DimensionMismatch(string("array size $(length(A)) ",
        "must be divisible by the product of the new dimensions $dims")))
    pre = _before_colon(dims...)
    post = _after_colon(dims...)
    _any_colon(post...) && throw1(dims)
    sz, remainder = divrem(length(A), prod(pre)*prod(post))
    remainder == 0 || throw2(A, dims)
    (pre..., Int(sz), post...)
end
@inline _any_colon() = false
@inline _any_colon(dim::Colon, tail...) = true
@inline _any_colon(dim::Any, tail...) = _any_colon(tail...)
@inline _before_colon(dim::Any, tail...) = (dim, _before_colon(tail...)...)
@inline _before_colon(dim::Colon, tail...) = ()
@inline _after_colon(dim::Any, tail...) =  _after_colon(tail...)
@inline _after_colon(dim::Colon, tail...) = tail

reshape(parent::AbstractArray{T,N}, ndims::Val{N}) where {T,N} = parent
function reshape(parent::AbstractArray, ndims::Val{N}) where N
    reshape(parent, rdims(Val(N), axes(parent)))
end

# Move elements from inds to out until out reaches the desired
# dimensionality N, either filling with OneTo(1) or collapsing the
# product of trailing dims into the last element
rdims_trailing(l, inds...) = length(l) * rdims_trailing(inds...)
rdims_trailing(l) = length(l)
rdims(out::Val{N}, inds::Tuple) where {N} = rdims(ntuple(Returns(OneTo(1)), Val(N)), inds)
rdims(out::Tuple{}, inds::Tuple{}) = () # N == 0, M == 0
rdims(out::Tuple{}, inds::Tuple{Any}) = ()
rdims(out::Tuple{}, inds::NTuple{M,Any}) where {M} = ()
rdims(out::Tuple{Any}, inds::Tuple{}) = out # N == 1, M == 0
rdims(out::NTuple{N,Any}, inds::Tuple{}) where {N} = out # N > 1, M == 0
rdims(out::Tuple{Any}, inds::Tuple{Any}) = inds # N == 1, M == 1
rdims(out::Tuple{Any}, inds::NTuple{M,Any}) where {M} = (oneto(rdims_trailing(inds...)),) # N == 1, M > 1
rdims(out::NTuple{N,Any}, inds::NTuple{N,Any}) where {N} = inds # N > 1, M == N
rdims(out::NTuple{N,Any}, inds::NTuple{M,Any}) where {N,M} = (first(inds), rdims(tail(out), tail(inds))...) # N > 1, M > 1, M != N


# _reshape on Array returns an Array
_reshape(parent::Vector, dims::Dims{1}) = parent
_reshape(parent::Array, dims::Dims{1}) = reshape(parent, dims)
_reshape(parent::Array, dims::Dims) = reshape(parent, dims)

# When reshaping Vector->Vector, don't wrap with a ReshapedArray
function _reshape(v::AbstractVector, dims::Dims{1})
    require_one_based_indexing(v)
    len = dims[1]
    len == length(v) || _throw_dmrs(length(v), "length", len)
    v
end
# General reshape
function _reshape(parent::AbstractArray, dims::Dims)
    n = length(parent)
    prod(dims) == n || _throw_dmrs(n, "size", dims)
    __reshape((parent, IndexStyle(parent)), dims)
end

@noinline function _throw_dmrs(n, str, dims)
    throw(DimensionMismatch("parent has $n elements, which is incompatible with $str $dims"))
end

# Reshaping a ReshapedArray
_reshape(v::ReshapedArray{<:Any,1}, dims::Dims{1}) = _reshape(v.parent, dims)
_reshape(R::ReshapedArray, dims::Dims) = _reshape(R.parent, dims)

function __reshape(p::Tuple{AbstractArray,IndexStyle}, dims::Dims)
    parent = p[1]
    strds = front(size_to_strides(map(length, axes(parent))..., 1))
    strds1 = map(s->max(1,Int(s)), strds)  # for resizing empty arrays
    mi = map(SignedMultiplicativeInverse, strds1)
    ReshapedArray(parent, dims, reverse(mi))
end

function __reshape(p::Tuple{AbstractArray{<:Any,0},IndexCartesian}, dims::Dims)
    parent = p[1]
    ReshapedArray(parent, dims, ())
end

function __reshape(p::Tuple{AbstractArray,IndexLinear}, dims::Dims)
    parent = p[1]
    ReshapedArray(parent, dims, ())
end

size(A::ReshapedArray) = A.dims
length(A::ReshapedArray) = length(parent(A))
similar(A::ReshapedArray, eltype::Type, dims::Dims) = similar(parent(A), eltype, dims)
IndexStyle(::Type{<:ReshapedArrayLF}) = IndexLinear()
parent(A::ReshapedArray) = A.parent
parentindices(A::ReshapedArray) = map(oneto, size(parent(A)))
reinterpret(::Type{T}, A::ReshapedArray, dims::Dims) where {T} = reinterpret(T, parent(A), dims)
elsize(::Type{<:ReshapedArray{<:Any,<:Any,P}}) where {P} = elsize(P)

unaliascopy(A::ReshapedArray) = typeof(A)(unaliascopy(A.parent), A.dims, A.mi)
dataids(A::ReshapedArray) = dataids(A.parent)

@inline ind2sub_rs(ax, ::Tuple{}, i::Int) = (i,)
@inline ind2sub_rs(ax, strds, i) = _ind2sub_rs(ax, strds, i - 1)
@inline _ind2sub_rs(ax, ::Tuple{}, ind) = (ind + first(ax[end]),)
@inline function _ind2sub_rs(ax, strds, ind)
    d, r = divrem(ind, strds[1])
    (_ind2sub_rs(front(ax), tail(strds), r)..., d + first(ax[end]))
end
offset_if_vec(i::Integer, axs::Tuple{<:AbstractUnitRange}) = i + first(axs[1]) - 1
offset_if_vec(i::Integer, axs::Tuple) = i

@inline function isassigned(A::ReshapedArrayLF, index::Int)
    @boundscheck checkbounds(Bool, A, index) || return false
    indexparent = index - firstindex(A) + firstindex(parent(A))
    @inbounds ret = isassigned(parent(A), indexparent)
    ret
end
@inline function isassigned(A::ReshapedArray{T,N}, indices::Vararg{Int, N}) where {T,N}
    @boundscheck checkbounds(Bool, A, indices...) || return false
    axp = axes(A.parent)
    i = offset_if_vec(_sub2ind(size(A), indices...), axp)
    I = ind2sub_rs(axp, A.mi, i)
    @inbounds isassigned(A.parent, I...)
end

@inline function getindex(A::ReshapedArrayLF, index::Int)
    @boundscheck checkbounds(A, index)
    indexparent = index - firstindex(A) + firstindex(parent(A))
    @inbounds ret = parent(A)[indexparent]
    ret
end
@inline function getindex(A::ReshapedArray{T,N}, indices::Vararg{Int,N}) where {T,N}
    @boundscheck checkbounds(A, indices...)
    _unsafe_getindex(A, indices...)
end
@inline function getindex(A::ReshapedArray, index::ReshapedIndex)
    @boundscheck checkbounds(parent(A), index.parentindex)
    @inbounds ret = parent(A)[index.parentindex]
    ret
end

@inline function _unsafe_getindex(A::ReshapedArray{T,N}, indices::Vararg{Int,N}) where {T,N}
    axp = axes(A.parent)
    i = offset_if_vec(_sub2ind(size(A), indices...), axp)
    I = ind2sub_rs(axp, A.mi, i)
    _unsafe_getindex_rs(parent(A), I)
end
@inline _unsafe_getindex_rs(A, i::Integer) = (@inbounds ret = A[i]; ret)
@inline _unsafe_getindex_rs(A, I) = (@inbounds ret = A[I...]; ret)

@inline function setindex!(A::ReshapedArrayLF, val, index::Int)
    @boundscheck checkbounds(A, index)
    indexparent = index - firstindex(A) + firstindex(parent(A))
    @inbounds parent(A)[indexparent] = val
    val
end
@inline function setindex!(A::ReshapedArray{T,N}, val, indices::Vararg{Int,N}) where {T,N}
    @boundscheck checkbounds(A, indices...)
    _unsafe_setindex!(A, val, indices...)
end
@inline function setindex!(A::ReshapedArray, val, index::ReshapedIndex)
    @boundscheck checkbounds(parent(A), index.parentindex)
    @inbounds parent(A)[index.parentindex] = val
    val
end

@inline function _unsafe_setindex!(A::ReshapedArray{T,N}, val, indices::Vararg{Int,N}) where {T,N}
    axp = axes(A.parent)
    i = offset_if_vec(_sub2ind(size(A), indices...), axp)
    @inbounds parent(A)[ind2sub_rs(axes(A.parent), A.mi, i)...] = val
    val
end

# helpful error message for a common failure case
const ReshapedRange{T,N,A<:AbstractRange} = ReshapedArray{T,N,A,Tuple{}}
setindex!(A::ReshapedRange, val, index::Int) = _rs_setindex!_err()
setindex!(A::ReshapedRange{T,N}, val, indices::Vararg{Int,N}) where {T,N} = _rs_setindex!_err()
setindex!(A::ReshapedRange, val, index::ReshapedIndex) = _rs_setindex!_err()

@noinline _rs_setindex!_err() = error("indexed assignment fails for a reshaped range; consider calling collect")

unsafe_convert(::Type{Ptr{T}}, a::ReshapedArray{T}) where {T} = unsafe_convert(Ptr{T}, parent(a))

# Add a few handy specializations to further speed up views of reshaped ranges
const ReshapedUnitRange{T,N,A<:AbstractUnitRange} = ReshapedArray{T,N,A,Tuple{}}
viewindexing(I::Tuple{Slice, ReshapedUnitRange, Vararg{ScalarIndex}}) = IndexLinear()
viewindexing(I::Tuple{ReshapedRange, Vararg{ScalarIndex}}) = IndexLinear()
compute_stride1(s, inds, I::Tuple{ReshapedRange, Vararg{Any}}) = s*step(I[1].parent)
compute_offset1(parent::AbstractVector, stride1::Integer, I::Tuple{ReshapedRange}) =
    (@inline; first(I[1]) - first(axes1(I[1]))*stride1)
substrides(strds::NTuple{N,Int}, I::Tuple{ReshapedUnitRange, Vararg{Any}}) where N =
    (size_to_strides(strds[1], size(I[1])...)..., substrides(tail(strds), tail(I))...)
unsafe_convert(::Type{Ptr{T}}, V::SubArray{T,N,P,<:Tuple{Vararg{Union{RangeIndex,ReshapedUnitRange}}}}) where {T,N,P} =
    unsafe_convert(Ptr{T}, V.parent) + (first_index(V)-1)*sizeof(T)


_checkcontiguous(::Type{Bool}, A::AbstractArray) = false
# `strides(A::DenseArray)` calls `size_to_strides` by default.
# Thus it's OK to assume all `DenseArray`s are contiguously stored.
_checkcontiguous(::Type{Bool}, A::DenseArray) = true
_checkcontiguous(::Type{Bool}, A::ReshapedArray) = _checkcontiguous(Bool, parent(A))
_checkcontiguous(::Type{Bool}, A::FastContiguousSubArray) = _checkcontiguous(Bool, parent(A))

function strides(a::ReshapedArray)
    _checkcontiguous(Bool, a) && return size_to_strides(1, size(a)...)
    apsz::Dims = size(a.parent)
    apst::Dims = strides(a.parent)
    msz, mst, n = merge_adjacent_dim(apsz, apst) # Try to perform "lazy" reshape
    n == ndims(a.parent) && return size_to_strides(mst, size(a)...) # Parent is stridevector like
    return _reshaped_strides(size(a), 1, msz, mst, n, apsz, apst)
end

function _reshaped_strides(::Dims{0}, reshaped::Int, msz::Int, ::Int, ::Int, ::Dims, ::Dims)
    reshaped == msz && return ()
    throw(ArgumentError("Input is not strided."))
end
function _reshaped_strides(sz::Dims, reshaped::Int, msz::Int, mst::Int, n::Int, apsz::Dims, apst::Dims)
    st = reshaped * mst
    reshaped = reshaped * sz[1]
    if length(sz) > 1 && reshaped == msz && sz[2] != 1
        msz, mst, n = merge_adjacent_dim(apsz, apst, n + 1)
        reshaped = 1
    end
    sts = _reshaped_strides(tail(sz), reshaped, msz, mst, n, apsz, apst)
    return (st, sts...)
end

merge_adjacent_dim(::Dims{0}, ::Dims{0}) = 1, 1, 0
merge_adjacent_dim(apsz::Dims{1}, apst::Dims{1}) = apsz[1], apst[1], 1
function merge_adjacent_dim(apsz::Dims{N}, apst::Dims{N}, n::Int = 1) where {N}
    sz, st = apsz[n], apst[n]
    while n < N
        szₙ, stₙ = apsz[n+1], apst[n+1]
        if sz == 1
            sz, st = szₙ, stₙ
        elseif stₙ == st * sz || szₙ == 1
            sz *= szₙ
        else
            break
        end
        n += 1
    end
    return sz, st, n
end
W   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/reinterpretarray.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
Gives a reinterpreted view (of element type T) of the underlying array (of element type S).
If the size of `T` differs from the size of `S`, the array will be compressed/expanded in
the first dimension. The variant `reinterpret(reshape, T, a)` instead adds or consumes the first dimension
depending on the ratio of element sizes.
"""
struct ReinterpretArray{T,N,S,A<:AbstractArray{S},IsReshaped} <: AbstractArray{T, N}
    parent::A
    readable::Bool
    writable::Bool

    function throwbits(S::Type, T::Type, U::Type)
        @noinline
        throw(ArgumentError("cannot reinterpret `$(S)` as `$(T)`, type `$(U)` is not a bits type"))
    end
    function throwsize0(S::Type, T::Type, msg)
        @noinline
        throw(ArgumentError("cannot reinterpret a zero-dimensional `$(S)` array to `$(T)` which is of a $msg size"))
    end
    function throwsingleton(S::Type, T::Type)
        @noinline
        throw(ArgumentError("cannot reinterpret a `$(S)` array to `$(T)` which is a singleton type"))
    end

    global reinterpret

    @doc """
        reinterpret(T::DataType, A::AbstractArray)

    Construct a view of the array with the same binary data as the given
    array, but with `T` as element type.

    This function also works on "lazy" array whose elements are not computed until they are explicitly retrieved.
    For instance, `reinterpret` on the range `1:6` works similarly as on the dense vector `collect(1:6)`:

    ```jldoctest
    julia> reinterpret(Float32, UInt32[1 2 3 4 5])
    1×5 reinterpret(Float32, ::Matrix{UInt32}):
     1.0f-45  3.0f-45  4.0f-45  6.0f-45  7.0f-45

    julia> reinterpret(Complex{Int}, 1:6)
    3-element reinterpret(Complex{$Int}, ::UnitRange{$Int}):
     1 + 2im
     3 + 4im
     5 + 6im
    ```
    """
    function reinterpret(::Type{T}, a::A) where {T,N,S,A<:AbstractArray{S, N}}
        function thrownonint(S::Type, T::Type, dim)
            @noinline
            throw(ArgumentError("""
                cannot reinterpret an `$(S)` array to `$(T)` whose first dimension has size `$(dim)`.
                The resulting array would have non-integral first dimension.
                """))
        end
        function throwaxes1(S::Type, T::Type, ax1)
            @noinline
            throw(ArgumentError("cannot reinterpret a `$(S)` array to `$(T)` when the first axis is $ax1. Try reshaping first."))
        end
        isbitstype(T) || throwbits(S, T, T)
        isbitstype(S) || throwbits(S, T, S)
        (N != 0 || sizeof(T) == sizeof(S)) || throwsize0(S, T, "different")
        if N != 0 && sizeof(S) != sizeof(T)
            ax1 = axes(a)[1]
            dim = length(ax1)
            if issingletontype(T)
                issingletontype(S) || throwsingleton(S, T)
            else
                rem(dim*sizeof(S),sizeof(T)) == 0 || thrownonint(S, T, dim)
            end
            first(ax1) == 1 || throwaxes1(S, T, ax1)
        end
        readable = array_subpadding(T, S)
        writable = array_subpadding(S, T)
        new{T, N, S, A, false}(a, readable, writable)
    end
    reinterpret(::Type{T}, a::AbstractArray{T}) where {T} = a

    # With reshaping
    function reinterpret(::typeof(reshape), ::Type{T}, a::A) where {T,S,A<:AbstractArray{S}}
        function throwintmult(S::Type, T::Type)
            @noinline
            throw(ArgumentError("`reinterpret(reshape, T, a)` requires that one of `sizeof(T)` (got $(sizeof(T))) and `sizeof(eltype(a))` (got $(sizeof(S))) be an integer multiple of the other"))
        end
        function throwsize1(a::AbstractArray, T::Type)
            @noinline
            throw(ArgumentError("`reinterpret(reshape, $T, a)` where `eltype(a)` is $(eltype(a)) requires that `axes(a, 1)` (got $(axes(a, 1))) be equal to 1:$(sizeof(T) ÷ sizeof(eltype(a))) (from the ratio of element sizes)"))
        end
        function throwfromsingleton(S, T)
            @noinline
            throw(ArgumentError("`reinterpret(reshape, $T, a)` where `eltype(a)` is $S requires that $T be a singleton type, since $S is one"))
        end
        isbitstype(T) || throwbits(S, T, T)
        isbitstype(S) || throwbits(S, T, S)
        if sizeof(S) == sizeof(T)
            N = ndims(a)
        elseif sizeof(S) > sizeof(T)
            issingletontype(T) && throwsingleton(S, T)
            rem(sizeof(S), sizeof(T)) == 0 || throwintmult(S, T)
            N = ndims(a) + 1
        else
            issingletontype(S) && throwfromsingleton(S, T)
            rem(sizeof(T), sizeof(S)) == 0 || throwintmult(S, T)
            N = ndims(a) - 1
            N > -1 || throwsize0(S, T, "larger")
            axes(a, 1) == OneTo(sizeof(T) ÷ sizeof(S)) || throwsize1(a, T)
        end
        readable = array_subpadding(T, S)
        writable = array_subpadding(S, T)
        new{T, N, S, A, true}(a, readable, writable)
    end
    reinterpret(::typeof(reshape), ::Type{T}, a::AbstractArray{T}) where {T} = a
end

ReshapedReinterpretArray{T,N,S,A<:AbstractArray{S}} = ReinterpretArray{T,N,S,A,true}
NonReshapedReinterpretArray{T,N,S,A<:AbstractArray{S, N}} = ReinterpretArray{T,N,S,A,false}

"""
    reinterpret(reshape, T, A::AbstractArray{S}) -> B

Change the type-interpretation of `A` while consuming or adding a "channel dimension."

If `sizeof(T) = n*sizeof(S)` for `n>1`, `A`'s first dimension must be
of size `n` and `B` lacks `A`'s first dimension. Conversely, if `sizeof(S) = n*sizeof(T)` for `n>1`,
`B` gets a new first dimension of size `n`. The dimensionality is unchanged if `sizeof(T) == sizeof(S)`.

!!! compat "Julia 1.6"
    This method requires at least Julia 1.6.

# Examples

```jldoctest
julia> A = [1 2; 3 4]
2×2 Matrix{$Int}:
 1  2
 3  4

julia> reinterpret(reshape, Complex{Int}, A)    # the result is a vector
2-element reinterpret(reshape, Complex{$Int}, ::Matrix{$Int}) with eltype Complex{$Int}:
 1 + 3im
 2 + 4im

julia> a = [(1,2,3), (4,5,6)]
2-element Vector{Tuple{$Int, $Int, $Int}}:
 (1, 2, 3)
 (4, 5, 6)

julia> reinterpret(reshape, Int, a)             # the result is a matrix
3×2 reinterpret(reshape, $Int, ::Vector{Tuple{$Int, $Int, $Int}}) with eltype $Int:
 1  4
 2  5
 3  6
```
"""
reinterpret(::typeof(reshape), T::Type, a::AbstractArray)

reinterpret(::Type{T}, a::NonReshapedReinterpretArray) where {T} = reinterpret(T, a.parent)
reinterpret(::typeof(reshape), ::Type{T}, a::ReshapedReinterpretArray) where {T} = reinterpret(reshape, T, a.parent)

# Definition of StridedArray
StridedFastContiguousSubArray{T,N,A<:DenseArray} = FastContiguousSubArray{T,N,A}
StridedReinterpretArray{T,N,A<:Union{DenseArray,StridedFastContiguousSubArray},IsReshaped} = ReinterpretArray{T,N,S,A,IsReshaped} where S
StridedReshapedArray{T,N,A<:Union{DenseArray,StridedFastContiguousSubArray,StridedReinterpretArray}} = ReshapedArray{T,N,A}
StridedSubArray{T,N,A<:Union{DenseArray,StridedReshapedArray,StridedReinterpretArray},
    I<:Tuple{Vararg{Union{RangeIndex, ReshapedUnitRange, AbstractCartesianIndex}}}} = SubArray{T,N,A,I}
StridedArray{T,N} = Union{DenseArray{T,N}, StridedSubArray{T,N}, StridedReshapedArray{T,N}, StridedReinterpretArray{T,N}}
StridedVector{T} = StridedArray{T,1}
StridedMatrix{T} = StridedArray{T,2}
StridedVecOrMat{T} = Union{StridedVector{T}, StridedMatrix{T}}

strides(a::Union{DenseArray,StridedReshapedArray,StridedReinterpretArray}) = size_to_strides(1, size(a)...)
stride(A::Union{DenseArray,StridedReshapedArray,StridedReinterpretArray}, k::Integer) =
    k ≤ ndims(A) ? strides(A)[k] : length(A)

function strides(a::ReinterpretArray{T,<:Any,S,<:AbstractArray{S},IsReshaped}) where {T,S,IsReshaped}
    _checkcontiguous(Bool, a) && return size_to_strides(1, size(a)...)
    stp = strides(parent(a))
    els, elp = sizeof(T), sizeof(S)
    els == elp && return stp # 0dim parent is also handled here.
    IsReshaped && els < elp && return (1, _checked_strides(stp, els, elp)...)
    stp[1] == 1 || throw(ArgumentError("Parent must be contiguous in the 1st dimension!"))
    st′ = _checked_strides(tail(stp), els, elp)
    return IsReshaped ? st′ : (1, st′...)
end

@inline function _checked_strides(stp::Tuple, els::Integer, elp::Integer)
    if elp > els && rem(elp, els) == 0
        N = div(elp, els)
        return map(i -> N * i, stp)
    end
    drs = map(i -> divrem(elp * i, els), stp)
    all(i->iszero(i[2]), drs) ||
        throw(ArgumentError("Parent's strides could not be exactly divided!"))
    map(first, drs)
end

_checkcontiguous(::Type{Bool}, A::ReinterpretArray) = _checkcontiguous(Bool, parent(A))

similar(a::ReinterpretArray, T::Type, d::Dims) = similar(a.parent, T, d)

function check_readable(a::ReinterpretArray{T, N, S} where N) where {T,S}
    # See comment in check_writable
    if !a.readable && !array_subpadding(T, S)
        throw(PaddingError(T, S))
    end
end

function check_writable(a::ReinterpretArray{T, N, S} where N) where {T,S}
    # `array_subpadding` is relatively expensive (compared to a simple arrayref),
    # so it is cached in the array. However, it is computable at compile time if,
    # inference has the types available. By using this form of the check, we can
    # get the best of both worlds for the success case. If the types were not
    # available to inference, we simply need to check the field (relatively cheap)
    # and if they were we should be able to fold this check away entirely.
    if !a.writable && !array_subpadding(S, T)
        throw(PaddingError(T, S))
    end
end

## IndexStyle specializations

# For `reinterpret(reshape, T, a)` where we're adding a channel dimension and with
# `IndexStyle(a) == IndexLinear()`, it's advantageous to retain pseudo-linear indexing.
struct IndexSCartesian2{K} <: IndexStyle end   # K = sizeof(S) ÷ sizeof(T), a static-sized 2d cartesian iterator

IndexStyle(::Type{ReinterpretArray{T,N,S,A,false}}) where {T,N,S,A<:AbstractArray{S,N}} = IndexStyle(A)
function IndexStyle(::Type{ReinterpretArray{T,N,S,A,true}}) where {T,N,S,A<:AbstractArray{S}}
    if sizeof(T) < sizeof(S)
        IndexStyle(A) === IndexLinear() && return IndexSCartesian2{sizeof(S) ÷ sizeof(T)}()
        return IndexCartesian()
    end
    return IndexStyle(A)
end
IndexStyle(::IndexSCartesian2{K}, ::IndexSCartesian2{K}) where {K} = IndexSCartesian2{K}()

struct SCartesianIndex2{K}   # can't make <:AbstractCartesianIndex without N, and 2 would be a bit misleading
    i::Int
    j::Int
end
to_index(i::SCartesianIndex2) = i

struct SCartesianIndices2{K,R<:AbstractUnitRange{Int}} <: AbstractMatrix{SCartesianIndex2{K}}
    indices2::R
end
SCartesianIndices2{K}(indices2::AbstractUnitRange{Int}) where {K} = (@assert K::Int > 1; SCartesianIndices2{K,typeof(indices2)}(indices2))

eachindex(::IndexSCartesian2{K}, A::ReshapedReinterpretArray) where {K} = SCartesianIndices2{K}(eachindex(IndexLinear(), parent(A)))
@inline function eachindex(style::IndexSCartesian2{K}, A::AbstractArray, B::AbstractArray...) where {K}
    iter = eachindex(style, A)
    _all_match_first(C->eachindex(style, C), iter, B...) || throw_eachindex_mismatch_indices(IndexSCartesian2{K}(), axes(A), axes.(B)...)
    return iter
end

size(iter::SCartesianIndices2{K}) where K = (K, length(iter.indices2))
axes(iter::SCartesianIndices2{K}) where K = (OneTo(K), iter.indices2)

first(iter::SCartesianIndices2{K}) where {K} = SCartesianIndex2{K}(1, first(iter.indices2))
last(iter::SCartesianIndices2{K}) where {K}  = SCartesianIndex2{K}(K, last(iter.indices2))

@inline function getindex(iter::SCartesianIndices2{K}, i::Int, j::Int) where {K}
    @boundscheck checkbounds(iter, i, j)
    return SCartesianIndex2{K}(i, iter.indices2[j])
end

function iterate(iter::SCartesianIndices2{K}) where {K}
    ret = iterate(iter.indices2)
    ret === nothing && return nothing
    item2, state2 = ret
    return SCartesianIndex2{K}(1, item2), (1, item2, state2)
end

function iterate(iter::SCartesianIndices2{K}, (state1, item2, state2)) where {K}
    if state1 < K
        item1 = state1 + 1
        return SCartesianIndex2{K}(item1, item2), (item1, item2, state2)
    end
    ret = iterate(iter.indices2, state2)
    ret === nothing && return nothing
    item2, state2 = ret
    return SCartesianIndex2{K}(1, item2), (1, item2, state2)
end

SimdLoop.simd_outer_range(iter::SCartesianIndices2) = iter.indices2
SimdLoop.simd_inner_length(::SCartesianIndices2{K}, ::Any) where K = K
@inline function SimdLoop.simd_index(::SCartesianIndices2{K}, Ilast::Int, I1::Int) where {K}
    SCartesianIndex2{K}(I1+1, Ilast)
end

_maybe_reshape(::IndexSCartesian2, A::ReshapedReinterpretArray, I...) = A

# fallbacks
function _getindex(::IndexSCartesian2, A::AbstractArray{T,N}, I::Vararg{Int, N}) where {T,N}
    @_propagate_inbounds_meta
    getindex(A, I...)
end
function _setindex!(::IndexSCartesian2, A::AbstractArray{T,N}, v, I::Vararg{Int, N}) where {T,N}
    @_propagate_inbounds_meta
    setindex!(A, v, I...)
end
# fallbacks for array types that use "pass-through" indexing (e.g., `IndexStyle(A) = IndexStyle(parent(A))`)
# but which don't handle SCartesianIndex2
function _getindex(::IndexSCartesian2, A::AbstractArray{T,N}, ind::SCartesianIndex2) where {T,N}
    @_propagate_inbounds_meta
    J = _ind2sub(tail(axes(A)), ind.j)
    getindex(A, ind.i, J...)
end
function _setindex!(::IndexSCartesian2, A::AbstractArray{T,N}, v, ind::SCartesianIndex2) where {T,N}
    @_propagate_inbounds_meta
    J = _ind2sub(tail(axes(A)), ind.j)
    setindex!(A, v, ind.i, J...)
end
eachindex(style::IndexSCartesian2, A::AbstractArray) = eachindex(style, parent(A))

## AbstractArray interface

parent(a::ReinterpretArray) = a.parent
dataids(a::ReinterpretArray) = dataids(a.parent)
unaliascopy(a::NonReshapedReinterpretArray{T}) where {T} = reinterpret(T, unaliascopy(a.parent))
unaliascopy(a::ReshapedReinterpretArray{T}) where {T} = reinterpret(reshape, T, unaliascopy(a.parent))

function size(a::NonReshapedReinterpretArray{T,N,S} where {N}) where {T,S}
    psize = size(a.parent)
    size1 = issingletontype(T) ? psize[1] : div(psize[1]*sizeof(S), sizeof(T))
    tuple(size1, tail(psize)...)
end
function size(a::ReshapedReinterpretArray{T,N,S} where {N}) where {T,S}
    psize = size(a.parent)
    sizeof(S) > sizeof(T) && return (div(sizeof(S), sizeof(T)), psize...)
    sizeof(S) < sizeof(T) && return tail(psize)
    return psize
end
size(a::NonReshapedReinterpretArray{T,0}) where {T} = ()

function axes(a::NonReshapedReinterpretArray{T,N,S} where {N}) where {T,S}
    paxs = axes(a.parent)
    f, l = first(paxs[1]), length(paxs[1])
    size1 = issingletontype(T) ? l : div(l*sizeof(S), sizeof(T))
    tuple(oftype(paxs[1], f:f+size1-1), tail(paxs)...)
end
function axes(a::ReshapedReinterpretArray{T,N,S} where {N}) where {T,S}
    paxs = axes(a.parent)
    sizeof(S) > sizeof(T) && return (OneTo(div(sizeof(S), sizeof(T))), paxs...)
    sizeof(S) < sizeof(T) && return tail(paxs)
    return paxs
end
axes(a::NonReshapedReinterpretArray{T,0}) where {T} = ()

has_offset_axes(a::ReinterpretArray) = has_offset_axes(a.parent)

elsize(::Type{<:ReinterpretArray{T}}) where {T} = sizeof(T)
unsafe_convert(::Type{Ptr{T}}, a::ReinterpretArray{T,N,S} where N) where {T,S} = Ptr{T}(unsafe_convert(Ptr{S},a.parent))

@inline @propagate_inbounds function getindex(a::NonReshapedReinterpretArray{T,0,S}) where {T,S}
    if isprimitivetype(T) && isprimitivetype(S)
        reinterpret(T, a.parent[])
    else
        a[firstindex(a)]
    end
end

@inline @propagate_inbounds getindex(a::ReinterpretArray) = a[firstindex(a)]

@inline @propagate_inbounds function getindex(a::ReinterpretArray{T,N,S}, inds::Vararg{Int, N}) where {T,N,S}
    check_readable(a)
    _getindex_ra(a, inds[1], tail(inds))
end

@inline @propagate_inbounds function getindex(a::ReinterpretArray{T,N,S}, i::Int) where {T,N,S}
    check_readable(a)
    if isa(IndexStyle(a), IndexLinear)
        return _getindex_ra(a, i, ())
    end
    # Convert to full indices here, to avoid needing multiple conversions in
    # the loop in _getindex_ra
    inds = _to_subscript_indices(a, i)
    isempty(inds) ? _getindex_ra(a, 1, ()) : _getindex_ra(a, inds[1], tail(inds))
end

@inline @propagate_inbounds function getindex(a::ReshapedReinterpretArray{T,N,S}, ind::SCartesianIndex2) where {T,N,S}
    check_readable(a)
    s = Ref{S}(a.parent[ind.j])
    GC.@preserve s begin
        tptr = Ptr{T}(unsafe_convert(Ref{S}, s))
        return unsafe_load(tptr, ind.i)
    end
end

@inline @propagate_inbounds function _getindex_ra(a::NonReshapedReinterpretArray{T,N,S}, i1::Int, tailinds::TT) where {T,N,S,TT}
    # Make sure to match the scalar reinterpret if that is applicable
    if sizeof(T) == sizeof(S) && (fieldcount(T) + fieldcount(S)) == 0
        if issingletontype(T) # singleton types
            @boundscheck checkbounds(a, i1, tailinds...)
            return T.instance
        end
        return reinterpret(T, a.parent[i1, tailinds...])
    else
        @boundscheck checkbounds(a, i1, tailinds...)
        ind_start, sidx = divrem((i1-1)*sizeof(T), sizeof(S))
        # Optimizations that avoid branches
        if sizeof(T) % sizeof(S) == 0
            # T is bigger than S and contains an integer number of them
            n = sizeof(T) ÷ sizeof(S)
            t = Ref{T}()
            GC.@preserve t begin
                sptr = Ptr{S}(unsafe_convert(Ref{T}, t))
                for i = 1:n
                     s = a.parent[ind_start + i, tailinds...]
                     unsafe_store!(sptr, s, i)
                end
            end
            return t[]
        elseif sizeof(S) % sizeof(T) == 0
            # S is bigger than T and contains an integer number of them
            s = Ref{S}(a.parent[ind_start + 1, tailinds...])
            GC.@preserve s begin
                tptr = Ptr{T}(unsafe_convert(Ref{S}, s))
                return unsafe_load(tptr + sidx)
            end
        else
            i = 1
            nbytes_copied = 0
            # This is a bit complicated to deal with partial elements
            # at both the start and the end. LLVM will fold as appropriate,
            # once it knows the data layout
            s = Ref{S}()
            t = Ref{T}()
            GC.@preserve s t begin
                sptr = Ptr{S}(unsafe_convert(Ref{S}, s))
                tptr = Ptr{T}(unsafe_convert(Ref{T}, t))
                while nbytes_copied < sizeof(T)
                    s[] = a.parent[ind_start + i, tailinds...]
                    nb = min(sizeof(S) - sidx, sizeof(T)-nbytes_copied)
                    memcpy(tptr + nbytes_copied, sptr + sidx, nb)
                    nbytes_copied += nb
                    sidx = 0
                    i += 1
                end
            end
            return t[]
        end
    end
end

@inline @propagate_inbounds function _getindex_ra(a::ReshapedReinterpretArray{T,N,S}, i1::Int, tailinds::TT) where {T,N,S,TT}
    # Make sure to match the scalar reinterpret if that is applicable
    if sizeof(T) == sizeof(S) && (fieldcount(T) + fieldcount(S)) == 0
        if issingletontype(T) # singleton types
            @boundscheck checkbounds(a, i1, tailinds...)
            return T.instance
        end
        return reinterpret(T, a.parent[i1, tailinds...])
    end
    @boundscheck checkbounds(a, i1, tailinds...)
    if sizeof(T) >= sizeof(S)
        t = Ref{T}()
        GC.@preserve t begin
            sptr = Ptr{S}(unsafe_convert(Ref{T}, t))
            if sizeof(T) > sizeof(S)
                # Extra dimension in the parent array
                n = sizeof(T) ÷ sizeof(S)
                if isempty(tailinds) && IndexStyle(a.parent) === IndexLinear()
                    offset = n * (i1 - firstindex(a))
                    for i = 1:n
                        s = a.parent[i + offset]
                        unsafe_store!(sptr, s, i)
                    end
                else
                    for i = 1:n
                        s = a.parent[i, i1, tailinds...]
                        unsafe_store!(sptr, s, i)
                    end
                end
            else
                # No extra dimension
                s = a.parent[i1, tailinds...]
                unsafe_store!(sptr, s)
            end
        end
        return t[]
    end
    # S is bigger than T and contains an integer number of them
    # n = sizeof(S) ÷ sizeof(T)
    s = Ref{S}()
    GC.@preserve s begin
        tptr = Ptr{T}(unsafe_convert(Ref{S}, s))
        s[] = a.parent[tailinds...]
        return unsafe_load(tptr, i1)
    end
end

@inline @propagate_inbounds function setindex!(a::NonReshapedReinterpretArray{T,0,S}, v) where {T,S}
    if isprimitivetype(S) && isprimitivetype(T)
        a.parent[] = reinterpret(S, v)
        return a
    end
    setindex!(a, v, firstindex(a))
end

@inline @propagate_inbounds setindex!(a::ReinterpretArray, v) = setindex!(a, v, firstindex(a))

@inline @propagate_inbounds function setindex!(a::ReinterpretArray{T,N,S}, v, inds::Vararg{Int, N}) where {T,N,S}
    check_writable(a)
    _setindex_ra!(a, v, inds[1], tail(inds))
end

@inline @propagate_inbounds function setindex!(a::ReinterpretArray{T,N,S}, v, i::Int) where {T,N,S}
    check_writable(a)
    if isa(IndexStyle(a), IndexLinear)
        return _setindex_ra!(a, v, i, ())
    end
    inds = _to_subscript_indices(a, i)
    _setindex_ra!(a, v, inds[1], tail(inds))
end

@inline @propagate_inbounds function setindex!(a::ReshapedReinterpretArray{T,N,S}, v, ind::SCartesianIndex2) where {T,N,S}
    check_writable(a)
    v = convert(T, v)::T
    s = Ref{S}(a.parent[ind.j])
    GC.@preserve s begin
        tptr = Ptr{T}(unsafe_convert(Ref{S}, s))
        unsafe_store!(tptr, v, ind.i)
    end
    a.parent[ind.j] = s[]
    return a
end

@inline @propagate_inbounds function _setindex_ra!(a::NonReshapedReinterpretArray{T,N,S}, v, i1::Int, tailinds::TT) where {T,N,S,TT}
    v = convert(T, v)::T
    # Make sure to match the scalar reinterpret if that is applicable
    if sizeof(T) == sizeof(S) && (fieldcount(T) + fieldcount(S)) == 0
        if issingletontype(T) # singleton types
            @boundscheck checkbounds(a, i1, tailinds...)
            # setindex! is a noop except for the index check
        else
            setindex!(a.parent, reinterpret(S, v), i1, tailinds...)
        end
    else
        @boundscheck checkbounds(a, i1, tailinds...)
        ind_start, sidx = divrem((i1-1)*sizeof(T), sizeof(S))
        # Optimizations that avoid branches
        if sizeof(T) % sizeof(S) == 0
            # T is bigger than S and contains an integer number of them
            t = Ref{T}(v)
            GC.@preserve t begin
                sptr = Ptr{S}(unsafe_convert(Ref{T}, t))
                n = sizeof(T) ÷ sizeof(S)
                for i = 1:n
                    s = unsafe_load(sptr, i)
                    a.parent[ind_start + i, tailinds...] = s
                end
            end
        elseif sizeof(S) % sizeof(T) == 0
            # S is bigger than T and contains an integer number of them
            s = Ref{S}(a.parent[ind_start + 1, tailinds...])
            GC.@preserve s begin
                tptr = Ptr{T}(unsafe_convert(Ref{S}, s))
                unsafe_store!(tptr + sidx, v)
                a.parent[ind_start + 1, tailinds...] = s[]
            end
        else
            t = Ref{T}(v)
            s = Ref{S}()
            GC.@preserve t s begin
                tptr = Ptr{UInt8}(unsafe_convert(Ref{T}, t))
                sptr = Ptr{UInt8}(unsafe_convert(Ref{S}, s))
                nbytes_copied = 0
                i = 1
                # Deal with any partial elements at the start. We'll have to copy in the
                # element from the original array and overwrite the relevant parts
                if sidx != 0
                    s[] = a.parent[ind_start + i, tailinds...]
                    nb = min((sizeof(S) - sidx) % UInt, sizeof(T) % UInt)
                    memcpy(sptr + sidx, tptr, nb)
                    nbytes_copied += nb
                    a.parent[ind_start + i, tailinds...] = s[]
                    i += 1
                    sidx = 0
                end
                # Deal with the main body of elements
                while nbytes_copied < sizeof(T) && (sizeof(T) - nbytes_copied) > sizeof(S)
                    nb = min(sizeof(S), sizeof(T) - nbytes_copied)
                    memcpy(sptr, tptr + nbytes_copied, nb)
                    nbytes_copied += nb
                    a.parent[ind_start + i, tailinds...] = s[]
                    i += 1
                end
                # Deal with trailing partial elements
                if nbytes_copied < sizeof(T)
                    s[] = a.parent[ind_start + i, tailinds...]
                    nb = min(sizeof(S), sizeof(T) - nbytes_copied)
                    memcpy(sptr, tptr + nbytes_copied, nb)
                    a.parent[ind_start + i, tailinds...] = s[]
                end
            end
        end
    end
    return a
end

@inline @propagate_inbounds function _setindex_ra!(a::ReshapedReinterpretArray{T,N,S}, v, i1::Int, tailinds::TT) where {T,N,S,TT}
    v = convert(T, v)::T
    # Make sure to match the scalar reinterpret if that is applicable
    if sizeof(T) == sizeof(S) && (fieldcount(T) + fieldcount(S)) == 0
        if issingletontype(T) # singleton types
            @boundscheck checkbounds(a, i1, tailinds...)
            # setindex! is a noop except for the index check
        else
            setindex!(a.parent, reinterpret(S, v), i1, tailinds...)
        end
    end
    @boundscheck checkbounds(a, i1, tailinds...)
    if sizeof(T) >= sizeof(S)
        t = Ref{T}(v)
        GC.@preserve t begin
            sptr = Ptr{S}(unsafe_convert(Ref{T}, t))
            if sizeof(T) > sizeof(S)
                # Extra dimension in the parent array
                n = sizeof(T) ÷ sizeof(S)
                if isempty(tailinds) && IndexStyle(a.parent) === IndexLinear()
                    offset = n * (i1 - firstindex(a))
                    for i = 1:n
                        s = unsafe_load(sptr, i)
                        a.parent[i + offset] = s
                    end
                else
                    for i = 1:n
                        s = unsafe_load(sptr, i)
                        a.parent[i, i1, tailinds...] = s
                    end
                end
            else # sizeof(T) == sizeof(S)
                # No extra dimension
                s = unsafe_load(sptr)
                a.parent[i1, tailinds...] = s
            end
        end
    else
        # S is bigger than T and contains an integer number of them
        s = Ref{S}()
        GC.@preserve s begin
            tptr = Ptr{T}(unsafe_convert(Ref{S}, s))
            s[] = a.parent[tailinds...]
            unsafe_store!(tptr, v, i1)
            a.parent[tailinds...] = s[]
        end
    end
    return a
end

# Padding
struct Padding
    offset::Int # 0-indexed offset of the next valid byte; sizeof(T) indicates trailing padding
    size::Int   # bytes of padding before a valid byte
end
function intersect(p1::Padding, p2::Padding)
    start = max(p1.offset, p2.offset)
    stop = min(p1.offset + p1.size, p2.offset + p2.size)
    Padding(start, max(0, stop-start))
end

struct PaddingError <: Exception
    S::Type
    T::Type
end

function showerror(io::IO, p::PaddingError)
    print(io, "Padding of type $(p.S) is not compatible with type $(p.T).")
end

"""
    CyclePadding(padding, total_size)

Cylces an iterator of `Padding` structs, restarting the padding at `total_size`.
E.g. if `padding` is all the padding in a struct and `total_size` is the total
aligned size of that array, `CyclePadding` will correspond to the padding in an
infinite vector of such structs.
"""
struct CyclePadding{P}
    padding::P
    total_size::Int
end
eltype(::Type{<:CyclePadding}) = Padding
IteratorSize(::Type{<:CyclePadding}) = IsInfinite()
isempty(cp::CyclePadding) = isempty(cp.padding)
function iterate(cp::CyclePadding)
    y = iterate(cp.padding)
    y === nothing && return nothing
    y[1], (0, y[2])
end
function iterate(cp::CyclePadding, state::Tuple)
    y = iterate(cp.padding, tail(state)...)
    y === nothing && return iterate(cp, (state[1]+cp.total_size,))
    Padding(y[1].offset+state[1], y[1].size), (state[1], tail(y)...)
end

"""
    Compute the location of padding in an isbits datatype. Recursive over the fields of that type.
"""
@assume_effects :foldable function padding(T::DataType, baseoffset::Int = 0)
    pads = Padding[]
    last_end::Int = baseoffset
    for i = 1:fieldcount(T)
        offset = baseoffset + Int(fieldoffset(T, i))
        fT = fieldtype(T, i)
        append!(pads, padding(fT, offset))
        if offset != last_end
            push!(pads, Padding(offset, offset-last_end))
        end
        last_end = offset + sizeof(fT)
    end
    if 0 < last_end - baseoffset < sizeof(T)
        push!(pads, Padding(baseoffset + sizeof(T), sizeof(T) - last_end + baseoffset))
    end
    return Core.svec(pads...)
end

function CyclePadding(T::DataType)
    a, s = datatype_alignment(T), sizeof(T)
    as = s + (a - (s % a)) % a
    pad = padding(T)
    if s != as
        pad = Core.svec(pad..., Padding(s, as - s))
    end
    CyclePadding(pad, as)
end

@assume_effects :total function array_subpadding(S, T)
    lcm_size = lcm(sizeof(S), sizeof(T))
    s, t = CyclePadding(S), CyclePadding(T)
    checked_size = 0
    # use of Stateful harms inference and makes this vulnerable to invalidation
    (pad, tstate) = let
        it = iterate(t)
        it === nothing && return true
        it
    end
    (ps, sstate) = let
        it = iterate(s)
        it === nothing && return false
        it
    end
    while checked_size < lcm_size
        while true
            # See if there's corresponding padding in S
            ps.offset > pad.offset && return false
            intersect(ps, pad) == pad && break
            ps, sstate = iterate(s, sstate)
        end
        checked_size = pad.offset + pad.size
        pad, tstate = iterate(t, tstate)
    end
    return true
end

@assume_effects :foldable function struct_subpadding(::Type{Out}, ::Type{In}) where {Out, In}
    padding(Out) == padding(In)
end

@assume_effects :foldable function packedsize(::Type{T}) where T
    pads = padding(T)
    return sizeof(T) - sum((p.size for p ∈ pads), init = 0)
end

@assume_effects :foldable ispacked(::Type{T}) where T = isempty(padding(T))

function _copytopacked!(ptr_out::Ptr{Out}, ptr_in::Ptr{In}) where {Out, In}
    writeoffset = 0
    for i ∈ 1:fieldcount(In)
        readoffset = fieldoffset(In, i)
        fT = fieldtype(In, i)
        if ispacked(fT)
            readsize = sizeof(fT)
            memcpy(ptr_out + writeoffset, ptr_in + readoffset, readsize)
            writeoffset += readsize
        else # nested padded type
            _copytopacked!(ptr_out + writeoffset, Ptr{fT}(ptr_in + readoffset))
            writeoffset += packedsize(fT)
        end
    end
end

function _copyfrompacked!(ptr_out::Ptr{Out}, ptr_in::Ptr{In}) where {Out, In}
    readoffset = 0
    for i ∈ 1:fieldcount(Out)
        writeoffset = fieldoffset(Out, i)
        fT = fieldtype(Out, i)
        if ispacked(fT)
            writesize = sizeof(fT)
            memcpy(ptr_out + writeoffset, ptr_in + readoffset, writesize)
            readoffset += writesize
        else # nested padded type
            _copyfrompacked!(Ptr{fT}(ptr_out + writeoffset), ptr_in + readoffset)
            readoffset += packedsize(fT)
        end
    end
end

@inline function _reinterpret(::Type{Out}, x::In) where {Out, In}
    # handle non-primitive types
    isbitstype(Out) || throw(ArgumentError("Target type for `reinterpret` must be isbits"))
    isbitstype(In) || throw(ArgumentError("Source type for `reinterpret` must be isbits"))
    inpackedsize = packedsize(In)
    outpackedsize = packedsize(Out)
    inpackedsize == outpackedsize ||
        throw(ArgumentError("Packed sizes of types $Out and $In do not match; got $outpackedsize \
            and $inpackedsize, respectively."))
    in = Ref{In}(x)
    out = Ref{Out}()
    if struct_subpadding(Out, In)
        # if packed the same, just copy
        GC.@preserve in out begin
            ptr_in = unsafe_convert(Ptr{In}, in)
            ptr_out = unsafe_convert(Ptr{Out}, out)
            memcpy(ptr_out, ptr_in, sizeof(Out))
        end
        return out[]
    else
        # mismatched padding
        GC.@preserve in out begin
            ptr_in = unsafe_convert(Ptr{In}, in)
            ptr_out = unsafe_convert(Ptr{Out}, out)

            if fieldcount(In) > 0 && ispacked(Out)
                _copytopacked!(ptr_out, ptr_in)
            elseif fieldcount(Out) > 0 && ispacked(In)
                _copyfrompacked!(ptr_out, ptr_in)
            else
                packed = Ref{NTuple{inpackedsize, UInt8}}()
                GC.@preserve packed begin
                    ptr_packed = unsafe_convert(Ptr{NTuple{inpackedsize, UInt8}}, packed)
                    _copytopacked!(ptr_packed, ptr_in)
                    _copyfrompacked!(ptr_out, ptr_packed)
                end
            end
        end
        return out[]
    end
end


# Reductions with IndexSCartesian2

function _mapreduce(f::F, op::OP, style::IndexSCartesian2{K}, A::AbstractArrayOrBroadcasted) where {F,OP,K}
    inds = eachindex(style, A)
    n = size(inds)[2]
    if n == 0
        return mapreduce_empty_iter(f, op, A, IteratorEltype(A))
    else
        return mapreduce_impl(f, op, A, first(inds), last(inds))
    end
end

@noinline function mapreduce_impl(f::F, op::OP, A::AbstractArrayOrBroadcasted,
                                  ifirst::SCI, ilast::SCI, blksize::Int) where {F,OP,SCI<:SCartesianIndex2{K}} where K
    if ilast.j - ifirst.j < blksize
        # sequential portion
        @inbounds a1 = A[ifirst]
        @inbounds a2 = A[SCI(2,ifirst.j)]
        v = op(f(a1), f(a2))
        @simd for i = ifirst.i + 2 : K
            @inbounds ai = A[SCI(i,ifirst.j)]
            v = op(v, f(ai))
        end
        # Remaining columns
        for j = ifirst.j+1 : ilast.j
            @simd for i = 1:K
                @inbounds ai = A[SCI(i,j)]
                v = op(v, f(ai))
            end
        end
        return v
    else
        # pairwise portion
        jmid = ifirst.j + (ilast.j - ifirst.j) >> 1
        v1 = mapreduce_impl(f, op, A, ifirst, SCI(K,jmid), blksize)
        v2 = mapreduce_impl(f, op, A, SCI(1,jmid+1), ilast, blksize)
        return op(v1, v2)
    end
end

mapreduce_impl(f::F, op::OP, A::AbstractArrayOrBroadcasted, ifirst::SCartesianIndex2, ilast::SCartesianIndex2) where {F,OP} =
    mapreduce_impl(f, op, A, ifirst, ilast, pairwise_blocksize(f, op))
O   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/bitarray.jl��      # This file is a part of Julia. License is MIT: https://julialang.org/license

## BitArray

# notes: bits are stored in contiguous chunks
#        unused bits must always be set to 0
"""
    BitArray{N} <: AbstractArray{Bool, N}

Space-efficient `N`-dimensional boolean array, using just one bit for each boolean value.

`BitArray`s pack up to 64 values into every 8 bytes, resulting in an 8x space efficiency
over `Array{Bool, N}` and allowing some operations to work on 64 values at once.

By default, Julia returns `BitArrays` from [broadcasting](@ref Broadcasting) operations
that generate boolean elements (including dotted-comparisons like `.==`) as well as from
the functions [`trues`](@ref) and [`falses`](@ref).

!!! note
    Due to its packed storage format, concurrent access to the elements of a `BitArray`
    where at least one of them is a write is not thread-safe.

"""
mutable struct BitArray{N} <: AbstractArray{Bool, N}
    chunks::Vector{UInt64}
    len::Int
    dims::NTuple{N,Int}
    function BitArray{N}(::UndefInitializer, dims::Vararg{Int,N}) where N
        n = 1
        i = 1
        for d in dims
            d >= 0 || throw(ArgumentError("dimension size must be ≥ 0, got $d for dimension $i"))
            n *= d
            i += 1
        end
        nc = num_bit_chunks(n)
        chunks = Vector{UInt64}(undef, nc)
        nc > 0 && (chunks[end] = UInt64(0))
        b = new(chunks, n)
        N != 1 && (b.dims = dims)
        return b
    end
end

# note: the docs for the two signatures are unified, but only
# the first one is recognized by the help system; it would be nice
# to fix this.
"""
    BitArray(undef, dims::Integer...)
    BitArray{N}(undef, dims::NTuple{N,Int})

Construct an undef [`BitArray`](@ref) with the given dimensions.
Behaves identically to the [`Array`](@ref) constructor. See [`undef`](@ref).

# Examples
```julia-repl
julia> BitArray(undef, 2, 2)
2×2 BitMatrix:
 0  0
 0  0

julia> BitArray(undef, (3, 1))
3×1 BitMatrix:
 0
 0
 0
```
"""
BitArray(::UndefInitializer, dims::Integer...) = BitArray(undef, map(Int,dims))
BitArray{N}(::UndefInitializer, dims::Integer...) where {N} = BitArray{N}(undef, map(Int,dims))::BitArray{N}
BitArray(::UndefInitializer, dims::NTuple{N,Integer}) where {N} = BitArray{N}(undef, map(Int, dims)...)
BitArray{N}(::UndefInitializer, dims::NTuple{N,Integer}) where {N} = BitArray{N}(undef, map(Int, dims)...)

const BitVector = BitArray{1}
const BitMatrix = BitArray{2}

BitVector() = BitVector(undef, 0)

"""
    BitVector(nt::Tuple{Vararg{Bool}})

Construct a `BitVector` from a tuple of `Bool`.
# Examples
```julia-repl
julia> nt = (true, false, true, false)
(true, false, true, false)

julia> BitVector(nt)
4-element BitVector:
 1
 0
 1
 0
```
"""
function BitVector(nt::Tuple{Vararg{Bool}})
    bv = BitVector(undef, length(nt))
    bv .= nt
end

## utility functions ##

length(B::BitArray) = B.len
size(B::BitVector) = (B.len,)
size(B::BitArray) = B.dims

@inline function size(B::BitVector, d::Integer)
    d < 1 && throw_boundserror(size(B), d)
    ifelse(d == 1, B.len, 1)
end

isassigned(B::BitArray, i::Int) = 1 <= i <= length(B)

IndexStyle(::Type{<:BitArray}) = IndexLinear()

## aux functions ##

const _msk64 = ~UInt64(0)
@inline _div64(l) = l >> 6
@inline _mod64(l) = l & 63
@inline _blsr(x)= x & (x-1) #zeros the last set bit. Has native instruction on many archs. needed in multidimensional.jl
@inline _msk_end(l::Int) = _msk64 >>> _mod64(-l)
@inline _msk_end(B::BitArray) = _msk_end(length(B))
num_bit_chunks(n::Int) = _div64(n+63)

@inline get_chunks_id(i::Int) = _div64(i-1)+1, _mod64(i-1)

function glue_src_bitchunks(src::Vector{UInt64}, k::Int, ks1::Int, msk_s0::UInt64, ls0::Int)
    @inbounds begin
        chunk = ((src[k] & msk_s0) >>> ls0)
        if ks1 > k && ls0 > 0
            chunk_n = (src[k + 1] & ~msk_s0)
            chunk |= (chunk_n << (64 - ls0))
        end
    end
    return chunk
end

function copy_chunks!(dest::Vector{UInt64}, pos_d::Int, src::Vector{UInt64}, pos_s::Int, numbits::Int)
    numbits == 0 && return
    if dest === src && pos_d > pos_s
        return copy_chunks_rtol!(dest, pos_d, pos_s, numbits)
    end

    kd0, ld0 = get_chunks_id(pos_d)
    kd1, ld1 = get_chunks_id(pos_d + numbits - 1)
    ks0, ls0 = get_chunks_id(pos_s)
    ks1, ls1 = get_chunks_id(pos_s + numbits - 1)

    delta_kd = kd1 - kd0
    delta_ks = ks1 - ks0

    u = _msk64
    if delta_kd == 0
        msk_d0 = ~(u << ld0) | (u << (ld1+1))
    else
        msk_d0 = ~(u << ld0)
        msk_d1 = (u << (ld1+1))
    end
    if delta_ks == 0
        msk_s0 = (u << ls0) & ~(u << (ls1+1))
    else
        msk_s0 = (u << ls0)
    end

    chunk_s0 = glue_src_bitchunks(src, ks0, ks1, msk_s0, ls0)

    dest[kd0] = (dest[kd0] & msk_d0) | ((chunk_s0 << ld0) & ~msk_d0)

    delta_kd == 0 && return

    for i = 1 : kd1 - kd0 - 1
        chunk_s1 = glue_src_bitchunks(src, ks0 + i, ks1, msk_s0, ls0)

        chunk_s = (chunk_s0 >>> (64 - ld0)) | (chunk_s1 << ld0)

        dest[kd0 + i] = chunk_s

        chunk_s0 = chunk_s1
    end

    if ks1 >= ks0 + delta_kd
        chunk_s1 = glue_src_bitchunks(src, ks0 + delta_kd, ks1, msk_s0, ls0)
    else
        chunk_s1 = UInt64(0)
    end

    chunk_s = (chunk_s0 >>> (64 - ld0)) | (chunk_s1 << ld0)

    dest[kd1] = (dest[kd1] & msk_d1) | (chunk_s & ~msk_d1)

    return
end

function copy_chunks_rtol!(chunks::Vector{UInt64}, pos_d::Int, pos_s::Int, numbits::Int)
    pos_d == pos_s && return
    pos_d < pos_s && return copy_chunks!(chunks, pos_d, chunks, pos_s, numbits)

    left = numbits
    s = min(left, 64)
    b = left - s
    ps = pos_s + b
    pd = pos_d + b
    u = _msk64
    while left > 0
        kd0, ld0 = get_chunks_id(pd)
        kd1, ld1 = get_chunks_id(pd + s - 1)
        ks0, ls0 = get_chunks_id(ps)
        ks1, ls1 = get_chunks_id(ps + s - 1)

        delta_kd = kd1 - kd0
        delta_ks = ks1 - ks0

        if delta_kd == 0
            msk_d0 = ~(u << ld0) | (u << (ld1+1))
        else
            msk_d0 = ~(u << ld0)
            msk_d1 = (u << (ld1+1))
        end
        if delta_ks == 0
            msk_s0 = (u << ls0) & ~(u << (ls1+1))
        else
            msk_s0 = (u << ls0)
        end

        chunk_s0 = glue_src_bitchunks(chunks, ks0, ks1, msk_s0, ls0) & ~(u << s)
        chunks[kd0] = (chunks[kd0] & msk_d0) | ((chunk_s0 << ld0) & ~msk_d0)

        if delta_kd != 0
            chunk_s = (chunk_s0 >>> (64 - ld0))

            chunks[kd1] = (chunks[kd1] & msk_d1) | (chunk_s & ~msk_d1)
        end

        left -= s
        s = min(left, 64)
        b = left - s
        ps = pos_s + b
        pd = pos_d + b
    end
end

function fill_chunks!(Bc::Array{UInt64}, x::Bool, pos::Int, numbits::Int)
    numbits <= 0 && return
    k0, l0 = get_chunks_id(pos)
    k1, l1 = get_chunks_id(pos+numbits-1)

    u = _msk64
    if k1 == k0
        msk0 = (u << l0) & ~(u << (l1+1))
    else
        msk0 = (u << l0)
        msk1 = ~(u << (l1+1))
    end
    @inbounds if x
        Bc[k0] |= msk0
        for k = k0+1:k1-1
            Bc[k] = u
        end
        k1 > k0 && (Bc[k1] |= msk1)
    else
        Bc[k0] &= ~msk0
        for k = k0+1:k1-1
            Bc[k] = 0
        end
        k1 > k0 && (Bc[k1] &= ~msk1)
    end
end

copy_to_bitarray_chunks!(dest::Vector{UInt64}, pos_d::Int, src::BitArray, pos_s::Int, numbits::Int) =
    copy_chunks!(dest, pos_d, src.chunks, pos_s, numbits)

# pack 8 Bools encoded as one contiguous UIn64 into a single byte, e.g.:
# 0000001:0000001:00000000:00000000:00000001:00000000:00000000:00000001 → 11001001 → 0xc9
function pack8bools(z::UInt64)
    z |= z >>> 7
    z |= z >>> 14
    z |= z >>> 28
    z &= 0xFF
    return z
end

function copy_to_bitarray_chunks!(Bc::Vector{UInt64}, pos_d::Int, C::Array{Bool}, pos_s::Int, numbits::Int)
    kd0, ld0 = get_chunks_id(pos_d)
    kd1, ld1 = get_chunks_id(pos_d + numbits - 1)

    delta_kd = kd1 - kd0

    u = _msk64
    if delta_kd == 0
        msk_d0 = msk_d1 = ~(u << ld0) | (u << (ld1+1))
        lt0 = ld1
    else
        msk_d0 = ~(u << ld0)
        msk_d1 = (u << (ld1+1))
        lt0 = 63
    end

    bind = kd0
    ind = pos_s
    @inbounds if ld0 > 0
        c = UInt64(0)
        for j = ld0:lt0
            c |= (UInt64(C[ind]) << j)
            ind += 1
        end
        Bc[kd0] = (Bc[kd0] & msk_d0) | (c & ~msk_d0)
        bind += 1
    end

    nc = _div64(numbits - ind + pos_s)
    nc8 = (nc >>> 3) << 3
    if nc8 > 0
        ind8 = 1
        P8 = Ptr{UInt64}(pointer(C, ind)) # unaligned i64 pointer
        @inbounds for i = 1:nc8
            c = UInt64(0)
            for j = 0:7
                # unaligned load
                c |= (pack8bools(unsafe_load(P8, ind8)) << (j<<3))
                ind8 += 1
            end
            Bc[bind] = c
            bind += 1
        end
        ind += (ind8-1) << 3
    end
    @inbounds for i = (nc8+1):nc
        c = UInt64(0)
        for j = 0:63
            c |= (UInt64(C[ind]) << j)
            ind += 1
        end
        Bc[bind] = c
        bind += 1
    end
    @inbounds if bind ≤ kd1
        @assert bind == kd1
        c = UInt64(0)
        for j = 0:ld1
            c |= (UInt64(C[ind]) << j)
            ind += 1
        end
        Bc[kd1] = (Bc[kd1] & msk_d1) | (c & ~msk_d1)
    end
end

## More definitions in multidimensional.jl

# auxiliary definitions used when filling a BitArray via a Vector{Bool} cache
# (e.g. when constructing from an iterable, or in broadcast!)

const bitcache_chunks = 64 # this can be changed
const bitcache_size = 64 * bitcache_chunks # do not change this

dumpbitcache(Bc::Vector{UInt64}, bind::Int, C::Vector{Bool}) =
    copy_to_bitarray_chunks!(Bc, ((bind - 1) << 6) + 1, C, 1, min(bitcache_size, (length(Bc)-bind+1) << 6))


## custom iterator ##
function iterate(B::BitArray, i::Int=0)
    i >= length(B) && return nothing
    (B.chunks[_div64(i)+1] & (UInt64(1)<<_mod64(i)) != 0, i+1)
end

## similar, fill!, copy! etc ##

similar(B::BitArray) = BitArray(undef, size(B))
similar(B::BitArray, dims::Int...) = BitArray(undef, dims)
similar(B::BitArray, dims::Dims) = BitArray(undef, dims...)

similar(B::BitArray, T::Type{Bool}, dims::Dims) = BitArray(undef, dims)
# changing type to a non-Bool returns an Array
# (this triggers conversions like float(bitvector) etc.)
similar(B::BitArray, T::Type, dims::Dims) = Array{T}(undef, dims)

function fill!(B::BitArray, x)
    y = convert(Bool, x)
    isempty(B) && return B
    Bc = B.chunks
    if !y
        fill!(Bc, 0)
    else
        fill!(Bc, _msk64)
        Bc[end] &= _msk_end(B)
    end
    return B
end

"""
    falses(dims)

Create a `BitArray` with all values set to `false`.

# Examples
```jldoctest
julia> falses(2,3)
2×3 BitMatrix:
 0  0  0
 0  0  0
```
"""
falses(dims::DimOrInd...) = falses(dims)
falses(dims::NTuple{N, Union{Integer, OneTo}}) where {N} = falses(map(to_dim, dims))
falses(dims::NTuple{N, Integer}) where {N} = fill!(BitArray(undef, dims), false)
falses(dims::Tuple{}) = fill!(BitArray(undef, dims), false)

"""
    trues(dims)

Create a `BitArray` with all values set to `true`.

# Examples
```jldoctest
julia> trues(2,3)
2×3 BitMatrix:
 1  1  1
 1  1  1
```
"""
trues(dims::DimOrInd...) = trues(dims)
trues(dims::NTuple{N, Union{Integer, OneTo}}) where {N} = trues(map(to_dim, dims))
trues(dims::NTuple{N, Integer}) where {N} = fill!(BitArray(undef, dims), true)
trues(dims::Tuple{}) = fill!(BitArray(undef, dims), true)

function one(x::BitMatrix)
    m, n = size(x)
    m == n || throw(DimensionMismatch("multiplicative identity defined only for square matrices"))
    a = falses(n, n)
    for i = 1:n
        a[i,i] = true
    end
    return a
end

function copyto!(dest::BitArray, src::BitArray)
    length(src) > length(dest) && throw(BoundsError(dest, length(dest)+1))
    destc = dest.chunks; srcc = src.chunks
    nc = min(length(destc), length(srcc))
    nc == 0 && return dest
    @inbounds begin
        for i = 1 : nc - 1
            destc[i] = srcc[i]
        end
        if length(src) == length(dest)
            destc[nc] = srcc[nc]
        else
            msk_s = _msk_end(src)
            msk_d = ~msk_s
            destc[nc] = (msk_d & destc[nc]) | (msk_s & srcc[nc])
        end
    end
    return dest
end

function unsafe_copyto!(dest::BitArray, doffs::Integer, src::Union{BitArray,Array}, soffs::Integer, n::Integer)
    copy_to_bitarray_chunks!(dest.chunks, Int(doffs), src, Int(soffs), Int(n))
    return dest
end

copyto!(dest::BitArray, doffs::Integer, src::Union{BitArray,Array}, soffs::Integer, n::Integer) =
    _copyto_int!(dest, Int(doffs), src, Int(soffs), Int(n))
function _copyto_int!(dest::BitArray, doffs::Int, src::Union{BitArray,Array}, soffs::Int, n::Int)
    n == 0 && return dest
    n < 0 && throw(ArgumentError("Number of elements to copy must be nonnegative."))
    soffs < 1 && throw(BoundsError(src, soffs))
    doffs < 1 && throw(BoundsError(dest, doffs))
    soffs+n-1 > length(src) && throw(BoundsError(src, length(src)+1))
    doffs+n-1 > length(dest) && throw(BoundsError(dest, length(dest)+1))
    return unsafe_copyto!(dest, doffs, src, soffs, n)
end

function copyto!(dest::BitArray, src::Array)
    length(src) > length(dest) && throw(BoundsError(dest, length(dest)+1))
    length(src) == 0 && return dest
    return unsafe_copyto!(dest, 1, src, 1, length(src))
end

function reshape(B::BitArray{N}, dims::NTuple{N,Int}) where N
    return dims == size(B) ? B : _bitreshape(B, dims)
end
reshape(B::BitArray, dims::Tuple{Vararg{Int}}) = _bitreshape(B, dims)
function _bitreshape(B::BitArray, dims::NTuple{N,Int}) where N
    prod(dims) == length(B) ||
        throw(DimensionMismatch("new dimensions $(dims) must be consistent with array size $(length(B))"))
    Br = BitArray{N}(undef, ntuple(i->0,Val(N))...)
    Br.chunks = B.chunks
    Br.len = prod(dims)
    N != 1 && (Br.dims = dims)
    return Br
end

## Constructors ##

function Array{T,N}(B::BitArray{N}) where {T,N}
    A = Array{T,N}(undef, size(B))
    Bc = B.chunks
    @inbounds for i = 1:length(A)
        A[i] = unsafe_bitgetindex(Bc, i)
    end
    return A
end

BitArray(A::AbstractArray{<:Any,N}) where {N} = BitArray{N}(A)

function BitArray{N}(A::AbstractArray{T,N}) where N where T
    B = BitArray(undef, convert(Dims{N}, size(A)::Dims{N}))
    _checkaxs(axes(B), axes(A))
    _copyto_bitarray!(B, A)
    return B::BitArray{N}
end

function _copyto_bitarray!(B::BitArray, A::AbstractArray)
    l = length(A)
    l == 0 && return B
    l > length(B) && throw(BoundsError(B, length(B)+1))
    Bc = B.chunks
    nc = num_bit_chunks(l)
    Ai = first(eachindex(A))
    @inbounds begin
        for i = 1:nc-1
            c = UInt64(0)
            for j = 0:63
                c |= (UInt64(convert(Bool, A[Ai])::Bool) << j)
                Ai = nextind(A, Ai)
            end
            Bc[i] = c
        end
        c = UInt64(0)
        tail = _mod64(l - 1) + 1
        for j = 0:tail-1
            c |= (UInt64(convert(Bool, A[Ai])::Bool) << j)
            Ai = nextind(A, Ai)
        end
        msk = _msk_end(tail)
        Bc[nc] = (c & msk) | (Bc[nc] & ~msk)
    end
    return B
end

reinterpret(::Type{Bool}, B::BitArray, dims::NTuple{N,Int}) where {N} = reinterpret(B, dims)
reinterpret(B::BitArray, dims::NTuple{N,Int}) where {N} = reshape(B, dims)

if nameof(@__MODULE__) === :Base  # avoid method overwrite
(::Type{T})(x::T) where {T<:BitArray} = copy(x)::T
BitArray(x::BitArray) = copy(x)
end

"""
    BitArray(itr)

Construct a [`BitArray`](@ref) generated by the given iterable object.
The shape is inferred from the `itr` object.

# Examples
```jldoctest
julia> BitArray([1 0; 0 1])
2×2 BitMatrix:
 1  0
 0  1

julia> BitArray(x+y == 3 for x = 1:2, y = 1:3)
2×3 BitMatrix:
 0  1  0
 1  0  0

julia> BitArray(x+y == 3 for x = 1:2 for y = 1:3)
6-element BitVector:
 0
 1
 0
 1
 0
 0
```
"""
BitArray(itr) = gen_bitarray(IteratorSize(itr), itr)
BitArray{N}(itr) where N = gen_bitarrayN(BitArray{N}, IteratorSize(itr), itr)

convert(::Type{T}, a::AbstractArray) where {T<:BitArray} = a isa T ? a : T(a)::T

# generic constructor from an iterable without compile-time info
# (we pass start(itr) explicitly to avoid a type-instability with filters)
gen_bitarray(isz::IteratorSize, itr) = gen_bitarray_from_itr(itr)

# generic iterable with known shape
function gen_bitarray(::HasShape, itr)
    B = BitArray(undef, size(itr))
    for (I,x) in zip(CartesianIndices(axes(itr)), itr)
        B[I] = x
    end
    return B
end

# generator with known shape or length
function gen_bitarray(::HasShape, itr::Generator)
    B = BitArray(undef, size(itr))
    return fill_bitarray_from_itr!(B, itr)
end
function gen_bitarray(::HasLength, itr)
    b = BitVector(undef, length(itr))
    return fill_bitarray_from_itr!(b, itr)
end

gen_bitarray(::IsInfinite, itr) =  throw(ArgumentError("infinite-size iterable used in BitArray constructor"))

gen_bitarrayN(::Type{BitVector}, itsz, itr)                        = gen_bitarray(itsz, itr)
gen_bitarrayN(::Type{BitVector}, itsz::HasShape{1}, itr)           = gen_bitarray(itsz, itr)
gen_bitarrayN(::Type{BitArray{N}}, itsz::HasShape{N}, itr) where N = gen_bitarray(itsz, itr)
# The first of these is just for ambiguity resolution
gen_bitarrayN(::Type{BitVector}, itsz::HasShape{N}, itr) where N      = throw(DimensionMismatch("cannot create a BitVector from a $N-dimensional iterator"))
gen_bitarrayN(@nospecialize(T::Type), itsz::HasShape{N}, itr) where N = throw(DimensionMismatch("cannot create a $T from a $N-dimensional iterator"))
gen_bitarrayN(@nospecialize(T::Type), itsz, itr) = throw(DimensionMismatch("cannot create a $T from a generic iterator"))

# The aux functions gen_bitarray_from_itr and fill_bitarray_from_itr! both
# use a Vector{Bool} cache for performance reasons

function gen_bitarray_from_itr(itr)
    B = empty!(BitVector(undef, bitcache_size))
    C = Vector{Bool}(undef, bitcache_size)
    Bc = B.chunks
    ind = 1
    cind = 1
    y = iterate(itr)
    while y !== nothing
        x, st = y
        @inbounds C[ind] = x
        ind += 1
        if ind > bitcache_size
            resize!(B, length(B) + bitcache_size)
            dumpbitcache(Bc, cind, C)
            cind += bitcache_chunks
            ind = 1
        end
        y = iterate(itr, st)
    end
    if ind > 1
        @inbounds C[ind:bitcache_size] .= false
        resize!(B, length(B) + ind - 1)
        dumpbitcache(Bc, cind, C)
    end
    return B
end

function fill_bitarray_from_itr!(B::BitArray, itr)
    n = length(B)
    C = Vector{Bool}(undef, bitcache_size)
    Bc = B.chunks
    ind = 1
    cind = 1
    y = iterate(itr)
    while y !== nothing
        x, st = y
        @inbounds C[ind] = x
        ind += 1
        if ind > bitcache_size
            dumpbitcache(Bc, cind, C)
            cind += bitcache_chunks
            ind = 1
        end
        y = iterate(itr, st)
    end
    if ind > 1
        @inbounds C[ind:bitcache_size] .= false
        dumpbitcache(Bc, cind, C)
    end
    return B
end


## Indexing: getindex ##

@inline function unsafe_bitgetindex(Bc::Vector{UInt64}, i::Int)
    i1, i2 = get_chunks_id(i)
    u = UInt64(1) << i2
    @inbounds r = (Bc[i1] & u) != 0
    return r
end

@inline function getindex(B::BitArray, i::Int)
    @boundscheck checkbounds(B, i)
    unsafe_bitgetindex(B.chunks, i)
end

## Indexing: setindex! ##

@inline function unsafe_bitsetindex!(Bc::Array{UInt64}, x::Bool, i::Int)
    i1, i2 = get_chunks_id(i)
    _unsafe_bitsetindex!(Bc, x, i1, i2)
end

@inline function _unsafe_bitsetindex!(Bc::Array{UInt64}, x::Bool, i1::Int, i2::Int)
    u = UInt64(1) << i2
    @inbounds begin
        c = Bc[i1]
        Bc[i1] = ifelse(x, c | u, c & ~u)
    end
end

@inline function setindex!(B::BitArray, x, i::Int)
    @boundscheck checkbounds(B, i)
    unsafe_bitsetindex!(B.chunks, convert(Bool, x), i)
    return B
end

indexoffset(i) = first(i)-1
indexoffset(::Colon) = 0

@propagate_inbounds function setindex!(B::BitArray, X::AbstractArray, J0::Union{Colon,AbstractUnitRange{Int}})
    _setindex!(IndexStyle(B), B, X, to_indices(B, (J0,))[1])
end

# Assigning an array of bools is more complicated, but we can still do some
# work on chunks by combining X and I 64 bits at a time to improve perf by ~40%
@inline function setindex!(B::BitArray, X::AbstractArray, I::BitArray)
    @boundscheck checkbounds(B, I)
    _unsafe_setindex!(B, X, I)
end
function _unsafe_setindex!(B::BitArray, X::AbstractArray, I::BitArray)
    Bc = B.chunks
    Ic = I.chunks
    length(Bc) == length(Ic) || throw_boundserror(B, I)
    lc = length(Bc)
    lx = length(X)
    last_chunk_len = _mod64(length(B)-1)+1

    Xi = first(eachindex(X))
    lastXi = last(eachindex(X))
    for i = 1:lc
        @inbounds Imsk = Ic[i]
        @inbounds C = Bc[i]
        u = UInt64(1)
        for j = 1:(i < lc ? 64 : last_chunk_len)
            if Imsk & u != 0
                Xi > lastXi && throw_setindex_mismatch(X, count(I))
                @inbounds x = convert(Bool, X[Xi])
                C = ifelse(x, C | u, C & ~u)
                Xi = nextind(X, Xi)
            end
            u <<= 1
        end
        @inbounds Bc[i] = C
    end
    if Xi != nextind(X, lastXi)
        throw_setindex_mismatch(X, count(I))
    end
    return B
end

## Dequeue functionality ##

function push!(B::BitVector, item)
    # convert first so we don't grow the bitarray if the assignment won't work
    item = convert(Bool, item)

    Bc = B.chunks

    l = _mod64(length(B))
    if l == 0
        _growend!(Bc, 1)
        Bc[end] = UInt64(0)
    end
    B.len += 1
    if item
        B[end] = true
    end
    return B
end

function append!(B::BitVector, items::BitVector)
    n0 = length(B)
    n1 = length(items)
    n1 == 0 && return B
    Bc = B.chunks
    k0 = length(Bc)
    k1 = num_bit_chunks(n0 + n1)
    if k1 > k0
        _growend!(Bc, k1 - k0)
        Bc[end] = UInt64(0)
    end
    B.len += n1
    copy_chunks!(Bc, n0+1, items.chunks, 1, n1)
    return B
end

append!(B::BitVector, items) = append!(B, BitVector(items))
append!(A::Vector{Bool}, items::BitVector) = append!(A, Array(items))

function prepend!(B::BitVector, items::BitVector)
    n0 = length(B)
    n1 = length(items)
    n1 == 0 && return B
    Bc = B.chunks
    k0 = length(Bc)
    k1 = num_bit_chunks(n0 + n1)
    if k1 > k0
        _growend!(Bc, k1 - k0)
        Bc[end] = UInt64(0)
    end
    B.len += n1
    copy_chunks!(Bc, 1 + n1, Bc, 1, n0)
    copy_chunks!(Bc, 1, items.chunks, 1, n1)
    return B
end

prepend!(B::BitVector, items) = prepend!(B, BitArray(items))
prepend!(A::Vector{Bool}, items::BitVector) = prepend!(A, Array(items))

function sizehint!(B::BitVector, sz::Integer)
    ccall(:jl_array_sizehint, Cvoid, (Any, UInt), B.chunks, num_bit_chunks(sz))
    return B
end

resize!(B::BitVector, n::Integer) = _resize_int!(B, Int(n))
function _resize_int!(B::BitVector, n::Int)
    n0 = length(B)
    n == n0 && return B
    n >= 0 || throw(BoundsError(B, n))
    if n < n0
        deleteat!(B, n+1:n0)
        return B
    end
    Bc = B.chunks
    k0 = length(Bc)
    k1 = num_bit_chunks(n)
    if k1 > k0
        _growend!(Bc, k1 - k0)
        Bc[end] = UInt64(0)
    end
    B.len = n
    return B
end

function pop!(B::BitVector)
    isempty(B) && throw(ArgumentError("argument must not be empty"))
    item = B[end]
    B[end] = false

    l = _mod64(length(B))
    l == 1 && _deleteend!(B.chunks, 1)
    B.len -= 1

    return item
end

function pushfirst!(B::BitVector, item)
    item = convert(Bool, item)

    Bc = B.chunks

    l = _mod64(length(B))
    if l == 0
        _growend!(Bc, 1)
        Bc[end] = UInt64(0)
    end
    B.len += 1
    if B.len == 1
        Bc[1] = item
        return B
    end
    for i = length(Bc) : -1 : 2
        Bc[i] = (Bc[i] << 1) | (Bc[i-1] >>> 63)
    end
    Bc[1] = UInt64(item) | (Bc[1] << 1)
    return B
end

function popfirst!(B::BitVector)
    isempty(B) && throw(ArgumentError("argument must not be empty"))
    @inbounds begin
        item = B[1]

        Bc = B.chunks

        for i = 1 : length(Bc) - 1
            Bc[i] = (Bc[i] >>> 1) | (Bc[i+1] << 63)
        end

        l = _mod64(length(B))
        if l == 1
            _deleteend!(Bc, 1)
        else
            Bc[end] >>>= 1
        end
        B.len -= 1
    end

    return item
end

insert!(B::BitVector, i::Integer, item) = _insert_int!(B, Int(i), item)
function _insert_int!(B::BitVector, i::Int, item)
    i = Int(i)
    n = length(B)
    1 <= i <= n+1 || throw(BoundsError(B, i))
    item = convert(Bool, item)

    Bc = B.chunks

    k, j = get_chunks_id(i)

    l = _mod64(length(B))
    if l == 0
        _growend!(Bc, 1)
        Bc[end] = UInt64(0)
    end
    B.len += 1

    for t = length(Bc) : -1 : k + 1
        Bc[t] = (Bc[t] << 1) | (Bc[t - 1] >>> 63)
    end

    msk_aft = (_msk64 << j)
    msk_bef = ~msk_aft
    Bc[k] = (msk_bef & Bc[k]) | ((msk_aft & Bc[k]) << 1)
    B[i] = item
    B
end

function _deleteat!(B::BitVector, i::Int)
    k, j = get_chunks_id(i)

    msk_bef = _msk64 >>> (63 - j)
    msk_aft = ~msk_bef
    msk_bef >>>= 1

    Bc = B.chunks

    @inbounds begin
        Bc[k] = (msk_bef & Bc[k]) | ((msk_aft & Bc[k]) >> 1)
        if length(Bc) > k
            Bc[k] |= (Bc[k + 1] << 63)
        end

        for t = k + 1 : length(Bc) - 1
            Bc[t] = (Bc[t] >>> 1) | (Bc[t + 1] << 63)
        end

        l = _mod64(length(B))

        if l == 1
            _deleteend!(Bc, 1)
        elseif length(Bc) > k
            Bc[end] >>>= 1
        end
    end

    B.len -= 1

    return B
end

function deleteat!(B::BitVector, i::Integer)
    i isa Bool && depwarn("passing Bool as an index is deprecated", :deleteat!)
    i = Int(i)
    n = length(B)
    1 <= i <= n || throw(BoundsError(B, i))

    return _deleteat!(B, i)
end

function deleteat!(B::BitVector, r::AbstractUnitRange{Int})
    n = length(B)
    i_f = first(r)
    i_l = last(r)
    1 <= i_f || throw(BoundsError(B, i_f))
    i_l <= n || throw(BoundsError(B, n+1))

    Bc = B.chunks
    new_l = length(B) - length(r)
    delta_k = num_bit_chunks(new_l) - length(Bc)

    copy_chunks!(Bc, i_f, Bc, i_l+1, n-i_l)

    delta_k < 0 && _deleteend!(Bc, -delta_k)

    B.len = new_l

    if new_l > 0
        Bc[end] &= _msk_end(new_l)
    end

    return B
end

function deleteat!(B::BitVector, inds)
    n = new_l = length(B)
    y = iterate(inds)
    y === nothing && return B

    Bc = B.chunks

    (p, s) = y
    checkbounds(B, p)
    p isa Bool && throw(ArgumentError("invalid index $p of type Bool"))
    q = p+1
    new_l -= 1
    y = iterate(inds, s)
    while y !== nothing
        (i, s) = y
        if !(q <= i <= n)
            i isa Bool && throw(ArgumentError("invalid index $i of type Bool"))
            i < q && throw(ArgumentError("indices must be unique and sorted"))
            throw(BoundsError(B, i))
        end
        new_l -= 1
        if i > q
            copy_chunks!(Bc, Int(p), Bc, Int(q), Int(i-q))
            p += i-q
        end
        q = i+1
        y = iterate(inds, s)
    end

    q <= n && copy_chunks!(Bc, Int(p), Bc, Int(q), Int(n-q+1))

    delta_k = num_bit_chunks(new_l) - length(Bc)
    delta_k < 0 && _deleteend!(Bc, -delta_k)

    B.len = new_l

    if new_l > 0
        Bc[end] &= _msk_end(new_l)
    end

    return B
end

function deleteat!(B::BitVector, inds::AbstractVector{Bool})
    length(inds) == length(B) || throw(BoundsError(B, inds))

    n = new_l = length(B)
    y = findfirst(inds)
    y === nothing && return B

    Bc = B.chunks

    p = y
    s = y + 1
    checkbounds(B, p)
    q = p + 1
    new_l -= 1
    y = findnext(inds, s)
    while y !== nothing
        i = y
        s = y + 1
        new_l -= 1
        if i > q
            copy_chunks!(Bc, Int(p), Bc, Int(q), Int(i-q))
            p += i - q
        end
        q = i + 1
        y = findnext(inds, s)
    end

    q <= n && copy_chunks!(Bc, Int(p), Bc, Int(q), Int(n - q + 1))

    delta_k = num_bit_chunks(new_l) - length(Bc)
    delta_k < 0 && _deleteend!(Bc, -delta_k)

    B.len = new_l

    if new_l > 0
        Bc[end] &= _msk_end(new_l)
    end

    return B
end

keepat!(B::BitVector, inds) = _keepat!(B, inds)
keepat!(B::BitVector, inds::AbstractVector{Bool}) = _keepat!(B, inds)

function splice!(B::BitVector, i::Integer)
    # TODO: after deprecation remove the four lines below
    #       as v = B[i] is enough to do both bounds checking
    #       and Bool check then just pass Int(i) to _deleteat!
    i isa Bool && depwarn("passing Bool as an index is deprecated", :splice!)
    i = Int(i)
    n = length(B)
    1 <= i <= n || throw(BoundsError(B, i))

    v = B[i]   # TODO: change to a copy if/when subscripting becomes an ArrayView
    _deleteat!(B, i)
    return v
end

const _default_bit_splice = BitVector()

function splice!(B::BitVector, r::Union{AbstractUnitRange{Int}, Integer}, ins::AbstractArray = _default_bit_splice)
    r isa Bool && depwarn("passing Bool as an index is deprecated", :splice!)
    _splice_int!(B, isa(r, AbstractUnitRange{Int}) ? r : Int(r), ins)
end

function _splice_int!(B::BitVector, r, ins)
    n = length(B)
    i_f, i_l = first(r), last(r)
    1 <= i_f <= n+1 || throw(BoundsError(B, i_f))
    i_l <= n || throw(BoundsError(B, n+1))

    Bins = convert(BitArray, ins)

    if (i_f > n)
        append!(B, Bins)
        return BitVector()
    end

    v = B[r]  # TODO: change to a copy if/when subscripting becomes an ArrayView

    Bc = B.chunks

    lins = length(Bins)
    ldel = length(r)

    new_l = length(B) + lins - ldel
    delta_k = num_bit_chunks(new_l) - length(Bc)

    delta_k > 0 && _growend!(Bc, delta_k)

    copy_chunks!(Bc, i_f+lins, Bc, i_l+1, n-i_l)
    copy_chunks!(Bc, i_f, Bins.chunks, 1, lins)

    delta_k < 0 && _deleteend!(Bc, -delta_k)

    B.len = new_l

    if new_l > 0
        Bc[end] &= _msk_end(new_l)
    end

    return v
end

function splice!(B::BitVector, r::Union{AbstractUnitRange{Int}, Integer}, ins)
    Bins = BitVector(undef, length(ins))
    i = 1
    for x in ins
        Bins[i] = Bool(x)
        i += 1
    end
    return splice!(B, r, Bins)
end


function empty!(B::BitVector)
    _deleteend!(B.chunks, length(B.chunks))
    B.len = 0
    return B
end

## Unary operators ##

function (-)(B::BitArray)
    A = zeros(Int, size(B))
    l = length(B)
    l == 0 && return A
    Bc = B.chunks
    ind = 1
    for i = 1:length(Bc)-1
        u = UInt64(1)
        c = Bc[i]
        for j = 1:64
            if c & u != 0
                A[ind] = -1
            end
            ind += 1
            u <<= 1
        end
    end
    u = UInt64(1)
    c = Bc[end]
    for j = 0:_mod64(l-1)
        if c & u != 0
            A[ind] = -1
        end
        ind += 1
        u <<= 1
    end
    return A
end

## Binary arithmetic operators ##

for f in (:+, :-)
    @eval function ($f)(A::BitArray, B::BitArray)
        r = Array{Int}(undef, promote_shape(size(A), size(B)))
        ay, by = iterate(A), iterate(B)
        ri = 1
        # promote_shape guarantees that A and B have the
        # same iteration space
        while ay !== nothing
            @inbounds r[ri] = ($f)(ay[1], by[1])
            ri += 1
            ay, by = iterate(A, ay[2]), iterate(B, by[2])
        end
        return r
    end
end

for f in (:/, :\)
    @eval begin
        ($f)(A::Union{BitMatrix,BitVector}, B::Union{BitMatrix,BitVector}) = ($f)(Array(A), Array(B))
    end
end
(/)(B::BitArray, x::Number) = (/)(Array(B), x)
(/)(x::Number, B::BitArray) = (/)(x, Array(B))

## promotion to complex ##

# TODO?

## comparison operators ##

function (==)(A::BitArray, B::BitArray)
    size(A) != size(B) && return false
    return A.chunks == B.chunks
end


## Data movement ##

# TODO some of this could be optimized

_reverse(A::BitArray, d::Tuple{Integer}) = _reverse(A, d[1])
function _reverse(A::BitArray, d::Int)
    nd = ndims(A)
    1 ≤ d ≤ nd || throw(ArgumentError("dimension $d is not 1 ≤ $d ≤ $nd"))
    sd = size(A, d)
    sd == 1 && return copy(A)

    B = similar(A)

    nnd = 0
    for i = 1:nd
        nnd += size(A,i)==1 || i==d
    end
    if nnd == nd
        # reverse along the only non-singleton dimension
        for i = 1:sd
            B[i] = A[sd+1-i]
        end
        return B
    end

    d_in = size(A)
    leading = d_in[1:(d-1)]
    M = prod(leading)
    N = length(A)
    stride = M * sd

    if M == 1
        for j = 0:stride:(N-stride)
            for i = 1:sd
                ri = sd+1-i
                B[j + ri] = A[j + i]
            end
        end
    else
        for i = 1:sd
            ri = sd+1-i
            for j=0:stride:(N-stride)
                offs = j + 1 + (i-1)*M
                boffs = j + 1 + (ri-1)*M
                copy_chunks!(B.chunks, boffs, A.chunks, offs, M)
            end
        end
    end
    return B
end

function _reverse!(B::BitVector, ::Colon)
    # Basic idea: each chunk is divided into two blocks of size k = n % 64, and
    # h = 64 - k. Walk from either end (with indices i and j) reversing chunks
    # and separately ORing their two blocks into place.
    #
    #           chunk 3                  chunk 2                  chunk 1
    # ┌───────────────┬───────┐┌───────────────┬───────┐┌───────────────┬───────┐
    # │000000000000000│   E   ││       D       │   C   ││       B       │   A   │
    # └───────────────┴───────┘└───────────────┴───────┘└───────────────┴───────┘
    #                     k            h           k            h            k
    # yielding;
    # ┌───────────────┬───────┐┌───────────────┬───────┐┌───────────────┬───────┐
    # │000000000000000│  A'   ││      B'       │  C'   ││      D'       │  E'   │
    # └───────────────┴───────┘└───────────────┴───────┘└───────────────┴───────┘

    n = length(B)
    n == 0 && return B

    k = _mod64(n+63) + 1
    h = 64 - k

    i, j = 0, length(B.chunks)
    u = UInt64(0)
    v = bitreverse(B.chunks[j])
    B.chunks[j] = 0
    @inbounds while true
        i += 1
        if i == j
            break
        end
        u = bitreverse(B.chunks[i])
        B.chunks[i] = 0
        B.chunks[j] |= u >>> h
        B.chunks[i] |= v >>> h

        j -= 1
        if i == j
            break
        end
        v = bitreverse(B.chunks[j])
        B.chunks[j] = 0
        B.chunks[i] |= v << k
        B.chunks[j] |= u << k
    end

    if isodd(length(B.chunks))
        B.chunks[i] |= v >>> h
    else
        B.chunks[i] |= u << k
    end

    return B
end

function (<<)(B::BitVector, i::UInt)
    n = length(B)
    i == 0 && return copy(B)
    A = falses(n)
    i < n && copy_chunks!(A.chunks, 1, B.chunks, Int(i+1), Int(n-i))
    return A
end

function (>>>)(B::BitVector, i::UInt)
    n = length(B)
    i == 0 && return copy(B)
    A = falses(n)
    i < n && copy_chunks!(A.chunks, Int(i+1), B.chunks, 1, Int(n-i))
    return A
end

"""
    >>(B::BitVector, n) -> BitVector

Right bit shift operator, `B >> n`. For `n >= 0`, the result is `B`
with elements shifted `n` positions forward, filling with `false`
values. If `n < 0`, elements are shifted backwards. Equivalent to
`B << -n`.

# Examples
```jldoctest
julia> B = BitVector([true, false, true, false, false])
5-element BitVector:
 1
 0
 1
 0
 0

julia> B >> 1
5-element BitVector:
 0
 1
 0
 1
 0

julia> B >> -1
5-element BitVector:
 0
 1
 0
 0
 0
```
"""
(>>)(B::BitVector, i::Union{Int, UInt}) = B >>> i

# signed integer version of shift operators with handling of negative values
"""
    <<(B::BitVector, n) -> BitVector

Left bit shift operator, `B << n`. For `n >= 0`, the result is `B`
with elements shifted `n` positions backwards, filling with `false`
values. If `n < 0`, elements are shifted forwards. Equivalent to
`B >> -n`.

# Examples
```jldoctest
julia> B = BitVector([true, false, true, false, false])
5-element BitVector:
 1
 0
 1
 0
 0

julia> B << 1
5-element BitVector:
 0
 1
 0
 0
 0

julia> B << -1
5-element BitVector:
 0
 1
 0
 1
 0
```
"""
(<<)(B::BitVector, i::Int) = (i >=0 ? B << unsigned(i) : B >> unsigned(-i))

"""
    >>>(B::BitVector, n) -> BitVector

Unsigned right bitshift operator, `B >>> n`. Equivalent to `B >> n`. See [`>>`](@ref) for
details and examples.
"""
(>>>)(B::BitVector, i::Int) = (i >=0 ? B >> unsigned(i) : B << unsigned(-i))

circshift!(dest::BitVector, src::BitVector, i::Integer) = _circshift_int!(dest, src, Int(i))
function _circshift_int!(dest::BitVector, src::BitVector, i::Int)
    i = Int(i)
    length(dest) == length(src) || throw(ArgumentError("destination and source should be of same size"))
    n = length(dest)
    i %= n
    i == 0 && return (src === dest ? src : copyto!(dest, src))
    Bc = (src === dest ? copy(src.chunks) : src.chunks)
    if i > 0 # right
        copy_chunks!(dest.chunks, i+1, Bc, 1, n-i)
        copy_chunks!(dest.chunks, 1, Bc, n-i+1, i)
    else # left
        i = -i
        copy_chunks!(dest.chunks, 1, Bc, i+1, n-i)
        copy_chunks!(dest.chunks, n-i+1, Bc, 1, i)
    end
    return dest
end

circshift!(B::BitVector, i::Integer) = circshift!(B, B, i)

## count & find ##

function bitcount(Bc::Vector{UInt64}; init::T=0) where {T}
    n::T = init
    @inbounds for i = 1:length(Bc)
        n = (n + count_ones(Bc[i])) % T
    end
    return n
end

_count(::typeof(identity), B::BitArray, ::Colon, init) = bitcount(B.chunks; init)

function unsafe_bitfindnext(Bc::Vector{UInt64}, start::Int)
    chunk_start = _div64(start-1)+1
    within_chunk_start = _mod64(start-1)
    mask = _msk64 << within_chunk_start

    @inbounds begin
        if Bc[chunk_start] & mask != 0
            return (chunk_start-1) << 6 + trailing_zeros(Bc[chunk_start] & mask) + 1
        end

        for i = chunk_start+1:length(Bc)
            if Bc[i] != 0
                return (i-1) << 6 + trailing_zeros(Bc[i]) + 1
            end
        end
    end
    return nothing
end

# returns the index of the next true element, or nothing if all false
function findnext(B::BitArray, start::Integer)
    start = Int(start)
    start > 0 || throw(BoundsError(B, start))
    start > length(B) && return nothing
    unsafe_bitfindnext(B.chunks, start)
end

#findfirst(B::BitArray) = findnext(B, 1)  ## defined in array.jl

# aux function: same as findnext(~B, start), but performed without temporaries
function findnextnot(B::BitArray, start::Int)
    start > 0 || throw(BoundsError(B, start))
    start > length(B) && return nothing

    Bc = B.chunks
    l = length(Bc)
    l == 0 && return nothing

    chunk_start = _div64(start-1)+1
    within_chunk_start = _mod64(start-1)
    mask = ~(_msk64 << within_chunk_start)

    @inbounds if chunk_start < l
        if Bc[chunk_start] | mask != _msk64
            return (chunk_start-1) << 6 + trailing_ones(Bc[chunk_start] | mask) + 1
        end
        for i = chunk_start+1:l-1
            if Bc[i] != _msk64
                return (i-1) << 6 + trailing_ones(Bc[i]) + 1
            end
        end
        if Bc[l] != _msk_end(B)
            return (l-1) << 6 + trailing_ones(Bc[l]) + 1
        end
    elseif Bc[l] | mask != _msk_end(B)
        return (l-1) << 6 + trailing_ones(Bc[l] | mask) + 1
    end
    return nothing
end
findfirstnot(B::BitArray) = findnextnot(B,1)

# returns the index of the first matching element
function findnext(pred::Fix2{<:Union{typeof(isequal),typeof(==)},Bool},
                  B::BitArray, start::Integer)
    v = pred.x
    v == false && return findnextnot(B, Int(start))
    v == true && return findnext(B, start)
    return nothing
end
#findfirst(B::BitArray, v) = findnext(B, 1, v)  ## defined in array.jl

# returns the index of the first element for which the function returns true
findnext(testf::Function, B::BitArray, start::Integer) = _findnext_int(testf, B, Int(start))
function _findnext_int(testf::Function, B::BitArray, start::Int)
    f0::Bool = testf(false)
    f1::Bool = testf(true)
    !f0 && f1 && return findnext(B, start)
    f0 && !f1 && return findnextnot(B, start)

    start > 0 || throw(BoundsError(B, start))
    start > length(B) && return nothing
    f0 && f1 && return start
    return nothing # last case: !f0 && !f1
end
#findfirst(testf::Function, B::BitArray) = findnext(testf, B, 1)  ## defined in array.jl

function unsafe_bitfindprev(Bc::Vector{UInt64}, start::Int)
    chunk_start = _div64(start-1)+1
    mask = _msk_end(start)

    @inbounds begin
        if Bc[chunk_start] & mask != 0
            return (chunk_start-1) << 6 + (top_set_bit(Bc[chunk_start] & mask))
        end

        for i = (chunk_start-1):-1:1
            if Bc[i] != 0
                return (i-1) << 6 + (top_set_bit(Bc[i]))
            end
        end
    end
    return nothing
end

# returns the index of the previous true element, or nothing if all false
function findprev(B::BitArray, start::Integer)
    start = Int(start)
    start > 0 || return nothing
    start > length(B) && throw(BoundsError(B, start))
    unsafe_bitfindprev(B.chunks, start)
end

function findprevnot(B::BitArray, start::Int)
    start = Int(start)
    start > 0 || return nothing
    start > length(B) && throw(BoundsError(B, start))

    Bc = B.chunks

    chunk_start = _div64(start-1)+1
    mask = ~_msk_end(start)

    @inbounds begin
        if Bc[chunk_start] | mask != _msk64
            return (chunk_start-1) << 6 + (64 - leading_ones(Bc[chunk_start] | mask))
        end

        for i = chunk_start-1:-1:1
            if Bc[i] != _msk64
                return (i-1) << 6 + (64 - leading_ones(Bc[i]))
            end
        end
    end
    return nothing
end
findlastnot(B::BitArray) = findprevnot(B, length(B))

# returns the index of the previous matching element
function findprev(pred::Fix2{<:Union{typeof(isequal),typeof(==)},Bool},
                  B::BitArray, start::Integer)
    v = pred.x
    v == false && return findprevnot(B, Int(start))
    v == true && return findprev(B, start)
    return nothing
end
#findlast(B::BitArray, v) = findprev(B, 1, v)  ## defined in array.jl

# returns the index of the previous element for which the function returns true
findprev(testf::Function, B::BitArray, start::Integer) = _findprev_int(testf, B, Int(start))
function _findprev_int(testf::Function, B::BitArray, start::Int)
    f0::Bool = testf(false)
    f1::Bool = testf(true)
    !f0 && f1 && return findprev(B, start)
    f0 && !f1 && return findprevnot(B, start)

    start > 0 || return nothing
    start > length(B) && throw(BoundsError(B, start))
    f0 && f1 && return start
    return nothing # last case: !f0 && !f1
end
#findlast(testf::Function, B::BitArray) = findprev(testf, B, 1)  ## defined in array.jl

function findmax(a::BitArray)
    isempty(a) && throw(ArgumentError("BitArray must be non-empty"))
    m, mi = false, 1
    ti = 1
    ac = a.chunks
    for i = 1:length(ac)
        @inbounds k = trailing_zeros(ac[i])
        ti += k
        k == 64 || return (true, @inbounds keys(a)[ti])
    end
    return m, @inbounds keys(a)[mi]
end

function findmin(a::BitArray)
    isempty(a) && throw(ArgumentError("BitArray must be non-empty"))
    m, mi = true, 1
    ti = 1
    ac = a.chunks
    for i = 1:length(ac)-1
        @inbounds k = trailing_ones(ac[i])
        ti += k
        k == 64 || return (false, @inbounds keys(a)[ti])
    end
    l = Base._mod64(length(a)-1) + 1
    @inbounds k = trailing_ones(ac[end] & Base._msk_end(l))
    ti += k
    k == l || return (false, @inbounds keys(a)[ti])
    return (m, @inbounds keys(a)[mi])
end

# findall helper functions
# Generic case (>2 dimensions)
function allindices!(I, B::BitArray)
    ind = first(keys(B))
    for k = 1:length(B)
        I[k] = ind
        ind = nextind(B, ind)
    end
end

# Optimized case for vector
function allindices!(I, B::BitVector)
    I[:] .= 1:length(B)
end

# Optimized case for matrix
function allindices!(I, B::BitMatrix)
    k = 1
    for c = 1:size(B,2), r = 1:size(B,1)
        I[k] = CartesianIndex(r, c)
        k += 1
    end
end

@inline _overflowind(i1, irest::Tuple{}, size) = (i1, irest)
@inline function _overflowind(i1, irest, size)
    i2 = irest[1]
    while i1 > size[1]
        i1 -= size[1]
        i2 += 1
    end
    i2, irest = _overflowind(i2, tail(irest), tail(size))
    return (i1, (i2, irest...))
end

@inline _toind(i1, irest::Tuple{}) = i1
@inline _toind(i1, irest) = CartesianIndex(i1, irest...)

function findall(B::BitArray)
    nnzB = count(B)
    I = Vector{eltype(keys(B))}(undef, nnzB)
    nnzB == 0 && return I
    nnzB == length(B) && (allindices!(I, B); return I)
    Bc = B.chunks
    Bs = size(B)
    Bi = i1 = i = 1
    irest = ntuple(one, ndims(B) - 1)
    c = Bc[1]
    @inbounds while true
        while c == 0
            Bi == length(Bc) && return I
            i1 += 64
            Bi += 1
            c = Bc[Bi]
        end

        tz = trailing_zeros(c)
        c = _blsr(c)

        i1, irest = _overflowind(i1 + tz, irest, Bs)
        I[i] = _toind(i1, irest)
        i += 1
        i1 -= tz
    end
end

# For performance
findall(::typeof(!iszero), B::BitArray) = findall(B)

## Reductions ##

_sum(A::BitArray, dims)    = reduce(+, A, dims=dims)
_sum(B::BitArray, ::Colon) = count(B)

function all(B::BitArray)
    isempty(B) && return true
    Bc = B.chunks
    @inbounds begin
        for i = 1:length(Bc)-1
            Bc[i] == _msk64 || return false
        end
        Bc[end] == _msk_end(B) || return false
    end
    return true
end

function any(B::BitArray)
    isempty(B) && return false
    Bc = B.chunks
    @inbounds begin
        for i = 1:length(Bc)
            Bc[i] == 0 || return true
        end
    end
    return false
end

minimum(B::BitArray) = isempty(B) ? throw(ArgumentError("argument must be non-empty")) : all(B)
maximum(B::BitArray) = isempty(B) ? throw(ArgumentError("argument must be non-empty")) : any(B)

## map over bitarrays ##

# Specializing map is even more important for bitarrays than it is for generic
# arrays since there can be a 64x speedup by working at the level of Int64
# instead of looping bit-by-bit.

map(::Union{typeof(~), typeof(!)}, A::BitArray) = bit_map!(~, similar(A), A)
map(::typeof(zero), A::BitArray) = fill!(similar(A), false)
map(::typeof(one), A::BitArray) = fill!(similar(A), true)
map(::typeof(identity), A::BitArray) = copy(A)

map!(::Union{typeof(~), typeof(!)}, dest::BitArray, A::BitArray) = bit_map!(~, dest, A)
map!(::typeof(zero), dest::BitArray, A::BitArray) = fill!(dest, false)
map!(::typeof(one), dest::BitArray, A::BitArray) = fill!(dest, true)
map!(::typeof(identity), dest::BitArray, A::BitArray) = copyto!(dest, A)

for (T, f) in ((:(Union{typeof(&), typeof(*), typeof(min)}), :(&)),
               (:(Union{typeof(|), typeof(max)}),            :(|)),
               (:(Union{typeof(xor), typeof(!=)}),           :xor),
               (:(typeof(nand)),                             :nand),
               (:(typeof(nor)),                              :nor),
               (:(Union{typeof(>=), typeof(^)}),             :((p, q) -> p | ~q)),
               (:(typeof(<=)),                               :((p, q) -> ~p | q)),
               (:(typeof(==)),                               :((p, q) -> ~xor(p, q))),
               (:(typeof(<)),                                :((p, q) -> ~p & q)),
               (:(typeof(>)),                                :((p, q) -> p & ~q)))
    @eval map(::$T, A::BitArray, B::BitArray) = bit_map!($f, similar(A), A, B)
    @eval map!(::$T, dest::BitArray, A::BitArray, B::BitArray) = bit_map!($f, dest, A, B)
end

# If we were able to specialize the function to a known bitwise operation,
# map across the chunks. Otherwise, fall-back to the AbstractArray method that
# iterates bit-by-bit.
function bit_map!(f::F, dest::BitArray, A::BitArray) where F
    length(A) <= length(dest) || throw(DimensionMismatch("length of destination must be >= length of collection"))
    isempty(A) && return dest
    destc = dest.chunks
    Ac = A.chunks
    len_Ac = length(Ac)
    for i = 1:(len_Ac-1)
        destc[i] = f(Ac[i])
    end
    # the last effected UInt64's original content
    dest_last = destc[len_Ac]
    _msk = _msk_end(A)
    # first zero out the bits mask is going to change
    # then update bits by `or`ing with a masked RHS
    # DO NOT SEPARATE ONTO TO LINES.
    # Otherwise there will be bugs when Ac aliases destc
    destc[len_Ac] = (dest_last & (~_msk)) | f(Ac[len_Ac]) & _msk
    dest
end
function bit_map!(f::F, dest::BitArray, A::BitArray, B::BitArray) where F
    min_bitlen = min(length(A), length(B))
    min_bitlen <= length(dest) || throw(DimensionMismatch("length of destination must be >= length of smallest input collection"))
    isempty(A) && return dest
    isempty(B) && return dest
    destc = dest.chunks
    Ac = A.chunks
    Bc = B.chunks
    len_Ac = min(length(Ac), length(Bc))
    for i = 1:len_Ac-1
        destc[i] = f(Ac[i], Bc[i])
    end
    # the last effected UInt64's original content
    dest_last = destc[len_Ac]
    _msk = _msk_end(min_bitlen)
    # first zero out the bits mask is going to change
    # then update bits by `or`ing with a masked RHS
    # DO NOT SEPARATE ONTO TO LINES.
    # Otherwise there will be bugs when Ac or Bc aliases destc
    destc[len_Ac] = (dest_last & ~(_msk)) | f(Ac[end], Bc[end]) & _msk
    dest
end

## Filter ##

function filter(f, Bs::BitArray)
    boolmap::Array{Bool} = map(f, Bs)
    Bs[boolmap]
end


## Concatenation ##

function hcat(B::BitVector...)
    height = length(B[1])
    for j = 2:length(B)
        length(B[j]) == height ||
            throw(DimensionMismatch("dimensions must match: $j-th argument has length $(length(B[j])), should have $height"))
    end
    M = BitMatrix(undef, height, length(B))
    for j = 1:length(B)
        copy_chunks!(M.chunks, (height*(j-1))+1, B[j].chunks, 1, height)
    end
    return M
end

function vcat(V::BitVector...)
    n = 0
    for Vk in V
        n += length(Vk)
    end
    B = BitVector(undef, n)
    j = 1
    for Vk in V
        copy_chunks!(B.chunks, j, Vk.chunks, 1, length(Vk))
        j += length(Vk)
    end
    return B
end

function hcat(A::Union{BitMatrix,BitVector}...)
    nargs = length(A)
    nrows = size(A[1], 1)
    ncols = 0
    dense = true
    for j = 1:nargs
        Aj = A[j]
        nd = ndims(Aj)
        ncols += (nd==2 ? size(Aj,2) : 1)
        size(Aj, 1) == nrows ||
            throw(DimensionMismatch("row lengths must match: $j-th element has first dim $(size(Aj, 1)), should have $nrows"))
    end

    B = BitMatrix(undef, nrows, ncols)

    pos = 1
    for k = 1:nargs
        Ak = A[k]
        n = length(Ak)
        copy_chunks!(B.chunks, pos, Ak.chunks, 1, n)
        pos += n
    end
    return B
end

function vcat(A::BitMatrix...)
    nargs = length(A)
    nrows, nrowsA = 0, sizehint!(Int[], nargs)
    for a in A
        sz1 = size(a, 1)
        nrows += sz1
        push!(nrowsA, sz1)
    end
    ncols = size(A[1], 2)
    for j = 2:nargs
        size(A[j], 2) == ncols ||
        throw(DimensionMismatch("column lengths must match: $j-th element has second dim $(size(A[j], 2)), should have $ncols"))
    end
    B = BitMatrix(undef, nrows, ncols)
    Bc = B.chunks
    pos_d = 1
    pos_s = fill(1, nargs)
    for j = 1:ncols, k = 1:nargs
        copy_chunks!(Bc, pos_d, A[k].chunks, pos_s[k], nrowsA[k])
        pos_s[k] += nrowsA[k]
        pos_d += nrowsA[k]
    end
    return B
end

# general case, specialized for BitArrays and Integers
_cat(dims::Integer, X::Union{BitArray, Bool}...) = _cat(Int(dims)::Int, X...)
function _cat(dims::Int, X::Union{BitArray, Bool}...)
    dims = Int(dims)
    catdims = dims2cat(dims)
    shape = cat_shape(catdims, map(cat_size, X))
    A = falses(shape)
    return __cat(A, shape, catdims, X...)
end

# hvcat -> use fallbacks in abstractarray.jl


# BitArray I/O

write(s::IO, B::BitArray) = write(s, B.chunks)
function read!(s::IO, B::BitArray)
    n = length(B)
    Bc = B.chunks
    nc = length(read!(s, Bc))
    if length(Bc) > 0 && Bc[end] & _msk_end(n) ≠ Bc[end]
        Bc[end] &= _msk_end(n) # ensure that the BitArray is not broken
        throw(DimensionMismatch("read mismatch, found non-zero bits after BitArray length"))
    end
    return B
end

sizeof(B::BitArray) = sizeof(B.chunks)

function _split_rest(a::Union{Vector, BitVector}, n::Int)
    _check_length_split_rest(length(a), n)
    last_n = a[end-n+1:end]
    resize!(a, length(a) - n)
    return a, last_n
end
M   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/bitset.jl�0      # This file is a part of Julia. License is MIT: https://julialang.org/license

const Bits = Vector{UInt64}
const CHK0 = zero(UInt64)
const NO_OFFSET = Int === Int64 ? -one(Int) << 60 : -one(Int) << 29
# + NO_OFFSET must be small enough to stay < 0 when added with any offset.
#   An offset is in the range -2^57:2^57 (64-bits architectures)
#   or -2^26:2^26 (32-bits architectures)
# + when the offset is NO_OFFSET, the bits field *must* be empty
# + NO_OFFSET could be made to be > 0, but a negative one allows
#   a small optimization in the in(x, ::BitSet) method

mutable struct BitSet <: AbstractSet{Int}
    const bits::Vector{UInt64}
    # 1st stored Int equals 64*offset
    offset::Int

    BitSet() = new(resize!(Vector{UInt64}(undef, 4), 0), NO_OFFSET)
end

"""
    BitSet([itr])

Construct a sorted set of `Int`s generated by the given iterable object, or an
empty set. Implemented as a bit string, and therefore designed for dense integer sets.
If the set will be sparse (for example, holding a few
very large integers), use [`Set`](@ref) instead.
"""
BitSet(itr) = union!(BitSet(), itr)

# Special implementation for BitSet, which lacks a fast `length` method.
function union!(s::BitSet, itr)
    for x in itr
        push!(s, x)
    end
    return s
end

@inline intoffset(s::BitSet) = s.offset << 6

empty(s::BitSet, ::Type{Int}=Int) = BitSet()
emptymutable(s::BitSet, ::Type{Int}=Int) = BitSet()

copy(s1::BitSet) = copy!(BitSet(), s1)
copymutable(s::BitSet) = copy(s)

function copy!(dest::BitSet, src::BitSet)
    resize!(dest.bits, length(src.bits))
    copyto!(dest.bits, src.bits)
    dest.offset = src.offset
    dest
end

sizehint!(s::BitSet, n::Integer) = (sizehint!(s.bits, (n+63) >> 6); s)

function _bits_getindex(b::Bits, n::Int, offset::Int)
    ci = _div64(n) - offset + 1
    1 <= ci <= length(b) || return false
    @inbounds r = (b[ci] & (one(UInt64) << _mod64(n))) != 0
    r
end

function _bits_findnext(b::Bits, start::Int)
    # start is 0-based
    # @assert start >= 0
    _div64(start) + 1 > length(b) && return -1
    ind = unsafe_bitfindnext(b, start+1)
    ind === nothing ? -1 : ind - 1
end

function _bits_findprev(b::Bits, start::Int)
    # start is 0-based
    # @assert start <= 64 * length(b) - 1
    start >= 0 || return -1
    ind = unsafe_bitfindprev(b, start+1)
    ind === nothing ? -1 : ind - 1
end

# An internal function for setting the inclusion bit for a given integer
@inline function _setint!(s::BitSet, idx::Int, b::Bool)
    cidx = _div64(idx)
    len = length(s.bits)
    diff = cidx - s.offset
    if diff >= len
        b || return s # setting a bit to zero outside the set's bits is a no-op

        # we put the following test within one of the two branches,
        # with the NO_OFFSET trick, to avoid having to perform it at
        # each and every call to _setint!
        if s.offset == NO_OFFSET # initialize the offset
            # we assume isempty(s.bits)
            s.offset = cidx
            diff = 0
        end
        _growend0!(s.bits, diff - len + 1)
    elseif diff < 0
        b || return s
        _growbeg0!(s.bits, -diff)
        s.offset += diff
        diff = 0
    end
    _unsafe_bitsetindex!(s.bits, b, diff+1, _mod64(idx))
    s
end


# An internal function to resize a Bits object and ensure the newly allocated
# elements are zeroed (will become unnecessary if this behavior changes)
@inline function _growend0!(b::Bits, nchunks::Int)
    len = length(b)
    _growend!(b, nchunks)
    for i in len+1:length(b)
        @inbounds b[i] = CHK0 # resize! gives dirty memory
    end
end

@inline function _growbeg0!(b::Bits, nchunks::Int)
    _growbeg!(b, nchunks)
    for i in 1:nchunks
        @inbounds b[i] = CHK0
    end
end

function union!(s::BitSet, r::AbstractUnitRange{<:Integer})
    isempty(r) && return s
    a, b = Int(first(r)), Int(last(r))
    cidxa = _div64(a)
    cidxb = _div64(b)
    if s.offset == NO_OFFSET
        s.offset = cidxa
    end
    len = length(s.bits)
    diffa = cidxa - s.offset
    diffb = cidxb - s.offset

    # grow s.bits as necessary
    if diffb >= len
        _growend0!(s.bits, diffb - len + 1)
    end
    if diffa < 0
        _growbeg0!(s.bits, -diffa)
        s.offset = cidxa # s.offset += diffa
        diffb -= diffa
        diffa = 0
    end

    # update s.bits
    i = _mod64(a)
    j = _mod64(b)
    @inbounds if diffa == diffb
        s.bits[diffa + 1] |= (((~CHK0) >> i) << (i+63-j)) >> (63-j)
    else
        s.bits[diffa + 1] |= ((~CHK0) >> i) << i
        s.bits[diffb + 1] |= (~CHK0  << (63-j)) >> (63-j)
        for n = diffa+1:diffb-1
            s.bits[n+1] = ~CHK0
        end
    end
    s
end

function _matched_map!(f, s1::BitSet, s2::BitSet)
    left_false_is_false = f(false, false) == f(false, true) == false
    right_false_is_false = f(false, false) == f(true, false) == false

    # we must first handle the NO_OFFSET case; we could test for
    # isempty(s1) but it can be costly, so the user has to call
    # empty!(s1) herself before-hand to re-initialize to NO_OFFSET
    if s1.offset == NO_OFFSET
        return left_false_is_false ? s1 : copy!(s1, s2)
    elseif s2.offset == NO_OFFSET
        return right_false_is_false ? empty!(s1) : s1
    end
    s1.offset = _matched_map!(f, s1.bits, s1.offset, s2.bits, s2.offset,
                              left_false_is_false, right_false_is_false)
    s1
end

# An internal function that takes a pure function `f` and maps across two BitArrays
# allowing the lengths and offsets to be different and altering b1 with the result
# WARNING: the assumptions written in the else clauses must hold
function _matched_map!(f, a1::Bits, b1::Int, a2::Bits, b2::Int,
                       left_false_is_false::Bool, right_false_is_false::Bool)
    l1, l2 = length(a1), length(a2)
    bdiff = b2 - b1
    e1, e2 = l1+b1, l2+b2
    ediff = e2 - e1

    # map! over the common indices
    @inbounds for i = max(1, 1+bdiff):min(l1, l2+bdiff)
        a1[i] = f(a1[i], a2[i-bdiff])
    end

    if ediff > 0
        if left_false_is_false
            # We don't need to worry about the trailing bits — they're all false
        else # @assert f(false, x) == x
            _growend!(a1, ediff)
            # if a1 and a2 are not overlapping, we infer implied "false" values from a2
            for outer l1 = l1+1:bdiff
                @inbounds a1[l1] = CHK0
            end
            # update ediff in case l1 was updated
            ediff = e2 - l1 - b1
            # copy actual chunks from a2
            unsafe_copyto!(a1, l1+1, a2, l2+1-ediff, ediff)
            l1 = length(a1)
        end
    elseif ediff < 0
        if right_false_is_false
            # We don't need to worry about the trailing bits — they're all false
            _deleteend!(a1, min(l1, -ediff))
            # no need to update l1, as if bdiff > 0 (case below), then bdiff will
            # be smaller anyway than an updated l1
        else # @assert f(x, false) == x
            # We don't need to worry about the trailing bits — they already have the
            # correct value
        end
    end

    if bdiff < 0
        if left_false_is_false
            # We don't need to worry about the leading bits — they're all false
        else # @assert f(false, x) == x
            _growbeg!(a1, -bdiff)
            # if a1 and a2 are not overlapping, we infer implied "false" values from a2
            for i = l2+1:-bdiff
                @inbounds a1[i] = CHK0
            end
            b1 += bdiff # updated return value

            # copy actual chunks from a2
            unsafe_copyto!(a1, 1, a2, 1, min(-bdiff, l2))
        end
    elseif bdiff > 0
        if right_false_is_false
            # We don't need to worry about the trailing bits — they're all false
            _deletebeg!(a1, min(l1, bdiff))
            b1 += bdiff
        else # @assert f(x, false) == x
            # We don't need to worry about the trailing bits — they already have the
            # correct value
        end
    end
    b1 # the new offset
end

@inline push!(s::BitSet, n::Integer) = _setint!(s, Int(n), true)

push!(s::BitSet, ns::Integer...) = (for n in ns; push!(s, n); end; s)

@inline pop!(s::BitSet) = pop!(s, last(s))

@inline function pop!(s::BitSet, n::Integer)
    if n in s
        delete!(s, n)
        n
    else
        throw(KeyError(n))
    end
end

@inline function pop!(s::BitSet, n::Integer, default)
    if n in s
        delete!(s, n)
        n
    else
        default
    end
end

@inline _is_convertible_Int(n) = typemin(Int) <= n <= typemax(Int)
@inline delete!(s::BitSet, n::Int) = _setint!(s, n, false)
@inline delete!(s::BitSet, n::Integer) = _is_convertible_Int(n) ? delete!(s, Int(n)) : s

popfirst!(s::BitSet) = pop!(s, first(s))

function empty!(s::BitSet)
    empty!(s.bits)
    s.offset = NO_OFFSET
    s
end

isempty(s::BitSet) = _check0(s.bits, 1, length(s.bits))

# Mathematical set functions: union!, intersect!, setdiff!, symdiff!

union(s::BitSet, sets...) = union!(copy(s), sets...)
union!(s1::BitSet, s2::BitSet) = _matched_map!(|, s1, s2)

intersect(s1::BitSet, s2::BitSet) =
    length(s1.bits) < length(s2.bits) ? intersect!(copy(s1), s2) : intersect!(copy(s2), s1)

intersect!(s1::BitSet, s2::BitSet) = _matched_map!(&, s1, s2)

setdiff!(s1::BitSet, s2::BitSet) = _matched_map!((p, q) -> p & ~q, s1, s2)

function symdiff!(s::BitSet, ns)
    for x in ns
        int_symdiff!(s, x)
    end
    return s
end

function symdiff!(s::BitSet, ns::AbstractSet)
    for x in ns
        int_symdiff!(s, x)
    end
    return s
end

function int_symdiff!(s::BitSet, n::Integer)
    n0 = Int(n)
    val = !(n0 in s)
    _setint!(s, n0, val)
    s
end

symdiff!(s1::BitSet, s2::BitSet) = _matched_map!(xor, s1, s2)

filter!(f, s::BitSet) = unsafe_filter!(f, s)

@inline in(n::Int, s::BitSet) = _bits_getindex(s.bits, n, s.offset)
@inline in(n::Integer, s::BitSet) = _is_convertible_Int(n) ? in(Int(n), s) : false

function iterate(s::BitSet, (word, idx) = (CHK0, 0))
    while word == 0
        idx == length(s.bits) && return nothing
        idx += 1
        word = @inbounds s.bits[idx]
    end
    trailing_zeros(word) + (idx - 1 + s.offset) << 6, (_blsr(word), idx)
end

@noinline _throw_bitset_notempty_error() =
    throw(ArgumentError("collection must be non-empty"))

function first(s::BitSet)
    idx = _bits_findnext(s.bits, 0)
    idx == -1 ? _throw_bitset_notempty_error() : idx + intoffset(s)
end

function last(s::BitSet)
    idx = _bits_findprev(s.bits, (length(s.bits) << 6) - 1)
    idx == -1 ? _throw_bitset_notempty_error() : idx + intoffset(s)
end

length(s::BitSet) = bitcount(s.bits) # = mapreduce(count_ones, +, s.bits; init=0)

function show(io::IO, s::BitSet)
    print(io, "BitSet([")
    first = true
    for n in s
        !first && print(io, ", ")
        print(io, n)
        first = false
    end
    print(io, "])")
end

function _check0(a::Vector{UInt64}, b::Int, e::Int)
    @inbounds for i in b:e
        a[i] == CHK0 || return false
    end
    true
end

function ==(s1::BitSet, s2::BitSet)
    # Swap so s1 has always the smallest offset
    if s1.offset > s2.offset
        s1, s2 = s2, s1
    end
    a1 = s1.bits
    a2 = s2.bits
    b1, b2 = s1.offset, s2.offset
    l1, l2 = length(a1), length(a2)
    e1 = l1+b1
    overlap0 = max(0, e1 - b2)
    included = overlap0 >= l2  # whether a2's indices are included in a1's
    overlap  = included ? l2 : overlap0

    # Ensure non-overlap chunks are zero (unlikely)
    _check0(a1, 1, l1-overlap0) || return false
    if included
        _check0(a1, b2-b1+l2+1, l1) || return false
    else
        _check0(a2, 1+overlap, l2) || return false
    end

    # compare overlap values
    if overlap > 0
        t1 = @_gc_preserve_begin a1
        t2 = @_gc_preserve_begin a2
        memcmp(pointer(a1, b2-b1+1), pointer(a2), overlap<<3) == 0 || return false
        @_gc_preserve_end t2
        @_gc_preserve_end t1
    end

    return true
end

function issubset(a::BitSet, b::BitSet)
    n = length(a.bits)
    shift = b.offset - a.offset
    i, j = shift, shift + length(b.bits)

    f(a, b) = a == a & b
    return (
        all(@inbounds iszero(a.bits[i]) for i in 1:min(n, i)) &&
        all(@inbounds f(a.bits[i], b.bits[i - shift]) for i in max(1, i+1):min(n, j)) &&
        all(@inbounds iszero(a.bits[i]) for i in max(1, j+1):n))
end
⊊(a::BitSet, b::BitSet) = a <= b && a != b


minimum(s::BitSet) = first(s)
maximum(s::BitSet) = last(s)
extrema(s::BitSet) = (first(s), last(s))
issorted(s::BitSet) = true
Q   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/multimedia.jl�>      # This file is a part of Julia. License is MIT: https://julialang.org/license

module Multimedia

import .Base: show, print, convert, repr

export AbstractDisplay, display, pushdisplay, popdisplay, displayable, redisplay,
    MIME, @MIME_str, istextmime,
    showable, TextDisplay

###########################################################################
# We define a singleton type MIME{mime symbol} for each MIME type, so
# that Julia's dispatch and overloading mechanisms can be used to
# dispatch show and to add conversions for new types.

"""
    MIME

A type representing a standard internet data format. "MIME" stands for
"Multipurpose Internet Mail Extensions", since the standard was originally
used to describe multimedia attachments to email messages.

A `MIME` object can be passed as the second argument to [`show`](@ref) to
request output in that format.

# Examples
```jldoctest
julia> show(stdout, MIME("text/plain"), "hi")
"hi"
```
"""
struct MIME{mime} end

"""
    @MIME_str

A convenience macro for writing [`MIME`](@ref) types, typically used when
adding methods to [`show`](@ref).
For example the syntax `show(io::IO, ::MIME"text/html", x::MyType) = ...`
could be used to define how to write an HTML representation of `MyType`.
"""
macro MIME_str(s)
    :(MIME{$(Expr(:quote, Symbol(s)))})
end

# fallback text/plain representation of any type:
show(io::IO, ::MIME"text/plain", x) = show(io, x)

MIME(s) = MIME{Symbol(s)}()
show(io::IO, ::MIME{mime}) where {mime} = print(io, "MIME type ", string(mime))
print(io::IO, ::MIME{mime}) where {mime} = print(io, mime)

###########################################################################
# For any type T one can define show(io, ::MIME"type", x::T) = ...
# in order to provide a way to export T as a given mime type.

"""
    showable(mime, x)

Return a boolean value indicating whether or not the object `x` can be written
as the given `mime` type.

(By default, this is determined automatically by the existence of the
corresponding [`show`](@ref) method for `typeof(x)`.  Some types provide custom `showable`
methods; for example, if the available MIME formats depend on the *value* of `x`.)

# Examples
```jldoctest
julia> showable(MIME("text/plain"), rand(5))
true

julia> showable("image/png", rand(5))
false
```
"""
showable(::MIME{mime}, @nospecialize x) where {mime} = hasmethod(show, Tuple{IO, MIME{mime}, typeof(x)})
showable(m::AbstractString, @nospecialize x) = showable(MIME(m), x)

"""
    show(io::IO, mime, x)

The [`display`](@ref) functions ultimately call `show` in order to write an object `x` as a
given `mime` type to a given I/O stream `io` (usually a memory buffer), if possible. In order
to provide a rich multimedia representation of a user-defined type `T`, it is only necessary
to define a new `show` method for `T`, via: `show(io, ::MIME"mime", x::T) = ...`,
where `mime` is a MIME-type string and the function body calls [`write`](@ref) (or similar) to write
that representation of `x` to `io`. (Note that the `MIME""` notation only supports
literal strings; to construct `MIME` types in a more flexible manner use
`MIME{Symbol("")}`.)

For example, if you define a `MyImage` type and know how to write it to a PNG file, you
could define a function `show(io, ::MIME"image/png", x::MyImage) = ...` to allow
your images to be displayed on any PNG-capable `AbstractDisplay` (such as IJulia). As usual, be sure
to `import Base.show` in order to add new methods to the built-in Julia function
`show`.

Technically, the `MIME"mime"` macro defines a singleton type for the given `mime` string,
which allows us to exploit Julia's dispatch mechanisms in determining how to display objects
of any given type.

The default MIME type is `MIME"text/plain"`. There is a fallback definition for `text/plain`
output that calls `show` with 2 arguments, so it is not always necessary to add a method
for that case. If a type benefits from custom human-readable output though,
`show(::IO, ::MIME"text/plain", ::T)` should be defined. For example, the `Day` type uses
`1 day` as the output for the `text/plain` MIME type, and `Day(1)` as the output of 2-argument `show`.

# Examples
```jldoctest
julia> struct Day
           n::Int
       end

julia> Base.show(io::IO, ::MIME"text/plain", d::Day) = print(io, d.n, " day")

julia> Day(1)
1 day
```

Container types generally implement 3-argument `show` by calling `show(io, MIME"text/plain"(), x)`
for elements `x`, with `:compact => true` set in an [`IOContext`](@ref) passed as the first argument.
"""
show(stream::IO, mime, x)
show(io::IO, m::AbstractString, x) = show(io, MIME(m), x)

"""
    repr(mime, x; context=nothing)

Return an `AbstractString` or `Vector{UInt8}` containing the representation of
`x` in the requested `mime` type, as written by [`show(io, mime, x)`](@ref) (throwing a
[`MethodError`](@ref) if no appropriate `show` is available). An `AbstractString` is
returned for MIME types with textual representations (such as `"text/html"` or
`"application/postscript"`), whereas binary data is returned as
`Vector{UInt8}`. (The function `istextmime(mime)` returns whether or not Julia
treats a given `mime` type as text.)

The optional keyword argument `context` can be set to `:key=>value` pair
or an `IO` or [`IOContext`](@ref) object whose attributes are used for the I/O
stream passed to `show`.

As a special case, if `x` is an `AbstractString` (for textual MIME types) or a
`Vector{UInt8}` (for binary MIME types), the `repr` function assumes that
`x` is already in the requested `mime` format and simply returns `x`. This
special case does not apply to the `"text/plain"` MIME type. This is useful so
that raw data can be passed to `display(m::MIME, x)`.

In particular, `repr("text/plain", x)` is typically a "pretty-printed" version
of `x` designed for human consumption.  See also [`repr(x)`](@ref) to instead
return a string corresponding to [`show(x)`](@ref) that may be closer to how
the value of `x` would be entered in Julia.

# Examples
```jldoctest
julia> A = [1 2; 3 4];

julia> repr("text/plain", A)
"2×2 Matrix{Int64}:\\n 1  2\\n 3  4"
```
"""
repr(m::MIME, x; context=nothing) = istextmime(m) ? _textrepr(m, x, context) : _binrepr(m, x, context)
repr(m::AbstractString, x; context=nothing) = repr(MIME(m), x; context=context)

# strings are shown escaped for text/plain
_textrepr(m::MIME, x, context) = String(__binrepr(m, x, context))
_textrepr(::MIME, x::AbstractString, context) = x
_textrepr(m::MIME"text/plain", x::AbstractString, context) = String(__binrepr(m, x, context))


function __binrepr(m::MIME, x, context)
    s = IOBuffer()
    if context === nothing
        show(s, m, x)
    else
        show(IOContext(s, context), m, x)
    end
    take!(s)
end
_binrepr(m::MIME, x, context) = __binrepr(m, x, context)
_binrepr(m::MIME, x::Vector{UInt8}, context) = x

"""
    istextmime(m::MIME)

Determine whether a MIME type is text data. MIME types are assumed to be binary
data except for a set of types known to be text data (possibly Unicode).

# Examples
```jldoctest
julia> istextmime(MIME("text/plain"))
true

julia> istextmime(MIME("image/png"))
false
```
"""
istextmime(m::MIME) = startswith(string(m), "text/")
istextmime(m::AbstractString) = istextmime(MIME(m))

for mime in ["application/atom+xml", "application/ecmascript",
             "application/javascript", "application/julia",
             "application/json", "application/postscript",
             "application/rdf+xml", "application/rss+xml",
             "application/x-latex", "application/xhtml+xml", "application/xml",
             "application/xml-dtd", "image/svg+xml", "model/vrml",
             "model/x3d+vrml", "model/x3d+xml"]
    global istextmime(::MIME{Symbol(mime)}) = true
end

###########################################################################
# We have an abstract AbstractDisplay class that can be subclassed in order to
# define new rich-display output devices.  A typical subclass should
# overload display(d::AbstractDisplay, m::MIME, x) for supported MIME types m,
# (typically using show, repr, ..., to get the MIME
# representation of x) and should also overload display(d::AbstractDisplay, x)
# to display x in whatever MIME type is preferred by the AbstractDisplay and
# is writable by x.  display(..., x) should throw a MethodError if x
# cannot be displayed.  The return value of display(...) is up to the
# AbstractDisplay type.

"""
    AbstractDisplay

Abstract supertype for rich display output devices. [`TextDisplay`](@ref) is a subtype
of this.
"""
abstract type AbstractDisplay end

# it is convenient to accept strings instead of ::MIME
display(d::AbstractDisplay, mime::AbstractString, @nospecialize x) = display(d, MIME(mime), x)
display(mime::AbstractString, @nospecialize x) = display(MIME(mime), x)

"""
    displayable(mime) -> Bool
    displayable(d::AbstractDisplay, mime) -> Bool

Return a boolean value indicating whether the given `mime` type (string) is displayable by
any of the displays in the current display stack, or specifically by the display `d` in the
second variant.
"""
displayable(d::AbstractDisplay, mime::AbstractString) = displayable(d, MIME(mime))
displayable(mime::AbstractString) = displayable(MIME(mime))

# simplest display, which only knows how to display text/plain

"""
    TextDisplay(io::IO)

Return a `TextDisplay <: AbstractDisplay`, which displays any object as the text/plain MIME type
(by default), writing the text representation to the given I/O stream. (This is how
objects are printed in the Julia REPL.)
"""
struct TextDisplay <: AbstractDisplay
    io::IO
end
display(d::TextDisplay, M::MIME"text/plain", @nospecialize x) = (show(d.io, M, x); println(d.io))
display(d::TextDisplay, @nospecialize x) = display(d, MIME"text/plain"(), x)

# if you explicitly call display("text/foo", x), it should work on a TextDisplay:
displayable(d::TextDisplay, M::MIME) = istextmime(M)
function display(d::TextDisplay, M::MIME, @nospecialize x)
    displayable(d, M) || throw(MethodError(display, (d, M, x)))
    show(d.io, M, x); println(d.io)
end

import Base: close, flush
flush(d::TextDisplay) = flush(d.io)
close(d::TextDisplay) = close(d.io)

###########################################################################
# We keep a stack of Displays, and calling display(x) uses the topmost
# AbstractDisplay that is capable of displaying x (doesn't throw an error)

const displays = AbstractDisplay[]

"""
    pushdisplay(d::AbstractDisplay)

Pushes a new display `d` on top of the global display-backend stack. Calling `display(x)` or
`display(mime, x)` will display `x` on the topmost compatible backend in the stack (i.e.,
the topmost backend that does not throw a [`MethodError`](@ref)).
"""
function pushdisplay(d::AbstractDisplay)
    global displays
    push!(displays, d)
end

"""
    popdisplay()
    popdisplay(d::AbstractDisplay)

Pop the topmost backend off of the display-backend stack, or the topmost copy of `d` in the
second variant.
"""
popdisplay() = pop!(displays)
function popdisplay(d::AbstractDisplay)
    for i = length(displays):-1:1
        if d == displays[i]
            return splice!(displays, i)
        end
    end
    throw(KeyError(d))
end
function reinit_displays()
    empty!(displays)
    pushdisplay(TextDisplay(stdout))
end

xdisplayable(D::AbstractDisplay, @nospecialize args...) = applicable(display, D, args...)

"""
    display(x)
    display(d::AbstractDisplay, x)
    display(mime, x)
    display(d::AbstractDisplay, mime, x)

Display `x` using the topmost applicable display in the display stack, typically using the
richest supported multimedia output for `x`, with plain-text [`stdout`](@ref) output as a fallback.
The `display(d, x)` variant attempts to display `x` on the given display `d` only, throwing
a [`MethodError`](@ref) if `d` cannot display objects of this type.

In general, you cannot assume that `display` output goes to `stdout` (unlike [`print(x)`](@ref) or
[`show(x)`](@ref)).  For example, `display(x)` may open up a separate window with an image.
`display(x)` means "show `x` in the best way you can for the current output device(s)."
If you want REPL-like text output that is guaranteed to go to `stdout`, use
[`show(stdout, "text/plain", x)`](@ref) instead.

There are also two variants with a `mime` argument (a MIME type string, such as
`"image/png"`), which attempt to display `x` using the requested MIME type *only*, throwing
a `MethodError` if this type is not supported by either the display(s) or by `x`. With these
variants, one can also supply the "raw" data in the requested MIME type by passing
`x::AbstractString` (for MIME types with text-based storage, such as text/html or
application/postscript) or `x::Vector{UInt8}` (for binary MIME types).

To customize how instances of a type are displayed, overload [`show`](@ref) rather than `display`,
as explained in the manual section on [custom pretty-printing](@ref man-custom-pretty-printing).
"""
function display(@nospecialize x)
    for i = length(displays):-1:1
        if xdisplayable(displays[i], x)
            try
                return display(displays[i], x)
            catch e
                isa(e, MethodError) && (e.f === display || e.f === show) ||
                    rethrow()
            end
        end
    end
    throw(MethodError(display, (x,)))
end

function display(m::MIME, @nospecialize x)
    for i = length(displays):-1:1
        if xdisplayable(displays[i], m, x)
            try
                return display(displays[i], m, x)
            catch e
                isa(e, MethodError) && e.f == display ||
                    rethrow()
            end
        end
    end
    throw(MethodError(display, (m, x)))
end

displayable(d::D, ::MIME{mime}) where {D<:AbstractDisplay,mime} =
    hasmethod(display, Tuple{D,MIME{mime},Any})

function displayable(m::MIME)
    for d in displays
        displayable(d, m) && return true
    end
    return false
end

###########################################################################
# The redisplay method can be overridden by a AbstractDisplay in order to
# update an existing display (instead of, for example, opening a new
# window), and is used by the IJulia interface to defer display
# until the next interactive prompt.  This is especially useful
# for Matlab/Pylab-like stateful plotting interfaces, where
# a plot is created and then modified many times (xlabel, title, etc.).

"""
    redisplay(x)
    redisplay(d::AbstractDisplay, x)
    redisplay(mime, x)
    redisplay(d::AbstractDisplay, mime, x)

By default, the `redisplay` functions simply call [`display`](@ref).
However, some display backends may override `redisplay` to modify an existing
display of `x` (if any).
Using `redisplay` is also a hint to the backend that `x` may be redisplayed
several times, and the backend may choose to defer the display until
(for example) the next interactive prompt.
"""
function redisplay(@nospecialize x)
    for i = length(displays):-1:1
        if xdisplayable(displays[i], x)
            try
                return redisplay(displays[i], x)
            catch e
                isa(e, MethodError) && e.f in (redisplay, display, show) ||
                    rethrow()
            end
        end
    end
    throw(MethodError(redisplay, (x,)))
end

function redisplay(m::Union{MIME,AbstractString}, @nospecialize x)
    for i = length(displays):-1:1
        if xdisplayable(displays[i], m, x)
            try
                return redisplay(displays[i], m, x)
            catch e
                isa(e, MethodError) && e.f in (redisplay, display) ||
                    rethrow()
            end
        end
    end
    throw(MethodError(redisplay, (m, x)))
end

# default redisplay is simply to call display
redisplay(d::AbstractDisplay, @nospecialize x) = display(d, x)
redisplay(d::AbstractDisplay, m::Union{MIME,AbstractString}, @nospecialize x) = display(d, m, x)

###########################################################################

end # module
K   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/some.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
    Some{T}

A wrapper type used in `Union{Some{T}, Nothing}` to distinguish between the absence
of a value ([`nothing`](@ref)) and the presence of a `nothing` value (i.e. `Some(nothing)`).

Use [`something`](@ref) to access the value wrapped by a `Some` object.
"""
struct Some{T}
    value::T
end

Some(::Type{T}) where {T} = Some{Type{T}}(T)

promote_rule(::Type{Some{T}}, ::Type{Some{S}}) where {T, S<:T} = Some{T}

nonnothingtype(::Type{T}) where {T} = typesplit(T, Nothing)
promote_rule(T::Type{Nothing}, S::Type) = Union{S, Nothing}
function promote_rule(T::Type{>:Nothing}, S::Type)
    R = nonnothingtype(T)
    R >: T && return Any
    T = R
    R = promote_type(T, S)
    return Union{R, Nothing}
end

function nonnothingtype_checked(T::Type)
    R = nonnothingtype(T)
    R >: T && error("could not compute non-nothing type")
    R <: Union{} && error("cannot convert a value to nothing for assignment")
    return R
end

convert(::Type{T}, x::T) where {T>:Nothing} = x
convert(::Type{T}, x) where {T>:Nothing} = convert(nonnothingtype_checked(T), x)
convert(::Type{Some{T}}, x::Some{T}) where {T} = x
convert(::Type{Some{T}}, x::Some) where {T} = Some{T}(convert(T, x.value))::Some{T}

function show(io::IO, x::Some)
    if get(io, :typeinfo, Any) == typeof(x)
        show(io, x.value)
    else
        print(io, "Some(")
        show(io, x.value)
        print(io, ')')
    end
end

"""
    notnothing(x)

Throw an error if `x === nothing`, and return `x` if not.
"""
notnothing(x::Any) = x
notnothing(::Nothing) = throw(ArgumentError("nothing passed to notnothing"))

"""
    isnothing(x)

Return `true` if `x === nothing`, and return `false` if not.

!!! compat "Julia 1.1"
    This function requires at least Julia 1.1.

See also [`something`](@ref), [`Base.notnothing`](@ref), [`ismissing`](@ref).
"""
isnothing(x) = x === nothing


"""
    something(x...)

Return the first value in the arguments which is not equal to [`nothing`](@ref),
if any. Otherwise throw an error.
Arguments of type [`Some`](@ref) are unwrapped.

See also [`coalesce`](@ref), [`skipmissing`](@ref), [`@something`](@ref).

# Examples
```jldoctest
julia> something(nothing, 1)
1

julia> something(Some(1), nothing)
1

julia> something(Some(nothing), 2) === nothing
true

julia> something(missing, nothing)
missing

julia> something(nothing, nothing)
ERROR: ArgumentError: No value arguments present
```
"""
function something end

something() = throw(ArgumentError("No value arguments present"))
something(x::Nothing, y...) = something(y...)
something(x::Some, y...) = x.value
something(x::Any, y...) = x


"""
    @something(x...)

Short-circuiting version of [`something`](@ref).

# Examples
```jldoctest
julia> f(x) = (println("f(\$x)"); nothing);

julia> a = 1;

julia> a = @something a f(2) f(3) error("Unable to find default for `a`")
1

julia> b = nothing;

julia> b = @something b f(2) f(3) error("Unable to find default for `b`")
f(2)
f(3)
ERROR: Unable to find default for `b`
[...]

julia> b = @something b f(2) f(3) Some(nothing)
f(2)
f(3)

julia> b === nothing
true
```

!!! compat "Julia 1.7"
    This macro is available as of Julia 1.7.
"""
macro something(args...)
    expr = :(nothing)
    for arg in reverse(args)
        expr = :(val = $(esc(arg)); val !== nothing ? val : ($expr))
    end
    something = GlobalRef(Base, :something)
    return :($something($expr))
end
K   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/dict.jlZZ      # This file is a part of Julia. License is MIT: https://julialang.org/license

function show(io::IO, t::AbstractDict{K,V}) where V where K
    recur_io = IOContext(io, :SHOWN_SET => t,
                             :typeinfo => eltype(t))

    limit = get(io, :limit, false)::Bool
    # show in a Julia-syntax-like form: Dict(k=>v, ...)
    print(io, typeinfo_prefix(io, t)[1])
    print(io, '(')
    if !isempty(t) && !show_circular(io, t)
        first = true
        n = 0
        for pair in t
            first || print(io, ", ")
            first = false
            show(recur_io, pair)
            n+=1
            limit && n >= 10 && (print(io, "…"); break)
        end
    end
    print(io, ')')
end

# Dict

# These can be changed, to trade off better performance for space
const global maxallowedprobe = 16
const global maxprobeshift   = 6

"""
    Dict([itr])

`Dict{K,V}()` constructs a hash table with keys of type `K` and values of type `V`.
Keys are compared with [`isequal`](@ref) and hashed with [`hash`](@ref).

Given a single iterable argument, constructs a [`Dict`](@ref) whose key-value pairs
are taken from 2-tuples `(key,value)` generated by the argument.

# Examples
```jldoctest
julia> Dict([("A", 1), ("B", 2)])
Dict{String, Int64} with 2 entries:
  "B" => 2
  "A" => 1
```

Alternatively, a sequence of pair arguments may be passed.

```jldoctest
julia> Dict("A"=>1, "B"=>2)
Dict{String, Int64} with 2 entries:
  "B" => 2
  "A" => 1
```
"""
mutable struct Dict{K,V} <: AbstractDict{K,V}
    # Metadata: empty => 0x00, removed => 0x7f, full => 0b1[7 most significant hash bits]
    slots::Vector{UInt8}
    keys::Array{K,1}
    vals::Array{V,1}
    ndel::Int
    count::Int
    age::UInt
    idxfloor::Int  # an index <= the indices of all used slots
    maxprobe::Int

    function Dict{K,V}() where V where K
        n = 16
        new(zeros(UInt8,n), Vector{K}(undef, n), Vector{V}(undef, n), 0, 0, 0, n, 0)
    end
    function Dict{K,V}(d::Dict{K,V}) where V where K
        new(copy(d.slots), copy(d.keys), copy(d.vals), d.ndel, d.count, d.age,
            d.idxfloor, d.maxprobe)
    end
    function Dict{K, V}(slots, keys, vals, ndel, count, age, idxfloor, maxprobe) where {K, V}
        new(slots, keys, vals, ndel, count, age, idxfloor, maxprobe)
    end
end
function Dict{K,V}(kv) where V where K
    h = Dict{K,V}()
    haslength(kv) && sizehint!(h, Int(length(kv))::Int)
    for (k,v) in kv
        h[k] = v
    end
    return h
end
Dict{K,V}(p::Pair) where {K,V} = setindex!(Dict{K,V}(), p.second, p.first)
function Dict{K,V}(ps::Pair...) where V where K
    h = Dict{K,V}()
    sizehint!(h, length(ps))
    for p in ps
        h[p.first] = p.second
    end
    return h
end
# Note the constructors of WeakKeyDict mirror these here, keep in sync.
Dict() = Dict{Any,Any}()
Dict(kv::Tuple{}) = Dict()
copy(d::Dict) = Dict(d)

const AnyDict = Dict{Any,Any}

Dict(ps::Pair{K,V}...) where {K,V} = Dict{K,V}(ps)
Dict(ps::Pair...)                  = Dict(ps)

function Dict(kv)
    try
        dict_with_eltype((K, V) -> Dict{K, V}, kv, eltype(kv))
    catch
        if !isiterable(typeof(kv)) || !all(x->isa(x,Union{Tuple,Pair}),kv)
            throw(ArgumentError("Dict(kv): kv needs to be an iterator of tuples or pairs"))
        else
            rethrow()
        end
    end
end

function grow_to!(dest::AbstractDict{K, V}, itr) where V where K
    y = iterate(itr)
    y === nothing && return dest
    ((k,v), st) = y
    dest2 = empty(dest, typeof(k), typeof(v))
    dest2[k] = v
    grow_to!(dest2, itr, st)
end

# this is a special case due to (1) allowing both Pairs and Tuples as elements,
# and (2) Pair being invariant. a bit annoying.
function grow_to!(dest::AbstractDict{K,V}, itr, st) where V where K
    y = iterate(itr, st)
    while y !== nothing
        (k,v), st = y
        if isa(k,K) && isa(v,V)
            dest[k] = v
        else
            new = empty(dest, promote_typejoin(K,typeof(k)), promote_typejoin(V,typeof(v)))
            merge!(new, dest)
            new[k] = v
            return grow_to!(new, itr, st)
        end
        y = iterate(itr, st)
    end
    return dest
end

empty(a::AbstractDict, ::Type{K}, ::Type{V}) where {K, V} = Dict{K, V}()

# Gets 7 most significant bits from the hash (hsh), first bit is 1
_shorthash7(hsh::UInt) = (hsh >> (8sizeof(UInt)-7))%UInt8 | 0x80

# hashindex (key, sz) - computes optimal position and shorthash7
#     idx - optimal position in the hash table
#     sh::UInt8 - short hash (7 highest hash bits)
function hashindex(key, sz)
    hsh = hash(key)::UInt
    idx = (((hsh % Int) & (sz-1)) + 1)::Int
    return idx, _shorthash7(hsh)
end

@propagate_inbounds isslotempty(h::Dict, i::Int) = h.slots[i] == 0x00
@propagate_inbounds isslotfilled(h::Dict, i::Int) = (h.slots[i] & 0x80) != 0
@propagate_inbounds isslotmissing(h::Dict, i::Int) = h.slots[i] == 0x7f

@constprop :none function rehash!(h::Dict{K,V}, newsz = length(h.keys)) where V where K
    olds = h.slots
    oldk = h.keys
    oldv = h.vals
    sz = length(olds)
    newsz = _tablesz(newsz)
    h.age += 1
    h.idxfloor = 1
    if h.count == 0
        resize!(h.slots, newsz)
        fill!(h.slots, 0x0)
        resize!(h.keys, newsz)
        resize!(h.vals, newsz)
        h.ndel = 0
        h.maxprobe = 0
        return h
    end

    slots = zeros(UInt8,newsz)
    keys = Vector{K}(undef, newsz)
    vals = Vector{V}(undef, newsz)
    age0 = h.age
    count = 0
    maxprobe = 0

    for i = 1:sz
        @inbounds if (olds[i] & 0x80) != 0
            k = oldk[i]
            v = oldv[i]
            index, sh = hashindex(k, newsz)
            index0 = index
            while slots[index] != 0
                index = (index & (newsz-1)) + 1
            end
            probe = (index - index0) & (newsz-1)
            probe > maxprobe && (maxprobe = probe)
            slots[index] = olds[i]
            keys[index] = k
            vals[index] = v
            count += 1
        end
    end

    @assert h.age == age0 "Multiple concurrent writes to Dict detected!"
    h.age += 1
    h.slots = slots
    h.keys = keys
    h.vals = vals
    h.count = count
    h.ndel = 0
    h.maxprobe = maxprobe
    return h
end

function sizehint!(d::Dict{T}, newsz) where T
    oldsz = length(d.slots)
    # limit new element count to max_values of the key type
    newsz = min(max(newsz, length(d)), max_values(T)::Int)
    # need at least 1.5n space to hold n elements
    newsz = _tablesz(cld(3 * newsz, 2))
    return newsz == oldsz ? d : rehash!(d, newsz)
end

"""
    empty!(collection) -> collection

Remove all elements from a `collection`.

# Examples
```jldoctest
julia> A = Dict("a" => 1, "b" => 2)
Dict{String, Int64} with 2 entries:
  "b" => 2
  "a" => 1

julia> empty!(A);

julia> A
Dict{String, Int64}()
```
"""
function empty!(h::Dict{K,V}) where V where K
    fill!(h.slots, 0x0)
    sz = length(h.slots)
    empty!(h.keys)
    empty!(h.vals)
    resize!(h.keys, sz)
    resize!(h.vals, sz)
    h.ndel = 0
    h.count = 0
    h.maxprobe = 0
    h.age += 1
    h.idxfloor = sz
    return h
end

# get the index where a key is stored, or -1 if not present
@assume_effects :terminates_locally function ht_keyindex(h::Dict{K,V}, key) where V where K
    isempty(h) && return -1
    sz = length(h.keys)
    iter = 0
    maxprobe = h.maxprobe
    maxprobe < sz || throw(AssertionError()) # This error will never trigger, but is needed for terminates_locally to be valid
    index, sh = hashindex(key, sz)
    keys = h.keys

    @inbounds while true
        isslotempty(h,index) && return -1
        if h.slots[index] == sh
            k = keys[index]
            if (key ===  k || isequal(key, k))
                return index
            end
        end

        index = (index & (sz-1)) + 1
        (iter += 1) > maxprobe && return -1
    end
    # This line is unreachable
end

# get (index, sh) for the key
#     index - where a key is stored, or -pos if not present
#             and the key would be inserted at pos
#     sh::UInt8 - short hash (7 highest hash bits)
# This version is for use by setindex! and get!
function ht_keyindex2_shorthash!(h::Dict{K,V}, key) where V where K
    sz = length(h.keys)
    iter = 0
    maxprobe = h.maxprobe
    index, sh = hashindex(key, sz)
    avail = 0
    keys = h.keys

    @inbounds while true
        if isslotempty(h,index)
            return (avail < 0 ? avail : -index), sh
        end

        if isslotmissing(h,index)
            if avail == 0
                # found an available slot, but need to keep scanning
                # in case "key" already exists in a later collided slot.
                avail = -index
            end
        elseif h.slots[index] == sh
            k = keys[index]
            if key === k || isequal(key, k)
                return index, sh
            end
        end

        index = (index & (sz-1)) + 1
        iter += 1
        iter > maxprobe && break
    end

    avail < 0 && return avail, sh

    maxallowed = max(maxallowedprobe, sz>>maxprobeshift)
    # Check if key is not present, may need to keep searching to find slot
    @inbounds while iter < maxallowed
        if !isslotfilled(h,index)
            h.maxprobe = iter
            return -index, sh
        end
        index = (index & (sz-1)) + 1
        iter += 1
    end

    rehash!(h, h.count > 64000 ? sz*2 : sz*4)

    return ht_keyindex2_shorthash!(h, key)
end

# Only for better backward compatibility. It can be removed in the future.
ht_keyindex2!(h::Dict, key) = ht_keyindex2_shorthash!(h, key)[1]

@propagate_inbounds function _setindex!(h::Dict, v, key, index, sh = _shorthash7(hash(key)))
    h.ndel -= isslotmissing(h, index)
    h.slots[index] = sh
    h.keys[index] = key
    h.vals[index] = v
    h.count += 1
    h.age += 1
    if index < h.idxfloor
        h.idxfloor = index
    end

    sz = length(h.keys)
    # Rehash now if necessary
    if (h.count + h.ndel)*3 > sz*2
        # > 2/3 full (including tombstones)
        rehash!(h, h.count > 64000 ? h.count*2 : h.count*4)
    end
    nothing
end

function setindex!(h::Dict{K,V}, v0, key0) where V where K
    if key0 isa K
        key = key0
    else
        key = convert(K, key0)::K
        if !(isequal(key, key0)::Bool)
            throw(ArgumentError("$(limitrepr(key0)) is not a valid key for type $K"))
        end
    end
    setindex!(h, v0, key)
end

function setindex!(h::Dict{K,V}, v0, key::K) where V where K
    v = v0 isa V ? v0 : convert(V, v0)::V
    index, sh = ht_keyindex2_shorthash!(h, key)

    if index > 0
        h.age += 1
        @inbounds h.keys[index] = key
        @inbounds h.vals[index] = v
    else
        @inbounds _setindex!(h, v, key, -index, sh)
    end

    return h
end

function setindex!(h::Dict{K,Any}, v, key::K) where K
    @nospecialize v
    index, sh = ht_keyindex2_shorthash!(h, key)

    if index > 0
        h.age += 1
        @inbounds h.keys[index] = key
        @inbounds h.vals[index] = v
    else
        @inbounds _setindex!(h, v, key, -index, sh)
    end

    return h
end


"""
    get!(collection, key, default)

Return the value stored for the given key, or if no mapping for the key is present, store
`key => default`, and return `default`.

# Examples
```jldoctest
julia> d = Dict("a"=>1, "b"=>2, "c"=>3);

julia> get!(d, "a", 5)
1

julia> get!(d, "d", 4)
4

julia> d
Dict{String, Int64} with 4 entries:
  "c" => 3
  "b" => 2
  "a" => 1
  "d" => 4
```
"""
get!(collection, key, default)

"""
    get!(f::Union{Function, Type}, collection, key)

Return the value stored for the given key, or if no mapping for the key is present, store
`key => f()`, and return `f()`.

This is intended to be called using `do` block syntax.

# Examples
```jldoctest
julia> squares = Dict{Int, Int}();

julia> function get_square!(d, i)
           get!(d, i) do
               i^2
           end
       end
get_square! (generic function with 1 method)

julia> get_square!(squares, 2)
4

julia> squares
Dict{Int64, Int64} with 1 entry:
  2 => 4
```
"""
get!(f::Callable, collection, key)

function get!(default::Callable, h::Dict{K,V}, key0) where V where K
    if key0 isa K
        key = key0
    else
        key = convert(K, key0)::K
        if !isequal(key, key0)
            throw(ArgumentError("$(limitrepr(key0)) is not a valid key for type $K"))
        end
    end
    return get!(default, h, key)
end

function get!(default::Callable, h::Dict{K,V}, key::K) where V where K
    index, sh = ht_keyindex2_shorthash!(h, key)

    index > 0 && return h.vals[index]

    age0 = h.age
    v = default()
    if !isa(v, V)
        v = convert(V, v)::V
    end
    if h.age != age0
        index, sh = ht_keyindex2_shorthash!(h, key)
    end
    if index > 0
        h.age += 1
        @inbounds h.keys[index] = key
        @inbounds h.vals[index] = v
    else
        @inbounds _setindex!(h, v, key, -index, sh)
    end
    return v
end

function getindex(h::Dict{K,V}, key) where V where K
    index = ht_keyindex(h, key)
    @inbounds return (index < 0) ? throw(KeyError(key)) : h.vals[index]::V
end

"""
    get(collection, key, default)

Return the value stored for the given key, or the given default value if no mapping for the
key is present.

!!! compat "Julia 1.7"
    For tuples and numbers, this function requires at least Julia 1.7.

# Examples
```jldoctest
julia> d = Dict("a"=>1, "b"=>2);

julia> get(d, "a", 3)
1

julia> get(d, "c", 3)
3
```
"""
get(collection, key, default)

function get(h::Dict{K,V}, key, default) where V where K
    index = ht_keyindex(h, key)
    @inbounds return (index < 0) ? default : h.vals[index]::V
end

"""
    get(f::Union{Function, Type}, collection, key)

Return the value stored for the given key, or if no mapping for the key is present, return
`f()`.  Use [`get!`](@ref) to also store the default value in the dictionary.

This is intended to be called using `do` block syntax

```julia
get(dict, key) do
    # default value calculated here
    time()
end
```
"""
get(::Callable, collection, key)

function get(default::Callable, h::Dict{K,V}, key) where V where K
    index = ht_keyindex(h, key)
    @inbounds return (index < 0) ? default() : h.vals[index]::V
end

"""
    haskey(collection, key) -> Bool

Determine whether a collection has a mapping for a given `key`.

# Examples
```jldoctest
julia> D = Dict('a'=>2, 'b'=>3)
Dict{Char, Int64} with 2 entries:
  'a' => 2
  'b' => 3

julia> haskey(D, 'a')
true

julia> haskey(D, 'c')
false
```
"""
haskey(h::Dict, key) = (ht_keyindex(h, key) >= 0)
in(key, v::KeySet{<:Any, <:Dict}) = (ht_keyindex(v.dict, key) >= 0)

"""
    getkey(collection, key, default)

Return the key matching argument `key` if one exists in `collection`, otherwise return `default`.

# Examples
```jldoctest
julia> D = Dict('a'=>2, 'b'=>3)
Dict{Char, Int64} with 2 entries:
  'a' => 2
  'b' => 3

julia> getkey(D, 'a', 1)
'a': ASCII/Unicode U+0061 (category Ll: Letter, lowercase)

julia> getkey(D, 'd', 'a')
'a': ASCII/Unicode U+0061 (category Ll: Letter, lowercase)
```
"""
function getkey(h::Dict{K,V}, key, default) where V where K
    index = ht_keyindex(h, key)
    @inbounds return (index<0) ? default : h.keys[index]::K
end

function _pop!(h::Dict, index)
    @inbounds val = h.vals[index]
    _delete!(h, index)
    return val
end

function pop!(h::Dict, key)
    index = ht_keyindex(h, key)
    return index > 0 ? _pop!(h, index) : throw(KeyError(key))
end

"""
    pop!(collection, key[, default])

Delete and return the mapping for `key` if it exists in `collection`, otherwise return
`default`, or throw an error if `default` is not specified.

# Examples
```jldoctest
julia> d = Dict("a"=>1, "b"=>2, "c"=>3);

julia> pop!(d, "a")
1

julia> pop!(d, "d")
ERROR: KeyError: key "d" not found
Stacktrace:
[...]

julia> pop!(d, "e", 4)
4
```
"""
pop!(collection, key, default)

function pop!(h::Dict, key, default)
    index = ht_keyindex(h, key)
    return index > 0 ? _pop!(h, index) : default
end

function pop!(h::Dict)
    isempty(h) && throw(ArgumentError("dict must be non-empty"))
    idx = skip_deleted_floor!(h)
    @inbounds key = h.keys[idx]
    @inbounds val = h.vals[idx]
    _delete!(h, idx)
    key => val
end

function _delete!(h::Dict{K,V}, index) where {K,V}
    @inbounds begin
    slots = h.slots
    sz = length(slots)
    _unsetindex!(h.keys, index)
    _unsetindex!(h.vals, index)
    # if the next slot is empty we don't need a tombstone
    # and can remove all tombstones that were required by the element we just deleted
    ndel = 1
    nextind = (index & (sz-1)) + 1
    if isslotempty(h, nextind)
        while true
            ndel -= 1
            slots[index] = 0x00
            index = ((index - 2) & (sz-1)) + 1
            isslotmissing(h, index) || break
        end
    else
        slots[index] = 0x7f
    end
    h.ndel += ndel
    h.count -= 1
    h.age += 1
    return h
    end
end

"""
    delete!(collection, key)

Delete the mapping for the given key in a collection, if any, and return the collection.

# Examples
```jldoctest
julia> d = Dict("a"=>1, "b"=>2)
Dict{String, Int64} with 2 entries:
  "b" => 2
  "a" => 1

julia> delete!(d, "b")
Dict{String, Int64} with 1 entry:
  "a" => 1

julia> delete!(d, "b") # d is left unchanged
Dict{String, Int64} with 1 entry:
  "a" => 1
```
"""
delete!(collection, key)

function delete!(h::Dict, key)
    index = ht_keyindex(h, key)
    if index > 0
        _delete!(h, index)
    end
    return h
end

function skip_deleted(h::Dict, i)
    L = length(h.slots)
    for i = i:L
        @inbounds if isslotfilled(h,i)
            return  i
        end
    end
    return 0
end
function skip_deleted_floor!(h::Dict)
    idx = skip_deleted(h, h.idxfloor)
    if idx != 0
        h.idxfloor = idx
    end
    idx
end

@propagate_inbounds _iterate(t::Dict{K,V}, i) where {K,V} = i == 0 ? nothing : (Pair{K,V}(t.keys[i],t.vals[i]), i == typemax(Int) ? 0 : i+1)
@propagate_inbounds function iterate(t::Dict)
    _iterate(t, skip_deleted(t, t.idxfloor))
end
@propagate_inbounds iterate(t::Dict, i) = _iterate(t, skip_deleted(t, i))

isempty(t::Dict) = (t.count == 0)
length(t::Dict) = t.count

@propagate_inbounds function Base.iterate(v::T, i::Int = v.dict.idxfloor) where T <: Union{KeySet{<:Any, <:Dict}, ValueIterator{<:Dict}}
    i == 0 && return nothing
    i = skip_deleted(v.dict, i)
    i == 0 && return nothing
    vals = T <: KeySet ? v.dict.keys : v.dict.vals
    (@inbounds vals[i], i == typemax(Int) ? 0 : i+1)
end

function filter!(pred, h::Dict{K,V}) where {K,V}
    h.count == 0 && return h
    @inbounds for i=1:length(h.slots)
        if ((h.slots[i] & 0x80) != 0) && !pred(Pair{K,V}(h.keys[i], h.vals[i]))
            _delete!(h, i)
        end
    end
    return h
end

function reduce(::typeof(merge), items::Vector{<:Dict})
    K = mapreduce(keytype, promote_type, items)
    V = mapreduce(valtype, promote_type, items)
    return reduce(merge!, items; init=Dict{K,V}())
end

function map!(f, iter::ValueIterator{<:Dict})
    dict = iter.dict
    vals = dict.vals
    # @inbounds is here so that it gets propagated to isslotfilled
    @inbounds for i = dict.idxfloor:lastindex(vals)
        if isslotfilled(dict, i)
            vals[i] = f(vals[i])
        end
    end
    return iter
end

function mergewith!(combine, d1::Dict{K, V}, d2::AbstractDict) where {K, V}
    haslength(d2) && sizehint!(d1, length(d1) + length(d2))
    for (k, v) in d2
        i, sh = ht_keyindex2_shorthash!(d1, k)
        if i > 0
            d1.vals[i] = combine(d1.vals[i], v)
        else
            if !(k isa K)
                k1 = convert(K, k)::K
                if !isequal(k, k1)
                    throw(ArgumentError("$(limitrepr(k)) is not a valid key for type $K"))
                end
                k = k1
            end
            if !isa(v, V)
                v = convert(V, v)::V
            end
            @inbounds _setindex!(d1, v, k, -i, sh)
        end
    end
    return d1
end

struct ImmutableDict{K,V} <: AbstractDict{K,V}
    parent::ImmutableDict{K,V}
    key::K
    value::V
    ImmutableDict{K,V}() where {K,V} = new() # represents an empty dictionary
    ImmutableDict{K,V}(key, value) where {K,V} = (empty = new(); new(empty, key, value))
    ImmutableDict{K,V}(parent::ImmutableDict, key, value) where {K,V} = new(parent, key, value)
end

"""
    ImmutableDict

`ImmutableDict` is a dictionary implemented as an immutable linked list,
which is optimal for small dictionaries that are constructed over many individual insertions.
Note that it is not possible to remove a value, although it can be partially overridden and hidden
by inserting a new value with the same key.

    ImmutableDict(KV::Pair)

Create a new entry in the `ImmutableDict` for a `key => value` pair

 - use `(key => value) in dict` to see if this particular combination is in the properties set
 - use `get(dict, key, default)` to retrieve the most recent value for a particular key

"""
ImmutableDict
ImmutableDict(KV::Pair{K,V}) where {K,V} = ImmutableDict{K,V}(KV[1], KV[2])
ImmutableDict(t::ImmutableDict{K,V}, KV::Pair) where {K,V} = ImmutableDict{K,V}(t, KV[1], KV[2])
ImmutableDict(t::ImmutableDict{K,V}, KV::Pair, rest::Pair...) where {K,V} =
    ImmutableDict(ImmutableDict(t, KV), rest...)
ImmutableDict(KV::Pair, rest::Pair...) = ImmutableDict(ImmutableDict(KV), rest...)

function in(key_value::Pair, dict::ImmutableDict, valcmp=(==))
    key, value = key_value
    while isdefined(dict, :parent)
        if isequal(dict.key, key)
            valcmp(value, dict.value) && return true
        end
        dict = dict.parent
    end
    return false
end

function haskey(dict::ImmutableDict, key)
    while isdefined(dict, :parent)
        isequal(dict.key, key) && return true
        dict = dict.parent
    end
    return false
end

function getindex(dict::ImmutableDict, key)
    while isdefined(dict, :parent)
        isequal(dict.key, key) && return dict.value
        dict = dict.parent
    end
    throw(KeyError(key))
end
function get(dict::ImmutableDict, key, default)
    while isdefined(dict, :parent)
        isequal(dict.key, key) && return dict.value
        dict = dict.parent
    end
    return default
end

function get(default::Callable, dict::ImmutableDict, key)
    while isdefined(dict, :parent)
        isequal(dict.key, key) && return dict.value
        dict = dict.parent
    end
    return default()
end

# this actually defines reverse iteration (e.g. it should not be used for merge/copy/filter type operations)
function iterate(d::ImmutableDict{K,V}, t=d) where {K, V}
    !isdefined(t, :parent) && return nothing
    (Pair{K,V}(t.key, t.value), t.parent)
end
length(t::ImmutableDict) = count(Returns(true), t)
isempty(t::ImmutableDict) = !isdefined(t, :parent)
empty(::ImmutableDict, ::Type{K}, ::Type{V}) where {K, V} = ImmutableDict{K,V}()

_similar_for(c::AbstractDict, ::Type{Pair{K,V}}, itr, isz, len) where {K, V} = empty(c, K, V)
_similar_for(c::AbstractDict, ::Type{T}, itr, isz, len) where {T} =
    throw(ArgumentError("for AbstractDicts, similar requires an element type of Pair;\n  if calling map, consider a comprehension instead"))
R   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/abstractset.jl�1      # This file is a part of Julia. License is MIT: https://julialang.org/license

eltype(::Type{<:AbstractSet{T}}) where {T} = @isdefined(T) ? T : Any
sizehint!(s::AbstractSet, n) = s

function copy!(dst::AbstractSet, src::AbstractSet)
    dst === src && return dst
    union!(empty!(dst), src)
end

## set operations (union, intersection, symmetric difference)

"""
    union(s, itrs...)
    ∪(s, itrs...)

Construct an object containing all distinct elements from all of the arguments.

The first argument controls what kind of container is returned.
If this is an array, it maintains the order in which elements first appear.

Unicode `∪` can be typed by writing `\\cup` then pressing tab in the Julia REPL, and in many editors.
This is an infix operator, allowing `s ∪ itr`.

See also [`unique`](@ref), [`intersect`](@ref), [`isdisjoint`](@ref), [`vcat`](@ref), [`Iterators.flatten`](@ref).

# Examples
```jldoctest
julia> union([1, 2], [3])
3-element Vector{Int64}:
 1
 2
 3

julia> union([4 2 3 4 4], 1:3, 3.0)
4-element Vector{Float64}:
 4.0
 2.0
 3.0
 1.0

julia> (0, 0.0) ∪ (-0.0, NaN)
3-element Vector{Real}:
   0
  -0.0
 NaN

julia> union(Set([1, 2]), 2:3)
Set{Int64} with 3 elements:
  2
  3
  1
```
"""
function union end

union(s, sets...) = union!(emptymutable(s, promote_eltype(s, sets...)), s, sets...)
union(s::AbstractSet) = copy(s)

const ∪ = union

"""
    union!(s::Union{AbstractSet,AbstractVector}, itrs...)

Construct the [`union`](@ref) of passed in sets and overwrite `s` with the result.
Maintain order with arrays.

$(_DOCS_ALIASING_WARNING)

# Examples
```jldoctest
julia> a = Set([3, 4, 5]);

julia> union!(a, 1:2:7);

julia> a
Set{Int64} with 5 elements:
  5
  4
  7
  3
  1
```
"""
function union!(s::AbstractSet, sets...)
    for x in sets
        union!(s, x)
    end
    return s
end

max_values(::Type) = typemax(Int)
max_values(T::Union{map(X -> Type{X}, BitIntegerSmall_types)...}) = 1 << (8*sizeof(T))
# saturated addition to prevent overflow with typemax(Int)
function max_values(T::Union)
    a = max_values(T.a)::Int
    b = max_values(T.b)::Int
    return max(a, b, a + b)
end
max_values(::Type{Bool}) = 2
max_values(::Type{Nothing}) = 1

function union!(s::AbstractSet{T}, itr) where T
    haslength(itr) && sizehint!(s, length(s) + Int(length(itr))::Int)
    for x in itr
        push!(s, x)
        length(s) == max_values(T) && break
    end
    return s
end

"""
    intersect(s, itrs...)
    ∩(s, itrs...)

Construct the set containing those elements which appear in all of the arguments.

The first argument controls what kind of container is returned.
If this is an array, it maintains the order in which elements first appear.

Unicode `∩` can be typed by writing `\\cap` then pressing tab in the Julia REPL, and in many editors.
This is an infix operator, allowing `s ∩ itr`.

See also [`setdiff`](@ref), [`isdisjoint`](@ref), [`issubset`](@ref Base.issubset), [`issetequal`](@ref).

!!! compat "Julia 1.8"
    As of Julia 1.8 intersect returns a result with the eltype of the
    type-promoted eltypes of the two inputs

# Examples
```jldoctest
julia> intersect([1, 2, 3], [3, 4, 5])
1-element Vector{Int64}:
 3

julia> intersect([1, 4, 4, 5, 6], [6, 4, 6, 7, 8])
2-element Vector{Int64}:
 4
 6

julia> intersect(1:16, 7:99)
7:16

julia> (0, 0.0) ∩ (-0.0, 0)
1-element Vector{Real}:
 0

julia> intersect(Set([1, 2]), BitSet([2, 3]), 1.0:10.0)
Set{Float64} with 1 element:
  2.0
```
"""
function intersect(s::AbstractSet, itr, itrs...)
    # heuristics to try to `intersect` with the shortest Set on the left
    if length(s)>50 && haslength(itr) && all(haslength, itrs)
        min_length, min_idx = findmin(length, itrs)
        if length(itr) > min_length
            new_itrs = setindex(itrs, itr, min_idx)
            return intersect(s, itrs[min_idx], new_itrs...)
        end
    end
    T = promote_eltype(s, itr, itrs...)
    if T == promote_eltype(s, itr)
        out = intersect(s, itr)
    else
        out = union!(emptymutable(s, T), s)
        intersect!(out, itr)
    end
    return intersect!(out, itrs...)
end
intersect(s) = union(s)
function intersect(s::AbstractSet, itr)
    if haslength(itr) && hasfastin(itr) && length(s) < length(itr)
        return mapfilter(in(itr), push!, s, emptymutable(s, promote_eltype(s, itr)))
    else
        return mapfilter(in(s), push!, itr, emptymutable(s, promote_eltype(s, itr)))
    end
end

const ∩ = intersect

"""
    intersect!(s::Union{AbstractSet,AbstractVector}, itrs...)

Intersect all passed in sets and overwrite `s` with the result.
Maintain order with arrays.

$(_DOCS_ALIASING_WARNING)
"""
function intersect!(s::AbstractSet, itrs...)
    for x in itrs
        intersect!(s, x)
    end
    return s
end
intersect!(s::AbstractSet, s2::AbstractSet) = filter!(in(s2), s)
intersect!(s::AbstractSet, itr) =
    intersect!(s, union!(emptymutable(s, eltype(itr)), itr))

"""
    setdiff(s, itrs...)

Construct the set of elements in `s` but not in any of the iterables in `itrs`.
Maintain order with arrays.

See also [`setdiff!`](@ref), [`union`](@ref) and [`intersect`](@ref).

# Examples
```jldoctest
julia> setdiff([1,2,3], [3,4,5])
2-element Vector{Int64}:
 1
 2
```
"""
setdiff(s::AbstractSet, itrs...) = setdiff!(copymutable(s), itrs...)
setdiff(s) = union(s)

"""
    setdiff!(s, itrs...)

Remove from set `s` (in-place) each element of each iterable from `itrs`.
Maintain order with arrays.

$(_DOCS_ALIASING_WARNING)

# Examples
```jldoctest
julia> a = Set([1, 3, 4, 5]);

julia> setdiff!(a, 1:2:6);

julia> a
Set{Int64} with 1 element:
  4
```
"""
function setdiff!(s::AbstractSet, itrs...)
    for x in itrs
        setdiff!(s, x)
    end
    return s
end
function setdiff!(s::AbstractSet, itr)
    for x in itr
        delete!(s, x)
    end
    return s
end


"""
    symdiff(s, itrs...)

Construct the symmetric difference of elements in the passed in sets.
When `s` is not an `AbstractSet`, the order is maintained.

See also [`symdiff!`](@ref), [`setdiff`](@ref), [`union`](@ref) and [`intersect`](@ref).

# Examples
```jldoctest
julia> symdiff([1,2,3], [3,4,5], [4,5,6])
3-element Vector{Int64}:
 1
 2
 6

julia> symdiff([1,2,1], [2, 1, 2])
Int64[]
```
"""
symdiff(s, sets...) = symdiff!(emptymutable(s, promote_eltype(s, sets...)), s, sets...)
symdiff(s) = symdiff!(copy(s))

"""
    symdiff!(s::Union{AbstractSet,AbstractVector}, itrs...)

Construct the symmetric difference of the passed in sets, and overwrite `s` with the result.
When `s` is an array, the order is maintained.
Note that in this case the multiplicity of elements matters.

$(_DOCS_ALIASING_WARNING)
"""
function symdiff!(s::AbstractSet, itrs...)
    for x in itrs
        symdiff!(s, x)
    end
    return s
end

symdiff!(s::AbstractSet, itr) = symdiff!(s::AbstractSet, Set(itr))

function symdiff!(s::AbstractSet, itr::AbstractSet)
    for x in itr
        x in s ? delete!(s, x) : push!(s, x)
    end
    return s
end

## non-strict subset comparison

const ⊆ = issubset
function ⊇ end
"""
    issubset(a, b) -> Bool
    ⊆(a, b) -> Bool
    ⊇(b, a) -> Bool

Determine whether every element of `a` is also in `b`, using [`in`](@ref).

See also [`⊊`](@ref), [`⊈`](@ref), [`∩`](@ref intersect), [`∪`](@ref union), [`contains`](@ref).

# Examples
```jldoctest
julia> issubset([1, 2], [1, 2, 3])
true

julia> [1, 2, 3] ⊆ [1, 2]
false

julia> [1, 2, 3] ⊇ [1, 2]
true
```
"""
issubset, ⊆, ⊇

const FASTIN_SET_THRESHOLD = 70

function issubset(a, b)
    if haslength(b) && (isa(a, AbstractSet) || !hasfastin(b))
        blen = length(b) # conditions above make this length computed only when needed
        # check a for too many unique elements
        if isa(a, AbstractSet) && length(a) > blen
            return false
        end
        # when `in` would be too slow and b is big enough, convert it to a Set
        # this threshold was empirically determined (cf. #26198)
        if !hasfastin(b) && blen > FASTIN_SET_THRESHOLD
            return issubset(a, Set(b))
        end
    end
    for elt in a
        elt in b || return false
    end
    return true
end

"""
    hasfastin(T)

Determine whether the computation `x ∈ collection` where `collection::T` can be considered
as a "fast" operation (typically constant or logarithmic complexity).
The definition `hasfastin(x) = hasfastin(typeof(x))` is provided for convenience so that instances
can be passed instead of types.
However the form that accepts a type argument should be defined for new types.
"""
hasfastin(::Type) = false
hasfastin(::Union{Type{<:AbstractSet},Type{<:AbstractDict},Type{<:AbstractRange}}) = true
hasfastin(x) = hasfastin(typeof(x))

⊇(a, b) = b ⊆ a

## strict subset comparison

function ⊊ end
function ⊋ end
"""
    ⊊(a, b) -> Bool
    ⊋(b, a) -> Bool

Determines if `a` is a subset of, but not equal to, `b`.

See also [`issubset`](@ref) (`⊆`), [`⊈`](@ref).

# Examples
```jldoctest
julia> (1, 2) ⊊ (1, 2, 3)
true

julia> (1, 2) ⊊ (1, 2)
false
```
"""
⊊, ⊋

⊊(a::AbstractSet, b::AbstractSet) = length(a) < length(b) && a ⊆ b
⊊(a::AbstractSet, b) = a ⊊ Set(b)
⊊(a, b::AbstractSet) = Set(a) ⊊ b
⊊(a, b) = Set(a) ⊊ Set(b)
⊋(a, b) = b ⊊ a

function ⊈ end
function ⊉ end
"""
    ⊈(a, b) -> Bool
    ⊉(b, a) -> Bool

Negation of `⊆` and `⊇`, i.e. checks that `a` is not a subset of `b`.

See also [`issubset`](@ref) (`⊆`), [`⊊`](@ref).

# Examples
```jldoctest
julia> (1, 2) ⊈ (2, 3)
true

julia> (1, 2) ⊈ (1, 2, 3)
false
```
"""
⊈, ⊉

⊈(a, b) = !⊆(a, b)
⊉(a, b) = b ⊈ a

## set equality comparison

"""
    issetequal(a, b) -> Bool

Determine whether `a` and `b` have the same elements. Equivalent
to `a ⊆ b && b ⊆ a` but more efficient when possible.

See also: [`isdisjoint`](@ref), [`union`](@ref).

# Examples
```jldoctest
julia> issetequal([1, 2], [1, 2, 3])
false

julia> issetequal([1, 2], [2, 1])
true
```
"""
issetequal(a::AbstractSet, b::AbstractSet) = a == b
issetequal(a::AbstractSet, b) = issetequal(a, Set(b))

function issetequal(a, b::AbstractSet)
    if haslength(a)
        # check b for too many unique elements
        length(a) < length(b) && return false
    end
    return issetequal(Set(a), b)
end

function issetequal(a, b)
    haslength(a) && return issetequal(a, Set(b))
    haslength(b) && return issetequal(b, Set(a))
    return issetequal(Set(a), Set(b))
end

## set disjoint comparison
"""
    isdisjoint(a, b) -> Bool

Determine whether the collections `a` and `b` are disjoint.
Equivalent to `isempty(a ∩ b)` but more efficient when possible.

See also: [`intersect`](@ref), [`isempty`](@ref), [`issetequal`](@ref).

!!! compat "Julia 1.5"
    This function requires at least Julia 1.5.

# Examples
```jldoctest
julia> isdisjoint([1, 2], [2, 3, 4])
false

julia> isdisjoint([3, 1], [2, 4])
true
```
"""
function isdisjoint(a, b)
    function _isdisjoint(a, b)
        hasfastin(b) && return !any(in(b), a)
        hasfastin(a) && return !any(in(a), b)
        haslength(b) && length(b) < FASTIN_SET_THRESHOLD &&
            return !any(in(b), a)
        return !any(in(Set(b)), a)
    end
    if haslength(a) && haslength(b) && length(b) < length(a)
        return _isdisjoint(b, a)
    end
    _isdisjoint(a, b)
end

function isdisjoint(a::AbstractRange{T}, b::AbstractRange{T}) where T
    (isempty(a) || isempty(b)) && return true
    fa, la = extrema(a)
    fb, lb = extrema(b)
    if (la < fb) | (lb < fa)
        return true
    else
        return _overlapping_range_isdisjoint(a, b)
    end
end

_overlapping_range_isdisjoint(a::AbstractRange{T}, b::AbstractRange{T}) where T = invoke(isdisjoint, Tuple{Any,Any}, a, b)

function _overlapping_range_isdisjoint(a::AbstractRange{T}, b::AbstractRange{T}) where T<:Integer
    if abs(step(a)) == abs(step(b))
        return mod(minimum(a), step(a)) != mod(minimum(b), step(a))
    else
        return invoke(isdisjoint, Tuple{Any,Any}, a, b)
    end
end

## partial ordering of sets by containment

==(a::AbstractSet, b::AbstractSet) = length(a) == length(b) && a ⊆ b
# convenience functions for AbstractSet
# (if needed, only their synonyms ⊊ and ⊆ must be specialized)
<( a::AbstractSet, b::AbstractSet) = a ⊊ b
<=(a::AbstractSet, b::AbstractSet) = a ⊆ b

## filtering sets

filter(pred, s::AbstractSet) = mapfilter(pred, push!, s, emptymutable(s))

# it must be safe to delete the current element while iterating over s:
unsafe_filter!(pred, s::AbstractSet) = mapfilter(!pred, delete!, s, s)

# TODO: delete mapfilter in favor of comprehensions/foldl/filter when competitive
function mapfilter(pred, f, itr, res)
    for x in itr
        pred(x) && f(res, x)
    end
    res
end
J   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/set.jl[      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
    Set{T} <: AbstractSet{T}

`Set`s are mutable containers that provide fast membership testing.

`Set`s have efficient implementations of set operations such as `in`, `union` and `intersect`.
Elements in a `Set` are unique, as determined by the elements' definition of `isequal`.
The order of elements in a `Set` is an implementation detail and cannot be relied on.

See also: [`AbstractSet`](@ref), [`BitSet`](@ref), [`Dict`](@ref),
[`push!`](@ref), [`empty!`](@ref), [`union!`](@ref), [`in`](@ref), [`isequal`](@ref)

# Examples
```jldoctest; filter = r"^  '.'"ma
julia> s = Set("aaBca")
Set{Char} with 3 elements:
  'a'
  'c'
  'B'

julia> push!(s, 'b')
Set{Char} with 4 elements:
  'a'
  'b'
  'B'
  'c'

julia> s = Set([NaN, 0.0, 1.0, 2.0]);

julia> -0.0 in s # isequal(0.0, -0.0) is false
false

julia> NaN in s # isequal(NaN, NaN) is true
true
```
"""
struct Set{T} <: AbstractSet{T}
    dict::Dict{T,Nothing}

    global _Set(dict::Dict{T,Nothing}) where {T} = new{T}(dict)
end

Set{T}() where {T} = _Set(Dict{T,Nothing}())
Set{T}(s::Set{T}) where {T} = _Set(Dict{T,Nothing}(s.dict))
Set{T}(itr) where {T} = union!(Set{T}(), itr)
Set() = Set{Any}()

function Set{T}(s::KeySet{T, <:Dict{T}}) where {T}
    d = s.dict
    slots = copy(d.slots)
    keys = copy(d.keys)
    vals = similar(d.vals, Nothing)
    _Set(Dict{T,Nothing}(slots, keys, vals, d.ndel, d.count, d.age, d.idxfloor, d.maxprobe))
end

Set(itr) = _Set(itr, IteratorEltype(itr))
_Set(itr, ::HasEltype) = Set{eltype(itr)}(itr)

function _Set(itr, ::EltypeUnknown)
    T = @default_eltype(itr)
    (isconcretetype(T) || T === Union{}) || return grow_to!(Set{T}(), itr)
    return Set{T}(itr)
end

empty(s::AbstractSet{T}, ::Type{U}=T) where {T,U} = Set{U}()

# return an empty set with eltype T, which is mutable (can be grown)
# by default, a Set is returned
emptymutable(s::AbstractSet{T}, ::Type{U}=T) where {T,U} = Set{U}()

_similar_for(c::AbstractSet, ::Type{T}, itr, isz, len) where {T} = empty(c, T)

function show(io::IO, s::Set)
    if isempty(s)
        if get(io, :typeinfo, Any) == typeof(s)
            print(io, "Set()")
        else
            show(io, typeof(s))
            print(io, "()")
        end
    else
        print(io, "Set(")
        show_vector(io, s)
        print(io, ')')
    end
end

isempty(s::Set) = isempty(s.dict)
length(s::Set)  = length(s.dict)
in(x, s::Set) = haskey(s.dict, x)

# This avoids hashing and probing twice and it works the same as
# in!(x, s::Set) = in(x, s) ? true : (push!(s, x); false)
function in!(x, s::Set)
    idx, sh = ht_keyindex2_shorthash!(s.dict, x)
    idx > 0 && return true
    _setindex!(s.dict, nothing, x, -idx, sh)
    return false
end

push!(s::Set, x) = (s.dict[x] = nothing; s)
pop!(s::Set, x) = (pop!(s.dict, x); x)
pop!(s::Set, x, default) = (x in s ? pop!(s, x) : default)

function pop!(s::Set)
    isempty(s) && throw(ArgumentError("set must be non-empty"))
    return pop!(s.dict)[1]
end

delete!(s::Set, x) = (delete!(s.dict, x); s)

copy(s::Set) = copymutable(s)

copymutable(s::Set{T}) where {T} = Set{T}(s)
# Set is the default mutable fall-back
copymutable(s::AbstractSet{T}) where {T} = Set{T}(s)

sizehint!(s::Set, newsz) = (sizehint!(s.dict, newsz); s)
empty!(s::Set) = (empty!(s.dict); s)
rehash!(s::Set) = (rehash!(s.dict); s)

iterate(s::Set, i...)       = iterate(KeySet(s.dict), i...)

# In case the size(s) is smaller than size(t) its more efficient to iterate through
# elements of s instead and only delete the ones also contained in t.
# The threshold for this decision boils down to a tradeoff between
# size(s) * cost(in() + delete!()) ≶ size(t) * cost(delete!())
# Empirical observations on Ints point towards a threshold of 0.8.
# To be on the safe side (e.g. cost(in) >>> cost(delete!) ) a
# conservative threshold of 0.5 was chosen.
function setdiff!(s::Set, t::Set)
    if 2 * length(s) < length(t)
        for x in s
            x in t && delete!(s, x)
        end
    else
        for x in t
            delete!(s, x)
        end
    end
    return s
end

"""
    unique(itr)

Return an array containing only the unique elements of collection `itr`,
as determined by [`isequal`](@ref), in the order that the first of each
set of equivalent elements originally appears. The element type of the
input is preserved.

See also: [`unique!`](@ref), [`allunique`](@ref), [`allequal`](@ref).

# Examples
```jldoctest
julia> unique([1, 2, 6, 2])
3-element Vector{Int64}:
 1
 2
 6

julia> unique(Real[1, 1.0, 2])
2-element Vector{Real}:
 1
 2
```
"""
function unique(itr)
    if isa(IteratorEltype(itr), HasEltype)
        T = eltype(itr)
        out = Vector{T}()
        seen = Set{T}()
        for x in itr
            !in!(x, seen) && push!(out, x)
        end
        return out
    end
    T = @default_eltype(itr)
    y = iterate(itr)
    y === nothing && return T[]
    x, i = y
    S = typeof(x)
    R = isconcretetype(T) ? T : S
    return _unique_from(itr, R[x], Set{R}((x,)), i)
end

_unique_from(itr, out, seen, i) = unique_from(itr, out, seen, i)
@inline function unique_from(itr, out::Vector{T}, seen, i) where T
    while true
        y = iterate(itr, i)
        y === nothing && break
        x, i = y
        S = typeof(x)
        if !(S === T || S <: T)
            R = promote_typejoin(S, T)
            seenR = convert(Set{R}, seen)
            outR = convert(Vector{R}, out)
            !in!(x, seenR) && push!(outR, x)
            return _unique_from(itr, outR, seenR, i)
        end
        !in!(x, seen) && push!(out, x)
    end
    return out
end

unique(r::AbstractRange) = allunique(r) ? r : oftype(r, r[begin:begin])

"""
    unique(f, itr)

Return an array containing one value from `itr` for each unique value produced by `f`
applied to elements of `itr`.

# Examples
```jldoctest
julia> unique(x -> x^2, [1, -1, 3, -3, 4])
3-element Vector{Int64}:
 1
 3
 4
```
This functionality can also be used to extract the *indices* of the first
occurrences of unique elements in an array:
```jldoctest
julia> a = [3.1, 4.2, 5.3, 3.1, 3.1, 3.1, 4.2, 1.7];

julia> i = unique(i -> a[i], eachindex(a))
4-element Vector{Int64}:
 1
 2
 3
 8

julia> a[i]
4-element Vector{Float64}:
 3.1
 4.2
 5.3
 1.7

julia> a[i] == unique(a)
true
```
"""
function unique(f, C; seen::Union{Nothing,Set}=nothing)
    out = Vector{eltype(C)}()
    if seen !== nothing
        for x in C
            !in!(f(x), seen) && push!(out, x)
        end
        return out
    end

    s = iterate(C)
    if s === nothing
        return out
    end
    (x, i) = s
    y = f(x)
    seen = Set{typeof(y)}()
    push!(seen, y)
    push!(out, x)

    return _unique!(f, out, C, seen, i)
end

function _unique!(f, out::AbstractVector, C, seen::Set, i)
    s = iterate(C, i)
    while s !== nothing
        (x, i) = s
        y = f(x)
        if y ∉ seen
            push!(out, x)
            if y isa eltype(seen)
                push!(seen, y)
            else
                seen2 = convert(Set{promote_typejoin(eltype(seen), typeof(y))}, seen)
                push!(seen2, y)
                return _unique!(f, out, C, seen2, i)
            end
        end
        s = iterate(C, i)
    end

    return out
end

"""
    unique!(f, A::AbstractVector)

Selects one value from `A` for each unique value produced by `f` applied to
elements of `A`, then return the modified A.

!!! compat "Julia 1.1"
    This method is available as of Julia 1.1.

# Examples
```jldoctest
julia> unique!(x -> x^2, [1, -1, 3, -3, 4])
3-element Vector{Int64}:
 1
 3
 4

julia> unique!(n -> n%3, [5, 1, 8, 9, 3, 4, 10, 7, 2, 6])
3-element Vector{Int64}:
 5
 1
 9

julia> unique!(iseven, [2, 3, 5, 7, 9])
2-element Vector{Int64}:
 2
 3
```
"""
function unique!(f, A::AbstractVector; seen::Union{Nothing,Set}=nothing)
    if length(A) <= 1
        return A
    end

    i = firstindex(A)::Int
    x = @inbounds A[i]
    y = f(x)
    if seen === nothing
        seen = Set{typeof(y)}()
    end
    push!(seen, y)
    return _unique!(f, A, seen, i, i+1)
end

function _unique!(f, A::AbstractVector, seen::Set, current::Integer, i::Integer)
    while i <= lastindex(A)
        x = @inbounds A[i]
        y = f(x)
        if y ∉ seen
            current += 1
            @inbounds A[current] = x
            if y isa eltype(seen)
                push!(seen, y)
            else
                seen2 = convert(Set{promote_typejoin(eltype(seen), typeof(y))}, seen)
                push!(seen2, y)
                return _unique!(f, A, seen2, current, i+1)
            end
        end
        i += 1
    end
    return resize!(A, current - firstindex(A)::Int + 1)::typeof(A)
end


# If A is not grouped, then we will need to keep track of all of the elements that we have
# seen so far.
_unique!(A::AbstractVector) = unique!(identity, A::AbstractVector)

# If A is grouped, so that each unique element is in a contiguous group, then we only
# need to keep track of one element at a time. We replace the elements of A with the
# unique elements that we see in the order that we see them. Once we have iterated
# through A, we resize A based on the number of unique elements that we see.
function _groupedunique!(A::AbstractVector)
    isempty(A) && return A
    idxs = eachindex(A)
    y = first(A)
    # We always keep the first element
    T = NTuple{2,Any} # just to eliminate `iterate(idxs)::Nothing` candidate
    it = iterate(idxs, (iterate(idxs)::T)[2])
    count = 1
    for x in Iterators.drop(A, 1)
        if !isequal(x, y)
            it = it::T
            y = A[it[1]] = x
            count += 1
            it = iterate(idxs, it[2])
        end
    end
    resize!(A, count)::typeof(A)
end

"""
    unique!(A::AbstractVector)

Remove duplicate items as determined by [`isequal`](@ref), then return the modified `A`.
`unique!` will return the elements of `A` in the order that they occur. If you do not care
about the order of the returned data, then calling `(sort!(A); unique!(A))` will be much
more efficient as long as the elements of `A` can be sorted.

# Examples
```jldoctest
julia> unique!([1, 1, 1])
1-element Vector{Int64}:
 1

julia> A = [7, 3, 2, 3, 7, 5];

julia> unique!(A)
4-element Vector{Int64}:
 7
 3
 2
 5

julia> B = [7, 6, 42, 6, 7, 42];

julia> sort!(B);  # unique! is able to process sorted data much more efficiently.

julia> unique!(B)
3-element Vector{Int64}:
  6
  7
 42
```
"""
function unique!(itr)
    if isa(itr, AbstractVector)
        if OrderStyle(eltype(itr)) === Ordered()
            (issorted(itr) || issorted(itr, rev=true)) && return _groupedunique!(itr)
        end
    end
    isempty(itr) && return itr
    return _unique!(itr)
end

"""
    allunique(itr) -> Bool

Return `true` if all values from `itr` are distinct when compared with [`isequal`](@ref).

See also: [`unique`](@ref), [`issorted`](@ref), [`allequal`](@ref).

# Examples
```jldoctest
julia> allunique([1, 2, 3])
true

julia> allunique([1, 2, 1, 2])
false

julia> allunique(Real[1, 1.0, 2])
false

julia> allunique([NaN, 2.0, NaN, 4.0])
false
```
"""
function allunique(C)
    if haslength(C)
        length(C) < 2 && return true
        length(C) < 32 && return _indexed_allunique(collect(C))
    end
    return _hashed_allunique(C)
end

function _hashed_allunique(C)
    seen = Set{eltype(C)}()
    x = iterate(C)
    if haslength(C) && length(C) > 1000
        for i in OneTo(1000)
            v, s = something(x)
            in!(v, seen) && return false
            x = iterate(C, s)
        end
        sizehint!(seen, length(C))
    end
    while x !== nothing
        v, s = x
        in!(v, seen) && return false
        x = iterate(C, s)
    end
    return true
end

allunique(::Union{AbstractSet,AbstractDict}) = true

allunique(r::AbstractRange) = !iszero(step(r)) || length(r) <= 1

allunique(A::StridedArray) = length(A) < 32 ? _indexed_allunique(A) : _hashed_allunique(A)

function _indexed_allunique(A)
    length(A) < 2 && return true
    iter = eachindex(A)
    I = iterate(iter)
    while I !== nothing
        i, s = I
        a = A[i]
        for j in Iterators.rest(iter, s)
            isequal(a, @inbounds A[j]) && return false
        end
        I = iterate(iter, s)
    end
    return true
end

function allunique(t::Tuple)
    length(t) < 32 || return _hashed_allunique(t)
    a = afoldl(true, tail(t)...) do b, x
        b & !isequal(first(t), x)
    end
    return a && allunique(tail(t))
end
allunique(t::Tuple{}) = true

"""
    allequal(itr) -> Bool

Return `true` if all values from `itr` are equal when compared with [`isequal`](@ref).

See also: [`unique`](@ref), [`allunique`](@ref).

!!! compat "Julia 1.8"
    The `allequal` function requires at least Julia 1.8.

# Examples
```jldoctest
julia> allequal([])
true

julia> allequal([1])
true

julia> allequal([1, 1])
true

julia> allequal([1, 2])
false

julia> allequal(Dict(:a => 1, :b => 1))
false
```
"""
allequal(itr) = isempty(itr) ? true : all(isequal(first(itr)), itr)

allequal(c::Union{AbstractSet,AbstractDict}) = length(c) <= 1

allequal(r::AbstractRange) = iszero(step(r)) || length(r) <= 1

filter!(f, s::Set) = unsafe_filter!(f, s)

const hashs_seed = UInt === UInt64 ? 0x852ada37cfe8e0ce : 0xcfe8e0ce
function hash(s::AbstractSet, h::UInt)
    hv = hashs_seed
    for x in s
        hv ⊻= hash(x)
    end
    hash(hv, h)
end

convert(::Type{T}, s::T) where {T<:AbstractSet} = s
convert(::Type{T}, s::AbstractSet) where {T<:AbstractSet} = T(s)::T


## replace/replace! ##

function check_count(count::Integer)
    count < 0 && throw(DomainError(count, "`count` must not be negative (got $count)"))
    return min(count, typemax(Int)) % Int
end

# TODO: use copy!, which is currently unavailable from here since it is defined in Future
_copy_oftype(x, ::Type{T}) where {T} = copyto!(similar(x, T), x)
# TODO: use similar() once deprecation is removed and it preserves keys
_copy_oftype(x::AbstractDict, ::Type{Pair{K,V}}) where {K,V} = merge!(empty(x, K, V), x)
_copy_oftype(x::AbstractSet, ::Type{T}) where {T} = union!(empty(x, T), x)

_copy_oftype(x::AbstractArray{T}, ::Type{T}) where {T} = copy(x)
_copy_oftype(x::AbstractDict{K,V}, ::Type{Pair{K,V}}) where {K,V} = copy(x)
_copy_oftype(x::AbstractSet{T}, ::Type{T}) where {T} = copy(x)

_similar_or_copy(x::Any) = similar(x)
_similar_or_copy(x::Any, ::Type{T}) where {T} = similar(x, T)
# Make a copy on construction since it is faster than inserting elements separately
_similar_or_copy(x::Union{AbstractDict,AbstractSet}) = copy(x)
_similar_or_copy(x::Union{AbstractDict,AbstractSet}, ::Type{T}) where {T} = _copy_oftype(x, T)

# to make replace/replace! work for a new container type Cont, only
# _replace!(new::Callable, res::Cont, A::Cont, count::Int)
# has to be implemented

"""
    replace!(A, old_new::Pair...; [count::Integer])

For each pair `old=>new` in `old_new`, replace all occurrences
of `old` in collection `A` by `new`.
Equality is determined using [`isequal`](@ref).
If `count` is specified, then replace at most `count` occurrences in total.
See also [`replace`](@ref replace(A, old_new::Pair...)).

# Examples
```jldoctest
julia> replace!([1, 2, 1, 3], 1=>0, 2=>4, count=2)
4-element Vector{Int64}:
 0
 4
 1
 3

julia> replace!(Set([1, 2, 3]), 1=>0)
Set{Int64} with 3 elements:
  0
  2
  3
```
"""
replace!(A, old_new::Pair...; count::Integer=typemax(Int)) =
    replace_pairs!(A, A, check_count(count), old_new)

function replace_pairs!(res, A, count::Int, old_new::Tuple{Vararg{Pair}})
    @inline function new(x)
        for o_n in old_new
            isequal(first(o_n), x) && return last(o_n)
        end
        return x # no replace
    end
    _replace!(new, res, A, count)
end

"""
    replace!(new::Union{Function, Type}, A; [count::Integer])

Replace each element `x` in collection `A` by `new(x)`.
If `count` is specified, then replace at most `count` values in total
(replacements being defined as `new(x) !== x`).

# Examples
```jldoctest
julia> replace!(x -> isodd(x) ? 2x : x, [1, 2, 3, 4])
4-element Vector{Int64}:
 2
 2
 6
 4

julia> replace!(Dict(1=>2, 3=>4)) do kv
           first(kv) < 3 ? first(kv)=>3 : kv
       end
Dict{Int64, Int64} with 2 entries:
  3 => 4
  1 => 3

julia> replace!(x->2x, Set([3, 6]))
Set{Int64} with 2 elements:
  6
  12
```
"""
replace!(new::Callable, A; count::Integer=typemax(Int)) =
    _replace!(new, A, A, check_count(count))

"""
    replace(A, old_new::Pair...; [count::Integer])

Return a copy of collection `A` where, for each pair `old=>new` in `old_new`,
all occurrences of `old` are replaced by `new`.
Equality is determined using [`isequal`](@ref).
If `count` is specified, then replace at most `count` occurrences in total.

The element type of the result is chosen using promotion (see [`promote_type`](@ref))
based on the element type of `A` and on the types of the `new` values in pairs.
If `count` is omitted and the element type of `A` is a `Union`, the element type
of the result will not include singleton types which are replaced with values of
a different type: for example, `Union{T,Missing}` will become `T` if `missing` is
replaced.

See also [`replace!`](@ref), [`splice!`](@ref), [`delete!`](@ref), [`insert!`](@ref).

!!! compat "Julia 1.7"
    Version 1.7 is required to replace elements of a `Tuple`.

# Examples
```jldoctest
julia> replace([1, 2, 1, 3], 1=>0, 2=>4, count=2)
4-element Vector{Int64}:
 0
 4
 1
 3

julia> replace([1, missing], missing=>0)
2-element Vector{Int64}:
 1
 0
```
"""
function replace(A, old_new::Pair...; count::Union{Integer,Nothing}=nothing)
    V = promote_valuetype(old_new...)
    if count isa Nothing
        T = promote_type(subtract_singletontype(eltype(A), old_new...), V)
        replace_pairs!(_similar_or_copy(A, T), A, typemax(Int), old_new)
    else
        U = promote_type(eltype(A), V)
        replace_pairs!(_similar_or_copy(A, U), A, check_count(count), old_new)
    end
end

promote_valuetype(x::Pair{K, V}) where {K, V} = V
promote_valuetype(x::Pair{K, V}, y::Pair...) where {K, V} =
    promote_type(V, promote_valuetype(y...))

# Subtract singleton types which are going to be replaced
function subtract_singletontype(::Type{T}, x::Pair{K}) where {T, K}
    if issingletontype(K)
        typesplit(T, K)
    else
        T
    end
end
subtract_singletontype(::Type{T}, x::Pair{K}, y::Pair...) where {T, K} =
    subtract_singletontype(subtract_singletontype(T, y...), x)

"""
    replace(new::Union{Function, Type}, A; [count::Integer])

Return a copy of `A` where each value `x` in `A` is replaced by `new(x)`.
If `count` is specified, then replace at most `count` values in total
(replacements being defined as `new(x) !== x`).

!!! compat "Julia 1.7"
    Version 1.7 is required to replace elements of a `Tuple`.

# Examples
```jldoctest
julia> replace(x -> isodd(x) ? 2x : x, [1, 2, 3, 4])
4-element Vector{Int64}:
 2
 2
 6
 4

julia> replace(Dict(1=>2, 3=>4)) do kv
           first(kv) < 3 ? first(kv)=>3 : kv
       end
Dict{Int64, Int64} with 2 entries:
  3 => 4
  1 => 3
```
"""
replace(new::Callable, A; count::Integer=typemax(Int)) =
    _replace!(new, _similar_or_copy(A), A, check_count(count))

# Handle ambiguities
replace!(a::Callable, b::Pair; count::Integer=-1) = throw(MethodError(replace!, (a, b)))
replace!(a::Callable, b::Pair, c::Pair; count::Integer=-1) = throw(MethodError(replace!, (a, b, c)))
replace(a::Callable, b::Pair; count::Integer=-1) = throw(MethodError(replace, (a, b)))
replace(a::Callable, b::Pair, c::Pair; count::Integer=-1) = throw(MethodError(replace, (a, b, c)))

### replace! for AbstractDict/AbstractSet

askey(k, ::AbstractDict) = k.first
askey(k, ::AbstractSet) = k

function _replace!(new::Callable, res::Union{AbstractDict,AbstractSet},
                   A::Union{AbstractDict,AbstractSet}, count::Int)
    @assert res isa AbstractDict && A isa AbstractDict ||
        res isa AbstractSet && A isa AbstractSet
    count == 0 && return res
    c = 0
    if res === A # cannot replace elements while iterating over A
        repl = Pair{eltype(A),eltype(A)}[]
        for x in A
            y = new(x)
            if x !== y
                push!(repl, x => y)
                c += 1
                c == count && break
            end
        end
        for oldnew in repl
            pop!(res, askey(first(oldnew), res))
        end
        for oldnew in repl
            push!(res, last(oldnew))
        end
    else
        for x in A
            y = new(x)
            if x !== y
                pop!(res, askey(x, res))
                push!(res, y)
                c += 1
                c == count && break
            end
        end
    end
    res
end

### replace! for AbstractArray

function _replace!(new::Callable, res::AbstractArray, A::AbstractArray, count::Int)
    c = 0
    if count >= length(A) # simpler loop allows for SIMD
        if res === A # for optimization only
            for i in eachindex(A)
                @inbounds Ai = A[i]
                y = new(Ai)
                @inbounds A[i] = y
            end
        else
            for i in eachindex(A)
                @inbounds Ai = A[i]
                y = new(Ai)
                @inbounds res[i] = y
            end
        end
    else
        for i in eachindex(A)
            @inbounds Ai = A[i]
            if c < count
                y = new(Ai)
                @inbounds res[i] = y
                c += (Ai !== y)
            else
                @inbounds res[i] = Ai
            end
        end
    end
    res
end

### specialization for Dict / Set

function _replace!(new::Callable, t::Dict{K,V}, A::AbstractDict, count::Int) where {K,V}
    # we ignore A, which is supposed to be equal to the destination t,
    # as it can generally be faster to just replace inline
    count == 0 && return t
    c = 0
    news = Pair{K,V}[]
    i = skip_deleted_floor!(t)
    @inbounds while i != 0
        k1, v1 = t.keys[i], t.vals[i]
        x1 = Pair{K,V}(k1, v1)
        x2 = new(x1)
        if x1 !== x2
            k2, v2 = first(x2), last(x2)
            if isequal(k1, k2)
                t.keys[i] = k2
                t.vals[i] = v2
                t.age += 1
            else
                _delete!(t, i)
                push!(news, x2)
            end
            c += 1
            c == count && break
        end
        i = i == typemax(Int) ? 0 : skip_deleted(t, i+1)
    end
    for n in news
        push!(t, n)
    end
    t
end

function _replace!(new::Callable, t::Set{T}, ::AbstractSet, count::Int) where {T}
    _replace!(t.dict, t.dict, count) do kv
        k = first(kv)
        k2 = new(k)
        k2 === k ? kv : k2 => nothing
    end
    t
end

### replace for tuples

function _replace(f::Callable, t::Tuple, count::Int)
    if count == 0 || isempty(t)
        t
    else
        x = f(t[1])
        (x, _replace(f, tail(t), count - !==(x, t[1]))...)
    end
end

replace(f::Callable, t::Tuple; count::Integer=typemax(Int)) =
    _replace(f, t, check_count(count))

function _replace(t::Tuple, count::Int, old_new::Tuple{Vararg{Pair}})
    _replace(t, count) do x
        @inline
        for o_n in old_new
            isequal(first(o_n), x) && return last(o_n)
        end
        return x
    end
end

replace(t::Tuple, old_new::Pair...; count::Integer=typemax(Int)) =
    _replace(t, check_count(count), old_new)
K   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/char.jl�0      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
The `AbstractChar` type is the supertype of all character implementations
in Julia. A character represents a Unicode code point, and can be converted
to an integer via the [`codepoint`](@ref) function in order to obtain the
numerical value of the code point, or constructed from the same integer.
These numerical values determine how characters are compared with `<` and `==`,
for example.  New `T <: AbstractChar` types should define a `codepoint(::T)`
method and a `T(::UInt32)` constructor, at minimum.

A given `AbstractChar` subtype may be capable of representing only a subset
of Unicode, in which case conversion from an unsupported `UInt32` value
may throw an error. Conversely, the built-in [`Char`](@ref) type represents
a *superset* of Unicode (in order to losslessly encode invalid byte streams),
in which case conversion of a non-Unicode value *to* `UInt32` throws an error.
The [`isvalid`](@ref) function can be used to check which codepoints are
representable in a given `AbstractChar` type.

Internally, an `AbstractChar` type may use a variety of encodings.  Conversion
via `codepoint(char)` will not reveal this encoding because it always returns the
Unicode value of the character. `print(io, c)` of any `c::AbstractChar`
produces an encoding determined by `io` (UTF-8 for all built-in `IO`
types), via conversion to `Char` if necessary.

`write(io, c)`, in contrast, may emit an encoding depending on
`typeof(c)`, and `read(io, typeof(c))` should read the same encoding as `write`.
New `AbstractChar` types must provide their own implementations of
`write` and `read`.
"""
AbstractChar

"""
    Char(c::Union{Number,AbstractChar})

`Char` is a 32-bit [`AbstractChar`](@ref) type that is the default representation
of characters in Julia. `Char` is the type used for character literals like `'x'`
and it is also the element type of [`String`](@ref).

In order to losslessly represent arbitrary byte streams stored in a `String`,
a `Char` value may store information that cannot be converted to a Unicode
codepoint — converting such a `Char` to `UInt32` will throw an error.
The [`isvalid(c::Char)`](@ref) function can be used to query whether `c`
represents a valid Unicode character.
"""
Char

@constprop :aggressive (::Type{T})(x::Number) where {T<:AbstractChar} = T(UInt32(x))
@constprop :aggressive AbstractChar(x::Number) = Char(x)
@constprop :aggressive (::Type{T})(x::AbstractChar) where {T<:Union{Number,AbstractChar}} = T(codepoint(x))
@constprop :aggressive (::Type{T})(x::AbstractChar) where {T<:Union{Int32,Int64}} = codepoint(x) % T
(::Type{T})(x::T) where {T<:AbstractChar} = x

"""
    ncodeunits(c::Char) -> Int

Return the number of code units required to encode a character as UTF-8.
This is the number of bytes which will be printed if the character is written
to an output stream, or `ncodeunits(string(c))` but computed efficiently.

!!! compat "Julia 1.1"
    This method requires at least Julia 1.1. In Julia 1.0 consider
    using `ncodeunits(string(c))`.
"""
ncodeunits(c::Char) = write(devnull, c) # this is surprisingly efficient

"""
    codepoint(c::AbstractChar) -> Integer

Return the Unicode codepoint (an unsigned integer) corresponding
to the character `c` (or throw an exception if `c` does not represent
a valid character). For `Char`, this is a `UInt32` value, but
`AbstractChar` types that represent only a subset of Unicode may
return a different-sized integer (e.g. `UInt8`).
"""
function codepoint end

@constprop :aggressive codepoint(c::Char) = UInt32(c)

struct InvalidCharError{T<:AbstractChar} <: Exception
    char::T
end
struct CodePointError{T<:Integer} <: Exception
    code::T
end
@noinline throw_invalid_char(c::AbstractChar) = throw(InvalidCharError(c))
@noinline throw_code_point_err(u::Integer) = throw(CodePointError(u))

function ismalformed(c::Char)
    u = bitcast(UInt32, c)
    l1 = leading_ones(u) << 3
    t0 = trailing_zeros(u) & 56
    (l1 == 8) | (l1 + t0 > 32) |
    (((u & 0x00c0c0c0) ⊻ 0x00808080) >> t0 != 0)
end

@inline is_overlong_enc(u::UInt32) = (u >> 24 == 0xc0) | (u >> 24 == 0xc1) | (u >> 21 == 0x0704) | (u >> 20 == 0x0f08)

function isoverlong(c::Char)
    u = bitcast(UInt32, c)
    is_overlong_enc(u)
end

# fallback: other AbstractChar types, by default, are assumed
#           not to support malformed or overlong encodings.

"""
    ismalformed(c::AbstractChar) -> Bool

Return `true` if `c` represents malformed (non-Unicode) data according to the
encoding used by `c`. Defaults to `false` for non-`Char` types.

See also [`show_invalid`](@ref).
"""
ismalformed(c::AbstractChar) = false

"""
    isoverlong(c::AbstractChar) -> Bool

Return `true` if `c` represents an overlong UTF-8 sequence. Defaults
to `false` for non-`Char` types.

See also [`decode_overlong`](@ref) and [`show_invalid`](@ref).
"""
isoverlong(c::AbstractChar) = false

@constprop :aggressive function UInt32(c::Char)
    # TODO: use optimized inline LLVM
    u = bitcast(UInt32, c)
    u < 0x80000000 && return u >> 24
    l1 = leading_ones(u)
    t0 = trailing_zeros(u) & 56
    (l1 == 1) | (8l1 + t0 > 32) |
    ((((u & 0x00c0c0c0) ⊻ 0x00808080) >> t0 != 0) | is_overlong_enc(u)) &&
        throw_invalid_char(c)
    u &= 0xffffffff >> l1
    u >>= t0
    ((u & 0x0000007f) >> 0) | ((u & 0x00007f00) >> 2) |
    ((u & 0x007f0000) >> 4) | ((u & 0x7f000000) >> 6)
end

"""
    decode_overlong(c::AbstractChar) -> Integer

When [`isoverlong(c)`](@ref) is `true`, `decode_overlong(c)` returns
the Unicode codepoint value of `c`. `AbstractChar` implementations
that support overlong encodings should implement `Base.decode_overlong`.
"""
function decode_overlong end

@constprop :aggressive function decode_overlong(c::Char)
    u = bitcast(UInt32, c)
    l1 = leading_ones(u)
    t0 = trailing_zeros(u) & 56
    u &= 0xffffffff >> l1
    u >>= t0
    ((u & 0x0000007f) >> 0) | ((u & 0x00007f00) >> 2) |
    ((u & 0x007f0000) >> 4) | ((u & 0x7f000000) >> 6)
end

@constprop :aggressive function Char(u::UInt32)
    u < 0x80 && return bitcast(Char, u << 24)
    u < 0x00200000 || throw_code_point_err(u)
    c = ((u << 0) & 0x0000003f) | ((u << 2) & 0x00003f00) |
        ((u << 4) & 0x003f0000) | ((u << 6) & 0x3f000000)
    c = u < 0x00000800 ? (c << 16) | 0xc0800000 :
        u < 0x00010000 ? (c << 08) | 0xe0808000 :
                         (c << 00) | 0xf0808080
    bitcast(Char, c)
end

@constprop :aggressive @noinline UInt32_cold(c::Char) = UInt32(c)
@constprop :aggressive function (T::Union{Type{Int8},Type{UInt8}})(c::Char)
    i = bitcast(Int32, c)
    i ≥ 0 ? ((i >>> 24) % T) : T(UInt32_cold(c))
end

@constprop :aggressive @noinline Char_cold(b::UInt32) = Char(b)
@constprop :aggressive function Char(b::Union{Int8,UInt8})
    0 ≤ b ≤ 0x7f ? bitcast(Char, (b % UInt32) << 24) : Char_cold(UInt32(b))
end

convert(::Type{AbstractChar}, x::Number) = Char(x) # default to Char
convert(::Type{T}, x::Number) where {T<:AbstractChar} = T(x)::T
convert(::Type{T}, x::AbstractChar) where {T<:Number} = T(x)::T
convert(::Type{T}, c::AbstractChar) where {T<:AbstractChar} = T(c)::T
convert(::Type{T}, c::T) where {T<:AbstractChar} = c

rem(x::AbstractChar, ::Type{T}) where {T<:Number} = rem(codepoint(x), T)

typemax(::Type{Char}) = bitcast(Char, typemax(UInt32))
typemin(::Type{Char}) = bitcast(Char, typemin(UInt32))

size(c::AbstractChar) = ()
size(c::AbstractChar, d::Integer) = d < 1 ? throw(BoundsError()) : 1
ndims(c::AbstractChar) = 0
ndims(::Type{<:AbstractChar}) = 0
length(c::AbstractChar) = 1
IteratorSize(::Type{Char}) = HasShape{0}()
firstindex(c::AbstractChar) = 1
lastindex(c::AbstractChar) = 1
getindex(c::AbstractChar) = c
getindex(c::AbstractChar, i::Integer) = i == 1 ? c : throw(BoundsError())
getindex(c::AbstractChar, I::Integer...) = all(x -> x == 1, I) ? c : throw(BoundsError())
first(c::AbstractChar) = c
last(c::AbstractChar) = c
eltype(::Type{T}) where {T<:AbstractChar} = T

iterate(c::AbstractChar, done=false) = done ? nothing : (c, true)
isempty(c::AbstractChar) = false
in(x::AbstractChar, y::AbstractChar) = x == y

==(x::Char, y::Char) = bitcast(UInt32, x) == bitcast(UInt32, y)
isless(x::Char, y::Char) = bitcast(UInt32, x) < bitcast(UInt32, y)
hash(x::Char, h::UInt) =
    hash_uint64(((bitcast(UInt32, x) + UInt64(0xd4d64234)) << 32) ⊻ UInt64(h))

first_utf8_byte(c::Char) = (bitcast(UInt32, c) >> 24) % UInt8

# fallbacks:
isless(x::AbstractChar, y::AbstractChar) = isless(Char(x), Char(y))
==(x::AbstractChar, y::AbstractChar) = Char(x) == Char(y)
hash(x::AbstractChar, h::UInt) = hash(Char(x), h)
widen(::Type{T}) where {T<:AbstractChar} = T

@inline -(x::AbstractChar, y::AbstractChar) = Int(x) - Int(y)
@inline function -(x::T, y::Integer) where {T<:AbstractChar}
    if x isa Char
        u = Int32((bitcast(UInt32, x) >> 24) % Int8)
        if u >= 0 # inline the runtime fast path
            z = u - y
            return 0 <= z < 0x80 ? bitcast(Char, (z % UInt32) << 24) : Char(UInt32(z))
        end
    end
    return T(Int32(x) - Int32(y))
end
@inline function +(x::T, y::Integer) where {T<:AbstractChar}
    if x isa Char
        u = Int32((bitcast(UInt32, x) >> 24) % Int8)
        if u >= 0 # inline the runtime fast path
            z = u + y
            return 0 <= z < 0x80 ? bitcast(Char, (z % UInt32) << 24) : Char(UInt32(z))
        end
    end
    return T(Int32(x) + Int32(y))
end
@inline +(x::Integer, y::AbstractChar) = y + x

# `print` should output UTF-8 by default for all AbstractChar types.
# (Packages may implement other IO subtypes to specify different encodings.)
# In contrast, `write(io, c)` outputs a `c` in an encoding determined by typeof(c).
print(io::IO, c::Char) = (write(io, c); nothing)
print(io::IO, c::AbstractChar) = print(io, Char(c)) # fallback: convert to output UTF-8

const hex_chars = UInt8['0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
                        'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i',
                        'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r',
                        's', 't', 'u', 'v', 'w', 'x', 'y', 'z']

function show_invalid(io::IO, c::Char)
    write(io, 0x27)
    u = bitcast(UInt32, c)
    while true
        a = hex_chars[((u >> 28) & 0xf) + 1]
        b = hex_chars[((u >> 24) & 0xf) + 1]
        write(io, 0x5c, UInt8('x'), a, b)
        (u <<= 8) == 0 && break
    end
    write(io, 0x27)
end

"""
    show_invalid(io::IO, c::AbstractChar)

Called by `show(io, c)` when [`isoverlong(c)`](@ref) or
[`ismalformed(c)`](@ref) return `true`.   Subclasses
of `AbstractChar` should define `Base.show_invalid` methods
if they support storing invalid character data.
"""
show_invalid

# show c to io, assuming UTF-8 encoded output
function show(io::IO, c::AbstractChar)
    if c <= '\\'
        b = c == '\0' ? 0x30 :
            c == '\a' ? 0x61 :
            c == '\b' ? 0x62 :
            c == '\t' ? 0x74 :
            c == '\n' ? 0x6e :
            c == '\v' ? 0x76 :
            c == '\f' ? 0x66 :
            c == '\r' ? 0x72 :
            c == '\e' ? 0x65 :
            c == '\'' ? 0x27 :
            c == '\\' ? 0x5c : 0xff
        if b != 0xff
            write(io, 0x27, 0x5c, b, 0x27)
            return
        end
    end
    if isoverlong(c) || ismalformed(c)
        show_invalid(io, c)
    elseif isprint(c)
        write(io, 0x27)
        print(io, c) # use print, not write, to use UTF-8 for any AbstractChar
        write(io, 0x27)
    else # unprintable, well-formed, non-overlong Unicode
        u = codepoint(c)
        write(io, 0x27, 0x5c, u <= 0x7f ? 0x78 : u <= 0xffff ? 0x75 : 0x55)
        d = max(2, 8 - (leading_zeros(u) >> 2))
        while 0 < d
            write(io, hex_chars[((u >> ((d -= 1) << 2)) & 0xf) + 1])
        end
        write(io, 0x27)
    end
    return
end

function show(io::IO, ::MIME"text/plain", c::T) where {T<:AbstractChar}
    show(io, c)
    get(io, :compact, false)::Bool && return
    if !ismalformed(c)
        print(io, ": ")
        if isoverlong(c)
            print(io, "[overlong] ")
            u = decode_overlong(c)
            c = T(u)
        else
            u = codepoint(c)
        end
        h = uppercase(string(u, base = 16, pad = 4))
        print(io, (isascii(c) ? "ASCII/" : ""), "Unicode U+", h)
    else
        print(io, ": Malformed UTF-8")
    end
    abr = Unicode.category_abbrev(c)
    str = Unicode.category_string(c)
    print(io, " (category ", abr, ": ", str, ")")
end
T   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/strings/basic.jl'b      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
The `AbstractString` type is the supertype of all string implementations in
Julia. Strings are encodings of sequences of [Unicode](https://unicode.org/)
code points as represented by the `AbstractChar` type. Julia makes a few assumptions
about strings:

* Strings are encoded in terms of fixed-size "code units"
  * Code units can be extracted with `codeunit(s, i)`
  * The first code unit has index `1`
  * The last code unit has index `ncodeunits(s)`
  * Any index `i` such that `1 ≤ i ≤ ncodeunits(s)` is in bounds
* String indexing is done in terms of these code units:
  * Characters are extracted by `s[i]` with a valid string index `i`
  * Each `AbstractChar` in a string is encoded by one or more code units
  * Only the index of the first code unit of an `AbstractChar` is a valid index
  * The encoding of an `AbstractChar` is independent of what precedes or follows it
  * String encodings are [self-synchronizing] – i.e. `isvalid(s, i)` is O(1)

[self-synchronizing]: https://en.wikipedia.org/wiki/Self-synchronizing_code

Some string functions that extract code units, characters or substrings from
strings error if you pass them out-of-bounds or invalid string indices. This
includes `codeunit(s, i)` and `s[i]`. Functions that do string
index arithmetic take a more relaxed approach to indexing and give you the
closest valid string index when in-bounds, or when out-of-bounds, behave as if
there were an infinite number of characters padding each side of the string.
Usually these imaginary padding characters have code unit length `1` but string
types may choose different "imaginary" character sizes as makes sense for their
implementations (e.g. substrings may pass index arithmetic through to the
underlying string they provide a view into). Relaxed indexing functions include
those intended for index arithmetic: `thisind`, `nextind` and `prevind`. This
model allows index arithmetic to work with out-of- bounds indices as
intermediate values so long as one never uses them to retrieve a character,
which often helps avoid needing to code around edge cases.

See also [`codeunit`](@ref), [`ncodeunits`](@ref), [`thisind`](@ref),
[`nextind`](@ref), [`prevind`](@ref).
"""
AbstractString

## required string functions ##

"""
    ncodeunits(s::AbstractString) -> Int

Return the number of code units in a string. Indices that are in bounds to
access this string must satisfy `1 ≤ i ≤ ncodeunits(s)`. Not all such indices
are valid – they may not be the start of a character, but they will return a
code unit value when calling `codeunit(s,i)`.

# Examples
```jldoctest
julia> ncodeunits("The Julia Language")
18

julia> ncodeunits("∫eˣ")
6

julia> ncodeunits('∫'), ncodeunits('e'), ncodeunits('ˣ')
(3, 1, 2)
```

See also [`codeunit`](@ref), [`checkbounds`](@ref), [`sizeof`](@ref),
[`length`](@ref), [`lastindex`](@ref).
"""
ncodeunits(s::AbstractString)

"""
    codeunit(s::AbstractString) -> Type{<:Union{UInt8, UInt16, UInt32}}

Return the code unit type of the given string object. For ASCII, Latin-1, or
UTF-8 encoded strings, this would be `UInt8`; for UCS-2 and UTF-16 it would be
`UInt16`; for UTF-32 it would be `UInt32`. The code unit type need not be
limited to these three types, but it's hard to think of widely used string
encodings that don't use one of these units. `codeunit(s)` is the same as
`typeof(codeunit(s,1))` when `s` is a non-empty string.

See also [`ncodeunits`](@ref).
"""
codeunit(s::AbstractString)

const CodeunitType = Union{Type{UInt8},Type{UInt16},Type{UInt32}}

"""
    codeunit(s::AbstractString, i::Integer) -> Union{UInt8, UInt16, UInt32}

Return the code unit value in the string `s` at index `i`. Note that

    codeunit(s, i) :: codeunit(s)

I.e. the value returned by `codeunit(s, i)` is of the type returned by
`codeunit(s)`.

# Examples
```jldoctest
julia> a = codeunit("Hello", 2)
0x65

julia> typeof(a)
UInt8
```

See also [`ncodeunits`](@ref), [`checkbounds`](@ref).
"""
@propagate_inbounds codeunit(s::AbstractString, i::Integer) = i isa Int ?
    throw(MethodError(codeunit, (s, i))) : codeunit(s, Int(i))

"""
    isvalid(s::AbstractString, i::Integer) -> Bool

Predicate indicating whether the given index is the start of the encoding of a
character in `s` or not. If `isvalid(s, i)` is true then `s[i]` will return the
character whose encoding starts at that index, if it's false, then `s[i]` will
raise an invalid index error or a bounds error depending on if `i` is in bounds.
In order for `isvalid(s, i)` to be an O(1) function, the encoding of `s` must be
[self-synchronizing](https://en.wikipedia.org/wiki/Self-synchronizing_code). This
is a basic assumption of Julia's generic string support.

See also [`getindex`](@ref), [`iterate`](@ref), [`thisind`](@ref),
[`nextind`](@ref), [`prevind`](@ref), [`length`](@ref).

# Examples
```jldoctest
julia> str = "αβγdef";

julia> isvalid(str, 1)
true

julia> str[1]
'α': Unicode U+03B1 (category Ll: Letter, lowercase)

julia> isvalid(str, 2)
false

julia> str[2]
ERROR: StringIndexError: invalid index [2], valid nearby indices [1]=>'α', [3]=>'β'
Stacktrace:
[...]
```
"""
@propagate_inbounds isvalid(s::AbstractString, i::Integer) = i isa Int ?
    throw(MethodError(isvalid, (s, i))) : isvalid(s, Int(i))

"""
    iterate(s::AbstractString, i::Integer) -> Union{Tuple{<:AbstractChar, Int}, Nothing}

Return a tuple of the character in `s` at index `i` with the index of the start
of the following character in `s`. This is the key method that allows strings to
be iterated, yielding a sequences of characters. If `i` is out of bounds in `s`
then a bounds error is raised. The `iterate` function, as part of the iteration
protocol may assume that `i` is the start of a character in `s`.

See also [`getindex`](@ref), [`checkbounds`](@ref).
"""
@propagate_inbounds iterate(s::AbstractString, i::Integer) = i isa Int ?
    throw(MethodError(iterate, (s, i))) : iterate(s, Int(i))

## basic generic definitions ##

eltype(::Type{<:AbstractString}) = Char # some string types may use another AbstractChar

"""
    sizeof(str::AbstractString)

Size, in bytes, of the string `str`. Equal to the number of code units in `str` multiplied by
the size, in bytes, of one code unit in `str`.

# Examples
```jldoctest
julia> sizeof("")
0

julia> sizeof("∀")
3
```
"""
sizeof(s::AbstractString) = ncodeunits(s)::Int * sizeof(codeunit(s)::CodeunitType)
firstindex(s::AbstractString) = 1
lastindex(s::AbstractString) = thisind(s, ncodeunits(s)::Int)
isempty(s::AbstractString) = iszero(ncodeunits(s)::Int)

function getindex(s::AbstractString, i::Integer)
    @boundscheck checkbounds(s, i)
    @inbounds return isvalid(s, i) ? (iterate(s, i)::NTuple{2,Any})[1] : string_index_err(s, i)
end

getindex(s::AbstractString, i::Colon) = s
# TODO: handle other ranges with stride ±1 specially?
# TODO: add more @propagate_inbounds annotations?
getindex(s::AbstractString, v::AbstractVector{<:Integer}) =
    sprint(io->(for i in v; write(io, s[i]) end), sizehint=length(v))
getindex(s::AbstractString, v::AbstractVector{Bool}) =
    throw(ArgumentError("logical indexing not supported for strings"))

function get(s::AbstractString, i::Integer, default)
# TODO: use ternary once @inbounds is expression-like
    if checkbounds(Bool, s, i)
        @inbounds return s[i]
    else
        return default
    end
end

## bounds checking ##

checkbounds(::Type{Bool}, s::AbstractString, i::Integer) =
    1 ≤ i ≤ ncodeunits(s)::Int
checkbounds(::Type{Bool}, s::AbstractString, r::AbstractRange{<:Integer}) =
    isempty(r) || (1 ≤ minimum(r) && maximum(r) ≤ ncodeunits(s)::Int)
checkbounds(::Type{Bool}, s::AbstractString, I::AbstractArray{<:Real}) =
    all(i -> checkbounds(Bool, s, i), I)
checkbounds(::Type{Bool}, s::AbstractString, I::AbstractArray{<:Integer}) =
    all(i -> checkbounds(Bool, s, i), I)
checkbounds(s::AbstractString, I::Union{Integer,AbstractArray}) =
    checkbounds(Bool, s, I) ? nothing : throw(BoundsError(s, I))

## construction, conversion, promotion ##

string() = ""
string(s::AbstractString) = s

Vector{UInt8}(s::AbstractString) = unsafe_wrap(Vector{UInt8}, String(s))
Array{UInt8}(s::AbstractString) = unsafe_wrap(Vector{UInt8}, String(s))
Vector{T}(s::AbstractString) where {T<:AbstractChar} = collect(T, s)

Symbol(s::AbstractString) = Symbol(String(s))
Symbol(x...) = Symbol(string(x...))

convert(::Type{T}, s::T) where {T<:AbstractString} = s
convert(::Type{T}, s::AbstractString) where {T<:AbstractString} = T(s)::T

## summary ##

function summary(io::IO, s::AbstractString)
    prefix = isempty(s) ? "empty" : string(ncodeunits(s), "-codeunit")
    print(io, prefix, " ", typeof(s))
end

## string & character concatenation ##

"""
    *(s::Union{AbstractString, AbstractChar}, t::Union{AbstractString, AbstractChar}...) -> AbstractString

Concatenate strings and/or characters, producing a [`String`](@ref). This is equivalent
to calling the [`string`](@ref) function on the arguments. Concatenation of built-in
string types always produces a value of type `String` but other string types may choose
to return a string of a different type as appropriate.

# Examples
```jldoctest
julia> "Hello " * "world"
"Hello world"

julia> 'j' * "ulia"
"julia"
```
"""
(*)(s1::Union{AbstractChar, AbstractString}, ss::Union{AbstractChar, AbstractString}...) = string(s1, ss...)

one(::Union{T,Type{T}}) where {T<:AbstractString} = convert(T, "")

## generic string comparison ##

"""
    cmp(a::AbstractString, b::AbstractString) -> Int

Compare two strings. Return `0` if both strings have the same length and the character
at each index is the same in both strings. Return `-1` if `a` is a prefix of `b`, or if
`a` comes before `b` in alphabetical order. Return `1` if `b` is a prefix of `a`, or if
`b` comes before `a` in alphabetical order (technically, lexicographical order by Unicode
code points).

# Examples
```jldoctest
julia> cmp("abc", "abc")
0

julia> cmp("ab", "abc")
-1

julia> cmp("abc", "ab")
1

julia> cmp("ab", "ac")
-1

julia> cmp("ac", "ab")
1

julia> cmp("α", "a")
1

julia> cmp("b", "β")
-1
```
"""
function cmp(a::AbstractString, b::AbstractString)
    a === b && return 0
    (iv1, iv2) = (iterate(a), iterate(b))
    while iv1 !== nothing && iv2 !== nothing
        (c, d) = (first(iv1)::AbstractChar, first(iv2)::AbstractChar)
        c ≠ d && return ifelse(c < d, -1, 1)
        (iv1, iv2) = (iterate(a, last(iv1)), iterate(b, last(iv2)))
    end
    return iv1 === nothing ? (iv2 === nothing ? 0 : -1) : 1
end

"""
    ==(a::AbstractString, b::AbstractString) -> Bool

Test whether two strings are equal character by character (technically, Unicode
code point by code point).

# Examples
```jldoctest
julia> "abc" == "abc"
true

julia> "abc" == "αβγ"
false
```
"""
==(a::AbstractString, b::AbstractString) = cmp(a, b) == 0

"""
    isless(a::AbstractString, b::AbstractString) -> Bool

Test whether string `a` comes before string `b` in alphabetical order
(technically, in lexicographical order by Unicode code points).

# Examples
```jldoctest
julia> isless("a", "b")
true

julia> isless("β", "α")
false

julia> isless("a", "a")
false
```
"""
isless(a::AbstractString, b::AbstractString) = cmp(a, b) < 0

# faster comparisons for symbols

@assume_effects :total function cmp(a::Symbol, b::Symbol)
    Int(sign(ccall(:strcmp, Int32, (Cstring, Cstring), a, b)))
end

isless(a::Symbol, b::Symbol) = cmp(a, b) < 0

# hashing

hash(s::AbstractString, h::UInt) = hash(String(s), h)

## character index arithmetic ##

"""
    length(s::AbstractString) -> Int
    length(s::AbstractString, i::Integer, j::Integer) -> Int

Return the number of characters in string `s` from indices `i` through `j`.

This is computed as the number of code unit indices from `i` to `j` which are
valid character indices. With only a single string argument, this computes
the number of characters in the entire string. With `i` and `j` arguments it
computes the number of indices between `i` and `j` inclusive that are valid
indices in the string `s`. In addition to in-bounds values, `i` may take the
out-of-bounds value `ncodeunits(s) + 1` and `j` may take the out-of-bounds
value `0`.

!!! note
    The time complexity of this operation is linear in general. That is, it
    will take the time proportional to the number of bytes or characters in
    the string because it counts the value on the fly. This is in contrast to
    the method for arrays, which is a constant-time operation.

See also [`isvalid`](@ref), [`ncodeunits`](@ref), [`lastindex`](@ref),
[`thisind`](@ref), [`nextind`](@ref), [`prevind`](@ref).

# Examples
```jldoctest
julia> length("jμΛIα")
5
```
"""
length(s::AbstractString) = @inbounds return length(s, 1, ncodeunits(s)::Int)

function length(s::AbstractString, i::Int, j::Int)
    @boundscheck begin
        0 < i ≤ ncodeunits(s)::Int+1 || throw(BoundsError(s, i))
        0 ≤ j < ncodeunits(s)::Int+1 || throw(BoundsError(s, j))
    end
    n = 0
    for k = i:j
        @inbounds n += isvalid(s, k)
    end
    return n
end

@propagate_inbounds length(s::AbstractString, i::Integer, j::Integer) =
    length(s, Int(i), Int(j))

"""
    thisind(s::AbstractString, i::Integer) -> Int

If `i` is in bounds in `s` return the index of the start of the character whose
encoding code unit `i` is part of. In other words, if `i` is the start of a
character, return `i`; if `i` is not the start of a character, rewind until the
start of a character and return that index. If `i` is equal to 0 or `ncodeunits(s)+1`
return `i`. In all other cases throw `BoundsError`.

# Examples
```jldoctest
julia> thisind("α", 0)
0

julia> thisind("α", 1)
1

julia> thisind("α", 2)
1

julia> thisind("α", 3)
3

julia> thisind("α", 4)
ERROR: BoundsError: attempt to access 2-codeunit String at index [4]
[...]

julia> thisind("α", -1)
ERROR: BoundsError: attempt to access 2-codeunit String at index [-1]
[...]
```
"""
thisind(s::AbstractString, i::Integer) = thisind(s, Int(i))

function thisind(s::AbstractString, i::Int)
    z = ncodeunits(s)::Int + 1
    i == z && return i
    @boundscheck 0 ≤ i ≤ z || throw(BoundsError(s, i))
    @inbounds while 1 < i && !(isvalid(s, i)::Bool)
        i -= 1
    end
    return i
end

"""
    prevind(str::AbstractString, i::Integer, n::Integer=1) -> Int

* Case `n == 1`

  If `i` is in bounds in `s` return the index of the start of the character whose
  encoding starts before index `i`. In other words, if `i` is the start of a
  character, return the start of the previous character; if `i` is not the start
  of a character, rewind until the start of a character and return that index.
  If `i` is equal to `1` return `0`.
  If `i` is equal to `ncodeunits(str)+1` return `lastindex(str)`.
  Otherwise throw `BoundsError`.

* Case `n > 1`

  Behaves like applying `n` times `prevind` for `n==1`. The only difference
  is that if `n` is so large that applying `prevind` would reach `0` then each remaining
  iteration decreases the returned value by `1`.
  This means that in this case `prevind` can return a negative value.

* Case `n == 0`

  Return `i` only if `i` is a valid index in `str` or is equal to `ncodeunits(str)+1`.
  Otherwise `StringIndexError` or `BoundsError` is thrown.

# Examples
```jldoctest
julia> prevind("α", 3)
1

julia> prevind("α", 1)
0

julia> prevind("α", 0)
ERROR: BoundsError: attempt to access 2-codeunit String at index [0]
[...]

julia> prevind("α", 2, 2)
0

julia> prevind("α", 2, 3)
-1
```
"""
prevind(s::AbstractString, i::Integer, n::Integer) = prevind(s, Int(i), Int(n))
prevind(s::AbstractString, i::Integer)             = prevind(s, Int(i))
prevind(s::AbstractString, i::Int)                 = prevind(s, i, 1)

function prevind(s::AbstractString, i::Int, n::Int)
    n < 0 && throw(ArgumentError("n cannot be negative: $n"))
    z = ncodeunits(s) + 1
    @boundscheck 0 < i ≤ z || throw(BoundsError(s, i))
    n == 0 && return thisind(s, i) == i ? i : string_index_err(s, i)
    while n > 0 && 1 < i
        @inbounds n -= isvalid(s, i -= 1)
    end
    return i - n
end

"""
    nextind(str::AbstractString, i::Integer, n::Integer=1) -> Int

* Case `n == 1`

  If `i` is in bounds in `s` return the index of the start of the character whose
  encoding starts after index `i`. In other words, if `i` is the start of a
  character, return the start of the next character; if `i` is not the start
  of a character, move forward until the start of a character and return that index.
  If `i` is equal to `0` return `1`.
  If `i` is in bounds but greater or equal to `lastindex(str)` return `ncodeunits(str)+1`.
  Otherwise throw `BoundsError`.

* Case `n > 1`

  Behaves like applying `n` times `nextind` for `n==1`. The only difference
  is that if `n` is so large that applying `nextind` would reach `ncodeunits(str)+1` then
  each remaining iteration increases the returned value by `1`. This means that in this
  case `nextind` can return a value greater than `ncodeunits(str)+1`.

* Case `n == 0`

  Return `i` only if `i` is a valid index in `s` or is equal to `0`.
  Otherwise `StringIndexError` or `BoundsError` is thrown.

# Examples
```jldoctest
julia> nextind("α", 0)
1

julia> nextind("α", 1)
3

julia> nextind("α", 3)
ERROR: BoundsError: attempt to access 2-codeunit String at index [3]
[...]

julia> nextind("α", 0, 2)
3

julia> nextind("α", 1, 2)
4
```
"""
nextind(s::AbstractString, i::Integer, n::Integer) = nextind(s, Int(i), Int(n))
nextind(s::AbstractString, i::Integer)             = nextind(s, Int(i))
nextind(s::AbstractString, i::Int)                 = nextind(s, i, 1)

function nextind(s::AbstractString, i::Int, n::Int)
    n < 0 && throw(ArgumentError("n cannot be negative: $n"))
    z = ncodeunits(s)
    @boundscheck 0 ≤ i ≤ z || throw(BoundsError(s, i))
    n == 0 && return thisind(s, i) == i ? i : string_index_err(s, i)
    while n > 0 && i < z
        @inbounds n -= isvalid(s, i += 1)
    end
    return i + n
end

## string index iteration type ##

struct EachStringIndex{T<:AbstractString}
    s::T
end
keys(s::AbstractString) = EachStringIndex(s)

length(e::EachStringIndex) = length(e.s)
first(::EachStringIndex) = 1
last(e::EachStringIndex) = lastindex(e.s)
iterate(e::EachStringIndex, state=firstindex(e.s)) = state > ncodeunits(e.s) ? nothing : (state, nextind(e.s, state))
eltype(::Type{<:EachStringIndex}) = Int

"""
    isascii(c::Union{AbstractChar,AbstractString}) -> Bool

Test whether a character belongs to the ASCII character set, or whether this is true for
all elements of a string.

# Examples
```jldoctest
julia> isascii('a')
true

julia> isascii('α')
false

julia> isascii("abc")
true

julia> isascii("αβγ")
false
```
For example, `isascii` can be used as a predicate function for [`filter`](@ref) or [`replace`](@ref)
to remove or replace non-ASCII characters, respectively:
```jldoctest
julia> filter(isascii, "abcdeγfgh") # discard non-ASCII chars
"abcdefgh"

julia> replace("abcdeγfgh", !isascii=>' ') # replace non-ASCII chars with spaces
"abcde fgh"
```
"""
isascii(c::Char) = bswap(reinterpret(UInt32, c)) < 0x80
isascii(s::AbstractString) = all(isascii, s)
isascii(c::AbstractChar) = UInt32(c) < 0x80

@inline function _isascii(code_units::AbstractVector{CU}, first, last) where {CU}
    r = zero(CU)
    for n = first:last
        @inbounds r |= code_units[n]
    end
    return 0 ≤ r < 0x80
end

#The chunking algorithm makes the last two chunks overlap inorder to keep the size fixed
@inline function  _isascii_chunks(chunk_size,cu::AbstractVector{CU}, first,last) where {CU}
    n=first
    while n <= last - chunk_size
        _isascii(cu,n,n+chunk_size-1) || return false
        n += chunk_size
    end
    return  _isascii(cu,last-chunk_size+1,last)
end
"""
    isascii(cu::AbstractVector{CU}) where {CU <: Integer} -> Bool

Test whether all values in the vector belong to the ASCII character set (0x00 to 0x7f).
This function is intended to be used by other string implementations that need a fast ASCII check.
"""
function isascii(cu::AbstractVector{CU}) where {CU <: Integer}
    chunk_size = 1024
    chunk_threshold =  chunk_size + (chunk_size ÷ 2)
    first = firstindex(cu);   last = lastindex(cu)
    l = last - first + 1
    l < chunk_threshold && return _isascii(cu,first,last)
    return _isascii_chunks(chunk_size,cu,first,last)
end

## string map, filter ##

function map(f, s::AbstractString)
    out = StringVector(max(4, sizeof(s)::Int÷sizeof(codeunit(s)::CodeunitType)))
    index = UInt(1)
    for c::AbstractChar in s
        c′ = f(c)
        isa(c′, AbstractChar) || throw(ArgumentError(
            "map(f, s::AbstractString) requires f to return AbstractChar; " *
            "try map(f, collect(s)) or a comprehension instead"))
        index + 3 > length(out) && resize!(out, unsigned(2 * length(out)))
        index += __unsafe_string!(out, convert(Char, c′), index)
    end
    resize!(out, index-1)
    sizehint!(out, index-1)
    return String(out)
end

function filter(f, s::AbstractString)
    out = IOBuffer(sizehint=sizeof(s))
    for c in s
        f(c) && write(out, c)
    end
    String(_unsafe_take!(out))
end

## string first and last ##

"""
    first(s::AbstractString, n::Integer)

Get a string consisting of the first `n` characters of `s`.

# Examples
```jldoctest
julia> first("∀ϵ≠0: ϵ²>0", 0)
""

julia> first("∀ϵ≠0: ϵ²>0", 1)
"∀"

julia> first("∀ϵ≠0: ϵ²>0", 3)
"∀ϵ≠"
```
"""
first(s::AbstractString, n::Integer) = @inbounds s[1:min(end, nextind(s, 0, n))]

"""
    last(s::AbstractString, n::Integer)

Get a string consisting of the last `n` characters of `s`.

# Examples
```jldoctest
julia> last("∀ϵ≠0: ϵ²>0", 0)
""

julia> last("∀ϵ≠0: ϵ²>0", 1)
"0"

julia> last("∀ϵ≠0: ϵ²>0", 3)
"²>0"
```
"""
last(s::AbstractString, n::Integer) = @inbounds s[max(1, prevind(s, ncodeunits(s)+1, n)):end]

"""
    reverseind(v, i)

Given an index `i` in [`reverse(v)`](@ref), return the corresponding index in
`v` so that `v[reverseind(v,i)] == reverse(v)[i]`. (This can be nontrivial in
cases where `v` contains non-ASCII characters.)

# Examples
```jldoctest
julia> s = "Julia🚀"
"Julia🚀"

julia> r = reverse(s)
"🚀ailuJ"

julia> for i in eachindex(s)
           print(r[reverseind(r, i)])
       end
Julia🚀
```
"""
reverseind(s::AbstractString, i::Integer) = thisind(s, ncodeunits(s)-i+1)

"""
    repeat(s::AbstractString, r::Integer)

Repeat a string `r` times. This can be written as `s^r`.

See also [`^`](@ref :^(::Union{AbstractString, AbstractChar}, ::Integer)).

# Examples
```jldoctest
julia> repeat("ha", 3)
"hahaha"
```
"""
repeat(s::AbstractString, r::Integer) = repeat(String(s), r)

"""
    ^(s::Union{AbstractString,AbstractChar}, n::Integer) -> AbstractString

Repeat a string or character `n` times. This can also be written as `repeat(s, n)`.

See also [`repeat`](@ref).

# Examples
```jldoctest
julia> "Test "^3
"Test Test Test "
```
"""
(^)(s::Union{AbstractString,AbstractChar}, r::Integer) = repeat(s, r)

# reverse-order iteration for strings and indices thereof
iterate(r::Iterators.Reverse{<:AbstractString}, i=lastindex(r.itr)) = i < firstindex(r.itr) ? nothing : (r.itr[i], prevind(r.itr, i))
iterate(r::Iterators.Reverse{<:EachStringIndex}, i=lastindex(r.itr.s)) = i < firstindex(r.itr.s) ? nothing : (i, prevind(r.itr.s, i))

## code unit access ##

"""
    CodeUnits(s::AbstractString)

Wrap a string (without copying) in an immutable vector-like object that accesses the code units
of the string's representation.
"""
struct CodeUnits{T,S<:AbstractString} <: DenseVector{T}
    s::S
    CodeUnits(s::S) where {S<:AbstractString} = new{codeunit(s),S}(s)
end

length(s::CodeUnits) = ncodeunits(s.s)
sizeof(s::CodeUnits{T}) where {T} = ncodeunits(s.s) * sizeof(T)
size(s::CodeUnits) = (length(s),)
elsize(s::Type{<:CodeUnits{T}}) where {T} = sizeof(T)
@propagate_inbounds getindex(s::CodeUnits, i::Int) = codeunit(s.s, i)
IndexStyle(::Type{<:CodeUnits}) = IndexLinear()
@inline iterate(s::CodeUnits, i=1) = (i % UInt) - 1 < length(s) ? (@inbounds s[i], i + 1) : nothing


write(io::IO, s::CodeUnits) = write(io, s.s)

unsafe_convert(::Type{Ptr{T}},    s::CodeUnits{T}) where {T} = unsafe_convert(Ptr{T}, s.s)
unsafe_convert(::Type{Ptr{Int8}}, s::CodeUnits{UInt8}) = unsafe_convert(Ptr{Int8}, s.s)

"""
    codeunits(s::AbstractString)

Obtain a vector-like object containing the code units of a string.
Returns a `CodeUnits` wrapper by default, but `codeunits` may optionally be defined
for new string types if necessary.

# Examples
```jldoctest
julia> codeunits("Juλia")
6-element Base.CodeUnits{UInt8, String}:
 0x4a
 0x75
 0xce
 0xbb
 0x69
 0x61
```
"""
codeunits(s::AbstractString) = CodeUnits(s)

function _split_rest(s::AbstractString, n::Int)
    lastind = lastindex(s)
    i = try
        prevind(s, lastind, n)
    catch e
        e isa BoundsError || rethrow()
        _check_length_split_rest(length(s), n)
    end
    last_n = SubString(s, nextind(s, i), lastind)
    front = s[begin:i]
    return front, last_n
end
U   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/strings/string.jl�Z      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
    StringIndexError(str, i)

An error occurred when trying to access `str` at index `i` that is not valid.
"""
struct StringIndexError <: Exception
    string::AbstractString
    index::Integer
end
@noinline string_index_err(s::AbstractString, i::Integer) =
    throw(StringIndexError(s, Int(i)))
function Base.showerror(io::IO, exc::StringIndexError)
    s = exc.string
    print(io, "StringIndexError: ", "invalid index [$(exc.index)]")
    if firstindex(s) <= exc.index <= ncodeunits(s)
        iprev = thisind(s, exc.index)
        inext = nextind(s, iprev)
        escprev = escape_string(s[iprev:iprev])
        if inext <= ncodeunits(s)
            escnext = escape_string(s[inext:inext])
            print(io, ", valid nearby indices [$iprev]=>'$escprev', [$inext]=>'$escnext'")
        else
            print(io, ", valid nearby index [$iprev]=>'$escprev'")
        end
    end
end

const ByteArray = Union{CodeUnits{UInt8,String}, Vector{UInt8},Vector{Int8}, FastContiguousSubArray{UInt8,1,CodeUnits{UInt8,String}}, FastContiguousSubArray{UInt8,1,Vector{UInt8}}, FastContiguousSubArray{Int8,1,Vector{Int8}}}

@inline between(b::T, lo::T, hi::T) where {T<:Integer} = (lo ≤ b) & (b ≤ hi)

"""
    String <: AbstractString

The default string type in Julia, used by e.g. string literals.

`String`s are immutable sequences of `Char`s. A `String` is stored internally as
a contiguous byte array, and while they are interpreted as being UTF-8 encoded,
they can be composed of any byte sequence. Use [`isvalid`](@ref) to validate
that the underlying byte sequence is valid as UTF-8.
"""
String

## constructors and conversions ##

# String constructor docstring from boot.jl, workaround for #16730
# and the unavailability of @doc in boot.jl context.
"""
    String(v::AbstractVector{UInt8})

Create a new `String` object using the data buffer from byte vector `v`.
If `v` is a `Vector{UInt8}` it will be truncated to zero length and future
modification of `v` cannot affect the contents of the resulting string.
To avoid truncation of `Vector{UInt8}` data, use `String(copy(v))`; for other
`AbstractVector` types, `String(v)` already makes a copy.

When possible, the memory of `v` will be used without copying when the `String`
object is created. This is guaranteed to be the case for byte vectors returned
by [`take!`](@ref) on a writable [`IOBuffer`](@ref) and by calls to
[`read(io, nb)`](@ref). This allows zero-copy conversion of I/O data to strings.
In other cases, `Vector{UInt8}` data may be copied, but `v` is truncated anyway
to guarantee consistent behavior.
"""
String(v::AbstractVector{UInt8}) = String(copyto!(StringVector(length(v)), v))
String(v::Vector{UInt8}) = ccall(:jl_array_to_string, Ref{String}, (Any,), v)

"""
    unsafe_string(p::Ptr{UInt8}, [length::Integer])

Copy a string from the address of a C-style (NUL-terminated) string encoded as UTF-8.
(The pointer can be safely freed afterwards.) If `length` is specified
(the length of the data in bytes), the string does not have to be NUL-terminated.

This function is labeled "unsafe" because it will crash if `p` is not
a valid memory address to data of the requested length.
"""
function unsafe_string(p::Union{Ptr{UInt8},Ptr{Int8}}, len::Integer)
    p == C_NULL && throw(ArgumentError("cannot convert NULL to string"))
    ccall(:jl_pchar_to_string, Ref{String}, (Ptr{UInt8}, Int), p, len)
end
function unsafe_string(p::Union{Ptr{UInt8},Ptr{Int8}})
    p == C_NULL && throw(ArgumentError("cannot convert NULL to string"))
    ccall(:jl_cstr_to_string, Ref{String}, (Ptr{UInt8},), p)
end

# This is @assume_effects :effect_free :nothrow :terminates_globally @ccall jl_alloc_string(n::Csize_t)::Ref{String},
# but the macro is not available at this time in bootstrap, so we write it manually.
@eval _string_n(n::Integer) = $(Expr(:foreigncall, QuoteNode(:jl_alloc_string), Ref{String}, Expr(:call, Expr(:core, :svec), :Csize_t), 1, QuoteNode((:ccall,0xe)), :(convert(Csize_t, n))))

"""
    String(s::AbstractString)

Create a new `String` from an existing `AbstractString`.
"""
String(s::AbstractString) = print_to_string(s)
@assume_effects :total String(s::Symbol) = unsafe_string(unsafe_convert(Ptr{UInt8}, s))

unsafe_wrap(::Type{Vector{UInt8}}, s::String) = ccall(:jl_string_to_array, Ref{Vector{UInt8}}, (Any,), s)
unsafe_wrap(::Type{Vector{UInt8}}, s::FastContiguousSubArray{UInt8,1,Vector{UInt8}}) = unsafe_wrap(Vector{UInt8}, pointer(s), size(s))

Vector{UInt8}(s::CodeUnits{UInt8,String}) = copyto!(Vector{UInt8}(undef, length(s)), s)
Vector{UInt8}(s::String) = Vector{UInt8}(codeunits(s))
Array{UInt8}(s::String)  = Vector{UInt8}(codeunits(s))

String(s::CodeUnits{UInt8,String}) = s.s

## low-level functions ##

pointer(s::String) = unsafe_convert(Ptr{UInt8}, s)
pointer(s::String, i::Integer) = pointer(s) + Int(i)::Int - 1

ncodeunits(s::String) = Core.sizeof(s)
codeunit(s::String) = UInt8

codeunit(s::String, i::Integer) = codeunit(s, Int(i))
@assume_effects :foldable @inline function codeunit(s::String, i::Int)
    @boundscheck checkbounds(s, i)
    b = GC.@preserve s unsafe_load(pointer(s, i))
    return b
end

## comparison ##

@assume_effects :total _memcmp(a::String, b::String) = @invoke _memcmp(a::Union{Ptr{UInt8},AbstractString},b::Union{Ptr{UInt8},AbstractString})

_memcmp(a::Union{Ptr{UInt8},AbstractString}, b::Union{Ptr{UInt8},AbstractString}) = _memcmp(a, b, min(sizeof(a), sizeof(b)))
function _memcmp(a::Union{Ptr{UInt8},AbstractString}, b::Union{Ptr{UInt8},AbstractString}, len::Int)
    GC.@preserve a b begin
        pa = unsafe_convert(Ptr{UInt8}, a)
        pb = unsafe_convert(Ptr{UInt8}, b)
        memcmp(pa, pb, len % Csize_t) % Int
    end
end

function cmp(a::String, b::String)
    al, bl = sizeof(a), sizeof(b)
    c = _memcmp(a, b)
    return c < 0 ? -1 : c > 0 ? +1 : cmp(al,bl)
end

==(a::String, b::String) = a===b

typemin(::Type{String}) = ""
typemin(::String) = typemin(String)

## thisind, nextind ##

@propagate_inbounds thisind(s::String, i::Int) = _thisind_str(s, i)

# s should be String or SubString{String}
@inline function _thisind_str(s, i::Int)
    i == 0 && return 0
    n = ncodeunits(s)
    i == n + 1 && return i
    @boundscheck between(i, 1, n) || throw(BoundsError(s, i))
    @inbounds b = codeunit(s, i)
    (b & 0xc0 == 0x80) & (i-1 > 0) || return i
    @inbounds b = codeunit(s, i-1)
    between(b, 0b11000000, 0b11110111) && return i-1
    (b & 0xc0 == 0x80) & (i-2 > 0) || return i
    @inbounds b = codeunit(s, i-2)
    between(b, 0b11100000, 0b11110111) && return i-2
    (b & 0xc0 == 0x80) & (i-3 > 0) || return i
    @inbounds b = codeunit(s, i-3)
    between(b, 0b11110000, 0b11110111) && return i-3
    return i
end

@propagate_inbounds nextind(s::String, i::Int) = _nextind_str(s, i)

# s should be String or SubString{String}
@inline function _nextind_str(s, i::Int)
    i == 0 && return 1
    n = ncodeunits(s)
    @boundscheck between(i, 1, n) || throw(BoundsError(s, i))
    @inbounds l = codeunit(s, i)
    (l < 0x80) | (0xf8 ≤ l) && return i+1
    if l < 0xc0
        i′ = @inbounds thisind(s, i)
        return i′ < i ? @inbounds(nextind(s, i′)) : i+1
    end
    # first continuation byte
    (i += 1) > n && return i
    @inbounds b = codeunit(s, i)
    b & 0xc0 ≠ 0x80 && return i
    ((i += 1) > n) | (l < 0xe0) && return i
    # second continuation byte
    @inbounds b = codeunit(s, i)
    b & 0xc0 ≠ 0x80 && return i
    ((i += 1) > n) | (l < 0xf0) && return i
    # third continuation byte
    @inbounds b = codeunit(s, i)
    ifelse(b & 0xc0 ≠ 0x80, i, i+1)
end

## checking UTF-8 & ACSII validity ##
#=
    The UTF-8 Validation is performed by a shift based DFA.
    ┌───────────────────────────────────────────────────────────────────┐
    │    UTF-8 DFA State Diagram    ┌──────────────2──────────────┐     │
    │                               ├────────3────────┐           │     │
    │                 ┌──────────┐  │     ┌─┐        ┌▼┐          │     │
    │      ASCII      │  UTF-8   │  ├─5──►│9├───1────► │          │     │
    │                 │          │  │     ├─┤        │ │         ┌▼┐    │
    │                 │  ┌─0─┐   │  ├─6──►│8├─1,7,9──►4├──1,7,9──► │    │
    │      ┌─0─┐      │  │   │   │  │     ├─┤        │ │         │ │    │
    │      │   │      │ ┌▼───┴┐  │  ├─11─►│7├──7,9───► │ ┌───────►3├─┐  │
    │     ┌▼───┴┐     │ │     │  ▼  │     └─┘        └─┘ │       │ │ │  │
    │     │  0  ├─────┘ │  1  ├─► ──┤                    │  ┌────► │ │  │
    │     └─────┘       │     │     │     ┌─┐            │  │    └─┘ │  │
    │                   └──▲──┘     ├─10─►│5├─────7──────┘  │        │  │
    │                      │        │     ├─┤               │        │  │
    │                      │        └─4──►│6├─────1,9───────┘        │  │
    │          INVALID     │              └─┘                        │  │
    │           ┌─*─┐      └──────────────────1,7,9──────────────────┘  │
    │          ┌▼───┴┐                                                  │
    │          │  2  ◄─── All undefined transitions result in state 2   │
    │          └─────┘                                                  │
    └───────────────────────────────────────────────────────────────────┘

        Validation States
            0 -> _UTF8_DFA_ASCII is the start state and will only stay in this state if the string is only ASCII characters
                        If the DFA ends in this state the string is ASCII only
            1 -> _UTF8_DFA_ACCEPT is the valid complete character state of the DFA once it has encountered a UTF-8 Unicode character
            2 -> _UTF8_DFA_INVALID is only reached by invalid bytes and once in this state it will not change
                    as seen by all 1s in that column of table below
            3 -> One valid continuation byte needed to return to state 0
        4,5,6 -> Two valid continuation bytes needed to return to state 0
        7,8,9 -> Three valids continuation bytes needed to return to state 0

                        Current State
                    0̲  1̲  2̲  3̲  4̲  5̲  6̲  7̲  8̲  9̲
                0 | 0  1  2  2  2  2  2  2  2  2
                1 | 2  2  2  1  3  2  3  2  4  4
                2 | 3  3  2  2  2  2  2  2  2  2
                3 | 4  4  2  2  2  2  2  2  2  2
                4 | 6  6  2  2  2  2  2  2  2  2
    Character   5 | 9  9  2  2  2  2  2  2  2  2     <- Next State
    Class       6 | 8  8  2  2  2  2  2  2  2  2
                7 | 2  2  2  1  3  3  2  4  4  2
                8 | 2  2  2  2  2  2  2  2  2  2
                9 | 2  2  2  1  3  2  3  4  4  2
               10 | 5  5  2  2  2  2  2  2  2  2
               11 | 7  7  2  2  2  2  2  2  2  2

           Shifts | 0  4 10 14 18 24  8 20 12 26

    The shifts that represent each state were derived using teh SMT solver Z3, to ensure when encoded into
    the rows the correct shift was a result.

    Each character class row is encoding 10 states with shifts as defined above. By shifting the bitsof a row by
    the current state then masking the result with 0x11110 give the shift for the new state


=#

#State type used by UTF-8 DFA
const _UTF8DFAState = UInt32
# Fill the table with 256 UInt64 representing the DFA transitions for all bytes
const _UTF8_DFA_TABLE = let # let block rather than function doesn't pollute base
    num_classes=12
    num_states=10
    bit_per_state = 6

    # These shifts were derived using a SMT solver
    state_shifts = [0, 4, 10, 14, 18, 24, 8, 20, 12, 26]

    character_classes = [   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                            0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                            0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                            0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                            0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                            0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                            0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                            0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                            1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
                            9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
                            7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
                            7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
                            8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
                            2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
                            10, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3,
                            11, 6, 6, 6, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8 ]

    # These are the rows discussed in comments above
    state_arrays = [ 0  1  2  2  2  2  2  2  2  2;
                     2  2  2  1  3  2  3  2  4  4;
                     3  3  2  2  2  2  2  2  2  2;
                     4  4  2  2  2  2  2  2  2  2;
                     6  6  2  2  2  2  2  2  2  2;
                     9  9  2  2  2  2  2  2  2  2;
                     8  8  2  2  2  2  2  2  2  2;
                     2  2  2  1  3  3  2  4  4  2;
                     2  2  2  2  2  2  2  2  2  2;
                     2  2  2  1  3  2  3  4  4  2;
                     5  5  2  2  2  2  2  2  2  2;
                     7  7  2  2  2  2  2  2  2  2]

    #This converts the state_arrays into the shift encoded _UTF8DFAState
    class_row = zeros(_UTF8DFAState, num_classes)

    for i = 1:num_classes
        row = _UTF8DFAState(0)
        for j in 1:num_states
            #Calculate the shift required for the next state
            to_shift = UInt8((state_shifts[state_arrays[i,j]+1]) )
            #Shift the next state into the position of the current state
            row = row | (_UTF8DFAState(to_shift) << state_shifts[j])
        end
        class_row[i]=row
    end

    map(c->class_row[c+1],character_classes)
end


const _UTF8_DFA_ASCII = _UTF8DFAState(0) #This state represents the start and end of any valid string
const _UTF8_DFA_ACCEPT = _UTF8DFAState(4) #This state represents the start and end of any valid string
const _UTF8_DFA_INVALID = _UTF8DFAState(10) # If the state machine is ever in this state just stop

# The dfa step is broken out so that it may be used in other functions. The mask was calculated to work with state shifts above
@inline _utf_dfa_step(state::_UTF8DFAState, byte::UInt8) = @inbounds (_UTF8_DFA_TABLE[byte+1] >> state) & _UTF8DFAState(0x0000001E)

@inline function _isvalid_utf8_dfa(state::_UTF8DFAState, bytes::AbstractVector{UInt8}, first::Int = firstindex(bytes), last::Int = lastindex(bytes))
    for i = first:last
       @inbounds state = _utf_dfa_step(state, bytes[i])
    end
    return (state)
end

@inline function  _find_nonascii_chunk(chunk_size,cu::AbstractVector{CU}, first,last) where {CU}
    n=first
    while n <= last - chunk_size
        _isascii(cu,n,n+chunk_size-1) || return n
        n += chunk_size
    end
    n= last-chunk_size+1
    _isascii(cu,n,last) || return n
    return nothing
end

##

# Classifcations of string
    # 0: neither valid ASCII nor UTF-8
    # 1: valid ASCII
    # 2: valid UTF-8
 byte_string_classify(s::AbstractString) = byte_string_classify(codeunits(s))


function byte_string_classify(bytes::AbstractVector{UInt8})
    chunk_size = 1024
    chunk_threshold =  chunk_size + (chunk_size ÷ 2)
    n = length(bytes)
    if n > chunk_threshold
        start = _find_nonascii_chunk(chunk_size,bytes,1,n)
        isnothing(start) && return 1
    else
        _isascii(bytes,1,n) && return 1
        start = 1
    end
    return _byte_string_classify_nonascii(bytes,start,n)
end

function _byte_string_classify_nonascii(bytes::AbstractVector{UInt8}, first::Int, last::Int)
    chunk_size = 256

    start = first
    stop = min(last,first + chunk_size - 1)
    state = _UTF8_DFA_ACCEPT
    while start <= last
        # try to process ascii chunks
        while state == _UTF8_DFA_ACCEPT
            _isascii(bytes,start,stop) || break
            (start = start + chunk_size) <= last || break
            stop = min(last,stop + chunk_size)
        end
        # Process non ascii chunk
        state = _isvalid_utf8_dfa(state,bytes,start,stop)
        state == _UTF8_DFA_INVALID && return 0

        start = start + chunk_size
        stop = min(last,stop + chunk_size)
    end
    return ifelse(state == _UTF8_DFA_ACCEPT,2,0)
end

isvalid(::Type{String}, bytes::AbstractVector{UInt8}) = (@inline byte_string_classify(bytes)) ≠ 0
isvalid(::Type{String}, s::AbstractString) =  (@inline byte_string_classify(s)) ≠ 0

@inline isvalid(s::AbstractString) = @inline isvalid(String, codeunits(s))

is_valid_continuation(c) = c & 0xc0 == 0x80

## required core functionality ##

@inline function iterate(s::String, i::Int=firstindex(s))
    (i % UInt) - 1 < ncodeunits(s) || return nothing
    b = @inbounds codeunit(s, i)
    u = UInt32(b) << 24
    between(b, 0x80, 0xf7) || return reinterpret(Char, u), i+1
    return iterate_continued(s, i, u)
end

function iterate_continued(s::String, i::Int, u::UInt32)
    u < 0xc0000000 && (i += 1; @goto ret)
    n = ncodeunits(s)
    # first continuation byte
    (i += 1) > n && @goto ret
    @inbounds b = codeunit(s, i)
    b & 0xc0 == 0x80 || @goto ret
    u |= UInt32(b) << 16
    # second continuation byte
    ((i += 1) > n) | (u < 0xe0000000) && @goto ret
    @inbounds b = codeunit(s, i)
    b & 0xc0 == 0x80 || @goto ret
    u |= UInt32(b) << 8
    # third continuation byte
    ((i += 1) > n) | (u < 0xf0000000) && @goto ret
    @inbounds b = codeunit(s, i)
    b & 0xc0 == 0x80 || @goto ret
    u |= UInt32(b); i += 1
@label ret
    return reinterpret(Char, u), i
end

@propagate_inbounds function getindex(s::String, i::Int)
    b = codeunit(s, i)
    u = UInt32(b) << 24
    between(b, 0x80, 0xf7) || return reinterpret(Char, u)
    return getindex_continued(s, i, u)
end

function getindex_continued(s::String, i::Int, u::UInt32)
    if u < 0xc0000000
        # called from `getindex` which checks bounds
        @inbounds isvalid(s, i) && @goto ret
        string_index_err(s, i)
    end
    n = ncodeunits(s)

    (i += 1) > n && @goto ret
    @inbounds b = codeunit(s, i) # cont byte 1
    b & 0xc0 == 0x80 || @goto ret
    u |= UInt32(b) << 16

    ((i += 1) > n) | (u < 0xe0000000) && @goto ret
    @inbounds b = codeunit(s, i) # cont byte 2
    b & 0xc0 == 0x80 || @goto ret
    u |= UInt32(b) << 8

    ((i += 1) > n) | (u < 0xf0000000) && @goto ret
    @inbounds b = codeunit(s, i) # cont byte 3
    b & 0xc0 == 0x80 || @goto ret
    u |= UInt32(b)
@label ret
    return reinterpret(Char, u)
end

getindex(s::String, r::AbstractUnitRange{<:Integer}) = s[Int(first(r)):Int(last(r))]

@inline function getindex(s::String, r::UnitRange{Int})
    isempty(r) && return ""
    i, j = first(r), last(r)
    @boundscheck begin
        checkbounds(s, r)
        @inbounds isvalid(s, i) || string_index_err(s, i)
        @inbounds isvalid(s, j) || string_index_err(s, j)
    end
    j = nextind(s, j) - 1
    n = j - i + 1
    ss = _string_n(n)
    GC.@preserve s ss unsafe_copyto!(pointer(ss), pointer(s, i), n)
    return ss
end

# nothrow because we know the start and end indices are valid
@assume_effects :nothrow length(s::String) = length_continued(s, 1, ncodeunits(s), ncodeunits(s))

# effects needed because @inbounds
@assume_effects :consistent :effect_free @inline function length(s::String, i::Int, j::Int)
    @boundscheck begin
        0 < i ≤ ncodeunits(s)+1 || throw(BoundsError(s, i))
        0 ≤ j < ncodeunits(s)+1 || throw(BoundsError(s, j))
    end
    j < i && return 0
    @inbounds i, k = thisind(s, i), i
    c = j - i + (i == k)
    @inbounds length_continued(s, i, j, c)
end

@assume_effects :terminates_locally @inline @propagate_inbounds function length_continued(s::String, i::Int, n::Int, c::Int)
    i < n || return c
    b = codeunit(s, i)
    while true
        while true
            (i += 1) ≤ n || return c
            0xc0 ≤ b ≤ 0xf7 && break
            b = codeunit(s, i)
        end
        l = b
        b = codeunit(s, i) # cont byte 1
        c -= (x = b & 0xc0 == 0x80)
        x & (l ≥ 0xe0) || continue

        (i += 1) ≤ n || return c
        b = codeunit(s, i) # cont byte 2
        c -= (x = b & 0xc0 == 0x80)
        x & (l ≥ 0xf0) || continue

        (i += 1) ≤ n || return c
        b = codeunit(s, i) # cont byte 3
        c -= (b & 0xc0 == 0x80)
    end
end

## overload methods for efficiency ##

isvalid(s::String, i::Int) = checkbounds(Bool, s, i) && thisind(s, i) == i

isascii(s::String) = isascii(codeunits(s))

# don't assume effects for general integers since we cannot know their implementation
@assume_effects :foldable repeat(c::Char, r::BitInteger) = @invoke repeat(c::Char, r::Integer)

"""
    repeat(c::AbstractChar, r::Integer) -> String

Repeat a character `r` times. This can equivalently be accomplished by calling
[`c^r`](@ref :^(::Union{AbstractString, AbstractChar}, ::Integer)).

# Examples
```jldoctest
julia> repeat('A', 3)
"AAA"
```
"""
function repeat(c::AbstractChar, r::Integer)
    c = Char(c)::Char
    r == 0 && return ""
    r < 0 && throw(ArgumentError("can't repeat a character $r times"))
    u = bswap(reinterpret(UInt32, c))
    n = 4 - (leading_zeros(u | 0xff) >> 3)
    s = _string_n(n*r)
    p = pointer(s)
    GC.@preserve s if n == 1
        memset(p, u % UInt8, r)
    elseif n == 2
        p16 = reinterpret(Ptr{UInt16}, p)
        for i = 1:r
            unsafe_store!(p16, u % UInt16, i)
        end
    elseif n == 3
        b1 = (u >> 0) % UInt8
        b2 = (u >> 8) % UInt8
        b3 = (u >> 16) % UInt8
        for i = 0:r-1
            unsafe_store!(p, b1, 3i + 1)
            unsafe_store!(p, b2, 3i + 2)
            unsafe_store!(p, b3, 3i + 3)
        end
    elseif n == 4
        p32 = reinterpret(Ptr{UInt32}, p)
        for i = 1:r
            unsafe_store!(p32, u, i)
        end
    end
    return s
end
X   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/strings/substring.jl1'      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
    SubString(s::AbstractString, i::Integer, j::Integer=lastindex(s))
    SubString(s::AbstractString, r::UnitRange{<:Integer})

Like [`getindex`](@ref), but returns a view into the parent string `s`
within range `i:j` or `r` respectively instead of making a copy.

The [`@views`](@ref) macro converts any string slices `s[i:j]` into
substrings `SubString(s, i, j)` in a block of code.

# Examples
```jldoctest
julia> SubString("abc", 1, 2)
"ab"

julia> SubString("abc", 1:2)
"ab"

julia> SubString("abc", 2)
"bc"
```
"""
struct SubString{T<:AbstractString} <: AbstractString
    string::T
    offset::Int
    ncodeunits::Int

    function SubString{T}(s::T, i::Int, j::Int) where T<:AbstractString
        i ≤ j || return new(s, 0, 0)
        @boundscheck begin
            checkbounds(s, i:j)
            @inbounds isvalid(s, i) || string_index_err(s, i)
            @inbounds isvalid(s, j) || string_index_err(s, j)
        end
        return new(s, i-1, nextind(s,j)-i)
    end
end

@propagate_inbounds SubString(s::T, i::Int, j::Int) where {T<:AbstractString} = SubString{T}(s, i, j)
@propagate_inbounds SubString(s::AbstractString, i::Integer, j::Integer=lastindex(s)) = SubString(s, Int(i), Int(j))
@propagate_inbounds SubString(s::AbstractString, r::AbstractUnitRange{<:Integer}) = SubString(s, first(r), last(r))

@propagate_inbounds function SubString(s::SubString, i::Int, j::Int)
    @boundscheck i ≤ j && checkbounds(s, i:j)
    SubString(s.string, s.offset+i, s.offset+j)
end

SubString(s::AbstractString) = SubString(s, 1, lastindex(s)::Int)
SubString{T}(s::T) where {T<:AbstractString} = SubString{T}(s, 1, lastindex(s)::Int)

@propagate_inbounds view(s::AbstractString, r::AbstractUnitRange{<:Integer}) = SubString(s, r)
@propagate_inbounds maybeview(s::AbstractString, r::AbstractUnitRange{<:Integer}) = view(s, r)
@propagate_inbounds maybeview(s::AbstractString, args...) = getindex(s, args...)

convert(::Type{SubString{S}}, s::AbstractString) where {S<:AbstractString} =
    SubString(convert(S, s))::SubString{S}
convert(::Type{T}, s::T) where {T<:SubString} = s

# Regex match allows only Union{String, SubString{String}} so define conversion to this type
convert(::Type{Union{String, SubString{String}}}, s::String) = s
convert(::Type{Union{String, SubString{String}}}, s::SubString{String}) = s
convert(::Type{Union{String, SubString{String}}}, s::AbstractString) = convert(String, s)::String

function String(s::SubString{String})
    parent = s.string
    copy = GC.@preserve parent unsafe_string(pointer(parent, s.offset+1), s.ncodeunits)
    return copy
end

ncodeunits(s::SubString) = s.ncodeunits
codeunit(s::SubString) = codeunit(s.string)::CodeunitType
length(s::SubString) = length(s.string, s.offset+1, s.offset+s.ncodeunits)

function codeunit(s::SubString, i::Integer)
    @boundscheck checkbounds(s, i)
    @inbounds return codeunit(s.string, s.offset + i)
end

function iterate(s::SubString, i::Integer=firstindex(s))
    i == ncodeunits(s)+1 && return nothing
    @boundscheck checkbounds(s, i)
    y = iterate(s.string, s.offset + i)
    y === nothing && return nothing
    c, i = y::Tuple{AbstractChar,Int}
    return c, i - s.offset
end

function getindex(s::SubString, i::Integer)
    @boundscheck checkbounds(s, i)
    @inbounds return getindex(s.string, s.offset + i)
end

isascii(ss::SubString{String}) = isascii(codeunits(ss))

function isvalid(s::SubString, i::Integer)
    ib = true
    @boundscheck ib = checkbounds(Bool, s, i)
    @inbounds return ib && isvalid(s.string, s.offset + i)::Bool
end

thisind(s::SubString{String}, i::Int) = _thisind_str(s, i)
nextind(s::SubString{String}, i::Int) = _nextind_str(s, i)

parent(s::SubString) = s.string
parentindices(s::SubString) = (s.offset + 1 : thisind(s.string, s.offset + s.ncodeunits),)

function ==(a::Union{String, SubString{String}}, b::Union{String, SubString{String}})
    sizeof(a) == sizeof(b) && _memcmp(a, b) == 0
end

function cmp(a::SubString{String}, b::SubString{String})
    c = _memcmp(a, b)
    return c < 0 ? -1 : c > 0 ? +1 : cmp(sizeof(a), sizeof(b))
end

# don't make unnecessary copies when passing substrings to C functions
cconvert(::Type{Ptr{UInt8}}, s::SubString{String}) = s
cconvert(::Type{Ptr{Int8}}, s::SubString{String}) = s

function unsafe_convert(::Type{Ptr{R}}, s::SubString{String}) where R<:Union{Int8, UInt8}
    convert(Ptr{R}, pointer(s.string)) + s.offset
end

pointer(x::SubString{String}) = pointer(x.string) + x.offset
pointer(x::SubString{String}, i::Integer) = pointer(x.string) + x.offset + (i-1)

function hash(s::SubString{String}, h::UInt)
    h += memhash_seed
    ccall(memhash, UInt, (Ptr{UInt8}, Csize_t, UInt32), s, sizeof(s), h % UInt32) + h
end

"""
    reverse(s::AbstractString) -> AbstractString

Reverses a string. Technically, this function reverses the codepoints in a string and its
main utility is for reversed-order string processing, especially for reversed
regular-expression searches. See also [`reverseind`](@ref) to convert indices in `s` to
indices in `reverse(s)` and vice-versa, and `graphemes` from module `Unicode` to
operate on user-visible "characters" (graphemes) rather than codepoints.
See also [`Iterators.reverse`](@ref) for
reverse-order iteration without making a copy. Custom string types must implement the
`reverse` function themselves and should typically return a string with the same type
and encoding. If they return a string with a different encoding, they must also override
`reverseind` for that string type to satisfy `s[reverseind(s,i)] == reverse(s)[i]`.

# Examples
```jldoctest
julia> reverse("JuliaLang")
"gnaLailuJ"
```

!!! note
    The examples below may be rendered differently on different systems.
    The comments indicate how they're supposed to be rendered

Combining characters can lead to surprising results:

```jldoctest
julia> reverse("ax̂e") # hat is above x in the input, above e in the output
"êxa"

julia> using Unicode

julia> join(reverse(collect(graphemes("ax̂e")))) # reverses graphemes; hat is above x in both in- and output
"ex̂a"
```
"""
function reverse(s::Union{String,SubString{String}})::String
    # Read characters forwards from `s` and write backwards to `out`
    out = _string_n(sizeof(s))
    offs = sizeof(s) + 1
    for c in s
        offs -= ncodeunits(c)
        __unsafe_string!(out, c, offs)
    end
    return out
end

string(a::String)            = String(a)
string(a::SubString{String}) = String(a)

function Symbol(s::SubString{String})
    return ccall(:jl_symbol_n, Ref{Symbol}, (Ptr{UInt8}, Int), s, sizeof(s))
end

@inline function __unsafe_string!(out, c::Char, offs::Integer) # out is a (new) String (or StringVector)
    x = bswap(reinterpret(UInt32, c))
    n = ncodeunits(c)
    GC.@preserve out begin
        unsafe_store!(pointer(out, offs), x % UInt8)
        n == 1 && return n
        x >>= 8
        unsafe_store!(pointer(out, offs+1), x % UInt8)
        n == 2 && return n
        x >>= 8
        unsafe_store!(pointer(out, offs+2), x % UInt8)
        n == 3 && return n
        x >>= 8
        unsafe_store!(pointer(out, offs+3), x % UInt8)
    end
    return n
end

@assume_effects :nothrow @inline function __unsafe_string!(out, s::String, offs::Integer)
    n = sizeof(s)
    GC.@preserve s out unsafe_copyto!(pointer(out, offs), pointer(s), n)
    return n
end

@inline function __unsafe_string!(out, s::SubString{String}, offs::Integer)
    n = sizeof(s)
    GC.@preserve s out unsafe_copyto!(pointer(out, offs), pointer(s), n)
    return n
end

@assume_effects :nothrow @inline function __unsafe_string!(out, s::Symbol, offs::Integer)
    n = sizeof(s)
    GC.@preserve s out unsafe_copyto!(pointer(out, offs), unsafe_convert(Ptr{UInt8},s), n)
    return n
end

# nothrow needed here because for v in a can't prove the indexing is inbounds.
@assume_effects :foldable :nothrow string(a::Union{Char, String, Symbol}...) = _string(a...)

string(a::Union{Char, String, SubString{String}, Symbol}...) = _string(a...)

function _string(a::Union{Char, String, SubString{String}, Symbol}...)
    n = 0
    for v in a
        # 4 types is too many for automatic Union-splitting, so we split manually
        # and allow one specializable call site per concrete type
        if v isa Char
            n += ncodeunits(v)
        elseif v isa String
            n += sizeof(v)
        elseif v isa SubString{String}
            n += sizeof(v)
        else
            n += sizeof(v::Symbol)
        end
    end
    out = _string_n(n)
    offs = 1
    for v in a
        if v isa Char
            offs += __unsafe_string!(out, v, offs)
        elseif v isa String || v isa SubString{String}
            offs += __unsafe_string!(out, v, offs)
        else
            offs += __unsafe_string!(out, v::Symbol, offs)
        end
    end
    return out
end

# don't assume effects for general integers since we cannot know their implementation
# not nothrow because r<0 throws
@assume_effects :foldable repeat(s::String, r::BitInteger) = @invoke repeat(s::String, r::Integer)

function repeat(s::Union{String, SubString{String}}, r::Integer)
    r < 0 && throw(ArgumentError("can't repeat a string $r times"))
    r == 0 && return ""
    r == 1 && return String(s)
    n = sizeof(s)
    out = _string_n(n*r)
    if n == 1 # common case: repeating a single-byte string
        @inbounds b = codeunit(s, 1)
        memset(unsafe_convert(Ptr{UInt8}, out), b, r)
    else
        for i = 0:r-1
            GC.@preserve s out unsafe_copyto!(pointer(out, i*n+1), pointer(s), n)
        end
    end
    return out
end

function filter(f, s::Union{String, SubString{String}})
    out = StringVector(sizeof(s))
    offset = 1
    for c in s
        if f(c)
            offset += __unsafe_string!(out, c, offset)
        end
    end
    resize!(out, offset-1)
    sizehint!(out, offset-1)
    return String(out)
end

getindex(s::AbstractString, r::AbstractUnitRange{<:Integer}) = SubString(s, r)
N   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/osutils.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
    @static

Partially evaluate an expression at parse time.

For example, `@static Sys.iswindows() ? foo : bar` will evaluate `Sys.iswindows()` and insert
either `foo` or `bar` into the expression.
This is useful in cases where a construct would be invalid on other platforms,
such as a `ccall` to a non-existent function.
`@static if Sys.isapple() foo end` and `@static foo <&&,||> bar` are also valid syntax.
"""
macro static(ex)
    if isa(ex, Expr)
        @label loop
        hd = ex.head
        if hd ∈ (:if, :elseif, :&&, :||)
            cond = Core.eval(__module__, ex.args[1])::Bool
            if xor(cond, hd === :||)
                return esc(ex.args[2])
            elseif length(ex.args) == 3
                br = ex.args[3]
                if br isa Expr && br.head === :elseif
                    ex = br
                    @goto loop
                else
                    return esc(ex.args[3])
                end
            elseif hd ∈ (:if, :elseif)
                return nothing
            else
                return cond
            end
        end
    end
    throw(ArgumentError("invalid @static macro"))
end
H   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/c.jl{Z      # This file is a part of Julia. License is MIT: https://julialang.org/license

# definitions related to C interface

import Core.Intrinsics: cglobal, bitcast

"""
    cglobal((symbol, library) [, type=Cvoid])

Obtain a pointer to a global variable in a C-exported shared library, specified exactly as
in [`ccall`](@ref).
Returns a `Ptr{Type}`, defaulting to `Ptr{Cvoid}` if no `Type` argument is
supplied.
The values can be read or written by [`unsafe_load`](@ref) or [`unsafe_store!`](@ref),
respectively.
"""
cglobal

"""
    CFunction struct

Garbage-collection handle for the return value from `@cfunction`
when the first argument is annotated with '\\\$'.
Like all `cfunction` handles, it should be passed to `ccall` as a `Ptr{Cvoid}`,
and will be converted automatically at the call site to the appropriate type.

See [`@cfunction`](@ref).
"""
mutable struct CFunction <: Ref{Cvoid}
    ptr::Ptr{Cvoid}
    f::Any
    _1::Ptr{Cvoid}
    _2::Ptr{Cvoid}
    let constructor = false end
end
unsafe_convert(::Type{Ptr{Cvoid}}, cf::CFunction) = cf.ptr

"""
    @cfunction(callable, ReturnType, (ArgumentTypes...,)) -> Ptr{Cvoid}
    @cfunction(\$callable, ReturnType, (ArgumentTypes...,)) -> CFunction

Generate a C-callable function pointer from the Julia function `callable`
for the given type signature.
To pass the return value to a `ccall`, use the argument type `Ptr{Cvoid}` in the signature.

Note that the argument type tuple must be a literal tuple, and not a tuple-valued variable or expression
(although it can include a splat expression). And that these arguments will be evaluated in global scope
during compile-time (not deferred until runtime).
Adding a '\\\$' in front of the function argument changes this to instead create a runtime closure
over the local variable `callable` (this is not supported on all architectures).

See [manual section on ccall and cfunction usage](@ref Calling-C-and-Fortran-Code).

# Examples
```julia-repl
julia> function foo(x::Int, y::Int)
           return x + y
       end

julia> @cfunction(foo, Int, (Int, Int))
Ptr{Cvoid} @0x000000001b82fcd0
```
"""
macro cfunction(f, rt, at)
    if !(isa(at, Expr) && at.head === :tuple)
        throw(ArgumentError("@cfunction argument types must be a literal tuple"))
    end
    at.head = :call
    pushfirst!(at.args, GlobalRef(Core, :svec))
    if isa(f, Expr) && f.head === :$
        fptr = f.args[1]
        typ = CFunction
    else
        fptr = QuoteNode(f)
        typ = Ptr{Cvoid}
    end
    cfun = Expr(:cfunction, typ, fptr, rt, at, QuoteNode(:ccall))
    return esc(cfun)
end

if ccall(:jl_is_char_signed, Ref{Bool}, ())
    const Cchar = Int8
else
    const Cchar = UInt8
end
"""
    Cchar

Equivalent to the native `char` c-type.
"""
Cchar

# The ccall here is equivalent to Sys.iswindows(), but that's not defined yet
@static if ccall(:jl_get_UNAME, Any, ()) === :NT
    const Clong = Int32
    const Culong = UInt32
    const Cwchar_t = UInt16
else
    const Clong = Int
    const Culong = UInt
    const Cwchar_t = Int32
end

"""
    Clong

Equivalent to the native `signed long` c-type.
"""
Clong

"""
    Culong

Equivalent to the native `unsigned long` c-type.
"""
Culong

"""
    Cwchar_t

Equivalent to the native `wchar_t` c-type ([`Int32`](@ref)).
"""
Cwchar_t

"""
    Cwstring

A C-style string composed of the native wide character type
[`Cwchar_t`](@ref)s. `Cwstring`s are NUL-terminated. For
C-style strings composed of the native character
type, see [`Cstring`](@ref). For more information
about string interoperability with C, see the
[manual](@ref man-bits-types).

"""
Cwstring

"""
    Cstring

A C-style string composed of the native character type
[`Cchar`](@ref)s. `Cstring`s are NUL-terminated. For
C-style strings composed of the native wide character
type, see [`Cwstring`](@ref). For more information
about string interoperability with C, see the
[manual](@ref man-bits-types).
"""
Cstring

@static if ccall(:jl_get_UNAME, Any, ()) !== :NT
    const sizeof_mode_t = ccall(:jl_sizeof_mode_t, Cint, ())
    if sizeof_mode_t == 2
        const Cmode_t = Int16
    elseif sizeof_mode_t == 4
        const Cmode_t = Int32
    elseif sizeof_mode_t == 8
        const Cmode_t = Int64
    end
end

# construction from pointers
Cstring(p::Union{Ptr{Int8},Ptr{UInt8},Ptr{Cvoid}}) = bitcast(Cstring, p)
Cwstring(p::Union{Ptr{Cwchar_t},Ptr{Cvoid}})       = bitcast(Cwstring, p)
Ptr{T}(p::Cstring) where {T<:Union{Int8,UInt8,Cvoid}} = bitcast(Ptr{T}, p)
Ptr{T}(p::Cwstring) where {T<:Union{Cwchar_t,Cvoid}}  = bitcast(Ptr{Cwchar_t}, p)

convert(::Type{Cstring}, p::Union{Ptr{Int8},Ptr{UInt8},Ptr{Cvoid}}) = Cstring(p)
convert(::Type{Cwstring}, p::Union{Ptr{Cwchar_t},Ptr{Cvoid}}) = Cwstring(p)
convert(::Type{Ptr{T}}, p::Cstring) where {T<:Union{Int8,UInt8,Cvoid}} = Ptr{T}(p)
convert(::Type{Ptr{T}}, p::Cwstring) where {T<:Union{Cwchar_t,Cvoid}} = Ptr{T}(p)

"""
    pointer(array [, index])

Get the native address of an array or string, optionally at a given location `index`.

This function is "unsafe". Be careful to ensure that a Julia reference to
`array` exists as long as this pointer will be used. The [`GC.@preserve`](@ref)
macro should be used to protect the `array` argument from garbage collection
within a given block of code.

Calling [`Ref(array[, index])`](@ref Ref) is generally preferable to this function as it guarantees validity.
"""
function pointer end

pointer(p::Cstring) = convert(Ptr{Cchar}, p)
pointer(p::Cwstring) = convert(Ptr{Cwchar_t}, p)

# comparisons against pointers (mainly to support `cstr==C_NULL`)
==(x::Union{Cstring,Cwstring}, y::Ptr) = pointer(x) == y
==(x::Ptr, y::Union{Cstring,Cwstring}) = x == pointer(y)

unsafe_string(s::Cstring) = unsafe_string(convert(Ptr{UInt8}, s))

# convert strings to String etc. to pass as pointers
cconvert(::Type{Cstring}, s::String) = s
cconvert(::Type{Cstring}, s::AbstractString) =
    cconvert(Cstring, String(s)::String)

function cconvert(::Type{Cwstring}, s::AbstractString)
    v = transcode(Cwchar_t, String(s))
    !isempty(v) && v[end] == 0 || push!(v, 0)
    return v
end

eltype(::Type{Cstring}) = Cchar
eltype(::Type{Cwstring}) = Cwchar_t

containsnul(p::Ptr, len) =
    C_NULL != ccall(:memchr, Ptr{Cchar}, (Ptr{Cchar}, Cint, Csize_t), p, 0, len)
containsnul(s::String) = containsnul(unsafe_convert(Ptr{Cchar}, s), sizeof(s))
containsnul(s::AbstractString) = '\0' in s

function unsafe_convert(::Type{Cstring}, s::Union{String,AbstractVector{UInt8}})
    p = unsafe_convert(Ptr{Cchar}, s)
    containsnul(p, sizeof(s)) &&
        throw(ArgumentError("embedded NULs are not allowed in C strings: $(repr(s))"))
    return Cstring(p)
end

function unsafe_convert(::Type{Cwstring}, v::Vector{Cwchar_t})
    for i = 1:length(v)-1
        v[i] == 0 &&
            throw(ArgumentError("embedded NULs are not allowed in C strings: $(repr(v))"))
    end
    v[end] == 0 ||
        throw(ArgumentError("C string data must be NUL terminated: $(repr(v))"))
    p = unsafe_convert(Ptr{Cwchar_t}, v)
    return Cwstring(p)
end

# symbols are guaranteed not to contain embedded NUL
cconvert(::Type{Cstring}, s::Symbol) = s
unsafe_convert(::Type{Cstring}, s::Symbol) = Cstring(unsafe_convert(Ptr{Cchar}, s))

@static if ccall(:jl_get_UNAME, Any, ()) === :NT
"""
    Base.cwstring(s)

Converts a string `s` to a NUL-terminated `Vector{Cwchar_t}`, suitable for passing to C
functions expecting a `Ptr{Cwchar_t}`. The main advantage of using this over the implicit
conversion provided by [`Cwstring`](@ref) is if the function is called multiple times with the
same argument.

This is only available on Windows.
"""
function cwstring(s::AbstractString)
    bytes = codeunits(String(s))
    0 in bytes && throw(ArgumentError("embedded NULs are not allowed in C strings: $(repr(s))"))
    return push!(transcode(UInt16, bytes), 0)
end
end

# transcoding between data in UTF-8 and UTF-16 for Windows APIs,
# and also UTF-32 for APIs using Cwchar_t on other platforms.

"""
    transcode(T, src)

Convert string data between Unicode encodings. `src` is either a
`String` or a `Vector{UIntXX}` of UTF-XX code units, where
`XX` is 8, 16, or 32. `T` indicates the encoding of the return value:
`String` to return a (UTF-8 encoded) `String` or `UIntXX`
to return a `Vector{UIntXX}` of UTF-`XX` data. (The alias [`Cwchar_t`](@ref)
can also be used as the integer type, for converting `wchar_t*` strings
used by external C libraries.)

The `transcode` function succeeds as long as the input data can be
reasonably represented in the target encoding; it always succeeds for
conversions between UTF-XX encodings, even for invalid Unicode data.

Only conversion to/from UTF-8 is currently supported.

# Examples
```jldoctest
julia> str = "αβγ"
"αβγ"

julia> transcode(UInt16, str)
3-element Vector{UInt16}:
 0x03b1
 0x03b2
 0x03b3

julia> transcode(String, transcode(UInt16, str))
"αβγ"
```
"""
function transcode end

transcode(::Type{T}, src::AbstractVector{T}) where {T<:Union{UInt8,UInt16,UInt32,Int32}} = src
transcode(::Type{T}, src::String) where {T<:Union{Int32,UInt32}} = T[T(c) for c in src]
transcode(::Type{T}, src::AbstractVector{UInt8}) where {T<:Union{Int32,UInt32}} =
    transcode(T, String(Vector(src)))
transcode(::Type{T}, src::CodeUnits{UInt8,String}) where {T<:Union{Int32,UInt32}} =
    transcode(T, String(src))

function transcode(::Type{UInt8}, src::Vector{<:Union{Int32,UInt32}})
    buf = IOBuffer()
    for c in src
        print(buf, Char(c))
    end
    take!(buf)
end
transcode(::Type{String}, src::String) = src
transcode(T, src::String) = transcode(T, codeunits(src))
transcode(::Type{String}, src) = String(transcode(UInt8, src))

function transcode(::Type{UInt16}, src::AbstractVector{UInt8})
    require_one_based_indexing(src)
    dst = UInt16[]
    i, n = 1, length(src)
    n > 0 || return dst
    sizehint!(dst, 2n)
    a = src[1]
    while true
        if i < n && -64 <= a % Int8 <= -12 # multi-byte character
            b = src[i += 1]
            if -64 <= (b % Int8) || a == 0xf4 && 0x8f < b
                # invalid UTF-8 (non-continuation or too-high code point)
                push!(dst, a)
                a = b; continue
            elseif a < 0xe0 # 2-byte UTF-8
                push!(dst, xor(0x3080, UInt16(a) << 6, b))
            elseif i < n # 3/4-byte character
                c = src[i += 1]
                if -64 <= (c % Int8) # invalid UTF-8 (non-continuation)
                    push!(dst, a, b)
                    a = c; continue
                elseif a < 0xf0 # 3-byte UTF-8
                    push!(dst, xor(0x2080, UInt16(a) << 12, UInt16(b) << 6, c))
                elseif i < n
                    d = src[i += 1]
                    if -64 <= (d % Int8) # invalid UTF-8 (non-continuation)
                        push!(dst, a, b, c)
                        a = d; continue
                    elseif a == 0xf0 && b < 0x90 # overlong encoding
                        push!(dst, xor(0x2080, UInt16(b) << 12, UInt16(c) << 6, d))
                    else # 4-byte UTF-8
                        push!(dst, 0xe5b8 + (UInt16(a) << 8) + (UInt16(b) << 2) + (c >> 4),
                                   xor(0xdc80, UInt16(c & 0xf) << 6, d))
                    end
                else # too short
                    push!(dst, a, b, c)
                    break
                end
            else # too short
                push!(dst, a, b)
                break
            end
        else # ASCII or invalid UTF-8 (continuation byte or too-high code point)
            push!(dst, a)
        end
        i < n || break
        a = src[i += 1]
    end
    return dst
end

function transcode(::Type{UInt8}, src::AbstractVector{UInt16})
    require_one_based_indexing(src)
    n = length(src)
    n == 0 && return UInt8[]

    # Precompute m = sizeof(dst).   This involves annoying duplication
    # of the loop over the src array.   However, this is not just an
    # optimization: it is problematic for security reasons to grow
    # dst dynamically, because Base.winprompt uses this function to
    # convert passwords to UTF-8 and we don't want to make unintentional
    # copies of the password data.
    a = src[1]
    i, m = 1, 0
    while true
        if a < 0x80
            m += 1
        elseif a < 0x800 # 2-byte UTF-8
            m += 2
        elseif a & 0xfc00 == 0xd800 && i < length(src)
            b = src[i += 1]
            if (b & 0xfc00) == 0xdc00 # 2-unit UTF-16 sequence => 4-byte UTF-8
                m += 4
            else
                m += 3
                a = b; continue
            end
        else
            # 1-unit high UTF-16 or unpaired high surrogate
            # either way, encode as 3-byte UTF-8 code point
            m += 3
        end
        i < n || break
        a = src[i += 1]
    end

    dst = StringVector(m)
    a = src[1]
    i, j = 1, 0
    while true
        if a < 0x80 # ASCII
            dst[j += 1] = a % UInt8
        elseif a < 0x800 # 2-byte UTF-8
            dst[j += 1] = 0xc0 | ((a >> 6) % UInt8)
            dst[j += 1] = 0x80 | ((a % UInt8) & 0x3f)
        elseif a & 0xfc00 == 0xd800 && i < n
            b = src[i += 1]
            if (b & 0xfc00) == 0xdc00
                # 2-unit UTF-16 sequence => 4-byte UTF-8
                a += 0x2840
                dst[j += 1] = 0xf0 | ((a >> 8) % UInt8)
                dst[j += 1] = 0x80 | ((a % UInt8) >> 2)
                dst[j += 1] = xor(0xf0, ((a % UInt8) << 4) & 0x3f, (b >> 6) % UInt8)
                dst[j += 1] = 0x80 | ((b % UInt8) & 0x3f)
            else
                dst[j += 1] = 0xe0 | ((a >> 12) % UInt8)
                dst[j += 1] = 0x80 | (((a >> 6) % UInt8) & 0x3f)
                dst[j += 1] = 0x80 | ((a % UInt8) & 0x3f)
                a = b; continue
            end
        else
            # 1-unit high UTF-16 or unpaired high surrogate
            # either way, encode as 3-byte UTF-8 code point
            dst[j += 1] = 0xe0 | ((a >> 12) % UInt8)
            dst[j += 1] = 0x80 | (((a >> 6) % UInt8) & 0x3f)
            dst[j += 1] = 0x80 | ((a % UInt8) & 0x3f)
        end
        i < n || break
        a = src[i += 1]
    end
    return dst
end

function unsafe_string(p::Ptr{T}, length::Integer) where {T<:Union{UInt16,UInt32,Cwchar_t}}
    transcode(String, unsafe_wrap(Array, p, length; own=false))
end
function unsafe_string(cw::Cwstring)
    p = convert(Ptr{Cwchar_t}, cw)
    n = 1
    while unsafe_load(p, n) != 0
        n += 1
    end
    return unsafe_string(p, n - 1)
end

# deferring (or un-deferring) ctrl-c handler for external C code that
# is not interrupt safe (see also issue #2622).  The sigatomic_begin/end
# functions should always be called in matched pairs, ideally via:
#            disable_sigint() do .. end
# reennable_sigint is provided so that immediate ctrl-c handling is
# re-enabled within a sigatomic region, e.g. inside a Julia callback function
# within a long-running C routine.
sigatomic_begin() = ccall(:jl_sigatomic_begin, Cvoid, ())
sigatomic_end() = ccall(:jl_sigatomic_end, Cvoid, ())

"""
    disable_sigint(f::Function)

Disable Ctrl-C handler during execution of a function on the current task,
for calling external code that may call julia code that is not interrupt safe.
Intended to be called using `do` block syntax as follows:

    disable_sigint() do
        # interrupt-unsafe code
        ...
    end

This is not needed on worker threads (`Threads.threadid() != 1`) since the
`InterruptException` will only be delivered to the master thread.
External functions that do not call julia code or julia runtime
automatically disable sigint during their execution.
"""
function disable_sigint(f::Function)
    sigatomic_begin()
    res = f()
    # Exception unwind sigatomic automatically
    sigatomic_end()
    res
end

"""
    reenable_sigint(f::Function)

Re-enable Ctrl-C handler during execution of a function.
Temporarily reverses the effect of [`disable_sigint`](@ref).
"""
function reenable_sigint(f::Function)
    sigatomic_end()
    res = f()
    # Exception unwind sigatomic automatically
    sigatomic_begin()
    res
end

"""
    exit_on_sigint(on::Bool)

Set `exit_on_sigint` flag of the julia runtime.  If `false`, Ctrl-C
(SIGINT) is capturable as [`InterruptException`](@ref) in `try` block.
This is the default behavior in REPL, any code run via `-e` and `-E`
and in Julia script run with `-i` option.

If `true`, `InterruptException` is not thrown by Ctrl-C.  Running code
upon such event requires [`atexit`](@ref).  This is the default
behavior in Julia script run without `-i` option.

!!! compat "Julia 1.5"
    Function `exit_on_sigint` requires at least Julia 1.5.
"""
function exit_on_sigint(on::Bool)
    ccall(:jl_exit_on_sigint, Cvoid, (Cint,), on)
end

function _ccallable(rt::Type, sigt::Type)
    ccall(:jl_extern_c, Cvoid, (Any, Any), rt, sigt)
end

function expand_ccallable(rt, def)
    if isa(def,Expr) && (def.head === :(=) || def.head === :function)
        sig = def.args[1]
        if sig.head === :(::)
            if rt === nothing
                rt = sig.args[2]
            end
            sig = sig.args[1]
        end
        if rt === nothing
            error("@ccallable requires a return type")
        end
        if sig.head === :call
            f = sig.args[1]
            if isa(f,Expr) && f.head === :(::)
                f = f.args[end]
            else
                f = :(typeof($f))
            end
            at = map(sig.args[2:end]) do a
                if isa(a,Expr) && a.head === :(::)
                    a.args[end]
                else
                    :Any
                end
            end
            return quote
                $(esc(def))
                _ccallable($(esc(rt)), $(Expr(:curly, :Tuple, esc(f), map(esc, at)...)))
            end
        end
    end
    error("expected method definition in @ccallable")
end

"""
    @ccallable(def)

Make the annotated function be callable from C using its name. This can, for example,
be used to expose functionality as a C-API when creating a custom Julia sysimage.
"""
macro ccallable(def)
    expand_ccallable(nothing, def)
end
macro ccallable(rt, def)
    expand_ccallable(rt, def)
end

# @ccall implementation
"""
    ccall_macro_parse(expression)

`ccall_macro_parse` is an implementation detail of `@ccall`.

It takes an expression like `:(printf("%d"::Cstring, value::Cuint)::Cvoid)`
returns: a tuple of `(function_name, return_type, arg_types, args)`

The above input outputs this:

    (:printf, :Cvoid, [:Cstring, :Cuint], ["%d", :value])
"""
function ccall_macro_parse(expr::Expr)
    # setup and check for errors
    if !Meta.isexpr(expr, :(::))
        throw(ArgumentError("@ccall needs a function signature with a return type"))
    end
    rettype = expr.args[2]

    call = expr.args[1]
    if !Meta.isexpr(call, :call)
        throw(ArgumentError("@ccall has to take a function call"))
    end

    # get the function symbols
    func = let f = call.args[1]
        if Meta.isexpr(f, :.)
            :(($(f.args[2]), $(f.args[1])))
        elseif Meta.isexpr(f, :$)
            f
        elseif f isa Symbol
            QuoteNode(f)
        else
            throw(ArgumentError("@ccall function name must be a symbol, a `.` node (e.g. `libc.printf`) or an interpolated function pointer (with `\$`)"))
        end
    end

    # detect varargs
    varargs = nothing
    argstart = 2
    callargs = call.args
    if length(callargs) >= 2 && Meta.isexpr(callargs[2], :parameters)
        argstart = 3
        varargs = callargs[2].args
    end

    # collect args and types
    args = []
    types = []

    function pusharg!(arg)
        if !Meta.isexpr(arg, :(::))
            throw(ArgumentError("args in @ccall need type annotations. '$arg' doesn't have one."))
        end
        push!(args, arg.args[1])
        push!(types, arg.args[2])
    end

    for i in argstart:length(callargs)
        pusharg!(callargs[i])
    end
    # add any varargs if necessary
    nreq = 0
    if !isnothing(varargs)
        if length(args) == 0
            throw(ArgumentError("C ABI prohibits vararg without one required argument"))
        end
        nreq = length(args)
        for a in varargs
            pusharg!(a)
        end
    end

    return func, rettype, types, args, nreq
end


function ccall_macro_lower(convention, func, rettype, types, args, nreq)
    statements = []

    # if interpolation was used, ensure the value is a function pointer at runtime.
    if Meta.isexpr(func, :$)
        push!(statements, Expr(:(=), :func, esc(func.args[1])))
        name = QuoteNode(func.args[1])
        func = :func
        check = quote
            if !isa(func, Ptr{Cvoid})
                name = $name
                throw(ArgumentError("interpolated function `$name` was not a Ptr{Cvoid}, but $(typeof(func))"))
            end
        end
        push!(statements, check)
    else
        func = esc(func)
    end

    return Expr(:block, statements...,
                Expr(:call, :ccall, func, Expr(:cconv, convention, nreq), esc(rettype),
                     Expr(:tuple, map(esc, types)...), map(esc, args)...))
end

"""
    @ccall library.function_name(argvalue1::argtype1, ...)::returntype
    @ccall function_name(argvalue1::argtype1, ...)::returntype
    @ccall \$function_pointer(argvalue1::argtype1, ...)::returntype

Call a function in a C-exported shared library, specified by
`library.function_name`, where `library` is a string constant or
literal. The library may be omitted, in which case the `function_name`
is resolved in the current process. Alternatively, `@ccall` may
also be used to call a function pointer `\$function_pointer`, such as
one returned by `dlsym`.

Each `argvalue` to `@ccall` is converted to the corresponding
`argtype`, by automatic insertion of calls to `unsafe_convert(argtype,
cconvert(argtype, argvalue))`. (See also the documentation for
[`unsafe_convert`](@ref Base.unsafe_convert) and [`cconvert`](@ref
Base.cconvert) for further details.) In most cases, this simply
results in a call to `convert(argtype, argvalue)`.


# Examples

    @ccall strlen(s::Cstring)::Csize_t

This calls the C standard library function:

    size_t strlen(char *)

with a Julia variable named `s`. See also `ccall`.

Varargs are supported with the following convention:

    @ccall printf("%s = %d"::Cstring ; "foo"::Cstring, foo::Cint)::Cint

The semicolon is used to separate required arguments (of which there
must be at least one) from variadic arguments.

Example using an external library:

    # C signature of g_uri_escape_string:
    # char *g_uri_escape_string(const char *unescaped, const char *reserved_chars_allowed, gboolean allow_utf8);

    const glib = "libglib-2.0"
    @ccall glib.g_uri_escape_string(my_uri::Cstring, ":/"::Cstring, true::Cint)::Cstring

The string literal could also be used directly before the function
name, if desired `"libglib-2.0".g_uri_escape_string(...`
"""
macro ccall(expr)
    return ccall_macro_lower(:ccall, ccall_macro_parse(expr)...)
end

macro ccall_effects(effects::UInt8, expr)
    return ccall_macro_lower((:ccall, effects), ccall_macro_parse(expr)...)
end
I   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/io.jlТ      # This file is a part of Julia. License is MIT: https://julialang.org/license

# Generic IO stubs -- all subtypes should implement these (if meaningful)

"""
    EOFError()

No more data was available to read from a file or stream.
"""
struct EOFError <: Exception end

"""
    SystemError(prefix::AbstractString, [errno::Int32])

A system call failed with an error code (in the `errno` global variable).
"""
struct SystemError <: Exception
    prefix::String
    errnum::Int32
    extrainfo
    SystemError(p::AbstractString, e::Integer, extrainfo) = new(p, e, extrainfo)
    SystemError(p::AbstractString, e::Integer) = new(p, e, nothing)
    SystemError(p::AbstractString) = new(p, Libc.errno(), nothing)
end

lock(::IO) = nothing
unlock(::IO) = nothing
reseteof(x::IO) = nothing

const SZ_UNBUFFERED_IO = 65536
buffer_writes(x::IO, bufsize=SZ_UNBUFFERED_IO) = x

"""
    isopen(object) -> Bool

Determine whether an object - such as a stream or timer
-- is not yet closed. Once an object is closed, it will never produce a new event.
However, since a closed stream may still have data to read in its buffer,
use [`eof`](@ref) to check for the ability to read data.
Use the `FileWatching` package to be notified when a stream might be writable or readable.

# Examples
```jldoctest
julia> io = open("my_file.txt", "w+");

julia> isopen(io)
true

julia> close(io)

julia> isopen(io)
false
```
"""
function isopen end

"""
    close(stream)

Close an I/O stream. Performs a [`flush`](@ref) first.
"""
function close end

"""
    closewrite(stream)

Shutdown the write half of a full-duplex I/O stream. Performs a [`flush`](@ref)
first. Notify the other end that no more data will be written to the underlying
file. This is not supported by all IO types.

# Examples
```jldoctest
julia> io = Base.BufferStream(); # this never blocks, so we can read and write on the same Task

julia> write(io, "request");

julia> # calling `read(io)` here would block forever

julia> closewrite(io);

julia> read(io, String)
"request"
```
"""
function closewrite end

"""
    flush(stream)

Commit all currently buffered writes to the given stream.
"""
function flush end

"""
    bytesavailable(io)

Return the number of bytes available for reading before a read from this stream or buffer will block.

# Examples
```jldoctest
julia> io = IOBuffer("JuliaLang is a GitHub organization");

julia> bytesavailable(io)
34
```
"""
function bytesavailable end

"""
    readavailable(stream)

Read available buffered data from a stream. Actual I/O is performed only if no
data has already been buffered. The result is a `Vector{UInt8}`.

!!! warning
    The amount of data returned is implementation-dependent; for example it can
    depend on the internal choice of buffer size. Other functions such as [`read`](@ref)
    should generally be used instead.
"""
function readavailable end

"""
    isreadable(io) -> Bool

Return `false` if the specified IO object is not readable.

# Examples
```jldoctest
julia> open("myfile.txt", "w") do io
           print(io, "Hello world!");
           isreadable(io)
       end
false

julia> open("myfile.txt", "r") do io
           isreadable(io)
       end
true

julia> rm("myfile.txt")
```
"""
isreadable(io::IO) = isopen(io)

"""
    iswritable(io) -> Bool

Return `false` if the specified IO object is not writable.

# Examples
```jldoctest
julia> open("myfile.txt", "w") do io
           print(io, "Hello world!");
           iswritable(io)
       end
true

julia> open("myfile.txt", "r") do io
           iswritable(io)
       end
false

julia> rm("myfile.txt")
```
"""
iswritable(io::IO) = isopen(io)

"""
    eof(stream) -> Bool

Test whether an I/O stream is at end-of-file. If the stream is not yet exhausted, this
function will block to wait for more data if necessary, and then return `false`. Therefore
it is always safe to read one byte after seeing `eof` return `false`. `eof` will return
`false` as long as buffered data is still available, even if the remote end of a connection
is closed.

# Examples
```jldoctest
julia> b = IOBuffer("my buffer");

julia> eof(b)
false

julia> seekend(b);

julia> eof(b)
true
```
"""
function eof end

function copy end
function wait_readnb end
function wait_close end

"""
    read(io::IO, T)

Read a single value of type `T` from `io`, in canonical binary representation.

Note that Julia does not convert the endianness for you. Use [`ntoh`](@ref) or
[`ltoh`](@ref) for this purpose.

    read(io::IO, String)

Read the entirety of `io`, as a `String` (see also [`readchomp`](@ref)).

# Examples
```jldoctest
julia> io = IOBuffer("JuliaLang is a GitHub organization");

julia> read(io, Char)
'J': ASCII/Unicode U+004A (category Lu: Letter, uppercase)

julia> io = IOBuffer("JuliaLang is a GitHub organization");

julia> read(io, String)
"JuliaLang is a GitHub organization"
```
"""
read(stream, t)
read(stream, ::Type{Union{}}, slurp...; kwargs...) = error("cannot read a value of type Union{}")


"""
    write(io::IO, x)

Write the canonical binary representation of a value to the given I/O stream or file.
Return the number of bytes written into the stream. See also [`print`](@ref) to
write a text representation (with an encoding that may depend upon `io`).

The endianness of the written value depends on the endianness of the host system.
Convert to/from a fixed endianness when writing/reading (e.g. using  [`htol`](@ref) and
[`ltoh`](@ref)) to get results that are consistent across platforms.

You can write multiple values with the same `write` call. i.e. the following are equivalent:

    write(io, x, y...)
    write(io, x) + write(io, y...)

# Examples
Consistent serialization:
```jldoctest
julia> fname = tempname(); # random temporary filename

julia> open(fname,"w") do f
           # Make sure we write 64bit integer in little-endian byte order
           write(f,htol(Int64(42)))
       end
8

julia> open(fname,"r") do f
           # Convert back to host byte order and host integer type
           Int(ltoh(read(f,Int64)))
       end
42
```

Merging write calls:
```jldoctest
julia> io = IOBuffer();

julia> write(io, "JuliaLang is a GitHub organization.", " It has many members.")
56

julia> String(take!(io))
"JuliaLang is a GitHub organization. It has many members."

julia> write(io, "Sometimes those members") + write(io, " write documentation.")
44

julia> String(take!(io))
"Sometimes those members write documentation."
```
User-defined plain-data types without `write` methods can be written when wrapped in a `Ref`:
```jldoctest
julia> struct MyStruct; x::Float64; end

julia> io = IOBuffer()
IOBuffer(data=UInt8[...], readable=true, writable=true, seekable=true, append=false, size=0, maxsize=Inf, ptr=1, mark=-1)

julia> write(io, Ref(MyStruct(42.0)))
8

julia> seekstart(io); read!(io, Ref(MyStruct(NaN)))
Base.RefValue{MyStruct}(MyStruct(42.0))
```
"""
function write end

read(s::IO, ::Type{UInt8}) = error(typeof(s)," does not support byte I/O")
write(s::IO, x::UInt8) = error(typeof(s)," does not support byte I/O")

"""
    unsafe_write(io::IO, ref, nbytes::UInt)

Copy `nbytes` from `ref` (converted to a pointer) into the `IO` object.

It is recommended that subtypes `T<:IO` override the following method signature
to provide more efficient implementations:
`unsafe_write(s::T, p::Ptr{UInt8}, n::UInt)`
"""
function unsafe_write(s::IO, p::Ptr{UInt8}, n::UInt)
    written::Int = 0
    for i = 1:n
        written += write(s, unsafe_load(p, i))
    end
    return written
end

"""
    unsafe_read(io::IO, ref, nbytes::UInt)

Copy `nbytes` from the `IO` stream object into `ref` (converted to a pointer).

It is recommended that subtypes `T<:IO` override the following method signature
to provide more efficient implementations:
`unsafe_read(s::T, p::Ptr{UInt8}, n::UInt)`
"""
function unsafe_read(s::IO, p::Ptr{UInt8}, n::UInt)
    for i = 1:n
        unsafe_store!(p, read(s, UInt8)::UInt8, i)
    end
    nothing
end

function peek(s::IO, ::Type{T}) where T
    mark(s)
    try read(s, T)::T
    finally
        reset(s)
    end
end

peek(s) = peek(s, UInt8)::UInt8

# Generic `open` methods

"""
    open_flags(; keywords...) -> NamedTuple

Compute the `read`, `write`, `create`, `truncate`, `append` flag value for
a given set of keyword arguments to [`open`](@ref) a [`NamedTuple`](@ref).
"""
function open_flags(;
    read     :: Union{Bool,Nothing} = nothing,
    write    :: Union{Bool,Nothing} = nothing,
    create   :: Union{Bool,Nothing} = nothing,
    truncate :: Union{Bool,Nothing} = nothing,
    append   :: Union{Bool,Nothing} = nothing,
)
    if write === true && read !== true && append !== true
        create   === nothing && (create   = true)
        truncate === nothing && (truncate = true)
    end

    if truncate === true || append === true
        write  === nothing && (write  = true)
        create === nothing && (create = true)
    end

    write    === nothing && (write    = false)
    read     === nothing && (read     = !write)
    create   === nothing && (create   = false)
    truncate === nothing && (truncate = false)
    append   === nothing && (append   = false)

    return (
        read = read,
        write = write,
        create = create,
        truncate = truncate,
        append = append,
    )
end

"""
    open(f::Function, args...; kwargs...)

Apply the function `f` to the result of `open(args...; kwargs...)` and close the resulting file
descriptor upon completion.

# Examples
```jldoctest
julia> write("myfile.txt", "Hello world!");

julia> open(io->read(io, String), "myfile.txt")
"Hello world!"

julia> rm("myfile.txt")
```
"""
function open(f::Function, args...; kwargs...)
    io = open(args...; kwargs...)
    try
        f(io)
    finally
        close(io)
    end
end

"""
    AbstractPipe

`AbstractPipe` is the abstract supertype for IO pipes that provide for communication between processes.

If `pipe isa AbstractPipe`, it must obey the following interface:

- `pipe.in` or `pipe.in_stream`, if present, must be of type `IO` and be used to provide input to the pipe
- `pipe.out` or `pipe.out_stream`, if present, must be of type `IO` and be used for output from the pipe
- `pipe.err` or `pipe.err_stream`, if present, must be of type `IO` and be used for writing errors from the pipe
"""
abstract type AbstractPipe <: IO end

function getproperty(pipe::AbstractPipe, name::Symbol)
    if name === :in || name === :in_stream || name === :out || name === :out_stream ||
       name === :err || name === :err_stream
        return getfield(pipe, name)::IO
    end
    return getfield(pipe, name)
end

function pipe_reader end
function pipe_writer end

for f in (:flush, :closewrite, :iswritable)
    @eval $(f)(io::AbstractPipe) = $(f)(pipe_writer(io)::IO)
end
write(io::AbstractPipe, byte::UInt8) = write(pipe_writer(io)::IO, byte)
write(to::IO, from::AbstractPipe) = write(to, pipe_reader(from))
unsafe_write(io::AbstractPipe, p::Ptr{UInt8}, nb::UInt) = unsafe_write(pipe_writer(io)::IO, p, nb)::Union{Int,UInt}
buffer_writes(io::AbstractPipe, args...) = buffer_writes(pipe_writer(io)::IO, args...)

for f in (
        # peek/mark interface
        :mark, :unmark, :reset, :ismarked,
        # Simple reader functions
        :read, :readavailable, :bytesavailable, :reseteof, :isreadable)
    @eval $(f)(io::AbstractPipe) = $(f)(pipe_reader(io)::IO)
end
read(io::AbstractPipe, byte::Type{UInt8}) = read(pipe_reader(io)::IO, byte)::UInt8
unsafe_read(io::AbstractPipe, p::Ptr{UInt8}, nb::UInt) = unsafe_read(pipe_reader(io)::IO, p, nb)
readuntil(io::AbstractPipe, arg::UInt8; kw...) = readuntil(pipe_reader(io)::IO, arg; kw...)
readuntil(io::AbstractPipe, arg::AbstractChar; kw...) = readuntil(pipe_reader(io)::IO, arg; kw...)
readuntil(io::AbstractPipe, arg::AbstractString; kw...) = readuntil(pipe_reader(io)::IO, arg; kw...)
readuntil(io::AbstractPipe, arg::AbstractVector; kw...) = readuntil(pipe_reader(io)::IO, arg; kw...)
readuntil_vector!(io::AbstractPipe, target::AbstractVector, keep::Bool, out) = readuntil_vector!(pipe_reader(io)::IO, target, keep, out)
readbytes!(io::AbstractPipe, target::AbstractVector{UInt8}, n=length(target)) = readbytes!(pipe_reader(io)::IO, target, n)
peek(io::AbstractPipe, ::Type{T}) where {T} = peek(pipe_reader(io)::IO, T)::T
wait_readnb(io::AbstractPipe, nb::Int) = wait_readnb(pipe_reader(io)::IO, nb)
eof(io::AbstractPipe) = eof(pipe_reader(io)::IO)::Bool

isopen(io::AbstractPipe) = isopen(pipe_writer(io)::IO) || isopen(pipe_reader(io)::IO)
close(io::AbstractPipe) = (close(pipe_writer(io)::IO); close(pipe_reader(io)::IO))
wait_close(io::AbstractPipe) = (wait_close(pipe_writer(io)::IO); wait_close(pipe_reader(io)::IO))


# Exception-safe wrappers (io = open(); try f(io) finally close(io))


"""
    write(filename::AbstractString, content)

Write the canonical binary representation of `content` to a file, which will be created if it does not exist yet or overwritten if it does exist.

Return the number of bytes written into the file.
"""
write(filename::AbstractString, a1, args...) = open(io->write(io, a1, args...), convert(String, filename)::String, "w")

"""
    read(filename::AbstractString)

Read the entire contents of a file as a `Vector{UInt8}`.

    read(filename::AbstractString, String)

Read the entire contents of a file as a string.

    read(filename::AbstractString, args...)

Open a file and read its contents. `args` is passed to `read`: this is equivalent to
`open(io->read(io, args...), filename)`.
"""
read(filename::AbstractString, args...) = open(io->read(io, args...), convert(String, filename)::String)

read(filename::AbstractString, ::Type{T}) where {T} = open(io->read(io, T), convert(String, filename)::String)

"""
    read!(stream::IO, array::AbstractArray)
    read!(filename::AbstractString, array::AbstractArray)

Read binary data from an I/O stream or file, filling in `array`.
"""
function read! end

read!(filename::AbstractString, a) = open(io->read!(io, a), convert(String, filename)::String)

"""
    readuntil(stream::IO, delim; keep::Bool = false)
    readuntil(filename::AbstractString, delim; keep::Bool = false)

Read a string from an I/O stream or a file, up to the given delimiter.
The delimiter can be a `UInt8`, `AbstractChar`, string, or vector.
Keyword argument `keep` controls whether the delimiter is included in the result.
The text is assumed to be encoded in UTF-8.

# Examples
```jldoctest
julia> write("my_file.txt", "JuliaLang is a GitHub organization.\\nIt has many members.\\n");

julia> readuntil("my_file.txt", 'L')
"Julia"

julia> readuntil("my_file.txt", '.', keep = true)
"JuliaLang is a GitHub organization."

julia> rm("my_file.txt")
```
"""
readuntil(filename::AbstractString, args...; kw...) = open(io->readuntil(io, args...; kw...), convert(String, filename)::String)

"""
    readline(io::IO=stdin; keep::Bool=false)
    readline(filename::AbstractString; keep::Bool=false)

Read a single line of text from the given I/O stream or file (defaults to `stdin`).
When reading from a file, the text is assumed to be encoded in UTF-8. Lines in the
input end with `'\\n'` or `"\\r\\n"` or the end of an input stream. When `keep` is
false (as it is by default), these trailing newline characters are removed from the
line before it is returned. When `keep` is true, they are returned as part of the
line.

# Examples
```jldoctest
julia> write("my_file.txt", "JuliaLang is a GitHub organization.\\nIt has many members.\\n");

julia> readline("my_file.txt")
"JuliaLang is a GitHub organization."

julia> readline("my_file.txt", keep=true)
"JuliaLang is a GitHub organization.\\n"

julia> rm("my_file.txt")
```
```julia-repl
julia> print("Enter your name: ")
Enter your name:

julia> your_name = readline()
Logan
"Logan"
```
"""
function readline(filename::AbstractString; keep::Bool=false)
    open(filename) do f
        readline(f, keep=keep)
    end
end

function readline(s::IO=stdin; keep::Bool=false)
    line = readuntil(s, 0x0a, keep=true)::Vector{UInt8}
    i = length(line)
    if keep || i == 0 || line[i] != 0x0a
        return String(line)
    elseif i < 2 || line[i-1] != 0x0d
        return String(resize!(line,i-1))
    else
        return String(resize!(line,i-2))
    end
end

"""
    readlines(io::IO=stdin; keep::Bool=false)
    readlines(filename::AbstractString; keep::Bool=false)

Read all lines of an I/O stream or a file as a vector of strings. Behavior is
equivalent to saving the result of reading [`readline`](@ref) repeatedly with the same
arguments and saving the resulting lines as a vector of strings.  See also
[`eachline`](@ref) to iterate over the lines without reading them all at once.

# Examples
```jldoctest
julia> write("my_file.txt", "JuliaLang is a GitHub organization.\\nIt has many members.\\n");

julia> readlines("my_file.txt")
2-element Vector{String}:
 "JuliaLang is a GitHub organization."
 "It has many members."

julia> readlines("my_file.txt", keep=true)
2-element Vector{String}:
 "JuliaLang is a GitHub organization.\\n"
 "It has many members.\\n"

julia> rm("my_file.txt")
```
"""
function readlines(filename::AbstractString; kw...)
    open(filename) do f
        readlines(f; kw...)
    end
end
readlines(s=stdin; kw...) = collect(eachline(s; kw...))

## byte-order mark, ntoh & hton ##

let a = UInt32[0x01020304]
    endian_bom = GC.@preserve a unsafe_load(convert(Ptr{UInt8}, pointer(a)))
    global ntoh, hton, ltoh, htol
    if endian_bom == 0x01
        ntoh(x) = x
        hton(x) = x
        ltoh(x) = bswap(x)
        htol(x) = bswap(x)
        const global ENDIAN_BOM = 0x01020304
    elseif endian_bom == 0x04
        ntoh(x) = bswap(x)
        hton(x) = bswap(x)
        ltoh(x) = x
        htol(x) = x
        const global ENDIAN_BOM = 0x04030201
    else
        error("seriously? what is this machine?")
    end
end

"""
    ENDIAN_BOM

The 32-bit byte-order-mark indicates the native byte order of the host machine.
Little-endian machines will contain the value `0x04030201`. Big-endian machines will contain
the value `0x01020304`.
"""
ENDIAN_BOM

"""
    ntoh(x)

Convert the endianness of a value from Network byte order (big-endian) to that used by the Host.
"""
ntoh(x)

"""
    hton(x)

Convert the endianness of a value from that used by the Host to Network byte order (big-endian).
"""
hton(x)

"""
    ltoh(x)

Convert the endianness of a value from Little-endian to that used by the Host.
"""
ltoh(x)

"""
    htol(x)

Convert the endianness of a value from that used by the Host to Little-endian.
"""
htol(x)


"""
    isreadonly(io) -> Bool

Determine whether a stream is read-only.

# Examples
```jldoctest
julia> io = IOBuffer("JuliaLang is a GitHub organization");

julia> isreadonly(io)
true

julia> io = IOBuffer();

julia> isreadonly(io)
false
```
"""
isreadonly(s) = isreadable(s) && !iswritable(s)

## binary I/O ##

write(io::IO, x) = throw(MethodError(write, (io, x)))
function write(io::IO, x1, xs...)
    written::Int = write(io, x1)
    for x in xs
        written += write(io, x)
    end
    return written
end

@noinline unsafe_write(s::IO, p::Ref{T}, n::Integer) where {T} =
    unsafe_write(s, unsafe_convert(Ref{T}, p)::Ptr, n) # mark noinline to ensure ref is gc-rooted somewhere (by the caller)
unsafe_write(s::IO, p::Ptr, n::Integer) = unsafe_write(s, convert(Ptr{UInt8}, p), convert(UInt, n))
write(s::IO, x::Ref{T}) where {T} = unsafe_write(s, x, Core.sizeof(T))
write(s::IO, x::Int8) = write(s, reinterpret(UInt8, x))
function write(s::IO, x::Union{Int16,UInt16,Int32,UInt32,Int64,UInt64,Int128,UInt128,Float16,Float32,Float64})
    return write(s, Ref(x))
end

write(s::IO, x::Bool) = write(s, UInt8(x))
write(to::IO, p::Ptr) = write(to, convert(UInt, p))

function write(s::IO, A::AbstractArray)
    if !isbitstype(eltype(A))
        error("`write` is not supported on non-isbits arrays")
    end
    nb = 0
    for a in A
        nb += write(s, a)
    end
    return nb
end

function write(s::IO, a::Array)
    if isbitstype(eltype(a))
        return GC.@preserve a unsafe_write(s, pointer(a), sizeof(a))
    else
        error("`write` is not supported on non-isbits arrays")
    end
end

function write(s::IO, a::SubArray{T,N,<:Array}) where {T,N}
    if !isbitstype(T) || !isa(a, StridedArray)
        return invoke(write, Tuple{IO, AbstractArray}, s, a)
    end
    elsz = elsize(a)
    colsz = size(a,1) * elsz
    GC.@preserve a if stride(a,1) != 1
        for idxs in CartesianIndices(size(a))
            unsafe_write(s, pointer(a, idxs), elsz)
        end
        return elsz * length(a)
    elseif N <= 1
        return unsafe_write(s, pointer(a, 1), colsz)
    else
        for colstart in CartesianIndices((1, size(a)[2:end]...))
            unsafe_write(s, pointer(a, colstart), colsz)
        end
        return colsz * trailingsize(a,2)
    end
end

function write(io::IO, c::Char)
    u = bswap(reinterpret(UInt32, c))
    n = 1
    while true
        write(io, u % UInt8)
        (u >>= 8) == 0 && return n
        n += 1
    end
end
# write(io, ::AbstractChar) is not defined: implementations
# must provide their own encoding-specific method.

function write(io::IO, s::Symbol)
    pname = unsafe_convert(Ptr{UInt8}, s)
    return unsafe_write(io, pname, ccall(:strlen, Csize_t, (Cstring,), pname))
end

function write(to::IO, from::IO)
    n = 0
    while !eof(from)
        n += write(to, readavailable(from))
    end
    return n
end

@noinline unsafe_read(s::IO, p::Ref{T}, n::Integer) where {T} = unsafe_read(s, unsafe_convert(Ref{T}, p)::Ptr, n) # mark noinline to ensure ref is gc-rooted somewhere (by the caller)
unsafe_read(s::IO, p::Ptr, n::Integer) = unsafe_read(s, convert(Ptr{UInt8}, p), convert(UInt, n))
read!(s::IO, x::Ref{T}) where {T} = (unsafe_read(s, x, Core.sizeof(T)); x)

read(s::IO, ::Type{Int8}) = reinterpret(Int8, read(s, UInt8))
function read(s::IO, T::Union{Type{Int16},Type{UInt16},Type{Int32},Type{UInt32},Type{Int64},Type{UInt64},Type{Int128},Type{UInt128},Type{Float16},Type{Float32},Type{Float64}})
    return read!(s, Ref{T}(0))[]::T
end

read(s::IO, ::Type{Bool}) = (read(s, UInt8) != 0)
read(s::IO, ::Type{Ptr{T}}) where {T} = convert(Ptr{T}, read(s, UInt))

function read!(s::IO, a::Array{UInt8})
    GC.@preserve a unsafe_read(s, pointer(a), sizeof(a))
    return a
end

function read!(s::IO, a::AbstractArray{T}) where T
    if isbitstype(T) && (a isa Array || a isa FastContiguousSubArray{T,<:Any,<:Array{T}})
        GC.@preserve a unsafe_read(s, pointer(a), sizeof(a))
    else
        for i in eachindex(a)
            a[i] = read(s, T)
        end
    end
    return a
end

function read(io::IO, ::Type{Char})
    b0 = read(io, UInt8)::UInt8
    l = 0x08 * (0x04 - UInt8(leading_ones(b0)))
    c = UInt32(b0) << 24
    if l ≤ 0x10
        s = 16
        while s ≥ l && !eof(io)::Bool
            peek(io) & 0xc0 == 0x80 || break
            b = read(io, UInt8)::UInt8
            c |= UInt32(b) << s
            s -= 8
        end
    end
    return reinterpret(Char, c)
end
# read(io, T) is not defined for other AbstractChar: implementations
# must provide their own encoding-specific method.

# readuntil_string is useful below since it has
# an optimized method for s::IOStream
readuntil_string(s::IO, delim::UInt8, keep::Bool) = String(readuntil(s, delim, keep=keep))::String

function readuntil(s::IO, delim::AbstractChar; keep::Bool=false)
    if delim ≤ '\x7f'
        return readuntil_string(s, delim % UInt8, keep)
    end
    out = IOBuffer()
    for c in readeach(s, Char)
        if c == delim
            keep && write(out, c)
            break
        end
        write(out, c)
    end
    return String(take!(out))
end

function readuntil(s::IO, delim::T; keep::Bool=false) where T
    out = (T === UInt8 ? StringVector(0) : Vector{T}())
    for c in readeach(s, T)
        if c == delim
            keep && push!(out, c)
            break
        end
        push!(out, c)
    end
    return out
end

# requires that indices for target are the integer unit range from firstindex to lastindex
# returns whether the delimiter was matched
# uses the Knuth–Morris–Pratt_algorithm, with the first and second cache entries unrolled
# For longer targets, the cache improves the big-O efficiency of scanning of sequences
# with repeated patterns
# Each cache entry tells us which index we should start the search at.
# We assume this is unlikely, so we only lazy-initialize as much of the cache as we need to use
# When we allocate the cache, we initialize it to 0 (and offset by the first index afterwards).
# Suppose target is:
#    Index:  1245689
#    Value: "aδcaδcx"
# We would set the cache to
#    0 0 0 1 2 3 4 0
# So after if we mismatch after the second aδc sequence,
# we can immediately jump back to index 5 (4 + 1).
function readuntil_vector!(io::IO, target::AbstractVector{T}, keep::Bool, out) where {T}
    first = firstindex(target)
    last = lastindex(target)
    len = last - first + 1
    if len < 1
        return true
    end
    pos = 0 # array-offset
    max_pos = 1 # array-offset in cache
    local cache # will be lazy initialized when needed
    output! = (isa(out, IO) ? write : push!)
    for c in readeach(io, T)
        # Backtrack until the next target character matches what was found
        while true
            c1 = target[pos + first]
            if c == c1
                pos += 1
                break
            elseif pos == 0
                break
            elseif pos == 1
                if !keep
                    output!(out, target[first])
                end
                pos = 0
            else
                # grow cache to contain up to `pos`
                if !@isdefined(cache)
                    cache = zeros(Int, len)
                end
                while max_pos < pos
                    ci = target[max_pos + first]
                    b = max_pos
                    max_pos += 1
                    while b != 0
                        b = cache[b]
                        cb = target[b + first]
                        if ci == cb
                            cache[max_pos] = b + 1
                            break
                        end
                    end
                end
                # read new position from cache
                pos1 = cache[pos]
                if !keep
                    # and add the removed prefix from the target to the output
                    # if not always keeping the match
                    for b in 1:(pos - pos1)
                        output!(out, target[b - 1 + first])
                    end
                end
                pos = pos1
            end
        end
        if keep || pos == 0
            output!(out, c)
        end
        pos == len && return true
    end
    if !keep
        # failed early without finishing the match,
        # add the partial match to the output
        # if not always keeping the match
        for b in 1:pos
            output!(out, target[b - 1 + first])
        end
    end
    return false
end

function readuntil(io::IO, target::AbstractString; keep::Bool=false)
    # small-string target optimizations
    x = Iterators.peel(target)
    isnothing(x) && return ""
    c, rest = x
    if isempty(rest) && c <= '\x7f'
        return readuntil_string(io, c % UInt8, keep)
    end
    # convert String to a utf8-byte-iterator
    if !(target isa String) && !(target isa SubString{String})
        target = String(target)
    end
    target = codeunits(target)::AbstractVector
    return String(readuntil(io, target, keep=keep))
end

function readuntil(io::IO, target::AbstractVector{T}; keep::Bool=false) where T
    out = (T === UInt8 ? StringVector(0) : Vector{T}())
    readuntil_vector!(io, target, keep, out)
    return out
end

"""
    readchomp(x)

Read the entirety of `x` as a string and remove a single trailing newline
if there is one. Equivalent to `chomp(read(x, String))`.

# Examples
```jldoctest
julia> write("my_file.txt", "JuliaLang is a GitHub organization.\\nIt has many members.\\n");

julia> readchomp("my_file.txt")
"JuliaLang is a GitHub organization.\\nIt has many members."

julia> rm("my_file.txt");
```
"""
readchomp(x) = chomp(read(x, String))

# read up to nb bytes into nb, returning # bytes read

"""
    readbytes!(stream::IO, b::AbstractVector{UInt8}, nb=length(b))

Read at most `nb` bytes from `stream` into `b`, returning the number of bytes read.
The size of `b` will be increased if needed (i.e. if `nb` is greater than `length(b)`
and enough bytes could be read), but it will never be decreased.
"""
function readbytes!(s::IO, b::AbstractArray{UInt8}, nb=length(b))
    require_one_based_indexing(b)
    olb = lb = length(b)
    nr = 0
    while nr < nb && !eof(s)
        a = read(s, UInt8)
        nr += 1
        if nr > lb
            lb = nr * 2
            resize!(b, lb)
        end
        b[nr] = a
    end
    if lb > olb
        resize!(b, nr) # shrink to just contain input data if was resized
    end
    return nr
end

"""
    read(s::IO, nb=typemax(Int))

Read at most `nb` bytes from `s`, returning a `Vector{UInt8}` of the bytes read.
"""
function read(s::IO, nb::Integer = typemax(Int))
    # Let readbytes! grow the array progressively by default
    # instead of taking of risk of over-allocating
    b = Vector{UInt8}(undef, nb == typemax(Int) ? 1024 : nb)
    nr = readbytes!(s, b, nb)
    return resize!(b, nr)
end

read(s::IO, ::Type{String}) = String(read(s)::Vector{UInt8})
read(s::IO, T::Type) = error("The IO stream does not support reading objects of type $T.")

## high-level iterator interfaces ##

struct EachLine{IOT <: IO}
    stream::IOT
    ondone::Function
    keep::Bool
    EachLine(stream::IO=stdin; ondone::Function=()->nothing, keep::Bool=false) =
        new{typeof(stream)}(stream, ondone, keep)
end

"""
    eachline(io::IO=stdin; keep::Bool=false)
    eachline(filename::AbstractString; keep::Bool=false)

Create an iterable `EachLine` object that will yield each line from an I/O stream
or a file. Iteration calls [`readline`](@ref) on the stream argument repeatedly with
`keep` passed through, determining whether trailing end-of-line characters are
retained. When called with a file name, the file is opened once at the beginning of
iteration and closed at the end. If iteration is interrupted, the file will be
closed when the `EachLine` object is garbage collected.

To iterate over each line of a `String`, `eachline(IOBuffer(str))` can be used.

[`Iterators.reverse`](@ref) can be used on an `EachLine` object to read the lines
in reverse order (for files, buffers, and other I/O streams supporting [`seek`](@ref)),
and [`first`](@ref) or [`last`](@ref) can be used to extract the initial or final
lines, respectively.

# Examples
```jldoctest
julia> write("my_file.txt", "JuliaLang is a GitHub organization.\\n It has many members.\\n");

julia> for line in eachline("my_file.txt")
           print(line)
       end
JuliaLang is a GitHub organization. It has many members.

julia> rm("my_file.txt");
```

!!! compat "Julia 1.8"
       Julia 1.8 is required to use `Iterators.reverse` or `last` with `eachline` iterators.
"""
function eachline(stream::IO=stdin; keep::Bool=false)
    EachLine(stream, keep=keep)::EachLine
end

function eachline(filename::AbstractString; keep::Bool=false)
    s = open(filename)
    EachLine(s, ondone=()->close(s), keep=keep)::EachLine
end

function iterate(itr::EachLine, state=nothing)
    eof(itr.stream) && return (itr.ondone(); nothing)
    (readline(itr.stream, keep=itr.keep), nothing)
end

eltype(::Type{<:EachLine}) = String

IteratorSize(::Type{<:EachLine}) = SizeUnknown()

isdone(itr::EachLine, state...) = eof(itr.stream)

# Reverse-order iteration for the EachLine iterator for seekable streams,
# which works by reading the stream from the end in 4kiB chunks.
function iterate(r::Iterators.Reverse{<:EachLine})
    p0 = position(r.itr.stream)
    seekend(r.itr.stream) # may throw if io is non-seekable
    p = position(r.itr.stream)
    # chunks = circular buffer of 4kiB blocks read from end of stream
    chunks = empty!(Vector{Vector{UInt8}}(undef, 2)) # allocate space for 2 buffers (common case)
    inewline = jnewline = 0
    while p > p0 && inewline == 0 # read chunks until we find a newline or we read whole file
        chunk = Vector{UInt8}(undef, min(4096, p-p0))
        p -= length(chunk)
        readbytes!(seek(r.itr.stream, p), chunk)
        pushfirst!(chunks, chunk)
        inewline = something(findlast(==(UInt8('\n')), chunk), 0)
        if length(chunks) == 1 && inewline == length(chunks[1])
            # found newline at end of file … keep looking
            jnewline = inewline
            inewline = something(findprev(==(UInt8('\n')), chunk, inewline-1), 0)
        end
    end
    return iterate(r, (; p0, p, chunks, ichunk=1, inewline, jchunk=length(chunks), jnewline = jnewline == 0 && !isempty(chunks) ? length(chunks[end]) : jnewline))
end
function iterate(r::Iterators.Reverse{<:EachLine}, state)
    function _stripnewline(keep, pos, data)
        # strip \n or \r\n from data[pos] by decrementing pos
        if !keep && pos > 0 && data[pos] == UInt8('\n')
            pos -= 1
            pos -= pos > 0 && data[pos] == UInt8('\r')
        end
        return pos
    end
    # state tuple: p0 = initial file position, p = current position,
    #              chunks = circular array of chunk buffers,
    #              current line is from chunks[ichunk][inewline+1] to chunks[jchunk][jnewline]
    p0, p, chunks, ichunk, inewline, jchunk, jnewline = state
    if inewline == 0 # no newline found, remaining line = rest of chunks (if any)
        isempty(chunks) && return (r.itr.ondone(); nothing)
        buf = IOBuffer(sizehint = ichunk==jchunk ? jnewline : 4096)
        while ichunk != jchunk
            write(buf, chunks[ichunk])
            ichunk = ichunk == length(chunks) ? 1 : ichunk + 1
        end
        chunk = chunks[jchunk]
        write(buf, view(chunk, 1:jnewline))
        buf.size = _stripnewline(r.itr.keep, buf.size, buf.data)
        empty!(chunks) # will cause next iteration to terminate
        seekend(r.itr.stream) # reposition to end of stream for isdone
        s = String(take!(buf))
    else
        # extract the string from chunks[ichunk][inewline+1] to chunks[jchunk][jnewline]
        if ichunk == jchunk # common case: current and previous newline in same chunk
            chunk = chunks[ichunk]
            s = String(view(chunk, inewline+1:_stripnewline(r.itr.keep, jnewline, chunk)))
        else
            buf = IOBuffer(sizehint=max(128, length(chunks[ichunk])-inewline+jnewline))
            write(buf, view(chunks[ichunk], inewline+1:length(chunks[ichunk])))
            i = ichunk
            while true
                i = i == length(chunks) ? 1 : i + 1
                i == jchunk && break
                write(buf, chunks[i])
            end
            write(buf, view(chunks[jchunk], 1:jnewline))
            buf.size = _stripnewline(r.itr.keep, buf.size, buf.data)
            s = String(take!(buf))

            # overwrite obsolete chunks (ichunk+1:jchunk)
            i = jchunk
            while i != ichunk
                chunk = chunks[i]
                p -= length(resize!(chunk, min(4096, p-p0)))
                readbytes!(seek(r.itr.stream, p), chunk)
                i = i == 1 ? length(chunks) : i - 1
            end
        end

        # find the newline previous to inewline
        jchunk = ichunk
        jnewline = inewline
        while true
            inewline = something(findprev(==(UInt8('\n')), chunks[ichunk], inewline-1), 0)
            inewline > 0 && break
            ichunk = ichunk == 1 ? length(chunks) : ichunk - 1
            ichunk == jchunk && break # found nothing — may need to read more chunks
            inewline = length(chunks[ichunk])+1 # start for next findprev
        end

        # read more chunks to look for a newline (should rarely happen)
        if inewline == 0 && p > p0
            ichunk = jchunk + 1
            while true
                chunk = Vector{UInt8}(undef, min(4096, p-p0))
                p -= length(chunk)
                readbytes!(seek(r.itr.stream, p), chunk)
                insert!(chunks, ichunk, chunk)
                inewline = something(findlast(==(UInt8('\n')), chunk), 0)
                (p == p0 || inewline > 0) && break
            end
        end
    end
    return (s, (; p0, p, chunks, ichunk, inewline, jchunk, jnewline))
end
isdone(r::Iterators.Reverse{<:EachLine}, state) = isempty(state.chunks)
isdone(r::Iterators.Reverse{<:EachLine}) = isdone(r.itr)

# use reverse iteration to get end of EachLines (if possible)
last(itr::EachLine) = first(Iterators.reverse(itr))

struct ReadEachIterator{T, IOT <: IO}
    stream::IOT
end

"""
    readeach(io::IO, T)

Return an iterable object yielding [`read(io, T)`](@ref).

See also [`skipchars`](@ref), [`eachline`](@ref), [`readuntil`](@ref).

!!! compat "Julia 1.6"
    `readeach` requires Julia 1.6 or later.

# Examples
```jldoctest
julia> io = IOBuffer("JuliaLang is a GitHub organization.\\n It has many members.\\n");

julia> for c in readeach(io, Char)
           c == '\\n' && break
           print(c)
       end
JuliaLang is a GitHub organization.
```
"""
readeach(stream::IOT, T::Type) where IOT<:IO = ReadEachIterator{T,IOT}(stream)

iterate(itr::ReadEachIterator{T}, state=nothing) where T =
    eof(itr.stream) ? nothing : (read(itr.stream, T), nothing)

eltype(::Type{ReadEachIterator{T}}) where T = T

IteratorSize(::Type{<:ReadEachIterator}) = SizeUnknown()

isdone(itr::ReadEachIterator, state...) = eof(itr.stream)

# IOStream Marking
# Note that these functions expect that io.mark exists for
# the concrete IO type. This may not be true for IO types
# not in base.

"""
    mark(s::IO)

Add a mark at the current position of stream `s`. Return the marked position.

See also [`unmark`](@ref), [`reset`](@ref), [`ismarked`](@ref).
"""
function mark(io::IO)
    io.mark = position(io)
end

"""
    unmark(s::IO)

Remove a mark from stream `s`. Return `true` if the stream was marked, `false` otherwise.

See also [`mark`](@ref), [`reset`](@ref), [`ismarked`](@ref).
"""
function unmark(io::IO)
    !ismarked(io) && return false
    io.mark = -1
    return true
end

"""
    reset(s::IO)

Reset a stream `s` to a previously marked position, and remove the mark. Return the
previously marked position. Throw an error if the stream is not marked.

See also [`mark`](@ref), [`unmark`](@ref), [`ismarked`](@ref).
"""
function reset(io::T) where T<:IO
    ismarked(io) || throw(ArgumentError("$T not marked"))
    m = io.mark
    seek(io, m)
    io.mark = -1 # must be after seek, or seek may fail
    return m
end

"""
    ismarked(s::IO)

Return `true` if stream `s` is marked.

See also [`mark`](@ref), [`unmark`](@ref), [`reset`](@ref).
"""
ismarked(io::IO) = io.mark >= 0

# Make sure all IO streams support flush, even if only as a no-op,
# to make it easier to write generic I/O code.

flush(io::IO) = nothing

"""
    skipchars(predicate, io::IO; linecomment=nothing)

Advance the stream `io` such that the next-read character will be the first remaining for
which `predicate` returns `false`. If the keyword argument `linecomment` is specified, all
characters from that character until the start of the next line are ignored.

# Examples
```jldoctest
julia> buf = IOBuffer("    text")
IOBuffer(data=UInt8[...], readable=true, writable=false, seekable=true, append=false, size=8, maxsize=Inf, ptr=1, mark=-1)

julia> skipchars(isspace, buf)
IOBuffer(data=UInt8[...], readable=true, writable=false, seekable=true, append=false, size=8, maxsize=Inf, ptr=5, mark=-1)

julia> String(readavailable(buf))
"text"
```
"""
function skipchars(predicate, io::IO; linecomment=nothing)
    for c in readeach(io, Char)
        if c === linecomment
            readline(io)
        elseif !predicate(c)
            skip(io, -ncodeunits(c))
            break
        end
    end
    return io
end

"""
    countlines(io::IO; eol::AbstractChar = '\\n')
    countlines(filename::AbstractString; eol::AbstractChar = '\\n')

Read `io` until the end of the stream/file and count the number of lines. To specify a file
pass the filename as the first argument. EOL markers other than `'\\n'` are supported by
passing them as the second argument.  The last non-empty line of `io` is counted even if it does not
end with the EOL, matching the length returned by [`eachline`](@ref) and [`readlines`](@ref).

To count lines of a `String`, `countlines(IOBuffer(str))` can be used.

# Examples
```jldoctest
julia> io = IOBuffer("JuliaLang is a GitHub organization.\\n");

julia> countlines(io)
1

julia> io = IOBuffer("JuliaLang is a GitHub organization.");

julia> countlines(io)
1

julia> eof(io) # counting lines moves the file pointer
true

julia> io = IOBuffer("JuliaLang is a GitHub organization.");

julia> countlines(io, eol = '.')
1
```
```jldoctest
julia> write("my_file.txt", "JuliaLang is a GitHub organization.\\n")
36

julia> countlines("my_file.txt")
1

julia> countlines("my_file.txt", eol = 'n')
4

julia> rm("my_file.txt")

```
"""
function countlines(io::IO; eol::AbstractChar='\n')
    isascii(eol) || throw(ArgumentError("only ASCII line terminators are supported"))
    aeol = UInt8(eol)
    a = Vector{UInt8}(undef, 8192)
    nl = nb = 0
    while !eof(io)
        nb = readbytes!(io, a)
        @simd for i=1:nb
            @inbounds nl += a[i] == aeol
        end
    end
    if nb > 0 && a[nb] != aeol
        nl += 1 # final line is not terminated with eol
    end
    nl
end

countlines(f::AbstractString; eol::AbstractChar = '\n') = open(io->countlines(io, eol = eol), f)::Int
O   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/iobuffer.jl�G      # This file is a part of Julia. License is MIT: https://julialang.org/license

## work with AbstractVector{UInt8} via I/O primitives ##

# Stateful string
mutable struct GenericIOBuffer{T<:AbstractVector{UInt8}} <: IO
    data::T # T should support: getindex, setindex!, length, copyto!, and resize!
    reinit::Bool # if true, data needs to be re-allocated (after take!)
    readable::Bool
    writable::Bool
    seekable::Bool # if not seekable, implementation is free to destroy (compact) past read data
    append::Bool # add data at end instead of at pointer
    size::Int # end pointer (and write pointer if append == true)
    maxsize::Int # fixed array size (typically pre-allocated)
    ptr::Int # read (and maybe write) pointer
    mark::Int # reset mark location for ptr (or <0 for no mark)

    function GenericIOBuffer{T}(data::T, readable::Bool, writable::Bool, seekable::Bool, append::Bool,
                                maxsize::Integer) where T<:AbstractVector{UInt8}
        require_one_based_indexing(data)
        new(data,false,readable,writable,seekable,append,length(data),maxsize,1,-1)
    end
end
const IOBuffer = GenericIOBuffer{Vector{UInt8}}

function GenericIOBuffer(data::T, readable::Bool, writable::Bool, seekable::Bool, append::Bool,
                         maxsize::Integer) where T<:AbstractVector{UInt8}
    GenericIOBuffer{T}(data, readable, writable, seekable, append, maxsize)
end

# allocate Vector{UInt8}s for IOBuffer storage that can efficiently become Strings
StringVector(n::Integer) = unsafe_wrap(Vector{UInt8}, _string_n(n))

# IOBuffers behave like Files. They are typically readable and writable. They are seekable. (They can be appendable).

"""
    IOBuffer([data::AbstractVector{UInt8}]; keywords...) -> IOBuffer

Create an in-memory I/O stream, which may optionally operate on a pre-existing array.

It may take optional keyword arguments:
- `read`, `write`, `append`: restricts operations to the buffer; see `open` for details.
- `truncate`: truncates the buffer size to zero length.
- `maxsize`: specifies a size beyond which the buffer may not be grown.
- `sizehint`: suggests a capacity of the buffer (`data` must implement `sizehint!(data, size)`).

When `data` is not given, the buffer will be both readable and writable by default.

# Examples
```jldoctest
julia> io = IOBuffer();

julia> write(io, "JuliaLang is a GitHub organization.", " It has many members.")
56

julia> String(take!(io))
"JuliaLang is a GitHub organization. It has many members."

julia> io = IOBuffer(b"JuliaLang is a GitHub organization.")
IOBuffer(data=UInt8[...], readable=true, writable=false, seekable=true, append=false, size=35, maxsize=Inf, ptr=1, mark=-1)

julia> read(io, String)
"JuliaLang is a GitHub organization."

julia> write(io, "This isn't writable.")
ERROR: ArgumentError: ensureroom failed, IOBuffer is not writeable

julia> io = IOBuffer(UInt8[], read=true, write=true, maxsize=34)
IOBuffer(data=UInt8[...], readable=true, writable=true, seekable=true, append=false, size=0, maxsize=34, ptr=1, mark=-1)

julia> write(io, "JuliaLang is a GitHub organization.")
34

julia> String(take!(io))
"JuliaLang is a GitHub organization"

julia> length(read(IOBuffer(b"data", read=true, truncate=false)))
4

julia> length(read(IOBuffer(b"data", read=true, truncate=true)))
0
```
"""
function IOBuffer(
        data::AbstractVector{UInt8};
        read::Union{Bool,Nothing}=nothing,
        write::Union{Bool,Nothing}=nothing,
        append::Union{Bool,Nothing}=nothing,
        truncate::Union{Bool,Nothing}=nothing,
        maxsize::Integer=typemax(Int),
        sizehint::Union{Integer,Nothing}=nothing)
    if maxsize < 0
        throw(ArgumentError("negative maxsize"))
    end
    if sizehint !== nothing
        sizehint!(data, sizehint)
    end
    flags = open_flags(read=read, write=write, append=append, truncate=truncate)
    buf = GenericIOBuffer(data, flags.read, flags.write, true, flags.append, Int(maxsize))
    if flags.truncate
        buf.size = 0
    end
    return buf
end

function IOBuffer(;
        read::Union{Bool,Nothing}=true,
        write::Union{Bool,Nothing}=true,
        append::Union{Bool,Nothing}=nothing,
        truncate::Union{Bool,Nothing}=true,
        maxsize::Integer=typemax(Int),
        sizehint::Union{Integer,Nothing}=nothing)
    size = sizehint !== nothing ? Int(sizehint) : maxsize != typemax(Int) ? Int(maxsize) : 32
    flags = open_flags(read=read, write=write, append=append, truncate=truncate)
    buf = IOBuffer(
        StringVector(size),
        read=flags.read,
        write=flags.write,
        append=flags.append,
        truncate=flags.truncate,
        maxsize=maxsize)
    fill!(buf.data, 0)
    return buf
end

# PipeBuffers behave like Unix Pipes. They are typically readable and writable, they act appendable, and are not seekable.

"""
    PipeBuffer(data::Vector{UInt8}=UInt8[]; maxsize::Integer = typemax(Int))

An [`IOBuffer`](@ref) that allows reading and performs writes by appending.
Seeking and truncating are not supported.
See [`IOBuffer`](@ref) for the available constructors.
If `data` is given, creates a `PipeBuffer` to operate on a data vector,
optionally specifying a size beyond which the underlying `Array` may not be grown.
"""
PipeBuffer(data::Vector{UInt8}=UInt8[]; maxsize::Int = typemax(Int)) =
    GenericIOBuffer(data,true,true,false,true,maxsize)
PipeBuffer(maxsize::Integer) = (x = PipeBuffer(StringVector(maxsize), maxsize = maxsize); x.size=0; x)

_similar_data(b::GenericIOBuffer, len::Int) = similar(b.data, len)
_similar_data(b::IOBuffer, len::Int) = StringVector(len)

function copy(b::GenericIOBuffer)
    ret = typeof(b)(b.reinit ? _similar_data(b, 0) : b.writable ?
                    copyto!(_similar_data(b, length(b.data)), b.data) : b.data,
                    b.readable, b.writable, b.seekable, b.append, b.maxsize)
    ret.size = b.size
    ret.ptr  = b.ptr
    return ret
end

show(io::IO, b::GenericIOBuffer) = print(io, "IOBuffer(data=UInt8[...], ",
                                      "readable=", b.readable, ", ",
                                      "writable=", b.writable, ", ",
                                      "seekable=", b.seekable, ", ",
                                      "append=",   b.append, ", ",
                                      "size=",     b.size, ", ",
                                      "maxsize=",  b.maxsize == typemax(Int) ? "Inf" : b.maxsize, ", ",
                                      "ptr=",      b.ptr, ", ",
                                      "mark=",     b.mark, ")")

@noinline function _throw_not_readable()
    # See https://github.com/JuliaLang/julia/issues/29688.
    throw(ArgumentError("read failed, IOBuffer is not readable"))
end

function unsafe_read(from::GenericIOBuffer, p::Ptr{UInt8}, nb::UInt)
    from.readable || _throw_not_readable()
    avail = bytesavailable(from)
    adv = min(avail, nb)
    GC.@preserve from unsafe_copyto!(p, pointer(from.data, from.ptr), adv)
    from.ptr += adv
    if nb > avail
        throw(EOFError())
    end
    nothing
end

function peek(from::GenericIOBuffer, T::Union{Type{Int16},Type{UInt16},Type{Int32},Type{UInt32},Type{Int64},Type{UInt64},Type{Int128},Type{UInt128},Type{Float16},Type{Float32},Type{Float64}})
    from.readable || _throw_not_readable()
    avail = bytesavailable(from)
    nb = sizeof(T)
    if nb > avail
        throw(EOFError())
    end
    GC.@preserve from begin
        ptr::Ptr{T} = pointer(from.data, from.ptr)
        x = unsafe_load(ptr)
    end
    return x
end

function read(from::GenericIOBuffer, T::Union{Type{Int16},Type{UInt16},Type{Int32},Type{UInt32},Type{Int64},Type{UInt64},Type{Int128},Type{UInt128},Type{Float16},Type{Float32},Type{Float64}})
    x = peek(from, T)
    from.ptr += sizeof(T)
    return x
end

function read_sub(from::GenericIOBuffer, a::AbstractArray{T}, offs, nel) where T
    require_one_based_indexing(a)
    from.readable || _throw_not_readable()
    if offs+nel-1 > length(a) || offs < 1 || nel < 0
        throw(BoundsError())
    end
    if isbitstype(T) && isa(a,Array)
        nb = UInt(nel * sizeof(T))
        GC.@preserve a unsafe_read(from, pointer(a, offs), nb)
    else
        for i = offs:offs+nel-1
            a[i] = read(from, T)
        end
    end
    return a
end

@inline function read(from::GenericIOBuffer, ::Type{UInt8})
    from.readable || _throw_not_readable()
    ptr = from.ptr
    size = from.size
    if ptr > size
        throw(EOFError())
    end
    @inbounds byte = from.data[ptr]::UInt8
    from.ptr = ptr + 1
    return byte
end

function peek(from::GenericIOBuffer, ::Type{UInt8})
    from.readable || _throw_not_readable()
    if from.ptr > from.size
        throw(EOFError())
    end
    return from.data[from.ptr]::UInt8
end

read(from::GenericIOBuffer, ::Type{Ptr{T}}) where {T} = convert(Ptr{T}, read(from, UInt))

isreadable(io::GenericIOBuffer) = io.readable
iswritable(io::GenericIOBuffer) = io.writable

# TODO: GenericIOBuffer is not iterable, so doesn't really have a length.
# This should maybe be sizeof() instead.
#length(io::GenericIOBuffer) = (io.seekable ? io.size : bytesavailable(io))
bytesavailable(io::GenericIOBuffer) = io.size - io.ptr + 1
position(io::GenericIOBuffer) = io.ptr-1

function skip(io::GenericIOBuffer, n::Integer)
    seekto = io.ptr + n
    n < 0 && return seek(io, seekto-1) # Does error checking
    io.ptr = min(seekto, io.size+1)
    return io
end

function seek(io::GenericIOBuffer, n::Integer)
    if !io.seekable
        ismarked(io) || throw(ArgumentError("seek failed, IOBuffer is not seekable and is not marked"))
        n == io.mark || throw(ArgumentError("seek failed, IOBuffer is not seekable and n != mark"))
    end
    # TODO: REPL.jl relies on the fact that this does not throw (by seeking past the beginning or end
    #       of an GenericIOBuffer), so that would need to be fixed in order to throw an error here
    #(n < 0 || n > io.size) && throw(ArgumentError("Attempted to seek outside IOBuffer boundaries."))
    #io.ptr = n+1
    io.ptr = max(min(n+1, io.size+1), 1)
    return io
end

function seekend(io::GenericIOBuffer)
    io.ptr = io.size+1
    return io
end

function truncate(io::GenericIOBuffer, n::Integer)
    io.writable || throw(ArgumentError("truncate failed, IOBuffer is not writeable"))
    io.seekable || throw(ArgumentError("truncate failed, IOBuffer is not seekable"))
    n < 0 && throw(ArgumentError("truncate failed, n bytes must be ≥ 0, got $n"))
    n > io.maxsize && throw(ArgumentError("truncate failed, $(n) bytes is exceeds IOBuffer maxsize $(io.maxsize)"))
    if io.reinit
        io.data = _similar_data(io, n)
        io.reinit = false
    elseif n > length(io.data)
        resize!(io.data, n)
    end
    io.data[io.size+1:n] .= 0
    io.size = n
    io.ptr = min(io.ptr, n+1)
    ismarked(io) && io.mark > n && unmark(io)
    return io
end

function compact(io::GenericIOBuffer)
    io.writable || throw(ArgumentError("compact failed, IOBuffer is not writeable"))
    io.seekable && throw(ArgumentError("compact failed, IOBuffer is seekable"))
    local ptr::Int, bytes_to_move::Int
    if ismarked(io) && io.mark < io.ptr
        if io.mark == 0 return end
        ptr = io.mark
        bytes_to_move = bytesavailable(io) + (io.ptr-io.mark)
    else
        ptr = io.ptr
        bytes_to_move = bytesavailable(io)
    end
    copyto!(io.data, 1, io.data, ptr, bytes_to_move)
    io.size -= ptr - 1
    io.ptr -= ptr - 1
    io.mark -= ptr - 1
    return io
end

@noinline function ensureroom_slowpath(io::GenericIOBuffer, nshort::UInt)
    io.writable || throw(ArgumentError("ensureroom failed, IOBuffer is not writeable"))
    if !io.seekable
        if !ismarked(io) && io.ptr > 1 && io.size <= io.ptr - 1
            io.ptr = 1
            io.size = 0
        else
            datastart = ismarked(io) ? io.mark : io.ptr
            if (io.size+nshort > io.maxsize) ||
                (datastart > 4096 && datastart > io.size - io.ptr) ||
                (datastart > 262144)
                # apply somewhat arbitrary heuristics to decide when to destroy
                # old, read data to make more room for new data
                compact(io)
            end
        end
    end
    return
end

@inline ensureroom(io::GenericIOBuffer, nshort::Int) = ensureroom(io, UInt(nshort))
@inline function ensureroom(io::GenericIOBuffer, nshort::UInt)
    if !io.writable || (!io.seekable && io.ptr > 1)
        ensureroom_slowpath(io, nshort)
    end
    n = min((nshort % Int) + (io.append ? io.size : io.ptr-1), io.maxsize)
    if io.reinit
        io.data = _similar_data(io, n)
        io.reinit = false
    else
        l = length(io.data)
        if n > l
            _growend!(io.data, (n - l) % UInt)
        end
    end
    return io
end

eof(io::GenericIOBuffer) = (io.ptr-1 == io.size)

function closewrite(io::GenericIOBuffer)
    io.writable = false
    # OR throw(_UVError("closewrite", UV_ENOTSOCK))
    nothing
end

@noinline function close(io::GenericIOBuffer{T}) where T
    io.readable = false
    io.writable = false
    io.seekable = false
    io.size = 0
    io.maxsize = 0
    io.ptr = 1
    io.mark = -1
    if io.writable
        resize!(io.data, 0)
    end
    nothing
end

isopen(io::GenericIOBuffer) = io.readable || io.writable || io.seekable || bytesavailable(io) > 0

"""
    take!(b::IOBuffer)

Obtain the contents of an `IOBuffer` as an array. Afterwards, the `IOBuffer` is reset to its initial state.

# Examples
```jldoctest
julia> io = IOBuffer();

julia> write(io, "JuliaLang is a GitHub organization.", " It has many members.")
56

julia> String(take!(io))
"JuliaLang is a GitHub organization. It has many members."
```
"""
function take!(io::GenericIOBuffer)
    ismarked(io) && unmark(io)
    if io.seekable
        nbytes = io.size
        data = copyto!(StringVector(nbytes), 1, io.data, 1, nbytes)
    else
        nbytes = bytesavailable(io)
        data = read!(io,StringVector(nbytes))
    end
    if io.writable
        io.ptr = 1
        io.size = 0
    end
    return data
end
function take!(io::IOBuffer)
    ismarked(io) && unmark(io)
    if io.seekable
        if io.writable
            if io.reinit
                data = StringVector(0)
            else
                data = resize!(io.data, io.size)
                io.reinit = true
            end
        else
            data = copyto!(StringVector(io.size), 1, io.data, 1, io.size)
        end
    else
        nbytes = bytesavailable(io)
        if io.writable
            data = io.data
            io.reinit = true
            _deletebeg!(data, io.ptr-1)
            resize!(data, nbytes)
        else
            data = read!(io, StringVector(nbytes))
        end
    end
    if io.writable
        io.ptr = 1
        io.size = 0
    end
    return data
end

"""
    _unsafe_take!(io::IOBuffer)

This simply returns the raw resized `io.data`, with no checks to be
sure that `io` is readable etcetera, and leaves `io` in an inconsistent
state.  This should only be used internally for performance-critical
`String` routines that immediately discard `io` afterwards, and it
*assumes* that `io` is writable and seekable.

It saves no allocations compared to `take!`, it just omits some checks.
"""
_unsafe_take!(io::IOBuffer) = resize!(io.data, io.size)

function write(to::IO, from::GenericIOBuffer)
    if to === from
        from.ptr = from.size + 1
        return 0
    end
    written::Int = GC.@preserve from unsafe_write(to, pointer(from.data, from.ptr), UInt(bytesavailable(from)))
    from.ptr += written
    return written
end

function unsafe_write(to::GenericIOBuffer, p::Ptr{UInt8}, nb::UInt)
    ensureroom(to, nb)
    ptr = (to.append ? to.size+1 : to.ptr)
    written = Int(min(nb, Int(length(to.data))::Int - ptr + 1))
    towrite = written
    d = to.data
    while towrite > 0
        @inbounds d[ptr] = unsafe_load(p)
        ptr += 1
        p += 1
        towrite -= 1
    end
    to.size = max(to.size, ptr - 1)
    if !to.append
        to.ptr += written
    end
    return written
end

@inline function write(to::GenericIOBuffer, a::UInt8)
    ensureroom(to, UInt(1))
    ptr = (to.append ? to.size+1 : to.ptr)
    if ptr > to.maxsize
        return 0
    else
        to.data[ptr] = a
    end
    to.size = max(to.size, ptr)
    if !to.append
        to.ptr += 1
    end
    return sizeof(UInt8)
end

readbytes!(io::GenericIOBuffer, b::Array{UInt8}, nb=length(b)) = readbytes!(io, b, Int(nb))
function readbytes!(io::GenericIOBuffer, b::Array{UInt8}, nb::Int)
    nr = min(nb, bytesavailable(io))
    if length(b) < nr
        resize!(b, nr)
    end
    read_sub(io, b, 1, nr)
    return nr
end
read(io::GenericIOBuffer) = read!(io,StringVector(bytesavailable(io)))
readavailable(io::GenericIOBuffer) = read(io)
read(io::GenericIOBuffer, nb::Integer) = read!(io,StringVector(min(nb, bytesavailable(io))))

function occursin(delim::UInt8, buf::IOBuffer)
    p = pointer(buf.data, buf.ptr)
    q = GC.@preserve buf ccall(:memchr,Ptr{UInt8},(Ptr{UInt8},Int32,Csize_t),p,delim,bytesavailable(buf))
    return q != C_NULL
end

function occursin(delim::UInt8, buf::GenericIOBuffer)
    data = buf.data
    for i = buf.ptr:buf.size
        @inbounds b = data[i]
        b == delim && return true
    end
    return false
end

function readuntil(io::GenericIOBuffer, delim::UInt8; keep::Bool=false)
    lb = 70
    A = StringVector(lb)
    nread = 0
    nout = 0
    data = io.data
    for i = io.ptr : io.size
        @inbounds b = data[i]
        nread += 1
        if keep || b != delim
            nout += 1
            if nout > lb
                lb = nout*2
                resize!(A, lb)
            end
            @inbounds A[nout] = b
        end
        if b == delim
            break
        end
    end
    io.ptr += nread
    if lb != nout
        resize!(A, nout)
    end
    A
end

# copy-free crc32c of IOBuffer:
function _crc32c(io::IOBuffer, nb::Integer, crc::UInt32=0x00000000)
    nb < 0 && throw(ArgumentError("number of bytes to checksum must be ≥ 0, got $nb"))
    io.readable || _throw_not_readable()
    n = min(nb, bytesavailable(io))
    n == 0 && return crc
    crc = GC.@preserve io unsafe_crc32c(pointer(io.data, io.ptr), n, crc)
    io.ptr += n
    return crc
end
_crc32c(io::IOBuffer, crc::UInt32=0x00000000) = _crc32c(io, bytesavailable(io), crc)
O   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/intfuncs.jl��      # This file is a part of Julia. License is MIT: https://julialang.org/license

## number-theoretic functions ##

"""
    gcd(x, y...)

Greatest common (positive) divisor (or zero if all arguments are zero).
The arguments may be integer and rational numbers.

!!! compat "Julia 1.4"
    Rational arguments require Julia 1.4 or later.

# Examples
```jldoctest
julia> gcd(6, 9)
3

julia> gcd(6, -9)
3

julia> gcd(6, 0)
6

julia> gcd(0, 0)
0

julia> gcd(1//3, 2//3)
1//3

julia> gcd(1//3, -2//3)
1//3

julia> gcd(1//3, 2)
1//3

julia> gcd(0, 0, 10, 15)
5
```
"""
function gcd(a::T, b::T) where T<:Integer
    while b != 0
        t = b
        b = rem(a, b)
        a = t
    end
    checked_abs(a)
end

function gcd(a::T, b::T) where T<:BitInteger
    a == 0 && return Base.checked_abs(b)
    b == 0 && return Base.checked_abs(a)
    if a isa Signed && a == typemin(T)
        if a == b
            Base.__throw_gcd_overflow(a, b)
        else
            a, b = b, a
        end
    end
    return _gcd(a, b)
end
@noinline __throw_gcd_overflow(a, b) =
    throw(OverflowError(LazyString("gcd(", a, ", ", b, ") overflows")))

function absdiff(x::T,y::T) where {T<:Unsigned}
    d = max(x,y) - min(x,y)
    d, d
end
function absdiff(x::T,y::T) where {T<:Signed}
    d = x - y
    abs(d), d
end
# binary GCD (aka Stein's) algorithm
# about 1.7x (2.1x) faster for random Int64s (Int128s)
# Unfortunately, we need to manually annotate this as `@assume_effects :terminates_locally` to work around #41694.
# Since this is used in the Rational constructor, constant folding is something we do care about here.
@assume_effects :terminates_locally function _gcd(ain::T, bin::T) where T<:BitInteger
    zb = trailing_zeros(bin)
    za = trailing_zeros(ain)
    a = abs(ain)
    b = abs(bin >> zb)
    k = min(za, zb)
    while a != 0
        a >>= za
        absd, diff = absdiff(a, b)
        za = trailing_zeros(diff)
        b = min(a, b)
        a = absd
    end
    r = b << k
    return r % T
end

"""
    lcm(x, y...)

Least common (positive) multiple (or zero if any argument is zero).
The arguments may be integer and rational numbers.

!!! compat "Julia 1.4"
    Rational arguments require Julia 1.4 or later.

# Examples
```jldoctest
julia> lcm(2, 3)
6

julia> lcm(-2, 3)
6

julia> lcm(0, 3)
0

julia> lcm(0, 0)
0

julia> lcm(1//3, 2//3)
2//3

julia> lcm(1//3, -2//3)
2//3

julia> lcm(1//3, 2)
2//1

julia> lcm(1, 3, 5, 7)
105
```
"""
function lcm(a::T, b::T) where T<:Integer
    # explicit a==0 test is to handle case of lcm(0, 0) correctly
    # explicit b==0 test is to handle case of lcm(typemin(T),0) correctly
    if a == 0 || b == 0
        return zero(a)
    else
        return checked_abs(checked_mul(a, div(b, gcd(b,a))))
    end
end

gcd(a::Integer) = checked_abs(a)
gcd(a::Rational) = checked_abs(a.num) // a.den
lcm(a::Union{Integer,Rational}) = gcd(a)
gcd(a::Unsigned, b::Signed) = gcd(promote(a, abs(b))...)
gcd(a::Signed, b::Unsigned) = gcd(promote(abs(a), b)...)
gcd(a::Real, b::Real) = gcd(promote(a,b)...)
lcm(a::Real, b::Real) = lcm(promote(a,b)...)
gcd(a::Real, b::Real, c::Real...) = gcd(a, gcd(b, c...))
lcm(a::Real, b::Real, c::Real...) = lcm(a, lcm(b, c...))
gcd(a::T, b::T) where T<:Real = throw(MethodError(gcd, (a,b)))
lcm(a::T, b::T) where T<:Real = throw(MethodError(lcm, (a,b)))

gcd(abc::AbstractArray{<:Real}) = reduce(gcd, abc; init=zero(eltype(abc)))
lcm(abc::AbstractArray{<:Real}) = reduce(lcm, abc; init=one(eltype(abc)))

function gcd(abc::AbstractArray{<:Integer})
    a = zero(eltype(abc))
    for b in abc
        a = gcd(a, b)
        if a == 1
            return a
        end
    end
    return a
end

# return (gcd(a, b), x, y) such that ax+by == gcd(a, b)
"""
    gcdx(a, b)

Computes the greatest common (positive) divisor of `a` and `b` and their Bézout
coefficients, i.e. the integer coefficients `u` and `v` that satisfy
``ua+vb = d = gcd(a, b)``. ``gcdx(a, b)`` returns ``(d, u, v)``.

The arguments may be integer and rational numbers.

!!! compat "Julia 1.4"
    Rational arguments require Julia 1.4 or later.

# Examples
```jldoctest
julia> gcdx(12, 42)
(6, -3, 1)

julia> gcdx(240, 46)
(2, -9, 47)
```

!!! note
    Bézout coefficients are *not* uniquely defined. `gcdx` returns the minimal
    Bézout coefficients that are computed by the extended Euclidean algorithm.
    (Ref: D. Knuth, TAoCP, 2/e, p. 325, Algorithm X.)
    For signed integers, these coefficients `u` and `v` are minimal in
    the sense that ``|u| < |b/d|`` and ``|v| < |a/d|``. Furthermore,
    the signs of `u` and `v` are chosen so that `d` is positive.
    For unsigned integers, the coefficients `u` and `v` might be near
    their `typemax`, and the identity then holds only via the unsigned
    integers' modulo arithmetic.
"""
Base.@assume_effects :terminates_locally function gcdx(a::Integer, b::Integer)
    T = promote_type(typeof(a), typeof(b))
    # a0, b0 = a, b
    s0, s1 = oneunit(T), zero(T)
    t0, t1 = s1, s0
    # The loop invariant is: s0*a0 + t0*b0 == a && s1*a0 + t1*b0 == b
    x = a % T
    y = b % T
    while y != 0
        q, r = divrem(x, y)
        x, y = y, r
        s0, s1 = s1, s0 - q*s1
        t0, t1 = t1, t0 - q*t1
    end
    x < 0 ? (-x, -s0, -t0) : (x, s0, t0)
end
gcdx(a::Real, b::Real) = gcdx(promote(a,b)...)
gcdx(a::T, b::T) where T<:Real = throw(MethodError(gcdx, (a,b)))

# multiplicative inverse of n mod m, error if none

"""
    invmod(n, m)

Take the inverse of `n` modulo `m`: `y` such that ``n y = 1 \\pmod m``,
and ``div(y,m) = 0``. This will throw an error if ``m = 0``, or if
``gcd(n,m) \\neq 1``.

# Examples
```jldoctest
julia> invmod(2, 5)
3

julia> invmod(2, 3)
2

julia> invmod(5, 6)
5
```
"""
function invmod(n::Integer, m::Integer)
    iszero(m) && throw(DomainError(m, "`m` must not be 0."))
    if n isa Signed && hastypemax(typeof(n))
        # work around inconsistencies in gcdx
        # https://github.com/JuliaLang/julia/issues/33781
        T = promote_type(typeof(n), typeof(m))
        n == typemin(typeof(n)) && m == typeof(n)(-1) && return T(0)
        n == typeof(n)(-1) && m == typemin(typeof(n)) && return T(-1)
    end
    g, x, y = gcdx(n, m)
    g != 1 && throw(DomainError((n, m), LazyString("Greatest common divisor is ", g, ".")))
    # Note that m might be negative here.
    if n isa Unsigned && hastypemax(typeof(n)) && x > typemax(n)>>1
        # x might have wrapped if it would have been negative
        # adding back m forces a correction
        x += m
    end
    # The postcondition is: mod(result * n, m) == mod(T(1), m) && div(result, m) == 0
    return mod(x, m)
end

# ^ for any x supporting *
to_power_type(x) = convert(Base._return_type(*, Tuple{typeof(x), typeof(x)}), x)
@noinline throw_domerr_powbysq(::Any, p) = throw(DomainError(p, LazyString(
    "Cannot raise an integer x to a negative power ", p, ".",
    "\nConvert input to float.")))
@noinline throw_domerr_powbysq(::Integer, p) = throw(DomainError(p, LazyString(
    "Cannot raise an integer x to a negative power ", p, ".",
    "\nMake x or ", p, " a float by adding a zero decimal ",
    "(e.g., 2.0^", p, " or 2^", float(p), " instead of 2^", p, ")",
    "or write 1/x^", -p, ", float(x)^", p, ", x^float(", p, ") or (x//1)^", p, ".")))
@noinline throw_domerr_powbysq(::AbstractMatrix, p) = throw(DomainError(p, LazyString(
    "Cannot raise an integer matrix x to a negative power ", p, ".",
    "\nMake x a float matrix by adding a zero decimal ",
    "(e.g., [2.0 1.0;1.0 0.0]^", p, " instead of [2 1;1 0]^", p, ")",
    "or write float(x)^", p, " or Rational.(x)^", p, ".")))
@assume_effects :terminates_locally function power_by_squaring(x_, p::Integer)
    x = to_power_type(x_)
    if p == 1
        return copy(x)
    elseif p == 0
        return one(x)
    elseif p == 2
        return x*x
    elseif p < 0
        isone(x) && return copy(x)
        isone(-x) && return iseven(p) ? one(x) : copy(x)
        throw_domerr_powbysq(x, p)
    end
    t = trailing_zeros(p) + 1
    p >>= t
    while (t -= 1) > 0
        x *= x
    end
    y = x
    while p > 0
        t = trailing_zeros(p) + 1
        p >>= t
        while (t -= 1) >= 0
            x *= x
        end
        y *= x
    end
    return y
end
power_by_squaring(x::Bool, p::Unsigned) = ((p==0) | x)
function power_by_squaring(x::Bool, p::Integer)
    p < 0 && !x && throw_domerr_powbysq(x, p)
    return (p==0) | x
end

^(x::T, p::T) where {T<:Integer} = power_by_squaring(x,p)
^(x::Number, p::Integer)  = power_by_squaring(x,p)

# x^p for any literal integer p is lowered to Base.literal_pow(^, x, Val(p))
# to enable compile-time optimizations specialized to p.
# However, we still need a fallback that calls the function ^ which may either
# mean Base.^ or something else, depending on context.
# We mark these @inline since if the target is marked @inline,
# we want to make sure that gets propagated,
# even if it is over the inlining threshold.
@inline literal_pow(f, x, ::Val{p}) where {p} = f(x,p)

# Restrict inlining to hardware-supported arithmetic types, which
# are fast enough to benefit from inlining.
const HWReal = Union{Int8,Int16,Int32,Int64,UInt8,UInt16,UInt32,UInt64,Float32,Float64}
const HWNumber = Union{HWReal, Complex{<:HWReal}, Rational{<:HWReal}}

# Inline x^2 and x^3 for Val
# (The first argument prevents unexpected behavior if a function ^
# is defined that is not equal to Base.^)
@inline literal_pow(::typeof(^), x::HWNumber, ::Val{0}) = one(x)
@inline literal_pow(::typeof(^), x::HWNumber, ::Val{1}) = x
@inline literal_pow(::typeof(^), x::HWNumber, ::Val{2}) = x*x
@inline literal_pow(::typeof(^), x::HWNumber, ::Val{3}) = x*x*x
@inline literal_pow(::typeof(^), x::HWNumber, ::Val{-1}) = inv(x)
@inline literal_pow(::typeof(^), x::HWNumber, ::Val{-2}) = (i=inv(x); i*i)

# don't use the inv(x) transformation here since float^p is slightly more accurate
@inline literal_pow(::typeof(^), x::AbstractFloat, ::Val{p}) where {p} = x^p
@inline literal_pow(::typeof(^), x::AbstractFloat, ::Val{-1}) = inv(x)

# for other types, define x^-n as inv(x)^n so that negative literal powers can
# be computed in a type-stable way even for e.g. integers.
@inline function literal_pow(f::typeof(^), x, ::Val{p}) where {p}
    if p < 0
        if x isa BitInteger64
            f(Float64(x), p) # inv would cause rounding, while Float64^Integer is able to compensate the inverse
        else
            f(inv(x), -p)
        end
    else
        f(x, p)
    end
end

# note: it is tempting to add optimized literal_pow(::typeof(^), x, ::Val{n})
#       methods here for various n, but this easily leads to method ambiguities
#       if anyone has defined literal_pow(::typeof(^), x::T, ::Val).

# b^p mod m

"""
    powermod(x::Integer, p::Integer, m)

Compute ``x^p \\pmod m``.

# Examples
```jldoctest
julia> powermod(2, 6, 5)
4

julia> mod(2^6, 5)
4

julia> powermod(5, 2, 20)
5

julia> powermod(5, 2, 19)
6

julia> powermod(5, 3, 19)
11
```
"""
function powermod(x::Integer, p::Integer, m::T) where T<:Integer
    p == 0 && return mod(one(m),m)
    # When the concrete type of p is signed and has the lowest value,
    # `p != 0 && p == -p` is equivalent to `p == typemin(typeof(p))` for 2's complement representation.
    # but will work for integer types like `BigInt` that don't have `typemin` defined
    # It needs special handling otherwise will cause overflow problem.
    if p == -p
        imod = invmod(x, m)
        rhalf = powermod(imod, -(p÷2), m)
        r::T = mod(widemul(rhalf, rhalf), m)
        isodd(p) && (r = mod(widemul(r, imod), m))
        #else odd
        return r
    elseif p < 0
        return powermod(invmod(x, m), -p, m)
    end
    (m == 1 || m == -1) && return zero(m)
    b = oftype(m,mod(x,m))  # this also checks for divide by zero

    t = prevpow(2, p)
    r = 1
    while true
        if p >= t
            r = mod(widemul(r,b),m)
            p -= t
        end
        t >>>= 1
        t <= 0 && break
        r = mod(widemul(r,r),m)
    end
    return r
end

# optimization: promote the modulus m to BigInt only once (cf. widemul in generic powermod above)
powermod(x::Integer, p::Integer, m::Union{Int128,UInt128}) = oftype(m, powermod(x, p, big(m)))

_nextpow2(x::Unsigned) = oneunit(x)<<(top_set_bit(x-oneunit(x)))
_nextpow2(x::Integer) = reinterpret(typeof(x),x < 0 ? -_nextpow2(unsigned(-x)) : _nextpow2(unsigned(x)))
_prevpow2(x::Unsigned) = one(x) << unsigned(top_set_bit(x)-1)
_prevpow2(x::Integer) = reinterpret(typeof(x),x < 0 ? -_prevpow2(unsigned(-x)) : _prevpow2(unsigned(x)))

"""
    ispow2(n::Number) -> Bool

Test whether `n` is an integer power of two.

See also [`count_ones`](@ref), [`prevpow`](@ref), [`nextpow`](@ref).

# Examples
```jldoctest
julia> ispow2(4)
true

julia> ispow2(5)
false

julia> ispow2(4.5)
false

julia> ispow2(0.25)
true

julia> ispow2(1//8)
true
```

!!! compat "Julia 1.6"
    Support for non-`Integer` arguments was added in Julia 1.6.
"""
ispow2(x::Number) = isreal(x) && ispow2(real(x))

ispow2(x::Integer) = x > 0 && count_ones(x) == 1

"""
    nextpow(a, x)

The smallest `a^n` not less than `x`, where `n` is a non-negative integer. `a` must be
greater than 1, and `x` must be greater than 0.

See also [`prevpow`](@ref).

# Examples
```jldoctest
julia> nextpow(2, 7)
8

julia> nextpow(2, 9)
16

julia> nextpow(5, 20)
25

julia> nextpow(4, 16)
16
```
"""
function nextpow(a::Real, x::Real)
    x <= 0 && throw(DomainError(x, "`x` must be positive."))
    # Special case fast path for x::Integer, a == 2.
    # This is a very common case. Constant prop will make sure that a call site
    # specified as `nextpow(2, x)` will get this special case inlined.
    a == 2 && isa(x, Integer) && return _nextpow2(x)
    a <= 1 && throw(DomainError(a, "`a` must be greater than 1."))
    x <= 1 && return one(a)
    n = ceil(Integer,log(a, x))
    # round-off error of log can go either direction, so need some checks
    p = a^(n-1)
    x > typemax(p) && throw(DomainError(x,"argument is beyond the range of type of the base"))
    p >= x && return p
    wp = a^n
    wp > p || throw(OverflowError("result is beyond the range of type of the base"))
    wp >= x && return wp
    wwp = a^(n+1)
    wwp > wp || throw(OverflowError("result is beyond the range of type of the base"))
    return wwp
end

"""
    prevpow(a, x)

The largest `a^n` not greater than `x`, where `n` is a non-negative integer.
`a` must be greater than 1, and `x` must not be less than 1.

See also [`nextpow`](@ref), [`isqrt`](@ref).

# Examples
```jldoctest
julia> prevpow(2, 7)
4

julia> prevpow(2, 9)
8

julia> prevpow(5, 20)
5

julia> prevpow(4, 16)
16
```
"""
function prevpow(a::T, x::Real) where T <: Real
    x < 1 && throw(DomainError(x, "`x` must be ≥ 1."))
    # See comment in nextpos() for a == special case.
    a == 2 && isa(x, Integer) && return _prevpow2(x)
    a <= 1 && throw(DomainError(a, "`a` must be greater than 1."))
    n = floor(Integer,log(a, x))
    # round-off error of log can go either direction, so need some checks
    p = a^n
    x > typemax(p) && throw(DomainError(x,"argument is beyond the range of type of the base"))
    if a isa Integer
        wp, overflow = mul_with_overflow(a, p)
        wp <= x && !overflow && return wp
    else
        wp = a^(n+1)
        wp <= x && return wp
    end
    p <= x && return p
    return a^(n-1)
end

## ndigits (number of digits) in base 10 ##

# decimal digits in an unsigned integer
const powers_of_ten = [
    0x0000000000000001, 0x000000000000000a, 0x0000000000000064, 0x00000000000003e8,
    0x0000000000002710, 0x00000000000186a0, 0x00000000000f4240, 0x0000000000989680,
    0x0000000005f5e100, 0x000000003b9aca00, 0x00000002540be400, 0x000000174876e800,
    0x000000e8d4a51000, 0x000009184e72a000, 0x00005af3107a4000, 0x00038d7ea4c68000,
    0x002386f26fc10000, 0x016345785d8a0000, 0x0de0b6b3a7640000, 0x8ac7230489e80000,
]
function bit_ndigits0z(x::Base.BitUnsigned64)
    lz = top_set_bit(x)
    nd = (1233*lz)>>12+1
    nd -= x < powers_of_ten[nd]
end
function bit_ndigits0z(x::UInt128)
    n = 0
    while x > 0x8ac7230489e80000 # 10e18
        x = div(x,0x8ac7230489e80000)
        n += 19
    end
    return n + ndigits0z(UInt64(x))
end

ndigits0z(x::BitSigned) = bit_ndigits0z(unsigned(abs(x)))
ndigits0z(x::BitUnsigned) = bit_ndigits0z(x)
ndigits0z(x::Integer) = ndigits0zpb(x, 10)

## ndigits with specified base ##

# The suffix "nb" stands for "negative base"
function ndigits0znb(x::Integer, b::Integer)
    d = 0
    if x isa Unsigned
        d += (x != 0)::Bool
        x = -signed(fld(x, -b))
    end
    # precondition: b < -1 && !(typeof(x) <: Unsigned)
    while x != 0
        x = cld(x,b)
        d += 1
    end
    return d
end

# do first division before conversion with signed here, which can otherwise overflow
ndigits0znb(x::Bool, b::Integer) = x % Int

# The suffix "pb" stands for "positive base"
function ndigits0zpb(x::Integer, b::Integer)
    # precondition: b > 1
    x == 0 && return 0
    b = Int(b)
    x = abs(x)
    if x isa Base.BitInteger
        x = unsigned(x)::Unsigned
        b == 2  && return top_set_bit(x)
        b == 8  && return (top_set_bit(x) + 2) ÷ 3
        b == 16 && return sizeof(x)<<1 - leading_zeros(x)>>2
        b == 10 && return bit_ndigits0z(x)
        if ispow2(b)
            dv, rm = divrem(top_set_bit(x), trailing_zeros(b))
            return iszero(rm) ? dv : dv + 1
        end
    end

    d = 0
    while x > typemax(Int)
        x = div(x,b)
        d += 1
    end
    x = div(x,b)
    d += 1

    m = 1
    while m <= x
        m *= b
        d += 1
    end
    return d
end

ndigits0zpb(x::Bool, b::Integer) = x % Int

# The suffix "0z" means that the output is 0 on input zero (cf. #16841)
"""
    ndigits0z(n::Integer, b::Integer=10)

Return 0 if `n == 0`, otherwise compute the number of digits in
integer `n` written in base `b` (i.e. equal to `ndigits(n, base=b)`
in this case).
The base `b` must not be in `[-1, 0, 1]`.

# Examples
```jldoctest
julia> Base.ndigits0z(0, 16)
0

julia> Base.ndigits(0, base=16)
1

julia> Base.ndigits0z(0)
0

julia> Base.ndigits0z(10, 2)
4

julia> Base.ndigits0z(10)
2
```

See also [`ndigits`](@ref).
"""
function ndigits0z(x::Integer, b::Integer)
    if b < -1
        ndigits0znb(x, b)
    elseif b > 1
        ndigits0zpb(x, b)
    else
        throw(DomainError(b, "The base must not be in `[-1, 0, 1]`."))
    end
end

# Extends the definition in base/int.jl
top_set_bit(x::Integer) = ceil(Integer, log2(x + oneunit(x)))

"""
    ndigits(n::Integer; base::Integer=10, pad::Integer=1)

Compute the number of digits in integer `n` written in base `base`
(`base` must not be in `[-1, 0, 1]`), optionally padded with zeros
to a specified size (the result will never be less than `pad`).

See also [`digits`](@ref), [`count_ones`](@ref).

# Examples
```jldoctest
julia> ndigits(0)
1

julia> ndigits(12345)
5

julia> ndigits(1022, base=16)
3

julia> string(1022, base=16)
"3fe"

julia> ndigits(123, pad=5)
5

julia> ndigits(-123)
3
```
"""
ndigits(x::Integer; base::Integer=10, pad::Integer=1) = max(pad, ndigits0z(x, base))

## integer to string functions ##

function bin(x::Unsigned, pad::Int, neg::Bool)
    m = top_set_bit(x)
    n = neg + max(pad, m)
    a = StringVector(n)
    # for i in 0x0:UInt(n-1) # automatic vectorization produces redundant codes
    #     @inbounds a[n - i] = 0x30 + (((x >> i) % UInt8)::UInt8 & 0x1)
    # end
    i = n
    @inbounds while i >= 4
        b = UInt32((x % UInt8)::UInt8)
        d = 0x30303030 + ((b * 0x08040201) >> 0x3) & 0x01010101
        a[i-3] = (d >> 0x00) % UInt8
        a[i-2] = (d >> 0x08) % UInt8
        a[i-1] = (d >> 0x10) % UInt8
        a[i]   = (d >> 0x18) % UInt8
        x >>= 0x4
        i -= 4
    end
    while i > neg
        @inbounds a[i] = 0x30 + ((x % UInt8)::UInt8 & 0x1)
        x >>= 0x1
        i -= 1
    end
    neg && (@inbounds a[1] = 0x2d) # UInt8('-')
    String(a)
end

function oct(x::Unsigned, pad::Int, neg::Bool)
    m = div(top_set_bit(x) + 2, 3)
    n = neg + max(pad, m)
    a = StringVector(n)
    i = n
    while i > neg
        @inbounds a[i] = 0x30 + ((x % UInt8)::UInt8 & 0x7)
        x >>= 0x3
        i -= 1
    end
    neg && (@inbounds a[1] = 0x2d) # UInt8('-')
    String(a)
end

# 2-digit decimal characters ("00":"99")
const _dec_d100 = UInt16[
# generating expression: UInt16[(0x30 + i % 10) << 0x8 + (0x30 + i ÷ 10) for i = 0:99]
#    0 0,    0 1,    0 2,    0 3, and so on in little-endian
  0x3030, 0x3130, 0x3230, 0x3330, 0x3430, 0x3530, 0x3630, 0x3730, 0x3830, 0x3930,
  0x3031, 0x3131, 0x3231, 0x3331, 0x3431, 0x3531, 0x3631, 0x3731, 0x3831, 0x3931,
  0x3032, 0x3132, 0x3232, 0x3332, 0x3432, 0x3532, 0x3632, 0x3732, 0x3832, 0x3932,
  0x3033, 0x3133, 0x3233, 0x3333, 0x3433, 0x3533, 0x3633, 0x3733, 0x3833, 0x3933,
  0x3034, 0x3134, 0x3234, 0x3334, 0x3434, 0x3534, 0x3634, 0x3734, 0x3834, 0x3934,
  0x3035, 0x3135, 0x3235, 0x3335, 0x3435, 0x3535, 0x3635, 0x3735, 0x3835, 0x3935,
  0x3036, 0x3136, 0x3236, 0x3336, 0x3436, 0x3536, 0x3636, 0x3736, 0x3836, 0x3936,
  0x3037, 0x3137, 0x3237, 0x3337, 0x3437, 0x3537, 0x3637, 0x3737, 0x3837, 0x3937,
  0x3038, 0x3138, 0x3238, 0x3338, 0x3438, 0x3538, 0x3638, 0x3738, 0x3838, 0x3938,
  0x3039, 0x3139, 0x3239, 0x3339, 0x3439, 0x3539, 0x3639, 0x3739, 0x3839, 0x3939
]

function append_c_digits(olength::Int, digits::Unsigned, buf, pos::Int)
    i = olength
    while i >= 2
        d, c = divrem(digits, 0x64)
        digits = oftype(digits, d)
        @inbounds d100 = _dec_d100[(c % Int) + 1]
        @inbounds buf[pos + i - 2] = d100 % UInt8
        @inbounds buf[pos + i - 1] = (d100 >> 0x8) % UInt8
        i -= 2
    end
    if i == 1
        @inbounds buf[pos] = UInt8('0') + rem(digits, 0xa) % UInt8
        i -= 1
    end
    return pos + olength
end

function append_nine_digits(digits::Unsigned, buf, pos::Int)
    if digits == 0
        for _ = 1:9
            @inbounds buf[pos] = UInt8('0')
            pos += 1
        end
        return pos
    end
    return @inline append_c_digits(9, digits, buf, pos) # force loop-unrolling on the length
end

function append_c_digits_fast(olength::Int, digits::Unsigned, buf, pos::Int)
    i = olength
    # n.b. olength may be larger than required to print all of `digits` (and will be padded
    # with zeros), but the printed number will be undefined if it is smaller, and may include
    # bits of both the high and low bytes.
    maxpow10 = 0x3b9aca00 # 10e9 as UInt32
    while i > 9 && digits > typemax(UInt)
        # do everything in cheap math chunks, using the processor's native math size
        d, c = divrem(digits, maxpow10)
        digits = oftype(digits, d)
        append_nine_digits(c % UInt32, buf, pos + i - 9)
        i -= 9
    end
    append_c_digits(i, digits % UInt, buf, pos)
    return pos + olength
end


function dec(x::Unsigned, pad::Int, neg::Bool)
    n = neg + ndigits(x, pad=pad)
    a = StringVector(n)
    append_c_digits_fast(n, x, a, 1)
    neg && (@inbounds a[1] = 0x2d) # UInt8('-')
    String(a)
end

function hex(x::Unsigned, pad::Int, neg::Bool)
    m = 2 * sizeof(x) - (leading_zeros(x) >> 2)
    n = neg + max(pad, m)
    a = StringVector(n)
    i = n
    while i >= 2
        b = (x % UInt8)::UInt8
        d1, d2 = b >> 0x4, b & 0xf
        @inbounds a[i-1] = d1 + ifelse(d1 > 0x9, 0x57, 0x30)
        @inbounds a[i]   = d2 + ifelse(d2 > 0x9, 0x57, 0x30)
        x >>= 0x8
        i -= 2
    end
    if i > neg
        d = (x % UInt8)::UInt8 & 0xf
        @inbounds a[i] = d + ifelse(d > 0x9, 0x57, 0x30)
    end
    neg && (@inbounds a[1] = 0x2d) # UInt8('-')
    String(a)
end

const base36digits = UInt8['0':'9';'a':'z']
const base62digits = UInt8['0':'9';'A':'Z';'a':'z']

function _base(base::Integer, x::Integer, pad::Int, neg::Bool)
    (x >= 0) | (base < 0) || throw(DomainError(x, "For negative `x`, `base` must be negative."))
    2 <= abs(base) <= 62 || throw(DomainError(base, "base must satisfy 2 ≤ abs(base) ≤ 62"))
    b = (base % Int)::Int
    digits = abs(b) <= 36 ? base36digits : base62digits
    n = neg + ndigits(x, base=b, pad=pad)
    a = StringVector(n)
    i = n
    @inbounds while i > neg
        if b > 0
            a[i] = digits[1 + (rem(x, b) % Int)::Int]
            x = div(x,b)
        else
            a[i] = digits[1 + (mod(x, -b) % Int)::Int]
            x = cld(x,b)
        end
        i -= 1
    end
    neg && (@inbounds a[1] = 0x2d) # UInt8('-')
    String(a)
end

split_sign(n::Integer) = unsigned(abs(n)), n < 0
split_sign(n::Unsigned) = n, false

"""
    string(n::Integer; base::Integer = 10, pad::Integer = 1)

Convert an integer `n` to a string in the given `base`,
optionally specifying a number of digits to pad to.

See also [`digits`](@ref), [`bitstring`](@ref), [`count_zeros`](@ref).

# Examples
```jldoctest
julia> string(5, base = 13, pad = 4)
"0005"

julia> string(-13, base = 5, pad = 4)
"-0023"
```
"""
function string(n::Integer; base::Integer = 10, pad::Integer = 1)
    pad = (min(max(pad, typemin(Int)), typemax(Int)) % Int)::Int
    if base == 2
        (n_positive, neg) = split_sign(n)
        bin(n_positive, pad, neg)
    elseif base == 8
        (n_positive, neg) = split_sign(n)
        oct(n_positive, pad, neg)
    elseif base == 10
        (n_positive, neg) = split_sign(n)
        dec(n_positive, pad, neg)
    elseif base == 16
        (n_positive, neg) = split_sign(n)
        hex(n_positive, pad, neg)
    else
        _base(base, base > 0 ? unsigned(abs(n)) : convert(Signed, n), pad, (base>0) & (n<0))
    end
end

string(b::Bool) = b ? "true" : "false"

"""
    bitstring(n)

A string giving the literal bit representation of a primitive type.

See also [`count_ones`](@ref), [`count_zeros`](@ref), [`digits`](@ref).

# Examples
```jldoctest
julia> bitstring(Int32(4))
"00000000000000000000000000000100"

julia> bitstring(2.2)
"0100000000000001100110011001100110011001100110011001100110011010"
```
"""
function bitstring(x::T) where {T}
    isprimitivetype(T) || throw(ArgumentError("$T not a primitive type"))
    sz = sizeof(T) * 8
    str = StringVector(sz)
    i = sz
    @inbounds while i >= 4
        b = UInt32(sizeof(T) == 1 ? bitcast(UInt8, x) : trunc_int(UInt8, x))
        d = 0x30303030 + ((b * 0x08040201) >> 0x3) & 0x01010101
        str[i-3] = (d >> 0x00) % UInt8
        str[i-2] = (d >> 0x08) % UInt8
        str[i-1] = (d >> 0x10) % UInt8
        str[i]   = (d >> 0x18) % UInt8
        x = lshr_int(x, 4)
        i -= 4
    end
    return String(str)
end

"""
    digits([T<:Integer], n::Integer; base::T = 10, pad::Integer = 1)

Return an array with element type `T` (default `Int`) of the digits of `n` in the given
base, optionally padded with zeros to a specified size. More significant digits are at
higher indices, such that `n == sum(digits[k]*base^(k-1) for k=1:length(digits))`.

See also [`ndigits`](@ref), [`digits!`](@ref),
and for base 2 also [`bitstring`](@ref), [`count_ones`](@ref).

# Examples
```jldoctest
julia> digits(10)
2-element Vector{Int64}:
 0
 1

julia> digits(10, base = 2)
4-element Vector{Int64}:
 0
 1
 0
 1

julia> digits(-256, base = 10, pad = 5)
5-element Vector{Int64}:
 -6
 -5
 -2
  0
  0

julia> n = rand(-999:999);

julia> n == evalpoly(13, digits(n, base = 13))
true
```
"""
digits(n::Integer; base::Integer = 10, pad::Integer = 1) =
    digits(typeof(base), n, base = base, pad = pad)

function digits(T::Type{<:Integer}, n::Integer; base::Integer = 10, pad::Integer = 1)
    digits!(zeros(T, ndigits(n, base=base, pad=pad)), n, base=base)
end

"""
    hastypemax(T::Type) -> Bool

Return `true` if and only if the extrema `typemax(T)` and `typemin(T)` are defined.
"""
hastypemax(::Base.BitIntegerType) = true
hastypemax(::Type{Bool}) = true
hastypemax(::Type{T}) where {T} = applicable(typemax, T) && applicable(typemin, T)

"""
    digits!(array, n::Integer; base::Integer = 10)

Fills an array of the digits of `n` in the given base. More significant digits are at higher
indices. If the array length is insufficient, the least significant digits are filled up to
the array length. If the array length is excessive, the excess portion is filled with zeros.

# Examples
```jldoctest
julia> digits!([2, 2, 2, 2], 10, base = 2)
4-element Vector{Int64}:
 0
 1
 0
 1

julia> digits!([2, 2, 2, 2, 2, 2], 10, base = 2)
6-element Vector{Int64}:
 0
 1
 0
 1
 0
 0
```
"""
function digits!(a::AbstractVector{T}, n::Integer; base::Integer = 10) where T<:Integer
    2 <= abs(base) || throw(DomainError(base, "base must be ≥ 2 or ≤ -2"))
    hastypemax(T) && abs(base) - 1 > typemax(T) &&
        throw(ArgumentError("type $T too small for base $base"))
    isempty(a) && return a

    if base > 0
        if ispow2(base) && n >= 0 && n isa Base.BitInteger && base <= typemax(Int)
            base = Int(base)
            k = trailing_zeros(base)
            c = base - 1
            for i in eachindex(a)
                a[i] = (n >> (k * (i - firstindex(a)))) & c
            end
        else
            for i in eachindex(a)
                n, d = divrem(n, base)
                a[i] = d
            end
        end
    else
        # manually peel one loop iteration for type stability
        n, d = fldmod(n, -base)
        a[firstindex(a)] = d
        n = -signed(n)
        for i in firstindex(a)+1:lastindex(a)
            n, d = fldmod(n, -base)
            a[i] = d
            n = -n
        end
    end
    return a
end

"""
    isqrt(n::Integer)

Integer square root: the largest integer `m` such that `m*m <= n`.

```jldoctest
julia> isqrt(5)
2
```
"""
isqrt(x::Integer) = oftype(x, trunc(sqrt(x)))

function isqrt(x::Union{Int64,UInt64,Int128,UInt128})
    x==0 && return x
    s = oftype(x, trunc(sqrt(x)))
    # fix with a Newton iteration, since conversion to float discards
    # too many bits.
    s = (s + div(x,s)) >> 1
    s*s > x ? s-1 : s
end

"""
    factorial(n::Integer)

Factorial of `n`. If `n` is an [`Integer`](@ref), the factorial is computed as an
integer (promoted to at least 64 bits). Note that this may overflow if `n` is not small,
but you can use `factorial(big(n))` to compute the result exactly in arbitrary precision.

See also [`binomial`](@ref).

# Examples
```jldoctest
julia> factorial(6)
720

julia> factorial(21)
ERROR: OverflowError: 21 is too large to look up in the table; consider using `factorial(big(21))` instead
Stacktrace:
[...]

julia> factorial(big(21))
51090942171709440000
```

# External links
* [Factorial](https://en.wikipedia.org/wiki/Factorial) on Wikipedia.
"""
function factorial(n::Integer)
    n < 0 && throw(DomainError(n, "`n` must be nonnegative."))
    f::typeof(n*n) = 1
    for i::typeof(n*n) = 2:n
        f *= i
    end
    return f
end

"""
    binomial(n::Integer, k::Integer)

The _binomial coefficient_ ``\\binom{n}{k}``, being the coefficient of the ``k``th term in
the polynomial expansion of ``(1+x)^n``.

If ``n`` is non-negative, then it is the number of ways to choose `k` out of `n` items:
```math
\\binom{n}{k} = \\frac{n!}{k! (n-k)!}
```
where ``n!`` is the [`factorial`](@ref) function.

If ``n`` is negative, then it is defined in terms of the identity
```math
\\binom{n}{k} = (-1)^k \\binom{k-n-1}{k}
```

See also [`factorial`](@ref).

# Examples
```jldoctest
julia> binomial(5, 3)
10

julia> factorial(5) ÷ (factorial(5-3) * factorial(3))
10

julia> binomial(-5, 3)
-35
```

# External links
* [Binomial coefficient](https://en.wikipedia.org/wiki/Binomial_coefficient) on Wikipedia.
"""
Base.@assume_effects :terminates_locally function binomial(n::T, k::T) where T<:Integer
    n0, k0 = n, k
    k < 0 && return zero(T)
    sgn = one(T)
    if n < 0
        n = -n + k - one(T)
        if isodd(k)
            sgn = -sgn
        end
    end
    k > n && return zero(T)
    (k == 0 || k == n) && return sgn
    k == 1 && return sgn*n
    if k > (n>>1)
        k = (n - k)
    end
    x = nn = n - k + one(T)
    nn += one(T)
    rr = T(2)
    while rr <= k
        xt = div(widemul(x, nn), rr)
        x = xt % T
        x == xt || throw(OverflowError(LazyString("binomial(", n0, ", ", k0, ") overflows")))
        rr += one(T)
        nn += one(T)
    end
    copysign(x, sgn)
end

"""
    binomial(x::Number, k::Integer)

The generalized binomial coefficient, defined for `k ≥ 0` by
the polynomial
```math
\\frac{1}{k!} \\prod_{j=0}^{k-1} (x - j)
```
When `k < 0` it returns zero.

For the case of integer `x`, this is equivalent to the ordinary
integer binomial coefficient
```math
\\binom{n}{k} = \\frac{n!}{k! (n-k)!}
```

Further generalizations to non-integer `k` are mathematically possible, but
involve the Gamma function and/or the beta function, which are
not provided by the Julia standard library but are available
in external packages such as [SpecialFunctions.jl](https://github.com/JuliaMath/SpecialFunctions.jl).

# External links
* [Binomial coefficient](https://en.wikipedia.org/wiki/Binomial_coefficient) on Wikipedia.
"""
function binomial(x::Number, k::Integer)
    k < 0 && return zero(x)/one(k)
    # we don't use prod(i -> (x-i+1), 1:k) / factorial(k),
    # and instead divide each term by i, to avoid spurious overflow.
    return prod(i -> (x-(i-1))/i, OneTo(k), init=oneunit(x)/one(k))
end
V   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/strings/strings.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

include("strings/search.jl")
include("strings/unicode.jl")

import .Unicode: textwidth, islowercase, isuppercase, isletter, isdigit, isnumeric, iscntrl, ispunct,
    isspace, isprint, isxdigit, lowercase, uppercase, titlecase, lowercasefirst, uppercasefirst

import .Iterators: PartitionIterator

include("strings/util.jl")
include("strings/io.jl")
U   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/strings/search.jl�N      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
An abstract type representing any sort of pattern matching expression
(typically a regular expression). `AbstractPattern` objects can be used to
match strings with [`match`](@ref).

!!! compat "Julia 1.6"
    This type is available in Julia 1.6 and later.
"""
abstract type AbstractPattern end

nothing_sentinel(i) = i == 0 ? nothing : i

function findnext(pred::Fix2{<:Union{typeof(isequal),typeof(==)},<:AbstractChar},
                  s::String, i::Integer)
    if i < 1 || i > sizeof(s)
        i == sizeof(s) + 1 && return nothing
        throw(BoundsError(s, i))
    end
    @inbounds isvalid(s, i) || string_index_err(s, i)
    c = pred.x
    c ≤ '\x7f' && return nothing_sentinel(_search(s, c % UInt8, i))
    while true
        i = _search(s, first_utf8_byte(c), i)
        i == 0 && return nothing
        pred(s[i]) && return i
        i = nextind(s, i)
    end
end

findfirst(pred::Fix2{<:Union{typeof(isequal),typeof(==)},<:Union{Int8,UInt8}}, a::ByteArray) =
    nothing_sentinel(_search(a, pred.x))

findnext(pred::Fix2{<:Union{typeof(isequal),typeof(==)},<:Union{Int8,UInt8}}, a::ByteArray, i::Integer) =
    nothing_sentinel(_search(a, pred.x, i))

findfirst(::typeof(iszero), a::ByteArray) = nothing_sentinel(_search(a, zero(UInt8)))
findnext(::typeof(iszero), a::ByteArray, i::Integer) = nothing_sentinel(_search(a, zero(UInt8), i))

function _search(a::Union{String,ByteArray}, b::Union{Int8,UInt8}, i::Integer = 1)
    if i < 1
        throw(BoundsError(a, i))
    end
    n = sizeof(a)
    if i > n
        return i == n+1 ? 0 : throw(BoundsError(a, i))
    end
    p = pointer(a)
    q = GC.@preserve a ccall(:memchr, Ptr{UInt8}, (Ptr{UInt8}, Int32, Csize_t), p+i-1, b, n-i+1)
    return q == C_NULL ? 0 : Int(q-p+1)
end

function _search(a::ByteArray, b::AbstractChar, i::Integer = 1)
    if isascii(b)
        _search(a,UInt8(b),i)
    else
        _search(a,codeunits(string(b)),i).start
    end
end

function findprev(pred::Fix2{<:Union{typeof(isequal),typeof(==)},<:AbstractChar},
                  s::String, i::Integer)
    c = pred.x
    c ≤ '\x7f' && return nothing_sentinel(_rsearch(s, c % UInt8, i))
    b = first_utf8_byte(c)
    while true
        i = _rsearch(s, b, i)
        i == 0 && return nothing
        pred(s[i]) && return i
        i = prevind(s, i)
    end
end

findlast(pred::Fix2{<:Union{typeof(isequal),typeof(==)},<:Union{Int8,UInt8}}, a::ByteArray) =
    nothing_sentinel(_rsearch(a, pred.x))

findprev(pred::Fix2{<:Union{typeof(isequal),typeof(==)},<:Union{Int8,UInt8}}, a::ByteArray, i::Integer) =
    nothing_sentinel(_rsearch(a, pred.x, i))

findlast(::typeof(iszero), a::ByteArray) = nothing_sentinel(_rsearch(a, zero(UInt8)))
findprev(::typeof(iszero), a::ByteArray, i::Integer) = nothing_sentinel(_rsearch(a, zero(UInt8), i))

function _rsearch(a::Union{String,ByteArray}, b::Union{Int8,UInt8}, i::Integer = sizeof(a))
    if i < 1
        return i == 0 ? 0 : throw(BoundsError(a, i))
    end
    n = sizeof(a)
    if i > n
        return i == n+1 ? 0 : throw(BoundsError(a, i))
    end
    p = pointer(a)
    q = GC.@preserve a ccall(:memrchr, Ptr{UInt8}, (Ptr{UInt8}, Int32, Csize_t), p, b, i)
    return q == C_NULL ? 0 : Int(q-p+1)
end

function _rsearch(a::ByteArray, b::AbstractChar, i::Integer = length(a))
    if isascii(b)
        _rsearch(a,UInt8(b),i)
    else
        _rsearch(a,codeunits(string(b)),i).start
    end
end

"""
    findfirst(pattern::AbstractString, string::AbstractString)
    findfirst(pattern::AbstractPattern, string::String)

Find the first occurrence of `pattern` in `string`. Equivalent to
[`findnext(pattern, string, firstindex(s))`](@ref).

# Examples
```jldoctest
julia> findfirst("z", "Hello to the world") # returns nothing, but not printed in the REPL

julia> findfirst("Julia", "JuliaLang")
1:5
```
"""
findfirst(pattern::AbstractString, string::AbstractString) =
    findnext(pattern, string, firstindex(string))

"""
    findfirst(ch::AbstractChar, string::AbstractString)

Find the first occurrence of character `ch` in `string`.

!!! compat "Julia 1.3"
    This method requires at least Julia 1.3.

# Examples
```jldoctest
julia> findfirst('a', "happy")
2

julia> findfirst('z', "happy") === nothing
true
```
"""
findfirst(ch::AbstractChar, string::AbstractString) = findfirst(==(ch), string)

"""
    findfirst(pattern::AbstractVector{<:Union{Int8,UInt8}},
              A::AbstractVector{<:Union{Int8,UInt8}})

Find the first occurrence of sequence `pattern` in vector `A`.

!!! compat "Julia 1.6"
    This method requires at least Julia 1.6.

# Examples
```jldoctest
julia> findfirst([0x52, 0x62], [0x40, 0x52, 0x62, 0x63])
2:3
```
"""
findfirst(pattern::AbstractVector{<:Union{Int8,UInt8}},
          A::AbstractVector{<:Union{Int8,UInt8}}) =
    _search(A, pattern, firstindex(A))

# AbstractString implementation of the generic findnext interface
function findnext(testf::Function, s::AbstractString, i::Integer)
    i = Int(i)
    z = ncodeunits(s) + 1
    1 ≤ i ≤ z || throw(BoundsError(s, i))
    @inbounds i == z || isvalid(s, i) || string_index_err(s, i)
    e = lastindex(s)
    while i <= e
        testf(@inbounds s[i]) && return i
        i = @inbounds nextind(s, i)
    end
    return nothing
end


in(c::AbstractChar, s::AbstractString) = (findfirst(isequal(c),s)!==nothing)

function _searchindex(s::Union{AbstractString,ByteArray},
                      t::Union{AbstractString,AbstractChar,Int8,UInt8},
                      i::Integer)
    x = Iterators.peel(t)
    if isnothing(x)
        return 1 <= i <= nextind(s,lastindex(s))::Int ? i :
               throw(BoundsError(s, i))
    end
    t1, trest = x
    while true
        i = findnext(isequal(t1),s,i)
        if i === nothing return 0 end
        ii = nextind(s, i)::Int
        a = Iterators.Stateful(trest)
        matched = all(splat(==), zip(SubString(s, ii), a))
        (isempty(a) && matched) && return i
        i = ii
    end
end

_searchindex(s::AbstractString, t::AbstractChar, i::Integer) = something(findnext(isequal(t), s, i), 0)

function _search_bloom_mask(c)
    UInt64(1) << (c & 63)
end

_nthbyte(s::String, i) = codeunit(s, i)
_nthbyte(t::AbstractVector, index) = t[index + (firstindex(t)-1)]

function _searchindex(s::String, t::String, i::Integer)
    # Check for fast case of a single byte
    lastindex(t) == 1 && return something(findnext(isequal(t[1]), s, i), 0)
    _searchindex(codeunits(s), codeunits(t), i)
end

function _searchindex(s::AbstractVector{<:Union{Int8,UInt8}},
                      t::AbstractVector{<:Union{Int8,UInt8}},
                      _i::Integer)
    sentinel = firstindex(s) - 1
    n = length(t)
    m = length(s)
    i = Int(_i) - sentinel
    (i < 1 || i > m+1) && throw(BoundsError(s, _i))

    if n == 0
        return 1 <= i <= m+1 ? max(1, i) : sentinel
    elseif m == 0
        return sentinel
    elseif n == 1
        return something(findnext(isequal(_nthbyte(t,1)), s, i), sentinel)
    end

    w = m - n
    if w < 0 || i - 1 > w
        return sentinel
    end

    bloom_mask = UInt64(0)
    skip = n - 1
    tlast = _nthbyte(t,n)
    for j in 1:n
        bloom_mask |= _search_bloom_mask(_nthbyte(t,j))
        if _nthbyte(t,j) == tlast && j < n
            skip = n - j - 1
        end
    end

    i -= 1
    while i <= w
        if _nthbyte(s,i+n) == tlast
            # check candidate
            j = 0
            while j < n - 1
                if _nthbyte(s,i+j+1) != _nthbyte(t,j+1)
                    break
                end
                j += 1
            end

            # match found
            if j == n - 1
                # restore in case `s` is an OffSetArray
                return i+firstindex(s)
            end

            # no match, try to rule out the next character
            if i < w && bloom_mask & _search_bloom_mask(_nthbyte(s,i+n+1)) == 0
                i += n
            else
                i += skip
            end
        elseif i < w
            if bloom_mask & _search_bloom_mask(_nthbyte(s,i+n+1)) == 0
                i += n
            end
        end
        i += 1
    end

    sentinel
end

function _search(s::Union{AbstractString,AbstractVector{<:Union{Int8,UInt8}}},
                 t::Union{AbstractString,AbstractChar,AbstractVector{<:Union{Int8,UInt8}}},
                 i::Integer)
    idx = _searchindex(s,t,i)
    if isempty(t)
        idx:idx-1
    elseif idx >= firstindex(s)
        idx:(idx + lastindex(t) - 1)
    else
        nothing
    end
end

"""
    findnext(pattern::AbstractString, string::AbstractString, start::Integer)
    findnext(pattern::AbstractPattern, string::String, start::Integer)

Find the next occurrence of `pattern` in `string` starting at position `start`.
`pattern` can be either a string, or a regular expression, in which case `string`
must be of type `String`.

The return value is a range of indices where the matching sequence is found, such that
`s[findnext(x, s, i)] == x`:

`findnext("substring", string, i)` == `start:stop` such that
`string[start:stop] == "substring"` and `i <= start`, or `nothing` if unmatched.

# Examples
```jldoctest
julia> findnext("z", "Hello to the world", 1) === nothing
true

julia> findnext("o", "Hello to the world", 6)
8:8

julia> findnext("Lang", "JuliaLang", 2)
6:9
```
"""
findnext(t::AbstractString, s::AbstractString, start::Integer) = _search(s, t, Int(start))

"""
    findnext(ch::AbstractChar, string::AbstractString, start::Integer)

Find the next occurrence of character `ch` in `string` starting at position `start`.

!!! compat "Julia 1.3"
    This method requires at least Julia 1.3.

# Examples
```jldoctest
julia> findnext('z', "Hello to the world", 1) === nothing
true

julia> findnext('o', "Hello to the world", 6)
8
```
"""
findnext(ch::AbstractChar, string::AbstractString, start::Integer) =
    findnext(==(ch), string, start)

"""
    findnext(pattern::AbstractVector{<:Union{Int8,UInt8}},
             A::AbstractVector{<:Union{Int8,UInt8}},
             start::Integer)

Find the next occurrence of the sequence `pattern` in vector `A` starting at position `start`.

!!! compat "Julia 1.6"
    This method requires at least Julia 1.6.

# Examples
```jldoctest
julia> findnext([0x52, 0x62], [0x52, 0x62, 0x72], 3) === nothing
true

julia> findnext([0x52, 0x62], [0x40, 0x52, 0x62, 0x52, 0x62], 3)
4:5
```
"""
findnext(pattern::AbstractVector{<:Union{Int8,UInt8}},
         A::AbstractVector{<:Union{Int8,UInt8}},
         start::Integer) =
    _search(A, pattern, start)

"""
    findlast(pattern::AbstractString, string::AbstractString)

Find the last occurrence of `pattern` in `string`. Equivalent to
[`findprev(pattern, string, lastindex(string))`](@ref).

# Examples
```jldoctest
julia> findlast("o", "Hello to the world")
15:15

julia> findfirst("Julia", "JuliaLang")
1:5
```
"""
findlast(pattern::AbstractString, string::AbstractString) =
    findprev(pattern, string, lastindex(string))

"""
    findlast(pattern::AbstractVector{<:Union{Int8,UInt8}},
             A::AbstractVector{<:Union{Int8,UInt8}})

Find the last occurrence of `pattern` in array `A`. Equivalent to
[`findprev(pattern, A, lastindex(A))`](@ref).

# Examples
```jldoctest
julia> findlast([0x52, 0x62], [0x52, 0x62, 0x52, 0x62])
3:4
```
"""
findlast(pattern::AbstractVector{<:Union{Int8,UInt8}},
         A::AbstractVector{<:Union{Int8,UInt8}}) =
    findprev(pattern, A, lastindex(A))

"""
    findlast(ch::AbstractChar, string::AbstractString)

Find the last occurrence of character `ch` in `string`.

!!! compat "Julia 1.3"
    This method requires at least Julia 1.3.

# Examples
```jldoctest
julia> findlast('p', "happy")
4

julia> findlast('z', "happy") === nothing
true
```
"""
findlast(ch::AbstractChar, string::AbstractString) = findlast(==(ch), string)

"""
    findall(
        pattern::Union{AbstractString,AbstractPattern},
        string::AbstractString;
        overlap::Bool = false,
    )
    findall(
        pattern::Vector{UInt8}
        A::Vector{UInt8};
        overlap::Bool = false,
    )

Return a `Vector{UnitRange{Int}}` of all the matches for `pattern` in `string`.
Each element of the returned vector is a range of indices where the
matching sequence is found, like the return value of [`findnext`](@ref).

If `overlap=true`, the matching sequences are allowed to overlap indices in the
original string, otherwise they must be from disjoint character ranges.

# Examples
```jldoctest
julia> findall("a", "apple")
1-element Vector{UnitRange{Int64}}:
 1:1

julia> findall("nana", "banana")
1-element Vector{UnitRange{Int64}}:
 3:6

julia> findall("a", "banana")
3-element Vector{UnitRange{Int64}}:
 2:2
 4:4
 6:6

julia> findall(UInt8[1,2], UInt8[1,2,3,1,2])
2-element Vector{UnitRange{Int64}}:
 1:2
 4:5
```

!!! compat "Julia 1.3"
     This method requires at least Julia 1.3.
"""

function findall(t::Union{AbstractString, AbstractPattern, AbstractVector{<:Union{Int8,UInt8}}},
                 s::Union{AbstractString, AbstractPattern, AbstractVector{<:Union{Int8,UInt8}}},
                 ; overlap::Bool=false)
    found = UnitRange{Int}[]
    i, e = firstindex(s), lastindex(s)
    while true
        r = findnext(t, s, i)
        isnothing(r) && break
        push!(found, r)
        j = overlap || isempty(r) ? first(r) : last(r)
        j > e && break
        @inbounds i = nextind(s, j)
    end
    return found
end

# AbstractString implementation of the generic findprev interface
function findprev(testf::Function, s::AbstractString, i::Integer)
    i = Int(i)
    z = ncodeunits(s) + 1
    0 ≤ i ≤ z || throw(BoundsError(s, i))
    i == z && return nothing
    @inbounds i == 0 || isvalid(s, i) || string_index_err(s, i)
    while i >= 1
        testf(@inbounds s[i]) && return i
        i = @inbounds prevind(s, i)
    end
    return nothing
end

function _rsearchindex(s::AbstractString,
                       t::Union{AbstractString,AbstractChar,Int8,UInt8},
                       i::Integer)
    if isempty(t)
        return 1 <= i <= nextind(s, lastindex(s))::Int ? i :
               throw(BoundsError(s, i))
    end
    t1, trest = Iterators.peel(Iterators.reverse(t))::NTuple{2,Any}
    while true
        i = findprev(isequal(t1), s, i)
        i === nothing && return 0
        ii = prevind(s, i)::Int
        a = Iterators.Stateful(trest)
        b = Iterators.Stateful(Iterators.reverse(
            pairs(SubString(s, 1, ii))))
        matched = all(splat(==), zip(a, (x[2] for x in b)))
        if matched && isempty(a)
            isempty(b) && return firstindex(s)
            return nextind(s, popfirst!(b)[1])::Int
        end
        i = ii
    end
end

function _rsearchindex(s::String, t::String, i::Integer)
    # Check for fast case of a single byte
    if lastindex(t) == 1
        return something(findprev(isequal(t[1]), s, i), 0)
    elseif lastindex(t) != 0
        j = i ≤ ncodeunits(s) ? nextind(s, i)-1 : i
        return _rsearchindex(codeunits(s), codeunits(t), j)
    elseif i > sizeof(s)
        return 0
    elseif i == 0
        return 1
    else
        return i
    end
end

function _rsearchindex(s::AbstractVector{<:Union{Int8,UInt8}}, t::AbstractVector{<:Union{Int8,UInt8}}, _k::Integer)
    sentinel = firstindex(s) - 1
    n = length(t)
    m = length(s)
    k = Int(_k) - sentinel
    k < 0 && throw(BoundsError(s, _k))

    if n == 0
        return 0 <= k <= m ? max(k, 1) : sentinel
    elseif m == 0
        return sentinel
    elseif n == 1
        return something(findprev(isequal(_nthbyte(t,1)), s, k), sentinel)
    end

    w = m - n
    if w < 0 || k <= 0
        return sentinel
    end

    bloom_mask = UInt64(0)
    skip = n - 1
    tfirst = _nthbyte(t,1)
    for j in n:-1:1
        bloom_mask |= _search_bloom_mask(_nthbyte(t,j))
        if _nthbyte(t,j) == tfirst && j > 1
            skip = j - 2
        end
    end

    i = min(k - n + 1, w + 1)
    while i > 0
        if _nthbyte(s,i) == tfirst
            # check candidate
            j = 1
            while j < n
                if _nthbyte(s,i+j) != _nthbyte(t,j+1)
                    break
                end
                j += 1
            end

            # match found, restore in case `s` is an OffsetArray
            if j == n
                return i + sentinel
            end

            # no match, try to rule out the next character
            if i > 1 && bloom_mask & _search_bloom_mask(_nthbyte(s,i-1)) == 0
                i -= n
            else
                i -= skip
            end
        elseif i > 1
            if bloom_mask & _search_bloom_mask(_nthbyte(s,i-1)) == 0
                i -= n
            end
        end
        i -= 1
    end

    sentinel
end

function _rsearch(s::Union{AbstractString,AbstractVector{<:Union{Int8,UInt8}}},
                  t::Union{AbstractString,AbstractChar,AbstractVector{<:Union{Int8,UInt8}}},
                  i::Integer)
    idx = _rsearchindex(s,t,i)
    if isempty(t)
        idx:idx-1
    elseif idx > firstindex(s) - 1
        idx:(idx + lastindex(t) - 1)
    else
        nothing
    end
end

"""
    findprev(pattern::AbstractString, string::AbstractString, start::Integer)

Find the previous occurrence of `pattern` in `string` starting at position `start`.

The return value is a range of indices where the matching sequence is found, such that
`s[findprev(x, s, i)] == x`:

`findprev("substring", string, i)` == `start:stop` such that
`string[start:stop] == "substring"` and `stop <= i`, or `nothing` if unmatched.

# Examples
```jldoctest
julia> findprev("z", "Hello to the world", 18) === nothing
true

julia> findprev("o", "Hello to the world", 18)
15:15

julia> findprev("Julia", "JuliaLang", 6)
1:5
```
"""
findprev(t::AbstractString, s::AbstractString, i::Integer) = _rsearch(s, t, Int(i))

"""
    findprev(ch::AbstractChar, string::AbstractString, start::Integer)

Find the previous occurrence of character `ch` in `string` starting at position `start`.

!!! compat "Julia 1.3"
    This method requires at least Julia 1.3.

# Examples
```jldoctest
julia> findprev('z', "Hello to the world", 18) === nothing
true

julia> findprev('o', "Hello to the world", 18)
15
```
"""
findprev(ch::AbstractChar, string::AbstractString, start::Integer) =
    findprev(==(ch), string, start)

"""
    findprev(pattern::AbstractVector{<:Union{Int8,UInt8}},
             A::AbstractVector{<:Union{Int8,UInt8}},
             start::Integer)

Find the previous occurrence of the sequence `pattern` in vector `A` starting at position `start`.

!!! compat "Julia 1.6"
    This method requires at least Julia 1.6.

# Examples
```jldoctest
julia> findprev([0x52, 0x62], [0x40, 0x52, 0x62, 0x52, 0x62], 3)
2:3
```
"""
findprev(pattern::AbstractVector{<:Union{Int8,UInt8}},
         A::AbstractVector{<:Union{Int8,UInt8}},
         start::Integer) =
    _rsearch(A, pattern, start)
"""
    occursin(needle::Union{AbstractString,AbstractPattern,AbstractChar}, haystack::AbstractString)

Determine whether the first argument is a substring of the second. If `needle`
is a regular expression, checks whether `haystack` contains a match.

# Examples
```jldoctest
julia> occursin("Julia", "JuliaLang is pretty cool!")
true

julia> occursin('a', "JuliaLang is pretty cool!")
true

julia> occursin(r"a.a", "aba")
true

julia> occursin(r"a.a", "abba")
false
```

See also [`contains`](@ref).
"""
occursin(needle::Union{AbstractString,AbstractChar}, haystack::AbstractString) =
    _searchindex(haystack, needle, firstindex(haystack)) != 0

"""
    occursin(haystack)

Create a function that checks whether its argument occurs in `haystack`, i.e.
a function equivalent to `needle -> occursin(needle, haystack)`.

The returned function is of type `Base.Fix2{typeof(occursin)}`.

!!! compat "Julia 1.6"
    This method requires Julia 1.6 or later.

# Examples
```jldoctest
julia> search_f = occursin("JuliaLang is a programming language");

julia> search_f("JuliaLang")
true

julia> search_f("Python")
false
```
"""
occursin(haystack) = Base.Fix2(occursin, haystack)

in(::AbstractString, ::AbstractString) = error("use occursin(needle, haystack) for string containment")
V   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/strings/unicode.jl�R      # This file is a part of Julia. License is MIT: https://julialang.org/license

# Various Unicode functionality from the utf8proc library
module Unicode

import Base: show, ==, hash, string, Symbol, isless, length, eltype,
             convert, isvalid, ismalformed, isoverlong, iterate

# whether codepoints are valid Unicode scalar values, i.e. 0-0xd7ff, 0xe000-0x10ffff

"""
    isvalid(value) -> Bool

Return `true` if the given value is valid for its type, which currently can be either
`AbstractChar` or `String` or `SubString{String}`.

# Examples
```jldoctest
julia> isvalid(Char(0xd800))
false

julia> isvalid(SubString(String(UInt8[0xfe,0x80,0x80,0x80,0x80,0x80]),1,2))
false

julia> isvalid(Char(0xd799))
true
```
"""
isvalid(value)

"""
    isvalid(T, value) -> Bool

Return `true` if the given value is valid for that type. Types currently can
be either `AbstractChar` or `String`. Values for `AbstractChar` can be of type `AbstractChar` or [`UInt32`](@ref).
Values for `String` can be of that type, `SubString{String}`, `Vector{UInt8}`,
or a contiguous subarray thereof.

# Examples
```jldoctest
julia> isvalid(Char, 0xd800)
false

julia> isvalid(String, SubString("thisisvalid",1,5))
true

julia> isvalid(Char, 0xd799)
true
```

!!! compat "Julia 1.6"
    Support for subarray values was added in Julia 1.6.
"""
isvalid(T,value)

isvalid(c::AbstractChar) = !ismalformed(c) & !isoverlong(c) & ((c ≤ '\ud7ff') | ('\ue000' ≤ c) & (c ≤ '\U10ffff'))
isvalid(::Type{<:AbstractChar}, c::Unsigned) = ((c ≤  0xd7ff ) | ( 0xe000  ≤ c) & (c ≤  0x10ffff ))
isvalid(::Type{T}, c::Integer) where {T<:AbstractChar}  = isvalid(T, Unsigned(c))
isvalid(::Type{<:AbstractChar}, c::AbstractChar)     = isvalid(c)

# utf8 category constants
const UTF8PROC_CATEGORY_CN = 0
const UTF8PROC_CATEGORY_LU = 1
const UTF8PROC_CATEGORY_LL = 2
const UTF8PROC_CATEGORY_LT = 3
const UTF8PROC_CATEGORY_LM = 4
const UTF8PROC_CATEGORY_LO = 5
const UTF8PROC_CATEGORY_MN = 6
const UTF8PROC_CATEGORY_MC = 7
const UTF8PROC_CATEGORY_ME = 8
const UTF8PROC_CATEGORY_ND = 9
const UTF8PROC_CATEGORY_NL = 10
const UTF8PROC_CATEGORY_NO = 11
const UTF8PROC_CATEGORY_PC = 12
const UTF8PROC_CATEGORY_PD = 13
const UTF8PROC_CATEGORY_PS = 14
const UTF8PROC_CATEGORY_PE = 15
const UTF8PROC_CATEGORY_PI = 16
const UTF8PROC_CATEGORY_PF = 17
const UTF8PROC_CATEGORY_PO = 18
const UTF8PROC_CATEGORY_SM = 19
const UTF8PROC_CATEGORY_SC = 20
const UTF8PROC_CATEGORY_SK = 21
const UTF8PROC_CATEGORY_SO = 22
const UTF8PROC_CATEGORY_ZS = 23
const UTF8PROC_CATEGORY_ZL = 24
const UTF8PROC_CATEGORY_ZP = 25
const UTF8PROC_CATEGORY_CC = 26
const UTF8PROC_CATEGORY_CF = 27
const UTF8PROC_CATEGORY_CS = 28
const UTF8PROC_CATEGORY_CO = 29

# strings corresponding to the category constants
const category_strings = [
    "Other, not assigned",
    "Letter, uppercase",
    "Letter, lowercase",
    "Letter, titlecase",
    "Letter, modifier",
    "Letter, other",
    "Mark, nonspacing",
    "Mark, spacing combining",
    "Mark, enclosing",
    "Number, decimal digit",
    "Number, letter",
    "Number, other",
    "Punctuation, connector",
    "Punctuation, dash",
    "Punctuation, open",
    "Punctuation, close",
    "Punctuation, initial quote",
    "Punctuation, final quote",
    "Punctuation, other",
    "Symbol, math",
    "Symbol, currency",
    "Symbol, modifier",
    "Symbol, other",
    "Separator, space",
    "Separator, line",
    "Separator, paragraph",
    "Other, control",
    "Other, format",
    "Other, surrogate",
    "Other, private use",
    "Invalid, too high",
    "Malformed, bad data",
]

const UTF8PROC_STABLE    = (1<<1)
const UTF8PROC_COMPAT    = (1<<2)
const UTF8PROC_COMPOSE   = (1<<3)
const UTF8PROC_DECOMPOSE = (1<<4)
const UTF8PROC_IGNORE    = (1<<5)
const UTF8PROC_REJECTNA  = (1<<6)
const UTF8PROC_NLF2LS    = (1<<7)
const UTF8PROC_NLF2PS    = (1<<8)
const UTF8PROC_NLF2LF    = (UTF8PROC_NLF2LS | UTF8PROC_NLF2PS)
const UTF8PROC_STRIPCC   = (1<<9)
const UTF8PROC_CASEFOLD  = (1<<10)
const UTF8PROC_CHARBOUND = (1<<11)
const UTF8PROC_LUMP      = (1<<12)
const UTF8PROC_STRIPMARK = (1<<13)

############################################################################

utf8proc_error(result) = error(unsafe_string(ccall(:utf8proc_errmsg, Cstring, (Cssize_t,), result)))

# static wrapper around user callback function
utf8proc_custom_func(codepoint::UInt32, callback::Any) =
    UInt32(callback(codepoint))::UInt32

function utf8proc_decompose(str, options, buffer, nwords, chartransform::typeof(identity))
    ret = ccall(:utf8proc_decompose, Int, (Ptr{UInt8}, Int, Ptr{UInt8}, Int, Cint),
                str, sizeof(str), buffer, nwords, options)
    ret < 0 && utf8proc_error(ret)
    return ret
end
function utf8proc_decompose(str, options, buffer, nwords, chartransform::T) where T
    ret = ccall(:utf8proc_decompose_custom, Int, (Ptr{UInt8}, Int, Ptr{UInt8}, Int, Cint, Ptr{Cvoid}, Ref{T}),
                str, sizeof(str), buffer, nwords, options,
                @cfunction(utf8proc_custom_func, UInt32, (UInt32, Ref{T})), chartransform)
    ret < 0 && utf8proc_error(ret)
    return ret
end

function utf8proc_map(str::Union{String,SubString{String}}, options::Integer, chartransform=identity)
    nwords = utf8proc_decompose(str, options, C_NULL, 0, chartransform)
    buffer = Base.StringVector(nwords*4)
    nwords = utf8proc_decompose(str, options, buffer, nwords, chartransform)
    nbytes = ccall(:utf8proc_reencode, Int, (Ptr{UInt8}, Int, Cint), buffer, nwords, options)
    nbytes < 0 && utf8proc_error(nbytes)
    return String(resize!(buffer, nbytes))
end

# from julia_charmap.h, used by julia_chartransform in the Unicode stdlib
const _julia_charmap = Dict{UInt32,UInt32}(
    0x025B => 0x03B5,
    0x00B5 => 0x03BC,
    0x00B7 => 0x22C5,
    0x0387 => 0x22C5,
    0x2212 => 0x002D,
    0x210F => 0x0127,
)

utf8proc_map(s::AbstractString, flags::Integer, chartransform=identity) = utf8proc_map(String(s), flags, chartransform)

# Documented in Unicode module
function normalize(
    s::AbstractString;
    stable::Bool=false,
    compat::Bool=false,
    compose::Bool=true,
    decompose::Bool=false,
    stripignore::Bool=false,
    rejectna::Bool=false,
    newline2ls::Bool=false,
    newline2ps::Bool=false,
    newline2lf::Bool=false,
    stripcc::Bool=false,
    casefold::Bool=false,
    lump::Bool=false,
    stripmark::Bool=false,
    chartransform=identity,
)
    flags = 0
    stable && (flags = flags | UTF8PROC_STABLE)
    compat && (flags = flags | UTF8PROC_COMPAT)
    # TODO: error if compose & decompose?
    if decompose
        flags = flags | UTF8PROC_DECOMPOSE
    elseif compose
        flags = flags | UTF8PROC_COMPOSE
    elseif compat || stripmark
        throw(ArgumentError("compat=true or stripmark=true require compose=true or decompose=true"))
    end
    stripignore && (flags = flags | UTF8PROC_IGNORE)
    rejectna && (flags = flags | UTF8PROC_REJECTNA)
    newline2ls + newline2ps + newline2lf > 1 && throw(ArgumentError("only one newline conversion may be specified"))
    newline2ls && (flags = flags | UTF8PROC_NLF2LS)
    newline2ps && (flags = flags | UTF8PROC_NLF2PS)
    newline2lf && (flags = flags | UTF8PROC_NLF2LF)
    stripcc && (flags = flags | UTF8PROC_STRIPCC)
    casefold && (flags = flags | UTF8PROC_CASEFOLD)
    lump && (flags = flags | UTF8PROC_LUMP)
    stripmark && (flags = flags | UTF8PROC_STRIPMARK)
    utf8proc_map(s, flags, chartransform)
end

function normalize(s::AbstractString, nf::Symbol)
    utf8proc_map(s, nf === :NFC ? (UTF8PROC_STABLE | UTF8PROC_COMPOSE) :
                    nf === :NFD ? (UTF8PROC_STABLE | UTF8PROC_DECOMPOSE) :
                    nf === :NFKC ? (UTF8PROC_STABLE | UTF8PROC_COMPOSE
                                   | UTF8PROC_COMPAT) :
                    nf === :NFKD ? (UTF8PROC_STABLE | UTF8PROC_DECOMPOSE
                                   | UTF8PROC_COMPAT) :
                    throw(ArgumentError(":$nf is not one of :NFC, :NFD, :NFKC, :NFKD")))
end

############################################################################

## character column width function ##
"""
    textwidth(c)

Give the number of columns needed to print a character.

# Examples
```jldoctest
julia> textwidth('α')
1

julia> textwidth('⛵')
2
```
"""
function textwidth(c::AbstractChar)
    ismalformed(c) && return 1
    Int(ccall(:utf8proc_charwidth, Cint, (UInt32,), c))
end

"""
    textwidth(s::AbstractString)

Give the number of columns needed to print a string.

# Examples
```jldoctest
julia> textwidth("March")
5
```
"""
textwidth(s::AbstractString) = mapreduce(textwidth, +, s; init=0)

"""
    lowercase(c::AbstractChar)

Convert `c` to lowercase.

See also [`uppercase`](@ref), [`titlecase`](@ref).

# Examples
```jldoctest
julia> lowercase('A')
'a': ASCII/Unicode U+0061 (category Ll: Letter, lowercase)

julia> lowercase('Ö')
'ö': Unicode U+00F6 (category Ll: Letter, lowercase)
```
"""
lowercase(c::T) where {T<:AbstractChar} = isascii(c) ? ('A' <= c <= 'Z' ? c + 0x20 : c) :
    T(ccall(:utf8proc_tolower, UInt32, (UInt32,), c))

"""
    uppercase(c::AbstractChar)

Convert `c` to uppercase.

See also [`lowercase`](@ref), [`titlecase`](@ref).

# Examples
```jldoctest
julia> uppercase('a')
'A': ASCII/Unicode U+0041 (category Lu: Letter, uppercase)

julia> uppercase('ê')
'Ê': Unicode U+00CA (category Lu: Letter, uppercase)
```
"""
uppercase(c::T) where {T<:AbstractChar} = isascii(c) ? ('a' <= c <= 'z' ? c - 0x20 : c) :
    T(ccall(:utf8proc_toupper, UInt32, (UInt32,), c))

"""
    titlecase(c::AbstractChar)

Convert `c` to titlecase. This may differ from uppercase for digraphs,
compare the example below.

See also [`uppercase`](@ref), [`lowercase`](@ref).

# Examples
```jldoctest
julia> titlecase('a')
'A': ASCII/Unicode U+0041 (category Lu: Letter, uppercase)

julia> titlecase('ǆ')
'ǅ': Unicode U+01C5 (category Lt: Letter, titlecase)

julia> uppercase('ǆ')
'Ǆ': Unicode U+01C4 (category Lu: Letter, uppercase)
```
"""
titlecase(c::T) where {T<:AbstractChar} = isascii(c) ? ('a' <= c <= 'z' ? c - 0x20 : c) :
    T(ccall(:utf8proc_totitle, UInt32, (UInt32,), c))

############################################################################

# returns UTF8PROC_CATEGORY code in 0:30 giving Unicode category
function category_code(c::AbstractChar)
    !ismalformed(c) ? category_code(UInt32(c)) : Cint(31)
end

function category_code(x::Integer)
    x ≤ 0x10ffff ? ccall(:utf8proc_category, Cint, (UInt32,), x) : Cint(30)
end

# more human-readable representations of the category code
function category_abbrev(c::AbstractChar)
    ismalformed(c) && return "Ma"
    c ≤ '\U10ffff' || return "In"
    unsafe_string(ccall(:utf8proc_category_string, Cstring, (UInt32,), c))
end

category_string(c) = category_strings[category_code(c)+1]

isassigned(c) = UTF8PROC_CATEGORY_CN < category_code(c) <= UTF8PROC_CATEGORY_CO

## libc character class predicates ##

"""
    islowercase(c::AbstractChar) -> Bool

Tests whether a character is a lowercase letter (according to the Unicode
standard's `Lowercase` derived property).

See also [`isuppercase`](@ref).

# Examples
```jldoctest
julia> islowercase('α')
true

julia> islowercase('Γ')
false

julia> islowercase('❤')
false
```
"""
islowercase(c::AbstractChar) = ismalformed(c) ? false : Bool(ccall(:utf8proc_islower, Cint, (UInt32,), UInt32(c)))

# true for Unicode upper and mixed case

"""
    isuppercase(c::AbstractChar) -> Bool

Tests whether a character is an uppercase letter (according to the Unicode
standard's `Uppercase` derived property).

See also [`islowercase`](@ref).

# Examples
```jldoctest
julia> isuppercase('γ')
false

julia> isuppercase('Γ')
true

julia> isuppercase('❤')
false
```
"""
isuppercase(c::AbstractChar) = ismalformed(c) ? false : Bool(ccall(:utf8proc_isupper, Cint, (UInt32,), UInt32(c)))

"""
    iscased(c::AbstractChar) -> Bool

Tests whether a character is cased, i.e. is lower-, upper- or title-cased.

See also [`islowercase`](@ref), [`isuppercase`](@ref).
"""
function iscased(c::AbstractChar)
    cat = category_code(c)
    return cat == UTF8PROC_CATEGORY_LU ||
           cat == UTF8PROC_CATEGORY_LT ||
           cat == UTF8PROC_CATEGORY_LL
end


"""
    isdigit(c::AbstractChar) -> Bool

Tests whether a character is a decimal digit (0-9).

See also: [`isletter`](@ref).

# Examples
```jldoctest
julia> isdigit('❤')
false

julia> isdigit('9')
true

julia> isdigit('α')
false
```
"""
isdigit(c::AbstractChar) = (c >= '0') & (c <= '9')

"""
    isletter(c::AbstractChar) -> Bool

Test whether a character is a letter.
A character is classified as a letter if it belongs to the Unicode general
category Letter, i.e. a character whose category code begins with 'L'.

See also: [`isdigit`](@ref).

# Examples
```jldoctest
julia> isletter('❤')
false

julia> isletter('α')
true

julia> isletter('9')
false
```
"""
isletter(c::AbstractChar) = UTF8PROC_CATEGORY_LU <= category_code(c) <= UTF8PROC_CATEGORY_LO

"""
    isnumeric(c::AbstractChar) -> Bool

Tests whether a character is numeric.
A character is classified as numeric if it belongs to the Unicode general category Number,
i.e. a character whose category code begins with 'N'.

Note that this broad category includes characters such as ¾ and ௰.
Use [`isdigit`](@ref) to check whether a character is a decimal digit between 0 and 9.

# Examples
```jldoctest
julia> isnumeric('௰')
true

julia> isnumeric('9')
true

julia> isnumeric('α')
false

julia> isnumeric('❤')
false
```
"""
isnumeric(c::AbstractChar) = UTF8PROC_CATEGORY_ND <= category_code(c) <= UTF8PROC_CATEGORY_NO

# following C++ only control characters from the Latin-1 subset return true

"""
    iscntrl(c::AbstractChar) -> Bool

Tests whether a character is a control character.
Control characters are the non-printing characters of the Latin-1 subset of Unicode.

# Examples
```jldoctest
julia> iscntrl('\\x01')
true

julia> iscntrl('a')
false
```
"""
iscntrl(c::AbstractChar) = c <= '\x1f' || '\x7f' <= c <= '\u9f'

"""
    ispunct(c::AbstractChar) -> Bool

Tests whether a character belongs to the Unicode general category Punctuation, i.e. a
character whose category code begins with 'P'.

# Examples
```jldoctest
julia> ispunct('α')
false

julia> ispunct('/')
true

julia> ispunct(';')
true
```
"""
ispunct(c::AbstractChar) = UTF8PROC_CATEGORY_PC <= category_code(c) <= UTF8PROC_CATEGORY_PO

# \u85 is the Unicode Next Line (NEL) character

"""
    isspace(c::AbstractChar) -> Bool

Tests whether a character is any whitespace character. Includes ASCII characters '\\t',
'\\n', '\\v', '\\f', '\\r', and ' ', Latin-1 character U+0085, and characters in Unicode
category Zs.

# Examples
```jldoctest
julia> isspace('\\n')
true

julia> isspace('\\r')
true

julia> isspace(' ')
true

julia> isspace('\\x20')
true
```
"""
@inline isspace(c::AbstractChar) =
    c == ' ' || '\t' <= c <= '\r' || c == '\u85' ||
    '\ua0' <= c && category_code(c) == UTF8PROC_CATEGORY_ZS

"""
    isprint(c::AbstractChar) -> Bool

Tests whether a character is printable, including spaces, but not a control character.

# Examples
```jldoctest
julia> isprint('\\x01')
false

julia> isprint('A')
true
```
"""
isprint(c::AbstractChar) = UTF8PROC_CATEGORY_LU <= category_code(c) <= UTF8PROC_CATEGORY_ZS

# true in principal if a printer would use ink

"""
    isxdigit(c::AbstractChar) -> Bool

Test whether a character is a valid hexadecimal digit. Note that this does not
include `x` (as in the standard `0x` prefix).

# Examples
```jldoctest
julia> isxdigit('a')
true

julia> isxdigit('x')
false
```
"""
isxdigit(c::AbstractChar) = '0'<=c<='9' || 'a'<=c<='f' || 'A'<=c<='F'

## uppercase, lowercase, and titlecase transformations ##

"""
    uppercase(s::AbstractString)

Return `s` with all characters converted to uppercase.

See also [`lowercase`](@ref), [`titlecase`](@ref), [`uppercasefirst`](@ref).

# Examples
```jldoctest
julia> uppercase("Julia")
"JULIA"
```
"""
uppercase(s::AbstractString) = map(uppercase, s)

"""
    lowercase(s::AbstractString)

Return `s` with all characters converted to lowercase.

See also [`uppercase`](@ref), [`titlecase`](@ref), [`lowercasefirst`](@ref).

# Examples
```jldoctest
julia> lowercase("STRINGS AND THINGS")
"strings and things"
```
"""
lowercase(s::AbstractString) = map(lowercase, s)

"""
    titlecase(s::AbstractString; [wordsep::Function], strict::Bool=true) -> String

Capitalize the first character of each word in `s`;
if `strict` is true, every other character is
converted to lowercase, otherwise they are left unchanged.
By default, all non-letters beginning a new grapheme are considered as word separators;
a predicate can be passed as the `wordsep` keyword to determine
which characters should be considered as word separators.
See also [`uppercasefirst`](@ref) to capitalize only the first
character in `s`.

See also [`uppercase`](@ref), [`lowercase`](@ref), [`uppercasefirst`](@ref).

# Examples
```jldoctest
julia> titlecase("the JULIA programming language")
"The Julia Programming Language"

julia> titlecase("ISS - international space station", strict=false)
"ISS - International Space Station"

julia> titlecase("a-a b-b", wordsep = c->c==' ')
"A-a B-b"
```
"""
function titlecase(s::AbstractString; wordsep::Function = !isletter, strict::Bool=true)
    startword = true
    state = Ref{Int32}(0)
    c0 = eltype(s)(0x00000000)
    b = IOBuffer()
    for c in s
        # Note: It would be better to have a word iterator following UAX#29,
        # similar to our grapheme iterator, but utf8proc does not yet have
        # this information.  At the very least we shouldn't break inside graphemes.
        if isgraphemebreak!(state, c0, c) && wordsep(c)
            print(b, c)
            startword = true
        else
            print(b, startword ? titlecase(c) : strict ? lowercase(c) : c)
            startword = false
        end
        c0 = c
    end
    return String(take!(b))
end

"""
    uppercasefirst(s::AbstractString) -> String

Return `s` with the first character converted to uppercase (technically "title
case" for Unicode). See also [`titlecase`](@ref) to capitalize the first
character of every word in `s`.

See also [`lowercasefirst`](@ref), [`uppercase`](@ref), [`lowercase`](@ref),
[`titlecase`](@ref).

# Examples
```jldoctest
julia> uppercasefirst("python")
"Python"
```
"""
function uppercasefirst(s::AbstractString)
    isempty(s) && return ""
    c = s[1]
    c′ = titlecase(c)
    c == c′ ? convert(String, s) :
    string(c′, SubString(s, nextind(s, 1)))
end

"""
    lowercasefirst(s::AbstractString)

Return `s` with the first character converted to lowercase.

See also [`uppercasefirst`](@ref), [`uppercase`](@ref), [`lowercase`](@ref),
[`titlecase`](@ref).

# Examples
```jldoctest
julia> lowercasefirst("Julia")
"julia"
```
"""
function lowercasefirst(s::AbstractString)
    isempty(s) && return ""
    c = s[1]
    c′ = lowercase(c)
    c == c′ ? convert(String, s) :
    string(c′, SubString(s, nextind(s, 1)))
end

############################################################################
# iterators for grapheme segmentation

isgraphemebreak(c1::AbstractChar, c2::AbstractChar) =
    ismalformed(c1) || ismalformed(c2) ||
    ccall(:utf8proc_grapheme_break, Bool, (UInt32, UInt32), c1, c2)

# Stateful grapheme break required by Unicode-9 rules: the string
# must be processed in sequence, with state initialized to Ref{Int32}(0).
# Requires utf8proc v2.0 or later.
function isgraphemebreak!(state::Ref{Int32}, c1::AbstractChar, c2::AbstractChar)
    if ismalformed(c1) || ismalformed(c2)
        state[] = 0
        return true
    end
    ccall(:utf8proc_grapheme_break_stateful, Bool,
          (UInt32, UInt32, Ref{Int32}), c1, c2, state)
end

struct GraphemeIterator{S<:AbstractString}
    s::S # original string (for generation of SubStrings)
end

# Documented in Unicode module
graphemes(s::AbstractString) = GraphemeIterator{typeof(s)}(s)

eltype(::Type{GraphemeIterator{S}}) where {S} = SubString{S}
eltype(::Type{GraphemeIterator{SubString{S}}}) where {S} = SubString{S}

function length(g::GraphemeIterator{S}) where {S}
    c0 = eltype(S)(0x00000000)
    n = 0
    state = Ref{Int32}(0)
    for c in g.s
        n += isgraphemebreak!(state, c0, c)
        c0 = c
    end
    return n
end

function iterate(g::GraphemeIterator, i_=(Int32(0),firstindex(g.s)))
    s = g.s
    statei, i = i_
    state = Ref{Int32}(statei)
    j = i
    y = iterate(s, i)
    y === nothing && return nothing
    c0, k = y
    while k <= ncodeunits(s) # loop until next grapheme is s[i:j]
        c, ℓ = iterate(s, k)::NTuple{2,Any}
        isgraphemebreak!(state, c0, c) && break
        j = k
        k = ℓ
        c0 = c
    end
    return (SubString(s, i, j), (state[], k))
end

==(g1::GraphemeIterator, g2::GraphemeIterator) = g1.s == g2.s
hash(g::GraphemeIterator, h::UInt) = hash(g.s, h)
isless(g1::GraphemeIterator, g2::GraphemeIterator) = isless(g1.s, g2.s)

show(io::IO, g::GraphemeIterator{S}) where {S} = print(io, "length-$(length(g)) GraphemeIterator{$S} for \"$(g.s)\"")

############################################################################

end # module
S   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/strings/util.jl��      # This file is a part of Julia. License is MIT: https://julialang.org/license

const Chars = Union{AbstractChar,Tuple{Vararg{AbstractChar}},AbstractVector{<:AbstractChar},Set{<:AbstractChar}}

# starts with and ends with predicates

"""
    startswith(s::AbstractString, prefix::AbstractString)

Return `true` if `s` starts with `prefix`. If `prefix` is a vector or set
of characters, test whether the first character of `s` belongs to that set.

See also [`endswith`](@ref), [`contains`](@ref).

# Examples
```jldoctest
julia> startswith("JuliaLang", "Julia")
true
```
"""
function startswith(a::AbstractString, b::AbstractString)
    i, j = iterate(a), iterate(b)
    while true
        j === nothing && return true # ran out of prefix: success!
        i === nothing && return false # ran out of source: failure
        i[1] == j[1] || return false # mismatch: failure
        i, j = iterate(a, i[2]), iterate(b, j[2])
    end
end
startswith(str::AbstractString, chars::Chars) = !isempty(str) && first(str)::AbstractChar in chars

"""
    endswith(s::AbstractString, suffix::AbstractString)

Return `true` if `s` ends with `suffix`. If `suffix` is a vector or set of
characters, test whether the last character of `s` belongs to that set.

See also [`startswith`](@ref), [`contains`](@ref).

# Examples
```jldoctest
julia> endswith("Sunday", "day")
true
```
"""
function endswith(a::AbstractString, b::AbstractString)
    a, b = Iterators.Reverse(a), Iterators.Reverse(b)
    i, j = iterate(a), iterate(b)
    while true
        j === nothing && return true # ran out of suffix: success!
        i === nothing && return false # ran out of source: failure
        i[1] == j[1] || return false # mismatch: failure
        i, j = iterate(a, i[2]), iterate(b, j[2])
    end
end
endswith(str::AbstractString, chars::Chars) = !isempty(str) && last(str) in chars

function startswith(a::Union{String, SubString{String}},
                    b::Union{String, SubString{String}})
    cub = ncodeunits(b)
    if ncodeunits(a) < cub
        false
    elseif _memcmp(a, b, sizeof(b)) == 0
        nextind(a, cub) == cub + 1 # check that end of `b` doesn't match a partial character in `a`
    else
        false
    end
end

"""
    startswith(io::IO, prefix::Union{AbstractString,Base.Chars})

Check if an `IO` object starts with a prefix.  See also [`peek`](@ref).
"""
function Base.startswith(io::IO, prefix::Base.Chars)
    mark(io)
    c = read(io, Char)
    reset(io)
    return c in prefix
end
function Base.startswith(io::IO, prefix::Union{String,SubString{String}})
    mark(io)
    s = read(io, ncodeunits(prefix))
    reset(io)
    return s == codeunits(prefix)
end
Base.startswith(io::IO, prefix::AbstractString) = startswith(io, String(prefix))

function endswith(a::Union{String, SubString{String}},
                  b::Union{String, SubString{String}})
    cub = ncodeunits(b)
    astart = ncodeunits(a) - ncodeunits(b) + 1
    if astart < 1
        false
    elseif GC.@preserve(a, _memcmp(pointer(a, astart), b, sizeof(b))) == 0
        thisind(a, astart) == astart # check that end of `b` doesn't match a partial character in `a`
    else
        false
    end
end

"""
    contains(haystack::AbstractString, needle)

Return `true` if `haystack` contains `needle`.
This is the same as `occursin(needle, haystack)`, but is provided for consistency with
`startswith(haystack, needle)` and `endswith(haystack, needle)`.

See also [`occursin`](@ref), [`in`](@ref), [`issubset`](@ref).

# Examples
```jldoctest
julia> contains("JuliaLang is pretty cool!", "Julia")
true

julia> contains("JuliaLang is pretty cool!", 'a')
true

julia> contains("aba", r"a.a")
true

julia> contains("abba", r"a.a")
false
```

!!! compat "Julia 1.5"
    The `contains` function requires at least Julia 1.5.
"""
contains(haystack::AbstractString, needle) = occursin(needle, haystack)

"""
    endswith(suffix)

Create a function that checks whether its argument ends with `suffix`, i.e.
a function equivalent to `y -> endswith(y, suffix)`.

The returned function is of type `Base.Fix2{typeof(endswith)}`, which can be
used to implement specialized methods.

!!! compat "Julia 1.5"
    The single argument `endswith(suffix)` requires at least Julia 1.5.

# Examples
```jldoctest
julia> endswith("Julia")("Ends with Julia")
true

julia> endswith("Julia")("JuliaLang")
false
```
"""
endswith(s) = Base.Fix2(endswith, s)

"""
    startswith(prefix)

Create a function that checks whether its argument starts with `prefix`, i.e.
a function equivalent to `y -> startswith(y, prefix)`.

The returned function is of type `Base.Fix2{typeof(startswith)}`, which can be
used to implement specialized methods.

!!! compat "Julia 1.5"
    The single argument `startswith(prefix)` requires at least Julia 1.5.

# Examples
```jldoctest
julia> startswith("Julia")("JuliaLang")
true

julia> startswith("Julia")("Ends with Julia")
false
```
"""
startswith(s) = Base.Fix2(startswith, s)

"""
    contains(needle)

Create a function that checks whether its argument contains `needle`, i.e.
a function equivalent to `haystack -> contains(haystack, needle)`.

The returned function is of type `Base.Fix2{typeof(contains)}`, which can be
used to implement specialized methods.
"""
contains(needle) = Base.Fix2(contains, needle)

"""
    chop(s::AbstractString; head::Integer = 0, tail::Integer = 1)

Remove the first `head` and the last `tail` characters from `s`.
The call `chop(s)` removes the last character from `s`.
If it is requested to remove more characters than `length(s)`
then an empty string is returned.

See also [`chomp`](@ref), [`startswith`](@ref), [`first`](@ref).

# Examples
```jldoctest
julia> a = "March"
"March"

julia> chop(a)
"Marc"

julia> chop(a, head = 1, tail = 2)
"ar"

julia> chop(a, head = 5, tail = 5)
""
```
"""
function chop(s::AbstractString; head::Integer = 0, tail::Integer = 1)
    if isempty(s)
        return SubString(s)
    end
    SubString(s, nextind(s, firstindex(s), head), prevind(s, lastindex(s), tail))
end

# TODO: optimization for the default case based on
# chop(s::AbstractString) = SubString(s, firstindex(s), prevind(s, lastindex(s)))

"""
    chopprefix(s::AbstractString, prefix::Union{AbstractString,Regex}) -> SubString

Remove the prefix `prefix` from `s`. If `s` does not start with `prefix`, a string equal to `s` is returned.

See also [`chopsuffix`](@ref).

!!! compat "Julia 1.8"
    This function is available as of Julia 1.8.

# Examples
```jldoctest
julia> chopprefix("Hamburger", "Ham")
"burger"

julia> chopprefix("Hamburger", "hotdog")
"Hamburger"
```
"""
function chopprefix(s::AbstractString, prefix::AbstractString)
    k = firstindex(s)
    i, j = iterate(s), iterate(prefix)
    while true
        j === nothing && i === nothing && return SubString(s, 1, 0) # s == prefix: empty result
        j === nothing && return @inbounds SubString(s, k) # ran out of prefix: success!
        i === nothing && return SubString(s) # ran out of source: failure
        i[1] == j[1] || return SubString(s) # mismatch: failure
        k = i[2]
        i, j = iterate(s, k), iterate(prefix, j[2])
    end
end

function chopprefix(s::Union{String, SubString{String}},
                    prefix::Union{String, SubString{String}})
    if startswith(s, prefix)
        SubString(s, 1 + ncodeunits(prefix))
    else
        SubString(s)
    end
end

"""
    chopsuffix(s::AbstractString, suffix::Union{AbstractString,Regex}) -> SubString

Remove the suffix `suffix` from `s`. If `s` does not end with `suffix`, a string equal to `s` is returned.

See also [`chopprefix`](@ref).

!!! compat "Julia 1.8"
    This function is available as of Julia 1.8.

# Examples
```jldoctest
julia> chopsuffix("Hamburger", "er")
"Hamburg"

julia> chopsuffix("Hamburger", "hotdog")
"Hamburger"
```
"""
function chopsuffix(s::AbstractString, suffix::AbstractString)
    a, b = Iterators.Reverse(s), Iterators.Reverse(suffix)
    k = lastindex(s)
    i, j = iterate(a), iterate(b)
    while true
        j === nothing && i === nothing && return SubString(s, 1, 0) # s == suffix: empty result
        j === nothing && return @inbounds SubString(s, firstindex(s), k) # ran out of suffix: success!
        i === nothing && return SubString(s) # ran out of source: failure
        i[1] == j[1] || return SubString(s) # mismatch: failure
        k = i[2]
        i, j = iterate(a, k), iterate(b, j[2])
    end
end

function chopsuffix(s::Union{String, SubString{String}},
                    suffix::Union{String, SubString{String}})
    if !isempty(suffix) && endswith(s, suffix)
        astart = ncodeunits(s) - ncodeunits(suffix) + 1
        @inbounds SubString(s, firstindex(s), prevind(s, astart))
    else
        SubString(s)
    end
end


"""
    chomp(s::AbstractString) -> SubString

Remove a single trailing newline from a string.

See also [`chop`](@ref).

# Examples
```jldoctest
julia> chomp("Hello\\n")
"Hello"
```
"""
function chomp(s::AbstractString)
    i = lastindex(s)
    (i < 1 || s[i] != '\n') && (return SubString(s, 1, i))
    j = prevind(s,i)
    (j < 1 || s[j] != '\r') && (return SubString(s, 1, j))
    return SubString(s, 1, prevind(s,j))
end
function chomp(s::String)
    i = lastindex(s)
    if i < 1 || codeunit(s,i) != 0x0a
        return @inbounds SubString(s, 1, i)
    elseif i < 2 || codeunit(s,i-1) != 0x0d
        return @inbounds SubString(s, 1, prevind(s, i))
    else
        return @inbounds SubString(s, 1, prevind(s, i-1))
    end
end

"""
    lstrip([pred=isspace,] str::AbstractString) -> SubString
    lstrip(str::AbstractString, chars) -> SubString

Remove leading characters from `str`, either those specified by `chars` or those for
which the function `pred` returns `true`.

The default behaviour is to remove leading whitespace and delimiters: see
[`isspace`](@ref) for precise details.

The optional `chars` argument specifies which characters to remove: it can be a single
character, or a vector or set of characters.

See also [`strip`](@ref) and [`rstrip`](@ref).

# Examples
```jldoctest
julia> a = lpad("March", 20)
"               March"

julia> lstrip(a)
"March"
```
"""
function lstrip(f, s::AbstractString)
    e = lastindex(s)
    for (i::Int, c::AbstractChar) in pairs(s)
        !f(c) && return @inbounds SubString(s, i, e)
    end
    SubString(s, e+1, e)
end
lstrip(s::AbstractString) = lstrip(isspace, s)
lstrip(s::AbstractString, chars::Chars) = lstrip(in(chars), s)
lstrip(::AbstractString, ::AbstractString) = throw(ArgumentError("Both arguments are strings. The second argument should be a `Char` or collection of `Char`s"))

"""
    rstrip([pred=isspace,] str::AbstractString) -> SubString
    rstrip(str::AbstractString, chars) -> SubString

Remove trailing characters from `str`, either those specified by `chars` or those for
which the function `pred` returns `true`.

The default behaviour is to remove trailing whitespace and delimiters: see
[`isspace`](@ref) for precise details.

The optional `chars` argument specifies which characters to remove: it can be a single
character, or a vector or set of characters.

See also [`strip`](@ref) and [`lstrip`](@ref).

# Examples
```jldoctest
julia> a = rpad("March", 20)
"March               "

julia> rstrip(a)
"March"
```
"""
function rstrip(f, s::AbstractString)
    for (i, c) in Iterators.reverse(pairs(s))
        f(c::AbstractChar) || return @inbounds SubString(s, 1, i::Int)
    end
    SubString(s, 1, 0)
end
rstrip(s::AbstractString) = rstrip(isspace, s)
rstrip(s::AbstractString, chars::Chars) = rstrip(in(chars), s)
rstrip(::AbstractString, ::AbstractString) = throw(ArgumentError("Both arguments are strings. The second argument should be a `Char` or collection of `Char`s"))


"""
    strip([pred=isspace,] str::AbstractString) -> SubString
    strip(str::AbstractString, chars) -> SubString

Remove leading and trailing characters from `str`, either those specified by `chars` or
those for which the function `pred` returns `true`.

The default behaviour is to remove leading and trailing whitespace and delimiters: see
[`isspace`](@ref) for precise details.

The optional `chars` argument specifies which characters to remove: it can be a single
character, vector or set of characters.

See also [`lstrip`](@ref) and [`rstrip`](@ref).

!!! compat "Julia 1.2"
    The method which accepts a predicate function requires Julia 1.2 or later.

# Examples
```jldoctest
julia> strip("{3, 5}\\n", ['{', '}', '\\n'])
"3, 5"
```
"""
strip(s::AbstractString) = lstrip(rstrip(s))
strip(s::AbstractString, chars::Chars) = lstrip(rstrip(s, chars), chars)
strip(::AbstractString, ::AbstractString) = throw(ArgumentError("Both arguments are strings. The second argument should be a `Char` or collection of `Char`s"))
strip(f, s::AbstractString) = lstrip(f, rstrip(f, s))

## string padding functions ##

"""
    lpad(s, n::Integer, p::Union{AbstractChar,AbstractString}=' ') -> String

Stringify `s` and pad the resulting string on the left with `p` to make it `n`
characters (in [`textwidth`](@ref)) long. If `s` is already `n` characters long, an equal
string is returned. Pad with spaces by default.

# Examples
```jldoctest
julia> lpad("March", 10)
"     March"
```
!!! compat "Julia 1.7"
    In Julia 1.7, this function was changed to use `textwidth` rather than a raw character (codepoint) count.
"""
lpad(s, n::Integer, p::Union{AbstractChar,AbstractString}=' ') = lpad(string(s)::AbstractString, n, string(p))

function lpad(
    s::Union{AbstractChar,AbstractString},
    n::Integer,
    p::Union{AbstractChar,AbstractString}=' ',
) :: String
    n = Int(n)::Int
    m = signed(n) - Int(textwidth(s))::Int
    m ≤ 0 && return string(s)
    l = textwidth(p)
    q, r = divrem(m, l)
    r == 0 ? string(p^q, s) : string(p^q, first(p, r), s)
end

"""
    rpad(s, n::Integer, p::Union{AbstractChar,AbstractString}=' ') -> String

Stringify `s` and pad the resulting string on the right with `p` to make it `n`
characters (in [`textwidth`](@ref)) long. If `s` is already `n` characters long, an equal
string is returned. Pad with spaces by default.

# Examples
```jldoctest
julia> rpad("March", 20)
"March               "
```
!!! compat "Julia 1.7"
    In Julia 1.7, this function was changed to use `textwidth` rather than a raw character (codepoint) count.
"""
rpad(s, n::Integer, p::Union{AbstractChar,AbstractString}=' ') = rpad(string(s)::AbstractString, n, string(p))

function rpad(
    s::Union{AbstractChar,AbstractString},
    n::Integer,
    p::Union{AbstractChar,AbstractString}=' ',
) :: String
    n = Int(n)::Int
    m = signed(n) - Int(textwidth(s))::Int
    m ≤ 0 && return string(s)
    l = textwidth(p)
    q, r = divrem(m, l)
    r == 0 ? string(s, p^q) : string(s, p^q, first(p, r))
end

"""
    eachsplit(str::AbstractString, dlm; limit::Integer=0, keepempty::Bool=true)
    eachsplit(str::AbstractString; limit::Integer=0, keepempty::Bool=false)

Split `str` on occurrences of the delimiter(s) `dlm` and return an iterator over the
substrings.  `dlm` can be any of the formats allowed by [`findnext`](@ref)'s first argument
(i.e. as a string, regular expression or a function), or as a single character or collection
of characters.

If `dlm` is omitted, it defaults to [`isspace`](@ref).

The optional keyword arguments are:
 - `limit`: the maximum size of the result. `limit=0` implies no maximum (default)
 - `keepempty`: whether empty fields should be kept in the result. Default is `false` without
   a `dlm` argument, `true` with a `dlm` argument.

See also [`split`](@ref).

!!! compat "Julia 1.8"
    The `eachsplit` function requires at least Julia 1.8.

# Examples
```jldoctest
julia> a = "Ma.rch"
"Ma.rch"

julia> b = eachsplit(a, ".")
Base.SplitIterator{String, String}("Ma.rch", ".", 0, true)

julia> collect(b)
2-element Vector{SubString{String}}:
 "Ma"
 "rch"
```
"""
function eachsplit end

# Forcing specialization on `splitter` improves performance (roughly 30% decrease in runtime)
# and prevents a major invalidation risk (1550 MethodInstances)
struct SplitIterator{S<:AbstractString,F}
    str::S
    splitter::F
    limit::Int
    keepempty::Bool
end

eltype(::Type{<:SplitIterator{T}}) where T = SubString{T}
eltype(::Type{<:SplitIterator{<:SubString{T}}}) where T = SubString{T}

IteratorSize(::Type{<:SplitIterator}) = SizeUnknown()

# i: the starting index of the substring to be extracted
# k: the starting index of the next substring to be extracted
# n: the number of splits returned so far; always less than iter.limit - 1 (1 for the rest)
function iterate(iter::SplitIterator, (i, k, n)=(firstindex(iter.str), firstindex(iter.str), 0))
    i - 1 > ncodeunits(iter.str)::Int && return nothing
    r = findnext(iter.splitter, iter.str, k)::Union{Nothing,Int,UnitRange{Int}}
    while r !== nothing && n != iter.limit - 1 && first(r) <= ncodeunits(iter.str)
        j, k = first(r), nextind(iter.str, last(r))::Int
        k_ = k <= j ? nextind(iter.str, j)::Int : k
        if i < k
            substr = @inbounds SubString(iter.str, i, prevind(iter.str, j)::Int)
            (iter.keepempty || i < j) && return (substr, (k, k_, n + 1))
            i = k
        end
        k = k_
        r = findnext(iter.splitter, iter.str, k)::Union{Nothing,Int,UnitRange{Int}}
    end
    iter.keepempty || i <= ncodeunits(iter.str) || return nothing
    @inbounds SubString(iter.str, i), (ncodeunits(iter.str) + 2, k, n + 1)
end

# Specialization for partition(s,n) to return a SubString
eltype(::Type{PartitionIterator{T}}) where {T<:AbstractString} = SubString{T}
# SubStrings do not nest
eltype(::Type{PartitionIterator{T}}) where {T<:SubString} = T

function iterate(itr::PartitionIterator{<:AbstractString}, state = firstindex(itr.c))
    state > ncodeunits(itr.c) && return nothing
    r = min(nextind(itr.c, state, itr.n - 1), lastindex(itr.c))
    return SubString(itr.c, state, r), nextind(itr.c, r)
end

eachsplit(str::T, splitter; limit::Integer=0, keepempty::Bool=true) where {T<:AbstractString} =
    SplitIterator(str, splitter, limit, keepempty)

eachsplit(str::T, splitter::Union{Tuple{Vararg{AbstractChar}},AbstractVector{<:AbstractChar},Set{<:AbstractChar}};
          limit::Integer=0, keepempty=true) where {T<:AbstractString} =
    eachsplit(str, in(splitter); limit, keepempty)

eachsplit(str::T, splitter::AbstractChar; limit::Integer=0, keepempty=true) where {T<:AbstractString} =
    eachsplit(str, isequal(splitter); limit, keepempty)

# a bit oddball, but standard behavior in Perl, Ruby & Python:
eachsplit(str::AbstractString; limit::Integer=0, keepempty=false) =
    eachsplit(str, isspace; limit, keepempty)

"""
    split(str::AbstractString, dlm; limit::Integer=0, keepempty::Bool=true)
    split(str::AbstractString; limit::Integer=0, keepempty::Bool=false)

Split `str` into an array of substrings on occurrences of the delimiter(s) `dlm`.  `dlm`
can be any of the formats allowed by [`findnext`](@ref)'s first argument (i.e. as a
string, regular expression or a function), or as a single character or collection of
characters.

If `dlm` is omitted, it defaults to [`isspace`](@ref).

The optional keyword arguments are:
 - `limit`: the maximum size of the result. `limit=0` implies no maximum (default)
 - `keepempty`: whether empty fields should be kept in the result. Default is `false` without
   a `dlm` argument, `true` with a `dlm` argument.

See also [`rsplit`](@ref), [`eachsplit`](@ref).

# Examples
```jldoctest
julia> a = "Ma.rch"
"Ma.rch"

julia> split(a, ".")
2-element Vector{SubString{String}}:
 "Ma"
 "rch"
```
"""
function split(str::T, splitter;
               limit::Integer=0, keepempty::Bool=true) where {T<:AbstractString}
    collect(eachsplit(str, splitter; limit, keepempty))
end

# a bit oddball, but standard behavior in Perl, Ruby & Python:
split(str::AbstractString;
      limit::Integer=0, keepempty::Bool=false) =
    split(str, isspace; limit, keepempty)

"""
    rsplit(s::AbstractString; limit::Integer=0, keepempty::Bool=false)
    rsplit(s::AbstractString, chars; limit::Integer=0, keepempty::Bool=true)

Similar to [`split`](@ref), but starting from the end of the string.

# Examples
```jldoctest
julia> a = "M.a.r.c.h"
"M.a.r.c.h"

julia> rsplit(a, ".")
5-element Vector{SubString{String}}:
 "M"
 "a"
 "r"
 "c"
 "h"

julia> rsplit(a, "."; limit=1)
1-element Vector{SubString{String}}:
 "M.a.r.c.h"

julia> rsplit(a, "."; limit=2)
2-element Vector{SubString{String}}:
 "M.a.r.c"
 "h"
```
"""
function rsplit end

function rsplit(str::T, splitter;
                limit::Integer=0, keepempty::Bool=true) where {T<:AbstractString}
    _rsplit(str, splitter, limit, keepempty, T <: SubString ? T[] : SubString{T}[])
end
function rsplit(str::T, splitter::Union{Tuple{Vararg{AbstractChar}},AbstractVector{<:AbstractChar},Set{<:AbstractChar}};
                limit::Integer=0, keepempty::Bool=true) where {T<:AbstractString}
    _rsplit(str, in(splitter), limit, keepempty, T <: SubString ? T[] : SubString{T}[])
end
function rsplit(str::T, splitter::AbstractChar;
                limit::Integer=0, keepempty::Bool=true) where {T<:AbstractString}
    _rsplit(str, isequal(splitter), limit, keepempty, T <: SubString ? T[] : SubString{T}[])
end

function _rsplit(str::AbstractString, splitter, limit::Integer, keepempty::Bool, strs::Array)
    n = lastindex(str)::Int
    r = something(findlast(splitter, str)::Union{Nothing,Int,UnitRange{Int}}, 0)
    j, k = first(r), last(r)
    while j > 0 && k > 0 && length(strs) != limit-1
        (keepempty || k < n) && pushfirst!(strs, @inbounds SubString(str,nextind(str,k)::Int,n))
        n = prevind(str, j)::Int
        r = something(findprev(splitter,str,n)::Union{Nothing,Int,UnitRange{Int}}, 0)
        j, k = first(r), last(r)
    end
    (keepempty || n > 0) && pushfirst!(strs, SubString(str,1,n))
    return strs
end
rsplit(str::AbstractString;
      limit::Integer=0, keepempty::Bool=false) =
    rsplit(str, isspace; limit=limit, keepempty=keepempty)

_replace(io, repl, str, r, pattern) = print(io, repl)
_replace(io, repl::Function, str, r, pattern) =
    print(io, repl(SubString(str, first(r), last(r))))
_replace(io, repl::Function, str, r, pattern::Function) =
    print(io, repl(str[first(r)]))

_pat_replacer(x) = x
_free_pat_replacer(x) = nothing

_pat_replacer(x::AbstractChar) = isequal(x)
_pat_replacer(x::Union{Tuple{Vararg{AbstractChar}},AbstractVector{<:AbstractChar},Set{<:AbstractChar}}) = in(x)

# note: leave str untyped here to make it easier for packages like StringViews to hook in
function _replace_init(str, pat_repl::NTuple{N, Pair}, count::Int) where N
    count < 0 && throw(DomainError(count, "`count` must be non-negative."))
    e1 = nextind(str, lastindex(str)) # sizeof(str)+1
    a = firstindex(str)
    patterns = map(p -> _pat_replacer(first(p)), pat_repl)
    replaces = map(last, pat_repl)
    rs = map(patterns) do p
        r = findnext(p, str, a)
        if r === nothing || first(r) == 0
            return e1+1:0
        end
        r isa Int && (r = r:r) # findnext / performance fix
        return r
    end
    return e1, patterns, replaces, rs, all(>(e1), map(first, rs))
end

# note: leave str untyped here to make it easier for packages like StringViews to hook in
function _replace_finish(io::IO, str, count::Int,
                         e1::Int, patterns::Tuple, replaces::Tuple, rs::Tuple)
    n = 1
    i = a = firstindex(str)
    while true
        p = argmin(map(first, rs)) # TODO: or argmin(rs), to pick the shortest first match ?
        r = rs[p]
        j, k = first(r), last(r)
        j > e1 && break
        if i == a || i <= k
            # copy out preserved portion
            GC.@preserve str unsafe_write(io, pointer(str, i), UInt(j-i))
            # copy out replacement string
            _replace(io, replaces[p], str, r, patterns[p])
        end
        if k < j
            i = j
            j == e1 && break
            k = nextind(str, j)
        else
            i = k = nextind(str, k)
        end
        n == count && break
        let k = k
            rs = map(patterns, rs) do p, r
                if first(r) < k
                    r = findnext(p, str, k)
                    if r === nothing || first(r) == 0
                        return e1+1:0
                    end
                    r isa Int && (r = r:r) # findnext / performance fix
                end
                return r
            end
        end
        n += 1
    end
    foreach(_free_pat_replacer, patterns)
    write(io, SubString(str, i))
    return io
end

# note: leave str untyped here to make it easier for packages like StringViews to hook in
function _replace_(io::IO, str, pat_repl::NTuple{N, Pair}, count::Int) where N
    if count == 0
        write(io, str)
        return io
    end
    e1, patterns, replaces, rs, notfound = _replace_init(str, pat_repl, count)
    if notfound
        foreach(_free_pat_replacer, patterns)
        write(io, str)
        return io
    end
    return _replace_finish(io, str, count, e1, patterns, replaces, rs)
end

# note: leave str untyped here to make it easier for packages like StringViews to hook in
function _replace_(str, pat_repl::NTuple{N, Pair}, count::Int) where N
    count == 0 && return String(str)
    e1, patterns, replaces, rs, notfound = _replace_init(str, pat_repl, count)
    if notfound
        foreach(_free_pat_replacer, patterns)
        return String(str)
    end
    out = IOBuffer(sizehint=floor(Int, 1.2sizeof(str)))
    return String(take!(_replace_finish(out, str, count, e1, patterns, replaces, rs)))
end

"""
    replace([io::IO], s::AbstractString, pat=>r, [pat2=>r2, ...]; [count::Integer])

Search for the given pattern `pat` in `s`, and replace each occurrence with `r`.
If `count` is provided, replace at most `count` occurrences.
`pat` may be a single character, a vector or a set of characters, a string,
or a regular expression.
If `r` is a function, each occurrence is replaced with `r(s)`
where `s` is the matched substring (when `pat` is a `AbstractPattern` or `AbstractString`) or
character (when `pat` is an `AbstractChar` or a collection of `AbstractChar`).
If `pat` is a regular expression and `r` is a [`SubstitutionString`](@ref), then capture group
references in `r` are replaced with the corresponding matched text.
To remove instances of `pat` from `string`, set `r` to the empty `String` (`""`).

The return value is a new string after the replacements.  If the `io::IO` argument
is supplied, the transformed string is instead written to `io` (returning `io`).
(For example, this can be used in conjunction with an [`IOBuffer`](@ref) to re-use
a pre-allocated buffer array in-place.)

Multiple patterns can be specified, and they will be applied left-to-right
simultaneously, so only one pattern will be applied to any character, and the
patterns will only be applied to the input text, not the replacements.

!!! compat "Julia 1.7"
    Support for multiple patterns requires version 1.7.

!!! compat "Julia 1.10"
    The `io::IO` argument requires version 1.10.

# Examples
```jldoctest
julia> replace("Python is a programming language.", "Python" => "Julia")
"Julia is a programming language."

julia> replace("The quick foxes run quickly.", "quick" => "slow", count=1)
"The slow foxes run quickly."

julia> replace("The quick foxes run quickly.", "quick" => "", count=1)
"The  foxes run quickly."

julia> replace("The quick foxes run quickly.", r"fox(es)?" => s"bus\\1")
"The quick buses run quickly."

julia> replace("abcabc", "a" => "b", "b" => "c", r".+" => "a")
"bca"
```
"""
replace(io::IO, s::AbstractString, pat_f::Pair...; count=typemax(Int)) =
    _replace_(io, String(s), pat_f, Int(count))

replace(s::AbstractString, pat_f::Pair...; count=typemax(Int)) =
    _replace_(String(s), pat_f, Int(count))


# TODO: allow transform as the first argument to replace?

# hex <-> bytes conversion

"""
    hex2bytes(itr)

Given an iterable `itr` of ASCII codes for a sequence of hexadecimal digits, returns a
`Vector{UInt8}` of bytes  corresponding to the binary representation: each successive pair
of hexadecimal digits in `itr` gives the value of one byte in the return vector.

The length of `itr` must be even, and the returned array has half of the length of `itr`.
See also [`hex2bytes!`](@ref) for an in-place version, and [`bytes2hex`](@ref) for the inverse.

!!! compat "Julia 1.7"
    Calling `hex2bytes` with iterators producing `UInt8` values requires
    Julia 1.7 or later. In earlier versions, you can `collect` the iterator
    before calling `hex2bytes`.

# Examples
```jldoctest
julia> s = string(12345, base = 16)
"3039"

julia> hex2bytes(s)
2-element Vector{UInt8}:
 0x30
 0x39

julia> a = b"01abEF"
6-element Base.CodeUnits{UInt8, String}:
 0x30
 0x31
 0x61
 0x62
 0x45
 0x46

julia> hex2bytes(a)
3-element Vector{UInt8}:
 0x01
 0xab
 0xef
```
"""
function hex2bytes end

hex2bytes(s) = hex2bytes!(Vector{UInt8}(undef, length(s)::Int >> 1), s)

# special case - valid bytes are checked in the generic implementation
function hex2bytes!(dest::AbstractArray{UInt8}, s::String)
    sizeof(s) != length(s) && throw(ArgumentError("input string must consist of hexadecimal characters only"))

    hex2bytes!(dest, transcode(UInt8, s))
end

"""
    hex2bytes!(dest::AbstractVector{UInt8}, itr)

Convert an iterable `itr` of bytes representing a hexadecimal string to its binary
representation, similar to [`hex2bytes`](@ref) except that the output is written in-place
to `dest`. The length of `dest` must be half the length of `itr`.

!!! compat "Julia 1.7"
    Calling hex2bytes! with iterators producing UInt8 requires
    version 1.7. In earlier versions, you can collect the iterable
    before calling instead.
"""
function hex2bytes!(dest::AbstractArray{UInt8}, itr)
    isodd(length(itr)) && throw(ArgumentError("length of iterable must be even"))
    @boundscheck 2*length(dest) != length(itr) && throw(ArgumentError("length of output array must be half of the length of input iterable"))
    iszero(length(itr)) && return dest

    next = iterate(itr)
    @inbounds for i in eachindex(dest)
        x,state = next::NTuple{2,Any}
        y,state = iterate(itr, state)::NTuple{2,Any}
        next = iterate(itr, state)
        dest[i] = number_from_hex(x) << 4 + number_from_hex(y)
    end

    return dest
end

@inline number_from_hex(c::AbstractChar) = number_from_hex(Char(c))
@inline number_from_hex(c::Char) = number_from_hex(UInt8(c))
@inline function number_from_hex(c::UInt8)
    UInt8('0') <= c <= UInt8('9') && return c - UInt8('0')
    c |= 0b0100000
    UInt8('a') <= c <= UInt8('f') && return c - UInt8('a') + 0x0a
    throw(ArgumentError("byte is not an ASCII hexadecimal digit"))
end

"""
    bytes2hex(itr) -> String
    bytes2hex(io::IO, itr)

Convert an iterator `itr` of bytes to its hexadecimal string representation, either
returning a `String` via `bytes2hex(itr)` or writing the string to an `io` stream
via `bytes2hex(io, itr)`.  The hexadecimal characters are all lowercase.

!!! compat "Julia 1.7"
    Calling `bytes2hex` with arbitrary iterators producing `UInt8` values requires
    Julia 1.7 or later. In earlier versions, you can `collect` the iterator
    before calling `bytes2hex`.

# Examples
```jldoctest
julia> a = string(12345, base = 16)
"3039"

julia> b = hex2bytes(a)
2-element Vector{UInt8}:
 0x30
 0x39

julia> bytes2hex(b)
"3039"
```
"""
function bytes2hex end

function bytes2hex(itr)
    eltype(itr) === UInt8 || throw(ArgumentError("eltype of iterator not UInt8"))
    b = Base.StringVector(2*length(itr))
    @inbounds for (i, x) in enumerate(itr)
        b[2i - 1] = hex_chars[1 + x >> 4]
        b[2i    ] = hex_chars[1 + x & 0xf]
    end
    return String(b)
end

function bytes2hex(io::IO, itr)
    eltype(itr) === UInt8 || throw(ArgumentError("eltype of iterator not UInt8"))
    for x in itr
        print(io, Char(hex_chars[1 + x >> 4]), Char(hex_chars[1 + x & 0xf]))
    end
end

# check for pure ASCII-ness
function ascii(s::String)
    for i in 1:sizeof(s)
        @inbounds codeunit(s, i) < 0x80 || __throw_invalid_ascii(s, i)
    end
    return s
end
@noinline __throw_invalid_ascii(s::String, i::Int) = throw(ArgumentError("invalid ASCII at index $i in $(repr(s))"))

"""
    ascii(s::AbstractString)

Convert a string to `String` type and check that it contains only ASCII data, otherwise
throwing an `ArgumentError` indicating the position of the first non-ASCII byte.

See also the [`isascii`](@ref) predicate to filter or replace non-ASCII characters.

# Examples
```jldoctest
julia> ascii("abcdeγfgh")
ERROR: ArgumentError: invalid ASCII at index 6 in "abcdeγfgh"
Stacktrace:
[...]

julia> ascii("abcdefgh")
"abcdefgh"
```
"""
ascii(x::AbstractString) = ascii(String(x))

Base.rest(s::Union{String,SubString{String}}, i=1) = SubString(s, i)
function Base.rest(s::AbstractString, st...)
    io = IOBuffer()
    for c in Iterators.rest(s, st...)
        print(io, c)
    end
    return String(take!(io))
end
Q   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/strings/io.jl�X      # This file is a part of Julia. License is MIT: https://julialang.org/license

## core text I/O ##

"""
    print([io::IO], xs...)

Write to `io` (or to the default output stream [`stdout`](@ref)
if `io` is not given) a canonical (un-decorated) text representation.
The representation used by `print` includes minimal formatting and tries to
avoid Julia-specific details.

`print` falls back to calling `show`, so most types should just define
`show`. Define `print` if your type has a separate "plain" representation.
For example, `show` displays strings with quotes, and `print` displays strings
without quotes.

See also [`println`](@ref), [`string`](@ref), [`printstyled`](@ref).

# Examples
```jldoctest
julia> print("Hello World!")
Hello World!
julia> io = IOBuffer();

julia> print(io, "Hello", ' ', :World!)

julia> String(take!(io))
"Hello World!"
```
"""
function print(io::IO, x)
    lock(io)
    try
        show(io, x)
    finally
        unlock(io)
    end
    return nothing
end

function print(io::IO, xs...)
    lock(io)
    try
        for x in xs
            print(io, x)
        end
    finally
        unlock(io)
    end
    return nothing
end

"""
    println([io::IO], xs...)

Print (using [`print`](@ref)) `xs` to `io` followed by a newline.
If `io` is not supplied, prints to the default output stream [`stdout`](@ref).

See also [`printstyled`](@ref) to add colors etc.

# Examples
```jldoctest
julia> println("Hello, world")
Hello, world

julia> io = IOBuffer();

julia> println(io, "Hello", ',', " world.")

julia> String(take!(io))
"Hello, world.\\n"
```
"""
println(io::IO, xs...) = print(io, xs..., "\n")

## conversion of general objects to strings ##

"""
    sprint(f::Function, args...; context=nothing, sizehint=0)

Call the given function with an I/O stream and the supplied extra arguments.
Everything written to this I/O stream is returned as a string.
`context` can be an [`IOContext`](@ref) whose properties will be used, a `Pair`
specifying a property and its value, or a tuple of `Pair` specifying multiple
properties and their values. `sizehint` suggests the capacity of the buffer (in
bytes).

The optional keyword argument `context` can be set to a `:key=>value` pair, a
tuple of `:key=>value` pairs, or an `IO` or [`IOContext`](@ref) object whose
attributes are used for the I/O stream passed to `f`.  The optional `sizehint`
is a suggested size (in bytes) to allocate for the buffer used to write the
string.

!!! compat "Julia 1.7"
    Passing a tuple to keyword `context` requires Julia 1.7 or later.

# Examples
```jldoctest
julia> sprint(show, 66.66666; context=:compact => true)
"66.6667"

julia> sprint(showerror, BoundsError([1], 100))
"BoundsError: attempt to access 1-element Vector{Int64} at index [100]"
```
"""
function sprint(f::Function, args...; context=nothing, sizehint::Integer=0)
    s = IOBuffer(sizehint=sizehint)
    if context isa Tuple
        f(IOContext(s, context...), args...)
    elseif context !== nothing
        f(IOContext(s, context), args...)
    else
        f(s, args...)
    end
    String(_unsafe_take!(s))
end

function _str_sizehint(x)
    if x isa Float64
        return 20
    elseif x isa Float32
        return 12
    elseif x isa String || x isa SubString{String}
        return sizeof(x)
    elseif x isa Char
        return ncodeunits(x)
    elseif x isa UInt64 || x isa UInt32
        return ndigits(x)
    elseif x isa Int64 || x isa Int32
        return ndigits(x) + (x < zero(x))
    else
        return 8
    end
end

function print_to_string(xs...)
    if isempty(xs)
        return ""
    end
    siz::Int = 0
    for x in xs
        siz += _str_sizehint(x)
    end
    # specialized for performance reasons
    s = IOBuffer(sizehint=siz)
    for x in xs
        print(s, x)
    end
    String(_unsafe_take!(s))
end

function string_with_env(env, xs...)
    if isempty(xs)
        return ""
    end
    siz::Int = 0
    for x in xs
        siz += _str_sizehint(x)
    end
    # specialized for performance reasons
    s = IOBuffer(sizehint=siz)
    env_io = IOContext(s, env)
    for x in xs
        print(env_io, x)
    end
    String(_unsafe_take!(s))
end

"""
    string(xs...)

Create a string from any values using the [`print`](@ref) function.

`string` should usually not be defined directly. Instead, define a method
`print(io::IO, x::MyType)`. If `string(x)` for a certain type needs to be
highly efficient, then it may make sense to add a method to `string` and
define `print(io::IO, x::MyType) = print(io, string(x))` to ensure the
functions are consistent.

See also: [`String`](@ref), [`repr`](@ref), [`sprint`](@ref), [`show`](@ref @show).

# Examples
```jldoctest
julia> string("a", 1, true)
"a1true"
```
"""
string(xs...) = print_to_string(xs...)

string(a::Symbol) = String(a)

# note: print uses an encoding determined by `io` (defaults to UTF-8), whereas
#       write uses an encoding determined by `s` (UTF-8 for `String`)
print(io::IO, s::AbstractString) = for c in s; print(io, c); end
write(io::IO, s::AbstractString) = (len = 0; for c in s; len += Int(write(io, c))::Int; end; len)
show(io::IO, s::AbstractString) = print_quoted(io, s)

# show elided string if more than `limit` characters
function show(
    io    :: IO,
    mime  :: MIME"text/plain",
    str   :: AbstractString;
    limit :: Union{Int, Nothing} = nothing,
)
    # compute limit in default case
    if limit === nothing
        get(io, :limit, false)::Bool || return show(io, str)
        limit = max(20, displaysize(io)[2])
        # one line in collection, seven otherwise
        get(io, :typeinfo, nothing) === nothing && (limit *= 7)
    end

    # early out for short strings
    len = ncodeunits(str)
    len ≤ limit - 2 && # quote chars
        return show(io, str)

    # these don't depend on string data
    units = codeunit(str) == UInt8 ? "bytes" : "code units"
    skip_text(skip) = " ⋯ $skip $units ⋯ "
    short = length(skip_text("")) + 4 # quote chars
    chars = max(limit, short + 1) - short # at least 1 digit

    # figure out how many characters to print in elided case
    chars -= d = ndigits(len - chars) # first adjustment
    chars += d - ndigits(len - chars) # second if needed
    chars = max(0, chars)

    # find head & tail, avoiding O(length(str)) computation
    head = nextind(str, 0, 1 + (chars + 1) ÷ 2)
    tail = prevind(str, len + 1, chars ÷ 2)

    # threshold: min chars skipped to make elision worthwhile
    t = short + ndigits(len - chars) - 1
    n = tail - head # skipped code units
    if 4t ≤ n || t ≤ n && t ≤ length(str, head, tail-1)
        skip = skip_text(n)
        show(io, SubString(str, 1:prevind(str, head)))
        printstyled(io, skip; color=:light_yellow, bold=true)
        show(io, SubString(str, tail))
    else
        show(io, str)
    end
end

# optimized methods to avoid iterating over chars
write(io::IO, s::Union{String,SubString{String}}) =
    GC.@preserve s Int(unsafe_write(io, pointer(s), reinterpret(UInt, sizeof(s))))::Int
print(io::IO, s::Union{String,SubString{String}}) = (write(io, s); nothing)

"""
    repr(x; context=nothing)

Create a string from any value using the [`show`](@ref) function.
You should not add methods to `repr`; define a `show` method instead.

The optional keyword argument `context` can be set to a `:key=>value` pair, a
tuple of `:key=>value` pairs, or an `IO` or [`IOContext`](@ref) object whose
attributes are used for the I/O stream passed to `show`.

Note that `repr(x)` is usually similar to how the value of `x` would
be entered in Julia.  See also [`repr(MIME("text/plain"), x)`](@ref) to instead
return a "pretty-printed" version of `x` designed more for human consumption,
equivalent to the REPL display of `x`.

!!! compat "Julia 1.7"
    Passing a tuple to keyword `context` requires Julia 1.7 or later.

# Examples
```jldoctest
julia> repr(1)
"1"

julia> repr(zeros(3))
"[0.0, 0.0, 0.0]"

julia> repr(big(1/3))
"0.333333333333333314829616256247390992939472198486328125"

julia> repr(big(1/3), context=:compact => true)
"0.333333"

```
"""
repr(x; context=nothing) = sprint(show, x; context=context)

limitrepr(x) = repr(x, context = :limit=>true)

# IOBuffer views of a (byte)string:

"""
    IOBuffer(string::String)

Create a read-only `IOBuffer` on the data underlying the given string.

# Examples
```jldoctest
julia> io = IOBuffer("Haho");

julia> String(take!(io))
"Haho"

julia> String(take!(io))
"Haho"
```
"""
IOBuffer(str::String) = IOBuffer(unsafe_wrap(Vector{UInt8}, str))
IOBuffer(s::SubString{String}) = IOBuffer(view(unsafe_wrap(Vector{UInt8}, s.string), s.offset + 1 : s.offset + sizeof(s)))

# join is implemented using IO

"""
    join([io::IO,] iterator [, delim [, last]])

Join any `iterator` into a single string, inserting the given delimiter (if any) between
adjacent items.  If `last` is given, it will be used instead of `delim` between the last
two items.  Each item of `iterator` is converted to a string via `print(io::IOBuffer, x)`.
If `io` is given, the result is written to `io` rather than returned as a `String`.

# Examples
```jldoctest
julia> join(["apples", "bananas", "pineapples"], ", ", " and ")
"apples, bananas and pineapples"

julia> join([1,2,3,4,5])
"12345"
```
"""
function join(io::IO, iterator, delim, last)
    first = true
    local prev
    for item in iterator
        if @isdefined prev
            first ? (first = false) : print(io, delim)
            print(io, prev)
        end
        prev = item
    end
    if @isdefined prev
        first || print(io, last)
        print(io, prev)
    end
    nothing
end
function join(io::IO, iterator, delim="")
    # Specialization of the above code when delim==last,
    # which lets us emit (compile) less code
    first = true
    for item in iterator
        first ? (first = false) : print(io, delim)
        print(io, item)
    end
end

join(iterator) = sprint(join, iterator)
join(iterator, delim) = sprint(join, iterator, delim)
join(iterator, delim, last) = sprint(join, iterator, delim, last)

## string escaping & unescaping ##

need_full_hex(c::Union{Nothing, AbstractChar}) = c !== nothing && isxdigit(c)
escape_nul(c::Union{Nothing, AbstractChar}) =
    (c !== nothing && '0' <= c <= '7') ? "\\x00" : "\\0"

"""
    escape_string(str::AbstractString[, esc]; keep = ())::AbstractString
    escape_string(io, str::AbstractString[, esc]; keep = ())::Nothing

General escaping of traditional C and Unicode escape sequences. The first form returns the
escaped string, the second prints the result to `io`.

Backslashes (`\\`) are escaped with a double-backslash (`"\\\\"`). Non-printable
characters are escaped either with their standard C escape codes, `"\\0"` for NUL (if
unambiguous), unicode code point (`"\\u"` prefix) or hex (`"\\x"` prefix).

The optional `esc` argument specifies any additional characters that should also be
escaped by a prepending backslash (`\"` is also escaped by default in the first form).

The argument `keep` specifies a collection of characters which are to be kept as
they are. Notice that `esc` has precedence here.

See also [`unescape_string`](@ref) for the reverse operation.

!!! compat "Julia 1.7"
    The `keep` argument is available as of Julia 1.7.

# Examples
```jldoctest
julia> escape_string("aaa\\nbbb")
"aaa\\\\nbbb"

julia> escape_string("aaa\\nbbb"; keep = '\\n')
"aaa\\nbbb"

julia> escape_string("\\xfe\\xff") # invalid utf-8
"\\\\xfe\\\\xff"

julia> escape_string(string('\\u2135','\\0')) # unambiguous
"ℵ\\\\0"

julia> escape_string(string('\\u2135','\\0','0')) # \\0 would be ambiguous
"ℵ\\\\x000"
```
"""
function escape_string(io::IO, s::AbstractString, esc=""; keep = ())
    a = Iterators.Stateful(s)
    for c::AbstractChar in a
        if c in esc
            print(io, '\\', c)
        elseif c in keep
            print(io, c)
        elseif isascii(c)
            c == '\0'          ? print(io, escape_nul(peek(a)::Union{AbstractChar,Nothing})) :
            c == '\e'          ? print(io, "\\e") :
            c == '\\'          ? print(io, "\\\\") :
            '\a' <= c <= '\r'  ? print(io, '\\', "abtnvfr"[Int(c)-6]) :
            isprint(c)         ? print(io, c) :
                                 print(io, "\\x", string(UInt32(c), base = 16, pad = 2))
        elseif !isoverlong(c) && !ismalformed(c)
            isprint(c)         ? print(io, c) :
            c <= '\x7f'        ? print(io, "\\x", string(UInt32(c), base = 16, pad = 2)) :
            c <= '\uffff'      ? print(io, "\\u", string(UInt32(c), base = 16, pad = need_full_hex(peek(a)::Union{AbstractChar,Nothing}) ? 4 : 2)) :
                                 print(io, "\\U", string(UInt32(c), base = 16, pad = need_full_hex(peek(a)::Union{AbstractChar,Nothing}) ? 8 : 4))
        else # malformed or overlong
            u = bswap(reinterpret(UInt32, c)::UInt32)
            while true
                print(io, "\\x", string(u % UInt8, base = 16, pad = 2))
                (u >>= 8) == 0 && break
            end
        end
    end
end

escape_string(s::AbstractString, esc=('\"',); keep = ()) =
    sprint((io)->escape_string(io, s, esc; keep = keep), sizehint=lastindex(s))

function print_quoted(io, s::AbstractString)
    print(io, '"')
    escape_string(io, s, ('\"','$')) #"# work around syntax highlighting problem
    print(io, '"')
end

# general unescaping of traditional C and Unicode escape sequences

# TODO: handle unescaping invalid UTF-8 sequences
"""
    unescape_string(str::AbstractString, keep = ())::AbstractString
    unescape_string(io, s::AbstractString, keep = ())::Nothing

General unescaping of traditional C and Unicode escape sequences. The first form returns
the escaped string, the second prints the result to `io`.
The argument `keep` specifies a collection of characters which (along with backlashes) are
to be kept as they are.

The following escape sequences are recognised:
 - Escaped backslash (`\\\\`)
 - Escaped double-quote (`\\\"`)
 - Standard C escape sequences (`\\a`, `\\b`, `\\t`, `\\n`, `\\v`, `\\f`, `\\r`, `\\e`)
 - Unicode BMP code points (`\\u` with 1-4 trailing hex digits)
 - All Unicode code points (`\\U` with 1-8 trailing hex digits; max value = 0010ffff)
 - Hex bytes (`\\x` with 1-2 trailing hex digits)
 - Octal bytes (`\\` with 1-3 trailing octal digits)

See also [`escape_string`](@ref).

# Examples
```jldoctest
julia> unescape_string("aaa\\\\nbbb") # C escape sequence
"aaa\\nbbb"

julia> unescape_string("\\\\u03c0") # unicode
"π"

julia> unescape_string("\\\\101") # octal
"A"

julia> unescape_string("aaa \\\\g \\\\n", ['g']) # using `keep` argument
"aaa \\\\g \\n"
```
"""
function unescape_string(io::IO, s::AbstractString, keep = ())
    a = Iterators.Stateful(s)
    for c in a
        if !isempty(a) && c == '\\'
            c = popfirst!(a)
            if c in keep
                print(io, '\\', c)
            elseif c == 'x' || c == 'u' || c == 'U'
                n = k = 0
                m = c == 'x' ? 2 :
                    c == 'u' ? 4 : 8
                while (k += 1) <= m && !isempty(a)
                    nc = peek(a)::AbstractChar
                    n = '0' <= nc <= '9' ? n<<4 + (nc-'0') :
                        'a' <= nc <= 'f' ? n<<4 + (nc-'a'+10) :
                        'A' <= nc <= 'F' ? n<<4 + (nc-'A'+10) : break
                    popfirst!(a)
                end
                if k == 1 || n > 0x10ffff
                    u = m == 4 ? 'u' : 'U'
                    throw(ArgumentError("invalid $(m == 2 ? "hex (\\x)" :
                                        "unicode (\\$u)") escape sequence"))
                end
                if m == 2 # \x escape sequence
                    write(io, UInt8(n))
                else
                    print(io, Char(n))
                end
            elseif '0' <= c <= '7'
                k = 1
                n = c-'0'
                while (k += 1) <= 3 && !isempty(a)
                    c = peek(a)::AbstractChar
                    n = ('0' <= c <= '7') ? n<<3 + c-'0' : break
                    popfirst!(a)
                end
                if n > 255
                    throw(ArgumentError("octal escape sequence out of range"))
                end
                write(io, UInt8(n))
            else
                print(io, c == 'a' ? '\a' :
                          c == 'b' ? '\b' :
                          c == 't' ? '\t' :
                          c == 'n' ? '\n' :
                          c == 'v' ? '\v' :
                          c == 'f' ? '\f' :
                          c == 'r' ? '\r' :
                          c == 'e' ? '\e' :
                          (c == '\\' || c == '"') ? c :
                          throw(ArgumentError("invalid escape sequence \\$c")))
            end
        else
            print(io, c)
        end
    end
end
unescape_string(s::AbstractString, keep = ()) =
    sprint(unescape_string, s, keep; sizehint=lastindex(s))

"""
    @b_str

Create an immutable byte (`UInt8`) vector using string syntax.

# Examples
```jldoctest
julia> v = b"12\\x01\\x02"
4-element Base.CodeUnits{UInt8, String}:
 0x31
 0x32
 0x01
 0x02

julia> v[2]
0x32
```
"""
macro b_str(s)
    v = codeunits(unescape_string(s))
    QuoteNode(v)
end

"""
    @raw_str -> String

Create a raw string without interpolation and unescaping.
The exception is that quotation marks still must be escaped. Backslashes
escape both quotation marks and other backslashes, but only when a sequence
of backslashes precedes a quote character. Thus, 2n backslashes followed by
a quote encodes n backslashes and the end of the literal while 2n+1 backslashes
followed by a quote encodes n backslashes followed by a quote character.

# Examples
```jldoctest
julia> println(raw"\\ \$x")
\\ \$x

julia> println(raw"\\"")
"

julia> println(raw"\\\\\\"")
\\"

julia> println(raw"\\\\x \\\\\\"")
\\\\x \\"
```
"""
macro raw_str(s); s; end

"""
    escape_raw_string(s::AbstractString)
    escape_raw_string(io, s::AbstractString)

Escape a string in the manner used for parsing raw string literals.
For each double-quote (`"`) character in input string `s`, this
function counts the number _n_ of preceding backslash (`\\`) characters,
and then increases there the number of backslashes from _n_ to 2_n_+1
(even for _n_ = 0). It also doubles a sequence of backslashes at the end
of the string.

This escaping convention is used in raw strings and other non-standard
string literals. (It also happens to be the escaping convention
expected by the Microsoft C/C++ compiler runtime when it parses a
command-line string into the argv[] array.)

See also [`escape_string`](@ref).
"""
function escape_raw_string(io, str::AbstractString)
    escapes = 0
    for c in str
        if c == '\\'
            escapes += 1
        else
            if c == '"'
                # if one or more backslashes are followed by
                # a double quote then escape all backslashes
                # and the double quote
                escapes = escapes * 2 + 1
            end
            while escapes > 0
                write(io, '\\')
                escapes -= 1
            end
            escapes = 0
            write(io, c)
        end
    end
    # also escape any trailing backslashes,
    # so they do not affect the closing quote
    while escapes > 0
        write(io, '\\')
        write(io, '\\')
        escapes -= 1
    end
end
escape_raw_string(str::AbstractString) = sprint(escape_raw_string, str;
                                                sizehint = lastindex(str) + 2)

## multiline strings ##

"""
    indentation(str::AbstractString; tabwidth=8) -> (Int, Bool)

Calculate the width of leading white space. Return the width and a flag to indicate
if the string is empty.

# Examples
```jldoctest
julia> Base.indentation("")
(0, true)

julia> Base.indentation("  a")
(2, false)

julia> Base.indentation("\\ta"; tabwidth=3)
(3, false)
```
"""
function indentation(str::AbstractString; tabwidth=8)
    count = 0
    for ch in str
        if ch == ' '
            count += 1
        elseif ch == '\t'
            count = div(count + tabwidth, tabwidth) * tabwidth
        else
            return count, false
        end
    end
    count, true
end

"""
    unindent(str::AbstractString, indent::Int; tabwidth=8)

Remove leading indentation from string.

See also `indent` from the [`MultilineStrings` package](https://github.com/invenia/MultilineStrings.jl).

# Examples
```jldoctest
julia> Base.unindent("   a\\n   b", 2)
" a\\n b"

julia> Base.unindent("\\ta\\n\\tb", 2, tabwidth=8)
"      a\\n      b"
```
"""
function unindent(str::AbstractString, indent::Int; tabwidth=8)
    indent == 0 && return str
    # Note: this loses the type of the original string
    buf = IOBuffer(sizehint=sizeof(str))
    cutting = true
    col = 0     # current column (0 based)
    for ch in str
        if cutting
            if ch == ' '
                col += 1
            elseif ch == '\t'
                col = div(col + tabwidth, tabwidth) * tabwidth
            elseif ch == '\n'
                # Now we need to output enough indentation
                for i = 1:col-indent
                    print(buf, ' ')
                end
                col = 0
                print(buf, '\n')
            else
                cutting = false
                # Now we need to output enough indentation to get to
                # correct place
                for i = 1:col-indent
                    print(buf, ' ')
                end
                col += 1
                print(buf, ch)
            end
        elseif ch == '\t'       # Handle internal tabs
            upd = div(col + tabwidth, tabwidth) * tabwidth
            # output the number of spaces that would have been seen
            # with original indentation
            for i = 1:(upd-col)
                print(buf, ' ')
            end
            col = upd
        elseif ch == '\n'
            cutting = true
            col = 0
            print(buf, '\n')
        else
            col += 1
            print(buf, ch)
        end
    end
    # If we were still "cutting" when we hit the end of the string,
    # we need to output the right number of spaces for the indentation
    if cutting
        for i = 1:col-indent
            print(buf, ' ')
        end
    end
    String(take!(buf))
end

function String(a::AbstractVector{Char})
    n = 0
    for v in a
        n += ncodeunits(v)
    end
    out = _string_n(n)
    offs = 1
    for v in a
        offs += __unsafe_string!(out, v, offs)
    end
    return out
end

function String(chars::AbstractVector{<:AbstractChar})
    sprint(sizehint=length(chars)) do io
        for c in chars
            print(io, c)
        end
    end
end
L   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/regex.jlzk      # This file is a part of Julia. License is MIT: https://julialang.org/license

## object-oriented Regex interface ##

include("pcre.jl")

const DEFAULT_COMPILER_OPTS = PCRE.UTF | PCRE.MATCH_INVALID_UTF | PCRE.ALT_BSUX | PCRE.UCP
const DEFAULT_MATCH_OPTS = PCRE.NO_UTF_CHECK

"""
    Regex(pattern[, flags]) <: AbstractPattern

A type representing a regular expression. `Regex` objects can be used to match strings
with [`match`](@ref).

`Regex` objects can be created using the [`@r_str`](@ref) string macro. The
`Regex(pattern[, flags])` constructor is usually used if the `pattern` string needs
to be interpolated. See the documentation of the string macro for details on flags.

!!! note
    To escape interpolated variables use `\\Q` and `\\E` (e.g. `Regex("\\\\Q\$x\\\\E")`)
"""
mutable struct Regex <: AbstractPattern
    pattern::String
    compile_options::UInt32
    match_options::UInt32
    regex::Ptr{Cvoid}

    function Regex(pattern::AbstractString, compile_options::Integer,
                   match_options::Integer)
        pattern = String(pattern)
        compile_options = UInt32(compile_options)
        match_options = UInt32(match_options)
        if (compile_options & ~PCRE.COMPILE_MASK) != 0
            throw(ArgumentError("invalid regex compile options: $compile_options"))
        end
        if (match_options & ~PCRE.EXECUTE_MASK) !=0
            throw(ArgumentError("invalid regex match options: $match_options"))
        end
        re = compile(new(pattern, compile_options, match_options, C_NULL))
        finalizer(re) do re
            re.regex == C_NULL || PCRE.free_re(re.regex)
        end
        re
    end
end

function Regex(pattern::AbstractString, flags::AbstractString)
    compile_options = DEFAULT_COMPILER_OPTS
    match_options = DEFAULT_MATCH_OPTS
    for f in flags
        if f == 'a'
            # instruct pcre2 to treat the strings as simple bytes (aka "ASCII"), not char encodings
            compile_options &= ~PCRE.UCP  # user can re-enable with (*UCP)
            compile_options &= ~PCRE.UTF # user can re-enable with (*UTF)
            compile_options &= ~PCRE.MATCH_INVALID_UTF # this would force on UTF
            match_options &= ~PCRE.NO_UTF_CHECK # if the user did force on UTF, we should check it for safety
        else
            compile_options |= f=='i' ? PCRE.CASELESS  :
                               f=='m' ? PCRE.MULTILINE :
                               f=='s' ? PCRE.DOTALL    :
                               f=='x' ? PCRE.EXTENDED  :
                               throw(ArgumentError("unknown regex flag: $f"))
        end
    end
    Regex(pattern, compile_options, match_options)
end
Regex(pattern::AbstractString) = Regex(pattern, DEFAULT_COMPILER_OPTS, DEFAULT_MATCH_OPTS)

function compile(regex::Regex)
    if regex.regex == C_NULL
        if PCRE.PCRE_COMPILE_LOCK === nothing
            regex.regex = PCRE.compile(regex.pattern, regex.compile_options)
            PCRE.jit_compile(regex.regex)
        else
            l = PCRE.PCRE_COMPILE_LOCK::Threads.SpinLock
            lock(l)
            try
                if regex.regex == C_NULL
                    regex.regex = PCRE.compile(regex.pattern, regex.compile_options)
                    PCRE.jit_compile(regex.regex)
                end
            finally
                unlock(l)
            end
        end
    end
    regex
end

"""
    @r_str -> Regex

Construct a regex, such as `r"^[a-z]*\$"`, without interpolation and unescaping (except for
quotation mark `"` which still has to be escaped). The regex also accepts one or more flags,
listed after the ending quote, to change its behaviour:

- `i` enables case-insensitive matching
- `m` treats the `^` and `\$` tokens as matching the start and end of individual lines, as
  opposed to the whole string.
- `s` allows the `.` modifier to match newlines.
- `x` enables "comment mode": whitespace is enabled except when escaped with `\\`, and `#`
  is treated as starting a comment.
- `a` enables ASCII mode (disables `UTF` and `UCP` modes). By default `\\B`, `\\b`, `\\D`,
  `\\d`, `\\S`, `\\s`, `\\W`, `\\w`, etc. match based on Unicode character properties. With
  this option, these sequences only match ASCII characters. This includes `\\u` also, which
  will emit the specified character value directly as a single byte, and not attempt to
  encode it into UTF-8. Importantly, this option allows matching against invalid UTF-8
  strings, by treating both matcher and target as simple bytes (as if they were ISO/IEC
  8859-1 / Latin-1 bytes) instead of as character encodings. In this case, this option is
  often combined with `s`. This option can be further refined by starting the pattern with
  (*UCP) or (*UTF).

See [`Regex`](@ref) if interpolation is needed.

# Examples
```jldoctest
julia> match(r"a+.*b+.*?d\$"ism, "Goodbye,\\nOh, angry,\\nBad world\\n")
RegexMatch("angry,\\nBad world")
```
This regex has the first three flags enabled.
"""
macro r_str(pattern, flags...) Regex(pattern, flags...) end

function show(io::IO, re::Regex)
    imsx = PCRE.CASELESS|PCRE.MULTILINE|PCRE.DOTALL|PCRE.EXTENDED
    ac = PCRE.UTF|PCRE.MATCH_INVALID_UTF|PCRE.UCP
    am = PCRE.NO_UTF_CHECK
    opts = re.compile_options
    mopts = re.match_options
    default = ((opts & ~imsx) | ac) == DEFAULT_COMPILER_OPTS
    if default
       if (opts & ac) == ac
           default = mopts == DEFAULT_MATCH_OPTS
       elseif (opts & ac) == 0
           default = mopts == (DEFAULT_MATCH_OPTS & ~am)
       else
           default = false
       end
   end
    if default
        print(io, "r\"")
        escape_raw_string(io, re.pattern)
        print(io, "\"")
        if (opts & PCRE.CASELESS ) != 0; print(io, "i"); end
        if (opts & PCRE.MULTILINE) != 0; print(io, "m"); end
        if (opts & PCRE.DOTALL   ) != 0; print(io, "s"); end
        if (opts & PCRE.EXTENDED ) != 0; print(io, "x"); end
        if (opts & ac            ) == 0; print(io, "a"); end
    else
        print(io, "Regex(")
        show(io, re.pattern)
        print(io, ", ")
        show(io, opts)
        print(io, ", ")
        show(io, mopts)
        print(io, ")")
    end
end

"""
`AbstractMatch` objects are used to represent information about matches found
in a string using an `AbstractPattern`.
"""
abstract type AbstractMatch end

"""
    RegexMatch <: AbstractMatch

A type representing a single match to a [`Regex`](@ref) found in a string.
Typically created from the [`match`](@ref) function.

The `match` field stores the substring of the entire matched string.
The `captures` field stores the substrings for each capture group, indexed by number.
To index by capture group name, the entire match object should be indexed instead,
as shown in the examples.
The location of the start of the match is stored in the `offset` field.
The `offsets` field stores the locations of the start of each capture group,
with 0 denoting a group that was not captured.

This type can be used as an iterator over the capture groups of the `Regex`,
yielding the substrings captured in each group.
Because of this, the captures of a match can be destructured.
If a group was not captured, `nothing` will be yielded instead of a substring.

Methods that accept a `RegexMatch` object are defined for [`iterate`](@ref),
[`length`](@ref), [`eltype`](@ref), [`keys`](@ref keys(::RegexMatch)), [`haskey`](@ref), and
[`getindex`](@ref), where keys are the the names or numbers of a capture group.
See [`keys`](@ref keys(::RegexMatch)) for more information.

# Examples
```jldoctest
julia> m = match(r"(?<hour>\\d+):(?<minute>\\d+)(am|pm)?", "11:30 in the morning")
RegexMatch("11:30", hour="11", minute="30", 3=nothing)

julia> m.match
"11:30"

julia> m.captures
3-element Vector{Union{Nothing, SubString{String}}}:
 "11"
 "30"
 nothing


julia> m["minute"]
"30"

julia> hr, min, ampm = m; # destructure capture groups by iteration

julia> hr
"11"
```
"""
struct RegexMatch <: AbstractMatch
    match::SubString{String}
    captures::Vector{Union{Nothing,SubString{String}}}
    offset::Int
    offsets::Vector{Int}
    regex::Regex
end

"""
    keys(m::RegexMatch) -> Vector

Return a vector of keys for all capture groups of the underlying regex.
A key is included even if the capture group fails to match.
That is, `idx` will be in the return value even if `m[idx] == nothing`.

Unnamed capture groups will have integer keys corresponding to their index.
Named capture groups will have string keys.

!!! compat "Julia 1.7"
    This method was added in Julia 1.7

# Examples
```jldoctest
julia> keys(match(r"(?<hour>\\d+):(?<minute>\\d+)(am|pm)?", "11:30"))
3-element Vector{Any}:
  "hour"
  "minute"
 3
```
"""
function keys(m::RegexMatch)
    idx_to_capture_name = PCRE.capture_names(m.regex.regex)
    return map(eachindex(m.captures)) do i
        # If the capture group is named, return it's name, else return it's index
        get(idx_to_capture_name, i, i)
    end
end

function show(io::IO, m::RegexMatch)
    print(io, "RegexMatch(")
    show(io, m.match)
    capture_keys = keys(m)
    if !isempty(capture_keys)
        print(io, ", ")
        for (i, capture_name) in enumerate(capture_keys)
            print(io, capture_name, "=")
            show(io, m.captures[i])
            if i < length(m)
                print(io, ", ")
            end
        end
    end
    print(io, ")")
end

# Capture group extraction
getindex(m::RegexMatch, idx::Integer) = m.captures[idx]
function getindex(m::RegexMatch, name::Union{AbstractString,Symbol})
    idx = PCRE.substring_number_from_name(m.regex.regex, name)
    idx <= 0 && error("no capture group named $name found in regex")
    m[idx]
end

haskey(m::RegexMatch, idx::Integer) = idx in eachindex(m.captures)
function haskey(m::RegexMatch, name::Union{AbstractString,Symbol})
    idx = PCRE.substring_number_from_name(m.regex.regex, name)
    return idx > 0
end

iterate(m::RegexMatch, args...) = iterate(m.captures, args...)
length(m::RegexMatch) = length(m.captures)
eltype(m::RegexMatch) = eltype(m.captures)

function occursin(r::Regex, s::AbstractString; offset::Integer=0)
    compile(r)
    return PCRE.exec_r(r.regex, String(s), offset, r.match_options)
end

function occursin(r::Regex, s::SubString{String}; offset::Integer=0)
    compile(r)
    return PCRE.exec_r(r.regex, s, offset, r.match_options)
end

"""
    startswith(s::AbstractString, prefix::Regex)

Return `true` if `s` starts with the regex pattern, `prefix`.

!!! note
    `startswith` does not compile the anchoring into the regular
    expression, but instead passes the anchoring as
    `match_option` to PCRE. If compile time is amortized,
    `occursin(r"^...", s)` is faster than `startswith(s, r"...")`.

See also [`occursin`](@ref) and [`endswith`](@ref).

!!! compat "Julia 1.2"
    This method requires at least Julia 1.2.

# Examples
```jldoctest
julia> startswith("JuliaLang", r"Julia|Romeo")
true
```
"""
function startswith(s::AbstractString, r::Regex)
    compile(r)
    return PCRE.exec_r(r.regex, String(s), 0, r.match_options | PCRE.ANCHORED)
end

function startswith(s::SubString{String}, r::Regex)
    compile(r)
    return PCRE.exec_r(r.regex, s, 0, r.match_options | PCRE.ANCHORED)
end

"""
    endswith(s::AbstractString, suffix::Regex)

Return `true` if `s` ends with the regex pattern, `suffix`.

!!! note
    `endswith` does not compile the anchoring into the regular
    expression, but instead passes the anchoring as
    `match_option` to PCRE. If compile time is amortized,
    `occursin(r"...\$", s)` is faster than `endswith(s, r"...")`.

See also [`occursin`](@ref) and [`startswith`](@ref).

!!! compat "Julia 1.2"
    This method requires at least Julia 1.2.

# Examples
```jldoctest
julia> endswith("JuliaLang", r"Lang|Roberts")
true
```
"""
function endswith(s::AbstractString, r::Regex)
    compile(r)
    return PCRE.exec_r(r.regex, String(s), 0, r.match_options | PCRE.ENDANCHORED)
end

function endswith(s::SubString{String}, r::Regex)
    compile(r)
    return PCRE.exec_r(r.regex, s, 0, r.match_options | PCRE.ENDANCHORED)
end

function chopprefix(s::AbstractString, prefix::Regex)
    m = match(prefix, s, firstindex(s), PCRE.ANCHORED)
    m === nothing && return SubString(s)
    return SubString(s, ncodeunits(m.match) + 1)
end

function chopsuffix(s::AbstractString, suffix::Regex)
    m = match(suffix, s, firstindex(s), PCRE.ENDANCHORED)
    m === nothing && return SubString(s)
    isempty(m.match) && return SubString(s)
    return SubString(s, firstindex(s), prevind(s, m.offset))
end


"""
    match(r::Regex, s::AbstractString[, idx::Integer[, addopts]])

Search for the first match of the regular expression `r` in `s` and return a [`RegexMatch`](@ref)
object containing the match, or nothing if the match failed. The matching substring can be
retrieved by accessing `m.match` and the captured sequences can be retrieved by accessing
`m.captures` The optional `idx` argument specifies an index at which to start the search.

# Examples
```jldoctest
julia> rx = r"a(.)a"
r"a(.)a"

julia> m = match(rx, "cabac")
RegexMatch("aba", 1="b")

julia> m.captures
1-element Vector{Union{Nothing, SubString{String}}}:
 "b"

julia> m.match
"aba"

julia> match(rx, "cabac", 3) === nothing
true
```
"""
function match end

function match(re::Regex, str::Union{SubString{String}, String}, idx::Integer,
               add_opts::UInt32=UInt32(0))
    compile(re)
    opts = re.match_options | add_opts
    matched, data = PCRE.exec_r_data(re.regex, str, idx-1, opts)
    if !matched
        PCRE.free_match_data(data)
        return nothing
    end
    n = div(PCRE.ovec_length(data), 2) - 1
    p = PCRE.ovec_ptr(data)
    mat = SubString(str, unsafe_load(p, 1)+1, prevind(str, unsafe_load(p, 2)+1))
    cap = Union{Nothing,SubString{String}}[unsafe_load(p,2i+1) == PCRE.UNSET ? nothing :
                                        SubString(str, unsafe_load(p,2i+1)+1,
                                                  prevind(str, unsafe_load(p,2i+2)+1)) for i=1:n]
    off = Int[ unsafe_load(p,2i+1)+1 for i=1:n ]
    result = RegexMatch(mat, cap, unsafe_load(p,1)+1, off, re)
    PCRE.free_match_data(data)
    return result
end

match(r::Regex, s::AbstractString) = match(r, s, firstindex(s))
match(r::Regex, s::AbstractString, i::Integer) = throw(ArgumentError(
    "regex matching is only available for the String type; use String(s) to convert"
))

findnext(re::Regex, str::Union{String,SubString}, idx::Integer) = _findnext_re(re, str, idx, C_NULL)

# TODO: return only start index and update deprecation
function _findnext_re(re::Regex, str::Union{String,SubString}, idx::Integer, match_data::Ptr{Cvoid})
    if idx > nextind(str,lastindex(str))
        throw(BoundsError())
    end
    opts = re.match_options
    compile(re)
    alloc = match_data == C_NULL
    if alloc
        matched, data = PCRE.exec_r_data(re.regex, str, idx-1, opts)
    else
        matched = PCRE.exec(re.regex, str, idx-1, opts, match_data)
        data = match_data
    end
    if matched
        p = PCRE.ovec_ptr(data)
        ans = (Int(unsafe_load(p,1))+1):prevind(str,Int(unsafe_load(p,2))+1)
    else
        ans = nothing
    end
    alloc && PCRE.free_match_data(data)
    return ans
end
findnext(r::Regex, s::AbstractString, idx::Integer) = throw(ArgumentError(
    "regex search is only available for the String type; use String(s) to convert"
))
findfirst(r::Regex, s::AbstractString) = findnext(r,s,firstindex(s))


"""
    findall(c::AbstractChar, s::AbstractString)

Return a vector `I` of the indices of `s` where `s[i] == c`. If there are no such
elements in `s`, return an empty array.

# Examples
```jldoctest
julia> findall('a', "batman")
2-element Vector{Int64}:
 2
 5
```

!!! compat "Julia 1.7"
     This method requires at least Julia 1.7.
"""
findall(c::AbstractChar, s::AbstractString) = findall(isequal(c),s)


"""
    count(
        pattern::Union{AbstractChar,AbstractString,AbstractPattern},
        string::AbstractString;
        overlap::Bool = false,
    )

Return the number of matches for `pattern` in `string`. This is equivalent to
calling `length(findall(pattern, string))` but more efficient.

If `overlap=true`, the matching sequences are allowed to overlap indices in the
original string, otherwise they must be from disjoint character ranges.

!!! compat "Julia 1.3"
     This method requires at least Julia 1.3.

!!! compat "Julia 1.7"
      Using a character as the pattern requires at least Julia 1.7.

# Examples
```jldoctest
julia> count('a', "JuliaLang")
2

julia> count(r"a(.)a", "cabacabac", overlap=true)
3

julia> count(r"a(.)a", "cabacabac")
2
```
"""
function count(t::Union{AbstractChar,AbstractString,AbstractPattern}, s::AbstractString; overlap::Bool=false)
    n = 0
    i, e = firstindex(s), lastindex(s)
    while true
        r = findnext(t, s, i)
        isnothing(r) && break
        n += 1
        j = overlap || isempty(r) ? first(r) : last(r)
        j > e && break
        @inbounds i = nextind(s, j)
    end
    return n
end

"""
    SubstitutionString(substr) <: AbstractString

Stores the given string `substr` as a `SubstitutionString`, for use in regular expression
substitutions. Most commonly constructed using the [`@s_str`](@ref) macro.

# Examples
```jldoctest
julia> SubstitutionString("Hello \\\\g<name>, it's \\\\1")
s"Hello \\g<name>, it's \\1"

julia> subst = s"Hello \\g<name>, it's \\1"
s"Hello \\g<name>, it's \\1"

julia> typeof(subst)
SubstitutionString{String}
```
"""
struct SubstitutionString{T<:AbstractString} <: AbstractString
    string::T
end

ncodeunits(s::SubstitutionString) = ncodeunits(s.string)::Int
codeunit(s::SubstitutionString) = codeunit(s.string)::CodeunitType
codeunit(s::SubstitutionString, i::Integer) = codeunit(s.string, i)::Union{UInt8, UInt16, UInt32}
isvalid(s::SubstitutionString, i::Integer) = isvalid(s.string, i)::Bool
iterate(s::SubstitutionString, i::Integer...) = iterate(s.string, i...)::Union{Nothing,Tuple{AbstractChar,Int}}

function show(io::IO, s::SubstitutionString)
    print(io, "s\"")
    escape_raw_string(io, s.string)
    print(io, "\"")
end

"""
    @s_str -> SubstitutionString

Construct a substitution string, used for regular expression substitutions.  Within the
string, sequences of the form `\\N` refer to the Nth capture group in the regex, and
`\\g<groupname>` refers to a named capture group with name `groupname`.

# Examples
```jldoctest
julia> msg = "#Hello# from Julia";

julia> replace(msg, r"#(.+)# from (?<from>\\w+)" => s"FROM: \\g<from>; MESSAGE: \\1")
"FROM: Julia; MESSAGE: Hello"
```
"""
macro s_str(string) SubstitutionString(string) end

# replacement

struct RegexAndMatchData
    re::Regex
    match_data::Ptr{Cvoid}
    RegexAndMatchData(re::Regex) = (compile(re); new(re, PCRE.create_match_data(re.regex)))
end

findnext(pat::RegexAndMatchData, str, i) = _findnext_re(pat.re, str, i, pat.match_data)

_pat_replacer(r::Regex) = RegexAndMatchData(r)

_free_pat_replacer(r::RegexAndMatchData) = PCRE.free_match_data(r.match_data)

replace_err(repl) = error("Bad replacement string: $repl")

function _write_capture(io::IO, group::Int, str, r, re::RegexAndMatchData)
    len = PCRE.substring_length_bynumber(re.match_data, group)
    # in the case of an optional group that doesn't match, len == 0
    len == 0 && return
    ensureroom(io, len+1)
    PCRE.substring_copy_bynumber(re.match_data, group,
        pointer(io.data, io.ptr), len+1)
    io.ptr += len
    io.size = max(io.size, io.ptr - 1)
    nothing
end
function _write_capture(io::IO, group::Int, str, r, re)
    group == 0 || replace_err("pattern is not a Regex")
    return print(io, SubString(str, r))
end


const SUB_CHAR = '\\'
const GROUP_CHAR = 'g'
const KEEP_ESC = [SUB_CHAR, GROUP_CHAR, '0':'9'...]

function _replace(io, repl_s::SubstitutionString, str, r, re)
    LBRACKET = '<'
    RBRACKET = '>'
    repl = unescape_string(repl_s.string, KEEP_ESC)
    i = firstindex(repl)
    e = lastindex(repl)
    while i <= e
        if repl[i] == SUB_CHAR
            next_i = nextind(repl, i)
            next_i > e && replace_err(repl)
            if repl[next_i] == SUB_CHAR
                write(io, SUB_CHAR)
                i = nextind(repl, next_i)
            elseif isdigit(repl[next_i])
                group = parse(Int, repl[next_i])
                i = nextind(repl, next_i)
                while i <= e
                    if isdigit(repl[i])
                        group = 10group + parse(Int, repl[i])
                        i = nextind(repl, i)
                    else
                        break
                    end
                end
                _write_capture(io, group, str, r, re)
            elseif repl[next_i] == GROUP_CHAR
                i = nextind(repl, next_i)
                if i > e || repl[i] != LBRACKET
                    replace_err(repl)
                end
                i = nextind(repl, i)
                i > e && replace_err(repl)
                groupstart = i
                while repl[i] != RBRACKET
                    i = nextind(repl, i)
                    i > e && replace_err(repl)
                end
                groupname = SubString(repl, groupstart, prevind(repl, i))
                if all(isdigit, groupname)
                    group = parse(Int, groupname)
                elseif re isa RegexAndMatchData
                    group = PCRE.substring_number_from_name(re.re.regex, groupname)
                    group < 0 && replace_err("Group $groupname not found in regex $(re.re)")
                else
                    group = -1
                end
                _write_capture(io, group, str, r, re)
                i = nextind(repl, i)
            else
                replace_err(repl)
            end
        else
            write(io, repl[i])
            i = nextind(repl, i)
        end
    end
end

struct RegexMatchIterator
    regex::Regex
    string::String
    overlap::Bool

    function RegexMatchIterator(regex::Regex, string::AbstractString, ovr::Bool=false)
        new(regex, string, ovr)
    end
end
compile(itr::RegexMatchIterator) = (compile(itr.regex); itr)
eltype(::Type{RegexMatchIterator}) = RegexMatch
IteratorSize(::Type{RegexMatchIterator}) = SizeUnknown()

function iterate(itr::RegexMatchIterator, (offset,prevempty)=(1,false))
    opts_nonempty = UInt32(PCRE.ANCHORED | PCRE.NOTEMPTY_ATSTART)
    while true
        mat = match(itr.regex, itr.string, offset,
                    prevempty ? opts_nonempty : UInt32(0))

        if mat === nothing
            if prevempty && offset <= sizeof(itr.string)
                offset = nextind(itr.string, offset)
                prevempty = false
                continue
            else
                break
            end
        else
            if itr.overlap
                if !isempty(mat.match)
                    offset = nextind(itr.string, mat.offset)
                else
                    offset = mat.offset
                end
            else
                offset = mat.offset + ncodeunits(mat.match)
            end
            return (mat, (offset, isempty(mat.match)))
        end
    end
    nothing
end

"""
    eachmatch(r::Regex, s::AbstractString; overlap::Bool=false)

Search for all matches of the regular expression `r` in `s` and return an iterator over the
matches. If `overlap` is `true`, the matching sequences are allowed to overlap indices in the
original string, otherwise they must be from distinct character ranges.

# Examples
```jldoctest
julia> rx = r"a.a"
r"a.a"

julia> m = eachmatch(rx, "a1a2a3a")
Base.RegexMatchIterator(r"a.a", "a1a2a3a", false)

julia> collect(m)
2-element Vector{RegexMatch}:
 RegexMatch("a1a")
 RegexMatch("a3a")

julia> collect(eachmatch(rx, "a1a2a3a", overlap = true))
3-element Vector{RegexMatch}:
 RegexMatch("a1a")
 RegexMatch("a2a")
 RegexMatch("a3a")
```
"""
eachmatch(re::Regex, str::AbstractString; overlap = false) =
    RegexMatchIterator(re, str, overlap)

## comparison ##

function ==(a::Regex, b::Regex)
    a.pattern == b.pattern && a.compile_options == b.compile_options && a.match_options == b.match_options
end

## hash ##
const hashre_seed = UInt === UInt64 ? 0x67e195eb8555e72d : 0xe32373e4
function hash(r::Regex, h::UInt)
    h += hashre_seed
    h = hash(r.pattern, h)
    h = hash(r.compile_options, h)
    h = hash(r.match_options, h)
end

## String operations ##

"""
    *(s::Regex, t::Union{Regex,AbstractString,AbstractChar}) -> Regex
    *(s::Union{Regex,AbstractString,AbstractChar}, t::Regex) -> Regex

Concatenate regexes, strings and/or characters, producing a [`Regex`](@ref).
String and character arguments must be matched exactly in the resulting regex,
meaning that the contained characters are devoid of any special meaning
(they are quoted with "\\Q" and "\\E").

!!! compat "Julia 1.3"
    This method requires at least Julia 1.3.

# Examples
```jldoctest
julia> match(r"Hello|Good bye" * ' ' * "world", "Hello world")
RegexMatch("Hello world")

julia> r = r"a|b" * "c|d"
r"(?:a|b)\\Qc|d\\E"

julia> match(r, "ac") == nothing
true

julia> match(r, "ac|d")
RegexMatch("ac|d")
```
"""
function *(r1::Union{Regex,AbstractString,AbstractChar}, rs::Union{Regex,AbstractString,AbstractChar}...)
    mask = PCRE.CASELESS | PCRE.MULTILINE | PCRE.DOTALL | PCRE.EXTENDED # imsx
    match_opts   = nothing # all args must agree on this
    compile_opts = nothing # all args must agree on this
    shared = mask
    for r in (r1, rs...)
        r isa Regex || continue
        if match_opts === nothing
            match_opts = r.match_options
            compile_opts = r.compile_options & ~mask
        else
            r.match_options == match_opts &&
                r.compile_options & ~mask == compile_opts ||
                throw(ArgumentError("cannot multiply regexes: incompatible options"))
        end
        shared &= r.compile_options
    end
    unshared = mask & ~shared
    Regex(string(wrap_string(r1, unshared), wrap_string.(rs, Ref(unshared))...), compile_opts | shared, match_opts)
end

*(r::Regex) = r # avoids wrapping r in a useless subpattern

wrap_string(r::Regex, unshared::UInt32) = string("(?", regex_opts_str(r.compile_options & unshared), ':', r.pattern, ')')
# if s contains raw"\E", split '\' and 'E' within two distinct \Q...\E groups:
wrap_string(s::AbstractString, ::UInt32) =  string("\\Q", replace(s, raw"\E" => raw"\\E\QE"), "\\E")
wrap_string(s::AbstractChar, ::UInt32) = string("\\Q", s, "\\E")

regex_opts_str(opts) = (isassigned(_regex_opts_str) ? _regex_opts_str[] : init_regex())[opts]

# UInt32 to String mapping for some compile options
const _regex_opts_str = Ref{ImmutableDict{UInt32,String}}()

@noinline init_regex() = _regex_opts_str[] = foldl(0:15, init=ImmutableDict{UInt32,String}()) do d, o
    opt = UInt32(0)
    str = ""
    if o & 1 != 0
        opt |= PCRE.CASELESS
        str *= 'i'
    end
    if o & 2 != 0
        opt |= PCRE.MULTILINE
        str *= 'm'
    end
    if o & 4 != 0
        opt |= PCRE.DOTALL
        str *= 's'
    end
    if o & 8 != 0
        opt |= PCRE.EXTENDED
        str *= 'x'
    end
    ImmutableDict(d, opt => str)
end


"""
    ^(s::Regex, n::Integer) -> Regex

Repeat a regex `n` times.

!!! compat "Julia 1.3"
    This method requires at least Julia 1.3.

# Examples
```jldoctest
julia> r"Test "^2
r"(?:Test ){2}"

julia> match(r"Test "^2, "Test Test ")
RegexMatch("Test Test ")
```
"""
^(r::Regex, i::Integer) = Regex(string("(?:", r.pattern, "){$i}"), r.compile_options, r.match_options)
K   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/pcre.jl�"      # This file is a part of Julia. License is MIT: https://julialang.org/license

## low-level pcre2 interface ##

module PCRE

import ..RefValue

# include($BUILDROOT/base/pcre_h.jl)
include(string(length(Core.ARGS) >= 2 ? Core.ARGS[2] : "", "pcre_h.jl"))

const PCRE_LIB = "libpcre2-8"

function create_match_context()
    JIT_STACK_START_SIZE = 32768
    JIT_STACK_MAX_SIZE = 1048576
    jit_stack = ccall((:pcre2_jit_stack_create_8, PCRE_LIB), Ptr{Cvoid},
                      (Csize_t, Csize_t, Ptr{Cvoid}),
                      JIT_STACK_START_SIZE, JIT_STACK_MAX_SIZE, C_NULL)
    ctx = ccall((:pcre2_match_context_create_8, PCRE_LIB),
                Ptr{Cvoid}, (Ptr{Cvoid},), C_NULL)
    ccall((:pcre2_jit_stack_assign_8, PCRE_LIB), Cvoid,
          (Ptr{Cvoid}, Ptr{Cvoid}, Ptr{Cvoid}), ctx, C_NULL, jit_stack)
    return ctx
end

THREAD_MATCH_CONTEXTS::Vector{Ptr{Cvoid}} = [C_NULL]

PCRE_COMPILE_LOCK = nothing

_tid() = Int(ccall(:jl_threadid, Int16, ())) + 1
_mth() = Int(Core.Intrinsics.atomic_pointerref(cglobal(:jl_n_threads, Cint), :acquire))

function get_local_match_context()
    tid = _tid()
    ctxs = THREAD_MATCH_CONTEXTS
    if length(ctxs) < tid
        # slow path to allocate it
        l = PCRE_COMPILE_LOCK::Threads.SpinLock
        lock(l)
        try
            ctxs = THREAD_MATCH_CONTEXTS
            if length(ctxs) < tid
                global THREAD_MATCH_CONTEXTS = ctxs = copyto!(fill(C_NULL, length(ctxs) + _mth()), ctxs)
            end
        finally
            unlock(l)
        end
    end
    ctx = @inbounds ctxs[tid]
    if ctx == C_NULL
        # slow path to allocate it
        ctx = create_match_context()
        THREAD_MATCH_CONTEXTS[tid] = ctx
    end
    return ctx
end

# supported options for different use cases

# arguments to pcre2_compile
const COMPILE_MASK      =
      ALT_BSUX          |
      ALT_CIRCUMFLEX    |
      ALT_VERBNAMES     |
      ANCHORED          |
      # AUTO_CALLOUT    |
      CASELESS          |
      DOLLAR_ENDONLY    |
      DOTALL            |
      # DUPNAMES        |
      ENDANCHORED       |
      EXTENDED          |
      EXTENDED_MORE     |
      FIRSTLINE         |
      LITERAL           |
      MATCH_INVALID_UTF |
      MATCH_UNSET_BACKREF |
      MULTILINE         |
      NEVER_BACKSLASH_C |
      NEVER_UCP         |
      NEVER_UTF         |
      NO_AUTO_CAPTURE   |
      NO_AUTO_POSSESS   |
      NO_DOTSTAR_ANCHOR |
      NO_START_OPTIMIZE |
      NO_UTF_CHECK      |
      UCP               |
      UNGREEDY          |
      USE_OFFSET_LIMIT  |
      UTF

# arguments to pcre2_set_newline
const COMPILE_NEWLINE_MASK = (
      NEWLINE_CR,
      NEWLINE_LF,
      NEWLINE_CRLF,
      NEWLINE_ANY,
      NEWLINE_ANYCRLF,
      NEWLINE_NUL)

# arguments to pcre2_set_compile_extra_options
const COMPILE_EXTRA_MASK            =
      EXTRA_ALLOW_SURROGATE_ESCAPES |
      EXTRA_ALT_BSUX                |
      EXTRA_BAD_ESCAPE_IS_LITERAL   |
      EXTRA_ESCAPED_CR_IS_LF        |
      EXTRA_MATCH_LINE              |
      EXTRA_MATCH_WORD

# arguments to match
const EXECUTE_MASK      =
      # ANCHORED        |
      # COPY_MATCHED_SUBJECT |
      # ENDANCHORED     |
      NOTBOL            |
      NOTEMPTY          |
      NOTEMPTY_ATSTART  |
      NOTEOL            |
      # NO_JIT          |
      NO_START_OPTIMIZE |
      NO_UTF_CHECK      |
      PARTIAL_HARD      |
      PARTIAL_SOFT


const UNSET = ~Csize_t(0)  # Indicates that an output vector element is unset

function info(regex::Ptr{Cvoid}, what::Integer, ::Type{T}) where T
    buf = RefValue{T}()
    ret = ccall((:pcre2_pattern_info_8, PCRE_LIB), Cint,
                (Ptr{Cvoid}, UInt32, Ptr{Cvoid}),
                regex, what, buf)
    if ret != 0
        error(ret == ERROR_NULL      ? "PCRE error: NULL regex object" :
              ret == ERROR_BADMAGIC  ? "PCRE error: invalid regex object" :
              ret == ERROR_BADOPTION ? "PCRE error: invalid option flags" :
                                       "PCRE error: unknown error ($ret)")
    end
    return buf[]
end

function ovec_length(match_data)
    n = ccall((:pcre2_get_ovector_count_8, PCRE_LIB), UInt32,
              (Ptr{Cvoid},), match_data)
    return 2Int(n)
end

function ovec_ptr(match_data)
    ptr = ccall((:pcre2_get_ovector_pointer_8, PCRE_LIB), Ptr{Csize_t},
                (Ptr{Cvoid},), match_data)
    return ptr
end

function compile(pattern::AbstractString, options::Integer)
    if !(pattern isa Union{String,SubString{String}})
        pattern = String(pattern)
    end
    errno = RefValue{Cint}(0)
    erroff = RefValue{Csize_t}(0)
    re_ptr = ccall((:pcre2_compile_8, PCRE_LIB), Ptr{Cvoid},
                   (Ptr{UInt8}, Csize_t, UInt32, Ref{Cint}, Ref{Csize_t}, Ptr{Cvoid}),
                   pattern, ncodeunits(pattern), options, errno, erroff, C_NULL)
    if re_ptr == C_NULL
        error("PCRE compilation error: $(err_message(errno[])) at offset $(erroff[])")
    end
    return re_ptr
end

function jit_compile(regex::Ptr{Cvoid})
    errno = ccall((:pcre2_jit_compile_8, PCRE_LIB), Cint,
                  (Ptr{Cvoid}, UInt32), regex, JIT_COMPLETE)
    errno == 0 && return true
    errno == ERROR_JIT_BADOPTION && return false
    error("PCRE JIT error: $(err_message(errno))")
end

free_match_data(match_data) =
    ccall((:pcre2_match_data_free_8, PCRE_LIB), Cvoid, (Ptr{Cvoid},), match_data)

free_re(re) =
    ccall((:pcre2_code_free_8, PCRE_LIB), Cvoid, (Ptr{Cvoid},), re)

free_jit_stack(stack) =
    ccall((:pcre2_jit_stack_free_8, PCRE_LIB), Cvoid, (Ptr{Cvoid},), stack)

free_match_context(context) =
    ccall((:pcre2_match_context_free_8, PCRE_LIB), Cvoid, (Ptr{Cvoid},), context)

function err_message(errno::Integer)
    buffer = Vector{UInt8}(undef, 1024)
    ret = ccall((:pcre2_get_error_message_8, PCRE_LIB), Cint,
                (Cint, Ptr{UInt8}, Csize_t), errno, buffer, length(buffer))
    ret == ERROR_BADDATA && error("PCRE error: invalid errno ($errno)")
    # TODO: seems like there should be a better way to get this string
    return GC.@preserve buffer unsafe_string(pointer(buffer))
end

function exec(re, subject, offset, options, match_data)
    if !(subject isa Union{String,SubString{String}})
        subject = String(subject)
    end
    rc = ccall((:pcre2_match_8, PCRE_LIB), Cint,
               (Ptr{Cvoid}, Ptr{UInt8}, Csize_t, Csize_t, UInt32, Ptr{Cvoid}, Ptr{Cvoid}),
               re, subject, ncodeunits(subject), offset, options, match_data, get_local_match_context())
    # rc == -1 means no match, -2 means partial match.
    rc < -2 && error("PCRE.exec error: $(err_message(rc))")
    return rc >= 0
end

function exec_r(re, subject, offset, options)
    match_data = create_match_data(re)
    ans = exec(re, subject, offset, options, match_data)
    free_match_data(match_data)
    return ans
end

function exec_r_data(re, subject, offset, options)
    match_data = create_match_data(re)
    ans = exec(re, subject, offset, options, match_data)
    return ans, match_data
end

function create_match_data(re)
    p = ccall((:pcre2_match_data_create_from_pattern_8, PCRE_LIB),
              Ptr{Cvoid}, (Ptr{Cvoid}, Ptr{Cvoid}), re, C_NULL)
    p == C_NULL && error("PCRE error: could not allocate memory")
    return p
end

function substring_number_from_name(re, name)
    n = ccall((:pcre2_substring_number_from_name_8, PCRE_LIB), Cint,
               (Ptr{Cvoid}, Cstring), re, name)
    return Int(n)
end

function substring_length_bynumber(match_data, number)
    s = RefValue{Csize_t}()
    rc = ccall((:pcre2_substring_length_bynumber_8, PCRE_LIB), Cint,
               (Ptr{Cvoid}, Cint, Ref{Csize_t}), match_data, number, s)
    if rc < 0
        rc == ERROR_UNSET && return 0
        error("PCRE error: $(err_message(rc))")
    end
    return Int(s[])
end

function substring_copy_bynumber(match_data, number, buf, buf_size)
    s = RefValue{Csize_t}(buf_size)
    rc = ccall((:pcre2_substring_copy_bynumber_8, PCRE_LIB), Cint,
               (Ptr{Cvoid}, UInt32, Ptr{UInt8}, Ref{Csize_t}),
               match_data, number, buf, s)
    rc < 0 && error("PCRE error: $(err_message(rc))")
    return Int(s[])
end

function capture_names(re)
    name_count = info(re, INFO_NAMECOUNT, UInt32)
    name_entry_size = info(re, INFO_NAMEENTRYSIZE, UInt32)
    nametable_ptr = info(re, INFO_NAMETABLE, Ptr{UInt8})
    names = Dict{Int,String}()
    for i = 1:name_count
        offset = (i-1)*name_entry_size + 1
        # The capture group index corresponding to name 'i' is stored as a
        # big-endian 16-bit value.
        high_byte = UInt16(unsafe_load(nametable_ptr, offset))
        low_byte = UInt16(unsafe_load(nametable_ptr, offset+1))
        idx = (high_byte << 8) | low_byte
        # The capture group name is a null-terminated string located directly
        # after the index.
        names[idx] = unsafe_string(nametable_ptr+offset+1)
    end
    return names
end

end # module
O   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/./pcre_h.jl/      const ALLOW_EMPTY_CLASS = UInt32(0x00000001)
const ALT_BSUX = UInt32(0x00000002)
const ALT_CIRCUMFLEX = UInt32(0x00200000)
const ALT_VERBNAMES = UInt32(0x00400000)
const ANCHORED = UInt32(0x80000000)
const AUTO_CALLOUT = UInt32(0x00000004)
const BSR_ANYCRLF = UInt32(2)
const BSR_UNICODE = UInt32(1)
const CALLOUT_BACKTRACK = UInt32(0x00000002)
const CALLOUT_STARTMATCH = UInt32(0x00000001)
const CASELESS = UInt32(0x00000008)
const CODE_UNIT_WIDTH = UInt32(8)
const CONFIG_BSR = UInt32(0)
const CONFIG_COMPILED_WIDTHS = UInt32(14)
const CONFIG_DEPTHLIMIT = UInt32(7)
const CONFIG_HEAPLIMIT = UInt32(12)
const CONFIG_JIT = UInt32(1)
const CONFIG_JITTARGET = UInt32(2)
const CONFIG_LINKSIZE = UInt32(3)
const CONFIG_MATCHLIMIT = UInt32(4)
const CONFIG_NEVER_BACKSLASH_C = UInt32(13)
const CONFIG_NEWLINE = UInt32(5)
const CONFIG_PARENSLIMIT = UInt32(6)
const CONFIG_RECURSIONLIMIT = UInt32(7)
const CONFIG_STACKRECURSE = UInt32(8)
const CONFIG_TABLES_LENGTH = UInt32(15)
const CONFIG_UNICODE = UInt32(9)
const CONFIG_UNICODE_VERSION = UInt32(10)
const CONFIG_VERSION = UInt32(11)
const CONVERT_GLOB = UInt32(0x00000010)
const CONVERT_GLOB_NO_STARSTAR = UInt32(0x00000050)
const CONVERT_GLOB_NO_WILD_SEPARATOR = UInt32(0x00000030)
const CONVERT_NO_UTF_CHECK = UInt32(0x00000002)
const CONVERT_POSIX_BASIC = UInt32(0x00000004)
const CONVERT_POSIX_EXTENDED = UInt32(0x00000008)
const CONVERT_UTF = UInt32(0x00000001)
const COPY_MATCHED_SUBJECT = UInt32(0x00004000)
const DFA_RESTART = UInt32(0x00000040)
const DFA_SHORTEST = UInt32(0x00000080)
const DOLLAR_ENDONLY = UInt32(0x00000010)
const DOTALL = UInt32(0x00000020)
const DUPNAMES = UInt32(0x00000040)
const ENDANCHORED = UInt32(0x20000000)
const ERROR_ALPHA_ASSERTION_UNKNOWN = Cint(195)
const ERROR_BACKSLASH_C_CALLER_DISABLED = Cint(183)
const ERROR_BACKSLASH_C_LIBRARY_DISABLED = Cint(185)
const ERROR_BACKSLASH_C_SYNTAX = Cint(168)
const ERROR_BACKSLASH_G_SYNTAX = Cint(157)
const ERROR_BACKSLASH_K_IN_LOOKAROUND = Cint(199)
const ERROR_BACKSLASH_K_SYNTAX = Cint(169)
const ERROR_BACKSLASH_N_IN_CLASS = Cint(171)
const ERROR_BACKSLASH_O_MISSING_BRACE = Cint(155)
const ERROR_BACKSLASH_U_CODE_POINT_TOO_BIG = Cint(177)
const ERROR_BADDATA = Cint((-29))
const ERROR_BADMAGIC = Cint((-31))
const ERROR_BADMODE = Cint((-32))
const ERROR_BADOFFSET = Cint((-33))
const ERROR_BADOFFSETLIMIT = Cint((-56))
const ERROR_BADOPTION = Cint((-34))
const ERROR_BADREPESCAPE = Cint((-57))
const ERROR_BADREPLACEMENT = Cint((-35))
const ERROR_BADSERIALIZEDDATA = Cint((-62))
const ERROR_BADSUBSPATTERN = Cint((-60))
const ERROR_BADSUBSTITUTION = Cint((-59))
const ERROR_BADUTFOFFSET = Cint((-36))
const ERROR_BAD_LITERAL_OPTIONS = Cint(192)
const ERROR_BAD_OPTIONS = Cint(117)
const ERROR_BAD_RELATIVE_REFERENCE = Cint(129)
const ERROR_BAD_SUBPATTERN_REFERENCE = Cint(115)
const ERROR_CALLOUT = Cint((-37))
const ERROR_CALLOUT_BAD_STRING_DELIMITER = Cint(182)
const ERROR_CALLOUT_NO_STRING_DELIMITER = Cint(181)
const ERROR_CALLOUT_NUMBER_TOO_BIG = Cint(138)
const ERROR_CALLOUT_STRING_TOO_LONG = Cint(172)
const ERROR_CLASS_INVALID_RANGE = Cint(150)
const ERROR_CLASS_RANGE_ORDER = Cint(108)
const ERROR_CODE_POINT_TOO_BIG = Cint(134)
const ERROR_CONDITION_ASSERTION_EXPECTED = Cint(128)
const ERROR_CONDITION_ATOMIC_ASSERTION_EXPECTED = Cint(198)
const ERROR_CONVERT_SYNTAX = Cint((-64))
const ERROR_DEFINE_TOO_MANY_BRANCHES = Cint(154)
const ERROR_DEPTHLIMIT = Cint((-53))
const ERROR_DFA_BADRESTART = Cint((-38))
const ERROR_DFA_RECURSE = Cint((-39))
const ERROR_DFA_UCOND = Cint((-40))
const ERROR_DFA_UFUNC = Cint((-41))
const ERROR_DFA_UINVALID_UTF = Cint((-66))
const ERROR_DFA_UITEM = Cint((-42))
const ERROR_DFA_WSSIZE = Cint((-43))
const ERROR_DUPLICATE_SUBPATTERN_NAME = Cint(143)
const ERROR_END_BACKSLASH = Cint(101)
const ERROR_END_BACKSLASH_C = Cint(102)
const ERROR_ESCAPE_INVALID_IN_CLASS = Cint(107)
const ERROR_ESCAPE_INVALID_IN_VERB = Cint(140)
const ERROR_HEAPLIMIT = Cint((-63))
const ERROR_HEAP_FAILED = Cint(121)
const ERROR_INTERNAL = Cint((-44))
const ERROR_INTERNAL_BAD_CODE = Cint(189)
const ERROR_INTERNAL_BAD_CODE_AUTO_POSSESS = Cint(180)
const ERROR_INTERNAL_BAD_CODE_IN_SKIP = Cint(190)
const ERROR_INTERNAL_BAD_CODE_LOOKBEHINDS = Cint(170)
const ERROR_INTERNAL_CODE_OVERFLOW = Cint(123)
const ERROR_INTERNAL_DUPMATCH = Cint((-65))
const ERROR_INTERNAL_MISSING_SUBPATTERN = Cint(153)
const ERROR_INTERNAL_OVERRAN_WORKSPACE = Cint(152)
const ERROR_INTERNAL_PARSED_OVERFLOW = Cint(163)
const ERROR_INTERNAL_STUDY_ERROR = Cint(131)
const ERROR_INTERNAL_UNEXPECTED_REPEAT = Cint(110)
const ERROR_INTERNAL_UNKNOWN_NEWLINE = Cint(156)
const ERROR_INVALID_AFTER_PARENS_QUERY = Cint(111)
const ERROR_INVALID_HEXADECIMAL = Cint(167)
const ERROR_INVALID_HYPHEN_IN_OPTIONS = Cint(194)
const ERROR_INVALID_OCTAL = Cint(164)
const ERROR_INVALID_SUBPATTERN_NAME = Cint(144)
const ERROR_JIT_BADOPTION = Cint((-45))
const ERROR_JIT_STACKLIMIT = Cint((-46))
const ERROR_LOOKBEHIND_INVALID_BACKSLASH_C = Cint(136)
const ERROR_LOOKBEHIND_NOT_FIXED_LENGTH = Cint(125)
const ERROR_LOOKBEHIND_TOO_COMPLICATED = Cint(135)
const ERROR_LOOKBEHIND_TOO_LONG = Cint(187)
const ERROR_MALFORMED_UNICODE_PROPERTY = Cint(146)
const ERROR_MARK_MISSING_ARGUMENT = Cint(166)
const ERROR_MATCHLIMIT = Cint((-47))
const ERROR_MISSING_CALLOUT_CLOSING = Cint(139)
const ERROR_MISSING_CLOSING_PARENTHESIS = Cint(114)
const ERROR_MISSING_COMMENT_CLOSING = Cint(118)
const ERROR_MISSING_CONDITION_CLOSING = Cint(124)
const ERROR_MISSING_NAME_TERMINATOR = Cint(142)
const ERROR_MISSING_OCTAL_OR_HEX_DIGITS = Cint(178)
const ERROR_MISSING_SQUARE_BRACKET = Cint(106)
const ERROR_MIXEDTABLES = Cint((-30))
const ERROR_NOMATCH = Cint((-1))
const ERROR_NOMEMORY = Cint((-48))
const ERROR_NOSUBSTRING = Cint((-49))
const ERROR_NOUNIQUESUBSTRING = Cint((-50))
const ERROR_NO_SURROGATES_IN_UTF16 = Cint(191)
const ERROR_NULL = Cint((-51))
const ERROR_NULL_PATTERN = Cint(116)
const ERROR_OCTAL_BYTE_TOO_BIG = Cint(151)
const ERROR_PARENS_QUERY_R_MISSING_CLOSING = Cint(158)
const ERROR_PARENTHESES_NEST_TOO_DEEP = Cint(119)
const ERROR_PARENTHESES_STACK_CHECK = Cint(133)
const ERROR_PARTIAL = Cint((-2))
const ERROR_PATTERN_STRING_TOO_LONG = Cint(188)
const ERROR_PATTERN_TOO_COMPLICATED = Cint(186)
const ERROR_PATTERN_TOO_LARGE = Cint(120)
const ERROR_POSIX_CLASS_NOT_IN_CLASS = Cint(112)
const ERROR_POSIX_NO_SUPPORT_COLLATING = Cint(113)
const ERROR_QUANTIFIER_INVALID = Cint(109)
const ERROR_QUANTIFIER_OUT_OF_ORDER = Cint(104)
const ERROR_QUANTIFIER_TOO_BIG = Cint(105)
const ERROR_QUERY_BARJX_NEST_TOO_DEEP = Cint(184)
const ERROR_RECURSELOOP = Cint((-52))
const ERROR_RECURSIONLIMIT = Cint((-53))
const ERROR_REPMISSINGBRACE = Cint((-58))
const ERROR_SCRIPT_RUN_NOT_AVAILABLE = Cint(196)
const ERROR_SUBPATTERN_NAMES_MISMATCH = Cint(165)
const ERROR_SUBPATTERN_NAME_EXPECTED = Cint(162)
const ERROR_SUBPATTERN_NAME_TOO_LONG = Cint(148)
const ERROR_SUBPATTERN_NUMBER_TOO_BIG = Cint(161)
const ERROR_SUPPORTED_ONLY_IN_UNICODE = Cint(193)
const ERROR_TOOMANYREPLACE = Cint((-61))
const ERROR_TOO_MANY_CAPTURES = Cint(197)
const ERROR_TOO_MANY_CONDITION_BRANCHES = Cint(127)
const ERROR_TOO_MANY_NAMED_SUBPATTERNS = Cint(149)
const ERROR_UCP_IS_DISABLED = Cint(175)
const ERROR_UNAVAILABLE = Cint((-54))
const ERROR_UNICODE_DISALLOWED_CODE_POINT = Cint(173)
const ERROR_UNICODE_NOT_SUPPORTED = Cint(132)
const ERROR_UNICODE_PROPERTIES_UNAVAILABLE = Cint(145)
const ERROR_UNKNOWN_ESCAPE = Cint(103)
const ERROR_UNKNOWN_POSIX_CLASS = Cint(130)
const ERROR_UNKNOWN_UNICODE_PROPERTY = Cint(147)
const ERROR_UNMATCHED_CLOSING_PARENTHESIS = Cint(122)
const ERROR_UNRECOGNIZED_AFTER_QUERY_P = Cint(141)
const ERROR_UNSET = Cint((-55))
const ERROR_UNSUPPORTED_ESCAPE_SEQUENCE = Cint(137)
const ERROR_UTF16_ERR1 = Cint((-24))
const ERROR_UTF16_ERR2 = Cint((-25))
const ERROR_UTF16_ERR3 = Cint((-26))
const ERROR_UTF32_ERR1 = Cint((-27))
const ERROR_UTF32_ERR2 = Cint((-28))
const ERROR_UTF8_ERR1 = Cint((-3))
const ERROR_UTF8_ERR10 = Cint((-12))
const ERROR_UTF8_ERR11 = Cint((-13))
const ERROR_UTF8_ERR12 = Cint((-14))
const ERROR_UTF8_ERR13 = Cint((-15))
const ERROR_UTF8_ERR14 = Cint((-16))
const ERROR_UTF8_ERR15 = Cint((-17))
const ERROR_UTF8_ERR16 = Cint((-18))
const ERROR_UTF8_ERR17 = Cint((-19))
const ERROR_UTF8_ERR18 = Cint((-20))
const ERROR_UTF8_ERR19 = Cint((-21))
const ERROR_UTF8_ERR2 = Cint((-4))
const ERROR_UTF8_ERR20 = Cint((-22))
const ERROR_UTF8_ERR21 = Cint((-23))
const ERROR_UTF8_ERR3 = Cint((-5))
const ERROR_UTF8_ERR4 = Cint((-6))
const ERROR_UTF8_ERR5 = Cint((-7))
const ERROR_UTF8_ERR6 = Cint((-8))
const ERROR_UTF8_ERR7 = Cint((-9))
const ERROR_UTF8_ERR8 = Cint((-10))
const ERROR_UTF8_ERR9 = Cint((-11))
const ERROR_UTF_IS_DISABLED = Cint(174)
const ERROR_VERB_ARGUMENT_NOT_ALLOWED = Cint(159)
const ERROR_VERB_NAME_TOO_LONG = Cint(176)
const ERROR_VERB_UNKNOWN = Cint(160)
const ERROR_VERSION_CONDITION_SYNTAX = Cint(179)
const ERROR_ZERO_RELATIVE_REFERENCE = Cint(126)
const EXTENDED = UInt32(0x00000080)
const EXTENDED_MORE = UInt32(0x01000000)
const EXTRA_ALLOW_LOOKAROUND_BSK = UInt32(0x00000040)
const EXTRA_ALLOW_SURROGATE_ESCAPES = UInt32(0x00000001)
const EXTRA_ALT_BSUX = UInt32(0x00000020)
const EXTRA_BAD_ESCAPE_IS_LITERAL = UInt32(0x00000002)
const EXTRA_ESCAPED_CR_IS_LF = UInt32(0x00000010)
const EXTRA_MATCH_LINE = UInt32(0x00000008)
const EXTRA_MATCH_WORD = UInt32(0x00000004)
const FIRSTLINE = UInt32(0x00000100)
const INFO_ALLOPTIONS = UInt32(0)
const INFO_ARGOPTIONS = UInt32(1)
const INFO_BACKREFMAX = UInt32(2)
const INFO_BSR = UInt32(3)
const INFO_CAPTURECOUNT = UInt32(4)
const INFO_DEPTHLIMIT = UInt32(21)
const INFO_EXTRAOPTIONS = UInt32(26)
const INFO_FIRSTBITMAP = UInt32(7)
const INFO_FIRSTCODETYPE = UInt32(6)
const INFO_FIRSTCODEUNIT = UInt32(5)
const INFO_FRAMESIZE = UInt32(24)
const INFO_HASBACKSLASHC = UInt32(23)
const INFO_HASCRORLF = UInt32(8)
const INFO_HEAPLIMIT = UInt32(25)
const INFO_JCHANGED = UInt32(9)
const INFO_JITSIZE = UInt32(10)
const INFO_LASTCODETYPE = UInt32(12)
const INFO_LASTCODEUNIT = UInt32(11)
const INFO_MATCHEMPTY = UInt32(13)
const INFO_MATCHLIMIT = UInt32(14)
const INFO_MAXLOOKBEHIND = UInt32(15)
const INFO_MINLENGTH = UInt32(16)
const INFO_NAMECOUNT = UInt32(17)
const INFO_NAMEENTRYSIZE = UInt32(18)
const INFO_NAMETABLE = UInt32(19)
const INFO_NEWLINE = UInt32(20)
const INFO_RECURSIONLIMIT = UInt32(21)
const INFO_SIZE = UInt32(22)
const JIT_COMPLETE = UInt32(0x00000001)
const JIT_INVALID_UTF = UInt32(0x00000100)
const JIT_PARTIAL_HARD = UInt32(0x00000004)
const JIT_PARTIAL_SOFT = UInt32(0x00000002)
const LITERAL = UInt32(0x02000000)
const MAJOR = UInt32(10)
const MATCH_INVALID_UTF = UInt32(0x04000000)
const MATCH_UNSET_BACKREF = UInt32(0x00000200)
const MINOR = UInt32(42)
const MULTILINE = UInt32(0x00000400)
const NEVER_BACKSLASH_C = UInt32(0x00100000)
const NEVER_UCP = UInt32(0x00000800)
const NEVER_UTF = UInt32(0x00001000)
const NEWLINE_ANY = UInt32(4)
const NEWLINE_ANYCRLF = UInt32(5)
const NEWLINE_CR = UInt32(1)
const NEWLINE_CRLF = UInt32(3)
const NEWLINE_LF = UInt32(2)
const NEWLINE_NUL = UInt32(6)
const NOTBOL = UInt32(0x00000001)
const NOTEMPTY = UInt32(0x00000004)
const NOTEMPTY_ATSTART = UInt32(0x00000008)
const NOTEOL = UInt32(0x00000002)
const NO_AUTO_CAPTURE = UInt32(0x00002000)
const NO_AUTO_POSSESS = UInt32(0x00004000)
const NO_DOTSTAR_ANCHOR = UInt32(0x00008000)
const NO_JIT = UInt32(0x00002000)
const NO_START_OPTIMIZE = UInt32(0x00010000)
const NO_UTF_CHECK = UInt32(0x40000000)
const PARTIAL_HARD = UInt32(0x00000020)
const PARTIAL_SOFT = UInt32(0x00000010)
const SUBSTITUTE_EXTENDED = UInt32(0x00000200)
const SUBSTITUTE_GLOBAL = UInt32(0x00000100)
const SUBSTITUTE_LITERAL = UInt32(0x00008000)
const SUBSTITUTE_MATCHED = UInt32(0x00010000)
const SUBSTITUTE_OVERFLOW_LENGTH = UInt32(0x00001000)
const SUBSTITUTE_REPLACEMENT_ONLY = UInt32(0x00020000)
const SUBSTITUTE_UNKNOWN_UNSET = UInt32(0x00000800)
const SUBSTITUTE_UNSET_EMPTY = UInt32(0x00000400)
const UCP = UInt32(0x00020000)
const UNGREEDY = UInt32(0x00040000)
const USE_OFFSET_LIMIT = UInt32(0x00800000)
const UTF = UInt32(0x00080000)
L   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/parse.jl@;      # This file is a part of Julia. License is MIT: https://julialang.org/license

import Base.Checked: add_with_overflow, mul_with_overflow

## string to integer functions ##

"""
    parse(type, str; base)

Parse a string as a number. For `Integer` types, a base can be specified
(the default is 10). For floating-point types, the string is parsed as a decimal
floating-point number.  `Complex` types are parsed from decimal strings
of the form `"R±Iim"` as a `Complex(R,I)` of the requested type; `"i"` or `"j"` can also be
used instead of `"im"`, and `"R"` or `"Iim"` are also permitted.
If the string does not contain a valid number, an error is raised.

!!! compat "Julia 1.1"
    `parse(Bool, str)` requires at least Julia 1.1.

# Examples
```jldoctest
julia> parse(Int, "1234")
1234

julia> parse(Int, "1234", base = 5)
194

julia> parse(Int, "afc", base = 16)
2812

julia> parse(Float64, "1.2e-3")
0.0012

julia> parse(Complex{Float64}, "3.2e-1 + 4.5im")
0.32 + 4.5im
```
"""
parse(T::Type, str; base = Int)
parse(::Type{Union{}}, slurp...; kwargs...) = error("cannot parse a value as Union{}")

function parse(::Type{T}, c::AbstractChar; base::Integer = 10) where T<:Integer
    a::Int = (base <= 36 ? 10 : 36)
    2 <= base <= 62 || throw(ArgumentError("invalid base: base must be 2 ≤ base ≤ 62, got $base"))
    d = '0' <= c <= '9' ? c-'0'    :
        'A' <= c <= 'Z' ? c-'A'+10 :
        'a' <= c <= 'z' ? c-'a'+a  : throw(ArgumentError("invalid digit: $(repr(c))"))
    d < base || throw(ArgumentError("invalid base $base digit $(repr(c))"))
    convert(T, d)
end

function parseint_iterate(s::AbstractString, startpos::Int, endpos::Int)
    (0 < startpos <= endpos) || (return Char(0), 0, 0)
    j = startpos
    c, startpos = iterate(s,startpos)::Tuple{Char, Int}
    c, startpos, j
end

function parseint_preamble(signed::Bool, base::Int, s::AbstractString, startpos::Int, endpos::Int)
    c, i, j = parseint_iterate(s, startpos, endpos)

    while isspace(c)
        c, i, j = parseint_iterate(s,i,endpos)
    end
    (j == 0) && (return 0, 0, 0)

    sgn = 1
    if signed
        if c == '-' || c == '+'
            (c == '-') && (sgn = -1)
            c, i, j = parseint_iterate(s,i,endpos)
        end
    end

    while isspace(c)
        c, i, j = parseint_iterate(s,i,endpos)
    end
    (j == 0) && (return 0, 0, 0)

    if base == 0
        if c == '0' && i <= endpos
            c, i = iterate(s,i)::Tuple{Char, Int}
            base = c=='b' ? 2 : c=='o' ? 8 : c=='x' ? 16 : 10
            if base != 10
                c, i, j = parseint_iterate(s,i,endpos)
            end
        else
            base = 10
        end
    end
    return sgn, base, j
end

# '0':'9' -> 0:9
# 'A':'Z' -> 10:35
# 'a':'z' -> 10:35 if base <= 36, 36:61 otherwise
# input outside of that is mapped to base
@inline function __convert_digit(_c::UInt32, base::UInt32)
    _0 = UInt32('0')
    _9 = UInt32('9')
    _A = UInt32('A')
    _a = UInt32('a')
    _Z = UInt32('Z')
    _z = UInt32('z')
    a = base <= 36 ? UInt32(10) : UInt32(36) # converting here instead of via a type assertion prevents typeassert related errors
    d = _0 <= _c <= _9 ? _c-_0             :
        _A <= _c <= _Z ? _c-_A+ UInt32(10) :
        _a <= _c <= _z ? _c-_a+a           :
        base
end


function tryparse_internal(::Type{T}, s::AbstractString, startpos::Int, endpos::Int, base_::Integer, raise::Bool) where T<:Integer
    sgn, base, i = parseint_preamble(T<:Signed, Int(base_), s, startpos, endpos)
    if sgn == 0 && base == 0 && i == 0
        raise && throw(ArgumentError("input string is empty or only contains whitespace"))
        return nothing
    end
    if !(2 <= base <= 62)
        raise && throw(ArgumentError(LazyString("invalid base: base must be 2 ≤ base ≤ 62, got ", base)))
        return nothing
    end
    if i == 0
        raise && throw(ArgumentError("premature end of integer: $(repr(SubString(s,startpos,endpos)))"))
        return nothing
    end
    c, i = parseint_iterate(s,i,endpos)
    if i == 0
        raise && throw(ArgumentError("premature end of integer: $(repr(SubString(s,startpos,endpos)))"))
        return nothing
    end

    base = convert(T, base)
    # Special case the common cases of base being 10 or 16 to avoid expensive runtime div
    m::T = base == 10 ? div(typemax(T) - T(9), T(10)) :
           base == 16 ? div(typemax(T) - T(15), T(16)) :
                        div(typemax(T) - base + 1, base)
    n::T = 0
    while n <= m
        # Fast path from `UInt32(::Char)`; non-ascii will be >= 0x80
        _c = reinterpret(UInt32, c) >> 24
        d::T = __convert_digit(_c, base % UInt32) # we know 2 <= base <= 62, so prevent an incorrect InexactError here
        if d >= base
            raise && throw(ArgumentError("invalid base $base digit $(repr(c)) in $(repr(SubString(s,startpos,endpos)))"))
            return nothing
        end
        n *= base
        n += d
        if i > endpos
            n *= sgn
            return n
        end
        c, i = iterate(s,i)::Tuple{Char, Int}
        isspace(c) && break
    end
    (T <: Signed) && (n *= sgn)
    while !isspace(c)
        # Fast path from `UInt32(::Char)`; non-ascii will be >= 0x80
        _c = reinterpret(UInt32, c) >> 24
        d::T = __convert_digit(_c, base % UInt32) # we know 2 <= base <= 62
        if d >= base
            raise && throw(ArgumentError("invalid base $base digit $(repr(c)) in $(repr(SubString(s,startpos,endpos)))"))
            return nothing
        end
        (T <: Signed) && (d *= sgn)

        n, ov_mul = mul_with_overflow(n, base)
        n, ov_add = add_with_overflow(n, d)
        if ov_mul | ov_add
            raise && throw(OverflowError("overflow parsing $(repr(SubString(s,startpos,endpos)))"))
            return nothing
        end
        (i > endpos) && return n
        c, i = iterate(s,i)::Tuple{Char, Int}
    end
    while i <= endpos
        c, i = iterate(s,i)::Tuple{Char, Int}
        if !isspace(c)
            raise && throw(ArgumentError("extra characters after whitespace in $(repr(SubString(s,startpos,endpos)))"))
            return nothing
        end
    end
    return n
end

function tryparse_internal(::Type{Bool}, sbuff::AbstractString,
        startpos::Int, endpos::Int, base::Integer, raise::Bool)
    if isempty(sbuff)
        raise && throw(ArgumentError("input string is empty"))
        return nothing
    end

    if isnumeric(sbuff[1])
        intres = tryparse_internal(UInt8, sbuff, startpos, endpos, base, false)
        (intres == 1) && return true
        (intres == 0) && return false
        raise && throw(ArgumentError("invalid Bool representation: $(repr(sbuff))"))
    end

    orig_start = startpos
    orig_end   = endpos

    # Ignore leading and trailing whitespace
    while startpos <= endpos && isspace(sbuff[startpos])
        startpos = nextind(sbuff, startpos)
    end
    while endpos >= startpos && isspace(sbuff[endpos])
        endpos = prevind(sbuff, endpos)
    end

    len = endpos - startpos + 1
    if sbuff isa Union{String, SubString{String}}
        p = pointer(sbuff) + startpos - 1
        truestr = "true"
        falsestr = "false"
        GC.@preserve sbuff truestr falsestr begin
            (len == 4) && (0 == memcmp(p, unsafe_convert(Ptr{UInt8}, truestr), 4)) && (return true)
            (len == 5) && (0 == memcmp(p, unsafe_convert(Ptr{UInt8}, falsestr), 5)) && (return false)
        end
    else
        (len == 4) && (SubString(sbuff, startpos:startpos+3) == "true") && (return true)
        (len == 5) && (SubString(sbuff, startpos:startpos+4) == "false") && (return false)
    end

    if raise
        substr = SubString(sbuff, orig_start, orig_end) # show input string in the error to avoid confusion
        if all(isspace, substr)
            throw(ArgumentError("input string only contains whitespace"))
        else
            throw(ArgumentError("invalid Bool representation: $(repr(substr))"))
        end
    end
    return nothing
end

@inline function check_valid_base(base)
    if 2 <= base <= 62
        return base
    end
    throw(ArgumentError("invalid base: base must be 2 ≤ base ≤ 62, got $base"))
end

"""
    tryparse(type, str; base)

Like [`parse`](@ref), but returns either a value of the requested type,
or [`nothing`](@ref) if the string does not contain a valid number.
"""
function tryparse(::Type{T}, s::AbstractString; base::Union{Nothing,Integer} = nothing) where {T<:Integer}
    # Zero base means, "figure it out"
    tryparse_internal(T, s, firstindex(s), lastindex(s), base===nothing ? 0 : check_valid_base(base), false)
end

function parse(::Type{T}, s::AbstractString; base::Union{Nothing,Integer} = nothing) where {T<:Integer}
    convert(T, tryparse_internal(T, s, firstindex(s), lastindex(s),
                                 base===nothing ? 0 : check_valid_base(base), true))
end
tryparse(::Type{Union{}}, slurp...; kwargs...) = error("cannot parse a value as Union{}")

## string to float functions ##

function tryparse(::Type{Float64}, s::String)
    hasvalue, val = ccall(:jl_try_substrtod, Tuple{Bool, Float64},
                          (Ptr{UInt8},Csize_t,Csize_t), s, 0, sizeof(s))
    hasvalue ? val : nothing
end
function tryparse(::Type{Float64}, s::SubString{String})
    hasvalue, val = ccall(:jl_try_substrtod, Tuple{Bool, Float64},
                          (Ptr{UInt8},Csize_t,Csize_t), s.string, s.offset, s.ncodeunits)
    hasvalue ? val : nothing
end
function tryparse_internal(::Type{Float64}, s::String, startpos::Int, endpos::Int)
    hasvalue, val = ccall(:jl_try_substrtod, Tuple{Bool, Float64},
                          (Ptr{UInt8},Csize_t,Csize_t), s, startpos-1, endpos-startpos+1)
    hasvalue ? val : nothing
end
function tryparse_internal(::Type{Float64}, s::SubString{String}, startpos::Int, endpos::Int)
    hasvalue, val = ccall(:jl_try_substrtod, Tuple{Bool, Float64},
                          (Ptr{UInt8},Csize_t,Csize_t), s.string, s.offset+startpos-1, endpos-startpos+1)
    hasvalue ? val : nothing
end
function tryparse(::Type{Float32}, s::String)
    hasvalue, val = ccall(:jl_try_substrtof, Tuple{Bool, Float32},
                          (Ptr{UInt8},Csize_t,Csize_t), s, 0, sizeof(s))
    hasvalue ? val : nothing
end
function tryparse(::Type{Float32}, s::SubString{String})
    hasvalue, val = ccall(:jl_try_substrtof, Tuple{Bool, Float32},
                          (Ptr{UInt8},Csize_t,Csize_t), s.string, s.offset, s.ncodeunits)
    hasvalue ? val : nothing
end
function tryparse_internal(::Type{Float32}, s::String, startpos::Int, endpos::Int)
    hasvalue, val = ccall(:jl_try_substrtof, Tuple{Bool, Float32},
                          (Ptr{UInt8},Csize_t,Csize_t), s, startpos-1, endpos-startpos+1)
    hasvalue ? val : nothing
end
function tryparse_internal(::Type{Float32}, s::SubString{String}, startpos::Int, endpos::Int)
    hasvalue, val = ccall(:jl_try_substrtof, Tuple{Bool, Float32},
                          (Ptr{UInt8},Csize_t,Csize_t), s.string, s.offset+startpos-1, endpos-startpos+1)
    hasvalue ? val : nothing
end
tryparse(::Type{T}, s::AbstractString) where {T<:Union{Float32,Float64}} = tryparse(T, String(s))
tryparse(::Type{Float16}, s::AbstractString) =
    convert(Union{Float16, Nothing}, tryparse(Float32, s))
tryparse_internal(::Type{Float16}, s::AbstractString, startpos::Int, endpos::Int) =
    convert(Union{Float16, Nothing}, tryparse_internal(Float32, s, startpos, endpos))

## string to complex functions ##

function tryparse_internal(::Type{Complex{T}}, s::Union{String,SubString{String}}, i::Int, e::Int, raise::Bool) where {T<:Real}
    # skip initial whitespace
    while i ≤ e && isspace(s[i])
        i = nextind(s, i)
    end
    if i > e
        raise && throw(ArgumentError("input string is empty or only contains whitespace"))
        return nothing
    end

    # find index of ± separating real/imaginary parts (if any)
    i₊ = something(findnext(in(('+','-')), s, i), 0)
    if i₊ == i # leading ± sign
        i₊ = something(findnext(in(('+','-')), s, i₊+1), 0)
    end
    if i₊ != 0 && s[prevind(s, i₊)] in ('e','E') # exponent sign
        i₊ = something(findnext(in(('+','-')), s, i₊+1), 0)
    end

    # find trailing im/i/j
    iᵢ = something(findprev(in(('m','i','j')), s, e), 0)
    if iᵢ > 0 && s[iᵢ] == 'm' # im
        iᵢ = prevind(s, iᵢ)
        if s[iᵢ] != 'i'
            raise && throw(ArgumentError("expected trailing \"im\", found only \"m\""))
            return nothing
        end
    end

    if i₊ == 0 # purely real or imaginary value
        if iᵢ > i && !(iᵢ == i+1 && s[i] in ('+','-')) # purely imaginary (not "±inf")
            x = tryparse_internal(T, s, i, prevind(s, iᵢ), raise)
            x === nothing && return nothing
            return Complex{T}(zero(x),x)
        else # purely real
            x = tryparse_internal(T, s, i, e, raise)
            x === nothing && return nothing
            return Complex{T}(x)
        end
    end

    if iᵢ < i₊
        raise && throw(ArgumentError("missing imaginary unit"))
        return nothing # no imaginary part
    end

    # parse real part
    re = tryparse_internal(T, s, i, prevind(s, i₊), raise)
    re === nothing && return nothing

    # parse imaginary part
    im = tryparse_internal(T, s, i₊+1, prevind(s, iᵢ), raise)
    im === nothing && return nothing

    return Complex{T}(re, s[i₊]=='-' ? -im : im)
end

# the ±1 indexing above for ascii chars is specific to String, so convert:
tryparse_internal(T::Type{Complex{S}}, s::AbstractString, i::Int, e::Int, raise::Bool) where S<:Real =
    tryparse_internal(T, String(s), i, e, raise)

# fallback methods for tryparse_internal
tryparse_internal(::Type{T}, s::AbstractString, startpos::Int, endpos::Int) where T<:Real =
    startpos == firstindex(s) && endpos == lastindex(s) ? tryparse(T, s) : tryparse(T, SubString(s, startpos, endpos))
function tryparse_internal(::Type{T}, s::AbstractString, startpos::Int, endpos::Int, raise::Bool) where T<:Real
    result = tryparse_internal(T, s, startpos, endpos)
    if raise && result === nothing
        _parse_failure(T, s, startpos, endpos)
    end
    return result
end
function tryparse_internal(::Type{T}, s::AbstractString, raise::Bool; kwargs...) where T<:Real
    result = tryparse(T, s; kwargs...)
    if raise && result === nothing
        _parse_failure(T, s)
    end
    return result
end
@noinline _parse_failure(T, s::AbstractString, startpos = firstindex(s), endpos = lastindex(s)) =
    throw(ArgumentError("cannot parse $(repr(s[startpos:endpos])) as $T"))

tryparse_internal(::Type{T}, s::AbstractString, startpos::Int, endpos::Int, raise::Bool) where T<:Integer =
    tryparse_internal(T, s, startpos, endpos, 10, raise)

parse(::Type{T}, s::AbstractString; kwargs...) where T<:Real =
    convert(T, tryparse_internal(T, s, true; kwargs...))
parse(::Type{T}, s::AbstractString) where T<:Complex =
    convert(T, tryparse_internal(T, s, firstindex(s), lastindex(s), true))

tryparse(T::Type{Complex{S}}, s::AbstractString) where S<:Real =
    tryparse_internal(T, s, firstindex(s), lastindex(s), false)
L   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/shell.jlC      # This file is a part of Julia. License is MIT: https://julialang.org/license

## shell-like command parsing ##

const shell_special = "#{}()[]<>|&*?~;"

# strips the end but respects the space when the string ends with "\\ "
function rstrip_shell(s::AbstractString)
    c_old = nothing
    for (i, c) in Iterators.reverse(pairs(s))
        i::Int; c::AbstractChar
        ((c == '\\') && c_old == ' ') && return SubString(s, 1, i+1)
        isspace(c) || return SubString(s, 1, i)
        c_old = c
    end
    SubString(s, 1, 0)
end

function shell_parse(str::AbstractString, interpolate::Bool=true;
                     special::AbstractString="", filename="none")
    last_arg = firstindex(str) # N.B.: This is used by REPLCompletions
    s = SubString(str, last_arg)
    s = rstrip_shell(lstrip(s))

    isempty(s) && return interpolate ? (Expr(:tuple,:()), last_arg) : ([], last_arg)

    in_single_quotes = false
    in_double_quotes = false

    args = []
    arg = []
    i = firstindex(s)
    st = Iterators.Stateful(pairs(s))
    update_last_arg = false # true after spaces or interpolate

    function push_nonempty!(list, x)
        if !isa(x,AbstractString) || !isempty(x)
            push!(list, x)
        end
        return nothing
    end
    function consume_upto!(list, s, i, j)
        push_nonempty!(list, s[i:prevind(s, j)::Int])
        something(peek(st), lastindex(s)::Int+1 => '\0').first::Int
    end
    function append_2to1!(list, innerlist)
        if isempty(innerlist); push!(innerlist, ""); end
        push!(list, copy(innerlist))
        empty!(innerlist)
    end

    C = eltype(str)
    P = Pair{Int,C}
    for (j, c) in st
        j, c = j::Int, c::C
        if !in_single_quotes && !in_double_quotes && isspace(c)
            update_last_arg = true
            i = consume_upto!(arg, s, i, j)
            append_2to1!(args, arg)
            while !isempty(st)
                # We've made sure above that we don't end in whitespace,
                # so updating `i` here is ok
                (i, c) = peek(st)::P
                isspace(c) || break
                popfirst!(st)
            end
        elseif interpolate && !in_single_quotes && c == '$'
            i = consume_upto!(arg, s, i, j)
            isempty(st) && error("\$ right before end of command")
            stpos, c = popfirst!(st)::P
            isspace(c) && error("space not allowed right after \$")
            if startswith(SubString(s, stpos), "var\"")
                # Disallow var"#" syntax in cmd interpolations.
                # TODO: Allow only identifiers after the $ for consistency with
                # string interpolation syntax (see #3150)
                ex, j = :var, stpos+3
            else
                # use parseatom instead of parse to respect filename (#28188)
                ex, j = Meta.parseatom(s, stpos, filename=filename)
            end
            last_arg = stpos + s.offset
            update_last_arg = true
            push!(arg, ex)
            s = SubString(s, j)
            Iterators.reset!(st, pairs(s))
            i = firstindex(s)
        else
            if update_last_arg
                last_arg = i + s.offset
                update_last_arg = false
            end
            if !in_double_quotes && c == '\''
                in_single_quotes = !in_single_quotes
                i = consume_upto!(arg, s, i, j)
            elseif !in_single_quotes && c == '"'
                in_double_quotes = !in_double_quotes
                i = consume_upto!(arg, s, i, j)
            elseif !in_single_quotes && c == '\\'
                if !isempty(st) && (peek(st)::P)[2] in ('\n', '\r')
                    i = consume_upto!(arg, s, i, j) + 1
                    if popfirst!(st)[2] == '\r' && (peek(st)::P)[2] == '\n'
                        i += 1
                        popfirst!(st)
                    end
                    while !isempty(st) && (peek(st)::P)[2] in (' ', '\t')
                        i = nextind(str, i)
                        _ = popfirst!(st)
                    end
                elseif in_double_quotes
                    isempty(st) && error("unterminated double quote")
                    k, c′ = peek(st)::P
                    if c′ == '"' || c′ == '$' || c′ == '\\'
                        i = consume_upto!(arg, s, i, j)
                        _ = popfirst!(st)
                    end
                else
                    isempty(st) && error("dangling backslash")
                    i = consume_upto!(arg, s, i, j)
                    _ = popfirst!(st)
                end
            elseif !in_single_quotes && !in_double_quotes && c in special
                error("parsing command `$str`: special characters \"$special\" must be quoted in commands")
            end
        end
    end

    if in_single_quotes; error("unterminated single quote"); end
    if in_double_quotes; error("unterminated double quote"); end

    push_nonempty!(arg, s[i:end])
    append_2to1!(args, arg)

    interpolate || return args, last_arg

    # construct an expression
    ex = Expr(:tuple)
    for arg in args
        push!(ex.args, Expr(:tuple, arg...))
    end
    return ex, last_arg
end

function shell_split(s::AbstractString)
    parsed = shell_parse(s, false)[1]
    args = String[]
    for arg in parsed
        push!(args, string(arg...))
    end
    args
end

function print_shell_word(io::IO, word::AbstractString, special::AbstractString = "")
    has_single = false
    has_special = false
    for c in word
        if isspace(c) || c=='\\' || c=='\'' || c=='"' || c=='$' || c in special
            has_special = true
            if c == '\''
                has_single = true
            end
        end
    end
    if isempty(word)
        print(io, "''")
    elseif !has_special
        print(io, word)
    elseif !has_single
        print(io, '\'', word, '\'')
    else
        print(io, '"')
        for c in word
            if c == '"' || c == '$'
                print(io, '\\')
            end
            print(io, c)
        end
        print(io, '"')
    end
    nothing
end

function print_shell_escaped(io::IO, cmd::AbstractString, args::AbstractString...;
                             special::AbstractString="")
    print_shell_word(io, cmd, special)
    for arg in args
        print(io, ' ')
        print_shell_word(io, arg, special)
    end
end
print_shell_escaped(io::IO; special::String="") = nothing

"""
    shell_escape(args::Union{Cmd,AbstractString...}; special::AbstractString="")

The unexported `shell_escape` function is the inverse of the unexported `shell_split` function:
it takes a string or command object and escapes any special characters in such a way that calling
`shell_split` on it would give back the array of words in the original command. The `special`
keyword argument controls what characters in addition to whitespace, backslashes, quotes and
dollar signs are considered to be special (default: none).

# Examples
```jldoctest
julia> Base.shell_escape("cat", "/foo/bar baz", "&&", "echo", "done")
"cat '/foo/bar baz' && echo done"

julia> Base.shell_escape("echo", "this", "&&", "that")
"echo this && that"
```
"""
shell_escape(args::AbstractString...; special::AbstractString="") =
    sprint((io, args...) -> print_shell_escaped(io, args..., special=special), args...)


function print_shell_escaped_posixly(io::IO, args::AbstractString...)
    first = true
    for arg in args
        first || print(io, ' ')
        # avoid printing quotes around simple enough strings
        # that any (reasonable) shell will definitely never consider them to be special
        have_single::Bool = false
        have_double::Bool = false
        function isword(c::AbstractChar)
            if '0' <= c <= '9' || 'a' <= c <= 'z' || 'A' <= c <= 'Z'
                # word characters
            elseif c == '_' || c == '/' || c == '+' || c == '-' || c == '.'
                # other common characters
            elseif c == '\''
                have_single = true
            elseif c == '"'
                have_double && return false # switch to single quoting
                have_double = true
            elseif !first && c == '='
                # equals is special if it is first (e.g. `env=val ./cmd`)
            else
                # anything else
                return false
            end
            return true
        end
        if isempty(arg)
            print(io, "''")
        elseif all(isword, arg)
            have_single && (arg = replace(arg, '\'' => "\\'"))
            have_double && (arg = replace(arg, '"' => "\\\""))
            print(io, arg)
        else
            print(io, '\'', replace(arg, '\'' => "'\\''"), '\'')
        end
        first = false
    end
end

"""
    shell_escape_posixly(args::Union{Cmd,AbstractString...})

The unexported `shell_escape_posixly` function
takes a string or command object and escapes any special characters in such a way that
it is safe to pass it as an argument to a posix shell.

# Examples
```jldoctest
julia> Base.shell_escape_posixly("cat", "/foo/bar baz", "&&", "echo", "done")
"cat '/foo/bar baz' '&&' echo done"

julia> Base.shell_escape_posixly("echo", "this", "&&", "that")
"echo this '&&' that"
```
"""
shell_escape_posixly(args::AbstractString...) =
    sprint(print_shell_escaped_posixly, args...)

"""
    shell_escape_csh(args::Union{Cmd,AbstractString...})
    shell_escape_csh(io::IO, args::Union{Cmd,AbstractString...})

This function quotes any metacharacters in the string arguments such
that the string returned can be inserted into a command-line for
interpretation by the Unix C shell (csh, tcsh), where each string
argument will form one word.

In contrast to a POSIX shell, csh does not support the use of the
backslash as a general escape character in double-quoted strings.
Therefore, this function wraps strings that might contain
metacharacters in single quotes, except for parts that contain single
quotes, which it wraps in double quotes instead. It switches between
these types of quotes as needed. Linefeed characters are escaped with
a backslash.

This function should also work for a POSIX shell, except if the input
string contains a linefeed (`"\\n"`) character.

See also: [`shell_escape_posixly`](@ref)
"""
function shell_escape_csh(io::IO, args::AbstractString...)
    first = true
    for arg in args
        first || write(io, ' ')
        first = false
        i = 1
        while true
            for (r,e) = (r"^[A-Za-z0-9/\._-]+\z"sa => "",
                         r"^[^']*\z"sa => "'", r"^[^\$\`\"]*\z"sa => "\"",
                         r"^[^']+"sa  => "'", r"^[^\$\`\"]+"sa  => "\"")
                if ((m = match(r, SubString(arg, i))) !== nothing)
                    write(io, e)
                    write(io, replace(m.match, '\n' => "\\\n"))
                    write(io, e)
                    i += ncodeunits(m.match)
                    break
                end
            end
            i <= lastindex(arg) || break
        end
    end
end
shell_escape_csh(args::AbstractString...) =
    sprint(shell_escape_csh, args...;
           sizehint = sum(sizeof.(args)) + length(args) * 3)

"""
    shell_escape_wincmd(s::AbstractString)
    shell_escape_wincmd(io::IO, s::AbstractString)

The unexported `shell_escape_wincmd` function escapes Windows `cmd.exe` shell
meta characters. It escapes `()!^<>&|` by placing a `^` in front. An `@` is
only escaped at the start of the string. Pairs of `"` characters and the
strings they enclose are passed through unescaped. Any remaining `"` is escaped
with `^` to ensure that the number of unescaped `"` characters in the result
remains even.

Since `cmd.exe` substitutes variable references (like `%USER%`) _before_
processing the escape characters `^` and `"`, this function makes no attempt to
escape the percent sign (`%`), the presence of `%` in the input may cause
severe breakage, depending on where the result is used.

Input strings with ASCII control characters that cannot be escaped (NUL, CR,
LF) will cause an `ArgumentError` exception.

The result is safe to pass as an argument to a command call being processed by
`CMD.exe /S /C " ... "` (with surrounding double-quote pair) and will be
received verbatim by the target application if the input does not contain `%`
(else this function will fail with an ArgumentError). The presence of `%` in
the input string may result in command injection vulnerabilities and may
invalidate any claim of suitability of the output of this function for use as
an argument to cmd (due to the ordering described above), so use caution when
assembling a string from various sources.

This function may be useful in concert with the `windows_verbatim` flag to
[`Cmd`](@ref) when constructing process pipelines.

```julia
wincmd(c::String) =
   run(Cmd(Cmd(["cmd.exe", "/s /c \\" \$c \\""]);
           windows_verbatim=true))
wincmd_echo(s::String) =
   wincmd("echo " * Base.shell_escape_wincmd(s))
wincmd_echo("hello \$(ENV["USERNAME"]) & the \\"whole\\" world! (=^I^=)")
```

But take note that if the input string `s` contains a `%`, the argument list
and echo'ed text may get corrupted, resulting in arbitrary command execution.
The argument can alternatively be passed as an environment variable, which
avoids the problem with `%` and the need for the `windows_verbatim` flag:

```julia
cmdargs = Base.shell_escape_wincmd("Passing args with %cmdargs% works 100%!")
run(setenv(`cmd /C echo %cmdargs%`, "cmdargs" => cmdargs))
```

!!! warning
    The argument parsing done by CMD when calling batch files (either inside
    `.bat` files or as arguments to them) is not fully compatible with the
    output of this function. In particular, the processing of `%` is different.

!!! important
    Due to a peculiar behavior of the CMD parser/interpreter, each command
    after a literal `|` character (indicating a command pipeline) must have
    `shell_escape_wincmd` applied twice since it will be parsed twice by CMD.
    This implies ENV variables would also be expanded twice!
    For example:
    ```julia
    to_print = "All for 1 & 1 for all!"
    to_print_esc = Base.shell_escape_wincmd(Base.shell_escape_wincmd(to_print))
    run(Cmd(Cmd(["cmd", "/S /C \\" break | echo \$(to_print_esc) \\""]), windows_verbatim=true))
    ```

With an I/O stream parameter `io`, the result will be written there,
rather than returned as a string.

See also [`escape_microsoft_c_args`](@ref), [`shell_escape_posixly`](@ref).

# Example
```jldoctest
julia> Base.shell_escape_wincmd("a^\\"^o\\"^u\\"")
"a^^\\"^o\\"^^u^\\""
```
"""
function shell_escape_wincmd(io::IO, s::AbstractString)
    # https://stackoverflow.com/a/4095133/1990689
    occursin(r"[\r\n\0]"sa, s) &&
        throw(ArgumentError("control character unsupported by CMD.EXE"))
    i = 1
    len = ncodeunits(s)
    if len > 0 && s[1] == '@'
        write(io, '^')
    end
    while i <= len
        c = s[i]
        if c == '"' && (j = findnext('"', s, nextind(s,i))) !== nothing
            write(io, SubString(s,i,j))
            i = j
        else
            if c in ('"', '(', ')', '!', '^', '<', '>', '&', '|')
                write(io, '^', c)
            else
                write(io, c)
            end
        end
        i = nextind(s,i)
    end
end
shell_escape_wincmd(s::AbstractString) = sprint(shell_escape_wincmd, s;
                                                sizehint = 2*sizeof(s))

"""
    escape_microsoft_c_args(args::Union{Cmd,AbstractString...})
    escape_microsoft_c_args(io::IO, args::Union{Cmd,AbstractString...})

Convert a collection of string arguments into a string that can be
passed to many Windows command-line applications.

Microsoft Windows passes the entire command line as a single string to
the application (unlike POSIX systems, where the shell splits the
command line into a list of arguments). Many Windows API applications
(including julia.exe), use the conventions of the [Microsoft C/C++
runtime](https://docs.microsoft.com/en-us/cpp/c-language/parsing-c-command-line-arguments)
to split that command line into a list of strings.

This function implements an inverse for a parser compatible with these rules.
It joins command-line arguments to be passed to a Windows
C/C++/Julia application into a command line, escaping or quoting the
meta characters space, TAB, double quote and backslash where needed.

See also [`shell_escape_wincmd`](@ref), [`escape_raw_string`](@ref).
"""
function escape_microsoft_c_args(io::IO, args::AbstractString...)
    # http://daviddeley.com/autohotkey/parameters/parameters.htm#WINCRULES
    first = true
    for arg in args
        if first
            first = false
        else
            write(io, ' ')  # separator
        end
        if isempty(arg) || occursin(r"[ \t\"]"sa, arg)
            # Julia raw strings happen to use the same escaping convention
            # as the argv[] parser in Microsoft's C runtime library.
            write(io, '"')
            escape_raw_string(io, arg)
            write(io, '"')
        else
            write(io, arg)
        end
    end
end
escape_microsoft_c_args(args::AbstractString...) =
    sprint(escape_microsoft_c_args, args...;
           sizehint = (sum(sizeof.(args)) + 3*length(args)))
K   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/show.jl
�     # This file is a part of Julia. License is MIT: https://julialang.org/license

using Core.Compiler: has_typevar

function show(io::IO, ::MIME"text/plain", u::UndefInitializer)
    show(io, u)
    get(io, :compact, false)::Bool && return
    print(io, ": array initializer with undefined values")
end

# first a few multiline show functions for types defined before the MIME type:

show(io::IO, ::MIME"text/plain", r::AbstractRange) = show(io, r) # always use the compact form for printing ranges

function show(io::IO, ::MIME"text/plain", r::LinRange)
    isempty(r) && return show(io, r)
    # show for LinRange, e.g.
    # range(1, stop=3, length=7)
    # 7-element LinRange{Float64}:
    #   1.0,1.33333,1.66667,2.0,2.33333,2.66667,3.0
    summary(io, r)
    println(io, ":")
    print_range(io, r)
end

function _isself(@nospecialize(ft))
    name = ft.name.mt.name
    mod = parentmodule(ft)  # NOTE: not necessarily the same as ft.name.mt.module
    return isdefined(mod, name) && ft == typeof(getfield(mod, name))
end

function show(io::IO, ::MIME"text/plain", f::Function)
    get(io, :compact, false)::Bool && return show(io, f)
    ft = typeof(f)
    name = ft.name.mt.name
    if isa(f, Core.IntrinsicFunction)
        print(io, f)
        id = Core.Intrinsics.bitcast(Int32, f)
        print(io, " (intrinsic function #$id)")
    elseif isa(f, Core.Builtin)
        print(io, name, " (built-in function)")
    else
        n = length(methods(f))
        m = n==1 ? "method" : "methods"
        sname = string(name)
        ns = (_isself(ft) || '#' in sname) ? sname : string("(::", ft, ")")
        what = startswith(ns, '@') ? "macro" : "generic function"
        print(io, ns, " (", what, " with $n $m)")
    end
end

show(io::IO, ::MIME"text/plain", c::ComposedFunction) = show(io, c)
show(io::IO, ::MIME"text/plain", c::Returns) = show(io, c)
show(io::IO, ::MIME"text/plain", s::Splat) = show(io, s)

const ansi_regex = r"(?s)(?:\x1B(?:[@-Z\\-_]|\[[0-?]*[ -/]*[@-~]))|."

# Pseudo-character representing an ANSI delimiter
struct ANSIDelimiter
    del::SubString{String}
end
ncodeunits(c::ANSIDelimiter) = ncodeunits(c.del)
textwidth(::ANSIDelimiter) = 0

# An iterator similar to `pairs(::String)` but whose values are Char or ANSIDelimiter
struct ANSIIterator
    captures::RegexMatchIterator
end
ANSIIterator(s::AbstractString) = ANSIIterator(eachmatch(ansi_regex, s))

IteratorSize(::Type{ANSIIterator}) = SizeUnknown()
eltype(::Type{ANSIIterator}) = Pair{Int, Union{Char,ANSIDelimiter}}
function iterate(I::ANSIIterator, (i, m_st)=(1, iterate(I.captures)))
    m_st === nothing && return nothing
    m, (j, new_m_st) = m_st
    c = lastindex(m.match) == 1 ? only(m.match) : ANSIDelimiter(m.match)
    return (i => c, (j, iterate(I.captures, (j, new_m_st))))
end
textwidth(I::ANSIIterator) = mapreduce(textwidth∘last, +, I; init=0)

function _truncate_at_width_or_chars(ignore_ANSI::Bool, str, width, rpad=false, chars="\r\n", truncmark="…")
    truncwidth = textwidth(truncmark)
    (width <= 0 || width < truncwidth) && return ""
    wid = truncidx = lastidx = 0
    # if str needs to be truncated, truncidx is the index of truncation.
    stop = false # once set, only ANSI delimiters will be kept as new characters.
    needANSIend = false # set if the last ANSI delimiter before truncidx is not "\033[0m".
    I = ignore_ANSI ? ANSIIterator(str) : pairs(str)
    for (i, c) in I
        if c isa ANSIDelimiter
            truncidx == 0 && (needANSIend = c != "\033[0m")
            lastidx = i + ncodeunits(c) - 1
        else
            stop && break
            wid += textwidth(c)
            truncidx == 0 && wid > (width - truncwidth) && (truncidx = lastidx)
            lastidx = i
            c in chars && break
            stop = wid >= width
        end
    end
    lastidx == 0 && return rpad ? ' '^width : ""
    str[lastidx] in chars && (lastidx = prevind(str, lastidx))
    ANSIend = needANSIend ? "\033[0m" : ""
    pad = rpad ? repeat(' ', max(0, width-wid)) : ""
    truncidx == 0 && (truncidx = lastidx)
    if lastidx < lastindex(str)
        return string(SubString(str, 1, truncidx), ANSIend, truncmark, pad)
    else
        return string(str, ANSIend, pad)
    end
end

function show(io::IO, ::MIME"text/plain", iter::Union{KeySet,ValueIterator})
    isempty(iter) && get(io, :compact, false)::Bool && return show(io, iter)
    summary(io, iter)
    isempty(iter) && return
    print(io, ". ", isa(iter,KeySet) ? "Keys" : "Values", ":")
    limit = get(io, :limit, false)::Bool
    if limit
        sz = displaysize(io)
        rows, cols = sz[1] - 3, sz[2]
        rows < 2 && (print(io, " …"); return)
        cols < 4 && (cols = 4)
        cols -= 2 # For prefix "  "
        rows -= 1 # For summary
    else
        rows = cols = typemax(Int)
    end

    for (i, v) in enumerate(iter)
        print(io, "\n  ")
        i == rows < length(iter) && (print(io, "⋮"); break)

        if limit
            str = sprint(show, v, context=io, sizehint=0)
            str = _truncate_at_width_or_chars(get(io, :color, false)::Bool, str, cols)
            print(io, str)
        else
            show(io, v)
        end
    end
end

function show(io::IO, ::MIME"text/plain", t::AbstractDict{K,V}) where {K,V}
    isempty(t) && return show(io, t)
    # show more descriptively, with one line per key/value pair
    recur_io = IOContext(io, :SHOWN_SET => t)
    limit = get(io, :limit, false)::Bool
    if !haskey(io, :compact)
        recur_io = IOContext(recur_io, :compact => true)
    end
    recur_io_k = IOContext(recur_io, :typeinfo=>keytype(t))
    recur_io_v = IOContext(recur_io, :typeinfo=>valtype(t))

    summary(io, t)
    isempty(t) && return
    print(io, ":")
    show_circular(io, t) && return
    if limit
        sz = displaysize(io)
        rows, cols = sz[1] - 3, sz[2]
        rows < 2   && (print(io, " …"); return)
        cols < 12  && (cols = 12) # Minimum widths of 2 for key, 4 for value
        cols -= 6 # Subtract the widths of prefix "  " separator " => "
        rows -= 1 # Subtract the summary

        # determine max key width to align the output, caching the strings
        hascolor = get(recur_io, :color, false)
        ks = Vector{String}(undef, min(rows, length(t)))
        vs = Vector{String}(undef, min(rows, length(t)))
        keywidth = 0
        valwidth = 0
        for (i, (k, v)) in enumerate(t)
            i > rows && break
            ks[i] = sprint(show, k, context=recur_io_k, sizehint=0)
            vs[i] = sprint(show, v, context=recur_io_v, sizehint=0)
            keywidth = clamp(hascolor ? textwidth(ANSIIterator(ks[i])) : textwidth(ks[i]), keywidth, cols)
            valwidth = clamp(hascolor ? textwidth(ANSIIterator(vs[i])) : textwidth(vs[i]), valwidth, cols)
        end
        if keywidth > max(div(cols, 2), cols - valwidth)
            keywidth = max(cld(cols, 3), cols - valwidth)
        end
    else
        rows = cols = typemax(Int)
    end

    for (i, (k, v)) in enumerate(t)
        print(io, "\n  ")
        if i == rows < length(t)
            print(io, rpad("⋮", keywidth), " => ⋮")
            break
        end

        if limit
            key = _truncate_at_width_or_chars(hascolor, ks[i], keywidth, true)
        else
            key = sprint(show, k, context=recur_io_k, sizehint=0)
        end
        print(recur_io, key)
        print(io, " => ")

        if limit
            val = _truncate_at_width_or_chars(hascolor, vs[i], cols - keywidth)
            print(io, val)
        else
            show(recur_io_v, v)
        end
    end
end

function summary(io::IO, t::AbstractSet)
    n = length(t)
    showarg(io, t, true)
    print(io, " with ", n, (n==1 ? " element" : " elements"))
end

function show(io::IO, ::MIME"text/plain", t::AbstractSet{T}) where T
    isempty(t) && return show(io, t)
    # show more descriptively, with one line per value
    recur_io = IOContext(io, :SHOWN_SET => t)
    limit = get(io, :limit, false)::Bool

    summary(io, t)
    isempty(t) && return
    print(io, ":")
    show_circular(io, t) && return
    if limit
        sz = displaysize(io)
        rows, cols = sz[1] - 3, sz[2]
        rows < 2   && (print(io, " …"); return)
        cols -= 2 # Subtract the width of prefix "  "
        cols < 4  && (cols = 4) # Minimum widths of 4 for value
        rows -= 1 # Subtract the summary
    else
        rows = cols = typemax(Int)
    end

    for (i, v) in enumerate(t)
        print(io, "\n  ")
        if i == rows < length(t)
            print(io, rpad("⋮", 2))
            break
        end

        if limit
            str = sprint(show, v, context=recur_io, sizehint=0)
            print(io, _truncate_at_width_or_chars(get(io, :color, false)::Bool, str, cols))
        else
            show(recur_io, v)
        end
    end
end

function show(io::IO, ::MIME"text/plain", opt::JLOptions)
    println(io, "JLOptions(")
    fields = fieldnames(JLOptions)
    nfields = length(fields)
    for (i, f) in enumerate(fields)
        v = getfield(opt, i)
        if isa(v, Ptr{UInt8})
            v = (v != C_NULL) ? unsafe_string(v) : ""
        elseif isa(v, Ptr{Ptr{UInt8}})
            v = unsafe_load_commands(v)
        end
        println(io, "  ", f, " = ", repr(v), i < nfields ? "," : "")
    end
    print(io, ")")
end

function show(io::IO, ::MIME"text/plain", t::Task)
    show(io, t)
    if istaskfailed(t)
        println(io)
        show_task_exception(io, t, indent = false)
    end
end


print(io::IO, s::Symbol) = (write(io,s); nothing)

"""
    IOContext

`IOContext` provides a mechanism for passing output configuration settings among [`show`](@ref) methods.

In short, it is an immutable dictionary that is a subclass of `IO`. It supports standard
dictionary operations such as [`getindex`](@ref), and can also be used as an I/O stream.
"""
struct IOContext{IO_t <: IO} <: AbstractPipe
    io::IO_t
    dict::ImmutableDict{Symbol, Any}

    function IOContext{IO_t}(io::IO_t, dict::ImmutableDict{Symbol, Any}) where IO_t<:IO
        @assert !(IO_t <: IOContext) "Cannot create `IOContext` from another `IOContext`."
        return new(io, dict)
    end
end

# (Note that TTY and TTYTerminal io types have a :color property.)
unwrapcontext(io::IO) = io, get(io,:color,false) ? ImmutableDict{Symbol,Any}(:color, true) : ImmutableDict{Symbol,Any}()
unwrapcontext(io::IOContext) = io.io, io.dict

function IOContext(io::IO, dict::ImmutableDict)
    io0 = unwrapcontext(io)[1]
    IOContext{typeof(io0)}(io0, dict)
end

convert(::Type{IOContext}, io::IO) = IOContext(unwrapcontext(io)...)::IOContext

IOContext(io::IO) = convert(IOContext, io)

function IOContext(io::IO, KV::Pair)
    io0, d = unwrapcontext(io)
    IOContext(io0, ImmutableDict{Symbol,Any}(d, KV[1], KV[2]))
end

"""
    IOContext(io::IO, context::IOContext)

Create an `IOContext` that wraps an alternate `IO` but inherits the properties of `context`.
"""
IOContext(io::IO, context::IO) = IOContext(unwrapcontext(io)[1], unwrapcontext(context)[2])

"""
    IOContext(io::IO, KV::Pair...)

Create an `IOContext` that wraps a given stream, adding the specified `key=>value` pairs to
the properties of that stream (note that `io` can itself be an `IOContext`).

 - use `(key => value) in io` to see if this particular combination is in the properties set
 - use `get(io, key, default)` to retrieve the most recent value for a particular key

The following properties are in common use:

 - `:compact`: Boolean specifying that values should be printed more compactly, e.g.
   that numbers should be printed with fewer digits. This is set when printing array
   elements. `:compact` output should not contain line breaks.
 - `:limit`: Boolean specifying that containers should be truncated, e.g. showing `…` in
   place of most elements.
 - `:displaysize`: A `Tuple{Int,Int}` giving the size in rows and columns to use for text
   output. This can be used to override the display size for called functions, but to
   get the size of the screen use the `displaysize` function.
 - `:typeinfo`: a `Type` characterizing the information already printed
   concerning the type of the object about to be displayed. This is mainly useful when
   displaying a collection of objects of the same type, so that redundant type information
   can be avoided (e.g. `[Float16(0)]` can be shown as "Float16[0.0]" instead
   of "Float16[Float16(0.0)]" : while displaying the elements of the array, the `:typeinfo`
   property will be set to `Float16`).
 - `:color`: Boolean specifying whether ANSI color/escape codes are supported/expected.
   By default, this is determined by whether `io` is a compatible terminal and by any
   `--color` command-line flag when `julia` was launched.

# Examples

```jldoctest
julia> io = IOBuffer();

julia> printstyled(IOContext(io, :color => true), "string", color=:red)

julia> String(take!(io))
"\\e[31mstring\\e[39m"

julia> printstyled(io, "string", color=:red)

julia> String(take!(io))
"string"
```

```jldoctest
julia> print(IOContext(stdout, :compact => false), 1.12341234)
1.12341234
julia> print(IOContext(stdout, :compact => true), 1.12341234)
1.12341
```

```jldoctest
julia> function f(io::IO)
           if get(io, :short, false)
               print(io, "short")
           else
               print(io, "loooooong")
           end
       end
f (generic function with 1 method)

julia> f(stdout)
loooooong
julia> f(IOContext(stdout, :short => true))
short
```
"""
IOContext(io::IO, KV::Pair, KVs::Pair...) = IOContext(IOContext(io, KV), KVs...)

show(io::IO, ctx::IOContext) = (print(io, "IOContext("); show(io, ctx.io); print(io, ")"))

pipe_reader(io::IOContext) = io.io
pipe_writer(io::IOContext) = io.io
lock(io::IOContext) = lock(io.io)
unlock(io::IOContext) = unlock(io.io)

in(key_value::Pair, io::IOContext) = in(key_value, io.dict, ===)
in(key_value::Pair, io::IO) = false
haskey(io::IOContext, key) = haskey(io.dict, key)
haskey(io::IO, key) = false
getindex(io::IOContext, key) = getindex(io.dict, key)
getindex(io::IO, key) = throw(KeyError(key))
get(io::IOContext, key, default) = get(io.dict, key, default)
get(io::IO, key, default) = default
keys(io::IOContext) = keys(io.dict)
keys(io::IO) = keys(ImmutableDict{Symbol,Any}())

displaysize(io::IOContext) = haskey(io, :displaysize) ? io[:displaysize]::Tuple{Int,Int} : displaysize(io.io)

show_circular(io::IO, @nospecialize(x)) = false
function show_circular(io::IOContext, @nospecialize(x))
    d = 1
    for (k, v) in io.dict
        if k === :SHOWN_SET
            if v === x
                print(io, "#= circular reference @-$d =#")
                return true
            end
            d += 1
        end
    end
    return false
end

"""
    show([io::IO = stdout], x)

Write a text representation of a value `x` to the output stream `io`. New types `T`
should overload `show(io::IO, x::T)`. The representation used by `show` generally
includes Julia-specific formatting and type information, and should be parseable
Julia code when possible.

[`repr`](@ref) returns the output of `show` as a string.

For a more verbose human-readable text output for objects of type `T`, define
`show(io::IO, ::MIME"text/plain", ::T)` in addition. Checking the `:compact`
[`IOContext`](@ref) key (often checked as `get(io, :compact, false)::Bool`)
of `io` in such methods is recommended,
since some containers show their elements by calling this method with
`:compact => true`.

See also [`print`](@ref), which writes un-decorated representations.

# Examples
```jldoctest
julia> show("Hello World!")
"Hello World!"
julia> print("Hello World!")
Hello World!
```
"""
show(io::IO, @nospecialize(x)) = show_default(io, x)

show(x) = show(stdout, x)

# avoid inferring show_default on the type of `x`
show_default(io::IO, @nospecialize(x)) = _show_default(io, inferencebarrier(x))

function _show_default(io::IO, @nospecialize(x))
    t = typeof(x)
    show(io, inferencebarrier(t)::DataType)
    print(io, '(')
    nf = nfields(x)
    nb = sizeof(x)::Int
    if nf != 0 || nb == 0
        if !show_circular(io, x)
            recur_io = IOContext(io, Pair{Symbol,Any}(:SHOWN_SET, x),
                                 Pair{Symbol,Any}(:typeinfo, Any))
            for i in 1:nf
                f = fieldname(t, i)
                if !isdefined(x, f)
                    print(io, undef_ref_str)
                else
                    show(recur_io, getfield(x, i))
                end
                if i < nf
                    print(io, ", ")
                end
            end
        end
    else
        print(io, "0x")
        r = Ref{Any}(x)
        GC.@preserve r begin
            p = unsafe_convert(Ptr{Cvoid}, r)
            for i in (nb - 1):-1:0
                print(io, string(unsafe_load(convert(Ptr{UInt8}, p + i)), base = 16, pad = 2))
            end
        end
    end
    print(io,')')
end

function active_module()
    isassigned(REPL_MODULE_REF) || return Main
    REPL = REPL_MODULE_REF[]
    return invokelatest(REPL.active_module)::Module
end

# Check if a particular symbol is exported from a standard library module
function is_exported_from_stdlib(name::Symbol, mod::Module)
    !isdefined(mod, name) && return false
    orig = getfield(mod, name)
    while !(mod === Base || mod === Core)
        activemod = active_module()
        parent = parentmodule(mod)
        if mod === activemod || mod === parent || parent === activemod
            return false
        end
        mod = parent
    end
    return isexported(mod, name) && isdefined(mod, name) && !isdeprecated(mod, name) && getfield(mod, name) === orig
end

function show_function(io::IO, f::Function, compact::Bool, fallback::Function)
    ft = typeof(f)
    mt = ft.name.mt
    if mt === Symbol.name.mt
        # uses shared method table
        fallback(io, f)
    elseif compact
        print(io, mt.name)
    elseif isdefined(mt, :module) && isdefined(mt.module, mt.name) &&
        getfield(mt.module, mt.name) === f
        mod = active_module()
        if is_exported_from_stdlib(mt.name, mt.module) || mt.module === mod
            show_sym(io, mt.name)
        else
            print(io, mt.module, ".")
            show_sym(io, mt.name)
        end
    else
        fallback(io, f)
    end
end

show(io::IO, f::Function) = show_function(io, f, get(io, :compact, false)::Bool, show_default)
print(io::IO, f::Function) = show_function(io, f, true, show)

function show(io::IO, f::Core.IntrinsicFunction)
    if !(get(io, :compact, false)::Bool)
        print(io, "Core.Intrinsics.")
    end
    print(io, nameof(f))
end

print(io::IO, f::Core.IntrinsicFunction) = print(io, nameof(f))

show(io::IO, ::Core.TypeofBottom) = print(io, "Union{}")
show(io::IO, ::MIME"text/plain", ::Core.TypeofBottom) = print(io, "Union{}")

function print_without_params(@nospecialize(x))
    b = unwrap_unionall(x)
    return isa(b, DataType) && b.name.wrapper === x
end

function io_has_tvar_name(io::IOContext, name::Symbol, @nospecialize(x))
    for (key, val) in io.dict
        if key === :unionall_env && val isa TypeVar && val.name === name && has_typevar(x, val)
            return true
        end
    end
    return false
end
io_has_tvar_name(io::IO, name::Symbol, @nospecialize(x)) = false

modulesof!(s::Set{Module}, x::TypeVar) = modulesof!(s, x.ub)
function modulesof!(s::Set{Module}, x::Type)
    x = unwrap_unionall(x)
    if x isa DataType
        push!(s, parentmodule(x))
    elseif x isa Union
        modulesof!(s, x.a)
        modulesof!(s, x.b)
    end
    s
end

# given an IO context for printing a type, reconstruct the proper type that
# we're attempting to represent.
# Union{T} where T is a degenerate case and is equal to T.ub, but we don't want
# to print them that way, so filter those out from our aliases completely.
function makeproper(io::IO, @nospecialize(x::Type))
    if io isa IOContext
        for (key, val) in io.dict
            if key === :unionall_env && val isa TypeVar
                x = UnionAll(val, x)
            end
        end
    end
    has_free_typevars(x) && return Any
    return x
end

function make_typealias(@nospecialize(x::Type))
    Any === x && return nothing
    x <: Tuple && return nothing
    mods = modulesof!(Set{Module}(), x)
    Core in mods && push!(mods, Base)
    aliases = Tuple{GlobalRef,SimpleVector}[]
    xenv = UnionAll[]
    for p in uniontypes(unwrap_unionall(x))
        p isa UnionAll && push!(xenv, p)
    end
    x isa UnionAll && push!(xenv, x)
    for mod in mods
        for name in unsorted_names(mod)
            if isdefined(mod, name) && !isdeprecated(mod, name) && isconst(mod, name)
                alias = getfield(mod, name)
                if alias isa Type && !has_free_typevars(alias) && !print_without_params(alias) && x <: alias
                    if alias isa UnionAll
                        (ti, env) = ccall(:jl_type_intersection_with_env, Any, (Any, Any), x, alias)::SimpleVector
                        # ti === Union{} && continue # impossible, since we already checked that x <: alias
                        env = env::SimpleVector
                        # TODO: In some cases (such as the following), the `env` is over-approximated.
                        #       We'd like to disable `fix_inferred_var_bound` since we'll already do that fix-up here.
                        #       (or detect and reverse the computation of it here).
                        #   T = Array{Array{T,1}, 1} where T
                        #   (ti, env) = ccall(:jl_type_intersection_with_env, Any, (Any, Any), T, Vector)
                        #   env[1].ub.var == T.var
                        applied = try
                                # this can fail if `x` contains a covariant
                                # union, and the non-matching branch of the
                                # union has additional restrictions on the
                                # bounds of the environment that are not met by
                                # the instantiation found above
                                alias{env...}
                            catch ex
                                ex isa TypeError || rethrow()
                                continue
                            end
                        for p in xenv
                            applied = rewrap_unionall(applied, p)
                        end
                        has_free_typevars(applied) && continue
                        applied === x || continue # it couldn't figure out the parameter matching
                    elseif alias === x
                        env = Core.svec()
                    else
                        continue # not a complete match
                    end
                    push!(aliases, (GlobalRef(mod, name), env))
                end
            end
        end
    end
    if length(aliases) == 1 # TODO: select the type with the "best" (shortest?) environment
        return aliases[1]
    end
end

isgensym(s::Symbol) = '#' in string(s)

function show_can_elide(p::TypeVar, wheres::Vector, elide::Int, env::SimpleVector, skip::Int)
    elide == 0 && return false
    wheres[elide] === p || return false
    for i = (elide + 1):length(wheres)
        v = wheres[i]::TypeVar
        has_typevar(v.lb, p) && return false
        has_typevar(v.ub, p) && return false
    end
    for i = 1:length(env)
        i == skip && continue
        has_typevar(env[i], p) && return false
    end
    return true
end

function show_typeparams(io::IO, env::SimpleVector, orig::SimpleVector, wheres::Vector)
    n = length(env)
    elide = length(wheres)
    function egal_var(p::TypeVar, @nospecialize o)
        return o isa TypeVar &&
            ccall(:jl_types_egal, Cint, (Any, Any), p.ub, o.ub) != 0 &&
            ccall(:jl_types_egal, Cint, (Any, Any), p.lb, o.lb) != 0
    end
    for i = n:-1:1
        p = env[i]
        if p isa TypeVar
            if i == n && egal_var(p, orig[i]) && show_can_elide(p, wheres, elide, env, i)
                n -= 1
                elide -= 1
            elseif p.lb === Union{} && isgensym(p.name) && show_can_elide(p, wheres, elide, env, i)
                elide -= 1
            elseif p.ub === Any && isgensym(p.name) && show_can_elide(p, wheres, elide, env, i)
                elide -= 1
            end
        end
    end
    if n > 0
        print(io, "{")
        for i = 1:n
            p = env[i]
            if p isa TypeVar
                if p.lb === Union{} && something(findfirst(@nospecialize(w) -> w === p, wheres), 0) > elide
                    print(io, "<:")
                    show(io, p.ub)
                elseif p.ub === Any && something(findfirst(@nospecialize(w) -> w === p, wheres), 0) > elide
                    print(io, ">:")
                    show(io, p.lb)
                else
                    show(io, p)
                end
            else
                show(io, p)
            end
            i < n && print(io, ", ")
        end
        print(io, "}")
    end
    resize!(wheres, elide)
    nothing
end

function show_typealias(io::IO, name::GlobalRef, x::Type, env::SimpleVector, wheres::Vector)
    if !(get(io, :compact, false)::Bool)
        # Print module prefix unless alias is visible from module passed to
        # IOContext. If :module is not set, default to Main (or current active module).
        # nothing can be used to force printing prefix.
        from = get(io, :module, active_module())
        if (from === nothing || !isvisible(name.name, name.mod, from))
            show(io, name.mod)
            print(io, ".")
        end
    end
    print(io, name.name)
    isempty(env) && return
    io = IOContext(io)
    for p in wheres
        io = IOContext(io, :unionall_env => p)
    end
    orig = getfield(name.mod, name.name)
    vars = TypeVar[]
    while orig isa UnionAll
        push!(vars, orig.var)
        orig = orig.body
    end
    show_typeparams(io, env, Core.svec(vars...), wheres)
    nothing
end

function make_wheres(io::IO, env::SimpleVector, @nospecialize(x::Type))
    seen = IdSet()
    wheres = TypeVar[]
    # record things printed by the context
    if io isa IOContext
        for (key, val) in io.dict
            if key === :unionall_env && val isa TypeVar && has_typevar(x, val)
                push!(seen, val)
            end
        end
    end
    # record things in x to print outermost
    while x isa UnionAll
        if !(x.var in seen)
            push!(seen, x.var)
            push!(wheres, x.var)
        end
        x = x.body
    end
    # record remaining things in env to print innermost
    for i = length(env):-1:1
        p = env[i]
        if p isa TypeVar && !(p in seen)
            push!(seen, p)
            pushfirst!(wheres, p)
        end
    end
    return wheres
end

function show_wheres(io::IO, wheres::Vector{TypeVar})
    isempty(wheres) && return
    io = IOContext(io)
    n = length(wheres)
    for i = 1:n
        p = wheres[i]
        print(io, n == 1 ? " where " : i == 1 ? " where {" : ", ")
        show(io, p)
        io = IOContext(io, :unionall_env => p)
    end
    n > 1 && print(io, "}")
    nothing
end

function show_typealias(io::IO, @nospecialize(x::Type))
    properx = makeproper(io, x)
    alias = make_typealias(properx)
    alias === nothing && return false
    wheres = make_wheres(io, alias[2], x)
    show_typealias(io, alias[1], x, alias[2], wheres)
    show_wheres(io, wheres)
    return true
end

function make_typealiases(@nospecialize(x::Type))
    aliases = SimpleVector[]
    Any === x && return aliases, Union{}
    x <: Tuple && return aliases, Union{}
    mods = modulesof!(Set{Module}(), x)
    Core in mods && push!(mods, Base)
    vars = Dict{Symbol,TypeVar}()
    xenv = UnionAll[]
    each = Any[]
    for p in uniontypes(unwrap_unionall(x))
        p isa UnionAll && push!(xenv, p)
        push!(each, rewrap_unionall(p, x))
    end
    x isa UnionAll && push!(xenv, x)
    for mod in mods
        for name in unsorted_names(mod)
            if isdefined(mod, name) && !isdeprecated(mod, name) && isconst(mod, name)
                alias = getfield(mod, name)
                if alias isa Type && !has_free_typevars(alias) && !print_without_params(alias) && !(alias <: Tuple)
                    (ti, env) = ccall(:jl_type_intersection_with_env, Any, (Any, Any), x, alias)::SimpleVector
                    ti === Union{} && continue
                    # make sure this alias wasn't from an unrelated part of the Union
                    mod2 = modulesof!(Set{Module}(), alias)
                    mod in mod2 || (mod === Base && Core in mods) || continue
                    env = env::SimpleVector
                    applied = alias
                    if !isempty(env)
                        applied = try
                                # this can fail if `x` contains a covariant
                                # union, and the non-matching branch of the
                                # union has additional restrictions on the
                                # bounds of the environment that are not met by
                                # the instantiation found above
                                alias{env...}
                            catch ex
                                ex isa TypeError || rethrow()
                                continue
                            end
                    end
                    ul = unionlen(applied)
                    for p in xenv
                        applied = rewrap_unionall(applied, p)
                    end
                    has_free_typevars(applied) && continue
                    applied <: x || continue # parameter matching didn't make a subtype
                    print_without_params(x) && (env = Core.svec())
                    for typ in each # check that the alias also fully subsumes at least component of the input
                        if typ <: applied
                            push!(aliases, Core.svec(GlobalRef(mod, name), env, applied, (ul, -length(env))))
                            break
                        end
                    end
                end
            end
        end
    end
    if isempty(aliases)
        return aliases, Union{}
    end
    sort!(aliases, by = x -> x[4]::Tuple{Int,Int}, rev = true) # heuristic sort by "best" environment
    let applied = Union{}
        applied1 = Union{}
        keep = SimpleVector[]
        prev = (0, 0)
        for alias in aliases
            alias4 = alias[4]::Tuple{Int,Int}
            if alias4[1] < 2
                if !(alias[3] <: applied)
                    applied1 = Union{applied1, alias[3]}
                    push!(keep, alias)
                end
            elseif alias4 == prev || !(alias[3] <: applied)
                applied = applied1 = Union{applied1, alias[3]}
                push!(keep, alias)
                prev = alias4
            end
        end
        return keep, applied1
    end
end

function show_unionaliases(io::IO, x::Union)
    properx = makeproper(io, x)
    aliases, applied = make_typealiases(properx)
    isempty(aliases) && return false
    first = true
    tvar = false
    for typ in uniontypes(x)
        if isa(typ, TypeVar)
            tvar = true # sort bare TypeVars to the end
            continue
        elseif rewrap_unionall(typ, properx) <: applied
            continue
        end
        print(io, first ? "Union{" : ", ")
        first = false
        show(io, typ)
    end
    if first && !tvar && length(aliases) == 1
        alias = aliases[1]
        env = alias[2]::SimpleVector
        wheres = make_wheres(io, env, x)
        show_typealias(io, alias[1], x, env, wheres)
        show_wheres(io, wheres)
    else
        for alias in aliases
            print(io, first ? "Union{" : ", ")
            first = false
            env = alias[2]::SimpleVector
            wheres = make_wheres(io, env, x)
            show_typealias(io, alias[1], x, env, wheres)
            show_wheres(io, wheres)
        end
        if tvar
            for typ in uniontypes(x)
                if isa(typ, TypeVar)
                    print(io, ", ")
                    show(io, typ)
                end
            end
        end
        print(io, "}")
    end
    return true
end

function show(io::IO, ::MIME"text/plain", @nospecialize(x::Type))
    if !print_without_params(x)
        properx = makeproper(io, x)
        if make_typealias(properx) !== nothing || (unwrap_unionall(x) isa Union && x <: make_typealiases(properx)[2])
            show(IOContext(io, :compact => true), x)
            if !(get(io, :compact, false)::Bool)
                printstyled(io, " (alias for "; color = :light_black)
                printstyled(IOContext(io, :compact => false), x, color = :light_black)
                printstyled(io, ")"; color = :light_black)
            end
            return
        end
    end
    show(io, x)
    # give a helpful hint for function types
    if x isa DataType && x !== UnionAll && !(get(io, :compact, false)::Bool)
        tn = x.name::Core.TypeName
        globname = isdefined(tn, :mt) ? tn.mt.name : nothing
        if is_global_function(tn, globname)
            print(io, " (singleton type of function ")
            show_sym(io, globname)
            print(io, ", subtype of Function)")
        end
    end
end

show(io::IO, @nospecialize(x::Type)) = _show_type(io, inferencebarrier(x))
function _show_type(io::IO, @nospecialize(x::Type))
    if print_without_params(x)
        show_type_name(io, (unwrap_unionall(x)::DataType).name)
        return
    elseif get(io, :compact, true)::Bool && show_typealias(io, x)
        return
    elseif x isa DataType
        show_datatype(io, x)
        return
    elseif x isa Union
        if get(io, :compact, true)::Bool && show_unionaliases(io, x)
            return
        end
        print(io, "Union")
        show_delim_array(io, uniontypes(x), '{', ',', '}', false)
        return
    end

    x = x::UnionAll
    wheres = TypeVar[]
    let io = IOContext(io)
        while x isa UnionAll
            var = x.var
            if var.name === :_ || io_has_tvar_name(io, var.name, x)
                counter = 1
                while true
                    newname = Symbol(var.name, counter)
                    if !io_has_tvar_name(io, newname, x)
                        var = TypeVar(newname, var.lb, var.ub)
                        x = x{var}
                        break
                    end
                    counter += 1
                end
            else
                x = x.body
            end
            push!(wheres, var)
            io = IOContext(io, :unionall_env => var)
        end
        if x isa DataType
            show_datatype(io, x, wheres)
        else
            show(io, x)
        end
    end
    show_wheres(io, wheres)
end

# Check whether 'sym' (defined in module 'parent') is visible from module 'from'
# If an object with this name exists in 'from', we need to check that it's the same binding
# and that it's not deprecated.
function isvisible(sym::Symbol, parent::Module, from::Module)
    owner = ccall(:jl_binding_owner, Ptr{Cvoid}, (Any, Any), parent, sym)
    from_owner = ccall(:jl_binding_owner, Ptr{Cvoid}, (Any, Any), from, sym)
    return owner !== C_NULL && from_owner === owner &&
        !isdeprecated(parent, sym) &&
        isdefined(from, sym) # if we're going to return true, force binding resolution
end

function is_global_function(tn::Core.TypeName, globname::Union{Symbol,Nothing})
    if globname !== nothing
        globname_str = string(globname::Symbol)
        if ('#' ∉ globname_str && '@' ∉ globname_str && isdefined(tn, :module) &&
                isbindingresolved(tn.module, globname) && isdefined(tn.module, globname) &&
                isconcretetype(tn.wrapper) && isa(getfield(tn.module, globname), tn.wrapper))
            return true
        end
    end
    return false
end

function show_type_name(io::IO, tn::Core.TypeName)
    if tn === UnionAll.name
        # by coincidence, `typeof(Type)` is a valid representation of the UnionAll type.
        # intercept this case and print `UnionAll` instead.
        return print(io, "UnionAll")
    end
    globname = isdefined(tn, :mt) ? tn.mt.name : nothing
    globfunc = is_global_function(tn, globname)
    sym = (globfunc ? globname : tn.name)::Symbol
    globfunc && print(io, "typeof(")
    quo = false
    if !(get(io, :compact, false)::Bool)
        # Print module prefix unless type is visible from module passed to
        # IOContext If :module is not set, default to Main (or current active module).
        # nothing can be used to force printing prefix
        from = get(io, :module, active_module())
        if isdefined(tn, :module) && (from === nothing || !isvisible(sym, tn.module, from))
            show(io, tn.module)
            print(io, ".")
            if globfunc && !is_id_start_char(first(string(sym)))
                print(io, ':')
                if sym in quoted_syms
                    print(io, '(')
                    quo = true
                end
            end
        end
    end
    show_sym(io, sym)
    quo      && print(io, ")")
    globfunc && print(io, ")")
    nothing
end

function maybe_kws_nt(x::DataType)
    x.name === typename(Pairs) || return nothing
    length(x.parameters) == 4 || return nothing
    x.parameters[1] === Symbol || return nothing
    p4 = x.parameters[4]
    if (isa(p4, DataType) && p4.name === typename(NamedTuple) && length(p4.parameters) == 2)
        syms, types = p4.parameters
        types isa DataType || return nothing
        x.parameters[2] === eltype(p4) || return nothing
        isa(syms, Tuple) || return nothing
        x.parameters[3] === typeof(syms) || return nothing
        return p4
    end
    return nothing
end

function show_datatype(io::IO, x::DataType, wheres::Vector{TypeVar}=TypeVar[])
    parameters = x.parameters::SimpleVector
    istuple = x.name === Tuple.name
    isnamedtuple = x.name === typename(NamedTuple)
    kwsnt = maybe_kws_nt(x)
    n = length(parameters)

    # Print tuple types with homogeneous tails longer than max_n compactly using `NTuple` or `Vararg`
    if istuple
        max_n = 3
        taillen = 1
        for i in (n-1):-1:1
            if parameters[i] === parameters[n]
                taillen += 1
            else
                break
            end
        end
        if n == taillen > max_n
            print(io, "NTuple{", n, ", ")
            show(io, parameters[1])
            print(io, "}")
        else
            print(io, "Tuple{")
            for i = 1:(taillen > max_n ? n-taillen : n)
                i > 1 && print(io, ", ")
                show(io, parameters[i])
            end
            if taillen > max_n
                print(io, ", Vararg{")
                show(io, parameters[n])
                print(io, ", ", taillen, "}")
            end
            print(io, "}")
        end
        return
    elseif isnamedtuple
        syms, types = parameters
        if syms isa Tuple && types isa DataType
            print(io, "@NamedTuple{")
            show_at_namedtuple(io, syms, types)
            print(io, "}")
            return
        end
    elseif get(io, :backtrace, false)::Bool && kwsnt !== nothing
        # simplify the type representation of keyword arguments
        # when printing signature of keyword method in the stack trace
        print(io, "@Kwargs{")
        show_at_namedtuple(io, kwsnt.parameters[1]::Tuple, kwsnt.parameters[2]::DataType)
        print(io, "}")
        return
    end

    show_type_name(io, x.name)
    show_typeparams(io, parameters, (unwrap_unionall(x.name.wrapper)::DataType).parameters, wheres)
end

function show_at_namedtuple(io::IO, syms::Tuple, types::DataType)
    first = true
    for i in 1:length(syms)
        if !first
            print(io, ", ")
        end
        print(io, syms[i])
        typ = types.parameters[i]
        if typ !== Any
            print(io, "::")
            show(io, typ)
        end
        first = false
    end
end

function show_supertypes(io::IO, typ::DataType)
    print(io, typ)
    while typ != Any
        typ = supertype(typ)
        print(io, " <: ", typ)
    end
end

show_supertypes(typ::DataType) = show_supertypes(stdout, typ)

"""
    @show exs...

Prints one or more expressions, and their results, to `stdout`, and returns the last result.

See also: [`show`](@ref), [`@info`](@ref man-logging), [`println`](@ref).

# Examples
```jldoctest
julia> x = @show 1+2
1 + 2 = 3
3

julia> @show x^2 x/2;
x ^ 2 = 9
x / 2 = 1.5
```
"""
macro show(exs...)
    blk = Expr(:block)
    for ex in exs
        push!(blk.args, :(println($(sprint(show_unquoted,ex)*" = "),
                                  repr(begin local value = $(esc(ex)) end))))
    end
    isempty(exs) || push!(blk.args, :value)
    return blk
end

function show(io::IO, tn::Core.TypeName)
    print(io, "typename(")
    show_type_name(io, tn)
    print(io, ")")
end

show(io::IO, ::Nothing) = print(io, "nothing")
show(io::IO, b::Bool) = print(io, get(io, :typeinfo, Any) === Bool ? (b ? "1" : "0") : (b ? "true" : "false"))
show(io::IO, n::Signed) = (write(io, string(n)); nothing)
show(io::IO, n::Unsigned) = print(io, "0x", string(n, pad = sizeof(n)<<1, base = 16))
print(io::IO, n::Unsigned) = print(io, string(n))

show(io::IO, p::Ptr) = print(io, typeof(p), " @0x$(string(UInt(p), base = 16, pad = Sys.WORD_SIZE>>2))")

has_tight_type(p::Pair) =
    typeof(p.first)  == typeof(p).parameters[1] &&
    typeof(p.second) == typeof(p).parameters[2]

isdelimited(io::IO, x) = true
isdelimited(io::IO, x::Function) = !isoperator(Symbol(x))

# !isdelimited means that the Pair is printed with "=>" (like in "1 => 2"),
# without its explicit type (like in "Pair{Integer,Integer}(1, 2)")
isdelimited(io::IO, p::Pair) = !(has_tight_type(p) || get(io, :typeinfo, Any) == typeof(p))

function gettypeinfos(io::IO, p::Pair)
    typeinfo = get(io, :typeinfo, Any)
    p isa typeinfo <: Pair ?
        fieldtype(typeinfo, 1) => fieldtype(typeinfo, 2) :
        Any => Any
end

function show(io::IO, p::Pair)
    isdelimited(io, p) && return show_pairtyped(io, p)
    typeinfos = gettypeinfos(io, p)
    for i = (1, 2)
        io_i = IOContext(io, :typeinfo => typeinfos[i])
        isdelimited(io_i, p[i]) || print(io, "(")
        show(io_i, p[i])
        isdelimited(io_i, p[i]) || print(io, ")")
        i == 1 && print(io, get(io, :compact, false)::Bool ? "=>" : " => ")
    end
end

function show_pairtyped(io::IO, p::Pair{K,V}) where {K,V}
    show(io, typeof(p))
    show(io, (p.first, p.second))
end

function show(io::IO, m::Module)
    if is_root_module(m)
        print(io, nameof(m))
    else
        print_fullname(io, m)
    end
end
# The call to print_fullname above was originally `print(io, join(fullname(m),"."))`,
# which allocates. The method below provides the same behavior without allocating.
# See https://github.com/JuliaLang/julia/pull/42773 for perf information.
function print_fullname(io::IO, m::Module)
    mp = parentmodule(m)
    if m === Main || m === Base || m === Core || mp === m
        show_sym(io, nameof(m))
    else
        print_fullname(io, mp)
        print(io, '.')
        show_sym(io, nameof(m))
    end
end

sourceinfo_slotnames(src::CodeInfo) = sourceinfo_slotnames(src.slotnames)
function sourceinfo_slotnames(slotnames::Vector{Symbol})
    names = Dict{String,Int}()
    printnames = Vector{String}(undef, length(slotnames))
    for i in eachindex(slotnames)
        if slotnames[i] === :var"#unused#"
            printnames[i] = "_"
            continue
        end
        name = string(slotnames[i])
        idx = get!(names, name, i)
        if idx != i || isempty(name)
            printname = "$name@_$i"
            idx > 0 && (printnames[idx] = "$name@_$idx")
            names[name] = 0
        else
            printname = name
        end
        printnames[i] = printname
    end
    return printnames
end

show(io::IO, l::Core.MethodInstance) = show_mi(io, l)

function show_mi(io::IO, l::Core.MethodInstance, from_stackframe::Bool=false)
    def = l.def
    if isa(def, Method)
        if isdefined(def, :generator) && l === def.generator
            print(io, "MethodInstance generator for ")
            show(io, def)
        else
            print(io, "MethodInstance for ")
            show_tuple_as_call(io, def.name, l.specTypes; qualified=true)
        end
    else
        print(io, "Toplevel MethodInstance thunk")
        # `thunk` is not very much information to go on. If this
        # MethodInstance is part of a stacktrace, it gets location info
        # added by other means.  But if it isn't, then we should try
        # to print a little more identifying information.
        if !from_stackframe
            linetable = l.uninferred.linetable
            line = isempty(linetable) ? "unknown" : (lt = linetable[1]::Union{LineNumberNode,Core.LineInfoNode}; string(lt.file, ':', lt.line))
            print(io, " from ", def, " starting at ", line)
        end
    end
end

# These sometimes show up as Const-values in InferenceFrameInfo signatures
show(io::IO, r::Core.Compiler.UnitRange) = show(io, r.start : r.stop)
show(io::IO, mime::MIME{Symbol("text/plain")}, r::Core.Compiler.UnitRange) = show(io, mime, r.start : r.stop)

function show(io::IO, mi_info::Core.Compiler.Timings.InferenceFrameInfo)
    mi = mi_info.mi
    def = mi.def
    if isa(def, Method)
        if isdefined(def, :generator) && mi === def.generator
            print(io, "InferenceFrameInfo generator for ")
            show(io, def)
        else
            print(io, "InferenceFrameInfo for ")
            argnames = [isa(a, Core.Const) ? (isa(a.val, Type) ? "" : a.val) : "" for a in mi_info.slottypes[1:mi_info.nargs]]
            show_tuple_as_call(io, def.name, mi.specTypes; argnames, qualified=true)
        end
    else
        linetable = mi.uninferred.linetable
        line = isempty(linetable) ? "" : (lt = linetable[1]; string(lt.file, ':', lt.line))
        print(io, "Toplevel InferenceFrameInfo thunk from ", def, " starting at ", line)
    end
end

function show(io::IO, tinf::Core.Compiler.Timings.Timing)
    print(io, "Core.Compiler.Timings.Timing(", tinf.mi_info, ") with ", length(tinf.children), " children")
end

function show_delim_array(io::IO, itr::Union{AbstractArray,SimpleVector}, op, delim, cl,
                          delim_one, i1=first(LinearIndices(itr)), l=last(LinearIndices(itr)))
    print(io, op)
    if !show_circular(io, itr)
        recur_io = IOContext(io, :SHOWN_SET => itr)
        first = true
        i = i1
        if l >= i1
            while true
                if !isassigned(itr, i)
                    print(io, undef_ref_str)
                else
                    x = itr[i]
                    show(recur_io, x)
                end
                i += 1
                if i > l
                    delim_one && first && print(io, delim)
                    break
                end
                first = false
                print(io, delim)
                print(io, ' ')
            end
        end
    end
    print(io, cl)
end

function show_delim_array(io::IO, itr, op, delim, cl, delim_one, i1=1, n=typemax(Int))
    print(io, op)
    if !show_circular(io, itr)
        recur_io = IOContext(io, :SHOWN_SET => itr)
        y = iterate(itr)
        first = true
        i0 = i1-1
        while i1 > 1 && y !== nothing
            y = iterate(itr, y[2])
            i1 -= 1
        end
        if y !== nothing
            typeinfo = get(io, :typeinfo, Any)
            while true
                x = y[1]
                y = iterate(itr, y[2])
                show(IOContext(recur_io, :typeinfo => itr isa typeinfo <: Tuple ?
                                             fieldtype(typeinfo, i1+i0) :
                                             typeinfo),
                     x)
                i1 += 1
                if y === nothing || i1 > n
                    delim_one && first && print(io, delim)
                    break
                end
                first = false
                print(io, delim)
                print(io, ' ')
            end
        end
    end
    print(io, cl)
end

show(io::IO, t::Tuple) = show_delim_array(io, t, '(', ',', ')', true)
show(io::IO, v::SimpleVector) = show_delim_array(io, v, "svec(", ',', ')', false)

show(io::IO, s::Symbol) = show_unquoted_quote_expr(io, s, 0, 0, 0)

## Abstract Syntax Tree (AST) printing ##

# Summary:
#   print(io, ex) defers to show_unquoted(io, ex)
#   show(io, ex) defers to show_unquoted(io, QuoteNode(ex))
#   show_unquoted(io, ex) does the heavy lifting
#
# AST printing should follow two rules:
#   1. Meta.parse(string(ex)) == ex
#   2. eval(Meta.parse(repr(ex))) == ex
#
# Rule 1 means that printing an expression should generate Julia code which
# could be reparsed to obtain the original expression. This code should be
# unambiguous and as readable as possible.
#
# Rule 2 means that showing an expression should generate a quoted version of
# print’s output. Parsing and then evaling this output should return the
# original expression.
#
# This is consistent with many other show methods, i.e.:
#   show(Set([1,2,3]))                     # ==> "Set{Int64}([2,3,1])"
#   eval(Meta.parse("Set{Int64}([2,3,1])")) # ==> An actual set
# While this isn’t true of ALL show methods, it is of all ASTs.

using Core.Compiler: TypedSlot, UnoptSlot

const ExprNode = Union{Expr, QuoteNode, UnoptSlot, LineNumberNode, SSAValue,
                       GotoNode, GotoIfNot, GlobalRef, PhiNode, PhiCNode, UpsilonNode,
                       ReturnNode}
# Operators have precedence levels from 1-N, and show_unquoted defaults to a
# precedence level of 0 (the fourth argument). The top-level print and show
# methods use a precedence of -1 to specially allow space-separated macro syntax.
# IOContext(io, :unquote_fallback => false) tells show_unquoted to treat any
# Expr whose head is :$ as if it is inside a quote, preventing fallback to the
# "unhandled" case: this is used by print/string to be lawful to Rule 1 above.
# On the contrary, show/repr have to follow Rule 2, requiring any Expr whose
# head is :$ and which is not inside a quote to fallback to the "unhandled" case:
# this is behavior is triggered by IOContext(io, :unquote_fallback => true)
print(        io::IO, ex::ExprNode)    = (show_unquoted(IOContext(io, :unquote_fallback => false), ex, 0, -1); nothing)
show(         io::IO, ex::ExprNode)    = show_unquoted_quote_expr(IOContext(io, :unquote_fallback => true), ex, 0, -1, 0)
show_unquoted(io::IO, ex)              = show_unquoted(io, ex, 0, 0)
show_unquoted(io::IO, ex, indent::Int) = show_unquoted(io, ex, indent, 0)
show_unquoted(io::IO, ex, ::Int,::Int) = show(io, ex)
show_unquoted(io::IO, ex, indent::Int, prec::Int, ::Int) = show_unquoted(io, ex, indent, prec)

## AST printing constants ##

const indent_width = 4
const quoted_syms = Set{Symbol}([:(:),:(::),:(:=),:(=),:(==),:(===),:(=>)])
const uni_syms = Set{Symbol}([:(::), :(<:), :(>:)])
const uni_ops = Set{Symbol}([:(+), :(-), :(!), :(¬), :(~), :(<:), :(>:), :(√), :(∛), :(∜), :(∓), :(±)])
const expr_infix_wide = Set{Symbol}([
    :(=), :(+=), :(-=), :(*=), :(/=), :(\=), :(^=), :(&=), :(|=), :(÷=), :(%=), :(>>>=), :(>>=), :(<<=),
    :(.=), :(.+=), :(.-=), :(.*=), :(./=), :(.\=), :(.^=), :(.&=), :(.|=), :(.÷=), :(.%=), :(.>>>=), :(.>>=), :(.<<=),
    :(&&), :(||), :(<:), :($=), :(⊻=), :(>:), :(-->),
    :(:=), :(≔), :(⩴), :(≕)])
const expr_infix = Set{Symbol}([:(:), :(->), :(::)])
const expr_infix_any = union(expr_infix, expr_infix_wide)
const expr_calls  = Dict(:call => ('(',')'), :calldecl => ('(',')'),
                         :ref => ('[',']'), :curly => ('{','}'), :(.) => ('(',')'))
const expr_parens = Dict(:tuple=>('(',')'), :vcat=>('[',']'),
                         :hcat =>('[',']'), :row =>('[',']'), :vect=>('[',']'),
                         :ncat =>('[',']'), :nrow =>('[',']'),
                         :braces=>('{','}'), :bracescat=>('{','}'))

## AST decoding helpers ##

is_id_start_char(c::AbstractChar) = ccall(:jl_id_start_char, Cint, (UInt32,), c) != 0
is_id_char(c::AbstractChar) = ccall(:jl_id_char, Cint, (UInt32,), c) != 0

"""
     isidentifier(s) -> Bool

Return whether the symbol or string `s` contains characters that are parsed as
a valid ordinary identifier (not a binary/unary operator) in Julia code;
see also [`Base.isoperator`](@ref).

Internally Julia allows any sequence of characters in a `Symbol` (except `\\0`s),
and macros automatically use variable names containing `#` in order to avoid
naming collision with the surrounding code. In order for the parser to
recognize a variable, it uses a limited set of characters (greatly extended by
Unicode). `isidentifier()` makes it possible to query the parser directly
whether a symbol contains valid characters.

# Examples
```jldoctest
julia> Meta.isidentifier(:x), Meta.isidentifier("1x")
(true, false)
```
"""
function isidentifier(s::AbstractString)
    x = Iterators.peel(s)
    isnothing(x) && return false
    (s == "true" || s == "false") && return false
    c, rest = x
    is_id_start_char(c) || return false
    return all(is_id_char, rest)
end
isidentifier(s::Symbol) = isidentifier(string(s))

is_op_suffix_char(c::AbstractChar) = ccall(:jl_op_suffix_char, Cint, (UInt32,), c) != 0

_isoperator(s) = ccall(:jl_is_operator, Cint, (Cstring,), s) != 0

"""
    isoperator(s::Symbol)

Return `true` if the symbol can be used as an operator, `false` otherwise.

# Examples
```jldoctest
julia> Meta.isoperator(:+), Meta.isoperator(:f)
(true, false)
```
"""
isoperator(s::Union{Symbol,AbstractString}) = _isoperator(s) || ispostfixoperator(s)

"""
    isunaryoperator(s::Symbol)

Return `true` if the symbol can be used as a unary (prefix) operator, `false` otherwise.

# Examples
```jldoctest
julia> Meta.isunaryoperator(:-), Meta.isunaryoperator(:√), Meta.isunaryoperator(:f)
(true, true, false)
```
"""
isunaryoperator(s::Symbol) = ccall(:jl_is_unary_operator, Cint, (Cstring,), s) != 0
is_unary_and_binary_operator(s::Symbol) = ccall(:jl_is_unary_and_binary_operator, Cint, (Cstring,), s) != 0
is_syntactic_operator(s::Symbol) = ccall(:jl_is_syntactic_operator, Cint, (Cstring,), s) != 0

"""
    isbinaryoperator(s::Symbol)

Return `true` if the symbol can be used as a binary (infix) operator, `false` otherwise.

# Examples
```jldoctest
julia> Meta.isbinaryoperator(:-), Meta.isbinaryoperator(:√), Meta.isbinaryoperator(:f)
(true, false, false)
```
"""
function isbinaryoperator(s::Symbol)
    return _isoperator(s) && (!isunaryoperator(s) || is_unary_and_binary_operator(s)) &&
        s !== Symbol("'")
end

"""
    ispostfixoperator(s::Union{Symbol,AbstractString})

Return `true` if the symbol can be used as a postfix operator, `false` otherwise.

# Examples
```jldoctest
julia> Meta.ispostfixoperator(Symbol("'")), Meta.ispostfixoperator(Symbol("'ᵀ")), Meta.ispostfixoperator(:-)
(true, true, false)
```
"""
function ispostfixoperator(s::Union{Symbol,AbstractString})
    s = String(s)::String
    return startswith(s, '\'') && all(is_op_suffix_char, SubString(s, 2))
end

"""
    operator_precedence(s::Symbol)

Return an integer representing the precedence of operator `s`, relative to
other operators. Higher-numbered operators take precedence over lower-numbered
operators. Return `0` if `s` is not a valid operator.

# Examples
```jldoctest
julia> Base.operator_precedence(:+), Base.operator_precedence(:*), Base.operator_precedence(:.)
(11, 12, 17)

julia> Base.operator_precedence(:sin), Base.operator_precedence(:+=), Base.operator_precedence(:(=))  # (Note the necessary parens on `:(=)`)
(0, 1, 1)
```
"""
operator_precedence(s::Symbol) = Int(ccall(:jl_operator_precedence, Cint, (Cstring,), s))
operator_precedence(x::Any) = 0 # fallback for generic expression nodes
const prec_assignment = operator_precedence(:(=))
const prec_pair = operator_precedence(:(=>))
const prec_control_flow = operator_precedence(:(&&))
const prec_arrow = operator_precedence(:(-->))
const prec_comparison = operator_precedence(:(>))
const prec_power = operator_precedence(:(^))
const prec_decl = operator_precedence(:(::))

"""
    operator_associativity(s::Symbol)

Return a symbol representing the associativity of operator `s`. Left- and right-associative
operators return `:left` and `:right`, respectively. Return `:none` if `s` is non-associative
or an invalid operator.

# Examples
```jldoctest
julia> Base.operator_associativity(:-), Base.operator_associativity(:+), Base.operator_associativity(:^)
(:left, :none, :right)

julia> Base.operator_associativity(:⊗), Base.operator_associativity(:sin), Base.operator_associativity(:→)
(:left, :none, :right)
```
"""
function operator_associativity(s::Symbol)
    if operator_precedence(s) in (prec_arrow, prec_assignment, prec_control_flow, prec_pair, prec_power) ||
        (isunaryoperator(s) && !is_unary_and_binary_operator(s)) || s === :<| || s === :||
        return :right
    elseif operator_precedence(s) in (0, prec_comparison) || s in (:+, :++, :*)
        return :none
    end
    return :left
end

is_quoted(ex)            = false
is_quoted(ex::QuoteNode) = true
is_quoted(ex::Expr)      = is_expr(ex, :quote, 1) || is_expr(ex, :inert, 1)

unquoted(ex::QuoteNode)  = ex.value
unquoted(ex::Expr)       = ex.args[1]

## AST printing helpers ##

function printstyled end
function with_output_color end

emphasize(io, str::AbstractString, col = Base.error_color()) = get(io, :color, false)::Bool ?
    printstyled(io, str; color=col, bold=true) :
    print(io, uppercase(str))

show_linenumber(io::IO, line)       = printstyled(io, "#= line ", line, " =#", color=:light_black)
show_linenumber(io::IO, line, file) = printstyled(io, "#= ", file, ":", line, " =#", color=:light_black)
show_linenumber(io::IO, line, file::Nothing) = show_linenumber(io, line)

# show a block, e g if/for/etc
function show_block(io::IO, head, args::Vector, body, indent::Int, quote_level::Int)
    print(io, head)
    if !isempty(args)
        print(io, ' ')
        if head === :elseif
            show_list(io, args, " ", indent, 0, quote_level)
        else
            show_list(io, args, ", ", indent, 0, quote_level)
        end
    end

    ind = head === :module || head === :baremodule ? indent : indent + indent_width
    exs = (is_expr(body, :block) || is_expr(body, :quote)) ? body.args : Any[body]
    for ex in exs
        print(io, '\n', " "^ind)
        show_unquoted(io, ex, ind, -1, quote_level)
    end
    print(io, '\n', " "^indent)
end
show_block(io::IO,head,    block,i::Int, quote_level::Int) = show_block(io,head, [], block,i, quote_level)
function show_block(io::IO, head, arg, block, i::Int, quote_level::Int)
    if is_expr(arg, :block) || is_expr(arg, :quote)
        show_block(io, head, arg.args, block, i, quote_level)
    else
        show_block(io, head, Any[arg], block, i, quote_level)
    end
end

# show an indented list
function show_list(io::IO, items, sep, indent::Int, prec::Int=0, quote_level::Int=0, enclose_operators::Bool=false,
                   kw::Bool=false)
    n = length(items)
    n == 0 && return
    indent += indent_width
    first = true
    for item in items
        !first && print(io, sep)
        parens = !is_quoted(item) &&
            (first && prec >= prec_power &&
             ((item isa Expr && item.head === :call && (callee = item.args[1]; isa(callee, Symbol) && callee in uni_ops)) ||
              (item isa Real && item < 0))) ||
            (enclose_operators && item isa Symbol && isoperator(item) && is_valid_identifier(item))
        parens && print(io, '(')
        if kw && is_expr(item, :kw, 2)
            item = item::Expr
            show_unquoted(io, Expr(:(=), item.args[1], item.args[2]), indent, parens ? 0 : prec, quote_level)
        elseif kw && is_expr(item, :(=), 2)
            item = item::Expr
            show_unquoted_expr_fallback(io, item, indent, quote_level)
        else
            show_unquoted(io, item, indent, parens ? 0 : prec, quote_level)
        end
        parens && print(io, ')')
        first = false
    end
end
# show an indented list inside the parens (op, cl)
function show_enclosed_list(io::IO, op, items, sep, cl, indent, prec=0, quote_level=0, encl_ops=false, kw::Bool=false)
    print(io, op)
    show_list(io, items, sep, indent, prec, quote_level, encl_ops, kw)
    print(io, cl)
end

function is_valid_identifier(sym)
    return isidentifier(sym) || (
        _isoperator(sym) &&
        !(sym in (Symbol("'"), :(::), :?)) &&
        !is_syntactic_operator(sym)
    )
end

# show a normal (non-operator) function call, e.g. f(x, y) or A[z]
# kw: `=` expressions are parsed with head `kw` in this context
function show_call(io::IO, head, func, func_args, indent, quote_level, kw::Bool)
    op, cl = expr_calls[head]
    if (isa(func, Symbol) && func !== :(:) && !(head === :. && isoperator(func))) ||
            (isa(func, Symbol) && !is_valid_identifier(func)) ||
            (isa(func, Expr) && (func.head === :. || func.head === :curly || func.head === :macroname)) ||
            isa(func, GlobalRef)
        show_unquoted(io, func, indent, 0, quote_level)
    else
        print(io, '(')
        show_unquoted(io, func, indent, 0, quote_level)
        print(io, ')')
    end
    if head === :(.)
        print(io, '.')
    end
    if !isempty(func_args) && isa(func_args[1], Expr) && (func_args[1]::Expr).head === :parameters
        print(io, op)
        show_list(io, func_args[2:end], ", ", indent, 0, quote_level, false, kw)
        print(io, "; ")
        show_list(io, (func_args[1]::Expr).args, ", ", indent, 0, quote_level, false, kw)
        print(io, cl)
    else
        show_enclosed_list(io, op, func_args, ", ", cl, indent, 0, quote_level, false, kw)
    end
end

# Print `sym` as it would appear as an identifier name in code
# * Print valid identifiers & operators literally; also macros names if allow_macroname=true
# * Escape invalid identifiers with var"" syntax
function show_sym(io::IO, sym::Symbol; allow_macroname=false)
    if is_valid_identifier(sym)
        print(io, sym)
    elseif allow_macroname && (sym_str = string(sym); startswith(sym_str, '@'))
        print(io, '@')
        show_sym(io, Symbol(sym_str[2:end]))
    else
        print(io, "var", repr(string(sym)))
    end
end

## AST printing ##

function show_unquoted(io::IO, val::SSAValue, ::Int, ::Int)
    if get(io, :maxssaid, typemax(Int))::Int < val.id
        # invalid SSAValue, print this in red for better recognition
        printstyled(io, "%", val.id; color=:red)
    else
        print(io, "%", val.id)
    end
end
show_unquoted(io::IO, sym::Symbol, ::Int, ::Int)        = show_sym(io, sym, allow_macroname=false)
show_unquoted(io::IO, ex::LineNumberNode, ::Int, ::Int) = show_linenumber(io, ex.line, ex.file)
show_unquoted(io::IO, ex::GotoNode, ::Int, ::Int)       = print(io, "goto %", ex.label)
show_unquoted(io::IO, ex::GlobalRef, ::Int, ::Int)      = show_globalref(io, ex)

function show_globalref(io::IO, ex::GlobalRef; allow_macroname=false)
    print(io, ex.mod)
    print(io, '.')
    quoted = !isidentifier(ex.name) && !startswith(string(ex.name), "@")
    parens = quoted && (!isoperator(ex.name) || (ex.name in quoted_syms))
    quoted && print(io, ':')
    parens && print(io, '(')
    show_sym(io, ex.name, allow_macroname=allow_macroname)
    parens && print(io, ')')
    nothing
end

function show_unquoted(io::IO, ex::UnoptSlot, ::Int, ::Int)
    typ = isa(ex, TypedSlot) ? ex.typ : Any
    slotid = ex.id
    slotnames = get(io, :SOURCE_SLOTNAMES, false)
    if (isa(slotnames, Vector{String}) &&
        slotid <= length(slotnames::Vector{String}))
        print(io, (slotnames::Vector{String})[slotid])
    else
        print(io, "_", slotid)
    end
    if typ !== Any && isa(ex, TypedSlot)
        print(io, "::", typ)
    end
end

function show_unquoted(io::IO, ex::QuoteNode, indent::Int, prec::Int)
    if isa(ex.value, Symbol)
        show_unquoted_quote_expr(io, ex.value, indent, prec, 0)
    else
        print(io, "\$(QuoteNode(")
        # QuoteNode does not allows for interpolation, so if ex.value is an
        # Expr it should be shown with quote_level equal to zero.
        # Calling show(io, ex.value) like this implicitly enforce that.
        show(io, ex.value)
        print(io, "))")
    end
end

function show_unquoted_quote_expr(io::IO, @nospecialize(value), indent::Int, prec::Int, quote_level::Int)
    if isa(value, Symbol)
        sym = value::Symbol
        if value in quoted_syms
            print(io, ":(", sym, ")")
        else
            if isidentifier(sym) || (_isoperator(sym) && sym !== Symbol("'"))
                print(io, ":", sym)
            else
                print(io, "Symbol(", repr(String(sym)), ")")
            end
        end
    else
        if isa(value,Expr) && value.head === :block
            value = value::Expr
            show_block(IOContext(io, beginsym=>false), "quote", value, indent, quote_level)
            print(io, "end")
        else
            print(io, ":(")
            show_unquoted(io, value, indent+2, -1, quote_level)  # +2 for `:(`
            print(io, ")")
        end
    end
end

function show_generator(io, ex::Expr, indent, quote_level)
    if ex.head === :flatten
        fg::Expr = ex
        ranges = Any[]
        while isa(fg, Expr) && fg.head === :flatten
            push!(ranges, (fg.args[1]::Expr).args[2:end])
            fg = (fg.args[1]::Expr).args[1]::Expr
        end
        push!(ranges, fg.args[2:end])
        show_unquoted(io, fg.args[1], indent, 0, quote_level)
        for r in ranges
            print(io, " for ")
            show_list(io, r, ", ", indent, 0, quote_level)
        end
    else
        show_unquoted(io, ex.args[1], indent, 0, quote_level)
        print(io, " for ")
        show_list(io, ex.args[2:end], ", ", indent, 0, quote_level)
    end
end

function valid_import_path(@nospecialize(ex), allow_as = true)
    if allow_as && is_expr(ex, :as) && length((ex::Expr).args) == 2
        ex = (ex::Expr).args[1]
    end
    return is_expr(ex, :(.)) && length((ex::Expr).args) > 0 && all(a->isa(a,Symbol), (ex::Expr).args)
end

function show_import_path(io::IO, ex, quote_level)
    if !isa(ex, Expr)
        show_unquoted(io, ex)
    elseif ex.head === :(:)
        show_import_path(io, ex.args[1], quote_level)
        print(io, ": ")
        for i = 2:length(ex.args)
            if i > 2
                print(io, ", ")
            end
            show_import_path(io, ex.args[i], quote_level)
        end
    elseif ex.head === :(.)
        for i = 1:length(ex.args)
            sym = ex.args[i]::Symbol
            if sym === :(.)
                print(io, '.')
            else
                if sym === :(..)
                    # special case for https://github.com/JuliaLang/julia/issues/49168
                    print(io, "(..)")
                else
                    show_sym(io, sym, allow_macroname=(i==length(ex.args)))
                end
                i < length(ex.args) && print(io, '.')
            end
        end
    else
        show_unquoted(io, ex, 0, 0, quote_level)
    end
end

# Wrap symbols for macro names to allow them to be printed literally
function allow_macroname(ex)
    if (ex isa Symbol && first(string(ex)) == '@') ||
       ex isa GlobalRef ||
       (is_expr(ex, :(.)) && length(ex.args) == 2 &&
        (is_expr(ex.args[2], :quote) || ex.args[2] isa QuoteNode))
       return Expr(:macroname, ex)
    else
        ex
    end
end

is_core_macro(arg::GlobalRef, macro_name::AbstractString) = is_core_macro(arg, Symbol(macro_name))
is_core_macro(arg::GlobalRef, macro_name::Symbol) = arg == GlobalRef(Core, macro_name)
is_core_macro(@nospecialize(arg), macro_name::AbstractString) = false
is_core_macro(@nospecialize(arg), macro_name::Symbol) = false

# symbol for IOContext flag signaling whether "begin" is treated
# as an ordinary symbol, which is true in indexing expressions.
const beginsym = gensym(:beginsym)

function show_unquoted_expr_fallback(io::IO, ex::Expr, indent::Int, quote_level::Int)
    print(io, "\$(Expr(")
    show(io, ex.head)
    for arg in ex.args
        print(io, ", ")
        show(io, arg)
    end
    print(io, "))")
end

# TODO: implement interpolated strings
function show_unquoted(io::IO, ex::Expr, indent::Int, prec::Int, quote_level::Int = 0)
    head, args, nargs = ex.head, ex.args, length(ex.args)
    unhandled = false
    # dot (i.e. "x.y"), but not compact broadcast exps
    if head === :(.) && (nargs != 2 || !is_expr(args[2], :tuple))
        # standalone .op
        if nargs == 1 && args[1] isa Symbol && isoperator(args[1]::Symbol)
            print(io, "(.", args[1], ")")
        elseif nargs == 2 && is_quoted(args[2])
            item = args[1]
            # field
            field = unquoted(args[2])
            parens = !is_quoted(item) && !(item isa Symbol && isidentifier(item)) && !is_expr(item, :(.))
            parens && print(io, '(')
            show_unquoted(io, item, indent, 0, quote_level)
            parens && print(io, ')')
            # .
            print(io, '.')
            # item
            if isa(field, Symbol)
                parens = field in quoted_syms
                quoted = parens || isoperator(field)
            else
                parens = quoted = true
            end
            quoted && print(io, ':')
            parens && print(io, '(')
            show_unquoted(io, field, indent, 0, quote_level)
            parens && print(io, ')')
        else
            unhandled = true
        end

    # infix (i.e. "x <: y" or "x = y")
    elseif (head in expr_infix_any && nargs==2)
        func_prec = operator_precedence(head)
        head_ = head in expr_infix_wide ? " $head " : head
        if func_prec <= prec
            show_enclosed_list(io, '(', args, head_, ')', indent, func_prec, quote_level, true)
        else
            show_list(io, args, head_, indent, func_prec, quote_level, true)
        end

    elseif head === :tuple
        print(io, "(")
        if nargs > 0 && is_expr(args[1], :parameters)
            arg1 = args[1]::Expr
            show_list(io, args[2:end], ", ", indent, 0, quote_level)
            nargs == 2 && print(io, ',')
            print(io, ";")
            if !isempty(arg1.args)
                print(io, " ")
            end
            show_list(io, arg1.args, ", ", indent, 0, quote_level, false, true)
        else
            show_list(io, args, ", ", indent, 0, quote_level)
            nargs == 1 && print(io, ',')
        end
        print(io, ")")

    # list-like forms, e.g. "[1, 2, 3]"
    elseif haskey(expr_parens, head) ||                          # :vcat etc.
        head === :typed_vcat || head === :typed_hcat || head === :typed_ncat
        # print the type and defer to the untyped case
        if head === :typed_vcat || head === :typed_hcat || head === :typed_ncat
            show_unquoted(io, args[1], indent, prec, quote_level)
            if head === :typed_vcat
                head = :vcat
            elseif head === :typed_hcat
                head = :hcat
            else
                head = :ncat
            end
            args = args[2:end]
            nargs = nargs - 1
        end
        op, cl = expr_parens[head]
        if head === :vcat || head === :bracescat
            sep = "; "
        elseif head === :hcat || head === :row
            sep = " "
        elseif head === :ncat || head === :nrow
            sep = ";"^args[1]::Int * " "
            args = args[2:end]
            nargs = nargs - 1
        else
            sep = ", "
        end
        head !== :row && head !== :nrow && print(io, op)
        show_list(io, args, sep, indent, 0, quote_level)
        if nargs <= 1 && (head === :vcat || head === :ncat)
            print(io, sep[1:end-1])
        end
        head !== :row && head !== :nrow && print(io, cl)

    # transpose
    elseif (head === Symbol("'") && nargs == 1) || (
        # ' with unicode suffix is a call expression
        head === :call && nargs == 2 && args[1] isa Symbol &&
        ispostfixoperator(args[1]::Symbol) && args[1]::Symbol !== Symbol("'")
    )
        op, arg1 = head === Symbol("'") ? (head, args[1]) : (args[1], args[2])
        if isa(arg1, Expr) || (isa(arg1, Symbol) && isoperator(arg1::Symbol))
            show_enclosed_list(io, '(', [arg1::Union{Expr, Symbol}], ", ", ')', indent, 0)
        else
            show_unquoted(io, arg1, indent, 0, quote_level)
        end
        print(io, op)

    # function call
    elseif head === :call && nargs >= 1
        func = args[1]
        fname = isa(func, GlobalRef) ? func.name : func
        func_prec = operator_precedence(fname)
        if func_prec > 0 || (isa(fname, Symbol) && fname in uni_ops)
            func = fname
        end
        func_args = args[2:end]

        # :kw exprs are only parsed inside parenthesized calls
        if any(a->is_expr(a, :kw), func_args) || (!isempty(func_args) && is_expr(func_args[1], :parameters))
            show_call(io, head, func, func_args, indent, quote_level, true)

        # scalar multiplication (i.e. "100x")
        elseif (func === :* &&
            length(func_args) == 2 && isa(func_args[1], Union{Int, Int64, Float32, Float64}) &&
            isa(func_args[2], Symbol) &&
            !in(string(func_args[2]::Symbol)[1], ('e', 'E', 'f', (func_args[1] == 0 && func_args[1] isa Integer ?
                                                                  # don't juxtapose 0 with b, o, x
                                                                  ('b', 'o', 'x') : ())...)))
            if func_prec <= prec
                show_enclosed_list(io, '(', func_args, "", ')', indent, func_prec, quote_level)
            else
                show_list(io, func_args, "", indent, func_prec, quote_level)
            end

        # unary operator (i.e. "!z")
        elseif isa(func,Symbol) && length(func_args) == 1 && func in uni_ops
            show_unquoted(io, func, indent, 0, quote_level)
            arg1 = func_args[1]
            if isa(arg1, Expr) || (isa(arg1, Symbol) && isoperator(arg1) && is_valid_identifier(arg1))
                show_enclosed_list(io, '(', func_args, ", ", ')', indent, func_prec)
            else
                show_unquoted(io, arg1, indent, func_prec, quote_level)
            end

        # binary operator (i.e. "x + y")
        elseif func_prec > 0 # is a binary operator
            func = func::Symbol    # operator_precedence returns func_prec == 0 for non-Symbol
            na = length(func_args)
            if (na == 2 || (na > 2 && func in (:+, :++, :*)) || (na == 3 && func === :(:))) &&
                    all(a -> !isa(a, Expr) || a.head !== :..., func_args)
                sep = func === :(:) ? "$func" : " $func "

                if func_prec <= prec
                    show_enclosed_list(io, '(', func_args, sep, ')', indent, func_prec, quote_level, true)
                else
                    show_list(io, func_args, sep, indent, func_prec, quote_level, true)
                end
            elseif na == 1
                # 1-argument call to normally-binary operator
                op, cl = expr_calls[head]
                print(io, "(")
                show_unquoted(io, func, indent, 0, quote_level)
                print(io, ")")
                show_enclosed_list(io, op, func_args, ", ", cl, indent, 0, quote_level)
            else
                show_call(io, head, func, func_args, indent, quote_level, true)
            end

        # normal function (i.e. "f(x,y)")
        else
            show_call(io, head, func, func_args, indent, quote_level, true)
        end

    # new expr
    elseif head === :new || head === :splatnew
        show_enclosed_list(io, "%$head(", args, ", ", ")", indent, 0, quote_level)

    # other call-like expressions ("A[1,2]", "T{X,Y}", "f.(X,Y)")
    elseif haskey(expr_calls, head) && nargs >= 1  # :ref/:curly/:calldecl/:(.)
        funcargslike = head === :(.) ? (args[2]::Expr).args : args[2:end]
        show_call(head === :ref ? IOContext(io, beginsym=>true) : io, head, args[1], funcargslike, indent, quote_level, head !== :curly)

    # comprehensions
    elseif head === :typed_comprehension && nargs == 2
        show_unquoted(io, args[1], indent, 0, quote_level)
        print(io, '[')
        show_generator(io, args[2], indent, quote_level)
        print(io, ']')

    elseif head === :comprehension && nargs == 1
        print(io, '[')
        show_generator(io, args[1], indent, quote_level)
        print(io, ']')

    elseif (head === :generator && nargs >= 2) || (head === :flatten && nargs == 1)
        print(io, '(')
        show_generator(io, ex, indent, quote_level)
        print(io, ')')

    elseif head === :filter && nargs == 2
        show_unquoted(io, args[2], indent, 0, quote_level)
        print(io, " if ")
        show_unquoted(io, args[1], indent, 0, quote_level)

    # comparison (i.e. "x < y < z")
    elseif head === :comparison && nargs >= 3 && (nargs&1==1)
        comp_prec = minimum(operator_precedence, args[2:2:end])
        if comp_prec <= prec
            show_enclosed_list(io, '(', args, " ", ')', indent, comp_prec, quote_level)
        else
            show_list(io, args, " ", indent, comp_prec, quote_level)
        end

    # function calls need to transform the function from :call to :calldecl
    # so that operators are printed correctly
    elseif head === :function && nargs==2 && is_expr(args[1], :call)
        show_block(IOContext(io, beginsym=>false), head, Expr(:calldecl, (args[1]::Expr).args...), args[2], indent, quote_level)
        print(io, "end")

    elseif (head === :function || head === :macro) && nargs == 1
        print(io, head, ' ')
        show_unquoted(IOContext(io, beginsym=>false), args[1])
        print(io, " end")

    elseif head === :do && nargs == 2
        iob = IOContext(io, beginsym=>false)
        show_unquoted(iob, args[1], indent, -1, quote_level)
        print(io, " do ")
        show_list(iob, (((args[2]::Expr).args[1])::Expr).args, ", ", 0, 0, quote_level)
        for stmt in (((args[2]::Expr).args[2])::Expr).args
            print(io, '\n', " "^(indent + indent_width))
            show_unquoted(iob, stmt, indent + indent_width, -1, quote_level)
        end
        print(io, '\n', " "^indent)
        print(io, "end")

    # block with argument
    elseif head in (:for,:while,:function,:macro,:if,:elseif,:let) && nargs==2
        if head === :function && is_expr(args[1], :...)
            # fix printing of "function (x...) x end"
            block_args = Expr(:tuple, args[1])
        else
            block_args = args[1]
        end
        if is_expr(args[2], :block)
            show_block(IOContext(io, beginsym=>false), head, block_args, args[2], indent, quote_level)
        else
            show_block(IOContext(io, beginsym=>false), head, block_args, Expr(:block, args[2]), indent, quote_level)
        end
        print(io, "end")

    elseif (head === :if || head === :elseif) && nargs == 3
        iob = IOContext(io, beginsym=>false)
        show_block(iob, head, args[1], args[2], indent, quote_level)
        arg3 = args[3]
        if isa(arg3, Expr) && arg3.head === :elseif
            show_unquoted(iob, arg3::Expr, indent, prec, quote_level)
        else
            show_block(iob, "else", arg3, indent, quote_level)
            print(io, "end")
        end

    elseif head === :module && nargs==3 && isa(args[1],Bool)
        show_block(IOContext(io, beginsym=>false), args[1] ? :module : :baremodule, args[2], args[3], indent, quote_level)
        print(io, "end")

    # type declaration
    elseif head === :struct && nargs==3
        show_block(IOContext(io, beginsym=>false), args[1] ? Symbol("mutable struct") : Symbol("struct"), args[2], args[3], indent, quote_level)
        print(io, "end")

    elseif head === :primitive && nargs == 2
        print(io, "primitive type ")
        show_list(io, args, ' ', indent, 0, quote_level)
        print(io, " end")

    elseif head === :abstract && nargs == 1
        print(io, "abstract type ")
        show_list(IOContext(io, beginsym=>false), args, ' ', indent, 0, quote_level)
        print(io, " end")

    # empty return (i.e. "function f() return end")
    elseif head === :return && nargs == 1 && args[1] === nothing
        print(io, head)

    # type annotation (i.e. "::Int")
    elseif head in uni_syms && nargs == 1
        print(io, head)
        show_unquoted(io, args[1], indent, 0, quote_level)

    # var-arg declaration or expansion
    # (i.e. "function f(L...) end" or "f(B...)")
    elseif head === :(...) && nargs == 1
        dotsprec = operator_precedence(:(:)) - 1
        parens = dotsprec <= prec
        parens && print(io, "(")
        show_unquoted(io, args[1], indent, dotsprec, quote_level)
        print(io, "...")
        parens && print(io, ")")

    elseif (nargs == 0 && head in (:break, :continue))
        print(io, head)

    elseif (nargs == 1 && head in (:return, :const)) ||
                          head in (:local,  :global)
        print(io, head, ' ')
        show_list(io, args, ", ", indent, 0, quote_level)

    elseif head === :export
        print(io, head, ' ')
        show_list(io, mapany(allow_macroname, args), ", ", indent)

    elseif head === :macrocall && nargs >= 2
        # handle some special syntaxes
        # `a b c`
        if is_core_macro(args[1], :var"@cmd")
            print(io, "`", args[3], "`")
        # 11111111111111111111, 0xfffffffffffffffff, 1111...many digits...
        elseif is_core_macro(args[1], :var"@int128_str") ||
               is_core_macro(args[1], :var"@uint128_str") ||
               is_core_macro(args[1], :var"@big_str")
            print(io, args[3])
        # x"y" and x"y"z
        elseif isa(args[1], Symbol) && nargs >= 3 && isa(args[3], String) &&
               startswith(string(args[1]::Symbol), "@") &&
               endswith(string(args[1]::Symbol), "_str")
            s = string(args[1]::Symbol)
            print(io, s[2:prevind(s,end,4)], "\"")
            escape_raw_string(io, args[3])
            print(io, "\"")
            if nargs == 4
                print(io, args[4])
            end
        # general case
        else
            # first show the line number argument as a comment
            if isa(args[2], LineNumberNode) || is_expr(args[2], :line)
                print(io, args[2], ' ')
            end
            # Use the functional syntax unless specifically designated with
            # prec=-1 and hide the line number argument from the argument list
            mname = allow_macroname(args[1])
            if prec >= 0
                show_call(io, :call, mname, args[3:end], indent, quote_level, false)
            else
                show_args = Vector{Any}(undef, nargs - 1)
                show_args[1] = mname
                show_args[2:end] = args[3:end]
                show_list(io, show_args, ' ', indent, 0, quote_level)
            end
        end

    elseif head === :macroname && nargs == 1
        arg1 = args[1]
        if arg1 isa Symbol
            show_sym(io, arg1, allow_macroname=true)
        elseif arg1 isa GlobalRef
            show_globalref(io, arg1, allow_macroname=true)
        elseif is_expr(arg1, :(.)) && length((arg1::Expr).args) == 2
            arg1 = arg1::Expr
            m = arg1.args[1]
            if m isa Symbol || m isa GlobalRef || is_expr(m, :(.), 2)
                show_unquoted(io, m)
            else
                print(io, "(")
                show_unquoted(io, m)
                print(io, ")")
            end
            print(io, '.')
            if is_expr(arg1.args[2], :quote)
                mname = (arg1.args[2]::Expr).args[1]
            else
                mname = (arg1.args[2]::QuoteNode).value
            end
            if mname isa Symbol
                show_sym(io, mname, allow_macroname=true)
            else
                show_unquoted(io, mname)
            end
        else
            show_unquoted(io, arg1)
        end

    elseif head === :line && 1 <= nargs <= 2
        show_linenumber(io, args...)

    elseif head === :try && 3 <= nargs <= 5
        iob = IOContext(io, beginsym=>false)
        show_block(iob, "try", args[1], indent, quote_level)
        if is_expr(args[3], :block)
            show_block(iob, "catch", args[2] === false ? Any[] : args[2], args[3]::Expr, indent, quote_level)
        end
        if nargs >= 5 && is_expr(args[5], :block)
            show_block(iob, "else", Any[], args[5]::Expr, indent, quote_level)
        end
        if nargs >= 4 && is_expr(args[4], :block)
            show_block(iob, "finally", Any[], args[4]::Expr, indent, quote_level)
        end
        print(io, "end")

    elseif head === :block
        # print as (...; ...; ...;) inside indexing expression
        if get(io, beginsym, false)
            print(io, '(')
            ind = indent + indent_width
            for i = 1:length(ex.args)
                if i > 1
                    # if there was only a comment before the first semicolon, the expression would get parsed as a NamedTuple
                    if !(i == 2 && ex.args[1] isa LineNumberNode)
                        print(io, ';')
                    end
                    print(io, "\n", ' '^ind)
                end
                show_unquoted(io, ex.args[i], ind, -1, quote_level)
            end
            if length(ex.args) < 2
                print(io, isempty(ex.args) ? ";;)" : ";)")
            else
                print(io, ')')
            end
        else
            show_block(io, "begin", ex, indent, quote_level)
            print(io, "end")
        end

    elseif head === :quote && nargs == 1 && isa(args[1], Symbol)
        show_unquoted_quote_expr(IOContext(io, beginsym=>false), args[1]::Symbol, indent, 0, quote_level+1)
    elseif head === :quote && !(get(io, :unquote_fallback, true)::Bool)
        if nargs == 1 && is_expr(args[1], :block)
            show_block(IOContext(io, beginsym=>false), "quote", Expr(:quote, (args[1]::Expr).args...), indent,
                       quote_level+1)
            print(io, "end")
        elseif nargs == 1
            print(io, ":(")
            show_unquoted(IOContext(io, beginsym=>false), args[1], indent+2, 0, quote_level+1)
            print(io, ")")
        else
            show_block(IOContext(io, beginsym=>false), "quote", ex, indent, quote_level+1)
            print(io, "end")
        end

    elseif head === :gotoifnot && nargs == 2 && isa(args[2], Int)
        print(io, "unless ")
        show_unquoted(io, args[1], indent, 0, quote_level)
        print(io, " goto %")
        print(io, args[2]::Int)

    elseif head === :string && nargs == 1 && isa(args[1], AbstractString)
        show(io, args[1])

    elseif head === :null
        print(io, "nothing")

    elseif head === :string
        print(io, '"')
        for x in args
            if !isa(x,AbstractString)
                print(io, "\$(")
                if isa(x,Symbol) && !(x in quoted_syms)
                    show_sym(io, x)
                else
                    show_unquoted(io, x, 0, 0, quote_level)
                end
                print(io, ")")
            else
                escape_string(io, String(x)::String, "\"\$")
            end
        end
        print(io, '"')

    elseif (head === :& || head === :$) && nargs == 1
        if head === :$
            quote_level -= 1
        end
        if head === :$ && get(io, :unquote_fallback, true)
            unhandled = true
        else
            print(io, head)
            a1 = args[1]
            parens = (isa(a1,Expr) && !in(a1.head, (:tuple, :$, :vect, :braces))) ||
                     (isa(a1,Symbol) && isoperator(a1))
            parens && print(io, "(")
            show_unquoted(io, a1, 0, 0, quote_level)
            parens && print(io, ")")
        end

    # `where` syntax
    elseif head === :where && nargs > 1
        parens = 1 <= prec
        parens && print(io, "(")
        show_unquoted(io, args[1], indent, operator_precedence(:(::)), quote_level)
        print(io, " where ")
        if nargs == 2
            show_unquoted(io, args[2], indent, 1, quote_level)
        else
            print(io, "{")
            show_list(io, args[2:end], ", ", indent, 0, quote_level)
            print(io, "}")
        end
        parens && print(io, ")")

    elseif (head === :import || head === :using) &&
           ((nargs == 1 && (valid_import_path(args[1]) ||
                           (is_expr(args[1], :(:)) &&
                            length((args[1]::Expr).args) > 1 &&
                            all(valid_import_path, (args[1]::Expr).args)))) ||
             all(valid_import_path, args))
        print(io, head)
        print(io, ' ')
        first = true
        for a in args
            if !first
                print(io, ", ")
            end
            first = false
            show_import_path(io, a, quote_level)
        end
    elseif head === :as && nargs == 2 && valid_import_path(args[1], false)
        show_import_path(io, args[1], quote_level)
        print(io, " as ")
        show_unquoted(io, args[2], indent, 0, quote_level)
    elseif head === :meta && nargs >= 2 && args[1] === :push_loc
        print(io, "# meta: location ", join(args[2:end], " "))
    elseif head === :meta && nargs == 1 && args[1] === :pop_loc
        print(io, "# meta: pop location")
    elseif head === :meta && nargs == 2 && args[1] === :pop_loc
        print(io, "# meta: pop locations ($(args[2]::Int))")
    # print anything else as "Expr(head, args...)"
    else
        unhandled = true
    end
    if unhandled
        show_unquoted_expr_fallback(io, ex, indent, quote_level)
    end
    nothing
end

demangle_function_name(name::Symbol) = Symbol(demangle_function_name(string(name)))
function demangle_function_name(name::AbstractString)
    demangle = split(name, '#')
    # kw sorters and impl methods use the name scheme `f#...`
    if length(demangle) >= 2 && demangle[1] != ""
        return demangle[1]
    end
    return name
end

# show the called object in a signature, given its type `ft`
# `io` should contain the UnionAll env of the signature
function show_signature_function(io::IO, @nospecialize(ft), demangle=false, fargname="", html=false, qualified=false)
    uw = unwrap_unionall(ft)
    if ft <: Function && isa(uw, DataType) && isempty(uw.parameters) && _isself(uw)
        uwmod = parentmodule(uw)
        if qualified && !is_exported_from_stdlib(uw.name.mt.name, uwmod) && uwmod !== Main
            print_within_stacktrace(io, uwmod, '.', bold=true)
        end
        s = sprint(show_sym, (demangle ? demangle_function_name : identity)(uw.name.mt.name), context=io)
        print_within_stacktrace(io, s, bold=true)
    elseif isType(ft) && (f = ft.parameters[1]; !isa(f, TypeVar))
        uwf = unwrap_unionall(f)
        parens = isa(f, UnionAll) && !(isa(uwf, DataType) && f === uwf.name.wrapper)
        parens && print(io, "(")
        print_within_stacktrace(io, f, bold=true)
        parens && print(io, ")")
    else
        if html
            print(io, "($fargname::<b>", ft, "</b>)")
        else
            print_within_stacktrace(io, "($fargname::", ft, ")", bold=true)
        end
    end
    nothing
end

function print_within_stacktrace(io, s...; color=:normal, bold=false)
    if get(io, :backtrace, false)::Bool
        printstyled(io, s...; color, bold)
    else
        print(io, s...)
    end
end

function show_tuple_as_call(out::IO, name::Symbol, sig::Type;
                            demangle=false, kwargs=nothing, argnames=nothing,
                            qualified=false, hasfirst=true)
    # print a method signature tuple for a lambda definition
    if sig === Tuple
        print(out, demangle ? demangle_function_name(name) : name, "(...)")
        return
    end
    tv = Any[]
    io = IOContext(IOBuffer(), out)
    env_io = io
    while isa(sig, UnionAll)
        push!(tv, sig.var)
        env_io = IOContext(env_io, :unionall_env => sig.var)
        sig = sig.body
    end
    n = 1
    sig = (sig::DataType).parameters
    if hasfirst
        show_signature_function(env_io, sig[1], demangle, "", false, qualified)
        n += 1
    end
    first = true
    print_within_stacktrace(io, "(", bold=true)
    show_argnames = argnames !== nothing && length(argnames) == length(sig)
    for i = n:length(sig)  # fixme (iter): `eachindex` with offset?
        first || print(io, ", ")
        first = false
        if show_argnames
            print_within_stacktrace(io, argnames[i]; color=:light_black)
        end
        print(io, "::")
        print_type_bicolor(env_io, sig[i]; use_color = get(io, :backtrace, false)::Bool)
    end
    if kwargs !== nothing
        print(io, "; ")
        first = true
        for (k, t) in kwargs
            first || print(io, ", ")
            first = false
            print_within_stacktrace(io, k; color=:light_black)
            if t == pairs(NamedTuple)
                # omit type annotation for splat keyword argument
                print(io, "...")
            else
                print(io, "::")
                print_type_bicolor(io, t; use_color = get(io, :backtrace, false)::Bool)
            end
        end
    end
    print_within_stacktrace(io, ")", bold=true)
    show_method_params(io, tv)
    str = String(take!(unwrapcontext(io)[1]))
    str = type_limited_string_from_context(out, str)
    print(out, str)
    nothing
end

function type_limited_string_from_context(out::IO, str::String)
    typelimitflag = get(out, :stacktrace_types_limited, nothing)
    if typelimitflag isa RefValue{Bool}
        sz = get(out, :displaysize, displaysize(out))::Tuple{Int, Int}
        str_lim = type_depth_limit(str, max(sz[2], 120))
        if sizeof(str_lim) < sizeof(str)
            typelimitflag[] = true
        end
        str = str_lim
    end
    return str
end

# limit nesting depth of `{ }` until string textwidth is less than `n`
function type_depth_limit(str::String, n::Int; maxdepth = nothing)
    depth = 0
    width_at = Int[]                       # total textwidth at each nesting depth
    depths = zeros(Int16, lastindex(str))  # depth at each character index
    levelcount = Int[]                     # number of nodes at each level
    strwid = 0
    st_0, st_backslash, st_squote, st_dquote = 0,1,2,4
    state::Int = st_0
    stateis(s) = (state & s) != 0
    quoted() = stateis(st_squote) || stateis(st_dquote)
    enter(s) = (state |= s)
    leave(s) = (state &= ~s)
    for (i, c) in ANSIIterator(str)
        if c isa ANSIDelimiter
            depths[i] = depth
            continue
        end

        if c == '\\' && quoted()
            enter(st_backslash)
        elseif c == '\''
            if stateis(st_backslash) || stateis(st_dquote)
            elseif stateis(st_squote)
                leave(st_squote)
            else
                enter(st_squote)
            end
        elseif c == '"'
            if stateis(st_backslash) || stateis(st_squote)
            elseif stateis(st_dquote)
                leave(st_dquote)
            else
                enter(st_dquote)
            end
        end
        if c == '}' && !quoted()
            depth -= 1
        end

        wid = textwidth(c)
        strwid += wid
        if depth > 0
            width_at[depth] += wid
        end
        depths[i] = depth

        if c == '{' && !quoted()
            depth += 1
            if depth > length(width_at)
                push!(width_at, 0)
                push!(levelcount, 0)
            end
            levelcount[depth] += 1
        end
        if c != '\\' && stateis(st_backslash)
            leave(st_backslash)
        end
    end
    if maxdepth === nothing
        limit_at = length(width_at) + 1
        while strwid > n
            limit_at -= 1
            limit_at <= 1 && break
            # add levelcount[] to include space taken by `…`
            strwid = strwid - width_at[limit_at] + levelcount[limit_at]
            if limit_at < length(width_at)
                # take away the `…` from the previous considered level
                strwid -= levelcount[limit_at+1]
            end
        end
    else
        limit_at = maxdepth
    end
    output = IOBuffer()
    prev = 0
    for (i, c) in ANSIIterator(str)
        di = depths[i]
        if di < limit_at
            if c isa ANSIDelimiter
                write(output, c.del)
            else
                write(output, c)
            end
        end
        if di > prev && di == limit_at
            write(output, "…")
        end
        prev = di
    end
    return String(take!(output))
end

function print_type_bicolor(io, type; kwargs...)
    str = sprint(show, type, context=io)
    print_type_bicolor(io, str; kwargs...)
end

function print_type_bicolor(io, str::String; color=:normal, inner_color=:light_black, use_color::Bool=true)
    i = findfirst('{', str)
    if !use_color # fix #41928
        print(io, str)
    elseif i === nothing
        printstyled(io, str; color=color)
    else
        printstyled(io, str[1:prevind(str,i)]; color=color)
        if endswith(str, "...")
            printstyled(io, str[i:prevind(str,end,3)]; color=inner_color)
            printstyled(io, "..."; color=color)
        else
            printstyled(io, str[i:end]; color=inner_color)
        end
    end
end

resolvebinding(@nospecialize(ex)) = ex
resolvebinding(ex::QuoteNode) = ex.value
resolvebinding(ex::Symbol) = resolvebinding(GlobalRef(Main, ex))
function resolvebinding(ex::Expr)
    if ex.head === :. && isa(ex.args[2], Symbol)
        parent = resolvebinding(ex.args[1])
        if isa(parent, Module)
            return resolvebinding(GlobalRef(parent, ex.args[2]))
        end
    end
    return nothing
end
function resolvebinding(ex::GlobalRef)
    isdefined(ex.mod, ex.name) || return nothing
    isconst(ex.mod, ex.name) || return nothing
    m = getfield(ex.mod, ex.name)
    isa(m, Module) || return nothing
    return m
end

function ismodulecall(ex::Expr)
    return ex.head === :call && (ex.args[1] === GlobalRef(Base,:getfield) ||
                                ex.args[1] === GlobalRef(Core,:getfield)) &&
           isa(resolvebinding(ex.args[2]), Module)
end

function show(io::IO, tv::TypeVar)
    # If we are in the `unionall_env`, the type-variable is bound
    # and the type constraints are already printed.
    # We don't need to print it again.
    # Otherwise, the lower bound should be printed if it is not `Bottom`
    # and the upper bound should be printed if it is not `Any`.
    in_env = (:unionall_env => tv) in io
    function show_bound(io::IO, @nospecialize(b))
        parens = isa(b,UnionAll) && !print_without_params(b)
        parens && print(io, "(")
        show(io, b)
        parens && print(io, ")")
    end
    lb, ub = tv.lb, tv.ub
    if !in_env && lb !== Bottom
        if ub === Any
            show_unquoted(io, tv.name)
            print(io, ">:")
            show_bound(io, lb)
        else
            show_bound(io, lb)
            print(io, "<:")
            show_unquoted(io, tv.name)
        end
    else
        show_unquoted(io, tv.name)
    end
    if !in_env && ub !== Any
        print(io, "<:")
        show_bound(io, ub)
    end
    nothing
end

function show(io::IO, vm::Core.TypeofVararg)
    print(io, "Vararg")
    if isdefined(vm, :T)
        print(io, "{")
        show(io, vm.T)
        if isdefined(vm, :N)
            print(io, ", ")
            show(io, vm.N)
        end
        print(io, "}")
    end
end

module IRShow
    const Compiler = Core.Compiler
    using Core.IR
    import ..Base
    import .Compiler: IRCode, TypedSlot, CFG, scan_ssa_use!,
        isexpr, compute_basic_blocks, block_for_inst, IncrementalCompact,
        Effects, ALWAYS_TRUE, ALWAYS_FALSE
    Base.getindex(r::Compiler.StmtRange, ind::Integer) = Compiler.getindex(r, ind)
    Base.size(r::Compiler.StmtRange) = Compiler.size(r)
    Base.first(r::Compiler.StmtRange) = Compiler.first(r)
    Base.last(r::Compiler.StmtRange) = Compiler.last(r)
    Base.length(is::Compiler.InstructionStream) = Compiler.length(is)
    Base.iterate(is::Compiler.InstructionStream, st::Int=1) = (st <= Compiler.length(is)) ? (is[st], st + 1) : nothing
    Base.getindex(is::Compiler.InstructionStream, idx::Int) = Compiler.getindex(is, idx)
    Base.getindex(node::Compiler.Instruction, fld::Symbol) = Compiler.getindex(node, fld)
    include("compiler/ssair/show.jl")

    const __debuginfo = Dict{Symbol, Any}(
        # :full => src -> Base.IRShow.statementidx_lineinfo_printer(src), # and add variable slot information
        :source => src -> Base.IRShow.statementidx_lineinfo_printer(src),
        # :oneliner => src -> Base.IRShow.statementidx_lineinfo_printer(Base.IRShow.PartialLineInfoPrinter, src),
        :none => src -> Base.IRShow.lineinfo_disabled,
        )
    const default_debuginfo = Ref{Symbol}(:none)
    debuginfo(sym) = sym === :default ? default_debuginfo[] : sym
end

function show(io::IO, src::CodeInfo; debuginfo::Symbol=:source)
    # Fix slot names and types in function body
    print(io, "CodeInfo(")
    lambda_io::IOContext = io
    if src.slotnames !== nothing
        lambda_io = IOContext(lambda_io, :SOURCE_SLOTNAMES => sourceinfo_slotnames(src))
    end
    if isempty(src.linetable) || src.linetable[1] isa LineInfoNode
        println(io)
        # TODO: static parameter values?
        # only accepts :source or :none, we can't have a fallback for default since
        # that would break code_typed(, debuginfo=:source) iff IRShow.default_debuginfo[] = :none
        IRShow.show_ir(lambda_io, src, IRShow.IRShowConfig(IRShow.__debuginfo[debuginfo](src)))
    else
        # this is a CodeInfo that has not been used as a method yet, so its locations are still LineNumberNodes
        body = Expr(:block)
        body.args = src.code
        show(lambda_io, body)
    end
    print(io, ")")
end

function show(io::IO, inferred::Core.Compiler.InferenceResult)
    mi = inferred.linfo
    tt = mi.specTypes.parameters[2:end]
    tts = join(["::$(t)" for t in tt], ", ")
    rettype = inferred.result
    if isa(rettype, Core.Compiler.InferenceState)
        rettype = rettype.bestguess
    end
    if isa(mi.def, Method)
        print(io, mi.def.name, "(", tts, " => ", rettype, ")")
    else
        print(io, "Toplevel MethodInstance thunk from ", mi.def, " => ", rettype)
    end
end

function show(io::IO, ::Core.Compiler.NativeInterpreter)
    print(io, "Core.Compiler.NativeInterpreter(...)")
end


function dump(io::IOContext, x::SimpleVector, n::Int, indent)
    if isempty(x)
        print(io, "empty SimpleVector")
        return
    end
    print(io, "SimpleVector")
    if n > 0
        for i = 1:length(x)
            println(io)
            print(io, indent, "  ", i, ": ")
            if isassigned(x,i)
                dump(io, x[i], n - 1, string(indent, "  "))
            else
                print(io, undef_ref_str)
            end
        end
    end
    nothing
end

function dump(io::IOContext, @nospecialize(x), n::Int, indent)
    if x === Union{}
        show(io, x)
        return
    end
    T = typeof(x)
    if isa(x, Function)
        print(io, x, " (function of type ", T, ")")
    else
        print(io, T)
    end
    nf = nfields(x)
    if nf > 0
        if n > 0 && !show_circular(io, x)
            recur_io = IOContext(io, Pair{Symbol,Any}(:SHOWN_SET, x))
            for field in 1:nf
                println(io)
                fname = string(fieldname(T, field))
                print(io, indent, "  ", fname, ": ")
                if isdefined(x,field)
                    dump(recur_io, getfield(x, field), n - 1, string(indent, "  "))
                else
                    print(io, undef_ref_str)
                end
            end
        end
    elseif !isa(x, Function)
        print(io, " ")
        show(io, x)
    end
    nothing
end

dump(io::IOContext, x::Module, n::Int, indent) = print(io, "Module ", x)
dump(io::IOContext, x::String, n::Int, indent) = (print(io, "String "); show(io, x))
dump(io::IOContext, x::Symbol, n::Int, indent) = print(io, typeof(x), " ", x)
dump(io::IOContext, x::Union,  n::Int, indent) = print(io, x)
dump(io::IOContext, x::Ptr,    n::Int, indent) = print(io, x)

function dump_elts(io::IOContext, x::Array, n::Int, indent, i0, i1)
    for i in i0:i1
        print(io, indent, "  ", i, ": ")
        if !isassigned(x,i)
            print(io, undef_ref_str)
        else
            dump(io, x[i], n - 1, string(indent, "  "))
        end
        i < i1 && println(io)
    end
end

function dump(io::IOContext, x::Array, n::Int, indent)
    print(io, "Array{", eltype(x), "}(", size(x), ")")
    if eltype(x) <: Number
        print(io, " ")
        show(io, x)
    else
        if n > 0 && !isempty(x) && !show_circular(io, x)
            println(io)
            recur_io = IOContext(io, :SHOWN_SET => x)
            lx = length(x)
            if get(io, :limit, false)::Bool
                dump_elts(recur_io, x, n, indent, 1, (lx <= 10 ? lx : 5))
                if lx > 10
                    println(io)
                    println(io, indent, "  ...")
                    dump_elts(recur_io, x, n, indent, lx - 4, lx)
                end
            else
                dump_elts(recur_io, x, n, indent, 1, lx)
            end
        end
    end
    nothing
end

# Types
function dump(io::IOContext, x::DataType, n::Int, indent)
    print(io, x)
    if x !== Any
        print(io, " <: ", supertype(x))
    end
    if n > 0 && !(x <: Tuple) && !isabstracttype(x)
        tvar_io::IOContext = io
        for tparam in x.parameters
            # approximately recapture the list of tvar parameterization
            # that may be used by the internal fields
            if isa(tparam, TypeVar)
                tvar_io = IOContext(tvar_io, :unionall_env => tparam)
            end
        end
        if x.name === _NAMEDTUPLE_NAME && !(x.parameters[1] isa Tuple)
            # named tuple type with unknown field names
            return
        end
        fields = fieldnames(x)
        fieldtypes = datatype_fieldtypes(x)
        for idx in 1:length(fields)
            println(io)
            print(io, indent, "  ", fields[idx], "::")
            print(tvar_io, fieldtypes[idx])
        end
    end
    nothing
end

const DUMP_DEFAULT_MAXDEPTH = 8

function dump(io::IO, @nospecialize(x); maxdepth=DUMP_DEFAULT_MAXDEPTH)
    dump(IOContext(io), x, maxdepth, "")
    println(io)
end

"""
    dump(x; maxdepth=$DUMP_DEFAULT_MAXDEPTH)

Show every part of the representation of a value.
The depth of the output is truncated at `maxdepth`.

# Examples
```jldoctest
julia> struct MyStruct
           x
           y
       end

julia> x = MyStruct(1, (2,3));

julia> dump(x)
MyStruct
  x: Int64 1
  y: Tuple{Int64, Int64}
    1: Int64 2
    2: Int64 3

julia> dump(x; maxdepth = 1)
MyStruct
  x: Int64 1
  y: Tuple{Int64, Int64}
```
"""
function dump(arg; maxdepth=DUMP_DEFAULT_MAXDEPTH)
    # this is typically used interactively, so default to being in Main (or current active module)
    mod = get(stdout, :module, active_module())
    dump(IOContext(stdout::IO, :limit => true, :module => mod), arg; maxdepth=maxdepth)
end

nocolor(io::IO) = IOContext(io, :color => false)
alignment_from_show(io::IO, x::Any) =
    textwidth(sprint(show, x, context=nocolor(io), sizehint=0))

"""
`alignment(io, X)` returns a tuple (left,right) showing how many characters are
needed on either side of an alignment feature such as a decimal point.

# Examples
```jldoctest
julia> Base.alignment(stdout, 42)
(2, 0)

julia> Base.alignment(stdout, 4.23)
(1, 3)

julia> Base.alignment(stdout, 1 + 10im)
(3, 5)
```
"""
alignment(io::IO, x::Any) = (0, alignment_from_show(io, x))
alignment(io::IO, x::Number) = (alignment_from_show(io, x), 0)
alignment(io::IO, x::Integer) = (alignment_from_show(io, x), 0)
function alignment(io::IO, x::Real)
    s = sprint(show, x, context=nocolor(io), sizehint=0)
    m = match(r"^(.*?)((?:[\.eEfF].*)?)$", s)
    m === nothing ? (textwidth(s), 0) :
                    (textwidth(m.captures[1]), textwidth(m.captures[2]))
end
function alignment(io::IO, x::Complex)
    s = sprint(show, x, context=nocolor(io), sizehint=0)
    m = match(r"^(.*[^ef][\+\-])(.*)$", s)
    m === nothing ? (textwidth(s), 0) :
                    (textwidth(m.captures[1]), textwidth(m.captures[2]))
end
function alignment(io::IO, x::Rational)
    s = sprint(show, x, context=nocolor(io), sizehint=0)
    m = match(r"^(.*?/)(/.*)$", s)
    m === nothing ? (textwidth(s), 0) :
                    (textwidth(m.captures[1]), textwidth(m.captures[2]))
end

function alignment(io::IO, x::Pair)
    fullwidth = alignment_from_show(io, x)
    if !isdelimited(io, x) # i.e. use "=>" for display
        ctx = IOContext(io, :typeinfo => gettypeinfos(io, x)[1])
        left = alignment_from_show(ctx, x.first)
        left += 2 * !isdelimited(ctx, x.first) # for parens around p.first
        left += !(get(io, :compact, false)::Bool) # spaces are added around "=>"
        (left+1, fullwidth-left-1) # +1 for the "=" part of "=>"
    else
        (0, fullwidth) # as for x::Any
    end
end

const undef_ref_str = "#undef"

show(io::IO, ::UndefInitializer) = print(io, "UndefInitializer()")

"""
    summary(io::IO, x)
    str = summary(x)

Print to a stream `io`, or return a string `str`, giving a brief description of
a value. By default returns `string(typeof(x))`, e.g. [`Int64`](@ref).

For arrays, returns a string of size and type info,
e.g. `10-element Array{Int64,1}`.

# Examples
```jldoctest
julia> summary(1)
"Int64"

julia> summary(zeros(2))
"2-element Vector{Float64}"
```
"""
summary(io::IO, x) = print(io, typeof(x))
function summary(x)
    io = IOBuffer()
    summary(io, x)
    String(take!(io))
end

## `summary` for AbstractArrays
# sizes such as 0-dimensional, 4-dimensional, 2x3
dims2string(d) = isempty(d) ? "0-dimensional" :
                 length(d) == 1 ? "$(d[1])-element" :
                 join(map(string,d), '×')

inds2string(inds) = join(map(_indsstring,inds), '×')
_indsstring(i) = string(i)
_indsstring(i::Union{IdentityUnitRange, Slice}) = string(i.indices)

# anything array-like gets summarized e.g. 10-element Array{Int64,1}
summary(io::IO, a::AbstractArray) = array_summary(io, a, axes(a))
function array_summary(io::IO, a, inds::Tuple{Vararg{OneTo}})
    print(io, dims2string(length.(inds)), " ")
    showarg(io, a, true)
end
function array_summary(io::IO, a, inds)
    print(io, dims2string(length.(inds)), " ")
    showarg(io, a, true)
    print(io, " with indices ", inds2string(inds))
end

## `summary` for Function
summary(io::IO, f::Function) = show(io, MIME"text/plain"(), f)

"""
    showarg(io::IO, x, toplevel)

Show `x` as if it were an argument to a function. This function is
used by [`summary`](@ref) to display type information in terms of sequences of
function calls on objects. `toplevel` is `true` if this is
the direct call from `summary` and `false` for nested (recursive) calls.

The fallback definition is to print `x` as "::\\\$(typeof(x))",
representing argument `x` in terms of its type. (The double-colon is
omitted if `toplevel=true`.) However, you can
specialize this function for specific types to customize printing.

# Example

A SubArray created as `view(a, :, 3, 2:5)`, where `a` is a
3-dimensional Float64 array, has type

    SubArray{Float64, 2, Array{Float64, 3}, Tuple{Colon, Int64, UnitRange{Int64}}, false}

The default `show` printing would display this full type.
However, the summary for SubArrays actually prints as

    2×4 view(::Array{Float64, 3}, :, 3, 2:5) with eltype Float64

because of a definition similar to

    function Base.showarg(io::IO, v::SubArray, toplevel)
        print(io, "view(")
        showarg(io, parent(v), false)
        print(io, ", ", join(v.indices, ", "))
        print(io, ')')
        toplevel && print(io, " with eltype ", eltype(v))
    end

Note that we're calling `showarg` recursively for the parent array
type, indicating that any recursed calls are not at the top level.
Printing the parent as `::Array{Float64,3}` is the fallback (non-toplevel)
behavior, because no specialized method for `Array` has been defined.
"""
function showarg(io::IO, T::Type, toplevel)
    toplevel || print(io, "::")
    print(io, "Type{", T, "}")
end
function showarg(io::IO, @nospecialize(x), toplevel)
    toplevel || print(io, "::")
    print(io, typeof(x))
end
# This method resolves an ambiguity for packages that specialize on eltype
function showarg(io::IO, a::Array{Union{}}, toplevel)
    toplevel || print(io, "::")
    print(io, typeof(a))
end

# Container specializations
function showarg(io::IO, v::SubArray, toplevel)
    print(io, "view(")
    showarg(io, parent(v), false)
    showindices(io, v.indices...)
    print(io, ')')
    toplevel && print(io, " with eltype ", eltype(v))
    return nothing
end
showindices(io, ::Slice, inds...) =
    (print(io, ", :"); showindices(io, inds...))
showindices(io, ind1, inds...) =
    (print(io, ", ", ind1); showindices(io, inds...))
showindices(io) = nothing

function showarg(io::IO, r::ReshapedArray, toplevel)
    print(io, "reshape(")
    showarg(io, parent(r), false)
    print(io, ", ", join(r.dims, ", "))
    print(io, ')')
    toplevel && print(io, " with eltype ", eltype(r))
    return nothing
end

function showarg(io::IO, r::NonReshapedReinterpretArray{T}, toplevel) where {T}
    print(io, "reinterpret(", T, ", ")
    showarg(io, parent(r), false)
    print(io, ')')
end

function showarg(io::IO, r::ReshapedReinterpretArray{T}, toplevel) where {T}
    print(io, "reinterpret(reshape, ", T, ", ")
    showarg(io, parent(r), false)
    print(io, ')')
    toplevel && print(io, " with eltype ", eltype(r))
    return nothing
end

# printing iterators from Base.Iterators

function show(io::IO, e::Iterators.Enumerate)
    print(io, "enumerate(")
    show(io, e.itr)
    print(io, ')')
end
show(io::IO, z::Iterators.Zip) = show_delim_array(io, z.is, "zip(", ',', ')', false)

# pretty printing for Iterators.Pairs
function Base.showarg(io::IO, r::Iterators.Pairs{<:Integer, <:Any, <:Any, T}, toplevel) where T<:AbstractArray
    print(io, "pairs(IndexLinear(), ::", T, ")")
end

function Base.showarg(io::IO, r::Iterators.Pairs{Symbol, <:Any, <:Any, T}, toplevel) where {T <: NamedTuple}
    print(io, "pairs(::NamedTuple)")
end

function Base.showarg(io::IO, r::Iterators.Pairs{<:Any, <:Any, I, D}, toplevel) where {D, I}
    print(io, "Iterators.Pairs(::", D, ", ::", I, ")")
end

# printing BitArrays

# (following functions not exported - mainly intended for debug)

function print_bit_chunk(io::IO, c::UInt64, l::Integer = 64)
    for s = 0:l-1
        d = (c >>> s) & 1
        print(io, "01"[d + 1])
        if (s + 1) & 7 == 0
            print(io, " ")
        end
    end
end

print_bit_chunk(c::UInt64, l::Integer) = print_bit_chunk(stdout, c, l)
print_bit_chunk(c::UInt64) = print_bit_chunk(stdout, c)

function bitshow(io::IO, B::BitArray)
    isempty(B) && return
    Bc = B.chunks
    for i = 1:length(Bc)-1
        print_bit_chunk(io, Bc[i])
        print(io, ": ")
    end
    l = _mod64(length(B)-1) + 1
    print_bit_chunk(io, Bc[end], l)
end
bitshow(B::BitArray) = bitshow(stdout, B)

bitstring(B::BitArray) = sprint(bitshow, B)

# printing OpaqueClosure
function show(io::IO, oc::Core.OpaqueClosure)
    A, R = typeof(oc).parameters
    show_tuple_as_call(io, Symbol(""), A; hasfirst=false)
    print(io, "::", R)
    print(io, "->◌")
end

function show(io::IO, ::MIME"text/plain", oc::Core.OpaqueClosure{A, R}) where {A, R}
    show(io, oc)
end
Z   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/compiler/ssair/show.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

# This file is not loaded into `Core.Compiler` but rather loaded into the context of
# `Base.IRShow` and thus does not participate in bootstrapping.

@nospecialize

if Pair != Base.Pair
import Base: Base, IOContext, string, join, sprint
IOContext(io::IO, KV::Pair) = IOContext(io, Base.Pair(KV[1], KV[2]))
length(s::String) = Base.length(s)
^(s::String, i::Int) = Base.:^(s, i)
end

import Base: show_unquoted
using Base: printstyled, with_output_color, prec_decl, @invoke

function Base.show(io::IO, cfg::CFG)
    print(io, "CFG with $(length(cfg.blocks)) blocks:")
    for (idx, block) in enumerate(cfg.blocks)
        print(io, "\n  bb ", idx)
        if block.stmts.start == block.stmts.stop
            print(io, " (stmt ", block.stmts.start, ")")
        else
            print(io, " (stmts ", block.stmts.start, ":", block.stmts.stop, ")")
        end
        if !isempty(block.succs)
            print(io, " → bb ")
            join(io, block.succs, ", ")
        end
    end
end

function print_stmt(io::IO, idx::Int, @nospecialize(stmt), used::BitSet, maxlength_idx::Int, color::Bool, show_type::Bool)
    if idx in used
        idx_s = string(idx)
        pad = " "^(maxlength_idx - length(idx_s) + 1)
        print(io, "%", idx_s, pad, "= ")
    else
        print(io, " "^(maxlength_idx + 4))
    end
    # TODO: `indent` is supposed to be the full width of the leader for correct alignment
    indent = 16
    if !color && stmt isa PiNode
        # when the outer context is already colored (green, for pending nodes), don't use the usual coloring printer
        print(io, "π (")
        show_unquoted(io, stmt.val, indent)
        print(io, ", ")
        print(io, stmt.typ)
        print(io, ")")
    elseif isexpr(stmt, :invoke) && length(stmt.args) >= 2 && isa(stmt.args[1], MethodInstance)
        stmt = stmt::Expr
        # TODO: why is this here, and not in Base.show_unquoted
        print(io, "invoke ")
        linfo = stmt.args[1]::Core.MethodInstance
        show_unquoted(io, stmt.args[2], indent)
        print(io, "(")
        # XXX: this is wrong if `sig` is not a concretetype method
        # more correct would be to use `fieldtype(sig, i)`, but that would obscure / discard Varargs information in show
        sig = linfo.specTypes == Tuple ? Core.svec() : Base.unwrap_unionall(linfo.specTypes).parameters::Core.SimpleVector
        print_arg(i) = sprint(; context=io) do io
            show_unquoted(io, stmt.args[i], indent)
            if (i - 1) <= length(sig)
                print(io, "::", sig[i - 1])
            end
        end
        join(io, (print_arg(i) for i = 3:length(stmt.args)), ", ")
        print(io, ")")
    # given control flow information, we prefer to print these with the basic block #, instead of the ssa %
    elseif isexpr(stmt, :enter) && length((stmt::Expr).args) == 1 && (stmt::Expr).args[1] isa Int
        print(io, "\$(Expr(:enter, #", (stmt::Expr).args[1]::Int, "))")
    elseif stmt isa GotoNode
        print(io, "goto #", stmt.label)
    elseif stmt isa PhiNode
        show_unquoted_phinode(io, stmt, indent, "#")
    elseif stmt isa GotoIfNot
        show_unquoted_gotoifnot(io, stmt, indent, "#")
    elseif stmt isa TypedSlot
        # call `show` with the type set to Any so it will not be shown, since
        # we will show the type ourselves.
        show_unquoted(io, SlotNumber(stmt.id), indent, show_type ? prec_decl : 0)
    # everything else in the IR, defer to the generic AST printer
    else
        show_unquoted(io, stmt, indent, show_type ? prec_decl : 0)
    end
    nothing
end

show_unquoted(io::IO, val::Argument, indent::Int, prec::Int) = show_unquoted(io, Core.SlotNumber(val.n), indent, prec)

show_unquoted(io::IO, stmt::PhiNode, indent::Int, ::Int) = show_unquoted_phinode(io, stmt, indent, "%")
function show_unquoted_phinode(io::IO, stmt::PhiNode, indent::Int, prefix::String)
    args = String[let
        e = stmt.edges[i]
        v = !isassigned(stmt.values, i) ? "#undef" :
            sprint(; context=io) do io′
                show_unquoted(io′, stmt.values[i], indent)
            end
        "$prefix$e => $v"
        end for i in 1:length(stmt.edges)
    ]
    print(io, "φ ", '(')
    join(io, args, ", ")
    print(io, ')')
end

function show_unquoted(io::IO, stmt::PhiCNode, indent::Int, ::Int)
    print(io, "φᶜ (")
    first = true
    for v in stmt.values
        first ? (first = false) : print(io, ", ")
        show_unquoted(io, v, indent)
    end
    print(io, ")")
end

function show_unquoted(io::IO, stmt::PiNode, indent::Int, ::Int)
    print(io, "π (")
    show_unquoted(io, stmt.val, indent)
    print(io, ", ")
    printstyled(io, stmt.typ, color=:cyan)
    print(io, ")")
end

function show_unquoted(io::IO, stmt::UpsilonNode, indent::Int, ::Int)
    print(io, "ϒ (")
    isdefined(stmt, :val) ?
        show_unquoted(io, stmt.val, indent) :
        print(io, "#undef")
    print(io, ")")
end

function show_unquoted(io::IO, stmt::ReturnNode, indent::Int, ::Int)
    if !isdefined(stmt, :val)
        print(io, "unreachable")
    else
        print(io, "return ")
        show_unquoted(io, stmt.val, indent)
    end
end

show_unquoted(io::IO, stmt::GotoIfNot, indent::Int, ::Int) = show_unquoted_gotoifnot(io, stmt, indent, "%")
function show_unquoted_gotoifnot(io::IO, stmt::GotoIfNot, indent::Int, prefix::String)
    print(io, "goto ", prefix, stmt.dest, " if not ")
    show_unquoted(io, stmt.cond, indent)
end

function compute_inlining_depth(linetable::Vector, iline::Int32)
    iline == 0 && return 1
    depth = -1
    while iline != 0
        depth += 1
        lineinfo = linetable[iline]::LineInfoNode
        iline = lineinfo.inlined_at
    end
    return depth
end

function should_print_ssa_type(@nospecialize node)
    if isa(node, Expr)
        return !(node.head in (:gc_preserve_begin, :gc_preserve_end, :meta, :enter, :leave))
    end
    return !isa(node, PiNode)   && !isa(node, GotoIfNot) &&
           !isa(node, GotoNode) && !isa(node, ReturnNode) &&
           !isa(node, QuoteNode)
end

function default_expr_type_printer(io::IO; @nospecialize(type), used::Bool, show_type::Bool=true, _...)
    show_type || return nothing
    printstyled(io, "::", type, color=(used ? :cyan : :light_black))
    return nothing
end

function normalize_method_name(m)
    if m isa Method
        return m.name
    elseif m isa MethodInstance
        return (m.def::Method).name
    elseif m isa Symbol
        return m
    else
        return Symbol("")
    end
end
@noinline method_name(m::LineInfoNode) = normalize_method_name(m.method)

# converts the linetable for line numbers
# into a list in the form:
#   1 outer-most-frame
#   2   inlined-frame
#   3     innermost-frame
function compute_loc_stack(linetable::Vector, line::Int32)
    stack = Int[]
    while line != 0
        entry = linetable[line]::LineInfoNode
        pushfirst!(stack, line)
        line = entry.inlined_at
    end
    return stack
end

"""
    Compute line number annotations for an IRCode

This functions compute three sets of annotations for each IR line. Take the following
example (taken from `@code_typed sin(1.0)`):

```
    **                                                    ***         **********
    35 6 ── %10  = :(Base.mul_float)(%%2, %%2)::Float64   │╻╷         sin_kernel
       │    %11  = :(Base.mul_float)(%10, %10)::Float64   ││╻          *
```

The three annotations are indicated with `*`. The first one is the line number of the
active function (printed once whenever the outer most line number changes). The second
is the inlining indicator. The number of lines indicate the level of nesting, with a
half-size line (╷) indicating the start of a scope and a full size line (│) indicating
a continuing scope. The last annotation is the most complicated one. It is a heuristic
way to print the name of the entered scope. What it attempts to do is print the outermost
scope that hasn't been printed before. Let's work a number of examples to see the impacts
and tradeoffs involved.

```
f() = leaf_function() # Deliberately not defined to end up in the IR verbatim
g() = f()
h() = g()
top_function() = h()
```

After inlining, we end up with:
```
1 1 ─ %1 = :(Main.leaf_function)()::Any   │╻╷╷ h
  └──      return %1                      │
```

We see that the only function printed is the outermost function. This certainly loses
some information, but the idea is that the outermost function would have the most
semantic meaning (in the context of the function we're looking at).

On the other hand, let's see what happens when we redefine f:
```
function f()
    leaf_function()
    leaf_function()
    leaf_function()
end
```

We get:
```
1 1 ─      :(Main.leaf_function)()::Any   │╻╷╷ h
  │        :(Main.leaf_function)()::Any   ││┃│  g
  │   %3 = :(Main.leaf_function)()::Any   │││┃   f
  └──      return %3                      │
```

Even though we were in the `f` scope since the first statement, it tooks us two statements
to catch up and print the intermediate scopes. Which scope is printed is indicated both
by the indentation of the method name and by an increased thickness of the appropriate
line for the scope.
"""
function compute_ir_line_annotations(code::IRCode)
    loc_annotations = String[]
    loc_methods = String[]
    loc_lineno = String[]
    cur_group = 1
    last_lineno = 0
    last_stack = Int[]
    last_printed_depth = 0
    linetable = code.linetable
    lines = code.stmts.line
    last_line = zero(eltype(lines))
    for idx in 1:length(lines)
        buf = IOBuffer()
        line = lines[idx]
        print(buf, "│")
        depth = compute_inlining_depth(linetable, line)
        iline = line
        lineno = 0
        loc_method = ""
        if line != 0
            stack = compute_loc_stack(linetable, line)
            lineno = linetable[stack[1]].line
            x = min(length(last_stack), length(stack))
            if length(stack) != 0
                # Compute the last depth that was in common
                first_mismatch = let last_stack=last_stack
                    findfirst(i->last_stack[i] != stack[i], 1:x)
                end
                # If the first mismatch is the last stack frame, that might just
                # be a line number mismatch in inner most frame. Ignore those
                if length(last_stack) == length(stack) && first_mismatch == length(stack)
                    last_entry, entry = linetable[last_stack[end]], linetable[stack[end]]
                    if method_name(last_entry) === method_name(entry) && last_entry.file === entry.file
                        first_mismatch = nothing
                    end
                end
                last_depth = something(first_mismatch, x+1)-1
                if min(depth, last_depth) > last_printed_depth
                    printing_depth = min(depth, last_printed_depth + 1)
                    last_printed_depth = printing_depth
                elseif length(stack) > length(last_stack) || first_mismatch !== nothing
                    printing_depth = min(depth, last_depth + 1)
                    last_printed_depth = printing_depth
                else
                    printing_depth = 0
                end
                stole_one = false
                if printing_depth != 0
                    for _ in 1:(printing_depth-1)
                        print(buf, "│")
                    end
                    if printing_depth <= last_depth-1 && first_mismatch === nothing
                        print(buf, "┃")
                        for _ in printing_depth+1:min(depth, last_depth)
                            print(buf, "│")
                        end
                    else
                        stole_one = true
                        print(buf, "╻")
                    end
                else
                    for _ in 1:min(depth, last_depth)
                        print(buf, "│")
                    end
                end
                print(buf, "╷"^max(0, depth - last_depth - stole_one))
                if printing_depth != 0
                    if length(stack) == printing_depth
                        loc_method = line
                    else
                        loc_method = stack[printing_depth + 1]
                    end
                    loc_method = method_name(linetable[loc_method])
                end
                loc_method = string(" "^printing_depth, loc_method)
            end
            last_stack = stack
            entry = linetable[line]
        end
        push!(loc_annotations, String(take!(buf)))
        push!(loc_lineno, (lineno != 0 && lineno != last_lineno) ? string(lineno) : "")
        push!(loc_methods, loc_method)
        last_line = line
        (lineno != 0) && (last_lineno = lineno)
        nothing
    end
    return (loc_annotations, loc_methods, loc_lineno)
end

Base.show(io::IO, code::Union{IRCode, IncrementalCompact}) = show_ir(io, code)

lineinfo_disabled(io::IO, linestart::String, idx::Int) = ""

function DILineInfoPrinter(linetable::Vector, showtypes::Bool=false)
    context = LineInfoNode[]
    context_depth = Ref(0)
    indent(s::String) = s^(max(context_depth[], 1) - 1)
    function emit_lineinfo_update(io::IO, linestart::String, lineidx::Int32)
        # internal configuration options:
        linecolor = :yellow
        collapse = showtypes ? false : true
        indent_all = true
        # convert lineidx to a vector
        if lineidx == typemin(Int32)
            # sentinel value: reset internal (and external) state
            pops = indent("└")
            if !isempty(pops)
                print(io, linestart)
                printstyled(io, pops; color=linecolor)
                println(io)
            end
            empty!(context)
            context_depth[] = 0
        elseif lineidx > 0 # just skip over lines with no debug info at all
            DI = LineInfoNode[]
            while lineidx != 0
                entry = linetable[lineidx]::LineInfoNode
                push!(DI, entry)
                lineidx = entry.inlined_at
            end
            # FOR DEBUGGING, or if you just like very excessive output:
            # this prints out the context in full for every statement
            #empty!(context)
            #context_depth[] = 0
            nframes = length(DI)
            nctx::Int = 0
            pop_skips = 0
            # compute the size of the matching prefix in the inlining information stack
            for i = 1:min(length(context), nframes)
                CtxLine = context[i]
                FrameLine = DI[nframes - i + 1]
                CtxLine === FrameLine || break
                nctx = i
            end
            update_line_only::Bool = false
            if collapse
                if nctx > 0
                    # check if we're adding more frames with the same method name,
                    # if so, drop all existing calls to it from the top of the context
                    # AND check if instead the context was previously printed that way
                    # but now has removed the recursive frames
                    let method = method_name(context[nctx]) # last matching frame
                        if (nctx < nframes && method_name(DI[nframes - nctx]) === method) ||
                           (nctx < length(context) && method_name(context[nctx + 1]) === method)
                            update_line_only = true
                            while nctx > 0 && method_name(context[nctx]) === method
                                nctx -= 1
                            end
                        end
                    end
                end
                # look at the first non-matching element to see if we are only changing the line number
                if !update_line_only && nctx < length(context) && nctx < nframes
                    let CtxLine = context[nctx + 1],
                        FrameLine = DI[nframes - nctx]
                        if method_name(CtxLine) === method_name(FrameLine)
                            update_line_only = true
                        end
                    end
                end
            elseif nctx < length(context) && nctx < nframes
                # look at the first non-matching element to see if we are only changing the line number
                let CtxLine = context[nctx + 1],
                    FrameLine = DI[nframes - nctx]
                    if CtxLine.file === FrameLine.file &&
                            method_name(CtxLine) === method_name(FrameLine)
                        update_line_only = true
                    end
                end
            end
            # examine what frames we're returning from
            if nctx < length(context)
                # compute the new inlining depth
                if collapse
                    npops = 1
                    let Prev = method_name(context[nctx + 1])
                        for i = (nctx + 2):length(context)
                            Next = method_name(context[i])
                            Prev === Next || (npops += 1)
                            Prev = Next
                        end
                    end
                else
                    npops = length(context) - nctx
                end
                resize!(context, nctx)
                update_line_only && (npops -= 1)
                if npops > 0
                    context_depth[] -= npops
                    print(io, linestart)
                    printstyled(io, indent("│"), "└"^npops; color=linecolor)
                    println(io)
                end
            end
            # now print the new frames
            while nctx < nframes
                frame::LineInfoNode = DI[nframes - nctx]
                nctx += 1
                started::Bool = false
                if !update_line_only && showtypes && !isa(frame.method, Symbol) && nctx != 1
                    print(io, linestart)
                    Base.with_output_color(linecolor, io) do io
                        print(io, indent("│"))
                        print(io, "┌ invoke ", frame.method)
                        println(io)
                    end
                    started = true
                end
                print(io, linestart)
                Base.with_output_color(linecolor, io) do io
                    print(io, indent("│"))
                    push!(context, frame)
                    if update_line_only
                        update_line_only = false
                    else
                        context_depth[] += 1
                        nctx != 1 && print(io, started ? "│" : "┌")
                    end
                    print(io, " @ ", frame.file)
                    if frame.line != typemax(frame.line) && frame.line != 0
                        print(io, ":", frame.line)
                    end
                    print(io, " within `", method_name(frame), "`")
                    if collapse
                        method = method_name(frame)
                        while nctx < nframes
                            frame = DI[nframes - nctx]
                            method_name(frame) === method || break
                            nctx += 1
                            push!(context, frame)
                            print(io, " @ ", frame.file, ":", frame.line)
                        end
                    end
                end
                println(io)
            end
            # FOR DEBUGGING `collapse`:
            # this double-checks the computation of context_depth
            #let Prev = method_name(context[1]),
            #    depth2 = 1
            #    for i = 2:nctx
            #        Next = method_name(context[i])
            #        (collapse && Prev === Next) || (depth2 += 1)
            #        Prev = Next
            #    end
            #    @assert context_depth[] == depth2
            #end
        end
        indent_all || return ""
        return sprint(io -> printstyled(io, indent("│"), color=linecolor), context=io)
    end
    return emit_lineinfo_update
end

"""
    IRShowConfig

- `line_info_preprinter(io::IO, indent::String, idx::Int)`` may print relevant info
  at the beginning of the line, and should at least print `indent`. It returns a
  string that will be printed after the final basic-block annotation.
- `line_info_postprinter(io::IO; type, used::Bool, show_type::Bool, idx::Int)` prints
  relevant information like type-annotation at the end of the statement
- `should_print_stmt(idx::Int) -> Bool`: whether the statement at index `idx` should be
  printed as part of the IR or not
- `bb_color`: color used for printing the basic block brackets on the left
"""
struct IRShowConfig
    line_info_preprinter
    line_info_postprinter
    should_print_stmt
    bb_color::Symbol
    function IRShowConfig(line_info_preprinter, line_info_postprinter=default_expr_type_printer;
                          should_print_stmt=Returns(true), bb_color::Symbol=:light_black)
        return new(line_info_preprinter, line_info_postprinter, should_print_stmt, bb_color)
    end
end

struct _UNDEF
    global const UNDEF = _UNDEF.instance
end

function _stmt(code::IRCode, idx::Int)
    stmts = code.stmts
    return isassigned(stmts.inst, idx) ? stmts[idx][:inst] : UNDEF
end
function _stmt(compact::IncrementalCompact, idx::Int)
    stmts = compact.result
    return isassigned(stmts.inst, idx) ? stmts[idx][:inst] : UNDEF
end
function _stmt(code::CodeInfo, idx::Int)
    code = code.code
    return isassigned(code, idx) ? code[idx] : UNDEF
end

function _type(code::IRCode, idx::Int)
    stmts = code.stmts
    return isassigned(stmts.type, idx) ? stmts[idx][:type] : UNDEF
end
function _type(compact::IncrementalCompact, idx::Int)
    stmts = compact.result
    return isassigned(stmts.type, idx) ? stmts[idx][:type] : UNDEF
end
function _type(code::CodeInfo, idx::Int)
    types = code.ssavaluetypes
    types isa Vector{Any} || return nothing
    return isassigned(types, idx) ? types[idx] : UNDEF
end

function statement_indices_to_labels(stmt, cfg::CFG)
    # convert statement index to labels, as expected by print_stmt
    if stmt isa Expr
        if stmt.head === :enter && length(stmt.args) == 1 && stmt.args[1] isa Int
            stmt = Expr(:enter, block_for_inst(cfg, stmt.args[1]::Int))
        end
    elseif isa(stmt, GotoIfNot)
        stmt = GotoIfNot(stmt.cond, block_for_inst(cfg, stmt.dest))
    elseif stmt isa GotoNode
        stmt = GotoNode(block_for_inst(cfg, stmt.label))
    elseif stmt isa PhiNode
        e = stmt.edges
        stmt = PhiNode(Int32[block_for_inst(cfg, Int(e[i])) for i in 1:length(e)], stmt.values)
    end
    return stmt
end

# Show a single statement, code.stmts[idx]/code.code[idx], in the context of the whole IRCode/CodeInfo.
# Returns the updated value of bb_idx.
# pop_new_node!(idx::Int; attach_after=false) -> (node_idx, new_node_inst, new_node_type)
#   may return a new node at the current index `idx`, which is printed before the statement
#   at index `idx`. This function is repeatedly called until it returns `nothing`.
#   to iterate nodes that are to be inserted after the statement, set `attach_after=true`.
function show_ir_stmt(io::IO, code::Union{IRCode, CodeInfo, IncrementalCompact}, idx::Int, config::IRShowConfig,
                      used::BitSet, cfg::CFG, bb_idx::Int; pop_new_node! = Returns(nothing), only_after::Bool=false)
    return show_ir_stmt(io, code, idx, config.line_info_preprinter, config.line_info_postprinter,
                        used, cfg, bb_idx; pop_new_node!, only_after, config.bb_color)
end

function show_ir_stmt(io::IO, code::Union{IRCode, CodeInfo, IncrementalCompact}, idx::Int, line_info_preprinter, line_info_postprinter,
                      used::BitSet, cfg::CFG, bb_idx::Int; pop_new_node! = Returns(nothing), only_after::Bool=false, bb_color=:light_black)
    stmt = _stmt(code, idx)
    type = _type(code, idx)
    max_bb_idx_size = length(string(length(cfg.blocks)))

    if isempty(used)
        maxlength_idx = 0
    else
        maxused = maximum(used)
        maxlength_idx = length(string(maxused))
    end

    if stmt === UNDEF
        # This is invalid, but do something useful rather
        # than erroring, to make debugging easier
        printstyled(io, "#UNDEF\n", color=:red)
        return bb_idx
    end

    i = 1
    function print_indentation(final::Bool=true)
        # Compute BB guard rail
        if bb_idx > length(cfg.blocks)
            # If invariants are violated, print a special leader
            linestart = " "^(max_bb_idx_size + 2) # not inside a basic block bracket
            inlining_indent = line_info_preprinter(io, linestart, i == 1 ? idx : 0)
            printstyled(io, "!!! ", "─"^max_bb_idx_size, color=bb_color)
        else
            bbrange = cfg.blocks[bb_idx].stmts
            # Print line info update
            linestart = idx == first(bbrange) ? "  " : sprint(io -> printstyled(io, "│ ", color=bb_color), context=io)
            linestart *= " "^max_bb_idx_size
            # idx == 0 means only indentation is printed, so we don't print linfos
            # multiple times if the are new nodes
            inlining_indent = line_info_preprinter(io, linestart, i == 1 ? idx : 0)

            if i == 1 && idx == first(bbrange)
                bb_idx_str = string(bb_idx)
                bb_pad = max_bb_idx_size - length(bb_idx_str)
                bb_type = length(cfg.blocks[bb_idx].preds) <= 1 ? "─" : "┄"
                printstyled(io, bb_idx_str, " ", bb_type, "─"^bb_pad, color=bb_color)
            elseif final && idx == last(bbrange) # print separator
                printstyled(io, "└", "─"^(1 + max_bb_idx_size), color=bb_color)
            else
                printstyled(io, "│ ", " "^max_bb_idx_size, color=bb_color)
            end
        end
        print(io, inlining_indent, " ")
    end

    # first, print new nodes that are to be inserted before the current statement
    function print_new_node(node; final::Bool=true)
        print_indentation(final)

        node_idx, new_node_inst, new_node_type = node
        @assert new_node_inst !== UNDEF # we filtered these out earlier
        show_type = should_print_ssa_type(new_node_inst)
        let maxlength_idx=maxlength_idx, show_type=show_type
            with_output_color(:green, io) do io′
                print_stmt(io′, node_idx, new_node_inst, used, maxlength_idx, false, show_type)
            end
        end

        if new_node_type === UNDEF # try to be robust against errors
            printstyled(io, "::#UNDEF", color=:red)
        else
            line_info_postprinter(io; type = new_node_type, used = node_idx in used, show_type, idx = node_idx)
        end
        println(io)
    end
    while (next = pop_new_node!(idx)) !== nothing
        only_after || print_new_node(next; final=false)
        i += 1
    end

    # peek at the nodes to be inserted after the current statement
    # (to determine of the statement itself is the final one)
    next = pop_new_node!(idx; attach_after=true)

    # then, print the current statement
    # FIXME: `only_after` is hack so that we can call this function to print uncompacted
    #        attach-after nodes when the current node has already been compated already
    if !only_after
        print_indentation(next===nothing)
        if code isa CodeInfo
            stmt = statement_indices_to_labels(stmt, cfg)
        end
        show_type = type !== nothing && should_print_ssa_type(stmt)
        print_stmt(io, idx, stmt, used, maxlength_idx, true, show_type)
        if type !== nothing # ignore types for pre-inference code
            if type === UNDEF
                # This is an error, but can happen if passes don't update their type information
                printstyled(io, "::#UNDEF", color=:red)
            else
                line_info_postprinter(io; type, used = idx in used, show_type, idx)
            end
        end
        println(io)
    end
    i += 1

    # finally, print new nodes that are to be inserted after the current statement
    while next !== nothing
        print_new_node(next)
        i += 1
        next = pop_new_node!(idx; attach_after=true)
    end

    # increment the basic block counter
    if bb_idx <= length(cfg.blocks)
        bbrange = cfg.blocks[bb_idx].stmts
        if bb_idx <= length(cfg.blocks) && idx == last(bbrange)
            bb_idx += 1
        end
    end

    return bb_idx
end

function _new_nodes_iter(stmts, new_nodes, new_nodes_info, new_nodes_idx)
    new_nodes_perm = filter(i -> isassigned(new_nodes.inst, i), 1:length(new_nodes))
    sort!(new_nodes_perm, by = x -> (x = new_nodes_info[x]; (x.pos, x.attach_after)))

    # separate iterators for the nodes that are inserted before resp. after each statement
    before_iter = Ref(1)
    after_iter = Ref(1)

    return function get_new_node(idx::Int; attach_after=false)
        iter = attach_after ? after_iter : before_iter
        iter[] <= length(new_nodes_perm) || return nothing
        node_idx = new_nodes_perm[iter[]]

        # skip nodes
        while node_idx < new_nodes_idx ||                           # already compacted
              idx > new_nodes_info[node_idx].pos ||                 # not interested in
              new_nodes_info[node_idx].attach_after != attach_after
            iter[] += 1
            iter[] > length(new_nodes_perm) && return nothing
            node_idx = new_nodes_perm[iter[]]
        end

        if new_nodes_info[node_idx].pos != idx ||
           new_nodes_info[node_idx].attach_after != attach_after
            return nothing
        end

        iter[] += 1
        new_node = new_nodes[node_idx]
        new_node_inst = isassigned(new_nodes.inst, node_idx) ? new_node[:inst] : UNDEF
        new_node_type = isassigned(new_nodes.type, node_idx) ? new_node[:type] : UNDEF
        node_idx += length(stmts)
        return node_idx, new_node_inst, new_node_type
    end
end

function new_nodes_iter(ir::IRCode, new_nodes_idx=1)
    stmts = ir.stmts
    new_nodes = ir.new_nodes.stmts
    new_nodes_info = ir.new_nodes.info
    return _new_nodes_iter(stmts, new_nodes, new_nodes_info, new_nodes_idx)
end

function new_nodes_iter(compact::IncrementalCompact)
    stmts = compact.result
    new_nodes = compact.new_new_nodes.stmts
    new_nodes_info = compact.new_new_nodes.info
    return _new_nodes_iter(stmts, new_nodes, new_nodes_info, 1)
end

# print only line numbers on the left, some of the method names and nesting depth on the right
function inline_linfo_printer(code::IRCode)
    loc_annotations, loc_methods, loc_lineno = compute_ir_line_annotations(code)
    max_loc_width = maximum(length, loc_annotations)
    max_lineno_width = maximum(length, loc_lineno)
    max_method_width = maximum(length, loc_methods)

    function (io::IO, indent::String, idx::Int)
        cols = (displaysize(io)::Tuple{Int,Int})[2]

        if idx == 0
            annotation = ""
            loc_method = ""
            lineno = ""
        elseif idx <= length(loc_annotations)
            # N.B.: The line array length not matching is invalid,
            # but let's be robust here
            annotation = loc_annotations[idx]
            loc_method = loc_methods[idx]
            lineno = loc_lineno[idx]
        else
            annotation = "!"
            loc_method = ""
            lineno = ""
        end
        # Print location information right aligned. If the line below is too long, it'll overwrite this,
        # but that's what we want.
        if get(io, :color, false)::Bool
            method_start_column = cols - max_method_width - max_loc_width - 2
            filler = " "^(max_loc_width-length(annotation))
            printstyled(io, "\e[$(method_start_column)G$(annotation)$(filler)$(loc_method)\e[1G", color = :light_black)
        end
        printstyled(io, lineno, " "^(max_lineno_width - length(lineno) + 1); color = :light_black)
        return ""
    end
end

_strip_color(s::String) = replace(s, r"\e\[\d+m"a => "")

function statementidx_lineinfo_printer(f, code::IRCode)
    printer = f(code.linetable)
    function (io::IO, indent::String, idx::Int)
        printer(io, indent, idx > 0 ? code.stmts[idx][:line] : typemin(Int32))
    end
end
function statementidx_lineinfo_printer(f, code::CodeInfo)
    printer = f(code.linetable)
    function (io::IO, indent::String, idx::Int)
        printer(io, indent, idx > 0 ? code.codelocs[idx] : typemin(Int32))
    end
end
statementidx_lineinfo_printer(code) = statementidx_lineinfo_printer(DILineInfoPrinter, code)

function stmts_used(io::IO, code::IRCode, warn_unset_entry=true)
    stmts = code.stmts
    used = BitSet()
    for stmt in stmts
        scan_ssa_use!(push!, used, stmt[:inst])
    end
    new_nodes = code.new_nodes.stmts
    for nn in 1:length(new_nodes)
        if isassigned(new_nodes.inst, nn)
            scan_ssa_use!(push!, used, new_nodes[nn][:inst])
        elseif warn_unset_entry
            printstyled(io, "ERROR: New node array has unset entry\n", color=:red)
            warn_unset_entry = false
        end
    end
    return used
end

function stmts_used(::IO, code::CodeInfo)
    stmts = code.code
    used = BitSet()
    for stmt in stmts
        scan_ssa_use!(push!, used, stmt)
    end
    return used
end

function default_config(code::IRCode; verbose_linetable=false)
    return IRShowConfig(verbose_linetable ? statementidx_lineinfo_printer(code)
                                          : inline_linfo_printer(code);
                        bb_color=:normal)
end
default_config(code::CodeInfo) = IRShowConfig(statementidx_lineinfo_printer(code))

function show_ir_stmts(io::IO, ir::Union{IRCode, CodeInfo, IncrementalCompact}, inds, config::IRShowConfig,
                       used::BitSet, cfg::CFG, bb_idx::Int; pop_new_node! = Returns(nothing))
    for idx in inds
        if config.should_print_stmt(ir, idx, used)
            bb_idx = show_ir_stmt(io, ir, idx, config, used, cfg, bb_idx; pop_new_node!)
        elseif bb_idx <= length(cfg.blocks) && idx == cfg.blocks[bb_idx].stmts.stop
            bb_idx += 1
        end
    end
    return bb_idx
end

function finish_show_ir(io::IO, cfg::CFG, config::IRShowConfig)
    max_bb_idx_size = length(string(length(cfg.blocks)))
    config.line_info_preprinter(io, " "^(max_bb_idx_size + 2), 0)
    return nothing
end

function show_ir(io::IO, ir::IRCode, config::IRShowConfig=default_config(ir);
                 pop_new_node! = new_nodes_iter(ir))
    used = stmts_used(io, ir)
    cfg = ir.cfg
    maxssaid = length(ir.stmts) + Core.Compiler.length(ir.new_nodes)
    let io = IOContext(io, :maxssaid=>maxssaid)
        show_ir_stmts(io, ir, 1:length(ir.stmts), config, used, cfg, 1; pop_new_node!)
    end
    finish_show_ir(io, cfg, config)
end

function show_ir(io::IO, ci::CodeInfo, config::IRShowConfig=default_config(ci);
                 pop_new_node! = Returns(nothing))
    used = stmts_used(io, ci)
    cfg = compute_basic_blocks(ci.code)
    let io = IOContext(io, :maxssaid=>length(ci.code))
        show_ir_stmts(io, ci, 1:length(ci.code), config, used, cfg, 1; pop_new_node!)
    end
    finish_show_ir(io, cfg, config)
end

function show_ir(io::IO, compact::IncrementalCompact, config::IRShowConfig=default_config(compact.ir))
    cfg = compact.ir.cfg


    # First print everything that has already been compacted

    # merge uses in uncompacted region into compacted uses
    used_compacted = BitSet(i for (i, x) in pairs(compact.used_ssas) if x != 0)
    used_uncompacted = stmts_used(io, compact.ir)
    for (i, ssa) = enumerate(compact.ssa_rename)
        if isa(ssa, SSAValue) && ssa.id in used_uncompacted
            push!(used_compacted, i)
        end
    end

    # while compacting, the end of the active result bb will not have been determined
    # (this is done post-hoc by `finish_current_bb!`), so determine it here from scratch.
    result_bbs = copy(compact.cfg_transform.result_bbs)
    if compact.active_result_bb <= length(result_bbs)
        # count the total number of nodes we'll add to this block
        input_bb_idx = block_for_inst(compact.ir.cfg, compact.idx)
        input_bb = compact.ir.cfg.blocks[input_bb_idx]
        count = 0
        for input_idx in input_bb.stmts.start:input_bb.stmts.stop
            pop_new_node! = new_nodes_iter(compact.ir)
            while pop_new_node!(input_idx) !== nothing
                count += 1
            end
            while pop_new_node!(input_idx; attach_after=true) !== nothing
                count += 1
            end
        end

        still_to_be_inserted = (last(input_bb.stmts) - compact.idx) + count

        result_bb = result_bbs[compact.active_result_bb]
        result_bbs[compact.active_result_bb] = Core.Compiler.BasicBlock(result_bb,
            Core.Compiler.StmtRange(first(result_bb.stmts), compact.result_idx+still_to_be_inserted))
    end
    compact_cfg = CFG(result_bbs, Int[first(result_bbs[i].stmts) for i in 2:length(result_bbs)])

    pop_new_node! = new_nodes_iter(compact)
    maxssaid = length(compact.result) + Core.Compiler.length(compact.new_new_nodes)
    bb_idx = let io = IOContext(io, :maxssaid=>maxssaid)
        show_ir_stmts(io, compact, 1:compact.result_idx-1, config, used_compacted,
                      compact_cfg, 1; pop_new_node!)
    end


    # Print uncompacted nodes from the original IR

    # print a separator
    (_, width) = displaysize(io)
    stmts = compact.ir.stmts
    indent = length(string(length(stmts)))
    # config.line_info_preprinter(io, "", compact.idx)
    printstyled(io, "─"^(width-indent-1), '\n', color=:red)

    # while compacting, the start of the active uncompacted bb will have been overwritten.
    # this manifests as a stmt range end that is less than the start, so correct that.
    inputs_bbs = copy(cfg.blocks)
    for (i, bb) in enumerate(inputs_bbs)
        if bb.stmts.stop < bb.stmts.start
            inputs_bbs[i] = Core.Compiler.BasicBlock(bb,
                Core.Compiler.StmtRange(last(bb.stmts), last(bb.stmts)))
            # this is not entirely correct, and will result in the bb starting again,
            # but is the best we can do without changing how `finish_current_bb!` works.
        end
    end
    uncompacted_cfg = CFG(inputs_bbs, Int[first(inputs_bbs[i].stmts) for i in 2:length(inputs_bbs)])

    pop_new_node! = new_nodes_iter(compact.ir, compact.new_nodes_idx)
    maxssaid = length(compact.ir.stmts) + Core.Compiler.length(compact.ir.new_nodes)
    let io = IOContext(io, :maxssaid=>maxssaid)
        # first show any new nodes to be attached after the last compacted statement
        if compact.idx > 1
            show_ir_stmt(io, compact.ir, compact.idx-1, config, used_uncompacted,
                        uncompacted_cfg, bb_idx; pop_new_node!, only_after=true)
        end

        # then show the actual uncompacted IR
        show_ir_stmts(io, compact.ir, compact.idx:length(stmts), config, used_uncompacted,
                      uncompacted_cfg, bb_idx; pop_new_node!)
    end

    finish_show_ir(io, uncompacted_cfg, config)
end

function effectbits_letter(effects::Effects, name::Symbol, suffix::Char)
    ft = fieldtype(Effects, name)
    if ft === UInt8
        prefix = getfield(effects, name) === ALWAYS_TRUE ? '+' :
                 getfield(effects, name) === ALWAYS_FALSE ? '!' : '?'
    elseif ft === Bool
        prefix = getfield(effects, name) ? '+' : '!'
    else
        error("unsupported effectbits type given")
    end
    return string(prefix, suffix)
end

function effectbits_color(effects::Effects, name::Symbol)
    ft = fieldtype(Effects, name)
    if ft === UInt8
        color = getfield(effects, name) === ALWAYS_TRUE ? :green :
                getfield(effects, name) === ALWAYS_FALSE ? :red : :yellow
    elseif ft === Bool
        color = getfield(effects, name) ? :green : :red
    else
        error("unsupported effectbits type given")
    end
    return color
end

function Base.show(io::IO, e::Effects)
    print(io, "(")
    printstyled(io, effectbits_letter(e, :consistent,  'c'); color=effectbits_color(e, :consistent))
    print(io, ',')
    printstyled(io, effectbits_letter(e, :effect_free, 'e'); color=effectbits_color(e, :effect_free))
    print(io, ',')
    printstyled(io, effectbits_letter(e, :nothrow,     'n'); color=effectbits_color(e, :nothrow))
    print(io, ',')
    printstyled(io, effectbits_letter(e, :terminates,  't'); color=effectbits_color(e, :terminates))
    print(io, ',')
    printstyled(io, effectbits_letter(e, :notaskstate, 's'); color=effectbits_color(e, :notaskstate))
    print(io, ',')
    printstyled(io, effectbits_letter(e, :inaccessiblememonly, 'm'); color=effectbits_color(e, :inaccessiblememonly))
    print(io, ',')
    printstyled(io, effectbits_letter(e, :noinbounds, 'i'); color=effectbits_color(e, :noinbounds))
    print(io, ')')
    e.nonoverlayed || printstyled(io, '′'; color=:red)
end

@specialize
P   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/arrayshow.jlB^      # This file is a part of Julia. License is MIT: https://julialang.org/license

# methods related to array printing

# Printing a value requires to take into account the :typeinfo property
# from the IO context; this property encodes (as a type) the type information
# that is supposed to have already been displayed concerning this value,
# so that redundancy can be avoided. For example, when printing an array of
# `Float16` values, the header "Float16" will be printed, and the values
# can simply be printed with the decimal representations:
# show(Float16(1)) -> "Float16(1.0)"
# show([Float16(1)]) -> "Float16[1.0]" (instead of "Float16[Float16(1.0)]")
# Similarly:
# show([[Float16(1)]]) -> "Array{Float16}[[1.0]]" (instead of "Array{Float16}[Float16[1.0]]")
#
# The array printing methods here can be grouped into two categories (and are annotated as such):
# 1) "typeinfo aware" : these are "API boundaries" functions, which will read the typeinfo
#    property from the context, and pass down to their value an updated property
#    according to its eltype; at each layer of nesting, only one "typeinfo aware"
#    function must be called;
# 2) "typeinfo agnostic": these are helper functions used by the first category; hence
#    they don't manipulate the typeinfo property, and let the printing routines
#    for their elements read directly the property set by their callers
#
# Non-annotated functions are even lower level (e.g. print_matrix_row), so they fall
# by default into category 2.
#
# The basic organization of this file is
# 1) printing with `display`
# 2) printing with `show`
# 3) Logic for displaying type information


## printing with `display`

"""
Unexported convenience function used in body of `replace_in_print_matrix`
methods. By default returns a string of the same width as original with a
centered cdot, used in printing of structural zeros of structured matrices.
Accept keyword args `c` for alternate single character marker.
"""
function replace_with_centered_mark(s::AbstractString;c::AbstractChar = '⋅')
    N = textwidth(ANSIIterator(s))
    return join(setindex!([" " for i=1:N],string(c),ceil(Int,N/2)))
end

const undef_ref_alignment = (3,3)

"""
`alignment(io, X, rows, cols, cols_if_complete, cols_otherwise, sep)` returns the
alignment for specified parts of array `X`, returning the (left,right) info.
It will look in X's `rows`, `cols` (both lists of indices)
and figure out what's needed to be fully aligned, for example looking all
the way down a column and finding out the maximum size of each element.
Parameter `sep::Integer` is number of spaces to put between elements.
`cols_if_complete` and `cols_otherwise` indicate screen width to use.
Alignment is reported as a vector of (left,right) tuples, one for each
column going across the screen.
"""
function alignment(io::IO, @nospecialize(X::AbstractVecOrMat),
        rows::AbstractVector{T}, cols::AbstractVector{V},
        cols_if_complete::Integer, cols_otherwise::Integer, sep::Integer,
        #= `size(X) may not infer, set this in caller =# ncols::Integer=size(X, 2)) where {T,V}
    a = Tuple{T, V}[]
    for j in cols # need to go down each column one at a time
        l = r = 0
        for i in rows # plumb down and see what largest element sizes are
            if isassigned(X,i,j)
                aij = alignment(io, X[i,j])::Tuple{Int,Int}
            else
                aij = undef_ref_alignment
            end
            l = max(l, aij[1]) # left characters
            r = max(r, aij[2]) # right characters
        end
        push!(a, (l, r)) # one tuple per column of X, pruned to screen width
        if length(a) > 1 && sum(map(sum,a)) + sep*length(a) >= cols_if_complete
            pop!(a) # remove this latest tuple if we're already beyond screen width
            break
        end
    end
    if 1 < length(a) < ncols
        while sum(map(sum,a)) + sep*length(a) >= cols_otherwise
            pop!(a)
        end
    end
    return a
end

"""
`print_matrix_row(io, X, A, i, cols, sep)` produces the aligned output for
a single matrix row X[i, cols] where the desired list of columns is given.
The corresponding alignment A is used, and the separation between elements
is specified as string sep.
`print_matrix_row` will also respect compact output for elements.
"""
function print_matrix_row(io::IO,
        @nospecialize(X::AbstractVecOrMat), A::Vector,
        i::Integer, cols::AbstractVector, sep::AbstractString,
        #= `axes(X)` may not infer, set this in caller =# idxlast::Integer=last(axes(X, 2)))
    for (k, j) = enumerate(cols)
        k > length(A) && break
        if isassigned(X,Int(i),Int(j)) # isassigned accepts only `Int` indices
            x = X[i,j]
            a = alignment(io, x)::Tuple{Int,Int}

            # First try 3-arg show
            sx = sprint(show, "text/plain", x, context=io, sizehint=0)

            # If the output contains line breaks, try 2-arg show instead.
            if occursin('\n', sx)
                sx = sprint(show, x, context=io, sizehint=0)
            end
        else
            a = undef_ref_alignment
            sx = undef_ref_str
        end
        l = repeat(" ", A[k][1]-a[1]) # pad on left and right as needed
        r = j == idxlast ? "" : repeat(" ", A[k][2]-a[2])
        prettysx = replace_in_print_matrix(X,i,j,sx)
        print(io, l, prettysx, r)
        if k < length(A); print(io, sep); end
    end
end


"""
`print_matrix_vdots` is used to show a series of vertical ellipsis instead
of a bunch of rows for long matrices. Not only is the string vdots shown
but it also repeated every M elements if desired.
"""
function print_matrix_vdots(io::IO, vdots::AbstractString,
                            A::Vector, sep::AbstractString, M::Integer, m::Integer,
                            pad_right::Bool = true)
    for k = 1:length(A)
        w = A[k][1] + A[k][2]
        if k % M == m
            l = repeat(" ", max(0, A[k][1]-length(vdots)))
            r = k == length(A) && !pad_right ?
                "" :
                repeat(" ", max(0, w-length(vdots)-length(l)))
            print(io, l, vdots, r)
        else
            (k != length(A) || pad_right) && print(io, repeat(" ", w))
        end
        if k < length(A); print(io, sep); end
    end
end

# typeinfo agnostic
"""
    print_matrix(io::IO, mat, pre, sep, post, hdots, vdots, ddots, hmod, vmod)

Prints a matrix with limited output size. If `io` sets `:limit` to true,
then only the corners of the matrix are printed, separated with vertical,
horizontal, and diagonal ellipses as appropriate.
Optional arguments are string pre (printed before the matrix, e.g. an opening bracket)
which will cause a corresponding same-size indent on following rows, and
string post (printed at the end of the last row of the matrix).
Also options to use different ellipsis characters hdots, vdots, ddots.
These are repeated every hmod or vmod elements.
"""
function print_matrix(io::IO, X::AbstractVecOrMat,
                      pre::AbstractString = " ",  # pre-matrix string
                      sep::AbstractString = "  ", # separator between elements
                      post::AbstractString = "",  # post-matrix string
                      hdots::AbstractString = "  \u2026  ",
                      vdots::AbstractString = "\u22ee",
                      ddots::AbstractString = "  \u22f1  ",
                      hmod::Integer = 5, vmod::Integer = 5)
    _print_matrix(io, inferencebarrier(X), pre, sep, post, hdots, vdots, ddots, hmod, vmod, unitrange(axes(X,1)), unitrange(axes(X,2)))
end

function _print_matrix(io, @nospecialize(X::AbstractVecOrMat), pre, sep, post, hdots, vdots, ddots, hmod, vmod, rowsA, colsA)
    hmod, vmod = Int(hmod)::Int, Int(vmod)::Int
    ncols, idxlast = length(colsA), last(colsA)
    if !(get(io, :limit, false)::Bool)
        screenheight = screenwidth = typemax(Int)
    else
        sz = displaysize(io)::Tuple{Int,Int}
        screenheight, screenwidth = sz[1] - 4, sz[2]
    end
    screenwidth -= length(pre)::Int + length(post)::Int
    presp = repeat(" ", length(pre)::Int)  # indent each row to match pre string
    postsp = ""
    @assert textwidth(hdots) == textwidth(ddots)
    sepsize = length(sep)::Int
    m, n = length(rowsA), length(colsA)
    # To figure out alignments, only need to look at as many rows as could
    # fit down screen. If screen has at least as many rows as A, look at A.
    # If not, then we only need to look at the first and last chunks of A,
    # each half a screen height in size.
    halfheight = div(screenheight,2)
    if m > screenheight
        rowsA = [rowsA[(0:halfheight-1) .+ firstindex(rowsA)]; rowsA[(end-div(screenheight-1,2)+1):end]]
    else
        rowsA = [rowsA;]
    end
    # Similarly for columns, only necessary to get alignments for as many
    # columns as could conceivably fit across the screen
    maxpossiblecols = div(screenwidth, 1+sepsize)
    if n > maxpossiblecols
        colsA = [colsA[(0:maxpossiblecols-1) .+ firstindex(colsA)]; colsA[(end-maxpossiblecols+1):end]]
    else
        colsA = [colsA;]
    end
    A = alignment(io, X, rowsA, colsA, screenwidth, screenwidth, sepsize, ncols)
    # Nine-slicing is accomplished using print_matrix_row repeatedly
    if m <= screenheight # rows fit vertically on screen
        if n <= length(A) # rows and cols fit so just print whole matrix in one piece
            for i in rowsA
                print(io, i == first(rowsA) ? pre : presp)
                print_matrix_row(io, X,A,i,colsA,sep,idxlast)
                print(io, i == last(rowsA) ? post : postsp)
                if i != last(rowsA); println(io); end
            end
        else # rows fit down screen but cols don't, so need horizontal ellipsis
            c = div(screenwidth-length(hdots)::Int+1,2)+1  # what goes to right of ellipsis
            Ralign = reverse(alignment(io, X, rowsA, reverse(colsA), c, c, sepsize, ncols)) # alignments for right
            c = screenwidth - sum(map(sum,Ralign)) - (length(Ralign)-1)*sepsize - length(hdots)::Int
            Lalign = alignment(io, X, rowsA, colsA, c, c, sepsize, ncols) # alignments for left of ellipsis
            for i in rowsA
                print(io, i == first(rowsA) ? pre : presp)
                print_matrix_row(io, X,Lalign,i,colsA[1:length(Lalign)],sep,idxlast)
                print(io, (i - first(rowsA)) % hmod == 0 ? hdots : repeat(" ", length(hdots)::Int))
                print_matrix_row(io, X, Ralign, i, (n - length(Ralign)) .+ colsA, sep, idxlast)
                print(io, i == last(rowsA) ? post : postsp)
                if i != last(rowsA); println(io); end
            end
        end
    else # rows don't fit so will need vertical ellipsis
        if n <= length(A) # rows don't fit, cols do, so only vertical ellipsis
            for i in rowsA
                print(io, i == first(rowsA) ? pre : presp)
                print_matrix_row(io, X,A,i,colsA,sep,idxlast)
                print(io, i == last(rowsA) ? post : postsp)
                if i != rowsA[end] || i == rowsA[halfheight]; println(io); end
                if i == rowsA[halfheight]
                    print(io, i == first(rowsA) ? pre : presp)
                    print_matrix_vdots(io, vdots, A, sep, vmod, 1, false)
                    print(io, i == last(rowsA) ? post : postsp * '\n')
                end
            end
        else # neither rows nor cols fit, so use all 3 kinds of dots
            c = div(screenwidth-length(hdots)::Int+1,2)+1
            Ralign = reverse(alignment(io, X, rowsA, reverse(colsA), c, c, sepsize, ncols))
            c = screenwidth - sum(map(sum,Ralign)) - (length(Ralign)-1)*sepsize - length(hdots)::Int
            Lalign = alignment(io, X, rowsA, colsA, c, c, sepsize, ncols)
            r = mod((length(Ralign)-n+1),vmod) # where to put dots on right half
            for i in rowsA
                print(io, i == first(rowsA) ? pre : presp)
                print_matrix_row(io, X,Lalign,i,colsA[1:length(Lalign)],sep,idxlast)
                print(io, (i - first(rowsA)) % hmod == 0 ? hdots : repeat(" ", length(hdots)::Int))
                print_matrix_row(io, X,Ralign,i,(n-length(Ralign)).+colsA,sep,idxlast)
                print(io, i == last(rowsA) ? post : postsp)
                if i != rowsA[end] || i == rowsA[halfheight]; println(io); end
                if i == rowsA[halfheight]
                    print(io, i == first(rowsA) ? pre : presp)
                    print_matrix_vdots(io, vdots, Lalign, sep, vmod, 1, true)
                    print(io, ddots)
                    print_matrix_vdots(io, vdots, Ralign, sep, vmod, r, false)
                    print(io, i == last(rowsA) ? post : postsp * '\n')
                end
            end
        end
        if isempty(rowsA)
            print(io, pre)
            print(io, vdots)
            length(colsA) > 1 && print(io, "    ", ddots)
            print(io, post)
        end
    end
end

# typeinfo agnostic
# n-dimensional arrays
show_nd(io::IO, a::AbstractArray, print_matrix::Function, show_full::Bool) =
    _show_nd(io, inferencebarrier(a), print_matrix, show_full, map(unitrange, axes(a)))

function _show_nd(io::IO, @nospecialize(a::AbstractArray), print_matrix::Function, show_full::Bool, axs::Tuple{Vararg{AbstractUnitRange}})
    limit = get(io, :limit, false)::Bool
    if isempty(a)
        return
    end
    tailinds = tail(tail(axs))
    nd = ndims(a)-2
    show_full || print(io, "[")
    Is = CartesianIndices(tailinds)
    lastidxs = first(Is).I
    reached_last_d = false
    for I in Is
        idxs = I.I
        if limit
            for i = 1:nd
                ii = idxs[i]
                ind = tailinds[i]
                if length(ind) > 10
                    if ii == ind[firstindex(ind)+3] && all(d->idxs[d]==first(tailinds[d]),1:i-1)
                        for j=i+1:nd
                            szj = length(axs[j+2])
                            indj = tailinds[j]
                            if szj>10 && first(indj)+2 < idxs[j] <= last(indj)-3
                                @goto skip
                            end
                        end
                        print(io, ";"^(i+2))
                        print(io, " \u2026 ")
                        show_full && print(io, "\n\n")
                        @goto skip
                    end
                    if ind[firstindex(ind)+2] < ii <= ind[end-3]
                        @goto skip
                    end
                end
            end
        end
        if show_full
            _show_nd_label(io, a, idxs)
        end
        slice = view(a, axs[1], axs[2], idxs...)
        if show_full
            print_matrix(io, slice)
            print(io, idxs == map(last,tailinds) ? "" : "\n\n")
        else
            idxdiff = lastidxs .- idxs .< 0
            if any(idxdiff)
                lastchangeindex = 2 + findlast(idxdiff)
                print(io, ";"^lastchangeindex)
                lastchangeindex == ndims(a) && (reached_last_d = true)
                print(io, " ")
            end
            print_matrix(io, slice)
        end
        @label skip
        lastidxs = idxs
    end
    if !show_full
        reached_last_d || print(io, ";"^(nd+2))
        print(io, "]")
    end
end

function _show_nd_label(io::IO, a::AbstractArray, idxs)
    print(io, "[:, :, ")
    for i = 1:length(idxs)-1
        print(io, idxs[i], ", ")
    end
    println(io, idxs[end], "] =")
end

# print_array: main helper functions for show(io, text/plain, array)
# typeinfo agnostic
# Note that this is for showing the content inside the array, and for `MIME"text/plain".
# There are `show(::IO, ::A) where A<:AbstractArray` methods that don't use this
# e.g. show_vector, show_zero_dim
print_array(io::IO, X::AbstractArray{<:Any, 0}) =
    isassigned(X) ? show(io, X[]) : print(io, undef_ref_str)
print_array(io::IO, X::AbstractVecOrMat) = print_matrix(io, X)
print_array(io::IO, X::AbstractArray) = show_nd(io, X, print_matrix, true)

# typeinfo aware
# implements: show(io::IO, ::MIME"text/plain", X::AbstractArray)
function show(io::IO, ::MIME"text/plain", X::AbstractArray)
    if isempty(X) && (get(io, :compact, false)::Bool || X isa Vector)
        return show(io, X)
    end
    # 0) show summary before setting :compact
    summary(io, X)
    isempty(X) && return
    print(io, ":")
    show_circular(io, X) && return

    # 1) compute new IOContext
    if !haskey(io, :compact) && length(axes(X, 2)) > 1
        io = IOContext(io, :compact => true)
    end
    if get(io, :limit, false)::Bool && eltype(X) === Method
        # override usual show method for Vector{Method}: don't abbreviate long lists
        io = IOContext(io, :limit => false)
    end

    if get(io, :limit, false)::Bool && displaysize(io)[1]-4 <= 0
        return print(io, " …")
    else
        println(io)
    end

    # 2) update typeinfo
    #
    # it must come after printing the summary, which can exploit :typeinfo itself
    # (e.g. views)
    # we assume this function is always called from top-level, i.e. that it's not nested
    # within another "show" method; hence we always print the summary, without
    # checking for current :typeinfo (this could be changed in the future)
    io = IOContext(io, :typeinfo => eltype(X))

    # 2) show actual content
    recur_io = IOContext(io, :SHOWN_SET => X)
    print_array(recur_io, X)
end

## printing with `show`

### non-Vector arrays

# _show_nonempty & _show_empty: main helper functions for show(io, X)
# typeinfo agnostic

"""
`_show_nonempty(io, X::AbstractMatrix, prefix)` prints matrix X with opening and closing square brackets,
preceded by `prefix`, supposed to encode the type of the elements.
"""
_show_nonempty(io::IO, X::AbstractMatrix, prefix::String) =
    _show_nonempty(io, inferencebarrier(X), prefix, false, axes(X))

function _show_nonempty(io::IO, @nospecialize(X::AbstractMatrix), prefix::String, drop_brackets::Bool, axs::Tuple{AbstractUnitRange,AbstractUnitRange})
    @assert !isempty(X)
    limit = get(io, :limit, false)::Bool
    indr, indc = axs
    nr, nc = length(indr), length(indc)
    rdots, cdots = false, false
    rr1, rr2 = unitrange(indr), 1:0
    cr1 = unitrange(indc)
    cr2 = first(cr1) .+ (0:-1)
    if limit
        if nr > 4
            rr1, rr2 = rr1[1:2], rr1[nr-1:nr]
            rdots = true
        end
        if nc > 4
            cr1, cr2 = cr1[1:2], cr1[nc-1:nc]
            cdots = true
        end
    end
    drop_brackets || print(io, prefix, "[")
    for rr in (rr1, rr2)
        for i in rr
            for cr in (cr1, cr2)
                for j in cr
                    j > first(cr) && print(io, " ")
                    if !isassigned(X,i,j)
                        print(io, undef_ref_str)
                    else
                        el = X[i,j]
                        show(io, el)
                    end
                end
                if last(cr) == last(indc)
                    i < last(indr) && print(io, "; ")
                elseif cdots
                    print(io, " \u2026 ")
                end
            end
        end
        last(rr) != last(indr) && rdots && print(io, "\u2026 ; ")
    end
    if !drop_brackets
        nc > 1 || print(io, ";;")
        print(io, "]")
    end
    return nothing
end


function _show_nonempty(io::IO, X::AbstractArray, prefix::String)
    print(io, prefix)
    show_nd(io, X, (io, slice) -> _show_nonempty(io, inferencebarrier(slice), prefix, true, axes(slice)), false)
end

# a specific call path is used to show vectors (show_vector)
_show_nonempty(::IO, ::AbstractVector, ::String) =
    error("_show_nonempty(::IO, ::AbstractVector, ::String) is not implemented")

_show_nonempty(io::IO, X::AbstractArray{T,0} where T, prefix::String) = print_array(io, X)

# NOTE: it's not clear how this method could use the :typeinfo attribute
function _show_empty(io::IO, X::Array)
    show(io, typeof(X))
    print(io, "(undef, ", join(size(X),", "), ')')
end
_show_empty(io, X::AbstractArray) = summary(io, X)

# typeinfo aware (necessarily)
function show(io::IO, X::AbstractArray)
    ndims(X) == 0 && return show_zero_dim(io, X)
    ndims(X) == 1 && return show_vector(io, X)
    prefix, implicit = typeinfo_prefix(io, X)
    if !implicit
        io = IOContext(io, :typeinfo => eltype(X))
    end
    isempty(X) ?
        _show_empty(io, X) :
        _show_nonempty(io, X, prefix)
end

### 0-dimensional arrays (#31481)
show_zero_dim(io::IO, X::BitArray{0}) = print(io, "BitArray(", Int(X[]), ")")
function show_zero_dim(io::IO, X::AbstractArray{T, 0}) where T
    if isassigned(X)
        print(io, "fill(")
        show(io, X[])
    else
        print(io, "Array{", T, ", 0}(")
        show(io, undef)
    end
    print(io, ")")
end

### Vector arrays

# typeinfo aware
# NOTE: v is not constrained to be a vector, as this function can work with iterables
# in general (it's used e.g. by show(::IO, ::Set))
function show_vector(io::IO, v, opn='[', cls=']')
    prefix, implicit = typeinfo_prefix(io, v)
    print(io, prefix)
    # directly or indirectly, the context now knows about eltype(v)
    if !implicit
        io = IOContext(io, :typeinfo => eltype(v))
    end
    limited = get(io, :limit, false)::Bool

    if limited && length(v) > 20
        axs1 = axes1(v)
        f, l = first(axs1), last(axs1)
        show_delim_array(io, v, opn, ",", "", false, f, f+9)
        print(io, "  …  ")
        show_delim_array(io, v, "", ",", cls, false, l-9, l)
    else
        show_delim_array(io, v, opn, ",", cls, false)
    end
end


## Logic for displaying type information

# given type `typeinfo` extracted from context, assuming a collection
# is being displayed, deduce the elements type; in spirit this is
# similar to `eltype` (except that we don't want a default fall-back
# returning Any, as this would cause incorrect printing in e.g. `Vector[Any[1]]`,
# because eltype(Vector) == Any so `Any` wouldn't be printed in `Any[1]`)
typeinfo_eltype(typeinfo) = nothing # element type not precisely known
typeinfo_eltype(typeinfo::Type{Union{}}, slurp...) = nothing
typeinfo_eltype(typeinfo::Type{<:AbstractArray{T}}) where {T} = eltype(typeinfo)
typeinfo_eltype(typeinfo::Type{<:AbstractDict{K,V}}) where {K,V} = eltype(typeinfo)
typeinfo_eltype(typeinfo::Type{<:AbstractSet{T}}) where {T} = eltype(typeinfo)


# types that can be parsed back accurately from their un-decorated representations
function typeinfo_implicit(@nospecialize(T))
    if T === Float64 || T === Int || T === Char || T === String || T === Symbol ||
        issingletontype(T)
        return true
    end
    return isconcretetype(T) &&
        ((T <: Array && typeinfo_implicit(eltype(T))) ||
         ((T <: Tuple || T <: Pair) && all(typeinfo_implicit, fieldtypes(T))) ||
         (T <: AbstractDict && typeinfo_implicit(keytype(T)) && typeinfo_implicit(valtype(T))))
end

# X not constrained, can be any iterable (cf. show_vector)
function typeinfo_prefix(io::IO, X)
    typeinfo = get(io, :typeinfo, Any)::Type

    if !(X isa typeinfo)
        typeinfo = Any
    end

    # what the context already knows about the eltype of X:
    eltype_ctx = typeinfo_eltype(typeinfo)
    eltype_X = eltype(X)

    if X isa AbstractDict
        if eltype_X == eltype_ctx
            sprint(show_type_name, typeof(X).name; context=io), false
        elseif !isempty(X) && typeinfo_implicit(keytype(X)) && typeinfo_implicit(valtype(X))
            sprint(show_type_name, typeof(X).name; context=io), true
        else
            sprint(print, typeof(X); context=io), false
        end
    else
        # Types hard-coded here are those which are created by default for a given syntax
        if eltype_X == eltype_ctx
            "", false
        elseif !isempty(X) && typeinfo_implicit(eltype_X)
            "", true
        elseif print_without_params(eltype_X)
            sprint(show_type_name, unwrap_unionall(eltype_X).name; context=io), false # Print "Array" rather than "Array{T,N}"
        else
            sprint(print, eltype_X; context=io), false
        end
    end
end
Q   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/methodshow.jl�?      # This file is a part of Julia. License is MIT: https://julialang.org/license

# Method and method table pretty-printing

const empty_sym = Symbol("")
function strip_gensym(sym)
    if sym === :var"#self#" || sym === :var"#unused#"
        return empty_sym
    end
    return Symbol(replace(String(sym), r"^(.*)#(.*#)?\d+$"sa => s"\1"))
end

function argtype_decl(env, n, @nospecialize(sig::DataType), i::Int, nargs, isva::Bool) # -> (argname, argtype)
    t = unwrapva(sig.parameters[min(i, end)])
    if i == nargs && isva
        va = sig.parameters[end]
        if isvarargtype(va) && (!isdefined(va, :N) || !isa(va.N, Int))
            t = va
        else
            ntotal = length(sig.parameters)
            isvarargtype(va) && (ntotal += va.N - 1)
            t = Vararg{t,ntotal-nargs+1}
        end
    end
    if isa(n,Expr)
        n = n.args[1]  # handle n::T in arg list
    end
    n = strip_gensym(n)
    local s
    if n === empty_sym
        s = ""
    else
        s = sprint(show_sym, n)
        t === Any && return s, ""
    end
    if isvarargtype(t)
        if !isdefined(t, :N)
            if unwrapva(t) === Any
                return string(s, "..."), ""
            else
                return s, string_with_env(env, unwrapva(t)) * "..."
            end
        end
        return s, string_with_env(env, "Vararg{", t.T, ", ", t.N, "}")
    end
    return s, string_with_env(env, t)
end

function method_argnames(m::Method)
    argnames = ccall(:jl_uncompress_argnames, Vector{Symbol}, (Any,), m.slot_syms)
    isempty(argnames) && return argnames
    return argnames[1:m.nargs]
end

function arg_decl_parts(m::Method, html=false)
    tv = Any[]
    sig = m.sig
    while isa(sig, UnionAll)
        push!(tv, sig.var)
        sig = sig.body
    end
    file, line = updated_methodloc(m)
    argnames = method_argnames(m)
    if length(argnames) >= m.nargs
        show_env = ImmutableDict{Symbol, Any}()
        for t in tv
            show_env = ImmutableDict(show_env, :unionall_env => t)
        end
        decls = Tuple{String,String}[argtype_decl(show_env, argnames[i], sig, i, m.nargs, m.isva)
                    for i = 1:m.nargs]
        decls[1] = ("", sprint(show_signature_function, unwrapva(sig.parameters[1]), false, decls[1][1], html,
                               context = show_env))
    else
        decls = Tuple{String,String}[("", "") for i = 1:length(sig.parameters::SimpleVector)]
    end
    return tv, decls, file, line
end

# NOTE: second argument is deprecated and is no longer used
function kwarg_decl(m::Method, kwtype = nothing)
    if m.sig !== Tuple # OpaqueClosure or Builtin
        kwtype = typeof(Core.kwcall)
        sig = rewrap_unionall(Tuple{kwtype, NamedTuple, (unwrap_unionall(m.sig)::DataType).parameters...}, m.sig)
        kwli = ccall(:jl_methtable_lookup, Any, (Any, Any, UInt), kwtype.name.mt, sig, get_world_counter())
        if kwli !== nothing
            kwli = kwli::Method
            slotnames = ccall(:jl_uncompress_argnames, Vector{Symbol}, (Any,), kwli.slot_syms)
            kws = filter(x -> !(x === empty_sym || '#' in string(x)), slotnames[(kwli.nargs + 1):end])
            # ensure the kwarg... is always printed last. The order of the arguments are not
            # necessarily the same as defined in the function
            i = findfirst(x -> endswith(string(x)::String, "..."), kws)
            if i !== nothing
                push!(kws, kws[i])
                deleteat!(kws, i)
            end
            isempty(kws) && push!(kws,  :var"...")
            return kws
        end
    end
    return Symbol[]
end

function show_method_params(io::IO, tv)
    if !isempty(tv)
        print(io, " where ")
        if length(tv) == 1
            show(io, tv[1])
        else
            print(io, "{")
            for i = 1:length(tv)
                if i > 1
                    print(io, ", ")
                end
                x = tv[i]
                show(io, x)
                io = IOContext(io, :unionall_env => x)
            end
            print(io, "}")
        end
    end
end

# In case the line numbers in the source code have changed since the code was compiled,
# allow packages to set a callback function that corrects them.
# (Used by Revise and perhaps other packages.)
# Any function `f` stored here must be consistent with the signature
#    f(m::Method)::Tuple{Union{Symbol,String}, Union{Int32,Int64}}
const methodloc_callback = Ref{Union{Function, Nothing}}(nothing)

function fixup_stdlib_path(path::String)
    # The file defining Base.Sys gets included after this file is included so make sure
    # this function is valid even in this intermediary state
    if isdefined(@__MODULE__, :Sys)
        BUILD_STDLIB_PATH = Sys.BUILD_STDLIB_PATH::String
        STDLIB = Sys.STDLIB::String
        if BUILD_STDLIB_PATH != STDLIB
            # BUILD_STDLIB_PATH gets defined in sysinfo.jl
            npath = normpath(path)
            npath′ = replace(npath, normpath(BUILD_STDLIB_PATH) => normpath(STDLIB))
            return npath == npath′ ? path : npath′
        end
    end
    return path
end

# This function does the method location updating
function updated_methodloc(m::Method)::Tuple{String, Int32}
    file, line = m.file, m.line
    if methodloc_callback[] !== nothing
        try
            file, line = invokelatest(methodloc_callback[], m)::Tuple{Union{Symbol,String}, Union{Int32,Int64}}
        catch
        end
    end
    file = fixup_stdlib_path(string(file))
    return file, Int32(line)
end

functionloc(m::Core.MethodInstance) = functionloc(m.def)

"""
    functionloc(m::Method)

Return a tuple `(filename,line)` giving the location of a `Method` definition.
"""
function functionloc(m::Method)
    file, ln = updated_methodloc(m)
    if ln <= 0
        error("could not determine location of method definition")
    end
    return (find_source_file(string(file)), ln)
end

"""
    functionloc(f::Function, types)

Return a tuple `(filename,line)` giving the location of a generic `Function` definition.
"""
functionloc(@nospecialize(f), @nospecialize(types)) = functionloc(which(f,types))

function functionloc(@nospecialize(f))
    mt = methods(f)
    if isempty(mt)
        if isa(f, Function)
            error("function has no definitions")
        else
            error("object is not callable")
        end
    end
    if length(mt) > 1
        error("function has multiple methods; please specify a type signature")
    end
    return functionloc(first(mt))
end

function sym_to_string(sym)
    if sym === :var"..."
        return "..."
    end
    s = String(sym)
    if endswith(s, "...")
        return string(sprint(show_sym, Symbol(s[1:end-3])), "...")
    else
        return sprint(show_sym, sym)
    end
end

# default compact view
show(io::IO, m::Method; kwargs...) = show_method(IOContext(io, :compact=>true), m; kwargs...)

show(io::IO, ::MIME"text/plain", m::Method; kwargs...) = show_method(io, m; kwargs...)

function show_method(io::IO, m::Method; modulecolor = :light_black, digit_align_width = 1)
    tv, decls, file, line = arg_decl_parts(m)
    sig = unwrap_unionall(m.sig)
    if sig === Tuple
        # Builtin
        print(io, m.name, "(...)")
        file = "none"
        line = 0
    else
        print(io, decls[1][2], "(")

        # arguments
        for (i,d) in enumerate(decls[2:end])
            printstyled(io, d[1], color=:light_black)
            if !isempty(d[2])
                print(io, "::")
                print_type_bicolor(io, d[2], color=:bold, inner_color=:normal)
            end
            i < length(decls)-1 && print(io, ", ")
        end

        kwargs = kwarg_decl(m)
        if !isempty(kwargs)
            print(io, "; ")
            for kw in kwargs
                skw = sym_to_string(kw)
                print(io, skw)
                if kw != last(kwargs)
                    print(io, ", ")
                end
            end
        end
        print(io, ")")
        show_method_params(io, tv)
    end

    if !(get(io, :compact, false)::Bool) # single-line mode
        println(io)
        digit_align_width += 4
    end
    # module & file, re-using function from errorshow.jl
    print_module_path_file(io, parentmodule(m), string(file), line; modulecolor, digit_align_width)
end

function show_method_list_header(io::IO, ms::MethodList, namefmt::Function)
    mt = ms.mt
    name = mt.name
    hasname = isdefined(mt.module, name) &&
              typeof(getfield(mt.module, name)) <: Function
    n = length(ms)
    m = n==1 ? "method" : "methods"
    print(io, "# $n $m")
    sname = string(name)
    namedisplay = namefmt(sname)
    if hasname
        what = (startswith(sname, '@') ?
                    "macro"
               : mt.module === Core && mt.defs isa Core.TypeMapEntry && (mt.defs.func::Method).sig === Tuple ?
                    "builtin function"
               : # else
                    "generic function")
        print(io, " for ", what, " ", namedisplay, " from ")

        col = get!(() -> popfirst!(STACKTRACE_MODULECOLORS), STACKTRACE_FIXEDCOLORS, parentmodule_before_main(ms.mt.module))

        printstyled(io, ms.mt.module, color=col)
    elseif '#' in sname
        print(io, " for anonymous function ", namedisplay)
    elseif mt === _TYPE_NAME.mt
        print(io, " for type constructor")
    else
        print(io, " for callable object")
    end
    !iszero(n) && print(io, ":")
end

# Determine the `modulecolor` value to pass to `show_method`
function _modulecolor(method::Method)
    mmt = get_methodtable(method)
    if mmt === nothing || mmt.module === parentmodule(method)
        return nothing
    end
    # `mmt` is only particularly relevant for external method tables. Since the primary
    # method table is shared, we now need to distinguish "primary" methods by trying to
    # check if there is a primary `DataType` to identify it with. c.f. how `jl_method_def`
    # would derive this same information (for the name).
    ft = argument_datatype((unwrap_unionall(method.sig)::DataType).parameters[1])
    # `ft` should be the type associated with the first argument in the method signature.
    # If it's `Type`, try to unwrap it again.
    if isType(ft)
        ft = argument_datatype(ft.parameters[1])
    end
    if ft === nothing || parentmodule(method) === parentmodule(ft) !== Core
        return nothing
    end
    m = parentmodule_before_main(method)
    return get!(() -> popfirst!(STACKTRACE_MODULECOLORS), STACKTRACE_FIXEDCOLORS, m)
end

function show_method_table(io::IO, ms::MethodList, max::Int=-1, header::Bool=true)
    mt = ms.mt
    name = mt.name
    hasname = isdefined(mt.module, name) &&
              typeof(getfield(mt.module, name)) <: Function
    if header
        show_method_list_header(io, ms, str -> "\""*str*"\"")
    end
    n = rest = 0
    local last

    last_shown_line_infos = get(io, :last_shown_line_infos, nothing)
    last_shown_line_infos === nothing || empty!(last_shown_line_infos)

    digit_align_width = length(string(max > 0 ? max : length(ms)))

    for meth in ms
        if max == -1 || n < max
            n += 1
            println(io)

            print(io, " ", lpad("[$n]", digit_align_width + 2), " ")

            show_method(io, meth; modulecolor=_modulecolor(meth))

            file, line = updated_methodloc(meth)
            if last_shown_line_infos !== nothing
                push!(last_shown_line_infos, (string(file), line))
            end
        else
            rest += 1
            last = meth
        end
    end
    if rest > 0
        println(io)
        if rest == 1
            show_method(io, last)
        else
            print(io, "... $rest methods not shown")
            if hasname
                print(io, " (use methods($name) to see them all)")
            end
        end
    end
    nothing
end

show(io::IO, ms::MethodList) = show_method_table(io, ms)
show(io::IO, ::MIME"text/plain", ms::MethodList) = show_method_table(io, ms)
show(io::IO, mt::Core.MethodTable) = show_method_table(io, MethodList(mt))

function inbase(m::Module)
    if m == Base
        true
    else
        parent = parentmodule(m)
        parent === m ? false : inbase(parent)
    end
end
fileurl(file) = let f = find_source_file(file); f === nothing ? "" : "file://"*f; end

function url(m::Method)
    M = parentmodule(m)
    (m.file === :null || m.file === :string) && return ""
    file = string(m.file)
    line = m.line
    line <= 0 || occursin(r"In\[[0-9]+\]"a, file) && return ""
    Sys.iswindows() && (file = replace(file, '\\' => '/'))
    libgit2_id = PkgId(UUID((0x76f85450_5226_5b5a,0x8eaa_529ad045b433)), "LibGit2")
    if inbase(M)
        if isempty(Base.GIT_VERSION_INFO.commit)
            # this url will only work if we're on a tagged release
            return "https://github.com/JuliaLang/julia/tree/v$VERSION/base/$file#L$line"
        else
            return "https://github.com/JuliaLang/julia/tree/$(Base.GIT_VERSION_INFO.commit)/base/$file#L$line"
        end
    elseif root_module_exists(libgit2_id)
        LibGit2 = root_module(libgit2_id)
        try
            d = dirname(file)
            return LibGit2.with(LibGit2.GitRepoExt(d)) do repo
                LibGit2.with(LibGit2.GitConfig(repo)) do cfg
                    u = LibGit2.get(cfg, "remote.origin.url", "")
                    u = (match(LibGit2.GITHUB_REGEX,u)::AbstractMatch).captures[1]
                    commit = string(LibGit2.head_oid(repo))
                    root = LibGit2.path(repo)
                    if startswith(file, root) || startswith(realpath(file), root)
                        "https://github.com/$u/tree/$commit/"*file[length(root)+1:end]*"#L$line"
                    else
                        fileurl(file)
                    end
                end
            end
        catch
            return fileurl(file)
        end
    else
        return fileurl(file)
    end
end

function show(io::IO, ::MIME"text/html", m::Method)
    tv, decls, file, line = arg_decl_parts(m, true)
    sig = unwrap_unionall(m.sig)
    if sig === Tuple
        # Builtin
        print(io, m.name, "(...) in ", parentmodule(m))
        return
    end
    print(io, decls[1][2], "(")
    join(
        io,
        String[
            isempty(d[2]) ? string(d[1]) : string(d[1], "::<b>", d[2] , "</b>") for d in decls[2:end]
        ],
        ", ",
        ", ",
    )
    kwargs = kwarg_decl(m)
    if !isempty(kwargs)
        print(io, "; <i>")
        join(io, map(sym_to_string, kwargs), ", ", ", ")
        print(io, "</i>")
    end
    print(io, ")")
    if !isempty(tv)
        print(io,"<i>")
        show_method_params(io, tv)
        print(io,"</i>")
    end
    print(io, " in ", parentmodule(m))
    if line > 0
        file, line = updated_methodloc(m)
        u = url(m)
        if isempty(u)
            print(io, " at ", file, ":", line)
        else
            print(io, """ at <a href="$u" target="_blank">""",
                  file, ":", line, "</a>")
        end
    end
end

function show(io::IO, mime::MIME"text/html", ms::MethodList)
    mt = ms.mt
    show_method_list_header(io, ms, str -> "<b>"*str*"</b>")
    print(io, "<ul>")
    for meth in ms
        print(io, "<li> ")
        show(io, mime, meth)
        print(io, "</li> ")
    end
    print(io, "</ul>")
end

show(io::IO, mime::MIME"text/html", mt::Core.MethodTable) = show(io, mime, MethodList(mt))

# pretty-printing of AbstractVector{Method}
function show(io::IO, mime::MIME"text/plain", mt::AbstractVector{Method})
    last_shown_line_infos = get(io, :last_shown_line_infos, nothing)
    last_shown_line_infos === nothing || empty!(last_shown_line_infos)
    first = true
    for (i, m) in enumerate(mt)
        first || println(io)
        first = false
        print(io, "[$(i)] ")
        show(io, m)
        file, line = updated_methodloc(m)
        if last_shown_line_infos !== nothing
            push!(last_shown_line_infos, (string(file), line))
        end
    end
    first && summary(io, mt)
    nothing
end

function show(io::IO, mime::MIME"text/html", mt::AbstractVector{Method})
    summary(io, mt)
    if !isempty(mt)
        print(io, ":<ul>")
        for d in mt
            print(io, "<li> ")
            show(io, mime, d)
        end
        print(io, "</ul>")
    end
    nothing
end
P   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/cartesian.jl�-      # This file is a part of Julia. License is MIT: https://julialang.org/license

module Cartesian

export @nloops, @nref, @ncall, @nexprs, @nextract, @nall, @nany, @ntuple, @nif

### Cartesian-specific macros

"""
    @nloops N itersym rangeexpr bodyexpr
    @nloops N itersym rangeexpr preexpr bodyexpr
    @nloops N itersym rangeexpr preexpr postexpr bodyexpr

Generate `N` nested loops, using `itersym` as the prefix for the iteration variables.
`rangeexpr` may be an anonymous-function expression, or a simple symbol `var` in which case
the range is `axes(var, d)` for dimension `d`.

Optionally, you can provide "pre" and "post" expressions. These get executed first and last,
respectively, in the body of each loop. For example:

    @nloops 2 i A d -> j_d = min(i_d, 5) begin
        s += @nref 2 A j
    end

would generate:

    for i_2 = axes(A, 2)
        j_2 = min(i_2, 5)
        for i_1 = axes(A, 1)
            j_1 = min(i_1, 5)
            s += A[j_1, j_2]
        end
    end

If you want just a post-expression, supply [`nothing`](@ref) for the pre-expression. Using
parentheses and semicolons, you can supply multi-statement expressions.
"""
macro nloops(N, itersym, rangeexpr, args...)
    _nloops(N, itersym, rangeexpr, args...)
end

function _nloops(N::Int, itersym::Symbol, arraysym::Symbol, args::Expr...)
    @gensym d
    _nloops(N, itersym, :($d->Base.axes($arraysym, $d)), args...)
end

function _nloops(N::Int, itersym::Symbol, rangeexpr::Expr, args::Expr...)
    if rangeexpr.head !== :->
        throw(ArgumentError("second argument must be an anonymous function expression to compute the range"))
    end
    if !(1 <= length(args) <= 3)
        throw(ArgumentError("number of arguments must be 1 ≤ length(args) ≤ 3, got $nargs"))
    end
    body = args[end]
    ex = Expr(:escape, body)
    for dim = 1:N
        itervar = inlineanonymous(itersym, dim)
        rng = inlineanonymous(rangeexpr, dim)
        preexpr = length(args) > 1 ? inlineanonymous(args[1], dim) : (:(nothing))
        postexpr = length(args) > 2 ? inlineanonymous(args[2], dim) : (:(nothing))
        ex = quote
            for $(esc(itervar)) = $(esc(rng))
                $(esc(preexpr))
                $ex
                $(esc(postexpr))
            end
        end
    end
    ex
end

"""
    @nref N A indexexpr

Generate expressions like `A[i_1, i_2, ...]`. `indexexpr` can either be an iteration-symbol
prefix, or an anonymous-function expression.

# Examples
```jldoctest
julia> @macroexpand Base.Cartesian.@nref 3 A i
:(A[i_1, i_2, i_3])
```
"""
macro nref(N::Int, A::Symbol, ex)
    vars = Any[ inlineanonymous(ex,i) for i = 1:N ]
    Expr(:escape, Expr(:ref, A, vars...))
end

"""
    @ncall N f sym...

Generate a function call expression. `sym` represents any number of function arguments, the
last of which may be an anonymous-function expression and is expanded into `N` arguments.

For example, `@ncall 3 func a` generates

    func(a_1, a_2, a_3)

while `@ncall 2 func a b i->c[i]` yields

    func(a, b, c[1], c[2])

"""
macro ncall(N::Int, f, args...)
    pre = args[1:end-1]
    ex = args[end]
    vars = Any[ inlineanonymous(ex,i) for i = 1:N ]
    Expr(:escape, Expr(:call, f, pre..., vars...))
end

"""
    @nexprs N expr

Generate `N` expressions. `expr` should be an anonymous-function expression.

# Examples
```jldoctest
julia> @macroexpand Base.Cartesian.@nexprs 4 i -> y[i] = A[i+j]
quote
    y[1] = A[1 + j]
    y[2] = A[2 + j]
    y[3] = A[3 + j]
    y[4] = A[4 + j]
end
```
"""
macro nexprs(N::Int, ex::Expr)
    exs = Any[ inlineanonymous(ex,i) for i = 1:N ]
    Expr(:escape, Expr(:block, exs...))
end

"""
    @nextract N esym isym

Generate `N` variables `esym_1`, `esym_2`, ..., `esym_N` to extract values from `isym`.
`isym` can be either a `Symbol` or anonymous-function expression.

`@nextract 2 x y` would generate

    x_1 = y[1]
    x_2 = y[2]

while `@nextract 3 x d->y[2d-1]` yields

    x_1 = y[1]
    x_2 = y[3]
    x_3 = y[5]

"""
macro nextract(N::Int, esym::Symbol, isym::Symbol)
    aexprs = Any[ Expr(:escape, Expr(:(=), inlineanonymous(esym, i), :(($isym)[$i]))) for i = 1:N ]
    Expr(:block, aexprs...)
end

macro nextract(N::Int, esym::Symbol, ex::Expr)
    aexprs = Any[ Expr(:escape, Expr(:(=), inlineanonymous(esym, i), inlineanonymous(ex,i))) for i = 1:N ]
    Expr(:block, aexprs...)
end

"""
    @nall N expr

Check whether all of the expressions generated by the anonymous-function expression `expr`
evaluate to `true`.

`@nall 3 d->(i_d > 1)` would generate the expression `(i_1 > 1 && i_2 > 1 && i_3 > 1)`. This
can be convenient for bounds-checking.
"""
macro nall(N::Int, criterion::Expr)
    if criterion.head !== :->
        throw(ArgumentError("second argument must be an anonymous function expression yielding the criterion"))
    end
    conds = Any[ Expr(:escape, inlineanonymous(criterion, i)) for i = 1:N ]
    Expr(:&&, conds...)
end

"""
    @nany N expr

Check whether any of the expressions generated by the anonymous-function expression `expr`
evaluate to `true`.

`@nany 3 d->(i_d > 1)` would generate the expression `(i_1 > 1 || i_2 > 1 || i_3 > 1)`.
"""
macro nany(N::Int, criterion::Expr)
    if criterion.head !== :->
        error("Second argument must be an anonymous function expression yielding the criterion")
    end
    conds = Any[ Expr(:escape, inlineanonymous(criterion, i)) for i = 1:N ]
    Expr(:||, conds...)
end

"""
    @ntuple N expr

Generates an `N`-tuple. `@ntuple 2 i` would generate `(i_1, i_2)`, and `@ntuple 2 k->k+1`
would generate `(2,3)`.
"""
macro ntuple(N::Int, ex)
    vars = Any[ inlineanonymous(ex,i) for i = 1:N ]
    Expr(:escape, Expr(:tuple, vars...))
end

"""
    @nif N conditionexpr expr
    @nif N conditionexpr expr elseexpr

Generates a sequence of `if ... elseif ... else ... end` statements. For example:

    @nif 3 d->(i_d >= size(A,d)) d->(error("Dimension ", d, " too big")) d->println("All OK")

would generate:

    if i_1 > size(A, 1)
        error("Dimension ", 1, " too big")
    elseif i_2 > size(A, 2)
        error("Dimension ", 2, " too big")
    else
        println("All OK")
    end
"""
macro nif(N, condition, operation...)
    # Handle the final "else"
    ex = esc(inlineanonymous(length(operation) > 1 ? operation[2] : operation[1], N))
    # Make the nested if statements
    for i = N-1:-1:1
        ex = Expr(:if, esc(inlineanonymous(condition,i)), esc(inlineanonymous(operation[1],i)), ex)
    end
    ex
end

## Utilities

# Simplify expressions like :(d->3:size(A,d)-3) given an explicit value for d
function inlineanonymous(ex::Expr, val)
    if ex.head !== :->
        throw(ArgumentError("not an anonymous function"))
    end
    if !isa(ex.args[1], Symbol)
        throw(ArgumentError("not a single-argument anonymous function"))
    end
    sym = ex.args[1]::Symbol
    ex = ex.args[2]::Expr
    exout = lreplace(ex, sym, val)
    exout = poplinenum(exout)
    exprresolve(exout)
end

# Given :i and 3, this generates :i_3
inlineanonymous(base::Symbol, ext) = Symbol(base,'_',ext)

# Replace a symbol by a value or a "coded" symbol
# E.g., for d = 3,
#    lreplace(:d, :d, 3) -> 3
#    lreplace(:i_d, :d, 3) -> :i_3
#    lreplace(:i_{d-1}, :d, 3) -> :i_2
# This follows LaTeX notation.
struct LReplace{S<:AbstractString}
    pat_sym::Symbol
    pat_str::S
    val::Int
end
LReplace(sym::Symbol, val::Integer) = LReplace(sym, string(sym), val)

lreplace(ex::Expr, sym::Symbol, val) = lreplace!(copy(ex), LReplace(sym, val))

function lreplace!(sym::Symbol, r::LReplace)
    sym == r.pat_sym && return r.val
    Symbol(lreplace!(string(sym), r))
end

function lreplace!(str::AbstractString, r::LReplace)
    i = firstindex(str)
    pat = r.pat_str
    j = firstindex(pat)
    matching = false
    local istart::Int
    while i <= ncodeunits(str)
        cstr = str[i]
        i = nextind(str, i)
        if !matching
            if cstr != '_' || i > ncodeunits(str)
                continue
            end
            istart = i
            cstr = str[i]
            i = nextind(str, i)
        end
        if j <= lastindex(pat)
            cr = pat[j]
            j = nextind(pat, j)
            if cstr == cr
                matching = true
            else
                matching = false
                j = firstindex(pat)
                i = istart
                continue
            end
        end
        if matching && j > lastindex(pat)
            if i > lastindex(str) || str[i] == '_'
                # We have a match
                return string(str[1:prevind(str, istart)], r.val, lreplace!(str[i:end], r))
            end
            matching = false
            j = firstindex(pat)
            i = istart
        end
    end
    str
end

function lreplace!(ex::Expr, r::LReplace)
    # Curly-brace notation, which acts like parentheses
    if ex.head === :curly && length(ex.args) == 2 && isa(ex.args[1], Symbol) && endswith(string(ex.args[1]::Symbol), "_")
        excurly = exprresolve(lreplace!(ex.args[2], r))
        if isa(excurly, Int)
            return Symbol(ex.args[1]::Symbol, excurly)
        else
            ex.args[2] = excurly
            return ex
        end
    end
    for i in 1:length(ex.args)
        ex.args[i] = lreplace!(ex.args[i], r)
    end
    ex
end

lreplace!(arg, r::LReplace) = arg


poplinenum(arg) = arg
function poplinenum(ex::Expr)
    if ex.head === :block
        if length(ex.args) == 1
            return ex.args[1]
        elseif length(ex.args) == 2 && isa(ex.args[1], LineNumberNode)
            return ex.args[2]
        elseif (length(ex.args) == 2 && isa(ex.args[1], Expr) && ex.args[1].head === :line)
            return ex.args[2]
        end
    end
    ex
end

## Resolve expressions at parsing time ##

const exprresolve_arith_dict = Dict{Symbol,Function}(:+ => +,
    :- => -, :* => *, :/ => /, :^ => ^, :div => div)
const exprresolve_cond_dict = Dict{Symbol,Function}(:(==) => ==,
    :(<) => <, :(>) => >, :(<=) => <=, :(>=) => >=)

function exprresolve_arith(ex::Expr)
    if ex.head === :call
        callee = ex.args[1]
        if isa(callee, Symbol)
            if haskey(exprresolve_arith_dict, callee) && all(Bool[isa(ex.args[i], Number) for i = 2:length(ex.args)])
                return true, exprresolve_arith_dict[callee](ex.args[2:end]...)
            end
        end
    end
    false, 0
end
exprresolve_arith(arg) = false, 0

exprresolve_conditional(b::Bool) = true, b
function exprresolve_conditional(ex::Expr)
    if ex.head === :call
        callee = ex.args[1]
        if isa(callee, Symbol)
            if callee ∈ keys(exprresolve_cond_dict) && isa(ex.args[2], Number) && isa(ex.args[3], Number)
                return true, exprresolve_cond_dict[callee](ex.args[2], ex.args[3])
            end
        end
    end
    false, false
end
exprresolve_conditional(arg) = false, false

exprresolve(arg) = arg
function exprresolve(ex::Expr)
    for i = 1:length(ex.args)
        ex.args[i] = exprresolve(ex.args[i])
    end
    # Handle simple arithmetic
    can_eval, result = exprresolve_arith(ex)
    if can_eval
        return result
    elseif ex.head === :call && (ex.args[1] === :+ || ex.args[1] === :-) && length(ex.args) == 3 && ex.args[3] == 0
        # simplify x+0 and x-0
        return ex.args[2]
    end
    # Resolve array references
    if ex.head === :ref && isa(ex.args[1], Array)
        for i = 2:length(ex.args)
            if !isa(ex.args[i], Real)
                return ex
            end
        end
        return ex.args[1][ex.args[2:end]...]
    end
    # Resolve conditionals
    if ex.head === :if
        can_eval, tf = exprresolve_conditional(ex.args[1])
        if can_eval
            ex = tf ? ex.args[2] : ex.args[3]
        end
    end
    ex
end

end
W   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/multidimensional.jld     # This file is a part of Julia. License is MIT: https://julialang.org/license

### Multidimensional iterators
module IteratorsMD
    import .Base: eltype, length, size, first, last, in, getindex, setindex!,
                  min, max, zero, oneunit, isless, eachindex,
                  convert, show, iterate, promote_rule

    import .Base: +, -, *, (:)
    import .Base: simd_outer_range, simd_inner_length, simd_index, setindex
    import .Base: to_indices, to_index, _to_indices1, _cutdim
    using .Base: IndexLinear, IndexCartesian, AbstractCartesianIndex, fill_to_length, tail,
        ReshapedArray, ReshapedArrayLF, OneTo, Fix1
    using .Base.Iterators: Reverse, PartitionIterator
    using .Base: @propagate_inbounds

    export CartesianIndex, CartesianIndices

    """
        CartesianIndex(i, j, k...)   -> I
        CartesianIndex((i, j, k...)) -> I

    Create a multidimensional index `I`, which can be used for
    indexing a multidimensional array `A`.  In particular, `A[I]` is
    equivalent to `A[i,j,k...]`.  One can freely mix integer and
    `CartesianIndex` indices; for example, `A[Ipre, i, Ipost]` (where
    `Ipre` and `Ipost` are `CartesianIndex` indices and `i` is an
    `Int`) can be a useful expression when writing algorithms that
    work along a single dimension of an array of arbitrary
    dimensionality.

    A `CartesianIndex` is sometimes produced by [`eachindex`](@ref), and
    always when iterating with an explicit [`CartesianIndices`](@ref).

    An `I::CartesianIndex` is treated as a "scalar" (not a container)
    for `broadcast`.   In order to iterate over the components of a
    `CartesianIndex`, convert it to a tuple with `Tuple(I)`.

    # Examples
    ```jldoctest
    julia> A = reshape(Vector(1:16), (2, 2, 2, 2))
    2×2×2×2 Array{Int64, 4}:
    [:, :, 1, 1] =
     1  3
     2  4

    [:, :, 2, 1] =
     5  7
     6  8

    [:, :, 1, 2] =
      9  11
     10  12

    [:, :, 2, 2] =
     13  15
     14  16

    julia> A[CartesianIndex((1, 1, 1, 1))]
    1

    julia> A[CartesianIndex((1, 1, 1, 2))]
    9

    julia> A[CartesianIndex((1, 1, 2, 1))]
    5
    ```

    !!! compat "Julia 1.10"
        Using a `CartesianIndex` as a "scalar" for `broadcast` requires
        Julia 1.10; in previous releases, use `Ref(I)`.
    """
    struct CartesianIndex{N} <: AbstractCartesianIndex{N}
        I::NTuple{N,Int}
        CartesianIndex{N}(index::NTuple{N,Integer}) where {N} = new(index)
    end

    CartesianIndex(index::NTuple{N,Integer}) where {N} = CartesianIndex{N}(index)
    CartesianIndex(index::Integer...) = CartesianIndex(index)
    CartesianIndex{N}(index::Vararg{Integer,N}) where {N} = CartesianIndex{N}(index)
    # Allow passing tuples smaller than N
    CartesianIndex{N}(index::Tuple) where {N} = CartesianIndex{N}(fill_to_length(index, 1, Val(N)))
    CartesianIndex{N}(index::Integer...) where {N} = CartesianIndex{N}(index)
    CartesianIndex{N}() where {N} = CartesianIndex{N}(())
    # Un-nest passed CartesianIndexes
    CartesianIndex(index::Union{Integer, CartesianIndex}...) = CartesianIndex(flatten(index))
    flatten(::Tuple{}) = ()
    flatten(I::Tuple{Any}) = Tuple(I[1])
    @inline flatten(I::Tuple) = (Tuple(I[1])..., flatten(tail(I))...)
    CartesianIndex(index::Tuple{Vararg{Union{Integer, CartesianIndex}}}) = CartesianIndex(index...)
    show(io::IO, i::CartesianIndex) = (print(io, "CartesianIndex"); show(io, i.I))

    # length
    length(::CartesianIndex{N}) where {N} = N
    length(::Type{CartesianIndex{N}}) where {N} = N

    # indexing
    getindex(index::CartesianIndex, i::Integer) = index.I[i]
    Base.get(A::AbstractArray, I::CartesianIndex, default) = get(A, I.I, default)
    eltype(::Type{T}) where {T<:CartesianIndex} = eltype(fieldtype(T, :I))

    # access to index tuple
    Tuple(index::CartesianIndex) = index.I

    Base.setindex(x::CartesianIndex,i,j) = CartesianIndex(Base.setindex(Tuple(x),i,j))

    # equality
    Base.:(==)(a::CartesianIndex{N}, b::CartesianIndex{N}) where N = a.I == b.I

    # zeros and ones
    zero(::CartesianIndex{N}) where {N} = zero(CartesianIndex{N})
    zero(::Type{CartesianIndex{N}}) where {N} = CartesianIndex(ntuple(Returns(0), Val(N)))
    oneunit(::CartesianIndex{N}) where {N} = oneunit(CartesianIndex{N})
    oneunit(::Type{CartesianIndex{N}}) where {N} = CartesianIndex(ntuple(Returns(1), Val(N)))

    # arithmetic, min/max
    @inline (-)(index::CartesianIndex{N}) where {N} =
        CartesianIndex{N}(map(-, index.I))
    @inline (+)(index1::CartesianIndex{N}, index2::CartesianIndex{N}) where {N} =
        CartesianIndex{N}(map(+, index1.I, index2.I))
    @inline (-)(index1::CartesianIndex{N}, index2::CartesianIndex{N}) where {N} =
        CartesianIndex{N}(map(-, index1.I, index2.I))
    @inline min(index1::CartesianIndex{N}, index2::CartesianIndex{N}) where {N} =
        CartesianIndex{N}(map(min, index1.I, index2.I))
    @inline max(index1::CartesianIndex{N}, index2::CartesianIndex{N}) where {N} =
        CartesianIndex{N}(map(max, index1.I, index2.I))

    @inline (*)(a::Integer, index::CartesianIndex{N}) where {N} = CartesianIndex{N}(map(x->a*x, index.I))
    @inline (*)(index::CartesianIndex, a::Integer) = *(a,index)

    # comparison
    isless(I1::CartesianIndex{N}, I2::CartesianIndex{N}) where {N} = isless(reverse(I1.I), reverse(I2.I))

    # conversions
    convert(::Type{T}, index::CartesianIndex{1}) where {T<:Number} = convert(T, index[1])
    convert(::Type{T}, index::CartesianIndex) where {T<:Tuple} = convert(T, index.I)

    # hashing
    const cartindexhash_seed = UInt == UInt64 ? 0xd60ca92f8284b8b0 : 0xf2ea7c2e
    function Base.hash(ci::CartesianIndex, h::UInt)
        h += cartindexhash_seed
        for i in ci.I
            h = hash(i, h)
        end
        return h
    end

    # nextind and prevind with CartesianIndex
    function Base.nextind(a::AbstractArray{<:Any,N}, i::CartesianIndex{N}) where {N}
        iter = CartesianIndices(axes(a))
        # might overflow
        I = inc(i.I, iter.indices)
        return I
    end
    function Base.prevind(a::AbstractArray{<:Any,N}, i::CartesianIndex{N}) where {N}
        iter = CartesianIndices(axes(a))
        # might underflow
        I = dec(i.I, iter.indices)
        return I
    end

    Base._ind2sub(t::Tuple, ind::CartesianIndex) = Tuple(ind)

    # Iteration over the elements of CartesianIndex cannot be supported until its length can be inferred,
    # see #23719
    Base.iterate(::CartesianIndex) =
        error("iteration is deliberately unsupported for CartesianIndex. Use `I` rather than `I...`, or use `Tuple(I)...`")

    # Iteration
    const OrdinalRangeInt = OrdinalRange{Int, Int}
    """
        CartesianIndices(sz::Dims) -> R
        CartesianIndices((istart:[istep:]istop, jstart:[jstep:]jstop, ...)) -> R

    Define a region `R` spanning a multidimensional rectangular range
    of integer indices. These are most commonly encountered in the
    context of iteration, where `for I in R ... end` will return
    [`CartesianIndex`](@ref) indices `I` equivalent to the nested loops

        for j = jstart:jstep:jstop
            for i = istart:istep:istop
                ...
            end
        end

    Consequently these can be useful for writing algorithms that
    work in arbitrary dimensions.

        CartesianIndices(A::AbstractArray) -> R

    As a convenience, constructing a `CartesianIndices` from an array makes a
    range of its indices.

    !!! compat "Julia 1.6"
        The step range method `CartesianIndices((istart:istep:istop, jstart:[jstep:]jstop, ...))`
        requires at least Julia 1.6.

    # Examples
    ```jldoctest
    julia> foreach(println, CartesianIndices((2, 2, 2)))
    CartesianIndex(1, 1, 1)
    CartesianIndex(2, 1, 1)
    CartesianIndex(1, 2, 1)
    CartesianIndex(2, 2, 1)
    CartesianIndex(1, 1, 2)
    CartesianIndex(2, 1, 2)
    CartesianIndex(1, 2, 2)
    CartesianIndex(2, 2, 2)

    julia> CartesianIndices(fill(1, (2,3)))
    CartesianIndices((2, 3))
    ```

    ## Conversion between linear and cartesian indices

    Linear index to cartesian index conversion exploits the fact that a
    `CartesianIndices` is an `AbstractArray` and can be indexed linearly:

    ```jldoctest
    julia> cartesian = CartesianIndices((1:3, 1:2))
    CartesianIndices((1:3, 1:2))

    julia> cartesian[4]
    CartesianIndex(1, 2)

    julia> cartesian = CartesianIndices((1:2:5, 1:2))
    CartesianIndices((1:2:5, 1:2))

    julia> cartesian[2, 2]
    CartesianIndex(3, 2)
    ```

    ## Broadcasting

    `CartesianIndices` support broadcasting arithmetic (+ and -) with a `CartesianIndex`.

    !!! compat "Julia 1.1"
        Broadcasting of CartesianIndices requires at least Julia 1.1.

    ```jldoctest
    julia> CIs = CartesianIndices((2:3, 5:6))
    CartesianIndices((2:3, 5:6))

    julia> CI = CartesianIndex(3, 4)
    CartesianIndex(3, 4)

    julia> CIs .+ CI
    CartesianIndices((5:6, 9:10))
    ```

    For cartesian to linear index conversion, see [`LinearIndices`](@ref).
    """
    struct CartesianIndices{N,R<:NTuple{N,OrdinalRangeInt}} <: AbstractArray{CartesianIndex{N},N}
        indices::R
    end

    CartesianIndices(::Tuple{}) = CartesianIndices{0,typeof(())}(())
    function CartesianIndices(inds::NTuple{N,OrdinalRange{<:Integer, <:Integer}}) where {N}
        indices = map(r->convert(OrdinalRangeInt, r), inds)
        CartesianIndices{N, typeof(indices)}(indices)
    end

    CartesianIndices(index::CartesianIndex) = CartesianIndices(index.I)
    CartesianIndices(inds::NTuple{N,Union{<:Integer,OrdinalRange{<:Integer}}}) where {N} =
        CartesianIndices(map(_convert2ind, inds))

    CartesianIndices(A::AbstractArray) = CartesianIndices(axes(A))

    _convert2ind(sz::Bool) = Base.OneTo(Int8(sz))
    _convert2ind(sz::Integer) = Base.OneTo(sz)
    _convert2ind(sz::AbstractUnitRange) = first(sz):last(sz)
    _convert2ind(sz::OrdinalRange) = first(sz):step(sz):last(sz)

    function show(io::IO, iter::CartesianIndices)
        print(io, "CartesianIndices(")
        show(io, map(_xform_index, iter.indices))
        print(io, ")")
    end
    _xform_index(i) = i
    _xform_index(i::OneTo) = i.stop
    show(io::IO, ::MIME"text/plain", iter::CartesianIndices) = show(io, iter)

    """
        (:)(start::CartesianIndex, [step::CartesianIndex], stop::CartesianIndex)

    Construct [`CartesianIndices`](@ref) from two `CartesianIndex` and an optional step.

    !!! compat "Julia 1.1"
        This method requires at least Julia 1.1.

    !!! compat "Julia 1.6"
        The step range method start:step:stop requires at least Julia 1.6.

    # Examples
    ```jldoctest
    julia> I = CartesianIndex(2,1);

    julia> J = CartesianIndex(3,3);

    julia> I:J
    CartesianIndices((2:3, 1:3))

    julia> I:CartesianIndex(1, 2):J
    CartesianIndices((2:1:3, 1:2:3))
    ```
    """
    (:)(I::CartesianIndex{N}, J::CartesianIndex{N}) where N =
        CartesianIndices(map((i,j) -> i:j, Tuple(I), Tuple(J)))
    (:)(I::CartesianIndex{N}, S::CartesianIndex{N}, J::CartesianIndex{N}) where N =
        CartesianIndices(map((i,s,j) -> i:s:j, Tuple(I), Tuple(S), Tuple(J)))

    promote_rule(::Type{CartesianIndices{N,R1}}, ::Type{CartesianIndices{N,R2}}) where {N,R1,R2} =
        CartesianIndices{N,Base.indices_promote_type(R1,R2)}

    convert(::Type{Tuple{}}, R::CartesianIndices{0}) = ()
    for RT in (OrdinalRange{Int, Int}, StepRange{Int, Int}, AbstractUnitRange{Int})
        @eval convert(::Type{NTuple{N,$RT}}, R::CartesianIndices{N}) where {N} =
            map(x->convert($RT, x), R.indices)
    end
    convert(::Type{NTuple{N,AbstractUnitRange}}, R::CartesianIndices{N}) where {N} =
        convert(NTuple{N,AbstractUnitRange{Int}}, R)
    convert(::Type{NTuple{N,UnitRange{Int}}}, R::CartesianIndices{N}) where {N} =
        UnitRange{Int}.(convert(NTuple{N,AbstractUnitRange}, R))
    convert(::Type{NTuple{N,UnitRange}}, R::CartesianIndices{N}) where {N} =
        UnitRange.(convert(NTuple{N,AbstractUnitRange}, R))
    convert(::Type{Tuple{Vararg{AbstractUnitRange{Int}}}}, R::CartesianIndices{N}) where {N} =
        convert(NTuple{N,AbstractUnitRange{Int}}, R)
    convert(::Type{Tuple{Vararg{AbstractUnitRange}}}, R::CartesianIndices) =
        convert(Tuple{Vararg{AbstractUnitRange{Int}}}, R)
    convert(::Type{Tuple{Vararg{UnitRange{Int}}}}, R::CartesianIndices{N}) where {N} =
        convert(NTuple{N,UnitRange{Int}}, R)
    convert(::Type{Tuple{Vararg{UnitRange}}}, R::CartesianIndices) =
        convert(Tuple{Vararg{UnitRange{Int}}}, R)

    convert(::Type{CartesianIndices{N,R}}, inds::CartesianIndices{N}) where {N,R} =
        CartesianIndices(convert(R, inds.indices))::CartesianIndices{N,R}

    # equality
    Base.:(==)(a::CartesianIndices{N}, b::CartesianIndices{N}) where N =
        all(map(==, a.indices, b.indices))
    Base.:(==)(a::CartesianIndices, b::CartesianIndices) = false

    # AbstractArray implementation
    Base.axes(iter::CartesianIndices{N,R}) where {N,R} = map(Base.axes1, iter.indices)
    Base.has_offset_axes(iter::CartesianIndices) = Base.has_offset_axes(iter.indices...)
    @propagate_inbounds function isassigned(iter::CartesianIndices{N,R}, I::Vararg{Int, N}) where {N,R}
        for i in 1:N
            isassigned(iter.indices[i], I[i]) || return false
        end
        return true
    end

    # getindex for a 0D CartesianIndices is necessary for disambiguation
    @propagate_inbounds function Base.getindex(iter::CartesianIndices{0,R}) where {R}
        CartesianIndex()
    end
    @inline function Base.getindex(iter::CartesianIndices{N,R}, I::Vararg{Int, N}) where {N,R}
        # Eagerly do boundscheck before calculating each item of the CartesianIndex so that
        # we can pass `@inbounds` hint to inside the map and generates more efficient SIMD codes (#42115)
        @boundscheck checkbounds(iter, I...)
        index = map(iter.indices, I) do r, i
            @inbounds getindex(r, i)
        end
        CartesianIndex(index)
    end

    # CartesianIndices act as a multidimensional range, so cartesian indexing of CartesianIndices
    # with compatible dimensions may be seen as indexing into the component ranges.
    # This may use the special indexing behavior implemented for ranges to return another CartesianIndices
    @inline function Base.getindex(iter::CartesianIndices{N,R},
        I::Vararg{Union{OrdinalRange{<:Integer, <:Integer}, Colon}, N}) where {N,R}
        @boundscheck checkbounds(iter, I...)
        indices = map(iter.indices, I) do r, i
            @inbounds getindex(r, i)
        end
        CartesianIndices(indices)
    end
    @propagate_inbounds function Base.getindex(iter::CartesianIndices{N},
        C::CartesianIndices{N}) where {N}
        getindex(iter, C.indices...)
    end
    @inline Base.getindex(iter::CartesianIndices{0}, ::CartesianIndices{0}) = iter

    # If dimensions permit, we may index into a CartesianIndices directly instead of constructing a SubArray wrapper
    @propagate_inbounds function Base.view(c::CartesianIndices{N}, r::Vararg{Union{OrdinalRange{<:Integer, <:Integer}, Colon},N}) where {N}
        getindex(c, r...)
    end
    @propagate_inbounds function Base.view(c::CartesianIndices{N}, C::CartesianIndices{N}) where {N}
        getindex(c, C)
    end

    eachindex(::IndexCartesian, A::AbstractArray) = CartesianIndices(axes(A))

    @inline function eachindex(::IndexCartesian, A::AbstractArray, B::AbstractArray...)
        axsA = axes(A)
        Base._all_match_first(axes, axsA, B...) || Base.throw_eachindex_mismatch_indices(IndexCartesian(), axes(A), axes.(B)...)
        CartesianIndices(axsA)
    end

    @inline function iterate(iter::CartesianIndices)
        iterfirst = first(iter)
        if !all(map(in, iterfirst.I, iter.indices))
            return nothing
        end
        iterfirst, iterfirst
    end
    @inline function iterate(iter::CartesianIndices, state)
        valid, I = __inc(state.I, iter.indices)
        valid || return nothing
        return CartesianIndex(I...), CartesianIndex(I...)
    end

    # increment & carry
    @inline function inc(state, indices)
        _, I = __inc(state, indices)
        return CartesianIndex(I...)
    end

    # Unlike ordinary ranges, CartesianIndices continues the iteration in the next column when the
    # current column is consumed. The implementation is written recursively to achieve this.
    # `iterate` returns `Union{Nothing, Tuple}`, we explicitly pass a `valid` flag to eliminate
    # the type instability inside the core `__inc` logic, and this gives better runtime performance.
    __inc(::Tuple{}, ::Tuple{}) = false, ()
    @inline function __inc(state::Tuple{Int}, indices::Tuple{OrdinalRangeInt})
        rng = indices[1]
        I = state[1] + step(rng)
        valid = __is_valid_range(I, rng) && state[1] != last(rng)
        return valid, (I, )
    end
    @inline function __inc(state::Tuple{Int,Int,Vararg{Int}}, indices::Tuple{OrdinalRangeInt,OrdinalRangeInt,Vararg{OrdinalRangeInt}})
        rng = indices[1]
        I = state[1] + step(rng)
        if __is_valid_range(I, rng) && state[1] != last(rng)
            return true, (I, tail(state)...)
        end
        valid, I = __inc(tail(state), tail(indices))
        return valid, (first(rng), I...)
    end

    @inline __is_valid_range(I, rng::AbstractUnitRange) = I in rng
    @inline function __is_valid_range(I, rng::OrdinalRange)
        if step(rng) > 0
            lo, hi = first(rng), last(rng)
        else
            lo, hi = last(rng), first(rng)
        end
        lo <= I <= hi
    end

    # 0-d cartesian ranges are special-cased to iterate once and only once
    iterate(iter::CartesianIndices{0}, done=false) = done ? nothing : (CartesianIndex(), true)

    size(iter::CartesianIndices) = map(length, iter.indices)

    length(iter::CartesianIndices) = prod(size(iter))

    # make CartesianIndices a multidimensional range
    Base.step(iter::CartesianIndices) = CartesianIndex(map(step, iter.indices))

    first(iter::CartesianIndices) = CartesianIndex(map(first, iter.indices))
    last(iter::CartesianIndices)  = CartesianIndex(map(last, iter.indices))

    # When used as indices themselves, CartesianIndices can simply become its tuple of ranges
    _to_indices1(A, inds, I1::CartesianIndices) = map(Fix1(to_index, A), I1.indices)
    _cutdim(inds::Tuple, I1::CartesianIndices) = split(inds, Val(ndims(I1)))[2]

    # but preserve CartesianIndices{0} as they consume a dimension.
    _to_indices1(A, inds, I1::CartesianIndices{0}) = (I1,)

    @inline in(i::CartesianIndex, r::CartesianIndices) = false
    @inline in(i::CartesianIndex{N}, r::CartesianIndices{N}) where {N} = all(map(in, i.I, r.indices))

    simd_outer_range(iter::CartesianIndices{0}) = iter
    function simd_outer_range(iter::CartesianIndices)
        CartesianIndices(tail(iter.indices))
    end

    simd_inner_length(iter::CartesianIndices{0}, ::CartesianIndex) = 1
    simd_inner_length(iter::CartesianIndices, I::CartesianIndex) = Base.length(iter.indices[1])

    simd_index(iter::CartesianIndices{0}, ::CartesianIndex, I1::Int) = first(iter)
    @propagate_inbounds simd_index(iter::CartesianIndices, Ilast::CartesianIndex, I1::Int) =
        CartesianIndex(iter.indices[1][I1+firstindex(iter.indices[1])], Ilast)

    # Split out the first N elements of a tuple
    @inline function split(t, V::Val)
        ref = ntuple(Returns(true), V)  # create a reference tuple of length N
        _split1(t, ref), _splitrest(t, ref)
    end
    @inline _split1(t, ref) = (t[1], _split1(tail(t), tail(ref))...)
    @inline _splitrest(t, ref) = _splitrest(tail(t), tail(ref))
    # exit either when we've exhausted the input or reference tuple
    _split1(::Tuple{}, ::Tuple{}) = ()
    _split1(::Tuple{}, ref) = ()
    _split1(t, ::Tuple{}) = ()
    _splitrest(::Tuple{}, ::Tuple{}) = ()
    _splitrest(t, ::Tuple{}) = t
    _splitrest(::Tuple{}, ref) = ()

    @inline function split(I::CartesianIndex, V::Val)
        i, j = split(I.I, V)
        CartesianIndex(i), CartesianIndex(j)
    end
    function split(R::CartesianIndices, V::Val)
        i, j = split(R.indices, V)
        CartesianIndices(i), CartesianIndices(j)
    end

    # reversed CartesianIndices iteration
    @inline function Base._reverse(iter::CartesianIndices, ::Colon)
        CartesianIndices(reverse.(iter.indices))
    end

    Base.@constprop :aggressive function Base._reverse(iter::CartesianIndices, dim::Integer)
        1 <= dim <= ndims(iter) || throw(ArgumentError(Base.LazyString("invalid dimension ", dim, " in reverse")))
        ndims(iter) == 1 && return Base._reverse(iter, :)
        indices = iter.indices
        return CartesianIndices(Base.setindex(indices, reverse(indices[dim]), dim))
    end

    Base.@constprop :aggressive function Base._reverse(iter::CartesianIndices, dims::Tuple{Vararg{Integer}})
        indices = iter.indices
        # use `sum` to force const fold
        dimrev = ntuple(i -> sum(==(i), dims; init = 0) == 1, Val(length(indices)))
        length(dims) == sum(dimrev) || throw(ArgumentError(Base.LazyString("invalid dimensions ", dims, " in reverse")))
        length(dims) == length(indices) && return Base._reverse(iter, :)
        indices′ = map((i, f) -> f ? (@noinline reverse(i)) : i, indices, dimrev)
        return CartesianIndices(indices′)
    end

    # fix ambiguity with array.jl:
    Base._reverse(iter::CartesianIndices{1}, dims::Tuple{Integer}) =
        Base._reverse(iter, first(dims))

    @inline function iterate(r::Reverse{<:CartesianIndices})
        iterfirst = last(r.itr)
        if !all(map(in, iterfirst.I, r.itr.indices))
            return nothing
        end
        iterfirst, iterfirst
    end
    @inline function iterate(r::Reverse{<:CartesianIndices}, state)
        valid, I = __dec(state.I, r.itr.indices)
        valid || return nothing
        return CartesianIndex(I...), CartesianIndex(I...)
    end

    # decrement & carry
    @inline function dec(state, indices)
        _, I = __dec(state, indices)
        return CartesianIndex(I...)
    end

    # decrement post check to avoid integer overflow
    @inline __dec(::Tuple{}, ::Tuple{}) = false, ()
    @inline function __dec(state::Tuple{Int}, indices::Tuple{OrdinalRangeInt})
        rng = indices[1]
        I = state[1] - step(rng)
        valid = __is_valid_range(I, rng) && state[1] != first(rng)
        return valid, (I,)
    end
    @inline function __dec(state::Tuple{Int,Int,Vararg{Int}}, indices::Tuple{OrdinalRangeInt,OrdinalRangeInt,Vararg{OrdinalRangeInt}})
        rng = indices[1]
        I = state[1] - step(rng)
        if __is_valid_range(I, rng) && state[1] != first(rng)
            return true, (I, tail(state)...)
        end
        valid, I = __dec(tail(state), tail(indices))
        return valid, (last(rng), I...)
    end

    # 0-d cartesian ranges are special-cased to iterate once and only once
    iterate(iter::Reverse{<:CartesianIndices{0}}, state=false) = state ? nothing : (CartesianIndex(), true)

    function Base.LinearIndices(inds::CartesianIndices{N,R}) where {N,R<:NTuple{N, AbstractUnitRange}}
        LinearIndices{N,R}(inds.indices)
    end
    function Base.LinearIndices(inds::CartesianIndices)
        indices = inds.indices
        if all(x->step(x)==1, indices)
            indices = map(rng->first(rng):last(rng), indices)
            LinearIndices{length(indices), typeof(indices)}(indices)
        else
            # Given the fact that StepRange 1:2:4 === 1:2:3, we lost the original size information
            # and thus cannot calculate the correct linear indices when the steps are not 1.
            throw(ArgumentError("LinearIndices for $(typeof(inds)) with non-1 step size is not yet supported."))
        end
    end

    # This is currently needed because converting to LinearIndices is only available when steps are
    # all 1
    # NOTE: this is only a temporary patch and could be possibly removed when StepRange support to
    # LinearIndices is done
    function Base.collect(inds::CartesianIndices{N, R}) where {N,R<:NTuple{N, AbstractUnitRange}}
        Base._collect_indices(axes(inds), inds)
    end
    function Base.collect(inds::CartesianIndices)
        dest = Array{eltype(inds), ndims(inds)}(undef, size(inds))
        i = 0
        @inbounds for a in inds
            dest[i+=1] = a
        end
        dest
    end

    # array operations
    Base.intersect(a::CartesianIndices{N}, b::CartesianIndices{N}) where N =
        CartesianIndices(intersect.(a.indices, b.indices))

    # Views of reshaped CartesianIndices are used for partitions — ensure these are fast
    const CartesianPartition{T<:CartesianIndex, P<:CartesianIndices, R<:ReshapedArray{T,1,P}} = SubArray{T,1,R,<:Tuple{AbstractUnitRange{Int}},false}
    eltype(::Type{PartitionIterator{T}}) where {T<:ReshapedArrayLF} = SubArray{eltype(T), 1, T, Tuple{UnitRange{Int}}, true}
    eltype(::Type{PartitionIterator{T}}) where {T<:ReshapedArray} = SubArray{eltype(T), 1, T, Tuple{UnitRange{Int}}, false}
    Iterators.IteratorEltype(::Type{<:PartitionIterator{T}}) where {T<:ReshapedArray} = Iterators.IteratorEltype(T)

    eltype(::Type{PartitionIterator{T}}) where {T<:OneTo} = UnitRange{eltype(T)}
    eltype(::Type{PartitionIterator{T}}) where {T<:Union{UnitRange, StepRange, StepRangeLen, LinRange}} = T
    Iterators.IteratorEltype(::Type{<:PartitionIterator{T}}) where {T<:Union{OneTo, UnitRange, StepRange, StepRangeLen, LinRange}} = Iterators.IteratorEltype(T)

    @inline function iterate(iter::CartesianPartition)
        isempty(iter) && return nothing
        f = first(iter)
        return (f, (f, 1))
    end
    @inline function iterate(iter::CartesianPartition, (state, n))
        n >= length(iter) && return nothing
        I = IteratorsMD.inc(state.I, iter.parent.parent.indices)
        return I, (I, n+1)
    end

    @inline function simd_outer_range(iter::CartesianPartition)
        # In general, the Cartesian Partition might start and stop in the middle of the outer
        # dimensions — thus the outer range of a CartesianPartition is itself a
        # CartesianPartition.
        mi = iter.parent.mi
        ci = iter.parent.parent
        ax, ax1 = axes(ci), Base.axes1(ci)
        subs = Base.ind2sub_rs(ax, mi, first(iter.indices[1]))
        vl, fl = Base._sub2ind(tail(ax), tail(subs)...), subs[1]
        vr, fr = divrem(last(iter.indices[1]) - 1, mi[end]) .+ (1, first(ax1))
        oci = CartesianIndices(tail(ci.indices))
        # A fake CartesianPartition to reuse the outer iterate fallback
        outer = @inbounds view(ReshapedArray(oci, (length(oci),), mi), vl:vr)
        init = @inbounds dec(oci[tail(subs)...].I, oci.indices) # real init state
        # Use Generator to make inner loop branchless
        @inline function skip_len_I(i::Int, I::CartesianIndex)
            l = i == 1 ? fl : first(ax1)
            r = i == length(outer) ? fr : last(ax1)
            l - first(ax1), r - l + 1, I
        end
        (skip_len_I(i, I) for (i, I) in Iterators.enumerate(Iterators.rest(outer, (init, 0))))
    end
    @inline function simd_outer_range(iter::CartesianPartition{CartesianIndex{2}})
        # But for two-dimensional Partitions the above is just a simple one-dimensional range
        # over the second dimension; we don't need to worry about non-rectangular staggers in
        # higher dimensions.
        mi = iter.parent.mi
        ci = iter.parent.parent
        ax, ax1 = axes(ci), Base.axes1(ci)
        fl, vl = Base.ind2sub_rs(ax, mi, first(iter.indices[1]))
        fr, vr = Base.ind2sub_rs(ax, mi, last(iter.indices[1]))
        outer = @inbounds CartesianIndices((ci.indices[2][vl:vr],))
        # Use Generator to make inner loop branchless
        @inline function skip_len_I(I::CartesianIndex{1})
            l = I == first(outer) ? fl : first(ax1)
            r = I == last(outer) ? fr : last(ax1)
            l - first(ax1), r - l + 1, I
        end
        (skip_len_I(I) for I in outer)
    end
    @inline simd_inner_length(iter::CartesianPartition, (_, len, _)::Tuple{Int,Int,CartesianIndex}) = len
    @propagate_inbounds simd_index(iter::CartesianPartition, (skip, _, I)::Tuple{Int,Int,CartesianIndex}, n::Int) =
        simd_index(iter.parent.parent, I, n + skip)
end  # IteratorsMD


using .IteratorsMD

## Bounds-checking with CartesianIndex
# Disallow linear indexing with CartesianIndex
function checkbounds(::Type{Bool}, A::AbstractArray, i::Union{CartesianIndex, AbstractArray{<:CartesianIndex}})
    @inline
    checkbounds_indices(Bool, axes(A), (i,))
end

@inline checkbounds_indices(::Type{Bool}, ::Tuple{}, I::Tuple{CartesianIndex,Vararg{Any}}) =
    checkbounds_indices(Bool, (), (I[1].I..., tail(I)...))
@inline checkbounds_indices(::Type{Bool}, IA::Tuple{Any}, I::Tuple{CartesianIndex,Vararg{Any}}) =
    checkbounds_indices(Bool, IA, (I[1].I..., tail(I)...))
@inline checkbounds_indices(::Type{Bool}, IA::Tuple, I::Tuple{CartesianIndex,Vararg{Any}}) =
    checkbounds_indices(Bool, IA, (I[1].I..., tail(I)...))

# Indexing into Array with mixtures of Integers and CartesianIndices is
# extremely performance-sensitive. While the abstract fallbacks support this,
# codegen has extra support for SIMDification that sub2ind doesn't (yet) support
@propagate_inbounds getindex(A::Array, i1::Union{Integer, CartesianIndex}, I::Union{Integer, CartesianIndex}...) =
    A[to_indices(A, (i1, I...))...]
@propagate_inbounds setindex!(A::Array, v, i1::Union{Integer, CartesianIndex}, I::Union{Integer, CartesianIndex}...) =
    (A[to_indices(A, (i1, I...))...] = v; A)

# Support indexing with an array of CartesianIndex{N}s
# Here we try to consume N of the indices (if there are that many available)
# The first two simply handle ambiguities
@inline function checkbounds_indices(::Type{Bool}, ::Tuple{},
        I::Tuple{AbstractArray{CartesianIndex{N}},Vararg{Any}}) where N
    checkindex(Bool, (), I[1]) & checkbounds_indices(Bool, (), tail(I))
end
@inline function checkbounds_indices(::Type{Bool}, IA::Tuple{Any},
        I::Tuple{AbstractArray{CartesianIndex{0}},Vararg{Any}})
    checkbounds_indices(Bool, IA, tail(I))
end
@inline function checkbounds_indices(::Type{Bool}, IA::Tuple{Any},
        I::Tuple{AbstractArray{CartesianIndex{N}},Vararg{Any}}) where N
    checkindex(Bool, IA, I[1]) & checkbounds_indices(Bool, (), tail(I))
end
@inline function checkbounds_indices(::Type{Bool}, IA::Tuple,
        I::Tuple{AbstractArray{CartesianIndex{N}},Vararg{Any}}) where N
    IA1, IArest = IteratorsMD.split(IA, Val(N))
    checkindex(Bool, IA1, I[1]) & checkbounds_indices(Bool, IArest, tail(I))
end


@inline function checkbounds_indices(::Type{Bool}, IA::Tuple{},
    I::Tuple{AbstractArray{Bool,N},Vararg{Any}}) where N
    return checkbounds_indices(Bool, IA, (LogicalIndex(I[1]), tail(I)...))
end
@inline function checkbounds_indices(::Type{Bool}, IA::Tuple,
    I::Tuple{AbstractArray{Bool,N},Vararg{Any}}) where N
    return checkbounds_indices(Bool, IA, (LogicalIndex(I[1]), tail(I)...))
end

function checkindex(::Type{Bool}, inds::Tuple, I::AbstractArray{<:CartesianIndex})
    b = true
    for i in I
        b &= checkbounds_indices(Bool, inds, (i,))
    end
    b
end
checkindex(::Type{Bool}, inds::Tuple, I::CartesianIndices) = all(checkindex.(Bool, inds, I.indices))

# combined count of all indices, including CartesianIndex and
# AbstractArray{CartesianIndex}
# rather than returning N, it returns an NTuple{N,Bool} so the result is inferable
@inline index_ndims(i1, I...) = (true, index_ndims(I...)...)
@inline function index_ndims(i1::CartesianIndex, I...)
    (map(Returns(true), i1.I)..., index_ndims(I...)...)
end
@inline function index_ndims(i1::AbstractArray{CartesianIndex{N}}, I...) where N
    (ntuple(Returns(true), Val(N))..., index_ndims(I...)...)
end
index_ndims() = ()

# combined dimensionality of all indices
# rather than returning N, it returns an NTuple{N,Bool} so the result is inferable
@inline index_dimsum(i1, I...) = (index_dimsum(I...)...,)
@inline index_dimsum(::Colon, I...) = (true, index_dimsum(I...)...)
@inline index_dimsum(::AbstractArray{Bool}, I...) = (true, index_dimsum(I...)...)
@inline function index_dimsum(::AbstractArray{<:Any,N}, I...) where N
    (ntuple(Returns(true), Val(N))..., index_dimsum(I...)...)
end
index_dimsum() = ()

# Recursively compute the lengths of a list of indices, without dropping scalars
index_lengths() = ()
@inline index_lengths(::Real, rest...) = (1, index_lengths(rest...)...)
@inline index_lengths(A::AbstractArray, rest...) = (length(A), index_lengths(rest...)...)

# shape of array to create for getindex() with indices I, dropping scalars
# returns a Tuple{Vararg{AbstractUnitRange}} of indices
index_shape() = ()
@inline index_shape(::Real, rest...) = index_shape(rest...)
@inline index_shape(A::AbstractArray, rest...) = (axes(A)..., index_shape(rest...)...)

"""
    LogicalIndex(mask)

The `LogicalIndex` type is a special vector that simply contains all indices I
where `mask[I]` is true. This specialized type does not support indexing
directly as doing so would require O(n) lookup time. `AbstractArray{Bool}` are
wrapped with `LogicalIndex` upon calling [`to_indices`](@ref).
"""
struct LogicalIndex{T, A<:AbstractArray{Bool}} <: AbstractVector{T}
    mask::A
    sum::Int
    LogicalIndex{T,A}(mask::A) where {T,A<:AbstractArray{Bool}} = new(mask, count(mask))
end
LogicalIndex(mask::AbstractVector{Bool}) = LogicalIndex{Int, typeof(mask)}(mask)
LogicalIndex(mask::AbstractArray{Bool, N}) where {N} = LogicalIndex{CartesianIndex{N}, typeof(mask)}(mask)
LogicalIndex{Int}(mask::AbstractArray) = LogicalIndex{Int, typeof(mask)}(mask)
size(L::LogicalIndex) = (L.sum,)
length(L::LogicalIndex) = L.sum
collect(L::LogicalIndex) = [i for i in L]
show(io::IO, r::LogicalIndex) = print(io,collect(r))
print_array(io::IO, X::LogicalIndex) = print_array(io, collect(X))
# Iteration over LogicalIndex is very performance-critical, but it also must
# support arbitrary AbstractArray{Bool}s with both Int and CartesianIndex.
# Thus the iteration state contains an index iterator and its state. We also
# keep track of the count of elements since we already know how many there
# should be -- this way we don't need to look at future indices to check done.
@inline function iterate(L::LogicalIndex{Int})
    r = LinearIndices(L.mask)
    iterate(L, (1, r))
end
@inline function iterate(L::LogicalIndex{<:CartesianIndex})
    r = CartesianIndices(axes(L.mask))
    iterate(L, (1, r))
end
@propagate_inbounds function iterate(L::LogicalIndex, s)
    # We're looking for the n-th true element, using iterator r at state i
    n = s[1]
    n > length(L) && return nothing
    #unroll once to help inference, cf issue #29418
    idx, i = iterate(tail(s)...)::Tuple{Any,Any}
    s = (n+1, s[2], i)
    L.mask[idx] && return (idx, s)
    while true
        idx, i = iterate(tail(s)...)::Tuple{Any,Any}
        s = (n+1, s[2], i)
        L.mask[idx] && return (idx, s)
    end
end
# When wrapping a BitArray, lean heavily upon its internals.
@inline function iterate(L::LogicalIndex{Int,<:BitArray})
    L.sum == 0 && return nothing
    Bc = L.mask.chunks
    return iterate(L, (1, 1, (), @inbounds Bc[1]))
end
@inline function iterate(L::LogicalIndex{<:CartesianIndex,<:BitArray})
    L.sum == 0 && return nothing
    Bc = L.mask.chunks
    irest = ntuple(one, ndims(L.mask)-1)
    return iterate(L, (1, 1, irest, @inbounds Bc[1]))
end
@inline function iterate(L::LogicalIndex{<:Any,<:BitArray}, (i1, Bi, irest, c))
    Bc = L.mask.chunks
    while c == 0
        Bi >= length(Bc) && return nothing
        i1 += 64
        @inbounds c = Bc[Bi+=1]
    end
    tz = trailing_zeros(c)
    c = _blsr(c)
    i1, irest = _overflowind(i1 + tz, irest, size(L.mask))
    return eltype(L)(i1, irest...), (i1 - tz, Bi, irest, c)
end

@inline checkbounds(::Type{Bool}, A::AbstractArray, I::LogicalIndex{<:Any,<:AbstractArray{Bool,1}}) =
    eachindex(IndexLinear(), A) == eachindex(IndexLinear(), I.mask)
@inline checkbounds(::Type{Bool}, A::AbstractArray, I::LogicalIndex) = axes(A) == axes(I.mask)
@inline checkindex(::Type{Bool}, indx::AbstractUnitRange, I::LogicalIndex) = (indx,) == axes(I.mask)
checkindex(::Type{Bool}, inds::Tuple, I::LogicalIndex) = checkbounds_indices(Bool, inds, axes(I.mask))

ensure_indexable(I::Tuple{}) = ()
@inline ensure_indexable(I::Tuple{Any, Vararg{Any}}) = (I[1], ensure_indexable(tail(I))...)
@inline ensure_indexable(I::Tuple{LogicalIndex, Vararg{Any}}) = (collect(I[1]), ensure_indexable(tail(I))...)

# In simple cases, we know that we don't need to use axes(A). Optimize those
# until Julia gets smart enough to elide the call on its own:
@inline to_indices(A, I::Tuple{Vararg{Union{Integer, CartesianIndex}}}) = to_indices(A, (), I)
# But some index types require more context spanning multiple indices
# CartesianIndex is unfolded outside the inner to_indices for better inference
_to_indices1(A, inds, I1::CartesianIndex) = map(Fix1(to_index, A), I1.I)
_cutdim(inds, I1::CartesianIndex) = IteratorsMD.split(inds, Val(length(I1)))[2]
# For arrays of CartesianIndex, we just skip the appropriate number of inds
_cutdim(inds, I1::AbstractArray{CartesianIndex{N}}) where {N} = IteratorsMD.split(inds, Val(N))[2]
# And boolean arrays behave similarly; they also skip their number of dimensions
_cutdim(inds::Tuple, I1::AbstractArray{Bool}) = IteratorsMD.split(inds, Val(ndims(I1)))[2]
# As an optimization, we allow trailing Array{Bool} and BitArray to be linear over trailing dimensions
@inline to_indices(A, inds, I::Tuple{Union{Array{Bool,N}, BitArray{N}}}) where {N} =
    (_maybe_linear_logical_index(IndexStyle(A), A, I[1]),)
_maybe_linear_logical_index(::IndexStyle, A, i) = to_index(A, i)
_maybe_linear_logical_index(::IndexLinear, A, i) = LogicalIndex{Int}(i)

# Colons get converted to slices by `uncolon`
_to_indices1(A, inds, I1::Colon) = (uncolon(inds),)

uncolon(::Tuple{}) = Slice(OneTo(1))
uncolon(inds::Tuple) = Slice(inds[1])

### From abstractarray.jl: Internal multidimensional indexing definitions ###
getindex(x::Union{Number,AbstractChar}, ::CartesianIndex{0}) = x
getindex(t::Tuple,  i::CartesianIndex{1}) = getindex(t, i.I[1])

# These are not defined on directly on getindex to avoid
# ambiguities for AbstractArray subtypes. See the note in abstractarray.jl

@inline function _getindex(l::IndexStyle, A::AbstractArray, I::Union{Real, AbstractArray}...)
    @boundscheck checkbounds(A, I...)
    return _unsafe_getindex(l, _maybe_reshape(l, A, I...), I...)
end
# But we can speed up IndexCartesian arrays by reshaping them to the appropriate dimensionality:
_maybe_reshape(::IndexLinear, A::AbstractArray, I...) = A
_maybe_reshape(::IndexCartesian, A::AbstractVector, I...) = A
@inline _maybe_reshape(::IndexCartesian, A::AbstractArray, I...) = __maybe_reshape(A, index_ndims(I...))
@inline __maybe_reshape(A::AbstractArray{T,N}, ::NTuple{N,Any}) where {T,N} = A
@inline __maybe_reshape(A::AbstractArray, ::NTuple{N,Any}) where {N} = reshape(A, Val(N))

function _unsafe_getindex(::IndexStyle, A::AbstractArray, I::Vararg{Union{Real, AbstractArray}, N}) where N
    # This is specifically not inlined to prevent excessive allocations in type unstable code
    shape = index_shape(I...)
    dest = similar(A, shape)
    map(length, axes(dest)) == map(length, shape) || throw_checksize_error(dest, shape)
    _unsafe_getindex!(dest, A, I...) # usually a generated function, don't allow it to impact inference result
    return dest
end

function _generate_unsafe_getindex!_body(N::Int)
    quote
        @inline
        D = eachindex(dest)
        Dy = iterate(D)
        @inbounds @nloops $N j d->I[d] begin
            # This condition is never hit, but at the moment
            # the optimizer is not clever enough to split the union without it
            Dy === nothing && return dest
            (idx, state) = Dy
            dest[idx] = @ncall $N getindex src j
            Dy = iterate(D, state)
        end
        return dest
    end
end

# Always index with the exactly indices provided.
@generated function _unsafe_getindex!(dest::AbstractArray, src::AbstractArray, I::Vararg{Union{Real, AbstractArray}, N}) where N
    _generate_unsafe_getindex!_body(N)
end

# manually written-out specializations for 1 and 2 arguments to save compile time
@eval function _unsafe_getindex!(dest::AbstractArray, src::AbstractArray, I::Vararg{Union{Real, AbstractArray},1})
    $(_generate_unsafe_getindex!_body(1))
end

@eval function _unsafe_getindex!(dest::AbstractArray, src::AbstractArray, I::Vararg{Union{Real, AbstractArray},2})
    $(_generate_unsafe_getindex!_body(2))
end

@noinline throw_checksize_error(A, sz) = throw(DimensionMismatch("output array is the wrong size; expected $sz, got $(size(A))"))

## setindex! ##
function _setindex!(l::IndexStyle, A::AbstractArray, x, I::Union{Real, AbstractArray}...)
    @inline
    @boundscheck checkbounds(A, I...)
    _unsafe_setindex!(l, _maybe_reshape(l, A, I...), x, I...)
    A
end

function _generate_unsafe_setindex!_body(N::Int)
    quote
        x′ = unalias(A, x)
        @nexprs $N d->(I_d = unalias(A, I[d]))
        idxlens = @ncall $N index_lengths I
        @ncall $N setindex_shape_check x′ (d->idxlens[d])
        Xy = iterate(x′)
        @inbounds @nloops $N i d->I_d begin
            # This is never reached, but serves as an assumption for
            # the optimizer that it does not need to emit error paths
            Xy === nothing && break
            (val, state) = Xy
            @ncall $N setindex! A val i
            Xy = iterate(x′, state)
        end
        A
    end
end

@generated function _unsafe_setindex!(::IndexStyle, A::AbstractArray, x, I::Vararg{Union{Real,AbstractArray}, N}) where N
    _generate_unsafe_setindex!_body(N)
end

@eval function _unsafe_setindex!(::IndexStyle, A::AbstractArray, x, I::Vararg{Union{Real,AbstractArray},1})
    $(_generate_unsafe_setindex!_body(1))
end

@eval function _unsafe_setindex!(::IndexStyle, A::AbstractArray, x, I::Vararg{Union{Real,AbstractArray},2})
    $(_generate_unsafe_setindex!_body(2))
end

diff(a::AbstractVector) = diff(a, dims=1)

"""
    diff(A::AbstractVector)
    diff(A::AbstractArray; dims::Integer)

Finite difference operator on a vector or a multidimensional array `A`. In the
latter case the dimension to operate on needs to be specified with the `dims`
keyword argument.

!!! compat "Julia 1.1"
    `diff` for arrays with dimension higher than 2 requires at least Julia 1.1.

# Examples
```jldoctest
julia> a = [2 4; 6 16]
2×2 Matrix{Int64}:
 2   4
 6  16

julia> diff(a, dims=2)
2×1 Matrix{Int64}:
  2
 10

julia> diff(vec(a))
3-element Vector{Int64}:
  4
 -2
 12
```
"""
function diff(a::AbstractArray{T,N}; dims::Integer) where {T,N}
    require_one_based_indexing(a)
    1 <= dims <= N || throw(ArgumentError("dimension $dims out of range (1:$N)"))

    r = axes(a)
    r0 = ntuple(i -> i == dims ? UnitRange(1, last(r[i]) - 1) : UnitRange(r[i]), N)
    r1 = ntuple(i -> i == dims ? UnitRange(2, last(r[i])) : UnitRange(r[i]), N)

    return view(a, r1...) .- view(a, r0...)
end
function diff(r::AbstractRange{T}; dims::Integer=1) where {T}
    dims == 1 || throw(ArgumentError("dimension $dims out of range (1:1)"))
    return [@inbounds r[i+1] - r[i] for i in firstindex(r):lastindex(r)-1]
end

### from abstractarray.jl

# In the common case where we have two views into the same parent, aliasing checks
# are _much_ easier and more important to get right
function mightalias(A::SubArray{T,<:Any,P}, B::SubArray{T,<:Any,P}) where {T,P}
    if !_parentsmatch(A.parent, B.parent)
        # We cannot do any better than the usual dataids check
        return !_isdisjoint(dataids(A), dataids(B))
    end
    # Now we know that A.parent === B.parent. This means that the indices of A
    # and B are the same length and indexing into the same dimensions. We can
    # just walk through them and check for overlaps: O(ndims(A)). We must finally
    # ensure that the indices don't alias with either parent
    return _indicesmightoverlap(A.indices, B.indices) ||
        !_isdisjoint(dataids(A.parent), _splatmap(dataids, B.indices)) ||
        !_isdisjoint(dataids(B.parent), _splatmap(dataids, A.indices))
end
_parentsmatch(A::AbstractArray, B::AbstractArray) = A === B
# Two reshape(::Array)s of the same size aren't `===` because they have different headers
_parentsmatch(A::Array, B::Array) = pointer(A) == pointer(B) && size(A) == size(B)

_indicesmightoverlap(A::Tuple{}, B::Tuple{}) = true
_indicesmightoverlap(A::Tuple{}, B::Tuple) = error("malformed subarray")
_indicesmightoverlap(A::Tuple, B::Tuple{}) = error("malformed subarray")
# For ranges, it's relatively cheap to construct the intersection
@inline function _indicesmightoverlap(A::Tuple{AbstractRange, Vararg{Any}}, B::Tuple{AbstractRange, Vararg{Any}})
    !isempty(intersect(A[1], B[1])) ? _indicesmightoverlap(tail(A), tail(B)) : false
end
# But in the common AbstractUnitRange case, there's an even faster shortcut
@inline function _indicesmightoverlap(A::Tuple{AbstractUnitRange, Vararg{Any}}, B::Tuple{AbstractUnitRange, Vararg{Any}})
    max(first(A[1]),first(B[1])) <= min(last(A[1]),last(B[1])) ? _indicesmightoverlap(tail(A), tail(B)) : false
end
# And we can check scalars against each other and scalars against arrays quite easily
@inline _indicesmightoverlap(A::Tuple{Real, Vararg{Any}}, B::Tuple{Real, Vararg{Any}}) =
    A[1] == B[1] ? _indicesmightoverlap(tail(A), tail(B)) : false
@inline _indicesmightoverlap(A::Tuple{Real, Vararg{Any}}, B::Tuple{AbstractArray, Vararg{Any}}) =
    A[1] in B[1] ? _indicesmightoverlap(tail(A), tail(B)) : false
@inline _indicesmightoverlap(A::Tuple{AbstractArray, Vararg{Any}}, B::Tuple{Real, Vararg{Any}}) =
    B[1] in A[1] ? _indicesmightoverlap(tail(A), tail(B)) : false
# And small arrays are quick, too
@inline function _indicesmightoverlap(A::Tuple{AbstractArray, Vararg{Any}}, B::Tuple{AbstractArray, Vararg{Any}})
    if length(A[1]) == 1
        return A[1][1] in B[1] ? _indicesmightoverlap(tail(A), tail(B)) : false
    elseif length(B[1]) == 1
        return B[1][1] in A[1] ? _indicesmightoverlap(tail(A), tail(B)) : false
    else
        # But checking larger arrays requires O(m*n) and is too much work
        return true
    end
end
# And in general, checking the intersection is too much work
_indicesmightoverlap(A::Tuple{Any, Vararg{Any}}, B::Tuple{Any, Vararg{Any}}) = true

"""
    fill!(A, x)

Fill array `A` with the value `x`. If `x` is an object reference, all elements will refer to
the same object. `fill!(A, Foo())` will return `A` filled with the result of evaluating
`Foo()` once.

# Examples
```jldoctest
julia> A = zeros(2,3)
2×3 Matrix{Float64}:
 0.0  0.0  0.0
 0.0  0.0  0.0

julia> fill!(A, 2.)
2×3 Matrix{Float64}:
 2.0  2.0  2.0
 2.0  2.0  2.0

julia> a = [1, 1, 1]; A = fill!(Vector{Vector{Int}}(undef, 3), a); a[1] = 2; A
3-element Vector{Vector{Int64}}:
 [2, 1, 1]
 [2, 1, 1]
 [2, 1, 1]

julia> x = 0; f() = (global x += 1; x); fill!(Vector{Int}(undef, 3), f())
3-element Vector{Int64}:
 1
 1
 1
```
"""
function fill!(A::AbstractArray{T}, x) where T
    xT = convert(T, x)
    for I in eachindex(A)
        @inbounds A[I] = xT
    end
    A
end

function copyto!(dest::AbstractArray{T1,N}, Rdest::CartesianIndices{N},
                  src::AbstractArray{T2,N}, Rsrc::CartesianIndices{N}) where {T1,T2,N}
    isempty(Rdest) && return dest
    if size(Rdest) != size(Rsrc)
        throw(ArgumentError("source and destination must have same size (got $(size(Rsrc)) and $(size(Rdest)))"))
    end
    checkbounds(dest, first(Rdest))
    checkbounds(dest, last(Rdest))
    checkbounds(src, first(Rsrc))
    checkbounds(src, last(Rsrc))
    src′ = unalias(dest, src)
    CRdest = CartesianIndices(Rdest)
    CRsrc = CartesianIndices(Rsrc)
    ΔI = first(CRdest) - first(CRsrc)
    if @generated
        quote
            @nloops $N i (n->CRsrc.indices[n]) begin
                @inbounds @nref($N,dest,n->Rdest.indices[n][i_n+ΔI[n]]) = @nref($N,src′,n->Rsrc.indices[n][i_n])
            end
        end
    else
        for I in CRsrc
            @inbounds dest[Rdest[I + ΔI]] = src′[Rsrc[I]]
        end
    end
    dest
end

"""
    copyto!(dest, Rdest::CartesianIndices, src, Rsrc::CartesianIndices) -> dest

Copy the block of `src` in the range of `Rsrc` to the block of `dest`
in the range of `Rdest`. The sizes of the two regions must match.

# Examples
```jldoctest
julia> A = zeros(5, 5);

julia> B = [1 2; 3 4];

julia> Ainds = CartesianIndices((2:3, 2:3));

julia> Binds = CartesianIndices(B);

julia> copyto!(A, Ainds, B, Binds)
5×5 Matrix{Float64}:
 0.0  0.0  0.0  0.0  0.0
 0.0  1.0  2.0  0.0  0.0
 0.0  3.0  4.0  0.0  0.0
 0.0  0.0  0.0  0.0  0.0
 0.0  0.0  0.0  0.0  0.0
```
"""
copyto!(::AbstractArray, ::CartesianIndices, ::AbstractArray, ::CartesianIndices)

# circshift!
circshift!(dest::AbstractArray, src, ::Tuple{}) = copyto!(dest, src)
"""
    circshift!(dest, src, shifts)

Circularly shift, i.e. rotate, the data in `src`, storing the result in
`dest`. `shifts` specifies the amount to shift in each dimension.

$(_DOCS_ALIASING_WARNING)

See also [`circshift`](@ref).
"""
@noinline function circshift!(dest::AbstractArray{T,N}, src, shiftamt::DimsInteger) where {T,N}
    dest === src && throw(ArgumentError("dest and src must be separate arrays"))
    inds = axes(src)
    axes(dest) == inds || throw(ArgumentError("indices of src and dest must match (got $inds and $(axes(dest)))"))
    isempty(src) && return dest
    _circshift!(dest, (), src, (), inds, fill_to_length(shiftamt, 0, Val(N)))
end

circshift!(dest::AbstractArray, src, shiftamt) =
    circshift!(dest, src, map(Integer, (shiftamt...,)))

# For each dimension, we copy the first half of src to the second half
# of dest, and the second half of src to the first half of dest. This
# uses a recursive bifurcation strategy so that these splits can be
# encoded by ranges, which means that we need only one call to `mod`
# per dimension rather than one call per index.
# `rdest` and `rsrc` are tuples-of-ranges that grow one dimension at a
# time; when all the dimensions have been filled in, you call `copyto!`
# for that block. In other words, in two dimensions schematically we
# have the following call sequence (--> means a call):
#   circshift!(dest, src, shiftamt) -->
#     _circshift!(dest, src, ("first half of dim1",)) -->
#       _circshift!(dest, src, ("first half of dim1", "first half of dim2")) --> copyto!
#       _circshift!(dest, src, ("first half of dim1", "second half of dim2")) --> copyto!
#     _circshift!(dest, src, ("second half of dim1",)) -->
#       _circshift!(dest, src, ("second half of dim1", "first half of dim2")) --> copyto!
#       _circshift!(dest, src, ("second half of dim1", "second half of dim2")) --> copyto!
@inline function _circshift!(dest, rdest, src, rsrc,
                             inds::Tuple{AbstractUnitRange,Vararg{Any}},
                             shiftamt::Tuple{Integer,Vararg{Any}})::typeof(dest)
    ind1, d = inds[1], shiftamt[1]
    s = mod(d, length(ind1))
    sf, sl = first(ind1)+s, last(ind1)-s
    r1, r2 = first(ind1):sf-1, sf:last(ind1)
    r3, r4 = first(ind1):sl, sl+1:last(ind1)
    tinds, tshiftamt = tail(inds), tail(shiftamt)
    _circshift!(dest, (rdest..., r1), src, (rsrc..., r4), tinds, tshiftamt)
    _circshift!(dest, (rdest..., r2), src, (rsrc..., r3), tinds, tshiftamt)
end
# At least one of inds, shiftamt is empty
function _circshift!(dest, rdest, src, rsrc, inds, shiftamt)
    copyto!(dest, CartesianIndices(rdest), src, CartesianIndices(rsrc))
end

# circcopy!
"""
    circcopy!(dest, src)

Copy `src` to `dest`, indexing each dimension modulo its length.
`src` and `dest` must have the same size, but can be offset in
their indices; any offset results in a (circular) wraparound. If the
arrays have overlapping indices, then on the domain of the overlap
`dest` agrees with `src`.

$(_DOCS_ALIASING_WARNING)

See also: [`circshift`](@ref).

# Examples
```julia-repl
julia> src = reshape(Vector(1:16), (4,4))
4×4 Array{Int64,2}:
 1  5   9  13
 2  6  10  14
 3  7  11  15
 4  8  12  16

julia> dest = OffsetArray{Int}(undef, (0:3,2:5))

julia> circcopy!(dest, src)
OffsetArrays.OffsetArray{Int64,2,Array{Int64,2}} with indices 0:3×2:5:
 8  12  16  4
 5   9  13  1
 6  10  14  2
 7  11  15  3

julia> dest[1:3,2:4] == src[1:3,2:4]
true
```
"""
function circcopy!(dest, src)
    dest === src && throw(ArgumentError("dest and src must be separate arrays"))
    indssrc, indsdest = axes(src), axes(dest)
    if (szsrc = map(length, indssrc)) != (szdest = map(length, indsdest))
        throw(DimensionMismatch("src and dest must have the same sizes (got $szsrc and $szdest)"))
    end
    shift = map((isrc, idest)->first(isrc)-first(idest), indssrc, indsdest)
    all(x->x==0, shift) && return copyto!(dest, src)
    _circcopy!(dest, (), indsdest, src, (), indssrc)
end

# This uses the same strategy described above for _circshift!
@inline function _circcopy!(dest, rdest, indsdest::Tuple{AbstractUnitRange,Vararg{Any}},
                            src,  rsrc,  indssrc::Tuple{AbstractUnitRange,Vararg{Any}})::typeof(dest)
    indd1, inds1 = indsdest[1], indssrc[1]
    l = length(indd1)
    s = mod(first(inds1)-first(indd1), l)
    sdf = first(indd1)+s
    rd1, rd2 = first(indd1):sdf-1, sdf:last(indd1)
    ssf = last(inds1)-s
    rs1, rs2 = first(inds1):ssf, ssf+1:last(inds1)
    tindsd, tindss = tail(indsdest), tail(indssrc)
    _circcopy!(dest, (rdest..., rd1), tindsd, src, (rsrc..., rs2), tindss)
    _circcopy!(dest, (rdest..., rd2), tindsd, src, (rsrc..., rs1), tindss)
end

# At least one of indsdest, indssrc are empty (and both should be, since we've checked)
function _circcopy!(dest, rdest, indsdest, src, rsrc, indssrc)
    copyto!(dest, CartesianIndices(rdest), src, CartesianIndices(rsrc))
end

### BitArrays

## getindex

# contiguous multidimensional indexing: if the first dimension is a range,
# we can get some performance from using copy_chunks!
@inline function _unsafe_getindex!(X::BitArray, B::BitArray, I0::Union{AbstractUnitRange{Int},Slice})
    copy_chunks!(X.chunks, 1, B.chunks, indexoffset(I0)+1, length(I0))
    return X
end

# Optimization where the inner dimension is contiguous improves perf dramatically
@generated function _unsafe_getindex!(X::BitArray, B::BitArray,
        I0::Union{Slice,UnitRange{Int}}, I::Union{Int,AbstractUnitRange{Int},Slice}...)
    N = length(I)
    quote
        $(Expr(:meta, :inline))
        @nexprs $N d->(I_d = I[d])

        idxlens = @ncall $N index_lengths I0 I

        f0 = indexoffset(I0)+1
        l0 = idxlens[1]

        gap_lst_1 = 0
        @nexprs $N d->(gap_lst_{d+1} = idxlens[d+1])
        stride = 1
        ind = f0
        @nexprs $N d->begin
            stride *= size(B, d)
            stride_lst_d = stride
            ind += stride * indexoffset(I_d)
            gap_lst_{d+1} *= stride
        end

        storeind = 1
        Xc, Bc = X.chunks, B.chunks
        @nloops($N, i, d->(1:idxlens[d+1]),
                d->nothing, # PRE
                d->(ind += stride_lst_d - gap_lst_d), # POST
                begin # BODY
                    copy_chunks!(Xc, storeind, Bc, ind, l0)
                    storeind += l0
                end)
        return X
    end
end

# in the general multidimensional non-scalar case, can we do about 10% better
# in most cases by manually hoisting the bitarray chunks access out of the loop
# (This should really be handled by the compiler or with an immutable BitArray)
@generated function _unsafe_getindex!(X::BitArray, B::BitArray, I::Union{Int,AbstractArray{Int}}...)
    N = length(I)
    quote
        $(Expr(:meta, :inline))
        stride_1 = 1
        @nexprs $N d->(stride_{d+1} = stride_d*size(B, d))
        $(Symbol(:offset_, N)) = 1
        ind = 0
        Xc, Bc = X.chunks, B.chunks
        @nloops $N i d->I[d] d->(@inbounds offset_{d-1} = offset_d + (i_d-1)*stride_d) begin
            ind += 1
            unsafe_bitsetindex!(Xc, unsafe_bitgetindex(Bc, offset_0), ind)
        end
        return X
    end
end

## setindex!

function copy_to_bitarray_chunks!(Bc::Vector{UInt64}, pos_d::Int, C::StridedArray, pos_s::Int, numbits::Int)
    bind = pos_d
    cind = pos_s
    lastind = pos_d + numbits - 1
    @inbounds while bind ≤ lastind
        unsafe_bitsetindex!(Bc, Bool(C[cind]), bind)
        bind += 1
        cind += 1
    end
end

# Note: the next two functions rely on the following definition of the conversion to Bool:
#   convert(::Type{Bool}, x::Real) = x==0 ? false : x==1 ? true : throw(InexactError(...))
# they're used to preemptively check in bulk when possible, which is much faster.
# Also, the functions can be overloaded for custom types T<:Real :
#  a) in the unlikely eventuality that they use a different logic for Bool conversion
#  b) to skip the check if not necessary
@inline try_bool_conversion(x::Real) =
    x == 0 || x == 1 || throw(InexactError(:try_bool_conversion, Bool, x))
@inline unchecked_bool_convert(x::Real) = x == 1

function copy_to_bitarray_chunks!(Bc::Vector{UInt64}, pos_d::Int, C::StridedArray{<:Real}, pos_s::Int, numbits::Int)
    @inbounds for i = (1:numbits) .+ (pos_s - 1)
        try_bool_conversion(C[i])
    end

    kd0, ld0 = get_chunks_id(pos_d)
    kd1, ld1 = get_chunks_id(pos_d + numbits - 1)

    delta_kd = kd1 - kd0

    u = _msk64
    if delta_kd == 0
        msk_d0 = msk_d1 = ~(u << ld0) | (u << (ld1+1))
        lt0 = ld1
    else
        msk_d0 = ~(u << ld0)
        msk_d1 = (u << (ld1+1))
        lt0 = 63
    end

    bind = kd0
    ind = pos_s
    @inbounds if ld0 > 0
        c = UInt64(0)
        for j = ld0:lt0
            c |= (UInt64(unchecked_bool_convert(C[ind])) << j)
            ind += 1
        end
        Bc[kd0] = (Bc[kd0] & msk_d0) | (c & ~msk_d0)
        bind += 1
    end

    nc = _div64(numbits - ind + pos_s)
    @inbounds for i = 1:nc
        c = UInt64(0)
        for j = 0:63
            c |= (UInt64(unchecked_bool_convert(C[ind])) << j)
            ind += 1
        end
        Bc[bind] = c
        bind += 1
    end

    @inbounds if bind ≤ kd1
        @assert bind == kd1
        c = UInt64(0)
        for j = 0:ld1
            c |= (UInt64(unchecked_bool_convert(C[ind])) << j)
            ind += 1
        end
        Bc[kd1] = (Bc[kd1] & msk_d1) | (c & ~msk_d1)
    end
end

# contiguous multidimensional indexing: if the first dimension is a range,
# we can get some performance from using copy_chunks!

@inline function setindex!(B::BitArray, X::Union{StridedArray,BitArray}, J0::Union{Colon,AbstractUnitRange{Int}})
    I0 = to_indices(B, (J0,))[1]
    @boundscheck checkbounds(B, I0)
    l0 = length(I0)
    setindex_shape_check(X, l0)
    l0 == 0 && return B
    f0 = indexoffset(I0)+1
    copy_to_bitarray_chunks!(B.chunks, f0, X, 1, l0)
    return B
end

@inline function setindex!(B::BitArray, X::Union{StridedArray,BitArray},
        I0::Union{Colon,AbstractUnitRange{Int}}, I::Union{Int,AbstractUnitRange{Int},Colon}...)
    J = to_indices(B, (I0, I...))
    @boundscheck checkbounds(B, J...)
    _unsafe_setindex!(B, X, J...)
end
@generated function _unsafe_setindex!(B::BitArray, X::Union{StridedArray,BitArray},
        I0::Union{Slice,AbstractUnitRange{Int}}, I::Union{Int,AbstractUnitRange{Int},Slice}...)
    N = length(I)
    quote
        idxlens = @ncall $N index_lengths I0 d->I[d]
        @ncall $N setindex_shape_check X idxlens[1] d->idxlens[d+1]
        isempty(X) && return B
        f0 = indexoffset(I0)+1
        l0 = idxlens[1]

        gap_lst_1 = 0
        @nexprs $N d->(gap_lst_{d+1} = idxlens[d+1])
        stride = 1
        ind = f0
        @nexprs $N d->begin
            stride *= size(B, d)
            stride_lst_d = stride
            ind += stride * indexoffset(I[d])
            gap_lst_{d+1} *= stride
        end

        refind = 1
        Bc = B.chunks
        @nloops($N, i, d->I[d],
                d->nothing, # PRE
                d->(ind += stride_lst_d - gap_lst_d), # POST
                begin # BODY
                    copy_to_bitarray_chunks!(Bc, ind, X, refind, l0)
                    refind += l0
                end)

        return B
    end
end

@propagate_inbounds function setindex!(B::BitArray, X::AbstractArray,
        I0::Union{Colon,AbstractUnitRange{Int}}, I::Union{Int,AbstractUnitRange{Int},Colon}...)
    _setindex!(IndexStyle(B), B, X, to_indices(B, (I0, I...))...)
end

## fill! contiguous views of BitArrays with a single value
function fill!(V::SubArray{Bool, <:Any, <:BitArray, <:Tuple{AbstractUnitRange{Int}}}, x)
    B = V.parent
    I0 = V.indices[1]
    l0 = length(I0)
    l0 == 0 && return V
    fill_chunks!(B.chunks, Bool(x), first(I0), l0)
    return V
end

fill!(V::SubArray{Bool, <:Any, <:BitArray, <:Tuple{AbstractUnitRange{Int}, Vararg{Union{Int,AbstractUnitRange{Int}}}}}, x) =
    _unsafe_fill_indices!(V.parent, x, V.indices...)

@generated function _unsafe_fill_indices!(B::BitArray, x,
        I0::AbstractUnitRange{Int}, I::Union{Int,AbstractUnitRange{Int}}...)
    N = length(I)
    quote
        y = Bool(x)
        idxlens = @ncall $N index_lengths I0 d->I[d]

        f0 = indexoffset(I0)+1
        l0 = idxlens[1]
        l0 == 0 && return B
        @nexprs $N d->(isempty(I[d]) && return B)

        gap_lst_1 = 0
        @nexprs $N d->(gap_lst_{d+1} = idxlens[d+1])
        stride = 1
        ind = f0
        @nexprs $N d->begin
            stride *= size(B, d)
            stride_lst_d = stride
            ind += stride * indexoffset(I[d])
            gap_lst_{d+1} *= stride
        end

        @nloops($N, i, d->I[d],
                d->nothing, # PRE
                d->(ind += stride_lst_d - gap_lst_d), # POST
                fill_chunks!(B.chunks, y, ind, l0) # BODY
                )

        return B
    end
end

## isassigned

@generated function isassigned(B::BitArray, I_0::Int, I::Int...)
    N = length(I)
    quote
        @nexprs $N d->(I_d = I[d])
        stride = 1
        index = I_0
        @nexprs $N d->begin
            l = size(B,d)
            stride *= l
            @boundscheck 1 <= I_{d-1} <= l || return false
            index += (I_d - 1) * stride
        end
        return isassigned(B, index)
    end
end

isassigned(a::AbstractArray, i::CartesianIndex) = isassigned(a, Tuple(i)...)
function isassigned(A::AbstractArray, i::Union{Integer, CartesianIndex}...)
    isa(i, Tuple{Vararg{Int}}) || return isassigned(A, CartesianIndex(to_indices(A, i)))
    @boundscheck checkbounds(Bool, A, i...) || return false
    S = IndexStyle(A)
    ninds = length(i)
    if (isa(S, IndexLinear) && ninds != 1)
        return @inbounds isassigned(A, _to_linear_index(A, i...))
    elseif (!isa(S, IndexLinear) && ninds != ndims(A))
        return @inbounds isassigned(A, _to_subscript_indices(A, i...)...)
    else
       try
            A[i...]
            true
        catch e
            if isa(e, BoundsError) || isa(e, UndefRefError)
                return false
            else
                rethrow()
            end
        end
    end
end

## permutedims

## Permute array dims ##

function permutedims(B::StridedArray, perm)
    dimsB = size(B)
    ndimsB = length(dimsB)
    (ndimsB == length(perm) && isperm(perm)) || throw(ArgumentError("no valid permutation of dimensions"))
    dimsP = ntuple(i->dimsB[perm[i]], ndimsB)::typeof(dimsB)
    P = similar(B, dimsP)
    permutedims!(P, B, perm)
end

function checkdims_perm(P::AbstractArray{TP,N}, B::AbstractArray{TB,N}, perm) where {TP,TB,N}
    indsB = axes(B)
    length(perm) == N || throw(ArgumentError("expected permutation of size $N, but length(perm)=$(length(perm))"))
    isperm(perm) || throw(ArgumentError("input is not a permutation"))
    indsP = axes(P)
    for i = 1:length(perm)
        indsP[i] == indsB[perm[i]] || throw(DimensionMismatch("destination tensor of incorrect size"))
    end
    nothing
end

for (V, PT, BT) in Any[((:N,), BitArray, BitArray), ((:T,:N), Array, StridedArray)]
    @eval @generated function permutedims!(P::$PT{$(V...)}, B::$BT{$(V...)}, perm) where $(V...)
        quote
            checkdims_perm(P, B, perm)

            #calculates all the strides
            native_strides = size_to_strides(1, size(B)...)
            strides_1 = 0
            @nexprs $N d->(strides_{d+1} = native_strides[perm[d]])

            #Creates offset, because indexing starts at 1
            offset = 1 - sum(@ntuple $N d->strides_{d+1})

            sumc = 0
            ind = 1
            @nloops($N, i, P,
                    d->(sumc += i_d*strides_{d+1}), # PRE
                    d->(sumc -= i_d*strides_{d+1}), # POST
                    begin # BODY
                        @inbounds P[ind] = B[sumc+offset]
                        ind += 1
                    end)

            return P
        end
    end
end

## unique across dim

# TODO: this doesn't fit into the new hashing scheme in any obvious way

struct Prehashed
    hash::UInt
end
hash(x::Prehashed) = x.hash

"""
    unique(A::AbstractArray; dims::Int)

Return unique regions of `A` along dimension `dims`.

# Examples
```jldoctest
julia> A = map(isodd, reshape(Vector(1:8), (2,2,2)))
2×2×2 Array{Bool, 3}:
[:, :, 1] =
 1  1
 0  0

[:, :, 2] =
 1  1
 0  0

julia> unique(A)
2-element Vector{Bool}:
 1
 0

julia> unique(A, dims=2)
2×1×2 Array{Bool, 3}:
[:, :, 1] =
 1
 0

[:, :, 2] =
 1
 0

julia> unique(A, dims=3)
2×2×1 Array{Bool, 3}:
[:, :, 1] =
 1  1
 0  0
```
"""
unique(A::AbstractArray; dims::Union{Colon,Integer} = :) = _unique_dims(A, dims)

_unique_dims(A::AbstractArray, dims::Colon) = invoke(unique, Tuple{Any}, A)

@generated function _unique_dims(A::AbstractArray{T,N}, dim::Integer) where {T,N}
    quote
        1 <= dim <= $N || return copy(A)
        hashes = zeros(UInt, axes(A, dim))

        # Compute hash for each row
        k = 0
        @nloops $N i A d->(if d == dim; k = i_d; end) begin
            @inbounds hashes[k] = hash(hashes[k], hash((@nref $N A i)))
        end

        # Collect index of first row for each hash
        uniquerow = similar(Array{Int}, axes(A, dim))
        firstrow = Dict{Prehashed,Int}()
        for k = axes(A, dim)
            uniquerow[k] = get!(firstrow, Prehashed(hashes[k]), k)
        end
        uniquerows = collect(values(firstrow))

        # Check for collisions
        collided = falses(axes(A, dim))
        @inbounds begin
            @nloops $N i A d->(if d == dim
                k = i_d
                j_d = uniquerow[k]
            else
                j_d = i_d
            end) begin
                if !isequal((@nref $N A j), (@nref $N A i))
                    collided[k] = true
                end
            end
        end

        if any(collided)
            nowcollided = similar(BitArray, axes(A, dim))
            while any(collided)
                # Collect index of first row for each collided hash
                empty!(firstrow)
                for j = axes(A, dim)
                    collided[j] || continue
                    uniquerow[j] = get!(firstrow, Prehashed(hashes[j]), j)
                end
                for v in values(firstrow)
                    push!(uniquerows, v)
                end

                # Check for collisions
                fill!(nowcollided, false)
                @nloops $N i A d->begin
                    if d == dim
                        k = i_d
                        j_d = uniquerow[k]
                        (!collided[k] || j_d == k) && continue
                    else
                        j_d = i_d
                    end
                end begin
                    if !isequal((@nref $N A j), (@nref $N A i))
                        nowcollided[k] = true
                    end
                end
                (collided, nowcollided) = (nowcollided, collided)
            end
        end

        @nref $N A d->d == dim ? sort!(uniquerows) : (axes(A, d))
    end
end

# Show for pairs() with Cartesian indices. Needs to be here rather than show.jl for bootstrap order
function Base.showarg(io::IO, r::Iterators.Pairs{<:Integer, <:Any, <:Any, T}, toplevel) where T <: Union{AbstractVector, Tuple}
    print(io, "pairs(::$T)")
end
function Base.showarg(io::IO, r::Iterators.Pairs{<:CartesianIndex, <:Any, <:Any, T}, toplevel) where T <: AbstractArray
    print(io, "pairs(::$T)")
end

function Base.showarg(io::IO, r::Iterators.Pairs{<:CartesianIndex, <:Any, <:Any, T}, toplevel) where T<:AbstractVector
    print(io, "pairs(IndexCartesian(), ::$T)")
end

## sortslices

"""
    sortslices(A; dims, alg::Algorithm=DEFAULT_UNSTABLE, lt=isless, by=identity, rev::Bool=false, order::Ordering=Forward)

Sort slices of an array `A`. The required keyword argument `dims` must
be either an integer or a tuple of integers. It specifies the
dimension(s) over which the slices are sorted.

E.g., if `A` is a matrix, `dims=1` will sort rows, `dims=2` will sort columns.
Note that the default comparison function on one dimensional slices sorts
lexicographically.

For the remaining keyword arguments, see the documentation of [`sort!`](@ref).

# Examples
```jldoctest
julia> sortslices([7 3 5; -1 6 4; 9 -2 8], dims=1) # Sort rows
3×3 Matrix{Int64}:
 -1   6  4
  7   3  5
  9  -2  8

julia> sortslices([7 3 5; -1 6 4; 9 -2 8], dims=1, lt=(x,y)->isless(x[2],y[2]))
3×3 Matrix{Int64}:
  9  -2  8
  7   3  5
 -1   6  4

julia> sortslices([7 3 5; -1 6 4; 9 -2 8], dims=1, rev=true)
3×3 Matrix{Int64}:
  9  -2  8
  7   3  5
 -1   6  4

julia> sortslices([7 3 5; 6 -1 -4; 9 -2 8], dims=2) # Sort columns
3×3 Matrix{Int64}:
  3   5  7
 -1  -4  6
 -2   8  9

julia> sortslices([7 3 5; 6 -1 -4; 9 -2 8], dims=2, alg=InsertionSort, lt=(x,y)->isless(x[2],y[2]))
3×3 Matrix{Int64}:
  5   3  7
 -4  -1  6
  8  -2  9

julia> sortslices([7 3 5; 6 -1 -4; 9 -2 8], dims=2, rev=true)
3×3 Matrix{Int64}:
 7   5   3
 6  -4  -1
 9   8  -2
```

# Higher dimensions

`sortslices` extends naturally to higher dimensions. E.g., if `A` is a
a 2x2x2 array, `sortslices(A, dims=3)` will sort slices within the 3rd dimension,
passing the 2x2 slices `A[:, :, 1]` and `A[:, :, 2]` to the comparison function.
Note that while there is no default order on higher-dimensional slices, you may
use the `by` or `lt` keyword argument to specify such an order.

If `dims` is a tuple, the order of the dimensions in `dims` is
relevant and specifies the linear order of the slices. E.g., if `A` is three
dimensional and `dims` is `(1, 2)`, the orderings of the first two dimensions
are re-arranged such that the slices (of the remaining third dimension) are sorted.
If `dims` is `(2, 1)` instead, the same slices will be taken,
but the result order will be row-major instead.

# Higher dimensional examples
```
julia> A = permutedims(reshape([4 3; 2 1; 'A' 'B'; 'C' 'D'], (2, 2, 2)), (1, 3, 2))
2×2×2 Array{Any, 3}:
[:, :, 1] =
 4  3
 2  1

[:, :, 2] =
 'A'  'B'
 'C'  'D'

julia> sortslices(A, dims=(1,2))
2×2×2 Array{Any, 3}:
[:, :, 1] =
 1  3
 2  4

[:, :, 2] =
 'D'  'B'
 'C'  'A'

julia> sortslices(A, dims=(2,1))
2×2×2 Array{Any, 3}:
[:, :, 1] =
 1  2
 3  4

[:, :, 2] =
 'D'  'C'
 'B'  'A'

julia> sortslices(reshape([5; 4; 3; 2; 1], (1,1,5)), dims=3, by=x->x[1,1])
1×1×5 Array{Int64, 3}:
[:, :, 1] =
 1

[:, :, 2] =
 2

[:, :, 3] =
 3

[:, :, 4] =
 4

[:, :, 5] =
 5
```
"""
function sortslices(A::AbstractArray; dims::Union{Integer, Tuple{Vararg{Integer}}}, kws...)
    _sortslices(A, Val{dims}(); kws...)
end

# Works around inference's lack of ability to recognize partial constness
struct DimSelector{dims, T}
    A::T
end
DimSelector{dims}(x::T) where {dims, T} = DimSelector{dims, T}(x)
(ds::DimSelector{dims, T})(i) where {dims, T} = i in dims ? axes(ds.A, i) : (:,)

_negdims(n, dims) = filter(i->!(i in dims), 1:n)

function compute_itspace(A, ::Val{dims}) where {dims}
    negdims = _negdims(ndims(A), dims)
    axs = Iterators.product(ntuple(DimSelector{dims}(A), ndims(A))...)
    vec(permutedims(collect(axs), (dims..., negdims...)))
end

function _sortslices(A::AbstractArray, d::Val{dims}; kws...) where dims
    itspace = compute_itspace(A, d)
    vecs = map(its->view(A, its...), itspace)
    p = sortperm(vecs; kws...)
    if ndims(A) == 2 && isa(dims, Integer) && isa(A, Array)
        # At the moment, the performance of the generic version is subpar
        # (about 5x slower). Hardcode a fast-path until we're able to
        # optimize this.
        return dims == 1 ? A[p, :] : A[:, p]
    else
        B = similar(A)
        for (x, its) in zip(p, itspace)
            B[its...] = vecs[x]
        end
        B
    end
end

getindex(b::Ref, ::CartesianIndex{0}) = getindex(b)
setindex!(b::Ref, x, ::CartesianIndex{0}) = setindex!(b, x)
P   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/broadcast.jl��      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
    Base.Broadcast

Module containing the broadcasting implementation.
"""
module Broadcast

using .Base.Cartesian
using .Base: Indices, OneTo, tail, to_shape, isoperator, promote_typejoin, promote_typejoin_union,
             _msk_end, unsafe_bitgetindex, bitcache_chunks, bitcache_size, dumpbitcache, unalias, negate
import .Base: copy, copyto!, axes
export broadcast, broadcast!, BroadcastStyle, broadcast_axes, broadcastable, dotview, @__dot__, BroadcastFunction

## Computing the result's axes: deprecated name
const broadcast_axes = axes

### Objects with customized broadcasting behavior should declare a BroadcastStyle

"""
`BroadcastStyle` is an abstract type and trait-function used to determine behavior of
objects under broadcasting. `BroadcastStyle(typeof(x))` returns the style associated
with `x`. To customize the broadcasting behavior of a type, one can declare a style
by defining a type/method pair

    struct MyContainerStyle <: BroadcastStyle end
    Base.BroadcastStyle(::Type{<:MyContainer}) = MyContainerStyle()

One then writes method(s) (at least [`similar`](@ref)) operating on
`Broadcasted{MyContainerStyle}`. There are also several pre-defined subtypes of `BroadcastStyle`
that you may be able to leverage; see the
[Interfaces chapter](@ref man-interfaces-broadcasting) for more information.
"""
abstract type BroadcastStyle end

struct Unknown <: BroadcastStyle end
BroadcastStyle(::Type{Union{}}, slurp...) = Unknown()  # ambiguity resolution

"""
`Broadcast.Style{C}()` defines a [`BroadcastStyle`](@ref) signaling through the type
parameter `C`. You can use this as an alternative to creating custom subtypes of `BroadcastStyle`,
for example

    Base.BroadcastStyle(::Type{<:MyContainer}) = Broadcast.Style{MyContainer}()
"""
struct Style{T} <: BroadcastStyle end

BroadcastStyle(::Type{<:Tuple}) = Style{Tuple}()

"""
`Broadcast.AbstractArrayStyle{N} <: BroadcastStyle` is the abstract supertype for any style
associated with an `AbstractArray` type.
The `N` parameter is the dimensionality, which can be handy for AbstractArray types
that only support specific dimensionalities:

    struct SparseMatrixStyle <: Broadcast.AbstractArrayStyle{2} end
    Base.BroadcastStyle(::Type{<:SparseMatrixCSC}) = SparseMatrixStyle()

For `AbstractArray` types that support arbitrary dimensionality, `N` can be set to `Any`:

    struct MyArrayStyle <: Broadcast.AbstractArrayStyle{Any} end
    Base.BroadcastStyle(::Type{<:MyArray}) = MyArrayStyle()

In cases where you want to be able to mix multiple `AbstractArrayStyle`s and keep track
of dimensionality, your style needs to support a [`Val`](@ref) constructor:

    struct MyArrayStyleDim{N} <: Broadcast.AbstractArrayStyle{N} end
    (::Type{<:MyArrayStyleDim})(::Val{N}) where N = MyArrayStyleDim{N}()

Note that if two or more `AbstractArrayStyle` subtypes conflict, broadcasting machinery
will fall back to producing `Array`s. If this is undesirable, you may need to
define binary [`BroadcastStyle`](@ref) rules to control the output type.

See also [`Broadcast.DefaultArrayStyle`](@ref).
"""
abstract type AbstractArrayStyle{N} <: BroadcastStyle end

"""
`Broadcast.ArrayStyle{MyArrayType}()` is a [`BroadcastStyle`](@ref) indicating that an object
behaves as an array for broadcasting. It presents a simple way to construct
[`Broadcast.AbstractArrayStyle`](@ref)s for specific `AbstractArray` container types.
Broadcast styles created this way lose track of dimensionality; if keeping track is important
for your type, you should create your own custom [`Broadcast.AbstractArrayStyle`](@ref).
"""
struct ArrayStyle{A<:AbstractArray} <: AbstractArrayStyle{Any} end
ArrayStyle{A}(::Val) where A = ArrayStyle{A}()

"""
`Broadcast.DefaultArrayStyle{N}()` is a [`BroadcastStyle`](@ref) indicating that an object
behaves as an `N`-dimensional array for broadcasting. Specifically, `DefaultArrayStyle` is
used for any
`AbstractArray` type that hasn't defined a specialized style, and in the absence of
overrides from other `broadcast` arguments the resulting output type is `Array`.
When there are multiple inputs to `broadcast`, `DefaultArrayStyle` "loses" to any other [`Broadcast.ArrayStyle`](@ref).
"""
struct DefaultArrayStyle{N} <: AbstractArrayStyle{N} end
DefaultArrayStyle(::Val{N}) where N = DefaultArrayStyle{N}()
DefaultArrayStyle{M}(::Val{N}) where {N,M} = DefaultArrayStyle{N}()
const DefaultVectorStyle = DefaultArrayStyle{1}
const DefaultMatrixStyle = DefaultArrayStyle{2}
BroadcastStyle(::Type{<:AbstractArray{T,N}}) where {T,N} = DefaultArrayStyle{N}()
BroadcastStyle(::Type{T}) where {T} = DefaultArrayStyle{ndims(T)}()

# `ArrayConflict` is an internal type signaling that two or more different `AbstractArrayStyle`
# objects were supplied as arguments, and that no rule was defined for resolving the
# conflict. The resulting output is `Array`. While this is the same output type
# produced by `DefaultArrayStyle`, `ArrayConflict` "poisons" the BroadcastStyle so that
# 3 or more arguments still return an `ArrayConflict`.
struct ArrayConflict <: AbstractArrayStyle{Any} end
ArrayConflict(::Val) = ArrayConflict()

### Binary BroadcastStyle rules
"""
    BroadcastStyle(::Style1, ::Style2) = Style3()

Indicate how to resolve different `BroadcastStyle`s. For example,

    BroadcastStyle(::Primary, ::Secondary) = Primary()

would indicate that style `Primary` has precedence over `Secondary`.
You do not have to (and generally should not) define both argument orders.
The result does not have to be one of the input arguments, it could be a third type.

Please see the [Interfaces chapter](@ref man-interfaces-broadcasting) of the manual for
more information.
"""
BroadcastStyle(::S, ::S) where S<:BroadcastStyle = S() # homogeneous types preserved
# Fall back to Unknown. This is necessary to implement argument-swapping
BroadcastStyle(::BroadcastStyle, ::BroadcastStyle) = Unknown()
# Unknown loses to everything
BroadcastStyle(::Unknown, ::Unknown) = Unknown()
BroadcastStyle(::S, ::Unknown) where S<:BroadcastStyle = S()
# Precedence rules
BroadcastStyle(a::AbstractArrayStyle{0}, b::Style{Tuple}) = b
BroadcastStyle(a::AbstractArrayStyle, ::Style{Tuple})    = a
BroadcastStyle(::A, ::A) where A<:ArrayStyle             = A()
BroadcastStyle(::ArrayStyle, ::ArrayStyle)               = Unknown()
BroadcastStyle(::A, ::A) where A<:AbstractArrayStyle     = A()
function BroadcastStyle(a::A, b::B) where {A<:AbstractArrayStyle{M},B<:AbstractArrayStyle{N}} where {M,N}
    if Base.typename(A) === Base.typename(B)
        return A(Val(max(M, N)))
    end
    return Unknown()
end
# Any specific array type beats DefaultArrayStyle
BroadcastStyle(a::AbstractArrayStyle{Any}, ::DefaultArrayStyle) = a
BroadcastStyle(a::AbstractArrayStyle{N}, ::DefaultArrayStyle{N}) where N = a
BroadcastStyle(a::AbstractArrayStyle{M}, ::DefaultArrayStyle{N}) where {M,N} =
    typeof(a)(Val(max(M, N)))

### Lazy-wrapper for broadcasting

# `Broadcasted` wrap the arguments to `broadcast(f, args...)`. A statement like
#    y = x .* (x .+ 1)
# will result in code that is essentially
#    y = copy(Broadcasted(*, x, Broadcasted(+, x, 1)))
# `broadcast!` results in `copyto!(dest, Broadcasted(...))`.

# The use of `Nothing` in place of a `BroadcastStyle` has a different
# application, in the fallback method
#    copyto!(dest, bc::Broadcasted) = copyto!(dest, convert(Broadcasted{Nothing}, bc))
# This allows methods
#    copyto!(dest::DestType,  bc::Broadcasted{Nothing})
# that specialize on `DestType` to be easily disambiguated from
# methods that instead specialize on `BroadcastStyle`,
#    copyto!(dest::AbstractArray, bc::Broadcasted{MyStyle})

struct Broadcasted{Style<:Union{Nothing,BroadcastStyle}, Axes, F, Args<:Tuple} <: Base.AbstractBroadcasted
    style::Style
    f::F
    args::Args
    axes::Axes          # the axes of the resulting object (may be bigger than implied by `args` if this is nested inside a larger `Broadcasted`)

    Broadcasted(style::Union{Nothing,BroadcastStyle}, f::Tuple, args::Tuple) = error() # disambiguation: tuple is not callable
    function Broadcasted(style::Union{Nothing,BroadcastStyle}, f::F, args::Tuple, axes=nothing) where {F}
        # using Core.Typeof rather than F preserves inferrability when f is a type
        return new{typeof(style), typeof(axes), Core.Typeof(f), typeof(args)}(style, f, args, axes)
    end

    function Broadcasted(f::F, args::Tuple, axes=nothing) where {F}
        Broadcasted(combine_styles(args...)::BroadcastStyle, f, args, axes)
    end

    function Broadcasted{Style}(f::F, args, axes=nothing) where {Style, F}
        return new{Style, typeof(axes), Core.Typeof(f), typeof(args)}(Style()::Style, f, args, axes)
    end

    function Broadcasted{Style,Axes,F,Args}(f, args, axes) where {Style,Axes,F,Args}
        return new{Style, Axes, F, Args}(Style()::Style, f, args, axes)
    end
end

struct AndAnd end
const andand = AndAnd()
broadcasted(::AndAnd, a, b) = broadcasted((a, b) -> a && b, a, b)
function broadcasted(::AndAnd, a, bc::Broadcasted)
    bcf = flatten(bc)
    broadcasted((a, args...) -> a && bcf.f(args...), a, bcf.args...)
end
struct OrOr end
const oror = OrOr()
broadcasted(::OrOr, a, b) = broadcasted((a, b) -> a || b, a, b)
function broadcasted(::OrOr, a, bc::Broadcasted)
    bcf = flatten(bc)
    broadcasted((a, args...) -> a || bcf.f(args...), a, bcf.args...)
end

Base.convert(::Type{Broadcasted{NewStyle}}, bc::Broadcasted{<:Any,Axes,F,Args}) where {NewStyle,Axes,F,Args} =
    Broadcasted{NewStyle,Axes,F,Args}(bc.f, bc.args, bc.axes)::Broadcasted{NewStyle,Axes,F,Args}

function Base.show(io::IO, bc::Broadcasted{Style}) where {Style}
    print(io, Broadcasted)
    # Only show the style parameter if we have a set of axes — representing an instantiated
    # "outermost" Broadcasted. The styles of nested Broadcasteds represent an intermediate
    # computation that is not relevant for dispatch, confusing, and just extra line noise.
    bc.axes isa Tuple && print(io, "{", Style, "}")
    print(io, "(", bc.f, ", ", bc.args, ")")
    nothing
end

## Allocating the output container
Base.similar(bc::Broadcasted, ::Type{T}) where {T} = similar(bc, T, axes(bc))
Base.similar(::Broadcasted{DefaultArrayStyle{N}}, ::Type{ElType}, dims) where {N,ElType} =
    similar(Array{ElType}, dims)
Base.similar(::Broadcasted{DefaultArrayStyle{N}}, ::Type{Bool}, dims) where N =
    similar(BitArray, dims)
# In cases of conflict we fall back on Array
Base.similar(::Broadcasted{ArrayConflict}, ::Type{ElType}, dims) where ElType =
    similar(Array{ElType}, dims)
Base.similar(::Broadcasted{ArrayConflict}, ::Type{Bool}, dims) =
    similar(BitArray, dims)

@inline Base.axes(bc::Broadcasted) = _axes(bc, bc.axes)
_axes(::Broadcasted, axes::Tuple) = axes
@inline _axes(bc::Broadcasted, ::Nothing)  = combine_axes(bc.args...)
_axes(bc::Broadcasted{<:AbstractArrayStyle{0}}, ::Nothing) = ()

@inline Base.axes(bc::Broadcasted{<:Any, <:NTuple{N}}, d::Integer) where N =
    d <= N ? axes(bc)[d] : OneTo(1)

BroadcastStyle(::Type{<:Broadcasted{Style}}) where {Style} = Style()
BroadcastStyle(::Type{<:Broadcasted{S}}) where {S<:Union{Nothing,Unknown}} =
    throw(ArgumentError("Broadcasted{Unknown} wrappers do not have a style assigned"))

argtype(::Type{BC}) where {BC<:Broadcasted} = fieldtype(BC, :args)
argtype(bc::Broadcasted) = argtype(typeof(bc))

@inline Base.eachindex(bc::Broadcasted) = _eachindex(axes(bc))
_eachindex(t::Tuple{Any}) = t[1]
_eachindex(t::Tuple) = CartesianIndices(t)

Base.IndexStyle(bc::Broadcasted) = IndexStyle(typeof(bc))
Base.IndexStyle(::Type{<:Broadcasted{<:Any,<:Tuple{Any}}}) = IndexLinear()
Base.IndexStyle(::Type{<:Broadcasted{<:Any}}) = IndexCartesian()

Base.LinearIndices(bc::Broadcasted{<:Any,<:Tuple{Any}}) = LinearIndices(axes(bc))::LinearIndices{1}

Base.ndims(bc::Broadcasted) = ndims(typeof(bc))
Base.ndims(::Type{<:Broadcasted{<:Any,<:NTuple{N,Any}}}) where {N} = N

Base.size(bc::Broadcasted) = map(length, axes(bc))
Base.length(bc::Broadcasted) = prod(size(bc))

function Base.iterate(bc::Broadcasted)
    iter = eachindex(bc)
    iterate(bc, (iter,))
end
Base.@propagate_inbounds function Base.iterate(bc::Broadcasted, s)
    y = iterate(s...)
    y === nothing && return nothing
    i, newstate = y
    return (bc[i], (s[1], newstate))
end

Base.IteratorSize(::Type{T}) where {T<:Broadcasted} = Base.HasShape{ndims(T)}()
Base.ndims(BC::Type{<:Broadcasted{<:Any,Nothing}}) = _maxndims(fieldtype(BC, :args))
Base.ndims(::Type{<:Broadcasted{<:AbstractArrayStyle{N},Nothing}}) where {N<:Integer} = N

_maxndims(T::Type{<:Tuple}) = reduce(max, (ntuple(n -> _ndims(fieldtype(T, n)), Base._counttuple(T))))
_maxndims(::Type{<:Tuple{T}}) where {T} = ndims(T)
_maxndims(::Type{<:Tuple{T}}) where {T<:Tuple} = _ndims(T)
function _maxndims(::Type{<:Tuple{T, S}}) where {T, S}
    return T<:Tuple || S<:Tuple ? max(_ndims(T), _ndims(S)) : max(ndims(T), ndims(S))
end

_ndims(x) = ndims(x)
_ndims(::Type{<:Tuple}) = 1

Base.IteratorEltype(::Type{<:Broadcasted}) = Base.EltypeUnknown()

## Instantiation fills in the "missing" fields in Broadcasted.
instantiate(x) = x

"""
    Broadcast.instantiate(bc::Broadcasted)

Construct and check the axes for the lazy Broadcasted object `bc`.

Custom [`BroadcastStyle`](@ref)s may override this default in cases where it is fast and easy
to compute and verify the resulting `axes` on-demand, leaving the `axis` field
of the `Broadcasted` object empty (populated with [`nothing`](@ref)).
"""
@inline function instantiate(bc::Broadcasted)
    if bc.axes isa Nothing # Not done via dispatch to make it easier to extend instantiate(::Broadcasted{Style})
        axes = combine_axes(bc.args...)
    else
        axes = bc.axes
        check_broadcast_axes(axes, bc.args...)
    end
    return Broadcasted(bc.style, bc.f, bc.args, axes)
end
instantiate(bc::Broadcasted{<:AbstractArrayStyle{0}}) = bc
# Tuples don't need axes, but when they have axes (for .= assignment), we need to check them (#33020)
instantiate(bc::Broadcasted{Style{Tuple}, Nothing}) = bc
function instantiate(bc::Broadcasted{Style{Tuple}})
    check_broadcast_axes(bc.axes, bc.args...)
    return bc
end
## Flattening

"""
    bcf = flatten(bc)

Create a "flat" representation of a lazy-broadcast operation.
From
   f.(a, g.(b, c), d)
we produce the equivalent of
   h.(a, b, c, d)
where
   h(w, x, y, z) = f(w, g(x, y), z)
In terms of its internal representation,
   Broadcasted(f, a, Broadcasted(g, b, c), d)
becomes
   Broadcasted(h, a, b, c, d)

This is an optional operation that may make custom implementation of broadcasting easier in
some cases.
"""
function flatten(bc::Broadcasted)
    isflat(bc) && return bc
    # concatenate the nested arguments into {a, b, c, d}
    args = cat_nested(bc)
    # build a function `makeargs` that takes a "flat" argument list and
    # and creates the appropriate input arguments for `f`, e.g.,
    #          makeargs = (w, x, y, z) -> (w, g(x, y), z)
    #
    # `makeargs` is built recursively and looks a bit like this:
    #     makeargs(w, x, y, z) = (w, makeargs1(x, y, z)...)
    #                          = (w, g(x, y), makeargs2(z)...)
    #                          = (w, g(x, y), z)
    let makeargs = make_makeargs(()->(), bc.args), f = bc.f
        newf = @inline function(args::Vararg{Any,N}) where N
            f(makeargs(args...)...)
        end
        return Broadcasted(bc.style, newf, args, bc.axes)
    end
end

const NestedTuple = Tuple{<:Broadcasted,Vararg{Any}}
isflat(bc::Broadcasted) = _isflat(bc.args)
_isflat(args::NestedTuple) = false
_isflat(args::Tuple) = _isflat(tail(args))
_isflat(args::Tuple{}) = true

cat_nested(t::Broadcasted, rest...) = (cat_nested(t.args...)..., cat_nested(rest...)...)
cat_nested(t::Any, rest...) = (t, cat_nested(rest...)...)
cat_nested() = ()

"""
    make_makeargs(makeargs_tail::Function, t::Tuple) -> Function

Each element of `t` is one (consecutive) node in a broadcast tree.
Ignoring `makeargs_tail` for the moment, the job of `make_makeargs` is
to return a function that takes in flattened argument list and returns a
tuple (each entry corresponding to an entry in `t`, having evaluated
the corresponding element in the broadcast tree). As an additional
complication, the passed in tuple may be longer than the number of leaves
in the subtree described by `t`. The `makeargs_tail` function should
be called on such additional arguments (but not the arguments consumed
by `t`).
"""
@inline make_makeargs(makeargs_tail, t::Tuple{}) = makeargs_tail
@inline function make_makeargs(makeargs_tail, t::Tuple)
    makeargs = make_makeargs(makeargs_tail, tail(t))
    (head, tail...)->(head, makeargs(tail...)...)
end
function make_makeargs(makeargs_tail, t::Tuple{<:Broadcasted, Vararg{Any}})
    bc = t[1]
    # c.f. the same expression in the function on leaf nodes above. Here
    # we recurse into siblings in the broadcast tree.
    let makeargs_tail = make_makeargs(makeargs_tail, tail(t)),
            # Here we recurse into children. It would be valid to pass in makeargs_tail
            # here, and not use it below. However, in that case, our recursion is no
            # longer purely structural because we're building up one argument (the closure)
            # while destructuing another.
            makeargs_head = make_makeargs((args...)->args, bc.args),
            f = bc.f
        # Create two functions, one that splits of the first length(bc.args)
        # elements from the tuple and one that yields the remaining arguments.
        # N.B. We can't call headargs on `args...` directly because
        # args is flattened (i.e. our children have not been evaluated
        # yet).
        headargs, tailargs = make_headargs(bc.args), make_tailargs(bc.args)
        return @inline function(args::Vararg{Any,N}) where N
            args1 = makeargs_head(args...)
            a, b = headargs(args1...), makeargs_tail(tailargs(args1...)...)
            (f(a...), b...)
        end
    end
end

@inline function make_headargs(t::Tuple)
    let headargs = make_headargs(tail(t))
        return @inline function(head, tail::Vararg{Any,N}) where N
            (head, headargs(tail...)...)
        end
    end
end
@inline function make_headargs(::Tuple{})
    return @inline function(tail::Vararg{Any,N}) where N
        ()
    end
end

@inline function make_tailargs(t::Tuple)
    let tailargs = make_tailargs(tail(t))
        return @inline function(head, tail::Vararg{Any,N}) where N
            tailargs(tail...)
        end
    end
end
@inline function make_tailargs(::Tuple{})
    return @inline function(tail::Vararg{Any,N}) where N
        tail
    end
end

## Broadcasting utilities ##

## logic for deciding the BroadcastStyle

"""
    combine_styles(cs...) -> BroadcastStyle

Decides which `BroadcastStyle` to use for any number of value arguments.
Uses [`BroadcastStyle`](@ref) to get the style for each argument, and uses
[`result_style`](@ref) to combine styles.

# Examples

```jldoctest
julia> Broadcast.combine_styles([1], [1 2; 3 4])
Base.Broadcast.DefaultArrayStyle{2}()
```
"""
function combine_styles end

combine_styles() = DefaultArrayStyle{0}()
combine_styles(c) = result_style(BroadcastStyle(typeof(c)))
combine_styles(c1, c2) = result_style(combine_styles(c1), combine_styles(c2))
@inline combine_styles(c1, c2, cs...) = result_style(combine_styles(c1), combine_styles(c2, cs...))

"""
    result_style(s1::BroadcastStyle[, s2::BroadcastStyle]) -> BroadcastStyle

Takes one or two `BroadcastStyle`s and combines them using [`BroadcastStyle`](@ref) to
determine a common `BroadcastStyle`.

# Examples

```jldoctest
julia> Broadcast.result_style(Broadcast.DefaultArrayStyle{0}(), Broadcast.DefaultArrayStyle{3}())
Base.Broadcast.DefaultArrayStyle{3}()

julia> Broadcast.result_style(Broadcast.Unknown(), Broadcast.DefaultArrayStyle{1}())
Base.Broadcast.DefaultArrayStyle{1}()
```
"""
function result_style end

result_style(s::BroadcastStyle) = s
result_style(s1::S, s2::S) where S<:BroadcastStyle = S()
# Test both orders so users typically only have to declare one order
result_style(s1, s2) = result_join(s1, s2, BroadcastStyle(s1, s2), BroadcastStyle(s2, s1))

# result_join is the final arbiter. Because `BroadcastStyle` for undeclared pairs results in Unknown,
# we defer to any case where the result of `BroadcastStyle` is known.
result_join(::Any, ::Any, ::Unknown, ::Unknown)   = Unknown()
result_join(::Any, ::Any, ::Unknown, s::BroadcastStyle) = s
result_join(::Any, ::Any, s::BroadcastStyle, ::Unknown) = s
# For AbstractArray types with specialized broadcasting and undefined precedence rules,
# we have to signal conflict. Because ArrayConflict is a subtype of AbstractArray,
# this will "poison" any future operations (if we instead returned `DefaultArrayStyle`, then for
# 3-array broadcasting the returned type would depend on argument order).
result_join(::AbstractArrayStyle, ::AbstractArrayStyle, ::Unknown, ::Unknown) =
    ArrayConflict()
# Fallbacks in case users define `rule` for both argument-orders (not recommended)
result_join(::Any, ::Any, ::S, ::S) where S<:BroadcastStyle = S()
@noinline function result_join(::S, ::T, ::U, ::V) where {S,T,U,V}
    error("""
conflicting broadcast rules defined
  Broadcast.BroadcastStyle(::$S, ::$T) = $U()
  Broadcast.BroadcastStyle(::$T, ::$S) = $V()
One of these should be undefined (and thus return Broadcast.Unknown).""")
end

# Indices utilities

"""
    combine_axes(As...) -> Tuple

Determine the result axes for broadcasting across all values in `As`.

```jldoctest
julia> Broadcast.combine_axes([1], [1 2; 3 4; 5 6])
(Base.OneTo(3), Base.OneTo(2))

julia> Broadcast.combine_axes(1, 1, 1)
()
```
"""
@inline combine_axes(A, B...) = broadcast_shape(axes(A), combine_axes(B...))
@inline combine_axes(A, B) = broadcast_shape(axes(A), axes(B))
combine_axes(A) = axes(A)

"""
    broadcast_shape(As...) -> Tuple

Determine the result axes for broadcasting across all axes (size Tuples) in `As`.

```jldoctest
julia> Broadcast.broadcast_shape((1,2), (2,1))
(2, 2)

julia> Broadcast.broadcast_shape((1,), (1,5), (4,5,3))
(4, 5, 3)
```
"""
function broadcast_shape end
# shape (i.e., tuple-of-indices) inputs
broadcast_shape(shape::Tuple) = shape
broadcast_shape(shape::Tuple, shape1::Tuple, shapes::Tuple...) = broadcast_shape(_bcs(shape, shape1), shapes...)
# _bcs consolidates two shapes into a single output shape
_bcs(::Tuple{}, ::Tuple{}) = ()
_bcs(::Tuple{}, newshape::Tuple) = (newshape[1], _bcs((), tail(newshape))...)
_bcs(shape::Tuple, ::Tuple{}) = (shape[1], _bcs(tail(shape), ())...)
function _bcs(shape::Tuple, newshape::Tuple)
    return (_bcs1(shape[1], newshape[1]), _bcs(tail(shape), tail(newshape))...)
end
# _bcs1 handles the logic for a single dimension
_bcs1(a::Integer, b::Integer) = a == 1 ? b : (b == 1 ? a : (a == b ? a : throw(DimensionMismatch("arrays could not be broadcast to a common size; got a dimension with lengths $a and $b"))))
_bcs1(a::Integer, b) = a == 1 ? b : (first(b) == 1 && last(b) == a ? b : throw(DimensionMismatch("arrays could not be broadcast to a common size; got a dimension with lengths $a and $(length(b))")))
_bcs1(a, b::Integer) = _bcs1(b, a)
_bcs1(a, b) = _bcsm(b, a) ? axistype(b, a) : (_bcsm(a, b) ? axistype(a, b) : throw(DimensionMismatch("arrays could not be broadcast to a common size; got a dimension with lengths $(length(a)) and $(length(b))")))
# _bcsm tests whether the second index is consistent with the first
_bcsm(a, b) = a == b || length(b) == 1
_bcsm(a, b::Number) = b == 1
_bcsm(a::Number, b::Number) = a == b || b == 1
# Ensure inferrability when dealing with axes of different AbstractUnitRange types
# (We may not want to define general promotion rules between, say, OneTo and Slice, but if
#  we get here we know the axes are at least consistent for the purposes of broadcasting)
axistype(a::T, b::T) where T = a
axistype(a::OneTo, b::OneTo) = OneTo{Int}(a)
axistype(a, b) = UnitRange{Int}(a)

## Check that all arguments are broadcast compatible with shape
# comparing one input against a shape
check_broadcast_shape(shp) = nothing
check_broadcast_shape(shp, ::Tuple{}) = nothing
check_broadcast_shape(::Tuple{}, ::Tuple{}) = nothing
function check_broadcast_shape(::Tuple{}, Ashp::Tuple)
    if any(ax -> length(ax) != 1, Ashp)
        throw(DimensionMismatch("cannot broadcast array to have fewer non-singleton dimensions"))
    end
    nothing
end
function check_broadcast_shape(shp, Ashp::Tuple)
    _bcsm(shp[1], Ashp[1]) || throw(DimensionMismatch("array could not be broadcast to match destination"))
    check_broadcast_shape(tail(shp), tail(Ashp))
end
@inline check_broadcast_axes(shp, A) = check_broadcast_shape(shp, axes(A))
# comparing many inputs
@inline function check_broadcast_axes(shp, A, As...)
    check_broadcast_axes(shp, A)
    check_broadcast_axes(shp, As...)
end

## Indexing manipulations
"""
    newindex(argument, I)
    newindex(I, keep, default)

Recompute index `I` such that it appropriately constrains broadcasted dimensions to the source.

Two methods are supported, both allowing for `I` to be specified as either a [`CartesianIndex`](@ref) or
an `Int`.

* `newindex(argument, I)` dynamically constrains `I` based upon the axes of `argument`.
* `newindex(I, keep, default)` constrains `I` using the pre-computed tuples `keeps` and `defaults`.
    * `keep` is a tuple of `Bool`s, where `keep[d] == true` means that dimension `d` in `I` should be preserved as is
    * `default` is a tuple of Integers, specifying what index to use in dimension `d` when `keep[d] == false`.
    Any remaining indices in `I` beyond the length of the `keep` tuple are truncated. The `keep` and `default`
    tuples may be created by `newindexer(argument)`.
"""
Base.@propagate_inbounds newindex(arg, I::CartesianIndex) = CartesianIndex(_newindex(axes(arg), I.I))
Base.@propagate_inbounds newindex(arg, I::Integer) = CartesianIndex(_newindex(axes(arg), (I,)))
Base.@propagate_inbounds _newindex(ax::Tuple, I::Tuple) = (ifelse(length(ax[1]) == 1, ax[1][1], I[1]), _newindex(tail(ax), tail(I))...)
Base.@propagate_inbounds _newindex(ax::Tuple{}, I::Tuple) = ()
Base.@propagate_inbounds _newindex(ax::Tuple, I::Tuple{}) = (ax[1][1], _newindex(tail(ax), ())...)
Base.@propagate_inbounds _newindex(ax::Tuple{}, I::Tuple{}) = ()

# If dot-broadcasting were already defined, this would be `ifelse.(keep, I, Idefault)`.
@inline newindex(I::CartesianIndex, keep, Idefault) = CartesianIndex(_newindex(I.I, keep, Idefault))
@inline newindex(i::Integer, keep::Tuple, idefault) = ifelse(keep[1], i, idefault[1])
@inline newindex(i::Integer, keep::Tuple{}, idefault) = CartesianIndex(())
@inline _newindex(I, keep, Idefault) =
    (ifelse(keep[1], I[1], Idefault[1]), _newindex(tail(I), tail(keep), tail(Idefault))...)
@inline _newindex(I, keep::Tuple{}, Idefault) = ()  # truncate if keep is shorter than I
@inline _newindex(I::Tuple{}, keep, Idefault) = ()  # or I is shorter
@inline _newindex(I::Tuple{}, keep::Tuple{}, Idefault) = () # or both

# newindexer(A) generates `keep` and `Idefault` (for use by `newindex` above)
# for a particular array `A`; `shapeindexer` does so for its axes.
@inline newindexer(A) = shapeindexer(axes(A))
@inline shapeindexer(ax) = _newindexer(ax)
@inline _newindexer(indsA::Tuple{}) = (), ()
@inline function _newindexer(indsA::Tuple)
    ind1 = indsA[1]
    keep, Idefault = _newindexer(tail(indsA))
    (Base.length(ind1)::Integer != 1, keep...), (first(ind1), Idefault...)
end

@inline function Base.getindex(bc::Broadcasted, I::Union{Integer,CartesianIndex})
    @boundscheck checkbounds(bc, I)
    @inbounds _broadcast_getindex(bc, I)
end
Base.@propagate_inbounds Base.getindex(
    bc::Broadcasted,
    i1::Union{Integer,CartesianIndex},
    i2::Union{Integer,CartesianIndex},
    I::Union{Integer,CartesianIndex}...,
) =
    bc[CartesianIndex((i1, i2, I...))]
Base.@propagate_inbounds Base.getindex(bc::Broadcasted) = bc[CartesianIndex(())]

@inline Base.checkbounds(bc::Broadcasted, I::Union{Integer,CartesianIndex}) =
    Base.checkbounds_indices(Bool, axes(bc), (I,)) || Base.throw_boundserror(bc, (I,))


"""
    _broadcast_getindex(A, I)

Index into `A` with `I`, collapsing broadcasted indices to their singleton indices as appropriate.
"""
Base.@propagate_inbounds _broadcast_getindex(A::Union{Ref,AbstractArray{<:Any,0},Number}, I) = A[] # Scalar-likes can just ignore all indices
Base.@propagate_inbounds _broadcast_getindex(::Ref{Type{T}}, I) where {T} = T
# Tuples are statically known to be singleton or vector-like
Base.@propagate_inbounds _broadcast_getindex(A::Tuple{Any}, I) = A[1]
Base.@propagate_inbounds _broadcast_getindex(A::Tuple, I) = A[I[1]]
# Everything else falls back to dynamically dropping broadcasted indices based upon its axes
Base.@propagate_inbounds _broadcast_getindex(A, I) = A[newindex(A, I)]

# In some cases, it's more efficient to sort out which dimensions should be dropped
# ahead of time (often when the size checks aren't able to be lifted out of the loop).
# The Extruded struct computes that information ahead of time and stores it as a pair
# of tuples to optimize indexing later. This is most commonly needed for `Array` and
# other `AbstractArray` subtypes that wrap `Array` and dynamically ask it for its size.
struct Extruded{T, K, D}
    x::T
    keeps::K    # A tuple of booleans, specifying which indices should be passed normally
    defaults::D # A tuple of integers, specifying the index to use when keeps[i] is false (as defaults[i])
end
@inline axes(b::Extruded) = axes(b.x)
Base.@propagate_inbounds _broadcast_getindex(b::Extruded, i) = b.x[newindex(i, b.keeps, b.defaults)]
extrude(x::AbstractArray) = Extruded(x, newindexer(x)...)
extrude(x) = x

# For Broadcasted
Base.@propagate_inbounds function _broadcast_getindex(bc::Broadcasted{<:Any,<:Any,<:Any,<:Any}, I)
    args = _getindex(bc.args, I)
    return _broadcast_getindex_evalf(bc.f, args...)
end
# Hack around losing Type{T} information in the final args tuple. Julia actually
# knows (in `code_typed`) the _value_ of these types, statically displaying them,
# but inference is currently skipping inferring the type of the types as they are
# transiently placed in a tuple as the argument list is lispily constructed. These
# additional methods recover type stability when a `Type` appears in one of the
# first two arguments of a function.
Base.@propagate_inbounds function _broadcast_getindex(bc::Broadcasted{<:Any,<:Any,<:Any,<:Tuple{Ref{Type{T}},Vararg{Any}}}, I) where {T}
    args = _getindex(tail(bc.args), I)
    return _broadcast_getindex_evalf(bc.f, T, args...)
end
Base.@propagate_inbounds function _broadcast_getindex(bc::Broadcasted{<:Any,<:Any,<:Any,<:Tuple{Any,Ref{Type{T}},Vararg{Any}}}, I) where {T}
    arg1 = _broadcast_getindex(bc.args[1], I)
    args = _getindex(tail(tail(bc.args)), I)
    return _broadcast_getindex_evalf(bc.f, arg1, T, args...)
end
Base.@propagate_inbounds function _broadcast_getindex(bc::Broadcasted{<:Any,<:Any,<:Any,<:Tuple{Ref{Type{T}},Ref{Type{S}},Vararg{Any}}}, I) where {T,S}
    args = _getindex(tail(tail(bc.args)), I)
    return _broadcast_getindex_evalf(bc.f, T, S, args...)
end

# Utilities for _broadcast_getindex
Base.@propagate_inbounds _getindex(args::Tuple, I) = (_broadcast_getindex(args[1], I), _getindex(tail(args), I)...)
Base.@propagate_inbounds _getindex(args::Tuple{Any}, I) = (_broadcast_getindex(args[1], I),)
Base.@propagate_inbounds _getindex(args::Tuple{}, I) = ()

@inline _broadcast_getindex_evalf(f::Tf, args::Vararg{Any,N}) where {Tf,N} = f(args...)  # not propagate_inbounds

"""
    Broadcast.broadcastable(x)

Return either `x` or an object like `x` such that it supports [`axes`](@ref), indexing, and its type supports [`ndims`](@ref).

If `x` supports iteration, the returned value should have the same `axes` and indexing
behaviors as [`collect(x)`](@ref).

If `x` is not an `AbstractArray` but it supports `axes`, indexing, and its type supports
`ndims`, then `broadcastable(::typeof(x))` may be implemented to just return itself.
Further, if `x` defines its own [`BroadcastStyle`](@ref), then it must define its
`broadcastable` method to return itself for the custom style to have any effect.

# Examples
```jldoctest
julia> Broadcast.broadcastable([1,2,3]) # like `identity` since arrays already support axes and indexing
3-element Vector{Int64}:
 1
 2
 3

julia> Broadcast.broadcastable(Int) # Types don't support axes, indexing, or iteration but are commonly used as scalars
Base.RefValue{Type{Int64}}(Int64)

julia> Broadcast.broadcastable("hello") # Strings break convention of matching iteration and act like a scalar instead
Base.RefValue{String}("hello")
```
"""
broadcastable(x::Union{Symbol,AbstractString,Function,UndefInitializer,Nothing,RoundingMode,Missing,Val,Ptr,AbstractPattern,Pair,IO,CartesianIndex}) = Ref(x)
broadcastable(::Type{T}) where {T} = Ref{Type{T}}(T)
broadcastable(x::Union{AbstractArray,Number,AbstractChar,Ref,Tuple,Broadcasted}) = x
# Default to collecting iterables — which will error for non-iterables
broadcastable(x) = collect(x)
broadcastable(::Union{AbstractDict, NamedTuple}) = throw(ArgumentError("broadcasting over dictionaries and `NamedTuple`s is reserved"))

## Computation of inferred result type, for empty and concretely inferred cases only
_broadcast_getindex_eltype(bc::Broadcasted) = combine_eltypes(bc.f, bc.args)
_broadcast_getindex_eltype(A) = eltype(A)  # Tuple, Array, etc.

eltypes(::Tuple{}) = Tuple{}
eltypes(t::Tuple{Any}) = Iterators.TupleOrBottom(_broadcast_getindex_eltype(t[1]))
eltypes(t::Tuple{Any,Any}) = Iterators.TupleOrBottom(_broadcast_getindex_eltype(t[1]), _broadcast_getindex_eltype(t[2]))
eltypes(t::Tuple) = (TT = eltypes(tail(t)); TT === Union{} ? Union{} : Iterators.TupleOrBottom(_broadcast_getindex_eltype(t[1]), TT.parameters...))
# eltypes(t::Tuple) = Iterators.TupleOrBottom(ntuple(i -> _broadcast_getindex_eltype(t[i]), Val(length(t)))...)

# Inferred eltype of result of broadcast(f, args...)
function combine_eltypes(f, args::Tuple)
    argT = eltypes(args)
    argT === Union{} && return Union{}
    return promote_typejoin_union(Base._return_type(f, argT))
end

## Broadcasting core

"""
    broadcast(f, As...)

Broadcast the function `f` over the arrays, tuples, collections, [`Ref`](@ref)s and/or scalars `As`.

Broadcasting applies the function `f` over the elements of the container arguments and the
scalars themselves in `As`. Singleton and missing dimensions are expanded to match the
extents of the other arguments by virtually repeating the value. By default, only a limited
number of types are considered scalars, including `Number`s, `String`s, `Symbol`s, `Type`s,
`Function`s and some common singletons like [`missing`](@ref) and [`nothing`](@ref). All other arguments are
iterated over or indexed into elementwise.

The resulting container type is established by the following rules:

 - If all the arguments are scalars or zero-dimensional arrays, it returns an unwrapped scalar.
 - If at least one argument is a tuple and all others are scalars or zero-dimensional arrays,
   it returns a tuple.
 - All other combinations of arguments default to returning an `Array`, but
   custom container types can define their own implementation and promotion-like
   rules to customize the result when they appear as arguments.

A special syntax exists for broadcasting: `f.(args...)` is equivalent to
`broadcast(f, args...)`, and nested `f.(g.(args...))` calls are fused into a
single broadcast loop.

# Examples
```jldoctest
julia> A = [1, 2, 3, 4, 5]
5-element Vector{Int64}:
 1
 2
 3
 4
 5

julia> B = [1 2; 3 4; 5 6; 7 8; 9 10]
5×2 Matrix{Int64}:
 1   2
 3   4
 5   6
 7   8
 9  10

julia> broadcast(+, A, B)
5×2 Matrix{Int64}:
  2   3
  5   6
  8   9
 11  12
 14  15

julia> parse.(Int, ["1", "2"])
2-element Vector{Int64}:
 1
 2

julia> abs.((1, -2))
(1, 2)

julia> broadcast(+, 1.0, (0, -2.0))
(1.0, -1.0)

julia> (+).([[0,2], [1,3]], Ref{Vector{Int}}([1,-1]))
2-element Vector{Vector{Int64}}:
 [1, 1]
 [2, 2]

julia> string.(("one","two","three","four"), ": ", 1:4)
4-element Vector{String}:
 "one: 1"
 "two: 2"
 "three: 3"
 "four: 4"

```
"""
broadcast(f::Tf, As...) where {Tf} = materialize(broadcasted(f, As...))

# special cases defined for performance
@inline broadcast(f, x::Number...) = f(x...)
@inline broadcast(f, t::NTuple{N,Any}, ts::Vararg{NTuple{N,Any}}) where {N} = map(f, t, ts...)

"""
    broadcast!(f, dest, As...)

Like [`broadcast`](@ref), but store the result of
`broadcast(f, As...)` in the `dest` array.
Note that `dest` is only used to store the result, and does not supply
arguments to `f` unless it is also listed in the `As`,
as in `broadcast!(f, A, A, B)` to perform `A[:] = broadcast(f, A, B)`.

# Examples
```jldoctest
julia> A = [1.0; 0.0]; B = [0.0; 0.0];

julia> broadcast!(+, B, A, (0, -2.0));

julia> B
2-element Vector{Float64}:
  1.0
 -2.0

julia> A
2-element Vector{Float64}:
 1.0
 0.0

julia> broadcast!(+, A, A, (0, -2.0));

julia> A
2-element Vector{Float64}:
  1.0
 -2.0
```
"""
broadcast!(f::Tf, dest, As::Vararg{Any,N}) where {Tf,N} = (materialize!(dest, broadcasted(f, As...)); dest)

"""
    broadcast_preserving_zero_d(f, As...)

Like [`broadcast`](@ref), except in the case of a 0-dimensional result where it returns a 0-dimensional container

Broadcast automatically unwraps zero-dimensional results to be just the element itself,
but in some cases it is necessary to always return a container — even in the 0-dimensional case.
"""
@inline function broadcast_preserving_zero_d(f, As...)
    bc = broadcasted(f, As...)
    r = materialize(bc)
    return length(axes(bc)) == 0 ? fill!(similar(bc, typeof(r)), r) : r
end
@inline broadcast_preserving_zero_d(f) = fill(f())
@inline broadcast_preserving_zero_d(f, as::Number...) = fill(f(as...))

"""
    Broadcast.materialize(bc)

Take a lazy `Broadcasted` object and compute the result
"""
@inline materialize(bc::Broadcasted) = copy(instantiate(bc))
materialize(x) = x

@inline function materialize!(dest, x)
    return materialize!(dest, instantiate(Broadcasted(identity, (x,), axes(dest))))
end

@inline function materialize!(dest, bc::Broadcasted{<:Any})
    return materialize!(combine_styles(dest, bc), dest, bc)
end
@inline function materialize!(::BroadcastStyle, dest, bc::Broadcasted{<:Any})
    return copyto!(dest, instantiate(Broadcasted(bc.style, bc.f, bc.args, axes(dest))))
end

## general `copy` methods
@inline copy(bc::Broadcasted{<:AbstractArrayStyle{0}}) = bc[CartesianIndex()]
copy(bc::Broadcasted{<:Union{Nothing,Unknown}}) =
    throw(ArgumentError("broadcasting requires an assigned BroadcastStyle"))

const NonleafHandlingStyles = Union{DefaultArrayStyle,ArrayConflict}

@inline function copy(bc::Broadcasted)
    ElType = combine_eltypes(bc.f, bc.args)
    if Base.isconcretetype(ElType)
        # We can trust it and defer to the simpler `copyto!`
        return copyto!(similar(bc, ElType), bc)
    end
    # When ElType is not concrete, use narrowing. Use the first output
    # value to determine the starting output eltype; copyto_nonleaf!
    # will widen `dest` as needed to accommodate later values.
    bc′ = preprocess(nothing, bc)
    iter = eachindex(bc′)
    y = iterate(iter)
    if y === nothing
        # if empty, take the ElType at face value
        return similar(bc′, ElType)
    end
    # Initialize using the first value
    I, state = y
    @inbounds val = bc′[I]
    dest = similar(bc′, typeof(val))
    @inbounds dest[I] = val
    # Now handle the remaining values
    # The typeassert gives inference a helping hand on the element type and dimensionality
    # (work-around for #28382)
    ElType′ = ElType === Union{} ? Any : ElType <: Type ? Type : ElType
    RT = dest isa AbstractArray ? AbstractArray{<:ElType′, ndims(dest)} : Any
    return copyto_nonleaf!(dest, bc′, iter, state, 1)::RT
end

## general `copyto!` methods
# The most general method falls back to a method that replaces Style->Nothing
# This permits specialization on typeof(dest) without introducing ambiguities
@inline copyto!(dest::AbstractArray, bc::Broadcasted) = copyto!(dest, convert(Broadcasted{Nothing}, bc))

# Performance optimization for the common identity scalar case: dest .= val
@inline function copyto!(dest::AbstractArray, bc::Broadcasted{<:AbstractArrayStyle{0}})
    # Typically, we must independently execute bc for every storage location in `dest`, but:
    # IF we're in the common no-op identity case with no nested args (like `dest .= val`),
    if bc.f === identity && bc.args isa Tuple{Any} && isflat(bc)
        # THEN we can just extract the argument and `fill!` the destination with it
        return fill!(dest, bc.args[1][])
    else
        # Otherwise, fall back to the default implementation like above
        return copyto!(dest, convert(Broadcasted{Nothing}, bc))
    end
end

# For broadcasted assignments like `broadcast!(f, A, ..., A, ...)`, where `A`
# appears on both the LHS and the RHS of the `.=`, then we know we're only
# going to make one pass through the array, and even though `A` is aliasing
# against itself, the mutations won't affect the result as the indices on the
# LHS and RHS will always match. This is not true in general, but with the `.op=`
# syntax it's fairly common for an argument to be `===` a source.
broadcast_unalias(dest, src) = dest === src ? src : unalias(dest, src)
broadcast_unalias(::Nothing, src) = src

# Preprocessing a `Broadcasted` does two things:
# * unaliases any arguments from `dest`
# * "extrudes" the arguments where it is advantageous to pre-compute the broadcasted indices
@inline preprocess(dest, bc::Broadcasted) = Broadcasted(bc.style, bc.f, preprocess_args(dest, bc.args), bc.axes)
preprocess(dest, x) = extrude(broadcast_unalias(dest, x))

@inline preprocess_args(dest, args::Tuple) = (preprocess(dest, args[1]), preprocess_args(dest, tail(args))...)
@inline preprocess_args(dest, args::Tuple{Any}) = (preprocess(dest, args[1]),)
@inline preprocess_args(dest, args::Tuple{}) = ()

# Specialize this method if all you want to do is specialize on typeof(dest)
@inline function copyto!(dest::AbstractArray, bc::Broadcasted{Nothing})
    axes(dest) == axes(bc) || throwdm(axes(dest), axes(bc))
    # Performance optimization: broadcast!(identity, dest, A) is equivalent to copyto!(dest, A) if indices match
    if bc.f === identity && bc.args isa Tuple{AbstractArray} # only a single input argument to broadcast!
        A = bc.args[1]
        if axes(dest) == axes(A)
            return copyto!(dest, A)
        end
    end
    bc′ = preprocess(dest, bc)
    # Performance may vary depending on whether `@inbounds` is placed outside the
    # for loop or not. (cf. https://github.com/JuliaLang/julia/issues/38086)
    @inbounds @simd for I in eachindex(bc′)
        dest[I] = bc′[I]
    end
    return dest
end

# Performance optimization: for BitArray outputs, we cache the result
# in a "small" Vector{Bool}, and then copy in chunks into the output
@inline function copyto!(dest::BitArray, bc::Broadcasted{Nothing})
    axes(dest) == axes(bc) || throwdm(axes(dest), axes(bc))
    ischunkedbroadcast(dest, bc) && return chunkedcopyto!(dest, bc)
    length(dest) < 256 && return invoke(copyto!, Tuple{AbstractArray, Broadcasted{Nothing}}, dest, bc)
    tmp = Vector{Bool}(undef, bitcache_size)
    destc = dest.chunks
    cind = 1
    bc′ = preprocess(dest, bc)
    @inbounds for P in Iterators.partition(eachindex(bc′), bitcache_size)
        ind = 1
        @simd for I in P
            tmp[ind] = bc′[I]
            ind += 1
        end
        @simd for i in ind:bitcache_size
            tmp[i] = false
        end
        dumpbitcache(destc, cind, tmp)
        cind += bitcache_chunks
    end
    return dest
end

# For some BitArray operations, we can work at the level of chunks. The trivial
# implementation just walks over the UInt64 chunks in a linear fashion.
# This requires three things:
#   1. The function must be known to work at the level of chunks (or can be converted to do so)
#   2. The only arrays involved must be BitArrays or scalar Bools
#   3. There must not be any broadcasting beyond scalar — all array sizes must match
# We could eventually allow for all broadcasting and other array types, but that
# requires very careful consideration of all the edge effects.
const ChunkableOp = Union{typeof(&), typeof(|), typeof(xor), typeof(~), typeof(identity),
    typeof(!), typeof(*), typeof(==)} # these are convertible to chunkable ops by liftfuncs
const BroadcastedChunkableOp{Style<:Union{Nothing,BroadcastStyle}, Axes, F<:ChunkableOp, Args<:Tuple} = Broadcasted{Style,Axes,F,Args}
ischunkedbroadcast(R, bc::BroadcastedChunkableOp) = ischunkedbroadcast(R, bc.args)
ischunkedbroadcast(R, args) = false
ischunkedbroadcast(R, args::Tuple{<:BitArray,Vararg{Any}}) = size(R) == size(args[1]) && ischunkedbroadcast(R, tail(args))
ischunkedbroadcast(R, args::Tuple{<:Bool,Vararg{Any}}) = ischunkedbroadcast(R, tail(args))
ischunkedbroadcast(R, args::Tuple{<:BroadcastedChunkableOp,Vararg{Any}}) = ischunkedbroadcast(R, args[1]) && ischunkedbroadcast(R, tail(args))
ischunkedbroadcast(R, args::Tuple{}) = true

# Convert compatible functions to chunkable ones. They must also be green-lighted as ChunkableOps
liftfuncs(bc::Broadcasted{<:Any,<:Any,<:Any}) = Broadcasted(bc.style, bc.f, map(liftfuncs, bc.args), bc.axes)
liftfuncs(bc::Broadcasted{<:Any,<:Any,typeof(sign)}) = Broadcasted(bc.style, identity, map(liftfuncs, bc.args), bc.axes)
liftfuncs(bc::Broadcasted{<:Any,<:Any,typeof(!)}) = Broadcasted(bc.style, ~, map(liftfuncs, bc.args), bc.axes)
liftfuncs(bc::Broadcasted{<:Any,<:Any,typeof(*)}) = Broadcasted(bc.style, &, map(liftfuncs, bc.args), bc.axes)
liftfuncs(bc::Broadcasted{<:Any,<:Any,typeof(==)}) = Broadcasted(bc.style, (~)∘(xor), map(liftfuncs, bc.args), bc.axes)
liftfuncs(x) = x

liftchunks(::Tuple{}) = ()
liftchunks(args::Tuple{<:BitArray,Vararg{Any}}) = (args[1].chunks, liftchunks(tail(args))...)
# Transform scalars to repeated scalars the size of a chunk
liftchunks(args::Tuple{<:Bool,Vararg{Any}}) = (ifelse(args[1], typemax(UInt64), UInt64(0)), liftchunks(tail(args))...)
ithchunk(i) = ()
Base.@propagate_inbounds ithchunk(i, c::Vector{UInt64}, args...) = (c[i], ithchunk(i, args...)...)
Base.@propagate_inbounds ithchunk(i, b::UInt64, args...) = (b, ithchunk(i, args...)...)
@inline function chunkedcopyto!(dest::BitArray, bc::Broadcasted)
    isempty(dest) && return dest
    f = flatten(liftfuncs(bc))
    args = liftchunks(f.args)
    dc = dest.chunks
    @simd for i in eachindex(dc)
        @inbounds dc[i] = f.f(ithchunk(i, args...)...)
    end
    @inbounds dc[end] &= Base._msk_end(dest)
    return dest
end


@noinline throwdm(axdest, axsrc) =
    throw(DimensionMismatch("destination axes $axdest are not compatible with source axes $axsrc"))

function restart_copyto_nonleaf!(newdest, dest, bc, val, I, iter, state, count)
    # Function barrier that makes the copying to newdest type stable
    for II in Iterators.take(iter, count)
        newdest[II] = dest[II]
    end
    newdest[I] = val
    return copyto_nonleaf!(newdest, bc, iter, state, count+1)
end

function copyto_nonleaf!(dest, bc::Broadcasted, iter, state, count)
    T = eltype(dest)
    while true
        y = iterate(iter, state)
        y === nothing && break
        I, state = y
        @inbounds val = bc[I]
        if val isa T
            @inbounds dest[I] = val
        else
            # This element type doesn't fit in dest. Allocate a new dest with wider eltype,
            # copy over old values, and continue
            newdest = Base.similar(bc, promote_typejoin(T, typeof(val)))
            return restart_copyto_nonleaf!(newdest, dest, bc, val, I, iter, state, count)
        end
        count += 1
    end
    return dest
end

## Tuple methods

@inline function copy(bc::Broadcasted{Style{Tuple}})
    dim = axes(bc)
    length(dim) == 1 || throw(DimensionMismatch("tuple only supports one dimension"))
    N = length(dim[1])
    return ntuple(k -> @inbounds(_broadcast_getindex(bc, k)), Val(N))
end

## scalar-range broadcast operations ##
# DefaultArrayStyle and \ are not available at the time of range.jl
broadcasted(::DefaultArrayStyle{1}, ::typeof(+), r::AbstractRange) = r

broadcasted(::DefaultArrayStyle{1}, ::typeof(-), r::AbstractRange) = range(-first(r), step=negate(step(r)), length=length(r))
broadcasted(::DefaultArrayStyle{1}, ::typeof(-), r::OrdinalRange) = range(-first(r), -last(r), step=negate(step(r)))
broadcasted(::DefaultArrayStyle{1}, ::typeof(-), r::StepRangeLen) = StepRangeLen(-r.ref, negate(r.step), length(r), r.offset)
broadcasted(::DefaultArrayStyle{1}, ::typeof(-), r::LinRange) = LinRange(-r.start, -r.stop, length(r))

# For #18336 we need to prevent promotion of the step type:
broadcasted(::DefaultArrayStyle{1}, ::typeof(+), r::AbstractRange, x::Number) = range(first(r) + x, step=step(r), length=length(r))
broadcasted(::DefaultArrayStyle{1}, ::typeof(+), x::Number, r::AbstractRange) = range(x + first(r), step=step(r), length=length(r))
broadcasted(::DefaultArrayStyle{1}, ::typeof(+), r::OrdinalRange, x::Integer) = range(first(r) + x, last(r) + x, step=step(r))
broadcasted(::DefaultArrayStyle{1}, ::typeof(+), x::Integer, r::OrdinalRange) = range(x + first(r), x + last(r), step=step(r))
broadcasted(::DefaultArrayStyle{1}, ::typeof(+), r::AbstractUnitRange, x::Integer) = range(first(r) + x, last(r) + x)
broadcasted(::DefaultArrayStyle{1}, ::typeof(+), x::Integer, r::AbstractUnitRange) = range(x + first(r), x + last(r))
broadcasted(::DefaultArrayStyle{1}, ::typeof(+), r::AbstractUnitRange, x::Real) = range(first(r) + x, length=length(r))
broadcasted(::DefaultArrayStyle{1}, ::typeof(+), x::Real, r::AbstractUnitRange) = range(x + first(r), length=length(r))
broadcasted(::DefaultArrayStyle{1}, ::typeof(+), r::StepRangeLen{T}, x::Number) where T =
    StepRangeLen{typeof(T(r.ref)+x)}(r.ref + x, r.step, length(r), r.offset)
broadcasted(::DefaultArrayStyle{1}, ::typeof(+), x::Number, r::StepRangeLen{T}) where T =
    StepRangeLen{typeof(x+T(r.ref))}(x + r.ref, r.step, length(r), r.offset)
broadcasted(::DefaultArrayStyle{1}, ::typeof(+), r::LinRange, x::Number) = LinRange(r.start + x, r.stop + x, length(r))
broadcasted(::DefaultArrayStyle{1}, ::typeof(+), x::Number, r::LinRange) = LinRange(x + r.start, x + r.stop, length(r))
broadcasted(::DefaultArrayStyle{1}, ::typeof(+), r1::AbstractRange, r2::AbstractRange) = r1 + r2

broadcasted(::DefaultArrayStyle{1}, ::typeof(-), r::AbstractRange, x::Number) = range(first(r) - x, step=step(r), length=length(r))
broadcasted(::DefaultArrayStyle{1}, ::typeof(-), x::Number, r::AbstractRange) = range(x - first(r), step=negate(step(r)), length=length(r))
broadcasted(::DefaultArrayStyle{1}, ::typeof(-), r::OrdinalRange, x::Integer) = range(first(r) - x, last(r) - x, step=step(r))
broadcasted(::DefaultArrayStyle{1}, ::typeof(-), x::Integer, r::OrdinalRange) = range(x - first(r), x - last(r), step=negate(step(r)))
broadcasted(::DefaultArrayStyle{1}, ::typeof(-), r::AbstractUnitRange, x::Integer) = range(first(r) - x, last(r) - x)
broadcasted(::DefaultArrayStyle{1}, ::typeof(-), r::AbstractUnitRange, x::Real) = range(first(r) - x, length=length(r))
broadcasted(::DefaultArrayStyle{1}, ::typeof(-), r::StepRangeLen{T}, x::Number) where T =
    StepRangeLen{typeof(T(r.ref)-x)}(r.ref - x, r.step, length(r), r.offset)
broadcasted(::DefaultArrayStyle{1}, ::typeof(-), x::Number, r::StepRangeLen{T}) where T =
    StepRangeLen{typeof(x-T(r.ref))}(x - r.ref, negate(r.step), length(r), r.offset)
broadcasted(::DefaultArrayStyle{1}, ::typeof(-), r::LinRange, x::Number) = LinRange(r.start - x, r.stop - x, length(r))
broadcasted(::DefaultArrayStyle{1}, ::typeof(-), x::Number, r::LinRange) = LinRange(x - r.start, x - r.stop, length(r))
broadcasted(::DefaultArrayStyle{1}, ::typeof(-), r1::AbstractRange, r2::AbstractRange) = r1 - r2

# at present Base.range_start_step_length(1,0,5) is an error, so for 0 .* (-2:2) we explicitly construct StepRangeLen:
broadcasted(::DefaultArrayStyle{1}, ::typeof(*), x::Number, r::AbstractRange) = StepRangeLen(x*first(r), x*step(r), length(r))
broadcasted(::DefaultArrayStyle{1}, ::typeof(*), x::Number, r::StepRangeLen{T}) where {T} =
    StepRangeLen{typeof(x*T(r.ref))}(x*r.ref, x*r.step, length(r), r.offset)
broadcasted(::DefaultArrayStyle{1}, ::typeof(*), x::Number, r::LinRange) = LinRange(x * r.start, x * r.stop, r.len)
broadcasted(::DefaultArrayStyle{1}, ::typeof(*), x::AbstractFloat, r::OrdinalRange) =
    Base.range_start_step_length(x*first(r), x*step(r), length(r))  # 0.2 .* (-2:2) needs TwicePrecision
# separate in case of noncommutative multiplication:
broadcasted(::DefaultArrayStyle{1}, ::typeof(*), r::AbstractRange, x::Number) = StepRangeLen(first(r)*x, step(r)*x, length(r))
broadcasted(::DefaultArrayStyle{1}, ::typeof(*), r::StepRangeLen{T}, x::Number) where {T} =
    StepRangeLen{typeof(T(r.ref)*x)}(r.ref*x, r.step*x, length(r), r.offset)
broadcasted(::DefaultArrayStyle{1}, ::typeof(*), r::LinRange, x::Number) = LinRange(r.start * x, r.stop * x, r.len)
broadcasted(::DefaultArrayStyle{1}, ::typeof(*), r::OrdinalRange, x::AbstractFloat) =
    Base.range_start_step_length(first(r)*x, step(r)*x, length(r))

#broadcasted(::DefaultArrayStyle{1}, ::typeof(/), r::AbstractRange, x::Number) = range(first(r)/x, last(r)/x, length=length(r))
broadcasted(::DefaultArrayStyle{1}, ::typeof(/), r::AbstractRange, x::Number) = range(first(r)/x, step=step(r)/x, length=length(r))
broadcasted(::DefaultArrayStyle{1}, ::typeof(/), r::StepRangeLen{T}, x::Number) where {T} =
    StepRangeLen{typeof(T(r.ref)/x)}(r.ref/x, r.step/x, length(r), r.offset)
broadcasted(::DefaultArrayStyle{1}, ::typeof(/), r::LinRange, x::Number) = LinRange(r.start / x, r.stop / x, r.len)

broadcasted(::DefaultArrayStyle{1}, ::typeof(\), x::Number, r::AbstractRange) = range(x\first(r), step=x\step(r), length=length(r))
broadcasted(::DefaultArrayStyle{1}, ::typeof(\), x::Number, r::StepRangeLen) = StepRangeLen(x\r.ref, x\r.step, length(r), r.offset)
broadcasted(::DefaultArrayStyle{1}, ::typeof(\), x::Number, r::LinRange) = LinRange(x \ r.start, x \ r.stop, r.len)

broadcasted(::DefaultArrayStyle{1}, ::typeof(big), r::UnitRange) = big(r.start):big(last(r))
broadcasted(::DefaultArrayStyle{1}, ::typeof(big), r::StepRange) = big(r.start):big(r.step):big(last(r))
broadcasted(::DefaultArrayStyle{1}, ::typeof(big), r::StepRangeLen) = StepRangeLen(big(r.ref), big(r.step), length(r), r.offset)
broadcasted(::DefaultArrayStyle{1}, ::typeof(big), r::LinRange) = LinRange(big(r.start), big(r.stop), length(r))

## CartesianIndices
broadcasted(::typeof(+), I::CartesianIndices{N}, j::CartesianIndex{N}) where N =
    CartesianIndices(map((rng, offset)->rng .+ offset, I.indices, Tuple(j)))
broadcasted(::typeof(+), j::CartesianIndex{N}, I::CartesianIndices{N}) where N =
    I .+ j
broadcasted(::typeof(-), I::CartesianIndices{N}, j::CartesianIndex{N}) where N =
    CartesianIndices(map((rng, offset)->rng .- offset, I.indices, Tuple(j)))
function broadcasted(::typeof(-), j::CartesianIndex{N}, I::CartesianIndices{N}) where N
    diffrange(offset, rng) = range(offset-last(rng), length=length(rng), step=step(rng))
    Iterators.reverse(CartesianIndices(map(diffrange, Tuple(j), I.indices)))
end

## In specific instances, we can broadcast masked BitArrays whole chunks at a time
# Very intentionally do not support much functionality here: scalar indexing would be O(n)
struct BitMaskedBitArray{N,M}
    parent::BitArray{N}
    mask::BitArray{M}
    BitMaskedBitArray{N,M}(parent, mask) where {N,M} = new(parent, mask)
end
@inline function BitMaskedBitArray(parent::BitArray{N}, mask::BitArray{M}) where {N,M}
    @boundscheck checkbounds(parent, mask)
    BitMaskedBitArray{N,M}(parent, mask)
end
Base.@propagate_inbounds dotview(B::BitArray, i::BitArray) = BitMaskedBitArray(B, i)
Base.show(io::IO, B::BitMaskedBitArray) = foreach(arg->show(io, arg), (typeof(B), (B.parent, B.mask)))
# Override materialize! to prevent the BitMaskedBitArray from escaping to an overridable method
@inline materialize!(B::BitMaskedBitArray, bc::Broadcasted{<:Any,<:Any,typeof(identity),Tuple{Bool}}) = fill!(B, bc.args[1])
@inline materialize!(B::BitMaskedBitArray, bc::Broadcasted{<:Any}) = materialize!(@inbounds(view(B.parent, B.mask)), bc)
function Base.fill!(B::BitMaskedBitArray, b::Bool)
    Bc = B.parent.chunks
    Ic = B.mask.chunks
    @inbounds if b
        for i = 1:length(Bc)
            Bc[i] |= Ic[i]
        end
    else
        for i = 1:length(Bc)
            Bc[i] &= ~Ic[i]
        end
    end
    return B
end


############################################################

# x[...] .= f.(y...) ---> broadcast!(f, dotview(x, ...), y...).
# The dotview function defaults to getindex, but we override it in
# a few cases to get the expected in-place behavior without affecting
# explicit calls to view.   (All of this can go away if slices
# are changed to generate views by default.)

Base.@propagate_inbounds dotview(args...) = Base.maybeview(args...)

############################################################
# The parser turns @. into a call to the __dot__ macro,
# which converts all function calls and assignments into
# broadcasting "dot" calls/assignments:

dottable(x) = false # avoid dotting spliced objects (e.g. view calls inserted by @view)
# don't add dots to dot operators
dottable(x::Symbol) = (!isoperator(x) || first(string(x)) != '.' || x === :..) && x !== :(:)
dottable(x::Expr) = x.head !== :$
undot(x) = x
function undot(x::Expr)
    if x.head === :.=
        Expr(:(=), x.args...)
    elseif x.head === :block # occurs in for x=..., y=...
        Expr(:block, Base.mapany(undot, x.args)...)
    else
        x
    end
end
__dot__(x) = x
function __dot__(x::Expr)
    dotargs = Base.mapany(__dot__, x.args)
    if x.head === :call && dottable(x.args[1])
        Expr(:., dotargs[1], Expr(:tuple, dotargs[2:end]...))
    elseif x.head === :comparison
        Expr(:comparison, (iseven(i) && dottable(arg) && arg isa Symbol && isoperator(arg) ?
                               Symbol('.', arg) : arg for (i, arg) in pairs(dotargs))...)
    elseif x.head === :$
        x.args[1]
    elseif x.head === :let # don't add dots to `let x=...` assignments
        Expr(:let, undot(dotargs[1]), dotargs[2])
    elseif x.head === :for # don't add dots to for x=... assignments
        Expr(:for, undot(dotargs[1]), dotargs[2])
    elseif (x.head === :(=) || x.head === :function || x.head === :macro) &&
           Meta.isexpr(x.args[1], :call) # function or macro definition
        Expr(x.head, x.args[1], dotargs[2])
    elseif x.head === :(<:) || x.head === :(>:)
        tmp = x.head === :(<:) ? :.<: : :.>:
        Expr(:call, tmp, dotargs...)
    else
        head = String(x.head)::String
        if last(head) == '=' && first(head) != '.' || head == "&&" || head == "||"
            Expr(Symbol('.', head), dotargs...)
        else
            Expr(x.head, dotargs...)
        end
    end
end
"""
    @. expr

Convert every function call or operator in `expr` into a "dot call"
(e.g. convert `f(x)` to `f.(x)`), and convert every assignment in `expr`
to a "dot assignment" (e.g. convert `+=` to `.+=`).

If you want to *avoid* adding dots for selected function calls in
`expr`, splice those function calls in with `\$`.  For example,
`@. sqrt(abs(\$sort(x)))` is equivalent to `sqrt.(abs.(sort(x)))`
(no dot for `sort`).

(`@.` is equivalent to a call to `@__dot__`.)

# Examples
```jldoctest
julia> x = 1.0:3.0; y = similar(x);

julia> @. y = x + 3 * sin(x)
3-element Vector{Float64}:
 3.5244129544236893
 4.727892280477045
 3.4233600241796016
```
"""
macro __dot__(x)
    esc(__dot__(x))
end

@inline function broadcasted_kwsyntax(f, args...; kwargs...)
    if isempty(kwargs) # some BroadcastStyles dispatch on `f`, so try to preserve its type
        return broadcasted(f, args...)
    else
        return broadcasted((args...) -> f(args...; kwargs...), args...)
    end
end
@inline function broadcasted(f::F, args...) where {F}
    args′ = map(broadcastable, args)
    broadcasted(combine_styles(args′...), f, args′...)
end
# Due to the current Type{T}/DataType specialization heuristics within Tuples,
# the totally generic varargs broadcasted(f, args...) method above loses Type{T}s in
# mapping broadcastable across the args. These additional methods with explicit
# arguments ensure we preserve Type{T}s in the first or second argument position.
@inline function broadcasted(f::F, arg1, args...) where {F}
    arg1′ = broadcastable(arg1)
    args′ = map(broadcastable, args)
    broadcasted(combine_styles(arg1′, args′...), f, arg1′, args′...)
end
@inline function broadcasted(f::F, arg1, arg2, args...) where {F}
    arg1′ = broadcastable(arg1)
    arg2′ = broadcastable(arg2)
    args′ = map(broadcastable, args)
    broadcasted(combine_styles(arg1′, arg2′, args′...), f, arg1′, arg2′, args′...)
end
@inline broadcasted(style::BroadcastStyle, f::F, args...) where {F} = Broadcasted(style, f, args)

"""
    BroadcastFunction{F} <: Function

Represents the "dotted" version of an operator, which broadcasts the operator over its
arguments, so `BroadcastFunction(op)` is functionally equivalent to `(x...) -> (op).(x...)`.

Can be created by just passing an operator preceded by a dot to a higher-order function.

# Examples
```jldoctest
julia> a = [[1 3; 2 4], [5 7; 6 8]];

julia> b = [[9 11; 10 12], [13 15; 14 16]];

julia> map(.*, a, b)
2-element Vector{Matrix{Int64}}:
 [9 33; 20 48]
 [65 105; 84 128]

julia> Base.BroadcastFunction(+)(a, b) == a .+ b
true
```

!!! compat "Julia 1.6"
    `BroadcastFunction` and the standalone `.op` syntax are available as of Julia 1.6.
"""
struct BroadcastFunction{F} <: Function
    f::F
end

@inline (op::BroadcastFunction)(x...; kwargs...) = op.f.(x...; kwargs...)

function Base.show(io::IO, op::BroadcastFunction)
    print(io, BroadcastFunction, '(')
    show(io, op.f)
    print(io, ')')
    nothing
end
Base.show(io::IO, ::MIME"text/plain", op::BroadcastFunction) = show(io, op)

end # module
N   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/missing.jl 7      # This file is a part of Julia. License is MIT: https://julialang.org/license

# Missing, missing and ismissing are defined in essentials.jl

show(io::IO, x::Missing) = print(io, "missing")

"""
    MissingException(msg)

Exception thrown when a [`missing`](@ref) value is encountered in a situation
where it is not supported. The error message, in the `msg` field
may provide more specific details.
"""
struct MissingException <: Exception
    msg::AbstractString
end

showerror(io::IO, ex::MissingException) =
    print(io, "MissingException: ", ex.msg)

"""
    nonmissingtype(T::Type)

If `T` is a union of types containing `Missing`, return a new type with
`Missing` removed.

# Examples
```jldoctest
julia> nonmissingtype(Union{Int64,Missing})
Int64

julia> nonmissingtype(Any)
Any
```

!!! compat "Julia 1.3"
    This function is exported as of Julia 1.3.
"""
nonmissingtype(::Type{T}) where {T} = typesplit(T, Missing)

function nonmissingtype_checked(T::Type)
    R = nonmissingtype(T)
    R >: T && error("could not compute non-missing type")
    R <: Union{} && error("cannot convert a value to missing for assignment")
    return R
end

promote_rule(T::Type{Missing}, S::Type) = Union{S, Missing}
promote_rule(T::Type{Union{Nothing, Missing}}, S::Type) = Union{S, Nothing, Missing}
function promote_rule(T::Type{>:Union{Nothing, Missing}}, S::Type)
    R = nonnothingtype(T)
    R >: T && return Any
    T = R
    R = nonmissingtype(T)
    R >: T && return Any
    T = R
    R = promote_type(T, S)
    return Union{R, Nothing, Missing}
end
function promote_rule(T::Type{>:Missing}, S::Type)
    R = nonmissingtype(T)
    R >: T && return Any
    T = R
    R = promote_type(T, S)
    return Union{R, Missing}
end

convert(::Type{T}, x::T) where {T>:Missing} = x
convert(::Type{T}, x::T) where {T>:Union{Missing, Nothing}} = x
convert(::Type{T}, x) where {T>:Missing} = convert(nonmissingtype_checked(T), x)
convert(::Type{T}, x) where {T>:Union{Missing, Nothing}} = convert(nonmissingtype_checked(nonnothingtype_checked(T)), x)

# Comparison operators
==(::Missing, ::Missing) = missing
==(::Missing, ::Any) = missing
==(::Any, ::Missing) = missing
# To fix ambiguity
==(::Missing, ::WeakRef) = missing
==(::WeakRef, ::Missing) = missing
isequal(::Missing, ::Missing) = true
isequal(::Missing, ::Any) = false
isequal(::Any, ::Missing) = false
<(::Missing, ::Missing) = missing
<(::Missing, ::Any) = missing
<(::Any, ::Missing) = missing
isless(::Missing, ::Missing) = false
isless(::Missing, ::Any) = false
isless(::Any, ::Missing) = true
isapprox(::Missing, ::Missing; kwargs...) = missing
isapprox(::Missing, ::Any; kwargs...) = missing
isapprox(::Any, ::Missing; kwargs...) = missing

# Unary operators/functions
for f in (:(!), :(~), :(+), :(-), :(*), :(&), :(|), :(xor),
          :(zero), :(one), :(oneunit),
          :(isfinite), :(isinf), :(isodd),
          :(isinteger), :(isreal), :(isnan),
          :(iszero), :(transpose), :(adjoint), :(float), :(complex), :(conj),
          :(abs), :(abs2), :(iseven), :(ispow2),
          :(real), :(imag), :(sign), :(inv))
    @eval ($f)(::Missing) = missing
end
for f in (:(Base.zero), :(Base.one), :(Base.oneunit))
    @eval ($f)(::Type{Missing}) = missing
    @eval function $(f)(::Type{Union{T, Missing}}) where T
        T === Any && throw(MethodError($f, (Any,)))  # To prevent StackOverflowError
        $f(T)
    end
end
for f in (:(Base.float), :(Base.complex))
    @eval $f(::Type{Missing}) = Missing
    @eval function $f(::Type{Union{T, Missing}}) where T
        T === Any && throw(MethodError($f, (Any,)))  # To prevent StackOverflowError
        Union{$f(T), Missing}
    end
end

# Binary operators/functions
for f in (:(+), :(-), :(*), :(/), :(^), :(mod), :(rem))
    @eval begin
        # Scalar with missing
        ($f)(::Missing, ::Missing) = missing
        ($f)(::Missing, ::Number)  = missing
        ($f)(::Number,  ::Missing) = missing
    end
end

div(::Missing, ::Missing, r::RoundingMode) = missing
div(::Missing, ::Number, r::RoundingMode) = missing
div(::Number, ::Missing, r::RoundingMode) = missing

min(::Missing, ::Missing) = missing
min(::Missing, ::Any)     = missing
min(::Any,     ::Missing) = missing
max(::Missing, ::Missing) = missing
max(::Missing, ::Any)     = missing
max(::Any,     ::Missing) = missing

missing_conversion_msg(@nospecialize T) =
    LazyString("cannot convert a missing value to type ", T, ": use Union{", T, ", Missing} instead")

# Rounding and related functions
round(::Missing, ::RoundingMode=RoundNearest; sigdigits::Integer=0, digits::Integer=0, base::Integer=0) = missing
round(::Type{>:Missing}, ::Missing, ::RoundingMode=RoundNearest) = missing
round(::Type{T}, ::Missing, ::RoundingMode=RoundNearest) where {T} =
    throw(MissingException(missing_conversion_msg(T)))
round(::Type{T}, x::Any, r::RoundingMode=RoundNearest) where {T>:Missing} = round(nonmissingtype_checked(T), x, r)
# to fix ambiguities
round(::Type{T}, x::Rational{Tr}, r::RoundingMode=RoundNearest) where {T>:Missing,Tr} = round(nonmissingtype_checked(T), x, r)
round(::Type{T}, x::Rational{Bool}, r::RoundingMode=RoundNearest) where {T>:Missing} = round(nonmissingtype_checked(T), x, r)

# Handle ceil, floor, and trunc separately as they have no RoundingMode argument
for f in (:(ceil), :(floor), :(trunc))
    @eval begin
        ($f)(::Missing; sigdigits::Integer=0, digits::Integer=0, base::Integer=0) = missing
        ($f)(::Type{>:Missing}, ::Missing) = missing
        ($f)(::Type{T}, ::Missing) where {T} = throw(MissingException(missing_conversion_msg(T)))
        ($f)(::Type{T}, x::Any) where {T>:Missing} = $f(nonmissingtype_checked(T), x)
        # to fix ambiguities
        ($f)(::Type{T}, x::Rational) where {T>:Missing} = $f(nonmissingtype_checked(T), x)
    end
end

# to avoid ambiguity warnings
(^)(::Missing, ::Integer) = missing

# Bit operators
(&)(::Missing, ::Missing) = missing
(&)(a::Missing, b::Bool) = ifelse(b, missing, false)
(&)(b::Bool, a::Missing) = ifelse(b, missing, false)
(&)(::Missing, ::Integer) = missing
(&)(::Integer, ::Missing) = missing
(|)(::Missing, ::Missing) = missing
(|)(a::Missing, b::Bool) = ifelse(b, true, missing)
(|)(b::Bool, a::Missing) = ifelse(b, true, missing)
(|)(::Missing, ::Integer) = missing
(|)(::Integer, ::Missing) = missing
xor(::Missing, ::Missing) = missing
xor(a::Missing, b::Bool) = missing
xor(b::Bool, a::Missing) = missing
xor(::Missing, ::Integer) = missing
xor(::Integer, ::Missing) = missing

*(d::Missing, x::Union{AbstractString,AbstractChar}) = missing
*(d::Union{AbstractString,AbstractChar}, x::Missing) = missing

function float(A::AbstractArray{Union{T, Missing}}) where {T}
    U = typeof(float(zero(T)))
    convert(AbstractArray{Union{U, Missing}}, A)
end
float(A::AbstractArray{Missing}) = A

"""
    skipmissing(itr)

Return an iterator over the elements in `itr` skipping [`missing`](@ref) values.
The returned object can be indexed using indices of `itr` if the latter is indexable.
Indices corresponding to missing values are not valid: they are skipped by [`keys`](@ref)
and [`eachindex`](@ref), and a `MissingException` is thrown when trying to use them.

Use [`collect`](@ref) to obtain an `Array` containing the non-`missing` values in
`itr`. Note that even if `itr` is a multidimensional array, the result will always
be a `Vector` since it is not possible to remove missings while preserving dimensions
of the input.

See also [`coalesce`](@ref), [`ismissing`](@ref), [`something`](@ref).

# Examples
```jldoctest
julia> x = skipmissing([1, missing, 2])
skipmissing(Union{Missing, Int64}[1, missing, 2])

julia> sum(x)
3

julia> x[1]
1

julia> x[2]
ERROR: MissingException: the value at index (2,) is missing
[...]

julia> argmax(x)
3

julia> collect(keys(x))
2-element Vector{Int64}:
 1
 3

julia> collect(skipmissing([1, missing, 2]))
2-element Vector{Int64}:
 1
 2

julia> collect(skipmissing([1 missing; 2 missing]))
2-element Vector{Int64}:
 1
 2
```
"""
skipmissing(itr) = SkipMissing(itr)

struct SkipMissing{T}
    x::T
end
IteratorSize(::Type{<:SkipMissing}) = SizeUnknown()
IteratorEltype(::Type{SkipMissing{T}}) where {T} = IteratorEltype(T)
eltype(::Type{SkipMissing{T}}) where {T} = nonmissingtype(eltype(T))

function iterate(itr::SkipMissing, state...)
    y = iterate(itr.x, state...)
    y === nothing && return nothing
    item, state = y
    while item === missing
        y = iterate(itr.x, state)
        y === nothing && return nothing
        item, state = y
    end
    item, state
end

IndexStyle(::Type{<:SkipMissing{T}}) where {T} = IndexStyle(T)
eachindex(itr::SkipMissing) =
    Iterators.filter(i -> @inbounds(itr.x[i]) !== missing, eachindex(itr.x))
keys(itr::SkipMissing) =
    Iterators.filter(i -> @inbounds(itr.x[i]) !== missing, keys(itr.x))
@propagate_inbounds function getindex(itr::SkipMissing, I...)
    v = itr.x[I...]
    v === missing && throw(MissingException(LazyString("the value at index ", I, " is missing")))
    v
end

function show(io::IO, s::SkipMissing)
    print(io, "skipmissing(")
    show(io, s.x)
    print(io, ')')
end

# Optimized mapreduce implementation
# The generic method is faster when !(eltype(A) >: Missing) since it does not need
# additional loops to identify the two first non-missing values of each block
mapreduce(f, op, itr::SkipMissing{<:AbstractArray}) =
    _mapreduce(f, op, IndexStyle(itr.x), eltype(itr.x) >: Missing ? itr : itr.x)

function _mapreduce(f, op, ::IndexLinear, itr::SkipMissing{<:AbstractArray})
    A = itr.x
    ai = missing
    inds = LinearIndices(A)
    i = first(inds)
    ilast = last(inds)
    for outer i in i:ilast
        @inbounds ai = A[i]
        ai !== missing && break
    end
    ai === missing && return mapreduce_empty(f, op, eltype(itr))
    a1::eltype(itr) = ai
    i == typemax(typeof(i)) && return mapreduce_first(f, op, a1)
    i += 1
    ai = missing
    for outer i in i:ilast
        @inbounds ai = A[i]
        ai !== missing && break
    end
    ai === missing && return mapreduce_first(f, op, a1)
    # We know A contains at least two non-missing entries: the result cannot be nothing
    something(mapreduce_impl(f, op, itr, first(inds), last(inds)))
end

_mapreduce(f, op, ::IndexCartesian, itr::SkipMissing) = mapfoldl(f, op, itr)

mapreduce_impl(f, op, A::SkipMissing, ifirst::Integer, ilast::Integer) =
    mapreduce_impl(f, op, A, ifirst, ilast, pairwise_blocksize(f, op))

# Returns nothing when the input contains only missing values, and Some(x) otherwise
@noinline function mapreduce_impl(f, op, itr::SkipMissing{<:AbstractArray},
                                  ifirst::Integer, ilast::Integer, blksize::Int)
    A = itr.x
    if ifirst > ilast
        return nothing
    elseif ifirst == ilast
        @inbounds a1 = A[ifirst]
        if a1 === missing
            return nothing
        else
            return Some(mapreduce_first(f, op, a1))
        end
    elseif ilast - ifirst < blksize
        # sequential portion
        ai = missing
        i = ifirst
        for outer i in i:ilast
            @inbounds ai = A[i]
            ai !== missing && break
        end
        ai === missing && return nothing
        a1 = ai::eltype(itr)
        i == typemax(typeof(i)) && return Some(mapreduce_first(f, op, a1))
        i += 1
        ai = missing
        for outer i in i:ilast
            @inbounds ai = A[i]
            ai !== missing && break
        end
        ai === missing && return Some(mapreduce_first(f, op, a1))
        a2 = ai::eltype(itr)
        i == typemax(typeof(i)) && return Some(op(f(a1), f(a2)))
        i += 1
        v = op(f(a1), f(a2))
        @simd for i = i:ilast
            @inbounds ai = A[i]
            if ai !== missing
                v = op(v, f(ai))
            end
        end
        return Some(v)
    else
        # pairwise portion
        imid = ifirst + (ilast - ifirst) >> 1
        v1 = mapreduce_impl(f, op, itr, ifirst, imid, blksize)
        v2 = mapreduce_impl(f, op, itr, imid+1, ilast, blksize)
        if v1 === nothing && v2 === nothing
            return nothing
        elseif v1 === nothing
            return v2
        elseif v2 === nothing
            return v1
        else
            return Some(op(something(v1), something(v2)))
        end
    end
end

"""
    filter(f, itr::SkipMissing{<:AbstractArray})

Return a vector similar to the array wrapped by the given `SkipMissing` iterator
but with all missing elements and those for which `f` returns `false` removed.

!!! compat "Julia 1.2"
    This method requires Julia 1.2 or later.

# Examples
```jldoctest
julia> x = [1 2; missing 4]
2×2 Matrix{Union{Missing, Int64}}:
 1         2
  missing  4

julia> filter(isodd, skipmissing(x))
1-element Vector{Int64}:
 1
```
"""
function filter(f, itr::SkipMissing{<:AbstractArray})
    y = similar(itr.x, eltype(itr), 0)
    for xi in itr.x
        if xi !== missing && f(xi)
            push!(y, xi)
        end
    end
    y
end

"""
    coalesce(x...)

Return the first value in the arguments which is not equal to [`missing`](@ref),
if any. Otherwise return `missing`.

See also [`skipmissing`](@ref), [`something`](@ref), [`@coalesce`](@ref).

# Examples

```jldoctest
julia> coalesce(missing, 1)
1

julia> coalesce(1, missing)
1

julia> coalesce(nothing, 1)  # returns `nothing`

julia> coalesce(missing, missing)
missing
```
"""
function coalesce end

coalesce() = missing
coalesce(x::Missing, y...) = coalesce(y...)
coalesce(x::Any, y...) = x


"""
    @coalesce(x...)

Short-circuiting version of [`coalesce`](@ref).

# Examples
```jldoctest
julia> f(x) = (println("f(\$x)"); missing);

julia> a = 1;

julia> a = @coalesce a f(2) f(3) error("`a` is still missing")
1

julia> b = missing;

julia> b = @coalesce b f(2) f(3) error("`b` is still missing")
f(2)
f(3)
ERROR: `b` is still missing
[...]
```

!!! compat "Julia 1.7"
    This macro is available as of Julia 1.7.
"""
macro coalesce(args...)
    expr = :(missing)
    for arg in reverse(args)
        expr = :((val = $arg) !== missing ? val : $expr)
    end
    return esc(:(let val; $expr; end))
end
N   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/version.jl*-      # This file is a part of Julia. License is MIT: https://julialang.org/license

## semantic version numbers (https://semver.org/)

const VerTuple = Tuple{Vararg{Union{UInt64,String}}}

const VInt = UInt32
"""
    VersionNumber

Version number type which follows the specifications of
[semantic versioning (semver)](https://semver.org/), composed of major, minor
and patch numeric values, followed by pre-release and build
alpha-numeric annotations.

`VersionNumber` objects can be compared with all of the standard comparison
operators (`==`, `<`, `<=`, etc.), with the result following semver rules.

See also [`@v_str`](@ref) to efficiently construct `VersionNumber` objects
from semver-format literal strings, [`VERSION`](@ref) for the `VersionNumber`
of Julia itself, and [Version Number Literals](@ref man-version-number-literals)
in the manual.

# Examples
```jldoctest
julia> a = VersionNumber(1, 2, 3)
v"1.2.3"

julia> a >= v"1.2"
true

julia> b = VersionNumber("2.0.1-rc1")
v"2.0.1-rc1"

julia> b >= v"2.0.1"
false
```
"""
struct VersionNumber
    major::VInt
    minor::VInt
    patch::VInt
    prerelease::VerTuple
    build::VerTuple

    function VersionNumber(major::VInt, minor::VInt, patch::VInt,
            pre::VerTuple,
            bld::VerTuple)
        major >= 0 || throw(ArgumentError("invalid negative major version: $major"))
        minor >= 0 || throw(ArgumentError("invalid negative minor version: $minor"))
        patch >= 0 || throw(ArgumentError("invalid negative patch version: $patch"))
        for ident in pre
            if ident isa Integer
                ident >= 0 || throw(ArgumentError("invalid negative pre-release identifier: $ident"))
            else
                if !occursin(r"^(?:|[0-9a-z-]*[a-z-][0-9a-z-]*)$"i, ident) ||
                    isempty(ident) && !(length(pre)==1 && isempty(bld))
                    throw(ArgumentError("invalid pre-release identifier: $(repr(ident))"))
                end
            end
        end
        for ident in bld
            if ident isa Integer
                ident >= 0 || throw(ArgumentError("invalid negative build identifier: $ident"))
            else
                if !occursin(r"^(?:|[0-9a-z-]*[a-z-][0-9a-z-]*)$"i, ident) ||
                    isempty(ident) && length(bld)!=1
                    throw(ArgumentError("invalid build identifier: $(repr(ident))"))
                end
            end
        end
        new(major, minor, patch, pre, bld)
    end
end
VersionNumber(major::Integer, minor::Integer = 0, patch::Integer = 0,
        pre::Tuple{Vararg{Union{Integer,AbstractString}}} = (),
        bld::Tuple{Vararg{Union{Integer,AbstractString}}} = ()) =
    VersionNumber(VInt(major), VInt(minor), VInt(patch),
        map(x->x isa Integer ? UInt64(x) : String(x), pre),
        map(x->x isa Integer ? UInt64(x) : String(x), bld))

VersionNumber(v::Tuple) = VersionNumber(v...)
VersionNumber(v::VersionNumber) = v

function print(io::IO, v::VersionNumber)
    v == typemax(VersionNumber) && return print(io, "∞")
    print(io, v.major)
    print(io, '.')
    print(io, v.minor)
    print(io, '.')
    print(io, v.patch)
    if !isempty(v.prerelease)
        print(io, '-')
        join(io, v.prerelease,'.')
    end
    if !isempty(v.build)
        print(io, '+')
        join(io, v.build,'.')
    end
end
show(io::IO, v::VersionNumber) = print(io, "v\"", v, "\"")

Broadcast.broadcastable(v::VersionNumber) = Ref(v)

const VERSION_REGEX = r"^
    v?                                      # prefix        (optional)
    (\d+)                                   # major         (required)
    (?:\.(\d+))?                            # minor         (optional)
    (?:\.(\d+))?                            # patch         (optional)
    (?:(-)|                                 # pre-release   (optional)
    ([a-z][0-9a-z-]*(?:\.[0-9a-z-]+)*|-(?:[0-9a-z-]+\.)*[0-9a-z-]+)?
    (?:(\+)|
    (?:\+((?:[0-9a-z-]+\.)*[0-9a-z-]+))?    # build         (optional)
    ))
$"ix

function split_idents(s::AbstractString)
    idents = eachsplit(s, '.')
    pidents = Union{UInt64,String}[occursin(r"^\d+$", ident) ? parse(UInt64, ident) : String(ident) for ident in idents]
    return tuple(pidents...)::VerTuple
end

function tryparse(::Type{VersionNumber}, v::AbstractString)
    v == "∞" && return typemax(VersionNumber)
    m = match(VERSION_REGEX, String(v)::String)
    m === nothing && return nothing
    major, minor, patch, minus, prerl, plus, build = m.captures
    major = parse(VInt, major::AbstractString)
    minor = minor !== nothing ? parse(VInt, minor) : VInt(0)
    patch = patch !== nothing ? parse(VInt, patch) : VInt(0)
    if prerl !== nothing && !isempty(prerl) && prerl[1] == '-'
        prerl = prerl[2:end] # strip leading '-'
    end
    prerl = prerl !== nothing ? split_idents(prerl) : minus !== nothing ? ("",) : ()
    build = build !== nothing ? split_idents(build) : plus  !== nothing ? ("",) : ()
    return VersionNumber(major, minor, patch, prerl::VerTuple, build::VerTuple)
end

function parse(::Type{VersionNumber}, v::AbstractString)
    ver = tryparse(VersionNumber, v)
    ver === nothing && throw(ArgumentError("invalid version string: $v"))
    return ver
end

VersionNumber(v::AbstractString) = parse(VersionNumber, v)

"""
    @v_str

String macro used to parse a string to a [`VersionNumber`](@ref).

# Examples
```jldoctest
julia> v"1.2.3"
v"1.2.3"

julia> v"2.0.1-rc1"
v"2.0.1-rc1"
```
"""
macro v_str(v); VersionNumber(v); end

function typemax(::Type{VersionNumber})
    ∞ = typemax(VInt)
    VersionNumber(∞, ∞, ∞, (), ("",))
end

typemin(::Type{VersionNumber}) = v"0-"

ident_cmp(a::Integer, b::Integer) = cmp(a, b)
ident_cmp(a::Integer, b::String ) = isempty(b) ? +1 : -1
ident_cmp(a::String,  b::Integer) = isempty(a) ? -1 : +1
ident_cmp(a::String,  b::String ) = cmp(a, b)

function ident_cmp(A::VerTuple, B::VerTuple)
    for (a, b) in Iterators.Zip{Tuple{VerTuple,VerTuple}}((A, B))
        c = ident_cmp(a, b)
        (c != 0) && return c
    end
    length(A) < length(B) ? -1 :
    length(B) < length(A) ? +1 : 0
end

function ==(a::VersionNumber, b::VersionNumber)
    (a.major != b.major) && return false
    (a.minor != b.minor) && return false
    (a.patch != b.patch) && return false
    (ident_cmp(a.prerelease, b.prerelease) != 0) && return false
    (ident_cmp(a.build, b.build) != 0) && return false
    return true
end

issupbuild(v::VersionNumber) = length(v.build)==1 && isempty(v.build[1])

function isless(a::VersionNumber, b::VersionNumber)
    (a.major < b.major) && return true
    (a.major > b.major) && return false
    (a.minor < b.minor) && return true
    (a.minor > b.minor) && return false
    (a.patch < b.patch) && return true
    (a.patch > b.patch) && return false
    (!isempty(a.prerelease) && isempty(b.prerelease)) && return true
    (isempty(a.prerelease) && !isempty(b.prerelease)) && return false
    c = ident_cmp(a.prerelease,b.prerelease)
    (c < 0) && return true
    (c > 0) && return false
    (!issupbuild(a) && issupbuild(b)) && return true
    (issupbuild(a) && !issupbuild(b)) && return false
    c = ident_cmp(a.build,b.build)
    (c < 0) && return true
    return false
end

function hash(v::VersionNumber, h::UInt)
    h += 0x8ff4ffdb75f9fede % UInt
    h = hash(v.major, h)
    h = hash(v.minor, h)
    h = hash(v.patch, h)
    h = hash(v.prerelease, ~h)
    h = hash(v.build, ~h)
end

lowerbound(v::VersionNumber) = VersionNumber(v.major, v.minor, v.patch, ("",), ())
upperbound(v::VersionNumber) = VersionNumber(v.major, v.minor, v.patch, (), ("",))

thispatch(v::VersionNumber) = VersionNumber(v.major, v.minor, v.patch)
thisminor(v::VersionNumber) = VersionNumber(v.major, v.minor, 0)
thismajor(v::VersionNumber) = VersionNumber(v.major, 0, 0)

nextpatch(v::VersionNumber) = v < thispatch(v) ? thispatch(v) : VersionNumber(v.major, v.minor, v.patch+1)
nextminor(v::VersionNumber) = v < thisminor(v) ? thisminor(v) : VersionNumber(v.major, v.minor+1, 0)
nextmajor(v::VersionNumber) = v < thismajor(v) ? thismajor(v) : VersionNumber(v.major+1, 0, 0)

## julia version info

"""
    VERSION

A [`VersionNumber`](@ref) object describing which version of Julia is in use. See also
[Version Number Literals](@ref man-version-number-literals).
"""
const VERSION = try
    ver = VersionNumber(VERSION_STRING)
    if !isempty(ver.prerelease) && !GIT_VERSION_INFO.tagged_commit
        if GIT_VERSION_INFO.build_number >= 0
            ver = VersionNumber(ver.major, ver.minor, ver.patch, (ver.prerelease..., GIT_VERSION_INFO.build_number), ver.build)
        else
            println("WARNING: no build number found for pre-release version")
            ver = VersionNumber(ver.major, ver.minor, ver.patch, (ver.prerelease..., "unknown"), ver.build)
        end
    elseif GIT_VERSION_INFO.build_number > 0
        println("WARNING: ignoring non-zero build number for VERSION")
    end
    ver
catch e
    println("while creating Base.VERSION, ignoring error $e")
    VersionNumber(0)
end

const libllvm_version = if endswith(libllvm_version_string, "jl")
    # strip the "jl" SONAME suffix (JuliaLang/julia#33058)
    # (LLVM does never report a prerelease version anyway)
    VersionNumber(libllvm_version_string[1:end-2])
else
    VersionNumber(libllvm_version_string)
end

libllvm_path() = ccall(:jl_get_libllvm, Any, ())

function banner(io::IO = stdout)
    if GIT_VERSION_INFO.tagged_commit
        commit_string = TAGGED_RELEASE_BANNER
    elseif isempty(GIT_VERSION_INFO.commit)
        commit_string = ""
    else
        days = Int(floor((ccall(:jl_clock_now, Float64, ()) - GIT_VERSION_INFO.fork_master_timestamp) / (60 * 60 * 24)))
        days = max(0, days)
        unit = days == 1 ? "day" : "days"
        distance = GIT_VERSION_INFO.fork_master_distance
        commit = GIT_VERSION_INFO.commit_short

        if distance == 0
            commit_string = "Commit $(commit) ($(days) $(unit) old master)"
        else
            branch = GIT_VERSION_INFO.branch
            commit_string = "$(branch)/$(commit) (fork: $(distance) commits, $(days) $(unit))"
        end
    end

    commit_date = isempty(Base.GIT_VERSION_INFO.date_string) ? "" : " ($(split(Base.GIT_VERSION_INFO.date_string)[1]))"

    if get(io, :color, false)::Bool
        c = text_colors
        tx = c[:normal] # text
        jl = c[:normal] # julia
        d1 = c[:bold] * c[:blue]    # first dot
        d2 = c[:bold] * c[:red]     # second dot
        d3 = c[:bold] * c[:green]   # third dot
        d4 = c[:bold] * c[:magenta] # fourth dot

        print(io,"""               $(d3)_$(tx)
           $(d1)_$(tx)       $(jl)_$(tx) $(d2)_$(d3)(_)$(d4)_$(tx)     |  Documentation: https://docs.julialang.org
          $(d1)(_)$(jl)     | $(d2)(_)$(tx) $(d4)(_)$(tx)    |
           $(jl)_ _   _| |_  __ _$(tx)   |  Type \"?\" for help, \"]?\" for Pkg help.
          $(jl)| | | | | | |/ _` |$(tx)  |
          $(jl)| | |_| | | | (_| |$(tx)  |  Version $(VERSION)$(commit_date)
         $(jl)_/ |\\__'_|_|_|\\__'_|$(tx)  |  $(commit_string)
        $(jl)|__/$(tx)                   |

        """)
    else
        print(io,"""
                       _
           _       _ _(_)_     |  Documentation: https://docs.julialang.org
          (_)     | (_) (_)    |
           _ _   _| |_  __ _   |  Type \"?\" for help, \"]?\" for Pkg help.
          | | | | | | |/ _` |  |
          | | |_| | | | (_| |  |  Version $(VERSION)$(commit_date)
         _/ |\\__'_|_|_|\\__'_|  |  $(commit_string)
        |__/                   |

        """)
    end
end
N   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/sysinfo.jlMD      # This file is a part of Julia. License is MIT: https://julialang.org/license

module Sys
@doc """
Provide methods for retrieving information about hardware and the operating system.
""" Sys

export BINDIR,
       STDLIB,
       CPU_THREADS,
       CPU_NAME,
       WORD_SIZE,
       ARCH,
       MACHINE,
       KERNEL,
       JIT,
       cpu_info,
       cpu_summary,
       uptime,
       loadavg,
       free_memory,
       total_memory,
       free_physical_memory,
       total_physical_memory,
       isapple,
       isbsd,
       isdragonfly,
       isfreebsd,
       islinux,
       isnetbsd,
       isopenbsd,
       isunix,
       iswindows,
       isjsvm,
       isexecutable,
       which

import ..Base: show

"""
    Sys.BINDIR::String

A string containing the full path to the directory containing the `julia` executable.
"""
global BINDIR::String = ccall(:jl_get_julia_bindir, Any, ())::String

"""
    Sys.STDLIB::String

A string containing the full path to the directory containing the `stdlib` packages.
"""
global STDLIB::String = "$BINDIR/../share/julia/stdlib/v$(VERSION.major).$(VERSION.minor)" # for bootstrap
# In case STDLIB change after julia is built, the variable below can be used
# to update cached method locations to updated ones.
const BUILD_STDLIB_PATH = STDLIB

# helper to avoid triggering precompile warnings

"""
    Sys.CPU_THREADS::Int

The number of logical CPU cores available in the system, i.e. the number of threads
that the CPU can run concurrently. Note that this is not necessarily the number of
CPU cores, for example, in the presence of
[hyper-threading](https://en.wikipedia.org/wiki/Hyper-threading).

See Hwloc.jl or CpuId.jl for extended information, including number of physical cores.
"""
global CPU_THREADS::Int = 1 # for bootstrap, changed on startup

"""
    Sys.ARCH::Symbol

A symbol representing the architecture of the build configuration.
"""
const ARCH = ccall(:jl_get_ARCH, Any, ())::Symbol


"""
    Sys.KERNEL::Symbol

A symbol representing the name of the operating system, as returned by `uname` of the build configuration.
"""
const KERNEL = ccall(:jl_get_UNAME, Any, ())::Symbol

"""
    Sys.MACHINE::String

A string containing the build triple.
"""
const MACHINE = Base.MACHINE::String

"""
    Sys.WORD_SIZE::Int

Standard word size on the current machine, in bits.
"""
const WORD_SIZE = Core.sizeof(Int) * 8

global SC_CLK_TCK::Clong, CPU_NAME::String, JIT::String

function __init__()
    env_threads = nothing
    if haskey(ENV, "JULIA_CPU_THREADS")
        env_threads = ENV["JULIA_CPU_THREADS"]
    end
    global CPU_THREADS = if env_threads !== nothing
        env_threads = tryparse(Int, env_threads)
        if !(env_threads isa Int && env_threads > 0)
            env_threads = Int(ccall(:jl_cpu_threads, Int32, ()))
            Core.print(Core.stderr, "WARNING: couldn't parse `JULIA_CPU_THREADS` environment variable. Defaulting Sys.CPU_THREADS to $env_threads.\n")
        end
        env_threads
    else
        Int(ccall(:jl_cpu_threads, Int32, ()))
    end
    global SC_CLK_TCK = ccall(:jl_SC_CLK_TCK, Clong, ())
    global CPU_NAME = ccall(:jl_get_cpu_name, Ref{String}, ())
    global JIT = ccall(:jl_get_JIT, Ref{String}, ())
    __init_build()
    nothing
end
# Populate the paths needed by sysimg compilation, e.g. `generate_precompile.jl`,
# without pulling in anything unnecessary like `CPU_NAME`
function __init_build()
    global BINDIR = ccall(:jl_get_julia_bindir, Any, ())::String
    vers = "v$(VERSION.major).$(VERSION.minor)"
    global STDLIB = abspath(BINDIR, "..", "share", "julia", "stdlib", vers)
    nothing
end

mutable struct UV_cpu_info_t
    model::Ptr{UInt8}
    speed::Int32
    cpu_times!user::UInt64
    cpu_times!nice::UInt64
    cpu_times!sys::UInt64
    cpu_times!idle::UInt64
    cpu_times!irq::UInt64
end
mutable struct CPUinfo
    model::String
    speed::Int32
    cpu_times!user::UInt64
    cpu_times!nice::UInt64
    cpu_times!sys::UInt64
    cpu_times!idle::UInt64
    cpu_times!irq::UInt64
    CPUinfo(model,speed,u,n,s,id,ir)=new(model,speed,u,n,s,id,ir)
end
CPUinfo(info::UV_cpu_info_t) = CPUinfo(unsafe_string(info.model), info.speed,
    info.cpu_times!user, info.cpu_times!nice, info.cpu_times!sys,
    info.cpu_times!idle, info.cpu_times!irq)

function _show_cpuinfo(io::IO, info::Sys.CPUinfo, header::Bool=true, prefix::AbstractString="    ")
    tck = SC_CLK_TCK
    if header
        println(io, info.model, ": ")
        print(io, " "^length(prefix))
        println(io, "    ", lpad("speed", 5), "    ", lpad("user", 9), "    ", lpad("nice", 9), "    ",
                lpad("sys", 9), "    ", lpad("idle", 9), "    ", lpad("irq", 9))
    end
    print(io, prefix)
    unit = tck > 0 ? " s  " : "    "
    tc = max(tck, 1)
    d(i, unit=unit) = lpad(string(round(Int64,i)), 9) * unit
    print(io,
          lpad(string(info.speed), 5), " MHz  ",
          d(info.cpu_times!user / tc), d(info.cpu_times!nice / tc), d(info.cpu_times!sys / tc),
          d(info.cpu_times!idle / tc), d(info.cpu_times!irq / tc, tck > 0 ? " s" : "  "))
    if tck <= 0
        print(io, "ticks")
    end
end

show(io::IO, info::CPUinfo) = _show_cpuinfo(io, info, true, "    ")

function _cpu_summary(io::IO, cpu::AbstractVector{CPUinfo}, i, j)
    if j-i < 9
        header = true
        for x = i:j
            header || println(io)
            _show_cpuinfo(io, cpu[x], header, "#$(x-i+1) ")
            header = false
        end
    else
        summary = CPUinfo(cpu[i].model,0,0,0,0,0,0)
        count = j - i + 1
        for x = i:j
            summary.speed += cpu[i].speed
            summary.cpu_times!user += cpu[x].cpu_times!user
            summary.cpu_times!nice += cpu[x].cpu_times!nice
            summary.cpu_times!sys += cpu[x].cpu_times!sys
            summary.cpu_times!idle += cpu[x].cpu_times!idle
            summary.cpu_times!irq += cpu[x].cpu_times!irq
        end
        summary.speed = div(summary.speed,count)
        _show_cpuinfo(io, summary, true, "#1-$(count) ")
    end
    println(io)
end

function cpu_summary(io::IO=stdout, cpu::AbstractVector{CPUinfo} = cpu_info())
    model = cpu[1].model
    first = 1
    for i = 2:length(cpu)
        if model != cpu[i].model
            _cpu_summary(io, cpu, first, i-1)
            first = i
        end
    end
    _cpu_summary(io, cpu, first, length(cpu))
end

function cpu_info()
    UVcpus = Ref{Ptr{UV_cpu_info_t}}()
    count = Ref{Int32}()
    err = ccall(:uv_cpu_info, Int32, (Ptr{Ptr{UV_cpu_info_t}}, Ptr{Int32}), UVcpus, count)
    Base.uv_error("uv_cpu_info", err)
    cpus = Vector{CPUinfo}(undef, count[])
    for i = 1:length(cpus)
        cpus[i] = CPUinfo(unsafe_load(UVcpus[], i))
    end
    ccall(:uv_free_cpu_info, Cvoid, (Ptr{UV_cpu_info_t}, Int32), UVcpus[], count[])
    return cpus
end

"""
    Sys.uptime()

Gets the current system uptime in seconds.
"""
function uptime()
    uptime_ = Ref{Float64}()
    err = ccall(:uv_uptime, Int32, (Ptr{Float64},), uptime_)
    Base.uv_error("uv_uptime", err)
    return uptime_[]
end

"""
    Sys.loadavg()

Get the load average. See: https://en.wikipedia.org/wiki/Load_(computing).
"""
function loadavg()
    loadavg_ = Vector{Float64}(undef, 3)
    ccall(:uv_loadavg, Cvoid, (Ptr{Float64},), loadavg_)
    return loadavg_
end

"""
    Sys.free_physical_memory()

Get the free memory of the system in bytes. The entire amount may not be available to the
current process; use `Sys.free_memory()` for the actually available amount.
"""
free_physical_memory() = ccall(:uv_get_free_memory, UInt64, ())

"""
    Sys.total_physical_memory()

Get the total memory in RAM (including that which is currently used) in bytes. The entire
amount may not be available to the current process; see `Sys.total_memory()`.
"""
total_physical_memory() = ccall(:uv_get_total_memory, UInt64, ())

"""
    Sys.free_memory()

Get the total free memory in RAM in bytes.
"""
free_memory() = ccall(:uv_get_available_memory, UInt64, ())

"""
    Sys.total_memory()

Get the total memory in RAM (including that which is currently used) in bytes.
This amount may be constrained, e.g., by Linux control groups. For the unconstrained
amount, see `Sys.total_physical_memory()`.
"""
function total_memory()
    constrained = ccall(:uv_get_constrained_memory, UInt64, ())
    physical = total_physical_memory()
    if 0 < constrained <= physical
        return constrained
    else
        return physical
    end
end

"""
    Sys.get_process_title()

Get the process title. On some systems, will always return an empty string.
"""
function get_process_title()
    buf = Vector{UInt8}(undef, 512)
    err = ccall(:uv_get_process_title, Cint, (Ptr{UInt8}, Cint), buf, 512)
    Base.uv_error("get_process_title", err)
    return unsafe_string(pointer(buf))
end

"""
    Sys.set_process_title(title::AbstractString)

Set the process title. No-op on some operating systems.
"""
function set_process_title(title::AbstractString)
    err = ccall(:uv_set_process_title, Cint, (Cstring,), title)
    Base.uv_error("set_process_title", err)
end

"""
    Sys.maxrss()

Get the maximum resident set size utilized in bytes.
See also:
    - man page of `getrusage`(2) on Linux and FreeBSD.
    - Windows API `GetProcessMemoryInfo`.
"""
maxrss() = ccall(:jl_maxrss, Csize_t, ())

"""
    Sys.isunix([os])

Predicate for testing if the OS provides a Unix-like interface.
See documentation in [Handling Operating System Variation](@ref).
"""
function isunix(os::Symbol)
    if iswindows(os)
        return false
    elseif islinux(os) || isbsd(os)
        return true
    elseif os === :Emscripten
        # Emscripten implements the POSIX ABI and provides traditional
        # Unix-style operating system functions such as file system support.
        # Therefore, we consider it a unix, even though this need not be
        # generally true for a jsvm embedding.
        return true
    else
        throw(ArgumentError("unknown operating system \"$os\""))
    end
end

"""
    Sys.islinux([os])

Predicate for testing if the OS is a derivative of Linux.
See documentation in [Handling Operating System Variation](@ref).
"""
islinux(os::Symbol) = (os === :Linux)

"""
    Sys.isbsd([os])

Predicate for testing if the OS is a derivative of BSD.
See documentation in [Handling Operating System Variation](@ref).

!!! note
    The Darwin kernel descends from BSD, which means that `Sys.isbsd()` is
    `true` on macOS systems. To exclude macOS from a predicate, use
    `Sys.isbsd() && !Sys.isapple()`.
"""
isbsd(os::Symbol) = (isfreebsd(os) || isopenbsd(os) || isnetbsd(os) || isdragonfly(os) || isapple(os))

"""
    Sys.isfreebsd([os])

Predicate for testing if the OS is a derivative of FreeBSD.
See documentation in [Handling Operating System Variation](@ref).

!!! note
    Not to be confused with `Sys.isbsd()`, which is `true` on FreeBSD but also on
    other BSD-based systems. `Sys.isfreebsd()` refers only to FreeBSD.
!!! compat "Julia 1.1"
    This function requires at least Julia 1.1.
"""
isfreebsd(os::Symbol) = (os === :FreeBSD)

"""
    Sys.isopenbsd([os])

Predicate for testing if the OS is a derivative of OpenBSD.
See documentation in [Handling Operating System Variation](@ref).

!!! note
    Not to be confused with `Sys.isbsd()`, which is `true` on OpenBSD but also on
    other BSD-based systems. `Sys.isopenbsd()` refers only to OpenBSD.
!!! compat "Julia 1.1"
    This function requires at least Julia 1.1.
"""
isopenbsd(os::Symbol) = (os === :OpenBSD)

"""
    Sys.isnetbsd([os])

Predicate for testing if the OS is a derivative of NetBSD.
See documentation in [Handling Operating System Variation](@ref).

!!! note
    Not to be confused with `Sys.isbsd()`, which is `true` on NetBSD but also on
    other BSD-based systems. `Sys.isnetbsd()` refers only to NetBSD.
!!! compat "Julia 1.1"
    This function requires at least Julia 1.1.
"""
isnetbsd(os::Symbol) = (os === :NetBSD)

"""
    Sys.isdragonfly([os])

Predicate for testing if the OS is a derivative of DragonFly BSD.
See documentation in [Handling Operating System Variation](@ref).

!!! note
    Not to be confused with `Sys.isbsd()`, which is `true` on DragonFly but also on
    other BSD-based systems. `Sys.isdragonfly()` refers only to DragonFly.
!!! compat "Julia 1.1"
    This function requires at least Julia 1.1.
"""
isdragonfly(os::Symbol) = (os === :DragonFly)

"""
    Sys.iswindows([os])

Predicate for testing if the OS is a derivative of Microsoft Windows NT.
See documentation in [Handling Operating System Variation](@ref).
"""
iswindows(os::Symbol) = (os === :Windows || os === :NT)

"""
    Sys.isapple([os])

Predicate for testing if the OS is a derivative of Apple Macintosh OS X or Darwin.
See documentation in [Handling Operating System Variation](@ref).
"""
isapple(os::Symbol) = (os === :Apple || os === :Darwin)

"""
    Sys.isjsvm([os])

Predicate for testing if Julia is running in a JavaScript VM (JSVM),
including e.g. a WebAssembly JavaScript embedding in a web browser.

!!! compat "Julia 1.2"
    This function requires at least Julia 1.2.
"""
isjsvm(os::Symbol) = (os === :Emscripten)

for f in (:isunix, :islinux, :isbsd, :isapple, :iswindows, :isfreebsd, :isopenbsd, :isnetbsd, :isdragonfly, :isjsvm)
    @eval $f() = $(getfield(@__MODULE__, f)(KERNEL))
end

if iswindows()
    function windows_version()
        verinfo = ccall(:GetVersion, UInt32, ())
        VersionNumber(verinfo & 0xFF, (verinfo >> 8) & 0xFF, verinfo >> 16)
    end
else
    windows_version() = v"0.0"
end

"""
    Sys.windows_version()

Return the version number for the Windows NT Kernel as a `VersionNumber`,
i.e. `v"major.minor.build"`, or `v"0.0.0"` if this is not running on Windows.
"""
windows_version

const WINDOWS_VISTA_VER = v"6.0"

"""
    Sys.isexecutable(path::String)

Return `true` if the given `path` has executable permissions.

!!! note
    Prior to Julia 1.6, this did not correctly interrogate filesystem
    ACLs on Windows, therefore it would return `true` for any
    file.  From Julia 1.6 on, it correctly determines whether the
    file is marked as executable or not.
"""
function isexecutable(path::String)
    # We use `access()` and `X_OK` to determine if a given path is
    # executable by the current user.  `X_OK` comes from `unistd.h`.
    X_OK = 0x01
    return ccall(:jl_fs_access, Cint, (Ptr{UInt8}, Cint), path, X_OK) == 0
end
isexecutable(path::AbstractString) = isexecutable(String(path))

"""
    Sys.which(program_name::String)

Given a program name, search the current `PATH` to find the first binary with
the proper executable permissions that can be run and return an absolute path
to it, or return `nothing` if no such program is available. If a path with
a directory in it is passed in for `program_name`, tests that exact path
for executable permissions only (with `.exe` and `.com` extensions added on
Windows platforms); no searching of `PATH` is performed.
"""
function which(program_name::String)
    if isempty(program_name)
       return nothing
    end
    # Build a list of program names that we're going to try
    program_names = String[]
    base_pname = basename(program_name)
    if iswindows()
        # If the file already has an extension, try that name first
        if !isempty(splitext(base_pname)[2])
            push!(program_names, base_pname)
        end

        # But also try appending .exe and .com`
        for pe in (".exe", ".com")
            push!(program_names, string(base_pname, pe))
        end
    else
        # On non-windows, we just always search for what we've been given
        push!(program_names, base_pname)
    end

    path_dirs = String[]
    program_dirname = dirname(program_name)
    # If we've been given a path that has a directory name in it, then we
    # check to see if that path exists.  Otherwise, we search the PATH.
    if isempty(program_dirname)
        # If we have been given just a program name (not a relative or absolute
        # path) then we should search `PATH` for it here:
        pathsep = iswindows() ? ';' : ':'
        path_dirs = map(abspath, eachsplit(get(ENV, "PATH", ""), pathsep))

        # On windows we always check the current directory as well
        if iswindows()
            pushfirst!(path_dirs, pwd())
        end
    else
        push!(path_dirs, abspath(program_dirname))
    end

    # Here we combine our directories with our program names, searching for the
    # first match among all combinations.
    for path_dir in path_dirs
        for pname in program_names
            program_path = joinpath(path_dir, pname)
            try
                # If we find something that matches our name and we can execute
                if isfile(program_path) && isexecutable(program_path)
                    return program_path
                end
            catch e
                # If we encounter a permission error, we skip this directory
                # and continue to the next directory in the PATH variable.
                if isa(e, Base.IOError) && e.code == Base.UV_EACCES
                    # Permission denied, continue searching
                    continue
                else
                    # Rethrow the exception if it's not a permission error
                    rethrow(e)
                end
            end
        end
    end

    # If we couldn't find anything, don't return anything
    nothing
end
which(program_name::AbstractString) = which(String(program_name))

end # module Sys
K   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/libc.jlW<      # This file is a part of Julia. License is MIT: https://julialang.org/license

module Libc
@doc """
Interface to libc, the C standard library.
""" Libc

import Base: transcode, windowserror, show
# these need to be defined seperately for bootstrapping but belong to Libc
import Base: memcpy, memmove, memset, memcmp
import Core.Intrinsics: bitcast

export FILE, TmStruct, strftime, strptime, getpid, gethostname, free, malloc, memcpy,
    memmove, memset, calloc, realloc, errno, strerror, flush_cstdio, systemsleep, time,
    transcode
if Sys.iswindows()
    export GetLastError, FormatMessage
end

include(string(length(Core.ARGS) >= 2 ? Core.ARGS[2] : "", "errno_h.jl"))  # include($BUILDROOT/base/errno_h.jl)

## RawFD ##

# Wrapper for an OS file descriptor (on both Unix and Windows)
"""
    RawFD

Primitive type which wraps the native OS file descriptor.
`RawFD`s can be passed to methods like [`stat`](@ref) to
discover information about the underlying file, and can
also be used to open streams, with the `RawFD` describing
the OS file backing the stream.
"""
primitive type RawFD 32 end
RawFD(fd::Integer) = bitcast(RawFD, Cint(fd))
RawFD(fd::RawFD) = fd
Base.cconvert(::Type{Cint}, fd::RawFD) = bitcast(Cint, fd)

dup(x::RawFD) = ccall((@static Sys.iswindows() ? :_dup : :dup), RawFD, (RawFD,), x)
dup(src::RawFD, target::RawFD) = systemerror("dup", -1 ==
    ccall((@static Sys.iswindows() ? :_dup2 : :dup2), Int32,
                (RawFD, RawFD), src, target))

show(io::IO, fd::RawFD) = print(io, "RawFD(", bitcast(UInt32, fd), ')')  # avoids invalidation via show_default

# Wrapper for an OS file descriptor (for Windows)
if Sys.iswindows()
    primitive type WindowsRawSocket sizeof(Ptr) * 8 end # On Windows file descriptors are HANDLE's and 64-bit on 64-bit Windows
    WindowsRawSocket(handle::Ptr{Cvoid}) = bitcast(WindowsRawSocket, handle)
    WindowsRawSocket(handle::WindowsRawSocket) = handle

    Base.cconvert(::Type{Ptr{Cvoid}}, fd::WindowsRawSocket) = bitcast(Ptr{Cvoid}, fd)
    _get_osfhandle(fd::RawFD) = ccall(:_get_osfhandle, WindowsRawSocket, (RawFD,), fd)
    _get_osfhandle(fd::WindowsRawSocket) = fd
    function dup(src::WindowsRawSocket)
        new_handle = Ref(WindowsRawSocket(Ptr{Cvoid}(-1)))
        my_process = ccall(:GetCurrentProcess, stdcall, Ptr{Cvoid}, ())
        DUPLICATE_SAME_ACCESS = 0x2
        status = ccall(:DuplicateHandle, stdcall, Int32,
            (Ptr{Cvoid}, WindowsRawSocket, Ptr{Cvoid}, Ptr{WindowsRawSocket}, UInt32, Int32, UInt32),
            my_process, src, my_process, new_handle, 0, false, DUPLICATE_SAME_ACCESS)
        windowserror("dup failed", status == 0)
        return new_handle[]
    end
    function dup(src::WindowsRawSocket, target::RawFD)
        fd = ccall(:_open_osfhandle, RawFD, (WindowsRawSocket, Int32), dup(src), 0)
        dup(fd, target)
        ccall(:_close, Int32, (RawFD,), fd)
        nothing
    end

else
    _get_osfhandle(fd::RawFD) = fd
end

## FILE (not auto-finalized) ##

struct FILE
    ptr::Ptr{Cvoid}
end

modestr(s::IO) = modestr(isreadable(s), iswritable(s))
modestr(r::Bool, w::Bool) = r ? (w ? "r+" : "r") : (w ? "w" : throw(ArgumentError("neither readable nor writable")))

function FILE(fd::RawFD, mode)
    FILEp = ccall((@static Sys.iswindows() ? :_fdopen : :fdopen), Ptr{Cvoid}, (Cint, Cstring), fd, mode)
    systemerror("fdopen", FILEp == C_NULL)
    FILE(FILEp)
end

function FILE(s::IO)
    f = FILE(dup(RawFD(fd(s))),modestr(s))
    seek(f, position(s))
    f
end

Base.unsafe_convert(T::Union{Type{Ptr{Cvoid}},Type{Ptr{FILE}}}, f::FILE) = convert(T, f.ptr)
Base.close(f::FILE) = systemerror("fclose", ccall(:fclose, Cint, (Ptr{Cvoid},), f.ptr) != 0)

function Base.seek(h::FILE, offset::Integer)
    systemerror("fseek", ccall(:fseek, Cint, (Ptr{Cvoid}, Clong, Cint),
                               h.ptr, offset, 0) != 0)
    h
end

Base.position(h::FILE) = ccall(:ftell, Clong, (Ptr{Cvoid},), h.ptr)

# flush C stdio output from external libraries

"""
    flush_cstdio()

Flushes the C `stdout` and `stderr` streams (which may have been written to by external C code).
"""
flush_cstdio() = ccall(:jl_flush_cstdio, Cvoid, ())

## time-related functions ##

# TODO: check for usleep errors?
if Sys.isunix()
    systemsleep(s::Real) = ccall(:usleep, Int32, (UInt32,), round(UInt32, s*1e6))
elseif Sys.iswindows()
    function systemsleep(s::Real)
        ccall(:Sleep, stdcall, Cvoid, (UInt32,), round(UInt32, s * 1e3))
        return Int32(0)
    end
else
    error("systemsleep undefined for this OS")
end
"""
    systemsleep(s::Real)

Suspends execution for `s` seconds.
This function does not yield to Julia's scheduler and therefore blocks
the Julia thread that it is running on for the duration of the sleep time.

See also [`sleep`](@ref).
"""
systemsleep

struct TimeVal
   sec::Int64
   usec::Int64
end

function TimeVal()
    tv = Ref{TimeVal}()
    status = ccall(:jl_gettimeofday, Cint, (Ref{TimeVal},), tv)
    status != 0 && error("unable to determine current time: ", status)
    return tv[]
end

"""
    TmStruct([seconds])

Convert a number of seconds since the epoch to broken-down format, with fields `sec`, `min`,
`hour`, `mday`, `month`, `year`, `wday`, `yday`, and `isdst`.
"""
mutable struct TmStruct
    sec::Int32
    min::Int32
    hour::Int32
    mday::Int32
    month::Int32
    year::Int32
    wday::Int32
    yday::Int32
    isdst::Int32
    # on some platforms the struct is 14 words, even though 9 are specified
    _10::Int32
    _11::Int32
    _12::Int32
    _13::Int32
    _14::Int32

    TmStruct(sec, min, hour, mday, month, year, wday, yday, isdst) =
        new(sec, min, hour, mday, month, year, wday, yday, isdst, 0,0,0,0,0)
    TmStruct() = new(0,0,0,0,0,0,0,0,0,0,0,0,0,0)
    function TmStruct(t::Real)
        t = floor(t)
        tm = TmStruct()
        # TODO: add support for UTC via gmtime_r()
        ccall(:localtime_r, Ptr{TmStruct}, (Ref{Int}, Ref{TmStruct}), t, tm)
        return tm
    end
end

"""
    strftime([format], time)

Convert time, given as a number of seconds since the epoch or a `TmStruct`, to a formatted
string using the given format. Supported formats are the same as those in the standard C
library.
"""
strftime(t) = strftime("%c", t)
strftime(fmt::AbstractString, t::Real) = strftime(fmt, TmStruct(t))
# Use wcsftime instead of strftime to support different locales
function strftime(fmt::AbstractString, tm::TmStruct)
    wctimestr = Vector{Cwchar_t}(undef, 128)
    n = ccall(:wcsftime, Csize_t, (Ptr{Cwchar_t}, Csize_t, Cwstring, Ref{TmStruct}),
              wctimestr, length(wctimestr), fmt, tm)
    n == 0 && return ""
    return transcode(String, resize!(wctimestr, n))
end

"""
    strptime([format], timestr)

Parse a formatted time string into a `TmStruct` giving the seconds, minute, hour, date, etc.
Supported formats are the same as those in the standard C library. On some platforms,
timezones will not be parsed correctly. If the result of this function will be passed to
`time` to convert it to seconds since the epoch, the `isdst` field should be filled in
manually. Setting it to `-1` will tell the C library to use the current system settings to
determine the timezone.
"""
strptime(timestr::AbstractString) = strptime("%c", timestr)
function strptime(fmt::AbstractString, timestr::AbstractString)
    tm = TmStruct()
    r = ccall(:strptime, Cstring, (Cstring, Cstring, Ref{TmStruct}), timestr, fmt, tm)
    # the following would tell mktime() that this is a local time, and that
    # it should try to guess the timezone. not sure if/how this should be
    # exposed in the API.
    # tm.isdst = -1
    if r == C_NULL
        # TODO: better error message
        throw(ArgumentError("invalid arguments"))
    end
    @static if Sys.isapple()
        # if we didn't explicitly parse the weekday or year day, use mktime
        # to fill them in automatically.
        if !occursin(r"([^%]|^)%(a|A|j|w|Ow)"a, fmt)
            ccall(:mktime, Int, (Ref{TmStruct},), tm)
        end
    end
    return tm
end

# system date in seconds

"""
    time(t::TmStruct) -> Float64

Converts a `TmStruct` struct to a number of seconds since the epoch.
"""
time(tm::TmStruct) = Float64(ccall(:mktime, Int, (Ref{TmStruct},), tm))

"""
    time() -> Float64

Get the system time in seconds since the epoch, with fairly high (typically, microsecond) resolution.
"""
time() = ccall(:jl_clock_now, Float64, ())

## process-related functions ##

"""
    getpid() -> Int32

Get Julia's process ID.
"""
getpid() = ccall(:uv_os_getpid, Int32, ())

## network functions ##

"""
    gethostname() -> String

Get the local machine's host name.
"""
function gethostname()
    hn = Vector{UInt8}(undef, 256)
    err = @static if Sys.iswindows()
        ccall(:gethostname, stdcall, Int32, (Ptr{UInt8}, UInt32), hn, length(hn))
    else
        ccall(:gethostname, Int32, (Ptr{UInt8}, UInt), hn, length(hn))
    end
    systemerror("gethostname", err != 0)
    return GC.@preserve hn unsafe_string(pointer(hn))
end

## system error handling ##

"""
    errno([code])

Get the value of the C library's `errno`. If an argument is specified, it is used to set the
value of `errno`.

The value of `errno` is only valid immediately after a `ccall` to a C library routine that
sets it. Specifically, you cannot call `errno` at the next prompt in a REPL, because lots of
code is executed between prompts.
"""
errno() = ccall(:jl_errno, Cint, ())
errno(e::Integer) = ccall(:jl_set_errno, Cvoid, (Cint,), e)

"""
    strerror(n=errno())

Convert a system call error code to a descriptive string
"""
strerror(e::Integer) = unsafe_string(ccall(:strerror, Cstring, (Int32,), e))
strerror() = strerror(errno())

"""
    GetLastError()

Call the Win32 `GetLastError` function [only available on Windows].
"""
function GetLastError end

"""
    FormatMessage(n=GetLastError())

Convert a Win32 system call error code to a descriptive string [only available on Windows].
"""
function FormatMessage end

if Sys.iswindows()
    GetLastError() = ccall(:GetLastError, stdcall, UInt32, ())

    FormatMessage(e) = FormatMessage(UInt32(e))
    function FormatMessage(e::UInt32=GetLastError())
        FORMAT_MESSAGE_ALLOCATE_BUFFER = UInt32(0x100)
        FORMAT_MESSAGE_FROM_SYSTEM = UInt32(0x1000)
        FORMAT_MESSAGE_IGNORE_INSERTS = UInt32(0x200)
        FORMAT_MESSAGE_MAX_WIDTH_MASK = UInt32(0xFF)
        lpMsgBuf = Ref{Ptr{UInt16}}()
        lpMsgBuf[] = 0
        len = ccall(:FormatMessageW, stdcall, UInt32, (UInt32, Ptr{Cvoid}, UInt32, UInt32, Ptr{Ptr{UInt16}}, UInt32, Ptr{Cvoid}),
                    FORMAT_MESSAGE_ALLOCATE_BUFFER | FORMAT_MESSAGE_FROM_SYSTEM | FORMAT_MESSAGE_IGNORE_INSERTS | FORMAT_MESSAGE_MAX_WIDTH_MASK,
                    C_NULL, e, 0, lpMsgBuf, 0, C_NULL)
        p = lpMsgBuf[]
        len == 0 && return ""
        buf = Vector{UInt16}(undef, len)
        GC.@preserve buf unsafe_copyto!(pointer(buf), p, len)
        ccall(:LocalFree, stdcall, Ptr{Cvoid}, (Ptr{Cvoid},), p)
        return transcode(String, buf)
    end
end

## Memory related ##
"""
    free(addr::Ptr)

Call `free` from the C standard library. Only use this on memory obtained from [`malloc`](@ref), not
on pointers retrieved from other C libraries. [`Ptr`](@ref) objects obtained from C libraries should
be freed by the free functions defined in that library, to avoid assertion failures if
multiple `libc` libraries exist on the system.
"""
free(p::Ptr) = ccall(:free, Cvoid, (Ptr{Cvoid},), p)
free(p::Cstring) = free(convert(Ptr{UInt8}, p))
free(p::Cwstring) = free(convert(Ptr{Cwchar_t}, p))

"""
    malloc(size::Integer) -> Ptr{Cvoid}

Call `malloc` from the C standard library.
"""
malloc(size::Integer) = ccall(:malloc, Ptr{Cvoid}, (Csize_t,), size)

"""
    realloc(addr::Ptr, size::Integer) -> Ptr{Cvoid}

Call `realloc` from the C standard library.

See warning in the documentation for [`free`](@ref) regarding only using this on memory originally
obtained from [`malloc`](@ref).
"""
realloc(p::Ptr, size::Integer) = ccall(:realloc, Ptr{Cvoid}, (Ptr{Cvoid}, Csize_t), p, size)

"""
    calloc(num::Integer, size::Integer) -> Ptr{Cvoid}

Call `calloc` from the C standard library.
"""
calloc(num::Integer, size::Integer) = ccall(:calloc, Ptr{Cvoid}, (Csize_t, Csize_t), num, size)


## Random numbers ##

# Access to very high quality (kernel) randomness
function getrandom!(A::Union{Array,Base.RefValue})
    ret = ccall(:uv_random, Cint, (Ptr{Cvoid}, Ptr{Cvoid}, Ptr{Cvoid}, Csize_t,   Cuint, Ptr{Cvoid}),
                                   C_NULL,     C_NULL,     A,          sizeof(A), 0,     C_NULL)
    Base.uv_error("getrandom", ret)
    return A
end
_make_uint64_seed() = getrandom!(Base.RefValue{UInt64}())[]

# To limit dependency on rand functionality implemented in the Random module,
# Libc.rand is used in Base (it also is independent from Random.seed, so is
# only affected by `Libc.srand(seed)` calls)
"""
    rand([T::Type]=UInt32)

Generate a random number of type `T`. `T` can be `UInt32` or `Float64`.
"""
rand() = ccall(:jl_rand, UInt64, ()) % UInt32
rand(::Type{UInt32}) = rand()
rand(::Type{Float64}) = rand() * 2.0^-32

"""
    srand([seed])

Set a value for the current global `seed`.
"""
function srand(seed::Integer=_make_uint64_seed())
    ccall(:jl_srand, Cvoid, (UInt64,), seed % UInt64)
end

struct Cpasswd
   username::Cstring
   uid::Culong
   gid::Culong
   shell::Cstring
   homedir::Cstring
   gecos::Cstring
   Cpasswd() = new(C_NULL, typemax(Culong), typemax(Culong), C_NULL, C_NULL, C_NULL)
end
mutable struct Cgroup
    groupname::Cstring # group name
    gid::Culong        # group ID
    mem::Ptr{Cstring}  # group members
    Cgroup() = new(C_NULL, typemax(Culong), C_NULL)
end
struct Passwd
    username::String
    uid::UInt
    gid::UInt
    shell::String
    homedir::String
    gecos::String
end
struct Group
    groupname::String
    gid::UInt
    mem::Vector{String}
end

function getpwuid(uid::Unsigned, throw_error::Bool=true)
    ref_pd = Ref(Cpasswd())
    ret = ccall(:uv_os_get_passwd2, Cint, (Ref{Cpasswd}, Culong), ref_pd, uid)
    if ret != 0
        throw_error && Base.uv_error("getpwuid", ret)
        return
    end
    pd = ref_pd[]
    pd = Passwd(
        pd.username == C_NULL ? "" : unsafe_string(pd.username),
        pd.uid,
        pd.gid,
        pd.shell == C_NULL ? "" : unsafe_string(pd.shell),
        pd.homedir == C_NULL ? "" : unsafe_string(pd.homedir),
        pd.gecos == C_NULL ? "" : unsafe_string(pd.gecos),
    )
    ccall(:uv_os_free_passwd, Cvoid, (Ref{Cpasswd},), ref_pd)
    return pd
end
function getgrgid(gid::Unsigned, throw_error::Bool=true)
    ref_gp = Ref(Cgroup())
    ret = ccall(:uv_os_get_group, Cint, (Ref{Cgroup}, Culong), ref_gp, gid)
    if ret != 0
        throw_error && Base.uv_error("getgrgid", ret)
        return
    end
    gp = ref_gp[]
    members = String[]
    if gp.mem != C_NULL
        while true
            mem = unsafe_load(gp.mem, length(members) + 1)
            mem == C_NULL && break
            push!(members, unsafe_string(mem))
        end
    end
    gp = Group(
         gp.groupname == C_NULL ? "" : unsafe_string(gp.groupname),
         gp.gid,
         members,
    )
    ccall(:uv_os_free_group, Cvoid, (Ref{Cgroup},), ref_gp)
    return gp
end

getuid() = ccall(:jl_getuid, Culong, ())
geteuid() = ccall(:jl_geteuid, Culong, ())

# Include dlopen()/dlpath() code
include("libdl.jl")
using .Libdl

end # module
P   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/./errno_h.jl�      const E2BIG = Int32(7)
const EACCES = Int32(13)
const EADDRINUSE = Int32(98)
const EADDRNOTAVAIL = Int32(99)
const EADV = Int32(68)
const EAFNOSUPPORT = Int32(97)
const EAGAIN = Int32(11)
const EALREADY = Int32(114)
const EBADE = Int32(52)
const EBADF = Int32(9)
const EBADFD = Int32(77)
const EBADMSG = Int32(74)
const EBADR = Int32(53)
const EBADRQC = Int32(56)
const EBADSLT = Int32(57)
const EBFONT = Int32(59)
const EBUSY = Int32(16)
const ECANCELED = Int32(125)
const ECHILD = Int32(10)
const ECHRNG = Int32(44)
const ECOMM = Int32(70)
const ECONNABORTED = Int32(103)
const ECONNREFUSED = Int32(111)
const ECONNRESET = Int32(104)
const EDEADLK = Int32(35)
const EDESTADDRREQ = Int32(89)
const EDOM = Int32(33)
const EDOTDOT = Int32(73)
const EDQUOT = Int32(122)
const EEXIST = Int32(17)
const EFAULT = Int32(14)
const EFBIG = Int32(27)
const EHOSTDOWN = Int32(112)
const EHOSTUNREACH = Int32(113)
const EHWPOISON = Int32(133)
const EIDRM = Int32(43)
const EILSEQ = Int32(84)
const EINPROGRESS = Int32(115)
const EINTR = Int32(4)
const EINVAL = Int32(22)
const EIO = Int32(5)
const EISCONN = Int32(106)
const EISDIR = Int32(21)
const EISNAM = Int32(120)
const EKEYEXPIRED = Int32(127)
const EKEYREJECTED = Int32(129)
const EKEYREVOKED = Int32(128)
const EL2HLT = Int32(51)
const EL2NSYNC = Int32(45)
const EL3HLT = Int32(46)
const EL3RST = Int32(47)
const ELIBACC = Int32(79)
const ELIBBAD = Int32(80)
const ELIBEXEC = Int32(83)
const ELIBMAX = Int32(82)
const ELIBSCN = Int32(81)
const ELNRNG = Int32(48)
const ELOOP = Int32(40)
const EMEDIUMTYPE = Int32(124)
const EMFILE = Int32(24)
const EMLINK = Int32(31)
const EMSGSIZE = Int32(90)
const EMULTIHOP = Int32(72)
const ENAMETOOLONG = Int32(36)
const ENAVAIL = Int32(119)
const ENETDOWN = Int32(100)
const ENETRESET = Int32(102)
const ENETUNREACH = Int32(101)
const ENFILE = Int32(23)
const ENOANO = Int32(55)
const ENOBUFS = Int32(105)
const ENOCSI = Int32(50)
const ENODATA = Int32(61)
const ENODEV = Int32(19)
const ENOENT = Int32(2)
const ENOEXEC = Int32(8)
const ENOKEY = Int32(126)
const ENOLCK = Int32(37)
const ENOLINK = Int32(67)
const ENOMEDIUM = Int32(123)
const ENOMEM = Int32(12)
const ENOMSG = Int32(42)
const ENONET = Int32(64)
const ENOPKG = Int32(65)
const ENOPROTOOPT = Int32(92)
const ENOSPC = Int32(28)
const ENOSR = Int32(63)
const ENOSTR = Int32(60)
const ENOSYS = Int32(38)
const ENOTBLK = Int32(15)
const ENOTCONN = Int32(107)
const ENOTDIR = Int32(20)
const ENOTEMPTY = Int32(39)
const ENOTNAM = Int32(118)
const ENOTRECOVERABLE = Int32(131)
const ENOTSOCK = Int32(88)
const ENOTTY = Int32(25)
const ENOTUNIQ = Int32(76)
const ENXIO = Int32(6)
const EOPNOTSUPP = Int32(95)
const EOVERFLOW = Int32(75)
const EOWNERDEAD = Int32(130)
const EPERM = Int32(1)
const EPFNOSUPPORT = Int32(96)
const EPIPE = Int32(32)
const EPROTO = Int32(71)
const EPROTONOSUPPORT = Int32(93)
const EPROTOTYPE = Int32(91)
const ERANGE = Int32(34)
const EREMCHG = Int32(78)
const EREMOTE = Int32(66)
const EREMOTEIO = Int32(121)
const ERESTART = Int32(85)
const ERFKILL = Int32(132)
const EROFS = Int32(30)
const ESHUTDOWN = Int32(108)
const ESOCKTNOSUPPORT = Int32(94)
const ESPIPE = Int32(29)
const ESRCH = Int32(3)
const ESRMNT = Int32(69)
const ESTALE = Int32(116)
const ESTRPIPE = Int32(86)
const ETIME = Int32(62)
const ETIMEDOUT = Int32(110)
const ETOOMANYREFS = Int32(109)
const ETXTBSY = Int32(26)
const EUCLEAN = Int32(117)
const EUNATCH = Int32(49)
const EUSERS = Int32(87)
const EXDEV = Int32(18)
const EXFULL = Int32(54)
L   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/libdl.jl4&      # This file is a part of Julia. License is MIT: https://julialang.org/license

module Libdl
@doc """
Interface to libdl. Provides dynamic linking support.
""" Libdl

import Base.DL_LOAD_PATH

export DL_LOAD_PATH, RTLD_DEEPBIND, RTLD_FIRST, RTLD_GLOBAL, RTLD_LAZY, RTLD_LOCAL,
    RTLD_NODELETE, RTLD_NOLOAD, RTLD_NOW, dlclose, dlopen, dlopen_e, dlsym, dlsym_e,
    dlpath, find_library, dlext, dllist

"""
    DL_LOAD_PATH

When calling [`dlopen`](@ref), the paths in this list will be searched first, in
order, before searching the system locations for a valid library handle.
"""
DL_LOAD_PATH

# note: constants to match JL_RTLD_* in src/julia.h, translated
#       to system-specific values by JL_RTLD macro in src/dlload.c
const RTLD_LOCAL     = 0x00000001
const RTLD_GLOBAL    = 0x00000002
const RTLD_LAZY      = 0x00000004
const RTLD_NOW       = 0x00000008
const RTLD_NODELETE  = 0x00000010
const RTLD_NOLOAD    = 0x00000020
const RTLD_DEEPBIND  = 0x00000040
const RTLD_FIRST     = 0x00000080

"""
    RTLD_DEEPBIND
    RTLD_FIRST
    RTLD_GLOBAL
    RTLD_LAZY
    RTLD_LOCAL
    RTLD_NODELETE
    RTLD_NOLOAD
    RTLD_NOW

Enum constant for [`dlopen`](@ref). See your platform man page for details, if
applicable.
"""
(RTLD_DEEPBIND, RTLD_FIRST, RTLD_GLOBAL, RTLD_LAZY, RTLD_LOCAL, RTLD_NODELETE, RTLD_NOLOAD, RTLD_NOW)

"""
    dlsym(handle, sym; throw_error::Bool = true)

Look up a symbol from a shared library handle, return callable function pointer on success.

If the symbol cannot be found, this method throws an error, unless the keyword argument
`throw_error` is set to `false`, in which case this method returns `nothing`.
"""
function dlsym(hnd::Ptr, s::Union{Symbol,AbstractString}; throw_error::Bool = true)
    hnd == C_NULL && throw(ArgumentError("NULL library handle"))
    val = Ref(Ptr{Cvoid}(0))
    symbol_found = ccall(:jl_dlsym, Cint,
        (Ptr{Cvoid}, Cstring, Ref{Ptr{Cvoid}}, Cint),
        hnd, s, val, Int64(throw_error)
    )
    if symbol_found == 0
        return nothing
    end
    return val[]
end

"""
    dlsym_e(handle, sym)

Look up a symbol from a shared library handle, silently return `C_NULL` on lookup failure.
This method is now deprecated in favor of `dlsym(handle, sym; throw_error=false)`.
"""
function dlsym_e(hnd::Ptr, s::Union{Symbol,AbstractString})
    return something(dlsym(hnd, s; throw_error=false), C_NULL)
end

"""
    dlopen(libfile::AbstractString [, flags::Integer]; throw_error:Bool = true)

Load a shared library, returning an opaque handle.

The extension given by the constant `dlext` (`.so`, `.dll`, or `.dylib`)
can be omitted from the `libfile` string, as it is automatically appended
if needed.   If `libfile` is not an absolute path name, then the paths
in the array `DL_LOAD_PATH` are searched for `libfile`, followed by the
system load path.

The optional flags argument is a bitwise-or of zero or more of `RTLD_LOCAL`, `RTLD_GLOBAL`,
`RTLD_LAZY`, `RTLD_NOW`, `RTLD_NODELETE`, `RTLD_NOLOAD`, `RTLD_DEEPBIND`, and `RTLD_FIRST`.
These are converted to the corresponding flags of the POSIX (and/or GNU libc and/or MacOS)
dlopen command, if possible, or are ignored if the specified functionality is not available
on the current platform. The default flags are platform specific. On MacOS the default
`dlopen` flags are `RTLD_LAZY|RTLD_DEEPBIND|RTLD_GLOBAL` while on other platforms the
defaults are `RTLD_LAZY|RTLD_DEEPBIND|RTLD_LOCAL`. An important usage of these flags is to
specify non default behavior for when the dynamic library loader binds library references to
exported symbols and if the bound references are put into process local or global scope. For
instance `RTLD_LAZY|RTLD_DEEPBIND|RTLD_GLOBAL` allows the library's symbols to be available
for usage in other shared libraries, addressing situations where there are dependencies
between shared libraries.

If the library cannot be found, this method throws an error, unless the keyword argument
`throw_error` is set to `false`, in which case this method returns `nothing`.

!!! note
     From Julia 1.6 on, this method replaces paths starting with `@executable_path/` with
     the path to the Julia executable, allowing for relocatable relative-path loads. In
     Julia 1.5 and earlier, this only worked on macOS.
"""
function dlopen end

dlopen(s::Symbol, flags::Integer = RTLD_LAZY | RTLD_DEEPBIND; kwargs...) =
    dlopen(string(s), flags; kwargs...)

function dlopen(s::AbstractString, flags::Integer = RTLD_LAZY | RTLD_DEEPBIND; throw_error::Bool = true)
    ret = ccall(:jl_load_dynamic_library, Ptr{Cvoid}, (Cstring,UInt32,Cint), s, flags, Cint(throw_error))
    if ret == C_NULL
        return nothing
    end
    return ret
end

"""
    dlopen(f::Function, args...; kwargs...)

Wrapper for usage with `do` blocks to automatically close the dynamic library once
control flow leaves the `do` block scope.

# Example
```julia
vendor = dlopen("libblas") do lib
    if Libdl.dlsym(lib, :openblas_set_num_threads; throw_error=false) !== nothing
        return :openblas
    else
        return :other
    end
end
```
"""
function dlopen(f::Function, args...; kwargs...)
    hdl = nothing
    try
        hdl = dlopen(args...; kwargs...)
        f(hdl)
    finally
        dlclose(hdl)
    end
end

"""
    dlopen_e(libfile::AbstractString [, flags::Integer])

Similar to [`dlopen`](@ref), except returns `C_NULL` instead of raising errors.
This method is now deprecated in favor of `dlopen(libfile::AbstractString [, flags::Integer]; throw_error=false)`.
"""
dlopen_e(args...) = something(dlopen(args...; throw_error=false), C_NULL)

"""
    dlclose(handle)

Close shared library referenced by handle.
"""
function dlclose(p::Ptr)
    0 == ccall(:jl_dlclose, Cint, (Ptr{Cvoid},), p)
end

"""
    dlclose(::Nothing)

For the very common pattern usage pattern of

    try
        hdl = dlopen(library_name)
        ... do something
    finally
        dlclose(hdl)
    end

We define a `dlclose()` method that accepts a parameter of type `Nothing`, so
that user code does not have to change its behavior for the case that `library_name`
was not found.
"""
function dlclose(p::Nothing)
end

"""
    find_library(names [, locations])

Searches for the first library in `names` in the paths in the `locations` list,
`DL_LOAD_PATH`, or system library paths (in that order) which can successfully be dlopen'd.
On success, the return value will be one of the names (potentially prefixed by one of the
paths in locations). This string can be assigned to a `global const` and used as the library
name in future `ccall`'s. On failure, it returns the empty string.
"""
function find_library(libnames, extrapaths=String[])
    for lib in libnames
        for path in extrapaths
            l = joinpath(path, lib)
            p = dlopen(l, RTLD_LAZY; throw_error=false)
            if p !== nothing
                dlclose(p)
                return l
            end
        end
        p = dlopen(lib, RTLD_LAZY; throw_error=false)
        if p !== nothing
            dlclose(p)
            return lib
        end
    end
    return ""
end
find_library(libname::Union{Symbol,AbstractString}, extrapaths=String[]) =
    find_library([string(libname)], extrapaths)

"""
    dlpath(handle::Ptr{Cvoid})

Given a library `handle` from `dlopen`, return the full path.
"""
function dlpath(handle::Ptr{Cvoid})
    p = ccall(:jl_pathname_for_handle, Cstring, (Ptr{Cvoid},), handle)
    s = unsafe_string(p)
    Sys.iswindows() && Libc.free(p)
    return s
end

"""
    dlpath(libname::Union{AbstractString, Symbol})

Get the full path of the library `libname`.

# Example
```julia-repl
julia> dlpath("libjulia")
```
"""
function dlpath(libname::Union{AbstractString, Symbol})
    handle = dlopen(libname)
    path = dlpath(handle)
    dlclose(handle)
    return path
end

if Sys.isapple()
    const dlext = "dylib"
elseif Sys.iswindows()
    const dlext = "dll"
else
    #assume Sys.islinux, or similar
    const dlext = "so"
end

"""
    dlext

File extension for dynamic libraries (e.g. dll, dylib, so) on the current platform.
"""
dlext

if (Sys.islinux() || Sys.isbsd()) && !Sys.isapple()
    struct dl_phdr_info
        # Base address of object
        addr::Cuint

        # Null-terminated name of object
        name::Ptr{UInt8}

        # Pointer to array of ELF program headers for this object
        phdr::Ptr{Cvoid}

        # Number of program headers for this object
        phnum::Cshort
    end

    # This callback function called by dl_iterate_phdr() on Linux and BSD's
    # DL_ITERATE_PHDR(3) on freebsd
    function dl_phdr_info_callback(di::dl_phdr_info, size::Csize_t, dynamic_libraries::Array{String,1})
        name = unsafe_string(di.name)
        push!(dynamic_libraries, name)
        return Cint(0)
    end
end

"""
    dllist()

Return the paths of dynamic libraries currently loaded in a `Vector{String}`.
"""
function dllist()
    dynamic_libraries = Vector{String}()

    @static if Sys.isapple()
        numImages = ccall(:_dyld_image_count, Cint, ())

        # start at 1 instead of 0 to skip self
        for i in 1:numImages-1
            name = unsafe_string(ccall(:_dyld_get_image_name, Cstring, (UInt32,), i))
            push!(dynamic_libraries, name)
        end
    elseif Sys.islinux() || Sys.isbsd()
        callback = @cfunction(dl_phdr_info_callback, Cint,
                              (Ref{dl_phdr_info}, Csize_t, Ref{Vector{String}}))
        ccall(:dl_iterate_phdr, Cint, (Ptr{Cvoid}, Ref{Vector{String}}), callback, dynamic_libraries)
        popfirst!(dynamic_libraries)
        filter!(!isempty, dynamic_libraries)
    elseif Sys.iswindows()
        ccall(:jl_dllist, Cint, (Any,), dynamic_libraries)
    else
        # unimplemented
    end

    return dynamic_libraries
end

end # module Libdl
N   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/logging.jl�Z      # This file is a part of Julia. License is MIT: https://julialang.org/license

module CoreLogging

import Base: isless, +, -, convert, show

export
    AbstractLogger,
    LogLevel,
    NullLogger,
    @debug,
    @info,
    @warn,
    @error,
    @logmsg,
    with_logger,
    current_logger,
    global_logger,
    disable_logging,
    SimpleLogger

#-------------------------------------------------------------------------------
# The AbstractLogger interface
"""
A logger controls how log records are filtered and dispatched.  When a log
record is generated, the logger is the first piece of user configurable code
which gets to inspect the record and decide what to do with it.
"""
abstract type AbstractLogger ; end

"""
    handle_message(logger, level, message, _module, group, id, file, line; key1=val1, ...)

Log a message to `logger` at `level`.  The logical location at which the
message was generated is given by module `_module` and `group`; the source
location by `file` and `line`. `id` is an arbitrary unique value (typically a
[`Symbol`](@ref)) to be used as a key to identify the log statement when
filtering.
"""
function handle_message end

"""
    shouldlog(logger, level, _module, group, id)

Return `true` when `logger` accepts a message at `level`, generated for
`_module`, `group` and with unique log identifier `id`.
"""
function shouldlog end

"""
    min_enabled_level(logger)

Return the minimum enabled level for `logger` for early filtering.  That is,
the log level below or equal to which all messages are filtered.
"""
function min_enabled_level end

"""
    catch_exceptions(logger)

Return `true` if the logger should catch exceptions which happen during log
record construction.  By default, messages are caught

By default all exceptions are caught to prevent log message generation from
crashing the program.  This lets users confidently toggle little-used
functionality - such as debug logging - in a production system.

If you want to use logging as an audit trail you should disable this for your
logger type.
"""
catch_exceptions(logger) = true


# Prevent invalidation when packages define custom loggers
# Using invoke in combination with @nospecialize eliminates backedges to these methods
Base.@constprop :none function _invoked_shouldlog(logger, level, _module, group, id)
    @nospecialize
    return invoke(
        shouldlog,
        Tuple{typeof(logger), typeof(level), typeof(_module), typeof(group), typeof(id)},
        logger, level, _module, group, id
    )::Bool
end

function _invoked_min_enabled_level(@nospecialize(logger))
    return invoke(min_enabled_level, Tuple{typeof(logger)}, logger)::LogLevel
end

function _invoked_catch_exceptions(@nospecialize(logger))
    return invoke(catch_exceptions, Tuple{typeof(logger)}, logger)::Bool
end

"""
    NullLogger()

Logger which disables all messages and produces no output - the logger
equivalent of /dev/null.
"""
struct NullLogger <: AbstractLogger; end

min_enabled_level(::NullLogger) = AboveMaxLevel
shouldlog(::NullLogger, args...) = false
handle_message(::NullLogger, args...; kwargs...) =
    (@nospecialize; error("Null logger handle_message() should not be called"))


#-------------------------------------------------------------------------------
# Standard log levels
"""
    LogLevel(level)

Severity/verbosity of a log record.

The log level provides a key against which potential log records may be
filtered, before any other work is done to construct the log record data
structure itself.

# Examples
```julia-repl
julia> Logging.LogLevel(0) == Logging.Info
true
```
"""
struct LogLevel
    level::Int32
end

LogLevel(level::LogLevel) = level

isless(a::LogLevel, b::LogLevel) = isless(a.level, b.level)
+(level::LogLevel, inc::Integer) = LogLevel(level.level+inc)
-(level::LogLevel, inc::Integer) = LogLevel(level.level-inc)
convert(::Type{LogLevel}, level::Integer) = LogLevel(level)

const BelowMinLevel = LogLevel(-1000001)
"""
    Debug

Alias for [`LogLevel(-1000)`](@ref LogLevel).
"""
const Debug         = LogLevel(   -1000)
"""
    Info

Alias for [`LogLevel(0)`](@ref LogLevel).
"""
const Info          = LogLevel(       0)
"""
    Warn

Alias for [`LogLevel(1000)`](@ref LogLevel).
"""
const Warn          = LogLevel(    1000)
"""
    Error

Alias for [`LogLevel(2000)`](@ref LogLevel).
"""
const Error         = LogLevel(    2000)
const AboveMaxLevel = LogLevel( 1000001)

# Global log limiting mechanism for super fast but inflexible global log limiting.
const _min_enabled_level = Ref{LogLevel}(Debug)

function show(io::IO, level::LogLevel)
    if     level == BelowMinLevel  print(io, "BelowMinLevel")
    elseif level == Debug          print(io, "Debug")
    elseif level == Info           print(io, "Info")
    elseif level == Warn           print(io, "Warn")
    elseif level == Error          print(io, "Error")
    elseif level == AboveMaxLevel  print(io, "AboveMaxLevel")
    else                           print(io, "LogLevel($(level.level))")
    end
end


#-------------------------------------------------------------------------------
# Logging macros

_logmsg_docs = """
    @debug message  [key=value | value ...]
    @info  message  [key=value | value ...]
    @warn  message  [key=value | value ...]
    @error message  [key=value | value ...]

    @logmsg level message [key=value | value ...]

Create a log record with an informational `message`.  For convenience, four
logging macros `@debug`, `@info`, `@warn` and `@error` are defined which log at
the standard severity levels `Debug`, `Info`, `Warn` and `Error`.  `@logmsg`
allows `level` to be set programmatically to any `LogLevel` or custom log level
types.

`message` should be an expression which evaluates to a string which is a human
readable description of the log event.  By convention, this string will be
formatted as markdown when presented.

The optional list of `key=value` pairs supports arbitrary user defined
metadata which will be passed through to the logging backend as part of the
log record.  If only a `value` expression is supplied, a key representing the
expression will be generated using [`Symbol`](@ref). For example, `x` becomes `x=x`,
and `foo(10)` becomes `Symbol("foo(10)")=foo(10)`.  For splatting a list of
key value pairs, use the normal splatting syntax, `@info "blah" kws...`.

There are some keys which allow automatically generated log data to be
overridden:

  * `_module=mod` can be used to specify a different originating module from
    the source location of the message.
  * `_group=symbol` can be used to override the message group (this is
    normally derived from the base name of the source file).
  * `_id=symbol` can be used to override the automatically generated unique
    message identifier.  This is useful if you need to very closely associate
    messages generated on different source lines.
  * `_file=string` and `_line=integer` can be used to override the apparent
    source location of a log message.

There's also some key value pairs which have conventional meaning:

  * `maxlog=integer` should be used as a hint to the backend that the message
    should be displayed no more than `maxlog` times.
  * `exception=ex` should be used to transport an exception with a log message,
    often used with `@error`. An associated backtrace `bt` may be attached
    using the tuple `exception=(ex,bt)`.

# Examples

```julia
@debug "Verbose debugging information.  Invisible by default"
@info  "An informational message"
@warn  "Something was odd.  You should pay attention"
@error "A non fatal error occurred"

x = 10
@info "Some variables attached to the message" x a=42.0

@debug begin
    sA = sum(A)
    "sum(A) = \$sA is an expensive operation, evaluated only when `shouldlog` returns true"
end

for i=1:10000
    @info "With the default backend, you will only see (i = \$i) ten times"  maxlog=10
    @debug "Algorithm1" i progress=i/10000
end
```
"""

# Get (module,filepath,line) for the location of the caller of a macro.
# Designed to be used from within the body of a macro.
macro _sourceinfo()
    esc(quote
        (__module__,
         __source__.file === nothing ? "?" : String(__source__.file::Symbol),
         __source__.line)
    end)
end

macro logmsg(level, exs...) logmsg_code((@_sourceinfo)..., esc(level), exs...) end
macro debug(exs...) logmsg_code((@_sourceinfo)..., :Debug, exs...) end
macro  info(exs...) logmsg_code((@_sourceinfo)..., :Info,  exs...) end
macro  warn(exs...) logmsg_code((@_sourceinfo)..., :Warn,  exs...) end
macro error(exs...) logmsg_code((@_sourceinfo)..., :Error, exs...) end

# Logging macros share documentation
@eval @doc $_logmsg_docs :(@logmsg)
@eval @doc $_logmsg_docs :(@debug)
@eval @doc $_logmsg_docs :(@info)
@eval @doc $_logmsg_docs :(@warn)
@eval @doc $_logmsg_docs :(@error)

_log_record_ids = Set{Symbol}()
# Generate a unique, stable, short, somewhat human readable identifier for a
# logging *statement*. The idea here is to have a key against which log events
# can be filtered and otherwise manipulated. The key should uniquely identify
# the source location in the originating module, but ideally should be stable
# across versions of the originating module, provided the log generating
# statement itself doesn't change.
function log_record_id(_module, level, message, log_kws)
    @nospecialize
    modname = _module === nothing ?  "" : join(fullname(_module), "_")
    # Use an arbitrarily chosen eight hex digits here. TODO: Figure out how to
    # make the id exactly the same on 32 and 64 bit systems.
    h = UInt32(hash(string(modname, level, message, log_kws)::String) & 0xFFFFFFFF)
    while true
        id = Symbol(modname, '_', string(h, base = 16, pad = 8))
        # _log_record_ids is a registry of log record ids for use during
        # compilation, to ensure uniqueness of ids.  Note that this state will
        # only persist during module compilation so it will be empty when a
        # precompiled module is loaded.
        if !(id in _log_record_ids)
            push!(_log_record_ids, id)
            return id
        end
        h += 1
    end
end

default_group(file) = Symbol(splitext(basename(file))[1])

function issimple(@nospecialize val)
    val isa String && return true
    val isa Symbol && return true
    val isa QuoteNode && return true
    val isa Number && return true
    val isa Char && return true
    if val isa Expr
        val.head === :quote && issimple(val.args[1]) && return true
        val.head === :inert && return true
    end
    return false
end
function issimplekw(@nospecialize val)
    if val isa Expr
        if val.head === :kw
            val = val.args[2]
            if val isa Expr && val.head === :escape
                issimple(val.args[1]) && return true
            end
        end
    end
    return false
end

# helper function to get the current logger, if enabled for the specified message type
@noinline Base.@constprop :none function current_logger_for_env(std_level::LogLevel, group, _module)
    logstate = @inline current_logstate()
    if std_level >= logstate.min_enabled_level || env_override_minlevel(group, _module)
        return logstate.logger
    end
    return nothing
end

# Generate code for logging macros
function logmsg_code(_module, file, line, level, message, exs...)
    @nospecialize
    log_data = process_logmsg_exs(_module, file, line, level, message, exs...)
    if !isa(message, Symbol) && issimple(message) && isempty(log_data.kwargs)
        logrecord = quote
            msg = $(message)
            kwargs = (;)
            true
        end
    elseif issimple(message) && all(issimplekw, log_data.kwargs)
        # if message and kwargs are just values and variables, we can avoid try/catch
        # complexity by adding the code for testing the UndefVarError by hand
        checkerrors = nothing
        for kwarg in reverse(log_data.kwargs)
            if isa(kwarg.args[2].args[1], Symbol)
                checkerrors = Expr(:if, Expr(:isdefined, kwarg.args[2]), checkerrors, Expr(:call, Expr(:core, :UndefVarError), QuoteNode(kwarg.args[2].args[1])))
            end
        end
        if isa(message, Symbol)
            message = esc(message)
            checkerrors = Expr(:if, Expr(:isdefined, message), checkerrors, Expr(:call, Expr(:core, :UndefVarError), QuoteNode(message.args[1])))
        end
        logrecord = quote
            let err = $checkerrors
                if err === nothing
                    msg = $(message)
                    kwargs = (;$(log_data.kwargs...))
                    true
                else
                    @invokelatest logging_error(logger, level, _module, group, id, file, line, err, false)
                    false
                end
            end
        end
    else
        logrecord = quote
            try
                msg = $(esc(message))
                kwargs = (;$(log_data.kwargs...))
                true
            catch err
                @invokelatest logging_error(logger, level, _module, group, id, file, line, err, true)
                false
            end
        end
    end
    return quote
        let
            level = $level
            # simplify std_level code emitted, if we know it is one of our global constants
            std_level = $(level isa Symbol ? :level : :(level isa $LogLevel ? level : convert($LogLevel, level)::$LogLevel))
            if std_level >= $(_min_enabled_level)[]
                group = $(log_data._group)
                _module = $(log_data._module)
                logger = $(current_logger_for_env)(std_level, group, _module)
                if !(logger === nothing)
                    id = $(log_data._id)
                    # Second chance at an early bail-out (before computing the message),
                    # based on arbitrary logger-specific logic.
                    if invokelatest($shouldlog, logger, level, _module, group, id)
                        file = $(log_data._file)
                        if file isa String
                            file = Base.fixup_stdlib_path(file)
                        end
                        line = $(log_data._line)
                        local msg, kwargs
                        $(logrecord) && invokelatest($handle_message,
                            logger, level, msg, _module, group, id, file, line;
                            kwargs...)
                    end
                end
            end
            nothing
        end
    end
end

function process_logmsg_exs(_orig_module, _file, _line, level, message, exs...)
    @nospecialize
    local _group, _id
    _module = _orig_module
    kwargs = Any[]
    for ex in exs
        if ex isa Expr && ex.head === :(=)
            k, v = ex.args
            if !(k isa Symbol)
                k = Symbol(k)
            end

            # Recognize several special keyword arguments
            if k === :_group
                _group = esc(v)
            elseif k === :_id
                _id = esc(v)
            elseif k === :_module
                _module = esc(v)
            elseif k === :_file
                _file = esc(v)
            elseif k === :_line
                _line = esc(v)
            else
                # Copy across key value pairs for structured log records
                push!(kwargs, Expr(:kw, k, esc(v)))
            end
        elseif ex isa Expr && ex.head === :... # Keyword splatting
            push!(kwargs, esc(ex))
        else # Positional arguments - will be converted to key value pairs automatically.
            push!(kwargs, Expr(:kw, Symbol(ex), esc(ex)))
        end
    end

    if !@isdefined(_group)
        _group = default_group_code(_file)
    end
    if !@isdefined(_id)
        _id = Expr(:quote, log_record_id(_orig_module, level, message, exs))
    end
    return (;_module, _group, _id, _file, _line, kwargs)
end

function default_group_code(file)
    @nospecialize
    if file isa String && isdefined(Base, :basename)
        QuoteNode(default_group(file))  # precompute if we can
    else
        ref = Ref{Symbol}()  # memoized run-time execution
        :(isassigned($ref) ? $ref[] : $ref[] = default_group(something($file, ""))::Symbol)
    end
end


# Report an error in log message creation
@noinline function logging_error(logger, level, _module, group, id,
                                 filepath, line, @nospecialize(err), real::Bool)
    @nospecialize
    if !_invoked_catch_exceptions(logger)
        real ? rethrow(err) : throw(err)
    end
    msg = try
              "Exception while generating log record in module $_module at $filepath:$line"
          catch ex
              LazyString("Exception handling log message: ", ex)
          end
    bt = real ? catch_backtrace() : backtrace()
    handle_message(
        logger, Error, msg, _module, :logevent_error, id, filepath, line;
        exception=(err,bt))
    nothing
end

# Log a message. Called from the julia C code; kwargs is in the format
# Any[key1,val1, ...] for simplicity in construction on the C side.
function logmsg_shim(level, message, _module, group, id, file, line, kwargs)
    @nospecialize
    real_kws = Any[(kwargs[i], kwargs[i+1]) for i in 1:2:length(kwargs)]
    @logmsg(convert(LogLevel, level), message,
            _module=_module, _id=id, _group=group,
            _file=String(file), _line=line, real_kws...)
    nothing
end

# LogState - a cache of data extracted from the logger, plus the logger itself.
struct LogState
    min_enabled_level::LogLevel
    logger::AbstractLogger
end

LogState(logger) = LogState(LogLevel(_invoked_min_enabled_level(logger)), logger)

function current_logstate()
    logstate = current_task().logstate
    return (logstate !== nothing ? logstate : _global_logstate)::LogState
end

function with_logstate(f::Function, logstate)
    @nospecialize
    t = current_task()
    old = t.logstate
    try
        t.logstate = logstate
        f()
    finally
        t.logstate = old
    end
end

#-------------------------------------------------------------------------------
# Control of the current logger and early log filtering

"""
    disable_logging(level)

Disable all log messages at log levels equal to or less than `level`.  This is
a *global* setting, intended to make debug logging extremely cheap when
disabled.

# Examples
```julia
Logging.disable_logging(Logging.Info) # Disable debug and info
```
"""
function disable_logging(level::LogLevel)
    _min_enabled_level[] = level + 1
end

let _debug_groups_include::Vector{Symbol} = Symbol[],
    _debug_groups_exclude::Vector{Symbol} = Symbol[],
    _debug_str::String = ""
global Base.@constprop :none function env_override_minlevel(group, _module)
    debug = get(ENV, "JULIA_DEBUG", "")
    if !(debug === _debug_str)
        _debug_str = debug
        empty!(_debug_groups_include)
        empty!(_debug_groups_exclude)
        for g in split(debug, ',')
            if !isempty(g)
                if startswith(g, "!")
                    if !isempty(g[2:end])
                        push!(_debug_groups_exclude, Symbol(g[2:end]))
                    end
                else
                    push!(_debug_groups_include, Symbol(g))
                end
            end
        end
        unique!(_debug_groups_include)
        unique!(_debug_groups_exclude)
    end

    if !(:all in _debug_groups_exclude) && (:all in _debug_groups_include || !isempty(_debug_groups_exclude))
        if isempty(_debug_groups_exclude)
            return true
        elseif isa(group, Symbol) && group in _debug_groups_exclude
            return false
        elseif isa(_module, Module) && (nameof(_module) in _debug_groups_exclude || nameof(Base.moduleroot(_module)) in _debug_groups_exclude)
            return false
        else
            return true
        end
    else
        if isempty(_debug_groups_include)
            return false
        elseif isa(group, Symbol) && group in _debug_groups_include
            return true
        elseif isa(_module, Module) && (nameof(_module) in _debug_groups_include || nameof(Base.moduleroot(_module)) in _debug_groups_include)
            return true
        else
            return false
        end
    end
    return false
end
end


"""
    global_logger()

Return the global logger, used to receive messages when no specific logger
exists for the current task.

    global_logger(logger)

Set the global logger to `logger`, and return the previous global logger.
"""
global_logger() = _global_logstate.logger

function global_logger(logger::AbstractLogger)
    prev = _global_logstate.logger
    global _global_logstate = LogState(logger)
    prev
end

"""
    with_logger(function, logger)

Execute `function`, directing all log messages to `logger`.

# Example

```julia
function test(x)
    @info "x = \$x"
end

with_logger(logger) do
    test(1)
    test([1,2])
end
```
"""
function with_logger(@nospecialize(f::Function), logger::AbstractLogger)
    with_logstate(f, LogState(logger))
end

"""
    current_logger()

Return the logger for the current task, or the global logger if none is
attached to the task.
"""
current_logger() = current_logstate().logger

const closed_stream = IOBuffer(UInt8[])
close(closed_stream)

#-------------------------------------------------------------------------------
# SimpleLogger
"""
    SimpleLogger([stream,] min_level=Info)

Simplistic logger for logging all messages with level greater than or equal to
`min_level` to `stream`. If stream is closed then messages with log level
greater or equal to `Warn` will be logged to `stderr` and below to `stdout`.
"""
struct SimpleLogger <: AbstractLogger
    stream::IO
    min_level::LogLevel
    message_limits::Dict{Any,Int}
end
SimpleLogger(stream::IO, level=Info) = SimpleLogger(stream, level, Dict{Any,Int}())
SimpleLogger(level=Info) = SimpleLogger(closed_stream, level)

shouldlog(logger::SimpleLogger, level, _module, group, id) =
    get(logger.message_limits, id, 1) > 0

min_enabled_level(logger::SimpleLogger) = logger.min_level

catch_exceptions(logger::SimpleLogger) = false

function handle_message(logger::SimpleLogger, level::LogLevel, message, _module, group, id,
                        filepath, line; kwargs...)
    @nospecialize
    maxlog = get(kwargs, :maxlog, nothing)
    if maxlog isa Core.BuiltinInts
        remaining = get!(logger.message_limits, id, Int(maxlog)::Int)
        logger.message_limits[id] = remaining - 1
        remaining > 0 || return
    end
    buf = IOBuffer()
    stream::IO = logger.stream
    if !(isopen(stream)::Bool)
        stream = stderr
    end
    iob = IOContext(buf, stream)
    levelstr = level == Warn ? "Warning" : string(level)
    msglines = eachsplit(chomp(convert(String, string(message))::String), '\n')
    msg1, rest = Iterators.peel(msglines)
    println(iob, "┌ ", levelstr, ": ", msg1)
    for msg in rest
        println(iob, "│ ", msg)
    end
    for (key, val) in kwargs
        key === :maxlog && continue
        println(iob, "│   ", key, " = ", val)
    end
    println(iob, "└ @ ", _module, " ", filepath, ":", line)
    write(stream, take!(buf))
    nothing
end

_global_logstate = LogState(SimpleLogger())

end # CoreLogging
R   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/linked_list.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

mutable struct IntrusiveLinkedList{T}
    # Invasive list requires that T have a field `.next >: U{T, Nothing}` and `.queue >: U{ILL{T}, Nothing}`
    head::Union{T, Nothing}
    tail::Union{T, Nothing}
    IntrusiveLinkedList{T}() where {T} = new{T}(nothing, nothing)
end

#const list_append!! = append!
#const list_deletefirst! = delete!

eltype(::Type{<:IntrusiveLinkedList{T}}) where {T} = @isdefined(T) ? T : Any

iterate(q::IntrusiveLinkedList) = (h = q.head; h === nothing ? nothing : (h, h))
iterate(q::IntrusiveLinkedList{T}, v::T) where {T} = (h = v.next; h === nothing ? nothing : (h, h))

isempty(q::IntrusiveLinkedList) = (q.head === nothing)

function length(q::IntrusiveLinkedList)
    i = 0
    head = q.head
    while head !== nothing
        i += 1
        head = head.next
    end
    return i
end

function list_append!!(q::IntrusiveLinkedList{T}, q2::IntrusiveLinkedList{T}) where T
    q === q2 && error("can't append list to itself")
    head2 = q2.head
    if head2 !== nothing
        tail2 = q2.tail::T
        q2.head = nothing
        q2.tail = nothing
        tail = q.tail
        q.tail = tail2
        if tail === nothing
            q.head = head2
        else
            tail.next = head2
        end
        while head2 !== nothing
            head2.queue = q
            head2 = head2.next
        end
    end
    return q
end

function push!(q::IntrusiveLinkedList{T}, val::T) where T
    val.queue === nothing || error("val already in a list")
    val.queue = q
    tail = q.tail
    if tail === nothing
        q.head = q.tail = val
    else
        tail.next = val
        q.tail = val
    end
    return q
end

function pushfirst!(q::IntrusiveLinkedList{T}, val::T) where T
    val.queue === nothing || error("val already in a list")
    val.queue = q
    head = q.head
    if head === nothing
        q.head = q.tail = val
    else
        val.next = head
        q.head = val
    end
    return q
end

function pop!(q::IntrusiveLinkedList{T}) where {T}
    val = q.tail::T
    list_deletefirst!(q, val) # expensive!
    return val
end

function popfirst!(q::IntrusiveLinkedList{T}) where {T}
    val = q.head::T
    list_deletefirst!(q, val) # cheap
    return val
end

# this function assumes `val` is found in `q`
function list_deletefirst!(q::IntrusiveLinkedList{T}, val::T) where T
    val.queue === q || return
    head = q.head::T
    if head === val
        if q.tail::T === val
            q.head = q.tail = nothing
        else
            q.head = val.next::T
        end
    else
        head_next = head.next::T
        while head_next !== val
            head = head_next
            head_next = head.next::T
        end
        if q.tail::T === val
            head.next = nothing
            q.tail = head
        else
            head.next = val.next::T
        end
    end
    val.next = nothing
    val.queue = nothing
    return q
end

#function list_deletefirst!(q::Array{T}, val::T) where T
#    i = findfirst(isequal(val), q)
#    i === nothing || deleteat!(q, i)
#    return q
#end


mutable struct LinkedListItem{T}
    # Adapter class to use any `T` in a LinkedList
    next::Union{LinkedListItem{T}, Nothing}
    queue::Union{IntrusiveLinkedList{LinkedListItem{T}}, Nothing}
    value::T
    LinkedListItem{T}(value::T) where {T} = new{T}(nothing, nothing, value)
end
const LinkedList{T} = IntrusiveLinkedList{LinkedListItem{T}}

# delegate methods, as needed
eltype(::Type{<:LinkedList{T}}) where {T} = @isdefined(T) ? T : Any
iterate(q::LinkedList) = (h = q.head; h === nothing ? nothing : (h.value, h))
iterate(q::IntrusiveLinkedList{LLT}, v::LLT) where {LLT<:LinkedListItem} = (h = v.next; h === nothing ? nothing : (h.value, h))
push!(q::LinkedList{T}, val::T) where {T} = push!(q, LinkedListItem{T}(val))
pushfirst!(q::LinkedList{T}, val::T) where {T} = pushfirst!(q, LinkedListItem{T}(val))
pop!(q::LinkedList) = invoke(pop!, Tuple{IntrusiveLinkedList,}, q).value
popfirst!(q::LinkedList) = invoke(popfirst!, Tuple{IntrusiveLinkedList,}, q).value
function list_deletefirst!(q::LinkedList{T}, val::T) where T
    h = q.head
    while h !== nothing
        if isequal(h.value, val)
            list_deletefirst!(q, h)
            break
        end
        h = h.next
    end
    return q
end
P   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/condition.jl)      # This file is a part of Julia. License is MIT: https://julialang.org/license

## thread/task locking abstraction

@noinline function concurrency_violation()
    # can be useful for debugging
    #try; error(); catch; ccall(:jlbacktrace, Cvoid, ()); end
    throw(ConcurrencyViolationError("lock must be held"))
end

"""
    AbstractLock

Abstract supertype describing types that
implement the synchronization primitives:
[`lock`](@ref), [`trylock`](@ref), [`unlock`](@ref), and [`islocked`](@ref).
"""
abstract type AbstractLock end
function lock end
function unlock end
function trylock end
function islocked end
unlockall(l::AbstractLock) = unlock(l) # internal function for implementing `wait`
relockall(l::AbstractLock, token::Nothing) = lock(l) # internal function for implementing `wait`
assert_havelock(l::AbstractLock, tid::Integer) =
    (islocked(l) && tid == Threads.threadid()) ? nothing : concurrency_violation()
assert_havelock(l::AbstractLock, tid::Task) =
    (islocked(l) && tid === current_task()) ? nothing : concurrency_violation()
assert_havelock(l::AbstractLock, tid::Nothing) = concurrency_violation()

"""
    AlwaysLockedST

This struct does not implement a real lock, but instead
pretends to be always locked on the original thread it was allocated on,
and simply ignores all other interactions.
It also does not synchronize tasks; for that use a real lock such as [`ReentrantLock`](@ref).
This can be used in the place of a real lock to, instead, simply and cheaply assert
that the operation is only occurring on a single cooperatively-scheduled thread.
It is thus functionally equivalent to allocating a real, recursive, task-unaware lock
immediately calling `lock` on it, and then never calling a matching `unlock`,
except that calling `lock` from another thread will throw a concurrency violation exception.
"""
struct AlwaysLockedST <: AbstractLock
    ownertid::Int16
    AlwaysLockedST() = new(Threads.threadid())
end
assert_havelock(l::AlwaysLockedST) = assert_havelock(l, l.ownertid)
lock(l::AlwaysLockedST) = assert_havelock(l)
unlock(l::AlwaysLockedST) = assert_havelock(l)
trylock(l::AlwaysLockedST) = l.ownertid == Threads.threadid()
islocked(::AlwaysLockedST) = true


## condition variables

"""
    GenericCondition

Abstract implementation of a condition object
for synchronizing tasks objects with a given lock.
"""
struct GenericCondition{L<:AbstractLock}
    waitq::IntrusiveLinkedList{Task}
    lock::L

    GenericCondition{L}() where {L<:AbstractLock} = new{L}(IntrusiveLinkedList{Task}(), L())
    GenericCondition{L}(l::L) where {L<:AbstractLock} = new{L}(IntrusiveLinkedList{Task}(), l)
    GenericCondition(l::AbstractLock) = new{typeof(l)}(IntrusiveLinkedList{Task}(), l)
end

assert_havelock(c::GenericCondition) = assert_havelock(c.lock)
lock(c::GenericCondition) = lock(c.lock)
unlock(c::GenericCondition) = unlock(c.lock)
trylock(c::GenericCondition) = trylock(c.lock)
islocked(c::GenericCondition) = islocked(c.lock)

lock(f, c::GenericCondition) = lock(f, c.lock)

# have waiter wait for c
function _wait2(c::GenericCondition, waiter::Task, first::Bool=false)
    ct = current_task()
    assert_havelock(c)
    if first
        pushfirst!(c.waitq, waiter)
    else
        push!(c.waitq, waiter)
    end
    # since _wait2 is similar to schedule, we should observe the sticky bit now
    if waiter.sticky && Threads.threadid(waiter) == 0 && !GC.in_finalizer()
        # Issue #41324
        # t.sticky && tid == 0 is a task that needs to be co-scheduled with
        # the parent task. If the parent (current_task) is not sticky we must
        # set it to be sticky.
        # XXX: Ideally we would be able to unset this
        ct.sticky = true
        tid = Threads.threadid()
        ccall(:jl_set_task_tid, Cint, (Any, Cint), waiter, tid-1)
    end
    return
end

"""
    wait([x])

Block the current task until some event occurs, depending on the type of the argument:

* [`Channel`](@ref): Wait for a value to be appended to the channel.
* [`Condition`](@ref): Wait for [`notify`](@ref) on a condition and return the `val`
  parameter passed to `notify`. Waiting on a condition additionally allows passing
  `first=true` which results in the waiter being put _first_ in line to wake up on `notify`
  instead of the usual first-in-first-out behavior.
* `Process`: Wait for a process or process chain to exit. The `exitcode` field of a process
  can be used to determine success or failure.
* [`Task`](@ref): Wait for a `Task` to finish. If the task fails with an exception, a
  `TaskFailedException` (which wraps the failed task) is thrown.
* [`RawFD`](@ref): Wait for changes on a file descriptor (see the `FileWatching` package).

If no argument is passed, the task blocks for an undefined period. A task can only be
restarted by an explicit call to [`schedule`](@ref) or [`yieldto`](@ref).

Often `wait` is called within a `while` loop to ensure a waited-for condition is met before
proceeding.
"""
function wait(c::GenericCondition; first::Bool=false)
    ct = current_task()
    _wait2(c, ct, first)
    token = unlockall(c.lock)
    try
        return wait()
    catch
        ct.queue === nothing || list_deletefirst!(ct.queue::IntrusiveLinkedList{Task}, ct)
        rethrow()
    finally
        relockall(c.lock, token)
    end
end

"""
    notify(condition, val=nothing; all=true, error=false)

Wake up tasks waiting for a condition, passing them `val`. If `all` is `true` (the default),
all waiting tasks are woken, otherwise only one is. If `error` is `true`, the passed value
is raised as an exception in the woken tasks.

Return the count of tasks woken up. Return 0 if no tasks are waiting on `condition`.
"""
@constprop :none notify(c::GenericCondition, @nospecialize(arg = nothing); all=true, error=false) = notify(c, arg, all, error)
function notify(c::GenericCondition, @nospecialize(arg), all, error)
    assert_havelock(c)
    cnt = 0
    while !isempty(c.waitq)
        t = popfirst!(c.waitq)
        schedule(t, arg, error=error)
        cnt += 1
        all || break
    end
    return cnt
end

notify_error(c::GenericCondition, err) = notify(c, err, true, true)

"""
    isempty(condition)

Return `true` if no tasks are waiting on the condition, `false` otherwise.
"""
isempty(c::GenericCondition) = isempty(c.waitq)


# default (Julia v1.0) is currently single-threaded
# (although it uses MT-safe versions, when possible)
"""
    Condition()

Create an edge-triggered event source that tasks can wait for. Tasks that call [`wait`](@ref) on a
`Condition` are suspended and queued. Tasks are woken up when [`notify`](@ref) is later called on
the `Condition`. Edge triggering means that only tasks waiting at the time [`notify`](@ref) is
called can be woken up. For level-triggered notifications, you must keep extra state to keep
track of whether a notification has happened. The [`Channel`](@ref) and [`Threads.Event`](@ref) types do
this, and can be used for level-triggered events.

This object is NOT thread-safe. See [`Threads.Condition`](@ref) for a thread-safe version.
"""
const Condition = GenericCondition{AlwaysLockedST}

lock(c::GenericCondition{AlwaysLockedST}) =
    throw(ArgumentError("`Condition` is not thread-safe. Please use `Threads.Condition` instead for multi-threaded code."))
unlock(c::GenericCondition{AlwaysLockedST}) =
    throw(ArgumentError("`Condition` is not thread-safe. Please use `Threads.Condition` instead for multi-threaded code."))
N   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/threads.jl)      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
Multithreading support.
"""
module Threads

global Condition # we'll define this later, make sure we don't import Base.Condition

include("threadingconstructs.jl")
include("atomics.jl")
include("locks-mt.jl")

end
Z   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/threadingconstructs.jl=      # This file is a part of Julia. License is MIT: https://julialang.org/license

export threadid, nthreads, @threads, @spawn,
       threadpool, nthreadpools

"""
    Threads.threadid() -> Int

Get the ID number of the current thread of execution. The master thread has
ID `1`.

# Examples
```julia-repl
julia> Threads.threadid()
1

julia> Threads.@threads for i in 1:4
          println(Threads.threadid())
       end
4
2
5
4
```

!!! note
    The thread that a task runs on may change if the task yields, which is known as [`Task Migration`](@ref man-task-migration).
    For this reason in most cases it is not safe to use `threadid()` to index into, say, a vector of buffer or stateful objects.

"""
threadid() = Int(ccall(:jl_threadid, Int16, ())+1)

# lower bound on the largest threadid()
"""
    Threads.maxthreadid() -> Int

Get a lower bound on the number of threads (across all thread pools) available
to the Julia process, with atomic-acquire semantics. The result will always be
greater than or equal to [`threadid()`](@ref) as well as `threadid(task)` for
any task you were able to observe before calling `maxthreadid`.
"""
maxthreadid() = Int(Core.Intrinsics.atomic_pointerref(cglobal(:jl_n_threads, Cint), :acquire))

"""
    Threads.nthreads(:default | :interactive) -> Int

Get the current number of threads within the specified thread pool. The threads in `:interactive`
have id numbers `1:nthreads(:interactive)`, and the threads in `:default` have id numbers in
`nthreads(:interactive) .+ (1:nthreads(:default))`.

See also `BLAS.get_num_threads` and `BLAS.set_num_threads` in the [`LinearAlgebra`](@ref
man-linalg) standard library, and `nprocs()` in the [`Distributed`](@ref man-distributed)
standard library and [`Threads.maxthreadid()`](@ref).
"""
nthreads(pool::Symbol) = threadpoolsize(pool)

function _nthreads_in_pool(tpid::Int8)
    p = unsafe_load(cglobal(:jl_n_threads_per_pool, Ptr{Cint}))
    return Int(unsafe_load(p, tpid + 1))
end

function _tpid_to_sym(tpid::Int8)
    if tpid == 0
        return :interactive
    elseif tpid == 1
        return :default
    elseif tpid == -1
        return :foreign
    else
        throw(ArgumentError("Unrecognized threadpool id $tpid"))
    end
end

function _sym_to_tpid(tp::Symbol)
    if tp === :interactive
        return Int8(0)
    elseif tp === :default
        return Int8(1)
    elseif tp == :foreign
        return Int8(-1)
    else
        throw(ArgumentError("Unrecognized threadpool name `$(repr(tp))`"))
    end
end

"""
    Threads.threadpool(tid = threadid()) -> Symbol

Returns the specified thread's threadpool; either `:default`, `:interactive`, or `:foreign`.
"""
function threadpool(tid = threadid())
    tpid = ccall(:jl_threadpoolid, Int8, (Int16,), tid-1)
    return _tpid_to_sym(tpid)
end

"""
    Threads.nthreadpools() -> Int

Returns the number of threadpools currently configured.
"""
nthreadpools() = Int(unsafe_load(cglobal(:jl_n_threadpools, Cint)))

"""
    Threads.threadpoolsize(pool::Symbol = :default) -> Int

Get the number of threads available to the default thread pool (or to the
specified thread pool).

See also: `BLAS.get_num_threads` and `BLAS.set_num_threads` in the
[`LinearAlgebra`](@ref man-linalg) standard library, and `nprocs()` in the
[`Distributed`](@ref man-distributed) standard library.
"""
function threadpoolsize(pool::Symbol = :default)
    if pool === :default || pool === :interactive
        tpid = _sym_to_tpid(pool)
    elseif pool == :foreign
        error("Threadpool size of `:foreign` is indeterminant")
    else
        error("invalid threadpool specified")
    end
    return _nthreads_in_pool(tpid)
end

"""
    threadpooltids(pool::Symbol)

Returns a vector of IDs of threads in the given pool.
"""
function threadpooltids(pool::Symbol)
    ni = _nthreads_in_pool(Int8(0))
    if pool === :interactive
        return collect(1:ni)
    elseif pool === :default
        return collect(ni+1:ni+_nthreads_in_pool(Int8(1)))
    else
        error("invalid threadpool specified")
    end
end

"""
    Threads.ngcthreads() -> Int

Returns the number of GC threads currently configured.
This includes both mark threads and concurrent sweep threads.
"""
ngcthreads() = Int(unsafe_load(cglobal(:jl_n_gcthreads, Cint))) + 1

function threading_run(fun, static)
    ccall(:jl_enter_threaded_region, Cvoid, ())
    n = threadpoolsize()
    tid_offset = threadpoolsize(:interactive)
    tasks = Vector{Task}(undef, n)
    for i = 1:n
        t = Task(() -> fun(i)) # pass in tid
        t.sticky = static
        if static
            ccall(:jl_set_task_tid, Cint, (Any, Cint), t, tid_offset + i-1)
        else
            # TODO: this should be the current pool (except interactive) if there
            # are ever more than two pools.
            @assert ccall(:jl_set_task_threadpoolid, Cint, (Any, Int8), t, _sym_to_tpid(:default)) == 1
        end
        tasks[i] = t
        schedule(t)
    end
    for i = 1:n
        Base._wait(tasks[i])
    end
    ccall(:jl_exit_threaded_region, Cvoid, ())
    failed_tasks = filter!(istaskfailed, tasks)
    if !isempty(failed_tasks)
        throw(CompositeException(map(TaskFailedException, failed_tasks)))
    end
end

function _threadsfor(iter, lbody, schedule)
    lidx = iter.args[1]         # index
    range = iter.args[2]
    quote
        local threadsfor_fun
        let range = $(esc(range))
        function threadsfor_fun(tid = 1; onethread = false)
            r = range # Load into local variable
            lenr = length(r)
            # divide loop iterations among threads
            if onethread
                tid = 1
                len, rem = lenr, 0
            else
                len, rem = divrem(lenr, threadpoolsize())
            end
            # not enough iterations for all the threads?
            if len == 0
                if tid > rem
                    return
                end
                len, rem = 1, 0
            end
            # compute this thread's iterations
            f = firstindex(r) + ((tid-1) * len)
            l = f + len - 1
            # distribute remaining iterations evenly
            if rem > 0
                if tid <= rem
                    f = f + (tid-1)
                    l = l + tid
                else
                    f = f + rem
                    l = l + rem
                end
            end
            # run this thread's iterations
            for i = f:l
                local $(esc(lidx)) = @inbounds r[i]
                $(esc(lbody))
            end
        end
        end
        if $(schedule === :dynamic || schedule === :default)
            threading_run(threadsfor_fun, false)
        elseif ccall(:jl_in_threaded_region, Cint, ()) != 0 # :static
            error("`@threads :static` cannot be used concurrently or nested")
        else # :static
            threading_run(threadsfor_fun, true)
        end
        nothing
    end
end

"""
    Threads.@threads [schedule] for ... end

A macro to execute a `for` loop in parallel. The iteration space is distributed to
coarse-grained tasks. This policy can be specified by the `schedule` argument. The
execution of the loop waits for the evaluation of all iterations.

See also: [`@spawn`](@ref Threads.@spawn) and
`pmap` in [`Distributed`](@ref man-distributed).

# Extended help

## Semantics

Unless stronger guarantees are specified by the scheduling option, the loop executed by
`@threads` macro have the following semantics.

The `@threads` macro executes the loop body in an unspecified order and potentially
concurrently. It does not specify the exact assignments of the tasks and the worker threads.
The assignments can be different for each execution. The loop body code (including any code
transitively called from it) must not make any assumptions about the distribution of
iterations to tasks or the worker thread in which they are executed. The loop body for each
iteration must be able to make forward progress independent of other iterations and be free
from data races. As such, invalid synchronizations across iterations may deadlock while
unsynchronized memory accesses may result in undefined behavior.

For example, the above conditions imply that:

- A lock taken in an iteration *must* be released within the same iteration.
- Communicating between iterations using blocking primitives like `Channel`s is incorrect.
- Write only to locations not shared across iterations (unless a lock or atomic operation is
  used).
- Unless the `:static` schedule is used, the value of [`threadid()`](@ref Threads.threadid)
  may change even within a single iteration. See [`Task Migration`](@ref man-task-migration).

## Schedulers

Without the scheduler argument, the exact scheduling is unspecified and varies across Julia
releases. Currently, `:dynamic` is used when the scheduler is not specified.

!!! compat "Julia 1.5"
    The `schedule` argument is available as of Julia 1.5.

### `:dynamic` (default)

`:dynamic` scheduler executes iterations dynamically to available worker threads. Current
implementation assumes that the workload for each iteration is uniform. However, this
assumption may be removed in the future.

This scheduling option is merely a hint to the underlying execution mechanism. However, a
few properties can be expected. The number of `Task`s used by `:dynamic` scheduler is
bounded by a small constant multiple of the number of available worker threads
([`Threads.threadpoolsize()`](@ref)). Each task processes contiguous regions of the
iteration space. Thus, `@threads :dynamic for x in xs; f(x); end` is typically more
efficient than `@sync for x in xs; @spawn f(x); end` if `length(xs)` is significantly
larger than the number of the worker threads and the run-time of `f(x)` is relatively
smaller than the cost of spawning and synchronizing a task (typically less than 10
microseconds).

!!! compat "Julia 1.8"
    The `:dynamic` option for the `schedule` argument is available and the default as of Julia 1.8.

### `:static`

`:static` scheduler creates one task per thread and divides the iterations equally among
them, assigning each task specifically to each thread. In particular, the value of
[`threadid()`](@ref Threads.threadid) is guaranteed to be constant within one iteration.
Specifying `:static` is an error if used from inside another `@threads` loop or from a
thread other than 1.

!!! note
    `:static` scheduling exists for supporting transition of code written before Julia 1.3.
    In newly written library functions, `:static` scheduling is discouraged because the
    functions using this option cannot be called from arbitrary worker threads.

## Example

To illustrate of the different scheduling strategies, consider the following function
`busywait` containing a non-yielding timed loop that runs for a given number of seconds.

```julia-repl
julia> function busywait(seconds)
            tstart = time_ns()
            while (time_ns() - tstart) / 1e9 < seconds
            end
        end

julia> @time begin
            Threads.@spawn busywait(5)
            Threads.@threads :static for i in 1:Threads.threadpoolsize()
                busywait(1)
            end
        end
6.003001 seconds (16.33 k allocations: 899.255 KiB, 0.25% compilation time)

julia> @time begin
            Threads.@spawn busywait(5)
            Threads.@threads :dynamic for i in 1:Threads.threadpoolsize()
                busywait(1)
            end
        end
2.012056 seconds (16.05 k allocations: 883.919 KiB, 0.66% compilation time)
```

The `:dynamic` example takes 2 seconds since one of the non-occupied threads is able
to run two of the 1-second iterations to complete the for loop.
"""
macro threads(args...)
    na = length(args)
    if na == 2
        sched, ex = args
        if sched isa QuoteNode
            sched = sched.value
        elseif sched isa Symbol
            # for now only allow quoted symbols
            sched = nothing
        end
        if sched !== :static && sched !== :dynamic
            throw(ArgumentError("unsupported schedule argument in @threads"))
        end
    elseif na == 1
        sched = :default
        ex = args[1]
    else
        throw(ArgumentError("wrong number of arguments in @threads"))
    end
    if !(isa(ex, Expr) && ex.head === :for)
        throw(ArgumentError("@threads requires a `for` loop expression"))
    end
    if !(ex.args[1] isa Expr && ex.args[1].head === :(=))
        throw(ArgumentError("nested outer loops are not currently supported by @threads"))
    end
    return _threadsfor(ex.args[1], ex.args[2], sched)
end

function _spawn_set_thrpool(t::Task, tp::Symbol)
    tpid = _sym_to_tpid(tp)
    if tpid == -1 || _nthreads_in_pool(tpid) == 0
        tpid = _sym_to_tpid(:default)
    end
    @assert ccall(:jl_set_task_threadpoolid, Cint, (Any, Int8), t, tpid) == 1
    nothing
end

"""
    Threads.@spawn [:default|:interactive] expr

Create a [`Task`](@ref) and [`schedule`](@ref) it to run on any available
thread in the specified threadpool (`:default` if unspecified). The task is
allocated to a thread once one becomes available. To wait for the task to
finish, call [`wait`](@ref) on the result of this macro, or call
[`fetch`](@ref) to wait and then obtain its return value.

Values can be interpolated into `@spawn` via `\$`, which copies the value
directly into the constructed underlying closure. This allows you to insert
the _value_ of a variable, isolating the asynchronous code from changes to
the variable's value in the current task.

!!! note
    The thread that the task runs on may change if the task yields, therefore `threadid()` should not
    be treated as constant for a task. See [`Task Migration`](@ref man-task-migration), and the broader
    [multi-threading](@ref man-multithreading) manual for further important caveats.
    See also the chapter on [threadpools](@ref man-threadpools).

!!! compat "Julia 1.3"
    This macro is available as of Julia 1.3.

!!! compat "Julia 1.4"
    Interpolating values via `\$` is available as of Julia 1.4.

!!! compat "Julia 1.9"
    A threadpool may be specified as of Julia 1.9.

# Examples
```julia-repl
julia> t() = println("Hello from ", Threads.threadid());

julia> tasks = fetch.([Threads.@spawn t() for i in 1:4]);
Hello from 1
Hello from 1
Hello from 3
Hello from 4
```
"""
macro spawn(args...)
    tp = QuoteNode(:default)
    na = length(args)
    if na == 2
        ttype, ex = args
        if ttype isa QuoteNode
            ttype = ttype.value
            if ttype !== :interactive && ttype !== :default
                throw(ArgumentError("unsupported threadpool in @spawn: $ttype"))
            end
            tp = QuoteNode(ttype)
        else
            tp = ttype
        end
    elseif na == 1
        ex = args[1]
    else
        throw(ArgumentError("wrong number of arguments in @spawn"))
    end

    letargs = Base._lift_one_interp!(ex)

    thunk = Base.replace_linenums!(:(()->($(esc(ex)))), __source__)
    var = esc(Base.sync_varname)
    quote
        let $(letargs...)
            local task = Task($thunk)
            task.sticky = false
            _spawn_set_thrpool(task, $(esc(tp)))
            if $(Expr(:islocal, var))
                put!($var, task)
            end
            schedule(task)
            task
        end
    end
end

# This is a stub that can be overloaded for downstream structures like `Channel`
function foreach end

# Scheduling traits that can be employed for downstream overloads
abstract type AbstractSchedule end
struct StaticSchedule <: AbstractSchedule end
struct FairSchedule <: AbstractSchedule end
N   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/atomics.jl�1      # This file is a part of Julia. License is MIT: https://julialang.org/license

using Core.Intrinsics: llvmcall

import .Base: setindex!, getindex, unsafe_convert
import .Base.Sys: ARCH, WORD_SIZE

export
    Atomic,
    atomic_cas!,
    atomic_xchg!,
    atomic_add!, atomic_sub!,
    atomic_and!, atomic_nand!, atomic_or!, atomic_xor!,
    atomic_max!, atomic_min!,
    atomic_fence
##
# Filter out unsupported atomic types on platforms
# - 128-bit atomics do not exist on AArch32.
# - Omitting 128-bit types on 32bit x86 and ppc64
# - LLVM doesn't currently support atomics on floats for ppc64
#   C++20 is adding limited support for atomics on float, but as of
#   now Clang does not support that yet.
if Sys.ARCH === :i686 || startswith(string(Sys.ARCH), "arm") ||
   Sys.ARCH === :powerpc64le || Sys.ARCH === :ppc64le
    const inttypes = (Int8, Int16, Int32, Int64,
                      UInt8, UInt16, UInt32, UInt64)
else
    const inttypes = (Int8, Int16, Int32, Int64, Int128,
                      UInt8, UInt16, UInt32, UInt64, UInt128)
end
const floattypes = (Float16, Float32, Float64)
const arithmetictypes = (inttypes..., floattypes...)
# TODO: Support Ptr
if Sys.ARCH === :powerpc64le || Sys.ARCH === :ppc64le
    const atomictypes = (inttypes..., Bool)
else
    const atomictypes = (arithmetictypes..., Bool)
end

const IntTypes = Union{inttypes...}
const FloatTypes = Union{floattypes...}
const ArithmeticTypes = Union{arithmetictypes...}
const AtomicTypes = Union{atomictypes...}

"""
    Threads.Atomic{T}

Holds a reference to an object of type `T`, ensuring that it is only
accessed atomically, i.e. in a thread-safe manner.

Only certain "simple" types can be used atomically, namely the
primitive boolean, integer, and float-point types. These are `Bool`,
`Int8`...`Int128`, `UInt8`...`UInt128`, and `Float16`...`Float64`.

New atomic objects can be created from a non-atomic values; if none is
specified, the atomic object is initialized with zero.

Atomic objects can be accessed using the `[]` notation:

# Examples
```jldoctest
julia> x = Threads.Atomic{Int}(3)
Base.Threads.Atomic{Int64}(3)

julia> x[] = 1
1

julia> x[]
1
```

Atomic operations use an `atomic_` prefix, such as [`atomic_add!`](@ref),
[`atomic_xchg!`](@ref), etc.
"""
mutable struct Atomic{T<:AtomicTypes}
    value::T
    Atomic{T}() where {T<:AtomicTypes} = new(zero(T))
    Atomic{T}(value) where {T<:AtomicTypes} = new(value)
end

Atomic() = Atomic{Int}()

"""
    Threads.atomic_cas!(x::Atomic{T}, cmp::T, newval::T) where T

Atomically compare-and-set `x`

Atomically compares the value in `x` with `cmp`. If equal, write
`newval` to `x`. Otherwise, leaves `x` unmodified. Returns the old
value in `x`. By comparing the returned value to `cmp` (via `===`) one
knows whether `x` was modified and now holds the new value `newval`.

For further details, see LLVM's `cmpxchg` instruction.

This function can be used to implement transactional semantics. Before
the transaction, one records the value in `x`. After the transaction,
the new value is stored only if `x` has not been modified in the mean
time.

# Examples
```jldoctest
julia> x = Threads.Atomic{Int}(3)
Base.Threads.Atomic{Int64}(3)

julia> Threads.atomic_cas!(x, 4, 2);

julia> x
Base.Threads.Atomic{Int64}(3)

julia> Threads.atomic_cas!(x, 3, 2);

julia> x
Base.Threads.Atomic{Int64}(2)
```
"""
function atomic_cas! end

"""
    Threads.atomic_xchg!(x::Atomic{T}, newval::T) where T

Atomically exchange the value in `x`

Atomically exchanges the value in `x` with `newval`. Returns the **old**
value.

For further details, see LLVM's `atomicrmw xchg` instruction.

# Examples
```jldoctest
julia> x = Threads.Atomic{Int}(3)
Base.Threads.Atomic{Int64}(3)

julia> Threads.atomic_xchg!(x, 2)
3

julia> x[]
2
```
"""
function atomic_xchg! end

"""
    Threads.atomic_add!(x::Atomic{T}, val::T) where T <: ArithmeticTypes

Atomically add `val` to `x`

Performs `x[] += val` atomically. Returns the **old** value. Not defined for
`Atomic{Bool}`.

For further details, see LLVM's `atomicrmw add` instruction.

# Examples
```jldoctest
julia> x = Threads.Atomic{Int}(3)
Base.Threads.Atomic{Int64}(3)

julia> Threads.atomic_add!(x, 2)
3

julia> x[]
5
```
"""
function atomic_add! end

"""
    Threads.atomic_sub!(x::Atomic{T}, val::T) where T <: ArithmeticTypes

Atomically subtract `val` from `x`

Performs `x[] -= val` atomically. Returns the **old** value. Not defined for
`Atomic{Bool}`.

For further details, see LLVM's `atomicrmw sub` instruction.

# Examples
```jldoctest
julia> x = Threads.Atomic{Int}(3)
Base.Threads.Atomic{Int64}(3)

julia> Threads.atomic_sub!(x, 2)
3

julia> x[]
1
```
"""
function atomic_sub! end

"""
    Threads.atomic_and!(x::Atomic{T}, val::T) where T

Atomically bitwise-and `x` with `val`

Performs `x[] &= val` atomically. Returns the **old** value.

For further details, see LLVM's `atomicrmw and` instruction.

# Examples
```jldoctest
julia> x = Threads.Atomic{Int}(3)
Base.Threads.Atomic{Int64}(3)

julia> Threads.atomic_and!(x, 2)
3

julia> x[]
2
```
"""
function atomic_and! end

"""
    Threads.atomic_nand!(x::Atomic{T}, val::T) where T

Atomically bitwise-nand (not-and) `x` with `val`

Performs `x[] = ~(x[] & val)` atomically. Returns the **old** value.

For further details, see LLVM's `atomicrmw nand` instruction.

# Examples
```jldoctest
julia> x = Threads.Atomic{Int}(3)
Base.Threads.Atomic{Int64}(3)

julia> Threads.atomic_nand!(x, 2)
3

julia> x[]
-3
```
"""
function atomic_nand! end

"""
    Threads.atomic_or!(x::Atomic{T}, val::T) where T

Atomically bitwise-or `x` with `val`

Performs `x[] |= val` atomically. Returns the **old** value.

For further details, see LLVM's `atomicrmw or` instruction.

# Examples
```jldoctest
julia> x = Threads.Atomic{Int}(5)
Base.Threads.Atomic{Int64}(5)

julia> Threads.atomic_or!(x, 7)
5

julia> x[]
7
```
"""
function atomic_or! end

"""
    Threads.atomic_xor!(x::Atomic{T}, val::T) where T

Atomically bitwise-xor (exclusive-or) `x` with `val`

Performs `x[] \$= val` atomically. Returns the **old** value.

For further details, see LLVM's `atomicrmw xor` instruction.

# Examples
```jldoctest
julia> x = Threads.Atomic{Int}(5)
Base.Threads.Atomic{Int64}(5)

julia> Threads.atomic_xor!(x, 7)
5

julia> x[]
2
```
"""
function atomic_xor! end

"""
    Threads.atomic_max!(x::Atomic{T}, val::T) where T

Atomically store the maximum of `x` and `val` in `x`

Performs `x[] = max(x[], val)` atomically. Returns the **old** value.

For further details, see LLVM's `atomicrmw max` instruction.

# Examples
```jldoctest
julia> x = Threads.Atomic{Int}(5)
Base.Threads.Atomic{Int64}(5)

julia> Threads.atomic_max!(x, 7)
5

julia> x[]
7
```
"""
function atomic_max! end

"""
    Threads.atomic_min!(x::Atomic{T}, val::T) where T

Atomically store the minimum of `x` and `val` in `x`

Performs `x[] = min(x[], val)` atomically. Returns the **old** value.

For further details, see LLVM's `atomicrmw min` instruction.

# Examples
```jldoctest
julia> x = Threads.Atomic{Int}(7)
Base.Threads.Atomic{Int64}(7)

julia> Threads.atomic_min!(x, 5)
7

julia> x[]
5
```
"""
function atomic_min! end

unsafe_convert(::Type{Ptr{T}}, x::Atomic{T}) where {T} = convert(Ptr{T}, pointer_from_objref(x))
setindex!(x::Atomic{T}, v) where {T} = setindex!(x, convert(T, v))

const llvmtypes = IdDict{Any,String}(
    Bool => "i8",  # julia represents bools with 8-bits for now. # TODO: is this okay?
    Int8 => "i8", UInt8 => "i8",
    Int16 => "i16", UInt16 => "i16",
    Int32 => "i32", UInt32 => "i32",
    Int64 => "i64", UInt64 => "i64",
    Int128 => "i128", UInt128 => "i128",
    Float16 => "half",
    Float32 => "float",
    Float64 => "double",
)
inttype(::Type{T}) where {T<:Integer} = T
inttype(::Type{Float16}) = Int16
inttype(::Type{Float32}) = Int32
inttype(::Type{Float64}) = Int64


import ..Base.gc_alignment

# All atomic operations have acquire and/or release semantics, depending on
# whether the load or store values. Most of the time, this is what one wants
# anyway, and it's only moderately expensive on most hardware.
for typ in atomictypes
    lt = llvmtypes[typ]
    ilt = llvmtypes[inttype(typ)]
    rt = "$lt, $lt*"
    irt = "$ilt, $ilt*"
    @eval getindex(x::Atomic{$typ}) =
        GC.@preserve x llvmcall($"""
                 %ptr = inttoptr i$WORD_SIZE %0 to $lt*
                 %rv = load atomic $rt %ptr acquire, align $(gc_alignment(typ))
                 ret $lt %rv
                 """, $typ, Tuple{Ptr{$typ}}, unsafe_convert(Ptr{$typ}, x))
    @eval setindex!(x::Atomic{$typ}, v::$typ) =
        GC.@preserve x llvmcall($"""
                 %ptr = inttoptr i$WORD_SIZE %0 to $lt*
                 store atomic $lt %1, $lt* %ptr release, align $(gc_alignment(typ))
                 ret void
                 """, Cvoid, Tuple{Ptr{$typ}, $typ}, unsafe_convert(Ptr{$typ}, x), v)

    # Note: atomic_cas! succeeded (i.e. it stored "new") if and only if the result is "cmp"
    if typ <: Integer
        @eval atomic_cas!(x::Atomic{$typ}, cmp::$typ, new::$typ) =
            GC.@preserve x llvmcall($"""
                     %ptr = inttoptr i$WORD_SIZE %0 to $lt*
                     %rs = cmpxchg $lt* %ptr, $lt %1, $lt %2 acq_rel acquire
                     %rv = extractvalue { $lt, i1 } %rs, 0
                     ret $lt %rv
                     """, $typ, Tuple{Ptr{$typ},$typ,$typ},
                     unsafe_convert(Ptr{$typ}, x), cmp, new)
    else
        @eval atomic_cas!(x::Atomic{$typ}, cmp::$typ, new::$typ) =
            GC.@preserve x llvmcall($"""
                     %iptr = inttoptr i$WORD_SIZE %0 to $ilt*
                     %icmp = bitcast $lt %1 to $ilt
                     %inew = bitcast $lt %2 to $ilt
                     %irs = cmpxchg $ilt* %iptr, $ilt %icmp, $ilt %inew acq_rel acquire
                     %irv = extractvalue { $ilt, i1 } %irs, 0
                     %rv = bitcast $ilt %irv to $lt
                     ret $lt %rv
                     """, $typ, Tuple{Ptr{$typ},$typ,$typ},
                     unsafe_convert(Ptr{$typ}, x), cmp, new)
    end

    arithmetic_ops = [:add, :sub]
    for rmwop in [arithmetic_ops..., :xchg, :and, :nand, :or, :xor, :max, :min]
        rmw = string(rmwop)
        fn = Symbol("atomic_", rmw, "!")
        if (rmw == "max" || rmw == "min") && typ <: Unsigned
            # LLVM distinguishes signedness in the operation, not the integer type.
            rmw = "u" * rmw
        end
        if rmwop in arithmetic_ops && !(typ <: ArithmeticTypes) continue end
        if typ <: Integer
            @eval $fn(x::Atomic{$typ}, v::$typ) =
                GC.@preserve x llvmcall($"""
                         %ptr = inttoptr i$WORD_SIZE %0 to $lt*
                         %rv = atomicrmw $rmw $lt* %ptr, $lt %1 acq_rel
                         ret $lt %rv
                         """, $typ, Tuple{Ptr{$typ}, $typ}, unsafe_convert(Ptr{$typ}, x), v)
        else
            rmwop === :xchg || continue
            @eval $fn(x::Atomic{$typ}, v::$typ) =
                GC.@preserve x llvmcall($"""
                         %iptr = inttoptr i$WORD_SIZE %0 to $ilt*
                         %ival = bitcast $lt %1 to $ilt
                         %irv = atomicrmw $rmw $ilt* %iptr, $ilt %ival acq_rel
                         %rv = bitcast $ilt %irv to $lt
                         ret $lt %rv
                         """, $typ, Tuple{Ptr{$typ}, $typ}, unsafe_convert(Ptr{$typ}, x), v)
        end
    end
end

# Provide atomic floating-point operations via atomic_cas!
const opnames = Dict{Symbol, Symbol}(:+ => :add, :- => :sub)
for op in [:+, :-, :max, :min]
    opname = get(opnames, op, op)
    @eval function $(Symbol("atomic_", opname, "!"))(var::Atomic{T}, val::T) where T<:FloatTypes
        IT = inttype(T)
        old = var[]
        while true
            new = $op(old, val)
            cmp = old
            old = atomic_cas!(var, cmp, new)
            reinterpret(IT, old) == reinterpret(IT, cmp) && return old
            # Temporary solution before we have gc transition support in codegen.
            ccall(:jl_gc_safepoint, Cvoid, ())
        end
    end
end

"""
    Threads.atomic_fence()

Insert a sequential-consistency memory fence

Inserts a memory fence with sequentially-consistent ordering
semantics. There are algorithms where this is needed, i.e. where an
acquire/release ordering is insufficient.

This is likely a very expensive operation. Given that all other atomic
operations in Julia already have acquire/release semantics, explicit
fences should not be necessary in most cases.

For further details, see LLVM's `fence` instruction.
"""
atomic_fence() = llvmcall("""
                          fence seq_cst
                          ret void
                          """, Cvoid, Tuple{})
O   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/locks-mt.jl	      # This file is a part of Julia. License is MIT: https://julialang.org/license

import .Base: unsafe_convert, lock, trylock, unlock, islocked, wait, notify, AbstractLock

export SpinLock

# Important Note: these low-level primitives defined here
#   are typically not for general usage

##########################################
# Atomic Locks
##########################################

"""
    SpinLock()

Create a non-reentrant, test-and-test-and-set spin lock.
Recursive use will result in a deadlock.
This kind of lock should only be used around code that takes little time
to execute and does not block (e.g. perform I/O).
In general, [`ReentrantLock`](@ref) should be used instead.

Each [`lock`](@ref) must be matched with an [`unlock`](@ref).
If [`!islocked(lck::SpinLock)`](@ref islocked) holds, [`trylock(lck)`](@ref trylock)
succeeds unless there are other tasks attempting to hold the lock "at the same time."

Test-and-test-and-set spin locks are quickest up to about 30ish
contending threads. If you have more contention than that, different
synchronization approaches should be considered.
"""
mutable struct SpinLock <: AbstractLock
    # we make this much larger than necessary to minimize false-sharing
    @atomic owned::Int
    SpinLock() = new(0)
end

# Note: this cannot assert that the lock is held by the correct thread, because we do not
# track which thread locked it. Users beware.
Base.assert_havelock(l::SpinLock) = islocked(l) ? nothing : Base.concurrency_violation()

function lock(l::SpinLock)
    while true
        if @inline trylock(l)
            return
        end
        ccall(:jl_cpu_suspend, Cvoid, ())
        # Temporary solution before we have gc transition support in codegen.
        ccall(:jl_gc_safepoint, Cvoid, ())
    end
end

function trylock(l::SpinLock)
    if l.owned == 0
        GC.disable_finalizers()
        p = @atomicswap :acquire l.owned = 1
        if p == 0
            return true
        end
        GC.enable_finalizers()
    end
    return false
end

function unlock(l::SpinLock)
    if (@atomicswap :release l.owned = 0) == 0
        error("unlock count must match lock count")
    end
    GC.enable_finalizers()
    ccall(:jl_cpu_wake, Cvoid, ())
    return
end

function islocked(l::SpinLock)
    return (@atomic :monotonic l.owned) != 0
end
K   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/lock.jl4      # This file is a part of Julia. License is MIT: https://julialang.org/license

const ThreadSynchronizer = GenericCondition{Threads.SpinLock}

# Advisory reentrant lock
"""
    ReentrantLock()

Creates a re-entrant lock for synchronizing [`Task`](@ref)s. The same task can
acquire the lock as many times as required (this is what the "Reentrant" part
of the name means). Each [`lock`](@ref) must be matched with an [`unlock`](@ref).

Calling 'lock' will also inhibit running of finalizers on that thread until the
corresponding 'unlock'. Use of the standard lock pattern illustrated below
should naturally be supported, but beware of inverting the try/lock order or
missing the try block entirely (e.g. attempting to return with the lock still
held):

This provides a acquire/release memory ordering on lock/unlock calls.

```
lock(l)
try
    <atomic work>
finally
    unlock(l)
end
```

If [`!islocked(lck::ReentrantLock)`](@ref islocked) holds, [`trylock(lck)`](@ref trylock)
succeeds unless there are other tasks attempting to hold the lock "at the same time."
"""
mutable struct ReentrantLock <: AbstractLock
    # offset = 16
    @atomic locked_by::Union{Task, Nothing}
    # offset32 = 20, offset64 = 24
    reentrancy_cnt::UInt32
    # offset32 = 24, offset64 = 28
    @atomic havelock::UInt8 # 0x0 = none, 0x1 = lock, 0x2 = conflict
    # offset32 = 28, offset64 = 32
    cond_wait::ThreadSynchronizer # 2 words
    # offset32 = 36, offset64 = 48
    # sizeof32 = 20, sizeof64 = 32
    # now add padding to make this a full cache line to minimize false sharing between objects
    _::NTuple{Int === Int32 ? 2 : 3, Int}
    # offset32 = 44, offset64 = 72 == sizeof+offset
    # sizeof32 = 28, sizeof64 = 56

    ReentrantLock() = new(nothing, 0x0000_0000, 0x00, ThreadSynchronizer())
end

assert_havelock(l::ReentrantLock) = assert_havelock(l, l.locked_by)

"""
    islocked(lock) -> Status (Boolean)

Check whether the `lock` is held by any task/thread.
This function alone should not be used for synchronization. However, `islocked` combined
with [`trylock`](@ref) can be used for writing the test-and-test-and-set or exponential
backoff algorithms *if it is supported by the `typeof(lock)`* (read its documentation).

# Extended help

For example, an exponential backoff can be implemented as follows if the `lock`
implementation satisfied the properties documented below.

```julia
nspins = 0
while true
    while islocked(lock)
        GC.safepoint()
        nspins += 1
        nspins > LIMIT && error("timeout")
    end
    trylock(lock) && break
    backoff()
end
```

## Implementation

A lock implementation is advised to define `islocked` with the following properties and note
it in its docstring.

* `islocked(lock)` is data-race-free.
* If `islocked(lock)` returns `false`, an immediate invocation of `trylock(lock)` must
  succeed (returns `true`) if there is no interference from other tasks.
"""
function islocked end
# Above docstring is a documentation for the abstract interface and not the one specific to
# `ReentrantLock`.

function islocked(rl::ReentrantLock)
    return (@atomic :monotonic rl.havelock) != 0
end

"""
    trylock(lock) -> Success (Boolean)

Acquire the lock if it is available,
and return `true` if successful.
If the lock is already locked by a different task/thread,
return `false`.

Each successful `trylock` must be matched by an [`unlock`](@ref).

Function `trylock` combined with [`islocked`](@ref) can be used for writing the
test-and-test-and-set or exponential backoff algorithms *if it is supported by the
`typeof(lock)`* (read its documentation).
"""
function trylock end
# Above docstring is a documentation for the abstract interface and not the one specific to
# `ReentrantLock`.

@inline function trylock(rl::ReentrantLock)
    ct = current_task()
    if rl.locked_by === ct
        #@assert rl.havelock !== 0x00
        rl.reentrancy_cnt += 0x0000_0001
        return true
    end
    return _trylock(rl, ct)
end
@noinline function _trylock(rl::ReentrantLock, ct::Task)
    GC.disable_finalizers()
    if (@atomicreplace :acquire rl.havelock 0x00 => 0x01).success
        #@assert rl.locked_by === nothing
        #@assert rl.reentrancy_cnt === 0
        rl.reentrancy_cnt = 0x0000_0001
        @atomic :release rl.locked_by = ct
        return true
    end
    GC.enable_finalizers()
    return false
end

"""
    lock(lock)

Acquire the `lock` when it becomes available.
If the lock is already locked by a different task/thread,
wait for it to become available.

Each `lock` must be matched by an [`unlock`](@ref).
"""
@inline function lock(rl::ReentrantLock)
    trylock(rl) || (@noinline function slowlock(rl::ReentrantLock)
        c = rl.cond_wait
        lock(c.lock)
        try
            while true
                if (@atomicreplace rl.havelock 0x01 => 0x02).old == 0x00 # :sequentially_consistent ? # now either 0x00 or 0x02
                    # it was unlocked, so try to lock it ourself
                    _trylock(rl, current_task()) && break
                else # it was locked, so now wait for the release to notify us
                    wait(c)
                end
            end
        finally
            unlock(c.lock)
        end
    end)(rl)
    return
end

"""
    unlock(lock)

Releases ownership of the `lock`.

If this is a recursive lock which has been acquired before, decrement an
internal counter and return immediately.
"""
@inline function unlock(rl::ReentrantLock)
    rl.locked_by === current_task() ||
        error(rl.reentrancy_cnt == 0x0000_0000 ? "unlock count must match lock count" : "unlock from wrong thread")
    (@noinline function _unlock(rl::ReentrantLock)
        n = rl.reentrancy_cnt - 0x0000_0001
        rl.reentrancy_cnt = n
        if n == 0x0000_00000
            @atomic :monotonic rl.locked_by = nothing
            if (@atomicswap :release rl.havelock = 0x00) == 0x02
                (@noinline function notifywaiters(rl)
                    cond_wait = rl.cond_wait
                    lock(cond_wait)
                    try
                        notify(cond_wait)
                    finally
                        unlock(cond_wait)
                    end
                end)(rl)
            end
            return true
        end
        return false
    end)(rl) && GC.enable_finalizers()
    nothing
end

function unlockall(rl::ReentrantLock)
    n = @atomicswap :not_atomic rl.reentrancy_cnt = 0x0000_0001
    unlock(rl)
    return n
end

function relockall(rl::ReentrantLock, n::UInt32)
    lock(rl)
    old = @atomicswap :not_atomic rl.reentrancy_cnt = n
    old == 0x0000_0001 || concurrency_violation()
    return
end

"""
    lock(f::Function, lock)

Acquire the `lock`, execute `f` with the `lock` held, and release the `lock` when `f`
returns. If the lock is already locked by a different task/thread, wait for it to become
available.

When this function returns, the `lock` has been released, so the caller should
not attempt to `unlock` it.

!!! compat "Julia 1.7"
    Using a [`Channel`](@ref) as the second argument requires Julia 1.7 or later.
"""
function lock(f, l::AbstractLock)
    lock(l)
    try
        return f()
    finally
        unlock(l)
    end
end

function trylock(f, l::AbstractLock)
    if trylock(l)
        try
            return f()
        finally
            unlock(l)
        end
    end
    return false
end

"""
    @lock l expr

Macro version of `lock(f, l::AbstractLock)` but with `expr` instead of `f` function.
Expands to:
```julia
lock(l)
try
    expr
finally
    unlock(l)
end
```
This is similar to using [`lock`](@ref) with a `do` block, but avoids creating a closure
and thus can improve the performance.
"""
macro lock(l, expr)
    quote
        temp = $(esc(l))
        lock(temp)
        try
            $(esc(expr))
        finally
            unlock(temp)
        end
    end
end

"""
    @lock_nofail l expr

Equivalent to `@lock l expr` for cases in which we can guarantee that the function
will not throw any error. In this case, avoiding try-catch can improve the performance.
See [`@lock`](@ref).
"""
macro lock_nofail(l, expr)
    quote
        temp = $(esc(l))
        lock(temp)
        val = $(esc(expr))
        unlock(temp)
        val
    end
end

@eval Threads begin
    """
        Threads.Condition([lock])

    A thread-safe version of [`Base.Condition`](@ref).

    To call [`wait`](@ref) or [`notify`](@ref) on a `Threads.Condition`, you must first call
    [`lock`](@ref) on it. When `wait` is called, the lock is atomically released during
    blocking, and will be reacquired before `wait` returns. Therefore idiomatic use
    of a `Threads.Condition` `c` looks like the following:

    ```
    lock(c)
    try
        while !thing_we_are_waiting_for
            wait(c)
        end
    finally
        unlock(c)
    end
    ```

    !!! compat "Julia 1.2"
        This functionality requires at least Julia 1.2.
    """
    const Condition = Base.GenericCondition{Base.ReentrantLock}

    """
    Special note for [`Threads.Condition`](@ref):

    The caller must be holding the [`lock`](@ref) that owns a `Threads.Condition` before calling this method.
    The calling task will be blocked until some other task wakes it,
    usually by calling [`notify`](@ref) on the same `Threads.Condition` object.
    The lock will be atomically released when blocking (even if it was locked recursively),
    and will be reacquired before returning.
    """
    wait(c::Condition)
end

"""
    Semaphore(sem_size)

Create a counting semaphore that allows at most `sem_size`
acquires to be in use at any time.
Each acquire must be matched with a release.

This provides a acquire & release memory ordering on acquire/release calls.
"""
mutable struct Semaphore
    sem_size::Int
    curr_cnt::Int
    cond_wait::Threads.Condition
    Semaphore(sem_size) = sem_size > 0 ? new(sem_size, 0, Threads.Condition()) : throw(ArgumentError("Semaphore size must be > 0"))
end

"""
    acquire(s::Semaphore)

Wait for one of the `sem_size` permits to be available,
blocking until one can be acquired.
"""
function acquire(s::Semaphore)
    lock(s.cond_wait)
    try
        while s.curr_cnt >= s.sem_size
            wait(s.cond_wait)
        end
        s.curr_cnt = s.curr_cnt + 1
    finally
        unlock(s.cond_wait)
    end
    return
end

"""
    acquire(f, s::Semaphore)

Execute `f` after acquiring from Semaphore `s`,
and `release` on completion or error.

For example, a do-block form that ensures only 2
calls of `foo` will be active at the same time:

```julia
s = Base.Semaphore(2)
@sync for _ in 1:100
    Threads.@spawn begin
        Base.acquire(s) do
            foo()
        end
    end
end
```

!!! compat "Julia 1.8"
    This method requires at least Julia 1.8.

"""
function acquire(f, s::Semaphore)
    acquire(s)
    try
        return f()
    finally
        release(s)
    end
end

"""
    release(s::Semaphore)

Return one permit to the pool,
possibly allowing another task to acquire it
and resume execution.
"""
function release(s::Semaphore)
    lock(s.cond_wait)
    try
        s.curr_cnt > 0 || error("release count must match acquire count")
        s.curr_cnt -= 1
        notify(s.cond_wait; all=false)
    finally
        unlock(s.cond_wait)
    end
    return
end


"""
    Event([autoreset=false])

Create a level-triggered event source. Tasks that call [`wait`](@ref) on an
`Event` are suspended and queued until [`notify`](@ref) is called on the `Event`.
After `notify` is called, the `Event` remains in a signaled state and
tasks will no longer block when waiting for it, until `reset` is called.

If `autoreset` is true, at most one task will be released from `wait` for
each call to `notify`.

This provides an acquire & release memory ordering on notify/wait.

!!! compat "Julia 1.1"
    This functionality requires at least Julia 1.1.

!!! compat "Julia 1.8"
    The `autoreset` functionality and memory ordering guarantee requires at least Julia 1.8.
"""
mutable struct Event
    notify::Threads.Condition
    autoreset::Bool
    @atomic set::Bool
    Event(autoreset::Bool=false) = new(Threads.Condition(), autoreset, false)
end

function wait(e::Event)
    if e.autoreset
        (@atomicswap :acquire_release e.set = false) && return
    else
        (@atomic e.set) && return # full barrier also
    end
    lock(e.notify) # acquire barrier
    try
        if e.autoreset
            (@atomicswap :acquire_release e.set = false) && return
        else
            e.set && return
        end
        wait(e.notify)
    finally
        unlock(e.notify) # release barrier
    end
    nothing
end

function notify(e::Event)
    lock(e.notify) # acquire barrier
    try
        if e.autoreset
            if notify(e.notify, all=false) == 0
                @atomic :release e.set = true
            end
        elseif !e.set
            @atomic :release e.set = true
            notify(e.notify)
        end
    finally
        unlock(e.notify)
    end
    nothing
end

"""
    reset(::Event)

Reset an [`Event`](@ref) back into an un-set state. Then any future calls to `wait` will
block until [`notify`](@ref) is called again.
"""
function reset(e::Event)
    @atomic e.set = false # full barrier
    nothing
end

@eval Threads begin
    import .Base: Event
    export Event
end
O   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/channels.jl�B      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
    AbstractChannel{T}

Representation of a channel passing objects of type `T`.
"""
abstract type AbstractChannel{T} end

push!(c::AbstractChannel, v) = (put!(c, v); c)
popfirst!(c::AbstractChannel) = take!(c)

"""
    Channel{T=Any}(size::Int=0)

Constructs a `Channel` with an internal buffer that can hold a maximum of `size` objects
of type `T`.
[`put!`](@ref) calls on a full channel block until an object is removed with [`take!`](@ref).

`Channel(0)` constructs an unbuffered channel. `put!` blocks until a matching `take!` is called.
And vice-versa.

Other constructors:

* `Channel()`: default constructor, equivalent to `Channel{Any}(0)`
* `Channel(Inf)`: equivalent to `Channel{Any}(typemax(Int))`
* `Channel(sz)`: equivalent to `Channel{Any}(sz)`

!!! compat "Julia 1.3"
    The default constructor `Channel()` and default `size=0` were added in Julia 1.3.
"""
mutable struct Channel{T} <: AbstractChannel{T}
    cond_take::Threads.Condition                 # waiting for data to become available
    cond_wait::Threads.Condition                 # waiting for data to become maybe available
    cond_put::Threads.Condition                  # waiting for a writeable slot
    @atomic state::Symbol
    excp::Union{Exception, Nothing}      # exception to be thrown when state !== :open

    data::Vector{T}
    @atomic n_avail_items::Int           # Available items for taking, can be read without lock
    sz_max::Int                          # maximum size of channel

    function Channel{T}(sz::Integer = 0) where T
        if sz < 0
            throw(ArgumentError("Channel size must be either 0, a positive integer or Inf"))
        end
        lock = ReentrantLock()
        cond_put, cond_take = Threads.Condition(lock), Threads.Condition(lock)
        cond_wait = (sz == 0 ? Threads.Condition(lock) : cond_take) # wait is distinct from take iff unbuffered
        return new(cond_take, cond_wait, cond_put, :open, nothing, Vector{T}(), 0, sz)
    end
end

function Channel{T}(sz::Float64) where T
    sz = (sz == Inf ? typemax(Int) : convert(Int, sz))
    return Channel{T}(sz)
end
Channel(sz=0) = Channel{Any}(sz)

# special constructors
"""
    Channel{T=Any}(func::Function, size=0; taskref=nothing, spawn=false, threadpool=nothing)

Create a new task from `func`, bind it to a new channel of type
`T` and size `size`, and schedule the task, all in a single call.
The channel is automatically closed when the task terminates.

`func` must accept the bound channel as its only argument.

If you need a reference to the created task, pass a `Ref{Task}` object via
the keyword argument `taskref`.

If `spawn=true`, the `Task` created for `func` may be scheduled on another thread
in parallel, equivalent to creating a task via [`Threads.@spawn`](@ref).

If `spawn=true` and the `threadpool` argument is not set, it defaults to `:default`.

If the `threadpool` argument is set (to `:default` or `:interactive`), this implies
that `spawn=true` and the new Task is spawned to the specified threadpool.

Return a `Channel`.

# Examples
```jldoctest
julia> chnl = Channel() do ch
           foreach(i -> put!(ch, i), 1:4)
       end;

julia> typeof(chnl)
Channel{Any}

julia> for i in chnl
           @show i
       end;
i = 1
i = 2
i = 3
i = 4
```

Referencing the created task:

```jldoctest
julia> taskref = Ref{Task}();

julia> chnl = Channel(taskref=taskref) do ch
           println(take!(ch))
       end;

julia> istaskdone(taskref[])
false

julia> put!(chnl, "Hello");
Hello

julia> istaskdone(taskref[])
true
```

!!! compat "Julia 1.3"
    The `spawn=` parameter was added in Julia 1.3. This constructor was added in Julia 1.3.
    In earlier versions of Julia, Channel used keyword arguments to set `size` and `T`, but
    those constructors are deprecated.

!!! compat "Julia 1.9"
    The `threadpool=` argument was added in Julia 1.9.

```jldoctest
julia> chnl = Channel{Char}(1, spawn=true) do ch
           for c in "hello world"
               put!(ch, c)
           end
       end
Channel{Char}(1) (2 items available)

julia> String(collect(chnl))
"hello world"
```
"""
function Channel{T}(func::Function, size=0; taskref=nothing, spawn=false, threadpool=nothing) where T
    chnl = Channel{T}(size)
    task = Task(() -> func(chnl))
    if threadpool === nothing
        threadpool = :default
    else
        spawn = true
    end
    task.sticky = !spawn
    bind(chnl, task)
    if spawn
        Threads._spawn_set_thrpool(task, threadpool)
        schedule(task) # start it on (potentially) another thread
    else
        yield(task) # immediately start it, yielding the current thread
    end
    isa(taskref, Ref{Task}) && (taskref[] = task)
    return chnl
end
Channel(func::Function, args...; kwargs...) = Channel{Any}(func, args...; kwargs...)

# This constructor is deprecated as of Julia v1.3, and should not be used.
# (Note that this constructor also matches `Channel(::Function)` w/out any kwargs, which is
# of course not deprecated.)
# We use `nothing` default values to check which arguments were set in order to throw the
# deprecation warning if users try to use `spawn=` with `ctype=` or `csize=`.
function Channel(func::Function; ctype=nothing, csize=nothing, taskref=nothing, spawn=nothing, threadpool=nothing)
    # The spawn= keyword argument was added in Julia v1.3, and cannot be used with the
    # deprecated keyword arguments `ctype=` or `csize=`.
    if (ctype !== nothing || csize !== nothing) && (spawn !== nothing || threadpool !== nothing)
        throw(ArgumentError("Cannot set `spawn=` or `threadpool=` in the deprecated constructor `Channel(f; ctype=Any, csize=0)`. Please use `Channel{T=Any}(f, size=0; taskref=nothing, spawn=false, threadpool=nothing)` instead!"))
    end
    # Set the actual default values for the arguments.
    ctype === nothing && (ctype = Any)
    csize === nothing && (csize = 0)
    spawn === nothing && (spawn = false)
    return Channel{ctype}(func, csize; taskref=taskref, spawn=spawn, threadpool=threadpool)
end

closed_exception() = InvalidStateException("Channel is closed.", :closed)

isbuffered(c::Channel) = c.sz_max==0 ? false : true

function check_channel_state(c::Channel)
    if !isopen(c)
        # if the monotonic load succeed, now do an acquire fence
        (@atomic :acquire c.state) === :open && concurrency_violation()
        excp = c.excp
        excp !== nothing && throw(excp)
        throw(closed_exception())
    end
end
"""
    close(c::Channel[, excp::Exception])

Close a channel. An exception (optionally given by `excp`), is thrown by:

* [`put!`](@ref) on a closed channel.
* [`take!`](@ref) and [`fetch`](@ref) on an empty, closed channel.
"""
close(c::Channel) = close(c, closed_exception()) # nospecialize on default arg seems to confuse makedocs
function close(c::Channel, @nospecialize(excp::Exception))
    lock(c)
    try
        c.excp = excp
        @atomic :release c.state = :closed
        notify_error(c.cond_take, excp)
        notify_error(c.cond_wait, excp)
        notify_error(c.cond_put, excp)
    finally
        unlock(c)
    end
    nothing
end

# Use acquire here to pair with release store in `close`, so that subsequent `isready` calls
# are forced to see `isready == true` if they see `isopen == false`. This means users must
# call `isopen` before `isready` if you are using the race-y APIs (or call `iterate`, which
# does this right for you).
isopen(c::Channel) = ((@atomic :acquire c.state) === :open)

"""
    bind(chnl::Channel, task::Task)

Associate the lifetime of `chnl` with a task.
`Channel` `chnl` is automatically closed when the task terminates.
Any uncaught exception in the task is propagated to all waiters on `chnl`.

The `chnl` object can be explicitly closed independent of task termination.
Terminating tasks have no effect on already closed `Channel` objects.

When a channel is bound to multiple tasks, the first task to terminate will
close the channel. When multiple channels are bound to the same task,
termination of the task will close all of the bound channels.

# Examples
```jldoctest
julia> c = Channel(0);

julia> task = @async foreach(i->put!(c, i), 1:4);

julia> bind(c,task);

julia> for i in c
           @show i
       end;
i = 1
i = 2
i = 3
i = 4

julia> isopen(c)
false
```

```jldoctest
julia> c = Channel(0);

julia> task = @async (put!(c, 1); error("foo"));

julia> bind(c, task);

julia> take!(c)
1

julia> put!(c, 1);
ERROR: TaskFailedException
Stacktrace:
[...]
    nested task error: foo
[...]
```
"""
function bind(c::Channel, task::Task)
    T = Task(() -> close_chnl_on_taskdone(task, c))
    T.sticky = false
    _wait2(task, T)
    return c
end

"""
    channeled_tasks(n::Int, funcs...; ctypes=fill(Any,n), csizes=fill(0,n))

A convenience method to create `n` channels and bind them to tasks started
from the provided functions in a single call. Each `func` must accept `n` arguments
which are the created channels. Channel types and sizes may be specified via
keyword arguments `ctypes` and `csizes` respectively. If unspecified, all channels are
of type `Channel{Any}(0)`.

Returns a tuple, `(Array{Channel}, Array{Task})`, of the created channels and tasks.
"""
function channeled_tasks(n::Int, funcs...; ctypes=fill(Any,n), csizes=fill(0,n))
    @assert length(csizes) == n
    @assert length(ctypes) == n

    chnls = map(i -> Channel{ctypes[i]}(csizes[i]), 1:n)
    tasks = Task[ Task(() -> f(chnls...)) for f in funcs ]

    # bind all tasks to all channels and schedule them
    foreach(t -> foreach(c -> bind(c, t), chnls), tasks)
    foreach(schedule, tasks)
    yield() # Allow scheduled tasks to run

    return (chnls, tasks)
end

function close_chnl_on_taskdone(t::Task, c::Channel)
    isopen(c) || return
    lock(c)
    try
        isopen(c) || return
        if istaskfailed(t)
            close(c, TaskFailedException(t))
            return
        end
        close(c)
    finally
        unlock(c)
    end
    nothing
end

struct InvalidStateException <: Exception
    msg::String
    state::Symbol
end
showerror(io::IO, ex::InvalidStateException) = print(io, "InvalidStateException: ", ex.msg)

"""
    put!(c::Channel, v)

Append an item `v` to the channel `c`. Blocks if the channel is full.

For unbuffered channels, blocks until a [`take!`](@ref) is performed by a different
task.

!!! compat "Julia 1.1"
    `v` now gets converted to the channel's type with [`convert`](@ref) as `put!` is called.
"""
function put!(c::Channel{T}, v) where T
    check_channel_state(c)
    v = convert(T, v)
    return isbuffered(c) ? put_buffered(c, v) : put_unbuffered(c, v)
end

# Atomically update channel n_avail, *assuming* we hold the channel lock.
function _increment_n_avail(c, inc)
    # We hold the channel lock so it's safe to non-atomically read and
    # increment c.n_avail_items
    newlen = c.n_avail_items + inc
    # Atomically store c.n_avail_items to prevent data races with other threads
    # reading this outside the lock.
    @atomic :monotonic c.n_avail_items = newlen
end

function put_buffered(c::Channel, v)
    lock(c)
    did_buffer = false
    try
        # Increment channel n_avail eagerly (before push!) to count data in the
        # buffer as well as offers from tasks which are blocked in wait().
        _increment_n_avail(c, 1)
        while length(c.data) == c.sz_max
            check_channel_state(c)
            wait(c.cond_put)
        end
        check_channel_state(c)
        push!(c.data, v)
        did_buffer = true
        # notify all, since some of the waiters may be on a "fetch" call.
        notify(c.cond_take, nothing, true, false)
    finally
        # Decrement the available items if this task had an exception before pushing the
        # item to the buffer (e.g., during `wait(c.cond_put)`):
        did_buffer || _increment_n_avail(c, -1)
        unlock(c)
    end
    return v
end

function put_unbuffered(c::Channel, v)
    lock(c)
    taker = try
        _increment_n_avail(c, 1)
        while isempty(c.cond_take.waitq)
            check_channel_state(c)
            notify(c.cond_wait)
            wait(c.cond_put)
        end
        check_channel_state(c)
        # unfair scheduled version of: notify(c.cond_take, v, false, false); yield()
        popfirst!(c.cond_take.waitq)
    finally
        _increment_n_avail(c, -1)
        unlock(c)
    end
    schedule(taker, v)
    yield()  # immediately give taker a chance to run, but don't block the current task
    return v
end

"""
    fetch(c::Channel)

Waits for and returns (without removing) the first available item from the `Channel`.
Note: `fetch` is unsupported on an unbuffered (0-size) `Channel`.

# Examples

Buffered channel:
```jldoctest
julia> c = Channel(3) do ch
           foreach(i -> put!(ch, i), 1:3)
       end;

julia> fetch(c)
1

julia> collect(c)  # item is not removed
3-element Vector{Any}:
 1
 2
 3
```
"""
fetch(c::Channel) = isbuffered(c) ? fetch_buffered(c) : fetch_unbuffered(c)
function fetch_buffered(c::Channel)
    lock(c)
    try
        while isempty(c.data)
            check_channel_state(c)
            wait(c.cond_take)
        end
        return c.data[1]
    finally
        unlock(c)
    end
end
fetch_unbuffered(c::Channel) = throw(ErrorException("`fetch` is not supported on an unbuffered Channel."))


"""
    take!(c::Channel)

Removes and returns a value from a [`Channel`](@ref) in order. Blocks until data is available.
For unbuffered channels, blocks until a [`put!`](@ref) is performed by a different task.

# Examples

Buffered channel:
```jldoctest
julia> c = Channel(1);

julia> put!(c, 1);

julia> take!(c)
1
```

Unbuffered channel:
```jldoctest
julia> c = Channel(0);

julia> task = Task(() -> put!(c, 1));

julia> schedule(task);

julia> take!(c)
1
```
"""
take!(c::Channel) = isbuffered(c) ? take_buffered(c) : take_unbuffered(c)
function take_buffered(c::Channel)
    lock(c)
    try
        while isempty(c.data)
            check_channel_state(c)
            wait(c.cond_take)
        end
        v = popfirst!(c.data)
        _increment_n_avail(c, -1)
        notify(c.cond_put, nothing, false, false) # notify only one, since only one slot has become available for a put!.
        return v
    finally
        unlock(c)
    end
end

# 0-size channel
function take_unbuffered(c::Channel{T}) where T
    lock(c)
    try
        check_channel_state(c)
        notify(c.cond_put, nothing, false, false)
        return wait(c.cond_take)::T
    finally
        unlock(c)
    end
end

"""
    isready(c::Channel)

Determines whether a [`Channel`](@ref) has a value stored in it.
Returns immediately, does not block.

For unbuffered channels returns `true` if there are tasks waiting on a [`put!`](@ref).

# Examples

Buffered channel:
```jldoctest
julia> c = Channel(1);

julia> isready(c)
false

julia> put!(c, 1);

julia> isready(c)
true
```

Unbuffered channel:
```jldoctest
julia> c = Channel();

julia> isready(c)  # no tasks waiting to put!
false

julia> task = Task(() -> put!(c, 1));

julia> schedule(task);  # schedule a put! task

julia> isready(c)
true
```

"""
isready(c::Channel) = n_avail(c) > 0
isempty(c::Channel) = n_avail(c) == 0
function n_avail(c::Channel)
    # Lock-free equivalent to `length(c.data) + length(c.cond_put.waitq)`
    @atomic :monotonic c.n_avail_items
end

lock(c::Channel) = lock(c.cond_take)
lock(f, c::Channel) = lock(f, c.cond_take)
unlock(c::Channel) = unlock(c.cond_take)
trylock(c::Channel) = trylock(c.cond_take)

"""
    wait(c::Channel)

Blocks until the `Channel` [`isready`](@ref).

```jldoctest
julia> c = Channel(1);

julia> isready(c)
false

julia> task = Task(() -> wait(c));

julia> schedule(task);

julia> istaskdone(task)  # task is blocked because channel is not ready
false

julia> put!(c, 1);

julia> istaskdone(task)  # task is now unblocked
true
```
"""
function wait(c::Channel)
    isready(c) && return
    lock(c)
    try
        while !isready(c)
            check_channel_state(c)
            wait(c.cond_wait)
        end
    finally
        unlock(c)
    end
    nothing
end

eltype(::Type{Channel{T}}) where {T} = T

show(io::IO, c::Channel) = print(io, typeof(c), "(", c.sz_max, ")")

function show(io::IO, ::MIME"text/plain", c::Channel)
    show(io, c)
    if !(get(io, :compact, false)::Bool)
        if !isopen(c)
            print(io, " (closed)")
        else
            n = n_avail(c)
            if n == 0
                print(io, " (empty)")
            else
                s = n == 1 ? "" : "s"
                print(io, " (", n, " item$s available)")
            end
        end
    end
end

function iterate(c::Channel, state=nothing)
    if isopen(c) || isready(c)
        try
            return (take!(c), nothing)
        catch e
            if isa(e, InvalidStateException) && e.state === :closed
                return nothing
            else
                rethrow()
            end
        end
    else
        return nothing
    end
end

IteratorSize(::Type{<:Channel}) = SizeUnknown()
L   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/partr.jl6      # This file is a part of Julia. License is MIT: https://julialang.org/license

module Partr

using ..Threads: SpinLock, maxthreadid, threadid

# a task minheap
mutable struct taskheap
    const lock::SpinLock
    const tasks::Vector{Task}
    @atomic ntasks::Int32
    @atomic priority::UInt16
    taskheap() = new(SpinLock(), Vector{Task}(undef, 256), zero(Int32), typemax(UInt16))
end


# multiqueue minheap state
const heap_d = UInt32(8)
const heaps = [Vector{taskheap}(undef, 0), Vector{taskheap}(undef, 0)]
const heaps_lock = [SpinLock(), SpinLock()]
const cong_unbias = [typemax(UInt32), typemax(UInt32)]


cong(max::UInt32, unbias::UInt32) =
    ccall(:jl_rand_ptls, UInt32, (UInt32, UInt32), max, unbias) + UInt32(1)

function unbias_cong(max::UInt32)
    return typemax(UInt32) - ((typemax(UInt32) % max) + UInt32(1))
end


function multiq_sift_up(heap::taskheap, idx::Int32)
    while idx > Int32(1)
        parent = (idx - Int32(2)) ÷ heap_d + Int32(1)
        if heap.tasks[idx].priority < heap.tasks[parent].priority
            t = heap.tasks[parent]
            heap.tasks[parent] = heap.tasks[idx]
            heap.tasks[idx] = t
            idx = parent
        else
            break
        end
    end
end


function multiq_sift_down(heap::taskheap, idx::Int32)
    if idx <= heap.ntasks
        for child = (heap_d * idx - heap_d + 2):(heap_d * idx + 1)
            child = Int(child)
            child > length(heap.tasks) && break
            if isassigned(heap.tasks, child) &&
                    heap.tasks[child].priority < heap.tasks[idx].priority
                t = heap.tasks[idx]
                heap.tasks[idx] = heap.tasks[child]
                heap.tasks[child] = t
                multiq_sift_down(heap, Int32(child))
            end
        end
    end
end


function multiq_size(tpid::Int8)
    nt = UInt32(Threads._nthreads_in_pool(tpid))
    tp = tpid + 1
    tpheaps = heaps[tp]
    heap_c = UInt32(2)
    heap_p = UInt32(length(tpheaps))

    if heap_c * nt <= heap_p
        return heap_p
    end

    @lock heaps_lock[tp] begin
        heap_p = UInt32(length(tpheaps))
        nt = UInt32(Threads._nthreads_in_pool(tpid))
        if heap_c * nt <= heap_p
            return heap_p
        end

        heap_p += heap_c * nt
        newheaps = Vector{taskheap}(undef, heap_p)
        copyto!(newheaps, tpheaps)
        for i = (1 + length(tpheaps)):heap_p
            newheaps[i] = taskheap()
        end
        heaps[tp] = newheaps
        cong_unbias[tp] = unbias_cong(heap_p)
    end

    return heap_p
end


function multiq_insert(task::Task, priority::UInt16)
    tpid = ccall(:jl_get_task_threadpoolid, Int8, (Any,), task)
    @assert tpid > -1
    heap_p = multiq_size(tpid)
    tp = tpid + 1

    task.priority = priority

    rn = cong(heap_p, cong_unbias[tp])
    tpheaps = heaps[tp]
    while !trylock(tpheaps[rn].lock)
        rn = cong(heap_p, cong_unbias[tp])
    end

    heap = tpheaps[rn]
    if heap.ntasks >= length(heap.tasks)
        resize!(heap.tasks, length(heap.tasks) * 2)
    end

    ntasks = heap.ntasks + Int32(1)
    @atomic :monotonic heap.ntasks = ntasks
    heap.tasks[ntasks] = task
    multiq_sift_up(heap, ntasks)
    priority = heap.priority
    if task.priority < priority
        @atomic :monotonic heap.priority = task.priority
    end
    unlock(heap.lock)

    return true
end


function multiq_deletemin()
    local rn1, rn2
    local prio1, prio2

    tid = Threads.threadid()
    tp = ccall(:jl_threadpoolid, Int8, (Int16,), tid-1) + 1
    if tp == 0 # Foreign thread
        return nothing
    end
    tpheaps = heaps[tp]

    @label retry
    GC.safepoint()
    heap_p = UInt32(length(tpheaps))
    for i = UInt32(0):heap_p
        if i == heap_p
            return nothing
        end
        rn1 = cong(heap_p, cong_unbias[tp])
        rn2 = cong(heap_p, cong_unbias[tp])
        prio1 = tpheaps[rn1].priority
        prio2 = tpheaps[rn2].priority
        if prio1 > prio2
            prio1 = prio2
            rn1 = rn2
        elseif prio1 == prio2 && prio1 == typemax(UInt16)
            continue
        end
        if trylock(tpheaps[rn1].lock)
            if prio1 == tpheaps[rn1].priority
                break
            end
            unlock(tpheaps[rn1].lock)
        end
    end

    heap = tpheaps[rn1]
    task = heap.tasks[1]
    if ccall(:jl_set_task_tid, Cint, (Any, Cint), task, tid-1) == 0
        unlock(heap.lock)
        @goto retry
    end
    ntasks = heap.ntasks
    @atomic :monotonic heap.ntasks = ntasks - Int32(1)
    heap.tasks[1] = heap.tasks[ntasks]
    Base._unsetindex!(heap.tasks, Int(ntasks))
    prio1 = typemax(UInt16)
    if ntasks > 1
        multiq_sift_down(heap, Int32(1))
        prio1 = heap.tasks[1].priority
    end
    @atomic :monotonic heap.priority = prio1
    unlock(heap.lock)

    return task
end

function multiq_check_empty()
    tid = Threads.threadid()
    tp = ccall(:jl_threadpoolid, Int8, (Int16,), tid-1) + 1
    if tp == 0 # Foreign thread
        return true
    end
    for i = UInt32(1):length(heaps[tp])
        if heaps[tp][i].ntasks != 0
            return false
        end
    end
    return true
end

end
K   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/task.jl�r      # This file is a part of Julia. License is MIT: https://julialang.org/license

## basic task functions and TLS

Core.Task(@nospecialize(f), reserved_stack::Int=0) = Core._Task(f, reserved_stack, ThreadSynchronizer())

# Container for a captured exception and its backtrace. Can be serialized.
struct CapturedException <: Exception
    ex::Any
    processed_bt::Vector{Any}

    function CapturedException(ex, bt_raw::Vector)
        # bt_raw MUST be a vector that can be processed by StackTraces.stacktrace
        # Typically the result of a catch_backtrace()

        # Process bt_raw so that it can be safely serialized
        bt_lines = process_backtrace(bt_raw, 100) # Limiting this to 100 lines.
        CapturedException(ex, bt_lines)
    end

    CapturedException(ex, processed_bt::Vector{Any}) = new(ex, processed_bt)
end

function showerror(io::IO, ce::CapturedException)
    showerror(io, ce.ex, ce.processed_bt, backtrace=true)
end

"""
    capture_exception(ex, bt) -> Exception

Returns an exception, possibly incorporating information from a backtrace `bt`. Defaults to returning [`CapturedException(ex, bt)`](@ref).

Used in [`asyncmap`](@ref) and [`asyncmap!`](@ref) to capture exceptions thrown during
the user-supplied function call.
"""
capture_exception(ex, bt) = CapturedException(ex, bt)

"""
    CompositeException

Wrap a `Vector` of exceptions thrown by a [`Task`](@ref) (e.g. generated from a remote worker over a channel
or an asynchronously executing local I/O write or a remote worker under `pmap`) with information about the series of exceptions.
For example, if a group of workers are executing several tasks, and multiple workers fail, the resulting `CompositeException` will
contain a "bundle" of information from each worker indicating where and why the exception(s) occurred.
"""
struct CompositeException <: Exception
    exceptions::Vector{Any}
    CompositeException() = new(Any[])
    CompositeException(exceptions) = new(exceptions)
end
length(c::CompositeException) = length(c.exceptions)
push!(c::CompositeException, ex) = push!(c.exceptions, ex)
pushfirst!(c::CompositeException, ex) = pushfirst!(c.exceptions, ex)
isempty(c::CompositeException) = isempty(c.exceptions)
iterate(c::CompositeException, state...) = iterate(c.exceptions, state...)
eltype(::Type{CompositeException}) = Any

function showerror(io::IO, ex::CompositeException)
    if !isempty(ex)
        showerror(io, ex.exceptions[1])
        remaining = length(ex) - 1
        if remaining > 0
            print(io, "\n\n...and ", remaining, " more exception", remaining > 1 ? "s" : "", ".\n")
        end
    else
        print(io, "CompositeException()\n")
    end
end

"""
    TaskFailedException

This exception is thrown by a [`wait(t)`](@ref) call when task `t` fails.
`TaskFailedException` wraps the failed task `t`.
"""
struct TaskFailedException <: Exception
    task::Task
end

function showerror(io::IO, ex::TaskFailedException, bt = nothing; backtrace=true)
    print(io, "TaskFailedException")
    if bt !== nothing && backtrace
        show_backtrace(io, bt)
    end
    println(io)
    printstyled(io, "\n    nested task error: ", color=error_color())
    show_task_exception(io, ex.task)
end

function show_task_exception(io::IO, t::Task; indent = true)
    stack = current_exceptions(t)
    b = IOBuffer()
    if isempty(stack)
        # exception stack buffer not available; probably a serialized task
        showerror(IOContext(b, io), t.result)
    else
        show_exception_stack(IOContext(b, io), stack)
    end
    str = String(take!(b))
    if indent
        str = replace(str, "\n" => "\n    ")
    end
    print(io, str)
end

function show(io::IO, t::Task)
    print(io, "Task ($(t.state)) @0x$(string(convert(UInt, pointer_from_objref(t)), base = 16, pad = Sys.WORD_SIZE>>2))")
end

"""
    @task

Wrap an expression in a [`Task`](@ref) without executing it, and return the [`Task`](@ref). This only
creates a task, and does not run it.

# Examples
```jldoctest
julia> a1() = sum(i for i in 1:1000);

julia> b = @task a1();

julia> istaskstarted(b)
false

julia> schedule(b);

julia> yield();

julia> istaskdone(b)
true
```
"""
macro task(ex)
    thunk = Base.replace_linenums!(:(()->$(esc(ex))), __source__)
    :(Task($thunk))
end

"""
    current_task()

Get the currently running [`Task`](@ref).
"""
current_task() = ccall(:jl_get_current_task, Ref{Task}, ())

# task states

const task_state_runnable = UInt8(0)
const task_state_done     = UInt8(1)
const task_state_failed   = UInt8(2)

const _state_index = findfirst(==(:_state), fieldnames(Task))
@eval function load_state_acquire(t)
    # TODO: Replace this by proper atomic operations when available
    @GC.preserve t llvmcall($("""
        %ptr = inttoptr i$(Sys.WORD_SIZE) %0 to i8*
        %rv = load atomic i8, i8* %ptr acquire, align 8
        ret i8 %rv
        """), UInt8, Tuple{Ptr{UInt8}},
        Ptr{UInt8}(pointer_from_objref(t) + fieldoffset(Task, _state_index)))
end

@inline function getproperty(t::Task, field::Symbol)
    if field === :state
        # TODO: this field name should be deprecated in 2.0
        st = load_state_acquire(t)
        if st === task_state_runnable
            return :runnable
        elseif st === task_state_done
            return :done
        elseif st === task_state_failed
            return :failed
        else
            @assert false
        end
    elseif field === :backtrace
        # TODO: this field name should be deprecated in 2.0
        return current_exceptions(t)[end][2]
    elseif field === :exception
        # TODO: this field name should be deprecated in 2.0
        return t._isexception ? t.result : nothing
    else
        return getfield(t, field)
    end
end

"""
    istaskdone(t::Task) -> Bool

Determine whether a task has exited.

# Examples
```jldoctest
julia> a2() = sum(i for i in 1:1000);

julia> b = Task(a2);

julia> istaskdone(b)
false

julia> schedule(b);

julia> yield();

julia> istaskdone(b)
true
```
"""
istaskdone(t::Task) = load_state_acquire(t) !== task_state_runnable

"""
    istaskstarted(t::Task) -> Bool

Determine whether a task has started executing.

# Examples
```jldoctest
julia> a3() = sum(i for i in 1:1000);

julia> b = Task(a3);

julia> istaskstarted(b)
false
```
"""
istaskstarted(t::Task) = ccall(:jl_is_task_started, Cint, (Any,), t) != 0

"""
    istaskfailed(t::Task) -> Bool

Determine whether a task has exited because an exception was thrown.

# Examples
```jldoctest
julia> a4() = error("task failed");

julia> b = Task(a4);

julia> istaskfailed(b)
false

julia> schedule(b);

julia> yield();

julia> istaskfailed(b)
true
```

!!! compat "Julia 1.3"
    This function requires at least Julia 1.3.
"""
istaskfailed(t::Task) = (load_state_acquire(t) === task_state_failed)

Threads.threadid(t::Task) = Int(ccall(:jl_get_task_tid, Int16, (Any,), t)+1)
function Threads.threadpool(t::Task)
    tpid = ccall(:jl_get_task_threadpoolid, Int8, (Any,), t)
    return Threads._tpid_to_sym(tpid)
end

task_result(t::Task) = t.result

task_local_storage() = get_task_tls(current_task())
function get_task_tls(t::Task)
    if t.storage === nothing
        t.storage = IdDict()
    end
    return (t.storage)::IdDict{Any,Any}
end

"""
    task_local_storage(key)

Look up the value of a key in the current task's task-local storage.
"""
task_local_storage(key) = task_local_storage()[key]

"""
    task_local_storage(key, value)

Assign a value to a key in the current task's task-local storage.
"""
task_local_storage(key, val) = (task_local_storage()[key] = val)

"""
    task_local_storage(body, key, value)

Call the function `body` with a modified task-local storage, in which `value` is assigned to
`key`; the previous value of `key`, or lack thereof, is restored afterwards. Useful
for emulating dynamic scoping.
"""
function task_local_storage(body::Function, key, val)
    tls = task_local_storage()
    hadkey = haskey(tls, key)
    old = get(tls, key, nothing)
    tls[key] = val
    try
        return body()
    finally
        hadkey ? (tls[key] = old) : delete!(tls, key)
    end
end

# just wait for a task to be done, no error propagation
function _wait(t::Task)
    if !istaskdone(t)
        donenotify = t.donenotify::ThreadSynchronizer
        lock(donenotify)
        try
            while !istaskdone(t)
                wait(donenotify)
            end
        finally
            unlock(donenotify)
        end
    end
    nothing
end

# have `waiter` wait for `t`
function _wait2(t::Task, waiter::Task)
    if !istaskdone(t)
        # since _wait2 is similar to schedule, we should observe the sticky
        # bit, even if we don't call `schedule` with early-return below
        if waiter.sticky && Threads.threadid(waiter) == 0 && !GC.in_finalizer()
            # Issue #41324
            # t.sticky && tid == 0 is a task that needs to be co-scheduled with
            # the parent task. If the parent (current_task) is not sticky we must
            # set it to be sticky.
            # XXX: Ideally we would be able to unset this
            current_task().sticky = true
            tid = Threads.threadid()
            ccall(:jl_set_task_tid, Cint, (Any, Cint), waiter, tid-1)
        end
        donenotify = t.donenotify::ThreadSynchronizer
        lock(donenotify)
        if !istaskdone(t)
            push!(donenotify.waitq, waiter)
            unlock(donenotify)
            return nothing
        else
            unlock(donenotify)
        end
    end
    schedule(waiter)
    nothing
end

function wait(t::Task)
    t === current_task() && error("deadlock detected: cannot wait on current task")
    _wait(t)
    if istaskfailed(t)
        throw(TaskFailedException(t))
    end
    nothing
end

"""
    fetch(x::Any)

Return `x`.
"""
fetch(@nospecialize x) = x

"""
    fetch(t::Task)

Wait for a [`Task`](@ref) to finish, then return its result value.
If the task fails with an exception, a [`TaskFailedException`](@ref) (which wraps the failed task)
is thrown.
"""
function fetch(t::Task)
    wait(t)
    return task_result(t)
end


## lexically-scoped waiting for multiple items

struct ScheduledAfterSyncException <: Exception
    values::Vector{Any}
end

function showerror(io::IO, ex::ScheduledAfterSyncException)
    print(io, "ScheduledAfterSyncException: ")
    if isempty(ex.values)
        print(io, "(no values)")
        return
    end
    show(io, ex.values[1])
    if length(ex.values) == 1
        print(io, " is")
    elseif length(ex.values) == 2
        print(io, " and one more ")
        print(io, nameof(typeof(ex.values[2])))
        print(io, " are")
    else
        print(io, " and ", length(ex.values) - 1, " more objects are")
    end
    print(io, " registered after the end of a `@sync` block")
end

function sync_end(c::Channel{Any})
    local c_ex
    while isready(c)
        r = take!(c)
        if isa(r, Task)
            _wait(r)
            if istaskfailed(r)
                if !@isdefined(c_ex)
                    c_ex = CompositeException()
                end
                push!(c_ex, TaskFailedException(r))
            end
        else
            try
                wait(r)
            catch e
                if !@isdefined(c_ex)
                    c_ex = CompositeException()
                end
                push!(c_ex, e)
            end
        end
    end
    close(c)

    # Capture all waitable objects scheduled after the end of `@sync` and
    # include them in the exception. This way, the user can check what was
    # scheduled by examining at the exception object.
    if isready(c)
        local racy
        for r in c
            if !@isdefined(racy)
                racy = []
            end
            push!(racy, r)
        end
        if @isdefined(racy)
            if !@isdefined(c_ex)
                c_ex = CompositeException()
            end
            # Since this is a clear programming error, show this exception first:
            pushfirst!(c_ex, ScheduledAfterSyncException(racy))
        end
    end

    if @isdefined(c_ex)
        throw(c_ex)
    end
    nothing
end

const sync_varname = gensym(:sync)

"""
    @sync

Wait until all lexically-enclosed uses of [`@async`](@ref), [`@spawn`](@ref Threads.@spawn), `@spawnat` and `@distributed`
are complete. All exceptions thrown by enclosed async operations are collected and thrown as
a [`CompositeException`](@ref).

# Examples
```julia-repl
julia> Threads.nthreads()
4

julia> @sync begin
           Threads.@spawn println("Thread-id \$(Threads.threadid()), task 1")
           Threads.@spawn println("Thread-id \$(Threads.threadid()), task 2")
       end;
Thread-id 3, task 1
Thread-id 1, task 2
```
"""
macro sync(block)
    var = esc(sync_varname)
    quote
        let $var = Channel(Inf)
            v = $(esc(block))
            sync_end($var)
            v
        end
    end
end

# schedule an expression to run asynchronously

"""
    @async

Wrap an expression in a [`Task`](@ref) and add it to the local machine's scheduler queue.

Values can be interpolated into `@async` via `\$`, which copies the value directly into the
constructed underlying closure. This allows you to insert the _value_ of a variable,
isolating the asynchronous code from changes to the variable's value in the current task.

!!! warning
    It is strongly encouraged to favor `Threads.@spawn` over `@async` always **even when no
    parallelism is required** especially in publicly distributed libraries.  This is
    because a use of `@async` disables the migration of the *parent* task across worker
    threads in the current implementation of Julia.  Thus, seemingly innocent use of
    `@async` in a library function can have a large impact on the performance of very
    different parts of user applications.

!!! compat "Julia 1.4"
    Interpolating values via `\$` is available as of Julia 1.4.
"""
macro async(expr)
    do_async_macro(expr, __source__)
end

# generate the code for @async, possibly wrapping the task in something before
# pushing it to the wait queue.
function do_async_macro(expr, linenums; wrap=identity)
    letargs = Base._lift_one_interp!(expr)

    thunk = Base.replace_linenums!(:(()->($(esc(expr)))), linenums)
    var = esc(sync_varname)
    quote
        let $(letargs...)
            local task = Task($thunk)
            if $(Expr(:islocal, var))
                put!($var, $(wrap(:task)))
            end
            schedule(task)
            task
        end
    end
end

# task wrapper that doesn't create exceptions wrapped in TaskFailedException
struct UnwrapTaskFailedException <: Exception
    task::Task
end

# common code for wait&fetch for UnwrapTaskFailedException
function unwrap_task_failed(f::Function, t::UnwrapTaskFailedException)
    try
        f(t.task)
    catch ex
        if ex isa TaskFailedException
            throw(ex.task.exception)
        else
            rethrow()
        end
    end
end

# the unwrapping for above task wrapper (gets triggered in sync_end())
wait(t::UnwrapTaskFailedException) = unwrap_task_failed(wait, t)

# same for fetching the tasks, for convenience
fetch(t::UnwrapTaskFailedException) = unwrap_task_failed(fetch, t)

# macro for running async code that doesn't throw wrapped exceptions
macro async_unwrap(expr)
    do_async_macro(expr, __source__, wrap=task->:(Base.UnwrapTaskFailedException($task)))
end

"""
    errormonitor(t::Task)

Print an error log to `stderr` if task `t` fails.

# Examples
```julia-repl
julia> Base._wait(errormonitor(Threads.@spawn error("task failed")))
Unhandled Task ERROR: task failed
Stacktrace:
[...]
```
"""
function errormonitor(t::Task)
    t2 = Task() do
        if istaskfailed(t)
            local errs = stderr
            try # try to display the failure atomically
                errio = IOContext(PipeBuffer(), errs::IO)
                emphasize(errio, "Unhandled Task ")
                display_error(errio, scrub_repl_backtrace(current_exceptions(t)))
                write(errs, errio)
            catch
                try # try to display the secondary error atomically
                    errio = IOContext(PipeBuffer(), errs::IO)
                    print(errio, "\nSYSTEM: caught exception while trying to print a failed Task notice: ")
                    display_error(errio, scrub_repl_backtrace(current_exceptions()))
                    write(errs, errio)
                    flush(errs)
                    # and then the actual error, as best we can
                    Core.print(Core.stderr, "while handling: ")
                    Core.println(Core.stderr, current_exceptions(t)[end][1])
                catch e
                    # give up
                    Core.print(Core.stderr, "\nSYSTEM: caught exception of type ", typeof(e).name.name,
                            " while trying to print a failed Task notice; giving up\n")
                end
            end
        end
        nothing
    end
    t2.sticky = false
    _wait2(t, t2)
    return t
end

# Capture interpolated variables in $() and move them to let-block
function _lift_one_interp!(e)
    letargs = Any[]  # store the new gensymed arguments
    _lift_one_interp_helper(e, false, letargs) # Start out _not_ in a quote context (false)
    letargs
end
_lift_one_interp_helper(v, _, _) = v
function _lift_one_interp_helper(expr::Expr, in_quote_context, letargs)
    if expr.head === :$
        if in_quote_context  # This $ is simply interpolating out of the quote
            # Now, we're out of the quote, so any _further_ $ is ours.
            in_quote_context = false
        else
            newarg = gensym()
            push!(letargs, :($(esc(newarg)) = $(esc(expr.args[1]))))
            return newarg  # Don't recurse into the lifted $() exprs
        end
    elseif expr.head === :quote
        in_quote_context = true   # Don't try to lift $ directly out of quotes
    elseif expr.head === :macrocall
        return expr  # Don't recur into macro calls, since some other macros use $
    end
    for (i,e) in enumerate(expr.args)
        expr.args[i] = _lift_one_interp_helper(e, in_quote_context, letargs)
    end
    expr
end


# add a wait-able object to the sync pool
macro sync_add(expr)
    var = esc(sync_varname)
    quote
        local ref = $(esc(expr))
        put!($var, ref)
        ref
    end
end

# runtime system hook called when a task finishes
function task_done_hook(t::Task)
    # `finish_task` sets `sigatomic` before entering this function
    err = istaskfailed(t)
    result = task_result(t)
    handled = false

    donenotify = t.donenotify
    if isa(donenotify, ThreadSynchronizer)
        lock(donenotify)
        try
            if !isempty(donenotify.waitq)
                handled = true
                notify(donenotify)
            end
        finally
            unlock(donenotify)
        end
    end

    if err && !handled && Threads.threadid() == 1
        if isa(result, InterruptException) && isdefined(Base, :active_repl_backend) &&
            active_repl_backend.backend_task._state === task_state_runnable && isempty(Workqueue) &&
            active_repl_backend.in_eval
            throwto(active_repl_backend.backend_task, result) # this terminates the task
        end
    end
    # Clear sigatomic before waiting
    sigatomic_end()
    try
        wait() # this will not return
    catch e
        # If an InterruptException happens while blocked in the event loop, try handing
        # the exception to the REPL task since the current task is done.
        # issue #19467
        if Threads.threadid() == 1 &&
            isa(e, InterruptException) && isdefined(Base, :active_repl_backend) &&
            active_repl_backend.backend_task._state === task_state_runnable && isempty(Workqueue) &&
            active_repl_backend.in_eval
            throwto(active_repl_backend.backend_task, e)
        else
            rethrow()
        end
    end
end


## scheduler and work queue

mutable struct IntrusiveLinkedListSynchronized{T}
    queue::IntrusiveLinkedList{T}
    lock::Threads.SpinLock
    IntrusiveLinkedListSynchronized{T}() where {T} = new(IntrusiveLinkedList{T}(), Threads.SpinLock())
end
isempty(W::IntrusiveLinkedListSynchronized) = isempty(W.queue)
length(W::IntrusiveLinkedListSynchronized) = length(W.queue)
function push!(W::IntrusiveLinkedListSynchronized{T}, t::T) where T
    lock(W.lock)
    try
        push!(W.queue, t)
    finally
        unlock(W.lock)
    end
    return W
end
function pushfirst!(W::IntrusiveLinkedListSynchronized{T}, t::T) where T
    lock(W.lock)
    try
        pushfirst!(W.queue, t)
    finally
        unlock(W.lock)
    end
    return W
end
function pop!(W::IntrusiveLinkedListSynchronized)
    lock(W.lock)
    try
        return pop!(W.queue)
    finally
        unlock(W.lock)
    end
end
function popfirst!(W::IntrusiveLinkedListSynchronized)
    lock(W.lock)
    try
        return popfirst!(W.queue)
    finally
        unlock(W.lock)
    end
end
function list_deletefirst!(W::IntrusiveLinkedListSynchronized{T}, t::T) where T
    lock(W.lock)
    try
        list_deletefirst!(W.queue, t)
    finally
        unlock(W.lock)
    end
    return W
end

const StickyWorkqueue = IntrusiveLinkedListSynchronized{Task}
global Workqueues::Vector{StickyWorkqueue} = [StickyWorkqueue()]
const Workqueues_lock = Threads.SpinLock()
const Workqueue = Workqueues[1] # default work queue is thread 1 // TODO: deprecate this variable

function workqueue_for(tid::Int)
    qs = Workqueues
    if length(qs) >= tid && isassigned(qs, tid)
        return @inbounds qs[tid]
    end
    # slow path to allocate it
    l = Workqueues_lock
    @lock l begin
        qs = Workqueues
        if length(qs) < tid
            nt = Threads.maxthreadid()
            @assert tid <= nt
            global Workqueues = qs = copyto!(typeof(qs)(undef, length(qs) + nt - 1), qs)
        end
        if !isassigned(qs, tid)
            @inbounds qs[tid] = StickyWorkqueue()
        end
        return @inbounds qs[tid]
    end
end

function enq_work(t::Task)
    (t._state === task_state_runnable && t.queue === nothing) || error("schedule: Task not runnable")

    # Sticky tasks go into their thread's work queue.
    if t.sticky
        tid = Threads.threadid(t)
        if tid == 0
            # The task is not yet stuck to a thread. Stick it to the current
            # thread and do the same to the parent task (the current task) so
            # that the tasks are correctly co-scheduled (issue #41324).
            # XXX: Ideally we would be able to unset this.
            if GC.in_finalizer()
                # The task was launched in a finalizer. There is no thread to sticky it
                # to, so just allow it to run anywhere as if it had been non-sticky.
                t.sticky = false
                @goto not_sticky
            else
                tid = Threads.threadid()
                ccall(:jl_set_task_tid, Cint, (Any, Cint), t, tid-1)
                current_task().sticky = true
            end
        end
        push!(workqueue_for(tid), t)
    else
        @label not_sticky
        tp = Threads.threadpool(t)
        if tp === :foreign || Threads.threadpoolsize(tp) == 1
            # There's only one thread in the task's assigned thread pool;
            # use its work queue.
            tid = (tp === :interactive) ? 1 : Threads.threadpoolsize(:interactive)+1
            ccall(:jl_set_task_tid, Cint, (Any, Cint), t, tid-1)
            push!(workqueue_for(tid), t)
        else
            # Otherwise, put the task in the multiqueue.
            Partr.multiq_insert(t, t.priority)
            tid = 0
        end
    end
    ccall(:jl_wakeup_thread, Cvoid, (Int16,), (tid - 1) % Int16)
    return t
end

schedule(t::Task) = enq_work(t)

"""
    schedule(t::Task, [val]; error=false)

Add a [`Task`](@ref) to the scheduler's queue. This causes the task to run constantly when the system
is otherwise idle, unless the task performs a blocking operation such as [`wait`](@ref).

If a second argument `val` is provided, it will be passed to the task (via the return value of
[`yieldto`](@ref)) when it runs again. If `error` is `true`, the value is raised as an exception in
the woken task.

!!! warning
    It is incorrect to use `schedule` on an arbitrary `Task` that has already been started.
    See [the API reference](@ref low-level-schedule-wait) for more information.

# Examples
```jldoctest
julia> a5() = sum(i for i in 1:1000);

julia> b = Task(a5);

julia> istaskstarted(b)
false

julia> schedule(b);

julia> yield();

julia> istaskstarted(b)
true

julia> istaskdone(b)
true
```
"""
function schedule(t::Task, @nospecialize(arg); error=false)
    # schedule a task to be (re)started with the given value or exception
    t._state === task_state_runnable || Base.error("schedule: Task not runnable")
    if error
        t.queue === nothing || Base.list_deletefirst!(t.queue::IntrusiveLinkedList{Task}, t)
        setfield!(t, :result, arg)
        setfield!(t, :_isexception, true)
    else
        t.queue === nothing || Base.error("schedule: Task not runnable")
        setfield!(t, :result, arg)
    end
    enq_work(t)
    return t
end

"""
    yield()

Switch to the scheduler to allow another scheduled task to run. A task that calls this
function is still runnable, and will be restarted immediately if there are no other runnable
tasks.
"""
function yield()
    ct = current_task()
    enq_work(ct)
    try
        wait()
    catch
        ct.queue === nothing || list_deletefirst!(ct.queue::IntrusiveLinkedList{Task}, ct)
        rethrow()
    end
end

@inline set_next_task(t::Task) = ccall(:jl_set_next_task, Cvoid, (Any,), t)

"""
    yield(t::Task, arg = nothing)

A fast, unfair-scheduling version of `schedule(t, arg); yield()` which
immediately yields to `t` before calling the scheduler.
"""
function yield(t::Task, @nospecialize(x=nothing))
    (t._state === task_state_runnable && t.queue === nothing) || error("yield: Task not runnable")
    t.result = x
    enq_work(current_task())
    set_next_task(t)
    return try_yieldto(ensure_rescheduled)
end

"""
    yieldto(t::Task, arg = nothing)

Switch to the given task. The first time a task is switched to, the task's function is
called with no arguments. On subsequent switches, `arg` is returned from the task's last
call to `yieldto`. This is a low-level call that only switches tasks, not considering states
or scheduling in any way. Its use is discouraged.
"""
function yieldto(t::Task, @nospecialize(x=nothing))
    # TODO: these are legacy behaviors; these should perhaps be a scheduler
    # state error instead.
    if t._state === task_state_done
        return x
    elseif t._state === task_state_failed
        throw(t.result)
    end
    t.result = x
    set_next_task(t)
    return try_yieldto(identity)
end

function try_yieldto(undo)
    try
        ccall(:jl_switch, Cvoid, ())
    catch
        undo(ccall(:jl_get_next_task, Ref{Task}, ()))
        rethrow()
    end
    ct = current_task()
    if ct._isexception
        exc = ct.result
        ct.result = nothing
        ct._isexception = false
        throw(exc)
    end
    result = ct.result
    ct.result = nothing
    return result
end

# yield to a task, throwing an exception in it
function throwto(t::Task, @nospecialize exc)
    t.result = exc
    t._isexception = true
    set_next_task(t)
    return try_yieldto(identity)
end

function ensure_rescheduled(othertask::Task)
    ct = current_task()
    W = workqueue_for(Threads.threadid())
    if ct !== othertask && othertask._state === task_state_runnable
        # we failed to yield to othertask
        # return it to the head of a queue to be retried later
        tid = Threads.threadid(othertask)
        Wother = tid == 0 ? W : workqueue_for(tid)
        pushfirst!(Wother, othertask)
    end
    # if the current task was queued,
    # also need to return it to the runnable state
    # before throwing an error
    list_deletefirst!(W, ct)
    nothing
end

function trypoptask(W::StickyWorkqueue)
    while !isempty(W)
        t = popfirst!(W)
        if t._state !== task_state_runnable
            # assume this somehow got queued twice,
            # probably broken now, but try discarding this switch and keep going
            # can't throw here, because it's probably not the fault of the caller to wait
            # and don't want to use print() here, because that may try to incur a task switch
            ccall(:jl_safe_printf, Cvoid, (Ptr{UInt8}, Int32...),
                "\nWARNING: Workqueue inconsistency detected: popfirst!(Workqueue).state !== :runnable\n")
            continue
        end
        return t
    end
    return Partr.multiq_deletemin()
end

checktaskempty = Partr.multiq_check_empty

@noinline function poptask(W::StickyWorkqueue)
    task = trypoptask(W)
    if !(task isa Task)
        task = ccall(:jl_task_get_next, Ref{Task}, (Any, Any, Any), trypoptask, W, checktaskempty)
    end
    set_next_task(task)
    nothing
end

function wait()
    GC.safepoint()
    W = workqueue_for(Threads.threadid())
    poptask(W)
    result = try_yieldto(ensure_rescheduled)
    process_events()
    # return when we come out of the queue
    return result
end

if Sys.iswindows()
    pause() = ccall(:Sleep, stdcall, Cvoid, (UInt32,), 0xffffffff)
else
    pause() = ccall(:pause, Cvoid, ())
end
X   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/threads_overloads.jll
      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
    Threads.foreach(f, channel::Channel;
                    schedule::Threads.AbstractSchedule=Threads.FairSchedule(),
                    ntasks=Threads.threadpoolsize())

Similar to `foreach(f, channel)`, but iteration over `channel` and calls to
`f` are split across `ntasks` tasks spawned by `Threads.@spawn`. This function
will wait for all internally spawned tasks to complete before returning.

If `schedule isa FairSchedule`, `Threads.foreach` will attempt to spawn tasks in a
manner that enables Julia's scheduler to more freely load-balance work items across
threads. This approach generally has higher per-item overhead, but may perform
better than `StaticSchedule` in concurrence with other multithreaded workloads.

If `schedule isa StaticSchedule`, `Threads.foreach` will spawn tasks in a manner
that incurs lower per-item overhead than `FairSchedule`, but is less amenable
to load-balancing. This approach thus may be more suitable for fine-grained,
uniform workloads, but may perform worse than `FairSchedule` in concurrence
with other multithreaded workloads.

# Examples
```julia-repl
julia> n = 20

julia> c = Channel{Int}(ch -> foreach(i -> put!(ch, i), 1:n), 1)

julia> d = Channel{Int}(n) do ch
           f = i -> put!(ch, i^2)
           Threads.foreach(f, c)
       end

julia> collect(d)
collect(d) = [1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400]
```

!!! compat "Julia 1.6"
    This function requires Julia 1.6 or later.
"""
function Threads.foreach(f, channel::Channel;
                         schedule::Threads.AbstractSchedule=Threads.FairSchedule(),
                         ntasks=Threads.threadpoolsize())
    apply = _apply_for_schedule(schedule)
    stop = Threads.Atomic{Bool}(false)
    @sync for _ in 1:ntasks
        Threads.@spawn try
            for item in channel
                $apply(f, item)
                # do `stop[] && break` after `f(item)` to avoid losing `item`.
                # this isn't super comprehensive since a task could still get
                # stuck on `take!` at `for item in channel`. We should think
                # about a more robust mechanism to avoid dropping items. See also
                # https://github.com/JuliaLang/julia/pull/34543#discussion_r422695217
                stop[] && break
            end
        catch
            stop[] = true
            rethrow()
        end
    end
    return nothing
end

_apply_for_schedule(::Threads.StaticSchedule) = (f, x) -> f(x)
_apply_for_schedule(::Threads.FairSchedule) = (f, x) -> wait(Threads.@spawn f(x))
R   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/weakkeydict.jlG      # This file is a part of Julia. License is MIT: https://julialang.org/license

# weak key dictionaries

"""
    WeakKeyDict([itr])

`WeakKeyDict()` constructs a hash table where the keys are weak
references to objects which may be garbage collected even when
referenced in a hash table.

See [`Dict`](@ref) for further help.  Note, unlike [`Dict`](@ref),
`WeakKeyDict` does not convert keys on insertion, as this would imply the key
object was unreferenced anywhere before insertion.

See also [`WeakRef`](@ref).
"""
mutable struct WeakKeyDict{K,V} <: AbstractDict{K,V}
    ht::Dict{WeakRef,V}
    lock::ReentrantLock
    finalizer::Function
    dirty::Bool

    # Constructors mirror Dict's
    function WeakKeyDict{K,V}() where V where K
        t = new(Dict{WeakRef,V}(), ReentrantLock(), identity, 0)
        t.finalizer = k -> t.dirty = true
        return t
    end
end
function WeakKeyDict{K,V}(kv) where V where K
    h = WeakKeyDict{K,V}()
    for (k,v) in kv
        h[k] = v
    end
    return h
end
WeakKeyDict{K,V}(p::Pair) where V where K = setindex!(WeakKeyDict{K,V}(), p.second, p.first)
function WeakKeyDict{K,V}(ps::Pair...) where V where K
    h = WeakKeyDict{K,V}()
    sizehint!(h, length(ps))
    for p in ps
        h[p.first] = p.second
    end
    return h
end
WeakKeyDict() = WeakKeyDict{Any,Any}()

WeakKeyDict(kv::Tuple{}) = WeakKeyDict()
copy(d::WeakKeyDict) = WeakKeyDict(d)

WeakKeyDict(ps::Pair{K,V}...)           where {K,V} = WeakKeyDict{K,V}(ps)
WeakKeyDict(ps::Pair{K}...)             where {K}   = WeakKeyDict{K,Any}(ps)
WeakKeyDict(ps::(Pair{K,V} where K)...) where {V}   = WeakKeyDict{Any,V}(ps)
WeakKeyDict(ps::Pair...)                            = WeakKeyDict{Any,Any}(ps)

function WeakKeyDict(kv)
    try
        Base.dict_with_eltype((K, V) -> WeakKeyDict{K, V}, kv, eltype(kv))
    catch
        if !isiterable(typeof(kv)) || !all(x->isa(x,Union{Tuple,Pair}),kv)
            throw(ArgumentError("WeakKeyDict(kv): kv needs to be an iterator of tuples or pairs"))
        else
            rethrow()
        end
    end
end

function _cleanup_locked(h::WeakKeyDict)
    if h.dirty
        h.dirty = false
        idx = skip_deleted_floor!(h.ht)
        while idx != 0
            if h.ht.keys[idx].value === nothing
                _delete!(h.ht, idx)
            end
            idx = skip_deleted(h.ht, idx + 1)
        end
    end
    return h
end

sizehint!(d::WeakKeyDict, newsz) = sizehint!(d.ht, newsz)
empty(d::WeakKeyDict, ::Type{K}, ::Type{V}) where {K, V} = WeakKeyDict{K, V}()

IteratorSize(::Type{<:WeakKeyDict}) = SizeUnknown()

islocked(wkh::WeakKeyDict) = islocked(wkh.lock)
lock(wkh::WeakKeyDict) = lock(wkh.lock)
unlock(wkh::WeakKeyDict) = unlock(wkh.lock)
lock(f, wkh::WeakKeyDict) = lock(f, wkh.lock)
trylock(f, wkh::WeakKeyDict) = trylock(f, wkh.lock)

function setindex!(wkh::WeakKeyDict{K}, v, key) where K
    !isa(key, K) && throw(ArgumentError("$(limitrepr(key)) is not a valid key for type $K"))
    # 'nothing' is not valid both because 'finalizer' will reject it,
    # and because we therefore use it as a sentinel value
    key === nothing && throw(ArgumentError("`nothing` is not a valid WeakKeyDict key"))
    lock(wkh) do
        _cleanup_locked(wkh)
        k = getkey(wkh.ht, key, nothing)
        if k === nothing
            finalizer(wkh.finalizer, key)
            k = WeakRef(key)
        else
            k.value = key
        end
        wkh.ht[k] = v
    end
    return wkh
end
function get!(wkh::WeakKeyDict{K}, key, default) where {K}
    v = lock(wkh) do
        if key !== nothing && haskey(wkh.ht, key)
            wkh.ht[key]
        else
            wkh[key] = default
        end
    end
    return v
end
function get!(default::Callable, wkh::WeakKeyDict{K}, key) where {K}
    v = lock(wkh) do
        if key !== nothing && haskey(wkh.ht, key)
            wkh.ht[key]
        else
            wkh[key] = default()
        end
    end
    return v
end

function getkey(wkh::WeakKeyDict{K}, kk, default) where K
    k = lock(wkh) do
        local k = getkey(wkh.ht, kk, nothing)
        k === nothing && return nothing
        return k.value
    end
    return k === nothing ? default : k::K
end

map!(f, iter::ValueIterator{<:WeakKeyDict})= map!(f, values(iter.dict.ht))

function get(wkh::WeakKeyDict{K}, key, default) where {K}
    key === nothing && throw(KeyError(nothing))
    lock(wkh) do
        return get(wkh.ht, key, default)
    end
end
function get(default::Callable, wkh::WeakKeyDict{K}, key) where {K}
    key === nothing && throw(KeyError(nothing))
    lock(wkh) do
        return get(default, wkh.ht, key)
    end
end
function pop!(wkh::WeakKeyDict{K}, key) where {K}
    key === nothing && throw(KeyError(nothing))
    lock(wkh) do
        return pop!(wkh.ht, key)
    end
end
function pop!(wkh::WeakKeyDict{K}, key, default) where {K}
    key === nothing && return default
    lock(wkh) do
        return pop!(wkh.ht, key, default)
    end
end
function delete!(wkh::WeakKeyDict, key)
    key === nothing && return wkh
    lock(wkh) do
        delete!(wkh.ht, key)
    end
    return wkh
end
function empty!(wkh::WeakKeyDict)
    lock(wkh) do
        empty!(wkh.ht)
    end
    return wkh
end
function haskey(wkh::WeakKeyDict{K}, key) where {K}
    key === nothing && return false
    lock(wkh) do
        return haskey(wkh.ht, key)
    end
end
function getindex(wkh::WeakKeyDict{K}, key) where {K}
    key === nothing && throw(KeyError(nothing))
    lock(wkh) do
        return getindex(wkh.ht, key)
    end
end
isempty(wkh::WeakKeyDict) = length(wkh) == 0
function length(t::WeakKeyDict)
    lock(t) do
        _cleanup_locked(t)
        return length(t.ht)
    end
end

function iterate(t::WeakKeyDict{K,V}, state...) where {K, V}
    return lock(t) do
        while true
            y = iterate(t.ht, state...)
            y === nothing && return nothing
            wkv, state = y
            k = wkv[1].value
            GC.safepoint() # ensure `k` is now gc-rooted
            k === nothing && continue # indicates `k` is scheduled for deletion
            kv = Pair{K,V}(k::K, wkv[2])
            return (kv, state)
        end
    end
end

filter!(f, d::WeakKeyDict) = filter_in_one_pass!(f, d)
J   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/env.jl?$      # This file is a part of Julia. License is MIT: https://julialang.org/license

if Sys.iswindows()
    const ERROR_ENVVAR_NOT_FOUND = UInt32(203)

    const env_dict = Dict{String, Vector{Cwchar_t}}()
    const env_lock = ReentrantLock()

    function memoized_env_lookup(str::AbstractString)
        # Windows environment variables have a different format from Linux / MacOS, and previously
        # incurred allocations because we had to convert a String to a Vector{Cwchar_t} each time
        # an environment variable was looked up. This function memoizes that lookup process, storing
        # the String => Vector{Cwchar_t} pairs in env_dict
        @lock env_lock begin
            var = get(env_dict, str, nothing)
            if isnothing(var)
                var = cwstring(str)
                env_dict[str] = var
            end
            return var
        end
    end

    _getenvlen(var::Vector{UInt16}) = ccall(:GetEnvironmentVariableW,stdcall,UInt32,(Ptr{UInt16},Ptr{UInt16},UInt32),var,C_NULL,0)
    _hasenv(s::Vector{UInt16}) = _getenvlen(s) != 0 || Libc.GetLastError() != ERROR_ENVVAR_NOT_FOUND
    _hasenv(s::AbstractString) = _hasenv(memoized_env_lookup(s))

    function access_env(onError::Function, str::AbstractString)
        var = memoized_env_lookup(str)
        len = _getenvlen(var)
        if len == 0
            return Libc.GetLastError() != ERROR_ENVVAR_NOT_FOUND ? "" : onError(str)
        end
        val = zeros(UInt16,len)
        ret = ccall(:GetEnvironmentVariableW,stdcall,UInt32,(Ptr{UInt16},Ptr{UInt16},UInt32),var,val,len)
        windowserror(:getenv, (ret == 0 && len != 1) || ret != len-1 || val[end] != 0)
        pop!(val) # NUL
        return transcode(String, val)
    end

    function _setenv(svar::AbstractString, sval::AbstractString, overwrite::Bool=true)
        var = memoized_env_lookup(svar)
        val = cwstring(sval)
        if overwrite || !_hasenv(var)
            ret = ccall(:SetEnvironmentVariableW,stdcall,Int32,(Ptr{UInt16},Ptr{UInt16}),var,val)
            windowserror(:setenv, ret == 0)
        end
    end

    function _unsetenv(svar::AbstractString)
        var = memoized_env_lookup(svar)
        ret = ccall(:SetEnvironmentVariableW,stdcall,Int32,(Ptr{UInt16},Ptr{UInt16}),var,C_NULL)
        windowserror(:setenv, ret == 0 && Libc.GetLastError() != ERROR_ENVVAR_NOT_FOUND)
    end
else # !windows
    _getenv(var::AbstractString) = ccall(:getenv, Cstring, (Cstring,), var)
    _hasenv(s::AbstractString) = _getenv(s) != C_NULL

    function access_env(onError::Function, var::AbstractString)
        val = _getenv(var)
        val == C_NULL ? onError(var) : unsafe_string(val)
    end

    function _setenv(var::AbstractString, val::AbstractString, overwrite::Bool=true)
        ret = ccall(:setenv, Int32, (Cstring,Cstring,Int32), var, val, overwrite)
        systemerror(:setenv, ret != 0)
    end

    function _unsetenv(var::AbstractString)
        ret = ccall(:unsetenv, Int32, (Cstring,), var)
        systemerror(:unsetenv, ret != 0)
    end
end # os test

## ENV: hash interface ##

"""
    EnvDict() -> EnvDict

A singleton of this type provides a hash table interface to environment variables.
"""
struct EnvDict <: AbstractDict{String,String}; end

"""
    ENV

Reference to the singleton `EnvDict`, providing a dictionary interface to system environment
variables.

(On Windows, system environment variables are case-insensitive, and `ENV` correspondingly converts
all keys to uppercase for display, iteration, and copying. Portable code should not rely on the
ability to distinguish variables by case, and should beware that setting an ostensibly lowercase
variable may result in an uppercase `ENV` key.)

!!! warning
    Mutating the environment is not thread-safe.

# Examples
```julia-repl
julia> ENV
Base.EnvDict with "50" entries:
  "SECURITYSESSIONID"            => "123"
  "USER"                         => "username"
  "MallocNanoZone"               => "0"
  ⋮                              => ⋮

julia> ENV["JULIA_EDITOR"] = "vim"
"vim"

julia> ENV["JULIA_EDITOR"]
"vim"
```

See also: [`withenv`](@ref), [`addenv`](@ref).
"""
const ENV = EnvDict()

const get_bool_env_truthy = (
    "t", "T",
    "true", "True", "TRUE",
    "y", "Y",
    "yes", "Yes", "YES",
    "1")
const get_bool_env_falsy = (
    "f", "F",
    "false", "False", "FALSE",
    "n", "N",
    "no", "No", "NO",
    "0")

"""
    Base.get_bool_env(name::String, default::Bool)::Union{Bool,Nothing}

Evaluate whether the value of environnment variable `name` is a truthy or falsy string,
and return `nothing` if it is not recognized as either. If the variable is not set, or is set to "",
return `default`.

Recognized values are the following, and their Capitalized and UPPERCASE forms:
    truthy: "t", "true", "y", "yes", "1"
    falsy:  "f", "false", "n", "no", "0"
"""
function get_bool_env(name::String, default::Bool)
    haskey(ENV, name) || return default
    val = ENV[name]
    if isempty(val)
        return default
    elseif val in get_bool_env_truthy
        return true
    elseif val in get_bool_env_falsy
        return false
    else
        return nothing
    end
end

getindex(::EnvDict, k::AbstractString) = access_env(k->throw(KeyError(k)), k)
get(::EnvDict, k::AbstractString, def) = access_env(Returns(def), k)
get(f::Callable, ::EnvDict, k::AbstractString) = access_env(k->f(), k)
function get!(default::Callable, ::EnvDict, k::AbstractString)
    haskey(ENV, k) && return ENV[k]
    ENV[k] = default()
end
in(k::AbstractString, ::KeySet{String, EnvDict}) = _hasenv(k)
pop!(::EnvDict, k::AbstractString) = (v = ENV[k]; _unsetenv(k); v)
pop!(::EnvDict, k::AbstractString, def) = haskey(ENV,k) ? pop!(ENV,k) : def
delete!(::EnvDict, k::AbstractString) = (_unsetenv(k); ENV)
setindex!(::EnvDict, v, k::AbstractString) = _setenv(k,string(v))
push!(::EnvDict, kv::Pair{<:AbstractString}) = setindex!(ENV, kv.second, kv.first)

if Sys.iswindows()
    GESW() = (pos = ccall(:GetEnvironmentStringsW, stdcall, Ptr{UInt16}, ()); (pos, pos))
    function winuppercase(s::AbstractString)
        isempty(s) && return s
        LOCALE_INVARIANT = 0x0000007f
        LCMAP_UPPERCASE  = 0x00000200
        ws = transcode(UInt16, String(s))
        result = ccall(:LCMapStringW, stdcall, Cint, (UInt32, UInt32, Ptr{UInt16}, Cint, Ptr{UInt16}, Cint),
                       LOCALE_INVARIANT, LCMAP_UPPERCASE, ws, length(ws), ws, length(ws))
        systemerror(:LCMapStringW, iszero(result))
        return transcode(String, ws)
    end
    function iterate(hash::EnvDict, block::Tuple{Ptr{UInt16},Ptr{UInt16}} = GESW())
        while true
            if unsafe_load(block[1]) == 0
                ccall(:FreeEnvironmentStringsW, stdcall, Int32, (Ptr{UInt16},), block[2])
                return nothing
            end
            pos = block[1]
            blk = block[2]
            len = ccall(:wcslen, UInt, (Ptr{UInt16},), pos)
            buf = Vector{UInt16}(undef, len)
            GC.@preserve buf unsafe_copyto!(pointer(buf), pos, len)
            env = transcode(String, buf)
            pos += (len + 1) * 2
            if !isempty(env)
                m = findnext('=', env, nextind(env, firstindex(env)))
            else
                m = nothing
            end
            if m === nothing
                @warn "malformed environment entry" env
                continue
            end
            return (Pair{String,String}(winuppercase(env[1:prevind(env, m)]), env[nextind(env, m):end]), (pos, blk))
        end
    end
else # !windows
    function iterate(::EnvDict, i=0)
        while true
            env = ccall(:jl_environ, Any, (Int32,), i)
            env === nothing && return nothing
            env = env::String
            m = findfirst('=', env)
            if m === nothing
                @warn "malformed environment entry" env
                continue
            end
            return (Pair{String,String}(env[1:prevind(env, m)], env[nextind(env, m):end]), i+1)
        end
    end
end # os-test

#TODO: Make these more efficient
function length(::EnvDict)
    i = 0
    for (k,v) in ENV
        i += 1
    end
    return i
end

function show(io::IO, ::EnvDict)
    for (k,v) = ENV
        println(io, "$k=$v")
    end
end

"""
    withenv(f, kv::Pair...)

Execute `f` in an environment that is temporarily modified (not replaced as in `setenv`)
by zero or more `"var"=>val` arguments `kv`. `withenv` is generally used via the
`withenv(kv...) do ... end` syntax. A value of `nothing` can be used to temporarily unset an
environment variable (if it is set). When `withenv` returns, the original environment has
been restored.

!!! warning
    Changing the environment is not thread-safe. For running external commands with a different
    environment from the parent process, prefer using [`addenv`](@ref) over `withenv`.
"""
function withenv(f, keyvals::Pair{T}...) where T<:AbstractString
    old = Dict{T,Any}()
    for (key,val) in keyvals
        old[key] = get(ENV,key,nothing)
        val !== nothing ? (ENV[key]=val) : delete!(ENV, key)
    end
    try f()
    finally
        for (key,val) in old
            val !== nothing ? (ENV[key]=val) : delete!(ENV, key)
        end
    end
end
withenv(f) = f() # handle empty keyvals case; see #10853
L   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/libuv.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

# Core definitions for interacting with the libuv library from Julia

include(string(length(Core.ARGS) >= 2 ? Core.ARGS[2] : "", "uv_constants.jl"))  # include($BUILDROOT/base/uv_constants.jl)

# convert UV handle data to julia object, checking for null
function uv_sizeof_handle(handle)
    if !(UV_UNKNOWN_HANDLE < handle < UV_HANDLE_TYPE_MAX)
        throw(DomainError(handle))
    end
    return ccall(:uv_handle_size, Csize_t, (Int32,), handle)
end

function uv_sizeof_req(req)
    if !(UV_UNKNOWN_REQ < req < UV_REQ_TYPE_MAX)
        throw(DomainError(req))
    end
    return ccall(:uv_req_size, Csize_t, (Int32,), req)
end

for h in uv_handle_types
@eval const $(Symbol("_sizeof_", lowercase(string(h)))) = uv_sizeof_handle($h)
end
for r in uv_req_types
@eval const $(Symbol("_sizeof_", lowercase(string(r)))) = uv_sizeof_req($r)
end

uv_handle_data(handle) = ccall(:jl_uv_handle_data, Ptr{Cvoid}, (Ptr{Cvoid},), handle)
uv_req_data(handle) = ccall(:jl_uv_req_data, Ptr{Cvoid}, (Ptr{Cvoid},), handle)
uv_req_set_data(req, data) = ccall(:jl_uv_req_set_data, Cvoid, (Ptr{Cvoid}, Any), req, data)
uv_req_set_data(req, data::Ptr{Cvoid}) = ccall(:jl_uv_req_set_data, Cvoid, (Ptr{Cvoid}, Ptr{Cvoid}), req, data)

macro handle_as(hand, typ)
    return quote
        local data = uv_handle_data($(esc(hand)))
        data == C_NULL && return
        unsafe_pointer_to_objref(data)::($(esc(typ)))
    end
end

associate_julia_struct(handle::Ptr{Cvoid}, @nospecialize(jlobj)) =
    ccall(:jl_uv_associate_julia_struct, Cvoid, (Ptr{Cvoid}, Any), handle, jlobj)
disassociate_julia_struct(uv) = disassociate_julia_struct(uv.handle)
disassociate_julia_struct(handle::Ptr{Cvoid}) =
    handle != C_NULL && ccall(:jl_uv_disassociate_julia_struct, Cvoid, (Ptr{Cvoid},), handle)

iolock_begin() = ccall(:jl_iolock_begin, Cvoid, ())
iolock_end() = ccall(:jl_iolock_end, Cvoid, ())

# A dict of all libuv handles that are being waited on somewhere in the system
# and should thus not be garbage collected
const uvhandles = IdDict()
const preserve_handle_lock = Threads.SpinLock()
function preserve_handle(x)
    lock(preserve_handle_lock)
    v = get(uvhandles, x, 0)::Int
    uvhandles[x] = v + 1
    unlock(preserve_handle_lock)
    nothing
end
function unpreserve_handle(x)
    lock(preserve_handle_lock)
    v = get(uvhandles, x, 0)::Int
    if v == 0
        unlock(preserve_handle_lock)
        error("unbalanced call to unpreserve_handle for $(typeof(x))")
    elseif v == 1
        pop!(uvhandles, x)
    else
        uvhandles[x] = v - 1
    end
    unlock(preserve_handle_lock)
    nothing
end

## Libuv error handling ##

struct IOError <: Exception
    msg::String
    code::Int32
    IOError(msg::AbstractString, code::Integer) = new(msg, code)
end

showerror(io::IO, e::IOError) = print(io, "IOError: ", e.msg)

function _UVError(pfx::AbstractString, code::Integer)
    code = Int32(code)
    IOError(string(pfx, ": ", struverror(code), " (", uverrorname(code), ")"), code)
end
function _UVError(pfx::AbstractString, code::Integer, sfxs::AbstractString...)
    code = Int32(code)
    IOError(string(pfx, ": ", struverror(code), " (", uverrorname(code), ")", " ", sfxs...), code)
end

struverror(err::Int32) = unsafe_string(ccall(:uv_strerror, Cstring, (Int32,), err))
uverrorname(err::Int32) = unsafe_string(ccall(:uv_err_name, Cstring, (Int32,), err))

uv_error(prefix::Symbol, c::Integer) = uv_error(string(prefix), c)
uv_error(prefix::AbstractString, c::Integer) = c < 0 ? throw(_UVError(prefix, c)) : nothing

## event loop ##

eventloop() = ccall(:jl_global_event_loop, Ptr{Cvoid}, ())

function uv_unref(h::Ptr{Cvoid})
    iolock_begin()
    ccall(:uv_unref, Cvoid, (Ptr{Cvoid},), h)
    iolock_end()
end

function uv_ref(h::Ptr{Cvoid})
    iolock_begin()
    ccall(:uv_ref, Cvoid, (Ptr{Cvoid},), h)
    iolock_end()
end

function process_events()
    return ccall(:jl_process_events, Int32, ())
end

function uv_alloc_buf end
function uv_readcb end
function uv_writecb_task end
function uv_shutdowncb_task end
function uv_return_spawn end
function uv_asynccb end
function uv_timercb end

function reinit_stdio()
    global stdin = init_stdio(ccall(:jl_stdin_stream, Ptr{Cvoid}, ()))
    global stdout = init_stdio(ccall(:jl_stdout_stream, Ptr{Cvoid}, ()))
    global stderr = init_stdio(ccall(:jl_stderr_stream, Ptr{Cvoid}, ()))
    opts = JLOptions()
    if opts.color != 0
        have_color = (opts.color == 1)
        if !isa(stdout, TTY)
            global stdout = IOContext(stdout, :color => have_color)
        end
        if !isa(stderr, TTY)
            global stderr = IOContext(stderr, :color => have_color)
        end
    end
    nothing
end

"""
    stdin::IO

Global variable referring to the standard input stream.
"""
:stdin

"""
    stdout::IO

Global variable referring to the standard out stream.
"""
:stdout

"""
    stderr::IO

Global variable referring to the standard error stream.
"""
:stderr
U   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/./uv_constants.jl�
      const uv_handle_types = [:UV_ASYNC, :UV_CHECK, :UV_FS_EVENT, :UV_FS_POLL, :UV_HANDLE, :UV_IDLE, :UV_NAMED_PIPE, :UV_POLL, :UV_PREPARE, :UV_PROCESS, :UV_STREAM, :UV_TCP, :UV_TIMER, :UV_TTY, :UV_UDP, :UV_SIGNAL, :UV_FILE]
const uv_req_types = [:UV_REQ, :UV_CONNECT, :UV_WRITE, :UV_SHUTDOWN, :UV_UDP_SEND, :UV_FS, :UV_WORK, :UV_GETADDRINFO, :UV_GETNAMEINFO, :UV_RANDOM,]
const uv_err_vals = [(:UV_E2BIG,(-(7))), (:UV_EACCES,(-(13))), (:UV_EADDRINUSE,(-(98))), (:UV_EADDRNOTAVAIL,(-(99))), (:UV_EAFNOSUPPORT,(-(97))), (:UV_EAGAIN,(-(11))), (:UV_EAI_ADDRFAMILY,(-3000)), (:UV_EAI_AGAIN,(-3001)), (:UV_EAI_BADFLAGS,(-3002)), (:UV_EAI_BADHINTS,(-3013)), (:UV_EAI_CANCELED,(-3003)), (:UV_EAI_FAIL,(-3004)), (:UV_EAI_FAMILY,(-3005)), (:UV_EAI_MEMORY,(-3006)), (:UV_EAI_NODATA,(-3007)), (:UV_EAI_NONAME,(-3008)), (:UV_EAI_OVERFLOW,(-3009)), (:UV_EAI_PROTOCOL,(-3014)), (:UV_EAI_SERVICE,(-3010)), (:UV_EAI_SOCKTYPE,(-3011)), (:UV_EALREADY,(-(114))), (:UV_EBADF,(-(9))), (:UV_EBUSY,(-(16))), (:UV_ECANCELED,(-(125))), (:UV_ECHARSET,(-4080)), (:UV_ECONNABORTED,(-(103))), (:UV_ECONNREFUSED,(-(111))), (:UV_ECONNRESET,(-(104))), (:UV_EDESTADDRREQ,(-(89))), (:UV_EEXIST,(-(17))), (:UV_EFAULT,(-(14))), (:UV_EFBIG,(-(27))), (:UV_EHOSTUNREACH,(-(113))), (:UV_EINTR,(-(4))), (:UV_EINVAL,(-(22))), (:UV_EIO,(-(5))), (:UV_EISCONN,(-(106))), (:UV_EISDIR,(-(21))), (:UV_ELOOP,(-(40))), (:UV_EMFILE,(-(24))), (:UV_EMSGSIZE,(-(90))), (:UV_ENAMETOOLONG,(-(36))), (:UV_ENETDOWN,(-(100))), (:UV_ENETUNREACH,(-(101))), (:UV_ENFILE,(-(23))), (:UV_ENOBUFS,(-(105))), (:UV_ENODEV,(-(19))), (:UV_ENOENT,(-(2))), (:UV_ENOMEM,(-(12))), (:UV_ENONET,(-(64))), (:UV_ENOPROTOOPT,(-(92))), (:UV_ENOSPC,(-(28))), (:UV_ENOSYS,(-(38))), (:UV_ENOTCONN,(-(107))), (:UV_ENOTDIR,(-(20))), (:UV_ENOTEMPTY,(-(39))), (:UV_ENOTSOCK,(-(88))), (:UV_ENOTSUP,(-(95))), (:UV_EOVERFLOW,(-(75))), (:UV_EPERM,(-(1))), (:UV_EPIPE,(-(32))), (:UV_EPROTO,(-(71))), (:UV_EPROTONOSUPPORT,(-(93))), (:UV_EPROTOTYPE,(-(91))), (:UV_ERANGE,(-(34))), (:UV_EROFS,(-(30))), (:UV_ESHUTDOWN,(-(108))), (:UV_ESPIPE,(-(29))), (:UV_ESRCH,(-(3))), (:UV_ETIMEDOUT,(-(110))), (:UV_ETXTBSY,(-(26))), (:UV_EXDEV,(-(18))), (:UV_UNKNOWN,(-4094)), (:UV_EOF,(-4095)), (:UV_ENXIO,(-(6))), (:UV_EMLINK,(-(31))), (:UV_EHOSTDOWN,(-(112))), (:UV_EREMOTEIO,(-(121))), (:UV_ENOTTY,(-(25))), (:UV_EFTYPE,(-4028)), (:UV_EILSEQ,(-(84))), (:UV_ESOCKTNOSUPPORT,(-(94))),]
let
    handles = [:UV_UNKNOWN_HANDLE, uv_handle_types..., :UV_HANDLE_TYPE_MAX]
    reqs = [:UV_UNKNOWN_REQ, uv_req_types..., :UV_REQ_TYPE_PRIVATE, :UV_REQ_TYPE_MAX]
    for i in 1:length(handles)
        @eval const $(handles[i]) = $(i - 1)
    end
    for i in 1:length(reqs)
        @eval const $(reqs[i]) = $(i - 1)
    end
    for (v, val) in uv_err_vals
        @eval const $v = $val
    end
end
Q   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/asyncevent.jl�)      # This file is a part of Julia. License is MIT: https://julialang.org/license

## async event notifications

"""
    AsyncCondition()

Create a async condition that wakes up tasks waiting for it
(by calling [`wait`](@ref) on the object)
when notified from C by a call to `uv_async_send`.
Waiting tasks are woken with an error when the object is closed (by [`close`](@ref)).
Use [`isopen`](@ref) to check whether it is still active.

This provides an implicit acquire & release memory ordering between the sending and waiting threads.
"""
mutable struct AsyncCondition
    @atomic handle::Ptr{Cvoid}
    cond::ThreadSynchronizer
    @atomic isopen::Bool
    @atomic set::Bool

    function AsyncCondition()
        this = new(Libc.malloc(_sizeof_uv_async), ThreadSynchronizer(), true, false)
        iolock_begin()
        associate_julia_struct(this.handle, this)
        err = ccall(:uv_async_init, Cint, (Ptr{Cvoid}, Ptr{Cvoid}, Ptr{Cvoid}),
            eventloop(), this, @cfunction(uv_asynccb, Cvoid, (Ptr{Cvoid},)))
        if err != 0
            #TODO: this codepath is currently not tested
            Libc.free(this.handle)
            this.handle = C_NULL
            throw(_UVError("uv_async_init", err))
        end
        finalizer(uvfinalize, this)
        iolock_end()
        return this
    end
end

"""
    AsyncCondition(callback::Function)

Create a async condition that calls the given `callback` function. The `callback` is passed one argument,
the async condition object itself.
"""
function AsyncCondition(cb::Function)
    async = AsyncCondition()
    t = @task begin
        unpreserve_handle(async)
        while _trywait(async)
            cb(async)
            isopen(async) || return
        end
    end
    # here we are mimicking parts of _trywait, in coordination with task `t`
    preserve_handle(async)
    @lock async.cond begin
        if async.set
            schedule(t)
        else
            _wait2(async.cond, t)
        end
    end
    return async
end

## timer-based notifications

"""
    Timer(delay; interval = 0)

Create a timer that wakes up tasks waiting for it (by calling [`wait`](@ref) on the timer object).

Waiting tasks are woken after an initial delay of at least `delay` seconds, and then repeating after
at least `interval` seconds again elapse. If `interval` is equal to `0`, the timer is only triggered
once. When the timer is closed (by [`close`](@ref)) waiting tasks are woken with an error. Use
[`isopen`](@ref) to check whether a timer is still active.

!!! note
    `interval` is subject to accumulating time skew. If you need precise events at a particular
    absolute time, create a new timer at each expiration with the difference to the next time computed.

!!! note
    A `Timer` requires yield points to update its state. For instance, `isopen(t::Timer)` cannot be
    used to timeout a non-yielding while loop.

"""
mutable struct Timer
    @atomic handle::Ptr{Cvoid}
    cond::ThreadSynchronizer
    @atomic isopen::Bool
    @atomic set::Bool

    function Timer(timeout::Real; interval::Real = 0.0)
        timeout ≥ 0 || throw(ArgumentError("timer cannot have negative timeout of $timeout seconds"))
        interval ≥ 0 || throw(ArgumentError("timer cannot have negative repeat interval of $interval seconds"))
        # libuv has a tendency to timeout 1 ms early, so we need +1 on the timeout (in milliseconds), unless it is zero
        timeoutms = ceil(UInt64, timeout * 1000) + !iszero(timeout)
        intervalms = ceil(UInt64, interval * 1000)
        loop = eventloop()

        this = new(Libc.malloc(_sizeof_uv_timer), ThreadSynchronizer(), true, false)
        associate_julia_struct(this.handle, this)
        iolock_begin()
        err = ccall(:uv_timer_init, Cint, (Ptr{Cvoid}, Ptr{Cvoid}), loop, this)
        @assert err == 0
        finalizer(uvfinalize, this)
        ccall(:uv_update_time, Cvoid, (Ptr{Cvoid},), loop)
        err = ccall(:uv_timer_start, Cint, (Ptr{Cvoid}, Ptr{Cvoid}, UInt64, UInt64),
            this, @cfunction(uv_timercb, Cvoid, (Ptr{Cvoid},)),
            timeoutms, intervalms)
        @assert err == 0
        iolock_end()
        return this
    end
end

unsafe_convert(::Type{Ptr{Cvoid}}, t::Timer) = t.handle
unsafe_convert(::Type{Ptr{Cvoid}}, async::AsyncCondition) = async.handle

# if this returns true, the object has been signaled
# if this returns false, the object is closed
function _trywait(t::Union{Timer, AsyncCondition})
    set = t.set
    if set
        # full barrier now for AsyncCondition
        t isa Timer || Core.Intrinsics.atomic_fence(:acquire_release)
    else
        if !isopen(t)
            close(t) # wait for the close to complete
            return false
        end
        iolock_begin()
        set = t.set
        if !set
            preserve_handle(t)
            lock(t.cond)
            try
                set = t.set
                if !set && t.handle != C_NULL # wait for set or handle, but not the isopen flag
                    iolock_end()
                    set = wait(t.cond)
                    unlock(t.cond)
                    iolock_begin()
                    lock(t.cond)
                end
            finally
                unlock(t.cond)
                unpreserve_handle(t)
            end
        end
        iolock_end()
    end
    @atomic :monotonic t.set = false
    return set
end

function wait(t::Union{Timer, AsyncCondition})
    _trywait(t) || throw(EOFError())
    nothing
end


isopen(t::Union{Timer, AsyncCondition}) = t.isopen && t.handle != C_NULL

function close(t::Union{Timer, AsyncCondition})
    t.handle == C_NULL && return # short-circuit path
    iolock_begin()
    if t.handle != C_NULL
        if t.isopen
            @atomic :monotonic t.isopen = false
            ccall(:jl_close_uv, Cvoid, (Ptr{Cvoid},), t)
        end
        # implement _trywait here without the auto-reset function, just waiting for the final close signal
        preserve_handle(t)
        lock(t.cond)
        try
            while t.handle != C_NULL
                iolock_end()
                wait(t.cond)
                unlock(t.cond)
                iolock_begin()
                lock(t.cond)
            end
        finally
            unlock(t.cond)
            unpreserve_handle(t)
        end
    end
    iolock_end()
    nothing
end

function uvfinalize(t::Union{Timer, AsyncCondition})
    iolock_begin()
    lock(t.cond)
    try
        if t.handle != C_NULL
            disassociate_julia_struct(t.handle) # not going to call the usual close hooks anymore
            if t.isopen
                @atomic :monotonic t.isopen = false
                ccall(:jl_close_uv, Cvoid, (Ptr{Cvoid},), t.handle)
            end
            @atomic :monotonic t.handle = C_NULL
            notify(t.cond, false)
        end
    finally
        unlock(t.cond)
    end
    iolock_end()
    nothing
end

function _uv_hook_close(t::Union{Timer, AsyncCondition})
    lock(t.cond)
    try
        @atomic :monotonic t.isopen = false
        Libc.free(@atomicswap :monotonic t.handle = C_NULL)
        notify(t.cond, false)
    finally
        unlock(t.cond)
    end
    nothing
end

function uv_asynccb(handle::Ptr{Cvoid})
    async = @handle_as handle AsyncCondition
    lock(async.cond) # acquire barrier
    try
        @atomic :release async.set = true
        notify(async.cond, true)
    finally
        unlock(async.cond)
    end
    nothing
end

function uv_timercb(handle::Ptr{Cvoid})
    t = @handle_as handle Timer
    lock(t.cond)
    try
        @atomic :monotonic t.set = true
        if ccall(:uv_timer_get_repeat, UInt64, (Ptr{Cvoid},), t) == 0
            # timer is stopped now
            if t.isopen
                @atomic :monotonic t.isopen = false
                ccall(:jl_close_uv, Cvoid, (Ptr{Cvoid},), t)
            end
        end
        notify(t.cond, true)
    finally
        unlock(t.cond)
    end
    nothing
end

"""
    sleep(seconds)

Block the current task for a specified number of seconds. The minimum sleep time is 1
millisecond or input of `0.001`.
"""
function sleep(sec::Real)
    sec ≥ 0 || throw(ArgumentError("cannot sleep for $sec seconds"))
    wait(Timer(sec))
    nothing
end

# timer with repeated callback
"""
    Timer(callback::Function, delay; interval = 0)

Create a timer that runs the function `callback` at each timer expiration.

Waiting tasks are woken and the function `callback` is called after an initial delay of `delay`
seconds, and then repeating with the given `interval` in seconds. If `interval` is equal to `0`, the
callback is only run once. The function `callback` is called with a single argument, the timer
itself. Stop a timer by calling `close`. The `callback` may still be run one final time, if the timer
has already expired.

# Examples

Here the first number is printed after a delay of two seconds, then the following numbers are
printed quickly.

```julia-repl
julia> begin
           i = 0
           cb(timer) = (global i += 1; println(i))
           t = Timer(cb, 2, interval=0.2)
           wait(t)
           sleep(0.5)
           close(t)
       end
1
2
3
```
"""
function Timer(cb::Function, timeout::Real; interval::Real=0.0)
    timer = Timer(timeout, interval=interval)
    t = @task begin
        unpreserve_handle(timer)
        while _trywait(timer)
            try
                cb(timer)
            catch err
                write(stderr, "Error in Timer:\n")
                showerror(stderr, err, catch_backtrace())
                return
            end
            isopen(timer) || return
        end
    end
    # here we are mimicking parts of _trywait, in coordination with task `t`
    preserve_handle(timer)
    @lock timer.cond begin
        if timer.set
            schedule(t)
        else
            _wait2(timer.cond, t)
        end
    end
    return timer
end

"""
    timedwait(testcb, timeout::Real; pollint::Real=0.1)

Waits until `testcb()` returns `true` or `timeout` seconds have passed, whichever is earlier.
The test function is polled every `pollint` seconds. The minimum value for `pollint` is 0.001 seconds,
that is, 1 millisecond.

Return `:ok` or `:timed_out`.
"""
function timedwait(testcb, timeout::Real; pollint::Real=0.1)
    pollint >= 1e-3 || throw(ArgumentError("pollint must be ≥ 1 millisecond"))
    start = time_ns()
    ns_timeout = 1e9 * timeout

    testcb() && return :ok

    t = Timer(pollint, interval=pollint)
    while _trywait(t) # stop if we ever get closed
        if testcb()
            close(t)
            return :ok
        elseif (time_ns() - start) > ns_timeout
            close(t)
            break
        end
    end
    return :timed_out
end
O   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/iostream.jlE      # This file is a part of Julia. License is MIT: https://julialang.org/license

## IOStream

const sizeof_ios_t = Int(ccall(:jl_sizeof_ios_t, Cint, ()))

"""
    IOStream

A buffered IO stream wrapping an OS file descriptor.
Mostly used to represent files returned by [`open`](@ref).
"""
mutable struct IOStream <: IO
    handle::Ptr{Cvoid}
    ios::Array{UInt8,1}
    name::String
    mark::Int64
    lock::ReentrantLock
    _dolock::Bool

    IOStream(name::AbstractString, buf::Array{UInt8,1}) = new(pointer(buf), buf, name, -1, ReentrantLock(), true)
end

function IOStream(name::AbstractString, finalize::Bool)
    buf = zeros(UInt8,sizeof_ios_t)
    x = IOStream(name, buf)
    if finalize
        finalizer(close, x)
    end
    return x
end
IOStream(name::AbstractString) = IOStream(name, true)

unsafe_convert(T::Type{Ptr{Cvoid}}, s::IOStream) = convert(T, pointer(s.ios))
show(io::IO, s::IOStream) = print(io, "IOStream(", s.name, ")")

macro _lock_ios(s, expr)
    s = esc(s)
    quote
        l = ($s)._dolock
        temp = ($s).lock
        l && lock(temp)
        val = $(esc(expr))
        l && unlock(temp)
        val
    end
end

"""
    fd(stream)

Return the file descriptor backing the stream or file. Note that this function only applies
to synchronous `File`'s and `IOStream`'s not to any of the asynchronous streams.
"""
fd(s::IOStream) = Int(ccall(:jl_ios_fd, Clong, (Ptr{Cvoid},), s.ios))

stat(s::IOStream) = stat(fd(s))

isopen(s::IOStream) = ccall(:ios_isopen, Cint, (Ptr{Cvoid},), s.ios) != 0

function close(s::IOStream)
    bad = @_lock_ios s ccall(:ios_close, Cint, (Ptr{Cvoid},), s.ios) != 0
    systemerror("close", bad)
end

function flush(s::IOStream)
    sigatomic_begin()
    bad = @_lock_ios s ccall(:ios_flush, Cint, (Ptr{Cvoid},), s.ios) != 0
    sigatomic_end()
    systemerror("flush", bad)
end

iswritable(s::IOStream) = ccall(:ios_get_writable, Cint, (Ptr{Cvoid},), s.ios)!=0

isreadable(s::IOStream) = ccall(:ios_get_readable, Cint, (Ptr{Cvoid},), s.ios)!=0

"""
    truncate(file, n)

Resize the file or buffer given by the first argument to exactly `n` bytes, filling
previously unallocated space with '\\0' if the file or buffer is grown.

# Examples
```jldoctest
julia> io = IOBuffer();

julia> write(io, "JuliaLang is a GitHub organization.")
35

julia> truncate(io, 15)
IOBuffer(data=UInt8[...], readable=true, writable=true, seekable=true, append=false, size=15, maxsize=Inf, ptr=16, mark=-1)

julia> String(take!(io))
"JuliaLang is a "

julia> io = IOBuffer();

julia> write(io, "JuliaLang is a GitHub organization.");

julia> truncate(io, 40);

julia> String(take!(io))
"JuliaLang is a GitHub organization.\\0\\0\\0\\0\\0"
```
"""
function truncate(s::IOStream, n::Integer)
    err = @_lock_ios s ccall(:ios_trunc, Cint, (Ptr{Cvoid}, Csize_t), s.ios, n) != 0
    systemerror("truncate", err)
    return s
end

"""
    seek(s, pos)

Seek a stream to the given position.

# Examples
```jldoctest
julia> io = IOBuffer("JuliaLang is a GitHub organization.");

julia> seek(io, 5);

julia> read(io, Char)
'L': ASCII/Unicode U+004C (category Lu: Letter, uppercase)
```
"""
function seek(s::IOStream, n::Integer)
    ret = @_lock_ios s ccall(:ios_seek, Int64, (Ptr{Cvoid}, Int64), s.ios, n)
    systemerror("seek", ret == -1)
    ret < -1 && error("seek failed")
    return s
end

"""
    seekstart(s)

Seek a stream to its beginning.

# Examples
```jldoctest
julia> io = IOBuffer("JuliaLang is a GitHub organization.");

julia> seek(io, 5);

julia> read(io, Char)
'L': ASCII/Unicode U+004C (category Lu: Letter, uppercase)

julia> seekstart(io);

julia> read(io, Char)
'J': ASCII/Unicode U+004A (category Lu: Letter, uppercase)
```
"""
seekstart(s::IO) = seek(s,0)

"""
    seekend(s)

Seek a stream to its end.
"""
function seekend(s::IOStream)
    err = @_lock_ios s ccall(:ios_seek_end, Int64, (Ptr{Cvoid},), s.ios) != 0
    systemerror("seekend", err)
    return s
end

"""
    skip(s, offset)

Seek a stream relative to the current position.

# Examples
```jldoctest
julia> io = IOBuffer("JuliaLang is a GitHub organization.");

julia> seek(io, 5);

julia> skip(io, 10);

julia> read(io, Char)
'G': ASCII/Unicode U+0047 (category Lu: Letter, uppercase)
```
"""
function skip(s::IOStream, delta::Integer)
    ret = @_lock_ios s ccall(:ios_skip, Int64, (Ptr{Cvoid}, Int64), s.ios, delta)
    systemerror("skip", ret == -1)
    ret < -1 && error("skip failed")
    return s
end

"""
    position(s)

Get the current position of a stream.

# Examples
```jldoctest
julia> io = IOBuffer("JuliaLang is a GitHub organization.");

julia> seek(io, 5);

julia> position(io)
5

julia> skip(io, 10);

julia> position(io)
15

julia> seekend(io);

julia> position(io)
35
```
"""
function position(s::IOStream)
    pos = @_lock_ios s ccall(:ios_pos, Int64, (Ptr{Cvoid},), s.ios)
    systemerror("position", pos == -1)
    return pos
end

function filesize(s::IOStream)
    sz = @_lock_ios s ccall(:ios_filesize, Int64, (Ptr{Cvoid},), s.ios)
    if sz == -1
        err = Libc.errno()
        throw(IOError(string("filesize: ", Libc.strerror(err), " for ", s.name), err))
    end
    return sz
end

_eof_nolock(s::IOStream) = ccall(:ios_eof_blocking, Cint, (Ptr{Cvoid},), s.ios) != 0
eof(s::IOStream) = @_lock_ios s _eof_nolock(s)

## constructing and opening streams ##

# "own" means the descriptor will be closed with the IOStream

"""
    fdio([name::AbstractString, ]fd::Integer[, own::Bool=false]) -> IOStream

Create an [`IOStream`](@ref) object from an integer file descriptor. If `own` is `true`, closing
this object will close the underlying descriptor. By default, an `IOStream` is closed when
it is garbage collected. `name` allows you to associate the descriptor with a named file.
"""
function fdio(name::AbstractString, fd::Integer, own::Bool=false)
    s = IOStream(name)
    ccall(:ios_fd, Ptr{Cvoid}, (Ptr{Cvoid}, Clong, Cint, Cint),
          s.ios, fd, 0, own)
    return s
end
fdio(fd::Integer, own::Bool=false) = fdio(string("<fd ",fd,">"), fd, own)

"""
    open(filename::AbstractString; lock = true, keywords...) -> IOStream

Open a file in a mode specified by five boolean keyword arguments:

| Keyword    | Description             | Default                                 |
|:-----------|:-----------------------|:----------------------------------------|
| `read`     | open for reading       | `!write`                                |
| `write`    | open for writing       | `truncate \\| append`                   |
| `create`   | create if non-existent | `!read & write \\| truncate \\| append` |
| `truncate` | truncate to zero size  | `!read & write`                         |
| `append`   | seek to end            | `false`                                 |

The default when no keywords are passed is to open files for reading only.
Returns a stream for accessing the opened file.

The `lock` keyword argument controls whether operations will be locked for
safe multi-threaded access.

!!! compat "Julia 1.5"
    The `lock` argument is available as of Julia 1.5.
"""
function open(fname::String; lock = true,
    read     :: Union{Bool,Nothing} = nothing,
    write    :: Union{Bool,Nothing} = nothing,
    create   :: Union{Bool,Nothing} = nothing,
    truncate :: Union{Bool,Nothing} = nothing,
    append   :: Union{Bool,Nothing} = nothing,
)
    flags = open_flags(
        read = read,
        write = write,
        create = create,
        truncate = truncate,
        append = append,
    )
    s = IOStream(string("<file ",fname,">"))
    if !lock
        s._dolock = false
    end
    systemerror("opening file $(repr(fname))",
                ccall(:ios_file, Ptr{Cvoid},
                      (Ptr{UInt8}, Cstring, Cint, Cint, Cint, Cint),
                      s.ios, fname, flags.read, flags.write, flags.create, flags.truncate) == C_NULL)
    if flags.append
        systemerror("seeking to end of file $fname", ccall(:ios_seek_end, Int64, (Ptr{Cvoid},), s.ios) != 0)
    end
    return s
end
open(fname::AbstractString; kwargs...) = open(convert(String, fname)::String; kwargs...)

"""
    open(filename::AbstractString, [mode::AbstractString]; lock = true) -> IOStream

Alternate syntax for open, where a string-based mode specifier is used instead of the five
booleans. The values of `mode` correspond to those from `fopen(3)` or Perl `open`, and are
equivalent to setting the following boolean groups:

| Mode | Description                   | Keywords                            |
|:-----|:------------------------------|:------------------------------------|
| `r`  | read                          | none                                |
| `w`  | write, create, truncate       | `write = true`                      |
| `a`  | write, create, append         | `append = true`                     |
| `r+` | read, write                   | `read = true, write = true`         |
| `w+` | read, write, create, truncate | `truncate = true, read = true`      |
| `a+` | read, write, create, append   | `append = true, read = true`        |

The `lock` keyword argument controls whether operations will be locked for
safe multi-threaded access.

# Examples
```jldoctest
julia> io = open("myfile.txt", "w");

julia> write(io, "Hello world!");

julia> close(io);

julia> io = open("myfile.txt", "r");

julia> read(io, String)
"Hello world!"

julia> write(io, "This file is read only")
ERROR: ArgumentError: write failed, IOStream is not writeable
[...]

julia> close(io)

julia> io = open("myfile.txt", "a");

julia> write(io, "This stream is not read only")
28

julia> close(io)

julia> rm("myfile.txt")
```

!!! compat "Julia 1.5"
    The `lock` argument is available as of Julia 1.5.
"""
function open(fname::AbstractString, mode::AbstractString; lock = true)
    mode == "r"  ? open(fname, lock = lock, read = true)                  :
    mode == "r+" ? open(fname, lock = lock, read = true, write = true)    :
    mode == "w"  ? open(fname, lock = lock, truncate = true)              :
    mode == "w+" ? open(fname, lock = lock, truncate = true, read = true) :
    mode == "a"  ? open(fname, lock = lock, append = true)                :
    mode == "a+" ? open(fname, lock = lock, append = true, read = true)   :
    throw(ArgumentError("invalid open mode: $mode"))
end

## low-level calls ##

function write(s::IOStream, b::UInt8)
    iswritable(s) || throw(ArgumentError("write failed, IOStream is not writeable"))
    Int(@_lock_ios s ccall(:ios_putc, Cint, (Cint, Ptr{Cvoid}), b, s.ios))
end

function unsafe_write(s::IOStream, p::Ptr{UInt8}, nb::UInt)
    iswritable(s) || throw(ArgumentError("write failed, IOStream is not writeable"))
    return Int(@_lock_ios s ccall(:ios_write, Csize_t, (Ptr{Cvoid}, Ptr{Cvoid}, Csize_t), s.ios, p, nb))
end

# num bytes available without blocking
bytesavailable(s::IOStream) = @_lock_ios s ccall(:jl_nb_available, Int32, (Ptr{Cvoid},), s.ios)

function readavailable(s::IOStream)
    lock(s.lock)
    nb = ccall(:jl_nb_available, Int32, (Ptr{Cvoid},), s.ios)
    if nb == 0
        ccall(:ios_fillbuf, Cssize_t, (Ptr{Cvoid},), s.ios)
        nb = ccall(:jl_nb_available, Int32, (Ptr{Cvoid},), s.ios)
    end
    a = Vector{UInt8}(undef, nb)
    nr = ccall(:ios_readall, Csize_t, (Ptr{Cvoid}, Ptr{Cvoid}, Csize_t), s, a, nb)
    if nr != nb
        unlock(s.lock)
        throw(EOFError())
    end
    unlock(s.lock)
    return a
end

function read(s::IOStream, ::Type{UInt8})
    b = @_lock_ios s ccall(:ios_getc, Cint, (Ptr{Cvoid},), s.ios)
    if b == -1
        throw(EOFError())
    end
    return b % UInt8
end

if ENDIAN_BOM == 0x04030201
function read(s::IOStream, T::Union{Type{Int16},Type{UInt16},Type{Int32},Type{UInt32},Type{Int64},Type{UInt64}})
    n = sizeof(T)
    l = s._dolock
    _lock = s.lock
    l && lock(_lock)
    if ccall(:jl_ios_buffer_n, Cint, (Ptr{Cvoid}, Csize_t), s.ios, n) != 0
        l && unlock(_lock)
        throw(EOFError())
    end
    x = ccall(:jl_ios_get_nbyte_int, UInt64, (Ptr{Cvoid}, Csize_t), s.ios, n) % T
    l && unlock(_lock)
    return x
end

read(s::IOStream, ::Type{Float16}) = reinterpret(Float16, read(s, Int16))
read(s::IOStream, ::Type{Float32}) = reinterpret(Float32, read(s, Int32))
read(s::IOStream, ::Type{Float64}) = reinterpret(Float64, read(s, Int64))
end

function unsafe_read(s::IOStream, p::Ptr{UInt8}, nb::UInt)
    nr = @_lock_ios s ccall(:ios_readall, Csize_t, (Ptr{Cvoid}, Ptr{Cvoid}, Csize_t), s, p, nb)
    if nr != nb
        throw(EOFError())
    end
    nothing
end

## text I/O ##

take!(s::IOStream) =
    @_lock_ios s ccall(:jl_take_buffer, Vector{UInt8}, (Ptr{Cvoid},), s.ios)

function readuntil(s::IOStream, delim::UInt8; keep::Bool=false)
    @_lock_ios s ccall(:jl_readuntil, Array{UInt8,1}, (Ptr{Cvoid}, UInt8, UInt8, UInt8), s.ios, delim, 0, !keep)
end

# like readuntil, above, but returns a String without requiring a copy
function readuntil_string(s::IOStream, delim::UInt8, keep::Bool)
    @_lock_ios s ccall(:jl_readuntil, Ref{String}, (Ptr{Cvoid}, UInt8, UInt8, UInt8), s.ios, delim, 1, !keep)
end

function readline(s::IOStream; keep::Bool=false)
    @_lock_ios s ccall(:jl_readuntil, Ref{String}, (Ptr{Cvoid}, UInt8, UInt8, UInt8), s.ios, '\n', 1, keep ? 0 : 2)
end

function readbytes_all!(s::IOStream,
                        b::Union{Array{UInt8}, FastContiguousSubArray{UInt8,<:Any,<:Array{UInt8}}},
                        nb::Integer)
    olb = lb = length(b)
    nr = 0
    let l = s._dolock, slock = s.lock
        l && lock(slock)
        GC.@preserve b while nr < nb
            if lb < nr+1
                try
                    lb = max(65536, (nr+1) * 2)
                    resize!(b, lb)
                catch
                    l && unlock(slock)
                    rethrow()
                end
            end
            thisr = Int(ccall(:ios_readall, Csize_t, (Ptr{Cvoid}, Ptr{Cvoid}, Csize_t),
                            s.ios, pointer(b, nr+1), min(lb-nr, nb-nr)))
            nr += thisr
            (nr == nb || thisr == 0 || _eof_nolock(s)) && break
        end
        l && unlock(slock)
    end
    if lb > olb && lb > nr
        resize!(b, max(olb, nr)) # shrink to just contain input data if was resized
    end
    return nr
end

function readbytes_some!(s::IOStream,
                         b::Union{Array{UInt8}, FastContiguousSubArray{UInt8,<:Any,<:Array{UInt8}}},
                         nb::Integer)
    olb = length(b)
    if nb > olb
        resize!(b, nb)
    end
    local nr
    @_lock_ios s begin
    nr = GC.@preserve b Int(ccall(:ios_read, Csize_t, (Ptr{Cvoid}, Ptr{Cvoid}, Csize_t),
                                  s.ios, pointer(b), nb))
    end
    lb = length(b)
    if lb > olb && lb > nr
        resize!(b, max(olb, nr)) # shrink to just contain input data if was resized
    end
    return nr
end

"""
    readbytes!(stream::IOStream, b::AbstractVector{UInt8}, nb=length(b); all::Bool=true)

Read at most `nb` bytes from `stream` into `b`, returning the number of bytes read.
The size of `b` will be increased if needed (i.e. if `nb` is greater than `length(b)`
and enough bytes could be read), but it will never be decreased.

If `all` is `true` (the default), this function will block repeatedly trying to read all
requested bytes, until an error or end-of-file occurs. If `all` is `false`, at most one
`read` call is performed, and the amount of data returned is device-dependent. Note that not
all stream types support the `all` option.
"""
function readbytes!(s::IOStream,
                    b::Union{Array{UInt8}, FastContiguousSubArray{UInt8,<:Any,<:Array{UInt8}}},
                    nb=length(b);
                    all::Bool=true)
    return all ? readbytes_all!(s, b, nb) : readbytes_some!(s, b, nb)
end

function read(s::IOStream)
    # First we try to fill the buffer. If that gives us the whole file,
    # copy it out and return. Otherwise look at the file size and use it
    # to prealloate space. Determining the size requires extra syscalls,
    # which we want to avoid for small files.
    @_lock_ios s begin
        nb = ccall(:ios_fillbuf, Cssize_t, (Ptr{Cvoid},), s.ios)
        if nb != -1
            b = StringVector(nb)
            readbytes_all!(s, b, nb)
        else
            sz = try # filesize is just a hint, so ignore if it fails
                filesize(s)
            catch ex
                ex isa IOError || rethrow()
                Int64(-1)
            end
            if sz > 0
                pos = position(s)
                if pos > 0
                    sz -= pos
                end
            end
            b = StringVector(sz < 0 ? 1024 : sz)
            nr = readbytes_all!(s, b, sz < 0 ? typemax(Int) : sz)
            resize!(b, nr)
        end
    end
    return b
end

"""
    read(s::IOStream, nb::Integer; all=true)

Read at most `nb` bytes from `s`, returning a `Vector{UInt8}` of the bytes read.

If `all` is `true` (the default), this function will block repeatedly trying to read all
requested bytes, until an error or end-of-file occurs. If `all` is `false`, at most one
`read` call is performed, and the amount of data returned is device-dependent. Note that not
all stream types support the `all` option.
"""
function read(s::IOStream, nb::Integer; all::Bool=true)
    # When all=false we have to allocate a buffer of the requested size upfront
    # since a single call will be made
    b = Vector{UInt8}(undef, all && nb == typemax(Int) ? 1024 : nb)
    nr = readbytes!(s, b, nb, all=all)
    resize!(b, nr)
    return b
end

## peek ##

function peek(s::IOStream, ::Type{UInt8})
    b = @_lock_ios s ccall(:ios_peekc, Cint, (Ptr{Cvoid},), s.ios)
    if b == -1
        throw(EOFError())
    end
    return b % UInt8
end
M   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/stream.jl��      # This file is a part of Julia. License is MIT: https://julialang.org/license

import .Libc: RawFD, dup
if Sys.iswindows()
    import .Libc: WindowsRawSocket
    const OS_HANDLE = WindowsRawSocket
    const INVALID_OS_HANDLE = WindowsRawSocket(Ptr{Cvoid}(-1))
else
    const OS_HANDLE = RawFD
    const INVALID_OS_HANDLE = RawFD(-1)
end


## types ##
abstract type IOServer end
"""
    LibuvServer

An abstract type for IOServers handled by libuv.

If `server isa LibuvServer`, it must obey the following interface:

- `server.handle` must be a `Ptr{Cvoid}`
- `server.status` must be an `Int`
- `server.cond` must be a `GenericCondition`
"""
abstract type LibuvServer <: IOServer end

function getproperty(server::LibuvServer, name::Symbol)
    if name === :handle
        return getfield(server, :handle)::Ptr{Cvoid}
    elseif name === :status
        return getfield(server, :status)::Int
    elseif name === :cond
        return getfield(server, :cond)::GenericCondition
    else
        return getfield(server, name)
    end
end

"""
    LibuvStream

An abstract type for IO streams handled by libuv.

If `stream isa LibuvStream`, it must obey the following interface:

- `stream.handle`, if present, must be a `Ptr{Cvoid}`
- `stream.status`, if present, must be an `Int`
- `stream.buffer`, if present, must be an `IOBuffer`
- `stream.sendbuf`, if present, must be a `Union{Nothing,IOBuffer}`
- `stream.cond`, if present, must be a `GenericCondition`
- `stream.lock`, if present, must be an `AbstractLock`
- `stream.throttle`, if present, must be an `Int`
"""
abstract type LibuvStream <: IO end

function getproperty(stream::LibuvStream, name::Symbol)
    if name === :handle
        return getfield(stream, :handle)::Ptr{Cvoid}
    elseif name === :status
        return getfield(stream, :status)::Int
    elseif name === :buffer
        return getfield(stream, :buffer)::IOBuffer
    elseif name === :sendbuf
        return getfield(stream, :sendbuf)::Union{Nothing,IOBuffer}
    elseif name === :cond
        return getfield(stream, :cond)::GenericCondition
    elseif name === :lock
        return getfield(stream, :lock)::AbstractLock
    elseif name === :throttle
        return getfield(stream, :throttle)::Int
    else
        return getfield(stream, name)
    end
end

# IO
# +- GenericIOBuffer{T<:AbstractArray{UInt8,1}} (not exported)
# +- AbstractPipe (not exported)
# .  +- Pipe
# .  +- Process (not exported)
# .  +- ProcessChain (not exported)
# +- DevNull (not exported)
# +- Filesystem.File
# +- LibuvStream (not exported)
# .  +- PipeEndpoint (not exported)
# .  +- TCPSocket
# .  +- TTY (not exported)
# .  +- UDPSocket
# .  +- BufferStream (FIXME: 2.0)
# +- IOBuffer = Base.GenericIOBuffer{Array{UInt8,1}}
# +- IOStream

# IOServer
# +- LibuvServer
# .  +- PipeServer
# .  +- TCPServer

# Redirectable = Union{IO, FileRedirect, Libc.RawFD} (not exported)

bytesavailable(s::LibuvStream) = bytesavailable(s.buffer)

function eof(s::LibuvStream)
    bytesavailable(s) > 0 && return false
    wait_readnb(s, 1)
    # This function is race-y if used from multiple threads, but we guarantee
    # it to never return true until the stream is definitively exhausted
    # and that we won't return true if there's a readerror pending (it'll instead get thrown).
    # This requires some careful ordering here (TODO: atomic loads)
    bytesavailable(s) > 0 && return false
    open = isreadable(s) # must precede readerror check
    s.readerror === nothing || throw(s.readerror)
    return !open
end

# Limit our default maximum read and buffer size,
# to avoid DoS-ing ourself into an OOM situation
const DEFAULT_READ_BUFFER_SZ = 10485760 # 10 MB

# manually limit our write size, if the OS doesn't support full-size writes
if Sys.iswindows()
    const MAX_OS_WRITE = UInt(0x1FF0_0000) # 511 MB (determined semi-empirically, limited to 31 MB on XP)
else
    const MAX_OS_WRITE = UInt(typemax(Csize_t))
end


const StatusUninit      = 0 # handle is allocated, but not initialized
const StatusInit        = 1 # handle is valid, but not connected/active
const StatusConnecting  = 2 # handle is in process of connecting
const StatusOpen        = 3 # handle is usable
const StatusActive      = 4 # handle is listening for read/write/connect events
const StatusClosing     = 5 # handle is closing / being closed
const StatusClosed      = 6 # handle is closed
const StatusEOF         = 7 # handle is a TTY that has seen an EOF event (pretends to be closed until reseteof is called)
const StatusPaused      = 8 # handle is Active, but not consuming events, and will transition to Open if it receives an event
function uv_status_string(x)
    s = x.status
    if x.handle == C_NULL
        if s == StatusClosed
            return "closed"
        elseif s == StatusUninit
            return "null"
        end
        return "invalid status"
    elseif s == StatusUninit
        return "uninit"
    elseif s == StatusInit
        return "init"
    elseif s == StatusConnecting
        return "connecting"
    elseif s == StatusOpen
        return "open"
    elseif s == StatusActive
        return "active"
    elseif s == StatusPaused
        return "paused"
    elseif s == StatusClosing
        return "closing"
    elseif s == StatusClosed
        return "closed"
    elseif s == StatusEOF
        return "eof"
    end
    return "invalid status"
end

mutable struct PipeEndpoint <: LibuvStream
    handle::Ptr{Cvoid}
    status::Int
    buffer::IOBuffer
    cond::ThreadSynchronizer
    readerror::Any
    sendbuf::Union{IOBuffer, Nothing}
    lock::ReentrantLock # advisory lock
    throttle::Int
    function PipeEndpoint(handle::Ptr{Cvoid}, status)
        p = new(handle,
                status,
                PipeBuffer(),
                ThreadSynchronizer(),
                nothing,
                nothing,
                ReentrantLock(),
                DEFAULT_READ_BUFFER_SZ)
        associate_julia_struct(handle, p)
        finalizer(uvfinalize, p)
        return p
    end
end

function PipeEndpoint()
    pipe = PipeEndpoint(Libc.malloc(_sizeof_uv_named_pipe), StatusUninit)
    iolock_begin()
    err = ccall(:uv_pipe_init, Cint, (Ptr{Cvoid}, Ptr{Cvoid}, Cint), eventloop(), pipe.handle, 0)
    uv_error("failed to create pipe endpoint", err)
    pipe.status = StatusInit
    iolock_end()
    return pipe
end

function PipeEndpoint(fd::OS_HANDLE)
    pipe = PipeEndpoint()
    iolock_begin()
    err = ccall(:uv_pipe_open, Int32, (Ptr{Cvoid}, OS_HANDLE), pipe.handle, fd)
    uv_error("pipe_open", err)
    pipe.status = StatusOpen
    iolock_end()
    return pipe
end
if OS_HANDLE != RawFD
    PipeEndpoint(fd::RawFD) = PipeEndpoint(Libc._get_osfhandle(fd))
end


mutable struct TTY <: LibuvStream
    handle::Ptr{Cvoid}
    status::Int
    buffer::IOBuffer
    cond::ThreadSynchronizer
    readerror::Any
    sendbuf::Union{IOBuffer, Nothing}
    lock::ReentrantLock # advisory lock
    throttle::Int
    @static if Sys.iswindows(); ispty::Bool; end
    function TTY(handle::Ptr{Cvoid}, status)
        tty = new(
            handle,
            status,
            PipeBuffer(),
            ThreadSynchronizer(),
            nothing,
            nothing,
            ReentrantLock(),
            DEFAULT_READ_BUFFER_SZ)
        associate_julia_struct(handle, tty)
        finalizer(uvfinalize, tty)
        @static if Sys.iswindows()
            tty.ispty = ccall(:jl_ispty, Cint, (Ptr{Cvoid},), handle) != 0
        end
        return tty
    end
end

function TTY(fd::OS_HANDLE)
    tty = TTY(Libc.malloc(_sizeof_uv_tty), StatusUninit)
    iolock_begin()
    err = ccall(:uv_tty_init, Int32, (Ptr{Cvoid}, Ptr{Cvoid}, OS_HANDLE, Int32),
        eventloop(), tty.handle, fd, 0)
    uv_error("TTY", err)
    tty.status = StatusOpen
    iolock_end()
    return tty
end
if OS_HANDLE != RawFD
    TTY(fd::RawFD) = TTY(Libc._get_osfhandle(fd))
end

show(io::IO, stream::LibuvServer) = print(io, typeof(stream), "(",
    _fd(stream), " ",
    uv_status_string(stream), ")")
show(io::IO, stream::LibuvStream) = print(io, typeof(stream), "(",
    _fd(stream), " ",
    uv_status_string(stream), ", ",
    bytesavailable(stream.buffer), " bytes waiting)")

# Shared LibuvStream object interface

function isreadable(io::LibuvStream)
    bytesavailable(io) > 0 && return true
    isopen(io) || return false
    io.status == StatusEOF && return false
    return ccall(:uv_is_readable, Cint, (Ptr{Cvoid},), io.handle) != 0
end

function iswritable(io::LibuvStream)
    isopen(io) || return false
    io.status == StatusClosing && return false
    return ccall(:uv_is_writable, Cint, (Ptr{Cvoid},), io.handle) != 0
end

lock(s::LibuvStream) = lock(s.lock)
unlock(s::LibuvStream) = unlock(s.lock)

setup_stdio(stream::LibuvStream, ::Bool) = (stream, false)
rawhandle(stream::LibuvStream) = stream.handle
unsafe_convert(::Type{Ptr{Cvoid}}, s::Union{LibuvStream, LibuvServer}) = s.handle

function init_stdio(handle::Ptr{Cvoid})
    iolock_begin()
    t = ccall(:jl_uv_handle_type, Int32, (Ptr{Cvoid},), handle)
    local io
    if t == UV_FILE
        fd = ccall(:jl_uv_file_handle, OS_HANDLE, (Ptr{Cvoid},), handle)
        # TODO: Replace ios.c file with libuv fs?
        # return File(fd)
        @static if Sys.iswindows()
            # TODO: Get ios.c to understand native handles
            fd = ccall(:_open_osfhandle, RawFD, (WindowsRawSocket, Int32), fd, 0)
        end
        # TODO: Get fdio to work natively with file descriptors instead of integers
        io = fdio(cconvert(Cint, fd))
    elseif t == UV_TTY
        io = TTY(handle, StatusOpen)
    elseif t == UV_TCP
        Sockets = require(PkgId(UUID((0x6462fe0b_24de_5631, 0x8697_dd941f90decc)), "Sockets"))
        io = Sockets.TCPSocket(handle, StatusOpen)
    elseif t == UV_NAMED_PIPE
        io = PipeEndpoint(handle, StatusOpen)
    else
        throw(ArgumentError("invalid stdio type: $t"))
    end
    iolock_end()
    return io
end

"""
    open(fd::OS_HANDLE) -> IO

Take a raw file descriptor wrap it in a Julia-aware IO type,
and take ownership of the fd handle.
Call `open(Libc.dup(fd))` to avoid the ownership capture
of the original handle.

!!! warning
    Do not call this on a handle that's already owned by some
    other part of the system.
"""
function open(h::OS_HANDLE)
    iolock_begin()
    t = ccall(:uv_guess_handle, Cint, (OS_HANDLE,), h)
    local io
    if t == UV_FILE
        @static if Sys.iswindows()
            # TODO: Get ios.c to understand native handles
            h = ccall(:_open_osfhandle, RawFD, (WindowsRawSocket, Int32), h, 0)
        end
        # TODO: Get fdio to work natively with file descriptors instead of integers
        io = fdio(cconvert(Cint, h))
    elseif t == UV_TTY
        io = TTY(h)
    elseif t == UV_TCP
        Sockets = require(PkgId(UUID((0x6462fe0b_24de_5631, 0x8697_dd941f90decc)), "Sockets"))
        io = Sockets.TCPSocket(h)
    elseif t == UV_NAMED_PIPE
        io = PipeEndpoint(h)
        @static if Sys.iswindows()
            if ccall(:jl_ispty, Cint, (Ptr{Cvoid},), io.handle) != 0
                # replace the Julia `PipeEndpoint` type with a `TTY` type,
                # if we detect that this is a cygwin pty object
                pipe_handle, pipe_status = io.handle, io.status
                io.status = StatusClosed
                io.handle = C_NULL
                io = TTY(pipe_handle, pipe_status)
            end
        end
    else
        throw(ArgumentError("invalid stdio type: $t"))
    end
    iolock_end()
    return io
end

if OS_HANDLE != RawFD
    function open(fd::RawFD)
        h = Libc.dup(Libc._get_osfhandle(fd)) # make a dup to steal ownership away from msvcrt
        try
            io = open(h)
            ccall(:_close, Cint, (RawFD,), fd) # on success, destroy the old libc handle
            return io
        catch ex
            ccall(:CloseHandle, stdcall, Cint, (OS_HANDLE,), h) # on failure, destroy the new nt handle
            rethrow(ex)
        end
    end
end

function isopen(x::Union{LibuvStream, LibuvServer})
    if x.status == StatusUninit || x.status == StatusInit || x.handle === C_NULL
        throw(ArgumentError("$x is not initialized"))
    end
    return x.status != StatusClosed
end

function check_open(x::Union{LibuvStream, LibuvServer})
    if !isopen(x) || x.status == StatusClosing
        throw(IOError("stream is closed or unusable", 0))
    end
end

function wait_readnb(x::LibuvStream, nb::Int)
    # fast path before iolock acquire
    bytesavailable(x.buffer) >= nb && return
    open = isopen(x) && x.status != StatusEOF # must precede readerror check
    x.readerror === nothing || throw(x.readerror)
    open || return
    iolock_begin()
    # repeat fast path after iolock acquire, before other expensive work
    bytesavailable(x.buffer) >= nb && (iolock_end(); return)
    open = isopen(x) && x.status != StatusEOF
    x.readerror === nothing || throw(x.readerror)
    open || (iolock_end(); return)
    # now do the "real" work
    oldthrottle = x.throttle
    preserve_handle(x)
    lock(x.cond)
    try
        while bytesavailable(x.buffer) < nb
            x.readerror === nothing || throw(x.readerror)
            isopen(x) || break
            x.status == StatusEOF && break
            x.throttle = max(nb, x.throttle)
            start_reading(x) # ensure we are reading
            iolock_end()
            wait(x.cond)
            unlock(x.cond)
            iolock_begin()
            lock(x.cond)
        end
    finally
        if isempty(x.cond)
            stop_reading(x) # stop reading iff there are currently no other read clients of the stream
        end
        if oldthrottle <= x.throttle <= nb
            # if we're interleaving readers, we might not get back to the "original" throttle
            # but we consider that an acceptable "risk", since we can't be quite sure what the intended value is now
            x.throttle = oldthrottle
        end
        unpreserve_handle(x)
        unlock(x.cond)
    end
    iolock_end()
    nothing
end

function closewrite(s::LibuvStream)
    iolock_begin()
    check_open(s)
    req = Libc.malloc(_sizeof_uv_shutdown)
    uv_req_set_data(req, C_NULL) # in case we get interrupted before arriving at the wait call
    err = ccall(:uv_shutdown, Int32, (Ptr{Cvoid}, Ptr{Cvoid}, Ptr{Cvoid}),
                req, s, @cfunction(uv_shutdowncb_task, Cvoid, (Ptr{Cvoid}, Cint)))
    if err < 0
        Libc.free(req)
        uv_error("shutdown", err)
    end
    ct = current_task()
    preserve_handle(ct)
    sigatomic_begin()
    uv_req_set_data(req, ct)
    iolock_end()
    status = try
        sigatomic_end()
        wait()::Cint
    finally
        # try-finally unwinds the sigatomic level, so need to repeat sigatomic_end
        sigatomic_end()
        iolock_begin()
        ct.queue === nothing || list_deletefirst!(ct.queue::IntrusiveLinkedList{Task}, ct)
        if uv_req_data(req) != C_NULL
            # req is still alive,
            # so make sure we won't get spurious notifications later
            uv_req_set_data(req, C_NULL)
        else
            # done with req
            Libc.free(req)
        end
        iolock_end()
        unpreserve_handle(ct)
    end
    if isopen(s)
        if status < 0 || ccall(:uv_is_readable, Cint, (Ptr{Cvoid},), s.handle) == 0
            close(s)
        end
    end
    if status < 0
        throw(_UVError("shutdown", status))
    end
    nothing
end

function wait_close(x::Union{LibuvStream, LibuvServer})
    preserve_handle(x)
    lock(x.cond)
    try
        while isopen(x)
            wait(x.cond)
        end
    finally
        unlock(x.cond)
        unpreserve_handle(x)
    end
    nothing
end

function close(stream::Union{LibuvStream, LibuvServer})
    iolock_begin()
    if stream.status == StatusInit
        ccall(:jl_forceclose_uv, Cvoid, (Ptr{Cvoid},), stream.handle)
        stream.status = StatusClosing
    elseif isopen(stream)
        if stream.status != StatusClosing
            ccall(:jl_close_uv, Cvoid, (Ptr{Cvoid},), stream.handle)
            stream.status = StatusClosing
        end
    end
    iolock_end()
    wait_close(stream)
    nothing
end

function uvfinalize(uv::Union{LibuvStream, LibuvServer})
    iolock_begin()
    if uv.handle != C_NULL
        disassociate_julia_struct(uv.handle) # not going to call the usual close hooks (so preserve_handle is not needed)
        if uv.status == StatusUninit
            Libc.free(uv.handle)
        elseif uv.status == StatusInit
            ccall(:jl_forceclose_uv, Cvoid, (Ptr{Cvoid},), uv.handle)
        elseif isopen(uv)
            if uv.status != StatusClosing
                ccall(:jl_close_uv, Cvoid, (Ptr{Cvoid},), uv.handle)
            end
        elseif uv.status == StatusClosed
            Libc.free(uv.handle)
        end
        uv.handle = C_NULL
        uv.status = StatusClosed
    end
    iolock_end()
    nothing
end

if Sys.iswindows()
    ispty(s::TTY) = s.ispty
    ispty(s::IO) = false
end

"""
    displaysize([io::IO]) -> (lines, columns)

Return the nominal size of the screen that may be used for rendering output to
this `IO` object.
If no input is provided, the environment variables `LINES` and `COLUMNS` are read.
If those are not set, a default size of `(24, 80)` is returned.

# Examples
```jldoctest
julia> withenv("LINES" => 30, "COLUMNS" => 100) do
           displaysize()
       end
(30, 100)
```

To get your TTY size,

```julia-repl
julia> displaysize(stdout)
(34, 147)
```
"""
displaysize(io::IO) = displaysize()
displaysize() = (parse(Int, get(ENV, "LINES",   "24")),
                 parse(Int, get(ENV, "COLUMNS", "80")))::Tuple{Int, Int}

function displaysize(io::TTY)
    check_open(io)

    local h::Int, w::Int
    default_size = displaysize()

    @static if Sys.iswindows()
        if ispty(io)
            # io is actually a libuv pipe but a cygwin/msys2 pty
            try
                h, w = parse.(Int, split(read(open(Base.Cmd(String["stty", "size"]), "r", io).out, String)))
                h > 0 || (h = default_size[1])
                w > 0 || (w = default_size[2])
                return h, w
            catch
                return default_size
            end
        end
    end

    s1 = Ref{Int32}(0)
    s2 = Ref{Int32}(0)
    iolock_begin()
    check_open(io)
    Base.uv_error("size (TTY)", ccall(:uv_tty_get_winsize,
                                      Int32, (Ptr{Cvoid}, Ptr{Int32}, Ptr{Int32}),
                                      io, s1, s2) != 0)
    iolock_end()
    w, h = s1[], s2[]
    h > 0 || (h = default_size[1])
    w > 0 || (w = default_size[2])
    return h, w
end

### Libuv callbacks ###

## BUFFER ##
## Allocate space in buffer (for immediate use)
function alloc_request(buffer::IOBuffer, recommended_size::UInt)
    ensureroom(buffer, Int(recommended_size))
    ptr = buffer.append ? buffer.size + 1 : buffer.ptr
    nb = min(length(buffer.data), buffer.maxsize) - ptr + 1
    return (Ptr{Cvoid}(pointer(buffer.data, ptr)), nb)
end

notify_filled(buffer::IOBuffer, nread::Int, base::Ptr{Cvoid}, len::UInt) = notify_filled(buffer, nread)

function notify_filled(buffer::IOBuffer, nread::Int)
    if buffer.append
        buffer.size += nread
    else
        buffer.ptr += nread
    end
    nothing
end

function alloc_buf_hook(stream::LibuvStream, size::UInt)
    throttle = UInt(stream.throttle)
    return alloc_request(stream.buffer, (size > throttle) ? throttle : size)
end

function uv_alloc_buf(handle::Ptr{Cvoid}, size::Csize_t, buf::Ptr{Cvoid})
    hd = uv_handle_data(handle)
    if hd == C_NULL
        ccall(:jl_uv_buf_set_len, Cvoid, (Ptr{Cvoid}, Csize_t), buf, 0)
        return nothing
    end
    stream = unsafe_pointer_to_objref(hd)::LibuvStream

    local data::Ptr{Cvoid}, newsize::Csize_t
    if stream.status != StatusActive
        data = C_NULL
        newsize = 0
    else
        (data, newsize) = alloc_buf_hook(stream, UInt(size))
        if data == C_NULL
            newsize = 0
        end
        # avoid aliasing of `nread` with `errno` in uv_readcb
        # or exceeding the Win32 maximum uv_buf_t len
        maxsize = @static Sys.iswindows() ? typemax(Cint) : typemax(Cssize_t)
        newsize > maxsize && (newsize = maxsize)
    end

    ccall(:jl_uv_buf_set_base, Cvoid, (Ptr{Cvoid}, Ptr{Cvoid}), buf, data)
    ccall(:jl_uv_buf_set_len, Cvoid, (Ptr{Cvoid}, Csize_t), buf, newsize)
    nothing
end

function uv_readcb(handle::Ptr{Cvoid}, nread::Cssize_t, buf::Ptr{Cvoid})
    stream_unknown_type = @handle_as handle LibuvStream
    nrequested = ccall(:jl_uv_buf_len, Csize_t, (Ptr{Cvoid},), buf)
    function readcb_specialized(stream::LibuvStream, nread::Int, nrequested::UInt)
        lock(stream.cond)
        if nread < 0
            if nread == UV_ENOBUFS && nrequested == 0
                # remind the client that stream.buffer is full
                notify(stream.cond)
            elseif nread == UV_EOF # libuv called uv_stop_reading already
                if stream.status != StatusClosing
                    stream.status = StatusEOF
                    notify(stream.cond)
                    if stream isa TTY
                        # stream can still be used by reseteof (or possibly write)
                    elseif !(stream isa PipeEndpoint) && ccall(:uv_is_writable, Cint, (Ptr{Cvoid},), stream.handle) != 0
                        # stream can still be used by write
                    else
                        # underlying stream is no longer useful: begin finalization
                        ccall(:jl_close_uv, Cvoid, (Ptr{Cvoid},), stream.handle)
                        stream.status = StatusClosing
                    end
                end
            else
                stream.readerror = _UVError("read", nread)
                notify(stream.cond)
                # This is a fatal connection error
                ccall(:jl_close_uv, Cvoid, (Ptr{Cvoid},), stream.handle)
                stream.status = StatusClosing
            end
        else
            notify_filled(stream.buffer, nread)
            notify(stream.cond)
        end
        unlock(stream.cond)

        # Stop background reading when
        # 1) there's nobody paying attention to the data we are reading
        # 2) we have accumulated a lot of unread data OR
        # 3) we have an alternate buffer that has reached its limit.
        if stream.status == StatusPaused ||
           (stream.status == StatusActive &&
            ((bytesavailable(stream.buffer) >= stream.throttle) ||
             (bytesavailable(stream.buffer) >= stream.buffer.maxsize)))
            # save cycles by stopping kernel notifications from arriving
            ccall(:uv_read_stop, Cint, (Ptr{Cvoid},), stream)
            stream.status = StatusOpen
        end
        nothing
    end
    readcb_specialized(stream_unknown_type, Int(nread), UInt(nrequested))
    nothing
end

function reseteof(x::TTY)
    iolock_begin()
    if x.status == StatusEOF
        x.status = StatusOpen
    end
    iolock_end()
    nothing
end

function _uv_hook_close(uv::Union{LibuvStream, LibuvServer})
    lock(uv.cond)
    try
        uv.status = StatusClosed
        # notify any listeners that exist on this libuv stream type
        notify(uv.cond)
    finally
        unlock(uv.cond)
    end
    nothing
end


##########################################
# Pipe Abstraction
#  (composed of two half-pipes: .in and .out)
##########################################

mutable struct Pipe <: AbstractPipe
    in::PipeEndpoint # writable
    out::PipeEndpoint # readable
end

"""
Construct an uninitialized Pipe object.

The appropriate end of the pipe will be automatically initialized if
the object is used in process spawning. This can be useful to easily
obtain references in process pipelines, e.g.:

```
julia> err = Pipe()

# After this `err` will be initialized and you may read `foo`'s
# stderr from the `err` pipe.
julia> run(pipeline(pipeline(`foo`, stderr=err), `cat`), wait=false)
```
"""
Pipe() = Pipe(PipeEndpoint(), PipeEndpoint())
pipe_reader(p::Pipe) = p.out
pipe_writer(p::Pipe) = p.in

function link_pipe!(pipe::Pipe;
                    reader_supports_async = false,
                    writer_supports_async = false)
     link_pipe!(pipe.out, reader_supports_async, pipe.in, writer_supports_async)
     return pipe
end

show(io::IO, stream::Pipe) = print(io,
    "Pipe(",
    _fd(stream.in), " ",
    uv_status_string(stream.in), " => ",
    _fd(stream.out), " ",
    uv_status_string(stream.out), ", ",
    bytesavailable(stream), " bytes waiting)")


## Functions for PipeEndpoint and PipeServer ##

function open_pipe!(p::PipeEndpoint, handle::OS_HANDLE)
    iolock_begin()
    if p.status != StatusInit
        error("pipe is already in use or has been closed")
    end
    err = ccall(:uv_pipe_open, Int32, (Ptr{Cvoid}, OS_HANDLE), p.handle, handle)
    uv_error("pipe_open", err)
    p.status = StatusOpen
    iolock_end()
    return p
end


function link_pipe!(read_end::PipeEndpoint, reader_supports_async::Bool,
                    write_end::PipeEndpoint, writer_supports_async::Bool)
    rd, wr = link_pipe(reader_supports_async, writer_supports_async)
    try
        try
            open_pipe!(read_end, rd)
        catch
            close_pipe_sync(rd)
            rethrow()
        end
        open_pipe!(write_end, wr)
    catch
        close_pipe_sync(wr)
        rethrow()
    end
    nothing
end

function link_pipe(reader_supports_async::Bool, writer_supports_async::Bool)
    UV_NONBLOCK_PIPE = 0x40
    fildes = Ref{Pair{OS_HANDLE, OS_HANDLE}}(INVALID_OS_HANDLE => INVALID_OS_HANDLE) # read (in) => write (out)
    err = ccall(:uv_pipe, Int32, (Ptr{Pair{OS_HANDLE, OS_HANDLE}}, Cint, Cint),
                fildes,
                reader_supports_async * UV_NONBLOCK_PIPE,
                writer_supports_async * UV_NONBLOCK_PIPE)
    uv_error("pipe", err)
    return fildes[]
end

if Sys.iswindows()
    function close_pipe_sync(handle::WindowsRawSocket)
        ccall(:CloseHandle, stdcall, Cint, (WindowsRawSocket,), handle)
        nothing
    end
else
    function close_pipe_sync(handle::RawFD)
        ccall(:close, Cint, (RawFD,), handle)
        nothing
    end
end

## Functions for any LibuvStream ##

# flow control

function start_reading(stream::LibuvStream)
    iolock_begin()
    if stream.status == StatusOpen
        if !isreadable(stream)
            error("tried to read a stream that is not readable")
        end
        # libuv may call the alloc callback immediately
        # for a TTY on Windows, so ensure the status is set first
        stream.status = StatusActive
        ret = ccall(:uv_read_start, Cint, (Ptr{Cvoid}, Ptr{Cvoid}, Ptr{Cvoid}),
                    stream, @cfunction(uv_alloc_buf, Cvoid, (Ptr{Cvoid}, Csize_t, Ptr{Cvoid})),
                    @cfunction(uv_readcb, Cvoid, (Ptr{Cvoid}, Cssize_t, Ptr{Cvoid})))
    elseif stream.status == StatusPaused
        stream.status = StatusActive
        ret = Int32(0)
    elseif stream.status == StatusActive
        ret = Int32(0)
    else
        ret = Int32(-1)
    end
    iolock_end()
    return ret
end

if Sys.iswindows()
    # the low performance version of stop_reading is required
    # on Windows due to a NT kernel bug that we can't use a blocking
    # stream for non-blocking (overlapped) calls,
    # and a ReadFile call blocking on one thread
    # causes all other operations on that stream to lockup
    function stop_reading(stream::LibuvStream)
        iolock_begin()
        if stream.status == StatusActive
            stream.status = StatusOpen
            ccall(:uv_read_stop, Cint, (Ptr{Cvoid},), stream)
        end
        iolock_end()
        nothing
    end
else
    function stop_reading(stream::LibuvStream)
        iolock_begin()
        if stream.status == StatusActive
            stream.status = StatusPaused
        end
        iolock_end()
        nothing
    end
end

# bulk read / write

readbytes!(s::LibuvStream, a::Vector{UInt8}, nb = length(a)) = readbytes!(s, a, Int(nb))
function readbytes!(s::LibuvStream, a::Vector{UInt8}, nb::Int)
    iolock_begin()
    sbuf = s.buffer
    @assert sbuf.seekable == false
    @assert sbuf.maxsize >= nb

    function wait_locked(s, buf, nb)
        while bytesavailable(buf) < nb
            s.readerror === nothing || throw(s.readerror)
            isopen(s) || break
            s.status != StatusEOF || break
            iolock_end()
            wait_readnb(s, nb)
            iolock_begin()
        end
    end

    if nb <= SZ_UNBUFFERED_IO # Under this limit we are OK with copying the array from the stream's buffer
        wait_locked(s, sbuf, nb)
    end
    if bytesavailable(sbuf) >= nb
        nread = readbytes!(sbuf, a, nb)
    else
        newbuf = PipeBuffer(a, maxsize=nb)
        newbuf.size = 0 # reset the write pointer to the beginning
        nread = try
            s.buffer = newbuf
            write(newbuf, sbuf)
            wait_locked(s, newbuf, nb)
            bytesavailable(newbuf)
        finally
            s.buffer = sbuf
        end
        compact(newbuf)
    end
    iolock_end()
    return nread
end

function read(stream::LibuvStream)
    wait_readnb(stream, typemax(Int))
    iolock_begin()
    bytes = take!(stream.buffer)
    iolock_end()
    return bytes
end

function unsafe_read(s::LibuvStream, p::Ptr{UInt8}, nb::UInt)
    iolock_begin()
    sbuf = s.buffer
    @assert sbuf.seekable == false
    @assert sbuf.maxsize >= nb

    function wait_locked(s, buf, nb)
        while bytesavailable(buf) < nb
            s.readerror === nothing || throw(s.readerror)
            isopen(s) || throw(EOFError())
            s.status != StatusEOF || throw(EOFError())
            iolock_end()
            wait_readnb(s, nb)
            iolock_begin()
        end
    end

    if nb <= SZ_UNBUFFERED_IO # Under this limit we are OK with copying the array from the stream's buffer
        wait_locked(s, sbuf, Int(nb))
    end
    if bytesavailable(sbuf) >= nb
        unsafe_read(sbuf, p, nb)
    else
        newbuf = PipeBuffer(unsafe_wrap(Array, p, nb), maxsize=Int(nb))
        newbuf.size = 0 # reset the write pointer to the beginning
        try
            s.buffer = newbuf
            write(newbuf, sbuf)
            wait_locked(s, newbuf, Int(nb))
        finally
            s.buffer = sbuf
        end
    end
    iolock_end()
    nothing
end

function read(this::LibuvStream, ::Type{UInt8})
    iolock_begin()
    sbuf = this.buffer
    @assert sbuf.seekable == false
    while bytesavailable(sbuf) < 1
        iolock_end()
        eof(this) && throw(EOFError())
        iolock_begin()
    end
    c = read(sbuf, UInt8)
    iolock_end()
    return c
end

function readavailable(this::LibuvStream)
    wait_readnb(this, 1) # unlike the other `read` family of functions, this one doesn't guarantee error reporting
    iolock_begin()
    buf = this.buffer
    @assert buf.seekable == false
    bytes = take!(buf)
    iolock_end()
    return bytes
end

function readuntil(x::LibuvStream, c::UInt8; keep::Bool=false)
    iolock_begin()
    buf = x.buffer
    @assert buf.seekable == false
    if !occursin(c, buf) # fast path checks first
        x.readerror === nothing || throw(x.readerror)
        if isopen(x) && x.status != StatusEOF
            preserve_handle(x)
            lock(x.cond)
            try
                while !occursin(c, x.buffer)
                    x.readerror === nothing || throw(x.readerror)
                    isopen(x) || break
                    x.status != StatusEOF || break
                    start_reading(x) # ensure we are reading
                    iolock_end()
                    wait(x.cond)
                    unlock(x.cond)
                    iolock_begin()
                    lock(x.cond)
                end
            finally
                if isempty(x.cond)
                    stop_reading(x) # stop reading iff there are currently no other read clients of the stream
                end
                unlock(x.cond)
                unpreserve_handle(x)
            end
        end
    end
    bytes = readuntil(buf, c, keep=keep)
    iolock_end()
    return bytes
end

uv_write(s::LibuvStream, p::Vector{UInt8}) = GC.@preserve p uv_write(s, pointer(p), UInt(sizeof(p)))

# caller must have acquired the iolock
function uv_write(s::LibuvStream, p::Ptr{UInt8}, n::UInt)
    uvw = uv_write_async(s, p, n)
    ct = current_task()
    preserve_handle(ct)
    sigatomic_begin()
    uv_req_set_data(uvw, ct)
    iolock_end()
    status = try
        sigatomic_end()
        # wait for the last chunk to complete (or error)
        # assume that any errors would be sticky,
        # (so we don't need to monitor the error status of the intermediate writes)
        wait()::Cint
    finally
        # try-finally unwinds the sigatomic level, so need to repeat sigatomic_end
        sigatomic_end()
        iolock_begin()
        ct.queue === nothing || list_deletefirst!(ct.queue::IntrusiveLinkedList{Task}, ct)
        if uv_req_data(uvw) != C_NULL
            # uvw is still alive,
            # so make sure we won't get spurious notifications later
            uv_req_set_data(uvw, C_NULL)
        else
            # done with uvw
            Libc.free(uvw)
        end
        iolock_end()
        unpreserve_handle(ct)
    end
    if status < 0
        throw(_UVError("write", status))
    end
    return Int(n)
end

# helper function for uv_write that returns the uv_write_t struct for the write
# rather than waiting on it, caller must hold the iolock
function uv_write_async(s::LibuvStream, p::Ptr{UInt8}, n::UInt)
    check_open(s)
    while true
        uvw = Libc.malloc(_sizeof_uv_write)
        uv_req_set_data(uvw, C_NULL) # in case we get interrupted before arriving at the wait call
        nwrite = min(n, MAX_OS_WRITE) # split up the write into chunks the OS can handle.
        # TODO: use writev instead of a loop
        err = ccall(:jl_uv_write,
                    Int32,
                    (Ptr{Cvoid}, Ptr{Cvoid}, UInt, Ptr{Cvoid}, Ptr{Cvoid}),
                    s, p, nwrite, uvw,
                    @cfunction(uv_writecb_task, Cvoid, (Ptr{Cvoid}, Cint)))
        if err < 0
            Libc.free(uvw)
            uv_error("write", err)
        end
        n -= nwrite
        p += nwrite
        if n == 0
            return uvw
        end
    end
end


# Optimized send
# - smaller writes are buffered, final uv write on flush or when buffer full
# - large isbits arrays are unbuffered and written directly

function unsafe_write(s::LibuvStream, p::Ptr{UInt8}, n::UInt)
    while true
        # try to add to the send buffer
        iolock_begin()
        buf = s.sendbuf
        buf === nothing && break
        totb = bytesavailable(buf) + n
        if totb < buf.maxsize
            nb = unsafe_write(buf, p, n)
            iolock_end()
            return nb
        end
        bytesavailable(buf) == 0 && break
        # perform flush(s)
        arr = take!(buf)
        uv_write(s, arr)
    end
    # perform the output to the kernel
    return uv_write(s, p, n)
end

function flush(s::LibuvStream)
    iolock_begin()
    buf = s.sendbuf
    if buf !== nothing
        if bytesavailable(buf) > 0
            arr = take!(buf)
            uv_write(s, arr)
            return
        end
    end
    uv_write(s, Ptr{UInt8}(Base.eventloop()), UInt(0)) # zero write from a random pointer to flush current queue
    return
end

function buffer_writes(s::LibuvStream, bufsize)
    sendbuf = PipeBuffer(bufsize)
    iolock_begin()
    s.sendbuf = sendbuf
    iolock_end()
    return s
end

## low-level calls to libuv ##

function write(s::LibuvStream, b::UInt8)
    buf = s.sendbuf
    if buf !== nothing
        iolock_begin()
        if bytesavailable(buf) + 1 < buf.maxsize
            n = write(buf, b)
            iolock_end()
            return n
        end
        iolock_end()
    end
    return write(s, Ref{UInt8}(b))
end

function uv_writecb_task(req::Ptr{Cvoid}, status::Cint)
    d = uv_req_data(req)
    if d != C_NULL
        uv_req_set_data(req, C_NULL) # let the Task know we got the writecb
        t = unsafe_pointer_to_objref(d)::Task
        schedule(t, status)
    else
        # no owner for this req, safe to just free it
        Libc.free(req)
    end
    nothing
end

function uv_shutdowncb_task(req::Ptr{Cvoid}, status::Cint)
    d = uv_req_data(req)
    if d != C_NULL
        uv_req_set_data(req, C_NULL) # let the Task know we got the shutdowncb
        t = unsafe_pointer_to_objref(d)::Task
        schedule(t, status)
    else
        # no owner for this req, safe to just free it
        Libc.free(req)
    end
    nothing
end


_fd(x::IOStream) = RawFD(fd(x))
_fd(x::Union{OS_HANDLE, RawFD}) = x

function _fd(x::Union{LibuvStream, LibuvServer})
    fd = Ref{OS_HANDLE}(INVALID_OS_HANDLE)
    if x.status != StatusUninit && x.status != StatusClosed && x.handle != C_NULL
        err = ccall(:uv_fileno, Int32, (Ptr{Cvoid}, Ptr{OS_HANDLE}), x.handle, fd)
        # handle errors by returning INVALID_OS_HANDLE
    end
    return fd[]
end

struct RedirectStdStream <: Function
    unix_fd::Int
    writable::Bool
end
for (f, writable, unix_fd) in
        ((:redirect_stdin, false, 0),
         (:redirect_stdout, true, 1),
         (:redirect_stderr, true, 2))
    @eval const ($f) = RedirectStdStream($unix_fd, $writable)
end
function _redirect_io_libc(stream, unix_fd::Int)
    posix_fd = _fd(stream)
    @static if Sys.iswindows()
        if 0 <= unix_fd <= 2
            ccall(:SetStdHandle, stdcall, Int32, (Int32, OS_HANDLE),
                -10 - unix_fd, Libc._get_osfhandle(posix_fd))
        end
    end
    dup(posix_fd, RawFD(unix_fd))
    nothing
end
function _redirect_io_global(io, unix_fd::Int)
    unix_fd == 0 && (global stdin = io)
    unix_fd == 1 && (global stdout = io)
    unix_fd == 2 && (global stderr = io)
    nothing
end
function (f::RedirectStdStream)(handle::Union{LibuvStream, IOStream})
    _redirect_io_libc(handle, f.unix_fd)
    c_sym = f.unix_fd == 0 ? cglobal(:jl_uv_stdin, Ptr{Cvoid}) :
            f.unix_fd == 1 ? cglobal(:jl_uv_stdout, Ptr{Cvoid}) :
            f.unix_fd == 2 ? cglobal(:jl_uv_stderr, Ptr{Cvoid}) :
            C_NULL
    c_sym == C_NULL || unsafe_store!(c_sym, handle.handle)
    _redirect_io_global(handle, f.unix_fd)
    return handle
end
function (f::RedirectStdStream)(::DevNull)
    nulldev = @static Sys.iswindows() ? "NUL" : "/dev/null"
    handle = open(nulldev, write=f.writable)
    _redirect_io_libc(handle, f.unix_fd)
    close(handle) # handle has been dup'ed in _redirect_io_libc
    _redirect_io_global(devnull, f.unix_fd)
    return devnull
end
function (f::RedirectStdStream)(io::AbstractPipe)
    io2 = (f.writable ? pipe_writer : pipe_reader)(io)
    f(io2)
    _redirect_io_global(io, f.unix_fd)
    return io
end
function (f::RedirectStdStream)(p::Pipe)
    if p.in.status == StatusInit && p.out.status == StatusInit
        link_pipe!(p)
    end
    io2 = getfield(p, f.writable ? :in : :out)
    f(io2)
    return p
end
(f::RedirectStdStream)() = f(Pipe())

# Deprecate these in v2 (RedirectStdStream support)
iterate(p::Pipe) = (p.out, 1)
iterate(p::Pipe, i::Int) = i == 1 ? (p.in, 2) : nothing
getindex(p::Pipe, key::Int) = key == 1 ? p.out : key == 2 ? p.in : throw(KeyError(key))

"""
    redirect_stdout([stream]) -> stream

Create a pipe to which all C and Julia level [`stdout`](@ref) output
will be redirected. Return a stream representing the pipe ends.
Data written to [`stdout`](@ref) may now be read from the `rd` end of
the pipe.

!!! note
    `stream` must be a compatible objects, such as an `IOStream`, `TTY`,
    `Pipe`, socket, or `devnull`.

See also [`redirect_stdio`](@ref).
"""
redirect_stdout

"""
    redirect_stderr([stream]) -> stream

Like [`redirect_stdout`](@ref), but for [`stderr`](@ref).

!!! note
    `stream` must be a compatible objects, such as an `IOStream`, `TTY`,
    `Pipe`, socket, or `devnull`.

See also [`redirect_stdio`](@ref).
"""
redirect_stderr

"""
    redirect_stdin([stream]) -> stream

Like [`redirect_stdout`](@ref), but for [`stdin`](@ref).
Note that the direction of the stream is reversed.

!!! note
    `stream` must be a compatible objects, such as an `IOStream`, `TTY`,
    `Pipe`, socket, or `devnull`.

See also [`redirect_stdio`](@ref).
"""
redirect_stdin

"""
    redirect_stdio(;stdin=stdin, stderr=stderr, stdout=stdout)

Redirect a subset of the streams `stdin`, `stderr`, `stdout`.
Each argument must be an `IOStream`, `TTY`, `Pipe`, socket, or `devnull`.

!!! compat "Julia 1.7"
    `redirect_stdio` requires Julia 1.7 or later.
"""
function redirect_stdio(;stdin=nothing, stderr=nothing, stdout=nothing)
    stdin  === nothing || redirect_stdin(stdin)
    stderr === nothing || redirect_stderr(stderr)
    stdout === nothing || redirect_stdout(stdout)
end

"""
    redirect_stdio(f; stdin=nothing, stderr=nothing, stdout=nothing)

Redirect a subset of the streams `stdin`, `stderr`, `stdout`,
call `f()` and restore each stream.

Possible values for each stream are:
* `nothing` indicating the stream should not be redirected.
* `path::AbstractString` redirecting the stream to the file at `path`.
* `io` an `IOStream`, `TTY`, `Pipe`, socket, or `devnull`.

# Examples
```julia-repl
julia> redirect_stdio(stdout="stdout.txt", stderr="stderr.txt") do
           print("hello stdout")
           print(stderr, "hello stderr")
       end

julia> read("stdout.txt", String)
"hello stdout"

julia> read("stderr.txt", String)
"hello stderr"
```

# Edge cases

It is possible to pass the same argument to `stdout` and `stderr`:
```julia-repl
julia> redirect_stdio(stdout="log.txt", stderr="log.txt", stdin=devnull) do
    ...
end
```

However it is not supported to pass two distinct descriptors of the same file.
```julia-repl
julia> io1 = open("same/path", "w")

julia> io2 = open("same/path", "w")

julia> redirect_stdio(f, stdout=io1, stderr=io2) # not supported
```
Also the `stdin` argument may not be the same descriptor as `stdout` or `stderr`.
```julia-repl
julia> io = open(...)

julia> redirect_stdio(f, stdout=io, stdin=io) # not supported
```

!!! compat "Julia 1.7"
    `redirect_stdio` requires Julia 1.7 or later.
"""
function redirect_stdio(f; stdin=nothing, stderr=nothing, stdout=nothing)

    function resolve(new::Nothing, oldstream, mode)
        (new=nothing, close=false, old=nothing)
    end
    function resolve(path::AbstractString, oldstream,mode)
        (new=open(path, mode), close=true, old=oldstream)
    end
    function resolve(new, oldstream, mode)
        (new=new, close=false, old=oldstream)
    end

    same_path(x, y) = false
    function same_path(x::AbstractString, y::AbstractString)
        # if x = y = "does_not_yet_exist.txt" then samefile will return false
        (abspath(x) == abspath(y)) || samefile(x,y)
    end
    if same_path(stderr, stdin)
        throw(ArgumentError("stdin and stderr cannot be the same path"))
    end
    if same_path(stdout, stdin)
        throw(ArgumentError("stdin and stdout cannot be the same path"))
    end

    new_in , close_in , old_in  = resolve(stdin , Base.stdin , "r")
    new_out, close_out, old_out = resolve(stdout, Base.stdout, "w")
    if same_path(stderr, stdout)
        # make sure that in case stderr = stdout = "same/path"
        # only a single io is used instead of opening the same file twice
        new_err, close_err, old_err = new_out, false, Base.stderr
    else
        new_err, close_err, old_err = resolve(stderr, Base.stderr, "w")
    end

    redirect_stdio(; stderr=new_err, stdin=new_in, stdout=new_out)

    try
        return f()
    finally
        redirect_stdio(;stderr=old_err, stdin=old_in, stdout=old_out)
        close_err && close(new_err)
        close_in  && close(new_in )
        close_out && close(new_out)
    end
end

function (f::RedirectStdStream)(thunk::Function, stream)
    stdold = f.unix_fd == 0 ? stdin :
             f.unix_fd == 1 ? stdout :
             f.unix_fd == 2 ? stderr :
             throw(ArgumentError("Not implemented to get old handle of fd except for stdio"))
    f(stream)
    try
        return thunk()
    finally
        f(stdold)
    end
end


"""
    redirect_stdout(f::Function, stream)

Run the function `f` while redirecting [`stdout`](@ref) to `stream`.
Upon completion, [`stdout`](@ref) is restored to its prior setting.
"""
redirect_stdout(f::Function, stream)

"""
    redirect_stderr(f::Function, stream)

Run the function `f` while redirecting [`stderr`](@ref) to `stream`.
Upon completion, [`stderr`](@ref) is restored to its prior setting.
"""
redirect_stderr(f::Function, stream)

"""
    redirect_stdin(f::Function, stream)

Run the function `f` while redirecting [`stdin`](@ref) to `stream`.
Upon completion, [`stdin`](@ref) is restored to its prior setting.
"""
redirect_stdin(f::Function, stream)

mark(x::LibuvStream)     = mark(x.buffer)
unmark(x::LibuvStream)   = unmark(x.buffer)
reset(x::LibuvStream)    = reset(x.buffer)
ismarked(x::LibuvStream) = ismarked(x.buffer)

function peek(s::LibuvStream, ::Type{T}) where T
    mark(s)
    try read(s, T)
    finally
        reset(s)
    end
end

# BufferStream's are non-OS streams, backed by a regular IOBuffer
mutable struct BufferStream <: LibuvStream
    buffer::IOBuffer
    cond::Threads.Condition
    readerror::Any
    buffer_writes::Bool
    lock::ReentrantLock # advisory lock
    status::Int

    BufferStream() = new(PipeBuffer(), Threads.Condition(), nothing, false, ReentrantLock(), StatusActive)
end

isopen(s::BufferStream) = s.status != StatusClosed

closewrite(s::BufferStream) = close(s)

function close(s::BufferStream)
    lock(s.cond) do
        s.status = StatusClosed
        notify(s.cond)
        nothing
    end
end
uvfinalize(s::BufferStream) = nothing
setup_stdio(stream::BufferStream, child_readable::Bool) = invoke(setup_stdio, Tuple{IO, Bool}, stream, child_readable)

function read(s::BufferStream, ::Type{UInt8})
    nread = lock(s.cond) do
        wait_readnb(s, 1)
        read(s.buffer, UInt8)
    end
    return nread
end
function unsafe_read(s::BufferStream, a::Ptr{UInt8}, nb::UInt)
    lock(s.cond) do
        wait_readnb(s, Int(nb))
        unsafe_read(s.buffer, a, nb)
        nothing
    end
end
bytesavailable(s::BufferStream) = bytesavailable(s.buffer)

isreadable(s::BufferStream) = (isopen(s) || bytesavailable(s) > 0) && s.buffer.readable
iswritable(s::BufferStream) = isopen(s) && s.buffer.writable

function wait_readnb(s::BufferStream, nb::Int)
    lock(s.cond) do
        while isopen(s) && bytesavailable(s.buffer) < nb
            wait(s.cond)
        end
    end
end

show(io::IO, s::BufferStream) = print(io, "BufferStream(bytes waiting=", bytesavailable(s.buffer), ", isopen=", isopen(s), ")")

function readuntil(s::BufferStream, c::UInt8; keep::Bool=false)
    bytes = lock(s.cond) do
        while isopen(s) && !occursin(c, s.buffer)
            wait(s.cond)
        end
        readuntil(s.buffer, c, keep=keep)
    end
    return bytes
end

function wait_close(s::BufferStream)
    lock(s.cond) do
        while isopen(s)
            wait(s.cond)
        end
    end
end

start_reading(s::BufferStream) = Int32(0)
stop_reading(s::BufferStream) = nothing

write(s::BufferStream, b::UInt8) = write(s, Ref{UInt8}(b))
function unsafe_write(s::BufferStream, p::Ptr{UInt8}, nb::UInt)
    nwrite = lock(s.cond) do
        rv = unsafe_write(s.buffer, p, nb)
        s.buffer_writes || notify(s.cond)
        rv
    end
    return nwrite
end

function eof(s::BufferStream)
    bytesavailable(s) > 0 && return false
    iseof = lock(s.cond) do
        wait_readnb(s, 1)
        return !isopen(s) && bytesavailable(s) <= 0
    end
    return iseof
end

# If buffer_writes is called, it will delay notifying waiters till a flush is called.
buffer_writes(s::BufferStream, bufsize=0) = (s.buffer_writes = true; s)
function flush(s::BufferStream)
    lock(s.cond) do
        notify(s.cond)
        nothing
    end
end

skip(s::BufferStream, n) = skip(s.buffer, n)
Q   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/filesystem.jl"      # This file is a part of Julia. License is MIT: https://julialang.org/license

## File Operations (Libuv-based) ##

module Filesystem

const S_IFDIR  = 0o040000  # directory
const S_IFCHR  = 0o020000  # character device
const S_IFBLK  = 0o060000  # block device
const S_IFREG  = 0o100000  # regular file
const S_IFIFO  = 0o010000  # fifo (named pipe)
const S_IFLNK  = 0o120000  # symbolic link
const S_IFSOCK = 0o140000  # socket file
const S_IFMT   = 0o170000

const S_ISUID = 0o4000  # set UID bit
const S_ISGID = 0o2000  # set GID bit
const S_ENFMT = S_ISGID # file locking enforcement
const S_ISVTX = 0o1000  # sticky bit

const S_IRUSR = 0o0400  # read by owner
const S_IWUSR = 0o0200  # write by owner
const S_IXUSR = 0o0100  # execute by owner
const S_IRWXU = 0o0700  # mask for owner permissions
const S_IRGRP = 0o0040  # read by group
const S_IWGRP = 0o0020  # write by group
const S_IXGRP = 0o0010  # execute by group
const S_IRWXG = 0o0070  # mask for group permissions
const S_IROTH = 0o0004  # read by other
const S_IWOTH = 0o0002  # write by other
const S_IXOTH = 0o0001  # execute by other
const S_IRWXO = 0o0007  # mask for other permissions

export File,
       StatStruct,
       # open,
       futime,
       write,
       JL_O_WRONLY,
       JL_O_RDONLY,
       JL_O_RDWR,
       JL_O_APPEND,
       JL_O_CREAT,
       JL_O_EXCL,
       JL_O_TRUNC,
       JL_O_TEMPORARY,
       JL_O_SHORT_LIVED,
       JL_O_SEQUENTIAL,
       JL_O_RANDOM,
       JL_O_NOCTTY,
       JL_O_NOCTTY,
       JL_O_NONBLOCK,
       JL_O_NDELAY,
       JL_O_SYNC,
       JL_O_FSYNC,
       JL_O_ASYNC,
       JL_O_LARGEFILE,
       JL_O_DIRECTORY,
       JL_O_NOFOLLOW,
       JL_O_CLOEXEC,
       JL_O_DIRECT,
       JL_O_NOATIME,
       JL_O_PATH,
       JL_O_TMPFILE,
       JL_O_DSYNC,
       JL_O_RSYNC,
       S_IRUSR, S_IWUSR, S_IXUSR, S_IRWXU,
       S_IRGRP, S_IWGRP, S_IXGRP, S_IRWXG,
       S_IROTH, S_IWOTH, S_IXOTH, S_IRWXO

import .Base:
    IOError, _UVError, _sizeof_uv_fs, check_open, close, eof, eventloop, fd, isopen,
    bytesavailable, position, read, read!, readavailable, seek, seekend, show,
    skip, stat, unsafe_read, unsafe_write, write, transcode, uv_error,
    setup_stdio, rawhandle, OS_HANDLE, INVALID_OS_HANDLE, windowserror, filesize

import .Base.RefValue

if Sys.iswindows()
    import .Base: cwstring
end

# Average buffer size including null terminator for several filesystem operations.
# On Windows we use the MAX_PATH = 260 value on Win32.
const AVG_PATH = Sys.iswindows() ? 260 : 512

# helper function to clean up libuv request
uv_fs_req_cleanup(req) = ccall(:uv_fs_req_cleanup, Cvoid, (Ptr{Cvoid},), req)

include("path.jl")
include("stat.jl")
include("file.jl")
include(string(length(Core.ARGS) >= 2 ? Core.ARGS[2] : "", "file_constants.jl"))  # include($BUILDROOT/base/file_constants.jl)

## Operations with File (fd) objects ##

abstract type AbstractFile <: IO end

mutable struct File <: AbstractFile
    open::Bool
    handle::OS_HANDLE
    File(fd::OS_HANDLE) = new(true, fd)
end
if OS_HANDLE !== RawFD
    File(fd::RawFD) = File(Libc._get_osfhandle(fd)) # TODO: calling close would now destroy the wrong handle
end

rawhandle(file::File) = file.handle
setup_stdio(file::File, ::Bool) = (file, false)

# Filesystem.open, not Base.open
function open(path::AbstractString, flags::Integer, mode::Integer=0)
    req = Libc.malloc(_sizeof_uv_fs)
    local handle
    try
        ret = ccall(:uv_fs_open, Int32,
                    (Ptr{Cvoid}, Ptr{Cvoid}, Cstring, Int32, Int32, Ptr{Cvoid}),
                    C_NULL, req, path, flags, mode, C_NULL)
        handle = ccall(:uv_fs_get_result, Cssize_t, (Ptr{Cvoid},), req)
        uv_fs_req_cleanup(req)
        ret < 0 && uv_error("open($(repr(path)), $flags, $mode)", ret)
    finally # conversion to Cstring could cause an exception
        Libc.free(req)
    end
    return File(OS_HANDLE(@static Sys.iswindows() ? Ptr{Cvoid}(handle) : Cint(handle)))
end

isopen(f::File) = f.open

function check_open(f::File)
    if !isopen(f)
        throw(ArgumentError("file is closed"))
    end
end

function close(f::File)
    if isopen(f)
        f.open = false
        err = ccall(:jl_fs_close, Int32, (OS_HANDLE,), f.handle)
        f.handle = INVALID_OS_HANDLE
        uv_error("close", err)
    end
    nothing
end

# sendfile is the most efficient way to copy from a file descriptor
function sendfile(dst::File, src::File, src_offset::Int64, bytes::Int)
    check_open(dst)
    check_open(src)
    while true
        result = ccall(:jl_fs_sendfile, Int32, (OS_HANDLE, OS_HANDLE, Int64, Csize_t),
                       src.handle, dst.handle, src_offset, bytes)
        uv_error("sendfile", result)
        nsent = result
        bytes -= nsent
        src_offset += nsent
        bytes <= 0 && break
    end
    nothing
end

function unsafe_write(f::File, buf::Ptr{UInt8}, len::UInt, offset::Int64=Int64(-1))
    check_open(f)
    err = ccall(:jl_fs_write, Int32, (OS_HANDLE, Ptr{UInt8}, Csize_t, Int64),
                f.handle, buf, len, offset)
    uv_error("write", err)
    return len
end

write(f::File, c::UInt8) = write(f, Ref{UInt8}(c))

function truncate(f::File, n::Integer)
    check_open(f)
    req = Libc.malloc(_sizeof_uv_fs)
    err = ccall(:uv_fs_ftruncate, Int32,
                (Ptr{Cvoid}, Ptr{Cvoid}, OS_HANDLE, Int64, Ptr{Cvoid}),
                C_NULL, req, f.handle, n, C_NULL)
    Libc.free(req)
    uv_error("ftruncate", err)
    return f
end

function futime(f::File, atime::Float64, mtime::Float64)
    check_open(f)
    req = Libc.malloc(_sizeof_uv_fs)
    err = ccall(:uv_fs_futime, Int32,
                (Ptr{Cvoid}, Ptr{Cvoid}, OS_HANDLE, Float64, Float64, Ptr{Cvoid}),
                C_NULL, req, f.handle, atime, mtime, C_NULL)
    Libc.free(req)
    uv_error("futime", err)
    return f
end

function read(f::File, ::Type{UInt8})
    check_open(f)
    ret = ccall(:jl_fs_read_byte, Int32, (OS_HANDLE,), f.handle)
    uv_error("read", ret)
    return ret % UInt8
end

function read(f::File, ::Type{Char})
    b0 = read(f, UInt8)
    l = 0x08 * (0x04 - UInt8(leading_ones(b0)))
    c = UInt32(b0) << 24
    if l ≤ 0x10
        s = 16
        while s ≥ l && !eof(f)
            # this works around lack of peek(::File)
            p = position(f)
            b = read(f, UInt8)
            if b & 0xc0 != 0x80
                seek(f, p)
                break
            end
            c |= UInt32(b) << s
            s -= 8
        end
    end
    return reinterpret(Char, c)
end

read(f::File, ::Type{T}) where {T<:AbstractChar} = T(read(f, Char)) # fallback

function unsafe_read(f::File, p::Ptr{UInt8}, nel::UInt)
    check_open(f)
    ret = ccall(:jl_fs_read, Int32, (OS_HANDLE, Ptr{Cvoid}, Csize_t),
                f.handle, p, nel)
    uv_error("read", ret)
    ret == nel || throw(EOFError())
    nothing
end

bytesavailable(f::File) = max(0, filesize(f) - position(f)) # position can be > filesize

eof(f::File) = bytesavailable(f) == 0

function readbytes!(f::File, b::Array{UInt8}, nb=length(b))
    nr = min(nb, bytesavailable(f))
    if length(b) < nr
        resize!(b, nr)
    end
    ret = ccall(:jl_fs_read, Int32, (OS_HANDLE, Ptr{Cvoid}, Csize_t),
                f.handle, b, nr)
    uv_error("read", ret)
    return ret
end
read(io::File) = read!(io, Base.StringVector(bytesavailable(io)))
readavailable(io::File) = read(io)
read(io::File, nb::Integer) = read!(io, Base.StringVector(min(nb, bytesavailable(io))))

const SEEK_SET = Int32(0)
const SEEK_CUR = Int32(1)
const SEEK_END = Int32(2)

function seek(f::File, n::Integer)
    ret = ccall(:jl_lseek, Int64, (OS_HANDLE, Int64, Int32), f.handle, n, SEEK_SET)
    ret == -1 && (@static Sys.iswindows() ? windowserror : systemerror)("seek")
    return f
end

function seekend(f::File)
    ret = ccall(:jl_lseek, Int64, (OS_HANDLE, Int64, Int32), f.handle, 0, SEEK_END)
    ret == -1 && (@static Sys.iswindows() ? windowserror : systemerror)("seekend")
    return f
end

function skip(f::File, n::Integer)
    ret = ccall(:jl_lseek, Int64, (OS_HANDLE, Int64, Int32), f.handle, n, SEEK_CUR)
    ret == -1 && (@static Sys.iswindows() ? windowserror : systemerror)("skip")
    return f
end

function position(f::File)
    check_open(f)
    ret = ccall(:jl_lseek, Int64, (OS_HANDLE, Int64, Int32), f.handle, 0, SEEK_CUR)
    ret == -1 && (@static Sys.iswindows() ? windowserror : systemerror)("lseek")
    return ret
end

fd(f::File) = f.handle
stat(f::File) = stat(f.handle)

function touch(f::File)
    @static if Sys.isunix()
        ret = ccall(:futimes, Cint, (Cint, Ptr{Cvoid}), fd(f), C_NULL)
        systemerror(:futimes, ret != 0)
    else
        t = time()
        futime(f, t, t)
    end
    f
end


end
K   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/path.jl.E      # This file is a part of Julia. License is MIT: https://julialang.org/license

export
    abspath,
    basename,
    dirname,
    expanduser,
    contractuser,
    homedir,
    isabspath,
    isdirpath,
    joinpath,
    normpath,
    realpath,
    relpath,
    splitdir,
    splitdrive,
    splitext,
    splitpath

if Sys.isunix()
    const path_separator    = "/"
    const path_separator_re = r"/+"sa
    const path_directory_re = r"(?:^|/)\.{0,2}$"sa
    const path_dir_splitter = r"^(.*?)(/+)([^/]*)$"sa
    const path_ext_splitter = r"^((?:.*/)?(?:\.|[^/\.])[^/]*?)(\.[^/\.]*|)$"sa

    splitdrive(path::String) = ("",path)
elseif Sys.iswindows()
    const path_separator    = "\\"
    const path_separator_re = r"[/\\]+"sa
    const path_absolute_re  = r"^(?:[A-Za-z]+:)?[/\\]"sa
    const path_directory_re = r"(?:^|[/\\])\.{0,2}$"sa
    const path_dir_splitter = r"^(.*?)([/\\]+)([^/\\]*)$"sa
    const path_ext_splitter = r"^((?:.*[/\\])?(?:\.|[^/\\\.])[^/\\]*?)(\.[^/\\\.]*|)$"sa

    function splitdrive(path::String)
        m = match(r"^([^\\]+:|\\\\[^\\]+\\[^\\]+|\\\\\?\\UNC\\[^\\]+\\[^\\]+|\\\\\?\\[^\\]+:|)(.*)$"sa, path)::AbstractMatch
        String(something(m.captures[1])), String(something(m.captures[2]))
    end
else
    error("path primitives for this OS need to be defined")
end


"""
    splitdrive(path::AbstractString) -> (AbstractString, AbstractString)

On Windows, split a path into the drive letter part and the path part. On Unix systems, the
first component is always the empty string.
"""
splitdrive(path::AbstractString)

"""
    homedir() -> String

Return the current user's home directory.

!!! note
    `homedir` determines the home directory via `libuv`'s `uv_os_homedir`. For details
    (for example on how to specify the home directory via environment variables), see the
    [`uv_os_homedir` documentation](http://docs.libuv.org/en/v1.x/misc.html#c.uv_os_homedir).
"""
function homedir()
    buf = Base.StringVector(AVG_PATH - 1) # space for null-terminator implied by StringVector
    sz = RefValue{Csize_t}(length(buf) + 1) # total buffer size including null
    while true
        rc = ccall(:uv_os_homedir, Cint, (Ptr{UInt8}, Ptr{Csize_t}), buf, sz)
        if rc == 0
            resize!(buf, sz[])
            return String(buf)
        elseif rc == Base.UV_ENOBUFS
            resize!(buf, sz[] - 1) # space for null-terminator implied by StringVector
        else
            uv_error("homedir()", rc)
        end
    end
end


if Sys.iswindows()
    isabspath(path::AbstractString) = occursin(path_absolute_re, path)
else
    isabspath(path::AbstractString) = startswith(path, '/')
end

"""
    isabspath(path::AbstractString) -> Bool

Determine whether a path is absolute (begins at the root directory).

# Examples
```jldoctest
julia> isabspath("/home")
true

julia> isabspath("home")
false
```
"""
isabspath(path::AbstractString)

"""
    isdirpath(path::AbstractString) -> Bool

Determine whether a path refers to a directory (for example, ends with a path separator).

# Examples
```jldoctest
julia> isdirpath("/home")
false

julia> isdirpath("/home/")
true
```
"""
isdirpath(path::String) = occursin(path_directory_re, splitdrive(path)[2])

"""
    splitdir(path::AbstractString) -> (AbstractString, AbstractString)

Split a path into a tuple of the directory name and file name.

# Examples
```jldoctest
julia> splitdir("/home/myuser")
("/home", "myuser")
```
"""
function splitdir(path::String)
    a, b = splitdrive(path)
    _splitdir_nodrive(a,b)
end

# Common splitdir functionality without splitdrive, needed for splitpath.
_splitdir_nodrive(path::String) = _splitdir_nodrive("", path)
function _splitdir_nodrive(a::String, b::String)
    m = match(path_dir_splitter,b)
    m === nothing && return (a,b)
    cs = m.captures
    getcapture(cs, i) = cs[i]::AbstractString
    c1, c2, c3 = getcapture(cs, 1), getcapture(cs, 2), getcapture(cs, 3)
    a = string(a, isempty(c1) ? c2[1] : c1)
    a, String(c3)
end

"""
    dirname(path::AbstractString) -> String

Get the directory part of a path. Trailing characters ('/' or '\\') in the path are
counted as part of the path.

# Examples
```jldoctest
julia> dirname("/home/myuser")
"/home"

julia> dirname("/home/myuser/")
"/home/myuser"
```

See also [`basename`](@ref).
"""
dirname(path::AbstractString) = splitdir(path)[1]

"""
    basename(path::AbstractString) -> String

Get the file name part of a path.

!!! note
    This function differs slightly from the Unix `basename` program, where trailing slashes are ignored,
    i.e. `\$ basename /foo/bar/` returns `bar`, whereas `basename` in Julia returns an empty string `""`.

# Examples
```jldoctest
julia> basename("/home/myuser/example.jl")
"example.jl"

julia> basename("/home/myuser/")
""
```

See also [`dirname`](@ref).
"""
basename(path::AbstractString) = splitdir(path)[2]

"""
    splitext(path::AbstractString) -> (String, String)

If the last component of a path contains one or more dots, split the path into everything before the
last dot and everything including and after the dot. Otherwise, return a tuple of the argument
unmodified and the empty string. "splitext" is short for "split extension".

# Examples
```jldoctest
julia> splitext("/home/myuser/example.jl")
("/home/myuser/example", ".jl")

julia> splitext("/home/myuser/example.tar.gz")
("/home/myuser/example.tar", ".gz")

julia> splitext("/home/my.user/example")
("/home/my.user/example", "")
```
"""
function splitext(path::String)
    a, b = splitdrive(path)
    m = match(path_ext_splitter, b)
    m === nothing && return (path,"")
    (a*something(m.captures[1])), String(something(m.captures[2]))
end

# NOTE: deprecated in 1.4
pathsep() = path_separator

"""
    splitpath(path::AbstractString) -> Vector{String}

Split a file path into all its path components. This is the opposite of
`joinpath`. Returns an array of substrings, one for each directory or file in
the path, including the root directory if present.

!!! compat "Julia 1.1"
    This function requires at least Julia 1.1.

# Examples
```jldoctest
julia> splitpath("/home/myuser/example.jl")
4-element Vector{String}:
 "/"
 "home"
 "myuser"
 "example.jl"
```
"""
splitpath(p::AbstractString) = splitpath(String(p))

function splitpath(p::String)
    drive, p = splitdrive(p)
    out = String[]
    isempty(p) && (pushfirst!(out,p))  # "" means the current directory.
    while !isempty(p)
        dir, base = _splitdir_nodrive(p)
        dir == p && (pushfirst!(out, dir); break)  # Reached root node.
        if !isempty(base)  # Skip trailing '/' in basename
            pushfirst!(out, base)
        end
        p = dir
    end
    if !isempty(drive)  # Tack the drive back on to the first element.
        out[1] = drive*out[1]  # Note that length(out) is always >= 1.
    end
    return out
end

if Sys.iswindows()

function joinpath(paths::Union{Tuple, AbstractVector})::String
    assertstring(x) = x isa AbstractString || throw(ArgumentError("path component is not a string: $(repr(x))"))

    isempty(paths) && throw(ArgumentError("collection of path components must be non-empty"))
    assertstring(paths[1])
    result_drive, result_path = splitdrive(paths[1])

    p_path = ""
    for i in firstindex(paths)+1:lastindex(paths)
        assertstring(paths[i])
        p_drive, p_path = splitdrive(paths[i])

        if startswith(p_path, ('\\', '/'))
            # second path is absolute
            if !isempty(p_drive) || !isempty(result_drive)
                result_drive = p_drive
            end
            result_path = p_path
            continue
        elseif !isempty(p_drive) && p_drive != result_drive
            if lowercase(p_drive) != lowercase(result_drive)
                # different drives, ignore the first path entirely
                result_drive = p_drive
                result_path = p_path
                continue
            end
        end

        # second path is relative to the first
        if !isempty(result_path) && result_path[end] ∉ ('\\', '/')
            result_path *= "\\"
        end

        result_path = result_path * p_path
    end

    # add separator between UNC and non-absolute path
    if !isempty(p_path) && result_path[1] ∉ ('\\', '/') && !isempty(result_drive) && result_drive[end] != ':'
        return result_drive * "\\" * result_path
    end

    return result_drive * result_path
end

else

function joinpath(paths::Union{Tuple, AbstractVector})::String
    assertstring(x) = x isa AbstractString || throw(ArgumentError("path component is not a string: $(repr(x))"))

    isempty(paths) && throw(ArgumentError("collection of path components must be non-empty"))
    assertstring(paths[1])
    path = paths[1]
    for i in firstindex(paths)+1:lastindex(paths)
        p = paths[i]
        assertstring(p)
        if isabspath(p)
            path = p
        elseif isempty(path) || path[end] == '/'
            path *= p
        else
            path *= "/" * p
        end
    end
    return path
end

end # os-test

joinpath(paths::AbstractString...)::String = joinpath(paths)

"""
    joinpath(parts::AbstractString...) -> String
    joinpath(parts::Vector{AbstractString}) -> String
    joinpath(parts::Tuple{AbstractString}) -> String

Join path components into a full path. If some argument is an absolute path or
(on Windows) has a drive specification that doesn't match the drive computed for
the join of the preceding paths, then prior components are dropped.

Note on Windows since there is a current directory for each drive, `joinpath("c:", "foo")`
represents a path relative to the current directory on drive "c:" so this is equal to "c:foo",
not "c:\\foo". Furthermore, `joinpath` treats this as a non-absolute path and ignores the drive
letter casing, hence `joinpath("C:\\A","c:b") = "C:\\A\\b"`.

# Examples
```jldoctest
julia> joinpath("/home/myuser", "example.jl")
"/home/myuser/example.jl"
```

```jldoctest
julia> joinpath(["/home/myuser", "example.jl"])
"/home/myuser/example.jl"
```
"""
joinpath

"""
    normpath(path::AbstractString) -> String

Normalize a path, removing "." and ".." entries and changing "/" to the canonical path separator
for the system.

# Examples
```jldoctest
julia> normpath("/home/myuser/../example.jl")
"/home/example.jl"

julia> normpath("Documents/Julia") == joinpath("Documents", "Julia")
true
```
"""
function normpath(path::String)
    isabs = isabspath(path)
    isdir = isdirpath(path)
    drive, path = splitdrive(path)
    parts = split(path, path_separator_re; keepempty=false)
    filter!(!=("."), parts)
    while true
        clean = true
        for j = 1:length(parts)-1
            if parts[j] != ".." && parts[j+1] == ".."
                deleteat!(parts, j:j+1)
                clean = false
                break
            end
        end
        clean && break
    end
    if isabs
        while !isempty(parts) && parts[1] == ".."
            popfirst!(parts)
        end
    elseif isempty(parts)
        push!(parts, ".")
    end
    path = join(parts, path_separator)
    if isabs
        path = path_separator*path
    end
    if isdir && !isdirpath(path)
        path *= path_separator
    end
    string(drive,path)
end

"""
    normpath(path::AbstractString, paths::AbstractString...) -> String

Convert a set of paths to a normalized path by joining them together and removing
"." and ".." entries. Equivalent to `normpath(joinpath(path, paths...))`.
"""
normpath(a::AbstractString, b::AbstractString...) = normpath(joinpath(a,b...))

"""
    abspath(path::AbstractString) -> String

Convert a path to an absolute path by adding the current directory if necessary.
Also normalizes the path as in [`normpath`](@ref).

# Example

If you are in a directory called `JuliaExample` and the data you are using is two levels up relative to the `JuliaExample` directory, you could write:

abspath("../../data")

Which gives a path like `"/home/JuliaUser/data/"`.

See also [`joinpath`](@ref), [`pwd`](@ref), [`expanduser`](@ref).
"""
function abspath(a::String)::String
    if !isabspath(a)
        cwd = pwd()
        a_drive, a_nodrive = splitdrive(a)
        if a_drive != "" && lowercase(splitdrive(cwd)[1]) != lowercase(a_drive)
            cwd = a_drive * path_separator
            a = joinpath(cwd, a_nodrive)
        else
            a = joinpath(cwd, a)
        end
    end
    return normpath(a)
end

"""
    abspath(path::AbstractString, paths::AbstractString...) -> String

Convert a set of paths to an absolute path by joining them together and adding the
current directory if necessary. Equivalent to `abspath(joinpath(path, paths...))`.
"""
abspath(a::AbstractString, b::AbstractString...) = abspath(joinpath(a,b...))

if Sys.iswindows()

function longpath(path::AbstractString)
    p = cwstring(path)
    buf = zeros(UInt16, length(p))
    while true
        n = ccall((:GetLongPathNameW, "kernel32"), stdcall,
            UInt32, (Ptr{UInt16}, Ptr{UInt16}, UInt32),
            p, buf, length(buf))
        windowserror(:longpath, n == 0)
        x = n < length(buf) # is the buffer big enough?
        resize!(buf, n) # shrink if x, grow if !x
        x && return transcode(String, buf)
    end
end

end # os-test


"""
    realpath(path::AbstractString) -> String

Canonicalize a path by expanding symbolic links and removing "." and ".." entries.
On case-insensitive case-preserving filesystems (typically Mac and Windows), the
filesystem's stored case for the path is returned.

(This function throws an exception if `path` does not exist in the filesystem.)
"""
function realpath(path::AbstractString)
    req = Libc.malloc(_sizeof_uv_fs)
    try
        ret = ccall(:uv_fs_realpath, Cint,
                    (Ptr{Cvoid}, Ptr{Cvoid}, Cstring, Ptr{Cvoid}),
                    C_NULL, req, path, C_NULL)
        if ret < 0
            uv_fs_req_cleanup(req)
            uv_error("realpath($(repr(path)))", ret)
        end
        path = unsafe_string(ccall(:jl_uv_fs_t_ptr, Cstring, (Ptr{Cvoid},), req))
        uv_fs_req_cleanup(req)
        return path
    finally
        Libc.free(req)
    end
end

if Sys.iswindows()
# on windows, ~ means "temporary file"
expanduser(path::AbstractString) = path
contractuser(path::AbstractString) = path
else
function expanduser(path::AbstractString)
    y = iterate(path)
    y === nothing && return path
    c, i = y::Tuple{eltype(path),Int}
    c != '~' && return path
    y = iterate(path, i)
    y === nothing && return homedir()
    y[1]::eltype(path) == '/' && return homedir() * path[i:end]
    throw(ArgumentError("~user tilde expansion not yet implemented"))
end
function contractuser(path::AbstractString)
    home = homedir()
    if path == home
        return "~"
    elseif startswith(path, home)
        return joinpath("~", relpath(path, home))
    else
        return path
    end
end
end


"""
    expanduser(path::AbstractString) -> AbstractString

On Unix systems, replace a tilde character at the start of a path with the current user's home directory.

See also: [`contractuser`](@ref).
"""
expanduser(path::AbstractString)

"""
    contractuser(path::AbstractString) -> AbstractString

On Unix systems, if the path starts with `homedir()`, replace it with a tilde character.

See also: [`expanduser`](@ref).
"""
contractuser(path::AbstractString)


"""
    relpath(path::AbstractString, startpath::AbstractString = ".") -> String

Return a relative filepath to `path` either from the current directory or from an optional
start directory. This is a path computation: the filesystem is not accessed to confirm the
existence or nature of `path` or `startpath`.

On Windows, case sensitivity is applied to every part of the path except drive letters. If
`path` and `startpath` refer to different drives, the absolute path of `path` is returned.
"""
function relpath(path::String, startpath::String = ".")
    isempty(path) && throw(ArgumentError("`path` must be non-empty"))
    isempty(startpath) && throw(ArgumentError("`startpath` must be non-empty"))
    curdir = "."
    pardir = ".."
    path == startpath && return curdir
    if Sys.iswindows()
        path_drive, path_without_drive = splitdrive(path)
        startpath_drive, startpath_without_drive = splitdrive(startpath)
        isempty(startpath_drive) && (startpath_drive = path_drive) # by default assume same as path drive
        uppercase(path_drive) == uppercase(startpath_drive) || return abspath(path) # if drives differ return first path
        path_arr  = split(abspath(path_drive * path_without_drive),      path_separator_re)
        start_arr = split(abspath(path_drive * startpath_without_drive), path_separator_re)
    else
        path_arr  = split(abspath(path),      path_separator_re)
        start_arr = split(abspath(startpath), path_separator_re)
    end
    i = 0
    while i < min(length(path_arr), length(start_arr))
        i += 1
        if path_arr[i] != start_arr[i]
            i -= 1
            break
        end
    end
    pathpart = join(path_arr[i+1:something(findlast(x -> !isempty(x), path_arr), 0)], path_separator)
    prefix_num = something(findlast(x -> !isempty(x), start_arr), 0) - i - 1
    if prefix_num >= 0
        prefix = pardir * path_separator
        relpath_ = isempty(pathpart)     ?
            (prefix^prefix_num) * pardir :
            (prefix^prefix_num) * pardir * path_separator * pathpart
    else
        relpath_ = pathpart
    end
    return isempty(relpath_) ? curdir :  relpath_
end
relpath(path::AbstractString, startpath::AbstractString) =
    relpath(String(path), String(startpath))

for f in (:isdirpath, :splitdir, :splitdrive, :splitext, :normpath, :abspath)
    @eval $f(path::AbstractString) = $f(String(path))
end
K   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/stat.jl]3      # This file is a part of Julia. License is MIT: https://julialang.org/license

# filesystem operations

export
    ctime,
    filemode,
    filesize,
    gperm,
    isblockdev,
    ischardev,
    isdir,
    isfifo,
    isfile,
    islink,
    ismount,
    ispath,
    issetgid,
    issetuid,
    issocket,
    issticky,
    lstat,
    mtime,
    operm,
    stat,
    uperm

struct StatStruct
    desc    :: Union{String, OS_HANDLE} # for show method, not included in equality or hash
    device  :: UInt
    inode   :: UInt
    mode    :: UInt
    nlink   :: Int
    uid     :: UInt
    gid     :: UInt
    rdev    :: UInt
    size    :: Int64
    blksize :: Int64
    blocks  :: Int64
    mtime   :: Float64
    ctime   :: Float64
end

@eval function Base.:(==)(x::StatStruct, y::StatStruct) # do not include `desc` in equality or hash
  $(let ex = true
        for fld in fieldnames(StatStruct)[2:end]
            ex = :(getfield(x, $(QuoteNode(fld))) === getfield(y, $(QuoteNode(fld))) && $ex)
        end
        Expr(:return, ex)
    end)
end
@eval function Base.hash(obj::StatStruct, h::UInt)
  $(quote
        $(Any[:(h = hash(getfield(obj, $(QuoteNode(fld))), h)) for fld in fieldnames(StatStruct)[2:end]]...)
        return h
    end)
end

StatStruct() = StatStruct("", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
StatStruct(buf::Union{Vector{UInt8},Ptr{UInt8}}) = StatStruct("", buf)
StatStruct(desc::Union{AbstractString, OS_HANDLE}, buf::Union{Vector{UInt8},Ptr{UInt8}}) = StatStruct(
    desc isa OS_HANDLE ? desc : String(desc),
    ccall(:jl_stat_dev,     UInt32,  (Ptr{UInt8},), buf),
    ccall(:jl_stat_ino,     UInt32,  (Ptr{UInt8},), buf),
    ccall(:jl_stat_mode,    UInt32,  (Ptr{UInt8},), buf),
    ccall(:jl_stat_nlink,   UInt32,  (Ptr{UInt8},), buf),
    ccall(:jl_stat_uid,     UInt32,  (Ptr{UInt8},), buf),
    ccall(:jl_stat_gid,     UInt32,  (Ptr{UInt8},), buf),
    ccall(:jl_stat_rdev,    UInt32,  (Ptr{UInt8},), buf),
    ccall(:jl_stat_size,    UInt64,  (Ptr{UInt8},), buf),
    ccall(:jl_stat_blksize, UInt64,  (Ptr{UInt8},), buf),
    ccall(:jl_stat_blocks,  UInt64,  (Ptr{UInt8},), buf),
    ccall(:jl_stat_mtime,   Float64, (Ptr{UInt8},), buf),
    ccall(:jl_stat_ctime,   Float64, (Ptr{UInt8},), buf),
)

function iso_datetime_with_relative(t, tnow)
    str = Libc.strftime("%FT%T%z", t)
    secdiff = t - tnow
    for (d, name) in ((24*60*60, "day"), (60*60, "hour"), (60, "minute"), (1, "second"))
        tdiff = round(Int, div(abs(secdiff), d))
        if tdiff != 0 # find first unit difference
            plural = tdiff == 1 ? "" : "s"
            when = secdiff < 0 ? "ago" : "in the future"
            return "$str ($tdiff $name$plural $when)"
        end
    end
    return "$str (just now)"
end


function getusername(uid::Unsigned)
    pwd = Libc.getpwuid(uid, false)
    pwd === nothing && return
    isempty(pwd.username) && return
    return pwd.username
end

function getgroupname(gid::Unsigned)
    gp = Libc.getgrgid(gid, false)
    gp === nothing && return
    isempty(gp.groupname) && return
    return gp.groupname
end

function show_statstruct(io::IO, st::StatStruct, oneline::Bool)
    print(io, oneline ? "StatStruct(" : "StatStruct for ")
    show(io, st.desc)
    oneline || print(io, "\n  ")
    print(io, " size: ", st.size, " bytes")
    oneline || print(io, "\n")
    print(io, " device: ", st.device)
    oneline || print(io, "\n ")
    print(io, " inode: ", st.inode)
    oneline || print(io, "\n  ")
    print(io, " mode: 0o", string(filemode(st), base = 8, pad = 6), " (", filemode_string(st), ")")
    oneline || print(io, "\n ")
    print(io, " nlink: ", st.nlink)
    oneline || print(io, "\n   ")
    print(io, " uid: $(st.uid)")
    username = getusername(st.uid)
    username === nothing || print(io, " (", username, ")")
    oneline || print(io, "\n   ")
    print(io, " gid: ", st.gid)
    groupname = getgroupname(st.gid)
    groupname === nothing || print(io, " (", groupname, ")")
    oneline || print(io, "\n  ")
    print(io, " rdev: ", st.rdev)
    oneline || print(io, "\n ")
    print(io, " blksz: ", st.blksize)
    oneline || print(io, "\n")
    print(io, " blocks: ", st.blocks)
    tnow = round(UInt, time())
    oneline || print(io, "\n ")
    print(io, " mtime: ", iso_datetime_with_relative(st.mtime, tnow))
    oneline || print(io, "\n ")
    print(io, " ctime: ", iso_datetime_with_relative(st.ctime, tnow))
    oneline && print(io, ")")
    return nothing
end

show(io::IO, st::StatStruct) = show_statstruct(io, st, true)
show(io::IO, ::MIME"text/plain", st::StatStruct) = show_statstruct(io, st, false)

# stat & lstat functions

macro stat_call(sym, arg1type, arg)
    return quote
        stat_buf = zeros(UInt8, Int(ccall(:jl_sizeof_stat, Int32, ())))
        r = ccall($(Expr(:quote, sym)), Int32, ($(esc(arg1type)), Ptr{UInt8}), $(esc(arg)), stat_buf)
        if !(r in (0, Base.UV_ENOENT, Base.UV_ENOTDIR, Base.UV_EINVAL))
            uv_error(string("stat(", repr($(esc(arg))), ")"), r)
        end
        st = StatStruct($(esc(arg)), stat_buf)
        if ispath(st) != (r == 0)
            error("stat returned zero type for a valid path")
        end
        return st
    end
end

stat(fd::OS_HANDLE)         = @stat_call jl_fstat OS_HANDLE fd
stat(path::AbstractString)  = @stat_call jl_stat  Cstring path
lstat(path::AbstractString) = @stat_call jl_lstat Cstring path
if RawFD !== OS_HANDLE
    global stat(fd::RawFD)  = stat(Libc._get_osfhandle(fd))
end
stat(fd::Integer)           = stat(RawFD(fd))

"""
    stat(file)

Return a structure whose fields contain information about the file.
The fields of the structure are:

| Name    | Description                                                        |
|:--------|:-------------------------------------------------------------------|
| desc    | The path or OS file descriptor                                     |
| size    | The size (in bytes) of the file                                    |
| device  | ID of the device that contains the file                            |
| inode   | The inode number of the file                                       |
| mode    | The protection mode of the file                                    |
| nlink   | The number of hard links to the file                               |
| uid     | The user id of the owner of the file                               |
| gid     | The group id of the file owner                                     |
| rdev    | If this file refers to a device, the ID of the device it refers to |
| blksize | The file-system preferred block size for the file                  |
| blocks  | The number of such blocks allocated                                |
| mtime   | Unix timestamp of when the file was last modified                  |
| ctime   | Unix timestamp of when the file's metadata was changed             |

"""
stat(path...) = stat(joinpath(path...))

"""
    lstat(file)

Like [`stat`](@ref), but for symbolic links gets the info for the link
itself rather than the file it refers to.
This function must be called on a file path rather than a file object or a file
descriptor.
"""
lstat(path...) = lstat(joinpath(path...))

# some convenience functions

const filemode_table = (
    [
        (S_IFLNK, "l"),
        (S_IFSOCK, "s"),  # Must appear before IFREG and IFDIR as IFSOCK == IFREG | IFDIR
        (S_IFREG, "-"),
        (S_IFBLK, "b"),
        (S_IFDIR, "d"),
        (S_IFCHR, "c"),
        (S_IFIFO, "p")
    ],
    [
        (S_IRUSR, "r"),
    ],
    [
        (S_IWUSR, "w"),
    ],
    [
        (S_IXUSR|S_ISUID, "s"),
        (S_ISUID, "S"),
        (S_IXUSR, "x")
    ],
    [
        (S_IRGRP, "r"),
    ],
    [
        (S_IWGRP, "w"),
    ],
    [
        (S_IXGRP|S_ISGID, "s"),
        (S_ISGID, "S"),
        (S_IXGRP, "x")
    ],
    [
        (S_IROTH, "r"),
    ],
    [
        (S_IWOTH, "w"),
    ],
    [
        (S_IXOTH|S_ISVTX, "t"),
        (S_ISVTX, "T"),
        (S_IXOTH, "x")
    ]
)

"""
    filemode(file)

Equivalent to `stat(file).mode`.
"""
filemode(st::StatStruct) = st.mode
filemode_string(st::StatStruct) = filemode_string(st.mode)
function filemode_string(mode)
    str = IOBuffer()
    for table in filemode_table
        complete = true
        for (bit, char) in table
            if mode & bit == bit
                write(str, char)
                complete = false
                break
            end
        end
        complete && write(str, "-")
    end
    return String(take!(str))
end

"""
    filesize(path...)

Equivalent to `stat(file).size`.
"""
filesize(st::StatStruct) = st.size

"""
    mtime(file)

Equivalent to `stat(file).mtime`.
"""
mtime(st::StatStruct) = st.mtime

"""
    ctime(file)

Equivalent to `stat(file).ctime`.
"""
ctime(st::StatStruct) = st.ctime

# mode type predicates

"""
    ispath(path) -> Bool

Return `true` if a valid filesystem entity exists at `path`,
otherwise returns `false`.
This is the generalization of [`isfile`](@ref), [`isdir`](@ref) etc.
"""
ispath(st::StatStruct) = filemode(st) & 0xf000 != 0x0000

"""
    isfifo(path) -> Bool

Return `true` if `path` is a FIFO, `false` otherwise.
"""
isfifo(st::StatStruct) = filemode(st) & 0xf000 == 0x1000

"""
    ischardev(path) -> Bool

Return `true` if `path` is a character device, `false` otherwise.
"""
ischardev(st::StatStruct) = filemode(st) & 0xf000 == 0x2000

"""
    isdir(path) -> Bool

Return `true` if `path` is a directory, `false` otherwise.

# Examples
```jldoctest
julia> isdir(homedir())
true

julia> isdir("not/a/directory")
false
```

See also [`isfile`](@ref) and [`ispath`](@ref).
"""
isdir(st::StatStruct) = filemode(st) & 0xf000 == 0x4000

"""
    isblockdev(path) -> Bool

Return `true` if `path` is a block device, `false` otherwise.
"""
isblockdev(st::StatStruct) = filemode(st) & 0xf000 == 0x6000

"""
    isfile(path) -> Bool

Return `true` if `path` is a regular file, `false` otherwise.

# Examples
```jldoctest
julia> isfile(homedir())
false

julia> filename = "test_file.txt";

julia> write(filename, "Hello world!");

julia> isfile(filename)
true

julia> rm(filename);

julia> isfile(filename)
false
```

See also [`isdir`](@ref) and [`ispath`](@ref).
"""
isfile(st::StatStruct) = filemode(st) & 0xf000 == 0x8000

"""
    islink(path) -> Bool

Return `true` if `path` is a symbolic link, `false` otherwise.
"""
islink(st::StatStruct) = filemode(st) & 0xf000 == 0xa000

"""
    issocket(path) -> Bool

Return `true` if `path` is a socket, `false` otherwise.
"""
issocket(st::StatStruct) = filemode(st) & 0xf000 == 0xc000

# mode permission predicates

"""
    issetuid(path) -> Bool

Return `true` if `path` has the setuid flag set, `false` otherwise.
"""
issetuid(st::StatStruct) = (filemode(st) & 0o4000) > 0

"""
    issetgid(path) -> Bool

Return `true` if `path` has the setgid flag set, `false` otherwise.
"""
issetgid(st::StatStruct) = (filemode(st) & 0o2000) > 0

"""
    issticky(path) -> Bool

Return `true` if `path` has the sticky bit set, `false` otherwise.
"""
issticky(st::StatStruct) = (filemode(st) & 0o1000) > 0

"""
    uperm(file)

Get the permissions of the owner of the file as a bitfield of

| Value | Description        |
|:------|:-------------------|
| 01    | Execute Permission |
| 02    | Write Permission   |
| 04    | Read Permission    |

For allowed arguments, see [`stat`](@ref).
"""
uperm(st::StatStruct) = UInt8((filemode(st) >> 6) & 0x7)

"""
    gperm(file)

Like [`uperm`](@ref) but gets the permissions of the group owning the file.
"""
gperm(st::StatStruct) = UInt8((filemode(st) >> 3) & 0x7)

"""
    operm(file)

Like [`uperm`](@ref) but gets the permissions for people who neither own the file nor are a member of
the group owning the file
"""
operm(st::StatStruct) = UInt8((filemode(st)     ) & 0x7)

# mode predicate methods for file names

for f in Symbol[
    :ispath,
    :isfifo,
    :ischardev,
    :isdir,
    :isblockdev,
    :isfile,
    :issocket,
    :issetuid,
    :issetgid,
    :issticky,
    :uperm,
    :gperm,
    :operm,
    :filemode,
    :filesize,
    :mtime,
    :ctime,
]
    @eval ($f)(path...)  = ($f)(stat(path...))
end

islink(path...) = islink(lstat(path...))

# samefile can be used for files and directories: #11145#issuecomment-99511194
function samefile(a::StatStruct, b::StatStruct)
    ispath(a) && ispath(b) && a.device == b.device && a.inode == b.inode
end

"""
    samefile(path_a::AbstractString, path_b::AbstractString)

Check if the paths `path_a` and `path_b` refer to the same existing file or directory.
"""
samefile(a::AbstractString, b::AbstractString) = samefile(stat(a), stat(b))

"""
    ismount(path) -> Bool

Return `true` if `path` is a mount point, `false` otherwise.
"""
function ismount(path...)
    path = joinpath(path...)
    isdir(path) || return false
    s1 = lstat(path)
    # Symbolic links cannot be mount points
    islink(s1) && return false
    parent_path = joinpath(path, "..")
    s2 = lstat(parent_path)
    # If a directory and its parent are on different devices,  then the
    # directory must be a mount point
    (s1.device != s2.device) && return true
    (s1.inode == s2.inode) && return true
    false
end
K   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/file.jl��      # This file is a part of Julia. License is MIT: https://julialang.org/license

# Operations with the file system (paths) ##

export
    cd,
    chmod,
    chown,
    cp,
    cptree,
    diskstat,
    hardlink,
    mkdir,
    mkpath,
    mktemp,
    mktempdir,
    mv,
    pwd,
    rename,
    readlink,
    readdir,
    rm,
    samefile,
    sendfile,
    symlink,
    tempdir,
    tempname,
    touch,
    unlink,
    walkdir

# get and set current directory

"""
    pwd() -> String

Get the current working directory.

See also: [`cd`](@ref), [`tempdir`](@ref).

# Examples
```julia-repl
julia> pwd()
"/home/JuliaUser"

julia> cd("/home/JuliaUser/Projects/julia")

julia> pwd()
"/home/JuliaUser/Projects/julia"
```
"""
function pwd()
    buf = Base.StringVector(AVG_PATH - 1) # space for null-terminator implied by StringVector
    sz = RefValue{Csize_t}(length(buf) + 1) # total buffer size including null
    while true
        rc = ccall(:uv_cwd, Cint, (Ptr{UInt8}, Ptr{Csize_t}), buf, sz)
        if rc == 0
            resize!(buf, sz[])
            return String(buf)
        elseif rc == Base.UV_ENOBUFS
            resize!(buf, sz[] - 1) # space for null-terminator implied by StringVector
        else
            uv_error("pwd()", rc)
        end
    end
end


"""
    cd(dir::AbstractString=homedir())

Set the current working directory.

See also: [`pwd`](@ref), [`mkdir`](@ref), [`mkpath`](@ref), [`mktempdir`](@ref).

# Examples
```julia-repl
julia> cd("/home/JuliaUser/Projects/julia")

julia> pwd()
"/home/JuliaUser/Projects/julia"

julia> cd()

julia> pwd()
"/home/JuliaUser"
```
"""
function cd(dir::AbstractString)
    err = ccall(:uv_chdir, Cint, (Cstring,), dir)
    err < 0 && uv_error("cd($(repr(dir)))", err)
    return nothing
end
cd() = cd(homedir())

if Sys.iswindows()
    function cd(f::Function, dir::AbstractString)
        old = pwd()
        try
            cd(dir)
            f()
       finally
            cd(old)
        end
    end
else
    function cd(f::Function, dir::AbstractString)
        fd = ccall(:open, Int32, (Cstring, Int32, UInt32...), :., 0)
        systemerror(:open, fd == -1)
        try
            cd(dir)
            f()
        finally
            systemerror(:fchdir, ccall(:fchdir, Int32, (Int32,), fd) != 0)
            systemerror(:close, ccall(:close, Int32, (Int32,), fd) != 0)
        end
    end
end
"""
    cd(f::Function, dir::AbstractString=homedir())

Temporarily change the current working directory to `dir`, apply function `f` and
finally return to the original directory.

# Examples
```julia-repl
julia> pwd()
"/home/JuliaUser"

julia> cd(readdir, "/home/JuliaUser/Projects/julia")
34-element Array{String,1}:
 ".circleci"
 ".freebsdci.sh"
 ".git"
 ".gitattributes"
 ".github"
 ⋮
 "test"
 "ui"
 "usr"
 "usr-staging"

julia> pwd()
"/home/JuliaUser"
```
"""
cd(f::Function) = cd(f, homedir())

function checkmode(mode::Integer)
    if !(0 <= mode <= 511)
        throw(ArgumentError("Mode must be between 0 and 511 = 0o777"))
    end
    mode
end

"""
    mkdir(path::AbstractString; mode::Unsigned = 0o777)

Make a new directory with name `path` and permissions `mode`. `mode` defaults to `0o777`,
modified by the current file creation mask. This function never creates more than one
directory. If the directory already exists, or some intermediate directories do not exist,
this function throws an error. See [`mkpath`](@ref) for a function which creates all
required intermediate directories.
Return `path`.

# Examples
```julia-repl
julia> mkdir("testingdir")
"testingdir"

julia> cd("testingdir")

julia> pwd()
"/home/JuliaUser/testingdir"
```
"""
function mkdir(path::AbstractString; mode::Integer = 0o777)
    req = Libc.malloc(_sizeof_uv_fs)
    try
        ret = ccall(:uv_fs_mkdir, Cint,
                    (Ptr{Cvoid}, Ptr{Cvoid}, Cstring, Cint, Ptr{Cvoid}),
                    C_NULL, req, path, checkmode(mode), C_NULL)
        if ret < 0
            uv_fs_req_cleanup(req)
            uv_error("mkdir($(repr(path)); mode=0o$(string(mode,base=8)))", ret)
        end
        uv_fs_req_cleanup(req)
        return path
    finally
        Libc.free(req)
    end
end

"""
    mkpath(path::AbstractString; mode::Unsigned = 0o777)

Create all intermediate directories in the `path` as required. Directories are created with
the permissions `mode` which defaults to `0o777` and is modified by the current file
creation mask. Unlike [`mkdir`](@ref), `mkpath` does not error if `path` (or parts of it)
already exists. However, an error will be thrown if `path` (or parts of it) points to an
existing file. Return `path`.

If `path` includes a filename you will probably want to use `mkpath(dirname(path))` to
avoid creating a directory using the filename.

# Examples
```julia-repl
julia> cd(mktempdir())

julia> mkpath("my/test/dir") # creates three directories
"my/test/dir"

julia> readdir()
1-element Array{String,1}:
 "my"

julia> cd("my")

julia> readdir()
1-element Array{String,1}:
 "test"

julia> readdir("test")
1-element Array{String,1}:
 "dir"

julia> mkpath("intermediate_dir/actually_a_directory.txt") # creates two directories
"intermediate_dir/actually_a_directory.txt"

julia> isdir("intermediate_dir/actually_a_directory.txt")
true

```
"""
function mkpath(path::AbstractString; mode::Integer = 0o777)
    isdirpath(path) && (path = dirname(path))
    dir = dirname(path)
    (path == dir || isdir(path)) && return path
    mkpath(dir, mode = checkmode(mode))
    try
        mkdir(path, mode = mode)
    catch err
        # If there is a problem with making the directory, but the directory
        # does in fact exist, then ignore the error. Else re-throw it.
        if !isa(err, IOError) || !isdir(path)
            rethrow()
        end
    end
    path
end

"""
    rm(path::AbstractString; force::Bool=false, recursive::Bool=false)

Delete the file, link, or empty directory at the given path. If `force=true` is passed, a
non-existing path is not treated as error. If `recursive=true` is passed and the path is a
directory, then all contents are removed recursively.

# Examples
```jldoctest
julia> mkpath("my/test/dir");

julia> rm("my", recursive=true)

julia> rm("this_file_does_not_exist", force=true)

julia> rm("this_file_does_not_exist")
ERROR: IOError: unlink("this_file_does_not_exist"): no such file or directory (ENOENT)
Stacktrace:
[...]
```
"""
function rm(path::AbstractString; force::Bool=false, recursive::Bool=false)
    if islink(path) || !isdir(path)
        try
            @static if Sys.iswindows()
                # is writable on windows actually means "is deletable"
                st = lstat(path)
                if ispath(st) && (filemode(st) & 0o222) == 0
                    chmod(path, 0o777)
                end
            end
            unlink(path)
        catch err
            if force && isa(err, IOError) && err.code==Base.UV_ENOENT
                return
            end
            rethrow()
        end
    else
        if recursive
            try
                for p in readdir(path)
                    rm(joinpath(path, p), force=force, recursive=true)
                end
            catch err
                if !(isa(err, IOError) && err.code==Base.UV_EACCES)
                    rethrow(err)
                end
            end
        end
        req = Libc.malloc(_sizeof_uv_fs)
        try
            ret = ccall(:uv_fs_rmdir, Cint, (Ptr{Cvoid}, Ptr{Cvoid}, Cstring, Ptr{Cvoid}), C_NULL, req, path, C_NULL)
            uv_fs_req_cleanup(req)
            if ret < 0 && !(force && ret == Base.UV_ENOENT)
                uv_error("rm($(repr(path)))", ret)
            end
            nothing
        finally
            Libc.free(req)
        end
    end
end


# The following use Unix command line facilities
function checkfor_mv_cp_cptree(src::AbstractString, dst::AbstractString, txt::AbstractString;
                                                          force::Bool=false)
    if ispath(dst)
        if force
            # Check for issue when: (src == dst) or when one is a link to the other
            # https://github.com/JuliaLang/julia/pull/11172#issuecomment-100391076
            if Base.samefile(src, dst)
                abs_src = islink(src) ? abspath(readlink(src)) : abspath(src)
                abs_dst = islink(dst) ? abspath(readlink(dst)) : abspath(dst)
                throw(ArgumentError(string("'src' and 'dst' refer to the same file/dir. ",
                                           "This is not supported.\n  ",
                                           "`src` refers to: $(abs_src)\n  ",
                                           "`dst` refers to: $(abs_dst)\n")))
            end
            rm(dst; recursive=true, force=true)
        else
            throw(ArgumentError(string("'$dst' exists. `force=true` ",
                                       "is required to remove '$dst' before $(txt).")))
        end
    end
end

function cptree(src::String, dst::String; force::Bool=false,
                                          follow_symlinks::Bool=false)
    isdir(src) || throw(ArgumentError("'$src' is not a directory. Use `cp(src, dst)`"))
    checkfor_mv_cp_cptree(src, dst, "copying"; force=force)
    mkdir(dst)
    for name in readdir(src)
        srcname = joinpath(src, name)
        if !follow_symlinks && islink(srcname)
            symlink(readlink(srcname), joinpath(dst, name))
        elseif isdir(srcname)
            cptree(srcname, joinpath(dst, name); force=force,
                                                 follow_symlinks=follow_symlinks)
        else
            sendfile(srcname, joinpath(dst, name))
        end
    end
end
cptree(src::AbstractString, dst::AbstractString; kwargs...) =
    cptree(String(src)::String, String(dst)::String; kwargs...)

"""
    cp(src::AbstractString, dst::AbstractString; force::Bool=false, follow_symlinks::Bool=false)

Copy the file, link, or directory from `src` to `dst`.
`force=true` will first remove an existing `dst`.

If `follow_symlinks=false`, and `src` is a symbolic link, `dst` will be created as a
symbolic link. If `follow_symlinks=true` and `src` is a symbolic link, `dst` will be a copy
of the file or directory `src` refers to.
Return `dst`.

!!! note
    The `cp` function is different from the `cp` command. The `cp` function always operates on
    the assumption that `dst` is a file, while the command does different things depending
    on whether `dst` is a directory or a file.
    Using `force=true` when `dst` is a directory will result in loss of all the contents present
    in the `dst` directory, and `dst` will become a file that has the contents of `src` instead.
"""
function cp(src::AbstractString, dst::AbstractString; force::Bool=false,
                                                      follow_symlinks::Bool=false)
    checkfor_mv_cp_cptree(src, dst, "copying"; force=force)
    if !follow_symlinks && islink(src)
        symlink(readlink(src), dst)
    elseif isdir(src)
        cptree(src, dst; force=force, follow_symlinks=follow_symlinks)
    else
        sendfile(src, dst)
    end
    dst
end

"""
    mv(src::AbstractString, dst::AbstractString; force::Bool=false)

Move the file, link, or directory from `src` to `dst`.
`force=true` will first remove an existing `dst`.
Return `dst`.

# Examples
```jldoctest; filter = r"Stacktrace:(\\n \\[[0-9]+\\].*)*"
julia> write("hello.txt", "world");

julia> mv("hello.txt", "goodbye.txt")
"goodbye.txt"

julia> "hello.txt" in readdir()
false

julia> readline("goodbye.txt")
"world"

julia> write("hello.txt", "world2");

julia> mv("hello.txt", "goodbye.txt")
ERROR: ArgumentError: 'goodbye.txt' exists. `force=true` is required to remove 'goodbye.txt' before moving.
Stacktrace:
 [1] #checkfor_mv_cp_cptree#10(::Bool, ::Function, ::String, ::String, ::String) at ./file.jl:293
[...]

julia> mv("hello.txt", "goodbye.txt", force=true)
"goodbye.txt"

julia> rm("goodbye.txt");

```
"""
function mv(src::AbstractString, dst::AbstractString; force::Bool=false)
    checkfor_mv_cp_cptree(src, dst, "moving"; force=force)
    rename(src, dst)
    dst
end

"""
    touch(path::AbstractString)
    touch(fd::File)

Update the last-modified timestamp on a file to the current time.

If the file does not exist a new file is created.

Return `path`.

# Examples
```julia-repl
julia> write("my_little_file", 2);

julia> mtime("my_little_file")
1.5273815391135583e9

julia> touch("my_little_file");

julia> mtime("my_little_file")
1.527381559163435e9
```

We can see the [`mtime`](@ref) has been modified by `touch`.
"""
function touch(path::AbstractString)
    f = open(path, JL_O_WRONLY | JL_O_CREAT, 0o0666)
    try
        touch(f)
    finally
        close(f)
    end
    path
end


"""
    tempdir()

Gets the path of the temporary directory. On Windows, `tempdir()` uses the first environment
variable found in the ordered list `TMP`, `TEMP`, `USERPROFILE`. On all other operating
systems, `tempdir()` uses the first environment variable found in the ordered list `TMPDIR`,
`TMP`, `TEMP`, and `TEMPDIR`. If none of these are found, the path `"/tmp"` is used.
"""
function tempdir()
    buf = Base.StringVector(AVG_PATH - 1) # space for null-terminator implied by StringVector
    sz = RefValue{Csize_t}(length(buf) + 1) # total buffer size including null
    while true
        rc = ccall(:uv_os_tmpdir, Cint, (Ptr{UInt8}, Ptr{Csize_t}), buf, sz)
        if rc == 0
            resize!(buf, sz[])
            return String(buf)
        elseif rc == Base.UV_ENOBUFS
            resize!(buf, sz[] - 1)  # space for null-terminator implied by StringVector
        else
            uv_error("tempdir()", rc)
        end
    end
end

"""
    prepare_for_deletion(path::AbstractString)

Prepares the given `path` for deletion by ensuring that all directories within that
`path` have write permissions, so that files can be removed from them.  This is
automatically invoked by methods such as `mktempdir()` to ensure that no matter what
weird permissions a user may have created directories with within the temporary prefix,
it will always be deleted.
"""
function prepare_for_deletion(path::AbstractString)
    # Nothing to do for non-directories
    if !isdir(path)
        return
    end

    try chmod(path, filemode(path) | 0o333)
    catch; end
    for (root, dirs, files) in walkdir(path; onerror=x->())
        for dir in dirs
            dpath = joinpath(root, dir)
            try chmod(dpath, filemode(dpath) | 0o333)
            catch; end
        end
    end
end

const TEMP_CLEANUP_MIN = Ref(1024)
const TEMP_CLEANUP_MAX = Ref(1024)
const TEMP_CLEANUP = Dict{String,Bool}()
const TEMP_CLEANUP_LOCK = ReentrantLock()

function temp_cleanup_later(path::AbstractString; asap::Bool=false)
    lock(TEMP_CLEANUP_LOCK)
    # each path should only be inserted here once, but if there
    # is a collision, let !asap win over asap: if any user might
    # still be using the path, don't delete it until process exit
    TEMP_CLEANUP[path] = get(TEMP_CLEANUP, path, true) & asap
    if length(TEMP_CLEANUP) > TEMP_CLEANUP_MAX[]
        temp_cleanup_purge()
        TEMP_CLEANUP_MAX[] = max(TEMP_CLEANUP_MIN[], 2*length(TEMP_CLEANUP))
    end
    unlock(TEMP_CLEANUP_LOCK)
    return nothing
end

function temp_cleanup_purge(; force::Bool=false)
    need_gc = Sys.iswindows()
    for (path, asap) in TEMP_CLEANUP
        try
            if (force || asap) && ispath(path)
                need_gc && GC.gc(true)
                need_gc = false
                prepare_for_deletion(path)
                rm(path, recursive=true, force=true)
            end
            !ispath(path) && delete!(TEMP_CLEANUP, path)
        catch ex
            @warn """
                Failed to clean up temporary path $(repr(path))
                $ex
                """ _group=:file
        end
    end
end

const temp_prefix = "jl_"

# Use `Libc.rand()` to generate random strings
function _rand_filename(len = 10)
    slug = Base.StringVector(len)
    chars = b"0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ"
    for i = 1:len
        slug[i] = chars[(Libc.rand() % length(chars)) + 1]
    end
    return String(slug)
end


# Obtain a temporary filename.
function tempname(parent::AbstractString=tempdir(); max_tries::Int = 100, cleanup::Bool=true)
    isdir(parent) || throw(ArgumentError("$(repr(parent)) is not a directory"))

    prefix = joinpath(parent, temp_prefix)
    filename = nothing
    for i in 1:max_tries
        filename = string(prefix, _rand_filename())
        if ispath(filename)
            filename = nothing
        else
            break
        end
    end

    if filename === nothing
        error("tempname: max_tries exhausted")
    end

    cleanup && temp_cleanup_later(filename)
    return filename
end

if Sys.iswindows()
# While this isn't a true analog of `mkstemp`, it _does_ create an
# empty file for us, ensuring that other simultaneous calls to
# `_win_mkstemp()` won't collide, so it's a better name for the
# function than `tempname()`.
function _win_mkstemp(temppath::AbstractString)
    tempp = cwstring(temppath)
    temppfx = cwstring(temp_prefix)
    tname = Vector{UInt16}(undef, 32767)
    uunique = ccall(:GetTempFileNameW, stdcall, UInt32,
                    (Ptr{UInt16}, Ptr{UInt16}, UInt32, Ptr{UInt16}),
                    tempp, temppfx, UInt32(0), tname)
    windowserror("GetTempFileName", uunique == 0)
    lentname = something(findfirst(iszero, tname))
    @assert lentname > 0
    resize!(tname, lentname - 1)
    return transcode(String, tname)
end

function mktemp(parent::AbstractString=tempdir(); cleanup::Bool=true)
    filename = _win_mkstemp(parent)
    cleanup && temp_cleanup_later(filename)
    return (filename, Base.open(filename, "r+"))
end

else # !windows

# Create and return the name of a temporary file along with an IOStream
function mktemp(parent::AbstractString=tempdir(); cleanup::Bool=true)
    b = joinpath(parent, temp_prefix * "XXXXXX")
    p = ccall(:mkstemp, Int32, (Cstring,), b) # modifies b
    systemerror(:mktemp, p == -1)
    cleanup && temp_cleanup_later(b)
    return (b, fdio(p, true))
end

end # os-test


"""
    tempname(parent=tempdir(); cleanup=true) -> String

Generate a temporary file path. This function only returns a path; no file is
created. The path is likely to be unique, but this cannot be guaranteed due to
the very remote possibility of two simultaneous calls to `tempname` generating
the same file name. The name is guaranteed to differ from all files already
existing at the time of the call to `tempname`.

When called with no arguments, the temporary name will be an absolute path to a
temporary name in the system temporary directory as given by `tempdir()`. If a
`parent` directory argument is given, the temporary path will be in that
directory instead.

The `cleanup` option controls whether the process attempts to delete the
returned path automatically when the process exits. Note that the `tempname`
function does not create any file or directory at the returned location, so
there is nothing to cleanup unless you create a file or directory there. If
you do and `clean` is `true` it will be deleted upon process termination.

!!! compat "Julia 1.4"
    The `parent` and `cleanup` arguments were added in 1.4. Prior to Julia 1.4
    the path `tempname` would never be cleaned up at process termination.

!!! warning

    This can lead to security holes if another process obtains the same
    file name and creates the file before you are able to. Open the file with
    `JL_O_EXCL` if this is a concern. Using [`mktemp()`](@ref) is also
    recommended instead.
"""
tempname()

"""
    mktemp(parent=tempdir(); cleanup=true) -> (path, io)

Return `(path, io)`, where `path` is the path of a new temporary file in `parent`
and `io` is an open file object for this path. The `cleanup` option controls whether
the temporary file is automatically deleted when the process exits.

!!! compat "Julia 1.3"
    The `cleanup` keyword argument was added in Julia 1.3. Relatedly, starting from 1.3,
    Julia will remove the temporary paths created by `mktemp` when the Julia process exits,
    unless `cleanup` is explicitly set to `false`.
"""
mktemp(parent)

"""
    mktempdir(parent=tempdir(); prefix=$(repr(temp_prefix)), cleanup=true) -> path

Create a temporary directory in the `parent` directory with a name
constructed from the given `prefix` and a random suffix, and return its path.
Additionally, on some platforms, any trailing `'X'` characters in `prefix` may be replaced
with random characters.
If `parent` does not exist, throw an error. The `cleanup` option controls whether
the temporary directory is automatically deleted when the process exits.

!!! compat "Julia 1.2"
    The `prefix` keyword argument was added in Julia 1.2.

!!! compat "Julia 1.3"
    The `cleanup` keyword argument was added in Julia 1.3. Relatedly, starting from 1.3,
    Julia will remove the temporary paths created by `mktempdir` when the Julia process
    exits, unless `cleanup` is explicitly set to `false`.

See also: [`mktemp`](@ref), [`mkdir`](@ref).
"""
function mktempdir(parent::AbstractString=tempdir();
    prefix::AbstractString=temp_prefix, cleanup::Bool=true)
    if isempty(parent) || occursin(path_separator_re, parent[end:end])
        # append a path_separator only if parent didn't already have one
        tpath = "$(parent)$(prefix)XXXXXX"
    else
        tpath = "$(parent)$(path_separator)$(prefix)XXXXXX"
    end

    req = Libc.malloc(_sizeof_uv_fs)
    try
        ret = ccall(:uv_fs_mkdtemp, Cint,
                    (Ptr{Cvoid}, Ptr{Cvoid}, Cstring, Ptr{Cvoid}),
                    C_NULL, req, tpath, C_NULL)
        if ret < 0
            uv_fs_req_cleanup(req)
            uv_error("mktempdir($(repr(parent)))", ret)
        end
        path = unsafe_string(ccall(:jl_uv_fs_t_path, Cstring, (Ptr{Cvoid},), req))
        uv_fs_req_cleanup(req)
        cleanup && temp_cleanup_later(path)
        return path
    finally
        Libc.free(req)
    end
end


"""
    mktemp(f::Function, parent=tempdir())

Apply the function `f` to the result of [`mktemp(parent)`](@ref) and remove the
temporary file upon completion.

See also: [`mktempdir`](@ref).
"""
function mktemp(fn::Function, parent::AbstractString=tempdir())
    (tmp_path, tmp_io) = mktemp(parent, cleanup=false)
    try
        fn(tmp_path, tmp_io)
    finally
        try
            close(tmp_io)
            ispath(tmp_path) && rm(tmp_path)
        catch ex
            @error "mktemp cleanup" _group=:file exception=(ex, catch_backtrace())
            # might be possible to remove later
            temp_cleanup_later(tmp_path, asap=true)
        end
    end
end

"""
    mktempdir(f::Function, parent=tempdir(); prefix=$(repr(temp_prefix)))

Apply the function `f` to the result of [`mktempdir(parent; prefix)`](@ref) and remove the
temporary directory all of its contents upon completion.

See also: [`mktemp`](@ref), [`mkdir`](@ref).

!!! compat "Julia 1.2"
    The `prefix` keyword argument was added in Julia 1.2.
"""
function mktempdir(fn::Function, parent::AbstractString=tempdir();
    prefix::AbstractString=temp_prefix)
    tmpdir = mktempdir(parent; prefix=prefix, cleanup=false)
    try
        fn(tmpdir)
    finally
        try
            if ispath(tmpdir)
                prepare_for_deletion(tmpdir)
                rm(tmpdir, recursive=true)
            end
        catch ex
            @error "mktempdir cleanup" _group=:file exception=(ex, catch_backtrace())
            # might be possible to remove later
            temp_cleanup_later(tmpdir, asap=true)
        end
    end
end

struct uv_dirent_t
    name::Ptr{UInt8}
    typ::Cint
end

"""
    readdir(dir::AbstractString=pwd();
        join::Bool = false,
        sort::Bool = true,
    ) -> Vector{String}

Return the names in the directory `dir` or the current working directory if not
given. When `join` is false, `readdir` returns just the names in the directory
as is; when `join` is true, it returns `joinpath(dir, name)` for each `name` so
that the returned strings are full paths. If you want to get absolute paths
back, call `readdir` with an absolute directory path and `join` set to true.

By default, `readdir` sorts the list of names it returns. If you want to skip
sorting the names and get them in the order that the file system lists them,
you can use `readdir(dir, sort=false)` to opt out of sorting.

See also: [`walkdir`](@ref).

!!! compat "Julia 1.4"
    The `join` and `sort` keyword arguments require at least Julia 1.4.

# Examples
```julia-repl
julia> cd("/home/JuliaUser/dev/julia")

julia> readdir()
30-element Array{String,1}:
 ".appveyor.yml"
 ".git"
 ".gitattributes"
 ⋮
 "ui"
 "usr"
 "usr-staging"

julia> readdir(join=true)
30-element Array{String,1}:
 "/home/JuliaUser/dev/julia/.appveyor.yml"
 "/home/JuliaUser/dev/julia/.git"
 "/home/JuliaUser/dev/julia/.gitattributes"
 ⋮
 "/home/JuliaUser/dev/julia/ui"
 "/home/JuliaUser/dev/julia/usr"
 "/home/JuliaUser/dev/julia/usr-staging"

julia> readdir("base")
145-element Array{String,1}:
 ".gitignore"
 "Base.jl"
 "Enums.jl"
 ⋮
 "version_git.sh"
 "views.jl"
 "weakkeydict.jl"

julia> readdir("base", join=true)
145-element Array{String,1}:
 "base/.gitignore"
 "base/Base.jl"
 "base/Enums.jl"
 ⋮
 "base/version_git.sh"
 "base/views.jl"
 "base/weakkeydict.jl"

julia> readdir(abspath("base"), join=true)
145-element Array{String,1}:
 "/home/JuliaUser/dev/julia/base/.gitignore"
 "/home/JuliaUser/dev/julia/base/Base.jl"
 "/home/JuliaUser/dev/julia/base/Enums.jl"
 ⋮
 "/home/JuliaUser/dev/julia/base/version_git.sh"
 "/home/JuliaUser/dev/julia/base/views.jl"
 "/home/JuliaUser/dev/julia/base/weakkeydict.jl"
```
"""
function readdir(dir::AbstractString; join::Bool=false, sort::Bool=true)
    # Allocate space for uv_fs_t struct
    req = Libc.malloc(_sizeof_uv_fs)
    try
        # defined in sys.c, to call uv_fs_readdir, which sets errno on error.
        err = ccall(:uv_fs_scandir, Int32, (Ptr{Cvoid}, Ptr{Cvoid}, Cstring, Cint, Ptr{Cvoid}),
                    C_NULL, req, dir, 0, C_NULL)
        err < 0 && uv_error("readdir($(repr(dir)))", err)

        # iterate the listing into entries
        entries = String[]
        ent = Ref{uv_dirent_t}()
        while Base.UV_EOF != ccall(:uv_fs_scandir_next, Cint, (Ptr{Cvoid}, Ptr{uv_dirent_t}), req, ent)
            name = unsafe_string(ent[].name)
            push!(entries, join ? joinpath(dir, name) : name)
        end

        # Clean up the request string
        uv_fs_req_cleanup(req)

        # sort entries unless opted out
        sort && sort!(entries)

        return entries
    finally
        Libc.free(req)
    end
end
readdir(; join::Bool=false, sort::Bool=true) =
    readdir(join ? pwd() : ".", join=join, sort=sort)

"""
    walkdir(dir; topdown=true, follow_symlinks=false, onerror=throw)

Return an iterator that walks the directory tree of a directory.
The iterator returns a tuple containing `(rootpath, dirs, files)`.
The directory tree can be traversed top-down or bottom-up.
If `walkdir` or `stat` encounters a `IOError` it will rethrow the error by default.
A custom error handling function can be provided through `onerror` keyword argument.
`onerror` is called with a `IOError` as argument.

See also: [`readdir`](@ref).

# Examples
```julia
for (root, dirs, files) in walkdir(".")
    println("Directories in \$root")
    for dir in dirs
        println(joinpath(root, dir)) # path to directories
    end
    println("Files in \$root")
    for file in files
        println(joinpath(root, file)) # path to files
    end
end
```

```julia-repl
julia> mkpath("my/test/dir");

julia> itr = walkdir("my");

julia> (root, dirs, files) = first(itr)
("my", ["test"], String[])

julia> (root, dirs, files) = first(itr)
("my/test", ["dir"], String[])

julia> (root, dirs, files) = first(itr)
("my/test/dir", String[], String[])
```
"""
function walkdir(root; topdown=true, follow_symlinks=false, onerror=throw)
    function _walkdir(chnl, root)
        tryf(f, p) = try
                f(p)
            catch err
                isa(err, IOError) || rethrow()
                try
                    onerror(err)
                catch err2
                    close(chnl, err2)
                end
                return
            end
        content = tryf(readdir, root)
        content === nothing && return
        dirs = Vector{eltype(content)}()
        files = Vector{eltype(content)}()
        for name in content
            path = joinpath(root, name)

            # If we're not following symlinks, then treat all symlinks as files
            if (!follow_symlinks && something(tryf(islink, path), true)) || !something(tryf(isdir, path), false)
                push!(files, name)
            else
                push!(dirs, name)
            end
        end

        if topdown
            push!(chnl, (root, dirs, files))
        end
        for dir in dirs
            _walkdir(chnl, joinpath(root, dir))
        end
        if !topdown
            push!(chnl, (root, dirs, files))
        end
        nothing
    end
    return Channel{Tuple{String,Vector{String},Vector{String}}}(chnl -> _walkdir(chnl, root))
end

function unlink(p::AbstractString)
    err = ccall(:jl_fs_unlink, Int32, (Cstring,), p)
    err < 0 && uv_error("unlink($(repr(p)))", err)
    nothing
end

# For move command
function rename(src::AbstractString, dst::AbstractString; force::Bool=false)
    err = ccall(:jl_fs_rename, Int32, (Cstring, Cstring), src, dst)
    # on error, default to cp && rm
    if err < 0
        cp(src, dst; force=force, follow_symlinks=false)
        rm(src; recursive=true)
    end
    nothing
end

function sendfile(src::AbstractString, dst::AbstractString)
    src_open = false
    dst_open = false
    local src_file, dst_file
    try
        src_file = open(src, JL_O_RDONLY)
        src_open = true
        dst_file = open(dst, JL_O_CREAT | JL_O_TRUNC | JL_O_WRONLY, filemode(src_file))
        dst_open = true

        bytes = filesize(stat(src_file))
        sendfile(dst_file, src_file, Int64(0), Int(bytes))
    finally
        if src_open && isopen(src_file)
            close(src_file)
        end
        if dst_open && isopen(dst_file)
            close(dst_file)
        end
    end
end

if Sys.iswindows()
    const UV_FS_SYMLINK_DIR      = 0x0001
    const UV_FS_SYMLINK_JUNCTION = 0x0002
    const UV__EPERM              = -4048
end

"""
    hardlink(src::AbstractString, dst::AbstractString)

Creates a hard link to an existing source file `src` with the name `dst`. The
destination, `dst`, must not exist.

See also: [`symlink`](@ref).

!!! compat "Julia 1.8"
    This method was added in Julia 1.8.
"""
function hardlink(src::AbstractString, dst::AbstractString)
    err = ccall(:jl_fs_hardlink, Int32, (Cstring, Cstring), src, dst)
    if err < 0
        msg = "hardlink($(repr(src)), $(repr(dst)))"
        uv_error(msg, err)
    end
    return nothing
end

"""
    symlink(target::AbstractString, link::AbstractString; dir_target = false)

Creates a symbolic link to `target` with the name `link`.

On Windows, symlinks must be explicitly declared as referring to a directory
or not.  If `target` already exists, by default the type of `link` will be auto-
detected, however if `target` does not exist, this function defaults to creating
a file symlink unless `dir_target` is set to `true`.  Note that if the user
sets `dir_target` but `target` exists and is a file, a directory symlink will
still be created, but dereferencing the symlink will fail, just as if the user
creates a file symlink (by calling `symlink()` with `dir_target` set to `false`
before the directory is created) and tries to dereference it to a directory.

Additionally, there are two methods of making a link on Windows; symbolic links
and junction points.  Junction points are slightly more efficient, but do not
support relative paths, so if a relative directory symlink is requested (as
denoted by `isabspath(target)` returning `false`) a symlink will be used, else
a junction point will be used.  Best practice for creating symlinks on Windows
is to create them only after the files/directories they reference are already
created.

See also: [`hardlink`](@ref).

!!! note
    This function raises an error under operating systems that do not support
    soft symbolic links, such as Windows XP.

!!! compat "Julia 1.6"
    The `dir_target` keyword argument was added in Julia 1.6.  Prior to this,
    symlinks to nonexistent paths on windows would always be file symlinks, and
    relative symlinks to directories were not supported.
"""
function symlink(target::AbstractString, link::AbstractString;
                 dir_target::Bool = false)
    @static if Sys.iswindows()
        if Sys.windows_version() < Sys.WINDOWS_VISTA_VER
            error("Windows XP does not support soft symlinks")
        end
    end
    flags = 0
    @static if Sys.iswindows()
        # If we're going to create a directory link, we need to know beforehand.
        # First, if `target` is not an absolute path, let's immediately resolve
        # it so that we can peek and see if it's a directory.
        resolved_target = target
        if !isabspath(target)
            resolved_target = joinpath(dirname(link), target)
        end

        # If it is a directory (or `dir_target` is set), we'll need to add one
        # of `UV_FS_SYMLINK_{DIR,JUNCTION}` to the flags, depending on whether
        # `target` is an absolute path or not.
        if (ispath(resolved_target) && isdir(resolved_target)) || dir_target
            if isabspath(target)
                flags |= UV_FS_SYMLINK_JUNCTION
            else
                flags |= UV_FS_SYMLINK_DIR
            end
        end
    end
    err = ccall(:jl_fs_symlink, Int32, (Cstring, Cstring, Cint), target, link, flags)
    if err < 0
        msg = "symlink($(repr(target)), $(repr(link)))"
        @static if Sys.iswindows()
            # creating file/directory symlinks requires Administrator privileges
            # while junction points apparently do not
            if flags & UV_FS_SYMLINK_JUNCTION == 0 && err == UV__EPERM
                msg = "On Windows, creating symlinks requires Administrator privileges.\n$msg"
            end
        end
        uv_error(msg, err)
    end
    return nothing
end

"""
    readlink(path::AbstractString) -> String

Return the target location a symbolic link `path` points to.
"""
function readlink(path::AbstractString)
    req = Libc.malloc(_sizeof_uv_fs)
    try
        ret = ccall(:uv_fs_readlink, Int32,
            (Ptr{Cvoid}, Ptr{Cvoid}, Cstring, Ptr{Cvoid}),
            C_NULL, req, path, C_NULL)
        if ret < 0
            uv_fs_req_cleanup(req)
            uv_error("readlink($(repr(path)))", ret)
            @assert false
        end
        tgt = unsafe_string(ccall(:jl_uv_fs_t_ptr, Cstring, (Ptr{Cvoid},), req))
        uv_fs_req_cleanup(req)
        return tgt
    finally
        Libc.free(req)
    end
end

"""
    chmod(path::AbstractString, mode::Integer; recursive::Bool=false)

Change the permissions mode of `path` to `mode`. Only integer `mode`s (e.g. `0o777`) are
currently supported. If `recursive=true` and the path is a directory all permissions in
that directory will be recursively changed.
Return `path`.

!!! note
     Prior to Julia 1.6, this did not correctly manipulate filesystem ACLs
     on Windows, therefore it would only set read-only bits on files.  It
     now is able to manipulate ACLs.
"""
function chmod(path::AbstractString, mode::Integer; recursive::Bool=false)
    err = ccall(:jl_fs_chmod, Int32, (Cstring, Cint), path, mode)
    err < 0 && uv_error("chmod($(repr(path)), 0o$(string(mode, base=8)))", err)
    if recursive && isdir(path)
        for p in readdir(path)
            if !islink(joinpath(path, p))
                chmod(joinpath(path, p), mode, recursive=true)
            end
        end
    end
    path
end

"""
    chown(path::AbstractString, owner::Integer, group::Integer=-1)

Change the owner and/or group of `path` to `owner` and/or `group`. If the value entered for `owner` or `group`
is `-1` the corresponding ID will not change. Only integer `owner`s and `group`s are currently supported.
Return `path`.
"""
function chown(path::AbstractString, owner::Integer, group::Integer=-1)
    err = ccall(:jl_fs_chown, Int32, (Cstring, Cint, Cint), path, owner, group)
    err < 0 && uv_error("chown($(repr(path)), $owner, $group)", err)
    path
end


# - http://docs.libuv.org/en/v1.x/fs.html#c.uv_fs_statfs (libuv function docs)
# - http://docs.libuv.org/en/v1.x/fs.html#c.uv_statfs_t (libuv docs of the returned struct)
"""
    DiskStat

Stores information about the disk in bytes. Populate by calling `diskstat`.
"""
struct DiskStat
    ftype::UInt64
    bsize::UInt64
    blocks::UInt64
    bfree::UInt64
    bavail::UInt64
    files::UInt64
    ffree::UInt64
    fspare::NTuple{4, UInt64} # reserved
end

function Base.getproperty(stats::DiskStat, field::Symbol)
    total = Int64(getfield(stats, :bsize) * getfield(stats, :blocks))
    available = Int64(getfield(stats, :bsize) * getfield(stats, :bavail))
    field === :total && return total
    field === :available && return available
    field === :used && return total - available
    return getfield(stats, field)
end

@eval Base.propertynames(stats::DiskStat) =
    $((fieldnames(DiskStat)[1:end-1]..., :available, :total, :used))

Base.show(io::IO, x::DiskStat) =
    print(io, "DiskStat(total=$(x.total), used=$(x.used), available=$(x.available))")

"""
    diskstat(path=pwd())

Returns statistics in bytes about the disk that contains the file or directory pointed at by
`path`. If no argument is passed, statistics about the disk that contains the current
working directory are returned.

!!! compat "Julia 1.8"
    This method was added in Julia 1.8.
"""
function diskstat(path::AbstractString=pwd())
    req = zeros(UInt8, _sizeof_uv_fs)
    err = ccall(:uv_fs_statfs, Cint, (Ptr{Cvoid}, Ptr{Cvoid}, Cstring, Ptr{Cvoid}),
                C_NULL, req, path, C_NULL)
    err < 0 && uv_error("diskstat($(repr(path)))", err)
    statfs_ptr = ccall(:jl_uv_fs_t_ptr, Ptr{Nothing}, (Ptr{Cvoid},), req)

    return unsafe_load(reinterpret(Ptr{DiskStat}, statfs_ptr))
end
W   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/./file_constants.jl�      const JL_O_WRONLY = 0o01
const JL_O_RDONLY = 0o00
const JL_O_RDWR = 0o02
const JL_O_APPEND = 0o02000
const JL_O_CREAT = 0o0100
const JL_O_EXCL = 0o0200
const JL_O_TRUNC = 0o01000
const JL_O_TEMPORARY = 0x0000
const JL_O_SHORT_LIVED = 0x0000
const JL_O_SEQUENTIAL = 0x0000
const JL_O_RANDOM = 0x0000
const JL_O_NOCTTY = 0o0400
const JL_O_NONBLOCK = 0o04000
const JL_O_NDELAY = 0o04000
const JL_O_SYNC = 0o04010000
const JL_O_FSYNC = 0o04010000
const JL_O_ASYNC = 0o020000
const JL_O_LARGEFILE = 0x0000
const JL_O_DIRECTORY = 0o0200000
const JL_O_NOFOLLOW = 0o0400000
const JL_O_CLOEXEC = 0o02000000
const JL_O_DIRECT = 0x0000
const JL_O_NOATIME = 0x0000
const JL_O_PATH = 0x0000
const JL_O_TMPFILE = 0x0000
const JL_O_DSYNC = 0o010000
const JL_O_RSYNC = 0o04010000
J   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/cmd.jl~F      # This file is a part of Julia. License is MIT: https://julialang.org/license

abstract type AbstractCmd end

# libuv process option flags
const UV_PROCESS_WINDOWS_VERBATIM_ARGUMENTS = UInt8(1 << 2)
const UV_PROCESS_DETACHED = UInt8(1 << 3)
const UV_PROCESS_WINDOWS_HIDE = UInt8(1 << 4)

struct Cmd <: AbstractCmd
    exec::Vector{String}
    ignorestatus::Bool
    flags::UInt32 # libuv process flags
    env::Union{Vector{String},Nothing}
    dir::String
    cpus::Union{Nothing,Vector{UInt16}}
    Cmd(exec::Vector{String}) =
        new(exec, false, 0x00, nothing, "", nothing)
    Cmd(cmd::Cmd, ignorestatus, flags, env, dir, cpus = nothing) =
        new(cmd.exec, ignorestatus, flags, env,
            dir === cmd.dir ? dir : cstr(dir), cpus)
    function Cmd(cmd::Cmd; ignorestatus::Bool=cmd.ignorestatus, env=cmd.env, dir::AbstractString=cmd.dir,
                 cpus::Union{Nothing,Vector{UInt16}} = cmd.cpus,
                 detach::Bool = 0 != cmd.flags & UV_PROCESS_DETACHED,
                 windows_verbatim::Bool = 0 != cmd.flags & UV_PROCESS_WINDOWS_VERBATIM_ARGUMENTS,
                 windows_hide::Bool = 0 != cmd.flags & UV_PROCESS_WINDOWS_HIDE)
        flags = detach * UV_PROCESS_DETACHED |
                windows_verbatim * UV_PROCESS_WINDOWS_VERBATIM_ARGUMENTS |
                windows_hide * UV_PROCESS_WINDOWS_HIDE
        new(cmd.exec, ignorestatus, flags, byteenv(env),
            dir === cmd.dir ? dir : cstr(dir), cpus)
    end
end

has_nondefault_cmd_flags(c::Cmd) =
    c.ignorestatus ||
    c.flags != 0x00 ||
    c.env !== nothing ||
    c.dir !== "" ||
    c.cpus !== nothing

"""
    Cmd(cmd::Cmd; ignorestatus, detach, windows_verbatim, windows_hide, env, dir)
    Cmd(exec::Vector{String})

Construct a new `Cmd` object, representing an external program and arguments, from `cmd`,
while changing the settings of the optional keyword arguments:

* `ignorestatus::Bool`: If `true` (defaults to `false`), then the `Cmd` will not throw an
  error if the return code is nonzero.
* `detach::Bool`: If `true` (defaults to `false`), then the `Cmd` will be run in a new
  process group, allowing it to outlive the `julia` process and not have Ctrl-C passed to
  it.
* `windows_verbatim::Bool`: If `true` (defaults to `false`), then on Windows the `Cmd` will
  send a command-line string to the process with no quoting or escaping of arguments, even
  arguments containing spaces. (On Windows, arguments are sent to a program as a single
  "command-line" string, and programs are responsible for parsing it into arguments. By
  default, empty arguments and arguments with spaces or tabs are quoted with double quotes
  `"` in the command line, and `\\` or `"` are preceded by backslashes.
  `windows_verbatim=true` is useful for launching programs that parse their command line in
  nonstandard ways.) Has no effect on non-Windows systems.
* `windows_hide::Bool`: If `true` (defaults to `false`), then on Windows no new console
  window is displayed when the `Cmd` is executed. This has no effect if a console is
  already open or on non-Windows systems.
* `env`: Set environment variables to use when running the `Cmd`. `env` is either a
  dictionary mapping strings to strings, an array of strings of the form `"var=val"`, an
  array or tuple of `"var"=>val` pairs. In order to modify (rather than replace) the
  existing environment, initialize `env` with `copy(ENV)` and then set `env["var"]=val` as
  desired.  To add to an environment block within a `Cmd` object without replacing all
  elements, use [`addenv()`](@ref) which will return a `Cmd` object with the updated environment.
* `dir::AbstractString`: Specify a working directory for the command (instead
  of the current directory).

For any keywords that are not specified, the current settings from `cmd` are used.

Note that the `Cmd(exec)` constructor does not create a copy of `exec`. Any subsequent changes to `exec` will be reflected in the `Cmd` object.

The most common way to construct a `Cmd` object is with command literals (backticks), e.g.

    `ls -l`

This can then be passed to the `Cmd` constructor to modify its settings, e.g.

    Cmd(`echo "Hello world"`, ignorestatus=true, detach=false)
"""
Cmd

hash(x::Cmd, h::UInt) = hash(x.exec, hash(x.env, hash(x.ignorestatus, hash(x.dir, hash(x.flags, h)))))
==(x::Cmd, y::Cmd) = x.exec == y.exec && x.env == y.env && x.ignorestatus == y.ignorestatus &&
                     x.dir == y.dir && isequal(x.flags, y.flags)

struct OrCmds <: AbstractCmd
    a::AbstractCmd
    b::AbstractCmd
    OrCmds(a::AbstractCmd, b::AbstractCmd) = new(a, b)
end

struct ErrOrCmds <: AbstractCmd
    a::AbstractCmd
    b::AbstractCmd
    ErrOrCmds(a::AbstractCmd, b::AbstractCmd) = new(a, b)
end

struct AndCmds <: AbstractCmd
    a::AbstractCmd
    b::AbstractCmd
    AndCmds(a::AbstractCmd, b::AbstractCmd) = new(a, b)
end

hash(x::AndCmds, h::UInt) = hash(x.a, hash(x.b, h))
==(x::AndCmds, y::AndCmds) = x.a == y.a && x.b == y.b

shell_escape(cmd::Cmd; special::AbstractString="") =
    shell_escape(cmd.exec..., special=special)
shell_escape_posixly(cmd::Cmd) =
    shell_escape_posixly(cmd.exec...)
shell_escape_csh(cmd::Cmd) =
    shell_escape_csh(cmd.exec...)
escape_microsoft_c_args(cmd::Cmd) =
    escape_microsoft_c_args(cmd.exec...)
escape_microsoft_c_args(io::IO, cmd::Cmd) =
    escape_microsoft_c_args(io::IO, cmd.exec...)

function show(io::IO, cmd::Cmd)
    print_env = cmd.env !== nothing
    print_dir = !isempty(cmd.dir)
    (print_env || print_dir) && print(io, "setenv(")
    print_cpus = cmd.cpus !== nothing
    print_cpus && print(io, "setcpuaffinity(")
    print(io, '`')
    join(io, map(cmd.exec) do arg
        replace(sprint(context=io) do io
            with_output_color(:underline, io) do io
                print_shell_word(io, arg, shell_special)
            end
        end, '`' => "\\`")
    end, ' ')
    print(io, '`')
    if print_cpus
        print(io, ", ")
        show(io, collect(Int, something(cmd.cpus)))
        print(io, ")")
    end
    print_env && (print(io, ","); show(io, cmd.env))
    print_dir && (print(io, "; dir="); show(io, cmd.dir))
    (print_dir || print_env) && print(io, ")")
    nothing
end

function show(io::IO, cmds::Union{OrCmds,ErrOrCmds})
    print(io, "pipeline(")
    show(io, cmds.a)
    print(io, ", ")
    print(io, isa(cmds, ErrOrCmds) ? "stderr=" : "stdout=")
    show(io, cmds.b)
    print(io, ")")
end

function show(io::IO, cmds::AndCmds)
    show(io, cmds.a)
    print(io, " & ")
    show(io, cmds.b)
end

const STDIN_NO  = 0
const STDOUT_NO = 1
const STDERR_NO = 2

struct FileRedirect
    filename::String
    append::Bool
    FileRedirect(filename::AbstractString, append::Bool) = FileRedirect(convert(String, filename), append)
    function FileRedirect(filename::String, append::Bool)
        if lowercase(filename) == (@static Sys.iswindows() ? "nul" : "/dev/null")
            @warn "For portability use devnull instead of a file redirect" maxlog=1
        end
        return new(filename, append)
    end
end

# setup_stdio ≈ cconvert
# rawhandle ≈ unsafe_convert
rawhandle(::DevNull) = C_NULL
rawhandle(x::OS_HANDLE) = x
if OS_HANDLE !== RawFD
    rawhandle(x::RawFD) = Libc._get_osfhandle(x)
end
setup_stdio(stdio::Union{DevNull,OS_HANDLE,RawFD}, ::Bool) = (stdio, false)

const Redirectable = Union{IO, FileRedirect, RawFD, OS_HANDLE}
const StdIOSet = NTuple{3, Redirectable}

struct CmdRedirect <: AbstractCmd
    cmd::AbstractCmd
    handle::Redirectable
    stream_no::Int
    readable::Bool
end
CmdRedirect(cmd, handle, stream_no) = CmdRedirect(cmd, handle, stream_no, stream_no == STDIN_NO)

function show(io::IO, cr::CmdRedirect)
    print(io, "pipeline(")
    show(io, cr.cmd)
    print(io, ", ")
    if cr.stream_no == STDOUT_NO
        print(io, "stdout")
    elseif cr.stream_no == STDERR_NO
        print(io, "stderr")
    elseif cr.stream_no == STDIN_NO
        print(io, "stdin")
    else
        print(io, cr.stream_no)
    end
    print(io, cr.readable ? "<" : ">")
    show(io, cr.handle)
    print(io, ")")
end

"""
    ignorestatus(command)

Mark a command object so that running it will not throw an error if the result code is non-zero.
"""
ignorestatus(cmd::Cmd) = Cmd(cmd, ignorestatus=true)
ignorestatus(cmd::Union{OrCmds,AndCmds}) =
    typeof(cmd)(ignorestatus(cmd.a), ignorestatus(cmd.b))

"""
    detach(command)

Mark a command object so that it will be run in a new process group, allowing it to outlive the julia process, and not have Ctrl-C interrupts passed to it.
"""
detach(cmd::Cmd) = Cmd(cmd; detach=true)

# like String(s), but throw an error if s contains NUL, since
# libuv requires NUL-terminated strings
function cstr(s)
    if Base.containsnul(s)
        throw(ArgumentError("strings containing NUL cannot be passed to spawned processes"))
    end
    return String(s)::String
end

# convert various env representations into an array of "key=val" strings
byteenv(env::AbstractArray{<:AbstractString}) =
    String[cstr(x) for x in env]
byteenv(env::AbstractDict) =
    String[cstr(string(k)*"="*string(v)) for (k,v) in env]
byteenv(env::Nothing) = nothing
byteenv(env::Union{AbstractVector{Pair{T,V}}, Tuple{Vararg{Pair{T,V}}}}) where {T<:AbstractString,V} =
    String[cstr(k*"="*string(v)) for (k,v) in env]

"""
    setenv(command::Cmd, env; dir)

Set environment variables to use when running the given `command`. `env` is either a
dictionary mapping strings to strings, an array of strings of the form `"var=val"`, or
zero or more `"var"=>val` pair arguments. In order to modify (rather than replace) the
existing environment, create `env` through `copy(ENV)` and then setting `env["var"]=val`
as desired, or use [`addenv`](@ref).

The `dir` keyword argument can be used to specify a working directory for the command.
`dir` defaults to the currently set `dir` for `command` (which is the current working
directory if not specified already).

See also [`Cmd`](@ref), [`addenv`](@ref), [`ENV`](@ref), [`pwd`](@ref).
"""
setenv(cmd::Cmd, env; dir=cmd.dir) = Cmd(cmd; env=byteenv(env), dir=dir)
setenv(cmd::Cmd, env::Pair{<:AbstractString}...; dir=cmd.dir) =
    setenv(cmd, env; dir=dir)
setenv(cmd::Cmd; dir=cmd.dir) = Cmd(cmd; dir=dir)

# split environment entry string into before and after first `=` (key and value)
function splitenv(e::String)
    i = findnext('=', e, 2)
    if i === nothing
        throw(ArgumentError("malformed environment entry"))
    end
    e[1:prevind(e, i)], e[nextind(e, i):end]
end

"""
    addenv(command::Cmd, env...; inherit::Bool = true)

Merge new environment mappings into the given [`Cmd`](@ref) object, returning a new `Cmd` object.
Duplicate keys are replaced.  If `command` does not contain any environment values set already,
it inherits the current environment at time of `addenv()` call if `inherit` is `true`.
Keys with value `nothing` are deleted from the env.

See also [`Cmd`](@ref), [`setenv`](@ref), [`ENV`](@ref).

!!! compat "Julia 1.6"
    This function requires Julia 1.6 or later.
"""
function addenv(cmd::Cmd, env::Dict; inherit::Bool = true)
    new_env = Dict{String,String}()
    if cmd.env === nothing
        if inherit
            merge!(new_env, ENV)
        end
    else
        for (k, v) in splitenv.(cmd.env)
            new_env[string(k)::String] = string(v)::String
        end
    end
    for (k, v) in env
        if v === nothing
            delete!(new_env, string(k)::String)
        else
            new_env[string(k)::String] = string(v)::String
        end
    end
    return setenv(cmd, new_env)
end

function addenv(cmd::Cmd, pairs::Pair{<:AbstractString}...; inherit::Bool = true)
    return addenv(cmd, Dict(k => v for (k, v) in pairs); inherit)
end

function addenv(cmd::Cmd, env::Vector{<:AbstractString}; inherit::Bool = true)
    return addenv(cmd, Dict(k => v for (k, v) in splitenv.(env)); inherit)
end

"""
    setcpuaffinity(original_command::Cmd, cpus) -> command::Cmd

Set the CPU affinity of the `command` by a list of CPU IDs (1-based) `cpus`.  Passing
`cpus = nothing` means to unset the CPU affinity if the `original_command` has any.

This function is supported only in Linux and Windows.  It is not supported in macOS because
libuv does not support affinity setting.

!!! compat "Julia 1.8"
    This function requires at least Julia 1.8.

# Examples

In Linux, the `taskset` command line program can be used to see how `setcpuaffinity` works.

```julia
julia> run(setcpuaffinity(`sh -c 'taskset -p \$\$'`, [1, 2, 5]));
pid 2273's current affinity mask: 13
```

Note that the mask value `13` reflects that the first, second, and the fifth bits (counting
from the least significant position) are turned on:

```julia
julia> 0b010011
0x13
```
"""
function setcpuaffinity end
setcpuaffinity(cmd::Cmd, ::Nothing) = Cmd(cmd; cpus = nothing)
setcpuaffinity(cmd::Cmd, cpus) = Cmd(cmd; cpus = collect(UInt16, cpus))

(&)(left::AbstractCmd, right::AbstractCmd) = AndCmds(left, right)
redir_out(src::AbstractCmd, dest::AbstractCmd) = OrCmds(src, dest)
redir_err(src::AbstractCmd, dest::AbstractCmd) = ErrOrCmds(src, dest)

# Stream Redirects
redir_out(dest::Redirectable, src::AbstractCmd) = CmdRedirect(src, dest, STDIN_NO)
redir_out(src::AbstractCmd, dest::Redirectable) = CmdRedirect(src, dest, STDOUT_NO)
redir_err(src::AbstractCmd, dest::Redirectable) = CmdRedirect(src, dest, STDERR_NO)

# File redirects
redir_out(src::AbstractCmd, dest::AbstractString) = CmdRedirect(src, FileRedirect(dest, false), STDOUT_NO)
redir_out(src::AbstractString, dest::AbstractCmd) = CmdRedirect(dest, FileRedirect(src, false), STDIN_NO)
redir_err(src::AbstractCmd, dest::AbstractString) = CmdRedirect(src, FileRedirect(dest, false), STDERR_NO)
redir_out_append(src::AbstractCmd, dest::AbstractString) = CmdRedirect(src, FileRedirect(dest, true), STDOUT_NO)
redir_err_append(src::AbstractCmd, dest::AbstractString) = CmdRedirect(src, FileRedirect(dest, true), STDERR_NO)

"""
    pipeline(command; stdin, stdout, stderr, append=false)

Redirect I/O to or from the given `command`. Keyword arguments specify which of the
command's streams should be redirected. `append` controls whether file output appends to the
file. This is a more general version of the 2-argument `pipeline` function.
`pipeline(from, to)` is equivalent to `pipeline(from, stdout=to)` when `from` is a command,
and to `pipeline(to, stdin=from)` when `from` is another kind of data source.

**Examples**:

```julia
run(pipeline(`dothings`, stdout="out.txt", stderr="errs.txt"))
run(pipeline(`update`, stdout="log.txt", append=true))
```
"""
function pipeline(cmd::AbstractCmd; stdin=nothing, stdout=nothing, stderr=nothing, append::Bool=false)
    if append && stdout === nothing && stderr === nothing
        throw(ArgumentError("append set to true, but no output redirections specified"))
    end
    if stdin !== nothing
        cmd = redir_out(stdin, cmd)
    end
    if stdout !== nothing
        cmd = append ? redir_out_append(cmd, stdout) : redir_out(cmd, stdout)
    end
    if stderr !== nothing
        cmd = append ? redir_err_append(cmd, stderr) : redir_err(cmd, stderr)
    end
    return cmd
end

pipeline(cmd::AbstractCmd, dest) = pipeline(cmd, stdout=dest)
pipeline(src::Union{Redirectable,AbstractString}, cmd::AbstractCmd) = pipeline(cmd, stdin=src)

"""
    pipeline(from, to, ...)

Create a pipeline from a data source to a destination. The source and destination can be
commands, I/O streams, strings, or results of other `pipeline` calls. At least one argument
must be a command. Strings refer to filenames. When called with more than two arguments,
they are chained together from left to right. For example, `pipeline(a,b,c)` is equivalent to
`pipeline(pipeline(a,b),c)`. This provides a more concise way to specify multi-stage
pipelines.

**Examples**:

```julia
run(pipeline(`ls`, `grep xyz`))
run(pipeline(`ls`, "out.txt"))
run(pipeline("out.txt", `grep xyz`))
```
"""
pipeline(a, b, c, d...) = pipeline(pipeline(a, b), c, d...)


## implementation of `cmd` syntax ##

cmd_interpolate(xs...) = cstr(string(map(cmd_interpolate1, xs)...))
cmd_interpolate1(x) = x
cmd_interpolate1(::Nothing) = throw(ArgumentError("`nothing` can not be interpolated into commands (`Cmd`)"))

arg_gen() = String[]
arg_gen(x::AbstractString) = String[cstr(x)]
function arg_gen(cmd::Cmd)
    if has_nondefault_cmd_flags(cmd)
        throw(ArgumentError("Non-default environment behavior is only permitted for the first interpolant."))
    end
    cmd.exec
end

function arg_gen(head)
    if isiterable(typeof(head))
        vals = String[]
        for x in head
            push!(vals, cmd_interpolate(x))
        end
        return vals
    else
        return String[cmd_interpolate(head)]
    end
end

function arg_gen(head, tail...)
    head = arg_gen(head)
    tail = arg_gen(tail...)
    vals = String[]
    for h = head, t = tail
        push!(vals, cmd_interpolate(h,t))
    end
    return vals
end

function cmd_gen(parsed)
    args = String[]
    if length(parsed) >= 1 && isa(parsed[1], Tuple{Cmd})
        cmd = (parsed[1]::Tuple{Cmd})[1]
        (ignorestatus, flags, env, dir) = (cmd.ignorestatus, cmd.flags, cmd.env, cmd.dir)
        append!(args, cmd.exec)
        for arg in tail(parsed)
            append!(args, Base.invokelatest(arg_gen, arg...)::Vector{String})
        end
        return Cmd(Cmd(args), ignorestatus, flags, env, dir)
    else
        for arg in parsed
            append!(args, arg_gen(arg...)::Vector{String})
        end
        return Cmd(args)
    end
end

"""
    @cmd str

Similar to `cmd`, generate a `Cmd` from the `str` string which represents the shell command(s) to be executed.
The [`Cmd`](@ref) object can be run as a process and can outlive the spawning julia process (see `Cmd` for more).

# Examples
```jldoctest
julia> cm = @cmd " echo 1 "
`echo 1`

julia> run(cm)
1
Process(`echo 1`, ProcessExited(0))
```
"""
macro cmd(str)
    cmd_ex = shell_parse(str, special=shell_special, filename=String(__source__.file))[1]
    return :(cmd_gen($(esc(cmd_ex))))
end
N   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/process.jl@X      # This file is a part of Julia. License is MIT: https://julialang.org/license

mutable struct Process <: AbstractPipe
    cmd::Cmd
    handle::Ptr{Cvoid}
    in::IO
    out::IO
    err::IO
    exitcode::Int64
    termsignal::Int32
    exitnotify::ThreadSynchronizer
    function Process(cmd::Cmd, handle::Ptr{Cvoid})
        this = new(cmd, handle, devnull, devnull, devnull,
                   typemin(fieldtype(Process, :exitcode)),
                   typemin(fieldtype(Process, :termsignal)),
                   ThreadSynchronizer())
        finalizer(uvfinalize, this)
        return this
    end
end
pipe_reader(p::Process) = p.out
pipe_writer(p::Process) = p.in

# Represents a whole pipeline of any number of related processes
# so the entire pipeline can be treated as one entity
mutable struct ProcessChain <: AbstractPipe
    processes::Vector{Process}
    in::IO
    out::IO
    err::IO
    function ProcessChain()
        return new(Process[], devnull, devnull, devnull)
    end
end
pipe_reader(p::ProcessChain) = p.out
pipe_writer(p::ProcessChain) = p.in

# release ownership of the libuv handle
function uvfinalize(proc::Process)
    if proc.handle != C_NULL
        iolock_begin()
        if proc.handle != C_NULL
            disassociate_julia_struct(proc.handle)
            ccall(:jl_close_uv, Cvoid, (Ptr{Cvoid},), proc.handle)
            proc.handle = C_NULL
        end
        iolock_end()
    end
    nothing
end

# called when the process dies
function uv_return_spawn(p::Ptr{Cvoid}, exit_status::Int64, termsignal::Int32)
    data = ccall(:jl_uv_process_data, Ptr{Cvoid}, (Ptr{Cvoid},), p)
    data == C_NULL && return
    proc = unsafe_pointer_to_objref(data)::Process
    proc.exitcode = exit_status
    proc.termsignal = termsignal
    disassociate_julia_struct(proc.handle) # ensure that data field is set to C_NULL
    ccall(:jl_close_uv, Cvoid, (Ptr{Cvoid},), proc.handle)
    proc.handle = C_NULL
    lock(proc.exitnotify)
    try
        notify(proc.exitnotify)
    finally
        unlock(proc.exitnotify)
    end
    nothing
end

# called when the libuv handle is destroyed
function _uv_hook_close(proc::Process)
    Libc.free(@atomicswap :not_atomic proc.handle = C_NULL)
    nothing
end

const SpawnIO  = Union{IO, RawFD, OS_HANDLE}
const SpawnIOs = Vector{SpawnIO} # convenience name for readability

function as_cpumask(cpus::Vector{UInt16})
    n = max(Int(maximum(cpus)), Int(ccall(:uv_cpumask_size, Cint, ())))
    cpumask = zeros(Bool, n)
    for i in cpus
        cpumask[i] = true
    end
    return cpumask
end

# handle marshalling of `Cmd` arguments from Julia to C
@noinline function _spawn_primitive(file, cmd::Cmd, stdio::SpawnIOs)
    loop = eventloop()
    cpumask = cmd.cpus
    cpumask === nothing || (cpumask = as_cpumask(cpumask))
    GC.@preserve stdio begin
        iohandles = Tuple{Cint, UInt}[ # assuming little-endian layout
            let h = rawhandle(io)
                h === C_NULL     ? (0x00, UInt(0)) :
                h isa OS_HANDLE  ? (0x02, UInt(cconvert(@static(Sys.iswindows() ? Ptr{Cvoid} : Cint), h))) :
                h isa Ptr{Cvoid} ? (0x04, UInt(h)) :
                error("invalid spawn handle $h from $io")
            end
            for io in stdio]
        handle = Libc.malloc(_sizeof_uv_process)
        disassociate_julia_struct(handle)
        (; exec, flags, env, dir) = cmd
        iolock_begin()
        err = ccall(:jl_spawn, Int32,
                  (Cstring, Ptr{Cstring}, Ptr{Cvoid}, Ptr{Cvoid},
                   Ptr{Tuple{Cint, UInt}}, Int,
                   UInt32, Ptr{Cstring}, Cstring, Ptr{Bool}, Csize_t, Ptr{Cvoid}),
            file, exec, loop, handle,
            iohandles, length(iohandles),
            flags,
            env === nothing ? C_NULL : env,
            isempty(dir) ? C_NULL : dir,
            cpumask === nothing ? C_NULL : cpumask,
            cpumask === nothing ? 0 : length(cpumask),
            @cfunction(uv_return_spawn, Cvoid, (Ptr{Cvoid}, Int64, Int32)))
        if err == 0
            pp = Process(cmd, handle)
            associate_julia_struct(handle, pp)
        else
            ccall(:jl_forceclose_uv, Cvoid, (Ptr{Cvoid},), handle) # will call free on handle eventually
        end
        iolock_end()
    end
    if err != 0
        throw(_UVError("could not spawn " * repr(cmd), err))
    end
    return pp
end

_spawn(cmds::AbstractCmd) = _spawn(cmds, SpawnIO[])

# optimization: we can spawn `Cmd` directly without allocating the ProcessChain
function _spawn(cmd::Cmd, stdios::SpawnIOs)
    isempty(cmd.exec) && throw(ArgumentError("cannot spawn empty command"))
    pp = setup_stdios(stdios) do stdios
        return _spawn_primitive(cmd.exec[1], cmd, stdios)
    end
    return pp
end

# assume that having a ProcessChain means that the stdio are setup
function _spawn(cmds::AbstractCmd, stdios::SpawnIOs)
    pp = setup_stdios(stdios) do stdios
        return _spawn(cmds, stdios, ProcessChain())
    end
    return pp
end

# helper function for making a copy of a SpawnIOs, with replacement
function _stdio_copy(stdios::SpawnIOs, fd::Int, @nospecialize replace)
    nio = max(fd, length(stdios))
    new = SpawnIOs(undef, nio)
    copyto!(fill!(new, devnull), stdios)
    new[fd] = replace
    return new
end

function _spawn(redirect::CmdRedirect, stdios::SpawnIOs, args...)
    fdnum = redirect.stream_no + 1
    io, close_io = setup_stdio(redirect.handle, redirect.readable)
    try
        stdios = _stdio_copy(stdios, fdnum, io)
        return _spawn(redirect.cmd, stdios, args...)
    finally
        close_io && close_stdio(io)
    end
end

function _spawn(cmds::OrCmds, stdios::SpawnIOs, chain::ProcessChain)
    in_pipe, out_pipe = link_pipe(false, false)
    try
        stdios_left = _stdio_copy(stdios, 2, out_pipe)
        _spawn(cmds.a, stdios_left, chain)
        stdios_right = _stdio_copy(stdios, 1, in_pipe)
        _spawn(cmds.b, stdios_right, chain)
    finally
        close_pipe_sync(out_pipe)
        close_pipe_sync(in_pipe)
    end
    return chain
end

function _spawn(cmds::ErrOrCmds, stdios::SpawnIOs, chain::ProcessChain)
    in_pipe, out_pipe = link_pipe(false, false)
    try
        stdios_left = _stdio_copy(stdios, 3, out_pipe)
        _spawn(cmds.a, stdios_left, chain)
        stdios_right = _stdio_copy(stdios, 1, in_pipe)
        _spawn(cmds.b, stdios_right, chain)
    finally
        close_pipe_sync(out_pipe)
        close_pipe_sync(in_pipe)
    end
    return chain
end

function _spawn(cmds::AndCmds, stdios::SpawnIOs, chain::ProcessChain)
    _spawn(cmds.a, stdios, chain)
    _spawn(cmds.b, stdios, chain)
    return chain
end

function _spawn(cmd::Cmd, stdios::SpawnIOs, chain::ProcessChain)
    isempty(cmd.exec) && throw(ArgumentError("cannot spawn empty command"))
    pp = _spawn_primitive(cmd.exec[1], cmd, stdios)
    push!(chain.processes, pp)
    return chain
end


# open the child end of each element of `stdios`, and initialize the parent end
function setup_stdios(f, stdios::SpawnIOs)
    nstdio = length(stdios)
    open_io = SpawnIOs(undef, nstdio)
    close_io = falses(nstdio)
    try
        for i in 1:nstdio
            open_io[i], close_io[i] = setup_stdio(stdios[i], i == 1)
        end
        pp = f(open_io)
        return pp
    finally
        for i in 1:nstdio
            close_io[i] && close_stdio(open_io[i])
        end
    end
end

function setup_stdio(stdio::PipeEndpoint, child_readable::Bool)
    if stdio.status == StatusInit
        # if the PipeEndpoint isn't open, set it to the parent end
        # and pass the other end to the child
        rd, wr = link_pipe(!child_readable, child_readable)
        try
            open_pipe!(stdio, child_readable ? wr : rd)
        catch
            close_pipe_sync(rd)
            close_pipe_sync(wr)
            rethrow()
        end
        child = child_readable ? rd : wr
        return (child, true)
    end
    # if it's already open, assume that it's already the child end
    # (since we can't do anything else)
    return (stdio, false)
end

function setup_stdio(stdio::Pipe, child_readable::Bool)
    if stdio.in.status == StatusInit && stdio.out.status == StatusInit
        link_pipe!(stdio)
    end
    io = child_readable ? stdio.out : stdio.in
    return (io, false)
end

setup_stdio(stdio::AbstractPipe, readable::Bool) =
    setup_stdio(readable ? pipe_reader(stdio) : pipe_writer(stdio), readable)

function setup_stdio(stdio::IOStream, child_readable::Bool)
    io = RawFD(fd(stdio))
    return (io, false)
end

function setup_stdio(stdio::FileRedirect, child_readable::Bool)
    if child_readable
        attr = JL_O_RDONLY
        perm = zero(S_IRUSR)
    else
        attr = JL_O_WRONLY | JL_O_CREAT
        attr |= stdio.append ? JL_O_APPEND : JL_O_TRUNC
        perm = S_IRUSR | S_IWUSR | S_IRGRP | S_IROTH
    end
    io = Filesystem.open(stdio.filename, attr, perm)
    return (io, true)
end

# incrementally move data between an arbitrary IO and a system Pipe,
# including copying the EOF (shutdown) when finished
# TODO: probably more efficient (when valid) to use `stdio` directly as the
#       PipeEndpoint buffer field in some cases
function setup_stdio(stdio::IO, child_readable::Bool)
    parent = PipeEndpoint()
    rd, wr = link_pipe(!child_readable, child_readable)
    try
        open_pipe!(parent, child_readable ? wr : rd)
    catch
        close_pipe_sync(rd)
        close_pipe_sync(wr)
        rethrow()
    end
    child = child_readable ? rd : wr
    try
        let in = (child_readable ? parent : stdio),
            out = (child_readable ? stdio : parent)
            @async try
                write(in, out)
            catch ex
                @warn "Process I/O error" exception=(ex, catch_backtrace())
            finally
                close(parent)
                child_readable || closewrite(stdio)
            end
        end
    catch
        close_pipe_sync(child)
        rethrow()
    end
    return (child, true)
end

close_stdio(stdio::OS_HANDLE) = close_pipe_sync(stdio)
close_stdio(stdio) = close(stdio)

# INTERNAL
# pad out stdio to have at least three elements,
# passing either `devnull` or the corresponding `stdio`
# A Redirectable can be any of:
#   - A system IO handle, to be passed to the child
#   - An uninitialized pipe, to be created
#   - devnull (to pass /dev/null for 0-2, or to leave undefined for fd > 2)
#   - An Filesystem.File or IOStream object to redirect the output to
#   - A FileRedirect, containing a string specifying a filename to be opened for the child

spawn_opts_swallow(stdios::StdIOSet) = SpawnIO[stdios...]
spawn_opts_inherit(stdios::StdIOSet) = SpawnIO[stdios...]
spawn_opts_swallow(in::Redirectable=devnull, out::Redirectable=devnull, err::Redirectable=devnull) =
    SpawnIO[in, out, err]
# pass original descriptors to child processes by default, because we might
# have already exhausted and closed the libuv object for our standard streams.
# ref issue #8529
spawn_opts_inherit(in::Redirectable=RawFD(0), out::Redirectable=RawFD(1), err::Redirectable=RawFD(2)) =
    SpawnIO[in, out, err]

function eachline(cmd::AbstractCmd; keep::Bool=false)
    out = PipeEndpoint()
    processes = _spawn(cmd, SpawnIO[devnull, out, stderr])
    # if the user consumes all the data, also check process exit status for success
    ondone = () -> (success(processes) || pipeline_error(processes); nothing)
    return EachLine(out, keep=keep, ondone=ondone)::EachLine
end

"""
    open(command, mode::AbstractString, stdio=devnull)

Run `command` asynchronously. Like `open(command, stdio; read, write)` except specifying
the read and write flags via a mode string instead of keyword arguments.
Possible mode strings are:

| Mode | Description | Keywords                         |
|:-----|:------------|:---------------------------------|
| `r`  | read        | none                             |
| `w`  | write       | `write = true`                   |
| `r+` | read, write | `read = true, write = true`      |
| `w+` | read, write | `read = true, write = true`      |
"""
function open(cmds::AbstractCmd, mode::AbstractString, stdio::Redirectable=devnull)
    if mode == "r+" || mode == "w+"
        return open(cmds, stdio, read = true, write = true)
    elseif mode == "r"
        return open(cmds, stdio)
    elseif mode == "w"
        return open(cmds, stdio, write = true)
    else
        throw(ArgumentError("mode must be \"r\", \"w\", \"r+\", or \"w+\", not $(repr(mode))"))
    end
end

# return a Process object to read-to/write-from the pipeline
"""
    open(command, stdio=devnull; write::Bool = false, read::Bool = !write)

Start running `command` asynchronously, and return a `process::IO` object.  If `read` is
true, then reads from the process come from the process's standard output and `stdio` optionally
specifies the process's standard input stream.  If `write` is true, then writes go to
the process's standard input and `stdio` optionally specifies the process's standard output
stream.
The process's standard error stream is connected to the current global `stderr`.
"""
function open(cmds::AbstractCmd, stdio::Redirectable=devnull; write::Bool=false, read::Bool=!write)
    if read && write
        stdio === devnull || throw(ArgumentError("no stream can be specified for `stdio` in read-write mode"))
        in = PipeEndpoint()
        out = PipeEndpoint()
        processes = _spawn(cmds, SpawnIO[in, out, stderr])
        processes.in = in
        processes.out = out
    elseif read
        out = PipeEndpoint()
        processes = _spawn(cmds, SpawnIO[stdio, out, stderr])
        processes.out = out
    elseif write
        in = PipeEndpoint()
        processes = _spawn(cmds, SpawnIO[in, stdio, stderr])
        processes.in = in
    else
        stdio === devnull || throw(ArgumentError("no stream can be specified for `stdio` in no-access mode"))
        processes = _spawn(cmds, SpawnIO[devnull, devnull, stderr])
    end
    return processes
end

"""
    open(f::Function, command, args...; kwargs...)

Similar to `open(command, args...; kwargs...)`, but calls `f(stream)` on the
resulting process stream, then closes the input stream and waits for the process
to complete. Return the value returned by `f` on success. Throw an error if the
process failed, or if the process attempts to print anything to stdout.
"""
function open(f::Function, cmds::AbstractCmd, args...; kwargs...)
    P = open(cmds, args...; kwargs...)
    function waitkill(P::Union{Process,ProcessChain})
        close(P)
        # 0.1 seconds after we hope it dies (from closing stdio),
        # we kill the process with SIGTERM (15)
        local t = Timer(0.1) do t
            process_running(P) && kill(P)
        end
        wait(P)
        close(t)
    end
    ret = try
        f(P)
    catch
        waitkill(P)
        rethrow()
    end
    close(P.in)
    if !(eof(P.out)::Bool)
        waitkill(P)
        throw(_UVError("open(do)", UV_EPIPE))
    end
    success(P) || pipeline_error(P)
    return ret
end

"""
    read(command::Cmd)

Run `command` and return the resulting output as an array of bytes.
"""
function read(cmd::AbstractCmd)
    procs = open(cmd, "r", devnull)
    bytes = read(procs.out)
    success(procs) || pipeline_error(procs)
    return bytes::Vector{UInt8}
end

"""
    read(command::Cmd, String)

Run `command` and return the resulting output as a `String`.
"""
read(cmd::AbstractCmd, ::Type{String}) = String(read(cmd))::String

"""
    run(command, args...; wait::Bool = true)

Run a command object, constructed with backticks (see the [Running External Programs](@ref)
section in the manual). Throws an error if anything goes wrong, including the process
exiting with a non-zero status (when `wait` is true).

The `args...` allow you to pass through file descriptors to the command, and are ordered
like regular unix file descriptors (eg `stdin, stdout, stderr, FD(3), FD(4)...`).

If `wait` is false, the process runs asynchronously. You can later wait for it and check
its exit status by calling `success` on the returned process object.

When `wait` is false, the process' I/O streams are directed to `devnull`.
When `wait` is true, I/O streams are shared with the parent process.
Use [`pipeline`](@ref) to control I/O redirection.
"""
function run(cmds::AbstractCmd, args...; wait::Bool = true)
    if wait
        ps = _spawn(cmds, spawn_opts_inherit(args...))
        success(ps) || pipeline_error(ps)
    else
        stdios = spawn_opts_swallow(args...)
        ps = _spawn(cmds, stdios)
        # for each stdio input argument, guess whether the user
        # passed a `stdio` placeholder object as input, and thus
        # might be able to use the return AbstractProcess as an IO object
        # (this really only applies to PipeEndpoint, Pipe, TCPSocket, or an AbstractPipe wrapping one of those)
        if length(stdios) > 0
            in = stdios[1]
            isa(in, IO) && (ps.in = in)
            if length(stdios) > 1
                out = stdios[2]
                isa(out, IO) && (ps.out = out)
                if length(stdios) > 2
                    err = stdios[3]
                    isa(err, IO) && (ps.err = err)
                end
            end
        end
    end
    return ps
end

# some common signal numbers that are usually available on all platforms
# and might be useful as arguments to `kill` or testing against `Process.termsignal`
const SIGHUP  = 1
const SIGINT  = 2
const SIGQUIT = 3 # !windows
const SIGKILL = 9
const SIGPIPE = 13 # !windows
const SIGTERM = 15

function test_success(proc::Process)
    @assert process_exited(proc)
    if proc.exitcode < 0
        #TODO: this codepath is not currently tested
        throw(_UVError("could not start process " * repr(proc.cmd), proc.exitcode))
    end
    return proc.exitcode == 0 && proc.termsignal == 0
end

function success(x::Process)
    wait(x)
    return test_success(x)
end
success(procs::Vector{Process}) = mapreduce(success, &, procs)
success(procs::ProcessChain) = success(procs.processes)

"""
    success(command)

Run a command object, constructed with backticks (see the [Running External Programs](@ref)
section in the manual), and tell whether it was successful (exited with a code of 0).
An exception is raised if the process cannot be started.
"""
success(cmd::AbstractCmd) = success(_spawn(cmd))


"""
    ProcessFailedException

Indicates problematic exit status of a process.
When running commands or pipelines, this is thrown to indicate
a nonzero exit code was returned (i.e. that the invoked process failed).
"""
struct ProcessFailedException <: Exception
    procs::Vector{Process}
end
ProcessFailedException(proc::Process) = ProcessFailedException([proc])

function showerror(io::IO, err::ProcessFailedException)
    if length(err.procs) == 1
        proc = err.procs[1]
        println(io, "failed process: ", proc, " [", proc.exitcode, "]")
    else
        println(io, "failed processes:")
        for proc in err.procs
            println(io, "  ", proc, " [", proc.exitcode, "]")
        end
    end
end

function pipeline_error(proc::Process)
    if !proc.cmd.ignorestatus
        throw(ProcessFailedException(proc))
    end
    nothing
end

function pipeline_error(procs::ProcessChain)
    failed = Process[]
    for p = procs.processes
        if !test_success(p) && !p.cmd.ignorestatus
            push!(failed, p)
        end
    end
    isempty(failed) && return nothing
    throw(ProcessFailedException(failed))
end

"""
    kill(p::Process, signum=Base.SIGTERM)

Send a signal to a process. The default is to terminate the process.
Returns successfully if the process has already exited, but throws an
error if killing the process failed for other reasons (e.g. insufficient
permissions).
"""
function kill(p::Process, signum::Integer=SIGTERM)
    iolock_begin()
    if process_running(p)
        @assert p.handle != C_NULL
        err = ccall(:uv_process_kill, Int32, (Ptr{Cvoid}, Int32), p.handle, signum)
        if err != 0 && err != UV_ESRCH
            throw(_UVError("kill", err))
        end
    end
    iolock_end()
    nothing
end
kill(ps::Vector{Process}, signum::Integer=SIGTERM) = for p in ps; kill(p, signum); end
kill(ps::ProcessChain, signum::Integer=SIGTERM) = kill(ps.processes, signum)

"""
    getpid(process) -> Int32

Get the child process ID, if it still exists.

!!! compat "Julia 1.1"
    This function requires at least Julia 1.1.
"""
function Libc.getpid(p::Process)
    # TODO: due to threading, this method is only weakly synchronized with the user application
    iolock_begin()
    ppid = Int32(0)
    if p.handle != C_NULL # e.g. process_running
        ppid = ccall(:jl_uv_process_pid, Int32, (Ptr{Cvoid},), p.handle)
    end
    iolock_end()
    ppid <= 0 && throw(_UVError("getpid", UV_ESRCH))
    return ppid
end

## process status ##

"""
    process_running(p::Process)

Determine whether a process is currently running.
"""
process_running(s::Process) = s.handle != C_NULL
process_running(s::Vector{Process}) = any(process_running, s)
process_running(s::ProcessChain) = process_running(s.processes)

"""
    process_exited(p::Process)

Determine whether a process has exited.
"""
process_exited(s::Process) = !process_running(s)
process_exited(s::Vector{Process}) = all(process_exited, s)
process_exited(s::ProcessChain) = process_exited(s.processes)

process_signaled(s::Process) = (s.termsignal > 0)

function process_status(s::Process)
    return process_running(s) ? "ProcessRunning" :
           process_signaled(s) ? "ProcessSignaled(" * string(s.termsignal) * ")" :
           process_exited(s) ? "ProcessExited(" * string(s.exitcode) * ")" :
           error("process status error")
end

function wait(x::Process)
    process_exited(x) && return
    iolock_begin()
    if !process_exited(x)
        preserve_handle(x)
        lock(x.exitnotify)
        iolock_end()
        try
            wait(x.exitnotify)
        finally
            unlock(x.exitnotify)
            unpreserve_handle(x)
        end
    else
        iolock_end()
    end
    nothing
end

wait(x::ProcessChain) = foreach(wait, x.processes)

show(io::IO, p::Process) = print(io, "Process(", p.cmd, ", ", process_status(p), ")")

# allow the elements of the Cmd to be accessed as an array or iterator
for f in (:length, :firstindex, :lastindex, :keys, :first, :last, :iterate)
    @eval $f(cmd::Cmd) = $f(cmd.exec)
end
Iterators.reverse(cmd::Cmd) = Iterators.reverse(cmd.exec)
eltype(::Type{Cmd}) = eltype(fieldtype(Cmd, :exec))
for f in (:iterate, :getindex)
    @eval $f(cmd::Cmd, i) = $f(cmd.exec, i)
end
R   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/ttyhascolor.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

if Sys.iswindows()
    ttyhascolor(term_type = nothing) = true
else
    function ttyhascolor(term_type = get(ENV, "TERM", ""))
        startswith(term_type, "xterm") && return true
        try
            @static if Sys.KERNEL === :FreeBSD
                return success(`tput AF 0`)
            else
                return success(`tput setaf 0`)
            end
        catch e
            return false
        end
    end
end
function get_have_color()
    global have_color
    have_color === nothing && (have_color = ttyhascolor())
    return have_color::Bool
end
in(key_value::Pair{Symbol,Bool}, ::TTY) = key_value.first === :color && key_value.second === get_have_color()
haskey(::TTY, key::Symbol) = key === :color
getindex(::TTY, key::Symbol) = key === :color ? get_have_color() : throw(KeyError(key))
get(::TTY, key::Symbol, default) = key === :color ? get_have_color() : default
S   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/secretbuffer.jl)      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
    Base.SecretBuffer()

An [`IOBuffer`](@ref)-like object where the contents will be securely wiped when garbage collected.

It is considered best practice to wipe the buffer using `Base.shred!(::SecretBuffer)` as
soon as the secure data are no longer required. When initializing with existing data, the
`SecretBuffer!` method is highly recommended to securely zero the passed argument. Avoid
initializing with and converting to `String`s as they are unable to be securely zeroed.

# Examples
```jldoctest
julia> s = Base.SecretBuffer()
SecretBuffer("*******")

julia> write(s, 's', 'e', 'c', 'r', 'e', 't')
6

julia> seek(s, 0); Char(read(s, UInt8))
's': ASCII/Unicode U+0073 (category Ll: Letter, lowercase)

julia> Base.shred!(s)
SecretBuffer("*******")

julia> eof(s)
true
```
"""
mutable struct SecretBuffer <: IO
    data::Vector{UInt8}
    size::Int
    ptr::Int

    function SecretBuffer(; sizehint=128)
        s = new(Vector{UInt8}(undef, sizehint), 0, 1)
        finalizer(final_shred!, s)
        return s
    end
end

"""
    SecretBuffer(str::AbstractString)

A convenience constructor to initialize a `SecretBuffer` from a non-secret string.

Strings are bad at keeping secrets because they are unable to be securely
zeroed or destroyed. Therefore, avoid using this constructor with secret data.
Instead of starting with a string, either construct the `SecretBuffer`
incrementally with `SecretBuffer()` and [`write`](@ref), or use a `Vector{UInt8}` with
the `Base.SecretBuffer!(::Vector{UInt8})` constructor.
"""
SecretBuffer(str::AbstractString) = SecretBuffer(String(str))
function SecretBuffer(str::String)
    buf = codeunits(str)
    s = SecretBuffer(sizehint=length(buf))
    for c in buf
        write(s, c)
    end
    seek(s, 0)
    s
end
convert(::Type{SecretBuffer}, s::AbstractString) = SecretBuffer(String(s))

"""
    SecretBuffer!(data::Vector{UInt8})

Initialize a new `SecretBuffer` from `data`, securely zeroing `data` afterwards.
"""
function SecretBuffer!(d::Vector{UInt8})
    len = length(d)
    s = SecretBuffer(sizehint=len)
    for i in 1:len
        write(s, d[i])
    end
    seek(s, 0)
    securezero!(d)
    s
end

function unsafe_SecretBuffer!(s::Cstring)
    if s == C_NULL
        throw(ArgumentError("cannot convert NULL to SecretBuffer"))
    end
    len = Int(ccall(:strlen, Csize_t, (Cstring,), s))
    unsafe_SecretBuffer!(convert(Ptr{UInt8}, s), len)
end
function unsafe_SecretBuffer!(p::Ptr{UInt8}, len=1)
    if p == C_NULL
        throw(ArgumentError("cannot convert NULL to SecretBuffer"))
    end
    s = SecretBuffer(sizehint=len)
    for i in 1:len
        write(s, unsafe_load(p, i))
    end
    seek(s, 0)
    unsafe_securezero!(p, len)
    s
end


show(io::IO, s::SecretBuffer) = print(io, "SecretBuffer(\"*******\")")

# Unlike other IO objects, equality is computed by value for convenience
==(s1::SecretBuffer, s2::SecretBuffer) = (s1.ptr == s2.ptr) && (s1.size == s2.size) && (UInt8(0) == _bufcmp(s1.data, s2.data, min(s1.size, s2.size)))
# Also attempt a constant time buffer comparison algorithm — the length of the secret might be
# inferred by a timing attack, but not its values.
@noinline function _bufcmp(data1::Vector{UInt8}, data2::Vector{UInt8}, sz::Int)
    res = UInt8(0)
    for i = 1:sz
        res |= xor(data1[i], data2[i])
    end
    return res
end
# All SecretBuffers hash the same to avoid leaking information or breaking consistency with ==
const _sb_hash = UInt === UInt32 ? 0x111c0925 : 0xb06061e370557428
hash(s::SecretBuffer, h::UInt) = hash(_sb_hash, h)


function write(io::SecretBuffer, b::UInt8)
    if io.ptr > length(io.data)
        # We need to resize! the array: do this manually to ensure no copies are left behind
        newdata = Vector{UInt8}(undef, (io.size+16)*2)
        copyto!(newdata, io.data)
        securezero!(io.data)
        io.data = newdata
    end
    io.size == io.ptr-1 && (io.size += 1)
    io.data[io.ptr] = b
    io.ptr += 1
    return 1
end

function write(io::IO, s::SecretBuffer)
    nb = 0
    for i in 1:s.size
        nb += write(io, s.data[i])
    end
    return nb
end

cconvert(::Type{Cstring}, s::SecretBuffer) = unsafe_convert(Cstring, s)
function unsafe_convert(::Type{Cstring}, s::SecretBuffer)
    # Ensure that no nuls appear in the valid region
    if any(==(0x00), s.data[i] for i in 1:s.size)
        throw(ArgumentError("`SecretBuffers` containing nul bytes cannot be converted to C strings"))
    end
    # Add a hidden nul byte just past the end of the valid region
    p = s.ptr
    s.ptr = s.size + 1
    write(s, '\0')
    s.ptr = p
    s.size -= 1
    return Cstring(unsafe_convert(Ptr{Cchar}, s.data))
end

seek(io::SecretBuffer, n::Integer) = (io.ptr = max(min(n+1, io.size+1), 1); io)
seekend(io::SecretBuffer) = seek(io, io.size+1)
skip(io::SecretBuffer, n::Integer) = seek(io, position(io) + n)

bytesavailable(io::SecretBuffer) = io.size - io.ptr + 1
position(io::SecretBuffer) = io.ptr-1
eof(io::SecretBuffer) = io.ptr > io.size
isempty(io::SecretBuffer) = io.size == 0
function peek(io::SecretBuffer, ::Type{UInt8})
    eof(io) && throw(EOFError())
    return io.data[io.ptr]
end
function read(io::SecretBuffer, ::Type{UInt8})
    eof(io) && throw(EOFError())
    byte = io.data[io.ptr]
    io.ptr += 1
    return byte
end

function final_shred!(s::SecretBuffer)
    !isshredded(s) && @async @warn("a SecretBuffer was `shred!`ed by the GC; use `shred!` manually after use to minimize exposure.")
    shred!(s)
end

"""
    shred!(s::SecretBuffer)

Shreds the contents of a `SecretBuffer` by securely zeroing its data and
resetting its pointer and size.
This function is used to securely erase the sensitive data held in the buffer,
reducing the potential for information leaks.

# Example
```julia
s = SecretBuffer()
write(s, 's', 'e', 'c', 'r', 'e', 't')
shred!(s)  # s is now empty
```
"""
function shred!(s::SecretBuffer)
    securezero!(s.data)
    s.ptr = 1
    s.size = 0
    return s
end

isshredded(s::SecretBuffer) = all(iszero, s.data)

"""
    shred!(f::Function, x)

Applies function `f` to the argument `x` and then shreds `x`.
This function is useful when you need to perform some operations on e.g. a
`SecretBuffer` and then want to ensure that it is securely shredded afterwards.
"""
function shred!(f::Function, x)
    try
        f(x)
    finally
        shred!(x)
    end
end
Q   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/floatfuncs.jlJ@      # This file is a part of Julia. License is MIT: https://julialang.org/license

## floating-point functions ##

copysign(x::Float64, y::Float64) = copysign_float(x, y)
copysign(x::Float32, y::Float32) = copysign_float(x, y)
copysign(x::Float32, y::Real) = copysign(x, Float32(y))
copysign(x::Float64, y::Real) = copysign(x, Float64(y))

flipsign(x::Float64, y::Float64) = bitcast(Float64, xor_int(bitcast(UInt64, x), and_int(bitcast(UInt64, y), 0x8000000000000000)))
flipsign(x::Float32, y::Float32) = bitcast(Float32, xor_int(bitcast(UInt32, x), and_int(bitcast(UInt32, y), 0x80000000)))
flipsign(x::Float32, y::Real) = flipsign(x, Float32(y))
flipsign(x::Float64, y::Real) = flipsign(x, Float64(y))

signbit(x::Float64) = signbit(bitcast(Int64, x))
signbit(x::Float32) = signbit(bitcast(Int32, x))
signbit(x::Float16) = signbit(bitcast(Int16, x))

"""
    maxintfloat(T=Float64)

The largest consecutive integer-valued floating-point number that is exactly represented in
the given floating-point type `T` (which defaults to `Float64`).

That is, `maxintfloat` returns the smallest positive integer-valued floating-point number
`n` such that `n+1` is *not* exactly representable in the type `T`.

When an `Integer`-type value is needed, use `Integer(maxintfloat(T))`.
"""
maxintfloat(::Type{Float64}) = 9007199254740992.
maxintfloat(::Type{Float32}) = Float32(16777216.)
maxintfloat(::Type{Float16}) = Float16(2048f0)
maxintfloat(x::T) where {T<:AbstractFloat} = maxintfloat(T)

"""
    maxintfloat(T, S)

The largest consecutive integer representable in the given floating-point type `T` that
also does not exceed the maximum integer representable by the integer type `S`.  Equivalently,
it is the minimum of `maxintfloat(T)` and [`typemax(S)`](@ref).
"""
maxintfloat(::Type{S}, ::Type{T}) where {S<:AbstractFloat, T<:Integer} = min(maxintfloat(S), S(typemax(T)))
maxintfloat() = maxintfloat(Float64)

isinteger(x::AbstractFloat) = (x - trunc(x) == 0)

"""
    round([T,] x, [r::RoundingMode])
    round(x, [r::RoundingMode]; digits::Integer=0, base = 10)
    round(x, [r::RoundingMode]; sigdigits::Integer, base = 10)

Rounds the number `x`.

Without keyword arguments, `x` is rounded to an integer value, returning a value of type
`T`, or of the same type of `x` if no `T` is provided. An [`InexactError`](@ref) will be
thrown if the value is not representable by `T`, similar to [`convert`](@ref).

If the `digits` keyword argument is provided, it rounds to the specified number of digits
after the decimal place (or before if negative), in base `base`.

If the `sigdigits` keyword argument is provided, it rounds to the specified number of
significant digits, in base `base`.

The [`RoundingMode`](@ref) `r` controls the direction of the rounding; the default is
[`RoundNearest`](@ref), which rounds to the nearest integer, with ties (fractional values
of 0.5) being rounded to the nearest even integer. Note that `round` may give incorrect
results if the global rounding mode is changed (see [`rounding`](@ref)).

# Examples
```jldoctest
julia> round(1.7)
2.0

julia> round(Int, 1.7)
2

julia> round(1.5)
2.0

julia> round(2.5)
2.0

julia> round(pi; digits=2)
3.14

julia> round(pi; digits=3, base=2)
3.125

julia> round(123.456; sigdigits=2)
120.0

julia> round(357.913; sigdigits=4, base=2)
352.0
```

!!! note
    Rounding to specified digits in bases other than 2 can be inexact when
    operating on binary floating point numbers. For example, the [`Float64`](@ref)
    value represented by `1.15` is actually *less* than 1.15, yet will be
    rounded to 1.2. For example:

    ```jldoctest
    julia> x = 1.15
    1.15

    julia> big(1.15)
    1.149999999999999911182158029987476766109466552734375

    julia> x < 115//100
    true

    julia> round(x, digits=1)
    1.2
    ```

# Extensions

To extend `round` to new numeric types, it is typically sufficient to define `Base.round(x::NewType, r::RoundingMode)`.
"""
round(T::Type, x)

function round(::Type{T}, x::AbstractFloat, r::RoundingMode) where {T<:Integer}
    r != RoundToZero && (x = round(x,r))
    trunc(T, x)
end

# NOTE: this relies on the current keyword dispatch behaviour (#9498).
function round(x::Real, r::RoundingMode=RoundNearest;
               digits::Union{Nothing,Integer}=nothing, sigdigits::Union{Nothing,Integer}=nothing, base::Union{Nothing,Integer}=nothing)
    if digits === nothing
        if sigdigits === nothing
            if base === nothing
                # avoid recursive calls
                throw(MethodError(round, (x,r)))
            else
                round(x,r)
                # or throw(ArgumentError("`round` cannot use `base` argument without `digits` or `sigdigits` arguments."))
            end
        else
            isfinite(x) || return float(x)
            _round_sigdigits(x, r, sigdigits, base === nothing ? 10 : base)
        end
    else
        if sigdigits === nothing
            isfinite(x) || return float(x)
            _round_digits(x, r, digits, base === nothing ? 10 : base)
        else
            throw(ArgumentError("`round` cannot use both `digits` and `sigdigits` arguments."))
        end
    end
end

trunc(x::Real; kwargs...) = round(x, RoundToZero; kwargs...)
floor(x::Real; kwargs...) = round(x, RoundDown; kwargs...)
ceil(x::Real; kwargs...)  = round(x, RoundUp; kwargs...)

round(x::Integer, r::RoundingMode) = x

# round x to multiples of 1/invstep
function _round_invstep(x, invstep, r::RoundingMode)
    y = round(x * invstep, r) / invstep
    if !isfinite(y)
        return x
    end
    return y
end

# round x to multiples of 1/(invstepsqrt^2)
# Using square root of step prevents overflowing
function _round_invstepsqrt(x, invstepsqrt, r::RoundingMode)
    y = round((x * invstepsqrt) * invstepsqrt, r) / invstepsqrt / invstepsqrt
    if !isfinite(y)
        return x
    end
    return y
end

# round x to multiples of step
function _round_step(x, step, r::RoundingMode)
    # TODO: use div with rounding mode
    y = round(x / step, r) * step
    if !isfinite(y)
        if x > 0
            return (r == RoundUp ? oftype(x, Inf) : zero(x))
        elseif x < 0
            return (r == RoundDown ? -oftype(x, Inf) : -zero(x))
        else
            return x
        end
    end
    return y
end

function _round_digits(x, r::RoundingMode, digits::Integer, base)
    fx = float(x)
    if digits >= 0
        invstep = oftype(fx, base)^digits
        if isfinite(invstep)
            return _round_invstep(fx, invstep, r)
        else
            invstepsqrt = oftype(fx, base)^oftype(fx, digits/2)
            return _round_invstepsqrt(fx, invstepsqrt, r)
        end
    else
        step = oftype(fx, base)^-digits
        return _round_step(fx, step, r)
    end
end

hidigit(x::Integer, base) = ndigits0z(x, base)
function hidigit(x::AbstractFloat, base)
    iszero(x) && return 0
    if base == 10
        return 1 + floor(Int, log10(abs(x)))
    elseif base == 2
        return 1 + exponent(x)
    else
        return 1 + floor(Int, log(base, abs(x)))
    end
end
hidigit(x::Real, base) = hidigit(float(x), base)

function _round_sigdigits(x, r::RoundingMode, sigdigits::Integer, base)
    h = hidigit(x, base)
    _round_digits(x, r, sigdigits-h, base)
end

# C-style round
function round(x::AbstractFloat, ::RoundingMode{:NearestTiesAway})
    y = trunc(x)
    ifelse(x==y,y,trunc(2*x-y))
end
# Java-style round
function round(x::T, ::RoundingMode{:NearestTiesUp}) where {T <: AbstractFloat}
    copysign(floor((x + (T(0.25) - eps(T(0.5)))) + (T(0.25) + eps(T(0.5)))), x)
end

function Base.round(x::AbstractFloat, ::typeof(RoundFromZero))
    signbit(x) ? round(x, RoundDown) : round(x, RoundUp)
end

# isapprox: approximate equality of numbers
"""
    isapprox(x, y; atol::Real=0, rtol::Real=atol>0 ? 0 : √eps, nans::Bool=false[, norm::Function])

Inexact equality comparison. Two numbers compare equal if their relative distance *or* their
absolute distance is within tolerance bounds: `isapprox` returns `true` if
`norm(x-y) <= max(atol, rtol*max(norm(x), norm(y)))`. The default `atol` (absolute tolerance) is zero and the
default `rtol` (relative tolerance) depends on the types of `x` and `y`. The keyword argument `nans` determines
whether or not NaN values are considered equal (defaults to false).

For real or complex floating-point values, if an `atol > 0` is not specified, `rtol` defaults to
the square root of [`eps`](@ref) of the type of `x` or `y`, whichever is bigger (least precise).
This corresponds to requiring equality of about half of the significant digits. Otherwise,
e.g. for integer arguments or if an `atol > 0` is supplied, `rtol` defaults to zero.

The `norm` keyword defaults to `abs` for numeric `(x,y)` and to `LinearAlgebra.norm` for
arrays (where an alternative `norm` choice is sometimes useful).
When `x` and `y` are arrays, if `norm(x-y)` is not finite (i.e. `±Inf`
or `NaN`), the comparison falls back to checking whether all elements of `x` and `y` are
approximately equal component-wise.

The binary operator `≈` is equivalent to `isapprox` with the default arguments, and `x ≉ y`
is equivalent to `!isapprox(x,y)`.

Note that `x ≈ 0` (i.e., comparing to zero with the default tolerances) is
equivalent to `x == 0` since the default `atol` is `0`.  In such cases, you should either
supply an appropriate `atol` (or use `norm(x) ≤ atol`) or rearrange your code (e.g.
use `x ≈ y` rather than `x - y ≈ 0`).   It is not possible to pick a nonzero `atol`
automatically because it depends on the overall scaling (the "units") of your problem:
for example, in `x - y ≈ 0`, `atol=1e-9` is an absurdly small tolerance if `x` is the
[radius of the Earth](https://en.wikipedia.org/wiki/Earth_radius) in meters,
but an absurdly large tolerance if `x` is the
[radius of a Hydrogen atom](https://en.wikipedia.org/wiki/Bohr_radius) in meters.

!!! compat "Julia 1.6"
    Passing the `norm` keyword argument when comparing numeric (non-array) arguments
    requires Julia 1.6 or later.

# Examples
```jldoctest
julia> isapprox(0.1, 0.15; atol=0.05)
true

julia> isapprox(0.1, 0.15; rtol=0.34)
true

julia> isapprox(0.1, 0.15; rtol=0.33)
false

julia> 0.1 + 1e-10 ≈ 0.1
true

julia> 1e-10 ≈ 0
false

julia> isapprox(1e-10, 0, atol=1e-8)
true

julia> isapprox([10.0^9, 1.0], [10.0^9, 2.0]) # using `norm`
true
```
"""
function isapprox(x::Number, y::Number;
                  atol::Real=0, rtol::Real=rtoldefault(x,y,atol),
                  nans::Bool=false, norm::Function=abs)
    x′, y′ = promote(x, y) # to avoid integer overflow
    x == y ||
        (isfinite(x) && isfinite(y) && norm(x-y) <= max(atol, rtol*max(norm(x′), norm(y′)))) ||
         (nans && isnan(x) && isnan(y))
end

function isapprox(x::Integer, y::Integer;
                  atol::Real=0, rtol::Real=rtoldefault(x,y,atol),
                  nans::Bool=false, norm::Function=abs)
    if norm === abs && atol < 1 && rtol == 0
        return x == y
    else
        return norm(x - y) <= max(atol, rtol*max(norm(x), norm(y)))
    end
end

"""
    isapprox(x; kwargs...) / ≈(x; kwargs...)

Create a function that compares its argument to `x` using `≈`, i.e. a function equivalent to `y -> y ≈ x`.

The keyword arguments supported here are the same as those in the 2-argument `isapprox`.

!!! compat "Julia 1.5"
    This method requires Julia 1.5 or later.
"""
isapprox(y; kwargs...) = x -> isapprox(x, y; kwargs...)

const ≈ = isapprox
"""
    x ≉ y

This is equivalent to `!isapprox(x,y)` (see [`isapprox`](@ref)).
"""
≉(args...; kws...) = !≈(args...; kws...)

# default tolerance arguments
rtoldefault(::Type{T}) where {T<:AbstractFloat} = sqrt(eps(T))
rtoldefault(::Type{<:Real}) = 0
function rtoldefault(x::Union{T,Type{T}}, y::Union{S,Type{S}}, atol::Real) where {T<:Number,S<:Number}
    rtol = max(rtoldefault(real(T)),rtoldefault(real(S)))
    return atol > 0 ? zero(rtol) : rtol
end

# fused multiply-add

"""
    fma(x, y, z)

Computes `x*y+z` without rounding the intermediate result `x*y`. On some systems this is
significantly more expensive than `x*y+z`. `fma` is used to improve accuracy in certain
algorithms. See [`muladd`](@ref).
"""
function fma end
function fma_emulated(a::Float32, b::Float32, c::Float32)::Float32
    ab = Float64(a) * b
    res = ab+c
    reinterpret(UInt64, res)&0x1fff_ffff!=0x1000_0000 && return res
    # yes error compensation is necessary. It sucks
    reslo = abs(c)>abs(ab) ? ab-(res - c) : c-(res - ab)
    res = iszero(reslo) ? res : (signbit(reslo) ? prevfloat(res) : nextfloat(res))
    return res
end

""" Splits a Float64 into a hi bit and a low bit where the high bit has 27 trailing 0s and the low bit has 26 trailing 0s"""
@inline function splitbits(x::Float64)
    hi = reinterpret(Float64, reinterpret(UInt64, x) & 0xffff_ffff_f800_0000)
    return hi, x-hi
end

function twomul(a::Float64, b::Float64)
    ahi, alo = splitbits(a)
    bhi, blo = splitbits(b)
    abhi = a*b
    blohi, blolo = splitbits(blo)
    ablo = alo*blohi - (((abhi - ahi*bhi) - alo*bhi) - ahi*blo) + blolo*alo
    return abhi, ablo
end

function fma_emulated(a::Float64, b::Float64,c::Float64)
    abhi, ablo = @inline twomul(a,b)
    if !isfinite(abhi+c) || isless(abs(abhi), nextfloat(0x1p-969)) || issubnormal(a) || issubnormal(b)
        aandbfinite = isfinite(a) && isfinite(b)
        if !(isfinite(c) && aandbfinite)
            return aandbfinite ? c : abhi+c
        end
        (iszero(a) || iszero(b)) && return abhi+c
        # The checks above satisfy exponent's nothrow precondition
        bias = Math._exponent_finite_nonzero(a) + Math._exponent_finite_nonzero(b)
        c_denorm = ldexp(c, -bias)
        if isfinite(c_denorm)
            # rescale a and b to [1,2), equivalent to ldexp(a, -exponent(a))
            issubnormal(a) && (a *= 0x1p52)
            issubnormal(b) && (b *= 0x1p52)
            a = reinterpret(Float64, (reinterpret(UInt64, a) & ~Base.exponent_mask(Float64)) | Base.exponent_one(Float64))
            b = reinterpret(Float64, (reinterpret(UInt64, b) & ~Base.exponent_mask(Float64)) | Base.exponent_one(Float64))
            c = c_denorm
            abhi, ablo = twomul(a,b)
            # abhi <= 4 -> isfinite(r)      (α)
            r = abhi+c
            # s ≈ 0                         (β)
            s = (abs(abhi) > abs(c)) ? (abhi-r+c+ablo) : (c-r+abhi+ablo)
            # α ⩓ β -> isfinite(sumhi)      (γ)
            sumhi = r+s
            # If result is subnormal, ldexp will cause double rounding because subnormals have fewer mantisa bits.
            # As such, we need to check whether round to even would lead to double rounding and manually round sumhi to avoid it.
            if issubnormal(ldexp(sumhi, bias))
                sumlo = r-sumhi+s
                # finite: See γ
                # non-zero: If sumhi == ±0., then ldexp(sumhi, bias) == ±0,
                # so we don't take this branch.
                bits_lost = -bias-Math._exponent_finite_nonzero(sumhi)-1022
                sumhiInt = reinterpret(UInt64, sumhi)
                if (bits_lost != 1) ⊻ (sumhiInt&1 == 1)
                    sumhi = nextfloat(sumhi, cmp(sumlo,0))
                end
            end
            return ldexp(sumhi, bias)
        end
        isinf(abhi) && signbit(c) == signbit(a*b) && return abhi
        # fall through
    end
    r = abhi+c
    s = (abs(abhi) > abs(c)) ? (abhi-r+c+ablo) : (c-r+abhi+ablo)
    return r+s
end
fma_llvm(x::Float32, y::Float32, z::Float32) = fma_float(x, y, z)
fma_llvm(x::Float64, y::Float64, z::Float64) = fma_float(x, y, z)

# Disable LLVM's fma if it is incorrect, e.g. because LLVM falls back
# onto a broken system libm; if so, use a software emulated fma
@assume_effects :consistent fma(x::Float32, y::Float32, z::Float32) = Core.Intrinsics.have_fma(Float32) ? fma_llvm(x,y,z) : fma_emulated(x,y,z)
@assume_effects :consistent fma(x::Float64, y::Float64, z::Float64) = Core.Intrinsics.have_fma(Float64) ? fma_llvm(x,y,z) : fma_emulated(x,y,z)

function fma(a::Float16, b::Float16, c::Float16)
    Float16(muladd(Float32(a), Float32(b), Float32(c))) #don't use fma if the hardware doesn't have it.
end

# This is necessary at least on 32-bit Intel Linux, since fma_llvm may
# have called glibc, and some broken glibc fma implementations don't
# properly restore the rounding mode
Rounding.setrounding_raw(Float32, Rounding.JL_FE_TONEAREST)
Rounding.setrounding_raw(Float64, Rounding.JL_FE_TONEAREST)
K   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/math.jl��      # This file is a part of Julia. License is MIT: https://julialang.org/license

module Math

export sin, cos, sincos, tan, sinh, cosh, tanh, asin, acos, atan,
       asinh, acosh, atanh, sec, csc, cot, asec, acsc, acot,
       sech, csch, coth, asech, acsch, acoth,
       sinpi, cospi, sincospi, tanpi, sinc, cosc,
       cosd, cotd, cscd, secd, sind, tand, sincosd,
       acosd, acotd, acscd, asecd, asind, atand,
       rad2deg, deg2rad,
       log, log2, log10, log1p, exponent, exp, exp2, exp10, expm1,
       cbrt, sqrt, fourthroot, significand,
       hypot, max, min, minmax, ldexp, frexp,
       clamp, clamp!, modf, ^, mod2pi, rem2pi,
       @evalpoly, evalpoly

import .Base: log, exp, sin, cos, tan, sinh, cosh, tanh, asin,
             acos, atan, asinh, acosh, atanh, sqrt, log2, log10,
             max, min, minmax, ^, exp2, muladd, rem,
             exp10, expm1, log1p, @constprop, @assume_effects

using .Base: sign_mask, exponent_mask, exponent_one,
            exponent_half, uinttype, significand_mask,
            significand_bits, exponent_bits, exponent_bias,
            exponent_max, exponent_raw_max

using Core.Intrinsics: sqrt_llvm

using .Base: IEEEFloat

@noinline function throw_complex_domainerror(f::Symbol, x)
    throw(DomainError(x,
        LazyString(f," was called with a negative real argument but will only return a complex result if called with a complex argument. Try ", f,"(Complex(x)).")))
end
@noinline function throw_complex_domainerror_neg1(f::Symbol, x)
    throw(DomainError(x,
        LazyString(f," was called with a real argument < -1 but will only return a complex result if called with a complex argument. Try ", f,"(Complex(x)).")))
end
@noinline function throw_exp_domainerror(x)
    throw(DomainError(x, LazyString(
        "Exponentiation yielding a complex result requires a ",
        "complex argument.\nReplace x^y with (x+0im)^y, ",
        "Complex(x)^y, or similar.")))
end

# non-type specific math functions

function two_mul(x::T, y::T) where {T<:Number}
    xy = x*y
    xy, fma(x, y, -xy)
end

@assume_effects :consistent @inline function two_mul(x::Float64, y::Float64)
    if Core.Intrinsics.have_fma(Float64)
        xy = x*y
        return xy, fma(x, y, -xy)
    end
    return Base.twomul(x,y)
end

@assume_effects :consistent @inline function two_mul(x::T, y::T) where T<: Union{Float16, Float32}
    if Core.Intrinsics.have_fma(T)
        xy = x*y
        return xy, fma(x, y, -xy)
    end
    xy = widen(x)*y
    Txy = T(xy)
    return Txy, T(xy-Txy)
end

"""
    clamp(x, lo, hi)

Return `x` if `lo <= x <= hi`. If `x > hi`, return `hi`. If `x < lo`, return `lo`. Arguments
are promoted to a common type.

See also [`clamp!`](@ref), [`min`](@ref), [`max`](@ref).

!!! compat "Julia 1.3"
    `missing` as the first argument requires at least Julia 1.3.

# Examples
```jldoctest
julia> clamp.([pi, 1.0, big(10)], 2.0, 9.0)
3-element Vector{BigFloat}:
 3.141592653589793238462643383279502884197169399375105820974944592307816406286198
 2.0
 9.0

julia> clamp.([11, 8, 5], 10, 6)  # an example where lo > hi
3-element Vector{Int64}:
  6
  6
 10
```
"""
clamp(x::X, lo::L, hi::H) where {X,L,H} =
    ifelse(x > hi, convert(promote_type(X,L,H), hi),
           ifelse(x < lo,
                  convert(promote_type(X,L,H), lo),
                  convert(promote_type(X,L,H), x)))

"""
    clamp(x, T)::T

Clamp `x` between `typemin(T)` and `typemax(T)` and convert the result to type `T`.

See also [`trunc`](@ref).

# Examples
```jldoctest
julia> clamp(200, Int8)
127

julia> clamp(-200, Int8)
-128

julia> trunc(Int, 4pi^2)
39
```
"""
clamp(x, ::Type{T}) where {T<:Integer} = clamp(x, typemin(T), typemax(T)) % T


"""
    clamp!(array::AbstractArray, lo, hi)

Restrict values in `array` to the specified range, in-place.
See also [`clamp`](@ref).

!!! compat "Julia 1.3"
    `missing` entries in `array` require at least Julia 1.3.

# Examples
```jldoctest
julia> row = collect(-4:4)';

julia> clamp!(row, 0, Inf)
1×9 adjoint(::Vector{Int64}) with eltype Int64:
 0  0  0  0  0  1  2  3  4

julia> clamp.((-4:4)', 0, Inf)
1×9 Matrix{Float64}:
 0.0  0.0  0.0  0.0  0.0  1.0  2.0  3.0  4.0
```
"""
function clamp!(x::AbstractArray, lo, hi)
    @inbounds for i in eachindex(x)
        x[i] = clamp(x[i], lo, hi)
    end
    x
end

"""
    clamp(x::Integer, r::AbstractUnitRange)

Clamp `x` to lie within range `r`.

!!! compat "Julia 1.6"
     This method requires at least Julia 1.6.
"""
clamp(x::Integer, r::AbstractUnitRange{<:Integer}) = clamp(x, first(r), last(r))

"""
    evalpoly(x, p)

Evaluate the polynomial ``\\sum_k x^{k-1} p[k]`` for the coefficients `p[1]`, `p[2]`, ...;
that is, the coefficients are given in ascending order by power of `x`.
Loops are unrolled at compile time if the number of coefficients is statically known, i.e.
when `p` is a `Tuple`.
This function generates efficient code using Horner's method if `x` is real, or using
a Goertzel-like [^DK62] algorithm if `x` is complex.

[^DK62]: Donald Knuth, Art of Computer Programming, Volume 2: Seminumerical Algorithms, Sec. 4.6.4.

!!! compat "Julia 1.4"
    This function requires Julia 1.4 or later.

# Example
```jldoctest
julia> evalpoly(2, (1, 2, 3))
17
```
"""
function evalpoly(x, p::Tuple)
    if @generated
        N = length(p.parameters::Core.SimpleVector)
        ex = :(p[end])
        for i in N-1:-1:1
            ex = :(muladd(x, $ex, p[$i]))
        end
        ex
    else
        _evalpoly(x, p)
    end
end

evalpoly(x, p::AbstractVector) = _evalpoly(x, p)

function _evalpoly(x, p)
    Base.require_one_based_indexing(p)
    N = length(p)
    ex = p[end]
    for i in N-1:-1:1
        ex = muladd(x, ex, p[i])
    end
    ex
end

function evalpoly(z::Complex, p::Tuple)
    if @generated
        N = length(p.parameters)
        a = :(p[end])
        b = :(p[end-1])
        as = []
        for i in N-2:-1:1
            ai = Symbol("a", i)
            push!(as, :($ai = $a))
            a = :(muladd(r, $ai, $b))
            b = :(muladd(-s, $ai, p[$i]))
        end
        ai = :a0
        push!(as, :($ai = $a))
        C = Expr(:block,
                 :(x = real(z)),
                 :(y = imag(z)),
                 :(r = x + x),
                 :(s = muladd(x, x, y*y)),
                 as...,
                 :(muladd($ai, z, $b)))
    else
        _evalpoly(z, p)
    end
end
evalpoly(z::Complex, p::Tuple{<:Any}) = p[1]


evalpoly(z::Complex, p::AbstractVector) = _evalpoly(z, p)

function _evalpoly(z::Complex, p)
    Base.require_one_based_indexing(p)
    length(p) == 1 && return p[1]
    N = length(p)
    a = p[end]
    b = p[end-1]

    x = real(z)
    y = imag(z)
    r = 2x
    s = muladd(x, x, y*y)
    for i in N-2:-1:1
        ai = a
        a = muladd(r, ai, b)
        b = muladd(-s, ai, p[i])
    end
    ai = a
    muladd(ai, z, b)
end

"""
    @horner(x, p...)

Evaluate `p[1] + x * (p[2] + x * (....))`, i.e. a polynomial via Horner's rule.

See also [`@evalpoly`](@ref), [`evalpoly`](@ref).
"""
macro horner(x, p...)
     xesc, pesc = esc(x), esc.(p)
    :(invoke(evalpoly, Tuple{Any, Tuple}, $xesc, ($(pesc...),)))
end

# Evaluate p[1] + z*p[2] + z^2*p[3] + ... + z^(n-1)*p[n].  This uses
# Horner's method if z is real, but for complex z it uses a more
# efficient algorithm described in Knuth, TAOCP vol. 2, section 4.6.4,
# equation (3).

"""
    @evalpoly(z, c...)

Evaluate the polynomial ``\\sum_k z^{k-1} c[k]`` for the coefficients `c[1]`, `c[2]`, ...;
that is, the coefficients are given in ascending order by power of `z`.  This macro expands
to efficient inline code that uses either Horner's method or, for complex `z`, a more
efficient Goertzel-like algorithm.

See also [`evalpoly`](@ref).

# Examples
```jldoctest
julia> @evalpoly(3, 1, 0, 1)
10

julia> @evalpoly(2, 1, 0, 1)
5

julia> @evalpoly(2, 1, 1, 1)
7
```
"""
macro evalpoly(z, p...)
    zesc, pesc = esc(z), esc.(p)
    :(evalpoly($zesc, ($(pesc...),)))
end

# polynomial evaluation using compensated summation.
# much more accurate, especially when lo can be combined with other rounding errors
Base.@assume_effects :terminates_locally @inline function exthorner(x, p::Tuple)
    hi, lo = p[end], zero(x)
    for i in length(p)-1:-1:1
        pi = getfield(p, i) # needed to prove consistency
        prod, err = two_mul(hi,x)
        hi = pi+prod
        lo = fma(lo, x, prod - (hi - pi) + err)
    end
    return hi, lo
end

"""
    rad2deg(x)

Convert `x` from radians to degrees.

See also [`deg2rad`](@ref).

# Examples
```jldoctest
julia> rad2deg(pi)
180.0
```
"""
rad2deg(z::AbstractFloat) = z * (180 / oftype(z, pi))

"""
    deg2rad(x)

Convert `x` from degrees to radians.

See also [`rad2deg`](@ref), [`sind`](@ref), [`pi`](@ref).

# Examples
```jldoctest
julia> deg2rad(90)
1.5707963267948966
```
"""
deg2rad(z::AbstractFloat) = z * (oftype(z, pi) / 180)
rad2deg(z::Real) = rad2deg(float(z))
deg2rad(z::Real) = deg2rad(float(z))
rad2deg(z::Number) = (z/pi)*180
deg2rad(z::Number) = (z*pi)/180

log(b::T, x::T) where {T<:Number} = log(x)/log(b)

"""
    log(b,x)

Compute the base `b` logarithm of `x`. Throws [`DomainError`](@ref) for negative
[`Real`](@ref) arguments.

# Examples
```jldoctest; filter = r"Stacktrace:(\\n \\[[0-9]+\\].*)*"
julia> log(4,8)
1.5

julia> log(4,2)
0.5

julia> log(-2, 3)
ERROR: DomainError with -2.0:
log was called with a negative real argument but will only return a complex result if called with a complex argument. Try log(Complex(x)).
Stacktrace:
 [1] throw_complex_domainerror(::Symbol, ::Float64) at ./math.jl:31
[...]

julia> log(2, -3)
ERROR: DomainError with -3.0:
log was called with a negative real argument but will only return a complex result if called with a complex argument. Try log(Complex(x)).
Stacktrace:
 [1] throw_complex_domainerror(::Symbol, ::Float64) at ./math.jl:31
[...]
```

!!! note
    If `b` is a power of 2 or 10, [`log2`](@ref) or [`log10`](@ref) should be used, as these will
    typically be faster and more accurate. For example,

    ```jldoctest
    julia> log(100,1000000)
    2.9999999999999996

    julia> log10(1000000)/2
    3.0
    ```
"""
log(b::Number, x::Number) = log(promote(b,x)...)

# type specific math functions

const libm = Base.libm_name

# functions with no domain error
"""
    sinh(x)

Compute hyperbolic sine of `x`.
"""
sinh(x::Number)

"""
    cosh(x)

Compute hyperbolic cosine of `x`.
"""
cosh(x::Number)

"""
    tanh(x)

Compute hyperbolic tangent of `x`.

See also [`tan`](@ref), [`atanh`](@ref).

# Examples

```jldoctest
julia> tanh.(-3:3f0)  # Here 3f0 isa Float32
7-element Vector{Float32}:
 -0.9950548
 -0.9640276
 -0.7615942
  0.0
  0.7615942
  0.9640276
  0.9950548

julia> tan.(im .* (1:3))
3-element Vector{ComplexF64}:
 0.0 + 0.7615941559557649im
 0.0 + 0.9640275800758169im
 0.0 + 0.9950547536867306im
```
"""
tanh(x::Number)

"""
    atan(y)
    atan(y, x)

Compute the inverse tangent of `y` or `y/x`, respectively.

For one argument, this is the angle in radians between the positive *x*-axis and the point
(1, *y*), returning a value in the interval ``[-\\pi/2, \\pi/2]``.

For two arguments, this is the angle in radians between the positive *x*-axis and the
point (*x*, *y*), returning a value in the interval ``[-\\pi, \\pi]``. This corresponds to a
standard [`atan2`](https://en.wikipedia.org/wiki/Atan2) function. Note that by convention
`atan(0.0,x)` is defined as ``\\pi`` and `atan(-0.0,x)` is defined as ``-\\pi`` when `x < 0`.

See also [`atand`](@ref) for degrees.

# Examples

```jldoctest
julia> rad2deg(atan(-1/√3))
-30.000000000000004

julia> rad2deg(atan(-1, √3))
-30.000000000000004

julia> rad2deg(atan(1, -√3))
150.0
```
"""
atan(x::Number)

"""
    asinh(x)

Compute the inverse hyperbolic sine of `x`.
"""
asinh(x::Number)


# utility for converting NaN return to DomainError
# the branch in nan_dom_err prevents its callers from inlining, so be sure to force it
# until the heuristics can be improved
@inline nan_dom_err(out, x) = isnan(out) & !isnan(x) ? throw(DomainError(x, "NaN result for non-NaN input.")) : out

# functions that return NaN on non-NaN argument for domain error
"""
    sin(x)

Compute sine of `x`, where `x` is in radians.

See also [`sind`](@ref), [`sinpi`](@ref), [`sincos`](@ref), [`cis`](@ref), [`asin`](@ref).

# Examples
```jldoctest
julia> round.(sin.(range(0, 2pi, length=9)'), digits=3)
1×9 Matrix{Float64}:
 0.0  0.707  1.0  0.707  0.0  -0.707  -1.0  -0.707  -0.0

julia> sind(45)
0.7071067811865476

julia> sinpi(1/4)
0.7071067811865475

julia> round.(sincos(pi/6), digits=3)
(0.5, 0.866)

julia> round(cis(pi/6), digits=3)
0.866 + 0.5im

julia> round(exp(im*pi/6), digits=3)
0.866 + 0.5im
```
"""
sin(x::Number)

"""
    cos(x)

Compute cosine of `x`, where `x` is in radians.

See also [`cosd`](@ref), [`cospi`](@ref), [`sincos`](@ref), [`cis`](@ref).
"""
cos(x::Number)

"""
    tan(x)

Compute tangent of `x`, where `x` is in radians.
"""
tan(x::Number)

"""
    asin(x)

Compute the inverse sine of `x`, where the output is in radians.

See also [`asind`](@ref) for output in degrees.

# Examples
```jldoctest
julia> asin.((0, 1/2, 1))
(0.0, 0.5235987755982989, 1.5707963267948966)

julia> asind.((0, 1/2, 1))
(0.0, 30.000000000000004, 90.0)
```
"""
asin(x::Number)

"""
    acos(x)

Compute the inverse cosine of `x`, where the output is in radians
"""
acos(x::Number)

"""
    acosh(x)

Compute the inverse hyperbolic cosine of `x`.
"""
acosh(x::Number)

"""
    atanh(x)

Compute the inverse hyperbolic tangent of `x`.
"""
atanh(x::Number)

"""
    log(x)

Compute the natural logarithm of `x`. Throws [`DomainError`](@ref) for negative
[`Real`](@ref) arguments. Use complex negative arguments to obtain complex results.

See also [`ℯ`](@ref), [`log1p`](@ref), [`log2`](@ref), [`log10`](@ref).

# Examples
```jldoctest; filter = r"Stacktrace:(\\n \\[[0-9]+\\].*)*"
julia> log(2)
0.6931471805599453

julia> log(-3)
ERROR: DomainError with -3.0:
log was called with a negative real argument but will only return a complex result if called with a complex argument. Try log(Complex(x)).
Stacktrace:
 [1] throw_complex_domainerror(::Symbol, ::Float64) at ./math.jl:31
[...]

julia> log.(exp.(-1:1))
3-element Vector{Float64}:
 -1.0
  0.0
  1.0
```
"""
log(x::Number)

"""
    log2(x)

Compute the logarithm of `x` to base 2. Throws [`DomainError`](@ref) for negative
[`Real`](@ref) arguments.

See also: [`exp2`](@ref), [`ldexp`](@ref), [`ispow2`](@ref).

# Examples
```jldoctest; filter = r"Stacktrace:(\\n \\[[0-9]+\\].*)*"
julia> log2(4)
2.0

julia> log2(10)
3.321928094887362

julia> log2(-2)
ERROR: DomainError with -2.0:
log2 was called with a negative real argument but will only return a complex result if called with a complex argument. Try log2(Complex(x)).
Stacktrace:
 [1] throw_complex_domainerror(f::Symbol, x::Float64) at ./math.jl:31
[...]

julia> log2.(2.0 .^ (-1:1))
3-element Vector{Float64}:
 -1.0
  0.0
  1.0
```
"""
log2(x)

"""
    log10(x)

Compute the logarithm of `x` to base 10.
Throws [`DomainError`](@ref) for negative [`Real`](@ref) arguments.

# Examples
```jldoctest; filter = r"Stacktrace:(\\n \\[[0-9]+\\].*)*"
julia> log10(100)
2.0

julia> log10(2)
0.3010299956639812

julia> log10(-2)
ERROR: DomainError with -2.0:
log10 was called with a negative real argument but will only return a complex result if called with a complex argument. Try log10(Complex(x)).
Stacktrace:
 [1] throw_complex_domainerror(f::Symbol, x::Float64) at ./math.jl:31
[...]
```
"""
log10(x)

"""
    log1p(x)

Accurate natural logarithm of `1+x`. Throws [`DomainError`](@ref) for [`Real`](@ref)
arguments less than -1.

# Examples
```jldoctest; filter = r"Stacktrace:(\\n \\[[0-9]+\\].*)*"
julia> log1p(-0.5)
-0.6931471805599453

julia> log1p(0)
0.0

julia> log1p(-2)
ERROR: DomainError with -2.0:
log1p was called with a real argument < -1 but will only return a complex result if called with a complex argument. Try log1p(Complex(x)).
Stacktrace:
 [1] throw_complex_domainerror(::Symbol, ::Float64) at ./math.jl:31
[...]
```
"""
log1p(x)

@inline function sqrt(x::Union{Float32,Float64})
    x < zero(x) && throw_complex_domainerror(:sqrt, x)
    sqrt_llvm(x)
end

"""
    sqrt(x)

Return ``\\sqrt{x}``. Throws [`DomainError`](@ref) for negative [`Real`](@ref) arguments.
Use complex negative arguments instead. The prefix operator `√` is equivalent to `sqrt`.

See also: [`hypot`](@ref).

# Examples
```jldoctest; filter = r"Stacktrace:(\\n \\[[0-9]+\\].*)*"
julia> sqrt(big(81))
9.0

julia> sqrt(big(-81))
ERROR: DomainError with -81.0:
NaN result for non-NaN input.
Stacktrace:
 [1] sqrt(::BigFloat) at ./mpfr.jl:501
[...]

julia> sqrt(big(complex(-81)))
0.0 + 9.0im

julia> .√(1:4)
4-element Vector{Float64}:
 1.0
 1.4142135623730951
 1.7320508075688772
 2.0
```
"""
sqrt(x)

"""
    fourthroot(x)

Return the fourth root of `x` by applying `sqrt` twice successively.
"""
fourthroot(x::Number) = sqrt(sqrt(x))

"""
    hypot(x, y)

Compute the hypotenuse ``\\sqrt{|x|^2+|y|^2}`` avoiding overflow and underflow.

This code is an implementation of the algorithm described in:
An Improved Algorithm for `hypot(a,b)`
by Carlos F. Borges
The article is available online at arXiv at the link
  https://arxiv.org/abs/1904.09481

    hypot(x...)

Compute the hypotenuse ``\\sqrt{\\sum |x_i|^2}`` avoiding overflow and underflow.

See also `norm` in the [`LinearAlgebra`](@ref man-linalg) standard library.

# Examples
```jldoctest; filter = r"Stacktrace:(\\n \\[[0-9]+\\].*)*"
julia> a = Int64(10)^10;

julia> hypot(a, a)
1.4142135623730951e10

julia> √(a^2 + a^2) # a^2 overflows
ERROR: DomainError with -2.914184810805068e18:
sqrt was called with a negative real argument but will only return a complex result if called with a complex argument. Try sqrt(Complex(x)).
Stacktrace:
[...]

julia> hypot(3, 4im)
5.0

julia> hypot(-5.7)
5.7

julia> hypot(3, 4im, 12.0)
13.0

julia> using LinearAlgebra

julia> norm([a, a, a, a]) == hypot(a, a, a, a)
true
```
"""
hypot(x::Number) = abs(float(x))
hypot(x::Number, y::Number) = _hypot(promote(float(x), y)...)
hypot(x::Number, y::Number, xs::Number...) = _hypot(promote(float(x), y, xs...))
function _hypot(x, y)
    # preserves unit
    axu = abs(x)
    ayu = abs(y)

    # unitless
    ax = axu / oneunit(axu)
    ay = ayu / oneunit(ayu)

    # Return Inf if either or both inputs is Inf (Compliance with IEEE754)
    if isinf(ax) || isinf(ay)
        return typeof(axu)(Inf)
    end

    # Order the operands
    if ay > ax
        axu, ayu = ayu, axu
        ax, ay = ay, ax
    end

    # Widely varying operands
    if ay <= ax*sqrt(eps(typeof(ax))/2)  #Note: This also gets ay == 0
        return axu
    end

    # Operands do not vary widely
    scale = eps(typeof(ax))*sqrt(floatmin(ax))  #Rescaling constant
    if ax > sqrt(floatmax(ax)/2)
        ax = ax*scale
        ay = ay*scale
        scale = inv(scale)
    elseif ay < sqrt(floatmin(ax))
        ax = ax/scale
        ay = ay/scale
    else
        scale = oneunit(scale)
    end
    h = sqrt(muladd(ax, ax, ay*ay))
    # This branch is correctly rounded but requires a native hardware fma.
    if Core.Intrinsics.have_fma(typeof(h))
        hsquared = h*h
        axsquared = ax*ax
        h -= (fma(-ay, ay, hsquared-axsquared) + fma(h, h,-hsquared) - fma(ax, ax, -axsquared))/(2*h)
    # This branch is within one ulp of correctly rounded.
    else
        if h <= 2*ay
            delta = h-ay
            h -= muladd(delta, delta-2*(ax-ay), ax*(2*delta - ax))/(2*h)
        else
            delta = h-ax
            h -= muladd(delta, delta, muladd(ay, (4*delta - ay), 2*delta*(ax - 2*ay)))/(2*h)
        end
    end
    return h*scale*oneunit(axu)
end
@inline function _hypot(x::Float32, y::Float32)
    if isinf(x) || isinf(y)
        return Inf32
    end
    _x, _y = Float64(x), Float64(y)
    return Float32(sqrt(muladd(_x, _x, _y*_y)))
end
@inline function _hypot(x::Float16, y::Float16)
    if isinf(x) || isinf(y)
        return Inf16
    end
    _x, _y = Float32(x), Float32(y)
    return Float16(sqrt(muladd(_x, _x, _y*_y)))
end
_hypot(x::ComplexF16, y::ComplexF16) = Float16(_hypot(ComplexF32(x), ComplexF32(y)))

function _hypot(x::NTuple{N,<:Number}) where {N}
    maxabs = maximum(abs, x)
    if isnan(maxabs) && any(isinf, x)
        return typeof(maxabs)(Inf)
    elseif (iszero(maxabs) || isinf(maxabs))
        return maxabs
    else
        return maxabs * sqrt(sum(y -> abs2(y / maxabs), x))
    end
end

function _hypot(x::NTuple{N,<:IEEEFloat}) where {N}
    T = eltype(x)
    infT = convert(T, Inf)
    x = abs.(x) # doesn't change result but enables computational shortcuts
    # note: any() was causing this to not inline for N=3 but mapreduce() was not
    mapreduce(==(infT), |, x) && return infT # return Inf even if an argument is NaN
    maxabs = reinterpret(T, maximum(z -> reinterpret(Signed, z), x)) # for abs(::IEEEFloat) values, a ::BitInteger cast does not change the result
    maxabs > zero(T) || return maxabs # catch NaN before the @fastmath below, but also shortcut 0 since we can (remove if no more @fastmath below)
    scale,invscale = scaleinv(maxabs)
     # @fastmath(+) to allow reassociation (see #48129)
    add_fast(x, y) = Core.Intrinsics.add_float_fast(x, y) # @fastmath is not available during bootstrap
    return scale * sqrt(mapreduce(y -> abs2(y * invscale), add_fast, x))
end

atan(y::Real, x::Real) = atan(promote(float(y),float(x))...)
atan(y::T, x::T) where {T<:AbstractFloat} = Base.no_op_err("atan", T)

_isless(x::T, y::T) where {T<:AbstractFloat} = (x < y) || (signbit(x) > signbit(y))
min(x::T, y::T) where {T<:AbstractFloat} = isnan(x) || ~isnan(y) && _isless(x, y) ? x : y
max(x::T, y::T) where {T<:AbstractFloat} = isnan(x) || ~isnan(y) && _isless(y, x) ? x : y
minmax(x::T, y::T) where {T<:AbstractFloat} = min(x, y), max(x, y)

_isless(x::Float16, y::Float16) = signbit(widen(x) - widen(y))

const has_native_fminmax = Sys.ARCH === :aarch64
@static if has_native_fminmax
    @eval begin
        Base.@assume_effects :total @inline llvm_min(x::Float64, y::Float64) = ccall("llvm.minimum.f64", llvmcall, Float64, (Float64, Float64), x, y)
        Base.@assume_effects :total @inline llvm_min(x::Float32, y::Float32) = ccall("llvm.minimum.f32", llvmcall, Float32, (Float32, Float32), x, y)
        Base.@assume_effects :total @inline llvm_max(x::Float64, y::Float64) = ccall("llvm.maximum.f64", llvmcall, Float64, (Float64, Float64), x, y)
        Base.@assume_effects :total @inline llvm_max(x::Float32, y::Float32) = ccall("llvm.maximum.f32", llvmcall, Float32, (Float32, Float32), x, y)
    end
end

function min(x::T, y::T) where {T<:Union{Float32,Float64}}
    @static if has_native_fminmax
        return llvm_min(x,y)
    end
    diff = x - y
    argmin = ifelse(signbit(diff), x, y)
    anynan = isnan(x)|isnan(y)
    return ifelse(anynan, diff, argmin)
end

function max(x::T, y::T) where {T<:Union{Float32,Float64}}
    @static if has_native_fminmax
        return llvm_max(x,y)
    end
    diff = x - y
    argmax = ifelse(signbit(diff), y, x)
    anynan = isnan(x)|isnan(y)
    return ifelse(anynan, diff, argmax)
end

function minmax(x::T, y::T) where {T<:Union{Float32,Float64}}
    @static if has_native_fminmax
        return llvm_min(x, y), llvm_max(x, y)
    end
    diff = x - y
    sdiff = signbit(diff)
    min, max = ifelse(sdiff, x, y), ifelse(sdiff, y, x)
    anynan = isnan(x)|isnan(y)
    return ifelse(anynan, diff, min), ifelse(anynan, diff, max)
end

"""
    ldexp(x, n)

Compute ``x \\times 2^n``.

# Examples
```jldoctest
julia> ldexp(5., 2)
20.0
```
"""
function ldexp(x::T, e::Integer) where T<:IEEEFloat
    xu = reinterpret(Unsigned, x)
    xs = xu & ~sign_mask(T)
    xs >= exponent_mask(T) && return x # NaN or Inf
    k = (xs >> significand_bits(T)) % Int
    if k == 0 # x is subnormal
        xs == 0 && return x # +-0
        m = leading_zeros(xs) - exponent_bits(T)
        ys = xs << unsigned(m)
        xu = ys | (xu & sign_mask(T))
        k = 1 - m
        # underflow, otherwise may have integer underflow in the following n + k
        e < -50000 && return flipsign(T(0.0), x)
    end
    # For cases where e of an Integer larger than Int make sure we properly
    # overflow/underflow; this is optimized away otherwise.
    if e > typemax(Int)
        return flipsign(T(Inf), x)
    elseif e < typemin(Int)
        return flipsign(T(0.0), x)
    end
    n = e % Int
    k += n
    # overflow, if k is larger than maximum possible exponent
    if k >= exponent_raw_max(T)
        return flipsign(T(Inf), x)
    end
    if k > 0 # normal case
        xu = (xu & ~exponent_mask(T)) | (rem(k, uinttype(T)) << significand_bits(T))
        return reinterpret(T, xu)
    else # subnormal case
        if k <= -significand_bits(T) # underflow
            # overflow, for the case of integer overflow in n + k
            e > 50000 && return flipsign(T(Inf), x)
            return flipsign(T(0.0), x)
        end
        k += significand_bits(T)
        # z = T(2.0) ^ (-significand_bits(T))
        z = reinterpret(T, rem(exponent_bias(T)-significand_bits(T), uinttype(T)) << significand_bits(T))
        xu = (xu & ~exponent_mask(T)) | (rem(k, uinttype(T)) << significand_bits(T))
        return z*reinterpret(T, xu)
    end
end
ldexp(x::Float16, q::Integer) = Float16(ldexp(Float32(x), q))

"""
    exponent(x) -> Int

Returns the largest integer `y` such that `2^y ≤ abs(x)`.
For a normalized floating-point number `x`, this corresponds to the exponent of `x`.

# Examples
```jldoctest
julia> exponent(8)
3

julia> exponent(64//1)
6

julia> exponent(6.5)
2

julia> exponent(16.0)
4

julia> exponent(3.142e-4)
-12
```
"""
function exponent(x::T) where T<:IEEEFloat
    @noinline throw1(x) = throw(DomainError(x, "Cannot be NaN or Inf."))
    @noinline throw2(x) = throw(DomainError(x, "Cannot be ±0.0."))
    xs = reinterpret(Unsigned, x) & ~sign_mask(T)
    xs >= exponent_mask(T) && throw1(x)
    k = Int(xs >> significand_bits(T))
    if k == 0 # x is subnormal
        xs == 0 && throw2(x)
        m = leading_zeros(xs) - exponent_bits(T)
        k = 1 - m
    end
    return k - exponent_bias(T)
end

# Like exponent, but assumes the nothrow precondition. For
# internal use only. Could be written as
# @assume_effects :nothrow exponent()
# but currently this form is easier on the compiler.
function _exponent_finite_nonzero(x::T) where T<:IEEEFloat
    # @precond :nothrow !isnan(x) && !isinf(x) && !iszero(x)
    xs = reinterpret(Unsigned, x) & ~sign_mask(T)
    k = rem(xs >> significand_bits(T), Int)
    if k == 0 # x is subnormal
        m = leading_zeros(xs) - exponent_bits(T)
        k = 1 - m
    end
    return k - exponent_bias(T)
end

"""
    significand(x)

Extract the significand (a.k.a. mantissa) of a floating-point number. If `x` is
a non-zero finite number, then the result will be a number of the same type and
sign as `x`, and whose absolute value is on the interval ``[1,2)``. Otherwise
`x` is returned.

# Examples
```jldoctest
julia> significand(15.2)
1.9

julia> significand(-15.2)
-1.9

julia> significand(-15.2) * 2^3
-15.2

julia> significand(-Inf), significand(Inf), significand(NaN)
(-Inf, Inf, NaN)
```
"""
function significand(x::T) where T<:IEEEFloat
    xu = reinterpret(Unsigned, x)
    xs = xu & ~sign_mask(T)
    xs >= exponent_mask(T) && return x # NaN or Inf
    if xs <= (~exponent_mask(T) & ~sign_mask(T)) # x is subnormal
        xs == 0 && return x # +-0
        m = unsigned(leading_zeros(xs) - exponent_bits(T))
        xs <<= m
        xu = xs | (xu & sign_mask(T))
    end
    xu = (xu & ~exponent_mask(T)) | exponent_one(T)
    return reinterpret(T, xu)
end

"""
    frexp(val)

Return `(x,exp)` such that `x` has a magnitude in the interval ``[1/2, 1)`` or 0,
and `val` is equal to ``x \\times 2^{exp}``.
# Examples
```jldoctest
julia> frexp(12.8)
(0.8, 4)
```
"""
function frexp(x::T) where T<:IEEEFloat
    xu = reinterpret(Unsigned, x)
    xs = xu & ~sign_mask(T)
    xs >= exponent_mask(T) && return x, 0 # NaN or Inf
    k = Int(xs >> significand_bits(T))
    if k == 0 # x is subnormal
        xs == 0 && return x, 0 # +-0
        m = leading_zeros(xs) - exponent_bits(T)
        xs <<= unsigned(m)
        xu = xs | (xu & sign_mask(T))
        k = 1 - m
    end
    k -= (exponent_bias(T) - 1)
    xu = (xu & ~exponent_mask(T)) | exponent_half(T)
    return reinterpret(T, xu), k
end

"""
    $(@__MODULE__).scaleinv(x)

Compute `(scale, invscale)` where `scale` and `invscale` are non-subnormal
(https://en.wikipedia.org/wiki/Subnormal_number) finite powers of two such that
`scale * invscale == 1` and `scale` is roughly on the order of `abs(x)`.
Inf, NaN, and zero inputs also result in finite nonzero outputs.
These values are useful to scale computations to prevent overflow and underflow
without round-off errors or division.

UNSTABLE DETAIL: For `x isa IEEEFLoat`, `scale` is chosen to be the
`prevpow(2,abs(x))` when possible, but is never less than floatmin(x) or greater
than inv(floatmin(x)). `Inf` and `NaN` resolve to `inv(floatmin(x))`. This
behavior is subject to change.

# Examples
```jldoctest
julia> $(@__MODULE__).scaleinv(7.5)
(4.0, 0.25)
```
"""
function scaleinv(x::T) where T<:IEEEFloat
    # by removing the sign and significand and restricting values to a limited range,
    # we can invert a number using bit-twiddling instead of division
    U = uinttype(T)
    umin = reinterpret(U, floatmin(T))
    umax = reinterpret(U, inv(floatmin(T)))
    emask = exponent_mask(T) # used to strip sign and significand
    u = clamp(reinterpret(U, x) & emask, umin, umax)
    scale = reinterpret(T, u)
    invscale = reinterpret(T, umin + umax - u) # inv(scale)
    return scale, invscale
end

# NOTE: This `rem` method is adapted from the msun `remainder` and `remainderf`
# functions, which are under the following license:
#
# Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
#
# Developed at SunSoft, a Sun Microsystems, Inc. business.
# Permission to use, copy, modify, and distribute this
# software is freely granted, provided that this notice
# is preserved.
function rem(x::T, p::T, ::RoundingMode{:Nearest}) where T<:IEEEFloat
    (iszero(p) || !isfinite(x) || isnan(p)) && return T(NaN)
    x == p && return copysign(zero(T), x)
    oldx = x
    x = abs(rem(x, 2p))  # 2p may overflow but that's okay
    p = abs(p)
    if p < 2 * floatmin(T)  # Check whether dividing p by 2 will underflow
        if 2x > p
            x -= p
            if 2x >= p
                x -= p
            end
        end
    else
        p_half = p / 2
        if x > p_half
            x -= p
            if x >= p_half
                x -= p
            end
        end
    end
    return flipsign(x, oldx)
end


"""
    modf(x)

Return a tuple `(fpart, ipart)` of the fractional and integral parts of a number. Both parts
have the same sign as the argument.

# Examples
```jldoctest
julia> modf(3.5)
(0.5, 3.0)

julia> modf(-3.5)
(-0.5, -3.0)
```
"""
modf(x) = isinf(x) ? (flipsign(zero(x), x), x) : (rem(x, one(x)), trunc(x))

function modf(x::T) where T<:IEEEFloat
    isinf(x) && return (copysign(zero(T), x), x)
    ix = trunc(x)
    rx = copysign(x - ix, x)
    return (rx, ix)
end

# @constprop aggressive to help the compiler see the switch between the integer and float
# variants for callers with constant `y`
@constprop :aggressive function ^(x::Float64, y::Float64)
    xu = reinterpret(UInt64, x)
    xu == reinterpret(UInt64, 1.0) && return 1.0
    # Exponents greater than this will always overflow or underflow.
    # Note that NaN can pass through this, but that will end up fine.
    if !(abs(y)<0x1.8p62)
        isnan(y) && return y
        y = sign(y)*0x1.8p62
    end
    yint = unsafe_trunc(Int64, y) # This is actually safe since julia freezes the result
    y == yint && return @noinline x^yint
    2*xu==0 && return abs(y)*Inf*(!(y>0)) # if x==0
    x<0 && throw_exp_domainerror(x) # |y| is small enough that y isn't an integer
    !isfinite(x) && return x*(y>0 || isnan(x))           # x is inf or NaN
    if xu < (UInt64(1)<<52) # x is subnormal
        xu = reinterpret(UInt64, x * 0x1p52) # normalize x
        xu &= ~sign_mask(Float64)
        xu -= UInt64(52) << 52 # mess with the exponent
    end
    return pow_body(xu, y)
end

@inline function pow_body(xu::UInt64, y::Float64)
    logxhi,logxlo = Base.Math._log_ext(xu)
    xyhi, xylo = two_mul(logxhi,y)
    xylo = muladd(logxlo, y, xylo)
    hi = xyhi+xylo
    return Base.Math.exp_impl(hi, xylo-(hi-xyhi), Val(:ℯ))
end

@constprop :aggressive function ^(x::T, y::T) where T <: Union{Float16, Float32}
    x == 1 && return one(T)
    # Exponents greater than this will always overflow or underflow.
    # Note that NaN can pass through this, but that will end up fine.
    max_exp = T == Float16 ? T(3<<14) : T(0x1.Ap30)
    if !(abs(y)<max_exp)
        isnan(y) && return y
        y = sign(y)*max_exp
    end
    yint = unsafe_trunc(Int32, y) # This is actually safe since julia freezes the result
    y == yint && return x^yint
    x < 0 && throw_exp_domainerror(x)
    !isfinite(x) && return x*(y>0 || isnan(x))
    x==0 && return abs(y)*T(Inf)*(!(y>0))
    return pow_body(x, y)
end

@inline function pow_body(x::T, y::T) where T <: Union{Float16, Float32}
    return T(exp2(log2(abs(widen(x))) * y))
end

# compensated power by squaring
@constprop :aggressive @inline function ^(x::Float64, n::Integer)
    n == 0 && return one(x)
    return pow_body(x, n)
end

@assume_effects :terminates_locally @noinline function pow_body(x::Float64, n::Integer)
    y = 1.0
    xnlo = ynlo = 0.0
    n == 3 && return x*x*x # keep compatibility with literal_pow
    if n < 0
        rx = inv(x)
        n==-2 && return rx*rx #keep compatibility with literal_pow
        isfinite(x) && (xnlo = -fma(x, rx, -1.) * rx)
        x = rx
        n = -n
    end
    while n > 1
        if n&1 > 0
            err = muladd(y, xnlo, x*ynlo)
            y, ynlo = two_mul(x,y)
            ynlo += err
        end
        err = x*2*xnlo
        x, xnlo = two_mul(x, x)
        xnlo += err
        n >>>= 1
    end
    err = muladd(y, xnlo, x*ynlo)
    return ifelse(isfinite(x) & isfinite(err), muladd(x, y, err), x*y)
end

function ^(x::Float32, n::Integer)
    n == -2 && return (i=inv(x); i*i)
    n == 3 && return x*x*x #keep compatibility with literal_pow
    n < 0 && return Float32(Base.power_by_squaring(inv(Float64(x)),-n))
    Float32(Base.power_by_squaring(Float64(x),n))
end
@inline ^(x::Float16, y::Integer) = Float16(Float32(x) ^ y)
@inline literal_pow(::typeof(^), x::Float16, ::Val{p}) where {p} = Float16(literal_pow(^,Float32(x),Val(p)))

## rem2pi-related calculations ##

function add22condh(xh::Float64, xl::Float64, yh::Float64, yl::Float64)
    # This algorithm, due to Dekker, computes the sum of two
    # double-double numbers and returns the high double. References:
    # [1] http://www.digizeitschriften.de/en/dms/img/?PID=GDZPPN001170007
    # [2] https://doi.org/10.1007/BF01397083
    r = xh+yh
    s = (abs(xh) > abs(yh)) ? (xh-r+yh+yl+xl) : (yh-r+xh+xl+yl)
    zh = r+s
    return zh
end

# multiples of pi/2, as double-double (ie with "tail")
const pi1o2_h  = 1.5707963267948966     # convert(Float64, pi * BigFloat(1/2))
const pi1o2_l  = 6.123233995736766e-17  # convert(Float64, pi * BigFloat(1/2) - pi1o2_h)

const pi2o2_h  = 3.141592653589793      # convert(Float64, pi * BigFloat(1))
const pi2o2_l  = 1.2246467991473532e-16 # convert(Float64, pi * BigFloat(1) - pi2o2_h)

const pi3o2_h  = 4.71238898038469       # convert(Float64, pi * BigFloat(3/2))
const pi3o2_l  = 1.8369701987210297e-16 # convert(Float64, pi * BigFloat(3/2) - pi3o2_h)

const pi4o2_h  = 6.283185307179586      # convert(Float64, pi * BigFloat(2))
const pi4o2_l  = 2.4492935982947064e-16 # convert(Float64, pi * BigFloat(2) - pi4o2_h)

"""
    rem2pi(x, r::RoundingMode)

Compute the remainder of `x` after integer division by `2π`, with the quotient rounded
according to the rounding mode `r`. In other words, the quantity

    x - 2π*round(x/(2π),r)

without any intermediate rounding. This internally uses a high precision approximation of
2π, and so will give a more accurate result than `rem(x,2π,r)`

- if `r == RoundNearest`, then the result is in the interval ``[-π, π]``. This will generally
  be the most accurate result. See also [`RoundNearest`](@ref).

- if `r == RoundToZero`, then the result is in the interval ``[0, 2π]`` if `x` is positive,.
  or ``[-2π, 0]`` otherwise. See also [`RoundToZero`](@ref).

- if `r == RoundDown`, then the result is in the interval ``[0, 2π]``.
  See also [`RoundDown`](@ref).
- if `r == RoundUp`, then the result is in the interval ``[-2π, 0]``.
  See also [`RoundUp`](@ref).

# Examples
```jldoctest
julia> rem2pi(7pi/4, RoundNearest)
-0.7853981633974485

julia> rem2pi(7pi/4, RoundDown)
5.497787143782138
```
"""
function rem2pi end
function rem2pi(x::Float64, ::RoundingMode{:Nearest})
    isnan(x) && return x
    isinf(x) && return NaN

    abs(x) < pi && return x

    n,y = rem_pio2_kernel(x)

    if iseven(n)
        if n & 2 == 2 # n % 4 == 2: add/subtract pi
            if y.hi <= 0
                return add22condh(y.hi,y.lo,pi2o2_h,pi2o2_l)
            else
                return add22condh(y.hi,y.lo,-pi2o2_h,-pi2o2_l)
            end
        else          # n % 4 == 0: add 0
            return y.hi+y.lo
        end
    else
        if n & 2 == 2 # n % 4 == 3: subtract pi/2
            return add22condh(y.hi,y.lo,-pi1o2_h,-pi1o2_l)
        else          # n % 4 == 1: add pi/2
            return add22condh(y.hi,y.lo,pi1o2_h,pi1o2_l)
        end
    end
end
function rem2pi(x::Float64, ::RoundingMode{:ToZero})
    isnan(x) && return x
    isinf(x) && return NaN

    ax = abs(x)
    ax <= 2*Float64(pi,RoundDown) && return x

    n,y = rem_pio2_kernel(ax)

    if iseven(n)
        if n & 2 == 2 # n % 4 == 2: add pi
            z = add22condh(y.hi,y.lo,pi2o2_h,pi2o2_l)
        else          # n % 4 == 0: add 0 or 2pi
            if y.hi > 0
                z = y.hi+y.lo
            else      # negative: add 2pi
                z = add22condh(y.hi,y.lo,pi4o2_h,pi4o2_l)
            end
        end
    else
        if n & 2 == 2 # n % 4 == 3: add 3pi/2
            z = add22condh(y.hi,y.lo,pi3o2_h,pi3o2_l)
        else          # n % 4 == 1: add pi/2
            z = add22condh(y.hi,y.lo,pi1o2_h,pi1o2_l)
        end
    end
    copysign(z,x)
end
function rem2pi(x::Float64, ::RoundingMode{:Down})
    isnan(x) && return x
    isinf(x) && return NaN

    if x < pi4o2_h
        if x >= 0
            return x
        elseif x > -pi4o2_h
            return add22condh(x,0.0,pi4o2_h,pi4o2_l)
        end
    end

    n,y = rem_pio2_kernel(x)

    if iseven(n)
        if n & 2 == 2 # n % 4 == 2: add pi
            return add22condh(y.hi,y.lo,pi2o2_h,pi2o2_l)
        else          # n % 4 == 0: add 0 or 2pi
            if y.hi > 0
                return y.hi+y.lo
            else      # negative: add 2pi
                return add22condh(y.hi,y.lo,pi4o2_h,pi4o2_l)
            end
        end
    else
        if n & 2 == 2 # n % 4 == 3: add 3pi/2
            return add22condh(y.hi,y.lo,pi3o2_h,pi3o2_l)
        else          # n % 4 == 1: add pi/2
            return add22condh(y.hi,y.lo,pi1o2_h,pi1o2_l)
        end
    end
end
function rem2pi(x::Float64, ::RoundingMode{:Up})
    isnan(x) && return x
    isinf(x) && return NaN

    if x > -pi4o2_h
        if x <= 0
            return x
        elseif x < pi4o2_h
            return add22condh(x,0.0,-pi4o2_h,-pi4o2_l)
        end
    end

    n,y = rem_pio2_kernel(x)

    if iseven(n)
        if n & 2 == 2 # n % 4 == 2: sub pi
            return add22condh(y.hi,y.lo,-pi2o2_h,-pi2o2_l)
        else          # n % 4 == 0: sub 0 or 2pi
            if y.hi < 0
                return y.hi+y.lo
            else      # positive: sub 2pi
                return add22condh(y.hi,y.lo,-pi4o2_h,-pi4o2_l)
            end
        end
    else
        if n & 2 == 2 # n % 4 == 3: sub pi/2
            return add22condh(y.hi,y.lo,-pi1o2_h,-pi1o2_l)
        else          # n % 4 == 1: sub 3pi/2
            return add22condh(y.hi,y.lo,-pi3o2_h,-pi3o2_l)
        end
    end
end

rem2pi(x::Float32, r::RoundingMode) = Float32(rem2pi(Float64(x), r))
rem2pi(x::Float16, r::RoundingMode) = Float16(rem2pi(Float64(x), r))
rem2pi(x::Int32, r::RoundingMode) = rem2pi(Float64(x), r)
function rem2pi(x::Int64, r::RoundingMode)
    fx = Float64(x)
    fx == x || throw(ArgumentError("Int64 argument to rem2pi is too large: $x"))
    rem2pi(fx, r)
end

"""
    mod2pi(x)

Modulus after division by `2π`, returning in the range ``[0,2π)``.

This function computes a floating point representation of the modulus after division by
numerically exact `2π`, and is therefore not exactly the same as `mod(x,2π)`, which would
compute the modulus of `x` relative to division by the floating-point number `2π`.

!!! note
    Depending on the format of the input value, the closest representable value to 2π may
    be less than 2π. For example, the expression `mod2pi(2π)` will not return `0`, because
    the intermediate value of `2*π` is a `Float64` and `2*Float64(π) < 2*big(π)`. See
    [`rem2pi`](@ref) for more refined control of this behavior.

# Examples
```jldoctest
julia> mod2pi(9*pi/4)
0.7853981633974481
```
"""
mod2pi(x) = rem2pi(x,RoundDown)

# generic fallback; for number types, promotion.jl does promotion

"""
    muladd(x, y, z)

Combined multiply-add: computes `x*y+z`, but allowing the add and multiply to be merged
with each other or with surrounding operations for performance.
For example, this may be implemented as an [`fma`](@ref) if the hardware supports it
efficiently.
The result can be different on different machines and can also be different on the same machine
due to constant propagation or other optimizations.
See [`fma`](@ref).

# Examples
```jldoctest
julia> muladd(3, 2, 1)
7

julia> 3 * 2 + 1
7
```
"""
muladd(x,y,z) = x*y+z


# helper functions for Libm functionality

"""
    highword(x)

Return the high word of `x` as a `UInt32`.
"""
@inline highword(x::Float64) = highword(reinterpret(UInt64, x))
@inline highword(x::UInt64)  = (x >>> 32) % UInt32
@inline highword(x::Float32) = reinterpret(UInt32, x)

@inline fromhighword(::Type{Float64}, u::UInt32) = reinterpret(Float64, UInt64(u) << 32)
@inline fromhighword(::Type{Float32}, u::UInt32) = reinterpret(Float32, u)


"""
    poshighword(x)

Return positive part of the high word of `x` as a `UInt32`.
"""
@inline poshighword(x::Float64) = poshighword(reinterpret(UInt64, x))
@inline poshighword(x::UInt64)  = highword(x) & 0x7fffffff
@inline poshighword(x::Float32) = highword(x) & 0x7fffffff

# More special functions
include("special/cbrt.jl")
include("special/exp.jl")
include("special/hyperbolic.jl")
include("special/trig.jl")
include("special/rem_pio2.jl")
include("special/log.jl")


# Float16 definitions

for func in (:sin,:cos,:tan,:asin,:acos,:atan,:cosh,:tanh,:asinh,:acosh,
             :atanh,:log,:log2,:log10,:sqrt,:fourthroot,:log1p)
    @eval begin
        $func(a::Float16) = Float16($func(Float32(a)))
        $func(a::ComplexF16) = ComplexF16($func(ComplexF32(a)))
    end
end

for func in (:exp,:exp2,:exp10,:sinh)
     @eval $func(a::ComplexF16) = ComplexF16($func(ComplexF32(a)))
end


atan(a::Float16,b::Float16) = Float16(atan(Float32(a),Float32(b)))
sincos(a::Float16) = Float16.(sincos(Float32(a)))

for f in (:sin, :cos, :tan, :asin, :atan, :acos,
          :sinh, :cosh, :tanh, :asinh, :acosh, :atanh,
          :exp, :exp2, :exp10, :expm1, :log, :log2, :log10, :log1p,
          :exponent, :sqrt, :cbrt, :sinpi, :cospi, :sincospi, :tanpi)
    @eval function ($f)(x::Real)
        xf = float(x)
        x === xf && throw(MethodError($f, (x,)))
        return ($f)(xf)
    end
    @eval $(f)(::Missing) = missing
end

for f in (:atan, :hypot, :log)
    @eval $(f)(::Missing, ::Missing) = missing
    @eval $(f)(::Number, ::Missing) = missing
    @eval $(f)(::Missing, ::Number) = missing
end

exp2(x::AbstractFloat) = 2^x
exp10(x::AbstractFloat) = 10^x
clamp(::Missing, lo, hi) = missing
fourthroot(::Missing) = missing

end # module
S   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/special/cbrt.jl+      # This file is a part of Julia. License is MIT: https://julialang.org/license

# Float32/Float64 based on C implementations from FDLIBM (http://www.netlib.org/fdlibm/)
# and FreeBSD:
#
## ====================================================
## Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
##
## Developed at SunPro, a Sun Microsystems, Inc. business.
## Permission to use, copy, modify, and distribute this
## software is freely granted, provided that this notice
## is preserved.
## ====================================================
## Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
## Debugged and optimized by Bruce D. Evans.

"""
    cbrt(x::Real)

Return the cube root of `x`, i.e. ``x^{1/3}``. Negative values are accepted
(returning the negative real root when ``x < 0``).

The prefix operator `∛` is equivalent to `cbrt`.

# Examples
```jldoctest
julia> cbrt(big(27))
3.0

julia> cbrt(big(-27))
-3.0
```
"""
cbrt(x::AbstractFloat) = x < 0 ? -(-x)^(1//3) : x^(1//3)

"""
    _approx_cbrt(x)

Approximate `cbrt` to 5 bits precision

    cbrt(2^e * (1+m)) ≈ 2^(e÷3) * (1 + (e%3+m)÷3)

where:
 - `e` is integral and >= 0
 - `m` is real and in [0, 1),
 - `÷` is integer division
 - `%` is integer remainder

The RHS is always >= the LHS and has a maximum relative error of about 1 in 16.
Adding a bias of -0.03306235651 to the `(e%3+m)÷3` term reduces the error to about 1 in
32.

With the IEEE floating point representation, for finite positive normal values, ordinary
integer division of the value in bits magically gives almost exactly the RHS of the above
provided we first subtract the exponent bias and later add it back.  We do the
subtraction virtually to keep e >= 0 so that ordinary integer division rounds towards
minus infinity; this is also efficient. All operations can be done in 32-bit.

These implementations assume that NaNs, infinities and zeros have already been filtered.
"""
@inline function _approx_cbrt(x::T) where {T<:Union{Float32,Float64}}
    # floor(UInt32, adj * exp2(k)) should be evaluated to 2 constants.
    adj = exponent_bias(T)*2/3 - 0.03306235651
    k = significand_bits(T) - (8*sizeof(T) - 32)

    u = highword(x) & 0x7fff_ffff
    if u >= Base.Math.highword(floatmin(T))
        v = div(u, UInt32(3)) + floor(UInt32, adj * exp2(k))
    else
        # subnormal
        x *= maxintfloat(T)
        adj -= exponent(maxintfloat(T))/3
        u = highword(x) & 0x7fff_ffff
        v = div(u, UInt32(3)) + floor(UInt32, adj * exp2(k))
    end
    return copysign(fromhighword(T, v), x)
end

@inline function _improve_cbrt(x::Float32, t::Float32)
    # Newton iterations solving
    #   t^2 - x/t == 0
    # with update
    #   t <- t*(t^3 + 2*x)/(2*t^3 + x)

    # Use double precision so that its terms can be arranged for efficiency
    # without causing overflow or underflow.
    xx = Float64(x)
    tt = Float64(t)

    # 1st step: 16 bits accuracy
    tt3 = tt^3
    tt *= (2*xx + tt3)/(x + 2*tt3)

    # 2nd step: 47 bits accuracy
    tt3 = tt^3
    tt *= (2*xx + tt3)/(x + 2*tt3)

    return Float32(tt)
end

@inline function _improve_cbrt(x::Float64, t::Float64)
    # cbrt to 23 bits:
    #
    #    cbrt(x) = t * cbrt(x / t^3) ~= t * P(t^3 / x)
    #
    # where P(r) is a polynomial of degree 4 that approximates 1/cbrt(r)
    # to within 2^-23.5 when |r - 1| < 1/10.  The rough approximation
    # has produced t such than |t/cbrt(x) - 1| ~< 1/32, and cubing this
    # gives us bounds for r = t^3/x.

    r = (t*t)*(t/x)
    t *= (@horner(r, 1.87595182427177009643, -1.88497979543377169875, 1.621429720105354466140) +
          r^3 * @horner(r, -0.758397934778766047437, 0.145996192886612446982))

    # Round t away from zero to 23 bits (sloppily except for ensuring that
    # the result is larger in magnitude than cbrt(x) but not much more than
    # 2 23-bit ulps larger).  With rounding towards zero, the error bound
    # would be ~5/6 instead of ~4/6.  With a maximum error of 2 23-bit ulps
    # in the rounded t, the infinite-precision error in the Newton
    # approximation barely affects third digit in the final error
    # 0.667; the error in the rounded t can be up to about 3 23-bit ulps
    # before the final error is larger than 0.667 ulps.

    u = reinterpret(UInt64, t)
    u = (u + 0x8000_0000) & UInt64(0xffff_ffff_c000_0000)
    t = reinterpret(Float64, u)

    # one step Newton iteration solving
    #   t^3 - x == 0
    # with update
    #   t <- t + t * (x/t^2 - t) / (3*t)

    # to 53 bits with error < 0.667 ulps
    s = t*t             # t*t is exact
    r = x/s             # error <= 0.5 ulps; |r| < |t|
    w = t+t             # t+t is exact
    r = (r - t)/(w + r) # r-t is exact; w+r ~= 3*t
    t = muladd(t, r, t) # error <= 0.5 + 0.5/3 + epsilon
    return t
end

function cbrt(x::Union{Float32,Float64})
    if !isfinite(x) || iszero(x)
        return x
    end
    t = _approx_cbrt(x)
    return _improve_cbrt(x, t)
end

function cbrt(a::Float16)
    if !isfinite(a) || iszero(a)
        return a
    end
    x = Float32(a)

    # 5 bit approximation. Simpler than _approx_cbrt since subnormals can not appear
    u = highword(x) & 0x7fff_ffff
    v = div(u, UInt32(3)) + 0x2a5119f2
    t = copysign(fromhighword(Float32, v), x)

    # 2 newton iterations
    t = 0.33333334f0 * (2f0*t + x/(t*t))
    t = 0.33333334f0 * (2f0*t + x/(t*t))
    return Float16(t)
end
R   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/special/exp.jlZ      # This file is a part of Julia. License is MIT: https://julialang.org/license

# magic rounding constant: 1.5*2^52 Adding, then subtracting it from a float rounds it to an Int.
# This works because eps(MAGIC_ROUND_CONST(T)) == one(T), so adding it to a smaller number aligns the lsb to the 1s place.
# Values for which this trick doesn't work are going to have outputs of 0 or Inf.
MAGIC_ROUND_CONST(::Type{Float64}) = 6.755399441055744e15
MAGIC_ROUND_CONST(::Type{Float32}) = 1.048576f7

# max, min, and subnormal arguments
# max_exp = T(exponent_bias(T)*log(base, big(2)) + log(base, 2 - big(2.0)^-significand_bits(T)))
MAX_EXP(n::Val{2}, ::Type{Float32}) = 128.0f0
MAX_EXP(n::Val{2}, ::Type{Float64}) = 1024.0
MAX_EXP(n::Val{:ℯ}, ::Type{Float32}) = 88.72284f0
MAX_EXP(n::Val{:ℯ}, ::Type{Float64}) = 709.7827128933841
MAX_EXP(n::Val{10}, ::Type{Float32}) = 38.53184f0
MAX_EXP(n::Val{10}, ::Type{Float64}) = 308.25471555991675

# min_exp = T(-(exponent_bias(T)+significand_bits(T)) * log(base, big(2)))
MIN_EXP(n::Val{2}, ::Type{Float32}) = -150.0f0
MIN_EXP(n::Val{2}, ::Type{Float64}) = -1075.0
MIN_EXP(n::Val{:ℯ}, ::Type{Float32}) = -103.97208f0
MIN_EXP(n::Val{:ℯ}, ::Type{Float64}) = -745.1332191019412
MIN_EXP(n::Val{10}, ::Type{Float32}) = -45.1545f0
MIN_EXP(n::Val{10}, ::Type{Float64}) = -323.60724533877976

# subnorm_exp = abs(log(base, floatmin(T)))
# these vals are positive since it's easier to take abs(x) than -abs(x)
SUBNORM_EXP(n::Val{2}, ::Type{Float32}) = 126.00001f0
SUBNORM_EXP(n::Val{2}, ::Type{Float64}) = 1022.0
SUBNORM_EXP(n::Val{:ℯ}, ::Type{Float32}) = 87.33655f0
SUBNORM_EXP(n::Val{:ℯ}, ::Type{Float64}) = 708.3964185322641
SUBNORM_EXP(n::Val{10}, ::Type{Float32}) = 37.92978f0
SUBNORM_EXP(n::Val{10}, ::Type{Float64}) = 307.6526555685887

# 256/log(base, 2) (For Float64 reductions)
LogBo256INV(::Val{2}, ::Type{Float64}) = 256.0
LogBo256INV(::Val{:ℯ}, ::Type{Float64}) = 369.3299304675746
LogBo256INV(::Val{10}, ::Type{Float64}) = 850.4135922911647

# -log(base, 2)/256 in upper and lower bits
# Upper is truncated to only have 34 bits of significand since N has at most
# ceil(log2(-MIN_EXP(base, Float64)*LogBo256INV(Val(2), Float64))) = 19 bits.
# This ensures no rounding when multiplying LogBo256U*N for FMAless hardware
LogBo256U(::Val{2}, ::Type{Float64}) = -0.00390625
LogBo256U(::Val{:ℯ}, ::Type{Float64}) = -0.002707606173999011
LogBo256U(::Val{10}, ::Type{Float64}) = -0.0011758984204561784
LogBo256L(::Val{2}, ::Type{Float64}) = 0.0
LogBo256L(::Val{:ℯ}, ::Type{Float64}) = -6.327543041662719e-14
LogBo256L(::Val{10}, ::Type{Float64}) = -1.0624811566412999e-13

# 1/log(base, 2) (For Float32 reductions)
LogBINV(::Val{2}, ::Type{Float32}) = 1.0f0
LogBINV(::Val{:ℯ}, ::Type{Float32}) = 1.442695f0
LogBINV(::Val{10}, ::Type{Float32}) = 3.321928f0

# -log(base, 2) in upper and lower bits
# Upper is truncated to only have 16 bits of significand since N has at most
# ceil(log2(-MIN_EXP(n, Float32)*LogBINV(Val(2), Float32))) = 8 bits.
# This ensures no rounding when multiplying LogBU*N for FMAless hardware
LogBU(::Val{2}, ::Type{Float32}) = -1.0f0
LogBU(::Val{:ℯ}, ::Type{Float32}) = -0.69314575f0
LogBU(::Val{10}, ::Type{Float32}) = -0.3010254f0
LogBL(::Val{2}, ::Type{Float32}) = 0.0f0
LogBL(::Val{:ℯ}, ::Type{Float32}) = -1.4286068f-6
LogBL(::Val{10}, ::Type{Float32}) = -4.605039f-6

# -log(base, 2) as a Float32 for Float16 version.
LogB(::Val{2}, ::Type{Float16}) = -1.0f0
LogB(::Val{:ℯ}, ::Type{Float16}) = -0.6931472f0
LogB(::Val{10}, ::Type{Float16}) = -0.30103f0

# Range reduced kernels
function expm1b_kernel(::Val{2}, x::Float64)
    return x * evalpoly(x, (0.6931471805599393, 0.24022650695910058,
                            0.05550411502333161, 0.009618129548366803))
end
function expm1b_kernel(::Val{:ℯ}, x::Float64)
    return x * evalpoly(x, (0.9999999999999912, 0.4999999999999997,
                            0.1666666857598779, 0.04166666857598777))
end
function expm1b_kernel(::Val{10}, x::Float64)
    return x * evalpoly(x, (2.3025850929940255, 2.6509490552391974,
                            2.034678825384765, 1.1712552025835192))
end

function expb_kernel(::Val{2}, x::Float32)
    return evalpoly(x, (1.0f0, 0.6931472f0, 0.2402265f0,
                        0.05550411f0, 0.009618025f0,
                        0.0013333423f0, 0.00015469732f0, 1.5316464f-5))
end
function expb_kernel(::Val{:ℯ}, x::Float32)
    return evalpoly(x, (1.0f0, 1.0f0, 0.5f0, 0.16666667f0,
                        0.041666217f0, 0.008333249f0,
                        0.001394858f0, 0.00019924171f0))
end
function expb_kernel(::Val{10}, x::Float32)
    return evalpoly(x, (1.0f0, 2.3025851f0, 2.650949f0,
                        2.0346787f0, 1.1712426f0, 0.53937745f0,
                        0.20788547f0, 0.06837386f0))
end

# Table stores data with 60 sig figs by using the fact that the first 12 bits of all the
# values would be the same if stored as regular Float64.
# This only gains 8 bits since the least significant 4 bits of the exponent
# of the small part are not the same for all table entries
const JU_MASK = typemax(UInt64)>>12
const JL_MASK = typemax(UInt64)>>8
const JU_CONST = 0x3FF0000000000000
const JL_CONST = 0x3C00000000000000


#function make_table(size)
#    t_array = zeros(UInt64, size);
#    for j in 1:size
#        val = 2.0^(BigFloat(j-1)/size)
#        valU = Float64(val, RoundDown)
#        valL = Float64(val-valU)
#        valU = reinterpret(UInt64, valU) & JU_MASK
#        valL = ((reinterpret(UInt64, valL) & JL_MASK)>>44)<<52
#        t_array[j] = valU | valL
#    end
#    return Tuple(t_array)
#end
#const J_TABLE = make_table(256);
const J_TABLE = (0x0000000000000000, 0xaac00b1afa5abcbe, 0x9b60163da9fb3335, 0xab502168143b0280, 0xadc02c9a3e778060,
                 0x656037d42e11bbcc, 0xa7a04315e86e7f84, 0x84c04e5f72f654b1, 0x8d7059b0d3158574, 0xa510650a0e3c1f88,
                 0xa8d0706b29ddf6dd, 0x83207bd42b72a836, 0x6180874518759bc8, 0xa4b092bdf66607df, 0x91409e3ecac6f383,
                 0x85d0a9c79b1f3919, 0x98a0b5586cf9890f, 0x94f0c0f145e46c85, 0x9010cc922b7247f7, 0xa210d83b23395deb,
                 0x4030e3ec32d3d1a2, 0xa5b0efa55fdfa9c4, 0xae40fb66affed31a, 0x8d41073028d7233e, 0xa4911301d0125b50,
                 0xa1a11edbab5e2ab5, 0xaf712abdc06c31cb, 0xae8136a814f204aa, 0xa661429aaea92ddf, 0xa9114e95934f312d,
                 0x82415a98c8a58e51, 0x58f166a45471c3c2, 0xab9172b83c7d517a, 0x70917ed48695bbc0, 0xa7718af9388c8de9,
                 0x94a1972658375d2f, 0x8e51a35beb6fcb75, 0x97b1af99f8138a1c, 0xa351bbe084045cd3, 0x9001c82f95281c6b,
                 0x9e01d4873168b9aa, 0xa481e0e75eb44026, 0xa711ed5022fcd91c, 0xa201f9c18438ce4c, 0x8dc2063b88628cd6,
                 0x935212be3578a819, 0x82a21f49917ddc96, 0x8d322bdda27912d1, 0x99b2387a6e756238, 0x8ac2451ffb82140a,
                 0x8ac251ce4fb2a63f, 0x93e25e85711ece75, 0x82b26b4565e27cdd, 0x9e02780e341ddf29, 0xa2d284dfe1f56380,
                 0xab4291ba7591bb6f, 0x86129e9df51fdee1, 0xa352ab8a66d10f12, 0xafb2b87fd0dad98f, 0xa572c57e39771b2e,
                 0x9002d285a6e4030b, 0x9d12df961f641589, 0x71c2ecafa93e2f56, 0xaea2f9d24abd886a, 0x86f306fe0a31b715,
                 0x89531432edeeb2fd, 0x8a932170fc4cd831, 0xa1d32eb83ba8ea31, 0x93233c08b26416ff, 0xab23496266e3fa2c,
                 0xa92356c55f929ff0, 0xa8f36431a2de883a, 0xa4e371a7373aa9ca, 0xa3037f26231e7549, 0xa0b38cae6d05d865,
                 0xa3239a401b7140ee, 0xad43a7db34e59ff6, 0x9543b57fbfec6cf4, 0xa083c32dc313a8e4, 0x7fe3d0e544ede173,
                 0x8ad3dea64c123422, 0xa943ec70df1c5174, 0xa413fa4504ac801b, 0x8bd40822c367a024, 0xaf04160a21f72e29,
                 0xa3d423fb27094689, 0xab8431f5d950a896, 0x88843ffa3f84b9d4, 0x48944e086061892d, 0xae745c2042a7d231,
                 0x9c946a41ed1d0057, 0xa1e4786d668b3236, 0x73c486a2b5c13cd0, 0xab1494e1e192aed1, 0x99c4a32af0d7d3de,
                 0xabb4b17dea6db7d6, 0x7d44bfdad5362a27, 0x9054ce41b817c114, 0x98e4dcb299fddd0d, 0xa564eb2d81d8abfe,
                 0xa5a4f9b2769d2ca6, 0x7a2508417f4531ee, 0xa82516daa2cf6641, 0xac65257de83f4eee, 0xabe5342b569d4f81,
                 0x879542e2f4f6ad27, 0xa8a551a4ca5d920e, 0xa7856070dde910d1, 0x99b56f4736b527da, 0xa7a57e27dbe2c4ce,
                 0x82958d12d497c7fd, 0xa4059c0827ff07cb, 0x9635ab07dd485429, 0xa245ba11fba87a02, 0x3c45c9268a5946b7,
                 0xa195d84590998b92, 0x9ba5e76f15ad2148, 0xa985f6a320dceb70, 0xa60605e1b976dc08, 0x9e46152ae6cdf6f4,
                 0xa636247eb03a5584, 0x984633dd1d1929fd, 0xa8e6434634ccc31f, 0xa28652b9febc8fb6, 0xa226623882552224,
                 0xa85671c1c70833f5, 0x60368155d44ca973, 0x880690f4b19e9538, 0xa216a09e667f3bcc, 0x7a36b052fa75173e,
                 0xada6c012750bdabe, 0x9c76cfdcddd47645, 0xae46dfb23c651a2e, 0xa7a6ef9298593ae4, 0xa9f6ff7df9519483,
                 0x59d70f7466f42e87, 0xaba71f75e8ec5f73, 0xa6f72f8286ead089, 0xa7a73f9a48a58173, 0x90474fbd35d7cbfd,
                 0xa7e75feb564267c8, 0x9b777024b1ab6e09, 0x986780694fde5d3f, 0x934790b938ac1cf6, 0xaaf7a11473eb0186,
                 0xa207b17b0976cfda, 0x9f17c1ed0130c132, 0x91b7d26a62ff86f0, 0x7057e2f336cf4e62, 0xabe7f3878491c490,
                 0xa6c80427543e1a11, 0x946814d2add106d9, 0xa1582589994cce12, 0x9998364c1eb941f7, 0xa9c8471a4623c7ac,
                 0xaf2857f4179f5b20, 0xa01868d99b4492ec, 0x85d879cad931a436, 0x99988ac7d98a6699, 0x9d589bd0a478580f,
                 0x96e8ace5422aa0db, 0x9ec8be05bad61778, 0xade8cf3216b5448b, 0xa478e06a5e0866d8, 0x85c8f1ae99157736,
                 0x959902fed0282c8a, 0xa119145b0b91ffc5, 0xab2925c353aa2fe1, 0xae893737b0cdc5e4, 0xa88948b82b5f98e4,
                 0xad395a44cbc8520e, 0xaf296bdd9a7670b2, 0xa1797d829fde4e4f, 0x7ca98f33e47a22a2, 0xa749a0f170ca07b9,
                 0xa119b2bb4d53fe0c, 0x7c79c49182a3f090, 0xa579d674194bb8d4, 0x7829e86319e32323, 0xaad9fa5e8d07f29d,
                 0xa65a0c667b5de564, 0x9c6a1e7aed8eb8bb, 0x963a309bec4a2d33, 0xa2aa42c980460ad7, 0xa16a5503b23e255c,
                 0x650a674a8af46052, 0x9bca799e1330b358, 0xa58a8bfe53c12e58, 0x90fa9e6b5579fdbf, 0x889ab0e521356eba,
                 0xa81ac36bbfd3f379, 0x97ead5ff3a3c2774, 0x97aae89f995ad3ad, 0xa5aafb4ce622f2fe, 0xa21b0e07298db665,
                 0x94db20ce6c9a8952, 0xaedb33a2b84f15fa, 0xac1b468415b749b0, 0xa1cb59728de55939, 0x92ab6c6e29f1c52a,
                 0xad5b7f76f2fb5e46, 0xa24b928cf22749e3, 0xa08ba5b030a10649, 0xafcbb8e0b79a6f1e, 0x823bcc1e904bc1d2,
                 0xafcbdf69c3f3a206, 0xa08bf2c25bd71e08, 0xa89c06286141b33c, 0x811c199bdd85529c, 0xa48c2d1cd9fa652b,
                 0x9b4c40ab5fffd07a, 0x912c544778fafb22, 0x928c67f12e57d14b, 0xa86c7ba88988c932, 0x71ac8f6d9406e7b5,
                 0xaa0ca3405751c4da, 0x750cb720dcef9069, 0xac5ccb0f2e6d1674, 0xa88cdf0b555dc3f9, 0xa2fcf3155b5bab73,
                 0xa1ad072d4a07897b, 0x955d1b532b08c968, 0xa15d2f87080d89f1, 0x93dd43c8eacaa1d6, 0x82ed5818dcfba487,
                 0x5fed6c76e862e6d3, 0xa77d80e316c98397, 0x9a0d955d71ff6075, 0x9c2da9e603db3285, 0xa24dbe7cd63a8314,
                 0x92ddd321f301b460, 0xa1ade7d5641c0657, 0xa72dfc97337b9b5e, 0xadae11676b197d16, 0xa42e264614f5a128,
                 0xa30e3b333b16ee11, 0x839e502ee78b3ff6, 0xaa7e653924676d75, 0x92de7a51fbc74c83, 0xa77e8f7977cdb73f,
                 0xa0bea4afa2a490d9, 0x948eb9f4867cca6e, 0xa1becf482d8e67f0, 0x91cee4aaa2188510, 0x9dcefa1bee615a27,
                 0xa66f0f9c1cb64129, 0x93af252b376bba97, 0xacdf3ac948dd7273, 0x99df50765b6e4540, 0x9faf6632798844f8,
                 0xa12f7bfdad9cbe13, 0xaeef91d802243c88, 0x874fa7c1819e90d8, 0xacdfbdba3692d513, 0x62efd3c22b8f71f1, 0x74afe9d96b2a23d9)

# :nothrow needed since the compiler can't prove `ind` is inbounds.
Base.@assume_effects :nothrow function table_unpack(ind::Int32)
    ind = ind & 255 + 1 # 255 == length(J_TABLE) - 1
    j = getfield(J_TABLE, ind) # use getfield so the compiler can prove consistent
    jU = reinterpret(Float64, JU_CONST | (j&JU_MASK))
    jL = reinterpret(Float64, JL_CONST | (j>>8))
    return jU, jL
end

# Method for Float64
# 1. Argument reduction: Reduce x to an r so that |r| <= log(b, 2)/512. Given x, base b,
#    find r and integers k, j such that
#       x = (k + j/256)*log(b, 2) + r,  0 <= j < 256, |r| <= log(b,2)/512.
#
# 2. Approximate b^r-1 by 3rd-degree minimax polynomial p_b(r) on the interval [-log(b,2)/512, log(b,2)/512].
#    Since the bounds on r are very tight, this is sufficient to be accurate to floating point epsilon.
#
# 3. Scale back: b^x = 2^k * 2^(j/256) * (1 + p_b(r))
#    Since the range of possible j is small, 2^(j/256) is stored for all possible values in slightly extended precision.

# Method for Float32
# 1. Argument reduction: Reduce x to an r so that |r| <= log(b, 2)/2. Given x, base b,
#    find r and integer N such that
#       x = N*log(b, 2) + r,  |r| <= log(b,2)/2.
#
# 2. Approximate b^r by 7th-degree minimax polynomial p_b(r) on the interval [-log(b,2)/2, log(b,2)/2].
# 3. Scale back: b^x = 2^N * p_b(r)
# For both, a little extra care needs to be taken if b^r is subnormal.
# The solution is to do the scaling back in 2 steps as just messing with the exponent wouldn't work.

@inline function exp_impl(x::Float64, base)
    T = Float64
    N_float = muladd(x, LogBo256INV(base, T), MAGIC_ROUND_CONST(T))
    N = reinterpret(UInt64, N_float) % Int32
    N_float -=  MAGIC_ROUND_CONST(T) #N_float now equals round(x*LogBo256INV(base, T))
    r = muladd(N_float, LogBo256U(base, T), x)
    r = muladd(N_float, LogBo256L(base, T), r)
    k = N >> 8
    jU, jL = table_unpack(N)
    small_part =  muladd(jU, expm1b_kernel(base, r), jL) + jU

    if !(abs(x) <= SUBNORM_EXP(base, T))
        x >= MAX_EXP(base, T) && return Inf
        x <= MIN_EXP(base, T) && return 0.0
        if k <= -53
            # The UInt64 forces promotion. (Only matters for 32 bit systems.)
            twopk = (k + UInt64(53)) << 52
            return reinterpret(T, twopk + reinterpret(UInt64, small_part))*0x1p-53
        end
        #k == 1024 && return (small_part * 2.0) * 2.0^1023
    end
    twopk = Int64(k) << 52
    return reinterpret(T, twopk + reinterpret(Int64, small_part))
end
# Computes base^(x+xlo). Used for pow.
@inline function exp_impl(x::Float64, xlo::Float64, base)
    T = Float64
    N_float = muladd(x, LogBo256INV(base, T), MAGIC_ROUND_CONST(T))
    N = reinterpret(UInt64, N_float) % Int32
    N_float -=  MAGIC_ROUND_CONST(T) #N_float now equals round(x*LogBo256INV(base, T))
    r = muladd(N_float, LogBo256U(base, T), x)
    r = muladd(N_float, LogBo256L(base, T), r)
    k = N >> 8
    jU, jL = table_unpack(N)
    kern = expm1b_kernel(base, r)
    very_small = muladd(kern, jU*xlo, jL)
    hi, lo = Base.canonicalize2(1.0, kern)
    small_part = fma(jU, hi, muladd(jU, (lo+xlo), very_small))
    if !(abs(x) <= SUBNORM_EXP(base, T))
        x >= MAX_EXP(base, T) && return Inf
        x <= MIN_EXP(base, T) && return 0.0
        if k <= -53
            # The UInt64 forces promotion. (Only matters for 32 bit systems.)
            twopk = (k + UInt64(53)) << 52
            return reinterpret(T, twopk + reinterpret(UInt64, small_part))*0x1p-53
        end
        #k == 1024 && return (small_part * 2.0) * 2.0^1023
    end
    twopk = Int64(k) << 52
    return reinterpret(T, twopk + reinterpret(Int64, small_part))
end
@inline function exp_impl_fast(x::Float64, base)
    T = Float64
    x >= MAX_EXP(base, T) && return Inf
    x <= -SUBNORM_EXP(base, T) && return 0.0
    N_float = muladd(x, LogBo256INV(base, T), MAGIC_ROUND_CONST(T))
    N = reinterpret(UInt64, N_float) % Int32
    N_float -=  MAGIC_ROUND_CONST(T) #N_float now equals round(x*LogBo256INV(base, T))
    r = muladd(N_float, LogBo256U(base, T), x)
    r = muladd(N_float, LogBo256L(base, T), r)
    k = N >> 8
    jU = reinterpret(Float64, JU_CONST | (@inbounds J_TABLE[N&255 + 1] & JU_MASK))
    small_part =  muladd(jU, expm1b_kernel(base, r), jU)
    twopk = Int64(k) << 52
    return reinterpret(T, twopk + reinterpret(Int64, small_part))
end

@inline function exp_impl(x::Float32, base)
    T = Float32
    N_float = round(x*LogBINV(base, T))
    N = unsafe_trunc(Int32, N_float)
    r = muladd(N_float, LogBU(base, T), x)
    r = muladd(N_float, LogBL(base, T), r)
    small_part = expb_kernel(base, r)
    power = (N+Int32(127))
    x > MAX_EXP(base, T) && return Inf32
    x < MIN_EXP(base, T) && return 0.0f0
    if x <= -SUBNORM_EXP(base, T)
        power += Int32(24)
        small_part *= Float32(0x1p-24)
    end
    if N == 128
        power -= Int32(1)
        small_part *= 2f0
    end
    return small_part * reinterpret(T, power << Int32(23))
end

@inline function exp_impl_fast(x::Float32, base)
    T = Float32
    x >= MAX_EXP(base, T) && return Inf32
    x <= -SUBNORM_EXP(base, T) && return 0f0
    N_float = round(x*LogBINV(base, T))
    N = unsafe_trunc(Int32, N_float)
    r = muladd(N_float, LogBU(base, T), x)
    r = muladd(N_float, LogBL(base, T), r)
    small_part = expb_kernel(base, r)
    twopk = reinterpret(T, (N+Int32(127)) << Int32(23))
    return twopk*small_part
end

@inline function exp_impl(a::Float16, base)
    T = Float32
    x = T(a)
    N_float = round(x*LogBINV(base, T))
    N = unsafe_trunc(Int32, N_float)
    r = muladd(N_float, LogB(base, Float16), x)
    small_part = expb_kernel(base, r)
    if !(abs(x) <= 25)
        x > 16 && return Inf16
        x < 25 && return zero(Float16)
    end
    twopk = reinterpret(T, (N+Int32(127)) << Int32(23))
    return Float16(twopk*small_part)
end

for (func, fast_func, base) in ((:exp2,  :exp2_fast,  Val(2)),
                                (:exp,   :exp_fast,   Val(:ℯ)),
                                (:exp10, :exp10_fast, Val(10)))
    @eval begin
        @noinline $func(x::Union{Float16,Float32,Float64}) = exp_impl(x, $base)
        @noinline $fast_func(x::Union{Float32,Float64}) = exp_impl_fast(x, $base)
    end
end

@doc """
    exp(x)

Compute the natural base exponential of `x`, in other words ``ℯ^x``.

See also [`exp2`](@ref), [`exp10`](@ref) and [`cis`](@ref).

# Examples
```jldoctest
julia> exp(1.0)
2.718281828459045

julia> exp(im * pi) ≈ cis(pi)
true
```
""" exp(x::Real)

"""
    exp2(x)

Compute the base 2 exponential of `x`, in other words ``2^x``.

See also [`ldexp`](@ref), [`<<`](@ref).

# Examples
```jldoctest
julia> exp2(5)
32.0

julia> 2^5
32

julia> exp2(63) > typemax(Int)
true
```
"""
exp2(x)

"""
    exp10(x)

Compute the base 10 exponential of `x`, in other words ``10^x``.

# Examples
```jldoctest
julia> exp10(2)
100.0

julia> 10^2
100
```
"""
exp10(x)

# functions with special cases for integer arguments
@inline function exp2(x::Base.BitInteger)
    if x > 1023
        Inf64
    elseif x <= -1023
        # if -1073 < x <= -1023 then Result will be a subnormal number
        # Hex literal with padding must be used to work on 32bit machine
        reinterpret(Float64, 0x0000_0000_0000_0001 << ((x + 1074) % UInt))
    else
        # We will cast everything to Int64 to avoid errors in case of Int128
        # If x is a Int128, and is outside the range of Int64, then it is not -1023<x<=1023
        reinterpret(Float64, (exponent_bias(Float64) + (x % Int64)) << (significand_bits(Float64) % UInt))
    end
end

# min and max arguments for expm1 by type
MAX_EXP(::Type{Float64}) =  709.7827128933845   # log 2^1023*(2-2^-52)
MIN_EXP(::Type{Float64}) = -37.42994775023705   # log 2^-54
MAX_EXP(::Type{Float32}) =  88.72284f0          # log 2^127 *(2-2^-23)
MIN_EXP(::Type{Float32}) = -17.32868f0          # log 2^-25
MAX_EXP(::Type{Float16}) =  Float16(11.09)      # log 2^15 *(2-2^-10)
MIN_EXP(::Type{Float16}) = -Float16(8.32)       # log 2^-12

Ln2INV(::Type{Float64}) = 1.4426950408889634
Ln2(::Type{Float64}) = -0.6931471805599453
Ln2INV(::Type{Float32}) = 1.442695f0
Ln2(::Type{Float32}) = -0.6931472f0

# log(.75) <= x <= log(1.25)
@inline function expm1_small(x::Float64)
    p = evalpoly(x, (0.16666666666666632, 0.04166666666666556, 0.008333333333401227,
                     0.001388888889068783, 0.00019841269447671544, 2.480157691845342e-5,
                     2.7558212415361945e-6, 2.758218402815439e-7, 2.4360682937111612e-8))
    p2 = exthorner(x, (1.0, .5, p))
    return fma(x, p2[1], x*p2[2])
end
@inline function expm1_small(x::Float32)
    p = evalpoly(x, (0.16666666f0, 0.041666627f0, 0.008333682f0,
                     0.0013908712f0, 0.0001933096f0))
    p2 = exthorner(x, (1f0, .5f0, p))
    return fma(x, p2[1], x*p2[2])
end

function expm1(x::Float64)
    T = Float64
    if -0.2876820724517809 <= x <= 0.22314355131420976
        return expm1_small(x)
    elseif !(abs(x)<=MIN_EXP(Float64))
        isnan(x) && return x
        x > MAX_EXP(Float64) && return Inf
        x < MIN_EXP(Float64) && return -1.0
    end

    N_float = muladd(x, LogBo256INV(Val(:ℯ), T), MAGIC_ROUND_CONST(T))
    N = reinterpret(UInt64, N_float) % Int32
    N_float -=  MAGIC_ROUND_CONST(T) #N_float now equals round(x*LogBo256INV(Val(:ℯ), T))
    r = muladd(N_float, LogBo256U(Val(:ℯ), T), x)
    r = muladd(N_float, LogBo256L(Val(:ℯ), T), r)
    k = Int64(N >> 8)
    jU, jL = table_unpack(N)
    p = expm1b_kernel(Val(:ℯ), r)
    twopk  = reinterpret(Float64, (1023+k) << 52)
    twopnk = reinterpret(Float64, (1023-k) << 52)
    k>=106 && return reinterpret(Float64, (1022+k) << 52)*(jU + muladd(jU, p, jL))*2
    k>=53 && return twopk*(jU + muladd(jU, p, (jL-twopnk)))
    k<=-2 && return twopk*(jU + muladd(jU, p, jL))-1
    return twopk*((jU-twopnk) + fma(jU, p, jL))
end

function expm1(x::Float32)
    x > MAX_EXP(Float32) && return Inf32
    x < MIN_EXP(Float32) && return -1f0
    if -0.2876821f0 <=x <= 0.22314355f0
        return expm1_small(x)
    end
    x = Float64(x)
    N_float = round(x*Ln2INV(Float64))
    N = unsafe_trunc(Int64, N_float)
    r = muladd(N_float, Ln2(Float64), x)
    hi = evalpoly(r, (1.0, .5, 0.16666667546642386, 0.041666183019487026,
                      0.008332997481506921, 0.0013966479175977883, 0.0002004037059220124))
    small_part = r*hi
    twopk = reinterpret(Float64, (N+1023) << 52)
    return Float32(muladd(twopk, small_part, twopk-1.0))
end

function expm1(x::Float16)
    x > MAX_EXP(Float16) && return Inf16
    x < MIN_EXP(Float16) && return Float16(-1.0)
    x = Float32(x)
    if -0.2876821f0 <=x <= 0.22314355f0
        return Float16(x*evalpoly(x, (1f0, .5f0, 0.16666628f0, 0.04166785f0, 0.008351848f0, 0.0013675707f0)))
    end
    N_float = round(x*Ln2INV(Float32))
    N = unsafe_trunc(Int32, N_float)
    r = muladd(N_float, Ln2(Float32), x)
    hi = evalpoly(r, (1f0, .5f0, 0.16666667f0, 0.041665863f0, 0.008333111f0, 0.0013981499f0, 0.00019983904f0))
    small_part = r*hi
    twopk = reinterpret(Float32, (N+Int32(127)) << Int32(23))
    return Float16(muladd(twopk, small_part, twopk-1f0))
end

"""
    expm1(x)

Accurately compute ``e^x-1``. It avoids the loss of precision involved in the direct
evaluation of exp(x)-1 for small values of x.
# Examples
```jldoctest
julia> expm1(1e-16)
1.0e-16

julia> exp(1e-16) - 1
0.0
```
"""
expm1(x)
Y   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/special/hyperbolic.jl�#      # This file is a part of Julia. License is MIT: https://julialang.org/license

# asinh, acosh, and atanh are heavily based on FDLIBM code:
# e_sinh.c, e_sinhf, e_cosh.c, e_coshf, s_tanh.c, s_tanhf.c, s_asinh.c,
# s_asinhf.c, e_acosh.c, e_coshf.c, e_atanh.c, and e_atanhf.c
# that are made available under the following licence:

# ====================================================
# Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
#
# Developed at SunSoft, a Sun Microsystems, Inc. business.
# Permission to use, copy, modify, and distribute this
# software is freely granted, provided that this notice
# is preserved.
# ====================================================


# Hyperbolic functions
# sinh methods
H_SMALL_X(::Type{Float64}) = 2.0^-28
H_MEDIUM_X(::Type{Float64}) = 22.0

H_SMALL_X(::Type{Float32}) = 2f-12
H_MEDIUM_X(::Type{Float32}) = 9f0

H_LARGE_X(::Type{Float64}) = 709.7822265633563 # nextfloat(709.7822265633562)

H_LARGE_X(::Type{Float32}) = 88.72283f0

SINH_SMALL_X(::Type{Float64}) = 2.1
SINH_SMALL_X(::Type{Float32}) = 3.0f0

# For Float64, use DoubleFloat scheme for extra accuracy
function sinh_kernel(x::Float64)
    x2, x2lo = two_mul(x,x)
    hi_order = evalpoly(x2, (8.333333333336817e-3, 1.9841269840165435e-4,
                             2.7557319381151335e-6, 2.5052096530035283e-8,
                             1.6059550718903307e-10, 7.634842144412119e-13,
                             2.9696954760355812e-15))
    hi,lo = exthorner(x2, (1.0, 0.16666666666666635, hi_order))
    return muladd(x, hi, muladd(x, lo, x*x2lo*0.16666666666666635))
end
# For Float32, using Float64 is simpler, faster, and doesn't require FMA
function sinh_kernel(x::Float32)
    x=Float64(x)
    res = evalpoly(x*x, (1.0, 0.1666666779967941, 0.008333336726447933,
                         0.00019841001151414065, 2.7555538207080807e-6,
                         2.5143389765825282e-8, 1.6260094552031644e-10))
    return Float32(res*x)
end

@inline function sinh16_kernel(x::Float32)
    res = evalpoly(x*x, (1.0f0, 0.16666667f0, 0.008333337f0, 0.00019841001f0,
                         2.7555539f-6, 2.514339f-8, 1.6260095f-10))
    return Float16(res*x)
end

function sinh(x::T) where T<:Union{Float32,Float64}
    # Method
    # mathematically sinh(x) is defined to be (exp(x)-exp(-x))/2
    #    1. Sometimes replace x by |x| (sinh(-x) = -sinh(x)).
    #    2. Find the branch and the expression to calculate and return it
    #      a)   0 <= x < SINH_SMALL_X
    #               approximate sinh(x) with a  minimax polynomial
    #      b)   SINH_SMALL_X <= x < H_LARGE_X
    #               return sinh(x) = (exp(x) - exp(-x))/2
    #      d)   H_LARGE_X  <= x
    #               return sinh(x) = exp(x/2)/2 * exp(x/2)
    #               Note that this branch automatically deals with Infs and NaNs

    absx = abs(x)
    if absx <= SINH_SMALL_X(T)
        return sinh_kernel(x)
    elseif absx >= H_LARGE_X(T)
        E = exp(T(.5)*absx)
        return copysign(T(.5)*E*E, x)
    end
    E = exp(absx)
    return copysign(T(.5)*(E - 1/E),x)
end

function Base.sinh(a::Float16)
    x = Float32(a)
    absx = abs(x)
    absx <= SINH_SMALL_X(Float32) && return sinh16_kernel(x)
    E = exp(absx)
    return Float16(copysign(.5f0*(E - 1/E),x))
end

COSH_SMALL_X(::Type{T}) where T= one(T)

function cosh_kernel(x2::Float32)
    return evalpoly(x2, (1.0f0, 0.49999997f0, 0.041666888f0, 0.0013882756f0, 2.549933f-5))
end

function cosh_kernel(x2::Float64)
    return evalpoly(x2, (1.0, 0.5000000000000002, 0.04166666666666269,
                         1.3888888889206764e-3, 2.4801587176784207e-5,
                         2.7557345825742837e-7, 2.0873617441235094e-9,
                         1.1663435515945578e-11))
end

function cosh(x::T) where T<:Union{Float32,Float64}
    # Method
    # mathematically cosh(x) is defined to be (exp(x)+exp(-x))/2
    #    1. Replace x by |x| (cosh(x) = cosh(-x)).
    #    2. Find the branch and the expression to calculate and return it
    #      a)   x <= COSH_SMALL_X
    #               approximate sinh(x) with a minimax polynomial
    #      b)   COSH_SMALL_X <= x < H_LARGE_X
    #               return cosh(x) = = (exp(x) + exp(-x))/2
    #      e)   H_LARGE_X  <= x
    #               return cosh(x) = exp(x/2)/2 * exp(x/2)
    #               Note that this branch automatically deals with Infs and NaNs

    absx = abs(x)
    if absx <= COSH_SMALL_X(T)
        return cosh_kernel(x*x)
    elseif absx >= H_LARGE_X(T)
        E = exp(T(.5)*absx)
        return T(.5)*E*E
    end
    E = exp(absx)
    return T(.5)*(E + 1/E)
end

# tanh methods
TANH_LARGE_X(::Type{Float64}) = 44.0
TANH_LARGE_X(::Type{Float32}) = 18.0f0
TANH_SMALL_X(::Type{Float64}) = 1.0
TANH_SMALL_X(::Type{Float32}) = 1.3862944f0       #2*log(2)
@inline function tanh_kernel(x::Float64)
    return evalpoly(x, (1.0, -0.33333333333332904, 0.13333333333267555,
                        -0.05396825393066753, 0.02186948742242217,
                        -0.008863215974794633, 0.003591910693118715,
                        -0.0014542587440487815, 0.0005825521659411748,
                        -0.00021647574085351332, 5.5752458452673005e-5))
end
@inline function tanh_kernel(x::Float32)
    return evalpoly(x, (1.0f0, -0.3333312f0, 0.13328037f0,
                        -0.05350336f0, 0.019975215f0, -0.0050525228f0))
end
function tanh(x::T) where T<:Union{Float32, Float64}
    # Method
    # mathematically tanh(x) is defined to be (exp(x)-exp(-x))/(exp(x)+exp(-x))
    #    1. reduce x to non-negative by tanh(-x) = -tanh(x).
    #    2. Find the branch and the expression to calculate and return it
    #      a) 0 <= x < H_SMALL_X
    #             Use a minimax polynomial over the range
    #      b) H_SMALL_X <= x < TANH_LARGE_X
    #           1 - 2/(exp(2x) + 1)
    #      c) TANH_LARGE_X <= x
    #            return 1
    abs2x = abs(2x)
    abs2x >= TANH_LARGE_X(T) && return copysign(one(T), x)
    abs2x <= TANH_SMALL_X(T) && return x*tanh_kernel(x*x)
    k = exp(abs2x)
    return copysign(1 - 2/(k+1), x)
end

# Inverse hyperbolic functions
AH_LN2(::Type{Float64}) = 6.93147180559945286227e-01
AH_LN2(::Type{Float32}) = 6.9314718246f-01
# asinh methods
function asinh(x::T) where T <: Union{Float32, Float64}
    # Method
    # mathematically asinh(x) = sign(x)*log(|x| + sqrt(x*x + 1))
    # is the principle value of the inverse hyperbolic sine
    # 1. Find the branch and the expression to calculate and return it
    #    a) |x| < 2^-28
    #        return x
    #    b) |x| < 2
    #        return sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
    #    c) 2 <= |x| < 2^28
    #        return sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1)))
    #    d) |x| >= 2^28
    #        return sign(x)*(log(x)+ln2))
    if !isfinite(x)
        return x
    end
    absx = abs(x)
    if absx < T(2)
        # in a)
        if absx < T(2)^-28
            return x
        end
        # in b)
        t = x*x
        w = log1p(absx + t/(T(1) + sqrt(T(1) + t)))
    elseif absx < T(2)^28
        # in c)
        t = absx
        w = log(T(2)*t + T(1)/(sqrt(x*x + T(1)) + t))
    else
        # in d)
        w = log(absx) + AH_LN2(T)
    end
    return copysign(w, x)
end

# acosh methods
@noinline acosh_domain_error(x) = throw(DomainError(x, "acosh(x) is only defined for x ≥ 1."))
function acosh(x::T) where T <: Union{Float32, Float64}
    # Method
    # mathematically acosh(x) if defined to be log(x + sqrt(x*x-1))
    # 1. Find the branch and the expression to calculate and return it
    #     a) x = 1
    #         return log1p(t+sqrt(2.0*t+t*t)) where t=x-1.
    #     b) 1 < x < 2
    #         return log1p(t+sqrt(2.0*t+t*t)) where t=x-1.
    #     c) 2 <= x <
    #         return log(2x-1/(sqrt(x*x-1)+x))
    #     d) x >= 2^28
    #         return log(x)+ln2
    # Special cases:
    #     if x < 1 throw DomainError

    isnan(x) && return x

    if x < T(1)
        return acosh_domain_error(x)
    elseif x == T(1)
        # in a)
        return T(0)
    elseif x < T(2)
        # in b)
        t = x - T(1)
        return log1p(t + sqrt(T(2)*t + t*t))
    elseif x < T(2)^28
        # in c)
        t = x*x
        return log(T(2)*x - T(1)/(x+sqrt(t - T(1))))
    else
        # in d)
        return log(x) + AH_LN2(T)
    end
end

# atanh methods
@noinline atanh_domain_error(x) = throw(DomainError(x, "atanh(x) is only defined for |x| ≤ 1."))
function atanh(x::T) where T <: Union{Float32, Float64}
    # Method
    # 1.Reduced x to positive by atanh(-x) = -atanh(x)
    # 2. Find the branch and the expression to calculate and return it
    #     a) 0 <= x < 0.5
    #         return 0.5*log1p(2x/(1-x))
    #     b) 0.5 <= x <= 1
    #         return 0.5*log((x+1)/(1-x))
    # Special cases:
    #    if |x| > 1 throw DomainError
    isnan(x) && return x

    absx = abs(x)

    if absx > 1
        atanh_domain_error(x)
    end
    if absx < T(0.5)
        # in a)
        t = log1p(T(2)*absx/(T(1)-absx))
    else
        # in b)
        t = log((T(1)+absx)/(T(1)-absx))
    end
    return T(0.5)*copysign(t, x)
end
S   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/special/trig.jl:�      # This file is a part of Julia. Except for the *_kernel functions (see below),
# license is MIT: https://julialang.org/license

struct DoubleFloat64
    hi::Float64
    lo::Float64
end
struct DoubleFloat32
    hi::Float64
end

# sin_kernel and cos_kernel functions are only valid for |x| < pi/4 = 0.7854
# translated from openlibm code: k_sin.c, k_cos.c, k_sinf.c, k_cosf.c.
# atan functions are based on openlibm code: s_atan.c, s_atanf.c.
# acos functions are based on openlibm code: e_acos.c, e_acosf.c.
# asin functions are based on openlibm code: e_asin.c, e_asinf.c. The above
# functions are made available under the following licence:

## Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
##
## Developed at SunPro, a Sun Microsystems, Inc. business.
## Permission to use, copy, modify, and distribute this
## software is freely granted, provided that this notice
## is preserved.

# Trigonometric functions
# sin methods
@noinline sin_domain_error(x) = throw(DomainError(x, "sin(x) is only defined for finite x."))
function sin(x::T) where T<:Union{Float32, Float64}
    absx = abs(x)
    if absx < T(pi)/4 #|x| ~<= pi/4, no need for reduction
        if absx < sqrt(eps(T))
            return x
        end
        return sin_kernel(x)
    elseif isnan(x)
        return x
    elseif isinf(x)
        sin_domain_error(x)
    end
    n, y = rem_pio2_kernel(x)
    n = n&3
    if n == 0
        return sin_kernel(y)
    elseif n == 1
        return cos_kernel(y)
    elseif n == 2
        return -sin_kernel(y)
    else
        return -cos_kernel(y)
    end
end

# Coefficients in 13th order polynomial approximation on [0; π/4]
#     sin(x) ≈ x + S1*x³ + S2*x⁵ + S3*x⁷ + S4*x⁹ + S5*x¹¹ + S6*x¹³
# D for double, S for sin, number is the order of x-1
const DS1 = -1.66666666666666324348e-01
const DS2 = 8.33333333332248946124e-03
const DS3 = -1.98412698298579493134e-04
const DS4 = 2.75573137070700676789e-06
const DS5 = -2.50507602534068634195e-08
const DS6 = 1.58969099521155010221e-10

"""
    sin_kernel(yhi, ylo)

Computes the sine on the interval [-π/4; π/4].
"""
@inline function sin_kernel(y::DoubleFloat64)
    y² = y.hi*y.hi
    y⁴ = y²*y²
    r  = @horner(y², DS2, DS3, DS4) + y²*y⁴*@horner(y², DS5, DS6)
    y³ = y²*y.hi
    y.hi-((y²*(0.5*y.lo-y³*r)-y.lo)-y³*DS1)
end
@inline function sin_kernel(y::Float64)
    y² =  y*y
    y⁴ =  y²*y²
    r  =  @horner(y², DS2, DS3, DS4) + y²*y⁴*@horner(y², DS5, DS6)
    y³ =  y²*y
    y+y³*(DS1+y²*r)
end

# sin_kernels accepting values from rem_pio2 in the Float32 case
@inline sin_kernel(x::Float32) = sin_kernel(DoubleFloat32(x))
@inline function sin_kernel(y::DoubleFloat32)
    S1 = -0.16666666641626524
    S2 = 0.008333329385889463
    z = y.hi*y.hi
    w = z*z
    r = @horner(z, -0.00019839334836096632, 2.718311493989822e-6)
    s = z*y.hi
    Float32((y.hi + s*@horner(z, S1, S2)) + s*w*r)
end

# cos methods
@noinline cos_domain_error(x) = throw(DomainError(x, "cos(x) is only defined for finite x."))
function cos(x::T) where T<:Union{Float32, Float64}
    absx = abs(x)
    if absx < T(pi)/4
        if absx < sqrt(eps(T)/T(2.0))
            return T(1.0)
        end
        return cos_kernel(x)
    elseif isnan(x)
        return x
    elseif isinf(x)
        cos_domain_error(x)
    else
        n, y = rem_pio2_kernel(x)
        n = n&3
        if n == 0
            return cos_kernel(y)
        elseif n == 1
            return -sin_kernel(y)
        elseif n == 2
            return -cos_kernel(y)
        else
            return sin_kernel(y)
        end
    end
end

const DC1 = 4.16666666666666019037e-02
const DC2 = -1.38888888888741095749e-03
const DC3 = 2.48015872894767294178e-05
const DC4 = -2.75573143513906633035e-07
const DC5 = 2.08757232129817482790e-09
const DC6 = -1.13596475577881948265e-11

"""
    cos_kernel(y)

Compute the cosine on the interval y∈[-π/4; π/4].
"""
@inline function cos_kernel(y::DoubleFloat64)
    y² = y.hi*y.hi
    y⁴ = y²*y²
    r  = y²*@horner(y², DC1, DC2, DC3) + y⁴*y⁴*@horner(y², DC4, DC5, DC6)
    half_y² = 0.5*y²
    w  = 1.0-half_y²
    w + (((1.0-w)-half_y²) + (y²*r-y.hi*y.lo))
end
@inline function cos_kernel(y::Float64)
    y² = y*y
    y⁴ = y²*y²
    r  = y²*@horner(y², DC1, DC2, DC3) + y⁴*y⁴*@horner(y², DC4, DC5, DC6)
    half_y² = 0.5*y²
    w  = 1.0-half_y²
    w + (((1.0-w)-half_y²) + (y²*r))
end

# cos_kernels accepting values from rem_pio2 in the Float32 case
cos_kernel(x::Float32) = cos_kernel(DoubleFloat32(x))
@inline function cos_kernel(y::DoubleFloat32)
    C0 = -0.499999997251031
    C1 = 0.04166662332373906
    y² = y.hi*y.hi
    y⁴ = y²*y²
    r = @horner(y², -0.001388676377460993, 2.439044879627741e-5)
    Float32(((1.0+y²*C0) + y⁴*C1) + (y⁴*y²)*r)
end

### sincos methods
@noinline sincos_domain_error(x) = throw(DomainError(x, "sincos(x) is only defined for finite x."))

"""
    sincos(x)

Simultaneously compute the sine and cosine of `x`, where `x` is in radians, returning
a tuple `(sine, cosine)`.

See also [`cis`](@ref), [`sincospi`](@ref), [`sincosd`](@ref).
"""
function sincos(x::T) where T<:Union{Float32, Float64}
    if abs(x) < T(pi)/4
        if x == zero(T)
            return x, one(T)
        end
        return sincos_kernel(x)
    elseif isnan(x)
        return x, x
    elseif isinf(x)
        sincos_domain_error(x)
    end
    n, y = rem_pio2_kernel(x)
    n = n&3
    # calculate both kernels at the reduced y...
    si, co = sincos_kernel(y)
    # ... and use the same selection scheme as above: (sin, cos, -sin, -cos) for
    # for sin and (cos, -sin, -cos, sin) for cos
    if n == 0
        return si, co
    elseif n == 1
        return co, -si
    elseif n == 2
        return -si, -co
    else
        return -co, si
    end
end

_sincos(x::AbstractFloat) = sincos(x)
_sincos(x) = (sin(x), cos(x))

sincos(x) = _sincos(float(x))


# There's no need to write specialized kernels, as inlining takes care of remo-
# ving superfluous calculations.
@inline sincos_kernel(y::Union{Float32, Float64, DoubleFloat32, DoubleFloat64}) = (sin_kernel(y), cos_kernel(y))

# tangent methods
@noinline tan_domain_error(x) = throw(DomainError(x, "tan(x) is only defined for finite x."))
function tan(x::T) where T<:Union{Float32, Float64}
    absx = abs(x)
    if absx < T(pi)/4
        if absx < sqrt(eps(T))/2 # first order dominates, but also allows tan(-0)=-0
            return x
        end
        return tan_kernel(x)
    elseif isnan(x)
        return x
    elseif isinf(x)
        tan_domain_error(x)
    end
    n, y = rem_pio2_kernel(x)
    if iseven(n)
        return tan_kernel(y,1)
    else
        return tan_kernel(y,-1)
    end
end

@inline tan_kernel(y::Float64) = tan_kernel(DoubleFloat64(y, 0.0), 1)
@inline function tan_kernel(y::DoubleFloat64, k)
    # kernel tan function on ~[-pi/4, pi/4] (except on -0)
    # Input y is assumed to be bounded by ~pi/4 in magnitude.
    # Input k indicates whether tan (if k = 1) or -1/tan (if k = -1) is returned.

    # Algorithm
    #    1. Since tan(-y) = -tan(y), we need only to consider positive y.
    #    2. Callers must return tan(-0) = -0 without calling here since our
    #       odd polynomial is not evaluated in a way that preserves -0.
    #       Callers may do the optimization tan(y) ~ y for tiny y.
    #    3. tan(y) is approximated by a odd polynomial of degree 27 on
    #       [0,0.67434]
    #                            3             27
    #           tan(y) ~ y + T1*y + ... + T13*y ≡ P(y)
    #       where
    #
    #                          |tan(y)         2     4            26   |     -59.2
    #        (tan(y)-P(y))/y = |----- - (1+T1*y +T2*y +.... +T13*y    )| <= 2
    #                          |  y                                    |
    #
    #       Note: tan(y+z) = tan(y) + tan'(y)*z
    #                  ~ tan(y) + (1+y*y)*z
    #       Therefore, for better accuracy in computing tan(y+z), let
    #             3      2      2       2       2
    #        r = y *(T2+y *(T3+y *(...+y *(T12+y *T13))))
    #       then
    #                     3    2
    #        tan(y+z) = y + (T1*y + (y *(r+z)+z))
    #
    #   4. For y in [0.67434,pi/4],  let z = pi/4 - y, then
    #        tan(y) = tan(pi/4-z) = (1-tan(z))/(1+tan(z))
    #               = 1 - 2*(tan(z) - (tan(z)^2)/(1+tan(z)))

    yhi = y.hi
    ylo = y.lo

    if abs(yhi) >= 0.6744
        if yhi < 0.0
            yhi = -yhi
            ylo = -ylo
        end
        # Then, accurately reduce y as "pio4hi"-yhi+"pio4lo"-ylo
        yhi = (pi/4 - yhi) + (3.06161699786838301793e-17 - ylo)
        # yhi is guaranteed to be exact, so ylo is identically zero
        ylo = 0.0
    end
    y² = yhi * yhi
    y⁴ = y² * y²

    # Break P(y)-T1*y³ = y^5*(T[2]+y^2*T[3]+...) into y⁵*r + y⁵*v where
    # r = T[2]+y^4*T[4]+...+y^20*T[12])
    # v = (y^2*(T[3]+y^4*T[5]+...+y^22*[T13]))
    r = @horner(y⁴,
        1.33333333333201242699e-01, # T2
        2.18694882948595424599e-02, # T4
        3.59207910759131235356e-03, # T6
        5.88041240820264096874e-04, # T8
        7.81794442939557092300e-05, # T10
        -1.85586374855275456654e-05) # T12
    v = y² * @horner(y⁴,
        5.39682539762260521377e-02, # T3
        8.86323982359930005737e-03, # T5
        1.45620945432529025516e-03, # T7
        2.46463134818469906812e-04, # T9
        7.14072491382608190305e-05, # T11
        2.59073051863633712884e-05) # T13
    # Precompute y³
    y³ = y² * yhi
    # Calculate  P(y)-y-T1*y³ =  y⁵*r + y⁵*v  = y²(y³*(r+v))
    r = ylo + y² * (y³ * (r + v) + ylo)
    # Calculate P(y)-y = r+T1*y³
    r += 3.33333333333334091986e-01*y³
    # Calculate w = r+y = P(y)
    Px = yhi + r
    if abs(y.hi) >= 0.6744
        # If the original y was above the threshold, then we calculate
        #     tan(y) = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
        #            ≈ 1 - 2*(P(z) - (P(z)^2)/(1+P(z)))
        # where z = y-π/4.
        return (signbit(y.hi) ? -1.0 : 1.0)*(k - 2*(yhi-(Px^2/(k+Px)-r)))
    end
    if k == 1
        # Else, we simply return w = P(y) if k == 1 (integer multiple from argument
        # reduction was even)...
        return Px
    else
        # ...or tan(y) ≈ -1.0/(y+r) if !(k == 1) (integer multiple from argument
        # reduction was odd). If 2ulp error is allowed, simply return the frac-
        # tion directly. Instead, we calculate it accurately.

        # Px0 is w with zeroed out low word
        Px0 = reinterpret(Float64, (reinterpret(UInt64, Px) >> 32) << 32)
        v = r - (Px0 - yhi) # Px0+v = r+y
        t = a = -1.0 / Px
        # zero out low word of t
        t = reinterpret(Float64, (reinterpret(UInt64, t) >> 32) << 32)
        s = 1.0 + t * Px0
        return t + a * (s + t * v)
    end
end

@inline tan_kernel(y::Float32) = tan_kernel(DoubleFloat32(y), 1)
@inline function tan_kernel(y::DoubleFloat32, k)
    # |tan(y)/y - t(y)| < 2**-25.5 (~[-2e-08, 2e-08]). */
    y² = y.hi*y.hi
    r  = @horner(y², 0.00297435743359967304927, 0.00946564784943673166728)
    t  = @horner(y², 0.0533812378445670393523, 0.0245283181166547278873)
    y⁴ = y²*y²
    y³ = y²*y.hi
    u  = @horner(y², 0.333331395030791399758, 0.133392002712976742718)
    Py  = (y.hi+y³*u)+(y³*y⁴)*(t+y⁴*r)
    if k == 1
        return Float32(Py)
    end

    return Float32(-1.0/Py)
end

# fallback methods
sin_kernel(x::Real) = sin(x)
cos_kernel(x::Real) = cos(x)
tan_kernel(x::Real) = tan(x)
sincos_kernel(x::Real) = sincos(x)

# Inverse trigonometric functions
# asin methods
ASIN_X_MIN_THRESHOLD(::Type{Float32}) = 2.0f0^-12
ASIN_X_MIN_THRESHOLD(::Type{Float64}) = sqrt(eps(Float64))

arc_p(t::Float64) =
    t*@horner(t,
    1.66666666666666657415e-01,
    -3.25565818622400915405e-01,
    2.01212532134862925881e-01,
    -4.00555345006794114027e-02,
    7.91534994289814532176e-04,
    3.47933107596021167570e-05)

arc_q(z::Float64) =
    @horner(z,
    1.0,
    -2.40339491173441421878e+00,
    2.02094576023350569471e+00,
    -6.88283971605453293030e-01,
    7.70381505559019352791e-02)

arc_p(t::Float32) =
    t*@horner(t,
    1.6666586697f-01,
    -4.2743422091f-02,
    -8.6563630030f-03)

arc_q(t::Float32) = @horner(t, 1.0f0, -7.0662963390f-01)

@inline arc_tRt(t) = arc_p(t)/arc_q(t)


@inline function asin_kernel(t::Float64, x::Float64)
    # we use that for 1/2 <= x < 1 we have
    #     asin(x) = pi/2-2*asin(sqrt((1-x)/2))
    # Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
    # then for x>0.98
    #     asin(x) = pi/2 - 2*(s+s*z*R(z))
    #         = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
    # For x<=0.98, let pio4_hi = pio2_hi/2, then
    #     f = hi part of s;
    #     c = sqrt(z) - f = (z-f*f)/(s+f)     ...f+c=sqrt(z)
    #  and
    #     asin(x) = pi/2 - 2*(s+s*z*R(z))
    #         = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
    #         = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
    pio2_lo = 6.12323399573676603587e-17
    s = sqrt_llvm(t)
    tRt = arc_tRt(t)
    if abs(x) >= 0.975 # |x| > 0.975
        return flipsign(pi/2 - (2.0*(s + s*tRt) - pio2_lo), x)
    else
        s0 = reinterpret(Float64, (reinterpret(UInt64, s) >> 32) << 32)
        c = (t - s0*s0)/(s + s0)
        p = 2.0*s*tRt - (pio2_lo - 2.0*c)
        q = pi/4 - 2.0*s0
        return flipsign(pi/4 - (p-q), x)
    end
end
@inline function asin_kernel(t::Float32, x::Float32)
    s = sqrt_llvm(Float64(t))
    tRt = arc_tRt(t) # rational approximation
    flipsign(Float32(pi/2 - 2*(s + s*tRt)), x)
end

@noinline asin_domain_error(x) = throw(DomainError(x, "asin(x) is not defined for |x| > 1."))
function asin(x::T) where T<:Union{Float32, Float64}
    # Since  asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
    # we approximate asin(x) on [0,0.5] by
    #     asin(x) = x + x*x^2*R(x^2)
    # where
    #     R(x^2) is a rational approximation of (asin(x)-x)/x^3
    # and its remez error is bounded by
    #     |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
    absx = abs(x)
    if absx >= T(1.0) # |x|>= 1
        if absx == T(1.0)
            return flipsign(T(pi)/2, x)
        end
        asin_domain_error(x)
    elseif absx < T(1.0)/2
        # if |x| sufficiently small, |x| is a good approximation
        if absx < ASIN_X_MIN_THRESHOLD(T)
            return x
        end
        return muladd(x, arc_tRt(x*x), x)
    end
    # else 1/2 <= |x| < 1
    t = (T(1.0) - absx)/2
    return asin_kernel(t, x)
end

# atan methods
ATAN_1_O_2_HI(::Type{Float64}) = 4.63647609000806093515e-01 # atan(0.5).hi
ATAN_2_O_2_HI(::Type{Float64}) = 7.85398163397448278999e-01 # atan(1.0).hi
ATAN_3_O_2_HI(::Type{Float64}) = 9.82793723247329054082e-01 # atan(1.5).hi
ATAN_INF_HI(::Type{Float64}) = 1.57079632679489655800e+00 # atan(Inf).hi

ATAN_1_O_2_HI(::Type{Float32}) = 4.6364760399f-01 # atan(0.5).hi
ATAN_2_O_2_HI(::Type{Float32}) = 7.8539812565f-01 # atan(1.0).hi
ATAN_3_O_2_HI(::Type{Float32}) = 9.8279368877f-01 # atan(1.5).hi
ATAN_INF_HI(::Type{Float32}) = 1.5707962513f+00 # atan(Inf).hi

ATAN_1_O_2_LO(::Type{Float64}) = 2.26987774529616870924e-17 # atan(0.5).lo
ATAN_2_O_2_LO(::Type{Float64}) = 3.06161699786838301793e-17 # atan(1.0).lo
ATAN_3_O_2_LO(::Type{Float64}) = 1.39033110312309984516e-17 # atan(1.5).lo
ATAN_INF_LO(::Type{Float64}) = 6.12323399573676603587e-17 # atan(Inf).lo

ATAN_1_O_2_LO(::Type{Float32}) = 5.0121582440f-09  # atan(0.5).lo
ATAN_2_O_2_LO(::Type{Float32}) = 3.7748947079f-08  # atan(1.0).lo
ATAN_3_O_2_LO(::Type{Float32}) = 3.4473217170f-08  # atan(1.5).lo
ATAN_INF_LO(::Type{Float32}) = 7.5497894159f-08  # atan(Inf).lo

ATAN_LARGE_X(::Type{Float64}) = 2.0^66 # seems too large? 2.0^60 gives the same
ATAN_SMALL_X(::Type{Float64}) = 2.0^-27
ATAN_LARGE_X(::Type{Float32}) = 2.0f0^26
ATAN_SMALL_X(::Type{Float32}) = 2.0f0^-12

atan_p(z::Float64, w::Float64) = z*@horner(w,
     3.33333333333329318027e-01,
     1.42857142725034663711e-01,
     9.09088713343650656196e-02,
     6.66107313738753120669e-02,
     4.97687799461593236017e-02,
     1.62858201153657823623e-02)
atan_q(w::Float64) = w*@horner(w,
     -1.99999999998764832476e-01,
     -1.11111104054623557880e-01,
     -7.69187620504482999495e-02,
     -5.83357013379057348645e-02,
     -3.65315727442169155270e-02)
atan_p(z::Float32, w::Float32) = z*@horner(w, 3.3333328366f-01,  1.4253635705f-01, 6.1687607318f-02)
atan_q(w::Float32) = w*@horner(w, -1.9999158382f-01, -1.0648017377f-01)
@inline function atan_pq(x)
    x² = x*x
    x⁴ = x²*x²
    # break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly
    atan_p(x², x⁴), atan_q(x⁴)
end

function atan(x::T) where T<:Union{Float32, Float64}
    # Method
    #   1. Reduce x to positive by atan(x) = -atan(-x).
    #   2. According to the integer k=4t+0.25 chopped, t=x, the argument
    #      is further reduced to one of the following intervals and the
    #      arctangent of t is evaluated by the corresponding formula:
    #
    #      [0,7/16]      atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
    #      [7/16,11/16]  atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
    #      [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
    #      [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
    #      [39/16,INF]   atan(x) = atan(INF) + atan( -1/t )
    #
    #  If isnan(x) is true, then the nan value will eventually be passed to
    #  atan_pq(x) and return the appropriate nan value.

    absx = abs(x)
    if absx >= ATAN_LARGE_X(T)
        return copysign(T(1.5707963267948966), x)
    end
    if absx < T(7/16)
        # no reduction needed
        if absx < ATAN_SMALL_X(T)
            return x
        end
        p, q = atan_pq(x)
        return x - x*(p + q)
    end
    xsign = sign(x)
    if absx < T(19/16) # 7/16 <= |x| < 19/16
        if absx < T(11/16) # 7/16 <= |x| <11/16
            hi = ATAN_1_O_2_HI(T)
            lo = ATAN_1_O_2_LO(T)
            x = (T(2.0)*absx - T(1.0))/(T(2.0) + absx)
        else # 11/16 <= |x| < 19/16
            hi = ATAN_2_O_2_HI(T)
            lo = ATAN_2_O_2_LO(T)
            x  = (absx - T(1.0))/(absx + T(1.0))
        end
    else
        if absx < T(39/16)  # 19/16 <= |x| < 39/16
            hi = ATAN_3_O_2_HI(T)
            lo = ATAN_3_O_2_LO(T)
            x = (absx - T(1.5))/(T(1.0) + T(1.5)*absx)
        else # 39/16 <= |x| < upper threshold (2.0^66 or 2.0f0^26)
            hi = ATAN_INF_HI(T)
            lo = ATAN_INF_LO(T)
            x  = -T(1.0)/absx
        end
    end
    # end of argument reduction
    p, q = atan_pq(x)
    z = hi - ((x*(p + q) - lo) - x)
    copysign(z, xsign)
end
# atan2 methods
ATAN2_PI_LO(::Type{Float32}) = -8.7422776573f-08
ATAN2_RATIO_BIT_SHIFT(::Type{Float32}) = 23
ATAN2_RATIO_THRESHOLD(::Type{Float32}) = 26

ATAN2_PI_LO(::Type{Float64}) = 1.2246467991473531772E-16
ATAN2_RATIO_BIT_SHIFT(::Type{Float64}) = 20
ATAN2_RATIO_THRESHOLD(::Type{Float64}) = 60

function atan(y::T, x::T) where T<:Union{Float32, Float64}
    # Method :
    #    M1) Reduce y to positive by atan2(y,x)=-atan2(-y,x).
    #    M2) Reduce x to positive by (if x and y are unexceptional):
    #        ARG (x+iy) = arctan(y/x)          ... if x > 0,
    #        ARG (x+iy) = pi - arctan[y/(-x)]   ... if x < 0,
    #
    # Special cases:
    #
    #    S1) ATAN2((anything), NaN ) is NaN;
    #    S2) ATAN2(NAN , (anything) ) is NaN;
    #    S3) ATAN2(+-0, +(anything but NaN)) is +-0  ;
    #    S4) ATAN2(+-0, -(anything but NaN)) is +-pi ;
    #    S5) ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
    #    S6) ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
    #    S7) ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
    #    S8) ATAN2(+-INF,+INF ) is +-pi/4 ;
    #    S9) ATAN2(+-INF,-INF ) is +-3pi/4;
    #    S10) ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
    if isnan(x) | isnan(y) # S1 or S2
        return isnan(x) ? x : y
    end

    if x == T(1.0) # then y/x = y and x > 0, see M2
        return atan(y)
    end
    # generate an m ∈ {0, 1, 2, 3} to branch off of
    m = 2*signbit(x) + 1*signbit(y)

    if iszero(y)
        if m == 0 || m == 1
            return y # atan(+-0, +anything) = +-0
        elseif m == 2
            return T(pi) # atan(+0, -anything) = pi
        elseif m == 3
            return -T(pi) # atan(-0, -anything) =-pi
        end
    elseif iszero(x)
        return flipsign(T(pi)/2, y)
    end

    if isinf(x)
        if isinf(y)
            if m == 0
                return T(pi)/4  # atan(+Inf), +Inf))
            elseif m == 1
                return -T(pi)/4 # atan(-Inf), +Inf))
            elseif m == 2
                return 3*T(pi)/4 # atan(+Inf, -Inf)
            elseif m == 3
                return -3*T(pi)/4 # atan(-Inf,-Inf)
            end
        else
            if m == 0
                return zero(T)  # atan(+...,+Inf) */
            elseif m == 1
                return -zero(T) # atan(-...,+Inf) */
            elseif m == 2
                return T(pi)    # atan(+...,-Inf) */
            elseif m == 3
                return -T(pi)   # atan(-...,-Inf) */
            end
        end
    end

    # x wasn't Inf, but y is
    isinf(y) && return copysign(T(pi)/2, y)

    ypw = poshighword(y)
    xpw = poshighword(x)
    # compute y/x for Float32
    k = reinterpret(Int32, ypw-xpw)>>ATAN2_RATIO_BIT_SHIFT(T)

    if k > ATAN2_RATIO_THRESHOLD(T) # |y/x| >  threshold
        z=T(pi)/2+T(0.5)*ATAN2_PI_LO(T)
        m&=1;
    elseif x<0 && k < -ATAN2_RATIO_THRESHOLD(T) # 0 > |y|/x > threshold
        z = zero(T)
    else #safe to do y/x
        z = atan(abs(y/x))
    end

    if m == 0
        return z # atan(+,+)
    elseif m == 1
        return -z # atan(-,+)
    elseif m == 2
        return T(pi)-(z-ATAN2_PI_LO(T)) # atan(+,-)
    else # default case m == 3
        return (z-ATAN2_PI_LO(T))-T(pi) # atan(-,-)
    end
end
# acos methods
ACOS_X_MIN_THRESHOLD(::Type{Float32}) = 2.0f0^-26
ACOS_X_MIN_THRESHOLD(::Type{Float64}) = 2.0^-57
PIO2_HI(::Type{Float32}) = 1.5707962513f+00
PIO2_LO(::Type{Float32}) = 7.5497894159f-08
PIO2_HI(::Type{Float64}) = 1.57079632679489655800e+00
PIO2_LO(::Type{Float64}) = 6.12323399573676603587e-17
ACOS_PI(::Type{Float32}) = 3.1415925026f+00
ACOS_PI(::Type{Float64}) = 3.14159265358979311600e+00
@inline ACOS_CORRECT_LOWWORD(::Type{Float32}, x) = reinterpret(Float32, (reinterpret(UInt32, x) & 0xfffff000))
@inline ACOS_CORRECT_LOWWORD(::Type{Float64}, x) = reinterpret(Float64, (reinterpret(UInt64, x) >> 32) << 32)

@noinline acos_domain_error(x) = throw(DomainError(x, "acos(x) not defined for |x| > 1"))
function acos(x::T) where T <: Union{Float32, Float64}
    # Method :
    #    acos(x)  = pi/2 - asin(x)
    #    acos(-x) = pi/2 + asin(x)
    # As a result, we use the same rational approximation (arc_tRt) as in asin.
    # See the comments in asin for more information about this approximation.
    # 1) For |x| <= 0.5
    #    acos(x) = pi/2 - (x + x*x^2*R(x^2))
    # 2) For x < -0.5
    #    acos(x) = pi - 2asin(sqrt((1 - |x|)/2))
    #        = pi - 0.5*(s+s*z*R(z))
    # where z=(1-|x|)/2, s=sqrt(z)
    # 3) For x > 0.5
    #     acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1 - x)/2)))
    #        = 2asin(sqrt((1 - x)/2))
    #        = 2s + 2s*z*R(z)     ...z=(1 - x)/2, s=sqrt(z)
    #        = 2f + (2c + 2s*z*R(z))
    #    where f=hi part of s, and c = (z - f*f)/(s + f) is the correction term
    #    for f so that f + c ~ sqrt(z).

    # Special cases:
    #    4) if x is NaN, return x itself;
    #    5) if |x|>1 throw warning.

    absx = abs(x)
    if absx >= T(1.0)
        # acos(-1) = π, acos(1) = 0
        absx == T(1.0) && return x > T(0.0) ? T(0.0) : T(pi)
        # acos(x) is not defined for |x| > 1
        acos_domain_error(x) # see 5) above
    elseif absx < T(1.0)/2 # see 1) above
        # if |x| sufficiently small, acos(x) ≈ pi/2
        absx < ACOS_X_MIN_THRESHOLD(T) && return T(pi)/2
        # if |x| < 0.5 we have acos(x) = pi/2 - (x + x*x^2*R(x^2))
        return PIO2_HI(T) - (x - (PIO2_LO(T) - x*arc_tRt(x*x)))
    end
    z = (T(1.0) - absx)*T(0.5)
    zRz = arc_tRt(z)
    s = sqrt_llvm(z)
    if x < T(0.0) # see 2) above
        return ACOS_PI(T) - T(2.0)*(s + (zRz*s - PIO2_LO(T)))
    else # see 3) above
        # if x > 0.5 we have
        # acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
        #         = 2asin(sqrt((1-x)/2))
        #         = 2s + 2s*z*R(z)    ...z=(1-x)/2, s=sqrt(z)
        #         = 2f + (2c + 2s*z*R(z))
        # where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
        # for f so that f+c ~ sqrt(z).
        df = ACOS_CORRECT_LOWWORD(T, s)
        c  = (z - df*df)/(s + df)
        return T(2.0)*(df + (zRz*s + c))
    end
end

# Uses minimax polynomial of sin(π * x) for π * x in [0, .25]
@inline function sinpi_kernel(x::Float64)
    sinpi_kernel_wide(x)
end
@inline function sinpi_kernel_wide(x::Float64)
    x² = x*x
    x⁴ = x²*x²
    r  = evalpoly(x², (2.5501640398773415, -0.5992645293202981, 0.08214588658006512,
                       -7.370429884921779e-3, 4.662827319453555e-4, -2.1717412523382308e-5))
    return muladd(3.141592653589793, x, x*muladd(-5.16771278004997,
                  x², muladd(x⁴, r,  1.2245907532225998e-16)))
end
@inline function sinpi_kernel(x::Float32)
    Float32(sinpi_kernel_wide(x))
end
@inline function sinpi_kernel_wide(x::Float32)
    x = Float64(x)
    return x*evalpoly(x*x, (3.1415926535762266, -5.167712769188119,
                            2.5501626483206374, -0.5992021090314925, 0.08100185277841528))
end

@inline function sinpi_kernel(x::Float16)
    Float16(sinpi_kernel_wide(x))
end
@inline function sinpi_kernel_wide(x::Float16)
    x = Float32(x)
    return x*evalpoly(x*x, (3.1415927f0, -5.1677127f0, 2.5501626f0, -0.5992021f0, 0.081001855f0))
end

# Uses minimax polynomial of cos(π * x) for π * x in [0, .25]
@inline function cospi_kernel(x::Float64)
    cospi_kernel_wide(x)
end
@inline function cospi_kernel_wide(x::Float64)
    x² = x*x
    r = x²*evalpoly(x², (4.058712126416765, -1.3352627688537357, 0.23533063027900392,
                         -0.025806887811869204, 1.9294917136379183e-3, -1.0368935675474665e-4))
    a_x² = 4.934802200544679 * x²
    a_x²lo = muladd(3.109686485461973e-16, x², muladd(4.934802200544679, x², -a_x²))

    w  = 1.0-a_x²
    return w + muladd(x², r, ((1.0-w)-a_x²) - a_x²lo)
end
@inline function cospi_kernel(x::Float32)
    Float32(cospi_kernel_wide(x))
end
@inline function cospi_kernel_wide(x::Float32)
    x = Float64(x)
    return evalpoly(x*x, (1.0, -4.934802200541122, 4.058712123568637,
                          -1.3352624040152927, 0.23531426791507182, -0.02550710082498761))
end
@inline function cospi_kernel(x::Float16)
    Float16(cospi_kernel_wide(x))
end
@inline function cospi_kernel_wide(x::Float16)
    x = Float32(x)
    return evalpoly(x*x, (1.0f0, -4.934802f0, 4.058712f0, -1.3352624f0, 0.23531426f0, -0.0255071f0))
end

"""
    sinpi(x)

Compute ``\\sin(\\pi x)`` more accurately than `sin(pi*x)`, especially for large `x`.

See also [`sind`](@ref), [`cospi`](@ref), [`sincospi`](@ref).
"""
function sinpi(_x::T) where T<:IEEEFloat
    x = abs(_x)
    if !isfinite(x)
        isnan(x) && return x
        throw(DomainError(x, "`x` cannot be infinite."))
    end
    # For large x, answers are all 1 or zero.
    x >= maxintfloat(T) && return copysign(zero(T), _x)

    # reduce to interval [0, 0.5]
    n = round(2*x)
    rx = float(muladd(T(-.5), n, x))
    n = Int64(n) & 3
    if n==0
        res = sinpi_kernel(rx)
    elseif n==1
        res = cospi_kernel(rx)
    elseif n==2
        res = zero(T)-sinpi_kernel(rx)
    else
        res = zero(T)-cospi_kernel(rx)
    end
    return ifelse(signbit(_x), -res, res)
end
"""
    cospi(x)

Compute ``\\cos(\\pi x)`` more accurately than `cos(pi*x)`, especially for large `x`.
"""
function cospi(x::T) where T<:IEEEFloat
    x = abs(x)
    if !isfinite(x)
        isnan(x) && return x
        throw(DomainError(x, "`x` cannot be infinite."))
    end
    # For large x, answers are all 1 or zero.
    x >= maxintfloat(T) && return one(T)

    # reduce to interval [0, 0.5]
    n = round(2*x)
    rx = float(muladd(T(-.5), n, x))
    n = Int64(n) & 3
    if n==0
        return cospi_kernel(rx)
    elseif n==1
        return zero(T)-sinpi_kernel(rx)
    elseif n==2
        return zero(T)-cospi_kernel(rx)
    else
        return sinpi_kernel(rx)
    end
end
"""
    sincospi(x)

Simultaneously compute [`sinpi(x)`](@ref) and [`cospi(x)`](@ref) (the sine and cosine of `π*x`,
where `x` is in radians), returning a tuple `(sine, cosine)`.

!!! compat "Julia 1.6"
    This function requires Julia 1.6 or later.

See also: [`cispi`](@ref), [`sincosd`](@ref), [`sinpi`](@ref).
"""
function sincospi(_x::T) where T<:IEEEFloat
    x = abs(_x)
    if !isfinite(x)
        isnan(x) && return x, x
        throw(DomainError(x, "`x` cannot be infinite."))
    end
    # For large x, answers are all 1 or zero.
    x >= maxintfloat(T) && return (copysign(zero(T), _x), one(T))

    # reduce to interval [0, 0.5]
    n = round(2*x)
    rx = float(muladd(T(-.5), n, x))
    n = Int64(n) & 3
    si, co = sinpi_kernel(rx),cospi_kernel(rx)
    if n==0
        si, co = si, co
    elseif n==1
        si, co  = co, zero(T)-si
    elseif n==2
        si, co  = zero(T)-si, zero(T)-co
    else
        si, co  = zero(T)-co, si
    end
    si = ifelse(signbit(_x), -si, si)
    return si, co
end

"""
    tanpi(x)

Compute ``\\tan(\\pi x)`` more accurately than `tan(pi*x)`, especially for large `x`.

!!! compat "Julia 1.10"
    This function requires at least Julia 1.10.

See also [`tand`](@ref), [`sinpi`](@ref), [`cospi`](@ref), [`sincospi`](@ref).
"""
function tanpi(_x::T) where T<:IEEEFloat
    # This is modified from sincospi.
    # Would it be faster or more accurate to make a tanpi_kernel?
    x = abs(_x)
    if !isfinite(x)
        isnan(x) && return x
        throw(DomainError(x, "`x` cannot be infinite."))
    end
    # For large x, answers are all zero.
    # All integer values for floats larger than maxintfloat are even.
    x >= maxintfloat(T) && return copysign(zero(T), _x)

    # reduce to interval [0, 0.5]
    n = round(2*x)
    rx = float(muladd(T(-.5), n, x))
    n = Int64(n) & 3
    si, co = sinpi_kernel_wide(rx), cospi_kernel_wide(rx)
    if n==0
        si, co = si, co
    elseif n==1
        si, co  = co, zero(T)-si
    elseif n==2
        si, co  = zero(T)-si, zero(T)-co
    else
        si, co  = zero(T)-co, si
    end
    si = ifelse(signbit(_x), -si, si)
    return float(T)(si / co)
end

sinpi(x::Integer) = x >= 0 ? zero(float(x)) : -zero(float(x))
cospi(x::Integer) = isodd(x) ? -one(float(x)) : one(float(x))
tanpi(x::Integer) = x >= 0 ? (isodd(x) ? -zero(float(x)) : zero(float(x))) :
                             (isodd(x) ? zero(float(x)) : -zero(float(x)))
sincospi(x::Integer) = (sinpi(x), cospi(x))
sinpi(x::AbstractFloat) = sin(pi*x)
cospi(x::AbstractFloat) = cos(pi*x)
sincospi(x::AbstractFloat) = sincos(pi*x)
tanpi(x::AbstractFloat) = tan(pi*x)
tanpi(x::Complex) = sinpi(x) / cospi(x) # Is there a better way to do this?

function sinpi(z::Complex{T}) where T
    F = float(T)
    zr, zi = reim(z)
    if isinteger(zr)
        # zr = ...,-2,-1,0,1,2,...
        # sin(pi*zr) == ±0
        # cos(pi*zr) == ±1
        # cosh(pi*zi) > 0
        s = copysign(zero(F),zr)
        c_pos = isa(zr,Integer) ? iseven(zr) : isinteger(zr/2)
        sh = sinh(pi*zi)
        Complex(s, c_pos ? sh : -sh)
    elseif isinteger(2*zr)
        # zr = ...,-1.5,-0.5,0.5,1.5,2.5,...
        # sin(pi*zr) == ±1
        # cos(pi*zr) == +0
        # sign(sinh(pi*zi)) == sign(zi)
        s_pos = isinteger((2*zr-1)/4)
        ch = cosh(pi*zi)
        Complex(s_pos ? ch : -ch, isnan(zi) ? zero(F) : copysign(zero(F),zi))
    elseif !isfinite(zr)
        if zi == 0 || isinf(zi)
            Complex(F(NaN), F(zi))
        else
            Complex(F(NaN), F(NaN))
        end
    else
        pizi = pi*zi
        sipi, copi = sincospi(zr)
        Complex(sipi*cosh(pizi), copi*sinh(pizi))
    end
end

function cospi(z::Complex{T}) where T
    F = float(T)
    zr, zi = reim(z)
    if isinteger(zr)
        # zr = ...,-2,-1,0,1,2,...
        # sin(pi*zr) == ±0
        # cos(pi*zr) == ±1
        # sign(sinh(pi*zi)) == sign(zi)
        # cosh(pi*zi) > 0
        s = copysign(zero(F),zr)
        c_pos = isa(zr,Integer) ? iseven(zr) : isinteger(zr/2)
        ch = cosh(pi*zi)
        Complex(c_pos ? ch : -ch, isnan(zi) ? s : -flipsign(s,zi))
    elseif isinteger(2*zr)
        # zr = ...,-1.5,-0.5,0.5,1.5,2.5,...
        # sin(pi*zr) == ±1
        # cos(pi*zr) == +0
        # sign(sinh(pi*zi)) == sign(zi)
        s_pos = isinteger((2*zr-1)/4)
        sh = sinh(pi*zi)
        Complex(zero(F), s_pos ? -sh : sh)
    elseif !isfinite(zr)
        if zi == 0
            Complex(F(NaN), isnan(zr) ? zero(F) : -flipsign(F(zi),zr))
        elseif isinf(zi)
            Complex(F(Inf), F(NaN))
        else
            Complex(F(NaN), F(NaN))
        end
    else
        pizi = pi*zi
        sipi, copi = sincospi(zr)
        Complex(copi*cosh(pizi), -sipi*sinh(pizi))
    end
end

function sincospi(z::Complex{T}) where T
    F = float(T)
    zr, zi = reim(z)
    if isinteger(zr)
        # zr = ...,-2,-1,0,1,2,...
        # sin(pi*zr) == ±0
        # cos(pi*zr) == ±1
        # cosh(pi*zi) > 0
        s = copysign(zero(F),zr)
        c_pos = isa(zr,Integer) ? iseven(zr) : isinteger(zr/2)
        pizi = pi*zi
        sh, ch = sinh(pizi), cosh(pizi)
        (
            Complex(s, c_pos ? sh : -sh),
            Complex(c_pos ? ch : -ch, isnan(zi) ? s : -flipsign(s,zi)),
        )
    elseif isinteger(2*zr)
        # zr = ...,-1.5,-0.5,0.5,1.5,2.5,...
        # sin(pi*zr) == ±1
        # cos(pi*zr) == +0
        # sign(sinh(pi*zi)) == sign(zi)
        s_pos = isinteger((2*zr-1)/4)
        pizi = pi*zi
        sh, ch = sinh(pizi), cosh(pizi)
        (
            Complex(s_pos ? ch : -ch, isnan(zi) ? zero(F) : copysign(zero(F),zi)),
            Complex(zero(F), s_pos ? -sh : sh),
        )
    elseif !isfinite(zr)
        if zi == 0
            Complex(F(NaN), F(zi)), Complex(F(NaN), isnan(zr) ? zero(F) : -flipsign(F(zi),zr))
        elseif isinf(zi)
            Complex(F(NaN), F(zi)), Complex(F(Inf), F(NaN))
        else
            Complex(F(NaN), F(NaN)), Complex(F(NaN), F(NaN))
        end
    else
        pizi = pi*zi
        sipi, copi = sincospi(zr)
        sihpi, cohpi = sinh(pizi), cosh(pizi)
        (
            Complex(sipi*cohpi, copi*sihpi),
            Complex(copi*cohpi, -sipi*sihpi),
        )
    end
end

"""
    fastabs(x::Number)

Faster `abs`-like function for rough magnitude comparisons.
`fastabs` is equivalent to `abs(x)` for most `x`,
but for complex `x` it computes `abs(real(x))+abs(imag(x))` rather
than requiring `hypot`.
"""
fastabs(x::Number) = abs(x)
fastabs(z::Complex) = abs(real(z)) + abs(imag(z))

# sinc and cosc are zero if the real part is Inf and imag is finite
isinf_real(x::Real) = isinf(x)
isinf_real(x::Complex) = isinf(real(x)) && isfinite(imag(x))
isinf_real(x::Number) = false

"""
    sinc(x)

Compute ``\\sin(\\pi x) / (\\pi x)`` if ``x \\neq 0``, and ``1`` if ``x = 0``.

See also [`cosc`](@ref), its derivative.
"""
sinc(x::Number) = _sinc(float(x))
sinc(x::Integer) = iszero(x) ? one(x) : zero(x)
_sinc(x::Number) = iszero(x) ? one(x) : isinf_real(x) ? zero(x) : sinpi(x)/(pi*x)
_sinc_threshold(::Type{Float64}) = 0.001
_sinc_threshold(::Type{Float32}) = 0.05f0
@inline _sinc(x::Union{T,Complex{T}}) where {T<:Union{Float32,Float64}} =
    fastabs(x) < _sinc_threshold(T) ? evalpoly(x^2, (T(1), -T(pi)^2/6, T(pi)^4/120)) : isinf_real(x) ? zero(x) : sinpi(x)/(pi*x)
_sinc(x::Float16) = Float16(_sinc(Float32(x)))
_sinc(x::ComplexF16) = ComplexF16(_sinc(ComplexF32(x)))

"""
    cosc(x)

Compute ``\\cos(\\pi x) / x - \\sin(\\pi x) / (\\pi x^2)`` if ``x \\neq 0``, and ``0`` if
``x = 0``. This is the derivative of `sinc(x)`.
"""
cosc(x::Number) = _cosc(float(x))
function _cosc(x::Number)
    # naive cosc formula is susceptible to catastrophic
    # cancellation error near x=0, so we use the Taylor series
    # for small enough |x|.
    if fastabs(x) < 0.5
        # generic Taylor series: π ∑ (-1)^n (πx)^{2n-1}/a(n) where
        # a(n) = (1+2n)*(2n-1)! (= OEIS A174549)
        s = (term = -(π*x))/3
        π²x² = term^2
        ε = eps(fastabs(term)) # error threshold to stop sum
        n = 1
        while true
            n += 1
            term *= π²x²/((1-2n)*(2n-2))
            s += (δs = term/(1+2n))
            fastabs(δs) ≤ ε && break
        end
        return π*s
    else
        return isinf_real(x) ? zero(x) : ((pi*x)*cospi(x)-sinpi(x))/((pi*x)*x)
    end
end
# hard-code Float64/Float32 Taylor series, with coefficients
#  Float64.([(-1)^n*big(pi)^(2n)/((2n+1)*factorial(2n-1)) for n = 1:6])
_cosc(x::Union{Float64,ComplexF64}) =
    fastabs(x) < 0.14 ? x*evalpoly(x^2, (-3.289868133696453, 3.2469697011334144, -1.1445109447325053, 0.2091827825412384, -0.023460810354558236, 0.001781145516372852)) :
    isinf_real(x) ? zero(x) : ((pi*x)*cospi(x)-sinpi(x))/((pi*x)*x)
_cosc(x::Union{Float32,ComplexF32}) =
    fastabs(x) < 0.26f0 ? x*evalpoly(x^2, (-3.289868f0, 3.2469697f0, -1.144511f0, 0.20918278f0)) :
    isinf_real(x) ? zero(x) : ((pi*x)*cospi(x)-sinpi(x))/((pi*x)*x)
_cosc(x::Float16) = Float16(_cosc(Float32(x)))
_cosc(x::ComplexF16) = ComplexF16(_cosc(ComplexF32(x)))

for (finv, f, finvh, fh, finvd, fd, fn) in ((:sec, :cos, :sech, :cosh, :secd, :cosd, "secant"),
                                            (:csc, :sin, :csch, :sinh, :cscd, :sind, "cosecant"),
                                            (:cot, :tan, :coth, :tanh, :cotd, :tand, "cotangent"))
    name = string(finv)
    hname = string(finvh)
    dname = string(finvd)
    @eval begin
        @doc """
            $($name)(x)

        Compute the $($fn) of `x`, where `x` is in radians.
        """ ($finv)(z::Number) = inv(($f)(z))
        @doc """
            $($hname)(x)

        Compute the hyperbolic $($fn) of `x`.
        """ ($finvh)(z::Number) = inv(($fh)(z))
        @doc """
            $($dname)(x)

        Compute the $($fn) of `x`, where `x` is in degrees.
        """ ($finvd)(z::Number) = inv(($fd)(z))
    end
end

for (tfa, tfainv, hfa, hfainv, fn) in ((:asec, :acos, :asech, :acosh, "secant"),
                                       (:acsc, :asin, :acsch, :asinh, "cosecant"),
                                       (:acot, :atan, :acoth, :atanh, "cotangent"))
    tname = string(tfa)
    hname = string(hfa)
    @eval begin
        @doc """
            $($tname)(x)
        Compute the inverse $($fn) of `x`, where the output is in radians. """ ($tfa)(y::Number) = ($tfainv)(inv(y))
        @doc """
            $($hname)(x)
        Compute the inverse hyperbolic $($fn) of `x`. """ ($hfa)(y::Number) = ($hfainv)(inv(y))
    end
end


# multiply in extended precision
function deg2rad_ext(x::Float64)
    m = 0.017453292519943295
    m_hi = 0.01745329238474369
    m_lo = 1.3519960527851425e-10

    u = 134217729.0*x # 0x1p27 + 1
    x_hi = u-(u-x)
    x_lo = x-x_hi

    y_hi = m*x
    y_lo = x_hi * m_lo + (x_lo* m_hi + ((x_hi*m_hi-y_hi) + x_lo*m_lo))

    DoubleFloat64(y_hi,y_lo)
end
deg2rad_ext(x::Float32) = DoubleFloat32(deg2rad(Float64(x)))
deg2rad_ext(x::Real) = deg2rad(x) # Fallback

function sind(x::Real)
    if isinf(x)
        return throw(DomainError(x, "`x` cannot be infinite."))
    elseif isnan(x)
        return x
    end

    rx = copysign(float(rem(x,360)),x)
    arx = abs(rx)

    if rx == zero(rx)
        return rx
    elseif arx < oftype(rx,45)
        return sin_kernel(deg2rad_ext(rx))
    elseif arx <= oftype(rx,135)
        y = deg2rad_ext(oftype(rx,90) - arx)
        return copysign(cos_kernel(y),rx)
    elseif arx == oftype(rx,180)
        return copysign(zero(rx),rx)
    elseif arx < oftype(rx,225)
        y = deg2rad_ext((oftype(rx,180) - arx)*sign(rx))
        return sin_kernel(y)
    elseif arx <= oftype(rx,315)
        y = deg2rad_ext(oftype(rx,270) - arx)
        return -copysign(cos_kernel(y),rx)
    else
        y = deg2rad_ext(rx - copysign(oftype(rx,360),rx))
        return sin_kernel(y)
    end
end

function cosd(x::Real)
    if isinf(x)
        return throw(DomainError(x, "`x` cannot be infinite."))
    elseif isnan(x)
        return x
    end

    rx = abs(float(rem(x,360)))

    if rx <= oftype(rx,45)
        return cos_kernel(deg2rad_ext(rx))
    elseif rx < oftype(rx,135)
        y = deg2rad_ext(oftype(rx,90) - rx)
        return sin_kernel(y)
    elseif rx <= oftype(rx,225)
        y = deg2rad_ext(oftype(rx,180) - rx)
        return -cos_kernel(y)
    elseif rx < oftype(rx,315)
        y = deg2rad_ext(rx - oftype(rx,270))
        return sin_kernel(y)
    else
        y = deg2rad_ext(oftype(rx,360) - rx)
        return cos_kernel(y)
    end
end

tand(x::Real) = sind(x) / cosd(x)

"""
    sincosd(x)

Simultaneously compute the sine and cosine of `x`, where `x` is in degrees.

!!! compat "Julia 1.3"
    This function requires at least Julia 1.3.
"""
sincosd(x) = (sind(x), cosd(x))
# It turns out that calling these functions separately yields better
# performance than considering each case and calling `sincos_kernel`.

sincosd(::Missing) = (missing, missing)

for (fd, f, fn) in ((:sind, :sin, "sine"), (:cosd, :cos, "cosine"), (:tand, :tan, "tangent"))
    for (fu, un) in ((:deg2rad, "degrees"),)
        name = string(fd)
        @eval begin
            @doc """
                $($name)(x)

            Compute $($fn) of `x`, where `x` is in $($un).
            If `x` is a matrix, `x` needs to be a square matrix.

            !!! compat "Julia 1.7"
                Matrix arguments require Julia 1.7 or later.
            """ ($fd)(x) = ($f)(($fu).(x))
        end
    end
end

for (fd, f, fn) in ((:asind, :asin, "sine"), (:acosd, :acos, "cosine"),
                    (:asecd, :asec, "secant"), (:acscd, :acsc, "cosecant"), (:acotd, :acot, "cotangent"))

    for (fu, un) in ((:rad2deg, "degrees"),)
        name = string(fd)
        @eval begin
            @doc """
                $($name)(x)

            Compute the inverse $($fn) of `x`, where the output is in $($un).
            If `x` is a matrix, `x` needs to be a square matrix.

            !!! compat "Julia 1.7"
                Matrix arguments require Julia 1.7 or later.
            """ ($fd)(x) = ($fu).(($f)(x))
        end
    end
end

"""
    atand(y)
    atand(y,x)

Compute the inverse tangent of `y` or `y/x`, respectively, where the output is in degrees.

!!! compat "Julia 1.7"
    The one-argument method supports square matrix arguments as of Julia 1.7.
"""
atand(y)    = rad2deg.(atan(y))
atand(y, x) = rad2deg.(atan(y,x))
W   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/special/rem_pio2.jl�&      # This file is a part of Julia. Except for the rem_pio2_kernel, and
# cody_waite_* methods (see below) license is MIT: https://julialang.org/license

# rem_pio2_kernel and cody_waite_* methods are heavily based on FDLIBM code:
# __ieee754_rem_pio2, that is made available under the following licence:

## Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
##
## Developed at SunPro, a Sun Microsystems, Inc. business.
## Permission to use, copy, modify, and distribute this
## software is freely granted, provided that this notice
## is preserved.

# Bits of 1/2π
#   1/2π == sum(x / 0x1p64^i for i,x = enumerate(INV_2PI))
# Can be obtained by:
#
#    setprecision(BigFloat, 4096)
#    I = 0.5/big(pi)
#    for i = 1:19
#        I *= 0x1p64
#        k = trunc(UInt64, I)
#        @printf "0x%016x,\n" k
#        I -= k
#    end

const INV_2PI = (
    0x28be_60db_9391_054a,
    0x7f09_d5f4_7d4d_3770,
    0x36d8_a566_4f10_e410,
    0x7f94_58ea_f7ae_f158,
    0x6dc9_1b8e_9093_74b8,
    0x0192_4bba_8274_6487,
    0x3f87_7ac7_2c4a_69cf,
    0xba20_8d7d_4bae_d121,
    0x3a67_1c09_ad17_df90,
    0x4e64_758e_60d4_ce7d,
    0x2721_17e2_ef7e_4a0e,
    0xc7fe_25ff_f781_6603,
    0xfbcb_c462_d682_9b47,
    0xdb4d_9fb3_c9f2_c26d,
    0xd3d1_8fd9_a797_fa8b,
    0x5d49_eeb1_faf9_7c5e,
    0xcf41_ce7d_e294_a4ba,
    0x9afe_d7ec_47e3_5742,
    0x1580_cc11_bf1e_daea)

@inline function cody_waite_2c_pio2(x::Float64, fn, n)
    pio2_1 = 1.57079632673412561417e+00
    pio2_1t = 6.07710050650619224932e-11

    z = muladd(-fn, pio2_1, x) # x - fn*pio2_1
    y1 = muladd(-fn, pio2_1t, z) # z - fn*pio2_1t
    y2 = muladd(-fn, pio2_1t, (z - y1)) # (z - y1) - fn*pio2_1t
    n, DoubleFloat64(y1, y2)
end

@inline function cody_waite_ext_pio2(x::Float64, xhp)
    pio2_1 = 1.57079632673412561417e+00
    pio2_1t = 6.07710050650619224932e-11
    pio2_2 = 6.07710050630396597660e-11
    pio2_2t = 2.02226624879595063154e-21
    pio2_3 = 2.02226624871116645580e-21
    pio2_3t = 8.47842766036889956997e-32

    fn = round(x*(2/pi)) # round to integer
    # on older systems, the above could be faster with
    # rf = 1.5/eps(Float64)
    # fn = (x*(2/pi)+rf)-rf

    r  = muladd(-fn, pio2_1, x) # x - fn*pio2_1
    w  = fn*pio2_1t # 1st round good to 85 bit
    j  = xhp>>20
    y1 = r-w
    high = highword(y1)
    i = j-((high>>20)&0x7ff)
    if i>16  # 2nd iteration needed, good to 118
        t  = r
        w  = fn*pio2_2
        r  = t-w
        w  = muladd(fn, pio2_2t,-((t-r)-w))
        y1 = r-w
        high = highword(y1)
        i = j-((high>>20)&0x7ff)
        if i>49 # 3rd iteration need, 151 bits acc
            t  = r # will cover all possible cases
            w  = fn*pio2_3
            r  = t-w
            w  = muladd(fn, pio2_3t, -((t-r)-w))
            y1 = r-w
        end
    end
    y2 = (r-y1)-w
    return unsafe_trunc(Int, fn), DoubleFloat64(y1, y2)
end


"""
    fromfraction(f::Int128)
Compute a tuple of values `(z1,z2)` such that
    ``z1 + z2 == f / 2^128``
and the significand of `z1` has 27 trailing zeros.
"""
function fromfraction(f::Int128)
    if f == 0
        return (0.0,0.0)
    end

    # 1. get leading term truncated to 26 bits
    s = ((f < 0) % UInt64) << 63     # sign bit
    x = abs(f) % UInt128             # magnitude
    n1 = Base.top_set_bit(x)          # ndigits0z(x,2)
    m1 = ((x >> (n1-26)) % UInt64) << 27
    d1 = ((n1-128+1021) % UInt64) << 52
    z1 = reinterpret(Float64, s | (d1 + m1))

    # 2. compute remaining term
    x2 = (x - (UInt128(m1) << (n1-53)))
    if x2 == 0
        return (z1, 0.0)
    end
    n2 = Base.top_set_bit(x2)
    m2 = (x2 >> (n2-53)) % UInt64
    d2 = ((n2-128+1021) % UInt64) << 52
    z2 = reinterpret(Float64,  s | (d2 + m2))
    return (z1,z2)
end

# XXX we want to mark :consistent-cy here so that this function can be concrete-folded,
# because the effect analysis currently can't prove it in the presence of `@inbounds` or
# `:boundscheck`, but still the accesses to `INV_2PI` are really safe here
Base.@assume_effects :consistent function paynehanek(x::Float64)
    # 1. Convert to form
    #
    #    x = X * 2^k,
    #
    # where 2^(n-1) <= X < 2^n  is an n-bit integer (n = 53, k = exponent(x)-52 )

    # Computations are integer based, so reinterpret x as UInt64
    u = reinterpret(UInt64, x)
    # Strip x of exponent bits and replace with ^1
    X = (u & significand_mask(Float64)) | (one(UInt64) << significand_bits(Float64))
    # Get k from formula above
    # k = exponent(x)-52
    raw_exponent = ((u & exponent_mask(Float64)) >> significand_bits(Float64)) % Int
    k = raw_exponent - exponent_bias(Float64) - significand_bits(Float64)

    # 2. Let α = 1/2π, then:
    #
    #    α*x mod 1 ≡ [(α*2^k mod 1)*X] mod 1
    #
    # so we can ignore the first k bits of α. Extract the next 3 64-bit parts of α.
    #
    # i.e. equivalent to
    #     setprecision(BigFloat,4096)
    #     α  = 1/(2*big(pi))
    #     A  = mod(ldexp(α,k), 1)
    #     z1 = ldexp(A,64)
    #     a1 = trunc(UInt64, z1)
    #     z2 = ldexp(z1-a1, 64)
    #     a2 = trunc(UInt64, z2)
    #     z3 = ldexp(z2-a2, 64)
    #     a3 = trunc(UInt64, z3)

    # This is equivalent to
    #     idx, shift = divrem(k, 64)
    # but divrem is slower.
    idx = k >> 6

    shift = k - (idx << 6)
    if shift == 0
        @inbounds a1 = INV_2PI[idx+1]
        @inbounds a2 = INV_2PI[idx+2]
        @inbounds a3 = INV_2PI[idx+3]
    else
        # use shifts to extract the relevant 64 bit window
        @inbounds a1 = (idx < 0 ? zero(UInt64) : INV_2PI[idx+1] << shift) | (INV_2PI[idx+2] >> (64 - shift))
        @inbounds a2 = (INV_2PI[idx+2] << shift) | (INV_2PI[idx+3] >> (64 - shift))
        @inbounds a3 = (INV_2PI[idx+3] << shift) | (INV_2PI[idx+4] >> (64 - shift))
    end

    # 3. Perform the multiplication:
    #
    #      X.  0  0  0
    #   ×  0. a1 a2 a3
    #   ==============
    #      _.  w  w  _
    #
    # (i.e. ignoring integer and lowest bit parts of result)

    w1 = UInt128(X*a1) << 64 # overflow becomes integer
    w2 = widemul(X,a2)
    w3 = widemul(X,a3) >> 64
    w = w1 + w2 + w3         # quotient fraction after division by 2π

    # adjust for sign of x
    w = flipsign(w,x)

    # 4. convert to quadrant, quotient fraction after division by π/2:
    q = (((w>>125)%Int +1)>>1) # nearest quadrant
    f = (w<<2) % Int128 # fraction part of quotient after division by π/2, taking values on [-0.5,0.5)

    # 5. convert quotient fraction to split precision Float64
    z_hi,z_lo = fromfraction(f)

    # 6. multiply by π/2
    pio2 = 1.5707963267948966
    pio2_hi = 1.5707963407039642
    pio2_lo = -1.3909067614167116e-8
    y_hi = (z_hi+z_lo)*pio2
    y_lo = (((z_hi*pio2_hi - y_hi) + z_hi*pio2_lo) + z_lo*pio2_hi) + z_lo*pio2_lo
    return q, DoubleFloat64(y_hi, y_lo)
end

"""
    rem_pio2_kernel(x::Union{Float32, Float64})
Calculate `x` divided by `π/2` accurately for arbitrarily large `x`.
Returns a pair `(k, r)`, where `k` is the quadrant of the result
(multiple of π/2) and `r` is the remainder, such that ``k * π/2 = x - r``.
The remainder is given as a double-double pair.
`k` is positive if `x > 0` and is negative if `x ≤ 0`.
"""
@inline function rem_pio2_kernel(x::Float64) # accurate to 1e-22
    xhp = poshighword(x)
    #  xhp <= highword(5pi/4) implies |x| ~<= 5pi/4,
    if xhp <= 0x400f6a7a
        #  last five bits of xhp == last five bits of highword(pi/2) or
        #  highword(2pi/2) implies |x| ~= pi/2 or 2pi/2,
        if (xhp & 0xfffff) == 0x921fb # use precise Cody Waite scheme
            return cody_waite_ext_pio2(x, xhp)
        end
        # use Cody Waite with two constants
        #  xhp <= highword(3pi/4) implies |x| ~<= 3pi/4
        if xhp <= 0x4002d97c
            if x > 0.0
                return cody_waite_2c_pio2(x, 1.0, 1)
            else
                return cody_waite_2c_pio2(x, -1.0, -1)
            end
        # 3pi/4 < |x| <= 5pi/4
        else
            if x > 0.0
                return cody_waite_2c_pio2(x, 2.0, 2)
            else
                return cody_waite_2c_pio2(x, -2.0, -2)
            end
        end
    end
    #  xhp <= highword(9pi/4) implies |x| ~<= 9pi/4
    if xhp <= 0x401c463b
        #  xhp <= highword(7pi/4) implies |x| ~<= 7pi/4
        if xhp <= 0x4015fdbc
            #  xhp == highword(3pi/2) implies |x| ~= 3pi/2
            if xhp == 0x4012d97c # use precise Cody Waite scheme
                return cody_waite_ext_pio2(x, xhp)
            end
            # use Cody Waite with two constants
            if x > 0.0
                return cody_waite_2c_pio2(x, 3.0, 3)
            else
                return cody_waite_2c_pio2(x, -3.0, -3)
            end
        # 7pi/4 < |x| =< 9pi/4
        else
            #  xhp == highword(4pi/2) implies |x| ~= 4pi/2
            if xhp == 0x401921fb # use precise Cody Waite scheme
                return cody_waite_ext_pio2(x, xhp)
            end
            # use Cody Waite with two constants
            if x > 0.0
                return cody_waite_2c_pio2(x, 4.0, 4)
            else
                return cody_waite_2c_pio2(x, -4.0, -4)
            end
        end
    end
    #  xhp < highword(2.0^20*pi/2) implies |x| ~< 2^20*pi/2
    if xhp < 0x413921fb # use precise Cody Waite scheme
        return cody_waite_ext_pio2(x, xhp)
    end
    # if |x| >= 2^20*pi/2 switch to Payne Hanek
    return paynehanek(x)
end

@inline function rem_pio2_kernel(x::Float32)
    xd = convert(Float64, x)
    # use Cody Waite reduction with two coefficients
    if abs(x) < Float32(pi*0x1p27) # x < 2^28 * pi/2
        fn = round(xd * (2/pi))
        r  = fma(fn, -pi/2, xd)
        y = fma(fn, -6.123233995736766e-17, r) # big(pi)/2 - pi/2 remainder
        return unsafe_trunc(Int, fn), DoubleFloat32(y)
    end
    n, y = @noinline paynehanek(xd)
    return n, DoubleFloat32(y.hi)
end
R   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/special/log.jl!h      # This file is a part of Julia. License is MIT: https://julialang.org/license

# Implementation of
#  "Table-driven Implementation of the Logarithm Function in IEEE Floating-point Arithmetic"
#  Tang, Ping-Tak Peter
#  ACM Trans. Math. Softw. (1990), 16(4):378--400
#  https://doi.org/10.1145/98267.98294

# Does not currently handle floating point flags (inexact, div-by-zero, etc).

import .Base.unsafe_trunc
import .Base.Math.@horner

# Float64 lookup table.
# to generate values:
  # N=39 # (can be up to N=42).
  # sN = 2.0^N
  # isN = 1.0/sN
  # s7 = 2.0^7
  # is7 = 1.0/s7
  # for j=0:128
  #   l_big = Base.log(big(1.0+j*is7))
  #   l_hi = isN*Float64(round(sN*l_big))
  #   l_lo = Float64(l_big-l_hi)
  #   j % 2 == 0 && print("\n    ")
  #   print("(",l_hi,",",l_lo,"),")
  # end

const t_log_Float64 = ((0.0,0.0),(0.007782140442941454,-8.865052917267247e-13),
    (0.015504186536418274,-4.530198941364935e-13),(0.0231670592820592,-5.248209479295644e-13),
    (0.03077165866670839,4.529814257790929e-14),(0.0383188643027097,-5.730994833076631e-13),
    (0.04580953603181115,-5.16945692881222e-13),(0.053244514518155484,6.567993368985218e-13),
    (0.06062462181580486,6.299848199383311e-13),(0.06795066190898069,-4.729424109166329e-13),
    (0.07522342123775161,-1.6408301585598662e-13),(0.08244366921098845,8.614512936087814e-14),
    (0.08961215869021544,-5.283050530808144e-13),(0.09672962645890948,-3.5836667430094137e-13),
    (0.10379679368088546,7.581073923016376e-13),(0.11081436634049169,-2.0157368416016215e-13),
    (0.11778303565552051,8.629474042969438e-13),(0.1247034785010328,-7.556920687451337e-14),
    (0.1315763577895268,-8.075373495358435e-13),(0.13840232285838283,7.363043577087051e-13),
    (0.14518200984457508,-7.718001336828099e-14),(0.15191604202664166,-7.996871607743758e-13),
    (0.15860503017574956,8.890223439724663e-13),(0.16524957289584563,-5.384682618788232e-13),
    (0.17185025692742784,-7.686134224018169e-13),(0.17840765747314435,-3.2605717931058157e-13),
    (0.18492233849428885,-2.7685884310448306e-13),(0.1913948530000198,-3.903387893794952e-13),
    (0.1978257433293038,6.160755775588723e-13),(0.20421554142922105,-5.30156516006026e-13),
    (0.21056476910780475,-4.55112422774782e-13),(0.21687393830143264,-8.182853292737783e-13),
    (0.22314355131493357,-7.238189921749681e-13),(0.22937410106533207,-4.86240001538379e-13),
    (0.23556607131286,-9.30945949519689e-14),(0.24171993688651128,6.338907368997553e-13),
    (0.24783616390413954,4.4171755371315547e-13),(0.25391520998164196,-6.785208495970588e-13),
    (0.25995752443668607,2.3999540484211735e-13),(0.2659635484978935,-7.555569400283742e-13),
    (0.27193371548310097,5.407904186145515e-13),(0.2778684510030871,3.692037508208009e-13),
    (0.28376817313073843,-9.3834172236637e-14),(0.28963329258294834,9.43339818951269e-14),
    (0.29546421289342106,4.148131870425857e-13),(0.3012613305781997,-3.7923164802093147e-14),
    (0.3070250352957373,-8.25463138725004e-13),(0.31275571000333,5.668653582900739e-13),
    (0.318453731119007,-4.723727821986367e-13),(0.32411946865431673,-1.0475750058776541e-13),
    (0.32975328637257917,-1.1118671389559323e-13),(0.33535554192167183,-5.339989292003297e-13),
    (0.3409265869704541,1.3912841212197566e-13),(0.3464667673470103,-8.017372713972018e-13),
    (0.35197642315688427,2.9391859187648e-13),(0.3574558889213222,4.815896111723205e-13),
    (0.3629054936900502,-6.817539406325327e-13),(0.36832556115950865,-8.009990055432491e-13),
    (0.3737164097929053,6.787566823158706e-13),(0.37907835293481185,1.5761203773969435e-13),
    (0.3844116989112081,-8.760375990774874e-13),(0.38971675114044046,-4.152515806343612e-13),
    (0.3949938082405424,3.2655698896907146e-13),(0.40024316412745975,-4.4704265010452445e-13),
    (0.4054651081078191,3.452764795203977e-13),(0.4106599249844294,8.390050778518307e-13),
    (0.4158278951435932,1.1776978751369214e-13),(0.4209692946442374,-1.0774341461609579e-13),
    (0.42608439531068143,2.186334329321591e-13),(0.43117346481813,2.413263949133313e-13),
    (0.4362367667745275,3.90574622098307e-13),(0.44127456080423144,6.437879097373207e-13),
    (0.44628710262804816,3.713514191959202e-13),(0.45127464413963025,-1.7166921336082432e-13),
    (0.4562374334818742,-2.8658285157914353e-13),(0.4611757151214988,6.713692791384601e-13),
    (0.46608972992544295,-8.437281040871276e-13),(0.4709797152190731,-2.821014384618127e-13),
    (0.4758459048698569,1.0701931762114255e-13),(0.4806885293455707,1.8119346366441111e-13),
    (0.4855078157816024,9.840465278232627e-14),(0.49030398804461583,5.780031989454028e-13),
    (0.49507726679803454,-1.8302857356041668e-13),(0.4998278695566114,-1.620740015674495e-13),
    (0.5045560107519123,4.83033149495532e-13),(0.5092619017905236,-7.156055317238212e-13),
    (0.5139457511013461,8.882123951857185e-13),(0.5186077642083546,-3.0900580513238243e-13),
    (0.5232481437651586,-6.10765519728515e-13),(0.5278670896204858,3.565996966334783e-13),
    (0.532464798869114,3.5782396591276384e-13),(0.5370414658973459,-4.622608700154458e-13),
    (0.5415972824321216,6.227976291722515e-13),(0.5461324375974073,7.283894727206574e-13),
    (0.5506471179523942,2.680964661521167e-13),(0.5551415075406112,-1.0960825046059278e-13),
    (0.5596157879353996,2.3119493838005378e-14),(0.5640701382853877,-5.846905800529924e-13),
    (0.5685047353526897,-2.1037482511444942e-14),(0.5729197535620187,-2.332318294558741e-13),
    (0.5773153650352469,-4.2333694288141915e-13),(0.5816917396350618,-4.3933937969737843e-13),
    (0.5860490450031648,4.1341647073835564e-13),(0.590387446602108,6.841763641591467e-14),
    (0.5947071077462169,4.758553400443064e-13),(0.5990081896452466,8.367967867475769e-13),
    (0.6032908514389419,-8.576373464665864e-13),(0.6075552502243227,2.1913281229340092e-13),
    (0.6118015411066153,-6.224284253643115e-13),(0.6160298772156239,-1.098359432543843e-13),
    (0.6202404097512044,6.531043137763365e-13),(0.6244332880123693,-4.758019902171077e-13),
    (0.6286086594227527,-3.785425126545704e-13),(0.6327666695706284,4.0939233218678666e-13),
    (0.636907462236195,8.742438391485829e-13),(0.6410311794206791,2.521818845684288e-13),
    (0.6451379613736208,-3.6081313604225574e-14),(0.649227946625615,-5.05185559242809e-13),
    (0.6533012720119586,7.869940332335532e-13),(0.6573580727090302,-6.702087696194906e-13),
    (0.6613984822452039,1.6108575753932459e-13),(0.6654226325445052,5.852718843625151e-13),
    (0.6694306539429817,-3.5246757297904794e-13),(0.6734226752123504,-1.8372084495629058e-13),
    (0.6773988235909201,8.860668981349492e-13),(0.6813592248072382,6.64862680714687e-13),
    (0.6853040030982811,6.383161517064652e-13),(0.6892332812385575,2.5144230728376075e-13),
    (0.6931471805601177,-1.7239444525614835e-13))

# Float32 lookup table
# to generate values:
  # N=16
  # sN = 2f0^N
  # isN = 1f0/sN
  # s7 = 2.0^7
  # is7 = 1.0/s7
  # for j=0:128
  #   j % 4 == 0 && print("\n    ")
  #   print(float64(Base.log(big(1.0+j*is7))),",")
  # end

const t_log_Float32 = (0.0,0.007782140442054949,0.015504186535965254,0.02316705928153438,
    0.030771658666753687,0.0383188643021366,0.0458095360312942,0.053244514518812285,
    0.06062462181643484,0.06795066190850775,0.07522342123758753,0.08244366921107459,
    0.08961215868968714,0.09672962645855111,0.10379679368164356,0.11081436634029011,
    0.11778303565638346,0.12470347850095724,0.13157635778871926,0.13840232285911913,
    0.1451820098444979,0.15191604202584197,0.15860503017663857,0.16524957289530717,
    0.17185025692665923,0.1784076574728183,0.184922338494012,0.19139485299962947,
    0.19782574332991987,0.2042155414286909,0.21056476910734964,0.21687393830061436,
    0.22314355131420976,0.22937410106484582,0.2355660713127669,0.24171993688714516,
    0.24783616390458127,0.25391520998096345,0.25995752443692605,0.26596354849713794,
    0.27193371548364176,0.2778684510034563,0.2837681731306446,0.28963329258304266,
    0.2954642128938359,0.3012613305781618,0.3070250352949119,0.3127557100038969,
    0.3184537311185346,0.324119468654212,0.329753286372468,0.3353555419211378,
    0.3409265869705932,0.34646676734620857,0.3519764231571782,0.3574558889218038,
    0.3629054936893685,0.3683255611587076,0.37371640979358406,0.37907835293496944,
    0.38441169891033206,0.3897167511400252,0.394993808240869,0.4002431641270127,
    0.4054651081081644,0.4106599249852684,0.415827895143711,0.42096929464412963,
    0.4260843953109001,0.4311734648183713,0.43623676677491807,0.4412745608048752,
    0.44628710262841953,0.45127464413945856,0.4562374334815876,0.46117571512217015,
    0.46608972992459924,0.470979715218791,0.4758459048699639,0.4806885293457519,
    0.4855078157817008,0.4903039880451938,0.4950772667978515,0.4998278695564493,
    0.5045560107523953,0.5092619017898079,0.5139457511022343,0.5186077642080457,
    0.5232481437645479,0.5278670896208424,0.5324647988694718,0.5370414658968836,
    0.5415972824327444,0.5461324375981357,0.5506471179526623,0.5551415075405016,
    0.5596157879354227,0.564070138284803,0.5685047353526688,0.5729197535617855,
    0.5773153650348236,0.5816917396346225,0.5860490450035782,0.5903874466021763,
    0.5947071077466928,0.5990081896460834,0.6032908514380843,0.6075552502245418,
    0.6118015411059929,0.616029877215514,0.6202404097518576,0.6244332880118935,
    0.6286086594223741,0.6327666695710378,0.6369074622370692,0.6410311794209312,
    0.6451379613735847,0.6492279466251099,0.6533012720127457,0.65735807270836,
    0.661398482245365,0.6654226325450905,0.6694306539426292,0.6734226752121667,
    0.6773988235918061,0.6813592248079031,0.6853040030989194,0.689233281238809,
    0.6931471805599453)

# truncate lower order bits (up to 26)
# ideally, this should be able to use ANDPD instructions, see #9868.
@inline function truncbits(x::Float64)
    reinterpret(Float64, reinterpret(UInt64,x) & 0xffff_ffff_f800_0000)
end

logb(::Type{Float32},::Val{2})  = 1.4426950408889634
logb(::Type{Float32},::Val{:ℯ}) = 1.0
logb(::Type{Float32},::Val{10}) = 0.4342944819032518
logbU(::Type{Float64},::Val{2})  = 1.4426950408889634
logbL(::Type{Float64},::Val{2})  = 2.0355273740931033e-17
logbU(::Type{Float64},::Val{:ℯ}) = 1.0
logbL(::Type{Float64},::Val{:ℯ}) = 0.0
logbU(::Type{Float64},::Val{10}) = 0.4342944819032518
logbL(::Type{Float64},::Val{10}) = 1.098319650216765e-17

# Procedure 1
# XXX we want to mark :consistent-cy here so that this function can be concrete-folded,
# because the effect analysis currently can't prove it in the presence of `@inbounds` or
# `:boundscheck`, but still the access to `t_log_Float64` is really safe here
Base.@assume_effects :consistent @inline function log_proc1(y::Float64,mf::Float64,F::Float64,f::Float64,base=Val(:ℯ))
    jp = unsafe_trunc(Int,128.0*F)-127

    ## Steps 1 and 2
    @inbounds hi,lo = t_log_Float64[jp]
    l_hi = mf* 0.6931471805601177 + hi
    l_lo = mf*-1.7239444525614835e-13 + lo

    ## Step 3
    # @inbounds u = f*c_invF[jp]
    # u = f/F
    # q = u*u*@horner(u,
    #                 -0x1.0_0000_0000_0001p-1,
    #                 +0x1.5_5555_5550_9ba5p-2,
    #                 -0x1.f_ffff_ffeb_6526p-3,
    #                 +0x1.9_99b4_dfed_6fe4p-3,
    #                 -0x1.5_5576_6647_2e04p-3)

    ## Step 3' (alternative)
    u = (2.0f)/(y+F)
    v = u*u
    q = u*v*@horner(v,
                    0.08333333333303913,
                    0.012500053168098584)

    ## Step 4
    m_hi = logbU(Float64, base)
    m_lo = logbL(Float64, base)
    return fma(m_hi, l_hi, fma(m_hi, (u + (q + l_lo)), m_lo*l_hi))
end

# Procedure 2
@inline function log_proc2(f::Float64,base=Val(:ℯ))
    ## Step 1
    g = 1.0/(2.0+f)
    u = 2.0*f*g
    v = u*u

    ## Step 2
    q = u*v*@horner(v,
                    0.08333333333333179,
                    0.012500000003771751,
                    0.0022321399879194482,
                    0.0004348877777076146)

    ## Step 3
    # based on:
    #   2(f-u) = 2(f(2+f)-2f)/(2+f) = 2f^2/(2+f) = fu
    #   2(f-u1-u2) - f*(u1+u2) = 0
    #   2(f-u1) - f*u1 = (2+f)u2
    #   u2 = (2(f-u1) - f*u1)/(2+f)

    m_hi = logbU(Float64, base)
    m_lo = logbL(Float64, base)
    return fma(m_hi, u, fma(m_lo, u, m_hi*fma(fma(-u,f,2(f-u)), g, q)))
end

# Procedure 1
# XXX we want to mark :consistent-cy here so that this function can be concrete-folded,
# because the effect analysis currently can't prove it in the presence of `@inbounds` or
# `:boundscheck`, but still the access to `t_log_Float32` is really safe here
Base.@assume_effects :consistent @inline function log_proc1(y::Float32,mf::Float32,F::Float32,f::Float32,base=Val(:ℯ))
    jp = unsafe_trunc(Int,128.0f0*F)-127

    ## Steps 1 and 2
    @inbounds hi = t_log_Float32[jp]
    l = mf*0.6931471805599453 + hi

    ## Step 3
    # @inbounds u = f*c_invF[jp]
    # q = u*u*@horner(u,
    #                 Float32(-0x1.00006p-1),
    #                 Float32(0x1.55546cp-2))

    ## Step 3' (alternative)
    u = (2f0f)/(y+F)
    v = u*u
    q = u*v*0.08333351f0

    ## Step 4
    Float32(logb(Float32, base)*(l + (u + q)))
end

# Procedure 2
@inline function log_proc2(f::Float32,base=Val(:ℯ))
    ## Step 1
    # compute in higher precision
    u64 = Float64(2f0*f)/(2.0+f)
    u = Float32(u64)
    v = u*u

    ## Step 2
    q = u*v*@horner(v,
                    0.08333332f0,
                    0.012512346f0)

    ## Step 3: not required

    ## Step 4
    Float32(logb(Float32, base)*(u64 + q))
end

log2(x::Float32)  = _log(x, Val(2),  :log2)
log(x::Float32)   = _log(x, Val(:ℯ), :log)
log10(x::Float32) = _log(x, Val(10), :log10)
log2(x::Float64)  = _log(x, Val(2),  :log2)
log(x::Float64)   = _log(x, Val(:ℯ), :log)
log10(x::Float64) = _log(x, Val(10), :log10)

function _log(x::Float64, base, func)
    if x > 0.0
        x == Inf && return x

        # Step 2
        if 0.9394130628134757 < x < 1.0644944589178595
            f = x-1.0
            return log_proc2(f, base)
        end

        # Step 3
        xu = reinterpret(UInt64,x)
        m = Int(xu >> 52) & 0x07ff
        if m == 0 # x is subnormal
            x *= 1.8014398509481984e16 # 0x1p54, normalise significand
            xu = reinterpret(UInt64,x)
            m = Int(xu >> 52) & 0x07ff - 54
        end
        m -= 1023
        y = reinterpret(Float64,(xu & 0x000f_ffff_ffff_ffff) | 0x3ff0_0000_0000_0000)

        mf = Float64(m)
        F = (y + 3.5184372088832e13) - 3.5184372088832e13 # 0x1p-7*round(0x1p7*y)
        f = y-F

        return log_proc1(y,mf,F,f,base)
    elseif x == 0.0
        -Inf
    elseif isnan(x)
        NaN
    else
        throw_complex_domainerror(func, x)
    end
end

function _log(x::Float32, base, func)
    if x > 0f0
        x == Inf32 && return x

        # Step 2
        if 0.939413f0 < x < 1.0644945f0
            f = x-1f0
            return log_proc2(f, base)
        end

        # Step 3
        xu = reinterpret(UInt32,x)
        m = Int(xu >> 23) & 0x00ff
        if m == 0 # x is subnormal
            x *= 3.3554432f7 # 0x1p25, normalise significand
            xu = reinterpret(UInt32,x)
            m = Int(xu >> 23) & 0x00ff - 25
        end
        m -= 127
        y = reinterpret(Float32,(xu & 0x007f_ffff) | 0x3f80_0000)

        mf = Float32(m)
        F = (y + 65536.0f0) - 65536.0f0 # 0x1p-7*round(0x1p7*y)
        f = y-F

        log_proc1(y,mf,F,f,base)
    elseif x == 0f0
        -Inf32
    elseif isnan(x)
        NaN32
    else
        throw_complex_domainerror(func, x)
    end
end


function log1p(x::Float64)
    if x > -1.0
        x == Inf && return x
        if -1.1102230246251565e-16 < x < 1.1102230246251565e-16
            return x # Inexact

        # Step 2
        elseif -0.06058693718652422 < x < 0.06449445891785943
            return log_proc2(x)
        end

        # Step 3
        z = 1.0 + x
        zu = reinterpret(UInt64,z)
        s = reinterpret(Float64,0x7fe0_0000_0000_0000 - (zu & 0xfff0_0000_0000_0000)) # 2^-m
        m = Int(zu >> 52) & 0x07ff - 1023 # z cannot be subnormal
        c = m > 0 ? 1.0-(z-x) : x-(z-1.0) # 1+x = z+c exactly
        y = reinterpret(Float64,(zu & 0x000f_ffff_ffff_ffff) | 0x3ff0_0000_0000_0000)

        mf = Float64(m)
        F = (y + 3.5184372088832e13) - 3.5184372088832e13 # 0x1p-7*round(0x1p7*y)
        f = (y - F) + c*s #2^m(F+f) = 1+x = z+c

        log_proc1(y,mf,F,f)
    elseif x == -1.0
        -Inf
    elseif isnan(x)
        NaN
    else
        throw_complex_domainerror_neg1(:log1p, x)
    end
end

function log1p(x::Float32)
    if x > -1f0
        x == Inf32 && return x
        if -5.9604645f-8 < x < 5.9604645f-8
            return x # Inexact
        # Step 2
        elseif -0.06058694f0 < x < 0.06449446f0
            return log_proc2(x)
        end

        # Step 3
        z = 1f0 + x
        zu = reinterpret(UInt32,z)
        s = reinterpret(Float32,0x7f000000 - (zu & 0xff80_0000)) # 2^-m
        m = Int(zu >> 23) & 0x00ff - 127 # z cannot be subnormal
        c = m > 0 ? 1f0-(z-x) : x-(z-1f0) # 1+x = z+c
        y = reinterpret(Float32,(zu & 0x007f_ffff) | 0x3f80_0000)

        mf = Float32(m)
        F = (y + 65536.0f0) - 65536.0f0 # 0x1p-7*round(0x1p7*y)
        f = (y - F) + s*c #2^m(F+f) = 1+x = z+c

        log_proc1(y,mf,F,f)
    elseif x == -1f0
        -Inf32
    elseif isnan(x)
        NaN32
    else
        throw_complex_domainerror_neg1(:log1p, x)
    end
end

#function make_compact_table(N)
#    table = Tuple{UInt64,Float64}[]
#    lo, hi = 0x1.69555p-1, 0x1.69555p0
#    for i in 0:N-1
#        # I am not fully sure why this is the right formula to use, but it apparently is
#        center = i/(2*N) + lo < 1 ? (i+.5)/(2*N) + lo : (i+.5)/N + hi -1
#        invc = Float64(center < 1 ? round(N/center)/N : round(2*N/center)/(N*2))
#        c = inv(big(invc))
#        logc = Float64(round(0x1p43*log(c))/0x1p43)
#        logctail = reinterpret(Float64, Float64(log(c) - logc))
#        p1 = (reinterpret(UInt64,invc) >> 45) % UInt8
#        push!(table, (p1|reinterpret(UInt64,logc),logctail))
#    end
#    return Tuple(table)
#end
#const t_log_table_compact = make_compact_table(128)
const t_log_table_compact = (
    (0xbfd62c82f2b9c8b5, 5.929407345889625e-15),
    (0xbfd5d1bdbf5808b4, -2.544157440035963e-14),
    (0xbfd57677174558b3, -3.443525940775045e-14),
    (0xbfd51aad872df8b2, -2.500123826022799e-15),
    (0xbfd4be5f957778b1, -8.929337133850617e-15),
    (0xbfd4618bc21c60b0, 1.7625431312172662e-14),
    (0xbfd404308686a8af, 1.5688303180062087e-15),
    (0xbfd3a64c556948ae, 2.9655274673691784e-14),
    (0xbfd347dd9a9880ad, 3.7923164802093147e-14),
    (0xbfd2e8e2bae120ac, 3.993416384387844e-14),
    (0xbfd2895a13de88ab, 1.9352855826489123e-14),
    (0xbfd2895a13de88ab, 1.9352855826489123e-14),
    (0xbfd22941fbcf78aa, -1.9852665484979036e-14),
    (0xbfd1c898c16998a9, -2.814323765595281e-14),
    (0xbfd1675cababa8a8, 2.7643769993528702e-14),
    (0xbfd1058bf9ae48a7, -4.025092402293806e-14),
    (0xbfd0a324e27390a6, -1.2621729398885316e-14),
    (0xbfd0402594b4d0a5, -3.600176732637335e-15),
    (0xbfd0402594b4d0a5, -3.600176732637335e-15),
    (0xbfcfb9186d5e40a4, 1.3029797173308663e-14),
    (0xbfcef0adcbdc60a3, 4.8230289429940886e-14),
    (0xbfce27076e2af0a2, -2.0592242769647135e-14),
    (0xbfcd5c216b4fc0a1, 3.149265065191484e-14),
    (0xbfcc8ff7c79aa0a0, 4.169796584527195e-14),
    (0xbfcc8ff7c79aa0a0, 4.169796584527195e-14),
    (0xbfcbc286742d909f, 2.2477465222466186e-14),
    (0xbfcaf3c94e80c09e, 3.6507188831790577e-16),
    (0xbfca23bc1fe2b09d, -3.827767260205414e-14),
    (0xbfca23bc1fe2b09d, -3.827767260205414e-14),
    (0xbfc9525a9cf4509c, -4.7641388950792196e-14),
    (0xbfc87fa06520d09b, 4.9278276214647115e-14),
    (0xbfc7ab890210e09a, 4.9485167661250996e-14),
    (0xbfc7ab890210e09a, 4.9485167661250996e-14),
    (0xbfc6d60fe719d099, -1.5003333854266542e-14),
    (0xbfc5ff3070a79098, -2.7194441649495324e-14),
    (0xbfc5ff3070a79098, -2.7194441649495324e-14),
    (0xbfc526e5e3a1b097, -2.99659267292569e-14),
    (0xbfc44d2b6ccb8096, 2.0472357800461955e-14),
    (0xbfc44d2b6ccb8096, 2.0472357800461955e-14),
    (0xbfc371fc201e9095, 3.879296723063646e-15),
    (0xbfc29552f81ff094, -3.6506824353335045e-14),
    (0xbfc1b72ad52f6093, -5.4183331379008994e-14),
    (0xbfc1b72ad52f6093, -5.4183331379008994e-14),
    (0xbfc0d77e7cd09092, 1.1729485484531301e-14),
    (0xbfc0d77e7cd09092, 1.1729485484531301e-14),
    (0xbfbfec9131dbe091, -3.811763084710266e-14),
    (0xbfbe27076e2b0090, 4.654729747598445e-14),
    (0xbfbe27076e2b0090, 4.654729747598445e-14),
    (0xbfbc5e548f5bc08f, -2.5799991283069902e-14),
    (0xbfba926d3a4ae08e, 3.7700471749674615e-14),
    (0xbfba926d3a4ae08e, 3.7700471749674615e-14),
    (0xbfb8c345d631a08d, 1.7306161136093256e-14),
    (0xbfb8c345d631a08d, 1.7306161136093256e-14),
    (0xbfb6f0d28ae5608c, -4.012913552726574e-14),
    (0xbfb51b073f06208b, 2.7541708360737882e-14),
    (0xbfb51b073f06208b, 2.7541708360737882e-14),
    (0xbfb341d7961be08a, 5.0396178134370583e-14),
    (0xbfb341d7961be08a, 5.0396178134370583e-14),
    (0xbfb16536eea38089, 1.8195060030168815e-14),
    (0xbfaf0a30c0118088, 5.213620639136504e-14),
    (0xbfaf0a30c0118088, 5.213620639136504e-14),
    (0xbfab42dd71198087, 2.532168943117445e-14),
    (0xbfab42dd71198087, 2.532168943117445e-14),
    (0xbfa77458f632c086, -5.148849572685811e-14),
    (0xbfa77458f632c086, -5.148849572685811e-14),
    (0xbfa39e87b9fec085, 4.6652946995830086e-15),
    (0xbfa39e87b9fec085, 4.6652946995830086e-15),
    (0xbf9f829b0e780084, -4.529814257790929e-14),
    (0xbf9f829b0e780084, -4.529814257790929e-14),
    (0xbf97b91b07d58083, -4.361324067851568e-14),
    (0xbf8fc0a8b0fc0082, -1.7274567499706107e-15),
    (0xbf8fc0a8b0fc0082, -1.7274567499706107e-15),
    (0xbf7fe02a6b100081, -2.298941004620351e-14),
    (0xbf7fe02a6b100081, -2.298941004620351e-14),
    (0x0000000000000080, 0.0),
    (0x0000000000000080, 0.0),
    (0x3f8010157589007e, -1.4902732911301337e-14),
    (0x3f9020565893807c, -3.527980389655325e-14),
    (0x3f98492528c9007a, -4.730054772033249e-14),
    (0x3fa0415d89e74078, 7.580310369375161e-15),
    (0x3fa466aed42e0076, -4.9893776716773285e-14),
    (0x3fa894aa149fc074, -2.262629393030674e-14),
    (0x3faccb73cdddc072, -2.345674491018699e-14),
    (0x3faeea31c006c071, -1.3352588834854848e-14),
    (0x3fb1973bd146606f, -3.765296820388875e-14),
    (0x3fb3bdf5a7d1e06d, 5.1128335719851986e-14),
    (0x3fb5e95a4d97a06b, -5.046674438470119e-14),
    (0x3fb700d30aeac06a, 3.1218748807418837e-15),
    (0x3fb9335e5d594068, 3.3871241029241416e-14),
    (0x3fbb6ac88dad6066, -1.7376727386423858e-14),
    (0x3fbc885801bc4065, 3.957125899799804e-14),
    (0x3fbec739830a2063, -5.2849453521890294e-14),
    (0x3fbfe89139dbe062, -3.767012502308738e-14),
    (0x3fc1178e8227e060, 3.1859736349078334e-14),
    (0x3fc1aa2b7e23f05f, 5.0900642926060466e-14),
    (0x3fc2d1610c86805d, 8.710783796122478e-15),
    (0x3fc365fcb015905c, 6.157896229122976e-16),
    (0x3fc4913d8333b05a, 3.821577743916796e-14),
    (0x3fc527e5e4a1b059, 3.9440046718453496e-14),
    (0x3fc6574ebe8c1057, 2.2924522154618074e-14),
    (0x3fc6f0128b757056, -3.742530094732263e-14),
    (0x3fc7898d85445055, -2.5223102140407338e-14),
    (0x3fc8beafeb390053, -1.0320443688698849e-14),
    (0x3fc95a5adcf70052, 1.0634128304268335e-14),
    (0x3fca93ed3c8ae050, -4.3425422595242564e-14),
    (0x3fcb31d8575bd04f, -1.2527395755711364e-14),
    (0x3fcbd087383be04e, -5.204008743405884e-14),
    (0x3fcc6ffbc6f0104d, -3.979844515951702e-15),
    (0x3fcdb13db0d4904b, -4.7955860343296286e-14),
    (0x3fce530effe7104a, 5.015686013791602e-16),
    (0x3fcef5ade4dd0049, -7.252318953240293e-16),
    (0x3fcf991c6cb3b048, 2.4688324156011588e-14),
    (0x3fd07138604d5846, 5.465121253624792e-15),
    (0x3fd0c42d67616045, 4.102651071698446e-14),
    (0x3fd1178e8227e844, -4.996736502345936e-14),
    (0x3fd16b5ccbacf843, 4.903580708156347e-14),
    (0x3fd1bf99635a6842, 5.089628039500759e-14),
    (0x3fd214456d0eb841, 1.1782016386565151e-14),
    (0x3fd2bef07cdc903f, 4.727452940514406e-14),
    (0x3fd314f1e1d3603e, -4.4204083338755686e-14),
    (0x3fd36b6776be103d, 1.548345993498083e-14),
    (0x3fd3c2527733303c, 2.1522127491642888e-14),
    (0x3fd419b423d5e83b, 1.1054030169005386e-14),
    (0x3fd4718dc271c83a, -5.534326352070679e-14),
    (0x3fd4c9e09e173039, -5.351646604259541e-14),
    (0x3fd522ae0738a038, 5.4612144489920215e-14),
    (0x3fd57bf753c8d037, 2.8136969901227338e-14),
    (0x3fd5d5bddf596036, -1.156568624616423e-14))

 @inline function log_tab_unpack(t::UInt64)
    invc = UInt64(t&UInt64(0xff)|0x1ff00)<<45
    logc = t&(~UInt64(0xff))
    return (reinterpret(Float64, invc), reinterpret(Float64, logc))
end

# Log implementation that returns 2 numbers which sum to give true value with about 68 bits of precision
# Since `log` only makes sense for positive exponents, we speed up the implementation by stealing the sign bit
# of the input for an extra bit of the exponent which is used to normalize subnormal inputs.
# Does not normalize results.
# Adapted and modified from https://github.com/ARM-software/optimized-routines/blob/master/math/pow.c
# Copyright (c) 2018-2020, Arm Limited. (which is also MIT licensed)
# note that this isn't an exact translation as this version compacts the table to reduce cache pressure.
function _log_ext(xu)
    # x = 2^k z; where z is in range [0x1.69555p-1,0x1.69555p-0) and exact.
    # The range is split into N subintervals.
    # The ith subinterval contains z and c is near the center of the interval.
    tmp = reinterpret(Int64, xu - 0x3fe6955500000000) #0x1.69555p-1
    i = (tmp >> 45) & 127
    z = reinterpret(Float64, xu - (tmp & 0xfff0000000000000))
    k = Float64(tmp >> 52)
    # log(x) = k*Ln2 + log(c) + log1p(z/c-1).
    # getfield instead of getindex to satisfy effect analysis not knowing whether this is inbounds
    t, logctail = getfield(t_log_table_compact, Int(i+1))
    invc, logc = log_tab_unpack(t)
    # Note: invc is j/N or j/N/2 where j is an integer in [N,2N) and
    # |z/c - 1| < 1/N, so r = z/c - 1 is exactly representable.
    r = fma(z, invc, -1.0)
    # k*Ln2 + log(c) + r.
    t1 = muladd(k, 0.6931471805598903, logc) #ln(2) hi part
    t2 = t1 + r
    lo1 = muladd(k, 5.497923018708371e-14, logctail) #ln(2) lo part
    lo2 = t1 - t2 + r
    ar = -0.5 * r
    ar2, lo3 = two_mul(r, ar)
    # k*Ln2 + log(c) + r + .5*r*r.
    hi = t2 + ar2
    lo4 = t2 - hi + ar2
    p = evalpoly(r, (-0x1.555555555556p-1, 0x1.0000000000006p-1, -0x1.999999959554ep-2, 0x1.555555529a47ap-2, -0x1.2495b9b4845e9p-2, 0x1.0002b8b263fc3p-2))
    lo = lo1 + lo2 + lo3 + muladd(r*ar2, p, lo4)
    return hi, lo
end
P   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/reducedim.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

## Functions to compute the reduced shape

# for reductions that expand 0 dims to 1
reduced_index(i::OneTo{T}) where {T} = OneTo(one(T))
reduced_index(i::Union{Slice, IdentityUnitRange}) = oftype(i, first(i):first(i))
reduced_index(i::AbstractUnitRange) =
    throw(ArgumentError(
"""
No method is implemented for reducing index range of type $(typeof(i)). Please implement
reduced_index for this index type or report this as an issue.
"""
    ))
reduced_indices(a::AbstractArrayOrBroadcasted, region) = reduced_indices(axes(a), region)

# for reductions that keep 0 dims as 0
reduced_indices0(a::AbstractArray, region) = reduced_indices0(axes(a), region)

function reduced_indices(inds::Indices{N}, d::Int) where N
    d < 1 && throw(ArgumentError("dimension must be ≥ 1, got $d"))
    if d == 1
        return (reduced_index(inds[1]), tail(inds)...)::typeof(inds)
    elseif 1 < d <= N
        return tuple(inds[1:d-1]..., oftype(inds[d], reduced_index(inds[d])), inds[d+1:N]...)::typeof(inds)
    else
        return inds
    end
end

function reduced_indices0(inds::Indices{N}, d::Int) where N
    d < 1 && throw(ArgumentError("dimension must be ≥ 1, got $d"))
    if d <= N
        ind = inds[d]
        rd = isempty(ind) ? ind : reduced_index(inds[d])
        if d == 1
            return (rd, tail(inds)...)::typeof(inds)
        else
            return tuple(inds[1:d-1]..., oftype(inds[d], rd), inds[d+1:N]...)::typeof(inds)
        end
    else
        return inds
    end
end

function reduced_indices(inds::Indices{N}, region) where N
    rinds = collect(inds)
    for i in region
        isa(i, Integer) || throw(ArgumentError("reduced dimension(s) must be integers"))
        d = Int(i)
        if d < 1
            throw(ArgumentError("region dimension(s) must be ≥ 1, got $d"))
        elseif d <= N
            rinds[d] = reduced_index(rinds[d])
        end
    end
    tuple(rinds...)::typeof(inds)
end

function reduced_indices0(inds::Indices{N}, region) where N
    rinds = collect(inds)
    for i in region
        isa(i, Integer) || throw(ArgumentError("reduced dimension(s) must be integers"))
        d = Int(i)
        if d < 1
            throw(ArgumentError("region dimension(s) must be ≥ 1, got $d"))
        elseif d <= N
            rind = rinds[d]
            rinds[d] = isempty(rind) ? rind : reduced_index(rind)
        end
    end
    tuple(rinds...)::typeof(inds)
end

###### Generic reduction functions #####

## initialization
# initarray! is only called by sum!, prod!, etc.
for (Op, initfun) in ((:(typeof(add_sum)), :zero), (:(typeof(mul_prod)), :one))
    @eval initarray!(a::AbstractArray{T}, ::Any, ::$(Op), init::Bool, src::AbstractArray) where {T} = (init && fill!(a, $(initfun)(T)); a)
end

initarray!(a::AbstractArray{T}, f, ::Union{typeof(min),typeof(max),typeof(_extrema_rf)},
    init::Bool, src::AbstractArray) where {T} = (init && mapfirst!(f, a, src); a)

for (Op, initval) in ((:(typeof(&)), true), (:(typeof(|)), false))
    @eval initarray!(a::AbstractArray, ::Any, ::$(Op), init::Bool, src::AbstractArray) = (init && fill!(a, $initval); a)
end

# reducedim_initarray is called by
reducedim_initarray(A::AbstractArrayOrBroadcasted, region, init, ::Type{R}) where {R} = fill!(similar(A,R,reduced_indices(A,region)), init)
reducedim_initarray(A::AbstractArrayOrBroadcasted, region, init::T) where {T} = reducedim_initarray(A, region, init, T)

# TODO: better way to handle reducedim initialization
#
# The current scheme is basically following Steven G. Johnson's original implementation
#
promote_union(T::Union) = promote_type(promote_union(T.a), promote_union(T.b))
promote_union(T) = T

_realtype(::Type{<:Complex}) = Real
_realtype(::Type{Complex{T}}) where T<:Real = T
_realtype(T::Type) = T
_realtype(::Union{typeof(abs),typeof(abs2)}, T) = _realtype(T)
_realtype(::Any, T) = T

function reducedim_init(f, op::Union{typeof(+),typeof(add_sum)}, A::AbstractArray, region)
    _reducedim_init(f, op, zero, sum, A, region)
end
function reducedim_init(f, op::Union{typeof(*),typeof(mul_prod)}, A::AbstractArray, region)
    _reducedim_init(f, op, one, prod, A, region)
end
function _reducedim_init(f, op, fv, fop, A, region)
    T = _realtype(f, promote_union(eltype(A)))
    if T !== Any && applicable(zero, T)
        x = f(zero(T))
        z = op(fv(x), fv(x))
        Tr = z isa T ? T : typeof(z)
    else
        z = fv(fop(f, A))
        Tr = typeof(z)
    end
    return reducedim_initarray(A, region, z, Tr)
end

# initialization when computing minima and maxima requires a little care
for (f1, f2, initval, typeextreme) in ((:min, :max, :Inf, :typemax), (:max, :min, :(-Inf), :typemin))
    @eval function reducedim_init(f, op::typeof($f1), A::AbstractArray, region)
        # First compute the reduce indices. This will throw an ArgumentError
        # if any region is invalid
        ri = reduced_indices(A, region)

        # Next, throw if reduction is over a region with length zero
        any(i -> isempty(axes(A, i)), region) && _empty_reduce_error()

        # Make a view of the first slice of the region
        A1 = view(A, ri...)

        if isempty(A1)
            # If the slice is empty just return non-view version as the initial array
            return map(f, A1)
        else
            # otherwise use the min/max of the first slice as initial value
            v0 = mapreduce(f, $f2, A1)

            T = _realtype(f, promote_union(eltype(A)))
            Tr = v0 isa T ? T : typeof(v0)

            # but NaNs and missing need to be avoided as initial values
            if v0 isa Number && isnan(v0)
                # v0 is NaN
                v0 = oftype(v0, $initval)
            elseif isunordered(v0)
                # v0 is missing or a third-party unordered value
                Tnm = nonmissingtype(Tr)
                # TODO: Some types, like BigInt, don't support typemin/typemax.
                # So a Matrix{Union{BigInt, Missing}} can still error here.
                v0 = $typeextreme(Tnm)
            end
            # v0 may have changed type.
            Tr = v0 isa T ? T : typeof(v0)

            return reducedim_initarray(A, region, v0, Tr)
        end
    end
end

function reducedim_init(f::ExtremaMap, op::typeof(_extrema_rf), A::AbstractArray, region)
    # First compute the reduce indices. This will throw an ArgumentError
    # if any region is invalid
    ri = reduced_indices(A, region)

    # Next, throw if reduction is over a region with length zero
    any(i -> isempty(axes(A, i)), region) && _empty_reduce_error()

    # Make a view of the first slice of the region
    A1 = view(A, ri...)

    isempty(A1) && return map(f, A1)
    # use the max/min of the first slice as initial value for non-empty cases
    v0 = reverse(mapreduce(f, op, A1)) # turn minmax to maxmin

    T = _realtype(f.f, promote_union(eltype(A)))
    Tmin = v0[1] isa T ? T : typeof(v0[1])
    Tmax = v0[2] isa T ? T : typeof(v0[2])

    # but NaNs and missing need to be avoided as initial values
    if v0[1] isa Number && isnan(v0[1])
        v0 = oftype(v0[1], Inf), oftype(v0[2], -Inf)
    elseif isunordered(v0[1])
        # v0 is missing or a third-party unordered value
        # TODO: Some types, like BigInt, don't support typemin/typemax.
        # So a Matrix{Union{BigInt, Missing}} can still error here.
        v0 = typemax(nonmissingtype(Tmin)), typemin(nonmissingtype(Tmax))
    end
    # v0 may have changed type.
    Tmin = v0[1] isa T ? T : typeof(v0[1])
    Tmax = v0[2] isa T ? T : typeof(v0[2])

    return reducedim_initarray(A, region, v0, Tuple{Tmin,Tmax})
end

reducedim_init(f::Union{typeof(abs),typeof(abs2)}, op::typeof(max), A::AbstractArray{T}, region) where {T} =
    reducedim_initarray(A, region, zero(f(zero(T))), _realtype(f, T))

reducedim_init(f, op::typeof(&), A::AbstractArrayOrBroadcasted, region) = reducedim_initarray(A, region, true)
reducedim_init(f, op::typeof(|), A::AbstractArrayOrBroadcasted, region) = reducedim_initarray(A, region, false)

# specialize to make initialization more efficient for common cases

let
    BitIntFloat = Union{BitInteger, IEEEFloat}
    T = Union{
        Any[AbstractArray{t} for t in uniontypes(BitIntFloat)]...,
        Any[AbstractArray{Complex{t}} for t in uniontypes(BitIntFloat)]...}

    global function reducedim_init(f, op::Union{typeof(+),typeof(add_sum)}, A::T, region)
        z = zero(f(zero(eltype(A))))
        reducedim_initarray(A, region, op(z, z))
    end
    global function reducedim_init(f, op::Union{typeof(*),typeof(mul_prod)}, A::T, region)
        u = one(f(one(eltype(A))))
        reducedim_initarray(A, region, op(u, u))
    end
end

## generic (map)reduction

has_fast_linear_indexing(a::AbstractArrayOrBroadcasted) = false
has_fast_linear_indexing(a::Array) = true
has_fast_linear_indexing(::Union{Number,Ref,AbstractChar}) = true  # 0d objects, for Broadcasted
has_fast_linear_indexing(bc::Broadcast.Broadcasted) =
    all(has_fast_linear_indexing, bc.args)

function check_reducedims(R, A)
    # Check whether R has compatible dimensions w.r.t. A for reduction
    #
    # It returns an integer value (useful for choosing implementation)
    # - If it reduces only along leading dimensions, e.g. sum(A, dims=1) or sum(A, dims=(1,2)),
    #   it returns the length of the leading slice. For the two examples above,
    #   it will be size(A, 1) or size(A, 1) * size(A, 2).
    # - Otherwise, e.g. sum(A, dims=2) or sum(A, dims=(1,3)), it returns 0.
    #
    ndims(R) <= ndims(A) || throw(DimensionMismatch("cannot reduce $(ndims(A))-dimensional array to $(ndims(R)) dimensions"))
    lsiz = 1
    had_nonreduc = false
    for i = 1:ndims(A)
        Ri, Ai = axes(R, i), axes(A, i)
        sRi, sAi = length(Ri), length(Ai)
        if sRi == 1
            if sAi > 1
                if had_nonreduc
                    lsiz = 0  # to reduce along i, but some previous dimensions were non-reducing
                else
                    lsiz *= sAi  # if lsiz was set to zero, it will stay to be zero
                end
            end
        else
            Ri == Ai || throw(DimensionMismatch("reduction on array with indices $(axes(A)) with output with indices $(axes(R))"))
            had_nonreduc = true
        end
    end
    return lsiz
end

"""
Extract first entry of slices of array A into existing array R.
"""
copyfirst!(R::AbstractArray, A::AbstractArray) = mapfirst!(identity, R, A)

function mapfirst!(f::F, R::AbstractArray, A::AbstractArray{<:Any,N}) where {N, F}
    lsiz = check_reducedims(R, A)
    t = _firstreducedslice(axes(R), axes(A))
    map!(f, R, view(A, t...))
end
# We know that the axes of R and A are compatible, but R might have a different number of
# dimensions than A, which is trickier than it seems due to offset arrays and type stability
_firstreducedslice(::Tuple{}, a::Tuple{}) = ()
_firstreducedslice(::Tuple, ::Tuple{}) = ()
@inline _firstreducedslice(::Tuple{}, a::Tuple) = (_firstslice(a[1]), _firstreducedslice((), tail(a))...)
@inline _firstreducedslice(r::Tuple, a::Tuple) = (length(r[1])==1 ? _firstslice(a[1]) : r[1], _firstreducedslice(tail(r), tail(a))...)
_firstslice(i::OneTo) = OneTo(1)
_firstslice(i::Slice) = Slice(_firstslice(i.indices))
_firstslice(i) = i[firstindex(i):firstindex(i)]

function _mapreducedim!(f, op, R::AbstractArray, A::AbstractArrayOrBroadcasted)
    lsiz = check_reducedims(R,A)
    isempty(A) && return R

    if has_fast_linear_indexing(A) && lsiz > 16
        # use mapreduce_impl, which is probably better tuned to achieve higher performance
        nslices = div(length(A), lsiz)
        ibase = first(LinearIndices(A))-1
        for i = 1:nslices
            @inbounds R[i] = op(R[i], mapreduce_impl(f, op, A, ibase+1, ibase+lsiz))
            ibase += lsiz
        end
        return R
    end
    indsAt, indsRt = safe_tail(axes(A)), safe_tail(axes(R)) # handle d=1 manually
    keep, Idefault = Broadcast.shapeindexer(indsRt)
    if reducedim1(R, A)
        # keep the accumulator as a local variable when reducing along the first dimension
        i1 = first(axes1(R))
        @inbounds for IA in CartesianIndices(indsAt)
            IR = Broadcast.newindex(IA, keep, Idefault)
            r = R[i1,IR]
            @simd for i in axes(A, 1)
                r = op(r, f(A[i, IA]))
            end
            R[i1,IR] = r
        end
    else
        @inbounds for IA in CartesianIndices(indsAt)
            IR = Broadcast.newindex(IA, keep, Idefault)
            @simd for i in axes(A, 1)
                R[i,IR] = op(R[i,IR], f(A[i,IA]))
            end
        end
    end
    return R
end

mapreducedim!(f, op, R::AbstractArray, A::AbstractArrayOrBroadcasted) =
    (_mapreducedim!(f, op, R, A); R)

reducedim!(op, R::AbstractArray{RT}, A::AbstractArrayOrBroadcasted) where {RT} =
    mapreducedim!(identity, op, R, A)

"""
    mapreduce(f, op, A::AbstractArray...; dims=:, [init])

Evaluates to the same as `reduce(op, map(f, A...); dims=dims, init=init)`, but is generally
faster because the intermediate array is avoided.

!!! compat "Julia 1.2"
    `mapreduce` with multiple iterators requires Julia 1.2 or later.

# Examples
```jldoctest
julia> a = reshape(Vector(1:16), (4,4))
4×4 Matrix{Int64}:
 1  5   9  13
 2  6  10  14
 3  7  11  15
 4  8  12  16

julia> mapreduce(isodd, *, a, dims=1)
1×4 Matrix{Bool}:
 0  0  0  0

julia> mapreduce(isodd, |, a, dims=1)
1×4 Matrix{Bool}:
 1  1  1  1
```
"""
mapreduce(f, op, A::AbstractArrayOrBroadcasted; dims=:, init=_InitialValue()) =
    _mapreduce_dim(f, op, init, A, dims)
mapreduce(f, op, A::AbstractArrayOrBroadcasted...; kw...) =
    reduce(op, map(f, A...); kw...)

_mapreduce_dim(f, op, nt, A::AbstractArrayOrBroadcasted, ::Colon) =
    mapfoldl_impl(f, op, nt, A)

_mapreduce_dim(f, op, ::_InitialValue, A::AbstractArrayOrBroadcasted, ::Colon) =
    _mapreduce(f, op, IndexStyle(A), A)

_mapreduce_dim(f, op, nt, A::AbstractArrayOrBroadcasted, dims) =
    mapreducedim!(f, op, reducedim_initarray(A, dims, nt), A)

_mapreduce_dim(f, op, ::_InitialValue, A::AbstractArrayOrBroadcasted, dims) =
    mapreducedim!(f, op, reducedim_init(f, op, A, dims), A)

"""
    reduce(f, A::AbstractArray; dims=:, [init])

Reduce 2-argument function `f` along dimensions of `A`. `dims` is a vector specifying the
dimensions to reduce, and the keyword argument `init` is the initial value to use in the
reductions. For `+`, `*`, `max` and `min` the `init` argument is optional.

The associativity of the reduction is implementation-dependent; if you need a particular
associativity, e.g. left-to-right, you should write your own loop or consider using
[`foldl`](@ref) or [`foldr`](@ref). See documentation for [`reduce`](@ref).

# Examples
```jldoctest
julia> a = reshape(Vector(1:16), (4,4))
4×4 Matrix{Int64}:
 1  5   9  13
 2  6  10  14
 3  7  11  15
 4  8  12  16

julia> reduce(max, a, dims=2)
4×1 Matrix{Int64}:
 13
 14
 15
 16

julia> reduce(max, a, dims=1)
1×4 Matrix{Int64}:
 4  8  12  16
```
"""
reduce(op, A::AbstractArray; kw...) = mapreduce(identity, op, A; kw...)

##### Specific reduction functions #####

"""
    count([f=identity,] A::AbstractArray; dims=:)

Count the number of elements in `A` for which `f` returns `true` over the given
dimensions.

!!! compat "Julia 1.5"
    `dims` keyword was added in Julia 1.5.

!!! compat "Julia 1.6"
    `init` keyword was added in Julia 1.6.

# Examples
```jldoctest
julia> A = [1 2; 3 4]
2×2 Matrix{Int64}:
 1  2
 3  4

julia> count(<=(2), A, dims=1)
1×2 Matrix{Int64}:
 1  1

julia> count(<=(2), A, dims=2)
2×1 Matrix{Int64}:
 2
 0
```
"""
count(A::AbstractArrayOrBroadcasted; dims=:, init=0) = count(identity, A; dims, init)
count(f, A::AbstractArrayOrBroadcasted; dims=:, init=0) = _count(f, A, dims, init)

_count(f, A::AbstractArrayOrBroadcasted, dims::Colon, init) = _simple_count(f, A, init)
_count(f, A::AbstractArrayOrBroadcasted, dims, init) = mapreduce(_bool(f), add_sum, A; dims, init)

"""
    count!([f=identity,] r, A)

Count the number of elements in `A` for which `f` returns `true` over the
singleton dimensions of `r`, writing the result into `r` in-place.

$(_DOCS_ALIASING_WARNING)

!!! compat "Julia 1.5"
    inplace `count!` was added in Julia 1.5.

# Examples
```jldoctest
julia> A = [1 2; 3 4]
2×2 Matrix{Int64}:
 1  2
 3  4

julia> count!(<=(2), [1 1], A)
1×2 Matrix{Int64}:
 1  1

julia> count!(<=(2), [1; 1], A)
2-element Vector{Int64}:
 2
 0
```
"""
count!(r::AbstractArray, A::AbstractArrayOrBroadcasted; init::Bool=true) = count!(identity, r, A; init=init)
count!(f, r::AbstractArray, A::AbstractArrayOrBroadcasted; init::Bool=true) =
    mapreducedim!(_bool(f), add_sum, initarray!(r, f, add_sum, init, A), A)

"""
    sum(A::AbstractArray; dims)

Sum elements of an array over the given dimensions.

# Examples
```jldoctest
julia> A = [1 2; 3 4]
2×2 Matrix{Int64}:
 1  2
 3  4

julia> sum(A, dims=1)
1×2 Matrix{Int64}:
 4  6

julia> sum(A, dims=2)
2×1 Matrix{Int64}:
 3
 7
```
"""
sum(A::AbstractArray; dims)

"""
    sum(f, A::AbstractArray; dims)

Sum the results of calling function `f` on each element of an array over the given
dimensions.

# Examples
```jldoctest
julia> A = [1 2; 3 4]
2×2 Matrix{Int64}:
 1  2
 3  4

julia> sum(abs2, A, dims=1)
1×2 Matrix{Int64}:
 10  20

julia> sum(abs2, A, dims=2)
2×1 Matrix{Int64}:
  5
 25
```
"""
sum(f, A::AbstractArray; dims)

"""
    sum!(r, A)

Sum elements of `A` over the singleton dimensions of `r`, and write results to `r`.

$(_DOCS_ALIASING_WARNING)

# Examples
```jldoctest
julia> A = [1 2; 3 4]
2×2 Matrix{Int64}:
 1  2
 3  4

julia> sum!([1; 1], A)
2-element Vector{Int64}:
 3
 7

julia> sum!([1 1], A)
1×2 Matrix{Int64}:
 4  6
```
"""
sum!(r, A)

"""
    prod(A::AbstractArray; dims)

Multiply elements of an array over the given dimensions.

# Examples
```jldoctest
julia> A = [1 2; 3 4]
2×2 Matrix{Int64}:
 1  2
 3  4

julia> prod(A, dims=1)
1×2 Matrix{Int64}:
 3  8

julia> prod(A, dims=2)
2×1 Matrix{Int64}:
  2
 12
```
"""
prod(A::AbstractArray; dims)

"""
    prod(f, A::AbstractArray; dims)

Multiply the results of calling the function `f` on each element of an array over the given
dimensions.

# Examples
```jldoctest
julia> A = [1 2; 3 4]
2×2 Matrix{Int64}:
 1  2
 3  4

julia> prod(abs2, A, dims=1)
1×2 Matrix{Int64}:
 9  64

julia> prod(abs2, A, dims=2)
2×1 Matrix{Int64}:
   4
 144
```
"""
prod(f, A::AbstractArray; dims)

"""
    prod!(r, A)

Multiply elements of `A` over the singleton dimensions of `r`, and write results to `r`.

$(_DOCS_ALIASING_WARNING)

# Examples
```jldoctest
julia> A = [1 2; 3 4]
2×2 Matrix{Int64}:
 1  2
 3  4

julia> prod!([1; 1], A)
2-element Vector{Int64}:
  2
 12

julia> prod!([1 1], A)
1×2 Matrix{Int64}:
 3  8
```
"""
prod!(r, A)

"""
    maximum(A::AbstractArray; dims)

Compute the maximum value of an array over the given dimensions. See also the
[`max(a,b)`](@ref) function to take the maximum of two or more arguments,
which can be applied elementwise to arrays via `max.(a,b)`.

See also: [`maximum!`](@ref), [`extrema`](@ref), [`findmax`](@ref), [`argmax`](@ref).

# Examples
```jldoctest
julia> A = [1 2; 3 4]
2×2 Matrix{Int64}:
 1  2
 3  4

julia> maximum(A, dims=1)
1×2 Matrix{Int64}:
 3  4

julia> maximum(A, dims=2)
2×1 Matrix{Int64}:
 2
 4
```
"""
maximum(A::AbstractArray; dims)

"""
    maximum(f, A::AbstractArray; dims)

Compute the maximum value by calling the function `f` on each element of an array over the given
dimensions.

# Examples
```jldoctest
julia> A = [1 2; 3 4]
2×2 Matrix{Int64}:
 1  2
 3  4

julia> maximum(abs2, A, dims=1)
1×2 Matrix{Int64}:
 9  16

julia> maximum(abs2, A, dims=2)
2×1 Matrix{Int64}:
  4
 16
```
"""
maximum(f, A::AbstractArray; dims)

"""
    maximum!(r, A)

Compute the maximum value of `A` over the singleton dimensions of `r`, and write results to `r`.

$(_DOCS_ALIASING_WARNING)

# Examples
```jldoctest
julia> A = [1 2; 3 4]
2×2 Matrix{Int64}:
 1  2
 3  4

julia> maximum!([1; 1], A)
2-element Vector{Int64}:
 2
 4

julia> maximum!([1 1], A)
1×2 Matrix{Int64}:
 3  4
```
"""
maximum!(r, A)

"""
    minimum(A::AbstractArray; dims)

Compute the minimum value of an array over the given dimensions. See also the
[`min(a,b)`](@ref) function to take the minimum of two or more arguments,
which can be applied elementwise to arrays via `min.(a,b)`.

See also: [`minimum!`](@ref), [`extrema`](@ref), [`findmin`](@ref), [`argmin`](@ref).

# Examples
```jldoctest
julia> A = [1 2; 3 4]
2×2 Matrix{Int64}:
 1  2
 3  4

julia> minimum(A, dims=1)
1×2 Matrix{Int64}:
 1  2

julia> minimum(A, dims=2)
2×1 Matrix{Int64}:
 1
 3
```
"""
minimum(A::AbstractArray; dims)

"""
    minimum(f, A::AbstractArray; dims)

Compute the minimum value by calling the function `f` on each element of an array over the given
dimensions.

# Examples
```jldoctest
julia> A = [1 2; 3 4]
2×2 Matrix{Int64}:
 1  2
 3  4

julia> minimum(abs2, A, dims=1)
1×2 Matrix{Int64}:
 1  4

julia> minimum(abs2, A, dims=2)
2×1 Matrix{Int64}:
 1
 9
```
"""
minimum(f, A::AbstractArray; dims)

"""
    minimum!(r, A)

Compute the minimum value of `A` over the singleton dimensions of `r`, and write results to `r`.

$(_DOCS_ALIASING_WARNING)

# Examples
```jldoctest
julia> A = [1 2; 3 4]
2×2 Matrix{Int64}:
 1  2
 3  4

julia> minimum!([1; 1], A)
2-element Vector{Int64}:
 1
 3

julia> minimum!([1 1], A)
1×2 Matrix{Int64}:
 1  2
```
"""
minimum!(r, A)

"""
    extrema(A::AbstractArray; dims) -> Array{Tuple}

Compute the minimum and maximum elements of an array over the given dimensions.

See also: [`minimum`](@ref), [`maximum`](@ref), [`extrema!`](@ref).

# Examples
```jldoctest
julia> A = reshape(Vector(1:2:16), (2,2,2))
2×2×2 Array{Int64, 3}:
[:, :, 1] =
 1  5
 3  7

[:, :, 2] =
  9  13
 11  15

julia> extrema(A, dims = (1,2))
1×1×2 Array{Tuple{Int64, Int64}, 3}:
[:, :, 1] =
 (1, 7)

[:, :, 2] =
 (9, 15)
```
"""
extrema(A::AbstractArray; dims)

"""
    extrema(f, A::AbstractArray; dims) -> Array{Tuple}

Compute the minimum and maximum of `f` applied to each element in the given dimensions
of `A`.

!!! compat "Julia 1.2"
    This method requires Julia 1.2 or later.
"""
extrema(f, A::AbstractArray; dims)

"""
    extrema!(r, A)

Compute the minimum and maximum value of `A` over the singleton dimensions of `r`, and write results to `r`.

$(_DOCS_ALIASING_WARNING)

!!! compat "Julia 1.8"
    This method requires Julia 1.8 or later.

# Examples
```jldoctest
julia> A = [1 2; 3 4]
2×2 Matrix{Int64}:
 1  2
 3  4

julia> extrema!([(1, 1); (1, 1)], A)
2-element Vector{Tuple{Int64, Int64}}:
 (1, 2)
 (3, 4)

julia> extrema!([(1, 1);; (1, 1)], A)
1×2 Matrix{Tuple{Int64, Int64}}:
 (1, 3)  (2, 4)
```
"""
extrema!(r, A)

"""
    all(A; dims)

Test whether all values along the given dimensions of an array are `true`.

# Examples
```jldoctest
julia> A = [true false; true true]
2×2 Matrix{Bool}:
 1  0
 1  1

julia> all(A, dims=1)
1×2 Matrix{Bool}:
 1  0

julia> all(A, dims=2)
2×1 Matrix{Bool}:
 0
 1
```
"""
all(A::AbstractArray; dims)

"""
    all(p, A; dims)

Determine whether predicate `p` returns `true` for all elements along the given dimensions of an array.

# Examples
```jldoctest
julia> A = [1 -1; 2 2]
2×2 Matrix{Int64}:
 1  -1
 2   2

julia> all(i -> i > 0, A, dims=1)
1×2 Matrix{Bool}:
 1  0

julia> all(i -> i > 0, A, dims=2)
2×1 Matrix{Bool}:
 0
 1
```
"""
all(::Function, ::AbstractArray; dims)

"""
    all!(r, A)

Test whether all values in `A` along the singleton dimensions of `r` are `true`, and write results to `r`.

$(_DOCS_ALIASING_WARNING)

# Examples
```jldoctest
julia> A = [true false; true false]
2×2 Matrix{Bool}:
 1  0
 1  0

julia> all!([1; 1], A)
2-element Vector{Int64}:
 0
 0

julia> all!([1 1], A)
1×2 Matrix{Int64}:
 1  0
```
"""
all!(r, A)

"""
    any(A; dims)

Test whether any values along the given dimensions of an array are `true`.

# Examples
```jldoctest
julia> A = [true false; true false]
2×2 Matrix{Bool}:
 1  0
 1  0

julia> any(A, dims=1)
1×2 Matrix{Bool}:
 1  0

julia> any(A, dims=2)
2×1 Matrix{Bool}:
 1
 1
```
"""
any(::AbstractArray; dims)

"""
    any(p, A; dims)

Determine whether predicate `p` returns `true` for any elements along the given dimensions of an array.

# Examples
```jldoctest
julia> A = [1 -1; 2 -2]
2×2 Matrix{Int64}:
 1  -1
 2  -2

julia> any(i -> i > 0, A, dims=1)
1×2 Matrix{Bool}:
 1  0

julia> any(i -> i > 0, A, dims=2)
2×1 Matrix{Bool}:
 1
 1
```
"""
any(::Function, ::AbstractArray; dims)

"""
    any!(r, A)

Test whether any values in `A` along the singleton dimensions of `r` are `true`, and write
results to `r`.

$(_DOCS_ALIASING_WARNING)

# Examples
```jldoctest
julia> A = [true false; true false]
2×2 Matrix{Bool}:
 1  0
 1  0

julia> any!([1; 1], A)
2-element Vector{Int64}:
 1
 1

julia> any!([1 1], A)
1×2 Matrix{Int64}:
 1  0
```
"""
any!(r, A)

for (fname, _fname, op) in [(:sum,     :_sum,     :add_sum), (:prod,    :_prod,    :mul_prod),
                            (:maximum, :_maximum, :max),     (:minimum, :_minimum, :min),
                            (:extrema, :_extrema, :_extrema_rf)]
    mapf = fname === :extrema ? :(ExtremaMap(f)) : :f
    @eval begin
        # User-facing methods with keyword arguments
        @inline ($fname)(a::AbstractArray; dims=:, kw...) = ($_fname)(a, dims; kw...)
        @inline ($fname)(f, a::AbstractArray; dims=:, kw...) = ($_fname)(f, a, dims; kw...)

        # Underlying implementations using dispatch
        ($_fname)(a, ::Colon; kw...) = ($_fname)(identity, a, :; kw...)
        ($_fname)(f, a, ::Colon; kw...) = mapreduce($mapf, $op, a; kw...)
    end
end

any(a::AbstractArray; dims=:)              = _any(a, dims)
any(f::Function, a::AbstractArray; dims=:) = _any(f, a, dims)
_any(a, ::Colon)                           = _any(identity, a, :)
all(a::AbstractArray; dims=:)              = _all(a, dims)
all(f::Function, a::AbstractArray; dims=:) = _all(f, a, dims)
_all(a, ::Colon)                           = _all(identity, a, :)

for (fname, op) in [(:sum, :add_sum), (:prod, :mul_prod),
                    (:maximum, :max), (:minimum, :min),
                    (:all, :&),       (:any, :|),
                    (:extrema, :_extrema_rf)]
    fname! = Symbol(fname, '!')
    _fname = Symbol('_', fname)
    mapf = fname === :extrema ? :(ExtremaMap(f)) : :f
    @eval begin
        $(fname!)(f::Function, r::AbstractArray, A::AbstractArray; init::Bool=true) =
            mapreducedim!($mapf, $(op), initarray!(r, $mapf, $(op), init, A), A)
        $(fname!)(r::AbstractArray, A::AbstractArray; init::Bool=true) = $(fname!)(identity, r, A; init=init)

        $(_fname)(A, dims; kw...)    = $(_fname)(identity, A, dims; kw...)
        $(_fname)(f, A, dims; kw...) = mapreduce($mapf, $(op), A; dims=dims, kw...)
    end
end

##### findmin & findmax #####
# The initial values of Rval are not used if the corresponding indices in Rind are 0.
#
function findminmax!(f, op, Rval, Rind, A::AbstractArray{T,N}) where {T,N}
    (isempty(Rval) || isempty(A)) && return Rval, Rind
    lsiz = check_reducedims(Rval, A)
    for i = 1:N
        axes(Rval, i) == axes(Rind, i) || throw(DimensionMismatch("Find-reduction: outputs must have the same indices"))
    end
    # If we're reducing along dimension 1, for efficiency we can make use of a temporary.
    # Otherwise, keep the result in Rval/Rind so that we traverse A in storage order.
    indsAt, indsRt = safe_tail(axes(A)), safe_tail(axes(Rval))
    keep, Idefault = Broadcast.shapeindexer(indsRt)
    ks = keys(A)
    y = iterate(ks)
    zi = zero(eltype(ks))
    if reducedim1(Rval, A)
        i1 = first(axes1(Rval))
        @inbounds for IA in CartesianIndices(indsAt)
            IR = Broadcast.newindex(IA, keep, Idefault)
            tmpRv = Rval[i1,IR]
            tmpRi = Rind[i1,IR]
            for i in axes(A,1)
                k, kss = y::Tuple
                tmpAv = f(A[i,IA])
                if tmpRi == zi || op(tmpRv, tmpAv)
                    tmpRv = tmpAv
                    tmpRi = k
                end
                y = iterate(ks, kss)
            end
            Rval[i1,IR] = tmpRv
            Rind[i1,IR] = tmpRi
        end
    else
        @inbounds for IA in CartesianIndices(indsAt)
            IR = Broadcast.newindex(IA, keep, Idefault)
            for i in axes(A, 1)
                k, kss = y::Tuple
                tmpAv = f(A[i,IA])
                tmpRv = Rval[i,IR]
                tmpRi = Rind[i,IR]
                if tmpRi == zi || op(tmpRv, tmpAv)
                    Rval[i,IR] = tmpAv
                    Rind[i,IR] = k
                end
                y = iterate(ks, kss)
            end
        end
    end
    Rval, Rind
end

"""
    findmin!(rval, rind, A) -> (minval, index)

Find the minimum of `A` and the corresponding linear index along singleton
dimensions of `rval` and `rind`, and store the results in `rval` and `rind`.
`NaN` is treated as less than all other values except `missing`.

$(_DOCS_ALIASING_WARNING)
"""
function findmin!(rval::AbstractArray, rind::AbstractArray, A::AbstractArray;
                  init::Bool=true)
    findminmax!(identity, isgreater, init && !isempty(A) ? fill!(rval, first(A)) : rval, fill!(rind,zero(eltype(keys(A)))), A)
end

"""
    findmin(A; dims) -> (minval, index)

For an array input, returns the value and index of the minimum over the given dimensions.
`NaN` is treated as less than all other values except `missing`.

# Examples
```jldoctest
julia> A = [1.0 2; 3 4]
2×2 Matrix{Float64}:
 1.0  2.0
 3.0  4.0

julia> findmin(A, dims=1)
([1.0 2.0], CartesianIndex{2}[CartesianIndex(1, 1) CartesianIndex(1, 2)])

julia> findmin(A, dims=2)
([1.0; 3.0;;], CartesianIndex{2}[CartesianIndex(1, 1); CartesianIndex(2, 1);;])
```
"""
findmin(A::AbstractArray; dims=:) = _findmin(A, dims)
_findmin(A, dims) = _findmin(identity, A, dims)

"""
    findmin(f, A; dims) -> (f(x), index)

For an array input, returns the value in the codomain and index of the corresponding value
which minimize `f` over the given dimensions.

# Examples
```jldoctest
julia> A = [-1.0 1; -0.5 2]
2×2 Matrix{Float64}:
 -1.0  1.0
 -0.5  2.0

julia> findmin(abs2, A, dims=1)
([0.25 1.0], CartesianIndex{2}[CartesianIndex(2, 1) CartesianIndex(1, 2)])

julia> findmin(abs2, A, dims=2)
([1.0; 0.25;;], CartesianIndex{2}[CartesianIndex(1, 1); CartesianIndex(2, 1);;])
```
"""
findmin(f, A::AbstractArray; dims=:) = _findmin(f, A, dims)

function _findmin(f, A, region)
    ri = reduced_indices0(A, region)
    if isempty(A)
        if prod(map(length, reduced_indices(A, region))) != 0
            throw(ArgumentError("collection slices must be non-empty"))
        end
        similar(A, promote_op(f, eltype(A)), ri), zeros(eltype(keys(A)), ri)
    else
        fA = f(first(A))
        findminmax!(f, isgreater, fill!(similar(A, _findminmax_inittype(f, A), ri), fA),
                    zeros(eltype(keys(A)), ri), A)
    end
end

"""
    findmax!(rval, rind, A) -> (maxval, index)

Find the maximum of `A` and the corresponding linear index along singleton
dimensions of `rval` and `rind`, and store the results in `rval` and `rind`.
`NaN` is treated as greater than all other values except `missing`.

$(_DOCS_ALIASING_WARNING)
"""
function findmax!(rval::AbstractArray, rind::AbstractArray, A::AbstractArray;
                  init::Bool=true)
    findminmax!(identity, isless, init && !isempty(A) ? fill!(rval, first(A)) : rval, fill!(rind,zero(eltype(keys(A)))), A)
end

"""
    findmax(A; dims) -> (maxval, index)

For an array input, returns the value and index of the maximum over the given dimensions.
`NaN` is treated as greater than all other values except `missing`.

# Examples
```jldoctest
julia> A = [1.0 2; 3 4]
2×2 Matrix{Float64}:
 1.0  2.0
 3.0  4.0

julia> findmax(A, dims=1)
([3.0 4.0], CartesianIndex{2}[CartesianIndex(2, 1) CartesianIndex(2, 2)])

julia> findmax(A, dims=2)
([2.0; 4.0;;], CartesianIndex{2}[CartesianIndex(1, 2); CartesianIndex(2, 2);;])
```
"""
findmax(A::AbstractArray; dims=:) = _findmax(A, dims)
_findmax(A, dims) = _findmax(identity, A, dims)

"""
    findmax(f, A; dims) -> (f(x), index)

For an array input, returns the value in the codomain and index of the corresponding value
which maximize `f` over the given dimensions.

# Examples
```jldoctest
julia> A = [-1.0 1; -0.5 2]
2×2 Matrix{Float64}:
 -1.0  1.0
 -0.5  2.0

julia> findmax(abs2, A, dims=1)
([1.0 4.0], CartesianIndex{2}[CartesianIndex(1, 1) CartesianIndex(2, 2)])

julia> findmax(abs2, A, dims=2)
([1.0; 4.0;;], CartesianIndex{2}[CartesianIndex(1, 1); CartesianIndex(2, 2);;])
```
"""
findmax(f, A::AbstractArray; dims=:) = _findmax(f, A, dims)

function _findmax(f, A, region)
    ri = reduced_indices0(A, region)
    if isempty(A)
        if prod(map(length, reduced_indices(A, region))) != 0
            throw(ArgumentError("collection slices must be non-empty"))
        end
        similar(A, promote_op(f, eltype(A)), ri), zeros(eltype(keys(A)), ri)
    else
        fA = f(first(A))
        findminmax!(f, isless, fill!(similar(A, _findminmax_inittype(f, A), ri), fA),
                    zeros(eltype(keys(A)), ri), A)
    end
end

function _findminmax_inittype(f, A::AbstractArray)
    T = _realtype(f, promote_union(eltype(A)))
    v0 = f(first(A))
    # First conditional: T is >: typeof(v0), so return it
    # Second conditional: handle missing specifically, as most often, f(missing) = missing;
    # certainly, some predicate functions return Bool, but not all.
    # Else, return the type of the transformation.
    Tr = v0 isa T ? T : Missing <: eltype(A) ? Union{Missing, typeof(v0)} : typeof(v0)
end

reducedim1(R, A) = length(axes1(R)) == 1

"""
    argmin(A; dims) -> indices

For an array input, return the indices of the minimum elements over the given dimensions.
`NaN` is treated as less than all other values except `missing`.

# Examples
```jldoctest
julia> A = [1.0 2; 3 4]
2×2 Matrix{Float64}:
 1.0  2.0
 3.0  4.0

julia> argmin(A, dims=1)
1×2 Matrix{CartesianIndex{2}}:
 CartesianIndex(1, 1)  CartesianIndex(1, 2)

julia> argmin(A, dims=2)
2×1 Matrix{CartesianIndex{2}}:
 CartesianIndex(1, 1)
 CartesianIndex(2, 1)
```
"""
argmin(A::AbstractArray; dims=:) = findmin(A; dims=dims)[2]

"""
    argmax(A; dims) -> indices

For an array input, return the indices of the maximum elements over the given dimensions.
`NaN` is treated as greater than all other values except `missing`.

# Examples
```jldoctest
julia> A = [1.0 2; 3 4]
2×2 Matrix{Float64}:
 1.0  2.0
 3.0  4.0

julia> argmax(A, dims=1)
1×2 Matrix{CartesianIndex{2}}:
 CartesianIndex(2, 1)  CartesianIndex(2, 2)

julia> argmax(A, dims=2)
2×1 Matrix{CartesianIndex{2}}:
 CartesianIndex(1, 2)
 CartesianIndex(2, 2)
```
"""
argmax(A::AbstractArray; dims=:) = findmax(A; dims=dims)[2]
Q   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/accumulate.jl�/      # This file is a part of Julia. License is MIT: https://julialang.org/license

# accumulate_pairwise slightly slower then accumulate, but more numerically
# stable in certain situations (e.g. sums).
# it does double the number of operations compared to accumulate,
# though for cheap operations like + this does not have much impact (20%)
function _accumulate_pairwise!(op::Op, c::AbstractVector{T}, v::AbstractVector, s, i1, n)::T where {T,Op}
    @inbounds if n < 128
        s_ = v[i1]
        c[i1] = op(s, s_)
        for i = i1+1:i1+n-1
            s_ = op(s_, v[i])
            c[i] = op(s, s_)
        end
    else
        n2 = n >> 1
        s_ = _accumulate_pairwise!(op, c, v, s, i1, n2)
        s_ = op(s_, _accumulate_pairwise!(op, c, v, op(s, s_), i1+n2, n-n2))
    end
    return s_
end

function accumulate_pairwise!(op::Op, result::AbstractVector, v::AbstractVector) where Op
    li = LinearIndices(v)
    li != LinearIndices(result) && throw(DimensionMismatch("input and output array sizes and indices must match"))
    n = length(li)
    n == 0 && return result
    i1 = first(li)
    @inbounds result[i1] = v1 = reduce_first(op,v[i1])
    n == 1 && return result
    _accumulate_pairwise!(op, result, v, v1, i1+1, n-1)
    return result
end

function accumulate_pairwise(op, v::AbstractVector{T}) where T
    out = similar(v, promote_op(op, T, T))
    return accumulate_pairwise!(op, out, v)
end


"""
    cumsum!(B, A; dims::Integer)

Cumulative sum of `A` along the dimension `dims`, storing the result in `B`. See also [`cumsum`](@ref).

$(_DOCS_ALIASING_WARNING)
"""
cumsum!(B::AbstractArray{T}, A; dims::Integer) where {T} =
    accumulate!(add_sum, B, A, dims=dims)

function cumsum!(out::AbstractArray, v::AbstractVector; dims::Integer=1)
    # we dispatch on the possibility of numerical stability issues
    _cumsum!(out, v, dims, ArithmeticStyle(eltype(out)))
end

function _cumsum!(out::AbstractArray{T}, v, dim, ::ArithmeticRounds) where {T}
    dim == 1 ? accumulate_pairwise!(add_sum, out, v) : copyto!(out, v)
end
function _cumsum!(out::AbstractArray, v, dim, ::ArithmeticUnknown)
    _cumsum!(out, v, dim, ArithmeticRounds())
end
function _cumsum!(out::AbstractArray{T}, v, dim, ::ArithmeticStyle) where {T}
    dim == 1 ? accumulate!(add_sum, out, v) : copyto!(out, v)
end

"""
    cumsum(A; dims::Integer)

Cumulative sum along the dimension `dims`. See also [`cumsum!`](@ref) to use a
preallocated output array, both for performance and to control the precision of
the output (e.g. to avoid overflow).

# Examples
```jldoctest
julia> a = [1 2 3; 4 5 6]
2×3 Matrix{Int64}:
 1  2  3
 4  5  6

julia> cumsum(a, dims=1)
2×3 Matrix{Int64}:
 1  2  3
 5  7  9

julia> cumsum(a, dims=2)
2×3 Matrix{Int64}:
 1  3   6
 4  9  15
```

!!! note
    The return array's `eltype` is `Int` for signed integers of less than system
    word size  and `UInt` for unsigned integers of less than system word size.
    To preserve `eltype` of arrays with small signed or unsigned integer
    `accumulate(+, A)` should be used.

    ```jldoctest
    julia> cumsum(Int8[100, 28])
    2-element Vector{Int64}:
     100
     128

    julia> accumulate(+,Int8[100, 28])
    2-element Vector{Int8}:
      100
     -128
    ```

    In the former case, the integers are widened to system word size and
    therefore the result is `Int64[100, 128]`. In the latter case, no such
    widening happens and integer overflow results in `Int8[100, -128]`.
"""
function cumsum(A::AbstractArray{T}; dims::Integer) where T
    out = similar(A, promote_op(add_sum, T, T))
    cumsum!(out, A, dims=dims)
end

"""
    cumsum(itr)

Cumulative sum of an iterator.

See also [`accumulate`](@ref) to apply functions other than `+`.

!!! compat "Julia 1.5"
    `cumsum` on a non-array iterator requires at least Julia 1.5.

# Examples
```jldoctest
julia> cumsum(1:3)
3-element Vector{Int64}:
 1
 3
 6

julia> cumsum((true, false, true, false, true))
(1, 1, 2, 2, 3)

julia> cumsum(fill(1, 2) for i in 1:3)
3-element Vector{Vector{Int64}}:
 [1, 1]
 [2, 2]
 [3, 3]
```
"""
cumsum(x::AbstractVector) = cumsum(x, dims=1)
cumsum(itr) = accumulate(add_sum, itr)


"""
    cumprod!(B, A; dims::Integer)

Cumulative product of `A` along the dimension `dims`, storing the result in `B`.
See also [`cumprod`](@ref).

$(_DOCS_ALIASING_WARNING)
"""
cumprod!(B::AbstractArray{T}, A; dims::Integer) where {T} =
    accumulate!(mul_prod, B, A, dims=dims)

"""
    cumprod!(y::AbstractVector, x::AbstractVector)

Cumulative product of a vector `x`, storing the result in `y`.
See also [`cumprod`](@ref).

$(_DOCS_ALIASING_WARNING)
"""
cumprod!(y::AbstractVector, x::AbstractVector) = cumprod!(y, x, dims=1)

"""
    cumprod(A; dims::Integer)

Cumulative product along the dimension `dim`. See also
[`cumprod!`](@ref) to use a preallocated output array, both for performance and
to control the precision of the output (e.g. to avoid overflow).

# Examples
```jldoctest
julia> a = Int8[1 2 3; 4 5 6];

julia> cumprod(a, dims=1)
2×3 Matrix{Int64}:
 1   2   3
 4  10  18

julia> cumprod(a, dims=2)
2×3 Matrix{Int64}:
 1   2    6
 4  20  120
```
"""
function cumprod(A::AbstractArray; dims::Integer)
    return accumulate(mul_prod, A, dims=dims)
end

"""
    cumprod(itr)

Cumulative product of an iterator.

See also [`cumprod!`](@ref), [`accumulate`](@ref), [`cumsum`](@ref).

!!! compat "Julia 1.5"
    `cumprod` on a non-array iterator requires at least Julia 1.5.

# Examples
```jldoctest
julia> cumprod(fill(1//2, 3))
3-element Vector{Rational{Int64}}:
 1//2
 1//4
 1//8

julia> cumprod((1, 2, 1, 3, 1))
(1, 2, 2, 6, 6)

julia> cumprod("julia")
5-element Vector{String}:
 "j"
 "ju"
 "jul"
 "juli"
 "julia"
```
"""
cumprod(x::AbstractVector) = cumprod(x, dims=1)
cumprod(itr) = accumulate(mul_prod, itr)


"""
    accumulate(op, A; dims::Integer, [init])

Cumulative operation `op` along the dimension `dims` of `A` (providing `dims` is optional
for vectors). An initial value `init` may optionally be provided by a keyword argument. See
also [`accumulate!`](@ref) to use a preallocated output array, both for performance and
to control the precision of the output (e.g. to avoid overflow).

For common operations there are specialized variants of `accumulate`,
see [`cumsum`](@ref), [`cumprod`](@ref). For a lazy version, see
[`Iterators.accumulate`](@ref).

!!! compat "Julia 1.5"
    `accumulate` on a non-array iterator requires at least Julia 1.5.

# Examples
```jldoctest
julia> accumulate(+, [1,2,3])
3-element Vector{Int64}:
 1
 3
 6

julia> accumulate(min, (1, -2, 3, -4, 5), init=0)
(0, -2, -2, -4, -4)

julia> accumulate(/, (2, 4, Inf), init=100)
(50.0, 12.5, 0.0)

julia> accumulate(=>, i^2 for i in 1:3)
3-element Vector{Any}:
          1
        1 => 4
 (1 => 4) => 9

julia> accumulate(+, fill(1, 3, 4))
3×4 Matrix{Int64}:
 1  4  7  10
 2  5  8  11
 3  6  9  12

julia> accumulate(+, fill(1, 2, 5), dims=2, init=100.0)
2×5 Matrix{Float64}:
 101.0  102.0  103.0  104.0  105.0
 101.0  102.0  103.0  104.0  105.0
```
"""
function accumulate(op, A; dims::Union{Nothing,Integer}=nothing, kw...)
    if dims === nothing && !(A isa AbstractVector)
        # This branch takes care of the cases not handled by `_accumulate!`.
        return collect(Iterators.accumulate(op, A; kw...))
    end
    nt = values(kw)
    if isempty(kw)
        out = similar(A, promote_op(op, eltype(A), eltype(A)))
    elseif keys(nt) === (:init,)
        out = similar(A, promote_op(op, typeof(nt.init), eltype(A)))
    else
        throw(ArgumentError("accumulate does not support the keyword arguments $(setdiff(keys(nt), (:init,)))"))
    end
    accumulate!(op, out, A; dims=dims, kw...)
end

function accumulate(op, xs::Tuple; init = _InitialValue())
    rf = BottomRF(op)
    ys, = afoldl(((), init), xs...) do (ys, acc), x
        acc = rf(acc, x)
        (ys..., acc), acc
    end
    return ys
end

"""
    accumulate!(op, B, A; [dims], [init])

Cumulative operation `op` on `A` along the dimension `dims`, storing the result in `B`.
Providing `dims` is optional for vectors.  If the keyword argument `init` is given, its
value is used to instantiate the accumulation.

$(_DOCS_ALIASING_WARNING)

See also [`accumulate`](@ref), [`cumsum!`](@ref), [`cumprod!`](@ref).

# Examples
```jldoctest
julia> x = [1, 0, 2, 0, 3];

julia> y = rand(5);

julia> accumulate!(+, y, x);

julia> y
5-element Vector{Float64}:
 1.0
 1.0
 3.0
 3.0
 6.0

julia> A = [1 2 3; 4 5 6];

julia> B = similar(A);

julia> accumulate!(-, B, A, dims=1)
2×3 Matrix{Int64}:
  1   2   3
 -3  -3  -3

julia> accumulate!(*, B, A, dims=2, init=10)
2×3 Matrix{Int64}:
 10   20    60
 40  200  1200
```
"""
function accumulate!(op, B, A; dims::Union{Integer, Nothing} = nothing, kw...)
    nt = values(kw)
    if isempty(kw)
        _accumulate!(op, B, A, dims, nothing)
    elseif keys(kw) === (:init,)
        _accumulate!(op, B, A, dims, Some(nt.init))
    else
        throw(ArgumentError("accumulate! does not support the keyword arguments $(setdiff(keys(nt), (:init,)))"))
    end
end

function _accumulate!(op, B, A, dims::Nothing, init::Union{Nothing, Some})
    throw(ArgumentError("Keyword argument dims must be provided for multidimensional arrays"))
end

function _accumulate!(op, B, A::AbstractVector, dims::Nothing, init::Nothing)
    isempty(A) && return B
    v1 = reduce_first(op, first(A))
    _accumulate1!(op, B, v1, A, 1)
end

function _accumulate!(op, B, A::AbstractVector, dims::Nothing, init::Some)
    isempty(A) && return B
    v1 = op(something(init), first(A))
    _accumulate1!(op, B, v1, A, 1)
end

function _accumulate!(op, B, A, dims::Integer, init::Union{Nothing, Some})
    dims > 0 || throw(ArgumentError("dims must be a positive integer"))
    inds_t = axes(A)
    axes(B) == inds_t || throw(DimensionMismatch("shape of B must match A"))
    dims > ndims(A) && return copyto!(B, A)
    isempty(inds_t[dims]) && return B
    if dims == 1
        # We can accumulate to a temporary variable, which allows
        # register usage and will be slightly faster
        ind1 = inds_t[1]
        @inbounds for I in CartesianIndices(tail(inds_t))
            if init === nothing
                tmp = reduce_first(op, A[first(ind1), I])
            else
                tmp = op(something(init), A[first(ind1), I])
            end
            B[first(ind1), I] = tmp
            for i_1 = first(ind1)+1:last(ind1)
                tmp = op(tmp, A[i_1, I])
                B[i_1, I] = tmp
            end
        end
    else
        R1 = CartesianIndices(axes(A)[1:dims-1])   # not type-stable
        R2 = CartesianIndices(axes(A)[dims+1:end])
        _accumulaten!(op, B, A, R1, inds_t[dims], R2, init) # use function barrier
    end
    return B
end

@noinline function _accumulaten!(op, B, A, R1, ind, R2, init::Nothing)
    # Copy the initial element in each 1d vector along dimension `dim`
    ii = first(ind)
    @inbounds for J in R2, I in R1
        B[I, ii, J] = reduce_first(op, A[I, ii, J])
    end
    # Accumulate
    @inbounds for J in R2, i in first(ind)+1:last(ind), I in R1
        B[I, i, J] = op(B[I, i-1, J], A[I, i, J])
    end
    B
end

@noinline function _accumulaten!(op, B, A, R1, ind, R2, init::Some)
    # Copy the initial element in each 1d vector along dimension `dim`
    ii = first(ind)
    @inbounds for J in R2, I in R1
        B[I, ii, J] = op(something(init), A[I, ii, J])
    end
    # Accumulate
    @inbounds for J in R2, i in first(ind)+1:last(ind), I in R1
        B[I, i, J] = op(B[I, i-1, J], A[I, i, J])
    end
    B
end

function _accumulate1!(op, B, v1, A::AbstractVector, dim::Integer)
    dim > 0 || throw(ArgumentError("dim must be a positive integer"))
    inds = LinearIndices(A)
    inds == LinearIndices(B) || throw(DimensionMismatch("LinearIndices of A and B don't match"))
    dim > 1 && return copyto!(B, A)
    (i1, state) = iterate(inds)::NTuple{2,Any} # We checked earlier that A isn't empty
    cur_val = v1
    B[i1] = cur_val
    next = iterate(inds, state)
    @inbounds while next !== nothing
        (i, state) = next
        cur_val = op(cur_val, A[i])
        B[i] = cur_val
        next = iterate(inds, state)
    end
    return B
end
X   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/permuteddimsarray.jl�'      # This file is a part of Julia. License is MIT: https://julialang.org/license

module PermutedDimsArrays

import Base: permutedims, permutedims!
export PermutedDimsArray

# Some day we will want storage-order-aware iteration, so put perm in the parameters
struct PermutedDimsArray{T,N,perm,iperm,AA<:AbstractArray} <: AbstractArray{T,N}
    parent::AA

    function PermutedDimsArray{T,N,perm,iperm,AA}(data::AA) where {T,N,perm,iperm,AA<:AbstractArray}
        (isa(perm, NTuple{N,Int}) && isa(iperm, NTuple{N,Int})) || error("perm and iperm must both be NTuple{$N,Int}")
        isperm(perm) || throw(ArgumentError(string(perm, " is not a valid permutation of dimensions 1:", N)))
        all(map(d->iperm[perm[d]]==d, 1:N)) || throw(ArgumentError(string(perm, " and ", iperm, " must be inverses")))
        new(data)
    end
end

"""
    PermutedDimsArray(A, perm) -> B

Given an AbstractArray `A`, create a view `B` such that the
dimensions appear to be permuted. Similar to `permutedims`, except
that no copying occurs (`B` shares storage with `A`).

See also [`permutedims`](@ref), [`invperm`](@ref).

# Examples
```jldoctest
julia> A = rand(3,5,4);

julia> B = PermutedDimsArray(A, (3,1,2));

julia> size(B)
(4, 3, 5)

julia> B[3,1,2] == A[1,2,3]
true
```
"""
function PermutedDimsArray(data::AbstractArray{T,N}, perm) where {T,N}
    length(perm) == N || throw(ArgumentError(string(perm, " is not a valid permutation of dimensions 1:", N)))
    iperm = invperm(perm)
    PermutedDimsArray{T,N,(perm...,),(iperm...,),typeof(data)}(data)
end

Base.parent(A::PermutedDimsArray) = A.parent
Base.size(A::PermutedDimsArray{T,N,perm}) where {T,N,perm} = genperm(size(parent(A)), perm)
Base.axes(A::PermutedDimsArray{T,N,perm}) where {T,N,perm} = genperm(axes(parent(A)), perm)
Base.has_offset_axes(A::PermutedDimsArray) = Base.has_offset_axes(A.parent)

Base.similar(A::PermutedDimsArray, T::Type, dims::Base.Dims) = similar(parent(A), T, dims)

Base.unsafe_convert(::Type{Ptr{T}}, A::PermutedDimsArray{T}) where {T} = Base.unsafe_convert(Ptr{T}, parent(A))

# It's OK to return a pointer to the first element, and indeed quite
# useful for wrapping C routines that require a different storage
# order than used by Julia. But for an array with unconventional
# storage order, a linear offset is ambiguous---is it a memory offset
# or a linear index?
Base.pointer(A::PermutedDimsArray, i::Integer) = throw(ArgumentError("pointer(A, i) is deliberately unsupported for PermutedDimsArray"))

function Base.strides(A::PermutedDimsArray{T,N,perm}) where {T,N,perm}
    s = strides(parent(A))
    ntuple(d->s[perm[d]], Val(N))
end
Base.elsize(::Type{<:PermutedDimsArray{<:Any, <:Any, <:Any, <:Any, P}}) where {P} = Base.elsize(P)

@inline function Base.getindex(A::PermutedDimsArray{T,N,perm,iperm}, I::Vararg{Int,N}) where {T,N,perm,iperm}
    @boundscheck checkbounds(A, I...)
    @inbounds val = getindex(A.parent, genperm(I, iperm)...)
    val
end
@inline function Base.setindex!(A::PermutedDimsArray{T,N,perm,iperm}, val, I::Vararg{Int,N}) where {T,N,perm,iperm}
    @boundscheck checkbounds(A, I...)
    @inbounds setindex!(A.parent, val, genperm(I, iperm)...)
    val
end

function Base.isassigned(A::PermutedDimsArray{T,N,perm,iperm}, I::Vararg{Int,N}) where {T,N,perm,iperm}
    @boundscheck checkbounds(Bool, A, I...) || return false
    @inbounds x = isassigned(A.parent, genperm(I, iperm)...)
    x
end

@inline genperm(I::NTuple{N,Any}, perm::Dims{N}) where {N} = ntuple(d -> I[perm[d]], Val(N))
@inline genperm(I, perm::AbstractVector{Int}) = genperm(I, (perm...,))

"""
    permutedims(A::AbstractArray, perm)

Permute the dimensions of array `A`. `perm` is a vector or a tuple of length `ndims(A)`
specifying the permutation.

See also [`permutedims!`](@ref), [`PermutedDimsArray`](@ref), [`transpose`](@ref), [`invperm`](@ref).

# Examples
```jldoctest
julia> A = reshape(Vector(1:8), (2,2,2))
2×2×2 Array{Int64, 3}:
[:, :, 1] =
 1  3
 2  4

[:, :, 2] =
 5  7
 6  8

julia> perm = (3, 1, 2); # put the last dimension first

julia> B = permutedims(A, perm)
2×2×2 Array{Int64, 3}:
[:, :, 1] =
 1  2
 5  6

[:, :, 2] =
 3  4
 7  8

julia> A == permutedims(B, invperm(perm)) # the inverse permutation
true
```

For each dimension `i` of `B = permutedims(A, perm)`, its corresponding dimension of `A`
will be `perm[i]`. This means the equality `size(B, i) == size(A, perm[i])` holds.

```jldoctest
julia> A = randn(5, 7, 11, 13);

julia> perm = [4, 1, 3, 2];

julia> B = permutedims(A, perm);

julia> size(B)
(13, 5, 11, 7)

julia> size(A)[perm] == ans
true
```
"""
function permutedims(A::AbstractArray, perm)
    dest = similar(A, genperm(axes(A), perm))
    permutedims!(dest, A, perm)
end

"""
    permutedims(m::AbstractMatrix)

Permute the dimensions of the matrix `m`, by flipping the elements across the diagonal of
the matrix. Differs from `LinearAlgebra`'s [`transpose`](@ref) in that the
operation is not recursive.

# Examples
```jldoctest; setup = :(using LinearAlgebra)
julia> a = [1 2; 3 4];

julia> b = [5 6; 7 8];

julia> c = [9 10; 11 12];

julia> d = [13 14; 15 16];

julia> X = [[a] [b]; [c] [d]]
2×2 Matrix{Matrix{Int64}}:
 [1 2; 3 4]     [5 6; 7 8]
 [9 10; 11 12]  [13 14; 15 16]

julia> permutedims(X)
2×2 Matrix{Matrix{Int64}}:
 [1 2; 3 4]  [9 10; 11 12]
 [5 6; 7 8]  [13 14; 15 16]

julia> transpose(X)
2×2 transpose(::Matrix{Matrix{Int64}}) with eltype Transpose{Int64, Matrix{Int64}}:
 [1 3; 2 4]  [9 11; 10 12]
 [5 7; 6 8]  [13 15; 14 16]
```
"""
permutedims(A::AbstractMatrix) = permutedims(A, (2,1))

"""
    permutedims(v::AbstractVector)

Reshape vector `v` into a `1 × length(v)` row matrix.
Differs from `LinearAlgebra`'s [`transpose`](@ref) in that
the operation is not recursive.

# Examples
```jldoctest; setup = :(using LinearAlgebra)
julia> permutedims([1, 2, 3, 4])
1×4 Matrix{Int64}:
 1  2  3  4

julia> V = [[[1 2; 3 4]]; [[5 6; 7 8]]]
2-element Vector{Matrix{Int64}}:
 [1 2; 3 4]
 [5 6; 7 8]

julia> permutedims(V)
1×2 Matrix{Matrix{Int64}}:
 [1 2; 3 4]  [5 6; 7 8]

julia> transpose(V)
1×2 transpose(::Vector{Matrix{Int64}}) with eltype Transpose{Int64, Matrix{Int64}}:
 [1 3; 2 4]  [5 7; 6 8]
```
"""
permutedims(v::AbstractVector) = reshape(v, (1, length(v)))

"""
    permutedims!(dest, src, perm)

Permute the dimensions of array `src` and store the result in the array `dest`. `perm` is a
vector specifying a permutation of length `ndims(src)`. The preallocated array `dest` should
have `size(dest) == size(src)[perm]` and is completely overwritten. No in-place permutation
is supported and unexpected results will happen if `src` and `dest` have overlapping memory
regions.

See also [`permutedims`](@ref).
"""
function permutedims!(dest, src::AbstractArray, perm)
    Base.checkdims_perm(dest, src, perm)
    P = PermutedDimsArray(dest, invperm(perm))
    _copy!(P, src)
    return dest
end

function Base.copyto!(dest::PermutedDimsArray{T,N}, src::AbstractArray{T,N}) where {T,N}
    checkbounds(dest, axes(src)...)
    _copy!(dest, src)
end
Base.copyto!(dest::PermutedDimsArray, src::AbstractArray) = _copy!(dest, src)

function _copy!(P::PermutedDimsArray{T,N,perm}, src) where {T,N,perm}
    # If dest/src are "close to dense," then it pays to be cache-friendly.
    # Determine the first permuted dimension
    d = 0  # d+1 will hold the first permuted dimension of src
    while d < ndims(src) && perm[d+1] == d+1
        d += 1
    end
    if d == ndims(src)
        copyto!(parent(P), src) # it's not permuted
    else
        R1 = CartesianIndices(axes(src)[1:d])
        d1 = findfirst(isequal(d+1), perm)::Int  # first permuted dim of dest
        R2 = CartesianIndices(axes(src)[d+2:d1-1])
        R3 = CartesianIndices(axes(src)[d1+1:end])
        _permutedims!(P, src, R1, R2, R3, d+1, d1)
    end
    return P
end

@noinline function _permutedims!(P::PermutedDimsArray, src, R1::CartesianIndices{0}, R2, R3, ds, dp)
    ip, is = axes(src, dp), axes(src, ds)
    for jo in first(ip):8:last(ip), io in first(is):8:last(is)
        for I3 in R3, I2 in R2
            for j in jo:min(jo+7, last(ip))
                for i in io:min(io+7, last(is))
                    @inbounds P[i, I2, j, I3] = src[i, I2, j, I3]
                end
            end
        end
    end
    P
end

@noinline function _permutedims!(P::PermutedDimsArray, src, R1, R2, R3, ds, dp)
    ip, is = axes(src, dp), axes(src, ds)
    for jo in first(ip):8:last(ip), io in first(is):8:last(is)
        for I3 in R3, I2 in R2
            for j in jo:min(jo+7, last(ip))
                for i in io:min(io+7, last(is))
                    for I1 in R1
                        @inbounds P[I1, i, I2, j, I3] = src[I1, i, I2, j, I3]
                    end
                end
            end
        end
    end
    P
end

const CommutativeOps = Union{typeof(+),typeof(Base.add_sum),typeof(min),typeof(max),typeof(Base._extrema_rf),typeof(|),typeof(&)}

function Base._mapreduce_dim(f, op::CommutativeOps, init::Base._InitialValue, A::PermutedDimsArray, dims::Colon)
    Base._mapreduce_dim(f, op, init, parent(A), dims)
end
function Base._mapreduce_dim(f::typeof(identity), op::Union{typeof(Base.mul_prod),typeof(*)}, init::Base._InitialValue, A::PermutedDimsArray{<:Union{Real,Complex}}, dims::Colon)
    Base._mapreduce_dim(f, op, init, parent(A), dims)
end

function Base.mapreducedim!(f, op::CommutativeOps, B::AbstractArray{T,N}, A::PermutedDimsArray{S,N,perm,iperm}) where {T,S,N,perm,iperm}
    C = PermutedDimsArray{T,N,iperm,perm,typeof(B)}(B) # make the inverse permutation for the output
    Base.mapreducedim!(f, op, C, parent(A))
    B
end
function Base.mapreducedim!(f::typeof(identity), op::Union{typeof(Base.mul_prod),typeof(*)}, B::AbstractArray{T,N}, A::PermutedDimsArray{<:Union{Real,Complex},N,perm,iperm}) where {T,N,perm,iperm}
    C = PermutedDimsArray{T,N,iperm,perm,typeof(B)}(B) # make the inverse permutation for the output
    Base.mapreducedim!(f, op, C, parent(A))
    B
end

function Base.showarg(io::IO, A::PermutedDimsArray{T,N,perm}, toplevel) where {T,N,perm}
    print(io, "PermutedDimsArray(")
    Base.showarg(io, parent(A), false)
    print(io, ", ", perm, ')')
    toplevel && print(io, " with eltype ", eltype(A))
    return nothing
end

end
O   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/ordering.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

module Order


import ..@__MODULE__, ..parentmodule
const Base = parentmodule(@__MODULE__)
import .Base:
    AbstractVector, @propagate_inbounds, isless, identity, getindex, reverse,
    +, -, !, &, <, |

## notions of element ordering ##

export # not exported by Base
    Ordering, Forward, Reverse,
    By, Lt, Perm,
    ReverseOrdering, ForwardOrdering,
    DirectOrdering,
    lt, ord, ordtype

"""
    Base.Order.Ordering

Abstract type which represents a total order on some set of elements.

Use [`Base.Order.lt`](@ref) to compare two elements according to the ordering.
"""
abstract type Ordering end

struct ForwardOrdering <: Ordering end

"""
    ReverseOrdering(fwd::Ordering=Forward)

A wrapper which reverses an ordering.

For a given `Ordering` `o`, the following holds for all  `a`, `b`:

    lt(ReverseOrdering(o), a, b) == lt(o, b, a)
"""
struct ReverseOrdering{Fwd<:Ordering} <: Ordering
    fwd::Fwd
end

ReverseOrdering(rev::ReverseOrdering) = rev.fwd
ReverseOrdering(fwd::Fwd) where {Fwd} = ReverseOrdering{Fwd}(fwd)
ReverseOrdering() = ReverseOrdering(ForwardOrdering())

"""
    reverse(o::Base.Ordering)

reverses ordering specified by `o`.

"""
reverse(o::Ordering) = ReverseOrdering(o)

const DirectOrdering = Union{ForwardOrdering,ReverseOrdering{ForwardOrdering}}

"""
    Base.Order.Forward

Default ordering according to [`isless`](@ref).
"""
const Forward = ForwardOrdering()

"""
    Base.Order.Reverse

Reverse ordering according to [`isless`](@ref).
"""
const Reverse = ReverseOrdering()

"""
    By(by, order::Ordering=Forward)

`Ordering` which applies `order` to elements after they have been transformed
by the function `by`.
"""
struct By{T, O} <: Ordering
    by::T
    order::O
end

# backwards compatibility with VERSION < v"1.5-"
By(by) = By(by, Forward)

"""
    Lt(lt)

`Ordering` that calls `lt(a, b)` to compare elements. `lt` must
obey the same rules as the `lt` parameter of [`sort!`](@ref).
"""
struct Lt{T} <: Ordering
    lt::T
end

"""
    Perm(order::Ordering, data::AbstractVector)

`Ordering` on the indices of `data` where `i` is less than `j` if `data[i]` is
less than `data[j]` according to `order`. In the case that `data[i]` and
`data[j]` are equal, `i` and `j` are compared by numeric value.
"""
struct Perm{O<:Ordering,V<:AbstractVector} <: Ordering
    order::O
    data::V
end

ReverseOrdering(by::By) = By(by.by, ReverseOrdering(by.order))
ReverseOrdering(perm::Perm) = Perm(ReverseOrdering(perm.order), perm.data)

"""
    lt(o::Ordering, a, b)

Test whether `a` is less than `b` according to the ordering `o`.
"""
lt(o::ForwardOrdering,       a, b) = isless(a,b)
lt(o::ReverseOrdering,       a, b) = lt(o.fwd,b,a)
lt(o::By,                    a, b) = lt(o.order,o.by(a),o.by(b))
lt(o::Lt,                    a, b) = o.lt(a,b)

@propagate_inbounds function lt(p::Perm, a::Integer, b::Integer)
    da = p.data[a]
    db = p.data[b]
    (lt(p.order, da, db)::Bool) | (!(lt(p.order, db, da)::Bool) & (a < b))
end

_ord(lt::typeof(isless), by::typeof(identity), order::Ordering) = order
_ord(lt::typeof(isless), by,                   order::Ordering) = By(by, order)

function _ord(lt, by, order::Ordering)
    if order === Forward
        return Lt((x, y) -> lt(by(x), by(y)))
    elseif order === Reverse
        return Lt((x, y) -> lt(by(y), by(x)))
    else
        error("Passing both lt= and order= arguments is ambiguous; please pass order=Forward or order=Reverse (or leave default)")
    end
end

"""
    ord(lt, by, rev::Union{Bool, Nothing}, order::Ordering=Forward)

Construct an [`Ordering`](@ref) object from the same arguments used by
[`sort!`](@ref).
Elements are first transformed by the function `by` (which may be
[`identity`](@ref)) and are then compared according to either the function `lt`
or an existing ordering `order`. `lt` should be [`isless`](@ref) or a function
that obeys the same rules as the `lt` parameter of [`sort!`](@ref). Finally,
the resulting order is reversed if `rev=true`.

Passing an `lt` other than `isless` along with an `order` other than
[`Base.Order.Forward`](@ref) or [`Base.Order.Reverse`](@ref) is not permitted,
otherwise all options are independent and can be used together in all possible
combinations.
"""
ord(lt, by, rev::Nothing, order::Ordering=Forward) = _ord(lt, by, order)

function ord(lt, by, rev::Bool, order::Ordering=Forward)
    o = _ord(lt, by, order)
    return rev ? ReverseOrdering(o) : o
end


# This function is not in use anywhere in Base but we observed
# use in sorting-related packages (#34719). It's probably best to move
# this functionality to those packages in the future; let's remind/force
# ourselves to deprecate this in v2.0.
# The following clause means `if VERSION < v"2.0-"` but it also works during
# bootstrap. For the same reason, we need to write `Int32` instead of `Cint`.
if ccall(:jl_ver_major, Int32, ()) < 2
    ordtype(o::ReverseOrdering, vs::AbstractArray) = ordtype(o.fwd, vs)
    ordtype(o::Perm,            vs::AbstractArray) = ordtype(o.order, o.data)
    # TODO: here, we really want the return type of o.by, without calling it
    ordtype(o::By,              vs::AbstractArray) = try typeof(o.by(vs[1])) catch; Any end
    ordtype(o::Ordering,        vs::AbstractArray) = eltype(vs)
end

end
K   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/sort.jl�     # This file is a part of Julia. License is MIT: https://julialang.org/license

module Sort

using Base.Order

using Base: copymutable, midpoint, require_one_based_indexing, uinttype,
    sub_with_overflow, add_with_overflow, OneTo, BitSigned, BitIntegerType, top_set_bit

import Base:
    sort,
    sort!,
    issorted,
    sortperm,
    to_indices

export # also exported by Base
    # order-only:
    issorted,
    searchsorted,
    searchsortedfirst,
    searchsortedlast,
    insorted,
    # order & algorithm:
    sort,
    sort!,
    sortperm,
    sortperm!,
    partialsort,
    partialsort!,
    partialsortperm,
    partialsortperm!,
    # algorithms:
    InsertionSort,
    QuickSort,
    MergeSort,
    PartialQuickSort

export # not exported by Base
    Algorithm,
    DEFAULT_UNSTABLE,
    DEFAULT_STABLE,
    SMALL_ALGORITHM,
    SMALL_THRESHOLD

abstract type Algorithm end

## functions requiring only ordering ##

function issorted(itr, order::Ordering)
    y = iterate(itr)
    y === nothing && return true
    prev, state = y
    y = iterate(itr, state)
    while y !== nothing
        this, state = y
        lt(order, this, prev) && return false
        prev = this
        y = iterate(itr, state)
    end
    return true
end

"""
    issorted(v, lt=isless, by=identity, rev::Bool=false, order::Ordering=Forward)

Test whether a collection is in sorted order. The keywords modify what
order is considered sorted, as described in the [`sort!`](@ref) documentation.

# Examples
```jldoctest
julia> issorted([1, 2, 3])
true

julia> issorted([(1, "b"), (2, "a")], by = x -> x[1])
true

julia> issorted([(1, "b"), (2, "a")], by = x -> x[2])
false

julia> issorted([(1, "b"), (2, "a")], by = x -> x[2], rev=true)
true

julia> issorted([1, 2, -2, 3], by=abs)
true
```
"""
issorted(itr;
    lt=isless, by=identity, rev::Union{Bool,Nothing}=nothing, order::Ordering=Forward) =
    issorted(itr, ord(lt,by,rev,order))

function partialsort!(v::AbstractVector, k::Union{Integer,OrdinalRange}, o::Ordering)
    _sort!(v, InitialOptimizations(ScratchQuickSort(k)), o, (;))
    maybeview(v, k)
end

maybeview(v, k) = view(v, k)
maybeview(v, k::Integer) = v[k]

"""
    partialsort!(v, k; by=identity, lt=isless, rev=false)

Partially sort the vector `v` in place so that the value at index `k` (or
range of adjacent values if `k` is a range) occurs
at the position where it would appear if the array were fully sorted. If `k` is a single
index, that value is returned; if `k` is a range, an array of values at those indices is
returned. Note that `partialsort!` may not fully sort the input array.

For the keyword arguments, see the documentation of [`sort!`](@ref).


# Examples
```jldoctest
julia> a = [1, 2, 4, 3, 4]
5-element Vector{Int64}:
 1
 2
 4
 3
 4

julia> partialsort!(a, 4)
4

julia> a
5-element Vector{Int64}:
 1
 2
 3
 4
 4

julia> a = [1, 2, 4, 3, 4]
5-element Vector{Int64}:
 1
 2
 4
 3
 4

julia> partialsort!(a, 4, rev=true)
2

julia> a
5-element Vector{Int64}:
 4
 4
 3
 2
 1
```
"""
partialsort!(v::AbstractVector, k::Union{Integer,OrdinalRange};
             lt=isless, by=identity, rev::Union{Bool,Nothing}=nothing, order::Ordering=Forward) =
    partialsort!(v, k, ord(lt,by,rev,order))

"""
    partialsort(v, k, by=identity, lt=isless, rev=false)

Variant of [`partialsort!`](@ref) that copies `v` before partially sorting it, thereby returning the
same thing as `partialsort!` but leaving `v` unmodified.
"""
partialsort(v::AbstractVector, k::Union{Integer,OrdinalRange}; kws...) =
    partialsort!(copymutable(v), k; kws...)

# reference on sorted binary search:
#   http://www.tbray.org/ongoing/When/200x/2003/03/22/Binary

# index of the first value of vector a that is greater than or equivalent to x;
# returns lastindex(v)+1 if x is greater than all values in v.
function searchsortedfirst(v::AbstractVector, x, lo::T, hi::T, o::Ordering)::keytype(v) where T<:Integer
    hi = hi + T(1)
    len = hi - lo
    @inbounds while len != 0
        half_len = len >>> 0x01
        m = lo + half_len
        if lt(o, v[m], x)
            lo = m + 1
            len -= half_len + 1
        else
            hi = m
            len = half_len
        end
    end
    return lo
end

# index of the last value of vector a that is less than or equivalent to x;
# returns firstindex(v)-1 if x is less than all values of v.
function searchsortedlast(v::AbstractVector, x, lo::T, hi::T, o::Ordering)::keytype(v) where T<:Integer
    u = T(1)
    lo = lo - u
    hi = hi + u
    @inbounds while lo < hi - u
        m = midpoint(lo, hi)
        if lt(o, x, v[m])
            hi = m
        else
            lo = m
        end
    end
    return lo
end

# returns the range of indices of v equivalent to x
# if v does not contain x, returns a 0-length range
# indicating the insertion point of x
function searchsorted(v::AbstractVector, x, ilo::T, ihi::T, o::Ordering)::UnitRange{keytype(v)} where T<:Integer
    u = T(1)
    lo = ilo - u
    hi = ihi + u
    @inbounds while lo < hi - u
        m = midpoint(lo, hi)
        if lt(o, v[m], x)
            lo = m
        elseif lt(o, x, v[m])
            hi = m
        else
            a = searchsortedfirst(v, x, max(lo,ilo), m, o)
            b = searchsortedlast(v, x, m, min(hi,ihi), o)
            return a : b
        end
    end
    return (lo + 1) : (hi - 1)
end

function searchsortedlast(a::AbstractRange{<:Real}, x::Real, o::DirectOrdering)::keytype(a)
    require_one_based_indexing(a)
    f, h, l = first(a), step(a), last(a)
    if lt(o, x, f)
        0
    elseif h == 0 || !lt(o, x, l)
        length(a)
    else
        n = round(Integer, (x - f) / h + 1)
        lt(o, x, a[n]) ? n - 1 : n
    end
end

function searchsortedfirst(a::AbstractRange{<:Real}, x::Real, o::DirectOrdering)::keytype(a)
    require_one_based_indexing(a)
    f, h, l = first(a), step(a), last(a)
    if !lt(o, f, x)
        1
    elseif h == 0 || lt(o, l, x)
        length(a) + 1
    else
        n = round(Integer, (x - f) / h + 1)
        lt(o, a[n], x) ? n + 1 : n
    end
end

function searchsortedlast(a::AbstractRange{<:Integer}, x::Real, o::DirectOrdering)::keytype(a)
    require_one_based_indexing(a)
    f, h, l = first(a), step(a), last(a)
    if lt(o, x, f)
        0
    elseif h == 0 || !lt(o, x, l)
        length(a)
    else
        if o isa ForwardOrdering
            fld(floor(Integer, x) - f, h) + 1
        else
            fld(ceil(Integer, x) - f, h) + 1
        end
    end
end

function searchsortedfirst(a::AbstractRange{<:Integer}, x::Real, o::DirectOrdering)::keytype(a)
    require_one_based_indexing(a)
    f, h, l = first(a), step(a), last(a)
    if !lt(o, f, x)
        1
    elseif h == 0 || lt(o, l, x)
        length(a) + 1
    else
        if o isa ForwardOrdering
            cld(ceil(Integer, x) - f, h) + 1
        else
            cld(floor(Integer, x) - f, h) + 1
        end
    end
end

searchsorted(a::AbstractRange{<:Real}, x::Real, o::DirectOrdering) =
    searchsortedfirst(a, x, o) : searchsortedlast(a, x, o)

for s in [:searchsortedfirst, :searchsortedlast, :searchsorted]
    @eval begin
        $s(v::AbstractVector, x, o::Ordering) = $s(v,x,firstindex(v),lastindex(v),o)
        $s(v::AbstractVector, x;
           lt=isless, by=identity, rev::Union{Bool,Nothing}=nothing, order::Ordering=Forward) =
            $s(v,x,ord(lt,by,rev,order))
    end
end

"""
    searchsorted(v, x; by=identity, lt=isless, rev=false)

Return the range of indices in `v` where values are equivalent to `x`, or an
empty range located at the insertion point if `v` does not contain values
equivalent to `x`. The vector `v` must be sorted according to the order defined
by the keywords. Refer to [`sort!`](@ref) for the meaning of the keywords and
the definition of equivalence. Note that the `by` function is applied to the
searched value `x` as well as the values in `v`.

The range is generally found using binary search, but there are optimized
implementations for some inputs.

See also: [`searchsortedfirst`](@ref), [`sort!`](@ref), [`insorted`](@ref), [`findall`](@ref).

# Examples
```jldoctest
julia> searchsorted([1, 2, 4, 5, 5, 7], 4) # single match
3:3

julia> searchsorted([1, 2, 4, 5, 5, 7], 5) # multiple matches
4:5

julia> searchsorted([1, 2, 4, 5, 5, 7], 3) # no match, insert in the middle
3:2

julia> searchsorted([1, 2, 4, 5, 5, 7], 9) # no match, insert at end
7:6

julia> searchsorted([1, 2, 4, 5, 5, 7], 0) # no match, insert at start
1:0

julia> searchsorted([1=>"one", 2=>"two", 2=>"two", 4=>"four"], 2=>"two", by=first) # compare the keys of the pairs
2:3
```
""" searchsorted

"""
    searchsortedfirst(v, x; by=identity, lt=isless, rev=false)

Return the index of the first value in `v` greater than or equivalent to `x`.
If `x` is greater than all values in `v`, return `lastindex(v) + 1`.

The vector `v` must be sorted according to the order defined by the keywords.
`insert!`ing `x` at the returned index will maintain the sorted order. Refer to
[`sort!`](@ref) for the meaning of the keywords and the definition of
"greater than" and equivalence. Note that the `by` function is applied to the
searched value `x` as well as the values in `v`.

The index is generally found using binary search, but there are optimized
implementations for some inputs.

See also: [`searchsortedlast`](@ref), [`searchsorted`](@ref), [`findfirst`](@ref).

# Examples
```jldoctest
julia> searchsortedfirst([1, 2, 4, 5, 5, 7], 4) # single match
3

julia> searchsortedfirst([1, 2, 4, 5, 5, 7], 5) # multiple matches
4

julia> searchsortedfirst([1, 2, 4, 5, 5, 7], 3) # no match, insert in the middle
3

julia> searchsortedfirst([1, 2, 4, 5, 5, 7], 9) # no match, insert at end
7

julia> searchsortedfirst([1, 2, 4, 5, 5, 7], 0) # no match, insert at start
1

julia> searchsortedfirst([1=>"one", 2=>"two", 4=>"four"], 3=>"three", by=first) # compare the keys of the pairs
3
```
""" searchsortedfirst

"""
    searchsortedlast(v, x; by=identity, lt=isless, rev=false)

Return the index of the last value in `v` less than or equivalent to `x`.
If `x` is less than all values in `v` the function returns `firstindex(v) - 1`.

The vector `v` must be sorted according to the order defined by the keywords.
Refer to [`sort!`](@ref) for the meaning of the keywords and the definition of
"less than" and equivalence. Note that the `by` function is applied to the
searched value `x` as well as the values in `v`.

The index is generally found using binary search, but there are optimized
implementations for some inputs

# Examples
```jldoctest
julia> searchsortedlast([1, 2, 4, 5, 5, 7], 4) # single match
3

julia> searchsortedlast([1, 2, 4, 5, 5, 7], 5) # multiple matches
5

julia> searchsortedlast([1, 2, 4, 5, 5, 7], 3) # no match, insert in the middle
2

julia> searchsortedlast([1, 2, 4, 5, 5, 7], 9) # no match, insert at end
6

julia> searchsortedlast([1, 2, 4, 5, 5, 7], 0) # no match, insert at start
0

julia> searchsortedlast([1=>"one", 2=>"two", 4=>"four"], 3=>"three", by=first) # compare the keys of the pairs
2
```
""" searchsortedlast

"""
    insorted(x, v; by=identity, lt=isless, rev=false) -> Bool

Determine whether a vector `v` contains any value equivalent to `x`.
The vector `v` must be sorted according to the order defined by the keywords.
Refer to [`sort!`](@ref) for the meaning of the keywords and the definition of
equivalence. Note that the `by` function is applied to the searched value `x`
as well as the values in `v`.

The check is generally done using binary search, but there are optimized
implementations for some inputs.

See also [`in`](@ref).

# Examples
```jldoctest
julia> insorted(4, [1, 2, 4, 5, 5, 7]) # single match
true

julia> insorted(5, [1, 2, 4, 5, 5, 7]) # multiple matches
true

julia> insorted(3, [1, 2, 4, 5, 5, 7]) # no match
false

julia> insorted(9, [1, 2, 4, 5, 5, 7]) # no match
false

julia> insorted(0, [1, 2, 4, 5, 5, 7]) # no match
false

julia> insorted(2=>"TWO", [1=>"one", 2=>"two", 4=>"four"], by=first) # compare the keys of the pairs
true
```

!!! compat "Julia 1.6"
     `insorted` was added in Julia 1.6.
"""
function insorted end
insorted(x, v::AbstractVector; kw...) = !isempty(searchsorted(v, x; kw...))
insorted(x, r::AbstractRange) = in(x, r)

## Alternative keyword management

macro getkw(syms...)
    getters = (getproperty(Sort, Symbol(:_, sym)) for sym in syms)
    Expr(:block, (:($(esc(:((kw, $sym) = $getter(v, o, kw))))) for (sym, getter) in zip(syms, getters))...)
end

for (sym, exp, type) in [
        (:lo, :(firstindex(v)), Integer),
        (:hi, :(lastindex(v)),  Integer),
        (:mn, :(throw(ArgumentError("mn is needed but has not been computed"))), :(eltype(v))),
        (:mx, :(throw(ArgumentError("mx is needed but has not been computed"))), :(eltype(v))),
        (:scratch, nothing, :(Union{Nothing, Vector})), # could have different eltype
        (:legacy_dispatch_entry, nothing, Union{Nothing, Algorithm})]
    usym = Symbol(:_, sym)
    @eval function $usym(v, o, kw)
        # using missing instead of nothing because scratch could === nothing.
        res = get(kw, $(Expr(:quote, sym)), missing)
        res !== missing && return kw, res::$type
        $sym = $exp
        (;kw..., $sym), $sym::$type
    end
end

## Scratch space management

"""
    make_scratch(scratch::Union{Nothing, Vector}, T::Type, len::Integer)

Returns `(s, t)` where `t` is an `AbstractVector` of type `T` with length at least `len`
that is backed by the `Vector` `s`. If `scratch !== nothing`, then `s === scratch`.

This function will allocate a new vector if `scratch === nothing`, `resize!` `scratch` if it
is too short, and `reinterpret` `scratch` if its eltype is not `T`.
"""
function make_scratch(scratch::Nothing, T::Type, len::Integer)
    s = Vector{T}(undef, len)
    s, s
end
function make_scratch(scratch::Vector{T}, ::Type{T}, len::Integer) where T
    len > length(scratch) && resize!(scratch, len)
    scratch, scratch
end
function make_scratch(scratch::Vector, T::Type, len::Integer)
    len_bytes = len * sizeof(T)
    len_scratch = div(len_bytes, sizeof(eltype(scratch)))
    len_scratch > length(scratch) && resize!(scratch, len_scratch)
    scratch, reinterpret(T, scratch)
end


## sorting algorithm components ##

"""
    _sort!(v::AbstractVector, a::Algorithm, o::Ordering, kw; t, offset)

An internal function that sorts `v` using the algorithm `a` under the ordering `o`,
subject to specifications provided in `kw` (such as `lo` and `hi` in which case it only
sorts `view(v, lo:hi)`)

Returns a scratch space if provided or constructed during the sort, or `nothing` if
no scratch space is present.

!!! note
    `_sort!` modifies but does not return `v`.

A returned scratch space will be a `Vector{T}` where `T` is usually the eltype of `v`. There
are some exceptions, for example if `eltype(v) == Union{Missing, T}` then the scratch space
may be be a `Vector{T}` due to `MissingOptimization` changing the eltype of `v` to `T`.

`t` is an appropriate scratch space for the algorithm at hand, to be accessed as
`t[i + offset]`. `t` is used for an algorithm to pass a scratch space back to itself in
internal or recursive calls.
"""
function _sort! end


"""
    MissingOptimization(next) <: Algorithm

Filter out missing values.

Missing values are placed after other values according to `DirectOrdering`s. This pass puts
them there and passes on a view into the original vector that excludes the missing values.
This pass is triggered for both `sort([1, missing, 3])` and `sortperm([1, missing, 3])`.
"""
struct MissingOptimization{T <: Algorithm} <: Algorithm
    next::T
end

struct WithoutMissingVector{T, U} <: AbstractVector{T}
    data::U
    function WithoutMissingVector(data; unsafe=false)
        if !unsafe && any(ismissing, data)
            throw(ArgumentError("data must not contain missing values"))
        end
        new{nonmissingtype(eltype(data)), typeof(data)}(data)
    end
end
Base.@propagate_inbounds function Base.getindex(v::WithoutMissingVector, i::Integer)
    out = v.data[i]
    @assert !(out isa Missing)
    out::eltype(v)
end
Base.@propagate_inbounds function Base.setindex!(v::WithoutMissingVector, x, i::Integer)
    v.data[i] = x
    v
end
Base.size(v::WithoutMissingVector) = size(v.data)
Base.axes(v::WithoutMissingVector) = axes(v.data)

"""
    send_to_end!(f::Function, v::AbstractVector; [lo, hi])

Send every element of `v` for which `f` returns `true` to the end of the vector and return
the index of the last element for which `f` returns `false`.

`send_to_end!(f, v, lo, hi)` is equivalent to `send_to_end!(f, view(v, lo:hi))+lo-1`

Preserves the order of the elements that are not sent to the end.
"""
function send_to_end!(f::F, v::AbstractVector; lo=firstindex(v), hi=lastindex(v)) where F <: Function
    i = lo
    @inbounds while i <= hi && !f(v[i])
        i += 1
    end
    j = i + 1
    @inbounds while j <= hi
        if !f(v[j])
            v[i], v[j] = v[j], v[i]
            i += 1
        end
        j += 1
    end
    i - 1
end
"""
    send_to_end!(f::Function, v::AbstractVector, o::DirectOrdering[, end_stable]; lo, hi)

Return `(a, b)` where `v[a:b]` are the elements that are not sent to the end.

If `o isa ReverseOrdering` then the "end" of `v` is `v[lo]`.

If `end_stable` is set, the elements that are sent to the end are stable instead of the
elements that are not
"""
@inline send_to_end!(f::F, v::AbstractVector, ::ForwardOrdering, end_stable=false; lo, hi) where F <: Function =
    end_stable ? (lo, hi-send_to_end!(!f, view(v, hi:-1:lo))) : (lo, send_to_end!(f, v; lo, hi))
@inline send_to_end!(f::F, v::AbstractVector, ::ReverseOrdering, end_stable=false; lo, hi) where F <: Function =
    end_stable ? (send_to_end!(!f, v; lo, hi)+1, hi) : (hi-send_to_end!(f, view(v, hi:-1:lo))+1, hi)


function _sort!(v::AbstractVector, a::MissingOptimization, o::Ordering, kw)
    @getkw lo hi
    if o isa DirectOrdering && eltype(v) >: Missing && nonmissingtype(eltype(v)) != eltype(v)
        lo, hi = send_to_end!(ismissing, v, o; lo, hi)
        _sort!(WithoutMissingVector(v, unsafe=true), a.next, o, (;kw..., lo, hi))
    elseif o isa Perm && o.order isa DirectOrdering && eltype(v) <: Integer &&
                eltype(o.data) >: Missing && nonmissingtype(eltype(o.data)) != eltype(o.data) &&
                all(i === j for (i,j) in zip(v, eachindex(o.data)))
        # TODO make this branch known at compile time
        # This uses a custom function because we need to ensure stability of both sides and
        # we can assume v is equal to eachindex(o.data) which allows a copying partition
        # without allocations.
        lo_i, hi_i = lo, hi
        cv = eachindex(o.data) # equal to copy(v)
        for i in lo:hi
            x = o.data[cv[i]]
            if ismissing(x) == (o.order == Reverse) # should x go at the beginning/end?
                v[lo_i] = i
                lo_i += 1
            else
                v[hi_i] = i
                hi_i -= 1
            end
        end
        reverse!(v, lo_i, hi)
        if o.order == Reverse
            lo = lo_i
        else
            hi = hi_i
        end

        _sort!(v, a.next, Perm(o.order, WithoutMissingVector(o.data, unsafe=true)), (;kw..., lo, hi))
    else
        _sort!(v, a.next, o, kw)
    end
end


"""
    IEEEFloatOptimization(next) <: Algorithm

Move NaN values to the end, partition by sign, and reinterpret the rest as unsigned integers.

IEEE floating point numbers (`Float64`, `Float32`, and `Float16`) compare the same as
unsigned integers with the bits with a few exceptions. This pass

This pass is triggered for both `sort([1.0, NaN, 3.0])` and `sortperm([1.0, NaN, 3.0])`.
"""
struct IEEEFloatOptimization{T <: Algorithm} <: Algorithm
    next::T
end

after_zero(::ForwardOrdering, x) = !signbit(x)
after_zero(::ReverseOrdering, x) = signbit(x)
is_concrete_IEEEFloat(T::Type) = T <: Base.IEEEFloat && isconcretetype(T)
function _sort!(v::AbstractVector, a::IEEEFloatOptimization, o::Ordering, kw)
    @getkw lo hi
    if is_concrete_IEEEFloat(eltype(v)) && o isa DirectOrdering
        lo, hi = send_to_end!(isnan, v, o, true; lo, hi)
        iv = reinterpret(uinttype(eltype(v)), v)
        j = send_to_end!(x -> after_zero(o, x), v; lo, hi)
        scratch = _sort!(iv, a.next, Reverse, (;kw..., lo, hi=j))
        if scratch === nothing # Union split
            _sort!(iv, a.next, Forward, (;kw..., lo=j+1, hi, scratch))
        else
            _sort!(iv, a.next, Forward, (;kw..., lo=j+1, hi, scratch))
        end
    elseif eltype(v) <: Integer && o isa Perm && o.order isa DirectOrdering && is_concrete_IEEEFloat(eltype(o.data))
        lo, hi = send_to_end!(i -> isnan(@inbounds o.data[i]), v, o.order, true; lo, hi)
        ip = reinterpret(uinttype(eltype(o.data)), o.data)
        j = send_to_end!(i -> after_zero(o.order, @inbounds o.data[i]), v; lo, hi)
        scratch = _sort!(v, a.next, Perm(Reverse, ip), (;kw..., lo, hi=j))
        if scratch === nothing # Union split
            _sort!(v, a.next, Perm(Forward, ip), (;kw..., lo=j+1, hi, scratch))
        else
            _sort!(v, a.next, Perm(Forward, ip), (;kw..., lo=j+1, hi, scratch))
        end
    else
        _sort!(v, a.next, o, kw)
    end
end


"""
    BoolOptimization(next) <: Algorithm

Sort `AbstractVector{Bool}`s using a specialized version of counting sort.

Accesses each element at most twice (one read and one write), and performs at most two
comparisons.
"""
struct BoolOptimization{T <: Algorithm} <: Algorithm
    next::T
end
_sort!(v::AbstractVector, a::BoolOptimization, o::Ordering, kw) = _sort!(v, a.next, o, kw)
function _sort!(v::AbstractVector{Bool}, ::BoolOptimization, o::Ordering, kw)
    first = lt(o, false, true) ? false : lt(o, true, false) ? true : return v
    @getkw lo hi scratch
    count = 0
    @inbounds for i in lo:hi
        if v[i] == first
            count += 1
        end
    end
    @inbounds v[lo:lo+count-1] .= first
    @inbounds v[lo+count:hi] .= !first
    scratch
end


"""
    IsUIntMappable(yes, no) <: Algorithm

Determines if the elements of a vector can be mapped to unsigned integers while preserving
their order under the specified ordering.

If they can be, dispatch to the `yes` algorithm and record the unsigned integer type that
the elements may be mapped to. Otherwise dispatch to the `no` algorithm.
"""
struct IsUIntMappable{T <: Algorithm, U <: Algorithm} <: Algorithm
    yes::T
    no::U
end
function _sort!(v::AbstractVector, a::IsUIntMappable, o::Ordering, kw)
    if UIntMappable(eltype(v), o) !== nothing
        _sort!(v, a.yes, o, kw)
    else
        _sort!(v, a.no, o, kw)
    end
end


"""
    Small{N}(small=SMALL_ALGORITHM, big) <: Algorithm

Sort inputs with `length(lo:hi) <= N` using the `small` algorithm. Otherwise use the `big`
algorithm.
"""
struct Small{N, T <: Algorithm, U <: Algorithm} <: Algorithm
    small::T
    big::U
end
Small{N}(small, big) where N = Small{N, typeof(small), typeof(big)}(small, big)
Small{N}(big) where N = Small{N}(SMALL_ALGORITHM, big)
function _sort!(v::AbstractVector, a::Small{N}, o::Ordering, kw) where N
    @getkw lo hi
    if (hi-lo) < N
        _sort!(v, a.small, o, kw)
    else
        _sort!(v, a.big, o, kw)
    end
end


struct InsertionSortAlg <: Algorithm end

"""
    InsertionSort

Use the insertion sort algorithm.

Insertion sort traverses the collection one element at a time, inserting
each element into its correct, sorted position in the output vector.

Characteristics:
* *stable*: preserves the ordering of elements that compare equal
(e.g. "a" and "A" in a sort of letters that ignores case).
* *in-place* in memory.
* *quadratic performance* in the number of elements to be sorted:
it is well-suited to small collections but should not be used for large ones.
"""
const InsertionSort = InsertionSortAlg()
const SMALL_ALGORITHM = InsertionSortAlg()

function _sort!(v::AbstractVector, ::InsertionSortAlg, o::Ordering, kw)
    @getkw lo hi scratch
    lo_plus_1 = (lo + 1)::Integer
    @inbounds for i = lo_plus_1:hi
        j = i
        x = v[i]
        while j > lo
            y = v[j-1]
            if !(lt(o, x, y)::Bool)
                break
            end
            v[j] = y
            j -= 1
        end
        v[j] = x
    end
    scratch
end


"""
    CheckSorted(next) <: Algorithm

Check if the input is already sorted and for large inputs, also check if it is
reverse-sorted. The reverse-sorted check is unstable.
"""
struct CheckSorted{T <: Algorithm} <: Algorithm
    next::T
end
function _sort!(v::AbstractVector, a::CheckSorted, o::Ordering, kw)
    @getkw lo hi scratch

    # For most arrays, a presorted check is cheap (overhead < 5%) and for most large
    # arrays it is essentially free (<1%).
    _issorted(v, lo, hi, o) && return scratch

    # For most large arrays, a reverse-sorted check is essentially free (overhead < 1%)
    if hi-lo >= 500 && _issorted(v, lo, hi, ReverseOrdering(o))
        # If reversing is valid, do so. This violates stability.
        reverse!(v, lo, hi)
        return scratch
    end

    _sort!(v, a.next, o, kw)
end


"""
    ComputeExtrema(next) <: Algorithm

Compute the extrema of the input under the provided order.

If the minimum is no less than the maximum, then the input is already sorted. Otherwise,
dispatch to the `next` algorithm.
"""
struct ComputeExtrema{T <: Algorithm} <: Algorithm
    next::T
end
function _sort!(v::AbstractVector, a::ComputeExtrema, o::Ordering, kw)
    @getkw lo hi scratch
    mn = mx = v[lo]
    @inbounds for i in (lo+1):hi
        vi = v[i]
        lt(o, vi, mn) && (mn = vi)
        lt(o, mx, vi) && (mx = vi)
    end

    lt(o, mn, mx) || return scratch # all same

    _sort!(v, a.next, o, (;kw..., mn, mx))
end


"""
    ConsiderCountingSort(counting=CountingSort(), next) <: Algorithm

If the input's range is small enough, use the `counting` algorithm. Otherwise, dispatch to
the `next` algorithm.

For most types, the threshold is if the range is shorter than half the length, but for types
larger than Int64, bitshifts are expensive and RadixSort is not viable, so the threshold is
much more generous.
"""
struct ConsiderCountingSort{T <: Algorithm, U <: Algorithm} <: Algorithm
    counting::T
    next::U
end
ConsiderCountingSort(next) = ConsiderCountingSort(CountingSort(), next)
function _sort!(v::AbstractVector{<:Integer}, a::ConsiderCountingSort, o::DirectOrdering, kw)
    @getkw lo hi mn mx
    range = maybe_unsigned(o === Reverse ? mn-mx : mx-mn)

    if range < (sizeof(eltype(v)) > 8 ? 5(hi-lo)-100 : div(hi-lo, 2))
        _sort!(v, a.counting, o, kw)
    else
        _sort!(v, a.next, o, kw)
    end
end
_sort!(v::AbstractVector, a::ConsiderCountingSort, o::Ordering, kw) = _sort!(v, a.next, o, kw)


"""
    CountingSort <: Algorithm

Use the counting sort algorithm.

`CountingSort` is an algorithm for sorting integers that runs in Θ(length + range) time and
space. It counts the number of occurrences of each value in the input and then iterates
through those counts repopulating the input with the values in sorted order.
"""
struct CountingSort <: Algorithm end
maybe_reverse(o::ForwardOrdering, x) = x
maybe_reverse(o::ReverseOrdering, x) = reverse(x)
function _sort!(v::AbstractVector{<:Integer}, ::CountingSort, o::DirectOrdering, kw)
    @getkw lo hi mn mx scratch
    range = maybe_unsigned(o === Reverse ? mn-mx : mx-mn)
    offs = 1 - (o === Reverse ? mx : mn)

    counts = fill(0, range+1) # TODO use scratch (but be aware of type stability)
    @inbounds for i = lo:hi
        counts[v[i] + offs] += 1
    end

    idx = lo
    @inbounds for i = maybe_reverse(o, 1:range+1)
        lastidx = idx + counts[i] - 1
        val = i-offs
        for j = idx:lastidx
            v[j] = val isa Unsigned && eltype(v) <: Signed ? signed(val) : val
        end
        idx = lastidx + 1
    end

    scratch
end


"""
    ConsiderRadixSort(radix=RadixSort(), next) <: Algorithm

If the number of bits in the input's range is small enough and the input supports efficient
bitshifts, use the `radix` algorithm. Otherwise, dispatch to the `next` algorithm.
"""
struct ConsiderRadixSort{T <: Algorithm, U <: Algorithm} <: Algorithm
    radix::T
    next::U
end
ConsiderRadixSort(next) = ConsiderRadixSort(RadixSort(), next)
function _sort!(v::AbstractVector, a::ConsiderRadixSort, o::DirectOrdering, kw)
    @getkw lo hi mn mx
    urange = uint_map(mx, o)-uint_map(mn, o)
    bits = unsigned(top_set_bit(urange))
    if sizeof(eltype(v)) <= 8 && bits+70 < 22log(hi-lo)
        _sort!(v, a.radix, o, kw)
    else
        _sort!(v, a.next, o, kw)
    end
end


"""
    RadixSort <: Algorithm

Use the radix sort algorithm.

`RadixSort` is a stable least significant bit first radix sort algorithm that runs in
`O(length * log(range))` time and linear space.

It first sorts the entire vector by the last `chunk_size` bits, then by the second
to last `chunk_size` bits, and so on. Stability means that it will not reorder two elements
that compare equal. This is essential so that the order introduced by earlier,
less significant passes is preserved by later passes.

Each pass divides the input into `2^chunk_size == mask+1` buckets. To do this, it
 * counts the number of entries that fall into each bucket
 * uses those counts to compute the indices to move elements of those buckets into
 * moves elements into the computed indices in the swap array
 * switches the swap and working array

`chunk_size` is larger for larger inputs and determined by an empirical heuristic.
"""
struct RadixSort <: Algorithm end
function _sort!(v::AbstractVector, a::RadixSort, o::DirectOrdering, kw)
    @getkw lo hi mn mx scratch
    umn = uint_map(mn, o)
    urange = uint_map(mx, o)-umn
    bits = unsigned(top_set_bit(urange))

    # At this point, we are committed to radix sort.
    u = uint_map!(v, lo, hi, o)

    # we subtract umn to avoid radixing over unnecessary bits. For example,
    # Int32[3, -1, 2] uint_maps to UInt32[0x80000003, 0x7fffffff, 0x80000002]
    # which uses all 32 bits, but once we subtract umn = 0x7fffffff, we are left with
    # UInt32[0x00000004, 0x00000000, 0x00000003] which uses only 3 bits, and
    # Float32[2.012, 400.0, 12.345] uint_maps to UInt32[0x3fff3b63, 0x3c37ffff, 0x414570a4]
    # which is reduced to UInt32[0x03c73b64, 0x00000000, 0x050d70a5] using only 26 bits.
    # the overhead for this subtraction is small enough that it is worthwhile in many cases.

    # this is faster than u[lo:hi] .-= umn as of v1.9.0-DEV.100
    @inbounds for i in lo:hi
        u[i] -= umn
    end

    scratch, t = make_scratch(scratch, eltype(v), hi-lo+1)
    tu = reinterpret(eltype(u), t)
    if radix_sort!(u, lo, hi, bits, tu, 1-lo)
        uint_unmap!(v, u, lo, hi, o, umn)
    else
        uint_unmap!(v, tu, lo, hi, o, umn, 1-lo)
    end
    scratch
end


"""
    ScratchQuickSort(next::Algorithm=SMALL_ALGORITHM) <: Algorithm
    ScratchQuickSort(lo::Union{Integer, Missing}, hi::Union{Integer, Missing}=lo, next::Algorithm=SMALL_ALGORITHM) <: Algorithm

Use the `ScratchQuickSort` algorithm with the `next` algorithm as a base case.

`ScratchQuickSort` is like `QuickSort`, but utilizes scratch space to operate faster and allow
for the possibility of maintaining stability.

If `lo` and `hi` are provided, finds and sorts the elements in the range `lo:hi`, reordering
but not necessarily sorting other elements in the process. If `lo` or `hi` is `missing`, it
is treated as the first or last index of the input, respectively.

`lo` and `hi` may be specified together as an `AbstractUnitRange`.

Characteristics:
  * *stable*: preserves the ordering of elements that compare equal
    (e.g. "a" and "A" in a sort of letters that ignores case).
  * *not in-place* in memory.
  * *divide-and-conquer*: sort strategy similar to [`QuickSort`](@ref).
  * *linear runtime* if `length(lo:hi)` is constant
  * *quadratic worst case runtime* in pathological cases
  (vanishingly rare for non-malicious input)
"""
struct ScratchQuickSort{L<:Union{Integer,Missing}, H<:Union{Integer,Missing}, T<:Algorithm} <: Algorithm
    lo::L
    hi::H
    next::T
end
ScratchQuickSort(next::Algorithm=SMALL_ALGORITHM) = ScratchQuickSort(missing, missing, next)
ScratchQuickSort(lo::Union{Integer, Missing}, hi::Union{Integer, Missing}) = ScratchQuickSort(lo, hi, SMALL_ALGORITHM)
ScratchQuickSort(lo::Union{Integer, Missing}, next::Algorithm=SMALL_ALGORITHM) = ScratchQuickSort(lo, lo, next)
ScratchQuickSort(r::OrdinalRange, next::Algorithm=SMALL_ALGORITHM) = ScratchQuickSort(first(r), last(r), next)

# select a pivot, partition v[lo:hi] according
# to the pivot, and store the result in t[lo:hi].
#
# sets `pivot_dest[pivot_index+pivot_index_offset] = pivot` and returns that index.
function partition!(t::AbstractVector, lo::Integer, hi::Integer, offset::Integer, o::Ordering,
        v::AbstractVector, rev::Bool, pivot_dest::AbstractVector, pivot_index_offset::Integer)
    # Ideally we would use `pivot_index = rand(lo:hi)`, but that requires Random.jl
    # and would mutate the global RNG in sorting.
    pivot_index = typeof(hi-lo)(hash(lo) % (hi-lo+1)) + lo
    @inbounds begin
        pivot = v[pivot_index]
        while lo < pivot_index
            x = v[lo]
            fx = rev ? !lt(o, x, pivot) : lt(o, pivot, x)
            t[(fx ? hi : lo) - offset] = x
            offset += fx
            lo += 1
        end
        while lo < hi
            x = v[lo+1]
            fx = rev ? lt(o, pivot, x) : !lt(o, x, pivot)
            t[(fx ? hi : lo) - offset] = x
            offset += fx
            lo += 1
        end
        pivot_index = lo-offset + pivot_index_offset
        pivot_dest[pivot_index] = pivot
    end

    # t_pivot_index = lo-offset (i.e. without pivot_index_offset)
    # t[t_pivot_index] is whatever it was before unless t is the pivot_dest
    # t[<t_pivot_index] <* pivot, stable
    # t[>t_pivot_index] >* pivot, reverse stable

    pivot_index
end

function _sort!(v::AbstractVector, a::ScratchQuickSort, o::Ordering, kw;
                t=nothing, offset=nothing, swap=false, rev=false)
    @getkw lo hi scratch

    if t === nothing
        scratch, t = make_scratch(scratch, eltype(v), hi-lo+1)
        offset = 1-lo
        kw = (;kw..., scratch)
    end

    while lo < hi && hi - lo > SMALL_THRESHOLD
        j = if swap
            partition!(v, lo+offset, hi+offset, offset, o, t, rev, v, 0)
        else
            partition!(t, lo, hi, -offset, o, v, rev, v, -offset)
        end
        swap = !swap

        # For ScratchQuickSort(), a.lo === a.hi === missing, so the first two branches get skipped
        if !ismissing(a.lo) && j <= a.lo # Skip sorting the lower part
            swap && copyto!(v, lo, t, lo+offset, j-lo)
            rev && reverse!(v, lo, j-1)
            lo = j+1
            rev = !rev
        elseif !ismissing(a.hi) && a.hi <= j # Skip sorting the upper part
            swap && copyto!(v, j+1, t, j+1+offset, hi-j)
            rev || reverse!(v, j+1, hi)
            hi = j-1
        elseif j-lo < hi-j
            # Sort the lower part recursively because it is smaller. Recursing on the
            # smaller part guarantees O(log(n)) stack space even on pathological inputs.
            _sort!(v, a, o, (;kw..., lo, hi=j-1); t, offset, swap, rev)
            lo = j+1
            rev = !rev
        else # Sort the higher part recursively
            _sort!(v, a, o, (;kw..., lo=j+1, hi); t, offset, swap, rev=!rev)
            hi = j-1
        end
    end
    hi < lo && return scratch
    swap && copyto!(v, lo, t, lo+offset, hi-lo+1)
    rev && reverse!(v, lo, hi)
    _sort!(v, a.next, o, (;kw..., lo, hi))
end


"""
    StableCheckSorted(next) <: Algorithm

Check if an input is sorted and/or reverse-sorted.

The definition of reverse-sorted is that for every pair of adjacent elements, the latter is
less than the former. This is stricter than `issorted(v, Reverse(o))` to avoid swapping pairs
of elements that compare equal.
"""
struct StableCheckSorted{T<:Algorithm} <: Algorithm
    next::T
end
function _sort!(v::AbstractVector, a::StableCheckSorted, o::Ordering, kw)
    @getkw lo hi scratch
    if _issorted(v, lo, hi, o)
        return scratch
    elseif _issorted(v, lo, hi, Lt((x, y) -> !lt(o, x, y)))
        # Reverse only if necessary. Using issorted(..., Reverse(o)) would violate stability.
        reverse!(v, lo, hi)
        return scratch
    end

    _sort!(v, a.next, o, kw)
end


# The return value indicates whether v is sorted (true) or t is sorted (false)
# This is one of the many reasons radix_sort! is not exported.
function radix_sort!(v::AbstractVector{U}, lo::Integer, hi::Integer, bits::Unsigned,
                     t::AbstractVector{U}, offset::Integer,
                     chunk_size=radix_chunk_size_heuristic(lo, hi, bits)) where U <: Unsigned
    # bits is unsigned for performance reasons.
    counts = Vector{Int}(undef, 1 << chunk_size + 1) # TODO use scratch for this

    shift = 0
    while true
        @noinline radix_sort_pass!(t, lo, hi, offset, counts, v, shift, chunk_size)
        # the latest data resides in t
        shift += chunk_size
        shift < bits || return false
        @noinline radix_sort_pass!(v, lo+offset, hi+offset, -offset, counts, t, shift, chunk_size)
        # the latest data resides in v
        shift += chunk_size
        shift < bits || return true
    end
end
function radix_sort_pass!(t, lo, hi, offset, counts, v, shift, chunk_size)
    mask = UInt(1) << chunk_size - 1  # mask is defined in pass so that the compiler
    @inbounds begin                   #  ↳ knows it's shape
        # counts[2:mask+2] will store the number of elements that fall into each bucket.
        # if chunk_size = 8, counts[2] is bucket 0x00 and counts[257] is bucket 0xff.
        counts .= 0
        for k in lo:hi
            x = v[k]                  # lookup the element
            i = (x >> shift)&mask + 2 # compute its bucket's index for this pass
            counts[i] += 1            # increment that bucket's count
        end

        counts[1] = lo + offset       # set target index for the first bucket
        cumsum!(counts, counts)       # set target indices for subsequent buckets
        # counts[1:mask+1] now stores indices where the first member of each bucket
        # belongs, not the number of elements in each bucket. We will put the first element
        # of bucket 0x00 in t[counts[1]], the next element of bucket 0x00 in t[counts[1]+1],
        # and the last element of bucket 0x00 in t[counts[2]-1].

        for k in lo:hi
            x = v[k]                  # lookup the element
            i = (x >> shift)&mask + 1 # compute its bucket's index for this pass
            j = counts[i]             # lookup the target index
            t[j] = x                  # put the element where it belongs
            counts[i] = j + 1         # increment the target index for the next
        end                           #  ↳ element in this bucket
    end
end
function radix_chunk_size_heuristic(lo::Integer, hi::Integer, bits::Unsigned)
    # chunk_size is the number of bits to radix over at once.
    # We need to allocate an array of size 2^chunk size, and on the other hand the higher
    # the chunk size the fewer passes we need. Theoretically, chunk size should be based on
    # the Lambert W function applied to length. Empirically, we use this heuristic:
    guess = min(10, log(maybe_unsigned(hi-lo))*3/4+3)
    # TODO the maximum chunk size should be based on architecture cache size.

    # We need iterations * chunk size ≥ bits, and these cld's
    # make an effort to get iterations * chunk size ≈ bits
    UInt8(cld(bits, cld(bits, guess)))
end

maybe_unsigned(x::Integer) = x # this is necessary to avoid calling unsigned on BigInt
maybe_unsigned(x::BitSigned) = unsigned(x)
function _issorted(v::AbstractVector, lo::Integer, hi::Integer, o::Ordering)
    @boundscheck checkbounds(v, lo:hi)
    @inbounds for i in (lo+1):hi
        lt(o, v[i], v[i-1]) && return false
    end
    true
end


## default sorting policy ##

"""
    InitialOptimizations(next) <: Algorithm

Attempt to apply a suite of low-cost optimizations to the input vector before sorting. These
optimizations may be automatically applied by the `sort!` family of functions when
`alg=InsertionSort`, `alg=MergeSort`, or `alg=QuickSort` is passed as an argument.

`InitialOptimizations` is an implementation detail and subject to change or removal in
future versions of Julia.

If `next` is stable, then `InitialOptimizations(next)` is also stable.

The specific optimizations attempted by `InitialOptimizations` are
[`MissingOptimization`](@ref), [`BoolOptimization`](@ref), dispatch to
[`InsertionSort`](@ref) for inputs with `length <= 10`, and [`IEEEFloatOptimization`](@ref).
"""
InitialOptimizations(next) = MissingOptimization(
    BoolOptimization(
        Small{10}(
            IEEEFloatOptimization(
                next))))
"""
    DEFAULT_STABLE

The default sorting algorithm.

This algorithm is guaranteed to be stable (i.e. it will not reorder elements that compare
equal). It makes an effort to be fast for most inputs.

The algorithms used by `DEFAULT_STABLE` are an implementation detail. See extended help
for the current dispatch system.

# Extended Help

`DEFAULT_STABLE` is composed of two parts: the [`InitialOptimizations`](@ref) and a hybrid
of Radix, Insertion, Counting, Quick sorts.

We begin with MissingOptimization because it has no runtime cost when it is not
triggered and can enable other optimizations to be applied later. For example,
BoolOptimization cannot apply to an `AbstractVector{Union{Missing, Bool}}`, but after
[`MissingOptimization`](@ref) is applied, that input will be converted into am
`AbstractVector{Bool}`.

We next apply [`BoolOptimization`](@ref) because it also has no runtime cost when it is not
triggered and when it is triggered, it is an incredibly efficient algorithm (sorting `Bool`s
is quite easy).

Next, we dispatch to [`InsertionSort`](@ref) for inputs with `length <= 10`. This dispatch
occurs before the [`IEEEFloatOptimization`](@ref) pass because the
[`IEEEFloatOptimization`](@ref)s are not beneficial for very small inputs.

To conclude the [`InitialOptimizations`](@ref), we apply [`IEEEFloatOptimization`](@ref).

After these optimizations, we branch on whether radix sort and related algorithms can be
applied to the input vector and ordering. We conduct this branch by testing if
`UIntMappable(v, order) !== nothing`. That is, we see if we know of a reversible mapping
from `eltype(v)` to `UInt` that preserves the ordering `order`. We perform this check after
the initial optimizations because they can change the input vector's type and ordering to
make them `UIntMappable`.

If the input is not [`UIntMappable`](@ref), then we perform a presorted check and dispatch
to [`ScratchQuickSort`](@ref).

Otherwise, we dispatch to [`InsertionSort`](@ref) for inputs with `length <= 40` and then
perform a presorted check ([`CheckSorted`](@ref)).

We check for short inputs before performing the presorted check to avoid the overhead of the
check for small inputs. Because the alternate dispatch is to [`InsertionSort`](@ref) which
has efficient `O(n)` runtime on presorted inputs, the check is not necessary for small
inputs.

We check if the input is reverse-sorted for long vectors (more than 500 elements) because
the check is essentially free unless the input is almost entirely reverse sorted.

Note that once the input is determined to be [`UIntMappable`](@ref), we know the order forms
a [total order](wikipedia.org/wiki/Total_order) over the inputs and so it is impossible to
perform an unstable sort because no two elements can compare equal unless they _are_ equal,
in which case switching them is undetectable. We utilize this fact to perform a more
aggressive reverse sorted check that will reverse the vector `[3, 2, 2, 1]`.

After these potential fast-paths are tried and failed, we [`ComputeExtrema`](@ref) of the
input. This computation has a fairly fast `O(n)` runtime, but we still try to delay it until
it is necessary.

Next, we [`ConsiderCountingSort`](@ref). If the range the input is small compared to its
length, we apply [`CountingSort`](@ref).

Next, we [`ConsiderRadixSort`](@ref). This is similar to the dispatch to counting sort,
but we conside rthe number of _bits_ in the range, rather than the range itself.
Consequently, we apply [`RadixSort`](@ref) for any reasonably long inputs that reach this
stage.

Finally, if the input has length less than 80, we dispatch to [`InsertionSort`](@ref) and
otherwise we dispatch to [`ScratchQuickSort`](@ref).
"""
const DEFAULT_STABLE = InitialOptimizations(
    IsUIntMappable(
        Small{40}(
            CheckSorted(
                ComputeExtrema(
                    ConsiderCountingSort(
                        ConsiderRadixSort(
                            Small{80}(
                                ScratchQuickSort())))))),
        StableCheckSorted(
            ScratchQuickSort())))
"""
    DEFAULT_UNSTABLE

An efficient sorting algorithm.

The algorithms used by `DEFAULT_UNSTABLE` are an implementation detail. They are currently
the same as those used by [`DEFAULT_STABLE`](@ref), but this is subject to change in future.
"""
const DEFAULT_UNSTABLE = DEFAULT_STABLE
const SMALL_THRESHOLD  = 20

function Base.show(io::IO, alg::Algorithm)
    print_tree(io, alg, 0)
end
function print_tree(io::IO, alg::Algorithm, cols::Int)
    print(io, "    "^cols)
    show_type(io, alg)
    print(io, '(')
    for (i, name) in enumerate(fieldnames(typeof(alg)))
        arg = getproperty(alg, name)
        i > 1 && print(io, ',')
        if arg isa Algorithm
            println(io)
            print_tree(io, arg, cols+1)
        else
            i > 1 && print(io, ' ')
            print(io, arg)
        end
    end
    print(io, ')')
end
show_type(io::IO, alg::Algorithm) = Base.show_type_name(io, typeof(alg).name)
show_type(io::IO, alg::Small{N}) where N = print(io, "Base.Sort.Small{$N}")

defalg(v::AbstractArray) = DEFAULT_STABLE
defalg(v::AbstractArray{<:Union{Number, Missing}}) = DEFAULT_UNSTABLE
defalg(v::AbstractArray{Missing}) = DEFAULT_UNSTABLE # for method disambiguation
defalg(v::AbstractArray{Union{}}) = DEFAULT_UNSTABLE # for method disambiguation

"""
    sort!(v; alg::Algorithm=defalg(v), lt=isless, by=identity, rev::Bool=false, order::Ordering=Forward)

Sort the vector `v` in place. A stable algorithm is used by default: the
ordering of elements that compare equal is preserved. A specific algorithm can
be selected via the `alg` keyword (see [Sorting Algorithms](@ref) for available
algorithms).

Elements are first transformed with the function `by` and then compared
according to either the function `lt` or the ordering `order`. Finally, the
resulting order is reversed if `rev=true` (this preserves forward stability:
elements that compare equal are not reversed). The current implemention applies
the `by` transformation before each comparison rather than once per element.

Passing an `lt` other than `isless` along with an `order` other than
[`Base.Order.Forward`](@ref) or [`Base.Order.Reverse`](@ref) is not permitted,
otherwise all options are independent and can be used together in all possible
combinations. Note that `order` can also include a "by" transformation, in
which case it is applied after that defined with the `by` keyword. For more
information on `order` values see the documentation on [Alternate
Orderings](@ref).

Relations between two elements are defined as follows (with "less" and
"greater" exchanged when `rev=true`):

* `x` is less than `y` if `lt(by(x), by(y))` (or `Base.Order.lt(order, by(x), by(y))`) yields true.
* `x` is greater than `y` if `y` is less than `x`.
* `x` and `y` are equivalent if neither is less than the other ("incomparable"
  is sometimes used as a synonym for "equivalent").

The result of `sort!` is sorted in the sense that every element is greater than
or equivalent to the previous one.

The `lt` function must define a strict weak order, that is, it must be

* irreflexive: `lt(x, x)` always yields `false`,
* asymmetric: if `lt(x, y)` yields `true` then `lt(y, x)` yields `false`,
* transitive: `lt(x, y) && lt(y, z)` implies `lt(x, z)`,
* transitive in equivalence: `!lt(x, y) && !lt(y, x)` and `!lt(y, z) && !lt(z,
  y)` together imply `!lt(x, z) && !lt(z, x)`. In words: if `x` and `y` are
  equivalent and `y` and `z` are equivalent then `x` and `z` must be
  equivalent.

For example `<` is a valid `lt` function for `Int` values but `≤` is not: it
violates irreflexivity. For `Float64` values even `<` is invalid as it violates
the fourth condition: `1.0` and `NaN` are equivalent and so are `NaN` and `2.0`
but `1.0` and `2.0` are not equivalent.

See also [`sort`](@ref), [`sortperm`](@ref), [`sortslices`](@ref),
[`partialsort!`](@ref), [`partialsortperm`](@ref), [`issorted`](@ref),
[`searchsorted`](@ref), [`insorted`](@ref), [`Base.Order.ord`](@ref).

# Examples
```jldoctest
julia> v = [3, 1, 2]; sort!(v); v
3-element Vector{Int64}:
 1
 2
 3

julia> v = [3, 1, 2]; sort!(v, rev = true); v
3-element Vector{Int64}:
 3
 2
 1

julia> v = [(1, "c"), (3, "a"), (2, "b")]; sort!(v, by = x -> x[1]); v
3-element Vector{Tuple{Int64, String}}:
 (1, "c")
 (2, "b")
 (3, "a")

julia> v = [(1, "c"), (3, "a"), (2, "b")]; sort!(v, by = x -> x[2]); v
3-element Vector{Tuple{Int64, String}}:
 (3, "a")
 (2, "b")
 (1, "c")

julia> sort(0:3, by=x->x-2, order=Base.Order.By(abs)) # same as sort(0:3, by=abs(x->x-2))
4-element Vector{Int64}:
 2
 1
 3
 0

julia> sort([2, NaN, 1, NaN, 3]) # correct sort with default lt=isless
5-element Vector{Float64}:
   1.0
   2.0
   3.0
 NaN
 NaN

julia> sort([2, NaN, 1, NaN, 3], lt=<) # wrong sort due to invalid lt. This behavior is undefined.
5-element Vector{Float64}:
   2.0
 NaN
   1.0
 NaN
   3.0
```
"""
function sort!(v::AbstractVector{T};
               alg::Algorithm=defalg(v),
               lt=isless,
               by=identity,
               rev::Union{Bool,Nothing}=nothing,
               order::Ordering=Forward,
               scratch::Union{Vector{T}, Nothing}=nothing) where T
    _sort!(v, maybe_apply_initial_optimizations(alg), ord(lt,by,rev,order), (;scratch))
    v
end

"""
    sort(v; alg::Algorithm=defalg(v), lt=isless, by=identity, rev::Bool=false, order::Ordering=Forward)

Variant of [`sort!`](@ref) that returns a sorted copy of `v` leaving `v` itself unmodified.

# Examples
```jldoctest
julia> v = [3, 1, 2];

julia> sort(v)
3-element Vector{Int64}:
 1
 2
 3

julia> v
3-element Vector{Int64}:
 3
 1
 2
```
"""
sort(v::AbstractVector; kws...) = sort!(copymutable(v); kws...)

## partialsortperm: the permutation to sort the first k elements of an array ##

"""
    partialsortperm(v, k; by=ientity, lt=isless, rev=false)

Return a partial permutation `I` of the vector `v`, so that `v[I]` returns values of a fully
sorted version of `v` at index `k`. If `k` is a range, a vector of indices is returned; if
`k` is an integer, a single index is returned. The order is specified using the same
keywords as `sort!`. The permutation is stable: the indices of equal elements
will appear in ascending order.

This function is equivalent to, but more efficient than, calling `sortperm(...)[k]`.

# Examples
```jldoctest
julia> v = [3, 1, 2, 1];

julia> v[partialsortperm(v, 1)]
1

julia> p = partialsortperm(v, 1:3)
3-element view(::Vector{Int64}, 1:3) with eltype Int64:
 2
 4
 3

julia> v[p]
3-element Vector{Int64}:
 1
 1
 2
```
"""
partialsortperm(v::AbstractVector, k::Union{Integer,OrdinalRange}; kwargs...) =
    partialsortperm!(similar(Vector{eltype(k)}, axes(v,1)), v, k; kwargs...)

"""
    partialsortperm!(ix, v, k; by=identity, lt=isless, rev=false)

Like [`partialsortperm`](@ref), but accepts a preallocated index vector `ix` the same size as
`v`, which is used to store (a permutation of) the indices of `v`.

`ix` is initialized to contain the indices of `v`.

(Typically, the indices of `v` will be `1:length(v)`, although if `v` has an alternative array type
with non-one-based indices, such as an `OffsetArray`, `ix` must share those same indices)

Upon return, `ix` is guaranteed to have the indices `k` in their sorted positions, such that

```julia
partialsortperm!(ix, v, k);
v[ix[k]] == partialsort(v, k)
```

The return value is the `k`th element of `ix` if `k` is an integer, or view into `ix` if `k` is
a range.

$(Base._DOCS_ALIASING_WARNING)

# Examples
```jldoctest
julia> v = [3, 1, 2, 1];

julia> ix = Vector{Int}(undef, 4);

julia> partialsortperm!(ix, v, 1)
2

julia> ix = [1:4;];

julia> partialsortperm!(ix, v, 2:3)
2-element view(::Vector{Int64}, 2:3) with eltype Int64:
 4
 3
```
 """
function partialsortperm!(ix::AbstractVector{<:Integer}, v::AbstractVector,
                          k::Union{Integer, OrdinalRange};
                          lt::Function=isless,
                          by::Function=identity,
                          rev::Union{Bool,Nothing}=nothing,
                          order::Ordering=Forward,
                          initialized::Bool=false)
    if axes(ix,1) != axes(v,1)
        throw(ArgumentError("The index vector is used as scratch space and must have the " *
                            "same length/indices as the source vector, $(axes(ix,1)) != $(axes(v,1))"))
    end
    @inbounds for i in eachindex(ix)
        ix[i] = i
    end

    # do partial quicksort
    _sort!(ix, InitialOptimizations(ScratchQuickSort(k)), Perm(ord(lt, by, rev, order), v), (;))

    maybeview(ix, k)
end

## sortperm: the permutation to sort an array ##

"""
    sortperm(A; alg::Algorithm=DEFAULT_UNSTABLE, lt=isless, by=identity, rev::Bool=false, order::Ordering=Forward, [dims::Integer])

Return a permutation vector or array `I` that puts `A[I]` in sorted order along the given dimension.
If `A` has more than one dimension, then the `dims` keyword argument must be specified. The order is specified
using the same keywords as [`sort!`](@ref). The permutation is guaranteed to be stable even
if the sorting algorithm is unstable: the indices of equal elements will appear in
ascending order.

See also [`sortperm!`](@ref), [`partialsortperm`](@ref), [`invperm`](@ref), [`indexin`](@ref).
To sort slices of an array, refer to [`sortslices`](@ref).

!!! compat "Julia 1.9"
    The method accepting `dims` requires at least Julia 1.9.

# Examples
```jldoctest
julia> v = [3, 1, 2];

julia> p = sortperm(v)
3-element Vector{Int64}:
 2
 3
 1

julia> v[p]
3-element Vector{Int64}:
 1
 2
 3

julia> A = [8 7; 5 6]
2×2 Matrix{Int64}:
 8  7
 5  6

julia> sortperm(A, dims = 1)
2×2 Matrix{Int64}:
 2  4
 1  3

julia> sortperm(A, dims = 2)
2×2 Matrix{Int64}:
 3  1
 2  4
```
"""
function sortperm(A::AbstractArray;
                  alg::Algorithm=DEFAULT_UNSTABLE,
                  lt=isless,
                  by=identity,
                  rev::Union{Bool,Nothing}=nothing,
                  order::Ordering=Forward,
                  scratch::Union{Vector{<:Integer}, Nothing}=nothing,
                  dims...) #to optionally specify dims argument
    if rev === true
        _sortperm(A; alg, order=ord(lt, by, true, order), scratch, dims...)
    else
        _sortperm(A; alg, order=ord(lt, by, nothing, order), scratch, dims...)
    end
end
function _sortperm(A::AbstractArray; alg, order, scratch, dims...)
    if order === Forward && isa(A,Vector) && eltype(A)<:Integer
        n = length(A)
        if n > 1
            min, max = extrema(A)
            (diff, o1) = sub_with_overflow(max, min)
            (rangelen, o2) = add_with_overflow(diff, oneunit(diff))
            if !(o1 || o2)::Bool && rangelen < div(n,2)
                return sortperm_int_range(A, rangelen, min)
            end
        end
    end
    ix = copymutable(LinearIndices(A))
    sort!(ix; alg, order = Perm(order, vec(A)), scratch, dims...)
end


"""
    sortperm!(ix, A; alg::Algorithm=DEFAULT_UNSTABLE, lt=isless, by=identity, rev::Bool=false, order::Ordering=Forward, [dims::Integer])

Like [`sortperm`](@ref), but accepts a preallocated index vector or array `ix` with the same `axes` as `A`.
`ix` is initialized to contain the values `LinearIndices(A)`.

$(Base._DOCS_ALIASING_WARNING)

!!! compat "Julia 1.9"
    The method accepting `dims` requires at least Julia 1.9.

# Examples
```jldoctest
julia> v = [3, 1, 2]; p = zeros(Int, 3);

julia> sortperm!(p, v); p
3-element Vector{Int64}:
 2
 3
 1

julia> v[p]
3-element Vector{Int64}:
 1
 2
 3

julia> A = [8 7; 5 6]; p = zeros(Int,2, 2);

julia> sortperm!(p, A; dims=1); p
2×2 Matrix{Int64}:
 2  4
 1  3

julia> sortperm!(p, A; dims=2); p
2×2 Matrix{Int64}:
 3  1
 2  4
```
"""
@inline function sortperm!(ix::AbstractArray{T}, A::AbstractArray;
                   alg::Algorithm=DEFAULT_UNSTABLE,
                   lt=isless,
                   by=identity,
                   rev::Union{Bool,Nothing}=nothing,
                   order::Ordering=Forward,
                   initialized::Bool=false,
                   scratch::Union{Vector{T}, Nothing}=nothing,
                   dims...) where T <: Integer #to optionally specify dims argument
    (typeof(A) <: AbstractVector) == (:dims in keys(dims)) && throw(ArgumentError("Dims argument incorrect for type $(typeof(A))"))
    axes(ix) == axes(A) || throw(ArgumentError("index array must have the same size/axes as the source array, $(axes(ix)) != $(axes(A))"))

    ix .= LinearIndices(A)
    if rev === true
        sort!(ix; alg, order=Perm(ord(lt, by, true, order), vec(A)), scratch, dims...)
    else
        sort!(ix; alg, order=Perm(ord(lt, by, nothing, order), vec(A)), scratch, dims...)
    end
end

# sortperm for vectors of few unique integers
function sortperm_int_range(x::Vector{<:Integer}, rangelen, minval)
    offs = 1 - minval
    n = length(x)

    counts = fill(0, rangelen+1)
    counts[1] = 1
    @inbounds for i = 1:n
        counts[x[i] + offs + 1] += 1
    end

    #cumsum!(counts, counts)
    @inbounds for i = 2:length(counts)
        counts[i] += counts[i-1]
    end

    P = Vector{Int}(undef, n)
    @inbounds for i = 1:n
        label = x[i] + offs
        P[counts[label]] = i
        counts[label] += 1
    end

    return P
end

## sorting multi-dimensional arrays ##

"""
    sort(A; dims::Integer, alg::Algorithm=defalg(A), lt=isless, by=identity, rev::Bool=false, order::Ordering=Forward)

Sort a multidimensional array `A` along the given dimension.
See [`sort!`](@ref) for a description of possible
keyword arguments.

To sort slices of an array, refer to [`sortslices`](@ref).

# Examples
```jldoctest
julia> A = [4 3; 1 2]
2×2 Matrix{Int64}:
 4  3
 1  2

julia> sort(A, dims = 1)
2×2 Matrix{Int64}:
 1  2
 4  3

julia> sort(A, dims = 2)
2×2 Matrix{Int64}:
 3  4
 1  2
```
"""
function sort(A::AbstractArray{T};
              dims::Integer,
              alg::Algorithm=defalg(A),
              lt=isless,
              by=identity,
              rev::Union{Bool,Nothing}=nothing,
              order::Ordering=Forward,
              scratch::Union{Vector{T}, Nothing}=nothing) where T
    dim = dims
    order = ord(lt,by,rev,order)
    n = length(axes(A, dim))
    if dim != 1
        pdims = (dim, setdiff(1:ndims(A), dim)...)  # put the selected dimension first
        Ap = permutedims(A, pdims)
        Av = vec(Ap)
        sort_chunks!(Av, n, maybe_apply_initial_optimizations(alg), order, scratch)
        permutedims(Ap, invperm(pdims))
    else
        Av = A[:]
        sort_chunks!(Av, n, maybe_apply_initial_optimizations(alg), order, scratch)
        reshape(Av, axes(A))
    end
end

@noinline function sort_chunks!(Av, n, alg, order, scratch)
    inds = LinearIndices(Av)
    sort_chunks!(Av, n, alg, order, scratch, first(inds), last(inds))
end

@noinline function sort_chunks!(Av, n, alg, order, scratch::Nothing, fst, lst)
    for lo = fst:n:lst
        s = _sort!(Av, alg, order, (; lo, hi=lo+n-1, scratch))
        s !== nothing && return sort_chunks!(Av, n, alg, order, s, lo+n, lst)
    end
    Av
end

@noinline function sort_chunks!(Av, n, alg, order, scratch::AbstractVector, fst, lst)
    for lo = fst:n:lst
        _sort!(Av, alg, order, (; lo, hi=lo+n-1, scratch))
    end
    Av
end


"""
    sort!(A; dims::Integer, alg::Algorithm=defalg(A), lt=isless, by=identity, rev::Bool=false, order::Ordering=Forward)

Sort the multidimensional array `A` along dimension `dims`.
See the one-dimensional version of [`sort!`](@ref) for a description of
possible keyword arguments.

To sort slices of an array, refer to [`sortslices`](@ref).

!!! compat "Julia 1.1"
    This function requires at least Julia 1.1.

# Examples
```jldoctest
julia> A = [4 3; 1 2]
2×2 Matrix{Int64}:
 4  3
 1  2

julia> sort!(A, dims = 1); A
2×2 Matrix{Int64}:
 1  2
 4  3

julia> sort!(A, dims = 2); A
2×2 Matrix{Int64}:
 1  2
 3  4
```
"""
function sort!(A::AbstractArray{T};
               dims::Integer,
               alg::Algorithm=defalg(A),
               lt=isless,
               by=identity,
               rev::Union{Bool,Nothing}=nothing,
               order::Ordering=Forward, # TODO stop eagerly over-allocating.
               scratch::Union{Vector{T}, Nothing}=Vector{T}(undef, size(A, dims))) where T
    __sort!(A, Val(dims), maybe_apply_initial_optimizations(alg), ord(lt, by, rev, order), scratch)
end
function __sort!(A::AbstractArray{T}, ::Val{K},
                alg::Algorithm,
                order::Ordering,
                scratch::Union{Vector{T}, Nothing}) where {K,T}
    nd = ndims(A)

    1 <= K <= nd || throw(ArgumentError("dimension out of range"))

    remdims = ntuple(i -> i == K ? 1 : axes(A, i), nd)
    for idx in CartesianIndices(remdims)
        Av = view(A, ntuple(i -> i == K ? Colon() : idx[i], nd)...)
        sort!(Av; alg, order, scratch)
    end
    A
end


## uint mapping to allow radix sorting primitives other than UInts ##

"""
    UIntMappable(T::Type, order::Ordering)

Return `typeof(uint_map(x::T, order))` if [`uint_map`](@ref) and
[`uint_unmap`](@ref) are implemented.

If either is not implemented, return `nothing`.
"""
UIntMappable(T::Type, order::Ordering) = nothing

"""
    uint_map(x, order::Ordering)::Unsigned

Map `x` to an un unsigned integer, maintaining sort order.

The map should be reversible with [`uint_unmap`](@ref), so `isless(order, a, b)` must be
a linear ordering for `a, b <: typeof(x)`. Satisfies
`isless(order, a, b) === (uint_map(a, order) < uint_map(b, order))`
and `x === uint_unmap(typeof(x), uint_map(x, order), order)`

See also: [`UIntMappable`](@ref) [`uint_unmap`](@ref)
"""
function uint_map end

"""
    uint_unmap(T::Type, u::Unsigned, order::Ordering)

Reconstruct the unique value `x::T` that uint_maps to `u`. Satisfies
`x === uint_unmap(T, uint_map(x::T, order), order)` for all `x <: T`.

See also: [`uint_map`](@ref) [`UIntMappable`](@ref)
"""
function uint_unmap end


### Primitive Types

# Integers
uint_map(x::Unsigned, ::ForwardOrdering) = x
uint_unmap(::Type{T}, u::T, ::ForwardOrdering) where T <: Unsigned = u

uint_map(x::Signed, ::ForwardOrdering) =
    unsigned(xor(x, typemin(x)))
uint_unmap(::Type{T}, u::Unsigned, ::ForwardOrdering) where T <: Signed =
    xor(signed(u), typemin(T))

UIntMappable(T::BitIntegerType, ::ForwardOrdering) = unsigned(T)

# Floats are not UIntMappable under regular orderings because they fail on NaN edge cases.
# uint mappings for floats are defined in Float, where the Left and Right orderings
# guarantee that there are no NaN values

# Chars
uint_map(x::Char, ::ForwardOrdering) = reinterpret(UInt32, x)
uint_unmap(::Type{Char}, u::UInt32, ::ForwardOrdering) = reinterpret(Char, u)
UIntMappable(::Type{Char}, ::ForwardOrdering) = UInt32

### Reverse orderings
uint_map(x, rev::ReverseOrdering) = ~uint_map(x, rev.fwd)
uint_unmap(T::Type, u::Unsigned, rev::ReverseOrdering) = uint_unmap(T, ~u, rev.fwd)
UIntMappable(T::Type, order::ReverseOrdering) = UIntMappable(T, order.fwd)


### Vectors

# Convert v to unsigned integers in place, maintaining sort order.
function uint_map!(v::AbstractVector, lo::Integer, hi::Integer, order::Ordering)
    u = reinterpret(UIntMappable(eltype(v), order), v)
    @inbounds for i in lo:hi
        u[i] = uint_map(v[i], order)
    end
    u
end

function uint_unmap!(v::AbstractVector, u::AbstractVector{U}, lo::Integer, hi::Integer,
                     order::Ordering, offset::U=zero(U),
                     index_offset::Integer=0) where U <: Unsigned
    @inbounds for i in lo:hi
        v[i] = uint_unmap(eltype(v), u[i+index_offset]+offset, order)
    end
    v
end


### Unused constructs for backward compatibility ###

## Old algorithms ##

struct QuickSortAlg     <: Algorithm end
struct MergeSortAlg     <: Algorithm end

"""
    PartialQuickSort{T <: Union{Integer,OrdinalRange}}

Indicate that a sorting function should use the partial quick sort algorithm.
`PartialQuickSort(k)` is like `QuickSort`, but is only required to find and
sort the elements that would end up in `v[k]` were `v` fully sorted.

Characteristics:
  * *not stable*: does not preserve the ordering of elements that
    compare equal (e.g. "a" and "A" in a sort of letters that
    ignores case).
  * *in-place* in memory.
  * *divide-and-conquer*: sort strategy similar to [`MergeSort`](@ref).

Note that `PartialQuickSort(k)` does not necessarily sort the whole array. For example,

```jldoctest
julia> x = rand(100);

julia> k = 50:100;

julia> s1 = sort(x; alg=QuickSort);

julia> s2 = sort(x; alg=PartialQuickSort(k));

julia> map(issorted, (s1, s2))
(true, false)

julia> map(x->issorted(x[k]), (s1, s2))
(true, true)

julia> s1[k] == s2[k]
true
```
"""
struct PartialQuickSort{T <: Union{Integer,OrdinalRange}} <: Algorithm
    k::T
end

"""
    QuickSort

Indicate that a sorting function should use the quick sort
algorithm, which is *not* stable.

Characteristics:
  * *not stable*: does not preserve the ordering of elements that
    compare equal (e.g. "a" and "A" in a sort of letters that
    ignores case).
  * *in-place* in memory.
  * *divide-and-conquer*: sort strategy similar to [`MergeSort`](@ref).
  * *good performance* for large collections.
"""
const QuickSort     = QuickSortAlg()

"""
    MergeSort

Indicate that a sorting function should use the merge sort
algorithm. Merge sort divides the collection into
subcollections and repeatedly merges them, sorting each
subcollection at each step, until the entire
collection has been recombined in sorted form.

Characteristics:
  * *stable*: preserves the ordering of elements that compare
    equal (e.g. "a" and "A" in a sort of letters that ignores
    case).
  * *not in-place* in memory.
  * *divide-and-conquer* sort strategy.
  * *good performance* for large collections but typically not quite as
    fast as [`QuickSort`](@ref).
"""
const MergeSort     = MergeSortAlg()

maybe_apply_initial_optimizations(alg::Algorithm) = alg
maybe_apply_initial_optimizations(alg::QuickSortAlg) = InitialOptimizations(alg)
maybe_apply_initial_optimizations(alg::MergeSortAlg) = InitialOptimizations(alg)
maybe_apply_initial_optimizations(alg::InsertionSortAlg) = InitialOptimizations(alg)

# selectpivot!
#
# Given 3 locations in an array (lo, mi, and hi), sort v[lo], v[mi], v[hi] and
# choose the middle value as a pivot
#
# Upon return, the pivot is in v[lo], and v[hi] is guaranteed to be
# greater than the pivot

@inline function selectpivot!(v::AbstractVector, lo::Integer, hi::Integer, o::Ordering)
    @inbounds begin
        mi = midpoint(lo, hi)

        # sort v[mi] <= v[lo] <= v[hi] such that the pivot is immediately in place
        if lt(o, v[lo], v[mi])
            v[mi], v[lo] = v[lo], v[mi]
        end

        if lt(o, v[hi], v[lo])
            if lt(o, v[hi], v[mi])
                v[hi], v[lo], v[mi] = v[lo], v[mi], v[hi]
            else
                v[hi], v[lo] = v[lo], v[hi]
            end
        end

        # return the pivot
        return v[lo]
    end
end

# partition!
#
# select a pivot, and partition v according to the pivot

function partition!(v::AbstractVector, lo::Integer, hi::Integer, o::Ordering)
    pivot = selectpivot!(v, lo, hi, o)
    # pivot == v[lo], v[hi] > pivot
    i, j = lo, hi
    @inbounds while true
        i += 1; j -= 1
        while lt(o, v[i], pivot); i += 1; end;
        while lt(o, pivot, v[j]); j -= 1; end;
        i >= j && break
        v[i], v[j] = v[j], v[i]
    end
    v[j], v[lo] = pivot, v[j]

    # v[j] == pivot
    # v[k] >= pivot for k > j
    # v[i] <= pivot for i < j
    return j
end

function sort!(v::AbstractVector, lo::Integer, hi::Integer, a::QuickSortAlg, o::Ordering)
    @inbounds while lo < hi
        hi-lo <= SMALL_THRESHOLD && return sort!(v, lo, hi, SMALL_ALGORITHM, o)
        j = partition!(v, lo, hi, o)
        if j-lo < hi-j
            # recurse on the smaller chunk
            # this is necessary to preserve O(log(n))
            # stack space in the worst case (rather than O(n))
            lo < (j-1) && sort!(v, lo, j-1, a, o)
            lo = j+1
        else
            j+1 < hi && sort!(v, j+1, hi, a, o)
            hi = j-1
        end
    end
    return v
end

sort!(v::AbstractVector{T}, lo::Integer, hi::Integer, a::MergeSortAlg, o::Ordering, t0::Vector{T}) where T =
    invoke(sort!, Tuple{typeof.((v, lo, hi, a, o))..., AbstractVector{T}}, v, lo, hi, a, o, t0) # For disambiguation
function sort!(v::AbstractVector{T}, lo::Integer, hi::Integer, a::MergeSortAlg, o::Ordering,
        t0::Union{AbstractVector{T}, Nothing}=nothing) where T
    @inbounds if lo < hi
        hi-lo <= SMALL_THRESHOLD && return sort!(v, lo, hi, SMALL_ALGORITHM, o)

        m = midpoint(lo, hi)

        t = t0 === nothing ? similar(v, m-lo+1) : t0
        length(t) < m-lo+1 && resize!(t, m-lo+1)
        Base.require_one_based_indexing(t)

        sort!(v, lo,  m,  a, o, t)
        sort!(v, m+1, hi, a, o, t)

        i, j = 1, lo
        while j <= m
            t[i] = v[j]
            i += 1
            j += 1
        end

        i, k = 1, lo
        while k < j <= hi
            if lt(o, v[j], t[i])
                v[k] = v[j]
                j += 1
            else
                v[k] = t[i]
                i += 1
            end
            k += 1
        end
        while k < j
            v[k] = t[i]
            k += 1
            i += 1
        end
    end

    return v
end

function sort!(v::AbstractVector, lo::Integer, hi::Integer, a::PartialQuickSort,
               o::Ordering)
    @inbounds while lo < hi
        hi-lo <= SMALL_THRESHOLD && return sort!(v, lo, hi, SMALL_ALGORITHM, o)
        j = partition!(v, lo, hi, o)

        if j <= first(a.k)
            lo = j+1
        elseif j >= last(a.k)
            hi = j-1
        else
            # recurse on the smaller chunk
            # this is necessary to preserve O(log(n))
            # stack space in the worst case (rather than O(n))
            if j-lo < hi-j
                lo < (j-1) && sort!(v, lo, j-1, a, o)
                lo = j+1
            else
                hi > (j+1) && sort!(v, j+1, hi, a, o)
                hi = j-1
            end
        end
    end
    return v
end

## Old extensibility mechanisms ##

# Support 3-, 5-, and 6-argument versions of sort! for calling into the internals in the old way
sort!(v::AbstractVector, a::Algorithm, o::Ordering) = sort!(v, firstindex(v), lastindex(v), a, o)
function sort!(v::AbstractVector, lo::Integer, hi::Integer, a::Algorithm, o::Ordering)
    _sort!(v, a, o, (; lo, hi, legacy_dispatch_entry=a))
    v
end
sort!(v::AbstractVector, lo::Integer, hi::Integer, a::Algorithm, o::Ordering, _) = sort!(v, lo, hi, a, o)
function sort!(v::AbstractVector, lo::Integer, hi::Integer, a::Algorithm, o::Ordering, scratch::Vector)
    _sort!(v, a, o, (; lo, hi, scratch, legacy_dispatch_entry=a))
    v
end

# Support dispatch on custom algorithms in the old way
# sort!(::AbstractVector, ::Integer, ::Integer, ::MyCustomAlgorithm, ::Ordering) = ...
function _sort!(v::AbstractVector, a::Algorithm, o::Ordering, kw)
    @getkw lo hi scratch legacy_dispatch_entry
    if legacy_dispatch_entry === a
        # This error prevents infinite recursion for unknown algorithms
        throw(ArgumentError("Base.Sort._sort!(::$(typeof(v)), ::$(typeof(a)), ::$(typeof(o)), ::Any) is not defined"))
    else
        sort!(v, lo, hi, a, o)
        scratch
    end
end

end # module Sort
V   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/binaryplatforms.jln�      # This file is a part of Julia. License is MIT: https://julialang.org/license

module BinaryPlatforms

export AbstractPlatform, Platform, HostPlatform, platform_dlext, tags, arch, os,
       os_version, libc, libgfortran_version, libstdcxx_version,
       cxxstring_abi, parse_dl_name_version, detect_libgfortran_version,
       detect_libstdcxx_version, detect_cxxstring_abi, call_abi, wordsize, triplet,
       select_platform, platforms_match, platform_name
import .Libc.Libdl

### Submodule with information about CPU features
include("cpuid.jl")
using .CPUID

# This exists to ease compatibility with old-style Platform objects
abstract type AbstractPlatform; end

"""
    Platform

A `Platform` represents all relevant pieces of information that a julia process may need
to know about its execution environment, such as the processor architecture, operating
system, libc implementation, etc...  It is, at its heart, a key-value mapping of tags
(such as `arch`, `os`, `libc`, etc...) to values (such as `"arch" => "x86_64"`, or
`"os" => "windows"`, etc...).  `Platform` objects are extensible in that the tag mapping
is open for users to add their own mappings to, as long as the mappings do not conflict
with the set of reserved tags: `arch`, `os`, `os_version`, `libc`, `call_abi`,
`libgfortran_version`, `libstdcxx_version`, `cxxstring_abi` and `julia_version`.

Valid tags and values are composed of alphanumeric and period characters.  All tags and
values will be lowercased when stored to reduce variation.

Example:

    Platform("x86_64", "windows"; cuda = "10.1")
"""
struct Platform <: AbstractPlatform
    tags::Dict{String,String}
    # The "compare strategy" allows selective overriding on how a tag is compared
    compare_strategies::Dict{String,Function}

    # Passing `tags` as a `Dict` avoids the need to infer different NamedTuple specializations
    function Platform(arch::String, os::String, _tags::Dict{String};
                      validate_strict::Bool = false,
                      compare_strategies::Dict{String,<:Function} = Dict{String,Function}())
        # A wee bit of normalization
        os = lowercase(os)
        arch = CPUID.normalize_arch(arch)

        tags = Dict{String,String}(
            "arch" => arch,
            "os" => os,
        )
        for (tag, value) in _tags
            value = value::Union{String,VersionNumber,Nothing}
            tag = lowercase(tag)
            if tag ∈ ("arch", "os")
                throw(ArgumentError("Cannot double-pass key $(tag)"))
            end

            # Drop `nothing` values; this means feature is not present or use default value.
            if value === nothing
                continue
            end

            # Normalize things that are known to be version numbers so that comparisons are easy.
            # Note that in our effort to be extremely compatible, we actually allow something that
            # doesn't parse nicely into a VersionNumber to persist, but if `validate_strict` is
            # set to `true`, it will cause an error later on.
            if tag ∈ ("libgfortran_version", "libstdcxx_version", "os_version")
                if isa(value, VersionNumber)
                    value = string(value)
                elseif isa(value, String)
                    v = tryparse(VersionNumber, value)
                    if isa(v, VersionNumber)
                        value = string(v)
                    end
                end
            end

            # Use `add_tag!()` to add the tag to our collection of tags
            add_tag!(tags, tag, string(value)::String)
        end

        # Auto-map call_abi and libc where necessary:
        if os == "linux" && !haskey(tags, "libc")
            # Default to `glibc` on Linux
            tags["libc"] = "glibc"
        end
        if os == "linux" && arch ∈ ("armv7l", "armv6l") && "call_abi" ∉ keys(tags)
            # default `call_abi` to `eabihf` on 32-bit ARM
            tags["call_abi"] = "eabihf"
        end

        # If the user is asking for strict validation, do so.
        if validate_strict
            validate_tags(tags)
        end

        # By default, we compare julia_version only against major and minor versions:
        if haskey(tags, "julia_version") && !haskey(compare_strategies, "julia_version")
            compare_strategies["julia_version"] = (a::String, b::String, a_comparator, b_comparator) -> begin
                a = VersionNumber(a)
                b = VersionNumber(b)
                return a.major == b.major && a.minor == b.minor
            end
        end

        return new(tags, compare_strategies)
    end
end

# Keyword interface (to avoid inference of specialized NamedTuple methods, use the Dict interface for `tags`)
function Platform(arch::String, os::String;
                  validate_strict::Bool = false,
                  compare_strategies::Dict{String,<:Function} = Dict{String,Function}(),
                  kwargs...)
    tags = Dict{String,Any}(String(tag)::String=>tagvalue(value) for (tag, value) in kwargs)
    return Platform(arch, os, tags; validate_strict, compare_strategies)
end

tagvalue(v::Union{String,VersionNumber,Nothing}) = v
tagvalue(v::Symbol) = String(v)
tagvalue(v::AbstractString) = convert(String, v)::String

# Simple tag insertion that performs a little bit of validation
function add_tag!(tags::Dict{String,String}, tag::String, value::String)
    # I know we said only alphanumeric and dots, but let's be generous so that we can expand
    # our support in the future while remaining as backwards-compatible as possible.  The
    # only characters that are absolutely disallowed right now are `-`, `+`, ` ` and things
    # that are illegal in filenames:
    nonos = raw"""+- /<>:"'\|?*"""
    if any(occursin(nono, tag) for nono in nonos)
        throw(ArgumentError("Invalid character in tag name \"$(tag)\"!"))
    end

    # Normalize and reject nonos
    value = lowercase(value)
    if any(occursin(nono, value) for nono in nonos)
        throw(ArgumentError("Invalid character in tag value \"$(value)\"!"))
    end
    tags[tag] = value
    return value
end

# Other `Platform` types can override this (I'm looking at you, `AnyPlatform`)
tags(p::Platform) = p.tags

# Make it act more like a dict
Base.getindex(p::AbstractPlatform, k::String) = getindex(tags(p), k)
Base.haskey(p::AbstractPlatform, k::String) = haskey(tags(p), k)
function Base.setindex!(p::AbstractPlatform, v::String, k::String)
    add_tag!(tags(p), k, v)
    return p
end

# Hash definition to ensure that it's stable
function Base.hash(p::Platform, h::UInt)
    h += 0x506c6174666f726d % UInt
    h = hash(p.tags, h)
    h = hash(p.compare_strategies, h)
    return h
end

# Simple equality definition; for compatibility testing, use `platforms_match()`
function Base.:(==)(a::Platform, b::Platform)
    return a.tags == b.tags && a.compare_strategies == b.compare_strategies
end


# Allow us to easily serialize Platform objects
function Base.repr(p::Platform; context=nothing)
    str = string(
        "Platform(",
        repr(arch(p)),
        ", ",
        repr(os(p)),
        "; ",
        join(("$(k) = $(repr(v))" for (k, v) in tags(p) if k ∉ ("arch", "os")), ", "),
        ")",
    )
end

# Make showing the platform a bit more palatable
function Base.show(io::IO, p::Platform)
    str = string(platform_name(p), " ", arch(p))
    # Add on all the other tags not covered by os/arch:
    other_tags = sort!(filter!(kv -> kv[1] ∉ ("os", "arch"), collect(tags(p))))
    if !isempty(other_tags)
        str = string(str, " {", join([string(k, "=", v) for (k, v) in other_tags], ", "), "}")
    end
    print(io, str)
end

function validate_tags(tags::Dict)
    throw_invalid_key(k) = throw(ArgumentError("Key \"$(k)\" cannot have value \"$(tags[k])\""))
    # Validate `arch`
    if tags["arch"] ∉ ("x86_64", "i686", "armv7l", "armv6l", "aarch64", "powerpc64le")
        throw_invalid_key("arch")
    end
    # Validate `os`
    if tags["os"] ∉ ("linux", "macos", "freebsd", "windows")
        throw_invalid_key("os")
    end
    # Validate `os`/`arch` combination
    throw_os_mismatch() = throw(ArgumentError("Invalid os/arch combination: $(tags["os"])/$(tags["arch"])"))
    if tags["os"] == "windows" && tags["arch"] ∉ ("x86_64", "i686", "armv7l", "aarch64")
        throw_os_mismatch()
    end
    if tags["os"] == "macos" && tags["arch"] ∉ ("x86_64", "aarch64")
        throw_os_mismatch()
    end

    # Validate `os`/`libc` combination
    throw_libc_mismatch() = throw(ArgumentError("Invalid os/libc combination: $(tags["os"])/$(tags["libc"])"))
    if tags["os"] == "linux"
        # Linux always has a `libc` entry
        if tags["libc"] ∉ ("glibc", "musl")
            throw_libc_mismatch()
        end
    else
        # Nothing else is allowed to have a `libc` entry
        if haskey(tags, "libc")
            throw_libc_mismatch()
        end
    end

    # Validate `os`/`arch`/`call_abi` combination
    throw_call_abi_mismatch() = throw(ArgumentError("Invalid os/arch/call_abi combination: $(tags["os"])/$(tags["arch"])/$(tags["call_abi"])"))
    if tags["os"] == "linux" && tags["arch"] ∈ ("armv7l", "armv6l")
        # If an ARM linux has does not have `call_abi` set to something valid, be sad.
        if !haskey(tags, "call_abi") || tags["call_abi"] ∉ ("eabihf", "eabi")
            throw_call_abi_mismatch()
        end
    else
        # Nothing else should have a `call_abi`.
        if haskey(tags, "call_abi")
            throw_call_abi_mismatch()
        end
    end

    # Validate `libgfortran_version` is a parsable `VersionNumber`
    throw_version_number(k) = throw(ArgumentError("\"$(k)\" cannot have value \"$(tags[k])\", must be a valid VersionNumber"))
    if "libgfortran_version" in keys(tags) && tryparse(VersionNumber, tags["libgfortran_version"]) === nothing
        throw_version_number("libgfortran_version")
    end

    # Validate `cxxstring_abi` is one of the two valid options:
    if "cxxstring_abi" in keys(tags) && tags["cxxstring_abi"] ∉ ("cxx03", "cxx11")
        throw_invalid_key("cxxstring_abi")
    end

    # Validate `libstdcxx_version` is a parsable `VersionNumber`
    if "libstdcxx_version" in keys(tags) && tryparse(VersionNumber, tags["libstdcxx_version"]) === nothing
        throw_version_number("libstdcxx_version")
    end
end

function set_compare_strategy!(p::Platform, key::String, f::Function)
    if !haskey(p.tags, key)
        throw(ArgumentError("Cannot set comparison strategy for nonexistent tag $(key)!"))
    end
    p.compare_strategies[key] = f
end

function get_compare_strategy(p::Platform, key::String, default = compare_default)
    if !haskey(p.tags, key)
        throw(ArgumentError("Cannot get comparison strategy for nonexistent tag $(key)!"))
    end
    return get(p.compare_strategies, key, default)
end
get_compare_strategy(p::AbstractPlatform, key::String, default = compare_default) = default


"""
    compare_default(a::String, b::String, a_requested::Bool, b_requested::Bool)

Default comparison strategy that falls back to `a == b`.  This only ever happens if both
`a` and `b` request this strategy, as any other strategy is preferable to this one.
"""
function compare_default(a::String, b::String, a_requested::Bool, b_requested::Bool)
    return a == b
end

"""
    compare_version_cap(a::String, b::String, a_comparator, b_comparator)

Example comparison strategy for `set_comparison_strategy!()` that implements a version
cap for host platforms that support _up to_ a particular version number.  As an example,
if an artifact is built for macOS 10.9, it can run on macOS 10.11, however if it were
built for macOS 10.12, it could not.  Therefore, the host platform of macOS 10.11 has a
version cap at `v"10.11"`.

Note that because both hosts and artifacts are represented with `Platform` objects it
is possible to call `platforms_match()` with two artifacts, a host and an artifact, an
artifact and a host, and even two hosts.  We attempt to do something intelligent for all
cases, but in the case of comparing version caps between two hosts, we return `true` only
if the two host platforms are in fact identical.
"""
function compare_version_cap(a::String, b::String, a_requested::Bool, b_requested::Bool)
    a = VersionNumber(a)
    b = VersionNumber(b)

    # If both b and a requested, then we fall back to equality:
    if a_requested && b_requested
        return a == b
    end

    # Otherwise, do the comparison between the the single version cap and the single version:
    if a_requested
        return b <= a
    else
        return a <= b
    end
end


"""
    HostPlatform(p::AbstractPlatform)

Convert a `Platform` to act like a "host"; e.g. if it has a version-bound tag such as
`"libstdcxx_version" => "3.4.26"`, it will treat that value as an upper bound, rather
than a characteristic.  `Platform` objects that define artifacts generally denote the
SDK or version that the artifact was built with, but for platforms, these versions are
generally the maximal version the platform can support.  The way this transformation
is implemented is to change the appropriate comparison strategies to treat these pieces
of data as bounds rather than points in any comparison.
"""
function HostPlatform(p::AbstractPlatform)
    if haskey(p, "os_version")
        set_compare_strategy!(p, "os_version", compare_version_cap)
    end
    if haskey(p, "libstdcxx_version")
        set_compare_strategy!(p, "libstdcxx_version", compare_version_cap)
    end
    return p
end

"""
    arch(p::AbstractPlatform)

Get the architecture for the given `Platform` object as a `String`.

# Examples
```jldoctest
julia> arch(Platform("aarch64", "Linux"))
"aarch64"

julia> arch(Platform("amd64", "freebsd"))
"x86_64"
```
"""
arch(p::AbstractPlatform) = get(tags(p), "arch", nothing)

"""
    os(p::AbstractPlatform)

Get the operating system for the given `Platform` object as a `String`.

# Examples
```jldoctest
julia> os(Platform("armv7l", "Linux"))
"linux"

julia> os(Platform("aarch64", "macos"))
"macos"
```
"""
os(p::AbstractPlatform) = get(tags(p), "os", nothing)

# As a special helper, it's sometimes useful to know the current OS at compile-time
function os()
    if Sys.iswindows()
        return "windows"
    elseif Sys.isapple()
        return "macos"
    elseif Sys.isbsd()
        return "freebsd"
    else
        return "linux"
    end
end

"""
    libc(p::AbstractPlatform)

Get the libc for the given `Platform` object as a `String`.  Returns `nothing` on
platforms with no explicit `libc` choices (which is most platforms).

# Examples
```jldoctest
julia> libc(Platform("armv7l", "Linux"))
"glibc"

julia> libc(Platform("aarch64", "linux"; libc="musl"))
"musl"

julia> libc(Platform("i686", "Windows"))
```
"""
libc(p::AbstractPlatform) = get(tags(p), "libc", nothing)

"""
    call_abi(p::AbstractPlatform)

Get the call ABI for the given `Platform` object as a `String`.  Returns `nothing` on
platforms with no explicit `call_abi` choices (which is most platforms).

# Examples
```jldoctest
julia> call_abi(Platform("armv7l", "Linux"))
"eabihf"

julia> call_abi(Platform("x86_64", "macos"))
```
"""
call_abi(p::AbstractPlatform) = get(tags(p), "call_abi", nothing)

const platform_names = Dict(
    "linux" => "Linux",
    "macos" => "macOS",
    "windows" => "Windows",
    "freebsd" => "FreeBSD",
    nothing => "Unknown",
)

"""
    platform_name(p::AbstractPlatform)

Get the "platform name" of the given platform, returning e.g. "Linux" or "Windows".
"""
function platform_name(p::AbstractPlatform)
    return platform_names[os(p)]
end

function VNorNothing(d::Dict, key)
    v = get(d, key, nothing)
    if v === nothing
        return nothing
    end
    return VersionNumber(v)::VersionNumber
end

"""
    libgfortran_version(p::AbstractPlatform)

Get the libgfortran version dictated by this `Platform` object as a `VersionNumber`,
or `nothing` if no compatibility bound is imposed.
"""
libgfortran_version(p::AbstractPlatform) = VNorNothing(tags(p), "libgfortran_version")

"""
    libstdcxx_version(p::AbstractPlatform)

Get the libstdc++ version dictated by this `Platform` object, or `nothing` if no
compatibility bound is imposed.
"""
libstdcxx_version(p::AbstractPlatform) = VNorNothing(tags(p), "libstdcxx_version")

"""
    cxxstring_abi(p::AbstractPlatform)

Get the c++ string ABI dictated by this `Platform` object, or `nothing` if no ABI is imposed.
"""
cxxstring_abi(p::AbstractPlatform) = get(tags(p), "cxxstring_abi", nothing)

"""
    os_version(p::AbstractPlatform)

Get the OS version dictated by this `Platform` object, or `nothing` if no OS version is
imposed/no data is available.  This is most commonly used by MacOS and FreeBSD objects
where we have high platform SDK fragmentation, and features are available only on certain
platform versions.
"""
os_version(p::AbstractPlatform) = VNorNothing(tags(p), "os_version")

"""
    wordsize(p::AbstractPlatform)

Get the word size for the given `Platform` object.

# Examples
```jldoctest
julia> wordsize(Platform("armv7l", "linux"))
32

julia> wordsize(Platform("x86_64", "macos"))
64
```
"""
wordsize(p::AbstractPlatform) = (arch(p) ∈ ("i686", "armv6l", "armv7l")) ? 32 : 64

"""
    triplet(p::AbstractPlatform; exclude_tags::Vector{String})

Get the target triplet for the given `Platform` object as a `String`.

# Examples
```jldoctest
julia> triplet(Platform("x86_64", "MacOS"))
"x86_64-apple-darwin"

julia> triplet(Platform("i686", "Windows"))
"i686-w64-mingw32"

julia> triplet(Platform("armv7l", "Linux"; libgfortran_version="3"))
"armv7l-linux-gnueabihf-libgfortran3"
```
"""
function triplet(p::AbstractPlatform)
    str = string(
        arch(p)::Union{Symbol,String},
        os_str(p),
        libc_str(p),
        call_abi_str(p),
    )

    # Tack on optional compiler ABI flags
    if libgfortran_version(p) !== nothing
        str = string(str, "-libgfortran", libgfortran_version(p).major)
    end
    if cxxstring_abi(p) !== nothing
        str = string(str, "-", cxxstring_abi(p))
    end
    if libstdcxx_version(p) !== nothing
        str = string(str, "-libstdcxx", libstdcxx_version(p).patch)
    end

    # Tack on all extra tags
    for (tag, val) in tags(p)
        if tag ∈ ("os", "arch", "libc", "call_abi", "libgfortran_version", "libstdcxx_version", "cxxstring_abi", "os_version")
            continue
        end
        str = string(str, "-", tag, "+", val)
    end
    return str
end

function os_str(p::AbstractPlatform)
    if os(p) == "linux"
        return "-linux"
    elseif os(p) == "macos"
        osvn = os_version(p)
        if osvn !== nothing
            return "-apple-darwin$(osvn.major)"
        else
            return "-apple-darwin"
        end
    elseif os(p) == "windows"
        return "-w64-mingw32"
    elseif os(p) == "freebsd"
        osvn = os_version(p)
        if osvn !== nothing
            return "-unknown-freebsd$(osvn.major).$(osvn.minor)"
        else
            return "-unknown-freebsd"
        end
    else
        return "-unknown"
    end
end

# Helper functions for Linux and FreeBSD libc/abi mishmashes
function libc_str(p::AbstractPlatform)
    lc = libc(p)
    if lc === nothing
        return ""
    elseif lc === "glibc"
        return "-gnu"
    else
        return string("-", lc)
    end
end
function call_abi_str(p::AbstractPlatform)
    cabi = call_abi(p)
    cabi === nothing ? "" : string(cabi::Union{Symbol,String})
end

Sys.isapple(p::AbstractPlatform) = os(p) == "macos"
Sys.islinux(p::AbstractPlatform) = os(p) == "linux"
Sys.iswindows(p::AbstractPlatform) = os(p) == "windows"
Sys.isfreebsd(p::AbstractPlatform) = os(p) == "freebsd"
Sys.isbsd(p::AbstractPlatform) = os(p) ∈ ("freebsd", "macos")
Sys.isunix(p::AbstractPlatform) = Sys.isbsd(p) || Sys.islinux(p)

const arch_mapping = Dict(
    "x86_64" => "(x86_|amd)64",
    "i686" => "i\\d86",
    "aarch64" => "(aarch64|arm64)",
    "armv7l" => "arm(v7l)?", # if we just see `arm-linux-gnueabihf`, we assume it's `armv7l`
    "armv6l" => "armv6l",
    "powerpc64le" => "p(ower)?pc64le",
)
# Keep this in sync with `CPUID.ISAs_by_family`
# These are the CPUID side of the microarchitectures targeted by GCC flags in BinaryBuilder.jl
const arch_march_isa_mapping = let
    function get_set(arch, name)
        all = CPUID.ISAs_by_family[arch]
        return all[findfirst(x -> x.first == name, all)].second
    end
    Dict(
        "i686" => [
            "pentium4" => get_set("i686", "pentium4"),
            "prescott" => get_set("i686", "prescott"),
        ],
        "x86_64" => [
            "x86_64" => get_set("x86_64", "x86_64"),
            "avx" => get_set("x86_64", "sandybridge"),
            "avx2" => get_set("x86_64", "haswell"),
            "avx512" => get_set("x86_64", "skylake_avx512"),
        ],
        "armv6l" => [
            "arm1176jzfs" => get_set("armv6l", "arm1176jzfs"),
        ],
        "armv7l" => [
            "armv7l" => get_set("armv7l", "armv7l"),
            "neonvfpv4" => get_set("armv7l", "armv7l+neon+vfpv4"),
        ],
        "aarch64" => [
            "armv8_0" => get_set("aarch64", "armv8.0-a"),
            "armv8_1" => get_set("aarch64", "armv8.1-a"),
            "armv8_2_crypto" => get_set("aarch64", "armv8.2-a+crypto"),
            "a64fx" => get_set("aarch64", "a64fx"),
            "apple_m1" => get_set("aarch64", "apple_m1"),
        ],
        "powerpc64le" => [
            "power8" => get_set("powerpc64le", "power8"),
        ]
    )
end
const os_mapping = Dict(
    "macos" => "-apple-darwin[\\d\\.]*",
    "freebsd" => "-(.*-)?freebsd[\\d\\.]*",
    "windows" => "-w64-mingw32",
    "linux" => "-(.*-)?linux",
)
const libc_mapping = Dict(
    "libc_nothing" => "",
    "glibc" => "-gnu",
    "musl" => "-musl",
)
const call_abi_mapping = Dict(
    "call_abi_nothing" => "",
    "eabihf" => "eabihf",
    "eabi" => "eabi",
)
const libgfortran_version_mapping = Dict(
    "libgfortran_nothing" => "",
    "libgfortran3" => "(-libgfortran3)|(-gcc4)", # support old-style `gccX` versioning
    "libgfortran4" => "(-libgfortran4)|(-gcc7)",
    "libgfortran5" => "(-libgfortran5)|(-gcc8)",
)
const cxxstring_abi_mapping = Dict(
    "cxxstring_nothing" => "",
    "cxx03" => "-cxx03",
    "cxx11" => "-cxx11",
)
const libstdcxx_version_mapping = Dict{String,String}(
    "libstdcxx_nothing" => "",
    "libstdcxx" => "-libstdcxx\\d+",
)

"""
    parse(::Type{Platform}, triplet::AbstractString)

Parses a string platform triplet back into a `Platform` object.
"""
function Base.parse(::Type{Platform}, triplet::String; validate_strict::Bool = false)
    # Helper function to collapse dictionary of mappings down into a regex of
    # named capture groups joined by "|" operators
    c(mapping) = string("(",join(["(?<$k>$v)" for (k, v) in mapping], "|"), ")")

    # We're going to build a mondo regex here to parse everything:
    triplet_regex = Regex(string(
        "^",
        # First, the core triplet; arch/os/libc/call_abi
        c(arch_mapping),
        c(os_mapping),
        c(libc_mapping),
        c(call_abi_mapping),
        # Next, optional things, like libgfortran/libstdcxx/cxxstring abi
        c(libgfortran_version_mapping),
        c(cxxstring_abi_mapping),
        c(libstdcxx_version_mapping),
        # Finally, the catch-all for extended tags
        "(?<tags>(?:-[^-]+\\+[^-]+)*)?",
        "\$",
    ))

    m = match(triplet_regex, triplet)
    if m !== nothing
        # Helper function to find the single named field within the giant regex
        # that is not `nothing` for each mapping we give it.
        get_field(m, mapping) = begin
            for k in keys(mapping)
                if m[k] !== nothing
                    # Convert our sentinel `nothing` values to actual `nothing`
                    if endswith(k, "_nothing")
                        return nothing
                    end
                    # Convert libgfortran/libstdcxx version numbers
                    if startswith(k, "libgfortran")
                        return VersionNumber(parse(Int,k[12:end]))
                    elseif startswith(k, "libstdcxx")
                        return VersionNumber(3, 4, parse(Int,m[k][11:end]))
                    else
                        return k
                    end
                end
            end
        end

        # Extract the information we're interested in:
        tags = Dict{String,Any}()
        arch = get_field(m, arch_mapping)
        os = get_field(m, os_mapping)
        tags["libc"] = get_field(m, libc_mapping)
        tags["call_abi"] = get_field(m, call_abi_mapping)
        tags["libgfortran_version"] = get_field(m, libgfortran_version_mapping)
        tags["libstdcxx_version"] = get_field(m, libstdcxx_version_mapping)
        tags["cxxstring_abi"] = get_field(m, cxxstring_abi_mapping)
        function split_tags(tagstr)
            tag_fields = split(tagstr, "-"; keepempty=false)
            if isempty(tag_fields)
                return Pair{String,String}[]
            end
            return map(v -> String(v[1]) => String(v[2]), split.(tag_fields, "+"))
        end
        merge!(tags, Dict(split_tags(m["tags"])))

        # Special parsing of os version number, if any exists
        function extract_os_version(os_name, pattern)
            m_osvn = match(pattern, m[os_name])
            if m_osvn !== nothing
                return VersionNumber(m_osvn.captures[1])
            end
            return nothing
        end
        os_version = nothing
        if os == "macos"
            os_version = extract_os_version("macos", r".*darwin([\d\.]+)"sa)
        end
        if os == "freebsd"
            os_version = extract_os_version("freebsd", r".*freebsd([\d.]+)"sa)
        end
        tags["os_version"] = os_version

        return Platform(arch, os, tags; validate_strict)
    end
    throw(ArgumentError("Platform `$(triplet)` is not an officially supported platform"))
end
Base.parse(::Type{Platform}, triplet::AbstractString; kwargs...) =
    parse(Platform, convert(String, triplet)::String; kwargs...)

function Base.tryparse(::Type{Platform}, triplet::AbstractString)
    try
        parse(Platform, triplet)
    catch e
        if isa(e, InterruptException)
            rethrow(e)
        end
        return nothing
    end
end

"""
    platform_dlext(p::AbstractPlatform = HostPlatform())

Return the dynamic library extension for the given platform, defaulting to the
currently running platform.  E.g. returns "so" for a Linux-based platform,
"dll" for a Windows-based platform, etc...
"""
function platform_dlext(p::AbstractPlatform = HostPlatform())
    if os(p) == "windows"
        return "dll"
    elseif os(p) == "macos"
        return "dylib"
    else
        return "so"
    end
end

"""
    parse_dl_name_version(path::String, platform::AbstractPlatform)

Given a path to a dynamic library, parse out what information we can
from the filename.  E.g. given something like "lib/libfoo.so.3.2",
this function returns `"libfoo", v"3.2"`.  If the path name is not a
valid dynamic library, this method throws an error.  If no soversion
can be extracted from the filename, as in "libbar.so" this method
returns `"libbar", nothing`.
"""
function parse_dl_name_version(path::String, os::String)
    # Use an extraction regex that matches the given OS
    local dlregex
    if os == "windows"
        # On Windows, libraries look like `libnettle-6.dll`
        dlregex = r"^(.*?)(?:-((?:[\.\d]+)*))?\.dll$"sa
    elseif os == "macos"
        # On OSX, libraries look like `libnettle.6.3.dylib`
        dlregex = r"^(.*?)((?:\.[\d]+)*)\.dylib$"sa
    else
        # On Linux and FreeBSD, libraries look like `libnettle.so.6.3.0`
        dlregex = r"^(.*?)\.so((?:\.[\d]+)*)$"sa
    end

    m = match(dlregex, basename(path))
    if m === nothing
        throw(ArgumentError("Invalid dynamic library path '$path'"))
    end

    # Extract name and version
    name = m.captures[1]
    version = m.captures[2]
    if version === nothing || isempty(version)
        version = nothing
    else
        version = VersionNumber(strip(version, '.'))
    end
    return name, version
end

# Adapter for `AbstractString`
function parse_dl_name_version(path::AbstractString, os::AbstractString)
    return parse_dl_name_version(string(path)::String, string(os)::String)
end

"""
    detect_libgfortran_version()

Inspects the current Julia process to determine the libgfortran version this Julia is
linked against (if any).
"""
function detect_libgfortran_version()
    libgfortran_paths = filter!(x -> occursin("libgfortran", x), Libdl.dllist())
    if isempty(libgfortran_paths)
        # One day, I hope to not be linking against libgfortran in base Julia
        return nothing
    end
    libgfortran_path = first(libgfortran_paths)

    name, version = parse_dl_name_version(libgfortran_path, os())
    if version === nothing
        # Even though we complain about this, we allow it to continue in the hopes that
        # we shall march on to a BRIGHTER TOMORROW.  One in which we are not shackled
        # by the constraints of libgfortran compiler ABIs upon our precious programming
        # languages; one where the mistakes of yesterday are mere memories and not
        # continual maintenance burdens upon the children of the dawn; one where numeric
        # code may be cleanly implemented in a modern language and not bestowed onto the
        # next generation by grizzled ancients, documented only with a faded yellow
        # sticky note that bears a hastily-scribbled "good luck".
        @warn("Unable to determine libgfortran version from '$(libgfortran_path)'")
    end
    return version
end

"""
    detect_libstdcxx_version(max_minor_version::Int=30)

Inspects the currently running Julia process to find out what version of libstdc++
it is linked against (if any).  `max_minor_version` is the latest version in the
3.4 series of GLIBCXX where the search is performed.
"""
function detect_libstdcxx_version(max_minor_version::Int=30)
    libstdcxx_paths = filter!(x -> occursin("libstdc++", x), Libdl.dllist())
    if isempty(libstdcxx_paths)
        # This can happen if we were built by clang, so we don't link against
        # libstdc++ at all.
        return nothing
    end

    # Brute-force our way through GLIBCXX_* symbols to discover which version we're linked against
    hdl = Libdl.dlopen(first(libstdcxx_paths))::Ptr{Cvoid}
    # Try all GLIBCXX versions down to GCC v4.8:
    # https://gcc.gnu.org/onlinedocs/libstdc++/manual/abi.html
    for minor_version in max_minor_version:-1:18
        if Libdl.dlsym(hdl, "GLIBCXX_3.4.$(minor_version)"; throw_error=false) !== nothing
            Libdl.dlclose(hdl)
            return VersionNumber("3.4.$(minor_version)")
        end
    end
    Libdl.dlclose(hdl)
    return nothing
end

"""
    detect_cxxstring_abi()

Inspects the currently running Julia process to see what version of the C++11 string ABI
it was compiled with (this is only relevant if compiled with `g++`; `clang` has no
incompatibilities yet, bless its heart).  In reality, this actually checks for symbols
within LLVM, but that is close enough for our purposes, as you can't mix configurations
between Julia and LLVM; they must match.
"""
function detect_cxxstring_abi()
    # First, if we're not linked against libstdc++, then early-exit because this doesn't matter.
    libstdcxx_paths = filter!(x -> occursin("libstdc++", x), Libdl.dllist())
    if isempty(libstdcxx_paths)
        # We were probably built by `clang`; we don't link against `libstdc++`` at all.
        return nothing
    end

    function open_libllvm(f::Function)
        for lib_name in (Base.libllvm_name, "libLLVM", "LLVM", "libLLVMSupport")
            hdl = Libdl.dlopen_e(lib_name)
            if hdl != C_NULL
                try
                    return f(hdl)
                finally
                    Libdl.dlclose(hdl)
                end
            end
        end
        error("Unable to open libLLVM!")
    end

    return open_libllvm() do hdl
        # Check for llvm::sys::getProcessTriple(), first without cxx11 tag:
        if Libdl.dlsym_e(hdl, "_ZN4llvm3sys16getProcessTripleEv") != C_NULL
            return "cxx03"
        elseif Libdl.dlsym_e(hdl, "_ZN4llvm3sys16getProcessTripleB5cxx11Ev") != C_NULL
            return "cxx11"
        else
            @warn("Unable to find llvm::sys::getProcessTriple() in libLLVM!")
            return nothing
        end
    end
end

"""
    host_triplet()

Build host triplet out of `Sys.MACHINE` and various introspective utilities that
detect compiler ABI values such as `libgfortran_version`, `libstdcxx_version` and
`cxxstring_abi`.  We do this without using any `Platform` tech as it must run before
we have much of that built.
"""
function host_triplet()
    str = Base.BUILD_TRIPLET

    if !occursin("-libgfortran", str)
        libgfortran_version = detect_libgfortran_version()
        if libgfortran_version !== nothing
            str = string(str, "-libgfortran", libgfortran_version.major)
        end
    end

    if !occursin("-cxx", str)
        cxxstring_abi = detect_cxxstring_abi()
        if cxxstring_abi !== nothing
            str = string(str, "-", cxxstring_abi)
        end
    end

    if !occursin("-libstdcxx", str)
        libstdcxx_version = detect_libstdcxx_version()
        if libstdcxx_version !== nothing
            str = string(str, "-libstdcxx", libstdcxx_version.patch)
        end
    end

    # Add on julia_version extended tag
    if !occursin("-julia_version+", str)
        str = string(str, "-julia_version+", VersionNumber(VERSION.major, VERSION.minor, VERSION.patch))
    end
    return str
end

"""
    HostPlatform()

Return the `Platform` object that corresponds to the current host system, with all
relevant comparison strategies set to host platform mode.  This is equivalent to:

    HostPlatform(parse(Platform, Base.BinaryPlatforms.host_triplet()))
"""
function HostPlatform()
    return HostPlatform(parse(Platform, host_triplet()))::Platform
end

"""
    platforms_match(a::AbstractPlatform, b::AbstractPlatform)

Return `true` if `a` and `b` are matching platforms, where matching is determined by
comparing all keys contained within the platform objects, and if both objects contain
entries for that key, they must match.  Comparison, by default, is performed using
the `==` operator, however this can be overridden on a key-by-key basis by adding
"comparison strategies" through `set_compare_strategy!(platform, key, func)`.

Note that as the comparison strategy is set on the `Platform` object, and not globally,
a custom comparison strategy is first looked for within the `a` object, then if none
is found, it is looked for in the `b` object.  Finally, if none is found in either, the
default of `==(ak, bk)` is used.  We throw an error if custom comparison strategies are
used on both `a` and `b` and they are not the same custom comparison.

The reserved tags `os_version` and `libstdcxx_version` use this mechanism to provide
bounded version constraints, where an artifact can specify that it was built using APIs
only available in macOS `v"10.11"` and later, or an artifact can state that it requires
a libstdc++ that is at least `v"3.4.22"`, etc...
"""
function platforms_match(a::AbstractPlatform, b::AbstractPlatform)
    for k in union(keys(tags(a)::Dict{String,String}), keys(tags(b)::Dict{String,String}))
        ak = get(tags(a), k, nothing)
        bk = get(tags(b), k, nothing)

        # Only continue if both `ak` and `bk` are not `nothing`
        if ak === nothing || bk === nothing
            continue
        end

        a_comp = get_compare_strategy(a, k)
        b_comp = get_compare_strategy(b, k)

        # Throw an error if `a` and `b` have both set non-default comparison strategies for `k`
        # and they're not the same strategy.
        if a_comp !== compare_default && b_comp !== compare_default && a_comp !== b_comp
            throw(ArgumentError("Cannot compare Platform objects with two different non-default comparison strategies for the same key \"$(k)\""))
        end

        # Select the custom comparator, if we have one.
        comparator = a_comp
        if b_comp !== compare_default
            comparator = b_comp
        end

        # Call the comparator, passing in which objects requested this comparison (one, the other, or both)
        # For some comparators this doesn't matter, but for non-symmetrical comparisons, it does.
        if !(comparator(ak, bk, a_comp === comparator, b_comp === comparator)::Bool)
            return false
        end
    end
    return true
end

function platforms_match(a::String, b::AbstractPlatform)
    return platforms_match(parse(Platform, a), b)
end
function platforms_match(a::AbstractPlatform, b::String)
    return platforms_match(a, parse(Platform, b))
end
platforms_match(a::String, b::String) = platforms_match(parse(Platform, a), parse(Platform, b))

# Adapters for AbstractString backedge avoidance
platforms_match(a::AbstractString, b::AbstractPlatform) = platforms_match(string(a)::String, b)
platforms_match(a::AbstractPlatform, b::AbstractString) = platforms_match(a, string(b)::String)
platforms_match(a::AbstractString, b::AbstractString) = platforms_match(string(a)::String, string(b)::String)


"""
    select_platform(download_info::Dict, platform::AbstractPlatform = HostPlatform())

Given a `download_info` dictionary mapping platforms to some value, choose
the value whose key best matches `platform`, returning `nothing` if no matches
can be found.

Platform attributes such as architecture, libc, calling ABI, etc... must all
match exactly, however attributes such as compiler ABI can have wildcards
within them such as `nothing` which matches any version of GCC.
"""
function select_platform(download_info::Dict, platform::AbstractPlatform = HostPlatform())
    ps = collect(filter(p -> platforms_match(p, platform), keys(download_info)))

    if isempty(ps)
        return nothing
    end

    # At this point, we may have multiple possibilities.  We now engage a multi-
    # stage selection algorithm, where we first sort the matches by how complete
    # the match is, e.g. preferring matches where the intersection of tags is
    # equal to the union of the tags:
    function match_loss(a, b)
        a_tags = Set(keys(tags(a)))
        b_tags = Set(keys(tags(b)))
        return length(union(a_tags, b_tags)) - length(intersect(a_tags, b_tags))
    end

    # We prefer these better matches, and secondarily reverse-sort by triplet so
    # as to generally choose the latest release (e.g. a `libgfortran5` tarball
    # over a `libgfortran3` tarball).
    sort!(ps, lt = (a, b) -> begin
        loss_a = match_loss(a, platform)
        loss_b = match_loss(b, platform)
        if loss_a != loss_b
            return loss_a < loss_b
        end
        return triplet(a) > triplet(b)
    end)

    # @invokelatest here to not get invalidated by new defs of `==(::Function, ::Function)`
    return @invokelatest getindex(download_info, first(ps))
end

# precompiles to reduce latency (see https://github.com/JuliaLang/julia/pull/43990#issuecomment-1025692379)
Dict{Platform,String}()[HostPlatform()] = ""
Platform("x86_64", "linux", Dict{String,Any}(); validate_strict=true)
Platform("x86_64", "linux", Dict{String,String}(); validate_strict=false)  # called this way from Artifacts.unpack_platform

end # module
L   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/cpuid.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

module CPUID

export cpu_isa

"""
    ISA(features::Set{UInt32})

A structure which represents the Instruction Set Architecture (ISA) of a
computer.  It holds the `Set` of features of the CPU.

The numerical values of the features are automatically generated from the C
source code of Julia and stored in the `features_h.jl` Julia file.
"""
struct ISA
    features::Set{UInt32}
end

Base.:<=(a::ISA, b::ISA) = a.features <= b.features
Base.:<(a::ISA,  b::ISA) = a.features <  b.features
Base.isless(a::ISA,  b::ISA) = a < b

include(string(length(Core.ARGS) >= 2 ? Core.ARGS[2] : "", "features_h.jl"))  # include($BUILDROOT/base/features_h.jl)

# Keep in sync with `arch_march_isa_mapping`.
const ISAs_by_family = Dict(
    "i686" => [
        # Source: https://gcc.gnu.org/onlinedocs/gcc/x86-Options.html.
        # Implicit in all sets, because always required by Julia: mmx, sse, sse2
        "pentium4" => ISA(Set{UInt32}()),
        "prescott" => ISA(Set((JL_X86_sse3,))),
    ],
    "x86_64" => [
        # Source: https://gcc.gnu.org/onlinedocs/gcc/x86-Options.html.
        # Implicit in all sets, because always required by x86-64 architecture: mmx, sse, sse2
        "x86_64" => ISA(Set{UInt32}()),
        "core2" => ISA(Set((JL_X86_sse3, JL_X86_ssse3))),
        "nehalem" => ISA(Set((JL_X86_sse3, JL_X86_ssse3, JL_X86_sse41, JL_X86_sse42, JL_X86_popcnt))),
        "sandybridge" => ISA(Set((JL_X86_sse3, JL_X86_ssse3, JL_X86_sse41, JL_X86_sse42, JL_X86_popcnt, JL_X86_avx, JL_X86_aes, JL_X86_pclmul))),
        "haswell" => ISA(Set((JL_X86_movbe, JL_X86_sse3, JL_X86_ssse3, JL_X86_sse41, JL_X86_sse42, JL_X86_popcnt, JL_X86_avx, JL_X86_avx2, JL_X86_aes, JL_X86_pclmul, JL_X86_fsgsbase, JL_X86_rdrnd, JL_X86_fma, JL_X86_bmi, JL_X86_bmi2, JL_X86_f16c))),
        "skylake" => ISA(Set((JL_X86_movbe, JL_X86_sse3, JL_X86_ssse3, JL_X86_sse41, JL_X86_sse42, JL_X86_popcnt, JL_X86_avx, JL_X86_avx2, JL_X86_aes, JL_X86_pclmul, JL_X86_fsgsbase, JL_X86_rdrnd, JL_X86_fma, JL_X86_bmi, JL_X86_bmi2, JL_X86_f16c, JL_X86_rdseed, JL_X86_adx, JL_X86_prfchw, JL_X86_clflushopt, JL_X86_xsavec, JL_X86_xsaves))),
        "skylake_avx512" => ISA(Set((JL_X86_movbe, JL_X86_sse3, JL_X86_ssse3, JL_X86_sse41, JL_X86_sse42, JL_X86_popcnt, JL_X86_pku, JL_X86_avx, JL_X86_avx2, JL_X86_aes, JL_X86_pclmul, JL_X86_fsgsbase, JL_X86_rdrnd, JL_X86_fma, JL_X86_bmi, JL_X86_bmi2, JL_X86_f16c, JL_X86_rdseed, JL_X86_adx, JL_X86_prfchw, JL_X86_clflushopt, JL_X86_xsavec, JL_X86_xsaves, JL_X86_avx512f, JL_X86_clwb, JL_X86_avx512vl, JL_X86_avx512bw, JL_X86_avx512dq, JL_X86_avx512cd))),
    ],
    "armv6l" => [
        # The only armv6l processor we know of that runs Julia on armv6l
        # We don't have a good way to tell the different armv6l variants apart through features,
        # and honestly we don't care much since it's basically this one chip that people want to use with Julia.
        "arm1176jzfs" => ISA(Set{UInt32}()),
    ],
    "armv7l" => [
        "armv7l" => ISA(Set{UInt32}()),
        "armv7l+neon" => ISA(Set((JL_AArch32_neon,))),
        "armv7l+neon+vfpv4" => ISA(Set((JL_AArch32_neon, JL_AArch32_vfp4))),
    ],
    "aarch64" => [
        # Implicit in all sets, because always required: fp, asimd
        "armv8.0-a" => ISA(Set{UInt32}()),
        "armv8.1-a" => ISA(Set((JL_AArch64_v8_1a, JL_AArch64_lse, JL_AArch64_crc, JL_AArch64_rdm))),
        "armv8.2-a+crypto" => ISA(Set((JL_AArch64_v8_2a, JL_AArch64_lse, JL_AArch64_crc, JL_AArch64_rdm, JL_AArch64_aes, JL_AArch64_sha2))),
        "a64fx" => ISA(Set((JL_AArch64_v8_2a, JL_AArch64_lse, JL_AArch64_crc, JL_AArch64_rdm, JL_AArch64_sha2, JL_AArch64_ccpp, JL_AArch64_complxnum, JL_AArch64_fullfp16, JL_AArch64_sve))),
        "apple_m1" => ISA(Set((JL_AArch64_v8_5a, JL_AArch64_lse, JL_AArch64_crc, JL_AArch64_rdm, JL_AArch64_aes, JL_AArch64_sha2, JL_AArch64_sha3, JL_AArch64_ccpp, JL_AArch64_complxnum, JL_AArch64_fp16fml, JL_AArch64_fullfp16, JL_AArch64_dotprod, JL_AArch64_rcpc, JL_AArch64_altnzcv))),
    ],
    "powerpc64le" => [
        # We have no way to test powerpc64le features yet, so we're only going to declare the lowest ISA:
        "power8" => ISA(Set{UInt32}()),
    ]
)

# Test a CPU feature exists on the currently-running host
test_cpu_feature(feature::UInt32) = ccall(:jl_test_cpu_feature, Bool, (UInt32,), feature)

# Normalize some variation in ARCH values (which typically come from `uname -m`)
function normalize_arch(arch::String)
    arch = lowercase(arch)
    if arch ∈ ("amd64",)
        arch = "x86_64"
    elseif arch ∈ ("i386", "i486", "i586")
        arch = "i686"
    elseif arch ∈ ("armv6",)
        arch = "armv6l"
    elseif arch ∈ ("arm", "armv7", "armv8", "armv8l")
        arch = "armv7l"
    elseif arch ∈ ("arm64",)
        arch = "aarch64"
    elseif arch ∈ ("ppc64le",)
        arch = "powerpc64le"
    end
    return arch
end

let
    # Collect all relevant features for the current architecture, if any.
    FEATURES = UInt32[]
    arch = normalize_arch(String(Sys.ARCH))
    if arch in keys(ISAs_by_family)
        for isa in ISAs_by_family[arch]
            unique!(append!(FEATURES, last(isa).features))
        end
    end

    # Use `@eval` to inline the list of features.
    @eval function cpu_isa()
        return ISA(Set{UInt32}(feat for feat in $(FEATURES) if test_cpu_feature(feat)))
    end
end

"""
    cpu_isa()

Return the [`ISA`](@ref) (instruction set architecture) of the current CPU.
"""
cpu_isa

end # module CPUID
Q   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/features_h.jl�      # X86 features
const JL_X86_sse3 = UInt32(0)
const JL_X86_pclmul = UInt32(1)
const JL_X86_ssse3 = UInt32(9)
const JL_X86_fma = UInt32(12)
const JL_X86_cx16 = UInt32(13)
const JL_X86_sse41 = UInt32(19)
const JL_X86_sse42 = UInt32(20)
const JL_X86_movbe = UInt32(22)
const JL_X86_popcnt = UInt32(23)
const JL_X86_aes = UInt32(25)
const JL_X86_xsave = UInt32(26)
const JL_X86_avx = UInt32(28)
const JL_X86_f16c = UInt32(29)
const JL_X86_rdrnd = UInt32(30)
const JL_X86_fsgsbase = UInt32(32 * 2 + 0)
const JL_X86_bmi = UInt32(32 * 2 + 3)
const JL_X86_avx2 = UInt32(32 * 2 + 5)
const JL_X86_bmi2 = UInt32(32 * 2 + 8)
const JL_X86_rtm = UInt32(32 * 2 + 11)
const JL_X86_avx512f = UInt32(32 * 2 + 16)
const JL_X86_avx512dq = UInt32(32 * 2 + 17)
const JL_X86_rdseed = UInt32(32 * 2 + 18)
const JL_X86_adx = UInt32(32 * 2 + 19)
const JL_X86_avx512ifma = UInt32(32 * 2 + 21)
const JL_X86_clflushopt = UInt32(32 * 2 + 23)
const JL_X86_clwb = UInt32(32 * 2 + 24)
const JL_X86_avx512pf = UInt32(32 * 2 + 26)
const JL_X86_avx512er = UInt32(32 * 2 + 27)
const JL_X86_avx512cd = UInt32(32 * 2 + 28)
const JL_X86_sha = UInt32(32 * 2 + 29)
const JL_X86_avx512bw = UInt32(32 * 2 + 30)
const JL_X86_avx512vl = UInt32(32 * 2 + 31)
const JL_X86_prefetchwt1 = UInt32(32 * 3 + 0)
const JL_X86_avx512vbmi = UInt32(32 * 3 + 1)
const JL_X86_pku = UInt32(32 * 3 + 4)
const JL_X86_waitpkg = UInt32(32 * 3 + 5)
const JL_X86_avx512vbmi2 = UInt32(32 * 3 + 6)
const JL_X86_shstk = UInt32(32 * 3 + 7)
const JL_X86_gfni = UInt32(32 * 3 + 8)
const JL_X86_vaes = UInt32(32 * 3 + 9)
const JL_X86_vpclmulqdq = UInt32(32 * 3 + 10)
const JL_X86_avx512vnni = UInt32(32 * 3 + 11)
const JL_X86_avx512bitalg = UInt32(32 * 3 + 12)
const JL_X86_avx512vpopcntdq = UInt32(32 * 3 + 14)
const JL_X86_rdpid = UInt32(32 * 3 + 22)
const JL_X86_cldemote = UInt32(32 * 3 + 25)
const JL_X86_movdiri = UInt32(32 * 3 + 27)
const JL_X86_movdir64b = UInt32(32 * 3 + 28)
const JL_X86_enqcmd = UInt32(32 * 3 + 29)
const JL_X86_uintr = UInt32(32 * 4 + 5)
const JL_X86_avx512vp2intersect = UInt32(32 * 4 + 8)
const JL_X86_serialize = UInt32(32 * 4 + 14)
const JL_X86_tsxldtrk = UInt32(32 * 4 + 16)
const JL_X86_pconfig = UInt32(32 * 4 + 18)
const JL_X86_amx_bf16 = UInt32(32 * 4 + 22)
const JL_X86_avx512fp16 = UInt32(32 * 4 + 23)
const JL_X86_amx_tile = UInt32(32 * 4 + 24)
const JL_X86_amx_int8 = UInt32(32 * 4 + 25)
const JL_X86_sahf = UInt32(32 * 5 + 0)
const JL_X86_lzcnt = UInt32(32 * 5 + 5)
const JL_X86_sse4a = UInt32(32 * 5 + 6)
const JL_X86_prfchw = UInt32(32 * 5 + 8)
const JL_X86_xop = UInt32(32 * 5 + 11)
const JL_X86_fma4 = UInt32(32 * 5 + 16)
const JL_X86_tbm = UInt32(32 * 5 + 21)
const JL_X86_mwaitx = UInt32(32 * 5 + 29)
const JL_X86_xsaveopt = UInt32(32 * 7 + 0)
const JL_X86_xsavec = UInt32(32 * 7 + 1)
const JL_X86_xsaves = UInt32(32 * 7 + 3)
const JL_X86_clzero = UInt32(32 * 8 + 0)
const JL_X86_wbnoinvd = UInt32(32 * 8 + 9)
const JL_X86_avxvnni = UInt32(32 * 9 + 4)
const JL_X86_avx512bf16 = UInt32(32 * 9 + 5)
const JL_X86_ptwrite = UInt32(32 * 10 + 4)

# AArch32 features
const JL_AArch32_neon = UInt32(12)
const JL_AArch32_vfp3 = UInt32(13)
const JL_AArch32_vfp4 = UInt32(16)
const JL_AArch32_hwdiv_arm = UInt32(17)
const JL_AArch32_hwdiv = UInt32(18)
const JL_AArch32_d32 = UInt32(19)
const JL_AArch32_crypto = UInt32(32 + 0)
const JL_AArch32_crc = UInt32(32 + 4)
const JL_AArch32_aclass = UInt32(32 * 2 + 0)
const JL_AArch32_rclass = UInt32(32 * 2 + 1)
const JL_AArch32_mclass = UInt32(32 * 2 + 2)
const JL_AArch32_v7 = UInt32(32 * 2 + 3)
const JL_AArch32_v8 = UInt32(32 * 2 + 4)
const JL_AArch32_v8_1a = UInt32(32 * 2 + 5)
const JL_AArch32_v8_2a = UInt32(32 * 2 + 6)
const JL_AArch32_v8_3a = UInt32(32 * 2 + 7)
const JL_AArch32_v8_m_main = UInt32(32 * 2 + 8)
const JL_AArch32_v8_4a = UInt32(32 * 2 + 9)
const JL_AArch32_v8_5a = UInt32(32 * 2 + 10)
const JL_AArch32_v8_6a = UInt32(32 * 2 + 11)

# AArch64 features
const JL_AArch64_aes = UInt32(4)
const JL_AArch64_sha2 = UInt32(6)
const JL_AArch64_crc = UInt32(7)
const JL_AArch64_lse = UInt32(8)
const JL_AArch64_fullfp16 = UInt32(9)
const JL_AArch64_rdm = UInt32(12)
const JL_AArch64_jsconv = UInt32(13)
const JL_AArch64_complxnum = UInt32(14)
const JL_AArch64_rcpc = UInt32(15)
const JL_AArch64_ccpp = UInt32(16)
const JL_AArch64_sha3 = UInt32(17)
const JL_AArch64_sm4 = UInt32(19)
const JL_AArch64_dotprod = UInt32(20)
const JL_AArch64_sve = UInt32(22)
const JL_AArch64_fp16fml = UInt32(23)
const JL_AArch64_dit = UInt32(24)
const JL_AArch64_rcpc_immo = UInt32(26)
const JL_AArch64_flagm = UInt32(27)
const JL_AArch64_ssbs = UInt32(28)
const JL_AArch64_sb = UInt32(29)
const JL_AArch64_pauth = UInt32(30)
const JL_AArch64_ccdp = UInt32(32 + 0)
const JL_AArch64_sve2 = UInt32(32 + 1)
const JL_AArch64_sve2_aes = UInt32(32 + 3)
const JL_AArch64_sve2_bitperm = UInt32(32 + 4)
const JL_AArch64_sve2_sha3 = UInt32(32 + 5)
const JL_AArch64_sve2_sm4 = UInt32(32 + 6)
const JL_AArch64_altnzcv = UInt32(32 + 7)
const JL_AArch64_fptoint = UInt32(32 + 8)
const JL_AArch64_f32mm = UInt32(32 + 10)
const JL_AArch64_f64mm = UInt32(32 + 11)
const JL_AArch64_i8mm = UInt32(32 + 13)
const JL_AArch64_bf16 = UInt32(32 + 14)
const JL_AArch64_rand = UInt32(32 + 16)
const JL_AArch64_bti = UInt32(32 + 17)
const JL_AArch64_mte = UInt32(32 + 18)
const JL_AArch64_v8_1a = UInt32(32 * 2 + 0)
const JL_AArch64_v8_2a = UInt32(32 * 2 + 1)
const JL_AArch64_v8_3a = UInt32(32 * 2 + 2)
const JL_AArch64_v8_4a = UInt32(32 * 2 + 3)
const JL_AArch64_v8_5a = UInt32(32 * 2 + 4)
const JL_AArch64_v8_6a = UInt32(32 * 2 + 5)

O   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/fastmath.jl8      # This file is a part of Julia. License is MIT: https://julialang.org/license

# Support for @fastmath

# This module provides versions of math functions that may violate
# strict IEEE semantics.

# This allows the following transformations. For more information see
# http://llvm.org/docs/LangRef.html#fast-math-flags:
# nnan: No NaNs - Allow optimizations to assume the arguments and
#       result are not NaN. Such optimizations are required to retain
#       defined behavior over NaNs, but the value of the result is
#       undefined.
# ninf: No Infs - Allow optimizations to assume the arguments and
#       result are not +/-Inf. Such optimizations are required to
#       retain defined behavior over +/-Inf, but the value of the
#       result is undefined.
# nsz:  No Signed Zeros - Allow optimizations to treat the sign of a
#       zero argument or result as insignificant.
# arcp: Allow Reciprocal - Allow optimizations to use the reciprocal
#       of an argument rather than perform division.
# fast: Fast - Allow algebraically equivalent transformations that may
#       dramatically change results in floating point (e.g.
#       reassociate). This flag implies all the others.

module FastMath

export @fastmath

import Core.Intrinsics: sqrt_llvm_fast, neg_float_fast,
    add_float_fast, sub_float_fast, mul_float_fast, div_float_fast,
    eq_float_fast, ne_float_fast, lt_float_fast, le_float_fast

const fast_op =
    Dict(# basic arithmetic
         :+ => :add_fast,
         :- => :sub_fast,
         :* => :mul_fast,
         :/ => :div_fast,
         :(==) => :eq_fast,
         :!= => :ne_fast,
         :< => :lt_fast,
         :<= => :le_fast,
         :> => :gt_fast,
         :>= => :ge_fast,
         :abs => :abs_fast,
         :abs2 => :abs2_fast,
         :cmp => :cmp_fast,
         :conj => :conj_fast,
         :inv => :inv_fast,
         :rem => :rem_fast,
         :sign => :sign_fast,
         :isfinite => :isfinite_fast,
         :isinf => :isinf_fast,
         :isnan => :isnan_fast,
         :issubnormal => :issubnormal_fast,
         # math functions
         :^ => :pow_fast,
         :acos => :acos_fast,
         :acosh => :acosh_fast,
         :angle => :angle_fast,
         :asin => :asin_fast,
         :asinh => :asinh_fast,
         :atan => :atan_fast,
         :atanh => :atanh_fast,
         :cbrt => :cbrt_fast,
         :cis => :cis_fast,
         :cos => :cos_fast,
         :cosh => :cosh_fast,
         :exp10 => :exp10_fast,
         :exp2 => :exp2_fast,
         :exp => :exp_fast,
         :expm1 => :expm1_fast,
         :hypot => :hypot_fast,
         :log10 => :log10_fast,
         :log1p => :log1p_fast,
         :log2 => :log2_fast,
         :log => :log_fast,
         :max => :max_fast,
         :min => :min_fast,
         :minmax => :minmax_fast,
         :sin => :sin_fast,
         :sincos => :sincos_fast,
         :sinh => :sinh_fast,
         :sqrt => :sqrt_fast,
         :tan => :tan_fast,
         :tanh => :tanh_fast,
         # reductions
         :maximum => :maximum_fast,
         :minimum => :minimum_fast,
         :maximum! => :maximum!_fast,
         :minimum! => :minimum!_fast)

const rewrite_op =
    Dict(:+= => :+,
         :-= => :-,
         :*= => :*,
         :/= => :/,
         :^= => :^)

function make_fastmath(expr::Expr)
    if expr.head === :quote
        return expr
    elseif expr.head === :call && expr.args[1] === :^ && expr.args[3] isa Integer
        # mimic Julia's literal_pow lowering of literal integer powers
        return Expr(:call, :(Base.FastMath.pow_fast), make_fastmath(expr.args[2]), Val{expr.args[3]}())
    end
    op = get(rewrite_op, expr.head, :nothing)
    if op !== :nothing
        var = expr.args[1]
        rhs = expr.args[2]
        if isa(var, Symbol)
            # simple assignment
            expr = :($var = $op($var, $rhs))
        end
        # It is hard to optimize array[i += 1] += 1
        # and array[end] += 1 without bugs. (#47241)
        # We settle for not optimizing the op= call.
    end
    Base.exprarray(make_fastmath(expr.head), Base.mapany(make_fastmath, expr.args))
end
function make_fastmath(symb::Symbol)
    fast_symb = get(fast_op, symb, :nothing)
    if fast_symb === :nothing
        return symb
    end
    :(Base.FastMath.$fast_symb)
end
make_fastmath(expr) = expr

"""
    @fastmath expr

Execute a transformed version of the expression, which calls functions that
may violate strict IEEE semantics. This allows the fastest possible operation,
but results are undefined -- be careful when doing this, as it may change numerical
results.

This sets the [LLVM Fast-Math flags](http://llvm.org/docs/LangRef.html#fast-math-flags),
and corresponds to the `-ffast-math` option in clang. See [the notes on performance
annotations](@ref man-performance-annotations) for more details.

# Examples
```jldoctest
julia> @fastmath 1+2
3

julia> @fastmath(sin(3))
0.1411200080598672
```
"""
macro fastmath(expr)
    make_fastmath(esc(expr))
end


# Basic arithmetic

const FloatTypes = Union{Float16,Float32,Float64}

sub_fast(x::FloatTypes) = neg_float_fast(x)

add_fast(x::T, y::T) where {T<:FloatTypes} = add_float_fast(x, y)
sub_fast(x::T, y::T) where {T<:FloatTypes} = sub_float_fast(x, y)
mul_fast(x::T, y::T) where {T<:FloatTypes} = mul_float_fast(x, y)
div_fast(x::T, y::T) where {T<:FloatTypes} = div_float_fast(x, y)

add_fast(x::T, y::T, zs::T...) where {T<:FloatTypes} =
    add_fast(add_fast(x, y), zs...)
mul_fast(x::T, y::T, zs::T...) where {T<:FloatTypes} =
    mul_fast(mul_fast(x, y), zs...)

@fastmath begin
    cmp_fast(x::T, y::T) where {T<:FloatTypes} = ifelse(x==y, 0, ifelse(x<y, -1, +1))
    log_fast(b::T, x::T) where {T<:FloatTypes} = log_fast(x)/log_fast(b)
end

eq_fast(x::T, y::T) where {T<:FloatTypes} = eq_float_fast(x, y)
ne_fast(x::T, y::T) where {T<:FloatTypes} = ne_float_fast(x, y)
lt_fast(x::T, y::T) where {T<:FloatTypes} = lt_float_fast(x, y)
le_fast(x::T, y::T) where {T<:FloatTypes} = le_float_fast(x, y)
gt_fast(x, y) = lt_fast(y, x)
ge_fast(x, y) = le_fast(y, x)

isinf_fast(x) = false
isfinite_fast(x) = true
isnan_fast(x) = false
issubnormal_fast(x) = false

# complex numbers

ComplexTypes = Union{ComplexF32, ComplexF64}

@fastmath begin
    abs_fast(x::ComplexTypes) = hypot(real(x), imag(x))
    abs2_fast(x::ComplexTypes) = real(x)*real(x) + imag(x)*imag(x)
    conj_fast(x::T) where {T<:ComplexTypes} = T(real(x), -imag(x))
    inv_fast(x::ComplexTypes) = conj(x) / abs2(x)
    sign_fast(x::ComplexTypes) = x == 0 ? float(zero(x)) : x/abs(x)

    add_fast(x::T, y::T) where {T<:ComplexTypes} =
        T(real(x)+real(y), imag(x)+imag(y))
    add_fast(x::Complex{T}, b::T) where {T<:FloatTypes} =
        Complex{T}(real(x)+b, imag(x))
    add_fast(a::T, y::Complex{T}) where {T<:FloatTypes} =
        Complex{T}(a+real(y), imag(y))

    sub_fast(x::T, y::T) where {T<:ComplexTypes} =
        T(real(x)-real(y), imag(x)-imag(y))
    sub_fast(x::Complex{T}, b::T) where {T<:FloatTypes} =
        Complex{T}(real(x)-b, imag(x))
    sub_fast(a::T, y::Complex{T}) where {T<:FloatTypes} =
        Complex{T}(a-real(y), -imag(y))

    mul_fast(x::T, y::T) where {T<:ComplexTypes} =
        T(real(x)*real(y) - imag(x)*imag(y),
          real(x)*imag(y) + imag(x)*real(y))
    mul_fast(x::Complex{T}, b::T) where {T<:FloatTypes} =
        Complex{T}(real(x)*b, imag(x)*b)
    mul_fast(a::T, y::Complex{T}) where {T<:FloatTypes} =
        Complex{T}(a*real(y), a*imag(y))

    @inline div_fast(x::T, y::T) where {T<:ComplexTypes} =
        T(real(x)*real(y) + imag(x)*imag(y),
          imag(x)*real(y) - real(x)*imag(y)) / abs2(y)
    div_fast(x::Complex{T}, b::T) where {T<:FloatTypes} =
        Complex{T}(real(x)/b, imag(x)/b)
    div_fast(a::T, y::Complex{T}) where {T<:FloatTypes} =
        Complex{T}(a*real(y), -a*imag(y)) / abs2(y)

    eq_fast(x::T, y::T) where {T<:ComplexTypes} =
        (real(x)==real(y)) & (imag(x)==imag(y))
    eq_fast(x::Complex{T}, b::T) where {T<:FloatTypes} =
        (real(x)==b) & (imag(x)==T(0))
    eq_fast(a::T, y::Complex{T}) where {T<:FloatTypes} =
        (a==real(y)) & (T(0)==imag(y))

    ne_fast(x::T, y::T) where {T<:ComplexTypes} = !(x==y)

    # Note: we use the same comparison for min, max, and minmax, so
    # that the compiler can convert between them
    max_fast(x::T, y::T) where {T<:FloatTypes} = ifelse(y > x, y, x)
    min_fast(x::T, y::T) where {T<:FloatTypes} = ifelse(y > x, x, y)
    minmax_fast(x::T, y::T) where {T<:FloatTypes} = ifelse(y > x, (x,y), (y,x))

    max_fast(x::T, y::T, z::T...) where {T<:FloatTypes} = max_fast(max_fast(x, y), z...)
    min_fast(x::T, y::T, z::T...) where {T<:FloatTypes} = min_fast(min_fast(x, y), z...)
end

# fall-back implementations and type promotion

for op in (:abs, :abs2, :conj, :inv, :sign)
    op_fast = fast_op[op]
    @eval begin
        # fall-back implementation for non-numeric types
        $op_fast(xs...) = $op(xs...)
    end
end

for op in (:+, :-, :*, :/, :(==), :!=, :<, :<=, :cmp, :rem, :min, :max, :minmax)
    op_fast = fast_op[op]
    @eval begin
        # fall-back implementation for non-numeric types
        $op_fast(xs...) = $op(xs...)
        # type promotion
        $op_fast(x::Number, y::Number, zs::Number...) =
            $op_fast(promote(x,y,zs...)...)
        # fall-back implementation that applies after promotion
        $op_fast(x::T,ys::T...) where {T<:Number} = $op(x,ys...)
    end
end


# Math functions
exp2_fast(x::Union{Float32,Float64})  = Base.Math.exp2_fast(x)
exp_fast(x::Union{Float32,Float64})   = Base.Math.exp_fast(x)
exp10_fast(x::Union{Float32,Float64}) = Base.Math.exp10_fast(x)

# builtins

pow_fast(x::Float32, y::Integer) = ccall("llvm.powi.f32.i32", llvmcall, Float32, (Float32, Int32), x, y)
pow_fast(x::Float64, y::Integer) = ccall("llvm.powi.f64.i32", llvmcall, Float64, (Float64, Int32), x, y)
pow_fast(x::FloatTypes, ::Val{p}) where {p} = pow_fast(x, p) # inlines already via llvm.powi
@inline pow_fast(x, v::Val) = Base.literal_pow(^, x, v)

sqrt_fast(x::FloatTypes) = sqrt_llvm_fast(x)
sincos_fast(v::FloatTypes) = sincos(v)

@inline function sincos_fast(v::Float16)
    s, c = sincos_fast(Float32(v))
    return Float16(s), Float16(c)
end
sincos_fast(v::AbstractFloat) = (sin_fast(v), cos_fast(v))
sincos_fast(v::Real) = sincos_fast(float(v)::AbstractFloat)
sincos_fast(v) = (sin_fast(v), cos_fast(v))


function rem_fast(x::T, y::T) where {T<:FloatTypes}
    return @fastmath copysign(Base.rem_internal(abs(x), abs(y)), x)
end

@fastmath begin
    hypot_fast(x::T, y::T) where {T<:FloatTypes} = sqrt(x*x + y*y)

    # complex numbers

    function cis_fast(x::T) where {T<:FloatTypes}
        s, c = sincos_fast(x)
        Complex{T}(c, s)
    end

    # See <http://en.cppreference.com/w/cpp/numeric/complex>
    pow_fast(x::T, y::T) where {T<:ComplexTypes} = exp(y*log(x))
    pow_fast(x::T, y::Complex{T}) where {T<:FloatTypes} = exp(y*log(x))
    pow_fast(x::Complex{T}, y::T) where {T<:FloatTypes} = exp(y*log(x))
    acos_fast(x::T) where {T<:ComplexTypes} =
        convert(T,π)/2 + im*log(im*x + sqrt(1-x*x))
    acosh_fast(x::ComplexTypes) = log(x + sqrt(x+1) * sqrt(x-1))
    angle_fast(x::ComplexTypes) = atan(imag(x), real(x))
    asin_fast(x::ComplexTypes) = -im*asinh(im*x)
    asinh_fast(x::ComplexTypes) = log(x + sqrt(1+x*x))
    atan_fast(x::ComplexTypes) = -im*atanh(im*x)
    atanh_fast(x::T) where {T<:ComplexTypes} = convert(T,1)/2*(log(1+x) - log(1-x))
    cis_fast(x::ComplexTypes) = exp(-imag(x)) * cis(real(x))
    cos_fast(x::ComplexTypes) = cosh(im*x)
    cosh_fast(x::T) where {T<:ComplexTypes} = convert(T,1)/2*(exp(x) + exp(-x))
    exp10_fast(x::T) where {T<:ComplexTypes} =
        exp10(real(x)) * cis(imag(x)*log(convert(T,10)))
    exp2_fast(x::T) where {T<:ComplexTypes} =
        exp2(real(x)) * cis(imag(x)*log(convert(T,2)))
    exp_fast(x::ComplexTypes) = exp(real(x)) * cis(imag(x))
    expm1_fast(x::ComplexTypes) = exp(x)-1
    log10_fast(x::T) where {T<:ComplexTypes} = log(x) / log(convert(T,10))
    log1p_fast(x::ComplexTypes) = log(1+x)
    log2_fast(x::T) where {T<:ComplexTypes} = log(x) / log(convert(T,2))
    log_fast(x::T) where {T<:ComplexTypes} = T(log(abs2(x))/2, angle(x))
    log_fast(b::T, x::T) where {T<:ComplexTypes} = T(log(x)/log(b))
    sin_fast(x::ComplexTypes) = -im*sinh(im*x)
    sinh_fast(x::T) where {T<:ComplexTypes} = convert(T,1)/2*(exp(x) - exp(-x))
    sqrt_fast(x::ComplexTypes) = sqrt(abs(x)) * cis(angle(x)/2)
    tan_fast(x::ComplexTypes) = -im*tanh(im*x)
    tanh_fast(x::ComplexTypes) = (a=exp(x); b=exp(-x); (a-b)/(a+b))
end

# fall-back implementations and type promotion

for f in (:acos, :acosh, :angle, :asin, :asinh, :atan, :atanh, :cbrt,
          :cis, :cos, :cosh, :exp10, :exp2, :exp, :expm1,
          :log10, :log1p, :log2, :log, :sin, :sinh, :sqrt, :tan,
          :tanh)
    f_fast = fast_op[f]
    @eval begin
        $f_fast(x) = $f(x)
    end
end

for f in (:^, :atan, :hypot, :log)
    f_fast = fast_op[f]
    @eval begin
        # fall-back implementation for non-numeric types
        $f_fast(x, y) = $f(x, y)
        # type promotion
        $f_fast(x::Number, y::Number) = $f_fast(promote(x, y)...)
        # fall-back implementation that applies after promotion
        $f_fast(x::T, y::T) where {T<:Number} = $f(x, y)
    end
end

# Reductions

maximum_fast(a; kw...) = Base.reduce(max_fast, a; kw...)
minimum_fast(a; kw...) = Base.reduce(min_fast, a; kw...)

maximum_fast(f, a; kw...) = Base.mapreduce(f, max_fast, a; kw...)
minimum_fast(f, a; kw...) = Base.mapreduce(f, min_fast, a; kw...)

Base.reducedim_init(f, ::typeof(max_fast), A::AbstractArray, region) =
    Base.reducedim_init(f, max, A::AbstractArray, region)
Base.reducedim_init(f, ::typeof(min_fast), A::AbstractArray, region) =
    Base.reducedim_init(f, min, A::AbstractArray, region)

maximum!_fast(r::AbstractArray, A::AbstractArray; kw...) =
    maximum!_fast(identity, r, A; kw...)
minimum!_fast(r::AbstractArray, A::AbstractArray; kw...) =
    minimum!_fast(identity, r, A; kw...)

maximum!_fast(f::Function, r::AbstractArray, A::AbstractArray; init::Bool=true) =
    Base.mapreducedim!(f, max_fast, Base.initarray!(r, f, max, init, A), A)
minimum!_fast(f::Function, r::AbstractArray, A::AbstractArray; init::Bool=true) =
    Base.mapreducedim!(f, min_fast, Base.initarray!(r, f, min, init, A), A)

end
L   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/Enums.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

module Enums

import Core.Intrinsics.bitcast
export Enum, @enum

function namemap end

"""
    Enum{T<:Integer}

The abstract supertype of all enumerated types defined with [`@enum`](@ref).
"""
abstract type Enum{T<:Integer} end

basetype(::Type{<:Enum{T}}) where {T<:Integer} = T

(::Type{T})(x::Enum{T2}) where {T<:Integer,T2<:Integer} = T(bitcast(T2, x))::T
Base.cconvert(::Type{T}, x::Enum{T2}) where {T<:Integer,T2<:Integer} = T(x)::T
Base.write(io::IO, x::Enum{T}) where {T<:Integer} = write(io, T(x))
Base.read(io::IO, ::Type{T}) where {T<:Enum} = T(read(io, basetype(T)))

"""
    _enum_hash(x::Enum, h::UInt)

Compute hash for an enum value `x`. This internal method will be specialized
for every enum type created through [`@enum`](@ref).
"""
_enum_hash(x::Enum, h::UInt) = invoke(hash, Tuple{Any, UInt}, x, h)
Base.hash(x::Enum, h::UInt) = _enum_hash(x, h)
Base.isless(x::T, y::T) where {T<:Enum} = isless(basetype(T)(x), basetype(T)(y))

Base.Symbol(x::Enum) = namemap(typeof(x))[Integer(x)]::Symbol

function _symbol(x::Enum)
    names = namemap(typeof(x))
    x = Integer(x)
    get(() -> Symbol("<invalid #$x>"), names, x)::Symbol
end

Base.print(io::IO, x::Enum) = print(io, _symbol(x))

function Base.show(io::IO, x::Enum)
    sym = _symbol(x)
    if !(get(io, :compact, false)::Bool)
        from = get(io, :module, Base.active_module())
        def = parentmodule(typeof(x))
        if from === nothing || !Base.isvisible(sym, def, from)
            show(io, def)
            print(io, ".")
        end
    end
    print(io, sym)
end

function Base.show(io::IO, ::MIME"text/plain", x::Enum)
    print(io, x, "::")
    show(IOContext(io, :compact => true), typeof(x))
    print(io, " = ")
    show(io, Integer(x))
end

function Base.show(io::IO, m::MIME"text/plain", t::Type{<:Enum})
    if isconcretetype(t)
        print(io, "Enum ")
        Base.show_datatype(io, t)
        print(io, ":")
        for x in instances(t)
            print(io, "\n", Symbol(x), " = ")
            show(io, Integer(x))
        end
    else
        invoke(show, Tuple{IO, MIME"text/plain", Type}, io, m, t)
    end
end

# generate code to test whether expr is in the given set of values
function membershiptest(expr, values)
    lo, hi = extrema(values)
    if length(values) == hi - lo + 1
        :($lo <= $expr <= $hi)
    elseif length(values) < 20
        foldl((x1,x2)->:($x1 || ($expr == $x2)), values[2:end]; init=:($expr == $(values[1])))
    else
        :($expr in $(Set(values)))
    end
end

# give Enum types scalar behavior in broadcasting
Base.broadcastable(x::Enum) = Ref(x)

@noinline enum_argument_error(typename, x) = throw(ArgumentError(string("invalid value for Enum $(typename): $x")))

"""
    @enum EnumName[::BaseType] value1[=x] value2[=y]

Create an `Enum{BaseType}` subtype with name `EnumName` and enum member values of
`value1` and `value2` with optional assigned values of `x` and `y`, respectively.
`EnumName` can be used just like other types and enum member values as regular values, such as

# Examples
```jldoctest fruitenum
julia> @enum Fruit apple=1 orange=2 kiwi=3

julia> f(x::Fruit) = "I'm a Fruit with value: \$(Int(x))"
f (generic function with 1 method)

julia> f(apple)
"I'm a Fruit with value: 1"

julia> Fruit(1)
apple::Fruit = 1
```

Values can also be specified inside a `begin` block, e.g.

```julia
@enum EnumName begin
    value1
    value2
end
```

`BaseType`, which defaults to [`Int32`](@ref), must be a primitive subtype of `Integer`.
Member values can be converted between the enum type and `BaseType`. `read` and `write`
perform these conversions automatically. In case the enum is created with a non-default
`BaseType`, `Integer(value1)` will return the integer `value1` with the type `BaseType`.

To list all the instances of an enum use `instances`, e.g.

```jldoctest fruitenum
julia> instances(Fruit)
(apple, orange, kiwi)
```

It is possible to construct a symbol from an enum instance:

```jldoctest fruitenum
julia> Symbol(apple)
:apple
```
"""
macro enum(T::Union{Symbol,Expr}, syms...)
    if isempty(syms)
        throw(ArgumentError("no arguments given for Enum $T"))
    end
    basetype = Int32
    typename = T
    if isa(T, Expr) && T.head === :(::) && length(T.args) == 2 && isa(T.args[1], Symbol)
        typename = T.args[1]
        basetype = Core.eval(__module__, T.args[2])
        if !isa(basetype, DataType) || !(basetype <: Integer) || !isbitstype(basetype)
            throw(ArgumentError("invalid base type for Enum $typename, $T=::$basetype; base type must be an integer primitive type"))
        end
    elseif !isa(T, Symbol)
        throw(ArgumentError("invalid type expression for enum $T"))
    end
    values = Vector{basetype}()
    seen = Set{Symbol}()
    namemap = Dict{basetype,Symbol}()
    lo = hi = i = zero(basetype)
    hasexpr = false

    if length(syms) == 1 && syms[1] isa Expr && syms[1].head === :block
        syms = syms[1].args
    end
    for s in syms
        s isa LineNumberNode && continue
        if isa(s, Symbol)
            if i == typemin(basetype) && !isempty(values)
                throw(ArgumentError("overflow in value \"$s\" of Enum $typename"))
            end
        elseif isa(s, Expr) &&
               (s.head === :(=) || s.head === :kw) &&
               length(s.args) == 2 && isa(s.args[1], Symbol)
            i = Core.eval(__module__, s.args[2]) # allow exprs, e.g. uint128"1"
            if !isa(i, Integer)
                throw(ArgumentError("invalid value for Enum $typename, $s; values must be integers"))
            end
            i = convert(basetype, i)
            s = s.args[1]
            hasexpr = true
        else
            throw(ArgumentError(string("invalid argument for Enum ", typename, ": ", s)))
        end
        s = s::Symbol
        if !Base.isidentifier(s)
            throw(ArgumentError("invalid name for Enum $typename; \"$s\" is not a valid identifier"))
        end
        if hasexpr && haskey(namemap, i)
            throw(ArgumentError("both $s and $(namemap[i]) have value $i in Enum $typename; values must be unique"))
        end
        namemap[i] = s
        push!(values, i)
        if s in seen
            throw(ArgumentError("name \"$s\" in Enum $typename is not unique"))
        end
        push!(seen, s)
        if length(values) == 1
            lo = hi = i
        else
            hi = max(hi, i)
        end
        i += oneunit(i)
    end
    blk = quote
        # enum definition
        Base.@__doc__(primitive type $(esc(typename)) <: Enum{$(basetype)} $(sizeof(basetype) * 8) end)
        function $(esc(typename))(x::Integer)
            $(membershiptest(:x, values)) || enum_argument_error($(Expr(:quote, typename)), x)
            return bitcast($(esc(typename)), convert($(basetype), x))
        end
        Enums.namemap(::Type{$(esc(typename))}) = $(esc(namemap))
        Base.typemin(x::Type{$(esc(typename))}) = $(esc(typename))($lo)
        Base.typemax(x::Type{$(esc(typename))}) = $(esc(typename))($hi)
        let type_hash = hash($(esc(typename)))
            # Use internal `_enum_hash` to allow users to specialize
            # `Base.hash` for their own enum types without overwriting the
            # method we would define here. This avoids a warning for
            # precompilation.
            Enums._enum_hash(x::$(esc(typename)), h::UInt) = hash(type_hash, hash(Integer(x), h))
        end
        let insts = (Any[ $(esc(typename))(v) for v in $values ]...,)
            Base.instances(::Type{$(esc(typename))}) = insts
        end
    end
    if isa(typename, Symbol)
        for (i, sym) in namemap
            push!(blk.args, :(const $(esc(sym)) = $(esc(typename))($i)))
        end
    end
    push!(blk.args, :nothing)
    blk.head = :toplevel
    return blk
end

end # module
J   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/gmp.jlĕ      # This file is a part of Julia. License is MIT: https://julialang.org/license

module GMP

export BigInt

import .Base: *, +, -, /, <, <<, >>, >>>, <=, ==, >, >=, ^, (~), (&), (|), xor, nand, nor,
             binomial, cmp, convert, div, divrem, factorial, cld, fld, gcd, gcdx, lcm, mod,
             ndigits, promote_rule, rem, show, isqrt, string, powermod, sum, prod,
             trailing_zeros, trailing_ones, count_ones, count_zeros, tryparse_internal,
             bin, oct, dec, hex, isequal, invmod, _prevpow2, _nextpow2, ndigits0zpb,
             widen, signed, unsafe_trunc, trunc, iszero, isone, big, flipsign, signbit,
             sign, hastypemax, isodd, iseven, digits!, hash, hash_integer, top_set_bit

if Clong == Int32
    const ClongMax = Union{Int8, Int16, Int32}
    const CulongMax = Union{UInt8, UInt16, UInt32}
else
    const ClongMax = Union{Int8, Int16, Int32, Int64}
    const CulongMax = Union{UInt8, UInt16, UInt32, UInt64}
end
const CdoubleMax = Union{Float16, Float32, Float64}

if Sys.iswindows()
    const libgmp = "libgmp-10.dll"
elseif Sys.isapple()
    const libgmp = "@rpath/libgmp.10.dylib"
else
    const libgmp = "libgmp.so.10"
end

version() = VersionNumber(unsafe_string(unsafe_load(cglobal((:__gmp_version, libgmp), Ptr{Cchar}))))
bits_per_limb() = Int(unsafe_load(cglobal((:__gmp_bits_per_limb, libgmp), Cint)))

const VERSION = version()
const BITS_PER_LIMB = bits_per_limb()

# GMP's mp_limb_t is by default a typedef of `unsigned long`, but can also be configured to be either
# `unsigned int` or `unsigned long long int`. The correct unsigned type is here named Limb, and must
# be used whenever mp_limb_t is in the signature of ccall'ed GMP functions.
if BITS_PER_LIMB == 32
    const Limb = UInt32
    const SLimbMax = Union{Int8, Int16, Int32}
    const ULimbMax = Union{UInt8, UInt16, UInt32}
elseif BITS_PER_LIMB == 64
    const Limb = UInt64
    const SLimbMax = Union{Int8, Int16, Int32, Int64}
    const ULimbMax = Union{UInt8, UInt16, UInt32, UInt64}
else
    error("GMP: cannot determine the type mp_limb_t (__gmp_bits_per_limb == $BITS_PER_LIMB)")
end

"""
    BigInt <: Signed

Arbitrary precision integer type.
"""
mutable struct BigInt <: Signed
    alloc::Cint
    size::Cint
    d::Ptr{Limb}

    function BigInt(; nbits::Integer=0)
        b = MPZ.init2!(new(), nbits)
        finalizer(cglobal((:__gmpz_clear, libgmp)), b)
        return b
    end
end

"""
    BigInt(x)

Create an arbitrary precision integer. `x` may be an `Int` (or anything that can be
converted to an `Int`). The usual mathematical operators are defined for this type, and
results are promoted to a [`BigInt`](@ref).

Instances can be constructed from strings via [`parse`](@ref), or using the `big`
string literal.

# Examples
```jldoctest
julia> parse(BigInt, "42")
42

julia> big"313"
313

julia> BigInt(10)^19
10000000000000000000
```
"""
BigInt(x)

"""
    ALLOC_OVERFLOW_FUNCTION

A reference that holds a boolean, if true, indicating julia is linked with a patched GMP that
does not abort on huge allocation and throws OutOfMemoryError instead.
"""
const ALLOC_OVERFLOW_FUNCTION = Ref(false)

function __init__()
    try
        if version().major != VERSION.major || bits_per_limb() != BITS_PER_LIMB
            msg = """The dynamically loaded GMP library (v\"$(version())\" with __gmp_bits_per_limb == $(bits_per_limb()))
                     does not correspond to the compile time version (v\"$VERSION\" with __gmp_bits_per_limb == $BITS_PER_LIMB).
                     Please rebuild Julia."""
            bits_per_limb() != BITS_PER_LIMB ? @error(msg) : @warn(msg)
        end

        ccall((:__gmp_set_memory_functions, libgmp), Cvoid,
              (Ptr{Cvoid},Ptr{Cvoid},Ptr{Cvoid}),
              cglobal(:jl_gc_counted_malloc),
              cglobal(:jl_gc_counted_realloc_with_old_size),
              cglobal(:jl_gc_counted_free_with_size))
        ZERO.alloc, ZERO.size, ZERO.d = 0, 0, C_NULL
        ONE.alloc, ONE.size, ONE.d = 1, 1, pointer(_ONE)
    catch ex
        Base.showerror_nostdio(ex, "WARNING: Error during initialization of module GMP")
    end
    # This only works with a patched version of GMP, ignore otherwise
    try
        ccall((:__gmp_set_alloc_overflow_function, libgmp), Cvoid,
              (Ptr{Cvoid},),
              cglobal(:jl_throw_out_of_memory_error))
        ALLOC_OVERFLOW_FUNCTION[] = true
    catch ex
        # ErrorException("ccall: could not find function...")
        if typeof(ex) != ErrorException
            rethrow()
        end
    end
end


module MPZ
# wrapping of libgmp functions
# - "output parameters" are labeled x, y, z, and are returned when appropriate
# - constant input parameters are labeled a, b, c
# - a method modifying its input has a "!" appended to its name, according to Julia's conventions
# - some convenient methods are added (in addition to the pure MPZ ones), e.g. `add(a, b) = add!(BigInt(), a, b)`
#   and `add!(x, a) = add!(x, x, a)`.
using ..GMP: BigInt, Limb, BITS_PER_LIMB, libgmp

const mpz_t = Ref{BigInt}
const bitcnt_t = Culong

gmpz(op::Symbol) = (Symbol(:__gmpz_, op), libgmp)

init!(x::BigInt) = (ccall((:__gmpz_init, libgmp), Cvoid, (mpz_t,), x); x)
init2!(x::BigInt, a) = (ccall((:__gmpz_init2, libgmp), Cvoid, (mpz_t, bitcnt_t), x, a); x)

realloc2!(x, a) = (ccall((:__gmpz_realloc2, libgmp), Cvoid, (mpz_t, bitcnt_t), x, a); x)
realloc2(a) = realloc2!(BigInt(), a)

sizeinbase(a::BigInt, b) = Int(ccall((:__gmpz_sizeinbase, libgmp), Csize_t, (mpz_t, Cint), a, b))

for (op, nbits) in (:add => :(BITS_PER_LIMB*(1 + max(abs(a.size), abs(b.size)))),
                    :sub => :(BITS_PER_LIMB*(1 + max(abs(a.size), abs(b.size)))),
                    :mul => 0, :fdiv_q => 0, :tdiv_q => 0, :cdiv_q => 0,
                    :fdiv_r => 0, :tdiv_r => 0, :cdiv_r => 0,
                    :gcd => 0, :lcm => 0, :and => 0, :ior => 0, :xor => 0)
    op! = Symbol(op, :!)
    @eval begin
        $op!(x::BigInt, a::BigInt, b::BigInt) = (ccall($(gmpz(op)), Cvoid, (mpz_t, mpz_t, mpz_t), x, a, b); x)
        $op(a::BigInt, b::BigInt) = $op!(BigInt(nbits=$nbits), a, b)
        $op!(x::BigInt, b::BigInt) = $op!(x, x, b)
    end
end

invert!(x::BigInt, a::BigInt, b::BigInt) =
    ccall((:__gmpz_invert, libgmp), Cint, (mpz_t, mpz_t, mpz_t), x, a, b)
invert(a::BigInt, b::BigInt) = invert!(BigInt(), a, b)
invert!(x::BigInt, b::BigInt) = invert!(x, x, b)

for op in (:add_ui, :sub_ui, :mul_ui, :mul_2exp, :fdiv_q_2exp, :pow_ui, :bin_ui)
    op! = Symbol(op, :!)
    @eval begin
        $op!(x::BigInt, a::BigInt, b) = (ccall($(gmpz(op)), Cvoid, (mpz_t, mpz_t, Culong), x, a, b); x)
        $op(a::BigInt, b) = $op!(BigInt(), a, b)
        $op!(x::BigInt, b) = $op!(x, x, b)
    end
end

ui_sub!(x::BigInt, a, b::BigInt) = (ccall((:__gmpz_ui_sub, libgmp), Cvoid, (mpz_t, Culong, mpz_t), x, a, b); x)
ui_sub(a, b::BigInt) = ui_sub!(BigInt(), a, b)

for op in (:scan1, :scan0)
    # when there is no meaningful answer, ccall returns typemax(Culong), where Culong can
    # be UInt32 (Windows) or UInt64; we return -1 in this case for all architectures
    @eval $op(a::BigInt, b) = Int(signed(ccall($(gmpz(op)), Culong, (mpz_t, Culong), a, b)))
end

mul_si!(x::BigInt, a::BigInt, b) = (ccall((:__gmpz_mul_si, libgmp), Cvoid, (mpz_t, mpz_t, Clong), x, a, b); x)
mul_si(a::BigInt, b) = mul_si!(BigInt(), a, b)
mul_si!(x::BigInt, b) = mul_si!(x, x, b)

for op in (:neg, :com, :sqrt, :set)
    op! = Symbol(op, :!)
    @eval begin
        $op!(x::BigInt, a::BigInt) = (ccall($(gmpz(op)), Cvoid, (mpz_t, mpz_t), x, a); x)
        $op(a::BigInt) = $op!(BigInt(), a)
    end
    op === :set && continue # MPZ.set!(x) would make no sense
    @eval $op!(x::BigInt) = $op!(x, x)
end

for (op, T) in ((:fac_ui, Culong), (:set_ui, Culong), (:set_si, Clong), (:set_d, Cdouble))
    op! = Symbol(op, :!)
    @eval begin
        $op!(x::BigInt, a) = (ccall($(gmpz(op)), Cvoid, (mpz_t, $T), x, a); x)
        $op(a) = $op!(BigInt(), a)
    end
end

popcount(a::BigInt) = Int(signed(ccall((:__gmpz_popcount, libgmp), Culong, (mpz_t,), a)))

mpn_popcount(d::Ptr{Limb}, s::Integer) = Int(ccall((:__gmpn_popcount, libgmp), Culong, (Ptr{Limb}, Csize_t), d, s))
mpn_popcount(a::BigInt) = mpn_popcount(a.d, abs(a.size))

function tdiv_qr!(x::BigInt, y::BigInt, a::BigInt, b::BigInt)
    ccall((:__gmpz_tdiv_qr, libgmp), Cvoid, (mpz_t, mpz_t, mpz_t, mpz_t), x, y, a, b)
    x, y
end
tdiv_qr(a::BigInt, b::BigInt) = tdiv_qr!(BigInt(), BigInt(), a, b)

powm!(x::BigInt, a::BigInt, b::BigInt, c::BigInt) =
    (ccall((:__gmpz_powm, libgmp), Cvoid, (mpz_t, mpz_t, mpz_t, mpz_t), x, a, b, c); x)
powm(a::BigInt, b::BigInt, c::BigInt) = powm!(BigInt(), a, b, c)
powm!(x::BigInt, b::BigInt, c::BigInt) = powm!(x, x, b, c)

function gcdext!(x::BigInt, y::BigInt, z::BigInt, a::BigInt, b::BigInt)
    ccall((:__gmpz_gcdext, libgmp), Cvoid, (mpz_t, mpz_t, mpz_t, mpz_t, mpz_t), x, y, z, a, b)
    x, y, z
end
gcdext(a::BigInt, b::BigInt) = gcdext!(BigInt(), BigInt(), BigInt(), a, b)

cmp(a::BigInt, b::BigInt) = Int(ccall((:__gmpz_cmp, libgmp), Cint, (mpz_t, mpz_t), a, b))
cmp_si(a::BigInt, b) = Int(ccall((:__gmpz_cmp_si, libgmp), Cint, (mpz_t, Clong), a, b))
cmp_ui(a::BigInt, b) = Int(ccall((:__gmpz_cmp_ui, libgmp), Cint, (mpz_t, Culong), a, b))
cmp_d(a::BigInt, b) = Int(ccall((:__gmpz_cmp_d, libgmp), Cint, (mpz_t, Cdouble), a, b))

mpn_cmp(a::Ptr{Limb}, b::Ptr{Limb}, c) = ccall((:__gmpn_cmp, libgmp), Cint, (Ptr{Limb}, Ptr{Limb}, Clong), a, b, c)
mpn_cmp(a::BigInt, b::BigInt, c) = mpn_cmp(a.d, b.d, c)

get_str!(x, a, b::BigInt) = (ccall((:__gmpz_get_str,libgmp), Ptr{Cchar}, (Ptr{Cchar}, Cint, mpz_t), x, a, b); x)
set_str!(x::BigInt, a, b) = Int(ccall((:__gmpz_set_str, libgmp), Cint, (mpz_t, Ptr{UInt8}, Cint), x, a, b))
get_d(a::BigInt) = ccall((:__gmpz_get_d, libgmp), Cdouble, (mpz_t,), a)

function export!(a::AbstractVector{T}, n::BigInt; order::Integer=-1, nails::Integer=0, endian::Integer=0) where {T<:Base.BitInteger}
    stride(a, 1) == 1 || throw(ArgumentError("a must have stride 1"))
    ndigits = cld(sizeinbase(n, 2), 8*sizeof(T) - nails)
    length(a) < ndigits && resize!(a, ndigits)
    count = Ref{Csize_t}()
    ccall((:__gmpz_export, libgmp), Ptr{T}, (Ptr{T}, Ref{Csize_t}, Cint, Csize_t, Cint, Csize_t, mpz_t),
        a, count, order, sizeof(T), endian, nails, n)
    @assert count[] ≤ length(a)
    return a, Int(count[])
end

limbs_write!(x::BigInt, a) = ccall((:__gmpz_limbs_write, libgmp), Ptr{Limb}, (mpz_t, Clong), x, a)
limbs_finish!(x::BigInt, a) = ccall((:__gmpz_limbs_finish, libgmp), Cvoid, (mpz_t, Clong), x, a)
import!(x::BigInt, a, b, c, d, e, f) = ccall((:__gmpz_import, libgmp), Cvoid,
    (mpz_t, Csize_t, Cint, Csize_t, Cint, Csize_t, Ptr{Cvoid}), x, a, b, c, d, e, f)

setbit!(x, a) = (ccall((:__gmpz_setbit, libgmp), Cvoid, (mpz_t, bitcnt_t), x, a); x)
tstbit(a::BigInt, b) = ccall((:__gmpz_tstbit, libgmp), Cint, (mpz_t, bitcnt_t), a, b) % Bool

end # module MPZ

const ZERO = BigInt()
const ONE  = BigInt()
const _ONE = Limb[1]

widen(::Type{Int128})  = BigInt
widen(::Type{UInt128}) = BigInt
widen(::Type{BigInt})  = BigInt

signed(x::BigInt) = x

BigInt(x::BigInt) = x
Signed(x::BigInt) = x

hastypemax(::Type{BigInt}) = false

function tryparse_internal(::Type{BigInt}, s::AbstractString, startpos::Int, endpos::Int, base_::Integer, raise::Bool)
    # don't make a copy in the common case where we are parsing a whole String
    bstr = startpos == firstindex(s) && endpos == lastindex(s) ? String(s) : String(SubString(s,startpos,endpos))

    sgn, base, i = Base.parseint_preamble(true,Int(base_),bstr,firstindex(bstr),lastindex(bstr))
    if !(2 <= base <= 62)
        raise && throw(ArgumentError("invalid base: base must be 2 ≤ base ≤ 62, got $base"))
        return nothing
    end
    if i == 0
        raise && throw(ArgumentError("premature end of integer: $(repr(bstr))"))
        return nothing
    end
    z = BigInt()
    if Base.containsnul(bstr)
        err = -1 # embedded NUL char (not handled correctly by GMP)
    else
        err = GC.@preserve bstr MPZ.set_str!(z, pointer(bstr)+(i-firstindex(bstr)), base)
    end
    if err != 0
        raise && throw(ArgumentError("invalid BigInt: $(repr(bstr))"))
        return nothing
    end
    flipsign!(z, sgn)
end

BigInt(x::Union{Clong,Int32}) = MPZ.set_si(x)
BigInt(x::Union{Culong,UInt32}) = MPZ.set_ui(x)
BigInt(x::Bool) = BigInt(UInt(x))

unsafe_trunc(::Type{BigInt}, x::Union{Float16,Float32,Float64}) = MPZ.set_d(x)

function BigInt(x::Float64)
    isinteger(x) || throw(InexactError(:BigInt, BigInt, x))
    unsafe_trunc(BigInt,x)
end

function trunc(::Type{BigInt}, x::Union{Float16,Float32,Float64})
    isfinite(x) || throw(InexactError(:trunc, BigInt, x))
    unsafe_trunc(BigInt,x)
end

BigInt(x::Float16) = BigInt(Float64(x))
BigInt(x::Float32) = BigInt(Float64(x))

function BigInt(x::Integer)
    # On 64-bit Windows, `Clong` is `Int32`, not `Int64`, so construction of
    # `Int64` constants, e.g. `BigInt(3)`, uses this method.
    isbits(x) && typemin(Clong) <= x <= typemax(Clong) && return BigInt((x % Clong)::Clong)
    nd = ndigits(x, base=2)
    z = MPZ.realloc2(nd)
    ux = unsigned(x < 0 ? -x : x)
    size = 0
    limbnbits = sizeof(Limb) << 3
    while nd > 0
        size += 1
        unsafe_store!(z.d, ux % Limb, size)
        ux >>= limbnbits
        nd -= limbnbits
    end
    z.size = x < 0 ? -size : size
    z
end


rem(x::BigInt, ::Type{Bool}) = !iszero(x) & unsafe_load(x.d) % Bool # never unsafe here

rem(x::BigInt, ::Type{T}) where T<:Union{SLimbMax,ULimbMax} =
    iszero(x) ? zero(T) : flipsign(unsafe_load(x.d) % T, x.size)

function rem(x::BigInt, ::Type{T}) where T<:Union{Base.BitUnsigned,Base.BitSigned}
    u = zero(T)
    for l = 1:min(abs(x.size), cld(sizeof(T), sizeof(Limb)))
        u += (unsafe_load(x.d, l) % T) << ((sizeof(Limb)<<3)*(l-1))
    end
    flipsign(u, x.size)
end

rem(x::Integer, ::Type{BigInt}) = BigInt(x)

isodd(x::BigInt) = MPZ.tstbit(x, 0)
iseven(x::BigInt) = !isodd(x)

function (::Type{T})(x::BigInt) where T<:Base.BitUnsigned
    if sizeof(T) < sizeof(Limb)
        convert(T, convert(Limb,x))
    else
        0 <= x.size <= cld(sizeof(T),sizeof(Limb)) || throw(InexactError(nameof(T), T, x))
        x % T
    end
end

function (::Type{T})(x::BigInt) where T<:Base.BitSigned
    n = abs(x.size)
    if sizeof(T) < sizeof(Limb)
        SLimb = typeof(Signed(one(Limb)))
        convert(T, convert(SLimb, x))
    else
        0 <= n <= cld(sizeof(T),sizeof(Limb)) || throw(InexactError(nameof(T), T, x))
        y = x % T
        ispos(x) ⊻ (y > 0) && throw(InexactError(nameof(T), T, x)) # catch overflow
        y
    end
end


Float64(n::BigInt, ::RoundingMode{:ToZero}) = MPZ.get_d(n)

function (::Type{T})(n::BigInt, ::RoundingMode{:ToZero}) where T<:Union{Float16,Float32}
    T(Float64(n,RoundToZero),RoundToZero)
end

function (::Type{T})(n::BigInt, ::RoundingMode{:Down}) where T<:CdoubleMax
    x = T(n,RoundToZero)
    x > n ? prevfloat(x) : x
end
function (::Type{T})(n::BigInt, ::RoundingMode{:Up}) where T<:CdoubleMax
    x = T(n,RoundToZero)
    x < n ? nextfloat(x) : x
end

function Float64(x::BigInt, ::RoundingMode{:Nearest})
    x == 0 && return 0.0
    xsize = abs(x.size)
    if xsize*BITS_PER_LIMB > 1024
        z = Inf64
    elseif xsize == 1
        z = Float64(unsafe_load(x.d))
    elseif Limb == UInt32 && xsize == 2
        z = Float64((unsafe_load(x.d, 2) % UInt64) << BITS_PER_LIMB + unsafe_load(x.d))
    else
        y1 = unsafe_load(x.d, xsize) % UInt64
        n = top_set_bit(y1)
        # load first 54(1 + 52 bits of fraction + 1 for rounding)
        y = y1 >> (n - (precision(Float64)+1))
        if Limb == UInt64
            y += n > precision(Float64) ? 0 : (unsafe_load(x.d, xsize-1) >> (10+n))
        else
            y += (unsafe_load(x.d, xsize-1) % UInt64) >> (n-22)
            y += n > (precision(Float64) - 32) ? 0 : (unsafe_load(x.d, xsize-2) >> (10+n))
        end
        y = (y + 1) >> 1 # round, ties up
        y &= ~UInt64(trailing_zeros(x) == (n-54 + (xsize-1)*BITS_PER_LIMB)) # fix last bit to round to even
        d = ((n+1021) % UInt64) << 52
        z = reinterpret(Float64, d+y)
        z = ldexp(z, (xsize-1)*BITS_PER_LIMB)
    end
    return flipsign(z, x.size)
end

function Float32(x::BigInt, ::RoundingMode{:Nearest})
    x == 0 && return 0f0
    xsize = abs(x.size)
    if xsize*BITS_PER_LIMB > 128
        z = Inf32
    elseif xsize == 1
        z = Float32(unsafe_load(x.d))
    else
        y1 = unsafe_load(x.d, xsize)
        n = BITS_PER_LIMB - leading_zeros(y1)
        # load first 25(1 + 23 bits of fraction + 1 for rounding)
        y = (y1 >> (n - (precision(Float32)+1))) % UInt32
        y += (n > precision(Float32) ? 0 : unsafe_load(x.d, xsize-1) >> (BITS_PER_LIMB - (25-n))) % UInt32
        y = (y + one(UInt32)) >> 1 # round, ties up
        y &= ~UInt32(trailing_zeros(x) == (n-25 + (xsize-1)*BITS_PER_LIMB)) # fix last bit to round to even
        d = ((n+125) % UInt32) << 23
        z = reinterpret(Float32, d+y)
        z = ldexp(z, (xsize-1)*BITS_PER_LIMB)
    end
    return flipsign(z, x.size)
end

function Float16(x::BigInt, ::RoundingMode{:Nearest})
    x == 0 && return Float16(0.0)
    y1 = unsafe_load(x.d)
    n = BITS_PER_LIMB - leading_zeros(y1)
    if n > 16 || abs(x.size) > 1
        z = Inf16
    else
        # load first 12(1 + 10 bits for fraction + 1 for rounding)
        y = (y1 >> (n - (precision(Float16)+1))) % UInt16
        y = (y + one(UInt16)) >> 1 # round, ties up
        y &= ~UInt16(trailing_zeros(x) == (n-12)) # fix last bit to round to even
        d = ((n+13) % UInt16) << 10
        z = reinterpret(Float16, d+y)
    end
    return flipsign(z, x.size)
end

Float64(n::BigInt) = Float64(n, RoundNearest)
Float32(n::BigInt) = Float32(n, RoundNearest)
Float16(n::BigInt) = Float16(n, RoundNearest)

promote_rule(::Type{BigInt}, ::Type{<:Integer}) = BigInt

"""
    big(x)

Convert a number to a maximum precision representation (typically [`BigInt`](@ref) or
`BigFloat`). See [`BigFloat`](@ref BigFloat(::Any, rounding::RoundingMode)) for
information about some pitfalls with floating-point numbers.
"""
function big end

big(::Type{<:Integer})  = BigInt
big(::Type{<:Rational}) = Rational{BigInt}

big(n::Integer) = convert(BigInt, n)

# Binary ops
for (fJ, fC) in ((:+, :add), (:-,:sub), (:*, :mul),
                 (:mod, :fdiv_r), (:rem, :tdiv_r),
                 (:gcd, :gcd), (:lcm, :lcm),
                 (:&, :and), (:|, :ior), (:xor, :xor))
    @eval begin
        ($fJ)(x::BigInt, y::BigInt) = MPZ.$fC(x, y)
    end
end

for (r, f) in ((RoundToZero, :tdiv_q),
               (RoundDown, :fdiv_q),
               (RoundUp, :cdiv_q))
    @eval div(x::BigInt, y::BigInt, ::typeof($r)) = MPZ.$f(x, y)
end

# For compat only. Remove in 2.0.
div(x::BigInt, y::BigInt) = div(x, y, RoundToZero)
fld(x::BigInt, y::BigInt) = div(x, y, RoundDown)
cld(x::BigInt, y::BigInt) = div(x, y, RoundUp)

/(x::BigInt, y::BigInt) = float(x)/float(y)

function invmod(x::BigInt, y::BigInt)
    z = zero(BigInt)
    ya = abs(y)
    if ya == 1
        return z
    end
    if (y==0 || MPZ.invert!(z, x, ya) == 0)
        throw(DomainError(y))
    end
    # GMP always returns a positive inverse; we instead want to
    # normalize such that div(z, y) == 0, i.e. we want a negative z
    # when y is negative.
    if y < 0
        MPZ.add!(z, y)
    end
    # The postcondition is: mod(z * x, y) == mod(big(1), m) && div(z, y) == 0
    return z
end

# More efficient commutative operations
for (fJ, fC) in ((:+, :add), (:*, :mul), (:&, :and), (:|, :ior), (:xor, :xor))
    fC! = Symbol(fC, :!)
    @eval begin
        ($fJ)(a::BigInt, b::BigInt, c::BigInt) = MPZ.$fC!(MPZ.$fC(a, b), c)
        ($fJ)(a::BigInt, b::BigInt, c::BigInt, d::BigInt) = MPZ.$fC!(MPZ.$fC!(MPZ.$fC(a, b), c), d)
        ($fJ)(a::BigInt, b::BigInt, c::BigInt, d::BigInt, e::BigInt) =
            MPZ.$fC!(MPZ.$fC!(MPZ.$fC!(MPZ.$fC(a, b), c), d), e)
    end
end

# Basic arithmetic without promotion
+(x::BigInt, c::CulongMax) = MPZ.add_ui(x, c)
+(c::CulongMax, x::BigInt) = x + c

-(x::BigInt, c::CulongMax) = MPZ.sub_ui(x, c)
-(c::CulongMax, x::BigInt) = MPZ.ui_sub(c, x)

+(x::BigInt, c::ClongMax) = c < 0 ? -(x, -(c % Culong)) : x + convert(Culong, c)
+(c::ClongMax, x::BigInt) = c < 0 ? -(x, -(c % Culong)) : x + convert(Culong, c)
-(x::BigInt, c::ClongMax) = c < 0 ? +(x, -(c % Culong)) : -(x, convert(Culong, c))
-(c::ClongMax, x::BigInt) = c < 0 ? -(x + -(c % Culong)) : -(convert(Culong, c), x)

*(x::BigInt, c::CulongMax) = MPZ.mul_ui(x, c)
*(c::CulongMax, x::BigInt) = x * c
*(x::BigInt, c::ClongMax) = MPZ.mul_si(x, c)
*(c::ClongMax, x::BigInt) = x * c

/(x::BigInt, y::Union{ClongMax,CulongMax}) = float(x)/y
/(x::Union{ClongMax,CulongMax}, y::BigInt) = x/float(y)

# unary ops
(-)(x::BigInt) = MPZ.neg(x)
(~)(x::BigInt) = MPZ.com(x)

<<(x::BigInt, c::UInt) = c == 0 ? x : MPZ.mul_2exp(x, c)
>>(x::BigInt, c::UInt) = c == 0 ? x : MPZ.fdiv_q_2exp(x, c)
>>>(x::BigInt, c::UInt) = x >> c

function trailing_zeros(x::BigInt)
    c = MPZ.scan1(x, 0)
    c == -1 && throw(DomainError(x, "`x` must be non-zero"))
    c
end

function trailing_ones(x::BigInt)
    c = MPZ.scan0(x, 0)
    c == -1 && throw(DomainError(x, "`x` must not be equal to -1"))
    c
end

function count_ones(x::BigInt)
    c = MPZ.popcount(x)
    c == -1 && throw(DomainError(x, "`x` cannot be negative"))
    c
end

# generic definition is not used to provide a better error message
function count_zeros(x::BigInt)
    c = MPZ.popcount(~x)
    c == -1 && throw(DomainError(x, "`x` must be negative"))
    c
end

"""
    count_ones_abs(x::BigInt)

Number of ones in the binary representation of abs(x).
"""
count_ones_abs(x::BigInt) = iszero(x) ? 0 : MPZ.mpn_popcount(x)

function top_set_bit(x::BigInt)
    isneg(x) && throw(DomainError(x, "top_set_bit only supports negative arguments when they have type BitSigned."))
    iszero(x) && return 0
    x.size * sizeof(Limb) << 3 - leading_zeros(GC.@preserve x unsafe_load(x.d, x.size))
end

divrem(x::BigInt, y::BigInt) = MPZ.tdiv_qr(x, y)
divrem(x::BigInt, y::Integer) = MPZ.tdiv_qr(x, big(y))

cmp(x::BigInt, y::BigInt) = sign(MPZ.cmp(x, y))
cmp(x::BigInt, y::ClongMax) = sign(MPZ.cmp_si(x, y))
cmp(x::BigInt, y::CulongMax) = sign(MPZ.cmp_ui(x, y))
cmp(x::BigInt, y::Integer) = cmp(x, big(y))
cmp(x::Integer, y::BigInt) = -cmp(y, x)

cmp(x::BigInt, y::CdoubleMax) = isnan(y) ? -1 : sign(MPZ.cmp_d(x, y))
cmp(x::CdoubleMax, y::BigInt) = -cmp(y, x)

isqrt(x::BigInt) = MPZ.sqrt(x)

^(x::BigInt, y::Culong) = MPZ.pow_ui(x, y)

function bigint_pow(x::BigInt, y::Integer)
    if y<0; throw(DomainError(y, "`y` cannot be negative.")); end
    @noinline throw1(y) =
        throw(OverflowError("exponent $y is too large and computation will overflow"))
    if x== 1; return x; end
    if x==-1; return isodd(y) ? x : -x; end
    if y>typemax(Culong)
       x==0 && return x

       #At this point, x is not 1, 0 or -1 and it is not possible to use
       #gmpz_pow_ui to compute the answer. Note that the magnitude of the
       #answer is:
       #- at least 2^(2^32-1) ≈ 10^(1.3e9) (if Culong === UInt32).
       #- at least 2^(2^64-1) ≈ 10^(5.5e18) (if Culong === UInt64).
       #
       #Assume that the answer will definitely overflow.

       throw1(y)
    end
    return x^convert(Culong, y)
end

^(x::BigInt , y::BigInt ) = bigint_pow(x, y)
^(x::BigInt , y::Bool   ) = y ? x : one(x)
^(x::BigInt , y::Integer) = bigint_pow(x, y)
^(x::Integer, y::BigInt ) = bigint_pow(BigInt(x), y)
^(x::Bool   , y::BigInt ) = Base.power_by_squaring(x, y)

function powermod(x::BigInt, p::BigInt, m::BigInt)
    r = MPZ.powm(x, p, m)
    return m < 0 && r > 0 ? MPZ.add!(r, m) : r # choose sign consistent with mod(x^p, m)
end

powermod(x::Integer, p::Integer, m::BigInt) = powermod(big(x), big(p), m)

function gcdx(a::BigInt, b::BigInt)
    if iszero(b) # shortcut this to ensure consistent results with gcdx(a,b)
        return a < 0 ? (-a,-ONE,b) : (a,one(BigInt),b)
        # we don't return the globals ONE and ZERO in case the user wants to
        # mutate the result
    end
    g, s, t = MPZ.gcdext(a, b)
    if t == 0
        # work around a difference in some versions of GMP
        if a == b
            return g, t, s
        elseif abs(a)==abs(b)
            return g, t, -s
        end
    end
    g, s, t
end

+(x::BigInt, y::BigInt, rest::BigInt...) = sum(tuple(x, y, rest...))
sum(arr::Union{AbstractArray{BigInt}, Tuple{BigInt, Vararg{BigInt}}}) =
    foldl(MPZ.add!, arr; init=BigInt(0))

function prod(arr::AbstractArray{BigInt})
    # compute first the needed number of bits for the result,
    # to avoid re-allocations;
    # GMP will always request n+m limbs for the result in MPZ.mul!,
    # if the arguments have n and m limbs; so we add all the bits
    # taken by the array elements, and add BITS_PER_LIMB to that,
    # to account for the rounding to limbs in MPZ.mul!
    # (BITS_PER_LIMB-1 would typically be enough, to which we add
    # 1 for the initial multiplication by init=1 in foldl)
    nbits = BITS_PER_LIMB
    for x in arr
        iszero(x) && return zero(BigInt)
        xsize = abs(x.size)
        lz = GC.@preserve x leading_zeros(unsafe_load(x.d, xsize))
        nbits += xsize * BITS_PER_LIMB - lz
    end
    init = BigInt(; nbits)
    MPZ.set_si!(init, 1)
    foldl(MPZ.mul!, arr; init)
end

factorial(x::BigInt) = isneg(x) ? BigInt(0) : MPZ.fac_ui(x)

function binomial(n::BigInt, k::Integer)
    k < 0 && return BigInt(0)
    k <= typemax(Culong) && return binomial(n, Culong(k))
    n < 0 && return isodd(k) ? -binomial(k - n - 1, k) : binomial(k - n - 1, k)
    κ = n - k
    κ < 0 && return BigInt(0)
    κ <= typemax(Culong) && return binomial(n, Culong(κ))
    throw(OverflowError("Computation would exceed memory"))
end
binomial(n::BigInt, k::Culong) = MPZ.bin_ui(n, k)

==(x::BigInt, y::BigInt) = cmp(x,y) == 0
==(x::BigInt, i::Integer) = cmp(x,i) == 0
==(i::Integer, x::BigInt) = cmp(x,i) == 0
==(x::BigInt, f::CdoubleMax) = isnan(f) ? false : cmp(x,f) == 0
==(f::CdoubleMax, x::BigInt) = isnan(f) ? false : cmp(x,f) == 0
iszero(x::BigInt) = x.size == 0
isone(x::BigInt) = x == Culong(1)

<=(x::BigInt, y::BigInt) = cmp(x,y) <= 0
<=(x::BigInt, i::Integer) = cmp(x,i) <= 0
<=(i::Integer, x::BigInt) = cmp(x,i) >= 0
<=(x::BigInt, f::CdoubleMax) = isnan(f) ? false : cmp(x,f) <= 0
<=(f::CdoubleMax, x::BigInt) = isnan(f) ? false : cmp(x,f) >= 0

<(x::BigInt, y::BigInt) = cmp(x,y) < 0
<(x::BigInt, i::Integer) = cmp(x,i) < 0
<(i::Integer, x::BigInt) = cmp(x,i) > 0
<(x::BigInt, f::CdoubleMax) = isnan(f) ? false : cmp(x,f) < 0
<(f::CdoubleMax, x::BigInt) = isnan(f) ? false : cmp(x,f) > 0
isneg(x::BigInt) = x.size < 0
ispos(x::BigInt) = x.size > 0

signbit(x::BigInt) = isneg(x)
flipsign!(x::BigInt, y::Integer) = (signbit(y) && (x.size = -x.size); x)
flipsign( x::BigInt, y::Integer) = signbit(y) ? -x : x
flipsign( x::BigInt, y::BigInt)  = signbit(y) ? -x : x
# above method to resolving ambiguities with flipsign(::T, ::T) where T<:Signed
function sign(x::BigInt)
    isneg(x) && return -one(x)
    ispos(x) && return one(x)
    return x
end

show(io::IO, x::BigInt) = print(io, string(x))

function string(n::BigInt; base::Integer = 10, pad::Integer = 1)
    base < 0 && return Base._base(Int(base), n, pad, (base>0) & (n.size<0))
    2 <= base <= 62 || throw(ArgumentError("base must be 2 ≤ base ≤ 62, got $base"))
    iszero(n) && pad < 1 && return ""
    nd1 = ndigits(n, base=base)
    nd  = max(nd1, pad)
    sv  = Base.StringVector(nd + isneg(n))
    GC.@preserve sv MPZ.get_str!(pointer(sv) + nd - nd1, base, n)
    @inbounds for i = (1:nd-nd1) .+ isneg(n)
        sv[i] = '0' % UInt8
    end
    isneg(n) && (sv[1] = '-' % UInt8)
    String(sv)
end

function digits!(a::AbstractVector{T}, n::BigInt; base::Integer = 10) where {T<:Integer}
    if base ≥ 2
        if base ≤ 62
            # fast path using mpz_get_str via string(n; base)
            s = codeunits(string(n; base))
            i, j = firstindex(a)-1, length(s)+1
            lasti = min(lastindex(a), firstindex(a) + length(s)-1 - isneg(n))
            while i < lasti
                # base ≤ 36: 0-9, plus a-z for 10-35
                # base > 36: 0-9, plus A-Z for 10-35 and a-z for 36..61
                x = s[j -= 1]
                a[i += 1] = base ≤ 36 ? (x>0x39 ? x-0x57 : x-0x30) : (x>0x39 ? (x>0x60 ? x-0x3d : x-0x37) : x-0x30)
            end
            lasti = lastindex(a)
            while i < lasti; a[i+=1] = zero(T); end
            return isneg(n) ? map!(-,a,a) : a
        elseif a isa StridedVector{<:Base.BitInteger} && stride(a,1) == 1 && ispow2(base) && base-1 ≤ typemax(T)
            # fast path using mpz_export
            origlen = length(a)
            _, writelen = MPZ.export!(a, n; nails = 8sizeof(T) - trailing_zeros(base))
            length(a) != origlen && resize!(a, origlen) # truncate to least-significant digits
            a[begin+writelen:end] .= zero(T)
            return isneg(n) ? map!(-,a,a) : a
        end
    end
    return invoke(digits!, Tuple{typeof(a), Integer}, a, n; base) # slow generic fallback
end

function ndigits0zpb(x::BigInt, b::Integer)
    b < 2 && throw(DomainError(b, "`b` cannot be less than 2."))
    x.size == 0 && return 0 # for consistency with other ndigits0z methods
    if ispow2(b) && 2 <= b <= 62 # GMP assumes b is in this range
        MPZ.sizeinbase(x, b)
    else
        # non-base 2 mpz_sizeinbase might return an answer 1 too big
        # use property that log(b, x) < ndigits(x, base=b) <= log(b, x) + 1
        n = MPZ.sizeinbase(x, 2)
        lb = log2(b) # assumed accurate to <1ulp (true for openlibm)
        q,r = divrem(n,lb)
        iq = Int(q)
        maxerr = q*eps(lb) # maximum error in remainder
        if r-1.0 < maxerr
            abs(x) >= big(b)^iq ? iq+1 : iq
        elseif lb-r < maxerr
            abs(x) >= big(b)^(iq+1) ? iq+2 : iq+1
        else
            iq+1
        end
    end
end

# Fast paths for nextpow(2, x::BigInt)
# below, ONE is always left-shifted by at least one digit, so a new BigInt is
# allocated, which can be safely mutated
_prevpow2(x::BigInt) = -2 <= x <= 2 ? x : flipsign!(ONE << (ndigits(x, base=2) - 1), x)
_nextpow2(x::BigInt) = count_ones_abs(x) <= 1 ? x : flipsign!(ONE << ndigits(x, base=2), x)

Base.checked_abs(x::BigInt) = abs(x)
Base.checked_neg(x::BigInt) = -x
Base.checked_add(a::BigInt, b::BigInt) = a + b
Base.checked_sub(a::BigInt, b::BigInt) = a - b
Base.checked_mul(a::BigInt, b::BigInt) = a * b
Base.checked_div(a::BigInt, b::BigInt) = div(a, b)
Base.checked_rem(a::BigInt, b::BigInt) = rem(a, b)
Base.checked_fld(a::BigInt, b::BigInt) = fld(a, b)
Base.checked_mod(a::BigInt, b::BigInt) = mod(a, b)
Base.checked_cld(a::BigInt, b::BigInt) = cld(a, b)
Base.add_with_overflow(a::BigInt, b::BigInt) = a + b, false
Base.sub_with_overflow(a::BigInt, b::BigInt) = a - b, false
Base.mul_with_overflow(a::BigInt, b::BigInt) = a * b, false

Base.deepcopy_internal(x::BigInt, stackdict::IdDict) = get!(() -> MPZ.set(x), stackdict, x)

## streamlined hashing for BigInt, by avoiding allocation from shifts ##

if Limb === UInt64 === UInt
    # On 64 bit systems we can define
    # an optimized version for BigInt of hash_integer (used e.g. for Rational{BigInt}),
    # and of hash

    using .Base: hash_uint

    function hash_integer(n::BigInt, h::UInt)
        GC.@preserve n begin
            s = n.size
            s == 0 && return hash_integer(0, h)
            p = convert(Ptr{UInt64}, n.d)
            b = unsafe_load(p)
            h ⊻= hash_uint(ifelse(s < 0, -b, b) ⊻ h)
            for k = 2:abs(s)
                h ⊻= hash_uint(unsafe_load(p, k) ⊻ h)
            end
            return h
        end
    end

    function hash(x::BigInt, h::UInt)
        GC.@preserve x begin
            sz = x.size
            sz == 0 && return hash(0, h)
            ptr = Ptr{UInt64}(x.d)
            if sz == 1
                return hash(unsafe_load(ptr), h)
            elseif sz == -1
                limb = unsafe_load(ptr)
                limb <= typemin(Int) % UInt && return hash(-(limb % Int), h)
            end
            pow = trailing_zeros(x)
            nd = Base.ndigits0z(x, 2)
            idx = (pow >>> 6) + 1
            shift = (pow & 63) % UInt
            upshift = BITS_PER_LIMB - shift
            asz = abs(sz)
            if shift == 0
                limb = unsafe_load(ptr, idx)
            else
                limb1 = unsafe_load(ptr, idx)
                limb2 = idx < asz ? unsafe_load(ptr, idx+1) : UInt(0)
                limb = limb2 << upshift | limb1 >> shift
            end
            if nd <= 1024 && nd - pow <= 53
                return hash(ldexp(flipsign(Float64(limb), sz), pow), h)
            end
            h = hash_integer(pow, h)
            h ⊻= hash_uint(flipsign(limb, sz) ⊻ h)
            for idx = idx+1:asz
                if shift == 0
                    limb = unsafe_load(ptr, idx)
                else
                    limb1 = limb2
                    if idx == asz
                        limb = limb1 >> shift
                        limb == 0 && break # don't hash leading zeros
                    else
                        limb2 = unsafe_load(ptr, idx+1)
                        limb = limb2 << upshift | limb1 >> shift
                    end
                end
                h ⊻= hash_uint(limb ⊻ h)
            end
            return h
        end
    end
end

module MPQ

# Rational{BigInt}
import .Base: unsafe_rational, __throw_rational_argerror_zero
import ..GMP: BigInt, MPZ, Limb, isneg, libgmp

gmpq(op::Symbol) = (Symbol(:__gmpq_, op), libgmp)

mutable struct _MPQ
    num_alloc::Cint
    num_size::Cint
    num_d::Ptr{Limb}
    den_alloc::Cint
    den_size::Cint
    den_d::Ptr{Limb}
    # to prevent GC
    rat::Rational{BigInt}
end

const mpq_t = Ref{_MPQ}

_MPQ(x::BigInt,y::BigInt) = _MPQ(x.alloc, x.size, x.d,
                                 y.alloc, y.size, y.d,
                                 unsafe_rational(BigInt, x, y))
_MPQ() = _MPQ(BigInt(), BigInt())
_MPQ(x::Rational{BigInt}) = _MPQ(x.num, x.den)

function sync_rational!(xq::_MPQ)
    xq.rat.num.alloc = xq.num_alloc
    xq.rat.num.size  = xq.num_size
    xq.rat.num.d     = xq.num_d
    xq.rat.den.alloc = xq.den_alloc
    xq.rat.den.size  = xq.den_size
    xq.rat.den.d     = xq.den_d
    return xq.rat
end

function Rational{BigInt}(num::BigInt, den::BigInt)
    if iszero(den)
        iszero(num) && __throw_rational_argerror_zero(BigInt)
        return set_si(flipsign(1, num), 0)
    end
    xq = _MPQ(MPZ.set(num), MPZ.set(den))
    ccall((:__gmpq_canonicalize, libgmp), Cvoid, (mpq_t,), xq)
    return sync_rational!(xq)
end

# define set, set_ui, set_si, set_z, and their inplace versions
function set!(z::Rational{BigInt}, x::Rational{BigInt})
    zq = _MPQ(z)
    ccall((:__gmpq_set, libgmp), Cvoid, (mpq_t, mpq_t), zq, _MPQ(x))
    return sync_rational!(zq)
end

function set_z!(z::Rational{BigInt}, x::BigInt)
    zq = _MPQ(z)
    ccall((:__gmpq_set_z, libgmp), Cvoid, (mpq_t, MPZ.mpz_t), zq, x)
    return sync_rational!(zq)
end

for (op, T) in ((:set, Rational{BigInt}), (:set_z, BigInt))
    op! = Symbol(op, :!)
    @eval $op(a::$T) = $op!(unsafe_rational(BigInt(), BigInt()), a)
end

# note that rationals returned from set_ui and set_si are not checked,
# set_ui(0, 0) will return 0//0 without errors, just like unsafe_rational
for (op, T1, T2) in ((:set_ui, Culong, Culong), (:set_si, Clong, Culong))
    op! = Symbol(op, :!)
    @eval begin
        function $op!(z::Rational{BigInt}, a, b)
            zq = _MPQ(z)
            ccall($(gmpq(op)), Cvoid, (mpq_t, $T1, $T2), zq, a, b)
            return sync_rational!(zq)
        end
        $op(a, b) = $op!(unsafe_rational(BigInt(), BigInt()), a, b)
    end
end

# define add, sub, mul, div, and their inplace versions
function add!(z::Rational{BigInt}, x::Rational{BigInt}, y::Rational{BigInt})
    if iszero(x.den) || iszero(y.den)
        if iszero(x.den) && iszero(y.den) && isneg(x.num) != isneg(y.num)
            throw(DivideError())
        end
        return set!(z, iszero(x.den) ? x : y)
    end
    zq = _MPQ(z)
    ccall((:__gmpq_add, libgmp), Cvoid,
          (mpq_t,mpq_t,mpq_t), zq, _MPQ(x), _MPQ(y))
    return sync_rational!(zq)
end

function sub!(z::Rational{BigInt}, x::Rational{BigInt}, y::Rational{BigInt})
    if iszero(x.den) || iszero(y.den)
        if iszero(x.den) && iszero(y.den) && isneg(x.num) == isneg(y.num)
            throw(DivideError())
        end
        iszero(x.den) && return set!(z, x)
        return set_si!(z, flipsign(-1, y.num), 0)
    end
    zq = _MPQ(z)
    ccall((:__gmpq_sub, libgmp), Cvoid,
          (mpq_t,mpq_t,mpq_t), zq, _MPQ(x), _MPQ(y))
    return sync_rational!(zq)
end

function mul!(z::Rational{BigInt}, x::Rational{BigInt}, y::Rational{BigInt})
    if iszero(x.den) || iszero(y.den)
        if iszero(x.num) || iszero(y.num)
            throw(DivideError())
        end
        return set_si!(z, ifelse(xor(isneg(x.num), isneg(y.num)), -1, 1), 0)
    end
    zq = _MPQ(z)
    ccall((:__gmpq_mul, libgmp), Cvoid,
          (mpq_t,mpq_t,mpq_t), zq, _MPQ(x), _MPQ(y))
    return sync_rational!(zq)
end

function div!(z::Rational{BigInt}, x::Rational{BigInt}, y::Rational{BigInt})
    if iszero(x.den)
        if iszero(y.den)
            throw(DivideError())
        end
        isneg(y.num) || return set!(z, x)
        return set_si!(z, flipsign(-1, x.num), 0)
    elseif iszero(y.den)
        return set_si!(z, 0, 1)
    elseif iszero(y.num)
        if iszero(x.num)
            throw(DivideError())
        end
        return set_si!(z, flipsign(1, x.num), 0)
    end
    zq = _MPQ(z)
    ccall((:__gmpq_div, libgmp), Cvoid,
          (mpq_t,mpq_t,mpq_t), zq, _MPQ(x), _MPQ(y))
    return sync_rational!(zq)
end

for (fJ, fC) in ((:+, :add), (:-, :sub), (:*, :mul), (://, :div))
    fC! = Symbol(fC, :!)
    @eval begin
        ($fC!)(x::Rational{BigInt}, y::Rational{BigInt}) = $fC!(x, x, y)
        (Base.$fJ)(x::Rational{BigInt}, y::Rational{BigInt}) = $fC!(unsafe_rational(BigInt(), BigInt()), x, y)
    end
end

function Base.cmp(x::Rational{BigInt}, y::Rational{BigInt})
    Int(ccall((:__gmpq_cmp, libgmp), Cint, (mpq_t, mpq_t), _MPQ(x), _MPQ(y)))
end

end # MPQ module

end # module
N   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/ryu/Ryu.jl�      module Ryu

using .Base.Libc
import .Base: significand_bits, significand_mask, exponent_bits, exponent_mask, exponent_bias, exponent_max, uinttype

include("utils.jl")
include("shortest.jl")
include("fixed.jl")
include("exp.jl")

"""
    Ryu.neededdigits(T)

Number of digits necessary to represent type `T` in fixed-precision decimal.
"""
neededdigits(::Type{Float64}) = 309 + 17
neededdigits(::Type{Float32}) = 39 + 9 + 2
neededdigits(::Type{Float16}) = 9 + 5 + 9

"""
    Ryu.writeshortest(x, plus=false, space=false, hash=true, precision=-1, expchar=UInt8('e'), padexp=false, decchar=UInt8('.'), typed=false, compact=false)
    Ryu.writeshortest(buf::Vector{UInt8}, pos::Int, x, args...)

Convert a float value `x` into its "shortest" decimal string, which can be parsed back to the same value.
This function allows achieving the `%g` printf format.
Note the 2nd method allows passing in a byte buffer and position directly; callers must ensure the buffer has sufficient room to hold the entire decimal string.

Various options for the output format include:
  * `plus`: for positive `x`, prefix decimal string with a `'+'` character
  * `space`: for positive `x`, prefix decimal string with a `' '` character; overridden if `plus=true`
  * `hash`: whether the decimal point should be written, even if no additional digits are needed for precision
  * `precision`: minimum number of digits to be included in the decimal string; extra `'0'` characters will be added for padding if necessary
  * `expchar`: character to use exponent component in scientific notation
  * `padexp`: whether two digits should always be written, even for single-digit exponents (e.g. `e+1` becomes `e+01`)
  * `decchar`: decimal point character to be used
  * `typed`: whether additional type information should be printed for `Float16` / `Float32`
  * `compact`: output will be limited to 6 significant digits
"""
function writeshortest(x::T,
        plus::Bool=false,
        space::Bool=false,
        hash::Bool=true,
        precision::Integer=-1,
        expchar::UInt8=UInt8('e'),
        padexp::Bool=false,
        decchar::UInt8=UInt8('.'),
        typed::Bool=false,
        compact::Bool=false) where {T <: Base.IEEEFloat}
    buf = Base.StringVector(neededdigits(T))
    pos = writeshortest(buf, 1, x, plus, space, hash, precision, expchar, padexp, decchar, typed, compact)
    return String(resize!(buf, pos - 1))
end

"""
    Ryu.writefixed(x, precision, plus=false, space=false, hash=false, decchar=UInt8('.'), trimtrailingzeros=false)
    Ryu.writefixed(buf::Vector{UInt8}, pos::Int, x, args...)

Convert a float value `x` into a "fixed" size decimal string of the provided precision.
This function allows achieving the `%f` printf format.
Note the 2nd method allows passing in a byte buffer and position directly; callers must ensure the buffer has sufficient room to hold the entire decimal string.

Various options for the output format include:
  * `plus`: for positive `x`, prefix decimal string with a `'+'` character
  * `space`: for positive `x`, prefix decimal string with a `' '` character; overridden if `plus=true`
  * `hash`: whether the decimal point should be written, even if no additional digits are needed for precision
  * `precision`: minimum number of significant digits to be included in the decimal string; extra `'0'` characters will be added for padding if necessary
  * `decchar`: decimal point character to be used
  * `trimtrailingzeros`: whether trailing zeros of fractional part should be removed
"""
function writefixed(x::T,
    precision::Integer,
    plus::Bool=false,
    space::Bool=false,
    hash::Bool=false,
    decchar::UInt8=UInt8('.'),
    trimtrailingzeros::Bool=false) where {T <: Base.IEEEFloat}
    buf = Base.StringVector(precision + neededdigits(T))
    pos = writefixed(buf, 1, x, precision, plus, space, hash, decchar, trimtrailingzeros)
    return String(resize!(buf, pos - 1))
end

"""
    Ryu.writeexp(x, precision, plus=false, space=false, hash=false, expchar=UInt8('e'), decchar=UInt8('.'), trimtrailingzeros=false)
    Ryu.writeexp(buf::Vector{UInt8}, pos::Int, x, args...)

Convert a float value `x` into a scientific notation decimal string.
This function allows achieving the `%e` printf format.
Note the 2nd method allows passing in a byte buffer and position directly; callers must ensure the buffer has sufficient room to hold the entire decimal string.

Various options for the output format include:
  * `plus`: for positive `x`, prefix decimal string with a `'+'` character
  * `space`: for positive `x`, prefix decimal string with a `' '` character; overridden if `plus=true`
  * `hash`: whether the decimal point should be written, even if no additional digits are needed for precision
  * `precision`: minimum number of significant digits to be included in the decimal string; extra `'0'` characters will be added for padding if necessary
  * `expchar`: character to use exponent component in scientific notation
  * `decchar`: decimal point character to be used
  * `trimtrailingzeros`: whether trailing zeros should be removed
"""
function writeexp(x::T,
    precision::Integer,
    plus::Bool=false,
    space::Bool=false,
    hash::Bool=false,
    expchar::UInt8=UInt8('e'),
    decchar::UInt8=UInt8('.'),
    trimtrailingzeros::Bool=false) where {T <: Base.IEEEFloat}
    buf = Base.StringVector(precision + neededdigits(T))
    pos = writeexp(buf, 1, x, precision, plus, space, hash, expchar, decchar, trimtrailingzeros)
    return String(resize!(buf, pos - 1))
end

function Base.show(io::IO, x::T, forceuntyped::Bool=false, fromprint::Bool=false) where {T <: Base.IEEEFloat}
    compact = get(io, :compact, false)::Bool
    buf = Base.StringVector(neededdigits(T))
    typed = !forceuntyped && !compact && get(io, :typeinfo, Any) != typeof(x)
    pos = writeshortest(buf, 1, x, false, false, true, -1,
        (x isa Float32 && !fromprint) ? UInt8('f') : UInt8('e'), false, UInt8('.'), typed, compact)
    write(io, resize!(buf, pos - 1))
    return
end

function Base.string(x::T) where {T <: Base.IEEEFloat}
    buf = Base.StringVector(neededdigits(T))
    pos = writeshortest(buf, 1, x, false, false, true, -1,
        UInt8('e'), false, UInt8('.'), false, false)
    return String(resize!(buf, pos - 1))
end

Base.print(io::IO, x::Union{Float16, Float32}) = show(io, x, true, true)

end # module
P   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/ryu/utils.jl $      const MANTISSA_MASK = Base.significand_mask(Float64)
const EXP_MASK = Base.exponent_mask(Float64) >> Base.significand_bits(Float64)

# Note: these are smaller than the values given in Figure 4 from the paper
# see https://github.com/ulfjack/ryu/issues/119
pow5_bitcount(::Type{Float16}) = 30
pow5_bitcount(::Type{Float32}) = 61
pow5_bitcount(::Type{Float64}) = 121

pow5_inv_bitcount(::Type{Float16}) = 30
pow5_inv_bitcount(::Type{Float32}) = 59
pow5_inv_bitcount(::Type{Float64}) = 122

qinvbound(::Type{Float16}) = 4
qinvbound(::Type{Float32}) = 9
qinvbound(::Type{Float64}) = 21

qbound(::Type{Float16}) = 15
qbound(::Type{Float32}) = 31
qbound(::Type{Float64}) = 63

"""
    Ryu.log10pow2(e::Integer)

Computes `floor(log10(2^e))`. This is valid for all `e < 1651`.
"""
log10pow2(e) = (e * 78913) >> 18


"""
    Ryu.log10pow5(e::Integer)

Computes `floor(log10(5^e))`. This is valid for all `e < 2621`.
"""
log10pow5(e) = (e * 732923) >> 20

"""
    Ryu.pow5bits(e)

Computes `e == 0 ? 1 : ceil(log2(5^e))`. This is valid for `e < 3529` (if performend in `Int32` arithmetic).
"""
pow5bits(e) = ((e * 1217359) >> 19) + 1

""""
     Ryu.mulshift(m::U, mula, j) where {U<:Unsigned}

Compute `(m * mul) >> j`, where `j >= 8*sizeof(U)`. The type of the results is the larger of `U` or `UInt32`.
"""
function mulshift(m::U, mul, j) where {U<:Unsigned}
    W = widen(U)
    nbits = 8*sizeof(U)
    return ((((W(m) * (mul % U)) >> nbits) + W(m) * (mul >> nbits)) >> (j - nbits)) % promote_type(U,UInt32)
end

indexforexp(e) = div(e + 15, 16)
pow10bitsforindex(idx) = 16 * idx + 120
lengthforindex(idx) = div(((Int64(16 * idx) * 1292913986) >> 32) + 1 + 16 + 8, 9)

"""
    Ryu.pow5(x, p)

Return `true` if `5^p` is a divisor of `x`.
"""
pow5(x, p) = x % (UInt64(5)^p) == 0

"""
    Ryu.pow2(x, p)

Return `true` if `2^p` is a divisor of `x`. In other words, if the trailing `p` bits of `x` are zero.
"""
pow2(x, p) = (x & ((Int64(1) << p) - 1)) == 0

"""
    Ryu.decimallength(v)

The number of decimal digits of the integer `v`.
"""
function decimallength(v)
    v >= 10000000000000000 && return 17
    v >= 1000000000000000 && return 16
    v >= 100000000000000 && return 15
    v >= 10000000000000 && return 14
    v >= 1000000000000 && return 13
    v >= 100000000000 && return 12
    v >= 10000000000 && return 11
    v >= 1000000000 && return 10
    v >= 100000000 && return 9
    v >= 10000000 && return 8
    v >= 1000000 && return 7
    v >= 100000 && return 6
    v >= 10000 && return 5
    v >= 1000 && return 4
    v >= 100 && return 3
    v >= 10 && return 2
    return 1
end
function decimallength(v::UInt32)
    v >= 100000000 && return 9
    v >= 10000000 && return 8
    v >= 1000000 && return 7
    v >= 100000 && return 6
    v >= 10000 && return 5
    v >= 1000 && return 4
    v >= 100 && return 3
    v >= 10 && return 2
    return 1
end
function decimallength(v::UInt16)
    v >= 10000 && return 5
    v >= 1000 && return 4
    v >= 100 && return 3
    v >= 10 && return 2
    return 1
end

function mulshiftinvsplit(::Type{T}, mv, mp, mm, i, j) where {T}
    mul = pow5invsplit_lookup(T, i)
    vr = mulshift(mv, mul, j)
    vp = mulshift(mp, mul, j)
    vm = mulshift(mm, mul, j)
    return vr, vp, vm
end

function mulshiftsplit(::Type{T}, mv, mp, mm, i, j) where {T}
    mul = pow5split_lookup(T, i)
    vr = mulshift(mv, mul, j)
    vp = mulshift(mp, mul, j)
    vm = mulshift(mm, mul, j)
    return vr, vp, vm
end

"""
    Ryu.umul256(a::UInt128, bHi::UInt64, bLo::UInt64)::Tuple{UInt128, UInt128}

Compute `p = a*b` where `b = bLo + bHi<<64`, returning the result as `pLo, pHi` where `p = pLo + pHi<<128`.
"""
function umul256(a::UInt128, bHi::UInt64, bLo::UInt64)
    aLo = a % UInt64
    aHi = (a >> 64) % UInt64

    b00 = UInt128(aLo) * bLo
    b01 = UInt128(aLo) * bHi
    b10 = UInt128(aHi) * bLo
    b11 = UInt128(aHi) * bHi

    b00Lo = b00 % UInt64
    b00Hi = (b00 >> 64) % UInt64

    mid1 = b10 + b00Hi
    mid1Lo = mid1 % UInt64
    mid1Hi = (mid1 >> 64) % UInt64

    mid2 = b01 + mid1Lo
    mid2Lo = mid2 % UInt64
    mid2Hi = (mid2 >> 64) % UInt64

    pHi = b11 + mid1Hi + mid2Hi
    pLo = (UInt128(mid2Lo) << 64) | b00Lo
    return pLo, pHi
end

"""
    Ryu.umul256_hi(a::UInt128, bHi::UInt64, bLo::UInt64)::UInt128

Compute `pHi = (a*b)>>128` where `b = bLo + bHi<<64`.
"""
umul256_hi(a::UInt128, bHi::UInt64, bLo::UInt64) = umul256(a, bHi, bLo)[2]

"""
    Ryu.mulshiftmod1e9(m, mula, mulb, mulc, j)::UInt32

Compute `(m * mul) >> j % 10^9` where `mul = mula + mulb<<64 + mulc<<128`, and `j >= 128`.
"""
function mulshiftmod1e9(m, mula, mulb, mulc, j)
    b0 = UInt128(m) * mula
    b1 = UInt128(m) * mulb
    b2 = UInt128(m) * mulc
    mid = b1 + ((b0 >> 64) % UInt64)
    s1 = b2 + ((mid >> 64) % UInt64)
    v = s1 >> (j - 128)
    multiplied = umul256_hi(v, 0x89705F4136B4A597, 0x31680A88F8953031)
    shifted = (multiplied >> 29) % UInt32
    return (v % UInt32) - UInt32(1000000000) * shifted
end

function append_sign(x, plus::Bool, space::Bool, buf, pos::Int)
    if signbit(x) && !isnan(x)  # suppress minus sign for signaling NaNs
        buf[pos] = UInt8('-')
        pos += 1
    elseif plus
        buf[pos] = UInt8('+')
        pos += 1
    elseif space
        buf[pos] = UInt8(' ')
        pos += 1
    end
    return pos
end


import Base: append_c_digits_fast as append_c_digits, append_nine_digits

function append_d_digits(olength::Int, digits::Unsigned, buf, pos::Int, decchar)
    newpos = append_c_digits(olength, digits, buf, pos + 1)
    @inbounds buf[pos] = buf[pos + 1]
    @inbounds buf[pos + 1] = decchar
    return newpos # == pos + olength + 1
end

const BIG_MASK = (big(1) << 64) - 1

const POW10_SPLIT = collect(Iterators.flatten(map(0:63) do idx
    pow10bits = pow10bitsforindex(idx)
    map(0:lengthforindex(idx)-1) do i
        v = (div(big(1) << pow10bits, big(10)^(9 * i)) + 1) % ((big(10)^9) << 136)
        return (UInt64(v & BIG_MASK), UInt64((v >> 64) & BIG_MASK), UInt64((v >> 128) & BIG_MASK))
    end
end))

function generateinversetables()
    POW10_OFFSET_2 = Vector{UInt16}(undef, 68 + 1)
    MIN_BLOCK_2 = fill(0xff, 68 + 1)
    POW10_SPLIT_2 = Tuple{UInt64, UInt64, UInt64}[]
    lowerCutoff = big(1) << (54 + 8)
    for idx = 0:67
        POW10_OFFSET_2[idx + 1] = length(POW10_SPLIT_2)
        i = 0
        while true
            v = ((big(10)^(9 * (i + 1)) >> (-(120 - 16 * idx))) % (big(10)^9) << (120 + 16))
            if MIN_BLOCK_2[idx + 1] == 0xff && ((v * lowerCutoff) >> 128) == 0
                i += 1
                continue
            end
            if MIN_BLOCK_2[idx + 1] == 0xff
                MIN_BLOCK_2[idx + 1] = i
            end
            v == 0 && break
            push!(POW10_SPLIT_2, ((v & BIG_MASK) % UInt64, ((v >> 64) & BIG_MASK) % UInt64, ((v >> 128) & BIG_MASK) % UInt64))
            i += 1
        end
    end
    POW10_OFFSET_2[end] = length(POW10_SPLIT_2)
    MIN_BLOCK_2[end] = 0x00

    return POW10_OFFSET_2, MIN_BLOCK_2, POW10_SPLIT_2
end

const POW10_OFFSET_2, MIN_BLOCK_2, POW10_SPLIT_2 = generateinversetables()

"""
    Ryu.pow5invsplit(T, i)

Compute `floor(2^k/5^i)+1`, where `k = pow5bits(i) - 1 + pow5_inv_bitcount(T)`. The result
is an unsigned integer twice as wide as `T` (i.e. a `UInt128` if `T == Float64`), with
`pow5_inv_bitcount(T)` significant bits.
"""
function pow5invsplit(::Type{T}, i) where {T<:AbstractFloat}
    W = widen(uinttype(T))
    pow = big(5)^i
    inv = div(big(1) << (ndigits(pow, base=2) - 1 + pow5_inv_bitcount(T)), pow) + 1
    return W(inv)
end

"""
    Ryu.pow5invsplit_lookup(T, i)

[`pow5invsplit`](@ref) computed via lookup table.
"""
function pow5invsplit_lookup end
for T in (Float64, Float32, Float16)
    e2_max = exponent_max(T) - precision(T) - 1
    i_max = log10pow2(e2_max)
    table_sym = Symbol("pow5invsplit_table_", string(T))
    @eval const $table_sym = Tuple(Any[pow5invsplit($T, i) for i = 0:$i_max])
    @eval pow5invsplit_lookup(::Type{$T}, i) = @inbounds($table_sym[i+1])
end


"""
    Ryu.pow5split(T, i)

Compute `floor(5^i/2^k)`, where `k = pow5bits(i) - pow5_bitcount(T)`. The result is an
unsigned integer twice as wide as `T` (i.e. a `UInt128` if `T == Float64`), with
`pow5_bitcount(T)` significant bits.
"""
function pow5split(::Type{T}, i) where {T<:AbstractFloat}
    W = widen(uinttype(T))
    pow = big(5)^i
    return W(pow >> (ndigits(pow, base=2) - pow5_bitcount(T)))
end

"""
    Ryu.pow5split_lookup(T, i)

[`pow5split`](@ref) computed via lookup table.
"""
function pow5split_lookup end
for T in (Float64, Float32, Float16)
    e2_min = 1 - exponent_bias(T) - significand_bits(T) - 2
    i_max = 1 - e2_min - log10pow5(-e2_min)
    table_sym = Symbol("pow5split_table_", string(T))
    @eval const $table_sym = Tuple(Any[pow5split($T, i) for i = 0:$i_max])
    @eval pow5split_lookup(::Type{$T}, i) = @inbounds($table_sym[i+1])
end

const DIGIT_TABLE16 = Base._dec_d100

const POW10_OFFSET = UInt16[
  0, 2, 5, 8, 12, 16, 21, 26, 32, 39,
  46, 54, 62, 71, 80, 90, 100, 111, 122, 134,
  146, 159, 173, 187, 202, 217, 233, 249, 266, 283,
  301, 319, 338, 357, 377, 397, 418, 440, 462, 485,
  508, 532, 556, 581, 606, 632, 658, 685, 712, 740,
  769, 798, 828, 858, 889, 920, 952, 984, 1017, 1050,
  1084, 1118, 1153, 1188
]
S   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/ryu/shortest.jl�:      """
    b, e10 = reduce_shortest(f[, maxsignif])

Reduce to shortest decimal representation where `abs(f) == b * 10^e10` and `b` is an
integer. If a `maxsignif` argument is provided, then `b < maxsignif`.
"""
@inline function reduce_shortest(f::T, maxsignif=nothing) where {T}
    U = uinttype(T)
    uf = reinterpret(U, f)
    m = uf & significand_mask(T)
    e = ((uf & exponent_mask(T)) >> significand_bits(T)) % Int

    ## Step 1
    #  mf * 2^ef == f
    mf = (one(U) << significand_bits(T)) | m
    ef = e - exponent_bias(T) - significand_bits(T)
    f_isinteger = mf & ((one(U) << -ef) - one(U)) == 0

    if ef > 0 || ef < -Base.significand_bits(T) || !f_isinteger
        # fixup subnormals
        if e == 0
            ef = 1 - exponent_bias(T) - significand_bits(T)
            mf = m
        end

        ## Step 2
        #  u * 2^e2 == (f + prevfloat(f))/2
        #  v * 2^e2 == f
        #  w * 2^e2 == (f + nextfloat(f))/2
        e2 = ef - 2
        mf_iseven = iseven(mf) # trailing bit of significand is zero

        v = U(4) * mf
        w = v + U(2)
        u_shift_half = m == 0 && e > 1 # if first element of binade, other than first normal one
        u = v - U(2) + u_shift_half

        ## Step 3
        #  a == floor(u * 2^e2 / 10^e10), exact if a_allzero
        #  b == floor(v * 2^e2 / 10^e10), exact if b_allzero
        #  c == floor(w * 2^e2 / 10^e10)
        a_allzero = false
        b_allzero = false
        b_lastdigit = 0x00
        if e2 >= 0
            q = log10pow2(e2) - (T == Float64 ? (e2 > 3) : 0)
            e10 = q
            k = pow5_inv_bitcount(T) + pow5bits(q) - 1
            i = -e2 + q + k
            a, b, c = mulshiftinvsplit(T, u, v, w, q, i)
            if T == Float32 || T == Float16
                if q != 0 && div(c - 1, 10) <= div(a, 10)
                    l = pow5_inv_bitcount(T) + pow5bits(q - 1) - 1
                    mul = pow5invsplit_lookup(T, q-1)
                    b_lastdigit = (mulshift(v, mul, -e2 + q - 1 + l) % 10) % UInt8
                end
            end
            if q <= qinvbound(T)
                if ((v % UInt32) - 5 * div(v, 5)) == 0
                    b_allzero = pow5(v, q)
                elseif mf_iseven
                    a_allzero = pow5(u, q)
                else
                    c -= pow5(w, q)
                end
            end
        else
            q = log10pow5(-e2) - (T == Float64 ? (-e2 > 1) : 0)
            e10 = q + e2
            i = -e2 - q
            k = pow5bits(i) - pow5_bitcount(T)
            j = q - k
            a, b, c = mulshiftsplit(T, u, v, w, i, j)
            if T == Float32 || T == Float16
                if q != 0 && div(c - 1, 10) <= div(a, 10)
                    j = q - 1 - (pow5bits(i + 1) - pow5_bitcount(T))
                    mul = pow5split_lookup(T, i+1)
                    b_lastdigit = (mulshift(v, mul, j) % 10) % UInt8
                end
            end
            if q <= 1
                b_allzero = true
                if mf_iseven
                    a_allzero = !u_shift_half
                else
                    c -= 1
                end
            elseif q < qbound(T)
                b_allzero = pow2(v, q - (T != Float64))
            end
        end

        ## Step 4: reduction
        if a_allzero || b_allzero
            # a) slow loop
            while true
                c_div10 = div(c, 10)
                a_div10 = div(a, 10)
                if c_div10 <= a_div10
                    break
                end
                a_mod10 = (a % UInt32) - UInt32(10) * (a_div10 % UInt32)
                b_div10 = div(b, 10)
                b_mod10 = (b % UInt32) - UInt32(10) * (b_div10 % UInt32)
                a_allzero &= a_mod10 == 0
                b_allzero &= b_lastdigit == 0
                b_lastdigit = b_mod10 % UInt8
                b = b_div10
                c = c_div10
                a = a_div10
                e10 += 1
            end
            if a_allzero
                while true
                    a_div10 = div(a, 10)
                    a_mod10 = (a % UInt32) - UInt32(10) * (a_div10 % UInt32)
                    if a_mod10 != 0 && (maxsignif === nothing || b < maxsignif)
                        break
                    end
                    c_div10 = div(c, 10)
                    b_div10 = div(b, 10)
                    b_mod10 = (b % UInt32) - UInt32(10) * (b_div10 % UInt32)
                    b_allzero &= b_lastdigit == 0
                    b_lastdigit = b_mod10 % UInt8
                    b = b_div10
                    c = c_div10
                    a = a_div10
                    e10 += 1
                end
            end
            if b_allzero && b_lastdigit == 5 && iseven(b)
                b_lastdigit = UInt8(4)
            end
            roundup = (b == a && (!mf_iseven || !a_allzero)) || b_lastdigit >= 5
        else
            # b) specialized for common case (99% Float64, 96% Float32)
            roundup = b_lastdigit >= 5
            c_div100 = div(c, 100)
            a_div100 = div(a, 100)
            if c_div100 > a_div100
                b_div100 = div(b, 100)
                b_mod100 = (b % UInt32) - UInt32(100) * (b_div100 % UInt32)
                roundup = b_mod100 >= 50
                b = b_div100
                c = c_div100
                a = a_div100
                e10 += 2
            end
            while true
                c_div10 = div(c, 10)
                a_div10 = div(a, 10)
                if c_div10 <= a_div10
                    break
                end
                b_div10 = div(b, 10)
                b_mod10 = (b % UInt32) - UInt32(10) * (b_div10 % UInt32)
                roundup = b_mod10 >= 5
                b = b_div10
                c = c_div10
                a = a_div10
                e10 += 1
            end
            roundup = (b == a || roundup)
        end
        if maxsignif !== nothing && b > maxsignif
            # reduce to max significant digits
            while true
                b_div10 = div(b, 10)
                b_mod10 = (b % UInt32) - UInt32(10) * (b_div10 % UInt32)
                if b <= maxsignif
                    break
                end
                b = b_div10
                roundup = (b_allzero && iseven(b)) ? b_mod10 > 5 : b_mod10 >= 5
                b_allzero &= b_mod10 == 0
                e10 += 1
            end
            b = b + roundup

            # remove trailing zeros
            while true
                b_div10 = div(b, 10)
                b_mod10 = (b % UInt32) - UInt32(10) * (b_div10 % UInt32)
                if b_mod10 != 0
                    break
                end
                b = b_div10
                e10 += 1
            end
        else
            b = b + roundup
        end
    else
        # c) specialized f an integer < 2^53
        b = mf >> -ef
        e10 = 0

        if maxsignif !== nothing && b > maxsignif
            b_allzero = true
            # reduce to max significant digits
            while true
                b_div10 = div(b, 10)
                b_mod10 = (b % UInt32) - UInt32(10) * (b_div10 % UInt32)
                if b <= maxsignif
                    break
                end
                b = b_div10
                roundup = (b_allzero && iseven(b)) ? b_mod10 > 5 : b_mod10 >= 5
                b_allzero &= b_mod10 == 0
                e10 += 1
            end
            b = b + roundup
        end
        while true
            b_div10 = div(b, 10)
            b_mod10 = (b % UInt32) - UInt32(10) * (b_div10 % UInt32)
            if b_mod10 != 0
                break
            end
            b = b_div10
            e10 += 1
        end
    end
    return b, e10
end

function writeshortest(buf::Vector{UInt8}, pos, x::T,
                       plus=false, space=false, hash=true,
                       precision=-1, expchar=UInt8('e'), padexp=false, decchar=UInt8('.'),
                       typed=false, compact=false) where {T}
    @assert 0 < pos <= length(buf)
    # special cases
    if x == 0
        if typed && x isa Float16
            @inbounds buf[pos] = UInt8('F')
            @inbounds buf[pos + 1] = UInt8('l')
            @inbounds buf[pos + 2] = UInt8('o')
            @inbounds buf[pos + 3] = UInt8('a')
            @inbounds buf[pos + 4] = UInt8('t')
            @inbounds buf[pos + 5] = UInt8('1')
            @inbounds buf[pos + 6] = UInt8('6')
            @inbounds buf[pos + 7] = UInt8('(')
            pos += 8
        end
        pos = append_sign(x, plus, space, buf, pos)
        @inbounds buf[pos] = UInt8('0')
        pos += 1
        if hash
            @inbounds buf[pos] = decchar
            pos += 1
        end
        if precision == -1
            @inbounds buf[pos] = UInt8('0')
            pos += 1
            if typed && x isa Float32
                @inbounds buf[pos] = UInt8('f')
                @inbounds buf[pos + 1] = UInt8('0')
                pos += 2
            end
            if typed && x isa Float16
                @inbounds buf[pos] = UInt8(')')
                pos += 1
            end
            return pos
        end
        while hash && precision > 1
            @inbounds buf[pos] = UInt8('0')
            pos += 1
            precision -= 1
        end
        if typed && x isa Float32
            @inbounds buf[pos] = UInt8('f')
            @inbounds buf[pos + 1] = UInt8('0')
            pos += 2
        end
        if typed && x isa Float16
            @inbounds buf[pos] = UInt8(')')
            pos += 1
        end
        return pos
    elseif isnan(x)
        pos = append_sign(x, plus, space, buf, pos)
        @inbounds buf[pos] = UInt8('N')
        @inbounds buf[pos + 1] = UInt8('a')
        @inbounds buf[pos + 2] = UInt8('N')
        if typed
            if x isa Float32
                @inbounds buf[pos + 3] = UInt8('3')
                @inbounds buf[pos + 4] = UInt8('2')
            elseif x isa Float16
                @inbounds buf[pos + 3] = UInt8('1')
                @inbounds buf[pos + 4] = UInt8('6')
            end
        end
        return pos + 3 + (typed && x isa Union{Float32, Float16} ? 2 : 0)
    elseif !isfinite(x)
        pos = append_sign(x, plus, space, buf, pos)
        @inbounds buf[pos] = UInt8('I')
        @inbounds buf[pos + 1] = UInt8('n')
        @inbounds buf[pos + 2] = UInt8('f')
        if typed
            if x isa Float32
                @inbounds buf[pos + 3] = UInt8('3')
                @inbounds buf[pos + 4] = UInt8('2')
            elseif x isa Float16
                @inbounds buf[pos + 3] = UInt8('1')
                @inbounds buf[pos + 4] = UInt8('6')
            end
        end
        return pos + 3 + (typed && x isa Union{Float32, Float16} ? 2 : 0)
    end

    output, nexp = reduce_shortest(x, compact ? 999_999 : nothing)

    if typed && x isa Float16
        @inbounds buf[pos] = UInt8('F')
        @inbounds buf[pos + 1] = UInt8('l')
        @inbounds buf[pos + 2] = UInt8('o')
        @inbounds buf[pos + 3] = UInt8('a')
        @inbounds buf[pos + 4] = UInt8('t')
        @inbounds buf[pos + 5] = UInt8('1')
        @inbounds buf[pos + 6] = UInt8('6')
        @inbounds buf[pos + 7] = UInt8('(')
        pos += 8
    end
    pos = append_sign(x, plus, space, buf, pos)

    olength = decimallength(output)
    exp_form = true
    pt = nexp + olength
    if -4 < pt <= (precision == -1 ? (T == Float16 ? 3 : 6) : precision) &&
        !(pt >= olength && abs(mod(x + 0.05, 10^(pt - olength)) - 0.05) > 0.05)
        exp_form = false
        if pt <= 0
            @inbounds buf[pos] = UInt8('0')
            pos += 1
            @inbounds buf[pos] = decchar
            pos += 1
            for _ = 1:abs(pt)
                @inbounds buf[pos] = UInt8('0')
                pos += 1
            end
        # elseif pt >= olength
            # nothing to do at this point
        # else
            # nothing to do at this point
        end
    else
        # make space for decchar
        pos += 1
    end

    append_c_digits(olength, output, buf, pos)

    if !exp_form
        if pt <= 0
            pos += olength
            precision -= olength
        elseif pt >= olength
            pos += olength
            precision -= olength
            for _ = 1:nexp
                @inbounds buf[pos] = UInt8('0')
                pos += 1
                precision -= 1
            end
            if hash
                @inbounds buf[pos] = decchar
                pos += 1
                if precision < 0
                    @inbounds buf[pos] = UInt8('0')
                    pos += 1
                end
            end
        else
            pointoff = olength - abs(nexp)
            # shift bytes after pointoff to make room for decchar
            ptr = pointer(buf)
            memmove(ptr + pos + pointoff, ptr + pos + pointoff - 1, olength - pointoff + 1)
            @inbounds buf[pos + pointoff] = decchar
            pos += olength + 1
            precision -= olength
        end
        if hash
            while precision > 0
                @inbounds buf[pos] = UInt8('0')
                pos += 1
                precision -= 1
            end
        end
        if typed && x isa Float32
            @inbounds buf[pos] = UInt8('f')
            @inbounds buf[pos + 1] = UInt8('0')
            pos += 2
        end
    else
        # move leading digit into place
        @inbounds buf[pos - 1] = buf[pos]
        if olength > 1 || hash
            @inbounds buf[pos] = decchar
            pos += olength
            precision -= olength
        end
        if hash
            if olength == 1
                @inbounds buf[pos] = UInt8('0')
                pos += 1
            end
            while precision > 0
                @inbounds buf[pos] = UInt8('0')
                pos += 1
                precision -= 1
            end
        end

        @inbounds buf[pos] = expchar
        pos += 1
        exp2 = nexp + olength - 1
        if exp2 < 0
            @inbounds buf[pos] = UInt8('-')
            pos += 1
            exp2 = -exp2
        elseif padexp
            @inbounds buf[pos] = UInt8('+')
            pos += 1
        end

        if exp2 >= 100
            c = exp2 % 10
            @inbounds d100 = DIGIT_TABLE16[(div(exp2, 10) % Int) + 1]
            @inbounds buf[pos] = d100 % UInt8
            @inbounds buf[pos + 1] = (d100 >> 0x8) % UInt8
            @inbounds buf[pos + 2] = UInt8('0') + (c % UInt8)
            pos += 3
        elseif exp2 >= 10
            @inbounds d100 = DIGIT_TABLE16[(exp2 % Int) + 1]
            @inbounds buf[pos] = d100 % UInt8
            @inbounds buf[pos + 1] = (d100 >> 0x8) % UInt8
            pos += 2
        else
            if padexp
                @inbounds buf[pos] = UInt8('0')
                pos += 1
            end
            @inbounds buf[pos] = UInt8('0') + (exp2 % UInt8)
            pos += 1
        end
    end
    if typed && x isa Float16
        @inbounds buf[pos] = UInt8(')')
        pos += 1
    end

    return pos
end
P   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/ryu/fixed.jl�      function writefixed(buf, pos, v::T,
    precision=-1, plus=false, space=false, hash=false,
    decchar=UInt8('.'), trimtrailingzeros=false) where {T <: Base.IEEEFloat}
    @assert 0 < pos <= length(buf)
    startpos = pos
    x = Float64(v)
    pos = append_sign(x, plus, space, buf, pos)

    # special cases
    if x == 0
        buf[pos] = UInt8('0')
        pos += 1
        if precision > 0 && !trimtrailingzeros
            buf[pos] = decchar
            pos += 1
            for _ = 1:precision
                buf[pos] = UInt8('0')
                pos += 1
            end
        elseif hash
            buf[pos] = decchar
            pos += 1
        end
        return pos
    elseif isnan(x)
        buf[pos] = UInt8('N')
        buf[pos + 1] = UInt8('a')
        buf[pos + 2] = UInt8('N')
        return pos + 3
    elseif !isfinite(x)
        buf[pos] = UInt8('I')
        buf[pos + 1] = UInt8('n')
        buf[pos + 2] = UInt8('f')
        return pos + 3
    end

    bits = Core.bitcast(UInt64, x)
    mant = bits & MANTISSA_MASK
    exp = Int((bits >> 52) & EXP_MASK)

    if exp == 0 # subnormal
        e2 = 1 - 1023 - 52
        m2 = mant
    else
        e2 = exp - 1023 - 52
        m2 = (Int64(1) << 52) | mant
    end
    nonzero = false
    if e2 >= -52
        idx = e2 < 0 ? 0 : indexforexp(e2)
        p10bits = pow10bitsforindex(idx)
        len = lengthforindex(idx)
        i = len - 1
        while i >= 0
            j = p10bits - e2
            mula, mulb, mulc = POW10_SPLIT[POW10_OFFSET[idx + 1] + i + 1]
            digits = mulshiftmod1e9(m2 << 8, mula, mulb, mulc, j + 8)
            if nonzero
                pos = append_nine_digits(digits, buf, pos)
            elseif digits != 0
                olength = decimallength(digits)
                pos = append_c_digits(olength, digits, buf, pos)
                nonzero = true
            end
            i -= 1
        end
    end
    if !nonzero
        buf[pos] = UInt8('0')
        pos += 1
    end
    hasfractional = false
    if precision > 0 || hash
        buf[pos] = decchar
        pos += 1
        hasfractional = true
    end
    if e2 < 0
        idx = div(-e2, 16)
        blocks = div(precision, 9) + 1
        roundUp = 0
        i = 0
        if blocks <= MIN_BLOCK_2[idx + 1]
            i = blocks
            for _ = 1:precision
                buf[pos] = UInt8('0')
                pos += 1
            end
        elseif i < MIN_BLOCK_2[idx + 1]
            i = MIN_BLOCK_2[idx + 1]
            for _ = 1:(9 * i)
                buf[pos] = UInt8('0')
                pos += 1
            end
        end
        while i < blocks
            j = 120 + (-e2 - 16 * idx)
            p = POW10_OFFSET_2[idx + 1] + UInt32(i) - MIN_BLOCK_2[idx + 1]
            if p >= POW10_OFFSET_2[idx + 2]
                for _ = 1:(precision - 9 * i)
                    buf[pos] = UInt8('0')
                    pos += 1
                end
                break
            end
            mula, mulb, mulc = POW10_SPLIT_2[p + 1]
            digits = mulshiftmod1e9(m2 << 8, mula, mulb, mulc, j + 8)
            if i < blocks - 1
                pos = append_nine_digits(digits, buf, pos)
            else
                maximum = precision - 9 * i
                lastDigit = 0
                k = 0
                while k < 9 - maximum
                    # global digits, lastDigit, k
                    lastDigit = digits % 10
                    digits = div(digits, 10)
                    k += 1
                end
                if lastDigit != 5
                    roundUp = lastDigit > 5 ? 1 : 0
                else
                    requiredTwos = -e2 - precision - 1
                    trailingZeros = requiredTwos <= 0 || (requiredTwos < 60 && pow2(m2, requiredTwos))
                    roundUp = trailingZeros ? 2 : 1 # 2 means round only if odd
                end
                if maximum > 0
                    pos = append_c_digits(maximum, digits, buf, pos)
                end
                break
            end
            i += 1
        end
        if roundUp != 0
            roundPos = pos
            dotPos = 1
            while true
                roundPos -= 1
                if roundPos == (startpos - 1) || (buf[roundPos] == UInt8('-')) || (plus && buf[roundPos] == UInt8('+')) || (space && buf[roundPos] == UInt8(' '))
                    buf[pos] = UInt8('0')
                    buf[roundPos + 1] = UInt8('1')
                    if dotPos > 1
                        buf[dotPos] = UInt8('0')
                        buf[dotPos + 1] = decchar
                        hasfractional = true
                    end
                    pos += 1
                    break
                end
                c = roundPos > 0 ? buf[roundPos] : 0x00
                if c == decchar
                    dotPos = roundPos
                    continue
                elseif c == UInt8('9')
                    buf[roundPos] = UInt8('0')
                    roundUp = 1
                    continue
                else
                    if roundUp == 2 && UInt8(c) % 2 == 0
                        break
                    end
                    buf[roundPos] = c + 1
                    break
                end
            end
        end
    else
        for _ = 1:precision
            buf[pos] = UInt8('0')
            pos += 1
        end
    end
    if trimtrailingzeros && hasfractional
        while buf[pos - 1] == UInt8('0')
            pos -= 1
        end
        if buf[pos - 1] == decchar && !hash
            pos -= 1
        end
    end
    return pos
end
N   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/ryu/exp.jl�      function writeexp(buf, pos, v::T,
    precision=-1, plus=false, space=false, hash=false,
    expchar=UInt8('e'), decchar=UInt8('.'), trimtrailingzeros=false) where {T <: Base.IEEEFloat}
    @assert 0 < pos <= length(buf)
    startpos = pos
    x = Float64(v)
    pos = append_sign(x, plus, space, buf, pos)

    # special cases
    if iszero(x)
        @inbounds buf[pos] = UInt8('0')
        pos += 1
        if precision > 0 && !trimtrailingzeros
            @inbounds buf[pos] = decchar
            pos += 1
            for _ = 1:precision
                @inbounds buf[pos] = UInt8('0')
                pos += 1
            end
        elseif hash
            @inbounds buf[pos] = decchar
            pos += 1
        end
        @inbounds buf[pos] = expchar
        @inbounds buf[pos + 1] = UInt8('+')
        @inbounds buf[pos + 2] = UInt8('0')
        @inbounds buf[pos + 3] = UInt8('0')
        return pos + 4
    elseif isnan(x)
        @inbounds buf[pos] = UInt8('N')
        @inbounds buf[pos + 1] = UInt8('a')
        @inbounds buf[pos + 2] = UInt8('N')
        return pos + 3
    elseif !isfinite(x)
        @inbounds buf[pos] = UInt8('I')
        @inbounds buf[pos + 1] = UInt8('n')
        @inbounds buf[pos + 2] = UInt8('f')
        return pos + 3
    end

    bits = Core.bitcast(UInt64, x)
    mant = bits & MANTISSA_MASK
    exp = Int((bits >> 52) & EXP_MASK)

    if iszero(exp)
        e2 = 1 - 1023 - 52
        m2 = mant
    else
        e2 = exp - 1023 - 52
        m2 = (Int64(1) << 52) | mant
    end
    nonzero = false
    precision += 1
    digits = zero(UInt32)
    printedDigits = 0
    availableDigits = 0
    e = 0
    if e2 >= -52
        idx = e2 < 0 ? 0 : indexforexp(e2)
        p10bits = pow10bitsforindex(idx)
        len = lengthforindex(idx)
        i = len - 1
        while i >= 0
            j = p10bits - e2
            #=@inbounds=# mula, mulb, mulc = POW10_SPLIT[POW10_OFFSET[idx + 1] + i + 1]
            digits = mulshiftmod1e9(m2 << 8, mula, mulb, mulc, j + 8)
            if !iszero(printedDigits)
                if printedDigits + 9 > precision
                    availableDigits = 9
                    break
                end
                pos = append_nine_digits(digits, buf, pos)
                printedDigits += 9
            elseif !iszero(digits)
                availableDigits = decimallength(digits)
                e = i * 9 + availableDigits - 1
                if availableDigits > precision
                    break
                end
                if precision > 1
                    pos = append_d_digits(availableDigits, digits, buf, pos, decchar)
                else
                    @inbounds buf[pos] = UInt8('0') + digits
                    pos += 1
                    if hash
                        @inbounds buf[pos] = decchar
                        pos += 1
                    end
                end
                printedDigits = availableDigits
                availableDigits = 0
            end
            i -= 1
        end
    end
    if e2 < 0 && iszero(availableDigits)
        idx = div(-e2, 16)
        i = Int(MIN_BLOCK_2[idx + 1])
        while i < 200
            j = 120 + (-e2 - 16 * idx)
            p = POW10_OFFSET_2[idx + 1] + i - MIN_BLOCK_2[idx + 1]
            if p >= POW10_OFFSET_2[idx + 2]
                digits = zero(UInt32)
            else
                #=@inbounds=# mula, mulb, mulc = POW10_SPLIT_2[p + 1]
                digits = mulshiftmod1e9(m2 << 8, mula, mulb, mulc, j + 8)
            end
            if !iszero(printedDigits)
                if printedDigits + 9 > precision
                    availableDigits = 9
                    break
                end
                pos = append_nine_digits(digits, buf, pos)
                printedDigits += 9
            elseif !iszero(digits)
                availableDigits = decimallength(digits)
                e = -(i + 1) * 9 + availableDigits - 1
                if availableDigits > precision
                    break
                end
                if precision > 1
                    pos = append_d_digits(availableDigits, digits, buf, pos, decchar)
                else
                    @inbounds buf[pos] = UInt8('0') + digits
                    pos += 1
                    if hash
                        @inbounds buf[pos] = decchar
                        pos += 1
                    end
                end
                printedDigits = availableDigits
                availableDigits = 0
            end
            i += 1
        end
    end
    maximum = precision - printedDigits
    if iszero(availableDigits)
        digits = zero(UInt32)
    end
    lastDigit = zero(UInt32)
    if availableDigits > maximum
        for k = 0:(availableDigits - maximum - 1)
            lastDigit = digits % UInt32(10)
            digits = div(digits, UInt32(10))
        end
    end
    roundUp = 0
    if lastDigit != 5
        roundUp = lastDigit > 5 ? 1 : 0
    else
        rexp = precision - e
        requiredTwos = -e2 - rexp
        trailingZeros = requiredTwos <= 0 ||
            (requiredTwos < 60 && pow2(m2, requiredTwos))
        if rexp < 0
            requiredFives = -rexp
            trailingZeros = trailingZeros & pow5(m2, requiredFives)
        end
        roundUp = trailingZeros ? 2 : 1
    end
    if !iszero(printedDigits)
        if iszero(digits)
            for _ = 1:maximum
                @inbounds buf[pos] = UInt8('0')
                pos += 1
            end
        else
            pos = append_c_digits(maximum, digits, buf, pos)
        end
    else
        if precision > 1
            pos = append_d_digits(maximum, digits, buf, pos, decchar)
        else
            @inbounds buf[pos] = UInt8('0') + digits
            pos += 1
            if hash
                @inbounds buf[pos] = decchar
                pos += 1
            end
        end
    end
    if !iszero(roundUp)
        roundPos = pos
        while true
            roundPos -= 1
            if roundPos == (startpos - 1) || (@inbounds buf[roundPos]) == UInt8('-') || (plus && (@inbounds buf[roundPos]) == UInt8('+')) || (space && (@inbounds buf[roundPos]) == UInt8(' '))
                @inbounds buf[roundPos + 1] = UInt8('1')
                e += 1
                break
            end
            c = roundPos > 0 ? (@inbounds buf[roundPos]) : 0x00
            if c == decchar
                continue
            elseif c == UInt8('9')
                @inbounds buf[roundPos] = UInt8('0')
                roundUp = 1
                continue
            else
                if roundUp == 2 && iseven(c)
                    break
                end
                @inbounds buf[roundPos] = c + 1
                break
            end
        end
    end
    if trimtrailingzeros
        while @inbounds buf[pos - 1] == UInt8('0')
            pos -= 1
        end
        if @inbounds buf[pos - 1] == decchar && !hash
            pos -= 1
        end
    end
    buf[pos] = expchar
    pos += 1
    if e < 0
        @inbounds buf[pos] = UInt8('-')
        pos += 1
        e = -e
    else
        @inbounds buf[pos] = UInt8('+')
        pos += 1
    end
    if e >= 100
        c = (e % 10) % UInt8
        @inbounds d100 = DIGIT_TABLE16[div(e, 10) + 1]
        @inbounds buf[pos] = d100 % UInt8
        @inbounds buf[pos + 1] = (d100 >> 0x8) % UInt8
        @inbounds buf[pos + 2] = UInt8('0') + c
        pos += 3
    else
        @inbounds d100 = DIGIT_TABLE16[e + 1]
        @inbounds buf[pos] = d100 % UInt8
        @inbounds buf[pos + 1] = (d100 >> 0x8) % UInt8
        pos += 2
    end
    return pos
end
K   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/mpfr.jl��      # This file is a part of Julia. License is MIT: https://julialang.org/license

module MPFR

export
    BigFloat,
    setprecision

import
    .Base: *, +, -, /, <, <=, ==, >, >=, ^, ceil, cmp, convert, copysign, div,
        inv, exp, exp2, exponent, factorial, floor, fma, muladd, hypot, isinteger,
        isfinite, isinf, isnan, ldexp, log, log2, log10, max, min, mod, modf,
        nextfloat, prevfloat, promote_rule, rem, rem2pi, round, show, float,
        sum, sqrt, string, print, trunc, precision, _precision, exp10, expm1, log1p,
        eps, signbit, sign, sin, cos, sincos, tan, sec, csc, cot, acos, asin, atan,
        cosh, sinh, tanh, sech, csch, coth, acosh, asinh, atanh, lerpi,
        cbrt, typemax, typemin, unsafe_trunc, floatmin, floatmax, rounding,
        setrounding, maxintfloat, widen, significand, frexp, tryparse, iszero,
        isone, big, _string_n, decompose, minmax,
        sinpi, cospi, sincospi, tanpi, sind, cosd, tand, asind, acosd, atand


using .Base.Libc
import ..Rounding: rounding_raw, setrounding_raw

import ..GMP: ClongMax, CulongMax, CdoubleMax, Limb, libgmp

import ..FastMath.sincos_fast

if Sys.iswindows()
    const libmpfr = "libmpfr-6.dll"
elseif Sys.isapple()
    const libmpfr = "@rpath/libmpfr.6.dylib"
else
    const libmpfr = "libmpfr.so.6"
end


version() = VersionNumber(unsafe_string(ccall((:mpfr_get_version,libmpfr), Ptr{Cchar}, ())))
patches() = split(unsafe_string(ccall((:mpfr_get_patches,libmpfr), Ptr{Cchar}, ())),' ')

function __init__()
    try
        # set exponent to full range by default
        set_emin!(get_emin_min())
        set_emax!(get_emax_max())
    catch ex
        Base.showerror_nostdio(ex, "WARNING: Error during initialization of module MPFR")
    end
    nothing
end

"""
    MPFR.MPFRRoundingMode

Matches the `mpfr_rnd_t` enum provided by MPFR, see
https://www.mpfr.org/mpfr-current/mpfr.html#Rounding-Modes

This is for internal use, and ensures that `ROUNDING_MODE[]` is type-stable.
"""
@enum MPFRRoundingMode begin
    MPFRRoundNearest
    MPFRRoundToZero
    MPFRRoundUp
    MPFRRoundDown
    MPFRRoundFromZero
    MPFRRoundFaithful
end

convert(::Type{MPFRRoundingMode}, ::RoundingMode{:Nearest})  = MPFRRoundNearest
convert(::Type{MPFRRoundingMode}, ::RoundingMode{:ToZero})   = MPFRRoundToZero
convert(::Type{MPFRRoundingMode}, ::RoundingMode{:Up})       = MPFRRoundUp
convert(::Type{MPFRRoundingMode}, ::RoundingMode{:Down})     = MPFRRoundDown
convert(::Type{MPFRRoundingMode}, ::RoundingMode{:FromZero}) = MPFRRoundFromZero

function convert(::Type{RoundingMode}, r::MPFRRoundingMode)
    if r == MPFRRoundNearest
        return RoundNearest
    elseif r == MPFRRoundToZero
        return RoundToZero
    elseif r == MPFRRoundUp
        return RoundUp
    elseif r == MPFRRoundDown
        return RoundDown
    elseif r == MPFRRoundFromZero
        return RoundFromZero
    else
        throw(ArgumentError("invalid MPFR rounding mode code: $r"))
    end
end

const ROUNDING_MODE = Ref{MPFRRoundingMode}(MPFRRoundNearest)
const DEFAULT_PRECISION = Ref{Clong}(256)

# Basic type and initialization definitions

"""
    BigFloat <: AbstractFloat

Arbitrary precision floating point number type.
"""
mutable struct BigFloat <: AbstractFloat
    prec::Clong
    sign::Cint
    exp::Clong
    d::Ptr{Limb}
    # _d::Buffer{Limb} # Julia gc handle for memory @ d
    _d::String # Julia gc handle for memory @ d (optimized)

    # Not recommended for general use:
    # used internally by, e.g. deepcopy
    global function _BigFloat(prec::Clong, sign::Cint, exp::Clong, d::String)
        # ccall-based version, inlined below
        #z = new(zero(Clong), zero(Cint), zero(Clong), C_NULL, d)
        #ccall((:mpfr_custom_init,libmpfr), Cvoid, (Ptr{Limb}, Clong), d, prec) # currently seems to be a no-op in mpfr
        #NAN_KIND = Cint(0)
        #ccall((:mpfr_custom_init_set,libmpfr), Cvoid, (Ref{BigFloat}, Cint, Clong, Ptr{Limb}), z, NAN_KIND, prec, d)
        #return z
        return new(prec, sign, exp, pointer(d), d)
    end

    function BigFloat(; precision::Integer=DEFAULT_PRECISION[])
        precision < 1 && throw(DomainError(precision, "`precision` cannot be less than 1."))
        nb = ccall((:mpfr_custom_get_size,libmpfr), Csize_t, (Clong,), precision)
        nb = (nb + Core.sizeof(Limb) - 1) ÷ Core.sizeof(Limb) # align to number of Limb allocations required for this
        #d = Vector{Limb}(undef, nb)
        d = _string_n(nb * Core.sizeof(Limb))
        EXP_NAN = Clong(1) - Clong(typemax(Culong) >> 1)
        return _BigFloat(Clong(precision), one(Cint), EXP_NAN, d) # +NAN
    end
end

rounding_raw(::Type{BigFloat}) = ROUNDING_MODE[]
setrounding_raw(::Type{BigFloat}, r::MPFRRoundingMode) = ROUNDING_MODE[]=r

rounding(::Type{BigFloat}) = convert(RoundingMode, rounding_raw(BigFloat))
setrounding(::Type{BigFloat}, r::RoundingMode) = setrounding_raw(BigFloat, convert(MPFRRoundingMode, r))


# overload the definition of unsafe_convert to ensure that `x.d` is assigned
# it may have been dropped in the event that the BigFloat was serialized
Base.unsafe_convert(::Type{Ref{BigFloat}}, x::Ptr{BigFloat}) = x
@inline function Base.unsafe_convert(::Type{Ref{BigFloat}}, x::Ref{BigFloat})
    x = x[]
    if x.d == C_NULL
        x.d = pointer(x._d)
    end
    return convert(Ptr{BigFloat}, Base.pointer_from_objref(x))
end

"""
    BigFloat(x::Union{Real, AbstractString} [, rounding::RoundingMode=rounding(BigFloat)]; [precision::Integer=precision(BigFloat)])

Create an arbitrary precision floating point number from `x`, with precision
`precision`. The `rounding` argument specifies the direction in which the result should be
rounded if the conversion cannot be done exactly. If not provided, these are set by the current global values.

`BigFloat(x::Real)` is the same as `convert(BigFloat,x)`, except if `x` itself is already
`BigFloat`, in which case it will return a value with the precision set to the current
global precision; `convert` will always return `x`.

`BigFloat(x::AbstractString)` is identical to [`parse`](@ref). This is provided for
convenience since decimal literals are converted to `Float64` when parsed, so
`BigFloat(2.1)` may not yield what you expect.

See also:
- [`@big_str`](@ref)
- [`rounding`](@ref) and [`setrounding`](@ref)
- [`precision`](@ref) and [`setprecision`](@ref)

!!! compat "Julia 1.1"
    `precision` as a keyword argument requires at least Julia 1.1.
    In Julia 1.0 `precision` is the second positional argument (`BigFloat(x, precision)`).

# Examples
```jldoctest
julia> BigFloat(2.1) # 2.1 here is a Float64
2.100000000000000088817841970012523233890533447265625

julia> BigFloat("2.1") # the closest BigFloat to 2.1
2.099999999999999999999999999999999999999999999999999999999999999999999999999986

julia> BigFloat("2.1", RoundUp)
2.100000000000000000000000000000000000000000000000000000000000000000000000000021

julia> BigFloat("2.1", RoundUp, precision=128)
2.100000000000000000000000000000000000007
```
"""
BigFloat(x, r::RoundingMode)

widen(::Type{Float64}) = BigFloat
widen(::Type{BigFloat}) = BigFloat

function BigFloat(x::BigFloat, r::MPFRRoundingMode=ROUNDING_MODE[]; precision::Integer=DEFAULT_PRECISION[])
    if precision == _precision(x)
        return x
    else
        z = BigFloat(;precision=precision)
        ccall((:mpfr_set, libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, MPFRRoundingMode),
              z, x, r)
        return z
    end
end

function _duplicate(x::BigFloat)
    z = BigFloat(;precision=_precision(x))
    ccall((:mpfr_set, libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Int32), z, x, 0)
    return z
end

# convert to BigFloat
for (fJ, fC) in ((:si,:Clong), (:ui,:Culong))
    @eval begin
        function BigFloat(x::($fC), r::MPFRRoundingMode=ROUNDING_MODE[]; precision::Integer=DEFAULT_PRECISION[])
            z = BigFloat(;precision=precision)
            ccall(($(string(:mpfr_set_,fJ)), libmpfr), Int32, (Ref{BigFloat}, $fC, MPFRRoundingMode), z, x, r)
            return z
        end
    end
end

function BigFloat(x::Float64, r::MPFRRoundingMode=ROUNDING_MODE[]; precision::Integer=DEFAULT_PRECISION[])
    z = BigFloat(;precision)
    # punt on the hard case where we might have to deal with rounding
    # we could use this path in all cases, but mpfr_set_d has a lot of overhead.
    if precision <= Base.significand_bits(Float64)
        ccall((:mpfr_set_d, libmpfr), Int32, (Ref{BigFloat}, Float64, MPFRRoundingMode), z, x, r)
        if isnan(x) && signbit(x) != signbit(z)
            z.sign = -z.sign
        end
        return z
    end
    z.sign = 1-2*signbit(x)
    if iszero(x) || !isfinite(x)
        if isinf(x)
            z.exp = Clong(2) - typemax(Clong)
        elseif isnan(x)
            z.exp = Clong(1) - typemax(Clong)
        else
            z.exp = - typemax(Clong)
        end
        return z
    end
    z.exp = 1 + exponent(x)
    # BigFloat doesn't have an implicit bit
    val = reinterpret(UInt64, significand(x))<<11 | typemin(Int64)
    nlimbs = (precision + 8*Core.sizeof(Limb) - 1) ÷ (8*Core.sizeof(Limb))

    # Limb is a CLong which is a UInt32 on windows (thank M$) which makes this more complicated and slower.
    if Limb === UInt64
        for i in 1:nlimbs-1
            unsafe_store!(z.d, 0x0, i)
        end
        unsafe_store!(z.d, val, nlimbs)
    else
        for i in 1:nlimbs-2
            unsafe_store!(z.d, 0x0, i)
        end
        unsafe_store!(z.d, val % UInt32, nlimbs-1)
        unsafe_store!(z.d, (val >> 32) % UInt32, nlimbs)
    end
    z
end

function BigFloat(x::BigInt, r::MPFRRoundingMode=ROUNDING_MODE[]; precision::Integer=DEFAULT_PRECISION[])
    z = BigFloat(;precision=precision)
    ccall((:mpfr_set_z, libmpfr), Int32, (Ref{BigFloat}, Ref{BigInt}, MPFRRoundingMode), z, x, r)
    return z
end

BigFloat(x::Integer; precision::Integer=DEFAULT_PRECISION[]) =
    BigFloat(BigInt(x)::BigInt, ROUNDING_MODE[]; precision=precision)
BigFloat(x::Integer, r::MPFRRoundingMode; precision::Integer=DEFAULT_PRECISION[]) =
    BigFloat(BigInt(x)::BigInt, r; precision=precision)

BigFloat(x::Union{Bool,Int8,Int16,Int32}, r::MPFRRoundingMode=ROUNDING_MODE[]; precision::Integer=DEFAULT_PRECISION[]) =
    BigFloat(convert(Clong, x), r; precision=precision)
BigFloat(x::Union{UInt8,UInt16,UInt32}, r::MPFRRoundingMode=ROUNDING_MODE[]; precision::Integer=DEFAULT_PRECISION[]) =
    BigFloat(convert(Culong, x), r; precision=precision)

BigFloat(x::Union{Float16,Float32}, r::MPFRRoundingMode=ROUNDING_MODE[]; precision::Integer=DEFAULT_PRECISION[]) =
    BigFloat(Float64(x), r; precision=precision)

function BigFloat(x::Rational, r::MPFRRoundingMode=ROUNDING_MODE[]; precision::Integer=DEFAULT_PRECISION[])
    setprecision(BigFloat, precision) do
        setrounding_raw(BigFloat, r) do
            BigFloat(numerator(x))::BigFloat / BigFloat(denominator(x))::BigFloat
        end
    end
end

function tryparse(::Type{BigFloat}, s::AbstractString; base::Integer=0, precision::Integer=DEFAULT_PRECISION[], rounding::MPFRRoundingMode=ROUNDING_MODE[])
    !isempty(s) && isspace(s[end]) && return tryparse(BigFloat, rstrip(s), base = base)
    z = BigFloat(precision=precision)
    err = ccall((:mpfr_set_str, libmpfr), Int32, (Ref{BigFloat}, Cstring, Int32, MPFRRoundingMode), z, s, base, rounding)
    err == 0 ? z : nothing
end

BigFloat(x::AbstractString, r::MPFRRoundingMode=ROUNDING_MODE[]; precision::Integer=DEFAULT_PRECISION[]) =
    parse(BigFloat, x; precision=precision, rounding=r)

Rational(x::BigFloat) = convert(Rational{BigInt}, x)
AbstractFloat(x::BigInt) = BigFloat(x)

float(::Type{BigInt}) = BigFloat

BigFloat(x::Real, r::RoundingMode; precision::Integer=DEFAULT_PRECISION[]) =
    BigFloat(x, convert(MPFRRoundingMode, r); precision=precision)::BigFloat
BigFloat(x::AbstractString, r::RoundingMode; precision::Integer=DEFAULT_PRECISION[]) =
    BigFloat(x, convert(MPFRRoundingMode, r); precision=precision)

## BigFloat -> Integer
_unchecked_cast(T, x::BigFloat, r::RoundingMode) = _unchecked_cast(T, x, convert(MPFRRoundingMode, r))

function _unchecked_cast(::Type{Int64}, x::BigFloat, r::MPFRRoundingMode)
    ccall((:__gmpfr_mpfr_get_sj,libmpfr), Cintmax_t, (Ref{BigFloat}, MPFRRoundingMode), x, r)
end

function _unchecked_cast(::Type{UInt64}, x::BigFloat, r::MPFRRoundingMode)
    ccall((:__gmpfr_mpfr_get_uj,libmpfr), Cuintmax_t, (Ref{BigFloat}, MPFRRoundingMode), x, r)
end

function _unchecked_cast(::Type{BigInt}, x::BigFloat, r::MPFRRoundingMode)
    z = BigInt()
    ccall((:mpfr_get_z, libmpfr), Int32, (Ref{BigInt}, Ref{BigFloat}, MPFRRoundingMode), z, x, r)
    return z
end

function _unchecked_cast(::Type{T}, x::BigFloat, r::MPFRRoundingMode) where T<:Union{Signed, Unsigned}
    CT = T <: Signed ? Int64 : UInt64
    typemax(T) < typemax(CT) ? _unchecked_cast(CT, x, r) : _unchecked_cast(BigInt, x, r)
end

function round(::Type{T}, x::BigFloat, r::Union{RoundingMode, MPFRRoundingMode}) where T<:Union{Signed, Unsigned}
    clear_flags()
    res = _unchecked_cast(T, x, r)
    if had_range_exception() || !(typemin(T) <= res <= typemax(T))
        throw(InexactError(:round, T, x))
    end
    return unsafe_trunc(T, res)
end

function round(::Type{BigInt}, x::BigFloat, r::Union{RoundingMode, MPFRRoundingMode})
    clear_flags()
    res = _unchecked_cast(BigInt, x, r)
    had_range_exception() && throw(InexactError(:round, BigInt, x))
    return res
end

round(::Type{T}, x::BigFloat, r::RoundingMode) where T<:Union{Signed, Unsigned} =
    invoke(round, Tuple{Type{<:Union{Signed, Unsigned}}, BigFloat, Union{RoundingMode, MPFRRoundingMode}}, T, x, r)
round(::Type{BigInt}, x::BigFloat, r::RoundingMode) =
    invoke(round, Tuple{Type{BigInt}, BigFloat, Union{RoundingMode, MPFRRoundingMode}}, BigInt, x, r)
round(::Type{<:Integer}, x::BigFloat, r::RoundingMode) = throw(MethodError(round, (Integer, x, r)))


unsafe_trunc(::Type{T}, x::BigFloat) where {T<:Integer} = unsafe_trunc(T, _unchecked_cast(T, x, RoundToZero))
unsafe_trunc(::Type{BigInt}, x::BigFloat) = _unchecked_cast(BigInt, x, RoundToZero)

# TODO: Ideally the base fallbacks for these would already exist
for (f, rnd) in zip((:trunc, :floor, :ceil, :round),
                 (RoundToZero, RoundDown, RoundUp, :(ROUNDING_MODE[])))
    @eval $f(::Type{T}, x::BigFloat) where T<:Union{Unsigned, Signed, BigInt} = round(T, x, $rnd)
    @eval $f(::Type{Integer}, x::BigFloat) = $f(BigInt, x)
end

function Bool(x::BigFloat)
    iszero(x) && return false
    isone(x) && return true
    throw(InexactError(:Bool, Bool, x))
end
function BigInt(x::BigFloat)
    isinteger(x) || throw(InexactError(:BigInt, BigInt, x))
    trunc(BigInt, x)
end

function (::Type{T})(x::BigFloat) where T<:Integer
    isinteger(x) || throw(InexactError(nameof(T), T, x))
    trunc(T,x)
end

## BigFloat -> AbstractFloat
_cpynansgn(x::AbstractFloat, y::BigFloat) = isnan(x) && signbit(x) != signbit(y) ? -x : x

Float64(x::BigFloat, r::MPFRRoundingMode=ROUNDING_MODE[]) =
    _cpynansgn(ccall((:mpfr_get_d,libmpfr), Float64, (Ref{BigFloat}, MPFRRoundingMode), x, r), x)
Float64(x::BigFloat, r::RoundingMode) = Float64(x, convert(MPFRRoundingMode, r))

Float32(x::BigFloat, r::MPFRRoundingMode=ROUNDING_MODE[]) =
    _cpynansgn(ccall((:mpfr_get_flt,libmpfr), Float32, (Ref{BigFloat}, MPFRRoundingMode), x, r), x)
Float32(x::BigFloat, r::RoundingMode) = Float32(x, convert(MPFRRoundingMode, r))

function Float16(x::BigFloat) :: Float16
    res = Float32(x)
    resi = reinterpret(UInt32, res)
    if (resi&0x7fffffff) < 0x38800000 # if Float16(res) is subnormal
        #shift so that the mantissa lines up where it would for normal Float16
        shift = 113-((resi & 0x7f800000)>>23)
        if shift<23
            resi |= 0x0080_0000 # set implicit bit
            resi >>= shift
        end
    end
    if (resi & 0x1fff == 0x1000) # if we are halfway between 2 Float16 values
        # adjust the value by 1 ULP in the direction that will make Float16(res) give the right answer
        res = nextfloat(res, cmp(x, res))
    end
    return res
end

promote_rule(::Type{BigFloat}, ::Type{<:Real}) = BigFloat
promote_rule(::Type{BigInt}, ::Type{<:AbstractFloat}) = BigFloat
promote_rule(::Type{BigFloat}, ::Type{<:AbstractFloat}) = BigFloat

big(::Type{<:AbstractFloat}) = BigFloat

big(x::AbstractFloat) = convert(BigFloat, x)

function Rational{BigInt}(x::AbstractFloat)
    isnan(x) && return zero(BigInt) // zero(BigInt)
    isinf(x) && return copysign(one(BigInt),x) // zero(BigInt)
    iszero(x) && return zero(BigInt) // one(BigInt)
    s = max(precision(x) - exponent(x), 0)
    BigInt(ldexp(x,s)) // (BigInt(1) << s)
end

# Basic arithmetic without promotion
for (fJ, fC) in ((:+,:add), (:*,:mul))
    @eval begin
        # BigFloat
        function ($fJ)(x::BigFloat, y::BigFloat)
            z = BigFloat()
            ccall(($(string(:mpfr_,fC)),libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, MPFRRoundingMode), z, x, y, ROUNDING_MODE[])
            return z
        end

        # Unsigned Integer
        function ($fJ)(x::BigFloat, c::CulongMax)
            z = BigFloat()
            ccall(($(string(:mpfr_,fC,:_ui)), libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Culong, MPFRRoundingMode), z, x, c, ROUNDING_MODE[])
            return z
        end
        ($fJ)(c::CulongMax, x::BigFloat) = ($fJ)(x,c)

        # Signed Integer
        function ($fJ)(x::BigFloat, c::ClongMax)
            z = BigFloat()
            ccall(($(string(:mpfr_,fC,:_si)), libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Clong, MPFRRoundingMode), z, x, c, ROUNDING_MODE[])
            return z
        end
        ($fJ)(c::ClongMax, x::BigFloat) = ($fJ)(x,c)

        # Float32/Float64
        function ($fJ)(x::BigFloat, c::CdoubleMax)
            z = BigFloat()
            ccall(($(string(:mpfr_,fC,:_d)), libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Cdouble, MPFRRoundingMode), z, x, c, ROUNDING_MODE[])
            return z
        end
        ($fJ)(c::CdoubleMax, x::BigFloat) = ($fJ)(x,c)

        # BigInt
        function ($fJ)(x::BigFloat, c::BigInt)
            z = BigFloat()
            ccall(($(string(:mpfr_,fC,:_z)), libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigInt}, MPFRRoundingMode), z, x, c, ROUNDING_MODE[])
            return z
        end
        ($fJ)(c::BigInt, x::BigFloat) = ($fJ)(x,c)
    end
end

for (fJ, fC) in ((:-,:sub), (:/,:div))
    @eval begin
        # BigFloat
        function ($fJ)(x::BigFloat, y::BigFloat)
            z = BigFloat()
            ccall(($(string(:mpfr_,fC)),libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, MPFRRoundingMode), z, x, y, ROUNDING_MODE[])
            return z
        end

        # Unsigned Int
        function ($fJ)(x::BigFloat, c::CulongMax)
            z = BigFloat()
            ccall(($(string(:mpfr_,fC,:_ui)), libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Culong, MPFRRoundingMode), z, x, c, ROUNDING_MODE[])
            return z
        end
        function ($fJ)(c::CulongMax, x::BigFloat)
            z = BigFloat()
            ccall(($(string(:mpfr_,:ui_,fC)), libmpfr), Int32, (Ref{BigFloat}, Culong, Ref{BigFloat}, MPFRRoundingMode), z, c, x, ROUNDING_MODE[])
            return z
        end

        # Signed Integer
        function ($fJ)(x::BigFloat, c::ClongMax)
            z = BigFloat()
            ccall(($(string(:mpfr_,fC,:_si)), libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Clong, MPFRRoundingMode), z, x, c, ROUNDING_MODE[])
            return z
        end
        function ($fJ)(c::ClongMax, x::BigFloat)
            z = BigFloat()
            ccall(($(string(:mpfr_,:si_,fC)), libmpfr), Int32, (Ref{BigFloat}, Clong, Ref{BigFloat}, MPFRRoundingMode), z, c, x, ROUNDING_MODE[])
            return z
        end

        # Float32/Float64
        function ($fJ)(x::BigFloat, c::CdoubleMax)
            z = BigFloat()
            ccall(($(string(:mpfr_,fC,:_d)), libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Cdouble, MPFRRoundingMode), z, x, c, ROUNDING_MODE[])
            return z
        end
        function ($fJ)(c::CdoubleMax, x::BigFloat)
            z = BigFloat()
            ccall(($(string(:mpfr_,:d_,fC)), libmpfr), Int32, (Ref{BigFloat}, Cdouble, Ref{BigFloat}, MPFRRoundingMode), z, c, x, ROUNDING_MODE[])
            return z
        end

        # BigInt
        function ($fJ)(x::BigFloat, c::BigInt)
            z = BigFloat()
            ccall(($(string(:mpfr_,fC,:_z)), libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigInt}, MPFRRoundingMode), z, x, c, ROUNDING_MODE[])
            return z
        end
        # no :mpfr_z_div function
    end
end

function -(c::BigInt, x::BigFloat)
    z = BigFloat()
    ccall((:mpfr_z_sub, libmpfr), Int32, (Ref{BigFloat}, Ref{BigInt}, Ref{BigFloat}, MPFRRoundingMode), z, c, x, ROUNDING_MODE[])
    return z
end

inv(x::BigFloat) = one(Clong) / x # faster than fallback one(x)/x

function fma(x::BigFloat, y::BigFloat, z::BigFloat)
    r = BigFloat()
    ccall(("mpfr_fma",libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, MPFRRoundingMode), r, x, y, z, ROUNDING_MODE[])
    return r
end

muladd(x::BigFloat, y::BigFloat, z::BigFloat) = fma(x, y, z)

# div
# BigFloat
function div(x::BigFloat, y::BigFloat)
    z = BigFloat()
    ccall((:mpfr_div,libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, MPFRRoundingMode), z, x, y, RoundToZero)
    ccall((:mpfr_trunc, libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}), z, z)
    return z
end

# Unsigned Int
function div(x::BigFloat, c::CulongMax)
    z = BigFloat()
    ccall((:mpfr_div_ui, libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Culong, MPFRRoundingMode), z, x, c, RoundToZero)
    ccall((:mpfr_trunc, libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}), z, z)
    return z
end
function div(c::CulongMax, x::BigFloat)
    z = BigFloat()
    ccall((:mpfr_ui_div, libmpfr), Int32, (Ref{BigFloat}, Culong, Ref{BigFloat}, MPFRRoundingMode), z, c, x, RoundToZero)
    ccall((:mpfr_trunc, libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}), z, z)
    return z
end

# Signed Integer
function div(x::BigFloat, c::ClongMax)
    z = BigFloat()
    ccall((:mpfr_div_si, libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Clong, MPFRRoundingMode), z, x, c, RoundToZero)
    ccall((:mpfr_trunc, libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}), z, z)
    return z
end
function div(c::ClongMax, x::BigFloat)
    z = BigFloat()
    ccall((:mpfr_si_div, libmpfr), Int32, (Ref{BigFloat}, Clong, Ref{BigFloat}, MPFRRoundingMode), z, c, x, RoundToZero)
    ccall((:mpfr_trunc, libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}), z, z)
    return z
end

# Float32/Float64
function div(x::BigFloat, c::CdoubleMax)
    z = BigFloat()
    ccall((:mpfr_div_d, libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Cdouble, MPFRRoundingMode), z, x, c, RoundToZero)
    ccall((:mpfr_trunc, libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}), z, z)
    return z
end
function div(c::CdoubleMax, x::BigFloat)
    z = BigFloat()
    ccall((:mpfr_d_div, libmpfr), Int32, (Ref{BigFloat}, Cdouble, Ref{BigFloat}, MPFRRoundingMode), z, c, x, RoundToZero)
    ccall((:mpfr_trunc, libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}), z, z)
    return z
end

# BigInt
function div(x::BigFloat, c::BigInt)
    z = BigFloat()
    ccall((:mpfr_div_z, libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigInt}, MPFRRoundingMode), z, x, c, RoundToZero)
    ccall((:mpfr_trunc, libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}), z, z)
    return z
end


# More efficient commutative operations
for (fJ, fC, fI) in ((:+, :add, 0), (:*, :mul, 1))
    @eval begin
        function ($fJ)(a::BigFloat, b::BigFloat, c::BigFloat)
            z = BigFloat()
            ccall(($(string(:mpfr_,fC)), libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, MPFRRoundingMode), z, a, b, ROUNDING_MODE[])
            ccall(($(string(:mpfr_,fC)), libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, MPFRRoundingMode), z, z, c, ROUNDING_MODE[])
            return z
        end
        function ($fJ)(a::BigFloat, b::BigFloat, c::BigFloat, d::BigFloat)
            z = BigFloat()
            ccall(($(string(:mpfr_,fC)), libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, MPFRRoundingMode), z, a, b, ROUNDING_MODE[])
            ccall(($(string(:mpfr_,fC)), libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, MPFRRoundingMode), z, z, c, ROUNDING_MODE[])
            ccall(($(string(:mpfr_,fC)), libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, MPFRRoundingMode), z, z, d, ROUNDING_MODE[])
            return z
        end
        function ($fJ)(a::BigFloat, b::BigFloat, c::BigFloat, d::BigFloat, e::BigFloat)
            z = BigFloat()
            ccall(($(string(:mpfr_,fC)), libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, MPFRRoundingMode), z, a, b, ROUNDING_MODE[])
            ccall(($(string(:mpfr_,fC)), libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, MPFRRoundingMode), z, z, c, ROUNDING_MODE[])
            ccall(($(string(:mpfr_,fC)), libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, MPFRRoundingMode), z, z, d, ROUNDING_MODE[])
            ccall(($(string(:mpfr_,fC)), libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, MPFRRoundingMode), z, z, e, ROUNDING_MODE[])
            return z
        end
    end
end

function -(x::BigFloat)
    z = BigFloat()
    ccall((:mpfr_neg, libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, MPFRRoundingMode), z, x, ROUNDING_MODE[])
    return z
end

function sqrt(x::BigFloat)
    isnan(x) && return x
    z = BigFloat()
    ccall((:mpfr_sqrt, libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, MPFRRoundingMode), z, x, ROUNDING_MODE[])
    isnan(z) && throw(DomainError(x, "NaN result for non-NaN input."))
    return z
end

sqrt(x::BigInt) = sqrt(BigFloat(x))

function ^(x::BigFloat, y::BigFloat)
    z = BigFloat()
    ccall((:mpfr_pow, libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, MPFRRoundingMode), z, x, y, ROUNDING_MODE[])
    return z
end

function ^(x::BigFloat, y::CulongMax)
    z = BigFloat()
    ccall((:mpfr_pow_ui, libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Culong, MPFRRoundingMode), z, x, y, ROUNDING_MODE[])
    return z
end

function ^(x::BigFloat, y::ClongMax)
    z = BigFloat()
    ccall((:mpfr_pow_si, libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Clong, MPFRRoundingMode), z, x, y, ROUNDING_MODE[])
    return z
end

function ^(x::BigFloat, y::BigInt)
    z = BigFloat()
    ccall((:mpfr_pow_z, libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigInt}, MPFRRoundingMode), z, x, y, ROUNDING_MODE[])
    return z
end

^(x::BigFloat, y::Integer)  = typemin(Clong)  <= y <= typemax(Clong)  ? x^Clong(y)  : x^BigInt(y)
^(x::BigFloat, y::Unsigned) = typemin(Culong) <= y <= typemax(Culong) ? x^Culong(y) : x^BigInt(y)

for f in (:exp, :exp2, :exp10, :expm1, :cosh, :sinh, :tanh, :sech, :csch, :coth, :cbrt)
    @eval function $f(x::BigFloat)
        z = BigFloat()
        ccall(($(string(:mpfr_,f)), libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, MPFRRoundingMode), z, x, ROUNDING_MODE[])
        return z
    end
end

function sincos_fast(v::BigFloat)
    s = BigFloat()
    c = BigFloat()
    ccall((:mpfr_sin_cos, libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, MPFRRoundingMode), s, c, v, ROUNDING_MODE[])
    return (s, c)
end
sincos(v::BigFloat) = sincos_fast(v)

# return log(2)
function big_ln2()
    c = BigFloat()
    ccall((:mpfr_const_log2, libmpfr), Cint, (Ref{BigFloat}, MPFRRoundingMode), c, MPFR.ROUNDING_MODE[])
    return c
end

function ldexp(x::BigFloat, n::Clong)
    z = BigFloat()
    ccall((:mpfr_mul_2si, libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Clong, MPFRRoundingMode), z, x, n, ROUNDING_MODE[])
    return z
end
function ldexp(x::BigFloat, n::Culong)
    z = BigFloat()
    ccall((:mpfr_mul_2ui, libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Culong, MPFRRoundingMode), z, x, n, ROUNDING_MODE[])
    return z
end
ldexp(x::BigFloat, n::ClongMax) = ldexp(x, convert(Clong, n))
ldexp(x::BigFloat, n::CulongMax) = ldexp(x, convert(Culong, n))
ldexp(x::BigFloat, n::Integer) = x * exp2(BigFloat(n))

function factorial(x::BigFloat)
    if x < 0 || !isinteger(x)
        throw(DomainError(x, "Must be a non-negative integer."))
    end
    ui = convert(Culong, x)
    z = BigFloat()
    ccall((:mpfr_fac_ui, libmpfr), Int32, (Ref{BigFloat}, Culong, MPFRRoundingMode), z, ui, ROUNDING_MODE[])
    return z
end

function hypot(x::BigFloat, y::BigFloat)
    z = BigFloat()
    ccall((:mpfr_hypot, libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, MPFRRoundingMode), z, x, y, ROUNDING_MODE[])
    return z
end

for f in (:log, :log2, :log10)
    @eval function $f(x::BigFloat)
        if x < 0
            throw(DomainError(x, string($f, " was called with a negative real argument but ",
                              "will only return a complex result if called ",
                              "with a complex argument. Try ", $f, "(complex(x)).")))
        end
        z = BigFloat()
        ccall(($(string(:mpfr_,f)), libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, MPFRRoundingMode), z, x, ROUNDING_MODE[])
        return z
    end
end

function log1p(x::BigFloat)
    if x < -1
        throw(DomainError(x, string("log1p was called with a real argument < -1 but ",
                          "will only return a complex result if called ",
                          "with a complex argument. Try log1p(complex(x)).")))
    end
    z = BigFloat()
    ccall((:mpfr_log1p, libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, MPFRRoundingMode), z, x, ROUNDING_MODE[])
    return z
end

# For `min`/`max`, general fallback for `AbstractFloat` is good enough.
# Only implement `minmax` and `_extrema_rf` to avoid repeated calls.
function minmax(x::BigFloat, y::BigFloat)
    isnan(x) && return x, x
    isnan(y) && return y, y
    Base.Math._isless(x, y) ? (x, y) : (y, x)
end

function Base._extrema_rf(x::NTuple{2,BigFloat}, y::NTuple{2,BigFloat})
    (x1, x2), (y1, y2) = x, y
    isnan(x1) && return x
    isnan(y1) && return y
    z1 = Base.Math._isless(x1, y1) ? x1 : y1
    z2 = Base.Math._isless(x2, y2) ? y2 : x2
    z1, z2
end

function modf(x::BigFloat)
    zint = BigFloat()
    zfloat = BigFloat()
    ccall((:mpfr_modf, libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, MPFRRoundingMode), zint, zfloat, x, ROUNDING_MODE[])
    return (zfloat, zint)
end

function rem(x::BigFloat, y::BigFloat)
    z = BigFloat()
    ccall((:mpfr_fmod, libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, MPFRRoundingMode), z, x, y, ROUNDING_MODE[])
    return z
end

function rem(x::BigFloat, y::BigFloat, ::RoundingMode{:Nearest})
    z = BigFloat()
    ccall((:mpfr_remainder, libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, MPFRRoundingMode), z, x, y, ROUNDING_MODE[])
    return z
end

# TODO: use a higher-precision BigFloat(pi) here?
rem2pi(x::BigFloat, r::RoundingMode) = rem(x, 2*BigFloat(pi), r)

function sum(arr::AbstractArray{BigFloat})
    z = BigFloat(0)
    for i in arr
        ccall((:mpfr_add, libmpfr), Int32,
            (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, MPFRRoundingMode), z, z, i, ROUNDING_MODE[])
    end
    return z
end

# Functions for which NaN results are converted to DomainError, following Base
for f in (:sin, :cos, :tan, :sec, :csc, :acos, :asin, :atan, :acosh, :asinh, :atanh, :sinpi, :cospi, :tanpi)
    @eval begin
        function ($f)(x::BigFloat)
            isnan(x) && return x
            z = BigFloat()
            ccall(($(string(:mpfr_,f)), libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, MPFRRoundingMode), z, x, ROUNDING_MODE[])
            isnan(z) && throw(DomainError(x, "NaN result for non-NaN input."))
            return z
        end
    end
end
sincospi(x::BigFloat) = (sinpi(x), cospi(x))

function atan(y::BigFloat, x::BigFloat)
    z = BigFloat()
    ccall((:mpfr_atan2, libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, MPFRRoundingMode), z, y, x, ROUNDING_MODE[])
    return z
end

# degree functions
for f in (:sin, :cos, :tan)
    @eval begin
        function ($(Symbol(f,:d)))(x::BigFloat)
            isnan(x) && return x
            z = BigFloat()
            ccall(($(string(:mpfr_,f,:u)), :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Culong, MPFRRoundingMode), z, x, 360, ROUNDING_MODE[])
            isnan(z) && throw(DomainError(x, "NaN result for non-NaN input."))
            return z
        end
        function ($(Symbol(:a,f,:d)))(x::BigFloat)
            isnan(x) && return x
            z = BigFloat()
            ccall(($(string(:mpfr_a,f,:u)), :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Culong, MPFRRoundingMode), z, x, 360, ROUNDING_MODE[])
            isnan(z) && throw(DomainError(x, "NaN result for non-NaN input."))
            return z
        end
    end
end
function atand(y::BigFloat, x::BigFloat)
    z = BigFloat()
    ccall((:mpfr_atan2u, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, Culong, MPFRRoundingMode), z, y, x, 360, ROUNDING_MODE[])
    return z
end


# Utility functions
==(x::BigFloat, y::BigFloat) = ccall((:mpfr_equal_p, libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}), x, y) != 0
<=(x::BigFloat, y::BigFloat) = ccall((:mpfr_lessequal_p, libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}), x, y) != 0
>=(x::BigFloat, y::BigFloat) = ccall((:mpfr_greaterequal_p, libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}), x, y) != 0
<(x::BigFloat, y::BigFloat) = ccall((:mpfr_less_p, libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}), x, y) != 0
>(x::BigFloat, y::BigFloat) = ccall((:mpfr_greater_p, libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}), x, y) != 0

function cmp(x::BigFloat, y::BigInt)
    isnan(x) && return 1
    ccall((:mpfr_cmp_z, libmpfr), Int32, (Ref{BigFloat}, Ref{BigInt}), x, y)
end
function cmp(x::BigFloat, y::ClongMax)
    isnan(x) && return 1
    ccall((:mpfr_cmp_si, libmpfr), Int32, (Ref{BigFloat}, Clong), x, y)
end
function cmp(x::BigFloat, y::CulongMax)
    isnan(x) && return 1
    ccall((:mpfr_cmp_ui, libmpfr), Int32, (Ref{BigFloat}, Culong), x, y)
end
cmp(x::BigFloat, y::Integer) = cmp(x,big(y))
cmp(x::Integer, y::BigFloat) = -cmp(y,x)

function cmp(x::BigFloat, y::CdoubleMax)
    isnan(x) && return isnan(y) ? 0 : 1
    isnan(y) && return -1
    ccall((:mpfr_cmp_d, libmpfr), Int32, (Ref{BigFloat}, Cdouble), x, y)
end
cmp(x::CdoubleMax, y::BigFloat) = -cmp(y,x)

==(x::BigFloat, y::Integer)    = !isnan(x) && cmp(x,y) == 0
==(x::Integer, y::BigFloat)    = y == x
==(x::BigFloat, y::CdoubleMax) = !isnan(x) && !isnan(y) && cmp(x,y) == 0
==(x::CdoubleMax, y::BigFloat) = y == x

<(x::BigFloat, y::Integer)    = !isnan(x) && cmp(x,y) < 0
<(x::Integer, y::BigFloat)    = !isnan(y) && cmp(y,x) > 0
<(x::BigFloat, y::CdoubleMax) = !isnan(x) && !isnan(y) && cmp(x,y) < 0
<(x::CdoubleMax, y::BigFloat) = !isnan(x) && !isnan(y) && cmp(y,x) > 0

<=(x::BigFloat, y::Integer)    = !isnan(x) && cmp(x,y) <= 0
<=(x::Integer, y::BigFloat)    = !isnan(y) && cmp(y,x) >= 0
<=(x::BigFloat, y::CdoubleMax) = !isnan(x) && !isnan(y) && cmp(x,y) <= 0
<=(x::CdoubleMax, y::BigFloat) = !isnan(x) && !isnan(y) && cmp(y,x) >= 0

signbit(x::BigFloat) = ccall((:mpfr_signbit, libmpfr), Int32, (Ref{BigFloat},), x) != 0
function sign(x::BigFloat)
    c = cmp(x, 0)
    (c == 0 || isnan(x)) && return x
    return c < 0 ? -one(x) : one(x)
end

function _precision(x::BigFloat)  # precision of an object of type BigFloat
    return ccall((:mpfr_get_prec, libmpfr), Clong, (Ref{BigFloat},), x)
end
precision(x::BigFloat; base::Integer=2) = _precision(x, base)

_precision(::Type{BigFloat}) = Int(DEFAULT_PRECISION[]) # default precision of the type BigFloat itself

"""
    setprecision([T=BigFloat,] precision::Int; base=2)

Set the precision (in bits, by default) to be used for `T` arithmetic.
If `base` is specified, then the precision is the minimum required to give
at least `precision` digits in the given `base`.

!!! warning

    This function is not thread-safe. It will affect code running on all threads, but
    its behavior is undefined if called concurrently with computations that use the
    setting.

!!! compat "Julia 1.8"
    The `base` keyword requires at least Julia 1.8.
"""
function setprecision(::Type{BigFloat}, precision::Integer; base::Integer=2)
    base > 1 || throw(DomainError(base, "`base` cannot be less than 2."))
    precision > 0 || throw(DomainError(precision, "`precision` cannot be less than 1."))
    DEFAULT_PRECISION[] = base == 2 ? precision : ceil(Int, precision * log2(base))
    return precision
end

setprecision(precision::Integer; base::Integer=2) = setprecision(BigFloat, precision; base)

maxintfloat(x::BigFloat) = BigFloat(2)^precision(x)
maxintfloat(::Type{BigFloat}) = BigFloat(2)^precision(BigFloat)

function copysign(x::BigFloat, y::BigFloat)
    z = BigFloat()
    ccall((:mpfr_copysign, libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Ref{BigFloat}, MPFRRoundingMode), z, x, y, ROUNDING_MODE[])
    return z
end

function exponent(x::BigFloat)
    if iszero(x) || !isfinite(x)
        throw(DomainError(x, "`x` must be non-zero and finite."))
    end
    # The '- 1' is to make it work as Base.exponent
    return ccall((:mpfr_get_exp, libmpfr), Clong, (Ref{BigFloat},), x) - 1
end

function frexp(x::BigFloat)
    z = BigFloat()
    c = Ref{Clong}()
    ccall((:mpfr_frexp, libmpfr), Int32, (Ptr{Clong}, Ref{BigFloat}, Ref{BigFloat}, MPFRRoundingMode), c, z, x, ROUNDING_MODE[])
    return (z, c[])
end

function significand(x::BigFloat)
    z = BigFloat()
    c = Ref{Clong}()
    ccall((:mpfr_frexp, libmpfr), Int32, (Ptr{Clong}, Ref{BigFloat}, Ref{BigFloat}, MPFRRoundingMode), c, z, x, ROUNDING_MODE[])
    # Double the significand to make it work as Base.significand
    ccall((:mpfr_mul_si, libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Clong, MPFRRoundingMode), z, z, 2, ROUNDING_MODE[])
    return z
end

function isinteger(x::BigFloat)
    return ccall((:mpfr_integer_p, libmpfr), Int32, (Ref{BigFloat},), x) != 0
end

for (f,R) in ((:roundeven, :Nearest),
              (:ceil, :Up),
              (:floor, :Down),
              (:trunc, :ToZero),
              (:round, :NearestTiesAway))
    @eval begin
        function round(x::BigFloat, ::RoundingMode{$(QuoteNode(R))})
            z = BigFloat()
            ccall(($(string(:mpfr_,f)), libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}), z, x)
            return z
        end
    end
end

function isinf(x::BigFloat)
    return ccall((:mpfr_inf_p, libmpfr), Int32, (Ref{BigFloat},), x) != 0
end

function isnan(x::BigFloat)
    return ccall((:mpfr_nan_p, libmpfr), Int32, (Ref{BigFloat},), x) != 0
end

isfinite(x::BigFloat) = !isinf(x) && !isnan(x)

iszero(x::BigFloat) = x == Clong(0)
isone(x::BigFloat) = x == Clong(1)

@eval typemax(::Type{BigFloat}) = $(BigFloat(Inf))
@eval typemin(::Type{BigFloat}) = $(BigFloat(-Inf))

function nextfloat!(x::BigFloat, n::Integer=1)
    signbit(n) && return prevfloat!(x, abs(n))
    for i = 1:n
        ccall((:mpfr_nextabove, libmpfr), Int32, (Ref{BigFloat},), x)
    end
    return x
end

function prevfloat!(x::BigFloat, n::Integer=1)
    signbit(n) && return nextfloat!(x, abs(n))
    for i = 1:n
        ccall((:mpfr_nextbelow, libmpfr), Int32, (Ref{BigFloat},), x)
    end
    return x
end

nextfloat(x::BigFloat, n::Integer=1) = n == 0 ? x : nextfloat!(_duplicate(x), n)
prevfloat(x::BigFloat, n::Integer=1) = n == 0 ? x : prevfloat!(_duplicate(x), n)

eps(::Type{BigFloat}) = nextfloat(BigFloat(1)) - BigFloat(1)

floatmin(::Type{BigFloat}) = nextfloat(zero(BigFloat))
floatmax(::Type{BigFloat}) = prevfloat(BigFloat(Inf))

"""
    setprecision(f::Function, [T=BigFloat,] precision::Integer; base=2)

Change the `T` arithmetic precision (in the given `base`) for the duration of `f`.
It is logically equivalent to:

    old = precision(BigFloat)
    setprecision(BigFloat, precision)
    f()
    setprecision(BigFloat, old)

Often used as `setprecision(T, precision) do ... end`

Note: `nextfloat()`, `prevfloat()` do not use the precision mentioned by
`setprecision`.

!!! compat "Julia 1.8"
    The `base` keyword requires at least Julia 1.8.
"""
function setprecision(f::Function, ::Type{T}, prec::Integer; kws...) where T
    old_prec = precision(T)
    setprecision(T, prec; kws...)
    try
        return f()
    finally
        setprecision(T, old_prec)
    end
end

setprecision(f::Function, prec::Integer; base::Integer=2) = setprecision(f, BigFloat, prec; base)

function string_mpfr(x::BigFloat, fmt::String)
    pc = Ref{Ptr{UInt8}}()
    n = ccall((:mpfr_asprintf,libmpfr), Cint,
              (Ptr{Ptr{UInt8}}, Ptr{UInt8}, Ref{BigFloat}...),
              pc, fmt, x)
    p = pc[]
    # convert comma decimal separator to dot
    for i = 1:n
        if unsafe_load(p, i) == UInt8(',')
            unsafe_store!(p, '.', i)
            break
        end
    end
    str = unsafe_string(p)
    ccall((:mpfr_free_str, libmpfr), Cvoid, (Ptr{UInt8},), p)
    return str
end

function _prettify_bigfloat(s::String)::String
    mantissa, exponent = eachsplit(s, 'e')
    if !occursin('.', mantissa)
        mantissa = string(mantissa, '.')
    end
    mantissa = rstrip(mantissa, '0')
    if endswith(mantissa, '.')
        mantissa = string(mantissa, '0')
    end
    expo = parse(Int, exponent)
    if -5 < expo < 6
        expo == 0 && return mantissa
        int, frac = eachsplit(mantissa, '.')
        if expo > 0
            expo < length(frac) ?
                string(int, frac[1:expo], '.', frac[expo+1:end]) :
                string(int, frac, '0'^(expo-length(frac)), '.', '0')
        else
            neg = startswith(int, '-')
            neg == true && (int = lstrip(int, '-'))
            @assert length(int) == 1
            string(neg ? '-' : "", '0', '.', '0'^(-expo-1), int, frac == "0" ? "" : frac)
        end
    else
        string(mantissa, 'e', exponent)
    end
end

function _string(x::BigFloat, fmt::String)::String
    isfinite(x) || return string(Float64(x))
    _prettify_bigfloat(string_mpfr(x, fmt))
end
_string(x::BigFloat) = _string(x, "%Re")
_string(x::BigFloat, k::Integer) = _string(x, "%.$(k)Re")

string(b::BigFloat) = _string(b)

print(io::IO, b::BigFloat) = print(io, string(b))
function show(io::IO, b::BigFloat)
    if get(io, :compact, false)::Bool
        print(io, _string(b, 5))
    else
        print(io, _string(b))
    end
end

# get/set exponent min/max
get_emax() = ccall((:mpfr_get_emax, libmpfr), Clong, ())
get_emax_min() = ccall((:mpfr_get_emax_min, libmpfr), Clong, ())
get_emax_max() = ccall((:mpfr_get_emax_max, libmpfr), Clong, ())

get_emin() = ccall((:mpfr_get_emin, libmpfr), Clong, ())
get_emin_min() = ccall((:mpfr_get_emin_min, libmpfr), Clong, ())
get_emin_max() = ccall((:mpfr_get_emin_max, libmpfr), Clong, ())

check_exponent_err(ret) = ret == 0 || throw(ArgumentError("Invalid MPFR exponent range"))
set_emax!(x) = check_exponent_err(ccall((:mpfr_set_emax, libmpfr), Cint, (Clong,), x))
set_emin!(x) = check_exponent_err(ccall((:mpfr_set_emin, libmpfr), Cint, (Clong,), x))

function Base.deepcopy_internal(x::BigFloat, stackdict::IdDict)
    get!(stackdict, x) do
        # d = copy(x._d)
        d = x._d
        d′ = GC.@preserve d unsafe_string(pointer(d), sizeof(d)) # creates a definitely-new String
        y = _BigFloat(x.prec, x.sign, x.exp, d′)
        #ccall((:mpfr_custom_move,libmpfr), Cvoid, (Ref{BigFloat}, Ptr{Limb}), y, d) # unnecessary
        return y
    end
end

function decompose(x::BigFloat)::Tuple{BigInt, Int, Int}
    isnan(x) && return 0, 0, 0
    isinf(x) && return x.sign, 0, 0
    x == 0 && return 0, 0, x.sign
    s = BigInt()
    s.size = cld(x.prec, 8*sizeof(Limb)) # limbs
    b = s.size * sizeof(Limb)            # bytes
    ccall((:__gmpz_realloc2, libgmp), Cvoid, (Ref{BigInt}, Culong), s, 8b) # bits
    memcpy(s.d, x.d, b)
    s, x.exp - 8b, x.sign
end

function lerpi(j::Integer, d::Integer, a::BigFloat, b::BigFloat)
    t = BigFloat(j)/d
    fma(t, b, fma(-t, a, a))
end

# flags
clear_flags() = ccall((:mpfr_clear_flags, libmpfr), Cvoid, ())
had_underflow() = ccall((:mpfr_underflow_p, libmpfr), Cint, ()) != 0
had_overflow() = ccall((:mpfr_underflow_p, libmpfr), Cint, ()) != 0
had_nan() = ccall((:mpfr_nanflag_p, libmpfr), Cint, ()) != 0
had_inexact_exception() = ccall((:mpfr_inexflag_p, libmpfr), Cint, ()) != 0
had_range_exception() = ccall((:mpfr_erangeflag_p, libmpfr), Cint, ()) != 0

end #module
T   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/combinatorics.jl�$      # This file is a part of Julia. License is MIT: https://julialang.org/license

# Factorials

const _fact_table64 = Vector{Int64}(undef, 20)
_fact_table64[1] = 1
for n in 2:20
    _fact_table64[n] = _fact_table64[n-1] * n
end

const _fact_table128 = Vector{UInt128}(undef, 34)
_fact_table128[1] = 1
for n in 2:34
    _fact_table128[n] = _fact_table128[n-1] * n
end

function factorial_lookup(n::Integer, table, lim)
    n < 0 && throw(DomainError(n, "`n` must not be negative."))
    n > lim && throw(OverflowError(string(n, " is too large to look up in the table; consider using `factorial(big(", n, "))` instead")))
    n == 0 && return one(n)
    @inbounds f = table[n]
    return oftype(n, f)
end

factorial(n::Int128) = factorial_lookup(n, _fact_table128, 33)
factorial(n::UInt128) = factorial_lookup(n, _fact_table128, 34)
factorial(n::Union{Int64,UInt64}) = factorial_lookup(n, _fact_table64, 20)

if Int === Int32
    factorial(n::Union{Int8,UInt8,Int16,UInt16}) = factorial(Int32(n))
    factorial(n::Union{Int32,UInt32}) = factorial_lookup(n, _fact_table64, 12)
else
    factorial(n::Union{Int8,UInt8,Int16,UInt16,Int32,UInt32}) = factorial(Int64(n))
end


# Basic functions for working with permutations

@inline function _foldoneto(op, acc, ::Val{N}) where N
    @assert N::Integer > 0
    if @generated
        quote
            acc_0 = acc
            Base.Cartesian.@nexprs $N i -> acc_{i} = op(acc_{i-1}, i)
            return $(Symbol(:acc_, N))
        end
    else
        for i in 1:N
            acc = op(acc, i)
        end
        return acc
    end
end

"""
    isperm(v) -> Bool

Return `true` if `v` is a valid permutation.

# Examples
```jldoctest
julia> isperm([1; 2])
true

julia> isperm([1; 3])
false
```
"""
isperm(A) = _isperm(A)

function _isperm(A)
    n = length(A)
    used = falses(n)
    for a in A
        (0 < a <= n) && (used[a] ⊻= true) || return false
    end
    true
end

isperm(p::Tuple{}) = true
isperm(p::Tuple{Int}) = p[1] == 1
isperm(p::Tuple{Int,Int}) = ((p[1] == 1) & (p[2] == 2)) | ((p[1] == 2) & (p[2] == 1))

function isperm(P::Tuple)
    valn = Val(length(P))
    _foldoneto(true, valn) do b,i
        s = _foldoneto(false, valn) do s, j
            s || P[j]==i
        end
        b&s
    end
end

isperm(P::Any32) = _isperm(P)

# swap columns i and j of a, in-place
function swapcols!(a::AbstractMatrix, i, j)
    i == j && return
    cols = axes(a,2)
    @boundscheck i in cols || throw(BoundsError(a, (:,i)))
    @boundscheck j in cols || throw(BoundsError(a, (:,j)))
    for k in axes(a,1)
        @inbounds a[k,i],a[k,j] = a[k,j],a[k,i]
    end
end

# swap rows i and j of a, in-place
function swaprows!(a::AbstractMatrix, i, j)
    i == j && return
    rows = axes(a,1)
    @boundscheck i in rows || throw(BoundsError(a, (:,i)))
    @boundscheck j in rows || throw(BoundsError(a, (:,j)))
    for k in axes(a,2)
        @inbounds a[i,k],a[j,k] = a[j,k],a[i,k]
    end
end

# like permute!! applied to each row of a, in-place in a (overwriting p).
function permutecols!!(a::AbstractMatrix, p::AbstractVector{<:Integer})
    require_one_based_indexing(a, p)
    count = 0
    start = 0
    while count < length(p)
        ptr = start = findnext(!iszero, p, start+1)::Int
        next = p[start]
        count += 1
        while next != start
            swapcols!(a, ptr, next)
            p[ptr] = 0
            ptr = next
            next = p[next]
            count += 1
        end
        p[ptr] = 0
    end
    a
end

function permute!!(a, p::AbstractVector{<:Integer})
    require_one_based_indexing(a, p)
    count = 0
    start = 0
    while count < length(a)
        ptr = start = findnext(!iszero, p, start+1)::Int
        temp = a[start]
        next = p[start]
        count += 1
        while next != start
            a[ptr] = a[next]
            p[ptr] = 0
            ptr = next
            next = p[next]
            count += 1
        end
        a[ptr] = temp
        p[ptr] = 0
    end
    a
end

"""
    permute!(v, p)

Permute vector `v` in-place, according to permutation `p`. No checking is done
to verify that `p` is a permutation.

To return a new permutation, use `v[p]`. This is generally faster than `permute!(v, p)`;
it is even faster to write into a pre-allocated output array with `u .= @view v[p]`.
(Even though `permute!` overwrites `v` in-place, it internally requires some allocation
to keep track of which elements have been moved.)

$(_DOCS_ALIASING_WARNING)

See also [`invpermute!`](@ref).

# Examples
```jldoctest
julia> A = [1, 1, 3, 4];

julia> perm = [2, 4, 3, 1];

julia> permute!(A, perm);

julia> A
4-element Vector{Int64}:
 1
 4
 3
 1
```
"""
permute!(v, p::AbstractVector) = (v .= v[p])

function invpermute!!(a, p::AbstractVector{<:Integer})
    require_one_based_indexing(a, p)
    count = 0
    start = 0
    while count < length(a)
        start = findnext(!iszero, p, start+1)::Int
        temp = a[start]
        next = p[start]
        count += 1
        while next != start
            temp_next = a[next]
            a[next] = temp
            temp = temp_next
            ptr = p[next]
            p[next] = 0
            next = ptr
            count += 1
        end
        a[next] = temp
        p[next] = 0
    end
    a
end

"""
    invpermute!(v, p)

Like [`permute!`](@ref), but the inverse of the given permutation is applied.

Note that if you have a pre-allocated output array (e.g. `u = similar(v)`),
it is quicker to instead employ `u[p] = v`.  (`invpermute!` internally
allocates a copy of the data.)

$(_DOCS_ALIASING_WARNING)

# Examples
```jldoctest
julia> A = [1, 1, 3, 4];

julia> perm = [2, 4, 3, 1];

julia> invpermute!(A, perm);

julia> A
4-element Vector{Int64}:
 4
 1
 3
 1
```
"""
invpermute!(v, p::AbstractVector) = (v[p] = v; v)

"""
    invperm(v)

Return the inverse permutation of `v`.
If `B = A[v]`, then `A == B[invperm(v)]`.

See also [`sortperm`](@ref), [`invpermute!`](@ref), [`isperm`](@ref), [`permutedims`](@ref).

# Examples
```jldoctest
julia> p = (2, 3, 1);

julia> invperm(p)
(3, 1, 2)

julia> v = [2; 4; 3; 1];

julia> invperm(v)
4-element Vector{Int64}:
 4
 1
 3
 2

julia> A = ['a','b','c','d'];

julia> B = A[v]
4-element Vector{Char}:
 'b': ASCII/Unicode U+0062 (category Ll: Letter, lowercase)
 'd': ASCII/Unicode U+0064 (category Ll: Letter, lowercase)
 'c': ASCII/Unicode U+0063 (category Ll: Letter, lowercase)
 'a': ASCII/Unicode U+0061 (category Ll: Letter, lowercase)

julia> B[invperm(v)]
4-element Vector{Char}:
 'a': ASCII/Unicode U+0061 (category Ll: Letter, lowercase)
 'b': ASCII/Unicode U+0062 (category Ll: Letter, lowercase)
 'c': ASCII/Unicode U+0063 (category Ll: Letter, lowercase)
 'd': ASCII/Unicode U+0064 (category Ll: Letter, lowercase)
```
"""
function invperm(a::AbstractVector)
    require_one_based_indexing(a)
    b = zero(a) # similar vector of zeros
    n = length(a)
    @inbounds for (i, j) in enumerate(a)
        ((1 <= j <= n) && b[j] == 0) ||
            throw(ArgumentError("argument is not a permutation"))
        b[j] = i
    end
    b
end

function invperm(p::Union{Tuple{},Tuple{Int},Tuple{Int,Int}})
    isperm(p) || throw(ArgumentError("argument is not a permutation"))
    p  # in dimensions 0-2, every permutation is its own inverse
end

function invperm(P::Tuple)
    valn = Val(length(P))
    ntuple(valn) do i
        s = _foldoneto(nothing, valn) do s, j
            s !== nothing && return s
            P[j]==i && return j
            nothing
        end
        s === nothing && throw(ArgumentError("argument is not a permutation"))
        s
    end
end

invperm(P::Any32) = Tuple(invperm(collect(P)))

#XXX This function should be moved to Combinatorics.jl but is currently used by Base.DSP.
"""
    nextprod(factors::Union{Tuple,AbstractVector}, n)

Next integer greater than or equal to `n` that can be written as ``\\prod k_i^{p_i}`` for integers
``p_1``, ``p_2``, etcetera, for factors ``k_i`` in `factors`.

# Examples
```jldoctest
julia> nextprod((2, 3), 105)
108

julia> 2^2 * 3^3
108
```

!!! compat "Julia 1.6"
    The method that accepts a tuple requires Julia 1.6 or later.
"""
function nextprod(a::Union{Tuple{Vararg{Integer}},AbstractVector{<:Integer}}, x::Real)
    if x > typemax(Int)
        throw(ArgumentError("unsafe for x > typemax(Int), got $x"))
    end
    k = length(a)
    v = fill(1, k)                    # current value of each counter
    mx = map(a -> nextpow(a,x), a)   # maximum value of each counter
    v[1] = mx[1]                      # start at first case that is >= x
    p::widen(Int) = mx[1]             # initial value of product in this case
    best = p
    icarry = 1

    while v[end] < mx[end]
        if p >= x
            best = p < best ? p : best  # keep the best found yet
            carrytest = true
            while carrytest
                p = div(p, v[icarry])
                v[icarry] = 1
                icarry += 1
                p *= a[icarry]
                v[icarry] *= a[icarry]
                carrytest = v[icarry] > mx[icarry] && icarry < k
            end
            if p < x
                icarry = 1
            end
        else
            while p < x
                p *= a[1]
                v[1] *= a[1]
            end
        end
    end
    # might overflow, but want predictable return type
    return mx[end] < best ? Int(mx[end]) : Int(best)
end
R   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/irrationals.jl�#      # This file is a part of Julia. License is MIT: https://julialang.org/license

## general machinery for irrational mathematical constants

"""
    AbstractIrrational <: Real

Number type representing an exact irrational value, which is automatically rounded to the correct precision in
arithmetic operations with other numeric quantities.

Subtypes `MyIrrational <: AbstractIrrational` should implement at least `==(::MyIrrational, ::MyIrrational)`,
`hash(x::MyIrrational, h::UInt)`, and `convert(::Type{F}, x::MyIrrational) where {F <: Union{BigFloat,Float32,Float64}}`.

If a subtype is used to represent values that may occasionally be rational (e.g. a square-root type that represents `√n`
for integers `n` will give a rational result when `n` is a perfect square), then it should also implement
`isinteger`, `iszero`, `isone`, and `==` with `Real` values (since all of these default to `false` for
`AbstractIrrational` types), as well as defining [`hash`](@ref) to equal that of the corresponding `Rational`.
"""
abstract type AbstractIrrational <: Real end

"""
    Irrational{sym} <: AbstractIrrational

Number type representing an exact irrational value denoted by the
symbol `sym`, such as [`π`](@ref pi), [`ℯ`](@ref) and [`γ`](@ref Base.MathConstants.eulergamma).

See also [`AbstractIrrational`](@ref).
"""
struct Irrational{sym} <: AbstractIrrational end

show(io::IO, x::Irrational{sym}) where {sym} = print(io, sym)

function show(io::IO, ::MIME"text/plain", x::Irrational{sym}) where {sym}
    if get(io, :compact, false)::Bool
        print(io, sym)
    else
        print(io, sym, " = ", string(float(x))[1:min(end,15)], "...")
    end
end

promote_rule(::Type{<:AbstractIrrational}, ::Type{Float16}) = Float16
promote_rule(::Type{<:AbstractIrrational}, ::Type{Float32}) = Float32
promote_rule(::Type{<:AbstractIrrational}, ::Type{<:AbstractIrrational}) = Float64
promote_rule(::Type{<:AbstractIrrational}, ::Type{T}) where {T<:Real} = promote_type(Float64, T)
promote_rule(::Type{S}, ::Type{T}) where {S<:AbstractIrrational,T<:Number} = promote_type(promote_type(S, real(T)), T)

AbstractFloat(x::AbstractIrrational) = Float64(x)::Float64
Float16(x::AbstractIrrational) = Float16(Float32(x)::Float32)
Complex{T}(x::AbstractIrrational) where {T<:Real} = Complex{T}(T(x))

# XXX this may change `DEFAULT_PRECISION`, thus not effect free
@assume_effects :total function Rational{T}(x::AbstractIrrational) where T<:Integer
    o = precision(BigFloat)
    p = 256
    while true
        setprecision(BigFloat, p)
        bx = BigFloat(x)
        r = rationalize(T, bx, tol=0)
        if abs(BigFloat(r) - bx) > eps(bx)
            setprecision(BigFloat, o)
            return r
        end
        p += 32
    end
end
Rational{BigInt}(x::AbstractIrrational) = throw(ArgumentError("Cannot convert an AbstractIrrational to a Rational{BigInt}: use rationalize(BigInt, x) instead"))

@assume_effects :total function (t::Type{T})(x::AbstractIrrational, r::RoundingMode) where T<:Union{Float32,Float64}
    setprecision(BigFloat, 256) do
        T(BigFloat(x)::BigFloat, r)
    end
end

float(::Type{<:AbstractIrrational}) = Float64

==(::Irrational{s}, ::Irrational{s}) where {s} = true
==(::AbstractIrrational, ::AbstractIrrational) = false

<(::Irrational{s}, ::Irrational{s}) where {s} = false
function <(x::AbstractIrrational, y::AbstractIrrational)
    Float64(x) != Float64(y) || throw(MethodError(<, (x, y)))
    return Float64(x) < Float64(y)
end

<=(::Irrational{s}, ::Irrational{s}) where {s} = true
<=(x::AbstractIrrational, y::AbstractIrrational) = x==y || x<y

# Irrationals, by definition, can't have a finite representation equal them exactly
==(x::AbstractIrrational, y::Real) = false
==(x::Real, y::AbstractIrrational) = false

# Irrational vs AbstractFloat
<(x::AbstractIrrational, y::Float64) = Float64(x,RoundUp) <= y
<(x::Float64, y::AbstractIrrational) = x <= Float64(y,RoundDown)
<(x::AbstractIrrational, y::Float32) = Float32(x,RoundUp) <= y
<(x::Float32, y::AbstractIrrational) = x <= Float32(y,RoundDown)
<(x::AbstractIrrational, y::Float16) = Float32(x,RoundUp) <= y
<(x::Float16, y::AbstractIrrational) = x <= Float32(y,RoundDown)
<(x::AbstractIrrational, y::BigFloat) = setprecision(precision(y)+32) do
    big(x) < y
end
<(x::BigFloat, y::AbstractIrrational) = setprecision(precision(x)+32) do
    x < big(y)
end

<=(x::AbstractIrrational, y::AbstractFloat) = x < y
<=(x::AbstractFloat, y::AbstractIrrational) = x < y

# Irrational vs Rational
@assume_effects :total function rationalize(::Type{T}, x::AbstractIrrational; tol::Real=0) where T
    return rationalize(T, big(x), tol=tol)
end
@assume_effects :total function lessrational(rx::Rational{<:Integer}, x::AbstractIrrational)
    # an @assume_effects :total version of `<` for determining if the rationalization of
    # an irrational number required rounding up or down
    return rx < big(x)
end
function <(x::AbstractIrrational, y::Rational{T}) where T
    T <: Unsigned && x < 0.0 && return true
    rx = rationalize(T, x)
    if lessrational(rx, x)
        return rx < y
    else
        return rx <= y
    end
end
function <(x::Rational{T}, y::AbstractIrrational) where T
    T <: Unsigned && y < 0.0 && return false
    ry = rationalize(T, y)
    if lessrational(ry, y)
        return x <= ry
    else
        return x < ry
    end
end
<(x::AbstractIrrational, y::Rational{BigInt}) = big(x) < y
<(x::Rational{BigInt}, y::AbstractIrrational) = x < big(y)

<=(x::AbstractIrrational, y::Rational) = x < y
<=(x::Rational, y::AbstractIrrational) = x < y

isfinite(::AbstractIrrational) = true
isinteger(::AbstractIrrational) = false
iszero(::AbstractIrrational) = false
isone(::AbstractIrrational) = false

hash(x::Irrational, h::UInt) = 3*objectid(x) - h

widen(::Type{T}) where {T<:Irrational} = T

zero(::AbstractIrrational) = false
zero(::Type{<:AbstractIrrational}) = false

one(::AbstractIrrational) = true
one(::Type{<:AbstractIrrational}) = true

sign(x::AbstractIrrational) = ifelse(x < zero(x), -1.0, 1.0)

-(x::AbstractIrrational) = -Float64(x)
for op in Symbol[:+, :-, :*, :/, :^]
    @eval $op(x::AbstractIrrational, y::AbstractIrrational) = $op(Float64(x),Float64(y))
end
*(x::Bool, y::AbstractIrrational) = ifelse(x, Float64(y), 0.0)

round(x::Irrational, r::RoundingMode) = round(float(x), r)

"""
    @irrational sym [val] def

Define a new `Irrational` value, `sym`, with arbitrary-precision definition in terms
of `BigFloat`s given by the expression `def`.

Optionally provide a pre-computed `Float64` value `val` which must equal `Float64(def)`.
`val` will be computed automatically if omitted.

An `AssertionError` is thrown when either `big(def) isa BigFloat` or `Float64(val) == Float64(def)`
returns `false`.

!!! warning
    This macro should not be used outside of `Base` Julia.

    The macro creates a new type `Irrational{:sym}` regardless of where it's invoked. This can
    lead to conflicting definitions if two packages define an irrational number with the same
    name but different values.


# Examples
```jldoctest
julia> Base.@irrational twoπ 2*big(π)

julia> twoπ
twoπ = 6.2831853071795...

julia> Base.@irrational sqrt2 1.4142135623730950488 √big(2)

julia> sqrt2
sqrt2 = 1.4142135623730...

julia> Base.@irrational sqrt2 1.4142135623730950488 big(2)
ERROR: AssertionError: big($(Expr(:escape, :sqrt2))) isa BigFloat

julia> Base.@irrational sqrt2 1.41421356237309 √big(2)
ERROR: AssertionError: Float64($(Expr(:escape, :sqrt2))) == Float64(big($(Expr(:escape, :sqrt2))))
```
"""
macro irrational(sym, val, def)
    irrational(sym, val, def)
end
macro irrational(sym, def)
    irrational(sym, :(big($(esc(sym)))), def)
end
function irrational(sym, val, def)
    esym = esc(sym)
    qsym = esc(Expr(:quote, sym))
    bigconvert = isa(def,Symbol) ? quote
        function Base.BigFloat(::Irrational{$qsym}, r::MPFR.MPFRRoundingMode=MPFR.ROUNDING_MODE[]; precision=precision(BigFloat))
            c = BigFloat(;precision=precision)
            ccall(($(string("mpfr_const_", def)), :libmpfr),
                  Cint, (Ref{BigFloat}, MPFR.MPFRRoundingMode), c, r)
            return c
        end
    end : quote
        function Base.BigFloat(::Irrational{$qsym}; precision=precision(BigFloat))
            setprecision(BigFloat, precision) do
                $(esc(def))
            end
        end
    end
    quote
        const $esym = Irrational{$qsym}()
        $bigconvert
        let v = $val, v64 = Float64(v), v32 = Float32(v)
            Base.Float64(::Irrational{$qsym}) = v64
            Base.Float32(::Irrational{$qsym}) = v32
        end
        @assert isa(big($esym), BigFloat)
        @assert Float64($esym) == Float64(big($esym))
        @assert Float32($esym) == Float32(big($esym))
    end
end

big(x::AbstractIrrational) = BigFloat(x)
big(::Type{<:AbstractIrrational}) = BigFloat

# align along = for nice Array printing
function alignment(io::IO, x::AbstractIrrational)
    m = match(r"^(.*?)(=.*)$", sprint(show, x, context=io, sizehint=0))
    m === nothing ? (length(sprint(show, x, context=io, sizehint=0)), 0) :
    (length(something(m.captures[1])), length(something(m.captures[2])))
end

# inv
inv(x::AbstractIrrational) = 1/x
T   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/mathconstants.jl�	      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
    Base.MathConstants

Module containing the mathematical constants.
See [`π`](@ref), [`ℯ`](@ref), [`γ`](@ref), [`φ`](@ref) and [`catalan`](@ref).
"""
module MathConstants

export π, pi, ℯ, e, γ, eulergamma, catalan, φ, golden

Base.@irrational π        pi
Base.@irrational ℯ        exp(big(1))
Base.@irrational γ        euler
Base.@irrational φ        (1+sqrt(big(5)))/2
Base.@irrational catalan  catalan

# aliases
"""
    π
    pi

The constant pi.

Unicode `π` can be typed by writing `\\pi` then pressing tab in the Julia REPL, and in many editors.

See also: [`sinpi`](@ref), [`sincospi`](@ref), [`deg2rad`](@ref).

# Examples
```jldoctest
julia> pi
π = 3.1415926535897...

julia> 1/2pi
0.15915494309189535
```
"""
π, const pi = π

"""
    ℯ
    e

The constant ℯ.

Unicode `ℯ` can be typed by writing `\\euler` and pressing tab in the Julia REPL, and in many editors.

See also: [`exp`](@ref), [`cis`](@ref), [`cispi`](@ref).

# Examples
```jldoctest
julia> ℯ
ℯ = 2.7182818284590...

julia> log(ℯ)
1

julia> ℯ^(im)π ≈ -1
true
```
"""
ℯ, const e = ℯ

"""
    γ
    eulergamma

Euler's constant.

# Examples
```jldoctest
julia> Base.MathConstants.eulergamma
γ = 0.5772156649015...

julia> dx = 10^-6;

julia> sum(-exp(-x) * log(x) for x in dx:dx:100) * dx
0.5772078382499133
```
"""
γ, const eulergamma = γ

"""
    φ
    golden

The golden ratio.

# Examples
```jldoctest
julia> Base.MathConstants.golden
φ = 1.6180339887498...

julia> (2ans - 1)^2 ≈ 5
true
```
"""
φ, const golden = φ

"""
    catalan

Catalan's constant.

# Examples
```jldoctest
julia> Base.MathConstants.catalan
catalan = 0.9159655941772...

julia> sum(log(x)/(1+x^2) for x in 1:0.01:10^6) * 0.01
0.9159466120554123
```
"""
catalan

# loop over types to prevent ambiguities for ^(::Number, x)
for T in (AbstractIrrational, Rational, Integer, Number, Complex)
    Base.:^(::Irrational{:ℯ}, x::T) = exp(x)
end
Base.literal_pow(::typeof(^), ::Irrational{:ℯ}, ::Val{p}) where {p} = exp(p)

Base.log(::Irrational{:ℯ}) = 1 # use 1 to correctly promote expressions like log(x)/log(ℯ)
Base.log(::Irrational{:ℯ}, x::Number) = log(x)

Base.sin(::Irrational{:π}) = 0.0
Base.cos(::Irrational{:π}) = -1.0
Base.sincos(::Irrational{:π}) = (0.0, -1.0)
Base.tan(::Irrational{:π}) = 0.0
Base.cot(::Irrational{:π}) = -1/0

end # module
K   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/meta.jl�>      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
Convenience functions for metaprogramming.
"""
module Meta

using ..CoreLogging

export quot,
       isexpr,
       isidentifier,
       isoperator,
       isunaryoperator,
       isbinaryoperator,
       ispostfixoperator,
       replace_sourceloc!,
       show_sexpr,
       @dump

using Base: isidentifier, isoperator, isunaryoperator, isbinaryoperator, ispostfixoperator
import Base: isexpr

"""
    Meta.quot(ex)::Expr

Quote expression `ex` to produce an expression with head `quote`. This can for
instance be used to represent objects of type `Expr` in the AST. See also the
manual section about [QuoteNode](@ref man-quote-node).

# Examples
```jldoctest
julia> eval(Meta.quot(:x))
:x

julia> dump(Meta.quot(:x))
Expr
  head: Symbol quote
  args: Array{Any}((1,))
    1: Symbol x

julia> eval(Meta.quot(:(1+2)))
:(1 + 2)
```
"""
quot(ex) = Expr(:quote, ex)

"""
    Meta.isexpr(ex, head[, n])::Bool

Return `true` if `ex` is an `Expr` with the given type `head` and optionally that
the argument list is of length `n`. `head` may be a `Symbol` or collection of
`Symbol`s. For example, to check that a macro was passed a function call
expression, you might use `isexpr(ex, :call)`.

# Examples
```jldoctest
julia> ex = :(f(x))
:(f(x))

julia> Meta.isexpr(ex, :block)
false

julia> Meta.isexpr(ex, :call)
true

julia> Meta.isexpr(ex, [:block, :call]) # multiple possible heads
true

julia> Meta.isexpr(ex, :call, 1)
false

julia> Meta.isexpr(ex, :call, 2)
true
```
"""
isexpr

"""
    replace_sourceloc!(location, expr)

Overwrite the caller source location for each macro call in `expr`, returning
the resulting AST.  This is useful when you need to wrap a macro inside a
macro, and want the inner macro to see the `__source__` location of the outer
macro.  For example:

```
macro test_is_one(ex)
    replace_sourceloc!(__source__, :(@test \$(esc(ex)) == 1))
end
@test_is_one 2
```

`@test` now reports the location of the call `@test_is_one 2` to the user,
rather than line 2 where `@test` is used as an implementation detail.
"""
function replace_sourceloc!(sourceloc, @nospecialize(ex))
    if ex isa Expr
        if ex.head === :macrocall
            ex.args[2] = sourceloc
        end
        map!(e -> replace_sourceloc!(sourceloc, e), ex.args, ex.args)
    end
    return ex
end


"""
    Meta.show_sexpr([io::IO,], ex)

Show expression `ex` as a lisp style S-expression.

# Examples
```jldoctest
julia> Meta.show_sexpr(:(f(x, g(y,z))))
(:call, :f, :x, (:call, :g, :y, :z))
```
"""
show_sexpr(ex) = show_sexpr(stdout, ex)
show_sexpr(io::IO, ex) = show_sexpr(io, ex, 0)
show_sexpr(io::IO, ex, indent::Int) = show(io, ex)

const sexpr_indent_width = 2

function show_sexpr(io::IO, ex::QuoteNode, indent::Int)
    inner = indent + sexpr_indent_width
    print(io, "(:quote, #QuoteNode\n", " "^inner)
    show_sexpr(io, ex.value, inner)
    print(io, '\n', " "^indent, ')')
end
function show_sexpr(io::IO, ex::Expr, indent::Int)
    inner = indent + sexpr_indent_width
    print(io, '(')
    show_sexpr(io, ex.head, inner)
    for arg in ex.args
        print(io, ex.head === :block ? ",\n"*" "^inner : ", ")
        show_sexpr(io, arg, inner)
    end
    if isempty(ex.args)
        print(io, ",)")
    else
        print(io, (ex.head === :block ? "\n"*" "^indent : ""), ')')
    end
end

"""
    @dump expr

Show every part of the representation of the given expression. Equivalent to
[`dump(:(expr))`](@ref dump).
"""
macro dump(expr)
    return :(dump($(QuoteNode(expr))))
end

"""
    lower(m, x)

Takes the expression `x` and returns an equivalent expression in lowered form
for executing in module `m`.
See also [`code_lowered`](@ref).
"""
lower(m::Module, @nospecialize(x)) = ccall(:jl_expand, Any, (Any, Any), x, m)

"""
    @lower [m] x

Return lowered form of the expression `x` in module `m`.
By default `m` is the module in which the macro is called.
See also [`lower`](@ref).
"""
macro lower(code)
    return :(lower($__module__, $(QuoteNode(code))))
end
macro lower(mod, code)
    return :(lower($(esc(mod)), $(QuoteNode(code))))
end


## interface to parser ##

"""
    ParseError(msg)

The expression passed to the [`parse`](@ref) function could not be interpreted as a valid Julia
expression.
"""
struct ParseError <: Exception
    msg::String
    detail::Any
end

ParseError(msg::AbstractString) = ParseError(msg, nothing)

function _parse_string(text::AbstractString, filename::AbstractString,
                       lineno::Integer, index::Integer, options)
    if index < 1 || index > ncodeunits(text) + 1
        throw(BoundsError(text, index))
    end
    ex, offset::Int = Core._parse(text, filename, lineno, index-1, options)
    ex, offset+1
end

"""
    parse(str, start; greedy=true, raise=true, depwarn=true, filename="none")

Parse the expression string and return an expression (which could later be
passed to eval for execution). `start` is the code unit index into `str` of the
first character to start parsing at (as with all string indexing, these are not
character indices). If `greedy` is `true` (default), `parse` will try to consume
as much input as it can; otherwise, it will stop as soon as it has parsed a
valid expression. Incomplete but otherwise syntactically valid expressions will
return `Expr(:incomplete, "(error message)")`. If `raise` is `true` (default),
syntax errors other than incomplete expressions will raise an error. If `raise`
is `false`, `parse` will return an expression that will raise an error upon
evaluation. If `depwarn` is `false`, deprecation warnings will be suppressed.
The `filename` argument is used to display diagnostics when an error is raised.

```jldoctest
julia> Meta.parse("(α, β) = 3, 5", 1) # start of string
(:((α, β) = (3, 5)), 16)

julia> Meta.parse("(α, β) = 3, 5", 1, greedy=false)
(:((α, β)), 9)

julia> Meta.parse("(α, β) = 3, 5", 16) # end of string
(nothing, 16)

julia> Meta.parse("(α, β) = 3, 5", 11) # index of 3
(:((3, 5)), 16)

julia> Meta.parse("(α, β) = 3, 5", 11, greedy=false)
(3, 13)
```
"""
function parse(str::AbstractString, pos::Integer;
               filename="none", greedy::Bool=true, raise::Bool=true, depwarn::Bool=true)
    ex, pos = _parse_string(str, String(filename), 1, pos, greedy ? :statement : :atom)
    if raise && isexpr(ex, :error)
        err = ex.args[1]
        if err isa String
            err = ParseError(err) # For flisp parser
        end
        throw(err)
    end
    return ex, pos
end

"""
    parse(str; raise=true, depwarn=true, filename="none")

Parse the expression string greedily, returning a single expression. An error is thrown if
there are additional characters after the first expression. If `raise` is `true` (default),
syntax errors will raise an error; otherwise, `parse` will return an expression that will
raise an error upon evaluation.  If `depwarn` is `false`, deprecation warnings will be
suppressed. The `filename` argument is used to display diagnostics when an error is raised.

```jldoctest; filter=r"(?<=Expr\\(:error).*|(?<=Expr\\(:incomplete).*"
julia> Meta.parse("x = 3")
:(x = 3)

julia> Meta.parse("1.0.2")
ERROR: ParseError:
# Error @ none:1:1
1.0.2
└──┘ ── invalid numeric constant
[...]

julia> Meta.parse("1.0.2"; raise = false)
:(\$(Expr(:error, "invalid numeric constant \"1.0.\"")))

julia> Meta.parse("x = ")
:(\$(Expr(:incomplete, "incomplete: premature end of input")))
```
"""
function parse(str::AbstractString;
               filename="none", raise::Bool=true, depwarn::Bool=true)
    ex, pos = parse(str, 1; filename, greedy=true, raise, depwarn)
    if isexpr(ex, :error)
        return ex
    end
    if pos <= ncodeunits(str)
        raise && throw(ParseError("extra token after end of expression"))
        return Expr(:error, "extra token after end of expression")
    end
    return ex
end

function parseatom(text::AbstractString, pos::Integer; filename="none", lineno=1)
    return _parse_string(text, String(filename), lineno, pos, :atom)
end

function parseall(text::AbstractString; filename="none", lineno=1)
    ex,_ = _parse_string(text, String(filename), lineno, 1, :all)
    return ex
end

"""
    partially_inline!(code::Vector{Any}, slot_replacements::Vector{Any},
                      type_signature::Type{<:Tuple}, static_param_values::Vector{Any},
                      slot_offset::Int, statement_offset::Int,
                      boundscheck::Symbol)

Return `code` after performing an in-place partial inlining pass on the Julia IR stored
within it.

The kind of inlining transformations performed by this function are those that are generally
possible given only a runtime type signature for a method invocation and the corresponding
method's lowered IR. Thus, this function is mainly useful when preparing Julia IR to be
emitted from a `@generated` function.

The performed transformations are:

- replace slot numbers in the range `1:length(slot_replacements)` with the corresponding items in `slot_replacements`
- increment other slot numbers by `slot_offset`
- substitute static parameter placeholders (e.g. `Expr(:static_parameter, 1)`) with the corresponding
values in `static_param_values`
- increment any statement indices present in the IR (`GotoNode`s, `SSAValue`s, etc.) by `statement_offset`
(useful when the caller plans to prepend new statements to the IR)
- turn off boundschecking (if `boundscheck === :off`) or propagate boundschecking (if `boundscheck === :propagate`)

This function is similar to `Core.Compiler.ssa_substitute!`, but works on pre-type-inference
IR instead of the optimizer's IR.
"""
function partially_inline!(code::Vector{Any}, slot_replacements::Vector{Any},
                           @nospecialize(type_signature)#=::Type{<:Tuple}=#,
                           static_param_values::Vector{Any},
                           slot_offset::Int, statement_offset::Int,
                           boundscheck::Symbol)
    for i = 1:length(code)
        isassigned(code, i) || continue
        code[i] = _partially_inline!(code[i], slot_replacements, type_signature,
                                     static_param_values, slot_offset,
                                     statement_offset, boundscheck)
    end
    return code
end

function _partially_inline!(@nospecialize(x), slot_replacements::Vector{Any},
                            @nospecialize(type_signature), static_param_values::Vector{Any},
                            slot_offset::Int, statement_offset::Int,
                            boundscheck::Symbol)
    if isa(x, Core.SSAValue)
        return Core.SSAValue(x.id + statement_offset)
    end
    if isa(x, Core.GotoNode)
        return Core.GotoNode(x.label + statement_offset)
    end
    if isa(x, Core.SlotNumber)
        id = x.id
        if 1 <= id <= length(slot_replacements)
            return slot_replacements[id]
        end
        return Core.SlotNumber(id + slot_offset)
    end
    if isa(x, Core.NewvarNode)
        return Core.NewvarNode(_partially_inline!(x.slot, slot_replacements, type_signature,
                                                  static_param_values, slot_offset,
                                                  statement_offset, boundscheck))
    end
    if isa(x, Core.PhiNode)
        partially_inline!(x.values, slot_replacements, type_signature, static_param_values,
                          slot_offset, statement_offset, boundscheck)
        x.edges .+= slot_offset
        return x
    end
    if isa(x, Core.ReturnNode)
        return Core.ReturnNode(
            _partially_inline!(x.val, slot_replacements, type_signature, static_param_values,
                               slot_offset, statement_offset, boundscheck),
        )
    end
    if isa(x, Core.GotoIfNot)
        return Core.GotoIfNot(
            _partially_inline!(x.cond, slot_replacements, type_signature, static_param_values,
                               slot_offset, statement_offset, boundscheck),
            x.dest + statement_offset,
        )
    end
    if isa(x, Expr)
        head = x.head
        if head === :static_parameter
            if isassigned(static_param_values, x.args[1])
                return QuoteNode(static_param_values[x.args[1]])
            end
            return x
        elseif head === :cfunction
            @assert !isa(type_signature, UnionAll) || !isempty(spvals)
            if !isa(x.args[2], QuoteNode) # very common no-op
                x.args[2] = _partially_inline!(x.args[2], slot_replacements, type_signature,
                                               static_param_values, slot_offset,
                                               statement_offset, boundscheck)
            end
            x.args[3] = _instantiate_type_in_env(x.args[3], type_signature, static_param_values)
            x.args[4] = Core.svec(Any[_instantiate_type_in_env(argt, type_signature, static_param_values) for argt in x.args[4]]...)
        elseif head === :foreigncall
            @assert !isa(type_signature, UnionAll) || !isempty(static_param_values)
            for i = 1:length(x.args)
                if i == 2
                    x.args[2] = _instantiate_type_in_env(x.args[2], type_signature, static_param_values)
                elseif i == 3
                    x.args[3] = Core.svec(Any[_instantiate_type_in_env(argt, type_signature, static_param_values) for argt in x.args[3]]...)
                elseif i == 4
                    @assert isa(x.args[4], Int)
                elseif i == 5
                    @assert isa((x.args[5]::QuoteNode).value, Union{Symbol, Tuple{Symbol, UInt8}})
                else
                    x.args[i] = _partially_inline!(x.args[i], slot_replacements,
                                                   type_signature, static_param_values,
                                                   slot_offset, statement_offset,
                                                   boundscheck)
                end
            end
        elseif head === :boundscheck
            if boundscheck === :propagate
                return x
            elseif boundscheck === :off
                return false
            else
                return true
            end
        elseif head === :gotoifnot
            x.args[1] = _partially_inline!(x.args[1], slot_replacements, type_signature,
                                           static_param_values, slot_offset,
                                           statement_offset, boundscheck)
            x.args[2] += statement_offset
        elseif head === :enter
            x.args[1] += statement_offset
        elseif head === :isdefined
            arg = x.args[1]
            # inlining a QuoteNode or literal into `Expr(:isdefined, x)` is invalid, replace with true
            if isa(arg, Core.SlotNumber)
                id = arg.id
                if 1 <= id <= length(slot_replacements)
                    replacement = slot_replacements[id]
                    if isa(replacement, Union{Core.SlotNumber, GlobalRef, Symbol})
                        return Expr(:isdefined, replacement)
                    else
                        @assert !isa(replacement, Expr)
                        return true
                    end
                end
                return Expr(:isdefined, Core.SlotNumber(id + slot_offset))
            elseif isexpr(arg, :static_parameter)
                if isassigned(static_param_values, arg.args[1])
                    return true
                end
                return x
            else
                @assert isa(arg, Union{GlobalRef, Symbol})
                return x
            end
        elseif !Core.Compiler.is_meta_expr_head(head)
            partially_inline!(x.args, slot_replacements, type_signature, static_param_values,
                              slot_offset, statement_offset, boundscheck)
        end
    end
    return x
end

_instantiate_type_in_env(x, spsig, spvals) = ccall(:jl_instantiate_type_in_env, Any, (Any, Any, Ptr{Any}), x, spsig, spvals)

end # module
R   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/stacktraces.jl�)      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
Tools for collecting and manipulating stack traces. Mainly used for building errors.
"""
module StackTraces


import Base: hash, ==, show
import Core: CodeInfo, MethodInstance

export StackTrace, StackFrame, stacktrace

"""
    StackFrame

Stack information representing execution context, with the following fields:

- `func::Symbol`

  The name of the function containing the execution context.

- `linfo::Union{Core.MethodInstance, Method, Module, Core.CodeInfo, Nothing}`

  The MethodInstance or CodeInfo containing the execution context (if it could be found), \
     or Module (for macro expansions)"

- `file::Symbol`

  The path to the file containing the execution context.

- `line::Int`

  The line number in the file containing the execution context.

- `from_c::Bool`

  True if the code is from C.

- `inlined::Bool`

  True if the code is from an inlined frame.

- `pointer::UInt64`

  Representation of the pointer to the execution context as returned by `backtrace`.

"""
struct StackFrame # this type should be kept platform-agnostic so that profiles can be dumped on one machine and read on another
    "the name of the function containing the execution context"
    func::Symbol
    "the path to the file containing the execution context"
    file::Symbol
    "the line number in the file containing the execution context"
    line::Int
    "the MethodInstance or CodeInfo containing the execution context (if it could be found), \
     or Module (for macro expansions)"
    linfo::Union{MethodInstance, Method, Module, CodeInfo, Nothing}
    "true if the code is from C"
    from_c::Bool
    "true if the code is from an inlined frame"
    inlined::Bool
    "representation of the pointer to the execution context as returned by `backtrace`"
    pointer::UInt64  # Large enough to be read losslessly on 32- and 64-bit machines.
end

StackFrame(func, file, line) = StackFrame(Symbol(func), Symbol(file), line,
                                          nothing, false, false, 0)

"""
    StackTrace

An alias for `Vector{StackFrame}` provided for convenience; returned by calls to
`stacktrace`.
"""
const StackTrace = Vector{StackFrame}

const empty_sym = Symbol("")
const UNKNOWN = StackFrame(empty_sym, empty_sym, -1, nothing, true, false, 0) # === lookup(C_NULL)


#=
If the StackFrame has function and line information, we consider two of them the same if
they share the same function/line information.
=#
function ==(a::StackFrame, b::StackFrame)
    return a.line == b.line && a.from_c == b.from_c && a.func == b.func && a.file == b.file && a.inlined == b.inlined # excluding linfo and pointer
end

function hash(frame::StackFrame, h::UInt)
    h += 0xf4fbda67fe20ce88 % UInt
    h = hash(frame.line, h)
    h = hash(frame.file, h)
    h = hash(frame.func, h)
    h = hash(frame.from_c, h)
    h = hash(frame.inlined, h)
    return h
end

"""
    lookup(pointer::Ptr{Cvoid}) -> Vector{StackFrame}

Given a pointer to an execution context (usually generated by a call to `backtrace`), looks
up stack frame context information. Returns an array of frame information for all functions
inlined at that point, innermost function first.
"""
Base.@constprop :none function lookup(pointer::Ptr{Cvoid})
    infos = ccall(:jl_lookup_code_address, Any, (Ptr{Cvoid}, Cint), pointer, false)::Core.SimpleVector
    pointer = convert(UInt64, pointer)
    isempty(infos) && return [StackFrame(empty_sym, empty_sym, -1, nothing, true, false, pointer)] # this is equal to UNKNOWN
    res = Vector{StackFrame}(undef, length(infos))
    for i in 1:length(infos)
        info = infos[i]::Core.SimpleVector
        @assert(length(info) == 6)
        res[i] = StackFrame(info[1]::Symbol, info[2]::Symbol, info[3]::Int, info[4], info[5]::Bool, info[6]::Bool, pointer)
    end
    return res
end

const top_level_scope_sym = Symbol("top-level scope")

function lookup(ip::Union{Base.InterpreterIP,Core.Compiler.InterpreterIP})
    code = ip.code
    if code === nothing
        # interpreted top-level expression with no CodeInfo
        return [StackFrame(top_level_scope_sym, empty_sym, 0, nothing, false, false, 0)]
    end
    codeinfo = (code isa MethodInstance ? code.uninferred : code)::CodeInfo
    # prepare approximate code info
    if code isa MethodInstance && (meth = code.def; meth isa Method)
        func = meth.name
        file = meth.file
        line = meth.line
    else
        func = top_level_scope_sym
        file = empty_sym
        line = Int32(0)
    end
    i = max(ip.stmt+1, 1)  # ip.stmt is 0-indexed
    if i > length(codeinfo.codelocs) || codeinfo.codelocs[i] == 0
        return [StackFrame(func, file, line, code, false, false, 0)]
    end
    lineinfo = codeinfo.linetable[codeinfo.codelocs[i]]::Core.LineInfoNode
    scopes = StackFrame[]
    while true
        inlined = lineinfo.inlined_at != 0
        push!(scopes, StackFrame(Base.IRShow.method_name(lineinfo)::Symbol, lineinfo.file, lineinfo.line, inlined ? nothing : code, false, inlined, 0))
        inlined || break
        lineinfo = codeinfo.linetable[lineinfo.inlined_at]::Core.LineInfoNode
    end
    return scopes
end

"""
    stacktrace([trace::Vector{Ptr{Cvoid}},] [c_funcs::Bool=false]) -> StackTrace

Return a stack trace in the form of a vector of `StackFrame`s. (By default stacktrace
doesn't return C functions, but this can be enabled.) When called without specifying a
trace, `stacktrace` first calls `backtrace`.
"""
Base.@constprop :none function stacktrace(trace::Vector{<:Union{Base.InterpreterIP,Core.Compiler.InterpreterIP,Ptr{Cvoid}}}, c_funcs::Bool=false)
    stack = StackTrace()
    for ip in trace
        for frame in lookup(ip)
            # Skip frames that come from C calls.
            if c_funcs || !frame.from_c
                push!(stack, frame)
            end
        end
    end
    return stack
end

Base.@constprop :none function stacktrace(c_funcs::Bool=false)
    stack = stacktrace(backtrace(), c_funcs)
    # Remove frame for this function (and any functions called by this function).
    remove_frames!(stack, :stacktrace)
    # also remove all of the non-Julia functions that led up to this point (if that list is non-empty)
    c_funcs && deleteat!(stack, 1:(something(findfirst(frame -> !frame.from_c, stack), 1) - 1))
    return stack
end

"""
    remove_frames!(stack::StackTrace, name::Symbol)

Takes a `StackTrace` (a vector of `StackFrames`) and a function name (a `Symbol`) and
removes the `StackFrame` specified by the function name from the `StackTrace` (also removing
all frames above the specified function). Primarily used to remove `StackTraces` functions
from the `StackTrace` prior to returning it.
"""
function remove_frames!(stack::StackTrace, name::Symbol)
    deleteat!(stack, 1:something(findlast(frame -> frame.func == name, stack), 0))
    return stack
end

function remove_frames!(stack::StackTrace, names::Vector{Symbol})
    deleteat!(stack, 1:something(findlast(frame -> frame.func in names, stack), 0))
    return stack
end

"""
    remove_frames!(stack::StackTrace, m::Module)

Return the `StackTrace` with all `StackFrame`s from the provided `Module` removed.
"""
function remove_frames!(stack::StackTrace, m::Module)
    filter!(f -> !from(f, m), stack)
    return stack
end

is_top_level_frame(f::StackFrame) = f.linfo isa CodeInfo || (f.linfo === nothing && f.func === top_level_scope_sym)

function show_spec_linfo(io::IO, frame::StackFrame)
    linfo = frame.linfo
    if linfo === nothing
        if frame.func === empty_sym
            print(io, "ip:0x", string(frame.pointer, base=16))
        elseif frame.func === top_level_scope_sym
            print(io, "top-level scope")
        else
            Base.print_within_stacktrace(io, Base.demangle_function_name(string(frame.func)), bold=true)
        end
    elseif linfo isa CodeInfo
        print(io, "top-level scope")
    elseif linfo isa Module
        Base.print_within_stacktrace(io, Base.demangle_function_name(string(frame.func)), bold=true)
    elseif linfo isa MethodInstance
        def = linfo.def
        if def isa Module
            Base.show_mi(io, linfo, #=from_stackframe=#true)
        else
            show_spec_sig(io, def, linfo.specTypes)
        end
    else
        m = linfo::Method
        show_spec_sig(io, m, m.sig)
    end
end

function show_spec_sig(io::IO, m::Method, @nospecialize(sig::Type))
    if get(io, :limit, :false)::Bool
        if !haskey(io, :displaysize)
            io = IOContext(io, :displaysize => displaysize(io))
        end
    end
    argnames = Base.method_argnames(m)
    argnames = replace(argnames, :var"#unused#" => :var"")
    if m.nkw > 0
        # rearrange call kw_impl(kw_args..., func, pos_args...) to func(pos_args...; kw_args)
        kwarg_types = Any[ fieldtype(sig, i) for i = 2:(1+m.nkw) ]
        uw = Base.unwrap_unionall(sig)::DataType
        pos_sig = Base.rewrap_unionall(Tuple{uw.parameters[(m.nkw+2):end]...}, sig)
        kwnames = argnames[2:(m.nkw+1)]
        for i = 1:length(kwnames)
            str = string(kwnames[i])::String
            if endswith(str, "...")
                kwnames[i] = Symbol(str[1:end-3])
            end
        end
        Base.show_tuple_as_call(io, m.name, pos_sig;
                                demangle=true,
                                kwargs=zip(kwnames, kwarg_types),
                                argnames=argnames[m.nkw+2:end])
    else
        Base.show_tuple_as_call(io, m.name, sig; demangle=true, argnames)
    end
end

function show(io::IO, frame::StackFrame)
    show_spec_linfo(io, frame)
    if frame.file !== empty_sym
        file_info = basename(string(frame.file))
        print(io, " at ")
        print(io, file_info, ":")
        if frame.line >= 0
            print(io, frame.line)
        else
            print(io, "?")
        end
    end
    if frame.inlined
        print(io, " [inlined]")
    end
end

function Base.parentmodule(frame::StackFrame)
    linfo = frame.linfo
    if linfo isa MethodInstance
        def = linfo.def
        if def isa Module
            return def
        else
            return (def::Method).module
        end
    elseif linfo isa Method
        return linfo.module
    elseif linfo isa Module
        return linfo
    else
        # The module is not always available (common reasons include
        # frames arising from the interpreter)
        nothing
    end
end

"""
    from(frame::StackFrame, filter_mod::Module) -> Bool

Return whether the `frame` is from the provided `Module`
"""
function from(frame::StackFrame, m::Module)
    return parentmodule(frame) === m
end

end
S   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/experimental.jl�0      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
    Experimental

!!! warning
    Types, methods, or macros defined in this module are experimental and subject
    to change and will not have deprecations. Caveat emptor.
"""
module Experimental

using Base: Threads, sync_varname
using Base.Meta

"""
    Const(A::Array)

Mark an Array as constant/read-only. The invariant guaranteed is that you will not
modify an Array (through another reference) within an `@aliasscope` scope.

!!! warning
    Experimental API. Subject to change without deprecation.
"""
struct Const{T,N} <: DenseArray{T,N}
    a::Array{T,N}
end

Base.IndexStyle(::Type{<:Const}) = IndexLinear()
Base.size(C::Const) = size(C.a)
Base.axes(C::Const) = axes(C.a)
@eval Base.getindex(A::Const, i1::Int) =
    (Base.@inline; Core.const_arrayref($(Expr(:boundscheck)), A.a, i1))
@eval Base.getindex(A::Const, i1::Int, i2::Int, I::Int...) =
  (Base.@inline; Core.const_arrayref($(Expr(:boundscheck)), A.a, i1, i2, I...))

"""
    @aliasscope expr

Allows the compiler to assume that all `Const`s are not being modified through stores
within this scope, even if the compiler can't prove this to be the case.

!!! warning
    Experimental API. Subject to change without deprecation.
"""
macro aliasscope(body)
    sym = gensym()
    quote
        $(Expr(:aliasscope))
        $sym = $(esc(body))
        $(Expr(:popaliasscope))
        $sym
    end
end


function sync_end(c::Channel{Any})
    if !isready(c)
        # there must be at least one item to begin with
        close(c)
        return
    end
    nremaining::Int = 0
    while true
        event = take!(c)
        if event === :__completion__
            nremaining -= 1
            if nremaining == 0
                break
            end
        else
            nremaining += 1
            schedule(Task(()->begin
                try
                    wait(event)
                    put!(c, :__completion__)
                catch e
                    close(c, e)
                end
            end))
        end
    end
    close(c)
    nothing
end

"""
    Experimental.@sync

Wait until all lexically-enclosed uses of `@async`, `@spawn`, `@spawnat` and `@distributed`
are complete, or at least one of them has errored. The first exception is immediately
rethrown. It is the responsibility of the user to cancel any still-running operations
during error handling.

!!! Note
    This interface is experimental and subject to change or removal without notice.
"""
macro sync(block)
    var = esc(sync_varname)
    quote
        let $var = Channel(Inf)
            v = $(esc(block))
            sync_end($var)
            v
        end
    end
end

"""
    Experimental.@optlevel n::Int

Set the optimization level (equivalent to the `-O` command line argument)
for code in the current module. Submodules inherit the setting of their
parent module.

Supported values are 0, 1, 2, and 3.

The effective optimization level is the minimum of that specified on the
command line and in per-module settings. If a `--min-optlevel` value is
set on the command line, that is enforced as a lower bound.
"""
macro optlevel(n::Int)
    return Expr(:meta, :optlevel, n)
end

"""
    Experimental.@max_methods n::Int

Set the maximum number of potentially-matching methods considered when running inference
for methods defined in the current module. This setting affects inference of calls with
incomplete knowledge of the argument types.

The benefit of this setting is to avoid excessive compilation and reduce invalidation risks
in poorly-inferred cases. For example, when `@max_methods 2` is set and there are two
potentially-matching methods returning different types inside a function body, then Julia
will compile subsequent calls for both types so that the compiled function body accounts
for both possibilities. Also the compiled code is vulnerable to invalidations that would
happen when either of the two methods gets invalidated. This speculative compilation and
these invalidations can be avoided by setting `@max_methods 1` and allowing the compiled
code to resort to runtime dispatch instead.

Supported values are `1`, `2`, `3`, `4`, and `default` (currently equivalent to `3`).
"""
macro max_methods(n::Int)
    0 < n < 5 || error("We must have that `1 <= max_methods <= 4`, but `max_methods = $n`.")
    return Expr(:meta, :max_methods, n)
end

"""
    Experimental.@max_methods n::Int function fname end

Set the maximum number of potentially-matching methods considered when running inference
for the generic function `fname`. Overrides any module-level or global inference settings
for max_methods. This setting is global for the entire generic function (or more precisely
the MethodTable).
"""
macro max_methods(n::Int, fdef::Expr)
    0 < n <= 255 || error("We must have that `1 <= max_methods <= 255`, but `max_methods = $n`.")
    (fdef.head === :function && length(fdef.args) == 1) || error("Second argument must be a function forward declaration")
    return :(typeof($(esc(fdef))).name.max_methods = $(UInt8(n)))
end

"""
    Experimental.@compiler_options optimize={0,1,2,3} compile={yes,no,all,min} infer={yes,no} max_methods={default,1,2,3,...}

Set compiler options for code in the enclosing module. Options correspond directly to
command-line options with the same name, where applicable. The following options
are currently supported:

  * `optimize`: Set optimization level.
  * `compile`: Toggle native code compilation. Currently only `min` is supported, which
    requests the minimum possible amount of compilation.
  * `infer`: Enable or disable type inference. If disabled, implies [`@nospecialize`](@ref).
  * `max_methods`: Maximum number of matching methods considered when running type inference.
"""
macro compiler_options(args...)
    opts = Expr(:block)
    for ex in args
        if isa(ex, Expr) && ex.head === :(=) && length(ex.args) == 2
            if ex.args[1] === :optimize
                push!(opts.args, Expr(:meta, :optlevel, ex.args[2]::Int))
            elseif ex.args[1] === :compile
                a = ex.args[2]
                a = #a === :no  ? 0 :
                    #a === :yes ? 1 :
                    #a === :all ? 2 :
                    a === :min ? 3 : error("invalid argument to \"compile\" option")
                push!(opts.args, Expr(:meta, :compile, a))
            elseif ex.args[1] === :infer
                a = ex.args[2]
                a = a === false || a === :no  ? 0 :
                    a === true  || a === :yes ? 1 : error("invalid argument to \"infer\" option")
                push!(opts.args, Expr(:meta, :infer, a))
            elseif ex.args[1] === :max_methods
                a = ex.args[2]
                a = a === :default ? 3 :
                  a isa Int ? ((0 < a < 5) ? a : error("We must have that `1 <= max_methods <= 4`, but `max_methods = $a`.")) :
                  error("invalid argument to \"max_methods\" option")
                push!(opts.args, Expr(:meta, :max_methods, a))
            else
                error("unknown option \"$(ex.args[1])\"")
            end
        else
            error("invalid option syntax")
        end
    end
    return opts
end

"""
    Experimental.@force_compile

Force compilation of the block or function (Julia's built-in interpreter is blocked from executing it).

# Examples

```
julia> occursin("interpreter", string(stacktrace(begin
           # with forced compilation
           Base.Experimental.@force_compile
           backtrace()
       end, true)))
false

julia> occursin("interpreter", string(stacktrace(begin
           # without forced compilation
           backtrace()
       end, true)))
true
```
"""
macro force_compile() Expr(:meta, :force_compile) end

# UI features for errors

"""
    Experimental.register_error_hint(handler, exceptiontype)

Register a "hinting" function `handler(io, exception)` that can
suggest potential ways for users to circumvent errors.  `handler`
should examine `exception` to see whether the conditions appropriate
for a hint are met, and if so generate output to `io`.
Packages should call `register_error_hint` from within their
`__init__` function.

For specific exception types, `handler` is required to accept additional arguments:

- `MethodError`: provide `handler(io, exc::MethodError, argtypes, kwargs)`,
  which splits the combined arguments into positional and keyword arguments.

When issuing a hint, the output should typically start with `\\n`.

If you define custom exception types, your `showerror` method can
support hints by calling [`Experimental.show_error_hints`](@ref).

# Example

```
julia> module Hinter

       only_int(x::Int)      = 1
       any_number(x::Number) = 2

       function __init__()
           Base.Experimental.register_error_hint(MethodError) do io, exc, argtypes, kwargs
               if exc.f == only_int
                    # Color is not necessary, this is just to show it's possible.
                    print(io, "\\nDid you mean to call ")
                    printstyled(io, "`any_number`?", color=:cyan)
               end
           end
       end

       end
```

Then if you call `Hinter.only_int` on something that isn't an `Int` (thereby triggering a `MethodError`), it issues the hint:

```
julia> Hinter.only_int(1.0)
ERROR: MethodError: no method matching only_int(::Float64)
Did you mean to call `any_number`?
Closest candidates are:
    ...
```

!!! compat "Julia 1.5"
    Custom error hints are available as of Julia 1.5.
!!! warning
    This interface is experimental and subject to change or removal without notice.
    To insulate yourself against changes, consider putting any registrations inside an
    `if isdefined(Base.Experimental, :register_error_hint) ... end` block.
"""
function register_error_hint(@nospecialize(handler), @nospecialize(exct::Type))
    list = get!(Vector{Any}, _hint_handlers, exct)
    push!(list, handler)
    return nothing
end

const _hint_handlers = IdDict{Type,Vector{Any}}()

"""
    Experimental.show_error_hints(io, ex, args...)

Invoke all handlers from [`Experimental.register_error_hint`](@ref) for the particular
exception type `typeof(ex)`. `args` must contain any other arguments expected by
the handler for that type.

!!! compat "Julia 1.5"
    Custom error hints are available as of Julia 1.5.
!!! warning
    This interface is experimental and subject to change or removal without notice.
"""
function show_error_hints(io, ex, args...)
    hinters = get(_hint_handlers, typeof(ex), nothing)
    isnothing(hinters) && return
    for handler in hinters
        try
            Base.invokelatest(handler, io, ex, args...)
        catch err
            tn = typeof(handler).name
            @error "Hint-handler $handler for $(typeof(ex)) in $(tn.module) caused an error"
        end
    end
end

# OpaqueClosure
include("opaque_closure.jl")

"""
    Experimental.@overlay mt [function def]

Define a method and add it to the method table `mt` instead of to the global method table.
This can be used to implement a method override mechanism. Regular compilation will not
consider these methods, and you should customize the compilation flow to look in these
method tables (e.g., using [`Core.Compiler.OverlayMethodTable`](@ref)).

"""
macro overlay(mt, def)
    def = macroexpand(__module__, def) # to expand @inline, @generated, etc
    if !isexpr(def, [:function, :(=)])
        error("@overlay requires a function Expr")
    end
    if isexpr(def.args[1], :call)
        def.args[1].args[1] = Expr(:overlay, mt, def.args[1].args[1])
    elseif isexpr(def.args[1], :where)
        def.args[1].args[1].args[1] = Expr(:overlay, mt, def.args[1].args[1].args[1])
    else
        error("@overlay requires a function Expr")
    end
    esc(def)
end

let new_mt(name::Symbol, mod::Module) = begin
        ccall(:jl_check_top_level_effect, Cvoid, (Any, Cstring), mod, "@MethodTable")
        ccall(:jl_new_method_table, Any, (Any, Any), name, mod)
    end
    @eval macro MethodTable(name::Symbol)
        esc(:(const $name = $$new_mt($(quot(name)), $(__module__))))
    end
end

"""
    Experimental.@MethodTable(name)

Create a new MethodTable in the current module, bound to `name`. This method table can be
used with the [`Experimental.@overlay`](@ref) macro to define methods for a function without
adding them to the global method table.
"""
:@MethodTable

end
U   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/opaque_closure.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
    @opaque ([type, ]args...) -> body

Marks a given closure as "opaque". Opaque closures capture the
world age of their creation (as opposed to their invocation).
This allows for more aggressive optimization of the capture
list, but trades off against the ability to inline opaque
closures at the call site, if their creation is not statically
visible.

An argument tuple type (`type`) may optionally be specified, to
specify allowed argument types in a more flexible way. In particular,
the argument type may be fixed length even if the function is variadic.

!!! warning
    This interface is experimental and subject to change or removal without notice.
"""
macro opaque(ex)
    esc(Expr(:opaque_closure, ex))
end

macro opaque(ty, ex)
    esc(Expr(:opaque_closure, ty, ex))
end

# OpaqueClosure construction from pre-inferred CodeInfo/IRCode
using Core.Compiler: IRCode
using Core: CodeInfo

function compute_ir_rettype(ir::IRCode)
    rt = Union{}
    for i = 1:length(ir.stmts)
        stmt = ir.stmts[i][:inst]
        if isa(stmt, Core.Compiler.ReturnNode) && isdefined(stmt, :val)
            rt = Core.Compiler.tmerge(Core.Compiler.argextype(stmt.val, ir), rt)
        end
    end
    return Core.Compiler.widenconst(rt)
end

function compute_oc_signature(ir::IRCode, nargs::Int, isva::Bool)
    argtypes = Vector{Any}(undef, nargs)
    for i = 1:nargs
        argtypes[i] = Core.Compiler.widenconst(ir.argtypes[i+1])
    end
    if isva
        lastarg = pop!(argtypes)
        if lastarg <: Tuple
            append!(argtypes, lastarg.parameters)
        else
            push!(argtypes, Vararg{Any})
        end
    end
    return Tuple{argtypes...}
end

function Core.OpaqueClosure(ir::IRCode, @nospecialize env...;
                            isva::Bool = false,
                            do_compile::Bool = true)
    # NOTE: we need ir.argtypes[1] == typeof(env)
    ir = Core.Compiler.copy(ir)
    nargs = length(ir.argtypes)-1
    sig = compute_oc_signature(ir, nargs, isva)
    rt = compute_ir_rettype(ir)
    src = ccall(:jl_new_code_info_uninit, Ref{CodeInfo}, ())
    src.slotnames = fill(:none, nargs+1)
    src.slotflags = fill(zero(UInt8), length(ir.argtypes))
    src.slottypes = copy(ir.argtypes)
    src.rettype = rt
    src = Core.Compiler.ir_to_codeinf!(src, ir)
    return generate_opaque_closure(sig, Union{}, rt, src, nargs, isva, env...; do_compile)
end

function Core.OpaqueClosure(src::CodeInfo, @nospecialize env...)
    src.inferred || throw(ArgumentError("Expected inferred src::CodeInfo"))
    mi = src.parent::Core.MethodInstance
    sig = Base.tuple_type_tail(mi.specTypes)
    method = mi.def::Method
    nargs = method.nargs-1
    isva = method.isva
    return generate_opaque_closure(sig, Union{}, src.rettype, src, nargs, isva, env...)
end

function generate_opaque_closure(@nospecialize(sig), @nospecialize(rt_lb), @nospecialize(rt_ub),
                                 src::CodeInfo, nargs::Int, isva::Bool, @nospecialize env...;
                                 mod::Module=@__MODULE__,
                                 lineno::Int=0,
                                 file::Union{Nothing,Symbol}=nothing,
                                 do_compile::Bool=true)
    return ccall(:jl_new_opaque_closure_from_code_info, Any, (Any, Any, Any, Any, Any, Cint, Any, Cint, Cint, Any, Cint),
        sig, rt_lb, rt_ub, mod, src, lineno, file, nargs, isva, env, do_compile)
end
O   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/deepcopy.jl      # This file is a part of Julia. License is MIT: https://julialang.org/license

# deep copying

# Note: deepcopy_internal(::Any, ::IdDict) is
#       only exposed for specialization by libraries

"""
    deepcopy(x)

Create a deep copy of `x`: everything is copied recursively, resulting in a fully
independent object. For example, deep-copying an array produces a new array whose elements
are deep copies of the original elements. Calling `deepcopy` on an object should generally
have the same effect as serializing and then deserializing it.

While it isn't normally necessary, user-defined types can override the default `deepcopy`
behavior by defining a specialized version of the function
`deepcopy_internal(x::T, dict::IdDict)` (which shouldn't otherwise be used),
where `T` is the type to be specialized for, and `dict` keeps track of objects copied
so far within the recursion. Within the definition, `deepcopy_internal` should be used
in place of `deepcopy`, and the `dict` variable should be
updated as appropriate before returning.
"""
function deepcopy(@nospecialize x)
    isbitstype(typeof(x)) && return x
    return deepcopy_internal(x, IdDict())::typeof(x)
end

deepcopy_internal(x::Union{Symbol,Core.MethodInstance,Method,GlobalRef,DataType,Union,UnionAll,Task,Regex},
                  stackdict::IdDict) = x
deepcopy_internal(x::Tuple, stackdict::IdDict) =
    ntuple(i->deepcopy_internal(x[i], stackdict), length(x))
deepcopy_internal(x::Module, stackdict::IdDict) = error("deepcopy of Modules not supported")

function deepcopy_internal(x::SimpleVector, stackdict::IdDict)
    if haskey(stackdict, x)
        return stackdict[x]
    end
    y = Core.svec(Any[deepcopy_internal(x[i], stackdict) for i = 1:length(x)]...)
    stackdict[x] = y
    return y
end

function deepcopy_internal(x::String, stackdict::IdDict)
    if haskey(stackdict, x)
        return stackdict[x]
    end
    y = GC.@preserve x unsafe_string(pointer(x), sizeof(x))
    stackdict[x] = y
    return y
end

function deepcopy_internal(@nospecialize(x), stackdict::IdDict)
    T = typeof(x)::DataType
    nf = nfields(x)
    if ismutable(x)
        if haskey(stackdict, x)
            return stackdict[x]
        end
        y = ccall(:jl_new_struct_uninit, Any, (Any,), T)
        stackdict[x] = y
        for i in 1:nf
            if isdefined(x, i)
                xi = getfield(x, i)
                xi = deepcopy_internal(xi, stackdict)::typeof(xi)
                ccall(:jl_set_nth_field, Cvoid, (Any, Csize_t, Any), y, i-1, xi)
            end
        end
    elseif nf == 0 || isbitstype(T)
        y = x
    else
        flds = Vector{Any}(undef, nf)
        for i in 1:nf
            if isdefined(x, i)
                xi = getfield(x, i)
                xi = deepcopy_internal(xi, stackdict)::typeof(xi)
                flds[i] = xi
            else
                nf = i - 1 # rest of tail must be undefined values
                break
            end
        end
        y = ccall(:jl_new_structv, Any, (Any, Ptr{Any}, UInt32), T, flds, nf)
    end
    return y::T
end

function deepcopy_internal(x::Array, stackdict::IdDict)
    if haskey(stackdict, x)
        return stackdict[x]::typeof(x)
    end
    _deepcopy_array_t(x, eltype(x), stackdict)
end

function _deepcopy_array_t(@nospecialize(x::Array), T, stackdict::IdDict)
    if isbitstype(T)
        return (stackdict[x]=copy(x))
    end
    dest = similar(x)
    stackdict[x] = dest
    for i = 1:length(x)
        if ccall(:jl_array_isassigned, Cint, (Any, Csize_t), x, i-1) != 0
            xi = ccall(:jl_arrayref, Any, (Any, Csize_t), x, i-1)
            if !isbits(xi)
                xi = deepcopy_internal(xi, stackdict)::typeof(xi)
            end
            ccall(:jl_arrayset, Cvoid, (Any, Any, Csize_t), dest, xi, i-1)
        end
    end
    return dest
end

function deepcopy_internal(x::Union{Dict,IdDict}, stackdict::IdDict)
    if haskey(stackdict, x)
        return stackdict[x]::typeof(x)
    end

    if isbitstype(eltype(x))
        return (stackdict[x] = copy(x))
    end

    dest = empty(x)
    stackdict[x] = dest
    for (k, v) in x
        dest[deepcopy_internal(k, stackdict)] = deepcopy_internal(v, stackdict)
    end
    dest
end

function deepcopy_internal(x::AbstractLock, stackdict::IdDict)
    if haskey(stackdict, x)
        return stackdict[x]
    end
    y = typeof(x)()
    stackdict[x] = y
    return y
end

function deepcopy_internal(x::GenericCondition, stackdict::IdDict)
    if haskey(stackdict, x)
        return stackdict[x]
    end
    y = typeof(x)(deepcopy_internal(x.lock, stackdict))
    stackdict[x] = y
    return y
end
O   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/download.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

Downloads() = require(PkgId(
        UUID((0xf43a241f_c20a_4ad4, 0x852c_f6b1247861c6)),
        "Downloads",
    ))

"""
    download(url::AbstractString, [path::AbstractString = tempname()]) -> path

Download a file from the given url, saving it to the location `path`, or if not
specified, a temporary path. Returns the path of the downloaded file.

!!! note
    Since Julia 1.6, this function is deprecated and is just a thin wrapper
    around `Downloads.download`. In new code, you should use that function
    directly instead of calling this.
"""
download(url::AbstractString, path::AbstractString) = do_download(url, path)
download(url::AbstractString) = do_download(url, nothing)

function do_download(url::AbstractString, path::Union{AbstractString, Nothing})
    depwarn("Base.download is deprecated; use Downloads.download instead", :download)
    invokelatest(Downloads().download, url, path)
end
R   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/summarysize.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

struct SummarySize
    seen::IdDict{Any,Any}
    frontier_x::Vector{Any}
    frontier_i::Vector{Int}
    exclude::Any
    chargeall::Any
end

"""
    Base.summarysize(obj; exclude=Union{...}, chargeall=Union{...}) -> Int

Compute the amount of memory, in bytes, used by all unique objects reachable from the argument.

# Keyword Arguments
- `exclude`: specifies the types of objects to exclude from the traversal.
- `chargeall`: specifies the types of objects to always charge the size of all of their
  fields, even if those fields would normally be excluded.

See also [`sizeof`](@ref).

# Examples
```jldoctest
julia> Base.summarysize(1.0)
8

julia> Base.summarysize(Ref(rand(100)))
848

julia> sizeof(Ref(rand(100)))
8
```
"""
function summarysize(obj;
                     exclude = Union{DataType, Core.TypeName, Core.MethodInstance},
                     chargeall = Union{Core.TypeMapEntry, Method})
    @nospecialize obj exclude chargeall
    ss = SummarySize(IdDict(), Any[], Int[], exclude, chargeall)
    size::Int = ss(obj)
    while !isempty(ss.frontier_x)
        # DFS heap traversal of everything without a specialization
        # BFS heap traversal of anything with a specialization
        x = ss.frontier_x[end]
        i = ss.frontier_i[end]
        val = nothing
        if isa(x, SimpleVector)
            nf = length(x)
            if isassigned(x, i)
                val = x[i]
            end
        elseif isa(x, Array)
            nf = length(x)
            if ccall(:jl_array_isassigned, Cint, (Any, UInt), x, i - 1) != 0
                val = x[i]
            end
        else
            nf = nfields(x)
            ft = typeof(x).types
            if !isbitstype(ft[i]) && isdefined(x, i)
                val = getfield(x, i)
            end
        end
        if nf > i
            ss.frontier_i[end] = i + 1
        else
            pop!(ss.frontier_x)
            pop!(ss.frontier_i)
        end
        if val !== nothing && !isa(val, Module) && (!isa(val, ss.exclude) || isa(x, ss.chargeall))
            size += ss(val)::Int
        end
    end
    return size
end

(ss::SummarySize)(@nospecialize obj) = _summarysize(ss, obj)
# define the general case separately to make sure it is not specialized for every type
@noinline function _summarysize(ss::SummarySize, @nospecialize obj)
    issingletontype(typeof(obj)) && return 0
    # NOTE: this attempts to discover multiple copies of the same immutable value,
    # and so is somewhat approximate.
    key = ccall(:jl_value_ptr, Ptr{Cvoid}, (Any,), obj)
    haskey(ss.seen, key) ? (return 0) : (ss.seen[key] = true)
    if nfields(obj) > 0
        push!(ss.frontier_x, obj)
        push!(ss.frontier_i, 1)
    end
    if isa(obj, UnionAll) || isa(obj, Union)
        # black-list of items that don't have a Core.sizeof
        sz = 2 * sizeof(Int)
    else
        sz = Core.sizeof(obj)
    end
    if sz == 0
        # 0-field mutable structs are not unique
        return gc_alignment(0)
    end
    return sz
end

(::SummarySize)(obj::Symbol) = 0
(::SummarySize)(obj::SummarySize) = 0

function (ss::SummarySize)(obj::String)
    key = ccall(:jl_value_ptr, Ptr{Cvoid}, (Any,), obj)
    haskey(ss.seen, key) ? (return 0) : (ss.seen[key] = true)
    return Core.sizeof(Int) + Core.sizeof(obj)
end

function (ss::SummarySize)(obj::DataType)
    key = pointer_from_objref(obj)
    haskey(ss.seen, key) ? (return 0) : (ss.seen[key] = true)
    size::Int = 7 * Core.sizeof(Int) + 6 * Core.sizeof(Int32)
    size += 4 * nfields(obj) + ifelse(Sys.WORD_SIZE == 64, 4, 0)
    size += ss(obj.parameters)::Int
    if isdefined(obj, :types)
        size += ss(obj.types)::Int
    end
    return size
end

function (ss::SummarySize)(obj::Core.TypeName)
    key = pointer_from_objref(obj)
    haskey(ss.seen, key) ? (return 0) : (ss.seen[key] = true)
    return Core.sizeof(obj) + (isdefined(obj, :mt) ? ss(obj.mt) : 0)
end

function (ss::SummarySize)(obj::Array)
    haskey(ss.seen, obj) ? (return 0) : (ss.seen[obj] = true)
    headersize = 4*sizeof(Int) + 8 + max(0, ndims(obj)-2)*sizeof(Int)
    size::Int = headersize
    datakey = unsafe_convert(Ptr{Cvoid}, obj)
    if !haskey(ss.seen, datakey)
        ss.seen[datakey] = true
        dsize = Core.sizeof(obj)
        T = eltype(obj)
        if isbitsunion(T)
            # add 1 union selector byte for each element
            dsize += length(obj)
        end
        size += dsize
        if !isempty(obj) && T !== Symbol && (!Base.allocatedinline(T) || (T isa DataType && !Base.datatype_pointerfree(T)))
            push!(ss.frontier_x, obj)
            push!(ss.frontier_i, 1)
        end
    end
    return size
end

function (ss::SummarySize)(obj::SimpleVector)
    key = pointer_from_objref(obj)
    haskey(ss.seen, key) ? (return 0) : (ss.seen[key] = true)
    size::Int = Core.sizeof(obj)
    if !isempty(obj)
        push!(ss.frontier_x, obj)
        push!(ss.frontier_i, 1)
    end
    return size
end

function (ss::SummarySize)(obj::Module)
    haskey(ss.seen, obj) ? (return 0) : (ss.seen[obj] = true)
    size::Int = Core.sizeof(obj)
    for binding in names(obj, all = true)
        if isdefined(obj, binding) && !isdeprecated(obj, binding)
            value = getfield(obj, binding)
            if !isa(value, Module) || parentmodule(value) === obj
                size += ss(value)::Int
                if isa(value, UnionAll)
                    value = unwrap_unionall(value)
                end
                if isa(value, DataType) && parentmodule(value) === obj && nameof(value) === binding
                    # charge a TypeName to its module (but not to the type)
                    size += ss(value.name)::Int
                end
            end
        end
    end
    return size
end

function (ss::SummarySize)(obj::Task)
    haskey(ss.seen, obj) ? (return 0) : (ss.seen[obj] = true)
    size::Int = Core.sizeof(obj)
    if isdefined(obj, :code)
        size += ss(obj.code)::Int
    end
    size += ss(obj.storage)::Int
    size += ss(obj.donenotify)::Int
    size += ss(obj.result)::Int
    # TODO: add stack size, and possibly traverse stack roots
    return size
end

(ss::SummarySize)(obj::BigInt) = _summarysize(ss, obj) + obj.alloc*sizeof(Base.GMP.Limb)
P   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/errorshow.jl<�      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
    showerror(io, e)

Show a descriptive representation of an exception object `e`.
This method is used to display the exception after a call to [`throw`](@ref).

# Examples
```jldoctest
julia> struct MyException <: Exception
           msg::String
       end

julia> function Base.showerror(io::IO, err::MyException)
           print(io, "MyException: ")
           print(io, err.msg)
       end

julia> err = MyException("test exception")
MyException("test exception")

julia> sprint(showerror, err)
"MyException: test exception"

julia> throw(MyException("test exception"))
ERROR: MyException: test exception
```
"""
showerror(io::IO, ex) = show(io, ex)

show_index(io::IO, x::Any) = show(io, x)
show_index(io::IO, x::Slice) = show_index(io, x.indices)
show_index(io::IO, x::LogicalIndex) = summary(io, x.mask)
show_index(io::IO, x::OneTo) = print(io, "1:", x.stop)
show_index(io::IO, x::Colon) = print(io, ':')

function showerror(io::IO, ex::Meta.ParseError)
    if isnothing(ex.detail)
        print(io, "ParseError(", repr(ex.msg), ")")
    else
        showerror(io, ex.detail)
    end
end

function showerror(io::IO, ex::BoundsError)
    print(io, "BoundsError")
    if isdefined(ex, :a)
        print(io, ": attempt to access ")
        summary(io, ex.a)
        if isdefined(ex, :i)
            print(io, " at index [")
            if ex.i isa AbstractRange
                print(io, ex.i)
            elseif ex.i isa AbstractString
                show(io, ex.i)
            else
                for (i, x) in enumerate(ex.i)
                    i > 1 && print(io, ", ")
                    show_index(io, x)
                end
            end
            print(io, ']')
        end
    end
    Experimental.show_error_hints(io, ex)
end

function showerror(io::IO, ex::TypeError)
    print(io, "TypeError: ")
    if ex.expected === Bool
        print(io, "non-boolean (", typeof(ex.got), ") used in boolean context")
    else
        if isvarargtype(ex.got)
            targs = (ex.got,)
        elseif isa(ex.got, Type)
            targs = ("Type{", ex.got, "}")
        else
            targs = ("a value of type $(typeof(ex.got))",)
        end
        if ex.context == ""
            ctx = "in $(ex.func)"
        elseif ex.func === Symbol("keyword argument")
            ctx = "in keyword argument $(ex.context)"
        else
            ctx = "in $(ex.func), in $(ex.context)"
        end
        print(io, ctx, ", expected ", ex.expected, ", got ", targs...)
    end
    Experimental.show_error_hints(io, ex)
end

function showerror(io::IO, ex, bt; backtrace=true)
    try
        showerror(io, ex)
    finally
        backtrace && show_backtrace(io, bt)
    end
end

function showerror(io::IO, ex::LoadError, bt; backtrace=true)
    !isa(ex.error, LoadError) && print(io, "LoadError: ")
    showerror(io, ex.error, bt, backtrace=backtrace)
    print(io, "\nin expression starting at $(ex.file):$(ex.line)")
end
showerror(io::IO, ex::LoadError) = showerror(io, ex, [])

function showerror(io::IO, ex::InitError, bt; backtrace=true)
    print(io, "InitError: ")
    showerror(io, ex.error, bt, backtrace=backtrace)
    print(io, "\nduring initialization of module ", ex.mod)
end
showerror(io::IO, ex::InitError) = showerror(io, ex, [])

function showerror(io::IO, ex::DomainError)
    if isa(ex.val, AbstractArray)
        compact = get(io, :compact, true)::Bool
        limit = get(io, :limit, true)::Bool
        print(IOContext(io, :compact => compact, :limit => limit),
              "DomainError with ", ex.val)
    else
        print(io, "DomainError with ", ex.val)
    end
    if isdefined(ex, :msg)
        print(io, ":\n", ex.msg)
    end
    Experimental.show_error_hints(io, ex)
    nothing
end

function showerror(io::IO, ex::SystemError)
    if @static(Sys.iswindows() ? ex.extrainfo isa WindowsErrorInfo : false)
        errstring = Libc.FormatMessage(ex.extrainfo.errnum)
        extrainfo = ex.extrainfo.extrainfo
    else
        errstring = Libc.strerror(ex.errnum)
        extrainfo = ex.extrainfo
    end
    if extrainfo === nothing
        print(io, "SystemError: $(ex.prefix): ", errstring)
    else
        print(io, "SystemError (with $extrainfo): $(ex.prefix): ", errstring)
    end
end

showerror(io::IO, ::DivideError) = print(io, "DivideError: integer division error")
showerror(io::IO, ::StackOverflowError) = print(io, "StackOverflowError:")
showerror(io::IO, ::UndefRefError) = print(io, "UndefRefError: access to undefined reference")
showerror(io::IO, ::EOFError) = print(io, "EOFError: read end of file")
function showerror(io::IO, ex::ErrorException)
    print(io, ex.msg)
    if ex.msg == "type String has no field data"
        println(io)
        print(io, "Use `codeunits(str)` instead.")
    end
end
showerror(io::IO, ex::KeyError) = (print(io, "KeyError: key ");
                                   show(io, ex.key);
                                   print(io, " not found"))
showerror(io::IO, ex::InterruptException) = print(io, "InterruptException:")
showerror(io::IO, ex::ArgumentError) = print(io, "ArgumentError: ", ex.msg)
showerror(io::IO, ex::DimensionMismatch) = print(io, "DimensionMismatch: ", ex.msg)
showerror(io::IO, ex::AssertionError) = print(io, "AssertionError: ", ex.msg)
showerror(io::IO, ex::OverflowError) = print(io, "OverflowError: ", ex.msg)

showerror(io::IO, ex::UndefKeywordError) =
    print(io, "UndefKeywordError: keyword argument `$(ex.var)` not assigned")

function showerror(io::IO, ex::UndefVarError)
    print(io, "UndefVarError: `$(ex.var)` not defined")
    Experimental.show_error_hints(io, ex)
end

function showerror(io::IO, ex::InexactError)
    print(io, "InexactError: ", ex.func, '(')
    nameof(ex.T) === ex.func || print(io, ex.T, ", ")
    print(io, ex.val, ')')
    Experimental.show_error_hints(io, ex)
end

function showerror(io::IO, ex::CanonicalIndexError)
    print(io, "CanonicalIndexError: ", ex.func, " not defined for ", ex.type)
end

typesof(@nospecialize args...) = Tuple{Any[ Core.Typeof(args[i]) for i in 1:length(args) ]...}

function print_with_compare(io::IO, @nospecialize(a::DataType), @nospecialize(b::DataType), color::Symbol)
    if a.name === b.name
        Base.show_type_name(io, a.name)
        n = length(a.parameters)
        n > 0 || return
        print(io, '{')
        for i = 1:n
            if i > length(b.parameters)
                printstyled(io, a.parameters[i], color=color)
            else
                print_with_compare(io::IO, a.parameters[i], b.parameters[i], color)
            end
            i < n && print(io, ',')
        end
        print(io, '}')
    else
        printstyled(io, a; color=color)
    end
end

function print_with_compare(io::IO, @nospecialize(a), @nospecialize(b), color::Symbol)
    if a === b
        print(io, a)
    else
        printstyled(io, a; color=color)
    end
end

function show_convert_error(io::IO, ex::MethodError, arg_types_param)
    # See #13033
    T = striptype(ex.args[1])
    if T === nothing
        print(io, "First argument to `convert` must be a Type, got ", ex.args[1])
    else
        p2 = arg_types_param[2]
        print_one_line = isa(T, DataType) && isa(p2, DataType) && T.name != p2.name
        printstyled(io, "Cannot `convert` an object of type ")
        print_one_line || printstyled(io, "\n  ")
        print_with_compare(io, p2, T, :light_green)
        printstyled(io, " to an object of type ")
        print_one_line || printstyled(io, "\n  ")
        print_with_compare(io, T, p2, :light_red)
    end
end

function showerror(io::IO, ex::MethodError)
    # ex.args is a tuple type if it was thrown from `invoke` and is
    # a tuple of the arguments otherwise.
    is_arg_types = isa(ex.args, DataType)
    arg_types = (is_arg_types ? ex.args : typesof(ex.args...))::DataType
    f = ex.f
    meth = methods_including_ambiguous(f, arg_types)
    if isa(meth, MethodList) && length(meth) > 1
        return showerror_ambiguous(io, meth, f, arg_types)
    end
    arg_types_param::SimpleVector = arg_types.parameters
    show_candidates = true
    print(io, "MethodError: ")
    ft = typeof(f)
    f_is_function = false
    kwargs = ()
    if f === Core.kwcall && !is_arg_types
        f = (ex.args::Tuple)[2]
        ft = typeof(f)
        arg_types_param = arg_types_param[3:end]
        kwargs = pairs(ex.args[1])
        ex = MethodError(f, ex.args[3:end::Int], ex.world)
    end
    name = ft.name.mt.name
    if f === Base.convert && length(arg_types_param) == 2 && !is_arg_types
        f_is_function = true
        show_convert_error(io, ex, arg_types_param)
    elseif f === mapreduce_empty || f === reduce_empty
        print(io, "reducing over an empty collection is not allowed; consider supplying `init` to the reducer")
        show_candidates = false
    elseif isempty(methods(f)) && isa(f, DataType) && isabstracttype(f)
        print(io, "no constructors have been defined for ", f)
    elseif isempty(methods(f)) && !isa(f, Function) && !isa(f, Type)
        print(io, "objects of type ", ft, " are not callable")
    else
        if ft <: Function && isempty(ft.parameters) && _isself(ft)
            f_is_function = true
        end
        print(io, "no method matching ")
        iob = IOContext(IOBuffer(), io)     # for type abbreviation as in #49795; some, like `convert(T, x)`, should not abbreviate
        show_signature_function(iob, isa(f, Type) ? Type{f} : typeof(f))
        print(iob, "(")
        for (i, typ) in enumerate(arg_types_param)
            print(iob, "::", typ)
            i == length(arg_types_param) || print(iob, ", ")
        end
        if !isempty(kwargs)
            print(iob, "; ")
            for (i, (k, v)) in enumerate(kwargs)
                print(iob, k, "::", typeof(v))
                i == length(kwargs)::Int || print(iob, ", ")
            end
        end
        print(iob, ")")
        str = String(take!(unwrapcontext(iob)[1]))
        str = type_limited_string_from_context(io, str)
        print(io, str)
    end
    # catch the two common cases of element-wise addition and subtraction
    if (f === Base.:+ || f === Base.:-) && length(arg_types_param) == 2
        # we need one array of numbers and one number, in any order
        if any(x -> x <: AbstractArray{<:Number}, arg_types_param) &&
            any(x -> x <: Number, arg_types_param)

            nounf = f === Base.:+ ? "addition" : "subtraction"
            varnames = ("scalar", "array")
            first, second = arg_types_param[1] <: Number ? varnames : reverse(varnames)
            fstring = f === Base.:+ ? "+" : "-"  # avoid depending on show_default for functions (invalidation)
            print(io, "\nFor element-wise $nounf, use broadcasting with dot syntax: $first .$fstring $second")
        end
    end
    if ft <: AbstractArray
        print(io, "\nUse square brackets [] for indexing an Array.")
    end
    # Check for local functions that shadow methods in Base
    if f_is_function && isdefined(Base, name)
        basef = getfield(Base, name)
        if basef !== ex.f && hasmethod(basef, arg_types)
            print(io, "\nYou may have intended to import ")
            show_unquoted(io, Expr(:., :Base, QuoteNode(name)))
        end
    end
    if (ex.world != typemax(UInt) && hasmethod(ex.f, arg_types) &&
        !hasmethod(ex.f, arg_types, world = ex.world))
        curworld = get_world_counter()
        print(io, "\nThe applicable method may be too new: running in world age $(ex.world), while current world is $(curworld).")
    end
    if !is_arg_types
        # Check for row vectors used where a column vector is intended.
        vec_args = []
        hasrows = false
        for arg in ex.args
            isrow = isa(arg,Array) && ndims(arg)::Int==2 && size(arg,1)::Int==1
            hasrows |= isrow
            push!(vec_args, isrow ? vec(arg) : arg)
        end
        if hasrows && applicable(f, vec_args...) && isempty(kwargs)
            print(io, "\n\nYou might have used a 2d row vector where a 1d column vector was required.",
                      "\nNote the difference between 1d column vector [1,2,3] and 2d row vector [1 2 3].",
                      "\nYou can convert to a column vector with the vec() function.")
        end
    end
    Experimental.show_error_hints(io, ex, arg_types_param, kwargs)
    show_candidates && try
        show_method_candidates(io, ex, kwargs)
    catch ex
        @error "Error showing method candidates, aborted" exception=ex,catch_backtrace()
    end
end

striptype(::Type{T}) where {T} = T
striptype(::Any) = nothing

function showerror_ambiguous(io::IO, meths, f, args)
    print(io, "MethodError: ")
    show_signature_function(io, isa(f, Type) ? Type{f} : typeof(f))
    print(io, "(")
    p = args.parameters
    for (i,a) in enumerate(p)
        print(io, "::", a)
        i < length(p) && print(io, ", ")
    end
    println(io, ") is ambiguous.\n\nCandidates:")
    sigfix = Any
    for m in meths
        print(io, "  ")
        show_method(io, m; digit_align_width=0)
        println(io)
        sigfix = typeintersect(m.sig, sigfix)
    end
    if isa(unwrap_unionall(sigfix), DataType) && sigfix <: Tuple
        let sigfix=sigfix
            if all(m->morespecific(sigfix, m.sig), meths)
                print(io, "\nPossible fix, define\n  ")
                Base.show_tuple_as_call(io, :function,  sigfix)
            else
                print(io, "To resolve the ambiguity, try making one of the methods more specific, or ")
                print(io, "adding a new method more specific than any of the existing applicable methods.")
            end
        end
        println(io)
    end
    nothing
end

#Show an error by directly calling jl_printf.
#Useful in Base submodule __init__ functions where stderr isn't defined yet.
function showerror_nostdio(err, msg::AbstractString)
    stderr_stream = ccall(:jl_stderr_stream, Ptr{Cvoid}, ())
    ccall(:jl_printf, Cint, (Ptr{Cvoid},Cstring), stderr_stream, msg)
    ccall(:jl_printf, Cint, (Ptr{Cvoid},Cstring), stderr_stream, ":\n")
    ccall(:jl_static_show, Csize_t, (Ptr{Cvoid},Any), stderr_stream, err)
    ccall(:jl_printf, Cint, (Ptr{Cvoid},Cstring), stderr_stream, "\n")
end

stacktrace_expand_basepaths()::Bool = Base.get_bool_env("JULIA_STACKTRACE_EXPAND_BASEPATHS", false) === true
stacktrace_contract_userdir()::Bool = Base.get_bool_env("JULIA_STACKTRACE_CONTRACT_HOMEDIR", true) === true
stacktrace_linebreaks()::Bool = Base.get_bool_env("JULIA_STACKTRACE_LINEBREAKS", false) === true

function show_method_candidates(io::IO, ex::MethodError, @nospecialize kwargs=())
    is_arg_types = isa(ex.args, DataType)
    arg_types = is_arg_types ? ex.args : typesof(ex.args...)
    arg_types_param = Any[arg_types.parameters...]
    # Displays the closest candidates of the given function by looping over the
    # functions methods and counting the number of matching arguments.
    f = ex.f
    ft = typeof(f)
    lines = []
    # These functions are special cased to only show if first argument is matched.
    special = f === convert || f === getindex || f === setindex!
    funcs = Tuple{Any,Vector{Any}}[(f, arg_types_param)]

    # An incorrect call method produces a MethodError for convert.
    # It also happens that users type convert when they mean call. So
    # pool MethodErrors for these two functions.
    if f === convert && !isempty(arg_types_param)
        at1 = arg_types_param[1]
        if isType(at1) && !Core.Compiler.has_free_typevars(at1)
            push!(funcs, (at1.parameters[1], arg_types_param[2:end]))
        end
    end

    for (func, arg_types_param) in funcs
        for method in methods(func)
            buf = IOBuffer()
            iob0 = iob = IOContext(buf, io)
            tv = Any[]
            if func isa Core.OpaqueClosure
                sig0 = signature_type(func, typeof(func).parameters[1])
            else
                sig0 = method.sig
            end
            while isa(sig0, UnionAll)
                push!(tv, sig0.var)
                iob = IOContext(iob, :unionall_env => sig0.var)
                sig0 = sig0.body
            end
            sig0 = sig0::DataType
            s1 = sig0.parameters[1]
            if sig0 === Tuple || !isa(func, rewrap_unionall(s1, method.sig))
                # function itself doesn't match or is a builtin
                continue
            else
                print(iob, "  ")
                show_signature_function(iob, s1)
            end
            print(iob, "(")
            t_i = copy(arg_types_param)
            right_matches = 0
            sig = sig0.parameters[2:end]
            for i = 1 : min(length(t_i), length(sig))
                i > 1 && print(iob, ", ")
                # If isvarargtype then it checks whether the rest of the input arguments matches
                # the varargtype
                if Base.isvarargtype(sig[i])
                    sigstr = (unwrapva(unwrap_unionall(sig[i])), "...")
                    j = length(t_i)
                else
                    sigstr = (sig[i],)
                    j = i
                end
                # Checks if the type of arg 1:i of the input intersects with the current method
                t_in = typeintersect(rewrap_unionall(Tuple{sig[1:i]...}, method.sig),
                                     rewrap_unionall(Tuple{t_i[1:j]...}, method.sig))
                # If the function is one of the special cased then it should break the loop if
                # the type of the first argument is not matched.
                t_in === Union{} && special && i == 1 && break
                if t_in === Union{}
                    if get(io, :color, false)::Bool
                        let sigstr=sigstr
                            Base.with_output_color(Base.error_color(), iob) do iob
                                print(iob, "::", sigstr...)
                            end
                        end
                    else
                        print(iob, "!Matched::", sigstr...)
                    end
                    # If there is no typeintersect then the type signature from the method is
                    # inserted in t_i this ensures if the type at the next i matches the type
                    # signature then there will be a type intersect
                    t_i[i] = sig[i]
                else
                    right_matches += j==i ? 1 : 0
                    print(iob, "::", sigstr...)
                end
            end
            special && right_matches == 0 && continue

            if length(t_i) > length(sig) && !isempty(sig) && Base.isvarargtype(sig[end])
                # It ensures that methods like f(a::AbstractString...) gets the correct
                # number of right_matches
                for t in arg_types_param[length(sig):end]
                    if t <: rewrap_unionall(unwrapva(unwrap_unionall(sig[end])), method.sig)
                        right_matches += 1
                    end
                end
            end

            if right_matches > 0 || length(arg_types_param) < 2
                if length(t_i) < length(sig)
                    # If the methods args is longer than input then the method
                    # arguments is printed as not a match
                    for (k, sigtype) in enumerate(sig[length(t_i)+1:end])
                        sigtype = isvarargtype(sigtype) ? unwrap_unionall(sigtype) : sigtype
                        if Base.isvarargtype(sigtype)
                            sigstr = (unwrapva(sigtype::Core.TypeofVararg), "...")
                        else
                            sigstr = (sigtype,)
                        end
                        if !((min(length(t_i), length(sig)) == 0) && k==1)
                            print(iob, ", ")
                        end
                        if k == 1 && Base.isvarargtype(sigtype)
                            # There wasn't actually a mismatch - the method match failed for
                            # some other reason, e.g. world age. Just print the sigstr.
                            print(iob, sigstr...)
                        elseif get(io, :color, false)::Bool
                            let sigstr=sigstr
                                Base.with_output_color(Base.error_color(), iob) do iob
                                    print(iob, "::", sigstr...)
                                end
                            end
                        else
                            print(iob, "!Matched::", sigstr...)
                        end
                    end
                end
                kwords = kwarg_decl(method)
                if !isempty(kwords)
                    print(iob, "; ")
                    join(iob, kwords, ", ")
                end
                print(iob, ")")
                show_method_params(iob0, tv)
                file, line = updated_methodloc(method)
                if file === nothing
                    file = string(method.file)
                end
                stacktrace_contract_userdir() && (file = contractuser(file))

                if !isempty(kwargs)::Bool
                    unexpected = Symbol[]
                    if isempty(kwords) || !(any(endswith(string(kword), "...") for kword in kwords))
                        for (k, v) in kwargs
                            if !(k::Symbol in kwords)
                                push!(unexpected, k::Symbol)
                            end
                        end
                    end
                    if !isempty(unexpected)
                        Base.with_output_color(Base.error_color(), iob) do iob
                            plur = length(unexpected) > 1 ? "s" : ""
                            print(iob, " got unsupported keyword argument$plur \"", join(unexpected, "\", \""), "\"")
                        end
                    end
                end
                if ex.world < reinterpret(UInt, method.primary_world)
                    print(iob, " (method too new to be called from this world context.)")
                elseif ex.world > reinterpret(UInt, method.deleted_world)
                    print(iob, " (method deleted before this world age.)")
                end
                println(iob)

                m = parentmodule_before_main(method)
                modulecolor = get!(() -> popfirst!(STACKTRACE_MODULECOLORS), STACKTRACE_FIXEDCOLORS, m)
                print_module_path_file(iob, m, string(file), line; modulecolor, digit_align_width = 3)

                # TODO: indicate if it's in the wrong world
                push!(lines, (buf, right_matches))
            end
        end
    end

    if !isempty(lines) # Display up to three closest candidates
        Base.with_output_color(:normal, io) do io
            print(io, "\n\nClosest candidates are:")
            sort!(lines, by = x -> -x[2])
            i = 0
            for line in lines
                println(io)
                if i >= 3
                    print(io, "  ...")
                    break
                end
                i += 1
                print(io, String(take!(line[1])))
            end
            println(io) # extra newline for spacing to stacktrace
        end
    end
end

# In case the line numbers in the source code have changed since the code was compiled,
# allow packages to set a callback function that corrects them.
# (Used by Revise and perhaps other packages.)
#
# Set this with
#     Base.update_stackframes_callback[] = my_updater!
# where my_updater! takes a single argument and works in-place. The argument will be a
# Vector{Any} storing tuples (sf::StackFrame, nrepetitions::Int), and the updater should
# replace `sf` as needed.
const update_stackframes_callback = Ref{Function}(identity)

const STACKTRACE_MODULECOLORS = Iterators.Stateful(Iterators.cycle([:magenta, :cyan, :green, :yellow]))
const STACKTRACE_FIXEDCOLORS = IdDict(Base => :light_black, Core => :light_black)

function show_full_backtrace(io::IO, trace::Vector; print_linebreaks::Bool)
    num_frames = length(trace)
    ndigits_max = ndigits(num_frames)

    println(io, "\nStacktrace:")

    for (i, (frame, n)) in enumerate(trace)
        print_stackframe(io, i, frame, n, ndigits_max, STACKTRACE_FIXEDCOLORS, STACKTRACE_MODULECOLORS)
        if i < num_frames
            println(io)
            print_linebreaks && println(io)
        end
    end
end

const BIG_STACKTRACE_SIZE = 50 # Arbitrary constant chosen here

function show_reduced_backtrace(io::IO, t::Vector)
    recorded_positions = IdDict{UInt, Vector{Int}}()
    #= For each frame of hash h, recorded_positions[h] is the list of indices i
    such that hash(t[i-1]) == h, ie the list of positions in which the
    frame appears just before. =#

    displayed_stackframes = []
    repeated_cycle = Tuple{Int,Int,Int}[]
    # First:  line to introuce the "cycle repetition" message
    # Second: length of the cycle
    # Third:  number of repetitions
    frame_counter = 1
    while frame_counter < length(t)
        (last_frame, n) = t[frame_counter]
        frame_counter += 1 # Indicating the next frame

        current_hash = hash(last_frame)
        positions = get(recorded_positions, current_hash, Int[])
        recorded_positions[current_hash] = push!(positions, frame_counter)

        repetitions = 0
        for index_p in length(positions)-1:-1:1 # More recent is more likely
            p = positions[index_p]
            cycle_length = frame_counter - p
            i = frame_counter
            j = p
            while i < length(t) && t[i] == t[j]
                i += 1
                j += 1
            end
            if j >= frame_counter-1
                #= At least one cycle repeated =#
                repetitions = div(i - frame_counter + 1, cycle_length)
                push!(repeated_cycle, (length(displayed_stackframes), cycle_length, repetitions))
                frame_counter += cycle_length * repetitions - 1
                break
            end
        end

        if repetitions==0
            push!(displayed_stackframes, (last_frame, n))
        end
    end

    try invokelatest(update_stackframes_callback[], displayed_stackframes) catch end

    println(io, "\nStacktrace:")

    ndigits_max = ndigits(length(t))

    push!(repeated_cycle, (0,0,0)) # repeated_cycle is never empty
    frame_counter = 1
    for i in 1:length(displayed_stackframes)
        (frame, n) = displayed_stackframes[i]

        print_stackframe(io, frame_counter, frame, n, ndigits_max, STACKTRACE_FIXEDCOLORS, STACKTRACE_MODULECOLORS)

        if i < length(displayed_stackframes)
            println(io)
            stacktrace_linebreaks() && println(io)
        end

        while repeated_cycle[1][1] == i # never empty because of the initial (0,0,0)
            cycle_length = repeated_cycle[1][2]
            repetitions = repeated_cycle[1][3]
            popfirst!(repeated_cycle)
            printstyled(io,
                "--- the last ", cycle_length, " lines are repeated ",
                  repetitions, " more time", repetitions>1 ? "s" : "", " ---", color = :light_black)
            if i < length(displayed_stackframes)
                println(io)
                stacktrace_linebreaks() && println(io)
            end
            frame_counter += cycle_length * repetitions
        end
        frame_counter += 1
    end
end


# Print a stack frame where the module color is determined by looking up the parent module in
# `modulecolordict`. If the module does not have a color, yet, a new one can be drawn
# from `modulecolorcycler`.
function print_stackframe(io, i, frame::StackFrame, n::Int, ndigits_max, modulecolordict, modulecolorcycler)
    m = Base.parentmodule(frame)
    modulecolor = if m !== nothing
        m = parentmodule_before_main(m)
        get!(() -> popfirst!(modulecolorcycler), modulecolordict, m)
    else
        :default
    end
    print_stackframe(io, i, frame, n, ndigits_max, modulecolor)
end

# Gets the topmost parent module that isn't Main
function parentmodule_before_main(m::Module)
    while parentmodule(m) !== m
        pm = parentmodule(m)
        pm == Main && break
        m = pm
    end
    m
end
parentmodule_before_main(x) = parentmodule_before_main(parentmodule(x))

# Print a stack frame where the module color is set manually with `modulecolor`.
function print_stackframe(io, i, frame::StackFrame, n::Int, ndigits_max, modulecolor)
    file, line = string(frame.file), frame.line
    file = fixup_stdlib_path(file)
    stacktrace_expand_basepaths() && (file = something(find_source_file(file), file))
    stacktrace_contract_userdir() && (file = contractuser(file))

    # Used by the REPL to make it possible to open
    # the location of a stackframe/method in the editor.
    if haskey(io, :last_shown_line_infos)
        push!(io[:last_shown_line_infos], (string(frame.file), frame.line))
    end

    inlined = getfield(frame, :inlined)
    modul = parentmodule(frame)

    digit_align_width = ndigits_max + 2

    # frame number
    print(io, " ", lpad("[" * string(i) * "]", digit_align_width))
    print(io, " ")

    StackTraces.show_spec_linfo(IOContext(io, :backtrace=>true), frame)
    if n > 1
        printstyled(io, " (repeats $n times)"; color=:light_black)
    end
    println(io)

    # @ Module path / file : line
    print_module_path_file(io, modul, file, line; modulecolor, digit_align_width)

    # inlined
    printstyled(io, inlined ? " [inlined]" : "", color = :light_black)
end

function print_module_path_file(io, modul, file, line; modulecolor = :light_black, digit_align_width = 0)
    printstyled(io, " " ^ digit_align_width * "@", color = :light_black)

    # module
    if modul !== nothing && modulecolor !== nothing
        print(io, " ")
        printstyled(io, modul, color = modulecolor)
    end

    # filepath
    stacktrace_expand_basepaths() && (file = something(find_source_file(file), file))
    stacktrace_contract_userdir() && (file = contractuser(file))
    print(io, " ")
    dir = dirname(file)
    !isempty(dir) && printstyled(io, dir, Filesystem.path_separator, color = :light_black)

    # filename, separator, line
    printstyled(io, basename(file), ":", line; color = :light_black, underline = true)
end

function show_backtrace(io::IO, t::Vector)
    if haskey(io, :last_shown_line_infos)
        empty!(io[:last_shown_line_infos])
    end

    # t is a pre-processed backtrace (ref #12856)
    if t isa Vector{Any}
        filtered = t
    else
        filtered = process_backtrace(t)
    end
    isempty(filtered) && return

    if length(filtered) == 1 && StackTraces.is_top_level_frame(filtered[1][1])
        f = filtered[1][1]::StackFrame
        if f.line == 0 && f.file === Symbol("")
            # don't show a single top-level frame with no location info
            return
        end
    end

    if length(filtered) > BIG_STACKTRACE_SIZE
        show_reduced_backtrace(IOContext(io, :backtrace => true), filtered)
        return
    else
        try invokelatest(update_stackframes_callback[], filtered) catch end
        # process_backtrace returns a Vector{Tuple{Frame, Int}}
        show_full_backtrace(io, filtered; print_linebreaks = stacktrace_linebreaks())
    end
    nothing
end


# For improved user experience, filter out frames for include() implementation
# - see #33065. See also #35371 for extended discussion of internal frames.
function _simplify_include_frames(trace)
    kept_frames = trues(length(trace))
    first_ignored = nothing
    for i in length(trace):-1:1
        frame::StackFrame, _ = trace[i]
        mod = parentmodule(frame)
        if first_ignored === nothing
            if mod === Base && frame.func === :_include
                # Hide include() machinery by default
                first_ignored = i
            end
        else
            first_ignored = first_ignored::Int
            # Hack: allow `mod==nothing` as a workaround for inlined functions.
            # TODO: Fix this by improving debug info.
            if mod in (Base,Core,nothing) && 1+first_ignored-i <= 5
                if frame.func === :eval
                    kept_frames[i:first_ignored] .= false
                    first_ignored = nothing
                end
            else
                # Bail out to avoid hiding frames in unexpected circumstances
                first_ignored = nothing
            end
        end
    end
    if first_ignored !== nothing
        kept_frames[1:first_ignored] .= false
    end
    return trace[kept_frames]
end

# Collapse frames that have the same location (in some cases)
function _collapse_repeated_frames(trace)
    kept_frames = trues(length(trace))
    last_frame = nothing
    for i in 1:length(trace)
        frame::StackFrame, _ = trace[i]
        if last_frame !== nothing && frame.file == last_frame.file && frame.line == last_frame.line
            #=
            Handles this case:

            f(g, a; kw...) = error();
            @inline f(a; kw...) = f(identity, a; kw...);
            f(1)

            which otherwise ends up as:

            [4] #f#4 <-- useless
            @ ./REPL[2]:1 [inlined]
            [5] f(a::Int64)
            @ Main ./REPL[2]:1
            =#
            if startswith(sprint(show, last_frame), "#")
                kept_frames[i-1] = false
            end

            #= Handles this case
            g(x, y=1, z=2) = error();
            g(1)

            which otherwise ends up as:

            [2] g(x::Int64, y::Int64, z::Int64)
            @ Main ./REPL[1]:1
            [3] g(x::Int64) <-- useless
            @ Main ./REPL[1]:1
            =#
            if frame.linfo isa MethodInstance && last_frame.linfo isa MethodInstance &&
                frame.linfo.def isa Method && last_frame.linfo.def isa Method
                m, last_m = frame.linfo.def::Method, last_frame.linfo.def::Method
                params, last_params = Base.unwrap_unionall(m.sig).parameters, Base.unwrap_unionall(last_m.sig).parameters
                if last_m.nkw != 0
                    pos_sig_params = last_params[(last_m.nkw+2):end]
                    issame = true
                    if pos_sig_params == params
                        kept_frames[i] = false
                    end
                end
                if length(last_params) > length(params)
                    issame = true
                    for i = 1:length(params)
                        issame &= params[i] == last_params[i]
                    end
                    if issame
                        kept_frames[i] = false
                    end
                end
            end

            # TODO: Detect more cases that can be collapsed
        end
        last_frame = frame
    end
    return trace[kept_frames]
end


function process_backtrace(t::Vector, limit::Int=typemax(Int); skipC = true)
    n = 0
    last_frame = StackTraces.UNKNOWN
    count = 0
    ret = Any[]
    for i in eachindex(t)
        lkups = t[i]
        if lkups isa StackFrame
            lkups = [lkups]
        else
            lkups = StackTraces.lookup(lkups)
        end
        for lkup in lkups
            if lkup === StackTraces.UNKNOWN
                continue
            end

            if (lkup.from_c && skipC)
                continue
            end
            code = lkup.linfo
            if code isa MethodInstance
                def = code.def
                if def isa Method && def.name !== :kwcall && def.sig <: Tuple{typeof(Core.kwcall),NamedTuple,Any,Vararg}
                    # hide kwcall() methods, which are probably internal keyword sorter methods
                    # (we print the internal method instead, after demangling
                    # the argument list, since it has the right line number info)
                    continue
                end
            elseif !lkup.from_c
                lkup.func === :kwcall && continue
            end
            count += 1
            if count > limit
                break
            end

            if lkup.file != last_frame.file || lkup.line != last_frame.line || lkup.func != last_frame.func || lkup.linfo !== last_frame.linfo
                if n > 0
                    push!(ret, (last_frame, n))
                end
                n = 1
                last_frame = lkup
            else
                n += 1
            end
        end
        count > limit && break
    end
    if n > 0
        push!(ret, (last_frame, n))
    end
    trace = _simplify_include_frames(ret)
    trace = _collapse_repeated_frames(trace)
    return trace
end

function show_exception_stack(io::IO, stack)
    # Display exception stack with the top of the stack first.  This ordering
    # means that the user doesn't have to scroll up in the REPL to discover the
    # root cause.
    nexc = length(stack)
    for i = nexc:-1:1
        if nexc != i
            printstyled(io, "\ncaused by: ", color=error_color())
        end
        exc, bt = stack[i]
        showerror(io, exc, bt, backtrace = bt!==nothing)
        i == 1 || println(io)
    end
end

# Defined here rather than error.jl for bootstrap ordering
function show(io::IO, ip::InterpreterIP)
    print(io, typeof(ip))
    if ip.code isa Core.CodeInfo
        print(io, " in top-level CodeInfo for $(ip.mod) at statement $(Int(ip.stmt))")
    else
        print(io, " in $(ip.code) at statement $(Int(ip.stmt))")
    end
end

# handler for displaying a hint in case the user tries to call
# the instance of a number (probably missing the operator)
# eg: (1 + 2)(3 + 4)
function noncallable_number_hint_handler(io, ex, arg_types, kwargs)
    @nospecialize
    if ex.f isa Number
        print(io, "\nMaybe you forgot to use an operator such as ")
        printstyled(io, "*, ^, %, / etc. ", color=:cyan)
        print(io, "?")
    end
end

Experimental.register_error_hint(noncallable_number_hint_handler, MethodError)

# Display a hint in case the user tries to use the + operator on strings
# (probably attempting concatenation)
function string_concatenation_hint_handler(io, ex, arg_types, kwargs)
    @nospecialize
    if (ex.f === +) && all(i -> i <: AbstractString, arg_types)
        print(io, "\nString concatenation is performed with ")
        printstyled(io, "*", color=:cyan)
        print(io, " (See also: https://docs.julialang.org/en/v1/manual/strings/#man-concatenation).")
    end
end

Experimental.register_error_hint(string_concatenation_hint_handler, MethodError)

# ExceptionStack implementation
size(s::ExceptionStack) = size(s.stack)
getindex(s::ExceptionStack, i::Int) = s.stack[i]

function show(io::IO, ::MIME"text/plain", stack::ExceptionStack)
    nexc = length(stack)
    printstyled(io, nexc, "-element ExceptionStack", nexc == 0 ? "" : ":\n")
    show_exception_stack(io, stack)
end
show(io::IO, stack::ExceptionStack) = show(io, MIME("text/plain"), stack)
O   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/initdefs.jl�C      # This file is a part of Julia. License is MIT: https://julialang.org/license

## initdefs.jl - initialization and runtime management definitions

"""
    PROGRAM_FILE

A string containing the script name passed to Julia from the command line. Note that the
script name remains unchanged from within included files. Alternatively see
[`@__FILE__`](@ref).
"""
global PROGRAM_FILE = ""

"""
    ARGS

An array of the command line arguments passed to Julia, as strings.
"""
const ARGS = String[]

"""
    exit(code=0)

Stop the program with an exit code. The default exit code is zero, indicating that the
program completed successfully. In an interactive session, `exit()` can be called with
the keyboard shortcut `^D`.
"""
exit(n) = ccall(:jl_exit, Cvoid, (Int32,), n)
exit() = exit(0)

const roottask = current_task()

is_interactive = false

"""
    isinteractive() -> Bool

Determine whether Julia is running an interactive session.
"""
isinteractive() = (is_interactive::Bool)

## package depots (registries, packages, environments) ##

"""
    DEPOT_PATH

A stack of "depot" locations where the package manager, as well as Julia's code
loading mechanisms, look for package registries, installed packages, named
environments, repo clones, cached compiled package images, and configuration
files. By default it includes:

1. `~/.julia` where `~` is the user home as appropriate on the system;
2. an architecture-specific shared system directory, e.g. `/usr/local/share/julia`;
3. an architecture-independent shared system directory, e.g. `/usr/share/julia`.

So `DEPOT_PATH` might be:
```julia
[joinpath(homedir(), ".julia"), "/usr/local/share/julia", "/usr/share/julia"]
```
The first entry is the "user depot" and should be writable by and owned by the
current user. The user depot is where: registries are cloned, new package versions
are installed, named environments are created and updated, package repos are cloned,
newly compiled package image files are saved, log files are written, development
packages are checked out by default, and global configuration data is saved. Later
entries in the depot path are treated as read-only and are appropriate for
registries, packages, etc. installed and managed by system administrators.

`DEPOT_PATH` is populated based on the [`JULIA_DEPOT_PATH`](@ref JULIA_DEPOT_PATH)
environment variable if set.

## DEPOT_PATH contents

Each entry in `DEPOT_PATH` is a path to a directory which contains subdirectories used by Julia for various purposes.
Here is an overview of some of the subdirectories that may exist in a depot:

* `artifacts`: Contains content that packages use for which Pkg manages the installation of.
* `clones`: Contains full clones of package repos. Maintained by `Pkg.jl` and used as a cache.
* `config`: Contains julia-level configuration such as a `startup.jl`
* `compiled`: Contains precompiled `*.ji` files for packages. Maintained by Julia.
* `dev`: Default directory for `Pkg.develop`. Maintained by `Pkg.jl` and the user.
* `environments`: Default package environments. For instance the global environment for a specific julia version. Maintained by `Pkg.jl`.
* `logs`: Contains logs of `Pkg` and `REPL` operations. Maintained by `Pkg.jl` and `Julia`.
* `packages`: Contains packages, some of which were explicitly installed and some which are implicit dependencies. Maintained by `Pkg.jl`.
* `registries`: Contains package registries. By default only `General`. Maintained by `Pkg.jl`.
* `scratchspaces`: Contains content that a package itself installs via the [`Scratch.jl`](https://github.com/JuliaPackaging/Scratch.jl) package. `Pkg.gc()` will delete content that is known to be unused.

!!! note
    Packages that want to store content should use the `scratchspaces` subdirectory via
    [`Scratch.jl`](https://github.com/JuliaPackaging/Scratch.jl) instead of creating new
    subdirectories in the depot root.

See also [`JULIA_DEPOT_PATH`](@ref JULIA_DEPOT_PATH), and
[Code Loading](@ref code-loading).
"""
const DEPOT_PATH = String[]

function append_default_depot_path!(DEPOT_PATH)
    path = joinpath(homedir(), ".julia")
    path in DEPOT_PATH || push!(DEPOT_PATH, path)
    path = abspath(Sys.BINDIR, "..", "local", "share", "julia")
    path in DEPOT_PATH || push!(DEPOT_PATH, path)
    path = abspath(Sys.BINDIR, "..", "share", "julia")
    path in DEPOT_PATH || push!(DEPOT_PATH, path)
    return DEPOT_PATH
end

function init_depot_path()
    empty!(DEPOT_PATH)
    if haskey(ENV, "JULIA_DEPOT_PATH")
        str = ENV["JULIA_DEPOT_PATH"]
        isempty(str) && return
        for path in eachsplit(str, Sys.iswindows() ? ';' : ':')
            if isempty(path)
                append_default_depot_path!(DEPOT_PATH)
            else
                path = expanduser(path)
                path in DEPOT_PATH || push!(DEPOT_PATH, path)
            end
        end
    else
        append_default_depot_path!(DEPOT_PATH)
    end
    nothing
end

## LOAD_PATH & ACTIVE_PROJECT ##

# JULIA_LOAD_PATH: split on `:` (or `;` on Windows)
# first empty entry is replaced with DEFAULT_LOAD_PATH, the rest are skipped
# entries starting with `@` are named environments:
#  - the first three `#`s in a named environment are replaced with version numbers
#  - `@stdlib` is a special name for the standard library and expands to its path

# if you want a current env setup, use direnv and
# have your .envrc do something like this:
#
#   export JULIA_LOAD_PATH="$(pwd):$JULIA_LOAD_PATH"
#
# this will inherit an existing JULIA_LOAD_PATH value or if there is none, leave
# a trailing empty entry in JULIA_LOAD_PATH which will be replaced with defaults.

const DEFAULT_LOAD_PATH = ["@", "@v#.#", "@stdlib"]

"""
    LOAD_PATH

An array of paths for `using` and `import` statements to consider as project
environments or package directories when loading code. It is populated based on
the [`JULIA_LOAD_PATH`](@ref JULIA_LOAD_PATH) environment variable if set;
otherwise it defaults to `["@", "@v#.#", "@stdlib"]`. Entries starting with `@`
have special meanings:

- `@` refers to the "current active environment", the initial value of which is
  initially determined by the [`JULIA_PROJECT`](@ref JULIA_PROJECT) environment
  variable or the `--project` command-line option.

- `@stdlib` expands to the absolute path of the current Julia installation's
  standard library directory.

- `@name` refers to a named environment, which are stored in depots (see
  [`JULIA_DEPOT_PATH`](@ref JULIA_DEPOT_PATH)) under the `environments`
  subdirectory. The user's named environments are stored in
  `~/.julia/environments` so `@name` would refer to the environment in
  `~/.julia/environments/name` if it exists and contains a `Project.toml` file.
  If `name` contains `#` characters, then they are replaced with the major, minor
  and patch components of the Julia version number. For example, if you are
  running Julia 1.2 then `@v#.#` expands to `@v1.2` and will look for an
  environment by that name, typically at `~/.julia/environments/v1.2`.

The fully expanded value of `LOAD_PATH` that is searched for projects and packages
can be seen by calling the `Base.load_path()` function.

See also
[`JULIA_LOAD_PATH`](@ref JULIA_LOAD_PATH),
[`JULIA_PROJECT`](@ref JULIA_PROJECT),
[`JULIA_DEPOT_PATH`](@ref JULIA_DEPOT_PATH), and
[Code Loading](@ref code-loading).
"""
const LOAD_PATH = copy(DEFAULT_LOAD_PATH)
# HOME_PROJECT is no longer used, here just to avoid breaking things
const HOME_PROJECT = Ref{Union{String,Nothing}}(nothing)
const ACTIVE_PROJECT = Ref{Union{String,Nothing}}(nothing) # Modify this only via `Base.set_active_project(proj)`
## Watchers for when the active project changes (e.g., Revise)
# Each should be a thunk, i.e., `f()`. To determine the current active project,
# the thunk can query `Base.active_project()`.
const active_project_callbacks = []

function current_project(dir::AbstractString)
    # look for project file in current dir and parents
    home = homedir()
    while true
        for proj in project_names
            file = joinpath(dir, proj)
            isfile_casesensitive(file) && return file
        end
        # bail at home directory
        dir == home && break
        old, dir = dir, dirname(dir)
        dir == old && break
    end
end

function current_project()
    dir = try pwd()
    catch err
        err isa IOError || rethrow()
        return nothing
    end
    return current_project(dir)
end

function parse_load_path(str::String)
    envs = String[]
    isempty(str) && return envs
    for env in eachsplit(str, Sys.iswindows() ? ';' : ':')
        if isempty(env)
            for env′ in DEFAULT_LOAD_PATH
                env′ in envs || push!(envs, env′)
            end
        else
            if env == "@."
                env = current_project()
                env === nothing && continue
            end
            env = expanduser(env)
            env in envs || push!(envs, env)
        end
    end
    return envs
end

function init_load_path()
    if haskey(ENV, "JULIA_LOAD_PATH")
        paths = parse_load_path(ENV["JULIA_LOAD_PATH"])
    else
        paths = filter!(env -> env !== nothing,
            String[env == "@." ? current_project() : env for env in DEFAULT_LOAD_PATH])
    end
    append!(empty!(LOAD_PATH), paths)
end

function init_active_project()
    project = (JLOptions().project != C_NULL ?
        unsafe_string(Base.JLOptions().project) :
        get(ENV, "JULIA_PROJECT", nothing))
    set_active_project(
        project === nothing ? nothing :
        project == "" ? nothing :
        startswith(project, "@") ? load_path_expand(project) : abspath(expanduser(project))
    )
end

## load path expansion: turn LOAD_PATH entries into concrete paths ##

function load_path_expand(env::AbstractString)::Union{String, Nothing}
    # named environment?
    if startswith(env, '@')
        # `@` in JULIA_LOAD_PATH is expanded early (at startup time)
        # if you put a `@` in LOAD_PATH manually, it's expanded late
        env == "@" && return active_project(false)
        env == "@." && return current_project()
        env == "@stdlib" && return Sys.STDLIB
        env = replace(env, '#' => VERSION.major, count=1)
        env = replace(env, '#' => VERSION.minor, count=1)
        env = replace(env, '#' => VERSION.patch, count=1)
        name = env[2:end]
        # look for named env in each depot
        for depot in DEPOT_PATH
            path = joinpath(depot, "environments", name)
            isdir(path) || continue
            for proj in project_names
                file = abspath(path, proj)
                isfile_casesensitive(file) && return file
            end
        end
        isempty(DEPOT_PATH) && return nothing
        return abspath(DEPOT_PATH[1], "environments", name, project_names[end])
    end
    # otherwise, it's a path
    path = abspath(env)
    if isdir(path)
        # directory with a project file?
        for proj in project_names
            file = joinpath(path, proj)
            isfile_casesensitive(file) && return file
        end
    end
    # package dir or path to project file
    return path
end
load_path_expand(::Nothing) = nothing

"""
    active_project()

Return the path of the active `Project.toml` file. See also [`Base.set_active_project`](@ref).
"""
function active_project(search_load_path::Bool=true)
    for project in (ACTIVE_PROJECT[],)
        project == "@" && continue
        project = load_path_expand(project)
        project === nothing && continue
        # while this seems well-inferred, nevertheless without the type annotation below
        # there are backedges here from abspath(::AbstractString, ::String)
        project = project::String
        if !isfile_casesensitive(project) && basename(project) ∉ project_names
            project = abspath(project, "Project.toml")
        end
        return project
    end
    search_load_path || return
    for project in LOAD_PATH
        project == "@" && continue
        project = load_path_expand(project)
        project === nothing && continue
        isfile_casesensitive(project) && return project
        ispath(project) && continue
        basename(project) in project_names && return project
    end
end

"""
    set_active_project(projfile::Union{AbstractString,Nothing})

Set the active `Project.toml` file to `projfile`. See also [`Base.active_project`](@ref).

!!! compat "Julia 1.8"
    This function requires at least Julia 1.8.
"""
function set_active_project(projfile::Union{AbstractString,Nothing})
    ACTIVE_PROJECT[] = projfile
    for f in active_project_callbacks
        try
            Base.invokelatest(f)
        catch
            @error "active project callback $f failed" maxlog=1
        end
    end
end


"""
    load_path()

Return the fully expanded value of [`LOAD_PATH`](@ref) that is searched for projects and
packages.

!!! note
    `load_path` may return a reference to a cached value so it is not safe to modify the
    returned vector.
"""
function load_path()
    cache = LOADING_CACHE[]
    cache !== nothing && return cache.load_path
    paths = String[]
    for env in LOAD_PATH
        path = load_path_expand(env)
        path !== nothing && path ∉ paths && push!(paths, path)
    end
    return paths
end

## atexit: register exit hooks ##

const atexit_hooks = Callable[
    () -> Filesystem.temp_cleanup_purge(force=true)
]
const _atexit_hooks_lock = ReentrantLock()
global _atexit_hooks_finished::Bool = false

"""
    atexit(f)

Register a zero- or one-argument function `f()` to be called at process exit.
`atexit()` hooks are called in last in first out (LIFO) order and run before
object finalizers.

If `f` has a method defined for one integer argument, it will be called as
`f(n::Int32)`, where `n` is the current exit code, otherwise it will be called
as `f()`.

!!! compat "Julia 1.9"
    The one-argument form requires Julia 1.9

Exit hooks are allowed to call `exit(n)`, in which case Julia will exit with
exit code `n` (instead of the original exit code). If more than one exit hook
calls `exit(n)`, then Julia will exit with the exit code corresponding to the
last called exit hook that calls `exit(n)`. (Because exit hooks are called in
LIFO order, "last called" is equivalent to "first registered".)

Note: Once all exit hooks have been called, no more exit hooks can be registered,
and any call to `atexit(f)` after all hooks have completed will throw an exception.
This situation may occur if you are registering exit hooks from background Tasks that
may still be executing concurrently during shutdown.
"""
function atexit(f::Function)
    Base.@lock _atexit_hooks_lock begin
        _atexit_hooks_finished && error("cannot register new atexit hook; already exiting.")
        pushfirst!(atexit_hooks, f)
        return nothing
    end
end

function _atexit(exitcode::Cint)
    # Don't hold the lock around the iteration, just in case any other thread executing in
    # parallel tries to register a new atexit hook while this is running. We don't want to
    # block that thread from proceeding, and we can allow it to register its hook which we
    # will immediately run here.
    while true
        local f
        Base.@lock _atexit_hooks_lock begin
            # If this is the last iteration, atomically disable atexit hooks to prevent
            # someone from registering a hook that will never be run.
            # (We do this inside the loop, so that it is atomic: no one can have registered
            #  a hook that never gets run, and we run all the hooks we know about until
            #  the vector is empty.)
            if isempty(atexit_hooks)
                global _atexit_hooks_finished = true
                break
            end

            f = popfirst!(atexit_hooks)
        end
        try
            if hasmethod(f, (Cint,))
                f(exitcode)
            else
                f()
            end
        catch ex
            showerror(stderr, ex)
            Base.show_backtrace(stderr, catch_backtrace())
            println(stderr)
        end
    end
end

## postoutput: register post output hooks ##
## like atexit but runs after any requested output.
## any hooks saved in the sysimage are cleared in Base._start
const postoutput_hooks = Callable[]

postoutput(f::Function) = (pushfirst!(postoutput_hooks, f); nothing)

function _postoutput()
    while !isempty(postoutput_hooks)
        f = popfirst!(postoutput_hooks)
        try
            f()
        catch ex
            showerror(stderr, ex)
            Base.show_backtrace(stderr, catch_backtrace())
            println(stderr)
        end
    end
end

## hook for disabling threaded libraries ##

library_threading_enabled = true
const disable_library_threading_hooks = []

function at_disable_library_threading(f)
    push!(disable_library_threading_hooks, f)
    if !library_threading_enabled
        disable_library_threading()
    end
    return
end

function disable_library_threading()
    global library_threading_enabled = false
    while !isempty(disable_library_threading_hooks)
        f = pop!(disable_library_threading_hooks)
        try
            f()
        catch err
            @warn("a hook from a library to disable threading failed:",
                  exception = (err, catch_backtrace()))
        end
    end
    return
end
Q   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/threadcall.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

const max_ccall_threads = parse(Int, get(ENV, "UV_THREADPOOL_SIZE", "4"))
const thread_notifiers = Union{Base.Condition, Nothing}[nothing for i in 1:max_ccall_threads]
const threadcall_restrictor = Semaphore(max_ccall_threads)

"""
    @threadcall((cfunc, clib), rettype, (argtypes...), argvals...)

The `@threadcall` macro is called in the same way as [`ccall`](@ref) but does the work
in a different thread. This is useful when you want to call a blocking C
function without causing the current `julia` thread to become blocked. Concurrency
is limited by size of the libuv thread pool, which defaults to 4 threads but
can be increased by setting the `UV_THREADPOOL_SIZE` environment variable and
restarting the `julia` process.

Note that the called function should never call back into Julia.
"""
macro threadcall(f, rettype, argtypes, argvals...)
    # check for usage errors
    isa(argtypes,Expr) && argtypes.head === :tuple ||
        error("threadcall: argument types must be a tuple")
    length(argtypes.args) == length(argvals) ||
        error("threadcall: wrong number of arguments to C function")

    # hygiene escape arguments
    f = esc(f)
    rettype = esc(rettype)
    argtypes = map(esc, argtypes.args)
    argvals = map(esc, argvals)

    # construct non-allocating wrapper to call C function
    wrapper = :(function (fptr::Ptr{Cvoid}, args_ptr::Ptr{Cvoid}, retval_ptr::Ptr{Cvoid})
        p = args_ptr
        # the rest of the body is created below
    end)
    body = wrapper.args[2].args
    args = Symbol[]
    for (i, T) in enumerate(argtypes)
        arg = Symbol("arg", i)
        push!(body, :($arg = unsafe_load(convert(Ptr{$T}, p))))
        push!(body, :(p += Core.sizeof($T)))
        push!(args, arg)
    end
    push!(body, :(ret = ccall(fptr, $rettype, ($(argtypes...),), $(args...))))
    push!(body, :(unsafe_store!(convert(Ptr{$rettype}, retval_ptr), ret)))
    push!(body, :(return Int(Core.sizeof($rettype))))

    # return code to generate wrapper function and send work request thread queue
    wrapper = Expr(:var"hygienic-scope", wrapper, @__MODULE__, __source__)
    return :(let fun_ptr = @cfunction($wrapper, Int, (Ptr{Cvoid}, Ptr{Cvoid}, Ptr{Cvoid}))
        # use cglobal to look up the function on the calling thread
        do_threadcall(fun_ptr, cglobal($f), $rettype, Any[$(argtypes...)], Any[$(argvals...)])
    end)
end

function do_threadcall(fun_ptr::Ptr{Cvoid}, cfptr::Ptr{Cvoid}, rettype::Type, argtypes::Vector, argvals::Vector)
    # generate function pointer
    c_notify_fun = @cfunction(
        function notify_fun(idx)
            global thread_notifiers
            notify(thread_notifiers[idx])
            return
        end, Cvoid, (Cint,))

    # cconvert, root and unsafe_convert arguments
    roots = Any[]
    args_size = isempty(argtypes) ? 0 : sum(Core.sizeof, argtypes)
    args_arr = Vector{UInt8}(undef, args_size)
    ptr = pointer(args_arr)
    for (T, x) in zip(argtypes, argvals)
        isbitstype(T) || throw(ArgumentError("threadcall requires isbits argument types"))
        y = cconvert(T, x)
        push!(roots, y)
        unsafe_store!(convert(Ptr{T}, ptr), unsafe_convert(T, y)::T)
        ptr += Core.sizeof(T)
    end

    # create return buffer
    ret_arr = Vector{UInt8}(undef, Core.sizeof(rettype))

    # wait for a worker thread to be available
    acquire(threadcall_restrictor)
    idx = findfirst(isequal(nothing), thread_notifiers)::Int
    thread_notifiers[idx] = Base.Condition()

    GC.@preserve args_arr ret_arr roots begin
        # queue up the work to be done
        ccall(:jl_queue_work, Cvoid,
            (Ptr{Cvoid}, Ptr{Cvoid}, Ptr{UInt8}, Ptr{UInt8}, Ptr{Cvoid}, Cint),
            fun_ptr, cfptr, args_arr, ret_arr, c_notify_fun, idx)

        # wait for a result & return it
        wait(thread_notifiers[idx])
        thread_notifiers[idx] = nothing
        release(threadcall_restrictor)

        r = unsafe_load(convert(Ptr{rettype}, pointer(ret_arr)))
    end
    return r
end
K   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/uuid.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
Represents a Universally Unique Identifier (UUID).
Can be built from one `UInt128` (all byte values), two `UInt64`, or four `UInt32`.
Conversion from a string will check the UUID validity.
"""
struct UUID
    value::UInt128
end
UUID(u::UUID) = u
UUID(u::NTuple{2, UInt64}) = UUID((UInt128(u[1]) << 64) | UInt128(u[2]))
UUID(u::NTuple{4, UInt32}) = UUID((UInt128(u[1]) << 96) | (UInt128(u[2]) << 64) |
                                  (UInt128(u[3]) << 32) | UInt128(u[4]))

function convert(::Type{NTuple{2, UInt64}}, uuid::UUID)
    bytes = uuid.value
    hi = UInt64((bytes >> 64) & 0xffffffffffffffff)
    lo = UInt64(bytes & 0xffffffffffffffff)
    return (hi, lo)
end

function convert(::Type{NTuple{4, UInt32}}, uuid::UUID)
    bytes = uuid.value
    hh = UInt32((bytes >> 96) & 0xffffffff)
    hl = UInt32((bytes >> 64) & 0xffffffff)
    lh = UInt32((bytes >> 32) & 0xffffffff)
    ll = UInt32(bytes & 0xffffffff)
    return (hh, hl, lh, ll)
end

UInt128(u::UUID) = u.value

let
    uuid_hash_seed = UInt === UInt64 ? 0xd06fa04f86f11b53 : 0x96a1f36d
    Base.hash(uuid::UUID, h::UInt) = hash(uuid_hash_seed, hash(convert(NTuple{2, UInt64}, uuid), h))
end

let
@inline function uuid_kernel(s, i, u)
    _c = UInt32(@inbounds codeunit(s, i))
    d = __convert_digit(_c, UInt32(16))
    d >= 16 && return nothing
    u <<= 4
    return u | d
end

function Base.tryparse(::Type{UUID}, s::AbstractString)
    u = UInt128(0)
    ncodeunits(s) != 36 && return nothing
    for i in 1:8
        u = uuid_kernel(s, i, u)
        u === nothing && return nothing
    end
    @inbounds codeunit(s, 9) == UInt8('-') || return nothing
    for i in 10:13
        u = uuid_kernel(s, i, u)
        u === nothing && return nothing
    end
    @inbounds codeunit(s, 14) == UInt8('-') || return nothing
    for i in 15:18
        u = uuid_kernel(s, i, u)
        u === nothing && return nothing
    end
    @inbounds codeunit(s, 19) == UInt8('-') || return nothing
    for i in 20:23
        u = uuid_kernel(s, i, u)
        u === nothing && return nothing
    end
    @inbounds codeunit(s, 24) == UInt8('-') || return nothing
    for i in 25:36
        u = uuid_kernel(s, i, u)
        u === nothing && return nothing
    end
    return Base.UUID(u)
end
end

let
    @noinline throw_malformed_uuid(s) = throw(ArgumentError("Malformed UUID string: $(repr(s))"))
    function Base.parse(::Type{UUID}, s::AbstractString)
        uuid = tryparse(UUID, s)
        return uuid === nothing ? throw_malformed_uuid(s) : uuid
    end
end

UUID(s::AbstractString) = parse(UUID, s)

let groupings = [36:-1:25; 23:-1:20; 18:-1:15; 13:-1:10; 8:-1:1]
    global string
    function string(u::UUID)
        u = u.value
        a = Base.StringVector(36)
        for i in groupings
            @inbounds a[i] = hex_chars[1 + u & 0xf]
            u >>= 4
        end
        @inbounds a[24] = a[19] = a[14] = a[9] = '-'
        return String(a)
    end
end

print(io::IO, u::UUID) = print(io, string(u))
show(io::IO, u::UUID) = print(io, "UUID(\"", u, "\")")

isless(a::UUID, b::UUID) = isless(a.value, b.value)

# give UUID scalar behavior in broadcasting
Base.broadcastable(x::UUID) = Ref(x)
L   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/pkgid.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

struct PkgId
    uuid::Union{UUID,Nothing}
    name::String

    PkgId(u::UUID, name::AbstractString) = new(UInt128(u) == 0 ? nothing : u, name)
    PkgId(::Nothing, name::AbstractString) = new(nothing, name)
end
PkgId(name::AbstractString) = PkgId(nothing, name)

function PkgId(m::Module, name::String = String(nameof(moduleroot(m))))
    uuid = UUID(ccall(:jl_module_uuid, NTuple{2, UInt64}, (Any,), m))
    UInt128(uuid) == 0 ? PkgId(name) : PkgId(uuid, name)
end

==(a::PkgId, b::PkgId) = a.uuid == b.uuid && a.name == b.name

function hash(pkg::PkgId, h::UInt)
    h += 0xc9f248583a0ca36c % UInt
    h = hash(pkg.uuid, h)
    h = hash(pkg.name, h)
    return h
end

show(io::IO, pkg::PkgId) =
    print(io, pkg.name, " [", pkg.uuid === nothing ? "top-level" : pkg.uuid, "]")

function binpack(pkg::PkgId)
    io = IOBuffer()
    write(io, UInt8(0))
    uuid = pkg.uuid
    write(io, uuid === nothing ? UInt128(0) : UInt128(uuid))
    write(io, pkg.name)
    return String(take!(io))
end

function binunpack(s::String)
    io = IOBuffer(s)
    @assert read(io, UInt8) === 0x00
    uuid = read(io, UInt128)
    name = read(io, String)
    return PkgId(UUID(uuid), name)
end
R   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/toml_parser.jl �      # This file is a part of Julia. License is MIT: https://julialang.org/license

module TOML

using Base: IdSet

# In case we do not have the Dates stdlib available
# we parse DateTime into these internal structs,
# note that these do not do any argument checking
struct Date
    year::Int
    month::Int
    day::Int
end
struct Time
    hour::Int
    minute::Int
    second::Int
    ms::Int
end
struct DateTime
    date::Date
    time::Time
end
DateTime(y, m, d, h, mi, s, ms) =
    DateTime(Date(y,m,d), Time(h, mi, s, ms))

const EOF_CHAR = typemax(Char)

const TOMLDict  = Dict{String, Any}

##########
# Parser #
##########

mutable struct Parser
    str::String
    # 1 character look ahead
    current_char::Char
    pos::Int
    # prevpos equals the startbyte of the look ahead character
    # prevpos-1 is therefore the end byte of the character we last ate
    prevpos::Int

    # File info
    column::Int
    line::Int

    # The function `take_substring` takes the substring from `marker` up
    # to `prevpos-1`.
    marker::Int

    # The current table that `key = value` entries are inserted into
    active_table::TOMLDict

    # As we parse dotted keys we store each part of the key in this cache
    # A future improvement would be to also store the spans of the keys
    # so that in error messages we could also show the previous key
    # definition in case of duplicated keys
    dotted_keys::Vector{String}

    # Strings in TOML can have line continuations ('\' as the last character
    # on a line. We store the byte ranges for each of these "chunks" in here
    chunks::Vector{UnitRange{Int}}

    # We need to keep track of those tables / arrays that are defined
    # inline since we are not allowed to add keys to those
    inline_tables::IdSet{TOMLDict}
    static_arrays::IdSet{Any}

    # [a.b.c.d] doesn't "define" the table [a]
    # so keys can later be added to [a], therefore
    # we need to keep track of what tables are
    # actually defined
    defined_tables::IdSet{TOMLDict}

    # The table we will finally return to the user
    root::TOMLDict

    # Filled in in case we are parsing a file to improve error messages
    filepath::Union{String, Nothing}

    # Get's populated with the Dates stdlib if it exists
    Dates::Union{Module, Nothing}
end

const DATES_PKGID = Base.PkgId(Base.UUID("ade2ca70-3891-5945-98fb-dc099432e06a"), "Dates")

function Parser(str::String; filepath=nothing)
    root = TOMLDict()
    l = Parser(
            str,                  # str
            EOF_CHAR,             # current_char
            firstindex(str),      # pos
            0,                    # prevpos
            0,                    # column
            1,                    # line
            0,                    # marker
            root,                 # active_table
            String[],             # dotted_keys
            UnitRange{Int}[],     # chunks
            IdSet{TOMLDict}(),    # inline_tables
            IdSet{Any}(),         # static_arrays
            IdSet{TOMLDict}(),    # defined_tables
            root,
            filepath,
            isdefined(Base, :maybe_root_module) ? Base.maybe_root_module(DATES_PKGID) : nothing,
        )
    startup(l)
    return l
end
function startup(l::Parser)
    # Populate our one character look-ahead
    c = eat_char(l)
    # Skip BOM
    if c === '\ufeff'
        l.column -= 1
        eat_char(l)
    end
end

Parser() = Parser("")
Parser(io::IO) = Parser(read(io, String))

function reinit!(p::Parser, str::String; filepath::Union{Nothing, String}=nothing)
    p.str = str
    p.current_char = EOF_CHAR
    p.pos = firstindex(str)
    p.prevpos = 0
    p.column = 0
    p.line = 1
    p.marker = 0
    p.root = TOMLDict()
    p.active_table = p.root
    empty!(p.dotted_keys)
    empty!(p.chunks)
    empty!(p.inline_tables)
    empty!(p.static_arrays)
    empty!(p.defined_tables)
    p.filepath = filepath
    startup(p)
    return p
end

##########
# Errors #
##########

throw_internal_error(msg) = error("internal TOML parser error: $msg")

# Many functions return a ParserError. We want this to bubble up
# all the way and have this error be returned to the user
# if the parse is called with `raise=false`. This macro
# makes that easier
@eval macro $(:var"try")(expr)
    return quote
        v = $(esc(expr))
        v isa ParserError && return v
        v
    end
end

# TODO: Check all of these are used
@enum ErrorType begin

    # Toplevel #
    ############
    ErrRedefineTableArray
    ErrExpectedNewLineKeyValue
    ErrAddKeyToInlineTable
    ErrAddArrayToStaticArray
    ErrArrayTreatedAsDictionary
    ErrExpectedEndOfTable
    ErrExpectedEndArrayOfTable

    # Keys #
    ########
    ErrExpectedEqualAfterKey
    # Check, are these the same?
    ErrDuplicatedKey
    ErrKeyAlreadyHasValue
    ErrInvalidBareKeyCharacter
    ErrEmptyBareKey

    # Values #
    ##########
    ErrUnexpectedEofExpectedValue
    ErrUnexpectedStartOfValue
    ErrGenericValueError

    # Arrays
    ErrExpectedCommaBetweenItemsArray

    # Inline tables
    ErrExpectedCommaBetweenItemsInlineTable
    ErrTrailingCommaInlineTable
    ErrInlineTableRedefine

    # Numbers
    ErrUnderscoreNotSurroundedByDigits
    ErrLeadingZeroNotAllowedInteger
    ErrOverflowError
    ErrLeadingDot
    ErrNoTrailingDigitAfterDot
    ErrTrailingUnderscoreNumber
    ErrSignInNonBase10Number

    # DateTime
    ErrParsingDateTime
    ErrOffsetDateNotSupported

    # Strings
    ErrNewLineInString
    ErrUnexpectedEndString
    ErrInvalidEscapeCharacter
    ErrInvalidUnicodeScalar
end

const err_message = Dict(
    ErrTrailingCommaInlineTable             => "trailing comma not allowed in inline table",
    ErrExpectedCommaBetweenItemsArray       => "expected comma between items in array",
    ErrExpectedCommaBetweenItemsInlineTable => "expected comma between items in inline table",
    ErrExpectedEndArrayOfTable              => "expected array of table to end with ']]'",
    ErrInvalidBareKeyCharacter              => "invalid bare key character",
    ErrRedefineTableArray                   => "tried to redefine an existing table as an array",
    ErrDuplicatedKey                        => "key already defined",
    ErrKeyAlreadyHasValue                   => "key already has a value",
    ErrEmptyBareKey                         => "bare key cannot be empty",
    ErrExpectedNewLineKeyValue              => "expected newline after key value pair",
    ErrNewLineInString                      => "newline character in single quoted string",
    ErrUnexpectedEndString                  => "string literal ended unexpectedly",
    ErrExpectedEndOfTable                   => "expected end of table ']'",
    ErrAddKeyToInlineTable                  => "tried to add a new key to an inline table",
    ErrInlineTableRedefine                  => "inline table overwrote key from other table",
    ErrArrayTreatedAsDictionary             => "tried to add a key to an array",
    ErrAddArrayToStaticArray                => "tried to append to a statically defined array",
    ErrGenericValueError                    => "failed to parse value",
    ErrLeadingZeroNotAllowedInteger         => "leading zero in integer not allowed",
    ErrUnderscoreNotSurroundedByDigits      => "underscore is not surrounded by digits",
    ErrUnexpectedStartOfValue               => "unexpected start of value",
    ErrOffsetDateNotSupported               => "offset date-time is not supported",
    ErrParsingDateTime                      => "parsing date/time value failed",
    ErrTrailingUnderscoreNumber             => "trailing underscore in number",
    ErrLeadingDot                           => "floats require a leading zero",
    ErrExpectedEqualAfterKey                => "expected equal sign after key",
    ErrNoTrailingDigitAfterDot              => "expected digit after dot",
    ErrOverflowError                        => "overflowed when parsing integer",
    ErrInvalidUnicodeScalar                 => "invalid unicode scalar",
    ErrInvalidEscapeCharacter               => "invalid escape character",
    ErrUnexpectedEofExpectedValue           => "unexpected end of file, expected a value",
    ErrSignInNonBase10Number                => "number not in base 10 is not allowed to have a sign",
)

for err in instances(ErrorType)
    @assert haskey(err_message, err) "$err does not have an error message"
end

mutable struct ParserError <: Exception
    type::ErrorType

    # Arbitrary data to store at the
    # call site to be used when formatting
    # the error
    data

    # These are filled in before returning from parse function
    str       ::Union{String,   Nothing}
    filepath  ::Union{String,   Nothing}
    line      ::Union{Int,      Nothing}
    column    ::Union{Int,      Nothing}
    pos       ::Union{Int,      Nothing} # position of parser when
    table     ::Union{TOMLDict, Nothing} # result parsed until error
end
ParserError(type, data) = ParserError(type, data, nothing, nothing, nothing, nothing, nothing, nothing)
ParserError(type) = ParserError(type, nothing)
# Defining these below can be useful when debugging code that erroneously returns a
# ParserError because you get a stacktrace to where the ParserError was created
#ParserError(type) = error(type)
#ParserError(type, data) = error(type,data)

# Many functions return either a T or a ParserError
const Err{T} = Union{T, ParserError}

function format_error_message_for_err_type(error::ParserError)
    msg = err_message[error.type]
    if error.type == ErrInvalidBareKeyCharacter
        c_escaped = escape_string(string(error.data)::String)
        msg *= ": '$c_escaped'"
    end
    return msg
end

# This is used in error formatting, for example,
# point_to_line("aa\nfoobar\n\bb", 4, 6) would return the strings:
# str1 = "foobar"
# str2 = "^^^"
# used to show the interval where an error happened
# Right now, it is only called with a == b
function point_to_line(str::AbstractString, a::Int, b::Int, context)
    @assert b >= a
    a = thisind(str, a)
    b = thisind(str, b)
    pos = something(findprev('\n', str, prevind(str, a)), 0) + 1
    io1 = IOContext(IOBuffer(), context)
    io2 = IOContext(IOBuffer(), context)
    while true
        if a <= pos <= b
            printstyled(io2, "^"; color=:light_green)
        else
            print(io2, " ")
        end
        it = iterate(str, pos)
        it === nothing && break
        c, pos = it
        c == '\n' && break
        print(io1, c)
    end
    return String(take!(io1.io)), String(take!(io2.io))
end

function Base.showerror(io::IO, err::ParserError)
    printstyled(io, "TOML Parser error:\n"; color=Base.error_color())
    f = something(err.filepath, "none")
    printstyled(io, f, ':', err.line, ':', err.column; bold=true)
    printstyled(io, " error: "; color=Base.error_color())
    println(io, format_error_message_for_err_type(err))
    # In this case we want the arrow to point one character
    pos = err.pos::Int
    err.type == ErrUnexpectedEofExpectedValue && (pos += 1)
    str1, err1 = point_to_line(err.str::String, pos, pos, io)
    @static if VERSION <= v"1.6.0-DEV.121"
        # See https://github.com/JuliaLang/julia/issues/36015
        format_fixer = get(io, :color, false)::Bool == true ? "\e[0m" : ""
        println(io, "$format_fixer  ", str1)
        print(io, "$format_fixer  ", err1)
    else
        println(io, "  ", str1)
        print(io, "  ", err1)
    end
end


################
# Parser utils #
################

@inline function next_char(l::Parser)::Char
    state = iterate(l.str, l.pos)
    l.prevpos = l.pos
    l.column += 1
    state === nothing && return EOF_CHAR
    c, pos = state
    l.pos = pos
    if c == '\n'
        l.line += 1
        l.column = 0
    end
    return c
end

@inline function eat_char(l::Parser)::Char
    c = l.current_char
    l.current_char = next_char(l)
    return c
end

@inline peek(l::Parser) = l.current_char

# Return true if the character was accepted. When a character
# is accepted it get's eaten and we move to the next character
@inline function accept(l::Parser, f::Union{Function, Char})::Bool
    c = peek(l)
    c == EOF_CHAR && return false
    ok = false
    if isa(f, Function)
        ok = f(c)
    elseif isa(f, Char)
        ok = c === f
    end
    ok && eat_char(l)
    return ok
end

# Return true if any character was accepted
function accept_batch(l::Parser, f::F)::Bool where {F}
    ok = false
    while accept(l, f)
        ok = true
    end
    return ok
end

# Return true if `f` was accepted `n` times
@inline function accept_n(l::Parser, n, f::F)::Bool where {F}
    for i in 1:n
        if !accept(l, f)
            return false
        end
    end
    return true
end

@inline iswhitespace(c::Char) = c == ' ' || c == '\t'
@inline isnewline(c::Char) = c == '\n' || c == '\r'

skip_ws(l::Parser) = accept_batch(l, iswhitespace)

skip_ws_nl_no_comment(l::Parser)::Bool = accept_batch(l, x -> iswhitespace(x) || isnewline(x))

function skip_ws_nl(l::Parser)::Bool
    skipped = false
    while true
        skipped_ws = accept_batch(l, x -> iswhitespace(x) || isnewline(x))
        skipped_comment = skip_comment(l)
        if !skipped_ws && !skipped_comment
            break
        end
        skipped = true
    end
    return skipped
end

# Returns true if a comment was skipped
function skip_comment(l::Parser)::Bool
    found_comment = accept(l, '#')
    if found_comment
        accept_batch(l, !isnewline)
    end
    return found_comment
end

skip_ws_comment(l::Parser) = skip_ws(l) && skip_comment(l)

@inline set_marker!(l::Parser) = l.marker = l.prevpos
take_substring(l::Parser) = SubString(l.str, l.marker:(l.prevpos-1))

############
# Toplevel #
############

# Driver, keeps parsing toplevel until we either get
# a `ParserError` or eof.
function parse(l::Parser)::TOMLDict
    v = tryparse(l)
    v isa ParserError && throw(v)
    return v
end

function tryparse(l::Parser)::Err{TOMLDict}
    while true
        skip_ws_nl(l)
        peek(l) == EOF_CHAR && break
        v = parse_toplevel(l)
        if v isa ParserError
            v.str      = l.str
            v.pos      = l.prevpos-1
            v.table    = l.root
            v.filepath = l.filepath
            v.line     = l.line
            v.column   = l.column-1
            return v
        end
    end
    return l.root
end

# Top level can be either a table key, an array of table statement
# or a key/value entry.
function parse_toplevel(l::Parser)::Err{Nothing}
    if accept(l, '[')
        l.active_table = l.root
        @try parse_table(l)
        skip_ws_comment(l)
        if !(peek(l) == '\n' || peek(l) == '\r' || peek(l) == '#' || peek(l) == EOF_CHAR)
            eat_char(l)
            return ParserError(ErrExpectedNewLineKeyValue)
        end
    else
        @try parse_entry(l, l.active_table)
        skip_ws_comment(l)
        # SPEC: "There must be a newline (or EOF) after a key/value pair."
        if !(peek(l) == '\n' || peek(l) == '\r' || peek(l) == '#' || peek(l) == EOF_CHAR)
            c = eat_char(l)
            return ParserError(ErrExpectedNewLineKeyValue)
        end
    end
end

function recurse_dict!(l::Parser, d::Dict, dotted_keys::AbstractVector{String}, check=true)::Err{TOMLDict}
    for i in 1:length(dotted_keys)
        d = d::TOMLDict
        key = dotted_keys[i]
        d = get!(TOMLDict, d, key)
        if d isa Vector
            d = d[end]
        end
        check && @try check_allowed_add_key(l, d, i == length(dotted_keys))
    end
    return d::TOMLDict
end

function check_allowed_add_key(l::Parser, d, check_defined=true)::Err{Nothing}
    if !(d isa Dict)
        return ParserError(ErrKeyAlreadyHasValue)
    elseif d isa Dict && d in l.inline_tables
        return ParserError(ErrAddKeyToInlineTable)
    elseif check_defined && d in l.defined_tables
        return ParserError(ErrDuplicatedKey)
    end
    return nothing
end

# Can only enter here from toplevel
function parse_table(l)
    if accept(l, '[')
        return parse_array_table(l)
    end
    table_key = @try parse_key(l)
    skip_ws(l)
    if !accept(l, ']')
        return ParserError(ErrExpectedEndOfTable)
    end
    l.active_table = @try recurse_dict!(l, l.root, table_key)
    push!(l.defined_tables, l.active_table)
    return
end

function parse_array_table(l)::Union{Nothing, ParserError}
    table_key = @try parse_key(l)
    skip_ws(l)
    if !(accept(l, ']') && accept(l, ']'))
        return ParserError(ErrExpectedEndArrayOfTable)
    end
    d = @try recurse_dict!(l, l.root, @view(table_key[1:end-1]), false)
    k = table_key[end]
    old = get!(() -> [], d, k)
    if old isa Vector
        if old in l.static_arrays
            return ParserError(ErrAddArrayToStaticArray)
        end
    else
        return ParserError(ErrArrayTreatedAsDictionary)
    end
    d_new = TOMLDict()
    push!(old, d_new)
    push!(l.defined_tables, d_new)
    l.active_table = d_new

    return
end

function parse_entry(l::Parser, d)::Union{Nothing, ParserError}
    key = @try parse_key(l)
    skip_ws(l)
    if !accept(l, '=')
        return ParserError(ErrExpectedEqualAfterKey)
    end
    if length(key) > 1
        d = @try recurse_dict!(l, d, @view(key[1:end-1]))
    end
    last_key_part = l.dotted_keys[end]

    v = get(d, last_key_part, nothing)
    if v !== nothing
        @try check_allowed_add_key(l, v)
    end

    skip_ws(l)
    value = @try parse_value(l)
    # Not allowed to overwrite a value with an inline dict
    if value isa Dict && haskey(d, last_key_part)
        return ParserError(ErrInlineTableRedefine)
    end
    # TODO: Performance, hashing `last_key_part` again here
    d[last_key_part] = value
    return
end


########
# Keys #
########

# SPEC: "Bare keys may only contain ASCII letters, ASCII digits, underscores,
# and dashes (A-Za-z0-9_-).
# Note that bare keys are allowed to be composed of only ASCII digits, e.g. 1234,
# but are always interpreted as strings."
@inline isvalid_barekey_char(c::Char) =
    'a' <= c <= 'z' ||
    'A' <= c <= 'Z' ||
    isdigit(c) ||
    c == '-' || c == '_'

# Current key...
function parse_key(l::Parser)
    empty!(l.dotted_keys)
    _parse_key(l)
end

# Recursively add dotted keys to `l.dotted_key`
function _parse_key(l::Parser)
    skip_ws(l)
    # SPEC: "A bare key must be non-empty,"
    if isempty(l.dotted_keys) && accept(l, '=')
        return ParserError(ErrEmptyBareKey)
    end
    keyval = if accept(l, '"')
        @try parse_string_start(l, false)
    elseif accept(l, '\'')
        @try parse_string_start(l, true)
    else
        set_marker!(l)
        if accept_batch(l, isvalid_barekey_char)
            if !(peek(l) == '.' || iswhitespace(peek(l)) || peek(l) == ']' || peek(l) == '=')
                c = eat_char(l)
                return ParserError(ErrInvalidBareKeyCharacter, c)
            end
            String(take_substring(l))
        else
            c = eat_char(l)
            return ParserError(ErrInvalidBareKeyCharacter, c)
        end
    end
    new_key = keyval
    push!(l.dotted_keys, new_key)
    # SPEC: "Whitespace around dot-separated parts is ignored."
    skip_ws(l)
    if accept(l, '.')
        skip_ws(l)
        @try _parse_key(l)
    end
    return l.dotted_keys
end


##########
# Values #
##########

function parse_value(l::Parser)
    val = if accept(l, '[')
        parse_array(l)
    elseif accept(l, '{')
        parse_inline_table(l)
    elseif accept(l, '"')
        parse_string_start(l, false)
    elseif accept(l, '\'')
        parse_string_start(l, true)
    elseif accept(l, 't')
        parse_bool(l, true)
    elseif accept(l, 'f')
        parse_bool(l, false)
    else
        parse_number_or_date_start(l)
    end
    if val === nothing
        return ParserError(ErrGenericValueError)
    end
    return val
end


#########
# Array #
#########

function push!!(v::Vector, el)
    # Since these types are typically non-inferrable, they are a big invalidation risk,
    # and since it's used by the package-loading infrastructure the cost of invalidation
    # is high. Therefore, this is written to reduce the "exposed surface area": e.g., rather
    # than writing `T[el]` we write it as `push!(Vector{T}(undef, 1), el)` so that there
    # is no ambiguity about what types of objects will be created.
    T = eltype(v)
    t = typeof(el)
    if el isa T || t === T
        push!(v, el::T)
        return v
    elseif T === Union{}
        out = Vector{t}(undef, 1)
        out[1] = el
        return out
    else
        if T isa Union
            newT = Any
        else
            newT = Union{T, typeof(el)}
        end
        new = Array{newT}(undef, length(v))
        copy!(new, v)
        return push!(new, el)
    end
end

function parse_array(l::Parser)::Err{Vector}
    skip_ws_nl(l)
    array = Vector{Union{}}()
    empty_array = accept(l, ']')
    while !empty_array
        v = @try parse_value(l)
        # TODO: Worth to function barrier this?
        array = push!!(array, v)
        # There can be an arbitrary number of newlines and comments before a value and before the closing bracket.
        skip_ws_nl(l)
        comma = accept(l, ',')
        skip_ws_nl(l)
        accept(l, ']') && break
        if !comma
            return ParserError(ErrExpectedCommaBetweenItemsArray)
        end
    end
    push!(l.static_arrays, array)
    return array
end


################
# Inline table #
################

function parse_inline_table(l::Parser)::Err{TOMLDict}
    dict = TOMLDict()
    push!(l.inline_tables, dict)
    skip_ws(l)
    accept(l, '}') && return dict
    while true
        @try parse_entry(l, dict)
        # SPEC: No newlines are allowed between the curly braces unless they are valid within a value.
        skip_ws(l)
        accept(l, '}') && return dict
        if accept(l, ',')
            skip_ws(l)
            if accept(l, '}')
                return ParserError(ErrTrailingCommaInlineTable)
            end
        else
            return ParserError(ErrExpectedCommaBetweenItemsInlineTable)
        end
    end
end


###########
# Numbers #
###########

parse_inf(l::Parser, sgn::Int) = accept(l, 'n') && accept(l, 'f') ? sgn * Inf : nothing
parse_nan(l::Parser) = accept(l, 'a') && accept(l, 'n') ? NaN : nothing

function parse_bool(l::Parser, v::Bool)::Union{Bool, Nothing}
    # Have eaten a 't' if `v` is true, otherwise have eaten a `f`.
    v ? (accept(l, 'r') && accept(l, 'u') && accept(l, 'e') && return true) :
        (accept(l, 'a') && accept(l, 'l') && accept(l, 's') && accept(l, 'e') && return false)
    return nothing
end

isvalid_hex(c::Char) = isdigit(c) || ('a' <= c <= 'f') || ('A' <= c <= 'F')
isvalid_oct(c::Char) = '0' <= c <= '7'
isvalid_binary(c::Char) = '0' <= c <= '1'

const ValidSigs = Union{typeof.([isvalid_hex, isvalid_oct, isvalid_binary, isdigit])...}
# This function eats things accepted by `f` but also allows eating `_` in between
# digits. Returns if it ate at lest one character and if it ate an underscore
function accept_batch_underscore(l::Parser, f::ValidSigs, fail_if_underscore=true)::Err{Tuple{Bool, Bool}}
    contains_underscore = false
    at_least_one = false
    last_underscore = false
    while true
        c = peek(l)
        if c == '_'
            contains_underscore = true
            if fail_if_underscore
                return ParserError(ErrUnderscoreNotSurroundedByDigits)
            end
            eat_char(l)
            fail_if_underscore = true
            last_underscore = true
        else
            # SPEC:  "Each underscore must be surrounded by at least one digit on each side."
            fail_if_underscore = false
            if f(c)
                at_least_one = true
                eat_char(l)
            else
                if last_underscore
                    return ParserError(ErrTrailingUnderscoreNumber)
                end
                return at_least_one, contains_underscore
            end
            last_underscore = false
        end
    end
end

function parse_number_or_date_start(l::Parser)
    integer = true
    read_dot = false

    set_marker!(l)
    sgn = 1
    parsed_sign = false
    if accept(l, '+')
        parsed_sign = true
    elseif accept(l, '-')
        parsed_sign = true
        sgn = -1
    end
    if accept(l, 'i')
        return parse_inf(l, sgn)
    elseif accept(l, 'n')
        return parse_nan(l)
    end

    if accept(l, '.')
        return ParserError(ErrLeadingDot)
    end

    # Zero is allowed to follow by a end value char, a base x, o, b or a dot
    readed_zero = false
    if accept(l, '0')
        readed_zero = true # Intentional bad grammar to remove the ambiguity in "read"...
        if ok_end_value(peek(l))
            return Int64(0)
        elseif accept(l, 'x')
            parsed_sign && return ParserError(ErrSignInNonBase10Number)
            ate, contains_underscore = @try accept_batch_underscore(l, isvalid_hex)
            ate && return parse_hex(l, contains_underscore)
        elseif accept(l, 'o')
            parsed_sign && return ParserError(ErrSignInNonBase10Number)
            ate, contains_underscore = @try accept_batch_underscore(l, isvalid_oct)
            ate && return parse_oct(l, contains_underscore)
        elseif accept(l, 'b')
            parsed_sign && return ParserError(ErrSignInNonBase10Number)
            ate, contains_underscore = @try accept_batch_underscore(l, isvalid_binary)
            ate && return parse_bin(l, contains_underscore)
        elseif accept(l, isdigit)
            return parse_local_time(l)
        end
    end

    read_underscore = false
    read_digit = accept(l, isdigit)
    if !readed_zero && !read_digit
        if peek(l) == EOF_CHAR
            return ParserError(ErrUnexpectedEofExpectedValue)
        else
            return ParserError(ErrUnexpectedStartOfValue)
        end
    end
    ate, contains_underscore = @try accept_batch_underscore(l, isdigit, readed_zero)
    read_underscore |= contains_underscore
    if (read_digit || ate) && ok_end_value(peek(l))
        return parse_int(l, contains_underscore)
    end
    # Done with integers here

    if !read_underscore
        # No underscores in date / times
        if peek(l) == '-'
            return parse_datetime(l)
        elseif peek(l) == ':'
            return parse_local_time(l)
        end
    end
    # Done with datetime / localtime here

    # can optionally read a . + digits and then exponent
    ate_dot = accept(l, '.')
    ate, contains_underscore = @try accept_batch_underscore(l, isdigit, true)
    if ate_dot && !ate
        return ParserError(ErrNoTrailingDigitAfterDot)
    end
    read_underscore |= contains_underscore
    if accept(l, x -> x == 'e' || x == 'E')
        accept(l, x-> x == '+' || x == '-')
        # SPEC: (which follows the same rules as decimal integer values but may include leading zeros)
        read_digit = accept_batch(l, isdigit)
        ate, read_underscore = @try accept_batch_underscore(l, isdigit, !read_digit)
        contains_underscore |= read_underscore
    end
    if !ok_end_value(peek(l))
        eat_char(l)
        return ParserError(ErrGenericValueError)
    end
    return parse_float(l, read_underscore)
end


function take_string_or_substring(l, contains_underscore)::SubString
    subs = take_substring(l)
    # Need to pass a AbstractString to `parse` so materialize it in case it
    # contains underscore.
    return contains_underscore ? SubString(filter(!=('_'), subs)) : subs
end

function parse_float(l::Parser, contains_underscore)::Err{Float64}
    s = take_string_or_substring(l, contains_underscore)
    v = Base.tryparse(Float64, s)
    v === nothing && return(ParserError(ErrGenericValueError))
    return v
end

for (name, T1, T2, n1, n2) in (("int", Int64,  Int128,  17,  33),
                               ("hex", UInt64, UInt128, 18,  34),
                               ("oct", UInt64, UInt128, 24,  45),
                               ("bin", UInt64, UInt128, 66, 130),
                               )
    @eval function $(Symbol("parse_", name))(l::Parser, contains_underscore, base=nothing)::Err{Union{$(T1), $(T2), BigInt}}
        s = take_string_or_substring(l, contains_underscore)
        len = length(s)
        v = try
            if len ≤ $(n1)
                Base.parse($(T1), s; base)
            elseif $(n1) < len ≤ $(n2)
                Base.parse($(T2), s; base)
            else
                Base.parse(BigInt, s; base)
            end
        catch e
            e isa Base.OverflowError && return(ParserError(ErrOverflowError))
            error("internal parser error: did not correctly discredit $(repr(s)) as an int")
        end
        return v
    end
end


##########################
# Date / Time / DateTime #
##########################

ok_end_value(c::Char) = iswhitespace(c) || c == '#' || c == EOF_CHAR || c == ']' ||
                               c == '}' || c == ',' || c == '\n'     || c == '\r'

#=
# https://tools.ietf.org/html/rfc3339

# Internet Protocols MUST generate four digit years in dates.

   date-fullyear   = 4DIGIT
   date-month      = 2DIGIT  ; 01-12
   date-mday       = 2DIGIT  ; 01-28, 01-29, 01-30, 01-31 based on
                             ; month/year
   time-hour       = 2DIGIT  ; 00-23
   time-minute     = 2DIGIT  ; 00-59
   time-second     = 2DIGIT  ; 00-58, 00-59, 00-60 based on leap second
                             ; rules
   time-secfrac    = "." 1*DIGIT
   time-numoffset  = ("+" / "-") time-hour ":" time-minute
   time-offset     = "Z" / time-numoffset

   partial-time    = time-hour ":" time-minute ":" time-second
                     [time-secfrac]
   full-date       = date-fullyear "-" date-month "-" date-mday
   full-time       = partial-time time-offset

   date-time       = full-date "T" full-time
=#

accept_two(l, f::F) where {F} = accept_n(l, 2, f) || return(ParserError(ErrParsingDateTime))
function parse_datetime(l)
    # Year has already been eaten when we reach here
    year = @try parse_int(l, false)
    year in 0:9999 || return ParserError(ErrParsingDateTime)

    # Month
    accept(l, '-') || return ParserError(ErrParsingDateTime)
    set_marker!(l)
    @try accept_two(l, isdigit)
    month = @try parse_int(l, false)
    month in 1:12 || return ParserError(ErrParsingDateTime)
    accept(l, '-') || return ParserError(ErrParsingDateTime)

    # Day
    set_marker!(l)
    @try accept_two(l, isdigit)
    day = @try parse_int(l, false)
    # Verify the real range in the constructor below
    day in 1:31 || return ParserError(ErrParsingDateTime)

    # We might have a local date now
    read_space = false
    if ok_end_value(peek(l))
        if (read_space = accept(l, ' '))
            if !isdigit(peek(l))
                return try_return_date(l, year, month, day)
            end
        else
            return try_return_date(l, year, month, day)
        end
    end
    if !read_space
        accept(l, 'T') || accept(l, 't') || return ParserError(ErrParsingDateTime)
    end

    h, m, s, ms = @try _parse_local_time(l)

    # Julia doesn't support offset times
    if !accept(l, 'Z')
        if accept(l, '+') || accept(l, '-')
            return ParserError(ErrOffsetDateNotSupported)
        end
    end

    if !ok_end_value(peek(l))
        return ParserError(ErrParsingDateTime)
    end

    # The DateTime parser verifies things like leap year for us
    return try_return_datetime(l, year, month, day, h, m, s, ms)
end

function try_return_datetime(p, year, month, day, h, m, s, ms)
    Dates = p.Dates
    if Dates !== nothing
        try
            return Dates.DateTime(year, month, day, h, m, s, ms)
        catch
            return ParserError(ErrParsingDateTime)
        end
    else
        return DateTime(year, month, day, h, m, s, ms)
    end
end

function try_return_date(p, year, month, day)
    Dates = p.Dates
    if Dates !== nothing
        try
            return Dates.Date(year, month, day)
        catch
            return ParserError(ErrParsingDateTime)
        end
    else
        return Date(year, month, day)
    end
end

function parse_local_time(l::Parser)
    h = @try parse_int(l, false)
    h in 0:23 || return ParserError(ErrParsingDateTime)
    _, m, s, ms = @try _parse_local_time(l, true)
    # TODO: Could potentially parse greater accuracy for the
    # fractional seconds here.
    return try_return_time(l, h, m, s, ms)
end

function try_return_time(p, h, m, s, ms)
    Dates = p.Dates
    if Dates !== nothing
        try
            return Dates.Time(h, m, s, ms)
        catch
            return ParserError(ErrParsingDateTime)
        end
    else
        return Time(h, m, s, ms)
    end
end

function _parse_local_time(l::Parser, skip_hour=false)::Err{NTuple{4, Int64}}
    # Hour has potentially been already parsed in
    # `parse_number_or_date_start` already
    if skip_hour
        hour = Int64(0)
    else
        set_marker!(l)
        @try accept_two(l, isdigit)
        hour = parse_int(l, false)
        hour in 0:23 || return ParserError(ErrParsingDateTime)
    end

    accept(l, ':') || return ParserError(ErrParsingDateTime)

    # minute
    set_marker!(l)
    @try accept_two(l, isdigit)
    minute = parse_int(l, false)
    minute in 0:59 || return ParserError(ErrParsingDateTime)

    accept(l, ':') || return ParserError(ErrParsingDateTime)

    # second
    set_marker!(l)
    @try accept_two(l, isdigit)
    second = parse_int(l, false)
    second in 0:59 || return ParserError(ErrParsingDateTime)

    # optional fractional second
    fractional_second = Int64(0)
    if accept(l, '.')
        set_marker!(l)
        found_fractional_digit = false
        for i in 1:3
            found_fractional_digit |= accept(l, isdigit)
        end
        if !found_fractional_digit
            return ParserError(ErrParsingDateTime)
        end
        # DateTime in base only manages 3 significant digits in fractional
        # second
        fractional_second = parse_int(l, false)
        # Truncate off the rest eventual digits
        accept_batch(l, isdigit)
    end
    return hour, minute, second, fractional_second
end


##########
# String #
##########

function parse_string_start(l::Parser, quoted::Bool)::Err{String}
    # Have eaten a `'` if `quoted` is true, otherwise have eaten a `"`
    multiline = false
    c = quoted ? '\'' : '"'
    if accept(l, c) # Eat second quote
        if !accept(l, c)
            return ""
        end
        accept(l, '\r') # Eat third quote
        accept(l, '\n') # Eat third quote
        multiline = true
    end
    return parse_string_continue(l, multiline, quoted)
end

@inline stop_candidates_multiline(x)         = x != '"'  &&  x != '\\'
@inline stop_candidates_singleline(x)        = x != '"'  &&  x != '\\' && x != '\n'
@inline stop_candidates_multiline_quoted(x)  = x != '\'' &&  x != '\\'
@inline stop_candidates_singleline_quoted(x) = x != '\'' &&  x != '\\' && x != '\n'

function parse_string_continue(l::Parser, multiline::Bool, quoted::Bool)::Err{String}
    start_chunk = l.prevpos
    q = quoted ? '\'' : '"'
    contains_backslash = false
    offset = multiline ? 3 : 1
    while true
        if peek(l) == EOF_CHAR
            return ParserError(ErrUnexpectedEndString)
        end
        if quoted
            accept_batch(l, multiline ? stop_candidates_multiline_quoted : stop_candidates_singleline_quoted)
        else
            accept_batch(l, multiline ? stop_candidates_multiline : stop_candidates_singleline)
        end
        if !multiline && peek(l) == '\n'
            return ParserError(ErrNewLineInString)
        end
        next_slash = peek(l) == '\\'
        if !next_slash
            # TODO: Doesn't handle values with e.g. format `""""str""""`
            if accept(l, q) && (!multiline || (accept(l, q) && accept(l, q)))
                push!(l.chunks, start_chunk:(l.prevpos-offset-1))
                return take_chunks(l, contains_backslash)
            end
        end
        c = eat_char(l) # eat the character we stopped at
        next_slash = c == '\\'
        if next_slash && !quoted
            if peek(l) == '\n' || peek(l) == '\r'
                push!(l.chunks, start_chunk:(l.prevpos-1-1)) # -1 due to eating the slash
                skip_ws_nl_no_comment(l)
                start_chunk = l.prevpos
            else
                c = eat_char(l) # eat the escaped character
                if c == 'u'  || c == 'U'
                    n = c == 'u' ? 4 : 6
                    set_marker!(l)
                    if !accept_n(l, n, isvalid_hex)
                        return ParserError(ErrInvalidUnicodeScalar)
                    end
                    codepoint = parse_int(l, false, 16)::Int64
                    #=
                    Unicode Scalar Value
                    ---------------------
                    Any Unicode code point except high-surrogate and
                    low-surrogate code points.  In other words, the ranges of
                    integers 0 to D7FF16 and E00016 to 10FFFF16 inclusive.
                    =#
                    if !(codepoint <= 0xD7FF || 0xE000 <= codepoint <= 0x10FFFF)
                        return ParserError(ErrInvalidUnicodeScalar)
                    end
                elseif c != 'b' && c != 't' && c != 'n' && c != 'f' && c != 'r' && c != '"' && c!= '\\'
                    return ParserError(ErrInvalidEscapeCharacter)
                end
                contains_backslash = true
            end
        end
    end
end

function take_chunks(l::Parser, unescape::Bool)::String
    nbytes = sum(length, l.chunks; init=0)
    str = Base._string_n(nbytes)
    offset = 1
    for chunk in l.chunks
        # The SubString constructor takes as an index the first byte of the
        # last character but we have the last byte.
        n = length(chunk)
        GC.@preserve str begin
            unsafe_copyto!(pointer(str, offset), pointer(l.str, first(chunk)), n)
        end
        offset += n
    end
    empty!(l.chunks)
    return unescape ? unescape_string(str) : str
end

end
N   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/linking.jl=      # This file is a part of Julia. License is MIT: https://julialang.org/license
module Linking

import Base.Libc: Libdl

# inlined LLD_jll
# These get calculated in __init__()
const PATH = Ref("")
const LIBPATH = Ref("")
const PATH_list = String[]
const LIBPATH_list = String[]
const lld_path = Ref{String}()
const lld_exe = Sys.iswindows() ? "lld.exe" : "lld"
const dsymutil_path = Ref{String}()
const dsymutil_exe = Sys.iswindows() ? "dsymutil.exe" : "dsymutil"

if Sys.iswindows()
    const LIBPATH_env = "PATH"
    const LIBPATH_default = ""
    const pathsep = ';'
elseif Sys.isapple()
    const LIBPATH_env = "DYLD_FALLBACK_LIBRARY_PATH"
    const LIBPATH_default = "~/lib:/usr/local/lib:/lib:/usr/lib"
    const pathsep = ':'
else
    const LIBPATH_env = "LD_LIBRARY_PATH"
    const LIBPATH_default = ""
    const pathsep = ':'
end

function adjust_ENV!(env::Dict, PATH::String, LIBPATH::String, adjust_PATH::Bool, adjust_LIBPATH::Bool)
    if adjust_LIBPATH
        LIBPATH_base = get(env, LIBPATH_env, expanduser(LIBPATH_default))
        if !isempty(LIBPATH_base)
            env[LIBPATH_env] = string(LIBPATH, pathsep, LIBPATH_base)
        else
            env[LIBPATH_env] = LIBPATH
        end
    end
    if adjust_PATH && (LIBPATH_env != "PATH" || !adjust_LIBPATH)
        if !isempty(get(env, "PATH", ""))
            env["PATH"] = string(PATH, pathsep, env["PATH"])
        else
            env["PATH"] = PATH
        end
    end
    return env
end

function __init_lld_path()
    # Prefer our own bundled lld, but if we don't have one, pick it up off of the PATH
    # If this is an in-tree build, `lld` will live in `tools`.  Otherwise, it'll be in `private_libexecdir`
    for bundled_lld_path in (joinpath(Sys.BINDIR, Base.PRIVATE_LIBEXECDIR, lld_exe),
                             joinpath(Sys.BINDIR, "..", "tools", lld_exe),
                             joinpath(Sys.BINDIR, lld_exe))
        if isfile(bundled_lld_path)
            lld_path[] = abspath(bundled_lld_path)
            return
        end
    end
    lld_path[] = something(Sys.which(lld_exe), lld_exe)
    return
end

function __init_dsymutil_path()
    #Same as with lld but for dsymutil
    for bundled_dsymutil_path in (joinpath(Sys.BINDIR, Base.PRIVATE_LIBEXECDIR, dsymutil_exe),
                             joinpath(Sys.BINDIR, "..", "tools", dsymutil_exe),
                             joinpath(Sys.BINDIR, dsymutil_exe))
        if isfile(bundled_dsymutil_path)
            dsymutil_path[] = abspath(bundled_dsymutil_path)
            return
        end
    end
    dsymutil_path[] = something(Sys.which(dsymutil_exe), dsymutil_exe)
    return
end

const VERBOSE = Ref{Bool}(false)

function __init__()
    VERBOSE[] = Base.get_bool_env("JULIA_VERBOSE_LINKING", false)

    __init_lld_path()
    __init_dsymutil_path()
    PATH[] = dirname(lld_path[])
    if Sys.iswindows()
        # On windows, the dynamic libraries (.dll) are in Sys.BINDIR ("usr\\bin")
        append!(LIBPATH_list, [abspath(Sys.BINDIR, Base.LIBDIR, "julia"), Sys.BINDIR])
    else
        append!(LIBPATH_list, [abspath(Sys.BINDIR, Base.LIBDIR, "julia"), abspath(Sys.BINDIR, Base.LIBDIR)])
    end
    LIBPATH[] = join(LIBPATH_list, pathsep)
    return
end

function lld(; adjust_PATH::Bool = true, adjust_LIBPATH::Bool = true)
    env = adjust_ENV!(copy(ENV), PATH[], LIBPATH[], adjust_PATH, adjust_LIBPATH)
    return Cmd(Cmd([lld_path[]]); env)
end

function dsymutil(; adjust_PATH::Bool = true, adjust_LIBPATH::Bool = true)
    env = adjust_ENV!(copy(ENV), PATH[], LIBPATH[], adjust_PATH, adjust_LIBPATH)
    return Cmd(Cmd([dsymutil_path[]]); env)
end

function ld()
    default_args = ``
    @static if Sys.iswindows()
        # LLD supports mingw style linking
        flavor = "gnu"
        m = Sys.ARCH == :x86_64 ? "i386pep" : "i386pe"
        default_args = `-m $m -Bdynamic --enable-auto-image-base --allow-multiple-definition`
    elseif Sys.isapple()
        flavor = "darwin"
        arch = Sys.ARCH == :aarch64 ? :arm64 : Sys.ARCH
        default_args = `-arch $arch -undefined dynamic_lookup -platform_version macos $(Base.MACOS_PRODUCT_VERSION) $(Base.MACOS_PLATFORM_VERSION)`
    else
        flavor = "gnu"
    end

    `$(lld()) -flavor $flavor $default_args`
end

const WHOLE_ARCHIVE = if Sys.isapple()
    "-all_load"
else
    "--whole-archive"
end

const NO_WHOLE_ARCHIVE = if Sys.isapple()
    ""
else
    "--no-whole-archive"
end

const SHARED = if Sys.isapple()
    "-dylib"
else
    "-shared"
end

is_debug() = ccall(:jl_is_debugbuild, Cint, ()) == 1
libdir() = abspath(Sys.BINDIR, Base.LIBDIR)
private_libdir() = abspath(Sys.BINDIR, Base.PRIVATE_LIBDIR)
if Sys.iswindows()
    shlibdir() = Sys.BINDIR
else
    shlibdir() = libdir()
end

function link_image_cmd(path, out)
    PRIVATE_LIBDIR = "-L$(private_libdir())"
    SHLIBDIR = "-L$(shlibdir())"
    LIBS = is_debug() ? ("-ljulia-debug", "-ljulia-internal-debug") :
                        ("-ljulia", "-ljulia-internal")
    @static if Sys.iswindows()
        LIBS = (LIBS..., "-lopenlibm", "-lssp", "-lgcc_s", "-lgcc", "-lmsvcrt")
    end

    V = VERBOSE[] ? "--verbose" : ""
    `$(ld()) $V $SHARED -o $out $WHOLE_ARCHIVE $path $NO_WHOLE_ARCHIVE $PRIVATE_LIBDIR $SHLIBDIR $LIBS`
end

function link_image(path, out, internal_stderr::IO=stderr, internal_stdout::IO=stdout)
    run(link_image_cmd(path, out), Base.DevNull(), internal_stderr, internal_stdout)
end

end # module Linking
N   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/loading.jl��     # This file is a part of Julia. License is MIT: https://julialang.org/license

# Base.require is the implementation for the `import` statement
const require_lock = ReentrantLock()

# Cross-platform case-sensitive path canonicalization

if Sys.isunix() && !Sys.isapple()
    # assume case-sensitive filesystems, don't have to do anything
    isfile_casesensitive(path) = isaccessiblefile(path)
elseif Sys.iswindows()
    # GetLongPathName Win32 function returns the case-preserved filename on NTFS.
    function isfile_casesensitive(path)
        isaccessiblefile(path) || return false  # Fail fast
        basename(Filesystem.longpath(path)) == basename(path)
    end
elseif Sys.isapple()
    # HFS+ filesystem is case-preserving. The getattrlist API returns
    # a case-preserved filename. In the rare event that HFS+ is operating
    # in case-sensitive mode, this will still work but will be redundant.

    # Constants from <sys/attr.h>
    const ATRATTR_BIT_MAP_COUNT = 5
    const ATTR_CMN_NAME = 1
    const BITMAPCOUNT = 1
    const COMMONATTR = 5
    const FSOPT_NOFOLLOW = 1  # Don't follow symbolic links

    const attr_list = zeros(UInt8, 24)
    attr_list[BITMAPCOUNT] = ATRATTR_BIT_MAP_COUNT
    attr_list[COMMONATTR] = ATTR_CMN_NAME

    # This essentially corresponds to the following C code:
    # attrlist attr_list;
    # memset(&attr_list, 0, sizeof(attr_list));
    # attr_list.bitmapcount = ATTR_BIT_MAP_COUNT;
    # attr_list.commonattr = ATTR_CMN_NAME;
    # struct Buffer {
    #    u_int32_t total_length;
    #    u_int32_t filename_offset;
    #    u_int32_t filename_length;
    #    char filename[max_filename_length];
    # };
    # Buffer buf;
    # getattrpath(path, &attr_list, &buf, sizeof(buf), FSOPT_NOFOLLOW);
    function isfile_casesensitive(path)
        isaccessiblefile(path) || return false
        path_basename = String(basename(path))
        local casepreserved_basename
        header_size = 12
        buf = Vector{UInt8}(undef, length(path_basename) + header_size + 1)
        while true
            ret = ccall(:getattrlist, Cint,
                        (Cstring, Ptr{Cvoid}, Ptr{Cvoid}, Csize_t, Culong),
                        path, attr_list, buf, sizeof(buf), FSOPT_NOFOLLOW)
            systemerror(:getattrlist, ret ≠ 0)
            filename_length = GC.@preserve buf unsafe_load(
              convert(Ptr{UInt32}, pointer(buf) + 8))
            if (filename_length + header_size) > length(buf)
                resize!(buf, filename_length + header_size)
                continue
            end
            casepreserved_basename =
              view(buf, (header_size+1):(header_size+filename_length-1))
            break
        end
        # Hack to compensate for inability to create a string from a subarray with no allocations.
        codeunits(path_basename) == casepreserved_basename && return true

        # If there is no match, it's possible that the file does exist but HFS+
        # performed unicode normalization. See  https://developer.apple.com/library/mac/qa/qa1235/_index.html.
        isascii(path_basename) && return false
        codeunits(Unicode.normalize(path_basename, :NFD)) == casepreserved_basename
    end
else
    # Generic fallback that performs a slow directory listing.
    function isfile_casesensitive(path)
        isaccessiblefile(path) || return false
        dir, filename = splitdir(path)
        any(readdir(dir) .== filename)
    end
end

# Check if the file is accessible. If stat fails return `false`

function isaccessibledir(dir)
    return try
        isdir(dir)
    catch err
        err isa IOError || rethrow()
        false
    end
end

function isaccessiblefile(file)
    return try
        isfile(file)
    catch err
        err isa IOError || rethrow()
        false
    end
end

function isaccessiblepath(path)
    return try
        ispath(path)
    catch err
        err isa IOError || rethrow()
        false
    end
end

## SHA1 ##

struct SHA1
    bytes::NTuple{20, UInt8}
end
function SHA1(bytes::Vector{UInt8})
    length(bytes) == 20 ||
        throw(ArgumentError("wrong number of bytes for SHA1 hash: $(length(bytes))"))
    return SHA1(ntuple(i->bytes[i], Val(20)))
end
SHA1(s::AbstractString) = SHA1(hex2bytes(s))
parse(::Type{SHA1}, s::AbstractString) = SHA1(s)
function tryparse(::Type{SHA1}, s::AbstractString)
    try
        return parse(SHA1, s)
    catch e
        if isa(e, ArgumentError)
            return nothing
        end
        rethrow(e)
    end
end

string(hash::SHA1) = bytes2hex(hash.bytes)
print(io::IO, hash::SHA1) = bytes2hex(io, hash.bytes)
show(io::IO, hash::SHA1) = print(io, "SHA1(\"", hash, "\")")

isless(a::SHA1, b::SHA1) = isless(a.bytes, b.bytes)
hash(a::SHA1, h::UInt) = hash((SHA1, a.bytes), h)
==(a::SHA1, b::SHA1) = a.bytes == b.bytes

# fake uuid5 function (for self-assigned UUIDs)
# TODO: delete and use real uuid5 once it's in stdlib

function uuid5(namespace::UUID, key::String)
    u::UInt128 = 0
    h = hash(namespace)
    for _ = 1:sizeof(u)÷sizeof(h)
        u <<= sizeof(h) << 3
        u |= (h = hash(key, h))
    end
    u &= 0xffffffffffff0fff3fffffffffffffff
    u |= 0x00000000000050008000000000000000
    return UUID(u)
end

const ns_dummy_uuid = UUID("fe0723d6-3a44-4c41-8065-ee0f42c8ceab")

function dummy_uuid(project_file::String)
    @lock require_lock begin
    cache = LOADING_CACHE[]
    if cache !== nothing
        uuid = get(cache.dummy_uuid, project_file, nothing)
        uuid === nothing || return uuid
    end
    project_path = try
        realpath(project_file)
    catch ex
        ex isa IOError || rethrow()
        project_file
    end
    uuid = uuid5(ns_dummy_uuid, project_path)
    if cache !== nothing
        cache.dummy_uuid[project_file] = uuid
    end
    return uuid
    end
end

## package path slugs: turning UUID + SHA1 into a pair of 4-byte "slugs" ##

const slug_chars = String(['A':'Z'; 'a':'z'; '0':'9'])

function slug(x::UInt32, p::Int)
    y::UInt32 = x
    sprint(sizehint=p) do io
        n = length(slug_chars)
        for i = 1:p
            y, d = divrem(y, n)
            write(io, slug_chars[1+d])
        end
    end
end

function package_slug(uuid::UUID, p::Int=5)
    crc = _crc32c(uuid)
    return slug(crc, p)
end

function version_slug(uuid::UUID, sha1::SHA1, p::Int=5)
    crc = _crc32c(uuid)
    crc = _crc32c(sha1.bytes, crc)
    return slug(crc, p)
end

mutable struct CachedTOMLDict
    path::String
    inode::UInt64
    mtime::Float64
    size::Int64
    hash::UInt32
    d::Dict{String, Any}
end

function CachedTOMLDict(p::TOML.Parser, path::String)
    s = stat(path)
    content = read(path)
    crc32 = _crc32c(content)
    TOML.reinit!(p, String(content); filepath=path)
    d = TOML.parse(p)
    return CachedTOMLDict(
        path,
        s.inode,
        s.mtime,
        s.size,
        crc32,
        d,
   )
end

function get_updated_dict(p::TOML.Parser, f::CachedTOMLDict)
    s = stat(f.path)
    # note, this might miss very rapid in-place updates, such that mtime is
    # identical but that is solvable by not doing in-place updates, and not
    # rapidly changing these files
    if s.inode != f.inode || s.mtime != f.mtime || f.size != s.size
        content = read(f.path)
        new_hash = _crc32c(content)
        if new_hash != f.hash
            f.inode = s.inode
            f.mtime = s.mtime
            f.size = s.size
            f.hash = new_hash
            TOML.reinit!(p, String(content); filepath=f.path)
            return f.d = TOML.parse(p)
        end
    end
    return f.d
end

struct LoadingCache
    load_path::Vector{String}
    dummy_uuid::Dict{String, UUID}
    env_project_file::Dict{String, Union{Bool, String}}
    project_file_manifest_path::Dict{String, Union{Nothing, String}}
    require_parsed::Set{String}
    identified_where::Dict{Tuple{PkgId, String}, Union{Nothing, Tuple{PkgId, Union{Nothing, String}}}}
    identified::Dict{String, Union{Nothing, Tuple{PkgId, Union{Nothing, String}}}}
    located::Dict{Tuple{PkgId, Union{String, Nothing}}, Union{Tuple{Union{String, Nothing}, Union{String, Nothing}}, Nothing}}
end
const LOADING_CACHE = Ref{Union{LoadingCache, Nothing}}(nothing)
LoadingCache() = LoadingCache(load_path(), Dict(), Dict(), Dict(), Set(), Dict(), Dict(), Dict())


struct TOMLCache
    p::TOML.Parser
    d::Dict{String, CachedTOMLDict}
end
const TOML_CACHE = TOMLCache(TOML.Parser(), Dict{String, Dict{String, Any}}())

parsed_toml(project_file::AbstractString) = parsed_toml(project_file, TOML_CACHE, require_lock)
function parsed_toml(project_file::AbstractString, toml_cache::TOMLCache, toml_lock::ReentrantLock)
    lock(toml_lock) do
        cache = LOADING_CACHE[]
        dd = if !haskey(toml_cache.d, project_file)
            d = CachedTOMLDict(toml_cache.p, project_file)
            toml_cache.d[project_file] = d
            d.d
        else
            d = toml_cache.d[project_file]
            # We are in a require call and have already parsed this TOML file
            # assume that it is unchanged to avoid hitting disk
            if cache !== nothing && project_file in cache.require_parsed
                d.d
            else
                get_updated_dict(toml_cache.p, d)
            end
        end
        if cache !== nothing
            push!(cache.require_parsed, project_file)
        end
        return dd
    end
end

## package identification: determine unique identity of package to be loaded ##

# Used by Pkg but not used in loading itself
function find_package(arg)
    pkgenv = identify_package_env(arg)
    pkgenv === nothing && return nothing
    pkg, env = pkgenv
    return locate_package(pkg, env)
end

"""
    Base.identify_package_env(name::String)::Union{Tuple{PkgId, String}, Nothing}
    Base.identify_package_env(where::Union{Module,PkgId}, name::String)::Union{Tuple{PkgId, String} Nothing}

Same as [`Base.identify_package`](@ref) except that the path to the environment where the package is identified
is also returned.
"""
identify_package_env(where::Module, name::String) = identify_package_env(PkgId(where), name)
function identify_package_env(where::PkgId, name::String)
    cache = LOADING_CACHE[]
    if cache !== nothing
        pkg_env = get(cache.identified_where, (where, name), nothing)
        pkg_env === nothing || return pkg_env
    end
    pkg_env = nothing
    if where.name === name
        pkg_env = where, nothing
    elseif where.uuid === nothing
        pkg_env = identify_package_env(name) # ignore `where`
    else
        for env in load_path()
            pkgid = manifest_deps_get(env, where, name)
            pkgid === nothing && continue # not found--keep looking
            if pkgid.uuid !== nothing
                pkg_env = pkgid, env # found in explicit environment--use it
            end
            break # found in implicit environment--return "not found"
        end
    end
    if cache !== nothing
        cache.identified_where[(where, name)] = pkg_env
    end
    return pkg_env
end
function identify_package_env(name::String)
    cache = LOADING_CACHE[]
    if cache !== nothing
        pkg_env = get(cache.identified, name, nothing)
        pkg_env === nothing || return pkg_env
    end
    pkg_env = nothing
    for env in load_path()
        pkg = project_deps_get(env, name)
        if pkg !== nothing
            pkg_env = pkg, env # found--return it
            break
        end
    end
    if cache !== nothing
        cache.identified[name] = pkg_env
    end
    return pkg_env
end

_nothing_or_first(x) = x === nothing ? nothing : first(x)

"""
    Base.identify_package(name::String)::Union{PkgId, Nothing}
    Base.identify_package(where::Union{Module,PkgId}, name::String)::Union{PkgId, Nothing}

Identify the package by its name from the current environment stack, returning
its `PkgId`, or `nothing` if it cannot be found.

If only the `name` argument is provided, it searches each environment in the
stack and its named direct dependencies.

There `where` argument provides the context from where to search for the
package: in this case it first checks if the name matches the context itself,
otherwise it searches all recursive dependencies (from the resolved manifest of
each environment) until it locates the context `where`, and from there
identifies the dependency with the corresponding name.

```julia-repl
julia> Base.identify_package("Pkg") # Pkg is a dependency of the default environment
Pkg [44cfe95a-1eb2-52ea-b672-e2afdf69b78f]

julia> using LinearAlgebra

julia> Base.identify_package(LinearAlgebra, "Pkg") # Pkg is not a dependency of LinearAlgebra
```
"""
identify_package(where::Module, name::String) = _nothing_or_first(identify_package_env(where, name))
identify_package(where::PkgId, name::String)  = _nothing_or_first(identify_package_env(where, name))
identify_package(name::String)                = _nothing_or_first(identify_package_env(name))

function locate_package_env(pkg::PkgId, stopenv::Union{String, Nothing}=nothing)
    cache = LOADING_CACHE[]
    if cache !== nothing
        pathenv = get(cache.located, (pkg, stopenv), nothing)
        pathenv === nothing || return pathenv
    end
    path = nothing
    env′ = nothing
    if pkg.uuid === nothing
        for env in load_path()
            env′ = env
            # look for the toplevel pkg `pkg.name` in this entry
            found = project_deps_get(env, pkg.name)
            if found !== nothing
                @assert found.name == pkg.name
                if found.uuid === nothing
                    # pkg.name is present in this directory or project file,
                    # return the path the entry point for the code, if it could be found
                    # otherwise, signal failure
                    path = implicit_manifest_uuid_path(env, pkg)
                    @goto done
                end
            end
            if !(loading_extension || precompiling_extension)
                stopenv == env && @goto done
            end
        end
    else
        for env in load_path()
            env′ = env
            path = manifest_uuid_path(env, pkg)
            # missing is used as a sentinel to stop looking further down in envs
            if path === missing
                path = nothing
                @goto done
            end
            if path !== nothing
                path = entry_path(path, pkg.name)
                @goto done
            end
            if !(loading_extension || precompiling_extension)
                stopenv == env && break
            end
        end
        # Allow loading of stdlibs if the name/uuid are given
        # e.g. if they have been explicitly added to the project/manifest
        mbypath = manifest_uuid_path(Sys.STDLIB, pkg)
        if mbypath isa String
            path = entry_path(mbypath, pkg.name)
            @goto done
        end
    end
    @label done
    if cache !== nothing
        cache.located[(pkg, stopenv)] = path, env′
    end
    return path, env′
end

"""
    Base.locate_package(pkg::PkgId)::Union{String, Nothing}

The path to the entry-point file for the package corresponding to the identifier
`pkg`, or `nothing` if not found. See also [`identify_package`](@ref).

```julia-repl
julia> pkg = Base.identify_package("Pkg")
Pkg [44cfe95a-1eb2-52ea-b672-e2afdf69b78f]

julia> Base.locate_package(pkg)
"/path/to/julia/stdlib/v$(VERSION.major).$(VERSION.minor)/Pkg/src/Pkg.jl"
```
"""
function locate_package(pkg::PkgId, stopenv::Union{String, Nothing}=nothing)::Union{Nothing,String}
    _nothing_or_first(locate_package_env(pkg, stopenv))
end

"""
    pathof(m::Module)

Return the path of the `m.jl` file that was used to `import` module `m`,
or `nothing` if `m` was not imported from a package.

Use [`dirname`](@ref) to get the directory part and [`basename`](@ref)
to get the file name part of the path.
"""
function pathof(m::Module)
    @lock require_lock begin
    pkgid = get(module_keys, m, nothing)
    pkgid === nothing && return nothing
    origin = get(pkgorigins, pkgid, nothing)
    origin === nothing && return nothing
    path = origin.path
    path === nothing && return nothing
    return fixup_stdlib_path(path)
    end
end

"""
    pkgdir(m::Module[, paths::String...])

Return the root directory of the package that declared module `m`,
or `nothing` if `m` was not declared in a package. Optionally further
path component strings can be provided to construct a path within the
package root.

To get the root directory of the package that implements the current module
the form `pkgdir(@__MODULE__)` can be used.

```julia-repl
julia> pkgdir(Foo)
"/path/to/Foo.jl"

julia> pkgdir(Foo, "src", "file.jl")
"/path/to/Foo.jl/src/file.jl"
```

!!! compat "Julia 1.7"
    The optional argument `paths` requires at least Julia 1.7.
"""
function pkgdir(m::Module, paths::String...)
    rootmodule = moduleroot(m)
    path = pathof(rootmodule)
    path === nothing && return nothing
    return joinpath(dirname(dirname(path)), paths...)
end

function get_pkgversion_from_path(path)
    project_file = locate_project_file(path)
    if project_file isa String
        d = parsed_toml(project_file)
        v = get(d, "version", nothing)
        if v !== nothing
            return VersionNumber(v::String)
        end
    end
    return nothing
end

"""
    pkgversion(m::Module)

Return the version of the package that imported module `m`,
or `nothing` if `m` was not imported from a package, or imported
from a package without a version field set.

The version is read from the package's Project.toml during package
load.

To get the version of the package that imported the current module
the form `pkgversion(@__MODULE__)` can be used.

!!! compat "Julia 1.9"
    This function was introduced in Julia 1.9.
"""
function pkgversion(m::Module)
    path = pkgdir(m)
    path === nothing && return nothing
    @lock require_lock begin
        v = get_pkgversion_from_path(path)
        pkgorigin = get(pkgorigins, PkgId(moduleroot(m)), nothing)
        # Cache the version
        if pkgorigin !== nothing && pkgorigin.version === nothing
            pkgorigin.version = v
        end
        return v
    end
end

## generic project & manifest API ##

const project_names = ("JuliaProject.toml", "Project.toml")
const manifest_names = ("JuliaManifest.toml", "Manifest.toml")
const preferences_names = ("JuliaLocalPreferences.toml", "LocalPreferences.toml")

function locate_project_file(env::String)
    for proj in project_names
        project_file = joinpath(env, proj)
        if isfile_casesensitive(project_file)
            return project_file
        end
    end
    return true
end

# classify the LOAD_PATH entry to be one of:
#  - `false`: nonexistent / nothing to see here
#  - `true`: `env` is an implicit environment
#  - `path`: the path of an explicit project file
function env_project_file(env::String)::Union{Bool,String}
    @lock require_lock begin
    cache = LOADING_CACHE[]
    if cache !== nothing
        project_file = get(cache.env_project_file, env, nothing)
        project_file === nothing || return project_file
    end
    if isdir(env)
        project_file = locate_project_file(env)
    elseif basename(env) in project_names && isfile_casesensitive(env)
        project_file = env
    else
        project_file = false
    end
    if cache !== nothing
        cache.env_project_file[env] = project_file
    end
    return project_file
    end
end

function project_deps_get(env::String, name::String)::Union{Nothing,PkgId}
    project_file = env_project_file(env)
    if project_file isa String
        pkg_uuid = explicit_project_deps_get(project_file, name)
        pkg_uuid === nothing || return PkgId(pkg_uuid, name)
    elseif project_file
        return implicit_project_deps_get(env, name)
    end
    return nothing
end

function manifest_deps_get(env::String, where::PkgId, name::String)::Union{Nothing,PkgId}
    uuid = where.uuid
    @assert uuid !== nothing
    project_file = env_project_file(env)
    if project_file isa String
        # first check if `where` names the Project itself
        proj = project_file_name_uuid(project_file, where.name)
        if proj == where
            # if `where` matches the project, use [deps] section as manifest, and stop searching
            pkg_uuid = explicit_project_deps_get(project_file, name)
            return PkgId(pkg_uuid, name)
        end
        d = parsed_toml(project_file)
        exts = get(d, "extensions", nothing)::Union{Dict{String, Any}, Nothing}
        if exts !== nothing
            # Check if `where` is an extension of the project
            if where.name in keys(exts) && where.uuid == uuid5(proj.uuid::UUID, where.name)
                # Extensions can load weak deps...
                weakdeps = get(d, "weakdeps", nothing)::Union{Dict{String, Any}, Nothing}
                if weakdeps !== nothing
                    wuuid = get(weakdeps, name, nothing)::Union{String, Nothing}
                    if wuuid !== nothing
                        return PkgId(UUID(wuuid), name)
                    end
                end
                # ... and they can load same deps as the project itself
                mby_uuid = explicit_project_deps_get(project_file, name)
                mby_uuid === nothing || return PkgId(mby_uuid, name)
            end
        end
        # look for manifest file and `where` stanza
        return explicit_manifest_deps_get(project_file, where, name)
    elseif project_file
        # if env names a directory, search it
        return implicit_manifest_deps_get(env, where, name)
    end
    return nothing
end

function manifest_uuid_path(env::String, pkg::PkgId)::Union{Nothing,String,Missing}
    project_file = env_project_file(env)
    if project_file isa String
        proj = project_file_name_uuid(project_file, pkg.name)
        if proj == pkg
            # if `pkg` matches the project, return the project itself
            return project_file_path(project_file)
        end
        mby_ext = project_file_ext_path(project_file, pkg.name)
        mby_ext === nothing || return mby_ext
        # look for manifest file and `where` stanza
        return explicit_manifest_uuid_path(project_file, pkg)
    elseif project_file
        # if env names a directory, search it
        return implicit_manifest_uuid_path(env, pkg)
    end
    return nothing
end


function find_ext_path(project_path::String, extname::String)
    extfiledir = joinpath(project_path, "ext", extname, extname * ".jl")
    isfile(extfiledir) && return extfiledir
    return joinpath(project_path, "ext", extname * ".jl")
end

function project_file_ext_path(project_file::String, name::String)
    d = parsed_toml(project_file)
    p = project_file_path(project_file)
    exts = get(d, "extensions", nothing)::Union{Dict{String, Any}, Nothing}
    if exts !== nothing
        if name in keys(exts)
            return find_ext_path(p, name)
        end
    end
    return nothing
end

# find project file's top-level UUID entry (or nothing)
function project_file_name_uuid(project_file::String, name::String)::PkgId
    d = parsed_toml(project_file)
    uuid′ = get(d, "uuid", nothing)::Union{String, Nothing}
    uuid = uuid′ === nothing ? dummy_uuid(project_file) : UUID(uuid′)
    name = get(d, "name", name)::String
    return PkgId(uuid, name)
end

function project_file_path(project_file::String)
    d = parsed_toml(project_file)
    joinpath(dirname(project_file), get(d, "path", "")::String)
end

# find project file's corresponding manifest file
function project_file_manifest_path(project_file::String)::Union{Nothing,String}
    @lock require_lock begin
    cache = LOADING_CACHE[]
    if cache !== nothing
        manifest_path = get(cache.project_file_manifest_path, project_file, missing)
        manifest_path === missing || return manifest_path
    end
    dir = abspath(dirname(project_file))
    d = parsed_toml(project_file)
    explicit_manifest = get(d, "manifest", nothing)::Union{String, Nothing}
    manifest_path = nothing
    if explicit_manifest !== nothing
        manifest_file = normpath(joinpath(dir, explicit_manifest))
        if isfile_casesensitive(manifest_file)
            manifest_path = manifest_file
        end
    end
    if manifest_path === nothing
        for mfst in manifest_names
            manifest_file = joinpath(dir, mfst)
            if isfile_casesensitive(manifest_file)
                manifest_path = manifest_file
                break
            end
        end
    end
    if cache !== nothing
        cache.project_file_manifest_path[project_file] = manifest_path
    end
    return manifest_path
    end
end

# given a directory (implicit env from LOAD_PATH) and a name,
# check if it is an implicit package
function entry_point_and_project_file_inside(dir::String, name::String)::Union{Tuple{Nothing,Nothing},Tuple{String,Nothing},Tuple{String,String}}
    path = normpath(joinpath(dir, "src", "$name.jl"))
    isfile_casesensitive(path) || return nothing, nothing
    for proj in project_names
        project_file = normpath(joinpath(dir, proj))
        isfile_casesensitive(project_file) || continue
        return path, project_file
    end
    return path, nothing
end

# given a project directory (implicit env from LOAD_PATH) and a name,
# find an entry point for `name`, and see if it has an associated project file
function entry_point_and_project_file(dir::String, name::String)::Union{Tuple{Nothing,Nothing},Tuple{String,Nothing},Tuple{String,String}}
    path = normpath(joinpath(dir, "$name.jl"))
    isfile_casesensitive(path) && return path, nothing
    dir = joinpath(dir, name)
    path, project_file = entry_point_and_project_file_inside(dir, name)
    path === nothing || return path, project_file
    dir = dir * ".jl"
    path, project_file = entry_point_and_project_file_inside(dir, name)
    path === nothing || return path, project_file
    return nothing, nothing
end

# given a path and a name, return the entry point
function entry_path(path::String, name::String)::Union{Nothing,String}
    isfile_casesensitive(path) && return normpath(path)
    path = normpath(joinpath(path, "src", "$name.jl"))
    isfile_casesensitive(path) && return path
    return nothing # source not found
end

## explicit project & manifest API ##

# find project file root or deps `name => uuid` mapping
# return `nothing` if `name` is not found
function explicit_project_deps_get(project_file::String, name::String)::Union{Nothing,UUID}
    d = parsed_toml(project_file)
    root_uuid = dummy_uuid(project_file)
    if get(d, "name", nothing)::Union{String, Nothing} === name
        uuid = get(d, "uuid", nothing)::Union{String, Nothing}
        return uuid === nothing ? root_uuid : UUID(uuid)
    end
    deps = get(d, "deps", nothing)::Union{Dict{String, Any}, Nothing}
    if deps !== nothing
        uuid = get(deps, name, nothing)::Union{String, Nothing}
        uuid === nothing || return UUID(uuid)
    end
    return nothing
end

function is_v1_format_manifest(raw_manifest::Dict{String})
    if haskey(raw_manifest, "manifest_format")
        mf = raw_manifest["manifest_format"]
        if mf isa Dict{String} && haskey(mf, "uuid")
            # the off-chance where an old format manifest has a dep called "manifest_format"
            return true
        end
        return false
    else
        return true
    end
end

# returns a deps list for both old and new manifest formats
function get_deps(raw_manifest::Dict)
    if is_v1_format_manifest(raw_manifest)
        return raw_manifest
    else
        # if the manifest has no deps, there won't be a `deps` field
        return get(Dict{String, Any}, raw_manifest, "deps")::Dict{String, Any}
    end
end

# find `where` stanza and return the PkgId for `name`
# return `nothing` if it did not find `where` (indicating caller should continue searching)
function explicit_manifest_deps_get(project_file::String, where::PkgId, name::String)::Union{Nothing,PkgId}
    manifest_file = project_file_manifest_path(project_file)
    manifest_file === nothing && return nothing # manifest not found--keep searching LOAD_PATH
    d = get_deps(parsed_toml(manifest_file))
    found_where = false
    found_name = false
    for (dep_name, entries) in d
        entries::Vector{Any}
        for entry in entries
            entry = entry::Dict{String, Any}
            uuid = get(entry, "uuid", nothing)::Union{String, Nothing}
            uuid === nothing && continue
            if UUID(uuid) === where.uuid
                found_where = true
                # deps is either a list of names (deps = ["DepA", "DepB"]) or
                # a table of entries (deps = {"DepA" = "6ea...", "DepB" = "55d..."}
                deps = get(entry, "deps", nothing)::Union{Vector{String}, Dict{String, Any}, Nothing}
                if deps isa Vector{String}
                    found_name = name in deps
                    break
                elseif deps isa Dict{String, Any}
                    deps = deps::Dict{String, Any}
                    for (dep, uuid) in deps
                        uuid::String
                        if dep === name
                            return PkgId(UUID(uuid), name)
                        end
                    end
                end
            else # Check for extensions
                extensions = get(entry, "extensions", nothing)
                if extensions !== nothing
                    if haskey(extensions, where.name) && where.uuid == uuid5(UUID(uuid), where.name)
                        found_where = true
                        if name == dep_name
                            return PkgId(UUID(uuid), name)
                        end
                        exts = extensions[where.name]::Union{String, Vector{String}}
                        if (exts isa String && name == exts) || (exts isa Vector{String} && name in exts)
                            weakdeps = get(entry, "weakdeps", nothing)::Union{Vector{String}, Dict{String, Any}, Nothing}
                            if weakdeps !== nothing
                                if weakdeps isa Vector{String}
                                    found_name = name in weakdeps
                                    break
                                elseif weakdeps isa Dict{String, Any}
                                    weakdeps = weakdeps::Dict{String, Any}
                                    for (dep, uuid) in weakdeps
                                        uuid::String
                                        if dep === name
                                            return PkgId(UUID(uuid), name)
                                        end
                                    end
                                end
                            end
                        end
                        # `name` is not an ext, do standard lookup as if this was the parent
                        return identify_package(PkgId(UUID(uuid), dep_name), name)
                    end
                end
            end
        end
    end
    found_where || return nothing
    found_name || return PkgId(name)
    # Only reach here if deps was not a dict which mean we have a unique name for the dep
    name_deps = get(d, name, nothing)::Union{Nothing, Vector{Any}}
    if name_deps === nothing || length(name_deps) != 1
        error("expected a single entry for $(repr(name)) in $(repr(project_file))")
    end
    entry = first(name_deps::Vector{Any})::Dict{String, Any}
    uuid = get(entry, "uuid", nothing)::Union{String, Nothing}
    uuid === nothing && return nothing
    return PkgId(UUID(uuid), name)
end

# find `uuid` stanza, return the corresponding path
function explicit_manifest_uuid_path(project_file::String, pkg::PkgId)::Union{Nothing,String,Missing}
    manifest_file = project_file_manifest_path(project_file)
    manifest_file === nothing && return nothing # no manifest, skip env

    d = get_deps(parsed_toml(manifest_file))
    entries = get(d, pkg.name, nothing)::Union{Nothing, Vector{Any}}
    if entries !== nothing
        for entry in entries
            entry = entry::Dict{String, Any}
            uuid = get(entry, "uuid", nothing)::Union{Nothing, String}
            uuid === nothing && continue
            if UUID(uuid) === pkg.uuid
                return explicit_manifest_entry_path(manifest_file, pkg, entry)
            end
        end
    end
    # Extensions
    for (name, entries) in d
        entries = entries::Vector{Any}
        for entry in entries
            uuid = get(entry, "uuid", nothing)::Union{Nothing, String}
            extensions = get(entry, "extensions", nothing)::Union{Nothing, Dict{String, Any}}
            if extensions !== nothing && haskey(extensions, pkg.name) && uuid !== nothing && uuid5(UUID(uuid), pkg.name) == pkg.uuid
                parent_path = locate_package(PkgId(UUID(uuid), name))
                if parent_path === nothing
                    error("failed to find source of parent package: \"$name\"")
                end
                p = normpath(dirname(parent_path), "..")
                return find_ext_path(p, pkg.name)
            end
        end
    end
    return nothing
end

function explicit_manifest_entry_path(manifest_file::String, pkg::PkgId, entry::Dict{String,Any})
    path = get(entry, "path", nothing)::Union{Nothing, String}
    if path !== nothing
        path = normpath(abspath(dirname(manifest_file), path))
        return path
    end
    hash = get(entry, "git-tree-sha1", nothing)::Union{Nothing, String}
    if hash === nothing
        mbypath = manifest_uuid_path(Sys.STDLIB, pkg)
        if mbypath isa String
            return entry_path(mbypath, pkg.name)
        end
        return nothing
    end
    hash = SHA1(hash)
    # Keep the 4 since it used to be the default
    uuid = pkg.uuid::UUID # checked within `explicit_manifest_uuid_path`
    for slug in (version_slug(uuid, hash), version_slug(uuid, hash, 4))
        for depot in DEPOT_PATH
            path = joinpath(depot, "packages", pkg.name, slug)
            ispath(path) && return abspath(path)
        end
    end
    # no depot contains the package, return missing to stop looking
    return missing
end

## implicit project & manifest API ##

# look for an entry point for `name` from a top-level package (no environment)
# otherwise return `nothing` to indicate the caller should keep searching
function implicit_project_deps_get(dir::String, name::String)::Union{Nothing,PkgId}
    path, project_file = entry_point_and_project_file(dir, name)
    if project_file === nothing
        path === nothing && return nothing
        return PkgId(name)
    end
    proj = project_file_name_uuid(project_file, name)
    proj.name == name || return nothing
    return proj
end

# look for an entry-point for `name`, check that UUID matches
# if there's a project file, look up `name` in its deps and return that
# otherwise return `nothing` to indicate the caller should keep searching
function implicit_manifest_deps_get(dir::String, where::PkgId, name::String)::Union{Nothing,PkgId}
    @assert where.uuid !== nothing
    project_file = entry_point_and_project_file(dir, where.name)[2]
    project_file === nothing && return nothing # a project file is mandatory for a package with a uuid
    proj = project_file_name_uuid(project_file, where.name)
    proj == where || return nothing # verify that this is the correct project file
    # this is the correct project, so stop searching here
    pkg_uuid = explicit_project_deps_get(project_file, name)
    return PkgId(pkg_uuid, name)
end

# look for an entry-point for `pkg` and return its path if UUID matches
function implicit_manifest_uuid_path(dir::String, pkg::PkgId)::Union{Nothing,String}
    path, project_file = entry_point_and_project_file(dir, pkg.name)
    if project_file === nothing
        pkg.uuid === nothing || return nothing
        return path
    end
    proj = project_file_name_uuid(project_file, pkg.name)
    proj == pkg || return nothing
    return path
end

## other code loading functionality ##

function find_source_file(path::AbstractString)
    (isabspath(path) || isfile(path)) && return path
    base_path = joinpath(Sys.BINDIR, DATAROOTDIR, "julia", "base", path)
    return isfile(base_path) ? normpath(base_path) : nothing
end

cache_file_entry(pkg::PkgId) = joinpath(
    "compiled",
    "v$(VERSION.major).$(VERSION.minor)",
    pkg.uuid === nothing ? ""       : pkg.name),
    pkg.uuid === nothing ? pkg.name : package_slug(pkg.uuid)

function find_all_in_cache_path(pkg::PkgId)
    paths = String[]
    entrypath, entryfile = cache_file_entry(pkg)
    for path in joinpath.(DEPOT_PATH, entrypath)
        isdir(path) || continue
        for file in readdir(path, sort = false) # no sort given we sort later
            if !((pkg.uuid === nothing && file == entryfile * ".ji") ||
                 (pkg.uuid !== nothing && startswith(file, entryfile * "_") &&
                  endswith(file, ".ji")))
                 continue
            end
            filepath = joinpath(path, file)
            isfile_casesensitive(filepath) && push!(paths, filepath)
        end
    end
    if length(paths) > 1
        # allocating the sort vector is less expensive than using sort!(.. by=mtime), which would
        # call the relatively slow mtime multiple times per path
        p = sortperm(mtime.(paths), rev = true)
        return paths[p]
    else
        return paths
    end
end

ocachefile_from_cachefile(cachefile) = string(chopsuffix(cachefile, ".ji"), ".", Base.Libc.dlext)
cachefile_from_ocachefile(cachefile) = string(chopsuffix(cachefile, ".$(Base.Libc.dlext)"), ".ji")


# use an Int counter so that nested @time_imports calls all remain open
const TIMING_IMPORTS = Threads.Atomic{Int}(0)

# these return either the array of modules loaded from the path / content given
# or an Exception that describes why it couldn't be loaded
# and it reconnects the Base.Docs.META
function _include_from_serialized(pkg::PkgId, path::String, ocachepath::Union{Nothing, String}, depmods::Vector{Any})
    assert_havelock(require_lock)
    timing_imports = TIMING_IMPORTS[] > 0
    try
    if timing_imports
        t_before = time_ns()
        cumulative_compile_timing(true)
        t_comp_before = cumulative_compile_time_ns()
    end

    if ocachepath !== nothing
        @debug "Loading object cache file $ocachepath for $pkg"
        sv = ccall(:jl_restore_package_image_from_file, Any, (Cstring, Any, Cint, Cstring), ocachepath, depmods, false, pkg.name)
    else
        @debug "Loading cache file $path for $pkg"
        sv = ccall(:jl_restore_incremental, Any, (Cstring, Any, Cint, Cstring), path, depmods, false, pkg.name)
    end
    if isa(sv, Exception)
        return sv
    end

    restored = register_restored_modules(sv, pkg, path)

    for M in restored
        M = M::Module
        if parentmodule(M) === M && PkgId(M) == pkg
            if timing_imports
                elapsed = round((time_ns() - t_before) / 1e6, digits = 1)
                comp_time, recomp_time = cumulative_compile_time_ns() .- t_comp_before
                print(lpad(elapsed, 9), " ms  ")
                parentid = get(EXT_PRIMED, pkg, nothing)
                if parentid !== nothing
                    print(parentid.name, " → ")
                end
                print(pkg.name)
                if comp_time > 0
                    printstyled(" ", Ryu.writefixed(Float64(100 * comp_time / (elapsed * 1e6)), 2), "% compilation time", color = Base.info_color())
                end
                if recomp_time > 0
                    perc = Float64(100 * recomp_time / comp_time)
                    printstyled(" (", perc < 1 ? "<1" : Ryu.writefixed(perc, 0), "% recompilation)", color = Base.warn_color())
                end
                println()
            end
            return M
        end
    end
    return ErrorException("Required dependency $pkg failed to load from a cache file.")

    finally
        timing_imports && cumulative_compile_timing(false)
    end
end

function register_restored_modules(sv::SimpleVector, pkg::PkgId, path::String)
    # This function is also used by PkgCacheInspector.jl
    restored = sv[1]::Vector{Any}
    for M in restored
        M = M::Module
        if isdefined(M, Base.Docs.META) && getfield(M, Base.Docs.META) !== nothing
            push!(Base.Docs.modules, M)
        end
        if parentmodule(M) === M
            register_root_module(M)
        end
    end

    # Register this cache path now - If Requires.jl is loaded, Revise may end
    # up looking at the cache path during the init callback.
    get!(PkgOrigin, pkgorigins, pkg).cachepath = path

    inits = sv[2]::Vector{Any}
    if !isempty(inits)
        unlock(require_lock) # temporarily _unlock_ during these callbacks
        try
            for (i, mod) in pairs(inits)
                run_module_init(mod, i)
            end
        finally
            lock(require_lock)
        end
    end
    return restored
end

function run_module_init(mod::Module, i::Int=1)
    # `i` informs ordering for the `@time_imports` report formatting
    if TIMING_IMPORTS[] == 0
        ccall(:jl_init_restored_module, Cvoid, (Any,), mod)
    else
        if isdefined(mod, :__init__)
            connector = i > 1 ? "├" : "┌"
            printstyled("               $connector ", color = :light_black)

            elapsedtime = time_ns()
            cumulative_compile_timing(true)
            compile_elapsedtimes = cumulative_compile_time_ns()

            ccall(:jl_init_restored_module, Cvoid, (Any,), mod)

            elapsedtime = (time_ns() - elapsedtime) / 1e6
            cumulative_compile_timing(false);
            comp_time, recomp_time = (cumulative_compile_time_ns() .- compile_elapsedtimes) ./ 1e6

            print(round(elapsedtime, digits=1), " ms $mod.__init__() ")
            if comp_time > 0
                printstyled(Ryu.writefixed(Float64(100 * comp_time / elapsedtime), 2), "% compilation time", color = Base.info_color())
            end
            if recomp_time > 0
                perc = Float64(100 * recomp_time / comp_time)
                printstyled(" (", perc < 1 ? "<1" : Ryu.writefixed(perc, 0), "% recompilation)", color = Base.warn_color())
            end
            println()
        end
    end
end

function run_package_callbacks(modkey::PkgId)
    run_extension_callbacks(modkey)
    assert_havelock(require_lock)
    unlock(require_lock)
    try
        for callback in package_callbacks
            invokelatest(callback, modkey)
        end
    catch
        # Try to continue loading if a callback errors
        errs = current_exceptions()
        @error "Error during package callback" exception=errs
    finally
        lock(require_lock)
    end
    nothing
end


##############
# Extensions #
##############

mutable struct ExtensionId
    const id::PkgId
    const parentid::PkgId # just need the name, for printing
    ntriggers::Int # how many more packages must be defined until this is loaded
end

const EXT_PRIMED = Dict{PkgId, PkgId}() # Extension -> Parent
const EXT_DORMITORY = Dict{PkgId,Vector{ExtensionId}}() # Trigger -> Extensions that can be triggered by it
const EXT_DORMITORY_FAILED = ExtensionId[]

function insert_extension_triggers(pkg::PkgId)
    pkg.uuid === nothing && return
    path_env_loc = locate_package_env(pkg)
    path_env_loc === nothing && return
    path, env_loc = path_env_loc
    if path === nothing || env_loc === nothing
        return
    end
    insert_extension_triggers(env_loc, pkg)
end

function insert_extension_triggers(env::String, pkg::PkgId)::Union{Nothing,Missing}
    project_file = env_project_file(env)
    if project_file isa String
        # Look in project for extensions to insert
        proj_pkg = project_file_name_uuid(project_file, pkg.name)
        if pkg == proj_pkg
            d_proj = parsed_toml(project_file)
            weakdeps = get(d_proj, "weakdeps", nothing)::Union{Nothing, Vector{String}, Dict{String,Any}}
            extensions = get(d_proj, "extensions", nothing)::Union{Nothing, Dict{String, Any}}
            extensions === nothing && return
            weakdeps === nothing && return
            if weakdeps isa Dict{String, Any}
                return _insert_extension_triggers(pkg, extensions, weakdeps)
            end
        end

        # Now look in manifest
        manifest_file = project_file_manifest_path(project_file)
        manifest_file === nothing && return
        d = get_deps(parsed_toml(manifest_file))
        for (dep_name, entries) in d
            entries::Vector{Any}
            for entry in entries
                entry = entry::Dict{String, Any}
                uuid = get(entry, "uuid", nothing)::Union{String, Nothing}
                uuid === nothing && continue
                if UUID(uuid) == pkg.uuid
                    weakdeps = get(entry, "weakdeps", nothing)::Union{Nothing, Vector{String}, Dict{String,Any}}
                    extensions = get(entry, "extensions", nothing)::Union{Nothing, Dict{String, Any}}
                    extensions === nothing && return
                    weakdeps === nothing && return
                    if weakdeps isa Dict{String, Any}
                        return _insert_extension_triggers(pkg, extensions, weakdeps)
                    end

                    d_weakdeps = Dict{String, Any}()
                    for (dep_name, entries) in d
                        dep_name in weakdeps || continue
                        entries::Vector{Any}
                        if length(entries) != 1
                            error("expected a single entry for $(repr(dep_name)) in $(repr(project_file))")
                        end
                        entry = first(entries)::Dict{String, Any}
                        uuid = entry["uuid"]::String
                        d_weakdeps[dep_name] = uuid
                    end
                    @assert length(d_weakdeps) == length(weakdeps)
                    return _insert_extension_triggers(pkg, extensions, d_weakdeps)
                end
            end
        end
    end
    return nothing
end

function _insert_extension_triggers(parent::PkgId, extensions::Dict{String, Any}, weakdeps::Dict{String, Any})
    for (ext, triggers) in extensions
        triggers = triggers::Union{String, Vector{String}}
        triggers isa String && (triggers = [triggers])
        id = PkgId(uuid5(parent.uuid, ext), ext)
        if id in keys(EXT_PRIMED) || haskey(Base.loaded_modules, id)
            continue  # extension is already primed or loaded, don't add it again
        end
        EXT_PRIMED[id] = parent
        gid = ExtensionId(id, parent, 1 + length(triggers))
        trigger1 = get!(Vector{ExtensionId}, EXT_DORMITORY, parent)
        push!(trigger1, gid)
        for trigger in triggers
            # TODO: Better error message if this lookup fails?
            uuid_trigger = UUID(weakdeps[trigger]::String)
            trigger_id = PkgId(uuid_trigger, trigger)
            if !haskey(Base.loaded_modules, trigger_id) || haskey(package_locks, trigger_id)
                trigger1 = get!(Vector{ExtensionId}, EXT_DORMITORY, trigger_id)
                push!(trigger1, gid)
            else
                gid.ntriggers -= 1
            end
        end
    end
end

loading_extension::Bool = false
precompiling_extension::Bool = false
function run_extension_callbacks(extid::ExtensionId)
    assert_havelock(require_lock)
    succeeded = try
        # Used by Distributed to now load extensions in the package callback
        global loading_extension = true
        _require_prelocked(extid.id)
        @debug "Extension $(extid.id.name) of $(extid.parentid.name) loaded"
        true
    catch
        # Try to continue loading if loading an extension errors
        errs = current_exceptions()
        @error "Error during loading of extension $(extid.id.name) of $(extid.parentid.name), \
                use `Base.retry_load_extensions()` to retry." exception=errs
        false
    finally
        global loading_extension = false
    end
    return succeeded
end

function run_extension_callbacks(pkgid::PkgId)
    assert_havelock(require_lock)
    # take ownership of extids that depend on this pkgid
    extids = pop!(EXT_DORMITORY, pkgid, nothing)
    extids === nothing && return
    for extid in extids
        if extid.ntriggers > 0
            # indicate pkgid is loaded
            extid.ntriggers -= 1
        end
        if extid.ntriggers < 0
            # indicate pkgid is loaded
            extid.ntriggers += 1
            succeeded = false
        else
            succeeded = true
        end
        if extid.ntriggers == 0
            # actually load extid, now that all dependencies are met,
            # and record the result
            succeeded = succeeded && run_extension_callbacks(extid)
            succeeded || push!(EXT_DORMITORY_FAILED, extid)
        end
    end
    return
end

"""
    retry_load_extensions()

Loads all the (not yet loaded) extensions that have their extension-dependencies loaded.
This is used in cases where the automatic loading of an extension failed
due to some problem with the extension. Instead of restarting the Julia session,
the extension can be fixed, and this function run.
"""
function retry_load_extensions()
    @lock require_lock begin
    # this copy is desired since run_extension_callbacks will release this lock
    # so this can still mutate the list to drop successful ones
    failed = copy(EXT_DORMITORY_FAILED)
    empty!(EXT_DORMITORY_FAILED)
    filter!(failed) do extid
        return !run_extension_callbacks(extid)
    end
    prepend!(EXT_DORMITORY_FAILED, failed)
    end
    return
end

"""
    get_extension(parent::Module, extension::Symbol)

Return the module for `extension` of `parent` or return `nothing` if the extension is not loaded.
"""
get_extension(parent::Module, ext::Symbol) = get_extension(PkgId(parent), ext)
function get_extension(parentid::PkgId, ext::Symbol)
    parentid.uuid === nothing && return nothing
    extid = PkgId(uuid5(parentid.uuid, string(ext)), string(ext))
    return get(loaded_modules, extid, nothing)
end

# End extensions

# should sync with the types of arguments of `stale_cachefile`
const StaleCacheKey = Tuple{Base.PkgId, UInt128, String, String}

"""
    Base.isprecompiled(pkg::PkgId; ignore_loaded::Bool=false)

Returns whether a given PkgId within the active project is precompiled.

By default this check observes the same approach that code loading takes
with respect to when different versions of dependencies are currently loaded
to that which is expected. To ignore loaded modules and answer as if in a
fresh julia session specify `ignore_loaded=true`.

!!! compat "Julia 1.10"
    This function requires at least Julia 1.10.
"""
function isprecompiled(pkg::PkgId;
        ignore_loaded::Bool=false,
        stale_cache::Dict{StaleCacheKey,Bool}=Dict{StaleCacheKey, Bool}(),
        cachepaths::Vector{String}=Base.find_all_in_cache_path(pkg),
        sourcepath::Union{String,Nothing}=Base.locate_package(pkg)
    )
    isnothing(sourcepath) && error("Cannot locate source for $(repr(pkg))")
    for path_to_try in cachepaths
        staledeps = stale_cachefile(sourcepath, path_to_try, ignore_loaded = true)
        if staledeps === true
            continue
        end
        staledeps, _ = staledeps::Tuple{Vector{Any}, Union{Nothing, String}}
        # finish checking staledeps module graph
        for i in 1:length(staledeps)
            dep = staledeps[i]
            dep isa Module && continue
            modpath, modkey, modbuild_id = dep::Tuple{String, PkgId, UInt128}
            modpaths = find_all_in_cache_path(modkey)
            for modpath_to_try in modpaths::Vector{String}
                stale_cache_key = (modkey, modbuild_id, modpath, modpath_to_try)::StaleCacheKey
                if get!(() -> stale_cachefile(stale_cache_key...; ignore_loaded) === true,
                        stale_cache, stale_cache_key)
                    continue
                end
                @goto check_next_dep
            end
            @goto check_next_path
            @label check_next_dep
        end
        try
            # update timestamp of precompilation file so that it is the first to be tried by code loading
            touch(path_to_try)
        catch ex
            # file might be read-only and then we fail to update timestamp, which is fine
            ex isa IOError || rethrow()
        end
        return true
        @label check_next_path
    end
    return false
end

# loads a precompile cache file, after checking stale_cachefile tests
function _tryrequire_from_serialized(modkey::PkgId, build_id::UInt128)
    assert_havelock(require_lock)
    loaded = nothing
    if root_module_exists(modkey)
        loaded = root_module(modkey)
    else
        loaded = start_loading(modkey)
        if loaded === nothing
            try
                modpath = locate_package(modkey)
                modpath === nothing && return nothing
                set_pkgorigin_version_path(modkey, String(modpath))
                loaded = _require_search_from_serialized(modkey, String(modpath), build_id)
            finally
                end_loading(modkey, loaded)
            end
            if loaded isa Module
                insert_extension_triggers(modkey)
                run_package_callbacks(modkey)
            end
        end
    end
    if !(loaded isa Module) || PkgId(loaded) != modkey
        return ErrorException("Required dependency $modkey failed to load from a cache file.")
    end
    return loaded
end

# loads a precompile cache file, ignoring stale_cachefile tests
# assuming all depmods are already loaded and everything is valid
function _tryrequire_from_serialized(modkey::PkgId, path::String, ocachepath::Union{Nothing, String}, sourcepath::String, depmods::Vector{Any})
    assert_havelock(require_lock)
    loaded = nothing
    if root_module_exists(modkey)
        loaded = root_module(modkey)
    else
        loaded = start_loading(modkey)
        if loaded === nothing
            try
                for i in 1:length(depmods)
                    dep = depmods[i]
                    dep isa Module && continue
                    _, depkey, depbuild_id = dep::Tuple{String, PkgId, UInt128}
                    @assert root_module_exists(depkey)
                    dep = root_module(depkey)
                    depmods[i] = dep
                end
                set_pkgorigin_version_path(modkey, sourcepath)
                loaded = _include_from_serialized(modkey, path, ocachepath, depmods)
            finally
                end_loading(modkey, loaded)
            end
            if loaded isa Module
                insert_extension_triggers(modkey)
                run_package_callbacks(modkey)
            end
        end
    end
    if !(loaded isa Module) || PkgId(loaded) != modkey
        return ErrorException("Required dependency $modkey failed to load from a cache file.")
    end
    return loaded
end

# loads a precompile cache file, ignoring stale_cachefile tests
# load the best available (non-stale) version of all dependent modules first
function _tryrequire_from_serialized(pkg::PkgId, path::String, ocachepath::Union{Nothing, String})
    assert_havelock(require_lock)
    local depmodnames
    io = open(path, "r")
    try
        iszero(isvalid_cache_header(io)) && return ArgumentError("Invalid header in cache file $path.")
        _, _, depmodnames, _, _, _, clone_targets, _ = parse_cache_header(io)
        pkgimage = !isempty(clone_targets)
        if pkgimage
            ocachepath !== nothing || return ArgumentError("Expected ocachepath to be provided")
            isfile(ocachepath) || return ArgumentError("Ocachepath $ocachepath is not a file.")
            ocachepath == ocachefile_from_cachefile(path) || return ArgumentError("$ocachepath is not the expected ocachefile")
            # TODO: Check for valid clone_targets?
            isvalid_pkgimage_crc(io, ocachepath) || return ArgumentError("Invalid checksum in cache file $ocachepath.")
        else
            @assert ocachepath === nothing
        end
        isvalid_file_crc(io) || return ArgumentError("Invalid checksum in cache file $path.")
    finally
        close(io)
    end
    ndeps = length(depmodnames)
    depmods = Vector{Any}(undef, ndeps)
    for i in 1:ndeps
        modkey, build_id = depmodnames[i]
        dep = _tryrequire_from_serialized(modkey, build_id)
        if !isa(dep, Module)
            return dep
        end
        depmods[i] = dep
    end
    # then load the file
    return _include_from_serialized(pkg, path, ocachepath, depmods)
end

# returns `nothing` if require found a precompile cache for this sourcepath, but couldn't load it
# returns the set of modules restored if the cache load succeeded
@constprop :none function _require_search_from_serialized(pkg::PkgId, sourcepath::String, build_id::UInt128)
    assert_havelock(require_lock)
    paths = find_all_in_cache_path(pkg)
    for path_to_try in paths::Vector{String}
        staledeps = stale_cachefile(pkg, build_id, sourcepath, path_to_try)
        if staledeps === true
            continue
        end
        staledeps, ocachefile = staledeps::Tuple{Vector{Any}, Union{Nothing, String}}
        # finish checking staledeps module graph
        for i in 1:length(staledeps)
            dep = staledeps[i]
            dep isa Module && continue
            modpath, modkey, modbuild_id = dep::Tuple{String, PkgId, UInt128}
            modpaths = find_all_in_cache_path(modkey)
            for modpath_to_try in modpaths
                modstaledeps = stale_cachefile(modkey, modbuild_id, modpath, modpath_to_try)
                if modstaledeps === true
                    continue
                end
                modstaledeps, modocachepath = modstaledeps::Tuple{Vector{Any}, Union{Nothing, String}}
                staledeps[i] = (modpath, modkey, modpath_to_try, modstaledeps, modocachepath)
                @goto check_next_dep
            end
            @debug "Rejecting cache file $path_to_try because required dependency $modkey with build ID $(UUID(modbuild_id)) is missing from the cache."
            @goto check_next_path
            @label check_next_dep
        end
        try
            touch(path_to_try) # update timestamp of precompilation file
        catch ex # file might be read-only and then we fail to update timestamp, which is fine
            ex isa IOError || rethrow()
        end
        # finish loading module graph into staledeps
        for i in 1:length(staledeps)
            dep = staledeps[i]
            dep isa Module && continue
            modpath, modkey, modcachepath, modstaledeps, modocachepath = dep::Tuple{String, PkgId, String, Vector{Any}, Union{Nothing, String}}
            dep = _tryrequire_from_serialized(modkey, modcachepath, modocachepath, modpath, modstaledeps)
            if !isa(dep, Module)
                @debug "Rejecting cache file $path_to_try because required dependency $modkey failed to load from cache file for $modcachepath." exception=dep
                @goto check_next_path
            end
            staledeps[i] = dep
        end
        restored = _include_from_serialized(pkg, path_to_try, ocachefile, staledeps)
        isa(restored, Module) && return restored
        @debug "Deserialization checks failed while attempting to load cache from $path_to_try" exception=restored
        continue
        @label check_next_path
    end
    return nothing
end

# to synchronize multiple tasks trying to import/using something
const package_locks = Dict{PkgId,Pair{Task,Threads.Condition}}()

debug_loading_deadlocks::Bool = true # Enable a slightly more expensive, but more complete algorithm that can handle simultaneous tasks.
                               # This only triggers if you have multiple tasks trying to load the same package at the same time,
                               # so it is unlikely to make a difference normally.
function start_loading(modkey::PkgId)
    # handle recursive calls to require
    assert_havelock(require_lock)
    loading = get(package_locks, modkey, nothing)
    if loading !== nothing
        # load already in progress for this module on the task
        task, cond = loading
        deps = String[modkey.name]
        pkgid = modkey
        assert_havelock(cond.lock)
        if debug_loading_deadlocks && current_task() !== task
            waiters = Dict{Task,Pair{Task,PkgId}}() # invert to track waiting tasks => loading tasks
            for each in package_locks
                cond2 = each[2][2]
                assert_havelock(cond2.lock)
                for waiting in cond2.waitq
                    push!(waiters, waiting => (each[2][1] => each[1]))
                end
            end
            while true
                running = get(waiters, task, nothing)
                running === nothing && break
                task, pkgid = running
                push!(deps, pkgid.name)
                task === current_task() && break
            end
        end
        if current_task() === task
            others = String[modkey.name] # repeat this to emphasize the cycle here
            for each in package_locks # list the rest of the packages being loaded too
                if each[2][1] === task
                    other = each[1].name
                    other == modkey.name || other == pkgid.name || push!(others, other)
                end
            end
            msg = sprint(deps, others) do io, deps, others
                print(io, "deadlock detected in loading ")
                join(io, deps, " -> ")
                print(io, " -> ")
                join(io, others, " && ")
            end
            throw(ConcurrencyViolationError(msg))
        end
        return wait(cond)
    end
    package_locks[modkey] = current_task() => Threads.Condition(require_lock)
    return
end

function end_loading(modkey::PkgId, @nospecialize loaded)
    loading = pop!(package_locks, modkey)
    notify(loading[2], loaded, all=true)
    nothing
end

# to notify downstream consumers that a module was successfully loaded
# Callbacks take the form (mod::Base.PkgId) -> nothing.
# WARNING: This is an experimental feature and might change later, without deprecation.
const package_callbacks = Any[]
# to notify downstream consumers that a file has been included into a particular module
# Callbacks take the form (mod::Module, filename::String) -> nothing
# WARNING: This is an experimental feature and might change later, without deprecation.
const include_callbacks = Any[]

# used to optionally track dependencies when requiring a module:
const _concrete_dependencies = Pair{PkgId,UInt128}[] # these dependency versions are "set in stone", and the process should try to avoid invalidating them
const _require_dependencies = Any[] # a list of (mod, path, mtime) tuples that are the file dependencies of the module currently being precompiled
const _track_dependencies = Ref(false) # set this to true to track the list of file dependencies
function _include_dependency(mod::Module, _path::AbstractString)
    prev = source_path(nothing)
    if prev === nothing
        path = abspath(_path)
    else
        path = normpath(joinpath(dirname(prev), _path))
    end
    if _track_dependencies[]
        @lock require_lock begin
        push!(_require_dependencies, (mod, path, mtime(path)))
        end
    end
    return path, prev
end

"""
    include_dependency(path::AbstractString)

In a module, declare that the file, directory, or symbolic link specified by `path`
(relative or absolute) is a dependency for precompilation; that is, the module will need
to be recompiled if the modification time of `path` changes.

This is only needed if your module depends on a path that is not used via [`include`](@ref). It has
no effect outside of compilation.
"""
function include_dependency(path::AbstractString)
    _include_dependency(Main, path)
    return nothing
end

# we throw PrecompilableError when a module doesn't want to be precompiled
import Core: PrecompilableError
function show(io::IO, ex::PrecompilableError)
    print(io, "Declaring __precompile__(false) is not allowed in files that are being precompiled.")
end
precompilableerror(ex::PrecompilableError) = true
precompilableerror(ex::WrappedException) = precompilableerror(ex.error)
precompilableerror(@nospecialize ex) = false

# Call __precompile__(false) at the top of a tile prevent it from being precompiled (false)
"""
    __precompile__(isprecompilable::Bool)

Specify whether the file calling this function is precompilable, defaulting to `true`.
If a module or file is *not* safely precompilable, it should call `__precompile__(false)` in
order to throw an error if Julia attempts to precompile it.
"""
@noinline function __precompile__(isprecompilable::Bool=true)
    if !isprecompilable && ccall(:jl_generating_output, Cint, ()) != 0
        throw(PrecompilableError())
    end
    nothing
end

# require always works in Main scope and loads files from node 1
const toplevel_load = Ref(true)

const _require_world_age = Ref{UInt}(typemax(UInt))

"""
    require(into::Module, module::Symbol)

This function is part of the implementation of [`using`](@ref) / [`import`](@ref), if a module is not
already defined in `Main`. It can also be called directly to force reloading a module,
regardless of whether it has been loaded before (for example, when interactively developing
libraries).

Loads a source file, in the context of the `Main` module, on every active node, searching
standard locations for files. `require` is considered a top-level operation, so it sets the
current `include` path but does not use it to search for files (see help for [`include`](@ref)).
This function is typically used to load library code, and is implicitly called by `using` to
load packages.

When searching for files, `require` first looks for package code in the global array
[`LOAD_PATH`](@ref). `require` is case-sensitive on all platforms, including those with
case-insensitive filesystems like macOS and Windows.

For more details regarding code loading, see the manual sections on [modules](@ref modules) and
[parallel computing](@ref code-availability).
"""
function require(into::Module, mod::Symbol)
    if _require_world_age[] != typemax(UInt)
        Base.invoke_in_world(_require_world_age[], __require, into, mod)
    else
        @invokelatest __require(into, mod)
    end
end

function __require(into::Module, mod::Symbol)
    @lock require_lock begin
    LOADING_CACHE[] = LoadingCache()
    try
        uuidkey_env = identify_package_env(into, String(mod))
        # Core.println("require($(PkgId(into)), $mod) -> $uuidkey_env")
        if uuidkey_env === nothing
            where = PkgId(into)
            if where.uuid === nothing
                hint, dots = begin
                    if isdefined(into, mod) && getfield(into, mod) isa Module
                        true, "."
                    elseif isdefined(parentmodule(into), mod) && getfield(parentmodule(into), mod) isa Module
                        true, ".."
                    else
                        false, ""
                    end
                end
                hint_message = hint ? ", maybe you meant `import/using $(dots)$(mod)`" : ""
                start_sentence = hint ? "Otherwise, run" : "Run"
                throw(ArgumentError("""
                    Package $mod not found in current path$hint_message.
                    - $start_sentence `import Pkg; Pkg.add($(repr(String(mod))))` to install the $mod package."""))
            else
                throw(ArgumentError("""
                Package $(where.name) does not have $mod in its dependencies:
                - You may have a partially installed environment. Try `Pkg.instantiate()`
                  to ensure all packages in the environment are installed.
                - Or, if you have $(where.name) checked out for development and have
                  added $mod as a dependency but haven't updated your primary
                  environment's manifest file, try `Pkg.resolve()`.
                - Otherwise you may need to report an issue with $(where.name)"""))
            end
        end
        uuidkey, env = uuidkey_env
        if _track_dependencies[]
            push!(_require_dependencies, (into, binpack(uuidkey), 0.0))
        end
        return _require_prelocked(uuidkey, env)
    finally
        LOADING_CACHE[] = nothing
    end
    end
end

require(uuidkey::PkgId) = @lock require_lock _require_prelocked(uuidkey)

const REPL_PKGID = PkgId(UUID("3fa0cd96-eef1-5676-8a61-b3b8758bbffb"), "REPL")

function _require_prelocked(uuidkey::PkgId, env=nothing)
    if _require_world_age[] != typemax(UInt)
        Base.invoke_in_world(_require_world_age[], __require_prelocked, uuidkey, env)
    else
        @invokelatest __require_prelocked(uuidkey, env)
    end
end

function __require_prelocked(uuidkey::PkgId, env=nothing)
    assert_havelock(require_lock)
    if !root_module_exists(uuidkey)
        newm = _require(uuidkey, env)
        if newm === nothing
            error("package `$(uuidkey.name)` did not define the expected \
                  module `$(uuidkey.name)`, check for typos in package module name")
        end
        insert_extension_triggers(uuidkey)
        # After successfully loading, notify downstream consumers
        run_package_callbacks(uuidkey)
        if uuidkey == REPL_PKGID
            REPL_MODULE_REF[] = newm
        end
    else
        newm = root_module(uuidkey)
    end
    return newm
end

mutable struct PkgOrigin
    path::Union{String,Nothing}
    cachepath::Union{String,Nothing}
    version::Union{VersionNumber,Nothing}
end
PkgOrigin() = PkgOrigin(nothing, nothing, nothing)
const pkgorigins = Dict{PkgId,PkgOrigin}()

const loaded_modules = Dict{PkgId,Module}()
const loaded_modules_order = Vector{Module}()
const module_keys = IdDict{Module,PkgId}() # the reverse

is_root_module(m::Module) = @lock require_lock haskey(module_keys, m)
root_module_key(m::Module) = @lock require_lock module_keys[m]

@constprop :none function register_root_module(m::Module)
    # n.b. This is called from C after creating a new module in `Base.__toplevel__`,
    # instead of adding them to the binding table there.
    @lock require_lock begin
    key = PkgId(m, String(nameof(m)))
    if haskey(loaded_modules, key)
        oldm = loaded_modules[key]
        if oldm !== m
            if (0 != ccall(:jl_generating_output, Cint, ())) && (JLOptions().incremental != 0)
                error("Replacing module `$(key.name)`")
            else
                @warn "Replacing module `$(key.name)`"
            end
        end
    end
    push!(loaded_modules_order, m)
    loaded_modules[key] = m
    module_keys[m] = key
    end
    nothing
end

register_root_module(Core)
register_root_module(Base)
register_root_module(Main)

# This is used as the current module when loading top-level modules.
# It has the special behavior that modules evaluated in it get added
# to the loaded_modules table instead of getting bindings.
baremodule __toplevel__
using Base
end

# get a top-level Module from the given key
root_module(key::PkgId) = @lock require_lock loaded_modules[key]
function root_module(where::Module, name::Symbol)
    key = identify_package(where, String(name))
    key isa PkgId || throw(KeyError(name))
    return root_module(key)
end
maybe_root_module(key::PkgId) = @lock require_lock get(loaded_modules, key, nothing)

root_module_exists(key::PkgId) = @lock require_lock haskey(loaded_modules, key)
loaded_modules_array() = @lock require_lock copy(loaded_modules_order)

function unreference_module(key::PkgId)
    if haskey(loaded_modules, key)
        m = pop!(loaded_modules, key)
        # need to ensure all modules are GC rooted; will still be referenced
        # in module_keys
    end
end

# whoever takes the package_locks[pkg] must call this function immediately
function set_pkgorigin_version_path(pkg::PkgId, path::Union{String,Nothing})
    assert_havelock(require_lock)
    pkgorigin = get!(PkgOrigin, pkgorigins, pkg)
    if path !== nothing
        # Pkg needs access to the version of packages in the sysimage.
        if Core.Compiler.generating_sysimg()
            pkgorigin.version = get_pkgversion_from_path(joinpath(dirname(path), ".."))
        end
    end
    pkgorigin.path = path
    nothing
end

# A hook to allow code load to use Pkg.precompile
const PKG_PRECOMPILE_HOOK = Ref{Function}()

# Returns `nothing` or the new(ish) module
function _require(pkg::PkgId, env=nothing)
    assert_havelock(require_lock)
    loaded = start_loading(pkg)
    loaded === nothing || return loaded

    last = toplevel_load[]
    try
        toplevel_load[] = false
        # perform the search operation to select the module file require intends to load
        path = locate_package(pkg, env)
        if path === nothing
            throw(ArgumentError("""
                Package $pkg is required but does not seem to be installed:
                 - Run `Pkg.instantiate()` to install all recorded dependencies.
                """))
        end
        set_pkgorigin_version_path(pkg, path)

        pkg_precompile_attempted = false # being safe to avoid getting stuck in a Pkg.precompile loop

        # attempt to load the module file via the precompile cache locations
        if JLOptions().use_compiled_modules != 0
            @label load_from_cache
            m = _require_search_from_serialized(pkg, path, UInt128(0))
            if m isa Module
                return m
            end
        end

        # if the module being required was supposed to have a particular version
        # but it was not handled by the precompile loader, complain
        for (concrete_pkg, concrete_build_id) in _concrete_dependencies
            if pkg == concrete_pkg
                @warn """Module $(pkg.name) with build ID $((UUID(concrete_build_id))) is missing from the cache.
                     This may mean $pkg does not support precompilation but is imported by a module that does."""
                if JLOptions().incremental != 0
                    # during incremental precompilation, this should be fail-fast
                    throw(PrecompilableError())
                end
            end
        end

        if JLOptions().use_compiled_modules != 0
            if (0 == ccall(:jl_generating_output, Cint, ())) || (JLOptions().incremental != 0)
                if !pkg_precompile_attempted && isinteractive() && isassigned(PKG_PRECOMPILE_HOOK)
                    pkg_precompile_attempted = true
                    unlock(require_lock)
                    try
                        @invokelatest PKG_PRECOMPILE_HOOK[](pkg.name, _from_loading = true)
                    finally
                        lock(require_lock)
                    end
                    @goto load_from_cache
                end
                # spawn off a new incremental pre-compile task for recursive `require` calls
                cachefile_or_module = maybe_cachefile_lock(pkg, path) do
                    # double-check now that we have lock
                    m = _require_search_from_serialized(pkg, path, UInt128(0))
                    m isa Module && return m
                    compilecache(pkg, path)
                end
                cachefile_or_module isa Module && return cachefile_or_module::Module
                cachefile = cachefile_or_module
                if isnothing(cachefile) # maybe_cachefile_lock returns nothing if it had to wait for another process
                    @goto load_from_cache # the new cachefile will have the newest mtime so will come first in the search
                elseif isa(cachefile, Exception)
                    if precompilableerror(cachefile)
                        verbosity = isinteractive() ? CoreLogging.Info : CoreLogging.Debug
                        @logmsg verbosity "Skipping precompilation since __precompile__(false). Importing $pkg."
                    else
                        @warn "The call to compilecache failed to create a usable precompiled cache file for $pkg" exception=m
                    end
                    # fall-through to loading the file locally if not incremental
                else
                    cachefile, ocachefile = cachefile::Tuple{String, Union{Nothing, String}}
                    m = _tryrequire_from_serialized(pkg, cachefile, ocachefile)
                    if !isa(m, Module)
                        @warn "The call to compilecache failed to create a usable precompiled cache file for $pkg" exception=m
                    else
                        return m
                    end
                end
                if JLOptions().incremental != 0
                    # during incremental precompilation, this should be fail-fast
                    throw(PrecompilableError())
                end
            end
        end

        # just load the file normally via include
        # for unknown dependencies
        uuid = pkg.uuid
        uuid = (uuid === nothing ? (UInt64(0), UInt64(0)) : convert(NTuple{2, UInt64}, uuid))
        old_uuid = ccall(:jl_module_uuid, NTuple{2, UInt64}, (Any,), __toplevel__)
        if uuid !== old_uuid
            ccall(:jl_set_module_uuid, Cvoid, (Any, NTuple{2, UInt64}), __toplevel__, uuid)
        end
        unlock(require_lock)
        try
            include(__toplevel__, path)
            loaded = get(loaded_modules, pkg, nothing)
        finally
            lock(require_lock)
            if uuid !== old_uuid
                ccall(:jl_set_module_uuid, Cvoid, (Any, NTuple{2, UInt64}), __toplevel__, old_uuid)
            end
        end
    finally
        toplevel_load[] = last
        end_loading(pkg, loaded)
    end
    return loaded
end

# Only used from test/precompile.jl
function _require_from_serialized(uuidkey::PkgId, path::String, ocachepath::Union{String, Nothing})
    @lock require_lock begin
    set_pkgorigin_version_path(uuidkey, nothing)
    newm = _tryrequire_from_serialized(uuidkey, path, ocachepath)
    newm isa Module || throw(newm)
    insert_extension_triggers(uuidkey)
    # After successfully loading, notify downstream consumers
    run_package_callbacks(uuidkey)
    return newm
    end
end


# relative-path load

"""
    include_string([mapexpr::Function,] m::Module, code::AbstractString, filename::AbstractString="string")

Like [`include`](@ref), except reads code from the given string rather than from a file.

The optional first argument `mapexpr` can be used to transform the included code before
it is evaluated: for each parsed expression `expr` in `code`, the `include_string` function
actually evaluates `mapexpr(expr)`.  If it is omitted, `mapexpr` defaults to [`identity`](@ref).

!!! compat "Julia 1.5"
    Julia 1.5 is required for passing the `mapexpr` argument.
"""
function include_string(mapexpr::Function, mod::Module, code::AbstractString,
                        filename::AbstractString="string")
    loc = LineNumberNode(1, Symbol(filename))
    try
        ast = Meta.parseall(code, filename=filename)
        @assert Meta.isexpr(ast, :toplevel)
        result = nothing
        line_and_ex = Expr(:toplevel, loc, nothing)
        for ex in ast.args
            if ex isa LineNumberNode
                loc = ex
                line_and_ex.args[1] = ex
                continue
            end
            ex = mapexpr(ex)
            # Wrap things to be eval'd in a :toplevel expr to carry line
            # information as part of the expr.
            line_and_ex.args[2] = ex
            result = Core.eval(mod, line_and_ex)
        end
        return result
    catch exc
        # TODO: Now that stacktraces are more reliable we should remove
        # LoadError and expose the real error type directly.
        rethrow(LoadError(filename, loc.line, exc))
    end
end

include_string(m::Module, txt::AbstractString, fname::AbstractString="string") =
    include_string(identity, m, txt, fname)

function source_path(default::Union{AbstractString,Nothing}="")
    s = current_task().storage
    if s !== nothing
        s = s::IdDict{Any,Any}
        if haskey(s, :SOURCE_PATH)
            return s[:SOURCE_PATH]::Union{Nothing,String}
        end
    end
    return default
end

function source_dir()
    p = source_path(nothing)
    return p === nothing ? pwd() : dirname(p)
end

"""
    Base.include([mapexpr::Function,] m::Module, path::AbstractString)

Evaluate the contents of the input source file in the global scope of module `m`.
Every module (except those defined with [`baremodule`](@ref)) has its own
definition of `include` omitting the `m` argument, which evaluates the file in that module.
Returns the result of the last evaluated expression of the input file. During including,
a task-local include path is set to the directory containing the file. Nested calls to
`include` will search relative to that path. This function is typically used to load source
interactively, or to combine files in packages that are broken into multiple source files.

The optional first argument `mapexpr` can be used to transform the included code before
it is evaluated: for each parsed expression `expr` in `path`, the `include` function
actually evaluates `mapexpr(expr)`.  If it is omitted, `mapexpr` defaults to [`identity`](@ref).

!!! compat "Julia 1.5"
    Julia 1.5 is required for passing the `mapexpr` argument.
"""
Base.include # defined in Base.jl

# Full include() implementation which is used after bootstrap
function _include(mapexpr::Function, mod::Module, _path::AbstractString)
    @noinline # Workaround for module availability in _simplify_include_frames
    path, prev = _include_dependency(mod, _path)
    for callback in include_callbacks # to preserve order, must come before eval in include_string
        invokelatest(callback, mod, path)
    end
    code = read(path, String)
    tls = task_local_storage()
    tls[:SOURCE_PATH] = path
    try
        return include_string(mapexpr, mod, code, path)
    finally
        if prev === nothing
            delete!(tls, :SOURCE_PATH)
        else
            tls[:SOURCE_PATH] = prev
        end
    end
end

"""
    evalfile(path::AbstractString, args::Vector{String}=String[])

Load the file into an anonymous module using [`include`](@ref), evaluate all expressions,
and return the value of the last expression.
The optional `args` argument can be used to set the input arguments of the script (i.e. the global `ARGS` variable).
Note that definitions (e.g. methods, globals) are evaluated in the anonymous module and do not affect the current module.

# Example

```jldoctest
julia> write("testfile.jl", \"\"\"
           @show ARGS
           1 + 1
       \"\"\");

julia> x = evalfile("testfile.jl", ["ARG1", "ARG2"]);
ARGS = ["ARG1", "ARG2"]

julia> x
2

julia> rm("testfile.jl")
```
"""
function evalfile(path::AbstractString, args::Vector{String}=String[])
    return Core.eval(Module(:__anon__),
        Expr(:toplevel,
             :(const ARGS = $args),
             :(eval(x) = $(Expr(:core, :eval))(__anon__, x)),
             :(include(x) = $(Expr(:top, :include))(__anon__, x)),
             :(include(mapexpr::Function, x) = $(Expr(:top, :include))(mapexpr, __anon__, x)),
             :(include($path))))
end
evalfile(path::AbstractString, args::Vector) = evalfile(path, String[args...])

function load_path_setup_code(load_path::Bool=true)
    code = """
    append!(empty!(Base.DEPOT_PATH), $(repr(map(abspath, DEPOT_PATH))))
    append!(empty!(Base.DL_LOAD_PATH), $(repr(map(abspath, DL_LOAD_PATH))))
    """
    if load_path
        load_path = map(abspath, Base.load_path())
        path_sep = Sys.iswindows() ? ';' : ':'
        any(path -> path_sep in path, load_path) &&
            error("LOAD_PATH entries cannot contain $(repr(path_sep))")
        code *= """
        append!(empty!(Base.LOAD_PATH), $(repr(load_path)))
        ENV["JULIA_LOAD_PATH"] = $(repr(join(load_path, Sys.iswindows() ? ';' : ':')))
        Base.set_active_project(nothing)
        """
    end
    return code
end

# this is called in the external process that generates precompiled package files
function include_package_for_output(pkg::PkgId, input::String, depot_path::Vector{String}, dl_load_path::Vector{String}, load_path::Vector{String},
                                    concrete_deps::typeof(_concrete_dependencies), source::Union{Nothing,String})
    append!(empty!(Base.DEPOT_PATH), depot_path)
    append!(empty!(Base.DL_LOAD_PATH), dl_load_path)
    append!(empty!(Base.LOAD_PATH), load_path)
    ENV["JULIA_LOAD_PATH"] = join(load_path, Sys.iswindows() ? ';' : ':')
    set_active_project(nothing)
    Base._track_dependencies[] = true
    get!(Base.PkgOrigin, Base.pkgorigins, pkg).path = input
    append!(empty!(Base._concrete_dependencies), concrete_deps)
    uuid_tuple = pkg.uuid === nothing ? (UInt64(0), UInt64(0)) : convert(NTuple{2, UInt64}, pkg.uuid)

    ccall(:jl_set_module_uuid, Cvoid, (Any, NTuple{2, UInt64}), Base.__toplevel__, uuid_tuple)
    if source !== nothing
        task_local_storage()[:SOURCE_PATH] = source
    end

    ccall(:jl_set_newly_inferred, Cvoid, (Any,), Core.Compiler.newly_inferred)
    Core.Compiler.track_newly_inferred.x = true
    try
        Base.include(Base.__toplevel__, input)
    catch ex
        precompilableerror(ex) || rethrow()
        @debug "Aborting `create_expr_cache'" exception=(ErrorException("Declaration of __precompile__(false) not allowed"), catch_backtrace())
        exit(125) # we define status = 125 means PrecompileableError
    finally
        Core.Compiler.track_newly_inferred.x = false
    end
end

const PRECOMPILE_TRACE_COMPILE = Ref{String}()
function create_expr_cache(pkg::PkgId, input::String, output::String, output_o::Union{Nothing, String},
                           concrete_deps::typeof(_concrete_dependencies), internal_stderr::IO = stderr, internal_stdout::IO = stdout)
    @nospecialize internal_stderr internal_stdout
    rm(output, force=true)   # Remove file if it exists
    output_o === nothing || rm(output_o, force=true)
    depot_path = map(abspath, DEPOT_PATH)
    dl_load_path = map(abspath, DL_LOAD_PATH)
    load_path = map(abspath, Base.load_path())
    path_sep = Sys.iswindows() ? ';' : ':'
    any(path -> path_sep in path, load_path) &&
        error("LOAD_PATH entries cannot contain $(repr(path_sep))")

    deps_strs = String[]
    function pkg_str(_pkg::PkgId)
        if _pkg.uuid === nothing
            "Base.PkgId($(repr(_pkg.name)))"
        else
            "Base.PkgId(Base.UUID(\"$(_pkg.uuid)\"), $(repr(_pkg.name)))"
        end
    end
    for (pkg, build_id) in concrete_deps
        push!(deps_strs, "$(pkg_str(pkg)) => $(repr(build_id))")
    end

    if output_o !== nothing
        cpu_target = get(ENV, "JULIA_CPU_TARGET", nothing)
        opt_level = Base.JLOptions().opt_level
        opts = `-O$(opt_level) --output-o $(output_o) --output-ji $(output) --output-incremental=yes`
    else
        cpu_target = nothing
        opts = `-O0 --output-ji $(output) --output-incremental=yes`
    end

    deps_eltype = sprint(show, eltype(concrete_deps); context = :module=>nothing)
    deps = deps_eltype * "[" * join(deps_strs, ",") * "]"
    trace = isassigned(PRECOMPILE_TRACE_COMPILE) ? `--trace-compile=$(PRECOMPILE_TRACE_COMPILE[])` : ``
    io = open(pipeline(addenv(`$(julia_cmd(;cpu_target)::Cmd) $(opts)
                              --startup-file=no --history-file=no --warn-overwrite=yes
                              --color=$(have_color === nothing ? "auto" : have_color ? "yes" : "no")
                              $trace
                              -`,
                              "OPENBLAS_NUM_THREADS" => 1,
                              "JULIA_NUM_THREADS" => 1),
                       stderr = internal_stderr, stdout = internal_stdout),
              "w", stdout)
    # write data over stdin to avoid the (unlikely) case of exceeding max command line size
    write(io.in, """
        empty!(Base.EXT_DORMITORY) # If we have a custom sysimage with `EXT_DORMITORY` prepopulated
        Base.precompiling_extension = $(loading_extension)
        Base.include_package_for_output($(pkg_str(pkg)), $(repr(abspath(input))), $(repr(depot_path)), $(repr(dl_load_path)),
            $(repr(load_path)), $deps, $(repr(source_path(nothing))))
        """)
    close(io.in)
    return io
end

function compilecache_dir(pkg::PkgId)
    entrypath, entryfile = cache_file_entry(pkg)
    return joinpath(DEPOT_PATH[1], entrypath)
end

function compilecache_path(pkg::PkgId, prefs_hash::UInt64; project::String=something(Base.active_project(), ""))::String
    entrypath, entryfile = cache_file_entry(pkg)
    cachepath = joinpath(DEPOT_PATH[1], entrypath)
    isdir(cachepath) || mkpath(cachepath)
    if pkg.uuid === nothing
        abspath(cachepath, entryfile) * ".ji"
    else
        crc = _crc32c(project)
        crc = _crc32c(unsafe_string(JLOptions().image_file), crc)
        crc = _crc32c(unsafe_string(JLOptions().julia_bin), crc)
        crc = _crc32c(ccall(:jl_cache_flags, UInt8, ()), crc)

        cpu_target = get(ENV, "JULIA_CPU_TARGET", nothing)
        if cpu_target === nothing
            cpu_target = unsafe_string(JLOptions().cpu_target)
        end
        crc = _crc32c(cpu_target, crc)

        crc = _crc32c(prefs_hash, crc)
        project_precompile_slug = slug(crc, 5)
        abspath(cachepath, string(entryfile, "_", project_precompile_slug, ".ji"))
    end
end

"""
    Base.compilecache(module::PkgId)

Creates a precompiled cache file for a module and all of its dependencies.
This can be used to reduce package load times. Cache files are stored in
`DEPOT_PATH[1]/compiled`. See [Module initialization and precompilation](@ref)
for important notes.
"""
function compilecache(pkg::PkgId, internal_stderr::IO = stderr, internal_stdout::IO = stdout)
    @nospecialize internal_stderr internal_stdout
    path = locate_package(pkg)
    path === nothing && throw(ArgumentError("$pkg not found during precompilation"))
    return compilecache(pkg, path, internal_stderr, internal_stdout)
end

const MAX_NUM_PRECOMPILE_FILES = Ref(10)

function compilecache(pkg::PkgId, path::String, internal_stderr::IO = stderr, internal_stdout::IO = stdout,
                      keep_loaded_modules::Bool = true)

    @nospecialize internal_stderr internal_stdout
    # decide where to put the resulting cache file
    cachepath = compilecache_dir(pkg)

    # build up the list of modules that we want the precompile process to preserve
    concrete_deps = copy(_concrete_dependencies)
    if keep_loaded_modules
        for mod in loaded_modules_array()
            if !(mod === Main || mod === Core || mod === Base)
                push!(concrete_deps, PkgId(mod) => module_build_id(mod))
            end
        end
    end
    # run the expression and cache the result
    verbosity = isinteractive() ? CoreLogging.Info : CoreLogging.Debug
    @logmsg verbosity "Precompiling $pkg"

    # create a temporary file in `cachepath` directory, write the cache in it,
    # write the checksum, _and then_ atomically move the file to `cachefile`.
    mkpath(cachepath)
    cache_objects = JLOptions().use_pkgimages != 0
    tmppath, tmpio = mktemp(cachepath)

    if cache_objects
        tmppath_o, tmpio_o = mktemp(cachepath)
        tmppath_so, tmpio_so = mktemp(cachepath)
    else
        tmppath_o = nothing
    end
    local p
    try
        close(tmpio)
        if cache_objects
            close(tmpio_o)
            close(tmpio_so)
        end
        p = create_expr_cache(pkg, path, tmppath, tmppath_o, concrete_deps, internal_stderr, internal_stdout)

        if success(p)
            if cache_objects
                # Run linker over tmppath_o
                Linking.link_image(tmppath_o, tmppath_so)
            end

            # Read preferences hash back from .ji file (we can't precompute because
            # we don't actually know what the list of compile-time preferences are without compiling)
            prefs_hash = preferences_hash(tmppath)
            cachefile = compilecache_path(pkg, prefs_hash)
            ocachefile = cache_objects ? ocachefile_from_cachefile(cachefile) : nothing

            # append checksum for so to the end of the .ji file:
            crc_so = UInt32(0)
            if cache_objects
                crc_so = open(_crc32c, tmppath_so, "r")
            end

            # append extra crc to the end of the .ji file:
            open(tmppath, "r+") do f
                if iszero(isvalid_cache_header(f))
                    error("Invalid header for $pkg in new cache file $(repr(tmppath)).")
                end
                seekend(f)
                write(f, crc_so)
                seekstart(f)
                write(f, _crc32c(f))
            end

            # inherit permission from the source file (and make them writable)
            chmod(tmppath, filemode(path) & 0o777 | 0o200)

            # prune the directory with cache files
            if pkg.uuid !== nothing
                entrypath, entryfile = cache_file_entry(pkg)
                cachefiles = filter!(x -> startswith(x, entryfile * "_") && endswith(x, ".ji"), readdir(cachepath))
                if length(cachefiles) >= MAX_NUM_PRECOMPILE_FILES[]
                    idx = findmin(mtime.(joinpath.(cachepath, cachefiles)))[2]
                    evicted_cachefile = joinpath(cachepath, cachefiles[idx])
                    @debug "Evicting file from cache" evicted_cachefile
                    rm(evicted_cachefile; force=true)
                    try
                        rm(ocachefile_from_cachefile(evicted_cachefile); force=true)
                        @static if Sys.isapple()
                            rm(ocachefile_from_cachefile(evicted_cachefile) * ".dSYM"; force=true, recursive=true)
                        end
                    catch e
                        e isa IOError || rethrow()
                    end
                end
            end

            if cache_objects
                try
                    rename(tmppath_so, ocachefile::String; force=true)
                catch e
                    e isa IOError || rethrow()
                    isfile(ocachefile::String) || rethrow()
                    # Windows prevents renaming a file that is in use so if there is a Julia session started
                    # with a package image loaded, we cannot rename that file.
                    # The code belows append a `_i` to the name of the cache file where `i` is the smallest number such that
                    # that cache file does not exist.
                    ocachename, ocacheext = splitext(ocachefile::String)
                    old_cachefiles = Set(readdir(cachepath))
                    num = 1
                    while true
                        ocachefile = ocachename * "_$num" * ocacheext
                        in(basename(ocachefile), old_cachefiles) || break
                        num += 1
                    end
                    # TODO: Risk for a race here if some other process grabs this name before us
                    cachefile = cachefile_from_ocachefile(ocachefile)
                    rename(tmppath_so, ocachefile::String; force=true)
                end
                @static if Sys.isapple()
                    run(`$(Linking.dsymutil()) $ocachefile`, Base.DevNull(), Base.DevNull(), Base.DevNull())
                end
            end
            # this is atomic according to POSIX (not Win32):
            rename(tmppath, cachefile; force=true)
            return cachefile, ocachefile
        end
    finally
        rm(tmppath, force=true)
        if cache_objects
            rm(tmppath_o::String, force=true)
            rm(tmppath_so, force=true)
        end
    end
    if p.exitcode == 125
        return PrecompilableError()
    else
        error("Failed to precompile $pkg to $(repr(tmppath)).")
    end
end

function module_build_id(m::Module)
    hi, lo = ccall(:jl_module_build_id, NTuple{2,UInt64}, (Any,), m)
    return (UInt128(hi) << 64) | lo
end

function isvalid_cache_header(f::IOStream)
    pkgimage = Ref{UInt8}()
    checksum = ccall(:jl_read_verify_header, UInt64, (Ptr{Cvoid}, Ptr{UInt8}, Ptr{Int64}, Ptr{Int64}), f.ios, pkgimage, Ref{Int64}(), Ref{Int64}()) # returns checksum id or zero

    if !iszero(checksum) && pkgimage[] != 0
        @debug "Cache header was for pkgimage"
        return UInt64(0) # We somehow read the header for a pkgimage and not a ji
    end
    return checksum
end
isvalid_file_crc(f::IOStream) = (_crc32c(seekstart(f), filesize(f) - 4) == read(f, UInt32))

function isvalid_pkgimage_crc(f::IOStream, ocachefile::String)
    seekstart(f) # TODO necessary
    seek(f, filesize(f) - 8)
    expected_crc_so = read(f, UInt32)
    crc_so = open(_crc32c, ocachefile, "r")
    expected_crc_so == crc_so
end

struct CacheHeaderIncludes
    id::PkgId
    filename::String
    mtime::Float64
    modpath::Vector{String}   # seemingly not needed in Base, but used by Revise
end

function parse_cache_header(f::IO)
    flags = read(f, UInt8)
    modules = Vector{Pair{PkgId, UInt64}}()
    while true
        n = read(f, Int32)
        n == 0 && break
        sym = String(read(f, n)) # module name
        uuid = UUID((read(f, UInt64), read(f, UInt64))) # pkg UUID
        build_id = read(f, UInt64) # build UUID (mostly just a timestamp)
        push!(modules, PkgId(uuid, sym) => build_id)
    end
    totbytes = read(f, Int64) # total bytes for file dependencies + preferences
    # read the list of requirements
    # and split the list into include and requires statements
    includes = CacheHeaderIncludes[]
    requires = Pair{PkgId, PkgId}[]
    while true
        n2 = read(f, Int32)
        totbytes -= 4
        if n2 == 0
            break
        end
        depname = String(read(f, n2))
        totbytes -= n2
        mtime = read(f, Float64)
        totbytes -= 8
        n1 = read(f, Int32)
        totbytes -= 4
        # map ids to keys
        modkey = (n1 == 0) ? PkgId("") : modules[n1].first
        modpath = String[]
        if n1 != 0
            # determine the complete module path
            while true
                n1 = read(f, Int32)
                totbytes -= 4
                if n1 == 0
                    break
                end
                push!(modpath, String(read(f, n1)))
                totbytes -= n1
            end
        end
        if depname[1] == '\0'
            push!(requires, modkey => binunpack(depname))
        else
            push!(includes, CacheHeaderIncludes(modkey, depname, mtime, modpath))
        end
    end
    prefs = String[]
    while true
        n2 = read(f, Int32)
        totbytes -= 4
        if n2 == 0
            break
        end
        push!(prefs, String(read(f, n2)))
        totbytes -= n2
    end
    prefs_hash = read(f, UInt64)
    totbytes -= 8
    srctextpos = read(f, Int64)
    totbytes -= 8
    @assert totbytes == 0 "header of cache file appears to be corrupt (totbytes == $(totbytes))"
    # read the list of modules that are required to be present during loading
    required_modules = Vector{Pair{PkgId, UInt128}}()
    while true
        n = read(f, Int32)
        n == 0 && break
        sym = String(read(f, n)) # module name
        uuid = UUID((read(f, UInt64), read(f, UInt64))) # pkg UUID
        build_id = UInt128(read(f, UInt64)) << 64
        build_id |= read(f, UInt64)
        push!(required_modules, PkgId(uuid, sym) => build_id)
    end
    l = read(f, Int32)
    clone_targets = read(f, l)

    return modules, (includes, requires), required_modules, srctextpos, prefs, prefs_hash, clone_targets, flags
end

function parse_cache_header(cachefile::String; srcfiles_only::Bool=false)
    io = open(cachefile, "r")
    try
        iszero(isvalid_cache_header(io)) && throw(ArgumentError("Invalid header in cache file $cachefile."))
        ret = parse_cache_header(io)
        srcfiles_only || return ret
        _, (includes, _), _, srctextpos, _... = ret
        srcfiles = srctext_files(io, srctextpos)
        delidx = Int[]
        for (i, chi) in enumerate(includes)
            chi.filename ∈ srcfiles || push!(delidx, i)
        end
        deleteat!(includes, delidx)
        return ret
    finally
        close(io)
    end
end

preferences_hash(f::IO) = parse_cache_header(f)[6]
function preferences_hash(cachefile::String)
    io = open(cachefile, "r")
    try
        if iszero(isvalid_cache_header(io))
            throw(ArgumentError("Invalid header in cache file $cachefile."))
        end
        return preferences_hash(io)
    finally
        close(io)
    end
end

function cache_dependencies(f::IO)
    _, (includes, _), modules, _... = parse_cache_header(f)
    return modules, map(chi -> (chi.filename, chi.mtime), includes)  # return just filename and mtime
end

function cache_dependencies(cachefile::String)
    io = open(cachefile, "r")
    try
        iszero(isvalid_cache_header(io)) && throw(ArgumentError("Invalid header in cache file $cachefile."))
        return cache_dependencies(io)
    finally
        close(io)
    end
end

function read_dependency_src(io::IO, filename::AbstractString)
    srctextpos = parse_cache_header(io)[4]
    srctextpos == 0 && error("no source-text stored in cache file")
    seek(io, srctextpos)
    return _read_dependency_src(io, filename)
end

function _read_dependency_src(io::IO, filename::AbstractString)
    while !eof(io)
        filenamelen = read(io, Int32)
        filenamelen == 0 && break
        fn = String(read(io, filenamelen))
        len = read(io, UInt64)
        if fn == filename
            return String(read(io, len))
        end
        seek(io, position(io) + len)
    end
    error(filename, " is not stored in the source-text cache")
end

function read_dependency_src(cachefile::String, filename::AbstractString)
    io = open(cachefile, "r")
    try
        iszero(isvalid_cache_header(io)) && throw(ArgumentError("Invalid header in cache file $cachefile."))
        return read_dependency_src(io, filename)
    finally
        close(io)
    end
end

function srctext_files(f::IO, srctextpos::Int64)
    files = Set{String}()
    srctextpos == 0 && return files
    seek(f, srctextpos)
    while !eof(f)
        filenamelen = read(f, Int32)
        filenamelen == 0 && break
        fn = String(read(f, filenamelen))
        len = read(f, UInt64)
        push!(files, fn)
        seek(f, position(f) + len)
    end
    return files
end

# Test to see if this UUID is mentioned in this `Project.toml`; either as
# the top-level UUID (e.g. that of the project itself), as a dependency,
# or as an extra/weakdep for Preferences.
function get_uuid_name(project::Dict{String, Any}, uuid::UUID)
    uuid_p = get(project, "uuid", nothing)::Union{Nothing, String}
    name = get(project, "name", nothing)::Union{Nothing, String}
    if name !== nothing && uuid_p !== nothing && UUID(uuid_p) == uuid
        return name
    end
    deps = get(project, "deps", nothing)::Union{Nothing, Dict{String, Any}}
    if deps !== nothing
        for (k, v) in deps
            if uuid == UUID(v::String)
                return k
            end
        end
    end
    for subkey in ("deps", "extras", "weakdeps")
        subsection = get(project, subkey, nothing)::Union{Nothing, Dict{String, Any}}
        if subsection !== nothing
            for (k, v) in subsection
                if uuid == UUID(v::String)
                    return k
                end
            end
        end
    end
    return nothing
end

function get_uuid_name(project_toml::String, uuid::UUID)
    project = parsed_toml(project_toml)
    return get_uuid_name(project, uuid)
end

# If we've asked for a specific UUID, this function will extract the prefs
# for that particular UUID.  Otherwise, it returns all preferences.
function filter_preferences(prefs::Dict{String, Any}, pkg_name)
    if pkg_name === nothing
        return prefs
    else
        return get(Dict{String, Any}, prefs, pkg_name)::Dict{String, Any}
    end
end

function collect_preferences(project_toml::String, uuid::Union{UUID,Nothing})
    # We'll return a list of dicts to be merged
    dicts = Dict{String, Any}[]

    project = parsed_toml(project_toml)
    pkg_name = nothing
    if uuid !== nothing
        # If we've been given a UUID, map that to the name of the package as
        # recorded in the preferences section.  If we can't find that mapping,
        # exit out, as it means there's no way preferences can be set for that
        # UUID, as we only allow actual dependencies to have preferences set.
        pkg_name = get_uuid_name(project, uuid)
        if pkg_name === nothing
            return dicts
        end
    end

    # Look first inside of `Project.toml` to see we have preferences embedded within there
    proj_preferences = get(Dict{String, Any}, project, "preferences")::Dict{String, Any}
    push!(dicts, filter_preferences(proj_preferences, pkg_name))

    # Next, look for `(Julia)LocalPreferences.toml` files next to this `Project.toml`
    project_dir = dirname(project_toml)
    for name in preferences_names
        toml_path = joinpath(project_dir, name)
        if isfile(toml_path)
            prefs = parsed_toml(toml_path)
            push!(dicts, filter_preferences(prefs, pkg_name))

            # If we find `JuliaLocalPreferences.toml`, don't look for `LocalPreferences.toml`
            break
        end
    end

    return dicts
end

"""
    recursive_prefs_merge(base::Dict, overrides::Dict...)

Helper function to merge preference dicts recursively, honoring overrides in nested
dictionaries properly.
"""
function recursive_prefs_merge(base::Dict{String, Any}, overrides::Dict{String, Any}...)
    new_base = Base._typeddict(base, overrides...)

    for override in overrides
        # Clear entries are keys that should be deleted from any previous setting.
        override_clear = get(override, "__clear__", nothing)
        if override_clear isa Vector{String}
            for k in override_clear
                delete!(new_base, k)
            end
        end

        for (k, override_k) in override
            # Note that if `base` has a mapping that is _not_ a `Dict`, and `override`
            new_base_k = get(new_base, k, nothing)
            if new_base_k isa Dict{String, Any} && override_k isa Dict{String, Any}
                new_base[k] = recursive_prefs_merge(new_base_k, override_k)
            else
                new_base[k] = override_k
            end
        end
    end
    return new_base
end

function get_preferences(uuid::Union{UUID,Nothing} = nothing)
    merged_prefs = Dict{String,Any}()
    for env in reverse(load_path())
        project_toml = env_project_file(env)
        if !isa(project_toml, String)
            continue
        end

        # Collect all dictionaries from the current point in the load path, then merge them in
        dicts = collect_preferences(project_toml, uuid)
        merged_prefs = recursive_prefs_merge(merged_prefs, dicts...)
    end
    return merged_prefs
end

function get_preferences_hash(uuid::Union{UUID, Nothing}, prefs_list::Vector{String})
    # Start from a predictable hash point to ensure that the same preferences always
    # hash to the same value, modulo changes in how Dictionaries are hashed.
    h = UInt(0)
    uuid === nothing && return UInt64(h)

    # Load the preferences
    prefs = get_preferences(uuid)

    # Walk through each name that's called out as a compile-time preference
    for name in prefs_list
        prefs_value = get(prefs, name, nothing)
        if prefs_value !== nothing
            h = hash(prefs_value, h)::UInt
        end
    end
    # We always return a `UInt64` so that our serialization format is stable
    return UInt64(h)
end

get_preferences_hash(m::Module, prefs_list::Vector{String}) = get_preferences_hash(PkgId(m).uuid, prefs_list)

# This is how we keep track of who is using what preferences at compile-time
const COMPILETIME_PREFERENCES = Dict{UUID,Set{String}}()

# In `Preferences.jl`, if someone calls `load_preference(@__MODULE__, key)` while we're precompiling,
# we mark that usage as a usage at compile-time and call this method, so that at the end of `.ji` generation,
# we can record the list of compile-time preferences and embed that into the `.ji` header
function record_compiletime_preference(uuid::UUID, key::String)
    pref = get!(Set{String}, COMPILETIME_PREFERENCES, uuid)
    push!(pref, key)
    return nothing
end
get_compiletime_preferences(uuid::UUID) = collect(get(Vector{String}, COMPILETIME_PREFERENCES, uuid))
get_compiletime_preferences(m::Module) = get_compiletime_preferences(PkgId(m).uuid)
get_compiletime_preferences(::Nothing) = String[]

function check_clone_targets(clone_targets)
    rejection_reason = ccall(:jl_check_pkgimage_clones, Any, (Ptr{Cchar},), clone_targets)
    if rejection_reason !== nothing
        return rejection_reason
    end
end

struct CacheFlags
    # OOICCDDP - see jl_cache_flags
    use_pkgimages::Bool
    debug_level::Int
    check_bounds::Int
    inline::Bool
    opt_level::Int

    function CacheFlags(f::UInt8)
        use_pkgimages = Bool(f & 1)
        debug_level = Int((f >> 1) & 3)
        check_bounds = Int((f >> 3) & 3)
        inline = Bool((f >> 5) & 1)
        opt_level = Int((f >> 6) & 3) # define OPT_LEVEL in statiddata_utils
        new(use_pkgimages, debug_level, check_bounds, inline, opt_level)
    end
end
CacheFlags(f::Int) = CacheFlags(UInt8(f))
CacheFlags() = CacheFlags(ccall(:jl_cache_flags, UInt8, ()))

function show(io::IO, cf::CacheFlags)
    print(io, "use_pkgimages = ", cf.use_pkgimages)
    print(io, ", debug_level = ", cf.debug_level)
    print(io, ", check_bounds = ", cf.check_bounds)
    print(io, ", inline = ", cf.inline)
    print(io, ", opt_level = ", cf.opt_level)
end

struct ImageTarget
    name::String
    flags::Int32
    ext_features::String
    features_en::Vector{UInt8}
    features_dis::Vector{UInt8}
end

function parse_image_target(io::IO)
    flags = read(io, Int32)
    nfeature = read(io, Int32)
    feature_en = read(io, 4*nfeature)
    feature_dis = read(io, 4*nfeature)
    name_len = read(io, Int32)
    name = String(read(io, name_len))
    ext_features_len = read(io, Int32)
    ext_features = String(read(io, ext_features_len))
    ImageTarget(name, flags, ext_features, feature_en, feature_dis)
end

function parse_image_targets(targets::Vector{UInt8})
    io = IOBuffer(targets)
    ntargets = read(io, Int32)
    targets = Vector{ImageTarget}(undef, ntargets)
    for i in 1:ntargets
        targets[i] = parse_image_target(io)
    end
    return targets
end

function current_image_targets()
    targets = @ccall jl_reflect_clone_targets()::Vector{UInt8}
    return parse_image_targets(targets)
end

struct FeatureName
    name::Cstring
    bit::UInt32 # bit index into a `uint32_t` array;
    llvmver::UInt32 # 0 if it is available on the oldest LLVM version we support
end

function feature_names()
    fnames = Ref{Ptr{FeatureName}}()
    nf = Ref{Csize_t}()
    @ccall jl_reflect_feature_names(fnames::Ptr{Ptr{FeatureName}}, nf::Ptr{Csize_t})::Cvoid
    if fnames[] == C_NULL
        @assert nf[] == 0
        return Vector{FeatureName}(undef, 0)
    end
    Base.unsafe_wrap(Array, fnames[], nf[], own=false)
end

function test_feature(features::Vector{UInt8}, feat::FeatureName)
    bitidx = feat.bit
    u8idx = div(bitidx, 8) + 1
    bit = bitidx % 8
    return (features[u8idx] & (1 << bit)) != 0
end

function show(io::IO, it::ImageTarget)
    print(io, it.name)
    if !isempty(it.ext_features)
        print(io, ",", it.ext_features)
    end
    print(io, "; flags=", it.flags)
    print(io, "; features_en=(")
    first = true
    for feat in feature_names()
        if test_feature(it.features_en, feat)
            name = Base.unsafe_string(feat.name)
            if first
                first = false
                print(io, name)
            else
                print(io, ", ", name)
            end
        end
    end
    print(io, ")")
    # Is feature_dis useful?
end

# Set by FileWatching.__init__()
global mkpidlock_hook
global trymkpidlock_hook
global parse_pidfile_hook

# The preferences hash is only known after precompilation so just assume no preferences.
# Also ignore the active project, which means that if all other conditions are equal,
# the same package cannot be precompiled from different projects and/or different preferences at the same time.
compilecache_pidfile_path(pkg::PkgId) = compilecache_path(pkg, UInt64(0); project="") * ".pidfile"

const compilecache_pidlock_stale_age = 10

# Allows processes to wait if another process is precompiling a given source already.
# The lock file mtime will be updated when held at most every `stale_age/2` seconds, with expected
# variance of 10 seconds or more being infrequent but not unusual.
# After `stale_age` seconds beyond the mtime of the lock file, the lock file is deleted and
# precompilation will proceed if the locking process no longer exists or after `stale_age * 5`
# seconds if the process does still exist.
# If the lock is held by another host, it will conservatively wait `stale_age * 5`
# seconds since processes cannot be checked remotely
function maybe_cachefile_lock(f, pkg::PkgId, srcpath::String; stale_age=compilecache_pidlock_stale_age)
    if @isdefined(mkpidlock_hook) && @isdefined(trymkpidlock_hook) && @isdefined(parse_pidfile_hook)
        pidfile = compilecache_pidfile_path(pkg)
        cachefile = invokelatest(trymkpidlock_hook, f, pidfile; stale_age)
        if cachefile === false
            pid, hostname, age = invokelatest(parse_pidfile_hook, pidfile)
            verbosity = isinteractive() ? CoreLogging.Info : CoreLogging.Debug
            if isempty(hostname) || hostname == gethostname()
                @logmsg verbosity "Waiting for another process (pid: $pid) to finish precompiling $pkg. Pidfile: $pidfile"
            else
                @logmsg verbosity "Waiting for another machine (hostname: $hostname, pid: $pid) to finish precompiling $pkg. Pidfile: $pidfile"
            end
            # wait until the lock is available, but don't actually acquire it
            # returning nothing indicates a process waited for another
            return invokelatest(mkpidlock_hook, Returns(nothing), pidfile; stale_age)
        end
        return cachefile
    else
        # for packages loaded before FileWatching.__init__()
        f()
    end
end
# returns true if it "cachefile.ji" is stale relative to "modpath.jl" and build_id for modkey
# otherwise returns the list of dependencies to also check
@constprop :none function stale_cachefile(modpath::String, cachefile::String; ignore_loaded::Bool = false)
    return stale_cachefile(PkgId(""), UInt128(0), modpath, cachefile; ignore_loaded)
end
@constprop :none function stale_cachefile(modkey::PkgId, build_id::UInt128, modpath::String, cachefile::String; ignore_loaded::Bool = false)
    io = open(cachefile, "r")
    try
        checksum = isvalid_cache_header(io)
        if iszero(checksum)
            @debug "Rejecting cache file $cachefile due to it containing an invalid cache header"
            return true # invalid cache file
        end
        modules, (includes, requires), required_modules, srctextpos, prefs, prefs_hash, clone_targets, flags = parse_cache_header(io)
        if isempty(modules)
            return true # ignore empty file
        end
        if ccall(:jl_match_cache_flags, UInt8, (UInt8,), flags) == 0
            @debug """
            Rejecting cache file $cachefile for $modkey since the flags are mismatched
              current session: $(CacheFlags())
              cache file:      $(CacheFlags(flags))
            """
            return true
        end
        pkgimage = !isempty(clone_targets)
        if pkgimage
            ocachefile = ocachefile_from_cachefile(cachefile)
            if JLOptions().use_pkgimages == 0
                # presence of clone_targets means native code cache
                @debug "Rejecting cache file $cachefile for $modkey since it would require usage of pkgimage"
                return true
            end
            rejection_reasons = check_clone_targets(clone_targets)
            if !isnothing(rejection_reasons)
                @debug("Rejecting cache file $cachefile for $modkey:",
                    Reasons=rejection_reasons,
                    var"Image Targets"=parse_image_targets(clone_targets),
                    var"Current Targets"=current_image_targets())
                return true
            end
            if !isfile(ocachefile)
                @debug "Rejecting cache file $cachefile for $modkey since pkgimage $ocachefile was not found"
                return true
            end
        else
            ocachefile = nothing
        end
        id = first(modules)
        if id.first != modkey && modkey != PkgId("")
            @debug "Rejecting cache file $cachefile for $modkey since it is for $id instead"
            return true
        end
        if build_id != UInt128(0)
            id_build = (UInt128(checksum) << 64) | id.second
            if id_build != build_id
                @debug "Ignoring cache file $cachefile for $modkey ($((UUID(id_build)))) since it is does not provide desired build_id ($((UUID(build_id))))"
                return true
            end
        end
        id = id.first
        modules = Dict{PkgId, UInt64}(modules)

        # Check if transitive dependencies can be fulfilled
        ndeps = length(required_modules)
        depmods = Vector{Any}(undef, ndeps)
        for i in 1:ndeps
            req_key, req_build_id = required_modules[i]
            # Module is already loaded
            if root_module_exists(req_key)
                M = root_module(req_key)
                if PkgId(M) == req_key && module_build_id(M) === req_build_id
                    depmods[i] = M
                elseif ignore_loaded
                    # Used by Pkg.precompile given that there it's ok to precompile different versions of loaded packages
                    @goto locate_branch
                else
                    @debug "Rejecting cache file $cachefile because module $req_key is already loaded and incompatible."
                    return true # Won't be able to fulfill dependency
                end
            else
                @label locate_branch
                path = locate_package(req_key)
                if path === nothing
                    @debug "Rejecting cache file $cachefile because dependency $req_key not found."
                    return true # Won't be able to fulfill dependency
                end
                depmods[i] = (path, req_key, req_build_id)
            end
        end

        # check if this file is going to provide one of our concrete dependencies
        # or if it provides a version that conflicts with our concrete dependencies
        # or neither
        skip_timecheck = false
        for (req_key, req_build_id) in _concrete_dependencies
            build_id = get(modules, req_key, UInt64(0))
            if build_id !== UInt64(0)
                build_id |= UInt128(checksum) << 64
                if build_id === req_build_id
                    skip_timecheck = true
                    break
                end
                @debug "Rejecting cache file $cachefile because it provides the wrong build_id (got $((UUID(build_id)))) for $req_key (want $(UUID(req_build_id)))"
                return true # cachefile doesn't provide the required version of the dependency
            end
        end

        # now check if this file is fresh relative to its source files
        if !skip_timecheck
            if !samefile(includes[1].filename, modpath) && !samefile(fixup_stdlib_path(includes[1].filename), modpath)
                @debug "Rejecting cache file $cachefile because it is for file $(includes[1].filename) not file $modpath"
                return true # cache file was compiled from a different path
            end
            for (modkey, req_modkey) in requires
                # verify that `require(modkey, name(req_modkey))` ==> `req_modkey`
                if identify_package(modkey, req_modkey.name) != req_modkey
                    @debug "Rejecting cache file $cachefile because uuid mapping for $modkey => $req_modkey has changed"
                    return true
                end
            end
            for chi in includes
                f, ftime_req = chi.filename, chi.mtime
                if !ispath(f)
                    _f = fixup_stdlib_path(f)
                    if isfile(_f) && startswith(_f, Sys.STDLIB)
                        # mtime is changed by extraction
                        @debug "Skipping mtime check for file $f used by $cachefile, since it is a stdlib"
                        continue
                    end
                    @debug "Rejecting stale cache file $cachefile because file $f does not exist"
                    return true
                end
                ftime = mtime(f)
                is_stale = ( ftime != ftime_req ) &&
                           ( ftime != floor(ftime_req) ) &&           # Issue #13606, PR #13613: compensate for Docker images rounding mtimes
                           ( ftime != ceil(ftime_req) ) &&            # PR: #47433 Compensate for CirceCI's truncating of timestamps in its caching
                           ( ftime != trunc(ftime_req, digits=6) ) && # Issue #20837, PR #20840: compensate for GlusterFS truncating mtimes to microseconds
                           ( ftime != 1.0 )  &&                       # PR #43090: provide compatibility with Nix mtime.
                           !( 0 < (ftime_req - ftime) < 1e-6 )        # PR #45552: Compensate for Windows tar giving mtimes that may be incorrect by up to one microsecond
                if is_stale
                    @debug "Rejecting stale cache file $cachefile (mtime $ftime_req) because file $f (mtime $ftime) has changed"
                    return true
                end
            end
        end

        if !isvalid_file_crc(io)
            @debug "Rejecting cache file $cachefile because it has an invalid checksum"
            return true
        end

        if pkgimage
            if !isvalid_pkgimage_crc(io, ocachefile::String)
                @debug "Rejecting cache file $cachefile because $ocachefile has an invalid checksum"
                return true
            end
        end

        curr_prefs_hash = get_preferences_hash(id.uuid, prefs)
        if prefs_hash != curr_prefs_hash
            @debug "Rejecting cache file $cachefile because preferences hash does not match 0x$(string(prefs_hash, base=16)) != 0x$(string(curr_prefs_hash, base=16))"
            return true
        end

        return depmods, ocachefile # fresh cachefile
    finally
        close(io)
    end
end

"""
    @__FILE__ -> String

Expand to a string with the path to the file containing the
macrocall, or an empty string if evaluated by `julia -e <expr>`.
Return `nothing` if the macro was missing parser source information.
Alternatively see [`PROGRAM_FILE`](@ref).
"""
macro __FILE__()
    __source__.file === nothing && return nothing
    return String(__source__.file::Symbol)
end

"""
    @__DIR__ -> String

Expand to a string with the absolute path to the directory of the file
containing the macrocall.
Return the current working directory if run from a REPL or if evaluated by `julia -e <expr>`.
"""
macro __DIR__()
    __source__.file === nothing && return nothing
    _dirname = dirname(String(__source__.file::Symbol))
    return isempty(_dirname) ? pwd() : abspath(_dirname)
end

"""
    precompile(f, argtypes::Tuple{Vararg{Any}})

Compile the given function `f` for the argument tuple (of types) `argtypes`, but do not execute it.
"""
function precompile(@nospecialize(f), @nospecialize(argtypes::Tuple))
    precompile(Tuple{Core.Typeof(f), argtypes...})
end

const ENABLE_PRECOMPILE_WARNINGS = Ref(false)
function precompile(@nospecialize(argt::Type))
    ret = ccall(:jl_compile_hint, Int32, (Any,), argt) != 0
    if !ret && ENABLE_PRECOMPILE_WARNINGS[]
        @warn "Inactive precompile statement" maxlog=100 form=argt _module=nothing _file=nothing _line=0
    end
    return ret
end

# Variants that work for `invoke`d calls for which the signature may not be sufficient
precompile(mi::Core.MethodInstance, world::UInt=get_world_counter()) =
    (ccall(:jl_compile_method_instance, Cvoid, (Any, Any, UInt), mi, C_NULL, world); return true)

"""
    precompile(f, argtypes::Tuple{Vararg{Any}}, m::Method)

Precompile a specific method for the given argument types. This may be used to precompile
a different method than the one that would ordinarily be chosen by dispatch, thus
mimicking `invoke`.
"""
function precompile(@nospecialize(f), @nospecialize(argtypes::Tuple), m::Method)
    precompile(Tuple{Core.Typeof(f), argtypes...}, m)
end

function precompile(@nospecialize(argt::Type), m::Method)
    atype, sparams = ccall(:jl_type_intersection_with_env, Any, (Any, Any), argt, m.sig)::SimpleVector
    mi = Core.Compiler.specialize_method(m, atype, sparams)
    return precompile(mi)
end

precompile(include_package_for_output, (PkgId, String, Vector{String}, Vector{String}, Vector{String}, typeof(_concrete_dependencies), Nothing))
precompile(include_package_for_output, (PkgId, String, Vector{String}, Vector{String}, Vector{String}, typeof(_concrete_dependencies), String))
precompile(create_expr_cache, (PkgId, String, String, String, typeof(_concrete_dependencies), IO, IO))
precompile(create_expr_cache, (PkgId, String, String, Nothing, typeof(_concrete_dependencies), IO, IO))
M   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/timing.jl�?      # This file is a part of Julia. License is MIT: https://julialang.org/license

# This type must be kept in sync with the C struct in src/gc.h
struct GC_Num
    allocd          ::Int64 # GC internal
    deferred_alloc  ::Int64 # GC internal
    freed           ::Int64 # GC internal
    malloc          ::Int64
    realloc         ::Int64
    poolalloc       ::Int64
    bigalloc        ::Int64
    freecall        ::Int64
    total_time      ::Int64
    total_allocd    ::Int64 # GC internal
    collect         ::Csize_t # GC internal
    pause           ::Cint
    full_sweep      ::Cint
    max_pause       ::Int64
    max_memory      ::Int64
    time_to_safepoint           ::Int64
    max_time_to_safepoint       ::Int64
    total_time_to_safepoint     ::Int64
    sweep_time      ::Int64
    mark_time       ::Int64
    total_sweep_time  ::Int64
    total_mark_time   ::Int64
    last_full_sweep ::Int64
end

gc_num() = ccall(:jl_gc_num, GC_Num, ())
reset_gc_stats() = ccall(:jl_gc_reset_stats, Cvoid, ())

# This type is to represent differences in the counters, so fields may be negative
struct GC_Diff
    allocd      ::Int64 # Bytes allocated
    malloc      ::Int64 # Number of GC aware malloc()
    realloc     ::Int64 # Number of GC aware realloc()
    poolalloc   ::Int64 # Number of pool allocation
    bigalloc    ::Int64 # Number of big (non-pool) allocation
    freecall    ::Int64 # Number of GC aware free()
    total_time  ::Int64 # Time spent in garbage collection
    pause       ::Int64 # Number of GC pauses
    full_sweep  ::Int64 # Number of GC full collection
end

gc_total_bytes(gc_num::GC_Num) =
    gc_num.allocd + gc_num.deferred_alloc + gc_num.total_allocd

function GC_Diff(new::GC_Num, old::GC_Num)
    # logic from `src/gc.c:jl_gc_total_bytes`
    old_allocd = gc_total_bytes(old)
    new_allocd = gc_total_bytes(new)
    return GC_Diff(new_allocd       - old_allocd,
                   new.malloc       - old.malloc,
                   new.realloc      - old.realloc,
                   new.poolalloc    - old.poolalloc,
                   new.bigalloc     - old.bigalloc,
                   new.freecall     - old.freecall,
                   new.total_time   - old.total_time,
                   new.pause        - old.pause,
                   new.full_sweep   - old.full_sweep)
end

function gc_alloc_count(diff::GC_Diff)
    diff.malloc + diff.realloc + diff.poolalloc + diff.bigalloc
end

# cumulative total time spent on compilation and recompilation, in nanoseconds
function cumulative_compile_time_ns()
    comp = ccall(:jl_cumulative_compile_time_ns, UInt64, ())
    recomp = ccall(:jl_cumulative_recompile_time_ns, UInt64, ())
    return comp, recomp
end

function cumulative_compile_timing(b::Bool)
    if b
        ccall(:jl_cumulative_compile_timing_enable, Cvoid, ())
    else
        ccall(:jl_cumulative_compile_timing_disable, Cvoid, ())
    end
    return
end

# total time spend in garbage collection, in nanoseconds
gc_time_ns() = ccall(:jl_gc_total_hrtime, UInt64, ())

"""
    Base.gc_live_bytes()

Return the total size (in bytes) of objects currently in memory.
This is computed as the total size of live objects after
the last garbage collection, plus the number of bytes allocated
since then.
"""
function gc_live_bytes()
    num = gc_num()
    Int(ccall(:jl_gc_live_bytes, Int64, ())) + num.allocd + num.deferred_alloc
end

"""
    Base.jit_total_bytes()

Return the total amount (in bytes) allocated by the just-in-time compiler
for e.g. native code and data.
"""
function jit_total_bytes()
    return ccall(:jl_jit_total_bytes, Csize_t, ())
end

# print elapsed time, return expression value
const _mem_units = ["byte", "KiB", "MiB", "GiB", "TiB", "PiB"]
const _cnt_units = ["", " k", " M", " G", " T", " P"]
function prettyprint_getunits(value, numunits, factor)
    if value == 0 || value == 1
        return (value, 1)
    end
    unit = ceil(Int, log(value) / log(factor))
    unit = min(numunits, unit)
    number = value/factor^(unit-1)
    return number, unit
end

function padded_nonzero_print(value, str, always_print = true)
    if always_print || value != 0
        blanks = "                "[1:(19 - length(str))]
        println(str, ":", blanks, value)
    end
end

function format_bytes(bytes) # also used by InteractiveUtils
    bytes, mb = prettyprint_getunits(bytes, length(_mem_units), Int64(1024))
    if mb == 1
        return string(Int(bytes), " ", _mem_units[mb], bytes==1 ? "" : "s")
    else
        return string(Ryu.writefixed(Float64(bytes), 3), " ", _mem_units[mb])
    end
end

function time_print(io::IO, elapsedtime, bytes=0, gctime=0, allocs=0, compile_time=0, recompile_time=0, newline=false; msg::Union{String,Nothing}=nothing)
    timestr = Ryu.writefixed(Float64(elapsedtime/1e9), 6)
    str = sprint() do io
        if msg isa String
            print(io, msg, ": ")
        else
            print(io, length(timestr) < 10 ? (" "^(10 - length(timestr))) : "")
        end
        print(io, timestr, " seconds")
        parens = bytes != 0 || allocs != 0 || gctime > 0 || compile_time > 0
        parens && print(io, " (")
        if bytes != 0 || allocs != 0
            allocs, ma = prettyprint_getunits(allocs, length(_cnt_units), Int64(1000))
            if ma == 1
                print(io, Int(allocs), _cnt_units[ma], allocs==1 ? " allocation: " : " allocations: ")
            else
                print(io, Ryu.writefixed(Float64(allocs), 2), _cnt_units[ma], " allocations: ")
            end
            print(io, format_bytes(bytes))
        end
        if gctime > 0
            if bytes != 0 || allocs != 0
                print(io, ", ")
            end
            print(io, Ryu.writefixed(Float64(100*gctime/elapsedtime), 2), "% gc time")
        end
        if compile_time > 0
            if bytes != 0 || allocs != 0 || gctime > 0
                print(io, ", ")
            end
            print(io, Ryu.writefixed(Float64(100*compile_time/elapsedtime), 2), "% compilation time")
        end
        if recompile_time > 0
            perc = Float64(100 * recompile_time / compile_time)
            # use "<1" to avoid the confusing UX of reporting 0% when it's >0%
            print(io, ": ", perc < 1 ? "<1" : Ryu.writefixed(perc, 0), "% of which was recompilation")
        end
        parens && print(io, ")")
        newline && print(io, "\n")
    end
    print(io, str)
    nothing
end

function timev_print(elapsedtime, diff::GC_Diff, compile_times; msg::Union{String,Nothing}=nothing)
    allocs = gc_alloc_count(diff)
    compile_time = first(compile_times)
    recompile_time = last(compile_times)
    time_print(stdout, elapsedtime, diff.allocd, diff.total_time, allocs, compile_time, recompile_time, true; msg)
    padded_nonzero_print(elapsedtime,       "elapsed time (ns)")
    padded_nonzero_print(diff.total_time,   "gc time (ns)")
    padded_nonzero_print(diff.allocd,       "bytes allocated")
    padded_nonzero_print(diff.poolalloc,    "pool allocs")
    padded_nonzero_print(diff.bigalloc,     "non-pool GC allocs")
    padded_nonzero_print(diff.malloc,       "malloc() calls", false)
    padded_nonzero_print(diff.realloc,      "realloc() calls", false)
    # always print number of frees if there are mallocs
    padded_nonzero_print(diff.freecall,     "free() calls", diff.malloc > 0)
    minor_collects = diff.pause - diff.full_sweep
    padded_nonzero_print(minor_collects,    "minor collections")
    padded_nonzero_print(diff.full_sweep,   "full collections")
end

# Like a try-finally block, except without introducing the try scope
# NOTE: This is deprecated and should not be used from user logic. A proper solution to
# this problem will be introduced in https://github.com/JuliaLang/julia/pull/39217
macro __tryfinally(ex, fin)
    Expr(:tryfinally,
       :($(esc(ex))),
       :($(esc(fin)))
       )
end

"""
    @time expr
    @time "description" expr

A macro to execute an expression, printing the time it took to execute, the number of
allocations, and the total number of bytes its execution caused to be allocated, before
returning the value of the expression. Any time spent garbage collecting (gc), compiling
new code, or recompiling invalidated code is shown as a percentage.

Optionally provide a description string to print before the time report.

In some cases the system will look inside the `@time` expression and compile some of the
called code before execution of the top-level expression begins. When that happens, some
compilation time will not be counted. To include this time you can run `@time @eval ...`.

See also [`@showtime`](@ref), [`@timev`](@ref), [`@timed`](@ref), [`@elapsed`](@ref),
[`@allocated`](@ref), and [`@allocations`](@ref).

!!! note
    For more serious benchmarking, consider the `@btime` macro from the BenchmarkTools.jl
    package which among other things evaluates the function multiple times in order to
    reduce noise.

!!! compat "Julia 1.8"
    The option to add a description was introduced in Julia 1.8.

    Recompilation time being shown separately from compilation time was introduced in Julia 1.8

```julia-repl
julia> x = rand(10,10);

julia> @time x * x;
  0.606588 seconds (2.19 M allocations: 116.555 MiB, 3.75% gc time, 99.94% compilation time)

julia> @time x * x;
  0.000009 seconds (1 allocation: 896 bytes)

julia> @time begin
           sleep(0.3)
           1+1
       end
  0.301395 seconds (8 allocations: 336 bytes)
2

julia> @time "A one second sleep" sleep(1)
A one second sleep: 1.005750 seconds (5 allocations: 144 bytes)

julia> for loop in 1:3
            @time loop sleep(1)
        end
1: 1.006760 seconds (5 allocations: 144 bytes)
2: 1.001263 seconds (5 allocations: 144 bytes)
3: 1.003676 seconds (5 allocations: 144 bytes)
```
"""
macro time(ex)
    quote
        @time nothing $(esc(ex))
    end
end
macro time(msg, ex)
    quote
        Experimental.@force_compile
        local stats = gc_num()
        local elapsedtime = time_ns()
        cumulative_compile_timing(true)
        local compile_elapsedtimes = cumulative_compile_time_ns()
        local val = @__tryfinally($(esc(ex)),
            (elapsedtime = time_ns() - elapsedtime;
            cumulative_compile_timing(false);
            compile_elapsedtimes = cumulative_compile_time_ns() .- compile_elapsedtimes)
        )
        local diff = GC_Diff(gc_num(), stats)
        local _msg = $(esc(msg))
        time_print(stdout, elapsedtime, diff.allocd, diff.total_time, gc_alloc_count(diff), first(compile_elapsedtimes), last(compile_elapsedtimes), true; msg=_msg)
        val
    end
end

"""
    @showtime expr

Like `@time` but also prints the expression being evaluated for reference.

!!! compat "Julia 1.8"
    This macro was added in Julia 1.8.

See also [`@time`](@ref).

```julia-repl
julia> @showtime sleep(1)
sleep(1): 1.002164 seconds (4 allocations: 128 bytes)
```
"""
macro showtime(ex)
    quote
        @time $(sprint(show_unquoted,ex)) $(esc(ex))
    end
end

"""
    @timev expr
    @timev "description" expr

This is a verbose version of the `@time` macro. It first prints the same information as
`@time`, then any non-zero memory allocation counters, and then returns the value of the
expression.

Optionally provide a description string to print before the time report.

!!! compat "Julia 1.8"
    The option to add a description was introduced in Julia 1.8.

See also [`@time`](@ref), [`@timed`](@ref), [`@elapsed`](@ref),
[`@allocated`](@ref), and [`@allocations`](@ref).

```julia-repl
julia> x = rand(10,10);

julia> @timev x * x;
  0.546770 seconds (2.20 M allocations: 116.632 MiB, 4.23% gc time, 99.94% compilation time)
elapsed time (ns): 546769547
gc time (ns):      23115606
bytes allocated:   122297811
pool allocs:       2197930
non-pool GC allocs:1327
malloc() calls:    36
realloc() calls:   5
GC pauses:         3

julia> @timev x * x;
  0.000010 seconds (1 allocation: 896 bytes)
elapsed time (ns): 9848
bytes allocated:   896
pool allocs:       1
```
"""
macro timev(ex)
    quote
        @timev nothing $(esc(ex))
    end
end
macro timev(msg, ex)
    quote
        Experimental.@force_compile
        local stats = gc_num()
        local elapsedtime = time_ns()
        cumulative_compile_timing(true)
        local compile_elapsedtimes = cumulative_compile_time_ns()
        local val = @__tryfinally($(esc(ex)),
            (elapsedtime = time_ns() - elapsedtime;
            cumulative_compile_timing(false);
            compile_elapsedtimes = cumulative_compile_time_ns() .- compile_elapsedtimes)
        )
        local diff = GC_Diff(gc_num(), stats)
        local _msg = $(esc(msg))
        timev_print(elapsedtime, diff, compile_elapsedtimes; msg=_msg)
        val
    end
end

"""
    @elapsed

A macro to evaluate an expression, discarding the resulting value, instead returning the
number of seconds it took to execute as a floating-point number.

In some cases the system will look inside the `@elapsed` expression and compile some of the
called code before execution of the top-level expression begins. When that happens, some
compilation time will not be counted. To include this time you can run `@elapsed @eval ...`.

See also [`@time`](@ref), [`@timev`](@ref), [`@timed`](@ref),
[`@allocated`](@ref), and [`@allocations`](@ref).

```julia-repl
julia> @elapsed sleep(0.3)
0.301391426
```
"""
macro elapsed(ex)
    quote
        Experimental.@force_compile
        local t0 = time_ns()
        $(esc(ex))
        (time_ns() - t0) / 1e9
    end
end

# total number of bytes allocated so far
gc_bytes(b::Ref{Int64}) = ccall(:jl_gc_get_total_bytes, Cvoid, (Ptr{Int64},), b)
# NOTE: gc_bytes() is deprecated
function gc_bytes()
    b = Ref{Int64}()
    gc_bytes(b)
    b[]
end

"""
    @allocated

A macro to evaluate an expression, discarding the resulting value, instead returning the
total number of bytes allocated during evaluation of the expression.

See also [`@allocations`](@ref), [`@time`](@ref), [`@timev`](@ref), [`@timed`](@ref),
and [`@elapsed`](@ref).

```julia-repl
julia> @allocated rand(10^6)
8000080
```
"""
macro allocated(ex)
    quote
        Experimental.@force_compile
        local b0 = Ref{Int64}(0)
        local b1 = Ref{Int64}(0)
        gc_bytes(b0)
        $(esc(ex))
        gc_bytes(b1)
        b1[] - b0[]
    end
end

"""
    @allocations

A macro to evaluate an expression, discard the resulting value, and instead return the
total number of allocations during evaluation of the expression.

See also [`@allocated`](@ref), [`@time`](@ref), [`@timev`](@ref), [`@timed`](@ref),
and [`@elapsed`](@ref).

```julia-repl
julia> @allocations rand(10^6)
2
```

!!! compat "Julia 1.9"
    This macro was added in Julia 1.9.
"""
macro allocations(ex)
    quote
        Experimental.@force_compile
        local stats = Base.gc_num()
        $(esc(ex))
        local diff = Base.GC_Diff(Base.gc_num(), stats)
        Base.gc_alloc_count(diff)
    end
end

"""
    @timed

A macro to execute an expression, and return the value of the expression, elapsed time,
total bytes allocated, garbage collection time, and an object with various memory allocation
counters.

In some cases the system will look inside the `@timed` expression and compile some of the
called code before execution of the top-level expression begins. When that happens, some
compilation time will not be counted. To include this time you can run `@timed @eval ...`.

See also [`@time`](@ref), [`@timev`](@ref), [`@elapsed`](@ref),
[`@allocated`](@ref), and [`@allocations`](@ref).

```julia-repl
julia> stats = @timed rand(10^6);

julia> stats.time
0.006634834

julia> stats.bytes
8000256

julia> stats.gctime
0.0055765

julia> propertynames(stats.gcstats)
(:allocd, :malloc, :realloc, :poolalloc, :bigalloc, :freecall, :total_time, :pause, :full_sweep)

julia> stats.gcstats.total_time
5576500
```

!!! compat "Julia 1.5"
    The return type of this macro was changed from `Tuple` to `NamedTuple` in Julia 1.5.
"""
macro timed(ex)
    quote
        Experimental.@force_compile
        local stats = gc_num()
        local elapsedtime = time_ns()
        local val = $(esc(ex))
        elapsedtime = time_ns() - elapsedtime
        local diff = GC_Diff(gc_num(), stats)
        (value=val, time=elapsedtime/1e9, bytes=diff.allocd, gctime=diff.total_time/1e9, gcstats=diff)
    end
end
K   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/util.jl2q      # This file is a part of Julia. License is MIT: https://julialang.org/license

## printing with color ##

const text_colors = Dict{Union{Symbol,Int},String}(
    :black         => "\033[30m",
    :red           => "\033[31m",
    :green         => "\033[32m",
    :yellow        => "\033[33m",
    :blue          => "\033[34m",
    :magenta       => "\033[35m",
    :cyan          => "\033[36m",
    :white         => "\033[37m",
    :light_black   => "\033[90m", # gray
    :light_red     => "\033[91m",
    :light_green   => "\033[92m",
    :light_yellow  => "\033[93m",
    :light_blue    => "\033[94m",
    :light_magenta => "\033[95m",
    :light_cyan    => "\033[96m",
    :light_white   => "\033[97m",
    :normal        => "\033[0m",
    :default       => "\033[39m",
    :bold          => "\033[1m",
    :italic        => "\033[3m",
    :underline     => "\033[4m",
    :blink         => "\033[5m",
    :reverse       => "\033[7m",
    :hidden        => "\033[8m",
    :nothing       => "",
)

for i in 0:255
    text_colors[i] = "\033[38;5;$(i)m"
end

const disable_text_style = Dict{Symbol,String}(
    :bold      => "\033[22m",
    :italic    => "\033[23m",
    :underline => "\033[24m",
    :blink     => "\033[25m",
    :reverse   => "\033[27m",
    :hidden    => "\033[28m",
    :normal    => "",
    :default   => "",
    :nothing   => "",
)

# Create a docstring with an automatically generated list
# of colors.
let color_syms = collect(Iterators.filter(x -> !isa(x, Integer), keys(text_colors))),
    formatting_syms = [:normal, :bold, :italic, :default]
    global const available_text_colors = cat(
        sort!(intersect(color_syms, formatting_syms), rev=true),
        sort!(setdiff(  color_syms, formatting_syms));
        dims=1)
end

const available_text_colors_docstring =
    string(join([string("`:", key,"`")
                 for key in available_text_colors], ",\n", ", or \n"))

"""Dictionary of color codes for the terminal.

Available colors are: $available_text_colors_docstring as well as the integers 0 to 255 inclusive.

The color `:default` will print text in the default color while the color `:normal`
will print text with all text properties (like boldness) reset.
Printing with the color `:nothing` will print the string without modifications.
"""
text_colors

function with_output_color(@nospecialize(f::Function), color::Union{Int, Symbol}, io::IO, args...;
        bold::Bool = false, italic::Bool = false, underline::Bool = false, blink::Bool = false,
        reverse::Bool = false, hidden::Bool = false)
    buf = IOBuffer()
    iscolor = get(io, :color, false)::Bool
    try f(IOContext(buf, io), args...)
    finally
        str = String(take!(buf))
        if !iscolor
            print(io, str)
        else
            bold && color === :bold && (color = :nothing)
            italic && color === :italic && (color = :nothing)
            underline && color === :underline && (color = :nothing)
            blink && color === :blink && (color = :nothing)
            reverse && color === :reverse && (color = :nothing)
            hidden && color === :hidden && (color = :nothing)
            enable_ansi  = get(text_colors, color, text_colors[:default]) *
                               (bold ? text_colors[:bold] : "") *
                               (italic ? text_colors[:italic] : "") *
                               (underline ? text_colors[:underline] : "") *
                               (blink ? text_colors[:blink] : "") *
                               (reverse ? text_colors[:reverse] : "") *
                               (hidden ? text_colors[:hidden] : "")

            disable_ansi = (hidden ? disable_text_style[:hidden] : "") *
                           (reverse ? disable_text_style[:reverse] : "") *
                           (blink ? disable_text_style[:blink] : "") *
                           (underline ? disable_text_style[:underline] : "") *
                           (bold ? disable_text_style[:bold] : "") *
                           (italic ? disable_text_style[:italic] : "") *
                               get(disable_text_style, color, text_colors[:default])
            first = true
            for line in eachsplit(str, '\n')
                first || print(buf, '\n')
                first = false
                isempty(line) && continue
                print(buf, enable_ansi, line, disable_ansi)
            end
            print(io, String(take!(buf)))
        end
    end
end

"""
    printstyled([io], xs...; bold::Bool=false, italic::Bool=false, underline::Bool=false, blink::Bool=false, reverse::Bool=false, hidden::Bool=false, color::Union{Symbol,Int}=:normal)

Print `xs` in a color specified as a symbol or integer, optionally in bold.

Keyword `color` may take any of the values $(Base.available_text_colors_docstring)
or an integer between 0 and 255 inclusive. Note that not all terminals support 256 colors.

Keywords `bold=true`, `italic=true`, `underline=true`, `blink=true` are self-explanatory.
Keyword `reverse=true` prints with foreground and background colors exchanged,
and `hidden=true` should be invisible in the terminal but can still be copied.
These properties can be used in any combination.

See also [`print`](@ref), [`println`](@ref), [`show`](@ref).

!!! note
    Not all terminals support italic output. Some terminals interpret italic as reverse or
    blink.

!!! compat "Julia 1.7"
    Keywords except `color` and `bold` were added in Julia 1.7.
!!! compat "Julia 1.10"
    Support for italic output was added in Julia 1.10.
"""
@constprop :none printstyled(io::IO, msg...; bold::Bool=false, italic::Bool=false, underline::Bool=false, blink::Bool=false, reverse::Bool=false, hidden::Bool=false, color::Union{Int,Symbol}=:normal) =
    with_output_color(print, color, io, msg...; bold=bold, italic=italic, underline=underline, blink=blink, reverse=reverse, hidden=hidden)
@constprop :none printstyled(msg...; bold::Bool=false, italic::Bool=false, underline::Bool=false, blink::Bool=false, reverse::Bool=false, hidden::Bool=false, color::Union{Int,Symbol}=:normal) =
    printstyled(stdout, msg...; bold=bold, italic=italic, underline=underline, blink=blink, reverse=reverse, hidden=hidden, color=color)

"""
    Base.julia_cmd(juliapath=joinpath(Sys.BINDIR, julia_exename()); cpu_target::Union{Nothing,String}=nothing)

Return a julia command similar to the one of the running process.
Propagates any of the `--cpu-target`, `--sysimage`, `--compile`, `--sysimage-native-code`,
`--compiled-modules`, `--pkgimages`, `--inline`, `--check-bounds`, `--optimize`, `--min-optlevel`, `-g`,
`--code-coverage`, `--track-allocation`, `--color`, `--startup-file`, and `--depwarn`
command line arguments that are not at their default values.

Among others, `--math-mode`, `--warn-overwrite`, and `--trace-compile` are notably not propagated currently.

Unless set to `nothing`, the `cpu_target` keyword argument can be used to override the CPU target set for the running process.

To get the julia command without propagated command line arguments, `julia_cmd()[1]` can be used.

!!! compat "Julia 1.1"
    Only the `--cpu-target`, `--sysimage`, `--depwarn`, `--compile` and `--check-bounds` flags were propagated before Julia 1.1.

!!! compat "Julia 1.5"
    The flags `--color` and `--startup-file` were added in Julia 1.5.

!!! compat "Julia 1.9"
    The keyword argument `cpu_target` was added.

    The flag `--pkgimages` was added in Julia 1.9.
"""
function julia_cmd(julia=joinpath(Sys.BINDIR, julia_exename()); cpu_target::Union{Nothing,String} = nothing)
    opts = JLOptions()
    if cpu_target === nothing
        cpu_target = unsafe_string(opts.cpu_target)
    end
    image_file = unsafe_string(opts.image_file)
    addflags = String[]
    let compile = if opts.compile_enabled == 0
                      "no"
                  elseif opts.compile_enabled == 2
                      "all"
                  elseif opts.compile_enabled == 3
                      "min"
                  else
                      "" # default = "yes"
                  end
        isempty(compile) || push!(addflags, "--compile=$compile")
    end
    let depwarn = if opts.depwarn == 1
                      "yes"
                  elseif opts.depwarn == 2
                      "error"
                  else
                      "" # default = "no"
                  end
        isempty(depwarn) || push!(addflags, "--depwarn=$depwarn")
    end
    let check_bounds = if opts.check_bounds == 1
                      "yes" # on
                  elseif opts.check_bounds == 2
                      "no" # off
                  else
                      "" # default = "auto"
                  end
        isempty(check_bounds) || push!(addflags, "--check-bounds=$check_bounds")
    end
    opts.can_inline == 0 && push!(addflags, "--inline=no")
    opts.use_compiled_modules == 0 && push!(addflags, "--compiled-modules=no")
    opts.opt_level == 2 || push!(addflags, "-O$(opts.opt_level)")
    opts.opt_level_min == 0 || push!(addflags, "--min-optlevel=$(opts.opt_level_min)")
    push!(addflags, "-g$(opts.debug_level)")
    if opts.code_coverage != 0
        # Forward the code-coverage flag only if applicable (if the filename is pid-dependent)
        coverage_file = (opts.output_code_coverage != C_NULL) ?  unsafe_string(opts.output_code_coverage) : ""
        if isempty(coverage_file) || occursin("%p", coverage_file)
            if opts.code_coverage == 1
                push!(addflags, "--code-coverage=user")
            elseif opts.code_coverage == 2
                push!(addflags, "--code-coverage=all")
            elseif opts.code_coverage == 3
                push!(addflags, "--code-coverage=@$(unsafe_string(opts.tracked_path))")
            end
            isempty(coverage_file) || push!(addflags, "--code-coverage=$coverage_file")
        end
    end
    if opts.malloc_log == 1
        push!(addflags, "--track-allocation=user")
    elseif opts.malloc_log == 2
        push!(addflags, "--track-allocation=all")
    elseif opts.malloc_log == 3
        push!(addflags, "--track-allocation=@$(unsafe_string(opts.tracked_path))")
    end
    if opts.color == 1
        push!(addflags, "--color=yes")
    elseif opts.color == 2
        push!(addflags, "--color=no")
    end
    if opts.startupfile == 2
        push!(addflags, "--startup-file=no")
    end
    if opts.use_sysimage_native_code == 0
        push!(addflags, "--sysimage-native-code=no")
    end
    if opts.use_pkgimages == 0
        push!(addflags, "--pkgimages=no")
    else
        # If pkgimage is set, malloc_log and code_coverage should not
        @assert opts.malloc_log == 0 && opts.code_coverage == 0
    end
    return `$julia -C $cpu_target -J$image_file $addflags`
end

function julia_exename()
    if !Base.isdebugbuild()
        return @static Sys.iswindows() ? "julia.exe" : "julia"
    else
        return @static Sys.iswindows() ? "julia-debug.exe" : "julia-debug"
    end
end

"""
    securezero!(o)

`securezero!` fills the memory associated with an object `o` with zeros.
Unlike `fill!(o,0)` and similar code, which might be optimized away by
the compiler for objects about to be discarded, the `securezero!` function
will always be called.
"""
function securezero! end
@noinline securezero!(a::AbstractArray{<:Number}) = fill!(a, 0)
@noinline unsafe_securezero!(p::Ptr{T}, len::Integer=1) where {T} =
    memset(p, 0, len*sizeof(T))
unsafe_securezero!(p::Ptr{Cvoid}, len::Integer=1) = Ptr{Cvoid}(unsafe_securezero!(Ptr{UInt8}(p), len))

"""
    Base.getpass(message::AbstractString) -> Base.SecretBuffer

Display a message and wait for the user to input a secret, returning an `IO`
object containing the secret.

!!! info "Windows"
    Note that on Windows, the secret might be displayed as it is typed; see
    `Base.winprompt` for securely retrieving username/password pairs from a
    graphical interface.
"""
function getpass end

# Note, this helper only works within `with_raw_tty()` on POSIX platforms!
function _getch()
    @static if Sys.iswindows()
        return UInt8(ccall(:_getch, Cint, ()))
    else
        return read(stdin, UInt8)
    end
end

const termios_size = Int(ccall(:jl_termios_size, Cint, ()))
make_termios() = zeros(UInt8, termios_size)

# These values seem to hold on all OSes we care about:
# glibc Linux, musl Linux, macOS, FreeBSD
@enum TCSETATTR_FLAGS TCSANOW=0 TCSADRAIN=1 TCSAFLUSH=2

function tcgetattr(fd::RawFD, termios)
    ret = ccall(:tcgetattr, Cint, (Cint, Ptr{Cvoid}), fd, termios)
    if ret != 0
        throw(IOError("tcgetattr failed", ret))
    end
end
function tcsetattr(fd::RawFD, termios, mode::TCSETATTR_FLAGS = TCSADRAIN)
    ret = ccall(:tcsetattr, Cint, (Cint, Cint, Ptr{Cvoid}), fd, Cint(mode), termios)
    if ret != 0
        throw(IOError("tcsetattr failed", ret))
    end
end
cfmakeraw(termios) = ccall(:cfmakeraw, Cvoid, (Ptr{Cvoid},), termios)

function with_raw_tty(f::Function, input::TTY)
    input === stdin || throw(ArgumentError("with_raw_tty only works for stdin"))
    fd = RawFD(0)

    # If we're on windows, we do nothing, as we have access to `_getch()` quite easily
    @static if Sys.iswindows()
        return f()
    end

    # Get the current terminal mode
    old_termios = make_termios()
    tcgetattr(fd, old_termios)
    try
        # Set a new, raw, terminal mode
        new_termios = copy(old_termios)
        cfmakeraw(new_termios)
        tcsetattr(fd, new_termios)

        # Call the user-supplied callback
        f()
    finally
        # Always restore the terminal mode
        tcsetattr(fd, old_termios)
    end
end

function getpass(input::TTY, output::IO, prompt::AbstractString)
    input === stdin || throw(ArgumentError("getpass only works for stdin"))
    with_raw_tty(stdin) do
        print(output, prompt, ": ")
        flush(output)
        s = SecretBuffer()
        plen = 0
        while true
            c = _getch()
            if c == 0xff || c == UInt8('\n') || c == UInt8('\r') || c == 0x04
                break # EOF or return
            elseif c == 0x00 || c == 0xe0
                _getch() # ignore function/arrow keys
            elseif c == UInt8('\b') && plen > 0
                plen -= 1 # delete last character on backspace
            elseif !iscntrl(Char(c)) && plen < 128
                write(s, c)
            end
        end
        return seekstart(s)
    end
end

# allow new getpass methods to be defined if stdin has been
# redirected to some custom stream, e.g. in IJulia.
getpass(prompt::AbstractString) = getpass(stdin, stdout, prompt)

"""
    prompt(message; default="") -> Union{String, Nothing}

Displays the `message` then waits for user input. Input is terminated when a newline (\\n)
is encountered or EOF (^D) character is entered on a blank line. If a `default` is provided
then the user can enter just a newline character to select the `default`.

See also `Base.winprompt` (for Windows) and `Base.getpass` for secure entry of passwords.

# Example

```julia-repl
julia> your_name = Base.prompt("Enter your name");
Enter your name: Logan

julia> your_name
"Logan"
```
"""
function prompt(input::IO, output::IO, message::AbstractString; default::AbstractString="")
    msg = !isempty(default) ? "$message [$default]: " : "$message: "
    print(output, msg)
    uinput = readline(input, keep=true)
    isempty(uinput) && return nothing  # Encountered an EOF
    uinput = chomp(uinput)
    isempty(uinput) ? default : uinput
end

# allow new prompt methods to be defined if stdin has been
# redirected to some custom stream, e.g. in IJulia.
prompt(message::AbstractString; default::AbstractString="") = prompt(stdin, stdout, message, default=default)

# Windows authentication prompt
if Sys.iswindows()
    struct CREDUI_INFO
        cbSize::UInt32
        parent::Ptr{Cvoid}
        pszMessageText::Ptr{UInt16}
        pszCaptionText::Ptr{UInt16}
        banner::Ptr{Cvoid}
    end

    const CREDUIWIN_GENERIC                 = 0x0001
    const CREDUIWIN_IN_CRED_ONLY            = 0x0020
    const CREDUIWIN_ENUMERATE_CURRENT_USER  = 0x0200

    const CRED_PACK_GENERIC_CREDENTIALS     = 0x0004

    const ERROR_SUCCESS                     = 0x0000
    const ERROR_CANCELLED                   = 0x04c7

    function winprompt(message, caption, default_username; prompt_username = true)
        # Step 1: Create an encrypted username/password bundle that will be used to set
        #         the default username (in theory could also provide a default password)
        credbuf = Vector{UInt8}(undef, 1024)
        credbufsize = Ref{UInt32}(sizeof(credbuf))
        succeeded = ccall((:CredPackAuthenticationBufferW, "credui.dll"), stdcall, Bool,
            (UInt32, Cwstring, Cwstring, Ptr{UInt8}, Ptr{UInt32}),
             CRED_PACK_GENERIC_CREDENTIALS, default_username, "", credbuf, credbufsize)
        if !succeeded
            credbuf = resize!(credbuf, credbufsize[])
            succeeded = ccall((:CredPackAuthenticationBufferW, "credui.dll"), stdcall, Bool,
                (UInt32, Cwstring, Cwstring, Ptr{UInt8}, Ptr{UInt32}),
                 CRED_PACK_GENERIC_CREDENTIALS, default_username, "", credbuf, credbufsize)
            @assert succeeded
        end

        # Step 2: Create the actual dialog
        #      2.1: Set up the window
        messageArr = Base.cwstring(message)
        captionArr = Base.cwstring(caption)
        pfSave = Ref{Bool}(false)
        cred = Ref{CREDUI_INFO}(CREDUI_INFO(sizeof(CREDUI_INFO), C_NULL, pointer(messageArr), pointer(captionArr), C_NULL))
        dwflags = CREDUIWIN_GENERIC | CREDUIWIN_ENUMERATE_CURRENT_USER
        if !prompt_username
            # Disable setting anything other than default_username
            dwflags |= CREDUIWIN_IN_CRED_ONLY
        end
        authPackage = Ref{Culong}(0)
        outbuf_data = Ref{Ptr{Cvoid}}(C_NULL)
        outbuf_size = Ref{Culong}(0)

        #      2.2: Do the actual request
        code = ccall((:CredUIPromptForWindowsCredentialsW, "credui.dll"), stdcall, UInt32, (Ptr{CREDUI_INFO}, UInt32, Ptr{Culong},
            Ptr{Cvoid}, Culong, Ptr{Ptr{Cvoid}}, Ptr{Culong}, Ptr{Bool}, UInt32), cred, 0, authPackage, credbuf, credbufsize[],
            outbuf_data, outbuf_size, pfSave, dwflags)

        #      2.3: If that failed for any reason other than the user canceling, error out.
        #           If the user canceled, just return nothing
        code == ERROR_CANCELLED && return nothing
        windowserror(:winprompt, code != ERROR_SUCCESS)

        # Step 3: Convert encrypted credentials back to plain text
        passbuf = Vector{UInt16}(undef, 1024)
        passlen = Ref{UInt32}(length(passbuf))
        usernamebuf = Vector{UInt16}(undef, 1024)
        usernamelen = Ref{UInt32}(length(usernamebuf))
        # Need valid buffers for domain, even though we don't care
        dummybuf = Vector{UInt16}(undef, 1024)
        succeeded = ccall((:CredUnPackAuthenticationBufferW, "credui.dll"), Bool,
            (UInt32, Ptr{Cvoid}, UInt32, Ptr{UInt16}, Ptr{UInt32}, Ptr{UInt16}, Ptr{UInt32}, Ptr{UInt16}, Ptr{UInt32}),
            0, outbuf_data[], outbuf_size[], usernamebuf, usernamelen, dummybuf, Ref{UInt32}(1024), passbuf, passlen)
        windowserror(:winprompt, !succeeded)

        # Step 4: Free the encrypted buffer
        # ccall(:SecureZeroMemory, Ptr{Cvoid}, (Ptr{Cvoid}, Csize_t), outbuf_data[], outbuf_size[]) - not an actual function
        unsafe_securezero!(outbuf_data[], outbuf_size[])
        ccall((:CoTaskMemFree, "ole32.dll"), Cvoid, (Ptr{Cvoid},), outbuf_data[])

        # Done.
        passbuf_ = passbuf[1:passlen[]-1]
        result = (String(transcode(UInt8, usernamebuf[1:usernamelen[]-1])),
                  SecretBuffer!(transcode(UInt8, passbuf_)))
        securezero!(passbuf_)
        securezero!(passbuf)

        return result
    end

end

unsafe_crc32c(a, n, crc) = ccall(:jl_crc32c, UInt32, (UInt32, Ptr{UInt8}, Csize_t), crc, a, n)

_crc32c(a::NTuple{<:Any, UInt8}, crc::UInt32=0x00000000) =
    unsafe_crc32c(Ref(a), length(a) % Csize_t, crc)
_crc32c(a::Union{Array{UInt8},FastContiguousSubArray{UInt8,N,<:Array{UInt8}} where N}, crc::UInt32=0x00000000) =
    unsafe_crc32c(a, length(a) % Csize_t, crc)

function _crc32c(s::Union{String, SubString{String}}, crc::UInt32=0x00000000)
    unsafe_crc32c(s, sizeof(s) % Csize_t, crc)
end

function _crc32c(io::IO, nb::Integer, crc::UInt32=0x00000000)
    nb < 0 && throw(ArgumentError("number of bytes to checksum must be ≥ 0, got $nb"))
    # use block size 24576=8192*3, since that is the threshold for
    # 3-way parallel SIMD code in the underlying jl_crc32c C function.
    buf = Vector{UInt8}(undef, min(nb, 24576))
    while !eof(io) && nb > 24576
        n = readbytes!(io, buf)
        crc = unsafe_crc32c(buf, n, crc)
        nb -= n
    end
    return unsafe_crc32c(buf, readbytes!(io, buf, min(nb, length(buf))), crc)
end
_crc32c(io::IO, crc::UInt32=0x00000000) = _crc32c(io, typemax(Int64), crc)
_crc32c(io::IOStream, crc::UInt32=0x00000000) = _crc32c(io, filesize(io)-position(io), crc)
_crc32c(uuid::UUID, crc::UInt32=0x00000000) = _crc32c(uuid.value, crc)
_crc32c(x::UInt128, crc::UInt32=0x00000000) =
    ccall(:jl_crc32c, UInt32, (UInt32, Ref{UInt128}, Csize_t), crc, x, 16)
_crc32c(x::UInt64, crc::UInt32=0x00000000) =
    ccall(:jl_crc32c, UInt32, (UInt32, Ref{UInt64}, Csize_t), crc, x, 8)
_crc32c(x::UInt32, crc::UInt32=0x00000000) =
    ccall(:jl_crc32c, UInt32, (UInt32, Ref{UInt32}, Csize_t), crc, x, 4)
_crc32c(x::UInt16, crc::UInt32=0x00000000) =
    ccall(:jl_crc32c, UInt32, (UInt32, Ref{UInt16}, Csize_t), crc, x, 2)
_crc32c(x::UInt8, crc::UInt32=0x00000000) =
    ccall(:jl_crc32c, UInt32, (UInt32, Ref{UInt8}, Csize_t), crc, x, 1)

"""
    @kwdef typedef

This is a helper macro that automatically defines a keyword-based constructor for the type
declared in the expression `typedef`, which must be a `struct` or `mutable struct`
expression. The default argument is supplied by declaring fields of the form `field::T =
default` or `field = default`. If no default is provided then the keyword argument becomes
a required keyword argument in the resulting type constructor.

Inner constructors can still be defined, but at least one should accept arguments in the
same form as the default inner constructor (i.e. one positional argument per field) in
order to function correctly with the keyword outer constructor.

!!! compat "Julia 1.1"
    `Base.@kwdef` for parametric structs, and structs with supertypes
    requires at least Julia 1.1.

!!! compat "Julia 1.9"
    This macro is exported as of Julia 1.9.

# Examples
```jldoctest
julia> @kwdef struct Foo
           a::Int = 1         # specified default
           b::String          # required keyword
       end
Foo

julia> Foo(b="hi")
Foo(1, "hi")

julia> Foo()
ERROR: UndefKeywordError: keyword argument `b` not assigned
Stacktrace:
[...]
```
"""
macro kwdef(expr)
    expr = macroexpand(__module__, expr) # to expand @static
    isexpr(expr, :struct) || error("Invalid usage of @kwdef")
    T = expr.args[2]
    if T isa Expr && T.head === :<:
        T = T.args[1]
    end

    params_ex = Expr(:parameters)
    call_args = Any[]

    _kwdef!(expr.args[3], params_ex.args, call_args)
    # Only define a constructor if the type has fields, otherwise we'll get a stack
    # overflow on construction
    if !isempty(params_ex.args)
        if T isa Symbol
            sig = :(($(esc(T)))($params_ex))
            call = :(($(esc(T)))($(call_args...)))
            body = Expr(:block, __source__, call)
            kwdefs = Expr(:function, sig, body)
        elseif isexpr(T, :curly)
            # if T == S{A<:AA,B<:BB}, define two methods
            #   S(...) = ...
            #   S{A,B}(...) where {A<:AA,B<:BB} = ...
            S = T.args[1]
            P = T.args[2:end]
            Q = Any[isexpr(U, :<:) ? U.args[1] : U for U in P]
            SQ = :($S{$(Q...)})
            body1 = Expr(:block, __source__, :(($(esc(S)))($(call_args...))))
            sig1 = :(($(esc(S)))($params_ex))
            def1 = Expr(:function, sig1, body1)
            body2 = Expr(:block, __source__, :(($(esc(SQ)))($(call_args...))))
            sig2 = :(($(esc(SQ)))($params_ex) where {$(esc.(P)...)})
            def2 = Expr(:function, sig2, body2)
            kwdefs = Expr(:block, def1, def2)
        else
            error("Invalid usage of @kwdef")
        end
    else
        kwdefs = nothing
    end
    return quote
        $(esc(:($Base.@__doc__ $expr)))
        $kwdefs
    end
end

# @kwdef helper function
# mutates arguments inplace
function _kwdef!(blk, params_args, call_args)
    for i in eachindex(blk.args)
        ei = blk.args[i]
        if ei isa Symbol
            #  var
            push!(params_args, ei)
            push!(call_args, ei)
        elseif ei isa Expr
            is_atomic = ei.head === :atomic
            ei = is_atomic ? first(ei.args) : ei # strip "@atomic" and add it back later
            is_const = ei.head === :const
            ei = is_const ? first(ei.args) : ei # strip "const" and add it back later
            # Note: `@atomic const ..` isn't valid, but reconstruct it anyway to serve a nice error
            if ei isa Symbol
                # const var
                push!(params_args, ei)
                push!(call_args, ei)
            elseif ei.head === :(=)
                lhs = ei.args[1]
                if lhs isa Symbol
                    #  var = defexpr
                    var = lhs
                elseif lhs isa Expr && lhs.head === :(::) && lhs.args[1] isa Symbol
                    #  var::T = defexpr
                    var = lhs.args[1]
                else
                    # something else, e.g. inline inner constructor
                    #   F(...) = ...
                    continue
                end
                defexpr = ei.args[2]  # defexpr
                push!(params_args, Expr(:kw, var, esc(defexpr)))
                push!(call_args, var)
                lhs = is_const ? Expr(:const, lhs) : lhs
                lhs = is_atomic ? Expr(:atomic, lhs) : lhs
                blk.args[i] = lhs # overrides arg
            elseif ei.head === :(::) && ei.args[1] isa Symbol
                # var::Typ
                var = ei.args[1]
                push!(params_args, var)
                push!(call_args, var)
            elseif ei.head === :block
                # can arise with use of @static inside type decl
                _kwdef!(ei, params_args, call_args)
            end
        end
    end
    blk
end

# testing

"""
    Base.runtests(tests=["all"]; ncores=ceil(Int, Sys.CPU_THREADS / 2),
                  exit_on_error=false, revise=false, [seed])

Run the Julia unit tests listed in `tests`, which can be either a string or an array of
strings, using `ncores` processors. If `exit_on_error` is `false`, when one test
fails, all remaining tests in other files will still be run; they are otherwise discarded,
when `exit_on_error == true`.
If `revise` is `true`, the `Revise` package is used to load any modifications to `Base` or
to the standard libraries before running the tests.
If a seed is provided via the keyword argument, it is used to seed the
global RNG in the context where the tests are run; otherwise the seed is chosen randomly.
"""
function runtests(tests = ["all"]; ncores::Int = ceil(Int, Sys.CPU_THREADS / 2),
                  exit_on_error::Bool=false,
                  revise::Bool=false,
                  seed::Union{BitInteger,Nothing}=nothing)
    if isa(tests,AbstractString)
        tests = split(tests)
    end
    exit_on_error && push!(tests, "--exit-on-error")
    revise && push!(tests, "--revise")
    seed !== nothing && push!(tests, "--seed=0x$(string(seed % UInt128, base=16))") # cast to UInt128 to avoid a minus sign
    ENV2 = copy(ENV)
    ENV2["JULIA_CPU_THREADS"] = "$ncores"
    pathsep = Sys.iswindows() ? ";" : ":"
    ENV2["JULIA_DEPOT_PATH"] = string(mktempdir(; cleanup = true), pathsep) # make sure the default depots can be loaded
    delete!(ENV2, "JULIA_LOAD_PATH")
    delete!(ENV2, "JULIA_PROJECT")
    try
        run(setenv(`$(julia_cmd()) $(joinpath(Sys.BINDIR,
            Base.DATAROOTDIR, "julia", "test", "runtests.jl")) $tests`, ENV2))
        nothing
    catch
        buf = PipeBuffer()
        original_load_path = copy(Base.LOAD_PATH); empty!(Base.LOAD_PATH); pushfirst!(Base.LOAD_PATH, "@stdlib")
        Base.require(Base, :InteractiveUtils).versioninfo(buf)
        empty!(Base.LOAD_PATH); append!(Base.LOAD_PATH, original_load_path)
        error("A test has failed. Please submit a bug report (https://github.com/JuliaLang/julia/issues)\n" *
              "including error messages above and the output of versioninfo():\n$(read(buf, String))")
    end
end

"""
    isdebugbuild()

Return `true` if julia is a debug version.
"""
function isdebugbuild()
    return ccall(:jl_is_debugbuild, Cint, ()) != 0
end
M   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/client.jl�M      # This file is a part of Julia. License is MIT: https://julialang.org/license

## client.jl - frontend handling command line options, environment setup,
##             and REPL

have_color = nothing
const default_color_warn = :yellow
const default_color_error = :light_red
const default_color_info = :cyan
const default_color_debug = :blue
const default_color_input = :normal
const default_color_answer = :normal
const color_normal = text_colors[:normal]

function repl_color(key, default)
    env_str = get(ENV, key, "")
    c = tryparse(Int, env_str)
    c_conv = something(c, Symbol(env_str))
    haskey(text_colors, c_conv) ? c_conv : default
end

error_color() = repl_color("JULIA_ERROR_COLOR", default_color_error)
warn_color()  = repl_color("JULIA_WARN_COLOR" , default_color_warn)
info_color()  = repl_color("JULIA_INFO_COLOR" , default_color_info)
debug_color()  = repl_color("JULIA_DEBUG_COLOR" , default_color_debug)

input_color()  = text_colors[repl_color("JULIA_INPUT_COLOR", default_color_input)]
answer_color() = text_colors[repl_color("JULIA_ANSWER_COLOR", default_color_answer)]

stackframe_lineinfo_color() = repl_color("JULIA_STACKFRAME_LINEINFO_COLOR", :bold)
stackframe_function_color() = repl_color("JULIA_STACKFRAME_FUNCTION_COLOR", :bold)

function repl_cmd(cmd, out)
    shell = shell_split(get(ENV, "JULIA_SHELL", get(ENV, "SHELL", "/bin/sh")))
    shell_name = Base.basename(shell[1])

    # Immediately expand all arguments, so that typing e.g. ~/bin/foo works.
    cmd.exec .= expanduser.(cmd.exec)

    if isempty(cmd.exec)
        throw(ArgumentError("no cmd to execute"))
    elseif cmd.exec[1] == "cd"
        new_oldpwd = pwd()
        if length(cmd.exec) > 2
            throw(ArgumentError("cd method only takes one argument"))
        elseif length(cmd.exec) == 2
            dir = cmd.exec[2]
            if dir == "-"
                if !haskey(ENV, "OLDPWD")
                    error("cd: OLDPWD not set")
                end
                dir = ENV["OLDPWD"]
            end
            cd(dir)
        else
            cd()
        end
        ENV["OLDPWD"] = new_oldpwd
        println(out, pwd())
    else
        @static if !Sys.iswindows()
            if shell_name == "fish"
                shell_escape_cmd = "begin; $(shell_escape_posixly(cmd)); and true; end"
            else
                shell_escape_cmd = "($(shell_escape_posixly(cmd))) && true"
            end
            cmd = `$shell -c $shell_escape_cmd`
        end
        try
            run(ignorestatus(cmd))
        catch
            # Windows doesn't shell out right now (complex issue), so Julia tries to run the program itself
            # Julia throws an exception if it can't find the program, but the stack trace isn't useful
            lasterr = current_exceptions()
            lasterr = ExceptionStack([(exception = e[1], backtrace = [] ) for e in lasterr])
            invokelatest(display_error, lasterr)
        end
    end
    nothing
end

# deprecated function--preserved for DocTests.jl
function ip_matches_func(ip, func::Symbol)
    for fr in StackTraces.lookup(ip)
        if fr === StackTraces.UNKNOWN || fr.from_c
            return false
        end
        fr.func === func && return true
    end
    return false
end

function scrub_repl_backtrace(bt)
    if bt !== nothing && !(bt isa Vector{Any}) # ignore our sentinel value types
        bt = bt isa Vector{StackFrame} ? copy(bt) : stacktrace(bt)
        # remove REPL-related frames from interactive printing
        eval_ind = findlast(frame -> !frame.from_c && frame.func === :eval, bt)
        eval_ind === nothing || deleteat!(bt, eval_ind:length(bt))
    end
    return bt
end
scrub_repl_backtrace(stack::ExceptionStack) =
    ExceptionStack(Any[(;x.exception, backtrace = scrub_repl_backtrace(x.backtrace)) for x in stack])

istrivialerror(stack::ExceptionStack) =
    length(stack) == 1 && length(stack[1].backtrace) ≤ 1 && !isa(stack[1].exception, MethodError)
    # frame 1 = top level; assumes already went through scrub_repl_backtrace; MethodError see #50803

function display_error(io::IO, stack::ExceptionStack)
    printstyled(io, "ERROR: "; bold=true, color=Base.error_color())
    show_exception_stack(IOContext(io, :limit => true), stack)
    println(io)
end
display_error(stack::ExceptionStack) = display_error(stderr, stack)

# these forms are depended on by packages outside Julia
function display_error(io::IO, er, bt)
    printstyled(io, "ERROR: "; bold=true, color=Base.error_color())
    showerror(IOContext(io, :limit => true), er, bt, backtrace = bt!==nothing)
    println(io)
end
display_error(er, bt=nothing) = display_error(stderr, er, bt)

function eval_user_input(errio, @nospecialize(ast), show_value::Bool)
    errcount = 0
    lasterr = nothing
    have_color = get(stdout, :color, false)::Bool
    while true
        try
            if have_color
                print(color_normal)
            end
            if lasterr !== nothing
                lasterr = scrub_repl_backtrace(lasterr)
                istrivialerror(lasterr) || setglobal!(Base.MainInclude, :err, lasterr)
                invokelatest(display_error, errio, lasterr)
                errcount = 0
                lasterr = nothing
            else
                ast = Meta.lower(Main, ast)
                value = Core.eval(Main, ast)
                setglobal!(Base.MainInclude, :ans, value)
                if !(value === nothing) && show_value
                    if have_color
                        print(answer_color())
                    end
                    try
                        invokelatest(display, value)
                    catch
                        @error "Evaluation succeeded, but an error occurred while displaying the value" typeof(value)
                        rethrow()
                    end
                end
            end
            break
        catch
            if errcount > 0
                @error "SYSTEM: display_error(errio, lasterr) caused an error"
            end
            errcount += 1
            lasterr = scrub_repl_backtrace(current_exceptions())
            setglobal!(Base.MainInclude, :err, lasterr)
            if errcount > 2
                @error "It is likely that something important is broken, and Julia will not be able to continue normally" errcount
                break
            end
        end
    end
    isa(stdin, TTY) && println()
    nothing
end

function _parse_input_line_core(s::String, filename::String)
    ex = Meta.parseall(s, filename=filename)
    if ex isa Expr && ex.head === :toplevel
        if isempty(ex.args)
            return nothing
        end
        last = ex.args[end]
        if last isa Expr && (last.head === :error || last.head === :incomplete)
            # if a parse error happens in the middle of a multi-line input
            # return only the error, so that none of the input is evaluated.
            return last
        end
    end
    return ex
end

function parse_input_line(s::String; filename::String="none", depwarn=true)
    # For now, assume all parser warnings are depwarns
    ex = if depwarn
        _parse_input_line_core(s, filename)
    else
        with_logger(NullLogger()) do
            _parse_input_line_core(s, filename)
        end
    end
    return ex
end
parse_input_line(s::AbstractString) = parse_input_line(String(s))

# detect the reason which caused an :incomplete expression
# from the error message
# NOTE: the error messages are defined in src/julia-parser.scm
function fl_incomplete_tag(msg::AbstractString)
    occursin("string", msg) && return :string
    occursin("comment", msg) && return :comment
    occursin("requires end", msg) && return :block
    occursin("\"`\"", msg) && return :cmd
    occursin("character", msg) && return :char
    return :other
end

incomplete_tag(ex) = :none
function incomplete_tag(ex::Expr)
    if ex.head !== :incomplete
        return :none
    elseif isempty(ex.args)
        return :other
    elseif ex.args[1] isa String
        return fl_incomplete_tag(ex.args[1])
    else
        return incomplete_tag(ex.args[1])
    end
end
incomplete_tag(exc::Meta.ParseError) = incomplete_tag(exc.detail)

function exec_options(opts)
    quiet                 = (opts.quiet != 0)
    startup               = (opts.startupfile != 2)
    history_file          = (opts.historyfile != 0)
    color_set             = (opts.color != 0) # --color!=auto
    global have_color     = color_set ? (opts.color == 1) : nothing # --color=on
    global is_interactive = (opts.isinteractive != 0)

    # pre-process command line argument list
    arg_is_program = !isempty(ARGS)
    repl = !arg_is_program
    cmds = unsafe_load_commands(opts.commands)
    for (cmd, arg) in cmds
        if cmd == 'e'
            arg_is_program = false
            repl = false
        elseif cmd == 'E'
            arg_is_program = false
            repl = false
        elseif cmd == 'L'
            # nothing
        elseif cmd == 'B' # --bug-report
            # If we're doing a bug report, don't load anything else. We will
            # spawn a child in which to execute these options.
            let InteractiveUtils = load_InteractiveUtils()
                InteractiveUtils.report_bug(arg)
            end
            return nothing
        else
            @warn "Unexpected command -$cmd'$arg'"
        end
    end

    # remove filename from ARGS
    global PROGRAM_FILE = arg_is_program ? popfirst!(ARGS) : ""

    # Load Distributed module only if any of the Distributed options have been specified.
    distributed_mode = (opts.worker == 1) || (opts.nprocs > 0) || (opts.machine_file != C_NULL)
    if distributed_mode
        let Distributed = require(PkgId(UUID((0x8ba89e20_285c_5b6f, 0x9357_94700520ee1b)), "Distributed"))
            Core.eval(Main, :(const Distributed = $Distributed))
            Core.eval(Main, :(using .Distributed))
        end

        invokelatest(Main.Distributed.process_opts, opts)
    end

    interactiveinput = (repl || is_interactive::Bool) && isa(stdin, TTY)
    is_interactive::Bool |= interactiveinput

    # load ~/.julia/config/startup.jl file
    if startup
        try
            load_julia_startup()
        catch
            invokelatest(display_error, scrub_repl_backtrace(current_exceptions()))
            !(repl || is_interactive::Bool) && exit(1)
        end
    end

    # process cmds list
    for (cmd, arg) in cmds
        if cmd == 'e'
            Core.eval(Main, parse_input_line(arg))
        elseif cmd == 'E'
            invokelatest(show, Core.eval(Main, parse_input_line(arg)))
            println()
        elseif cmd == 'L'
            # load file immediately on all processors
            if !distributed_mode
                include(Main, arg)
            else
                # TODO: Move this logic to Distributed and use a callback
                @sync for p in invokelatest(Main.procs)
                    @async invokelatest(Main.remotecall_wait, include, p, Main, arg)
                end
            end
        end
    end

    # load file
    if arg_is_program
        # program
        if !is_interactive::Bool
            exit_on_sigint(true)
        end
        try
            if PROGRAM_FILE == "-"
                include_string(Main, read(stdin, String), "stdin")
            else
                include(Main, PROGRAM_FILE)
            end
        catch
            invokelatest(display_error, scrub_repl_backtrace(current_exceptions()))
            if !is_interactive::Bool
                exit(1)
            end
        end
    end
    if repl || is_interactive::Bool
        if interactiveinput
            banner = (opts.banner != 0) # --banner!=no
        else
            banner = (opts.banner == 1) # --banner=yes
        end
        run_main_repl(interactiveinput, quiet, banner, history_file, color_set)
    end
    nothing
end

function _global_julia_startup_file()
    # If the user built us with a specific Base.SYSCONFDIR, check that location first for a startup.jl file
    # If it is not found, then continue on to the relative path based on Sys.BINDIR
    BINDIR = Sys.BINDIR
    SYSCONFDIR = Base.SYSCONFDIR
    if !isempty(SYSCONFDIR)
        p1 = abspath(BINDIR, SYSCONFDIR, "julia", "startup.jl")
        isfile(p1) && return p1
    end
    p2 = abspath(BINDIR, "..", "etc", "julia", "startup.jl")
    isfile(p2) && return p2
    return nothing
end

function _local_julia_startup_file()
    if !isempty(DEPOT_PATH)
        path = abspath(DEPOT_PATH[1], "config", "startup.jl")
        isfile(path) && return path
    end
    return nothing
end

function load_julia_startup()
    global_file = _global_julia_startup_file()
    (global_file !== nothing) && include(Main, global_file)
    local_file = _local_julia_startup_file()
    (local_file !== nothing) && include(Main, local_file)
    return nothing
end

const repl_hooks = []

"""
    atreplinit(f)

Register a one-argument function to be called before the REPL interface is initialized in
interactive sessions; this is useful to customize the interface. The argument of `f` is the
REPL object. This function should be called from within the `.julia/config/startup.jl`
initialization file.
"""
atreplinit(f::Function) = (pushfirst!(repl_hooks, f); nothing)

function __atreplinit(repl)
    for f in repl_hooks
        try
            f(repl)
        catch err
            showerror(stderr, err)
            println(stderr)
        end
    end
end
_atreplinit(repl) = invokelatest(__atreplinit, repl)

function load_InteractiveUtils(mod::Module=Main)
    # load interactive-only libraries
    if !isdefined(mod, :InteractiveUtils)
        try
            let InteractiveUtils = require(PkgId(UUID(0xb77e0a4c_d291_57a0_90e8_8db25a27a240), "InteractiveUtils"))
                Core.eval(mod, :(const InteractiveUtils = $InteractiveUtils))
                Core.eval(mod, :(using .InteractiveUtils))
                return InteractiveUtils
            end
        catch ex
            @warn "Failed to import InteractiveUtils into module $mod" exception=(ex, catch_backtrace())
        end
        return nothing
    end
    return getfield(mod, :InteractiveUtils)
end

global active_repl

# run the requested sort of evaluation loop on stdio
function run_main_repl(interactive::Bool, quiet::Bool, banner::Bool, history_file::Bool, color_set::Bool)
    load_InteractiveUtils()

    if interactive && isassigned(REPL_MODULE_REF)
        invokelatest(REPL_MODULE_REF[]) do REPL
            term_env = get(ENV, "TERM", @static Sys.iswindows() ? "" : "dumb")
            term = REPL.Terminals.TTYTerminal(term_env, stdin, stdout, stderr)
            banner && Base.banner(term)
            if term.term_type == "dumb"
                repl = REPL.BasicREPL(term)
                quiet || @warn "Terminal not fully functional"
            else
                repl = REPL.LineEditREPL(term, get(stdout, :color, false), true)
                repl.history_file = history_file
            end
            global active_repl = repl
            # Make sure any displays pushed in .julia/config/startup.jl ends up above the
            # REPLDisplay
            pushdisplay(REPL.REPLDisplay(repl))
            _atreplinit(repl)
            REPL.run_repl(repl, backend->(global active_repl_backend = backend))
        end
    else
        # otherwise provide a simple fallback
        if interactive && !quiet
            @warn "REPL provider not available: using basic fallback"
        end
        banner && Base.banner()
        let input = stdin
            if isa(input, File) || isa(input, IOStream)
                # for files, we can slurp in the whole thing at once
                ex = parse_input_line(read(input, String))
                if Meta.isexpr(ex, :toplevel)
                    # if we get back a list of statements, eval them sequentially
                    # as if we had parsed them sequentially
                    for stmt in ex.args
                        eval_user_input(stderr, stmt, true)
                    end
                    body = ex.args
                else
                    eval_user_input(stderr, ex, true)
                end
            else
                while isopen(input) || !eof(input)
                    if interactive
                        print("julia> ")
                        flush(stdout)
                    end
                    try
                        line = ""
                        ex = nothing
                        while !eof(input)
                            line *= readline(input, keep=true)
                            ex = parse_input_line(line)
                            if !(isa(ex, Expr) && ex.head === :incomplete)
                                break
                            end
                        end
                        eval_user_input(stderr, ex, true)
                    catch err
                        isa(err, InterruptException) ? print("\n\n") : rethrow()
                    end
                end
            end
        end
    end
    nothing
end

# MainInclude exists to hide Main.include and eval from `names(Main)`.
baremodule MainInclude
using ..Base
# These definitions calls Base._include rather than Base.include to get
# one-frame stacktraces for the common case of using include(fname) in Main.
include(mapexpr::Function, fname::AbstractString) = Base._include(mapexpr, Main, fname)
function include(fname::AbstractString)
    isa(fname, String) || (fname = Base.convert(String, fname)::String)
    Base._include(identity, Main, fname)
end
eval(x) = Core.eval(Main, x)

"""
    ans

A variable referring to the last computed value, automatically imported to the interactive prompt.
"""
global ans = nothing

"""
    err

A variable referring to the last thrown errors, automatically imported to the interactive prompt.
The thrown errors are collected in a stack of exceptions.
"""
global err = nothing

# weakly exposes ans and err variables to Main
export ans, err

end

"""
    eval(expr)

Evaluate an expression in the global scope of the containing module.
Every `Module` (except those defined with `baremodule`) has its own 1-argument
definition of `eval`, which evaluates expressions in that module.
"""
MainInclude.eval

"""
    include([mapexpr::Function,] path::AbstractString)

Evaluate the contents of the input source file in the global scope of the containing module.
Every module (except those defined with `baremodule`) has its own
definition of `include`, which evaluates the file in that module.
Returns the result of the last evaluated expression of the input file. During including,
a task-local include path is set to the directory containing the file. Nested calls to
`include` will search relative to that path. This function is typically used to load source
interactively, or to combine files in packages that are broken into multiple source files.
The argument `path` is normalized using [`normpath`](@ref) which will resolve
relative path tokens such as `..` and convert `/` to the appropriate path separator.

The optional first argument `mapexpr` can be used to transform the included code before
it is evaluated: for each parsed expression `expr` in `path`, the `include` function
actually evaluates `mapexpr(expr)`.  If it is omitted, `mapexpr` defaults to [`identity`](@ref).

Use [`Base.include`](@ref) to evaluate a file into another module.

!!! compat "Julia 1.5"
    Julia 1.5 is required for passing the `mapexpr` argument.
"""
MainInclude.include

function _start()
    empty!(ARGS)
    append!(ARGS, Core.ARGS)
    # clear any postoutput hooks that were saved in the sysimage
    empty!(Base.postoutput_hooks)
    try
        exec_options(JLOptions())
    catch
        invokelatest(display_error, scrub_repl_backtrace(current_exceptions()))
        exit(1)
    end
    if is_interactive && get(stdout, :color, false)
        print(color_normal)
    end
end
O   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/asyncmap.jl4      # This file is a part of Julia. License is MIT: https://julialang.org/license

using Base.Iterators: Enumerate

"""
    asyncmap(f, c...; ntasks=0, batch_size=nothing)

Uses multiple concurrent tasks to map `f` over a collection (or multiple
equal length collections). For multiple collection arguments, `f` is
applied elementwise.

`ntasks` specifies the number of tasks to run concurrently.
Depending on the length of the collections, if `ntasks` is unspecified,
up to 100 tasks will be used for concurrent mapping.

`ntasks` can also be specified as a zero-arg function. In this case, the
number of tasks to run in parallel is checked before processing every element and a new
task started if the value of `ntasks_func` is greater than the current number
of tasks.

If `batch_size` is specified, the collection is processed in batch mode. `f` must
then be a function that must accept a `Vector` of argument tuples and must
return a vector of results. The input vector will have a length of `batch_size` or less.

The following examples highlight execution in different tasks by returning
the `objectid` of the tasks in which the mapping function is executed.

First, with `ntasks` undefined, each element is processed in a different task.
```
julia> tskoid() = objectid(current_task());

julia> asyncmap(x->tskoid(), 1:5)
5-element Array{UInt64,1}:
 0x6e15e66c75c75853
 0x440f8819a1baa682
 0x9fb3eeadd0c83985
 0xebd3e35fe90d4050
 0x29efc93edce2b961

julia> length(unique(asyncmap(x->tskoid(), 1:5)))
5
```

With `ntasks=2` all elements are processed in 2 tasks.
```
julia> asyncmap(x->tskoid(), 1:5; ntasks=2)
5-element Array{UInt64,1}:
 0x027ab1680df7ae94
 0xa23d2f80cd7cf157
 0x027ab1680df7ae94
 0xa23d2f80cd7cf157
 0x027ab1680df7ae94

julia> length(unique(asyncmap(x->tskoid(), 1:5; ntasks=2)))
2
```

With `batch_size` defined, the mapping function needs to be changed to accept an array
of argument tuples and return an array of results. `map` is used in the modified mapping
function to achieve this.
```
julia> batch_func(input) = map(x->string("args_tuple: ", x, ", element_val: ", x[1], ", task: ", tskoid()), input)
batch_func (generic function with 1 method)

julia> asyncmap(batch_func, 1:5; ntasks=2, batch_size=2)
5-element Array{String,1}:
 "args_tuple: (1,), element_val: 1, task: 9118321258196414413"
 "args_tuple: (2,), element_val: 2, task: 4904288162898683522"
 "args_tuple: (3,), element_val: 3, task: 9118321258196414413"
 "args_tuple: (4,), element_val: 4, task: 4904288162898683522"
 "args_tuple: (5,), element_val: 5, task: 9118321258196414413"
```
"""
function asyncmap(f, c...; ntasks=0, batch_size=nothing)
    return async_usemap(f, c...; ntasks=ntasks, batch_size=batch_size)
end

function async_usemap(f, c...; ntasks=0, batch_size=nothing)
    ntasks = verify_ntasks(c[1], ntasks)
    batch_size = verify_batch_size(batch_size)

    if batch_size !== nothing
        exec_func = batch -> begin
            # extract the Refs from the input tuple
            batch_refs = map(x->x[1], batch)

            # and the args tuple....
            batched_args = map(x->x[2], batch)

            results = f(batched_args)
            foreach(x -> (batch_refs[x[1]].x = x[2]), enumerate(results))
        end
    else
        exec_func = (r,args) -> (r.x = f(args...))
    end
    chnl, worker_tasks = setup_chnl_and_tasks(exec_func, ntasks, batch_size)
    return wrap_n_exec_twice(chnl, worker_tasks, ntasks, exec_func, c...)
end

batch_size_err_str(batch_size) = string("batch_size must be specified as a positive integer. batch_size=", batch_size)
function verify_batch_size(batch_size)
    if batch_size === nothing
        return batch_size
    elseif isa(batch_size, Number)
        batch_size = Int(batch_size)
        batch_size < 1 && throw(ArgumentError(batch_size_err_str(batch_size)))
        return batch_size
    else
        throw(ArgumentError(batch_size_err_str(batch_size)))
    end
end


function verify_ntasks(iterable, ntasks)
    if !((isa(ntasks, Number) && (ntasks >= 0)) || isa(ntasks, Function))
        err = string("ntasks must be specified as a positive integer or a 0-arg function. ntasks=", ntasks)
        throw(ArgumentError(err))
    end

    if ntasks == 0
        if haslength(iterable)
            ntasks = max(1,min(100, length(iterable)))
        else
            ntasks = 100
        end
    end
    return ntasks
end

function wrap_n_exec_twice(chnl, worker_tasks, ntasks, exec_func, c...)
    # The driver task, creates a Ref object and writes it and the args tuple to
    # the communication channel for processing by a free worker task.
    push_arg_to_channel = (x...) -> (r=Ref{Any}(nothing); put!(chnl,(r,x));r)

    if isa(ntasks, Function)
        map_f = (x...) -> begin
            # check number of tasks every time, and start one if required.
            # number_tasks > optimal_number is fine, the other way around is inefficient.
            if length(worker_tasks) < ntasks()
                start_worker_task!(worker_tasks, exec_func, chnl)
            end
            push_arg_to_channel(x...)
        end
    else
        map_f = push_arg_to_channel
    end
    maptwice(map_f, chnl, worker_tasks, c...)
end

function maptwice(wrapped_f, chnl, worker_tasks, c...)
    # first run, returns a collection of Refs
    asyncrun_excp = nothing
    local asyncrun
    try
        asyncrun = map(wrapped_f, c...)
    catch ex
        if isa(ex,InvalidStateException)
            # channel could be closed due to exceptions in the async tasks,
            # we propagate those errors, if any, over the `put!` failing
            # in asyncrun due to a closed channel.
            asyncrun_excp = ex
        else
            rethrow()
        end
    end

    # close channel and wait for all worker tasks to finish
    close(chnl)

    # check and throw any exceptions from the worker tasks
    foreach(x->(v=fetch(x); isa(v, Exception) && throw(v)), worker_tasks)

    # check if there was a genuine problem with asyncrun
    (asyncrun_excp !== nothing) && throw(asyncrun_excp)

    if isa(asyncrun, Ref)
        # scalar case
        return asyncrun.x
    else
        # second run, extract values from the Refs and return
        return map(ref->ref.x, asyncrun)
    end
end

function setup_chnl_and_tasks(exec_func, ntasks, batch_size=nothing)
    if isa(ntasks, Function)
        nt = ntasks()::Int
        # start at least one worker task.
        if nt == 0
            nt = 1
        end
    else
        nt = ntasks::Int
    end

    # Use an unbuffered channel for communicating with the worker tasks. In the event
    # of an error in any of the worker tasks, the channel is closed. This
    # results in the `put!` in the driver task failing immediately.
    chnl = Channel(0)
    worker_tasks = []
    foreach(_ -> start_worker_task!(worker_tasks, exec_func, chnl, batch_size), 1:nt)
    yield()
    return (chnl, worker_tasks)
end

function start_worker_task!(worker_tasks, exec_func, chnl, batch_size=nothing)
    t = @async begin
        retval = nothing

        try
            if isa(batch_size, Number)
                while isopen(chnl)
                    # The mapping function expects an array of input args, as it processes
                    # elements in a batch.
                    batch_collection=Any[]
                    n = 0
                    for exec_data in chnl
                        push!(batch_collection, exec_data)
                        n += 1
                        (n == batch_size) && break
                    end
                    if n > 0
                        exec_func(batch_collection)
                    end
                end
            else
                for exec_data in chnl
                    exec_func(exec_data...)
                end
            end
        catch e
            close(chnl)
            retval = capture_exception(e, catch_backtrace())
        end
        retval
    end
    push!(worker_tasks, t)
end

# Special handling for some types.
function asyncmap(f, s::AbstractString; kwargs...)
    s2 = Vector{Char}(undef, length(s))
    asyncmap!(f, s2, s; kwargs...)
    return String(s2)
end

# map on a single BitArray returns a BitArray if the mapping function is boolean.
function asyncmap(f, b::BitArray; kwargs...)
    b2 = async_usemap(f, b; kwargs...)
    if eltype(b2) == Bool
        return BitArray(b2)
    end
    return b2
end

mutable struct AsyncCollector
    f
    results
    enumerator::Enumerate
    ntasks
    batch_size
    nt_check::Bool     # check number of tasks on every iteration

    AsyncCollector(f, r, en::Enumerate, ntasks, batch_size) = new(f, r, en, ntasks, batch_size, isa(ntasks, Function))
end

"""
    AsyncCollector(f, results, c...; ntasks=0, batch_size=nothing) -> iterator

Return an iterator which applies `f` to each element of `c` asynchronously
and collects output into `results`.

Keyword args `ntasks` and `batch_size` have the same behavior as in
[`asyncmap`](@ref). If `batch_size` is specified, `f` must
be a function which operates on an array of argument tuples.

!!! note
    `iterate(::AsyncCollector, state) -> (nothing, state)`. A successful return
    from `iterate` indicates that the next element from the input collection is
    being processed asynchronously. It blocks until a free worker task becomes
    available.

!!! note
    `for _ in AsyncCollector(f, results, c...; ntasks=1) end` is equivalent to
    `map!(f, results, c...)`.
"""
function AsyncCollector(f, results, c...; ntasks=0, batch_size=nothing)
    AsyncCollector(f, results, enumerate(zip(c...)), ntasks, batch_size)
end

mutable struct AsyncCollectorState
    chnl::Channel
    worker_tasks::Array{Task,1}
    enum_state      # enumerator state
    AsyncCollectorState(chnl::Channel, worker_tasks::Vector) =
        new(chnl, convert(Vector{Task}, worker_tasks))
end

function iterate(itr::AsyncCollector)
    itr.ntasks = verify_ntasks(itr.enumerator, itr.ntasks)
    itr.batch_size = verify_batch_size(itr.batch_size)

    chnl, worker_tasks = setup_chnl_and_tasks((i,args) -> (itr.results[i]=itr.f(args...)), itr.ntasks, itr.batch_size)
    return iterate(itr, AsyncCollectorState(chnl, worker_tasks))
end

function wait_done(itr::AsyncCollector, state::AsyncCollectorState)
    close(state.chnl)

    # wait for all tasks to finish
    foreach(x->(v=fetch(x); isa(v, Exception) && throw(v)), state.worker_tasks)
    empty!(state.worker_tasks)
end

function iterate(itr::AsyncCollector, state::AsyncCollectorState)
    if itr.nt_check && (length(state.worker_tasks) < itr.ntasks())
        start_worker_task!(state.worker_tasks, itr.f, state.chnl)
    end

    # Get index and mapped function arguments from enumeration iterator.
    y = isdefined(state, :enum_state) ?
        iterate(itr.enumerator, state.enum_state) :
        iterate(itr.enumerator)
    if y === nothing
        wait_done(itr, state)
        return nothing
    end
    (i, args), state.enum_state = y
    put!(state.chnl, (i, args))

    return (nothing, state)
end

"""
    AsyncGenerator(f, c...; ntasks=0, batch_size=nothing) -> iterator

Apply `f` to each element of `c` using at most `ntasks` asynchronous tasks.

Keyword args `ntasks` and `batch_size` have the same behavior as in
[`asyncmap`](@ref). If `batch_size` is specified, `f` must
be a function which operates on an array of argument tuples.

!!! note
    `collect(AsyncGenerator(f, c...; ntasks=1))` is equivalent to
    `map(f, c...)`.
"""
mutable struct AsyncGenerator
    collector::AsyncCollector
end

function AsyncGenerator(f, c...; ntasks=0)
    AsyncGenerator(AsyncCollector(f, Dict{Int,Any}(), c...; ntasks=ntasks))
end

mutable struct AsyncGeneratorState
    i::Int
    collector_done::Bool
    collector_state::AsyncCollectorState
    AsyncGeneratorState(i::Int) = new(i, false)
end

function iterate(itr::AsyncGenerator, state::AsyncGeneratorState=AsyncGeneratorState(0))
    state.i += 1

    results_dict = itr.collector.results
    while !state.collector_done && !haskey(results_dict, state.i)
        y = isdefined(state, :collector_state) ?
            iterate(itr.collector, state.collector_state) :
            iterate(itr.collector)
        if y === nothing
            # `check_done` waits for async tasks to finish. if we do not have the index
            # we are looking for, it is an error.
            state.collector_done = true
            break;
        end
        _, state.collector_state = y
    end
    state.collector_done && isempty(results_dict) && return nothing
    r = results_dict[state.i]
    delete!(results_dict, state.i)

    return (r, state)
end

# pass-through iterator traits to the iterable
# on which the mapping function is being applied
IteratorSize(::Type{AsyncGenerator}) = SizeUnknown()
IteratorEltype(::Type{AsyncGenerator}) = EltypeUnknown()
size(itr::AsyncGenerator) = size(itr.collector.enumerator)
length(itr::AsyncGenerator) = length(itr.collector.enumerator)

"""
    asyncmap!(f, results, c...; ntasks=0, batch_size=nothing)

Like [`asyncmap`](@ref), but stores output in `results` rather than
returning a collection.

$(_DOCS_ALIASING_WARNING)
"""
function asyncmap!(f, r, c1, c...; ntasks=0, batch_size=nothing)
    foreach(identity, AsyncCollector(f, r, c1, c...; ntasks=ntasks, batch_size=batch_size))
    r
end
Q   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/deprecated.jl�6      # This file is a part of Julia. License is MIT: https://julialang.org/license

# Deprecated functions and objects
#
# Please add new deprecations at the bottom of the file.
# A function deprecated in a release will be removed in the next one.
# Please also add a reference to the pull request which introduced the
# deprecation. For simple cases where a direct replacement is available,
# use @deprecate. @deprecate takes care of calling the replacement
# and of exporting the function.
#
# For more complex cases, move the body of the deprecated method in this file,
# and call depwarn() directly from inside it. The symbol depwarn() expects is
# the name of the function, which is used to ensure that the deprecation warning
# is only printed the first time for each call place.

"""
    @deprecate old new [export_old=true]

Deprecate method `old` and specify the replacement call `new`, defining a new method `old`
with the specified signature in the process.

To prevent `old` from being exported, set `export_old` to `false`.

!!! compat "Julia 1.5"
    As of Julia 1.5, functions defined by `@deprecate` do not print warning when `julia`
    is run without the `--depwarn=yes` flag set, as the default value of `--depwarn` option
    is `no`.  The warnings are printed from tests run by `Pkg.test()`.

# Examples
```jldoctest
julia> @deprecate old(x) new(x)
old (generic function with 1 method)

julia> @deprecate old(x) new(x) false
old (generic function with 1 method)
```

Calls to `@deprecate` without explicit type-annotations will define
deprecated methods accepting any number of positional and keyword
arguments of type `Any`.

!!! compat "Julia 1.9"
    Keyword arguments are forwarded when there is no explicit type
    annotation as of Julia 1.9. For older versions, you can manually
    forward positional and keyword arguments by doing `@deprecate
    old(args...; kwargs...) new(args...; kwargs...)`.

To restrict deprecation to a specific signature, annotate the
arguments of `old`. For example,
```jldoctest; filter = r"@ .*"a
julia> new(x::Int) = x;

julia> new(x::Float64) = 2x;

julia> @deprecate old(x::Int) new(x);

julia> methods(old)
# 1 method for generic function "old" from Main:
 [1] old(x::Int64)
     @ deprecated.jl:94
```
will define and deprecate a method `old(x::Int)` that mirrors `new(x::Int)` but will not
define nor deprecate the method `old(x::Float64)`.
"""
macro deprecate(old, new, export_old=true)
    function cannot_export_nonsymbol()
        error(
            "if the third `export_old` argument is not specified or `true`, the first",
            " argument must be of form",
            " (1) `f(...)` where `f` is a symbol,",
            " (2) `T{...}(...)` where `T` is a symbol, or",
            " (3) a symbol.",
        )
    end
    meta = Expr(:meta, :noinline)
    if isa(old, Expr) && (old.head === :call || old.head === :where)
        remove_linenums!(new)
        oldcall = sprint(show_unquoted, old)
        newcall = sprint(show_unquoted, new)
        # if old.head is a :where, step down one level to the :call to avoid code duplication below
        callexpr = old.head === :call ? old : old.args[1]
        if callexpr.head === :call
            fnexpr = callexpr.args[1]
            if fnexpr isa Expr && fnexpr.head === :curly
                fnexpr = fnexpr.args[1]
            end
            if export_old
                if fnexpr isa Symbol
                    maybe_export = Expr(:export, esc(fnexpr))
                else
                    cannot_export_nonsymbol()
                end
            else
                maybe_export = nothing
            end
        else
            error("invalid usage of @deprecate")
        end
        Expr(:toplevel,
            maybe_export,
            :($(esc(old)) = begin
                  $meta
                  depwarn($"`$oldcall` is deprecated, use `$newcall` instead.", Core.Typeof($(esc(fnexpr))).name.mt.name)
                  $(esc(new))
              end))
    else
        if export_old && !(old isa Symbol)
            cannot_export_nonsymbol()
        end
        Expr(:toplevel,
            export_old ? Expr(:export, esc(old)) : nothing,
            :(function $(esc(old))(args...; kwargs...)
                  $meta
                  depwarn($"`$old` is deprecated, use `$new` instead.", Core.Typeof($(esc(old))).name.mt.name)
                  $(esc(new))(args...; kwargs...)
              end))
    end
end

function depwarn(msg, funcsym; force::Bool=false)
    opts = JLOptions()
    if opts.depwarn == 2
        throw(ErrorException(msg))
    end
    deplevel = force || opts.depwarn == 1 ? CoreLogging.Warn : CoreLogging.BelowMinLevel
    @logmsg(
        deplevel,
        msg,
        _module=begin
            bt = backtrace()
            frame, caller = firstcaller(bt, funcsym)
            linfo = caller.linfo
            if linfo isa Core.MethodInstance
                def = linfo.def
                def isa Module ? def : def.module
            else
                Core    # TODO: Is it reasonable to attribute callers without linfo to Core?
            end
        end,
        _file=String(caller.file),
        _line=caller.line,
        _id=(frame,funcsym),
        _group=:depwarn,
        caller=caller,
        maxlog=funcsym === nothing ? nothing : 1
    )
    nothing
end

firstcaller(bt::Vector, ::Nothing) = Ptr{Cvoid}(0), StackTraces.UNKNOWN
firstcaller(bt::Vector, funcsym::Symbol) = firstcaller(bt, (funcsym,))
function firstcaller(bt::Vector, funcsyms)
    # Identify the calling line
    found = false
    for ip in bt
        lkups = StackTraces.lookup(ip)
        for lkup in lkups
            if lkup == StackTraces.UNKNOWN || lkup.from_c
                continue
            end
            if found
                return ip, lkup
            end
            found = lkup.func in funcsyms
            # look for constructor type name
            if !found
                li = lkup.linfo
                if li isa Core.MethodInstance
                    def = li.def
                    found = def isa Method && def.name in funcsyms
                end
            end
        end
    end
    return C_NULL, StackTraces.UNKNOWN
end

deprecate(m::Module, s::Symbol, flag=1) = ccall(:jl_deprecate_binding, Cvoid, (Any, Any, Cint), m, s, flag)

macro deprecate_binding(old, new, export_old=true, dep_message=:nothing, constant=true)
    dep_message === :nothing && (dep_message = ", use $new instead.")
    return Expr(:toplevel,
         export_old ? Expr(:export, esc(old)) : nothing,
         Expr(:const, Expr(:(=), esc(Symbol(string("_dep_message_",old))), esc(dep_message))),
         constant ? Expr(:const, Expr(:(=), esc(old), esc(new))) : Expr(:(=), esc(old), esc(new)),
         Expr(:call, :deprecate, __module__, Expr(:quote, old)))
end

macro deprecate_stdlib(old, mod, export_old=true, newname=old)
    rename = old === newname ? "" : " as `$newname`"
    dep_message = """: it has been moved to the standard library package `$mod`$rename.
                        Add `using $mod` to your imports."""
    new = GlobalRef(Base.root_module(Base, mod), newname)
    return Expr(:toplevel,
         export_old ? Expr(:export, esc(old)) : nothing,
         Expr(:const, Expr(:(=), esc(Symbol(string("_dep_message_",old))), esc(dep_message))),
         Expr(:const, Expr(:(=), esc(old), esc(new))),
         Expr(:call, :deprecate, __module__, Expr(:quote, old)))
end

macro deprecate_moved(old, new, export_old=true)
    eold = esc(old)
    emsg = string(old, " has been moved to the package ", new, ".jl.\n",
        "Run `Pkg.add(\"", new, "\")` to install it, restart Julia,\n",
        "and then run `using ", new, "` to load it.")
    return Expr(:toplevel,
        :($eold(args...; kwargs...) = error($emsg)),
        export_old ? Expr(:export, eold) : nothing,
        Expr(:call, :deprecate, __module__, Expr(:quote, old), 2))
end

# BEGIN 1.0 deprecations

@deprecate one(i::CartesianIndex)                    oneunit(i)
@deprecate one(I::Type{CartesianIndex{N}}) where {N} oneunit(I)

@deprecate BigFloat(x, prec::Int)                               BigFloat(x; precision=prec)
@deprecate BigFloat(x, prec::Int, rounding::RoundingMode)       BigFloat(x, rounding; precision=prec)
@deprecate BigFloat(x::Real, prec::Int)                         BigFloat(x; precision=prec)
@deprecate BigFloat(x::Real, prec::Int, rounding::RoundingMode) BigFloat(x, rounding; precision=prec)

# END 1.0 deprecations

# BEGIN 1.5 deprecations

"""
    isimmutable(v) -> Bool
!!! warning
    Consider using `!ismutable(v)` instead, as `isimmutable(v)` will be replaced by `!ismutable(v)` in a future release. (Since Julia 1.5)
Return `true` iff value `v` is immutable.  See [Mutable Composite Types](@ref)
for a discussion of immutability. Note that this function works on values, so if you give it
a type, it will tell you that a value of `DataType` is mutable.

# Examples
```jldoctest
julia> isimmutable(1)
true

julia> isimmutable([1,2])
false
```
"""
isimmutable(@nospecialize(x)) = !ismutable(x)
export isimmutable
# Note isimmutable is not @deprecated out of performance concerns

macro get!(h, key0, default)
    f, l = __source__.file, __source__.line
    @warn "`@get!(dict, key, default)` at $f:$l is deprecated, use `get!(()->default, dict, key)` instead."
    return quote
        get!(()->$(esc(default)), $(esc(h)), $(esc(key0)))
    end
end

pointer(V::SubArray{<:Any,<:Any,<:Array,<:Tuple{Vararg{RangeIndex}}}, is::Tuple) = pointer(V, CartesianIndex(is))

# END 1.5 deprecations

# BEGIN 1.6 deprecations

# These changed from SimpleVector to `MethodMatch`. These definitions emulate
# being a SimpleVector to ease transition for packages that make explicit
# use of (internal) APIs that return raw method matches.
iterate(match::Core.MethodMatch, field::Int=1) =
    field > nfields(match) ? nothing : (getfield(match, field), field+1)
getindex(match::Core.MethodMatch, field::Int) =
    getfield(match, field)


# these were internal functions, but some packages seem to be relying on them
tuple_type_head(T::Type) = fieldtype(T, 1)
tuple_type_cons(::Type, ::Type{Union{}}) = Union{}
function tuple_type_cons(::Type{S}, ::Type{T}) where T<:Tuple where S
    @_foldable_meta
    Tuple{S, T.parameters...}
end
function parameter_upper_bound(t::UnionAll, idx)
    @_foldable_meta
    return rewrap_unionall((unwrap_unionall(t)::DataType).parameters[idx], t)
end

# these were internal functions, but some packages seem to be relying on them
@deprecate cat_shape(dims, shape::Tuple{}, shapes::Tuple...) cat_shape(dims, shapes) false
cat_shape(dims, shape::Tuple{}) = () # make sure `cat_shape(dims, ())` do not recursively calls itself

@deprecate unsafe_indices(A) axes(A) false
@deprecate unsafe_length(r) length(r) false

# these were internal type aliases, but some packages seem to be relying on them
const Any16{N} = Tuple{Any,Any,Any,Any,Any,Any,Any,Any,
                        Any,Any,Any,Any,Any,Any,Any,Any,Vararg{Any,N}}
const All16{T,N} = Tuple{T,T,T,T,T,T,T,T,
                         T,T,T,T,T,T,T,T,Vararg{T,N}}

# END 1.6 deprecations

# BEGIN 1.7 deprecations

# the plan is to eventually overload getproperty to access entries of the dict
@noinline function getproperty(x::Pairs, s::Symbol)
    depwarn("use values(kwargs) and keys(kwargs) instead of kwargs.data and kwargs.itr", :getproperty, force=true)
    return getfield(x, s)
end

# This function was marked as experimental and not exported.
@deprecate catch_stack(task=current_task(); include_bt=true) current_exceptions(task; backtrace=include_bt) false

# END 1.7 deprecations

# BEGIN 1.8 deprecations

const var"@_inline_meta" = var"@inline"
const var"@_noinline_meta" = var"@noinline"
@deprecate getindex(t::Tuple, i::Real) t[convert(Int, i)]

# END 1.8 deprecations

# BEGIN 1.9 deprecations

# We'd generally like to avoid direct external access to internal fields
# Core.Compiler.is_inlineable and Core.Compiler.set_inlineable! move towards this direction,
# but we need to keep these around for compat
function getproperty(ci::CodeInfo, s::Symbol)
    s === :inlineable && return Core.Compiler.is_inlineable(ci)
    return getfield(ci, s)
end

function setproperty!(ci::CodeInfo, s::Symbol, v)
    s === :inlineable && return Core.Compiler.set_inlineable!(ci, v)
    return setfield!(ci, s, convert(fieldtype(CodeInfo, s), v))
end

@eval Threads nthreads() = threadpoolsize()

@eval Threads begin
    """
        resize_nthreads!(A, copyvalue=A[1])

    Resize the array `A` to length [`nthreads()`](@ref).   Any new
    elements that are allocated are initialized to `deepcopy(copyvalue)`,
    where `copyvalue` defaults to `A[1]`.

    This is typically used to allocate per-thread variables, and
    should be called in `__init__` if `A` is a global constant.

    !!! warning

        This function is deprecated, since as of Julia v1.9 the number of
        threads can change at run time. Instead, per-thread state should be
        created as needed based on the thread id of the caller.
    """
    function resize_nthreads!(A::AbstractVector, copyvalue=A[1])
        nthr = nthreads()
        nold = length(A)
        resize!(A, nthr)
        for i = nold+1:nthr
            A[i] = deepcopy(copyvalue)
        end
        return A
    end
end

# END 1.9 deprecations

# BEGIN 1.10 deprecations

"""
    @pure ex

`@pure` gives the compiler a hint for the definition of a pure function,
helping for type inference.

!!! warning
    This macro is intended for internal compiler use and may be subject to changes.

!!! warning
    In Julia 1.8 and higher, it is favorable to use [`@assume_effects`](@ref) instead of `@pure`.
    This is because `@assume_effects` allows a finer grained control over Julia's purity
    modeling and the effect system enables a wider range of optimizations.
"""
macro pure(ex)
    return esc(:(Base.@assume_effects :foldable $ex))
end

# END 1.10 deprecations
T   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/docs/basedocs.jl:     # This file is a part of Julia. License is MIT: https://julialang.org/license

module BaseDocs

@nospecialize # don't specialize on any arguments of the methods declared herein

struct Keyword
    name::Symbol
end
macro kw_str(text)
    return Keyword(Symbol(text))
end

"""
**Welcome to Julia $(string(VERSION)).** The full manual is available at

    https://docs.julialang.org

as well as many great tutorials and learning resources:

    https://julialang.org/learning/

For help on a specific function or macro, type `?` followed
by its name, e.g. `?cos`, or `?@time`, and press enter.
Type `;` to enter shell mode, `]` to enter package mode.

To exit the interactive session, type `CTRL-D` (press the
control key together with the `d` key), or type `exit()`.
"""
kw"help", kw"Julia", kw"julia", kw""

"""
    using

`using Foo` will load the module or package `Foo` and make its [`export`](@ref)ed names
available for direct use. Names can also be used via dot syntax (e.g. `Foo.foo` to access
the name `foo`), whether they are `export`ed or not.
See the [manual section about modules](@ref modules) for details.
"""
kw"using"

"""
    import

`import Foo` will load the module or package `Foo`.
Names from the imported `Foo` module can be accessed with dot syntax
(e.g. `Foo.foo` to access the name `foo`).
See the [manual section about modules](@ref modules) for details.
"""
kw"import"

"""
    export

`export` is used within modules to tell Julia which functions should be
made available to the user. For example: `export foo` makes the name
`foo` available when [`using`](@ref) the module.
See the [manual section about modules](@ref modules) for details.
"""
kw"export"

"""
    as

`as` is used as a keyword to rename an identifier brought into scope by
`import` or `using`, for the purpose of working around name conflicts as
well as for shortening names.  (Outside of `import` or `using` statements,
`as` is not a keyword and can be used as an ordinary identifier.)

`import LinearAlgebra as LA` brings the imported `LinearAlgebra` standard library
into scope as `LA`.

`import LinearAlgebra: eigen as eig, cholesky as chol` brings the `eigen` and `cholesky` methods
from `LinearAlgebra` into scope as `eig` and `chol` respectively.

`as` works with `using` only when individual identifiers are brought into scope.
For example, `using LinearAlgebra: eigen as eig` or `using LinearAlgebra: eigen as eig, cholesky as chol` works,
but `using LinearAlgebra as LA` is invalid syntax, since it is nonsensical to
rename *all* exported names from `LinearAlgebra` to `LA`.
"""
kw"as"

"""
    abstract type

`abstract type` declares a type that cannot be instantiated, and serves only as a node in the
type graph, thereby describing sets of related concrete types: those concrete types
which are their descendants. Abstract types form the conceptual hierarchy which makes
Julia’s type system more than just a collection of object implementations. For example:

```julia
abstract type Number end
abstract type Real <: Number end
```
[`Number`](@ref) has no supertype, whereas [`Real`](@ref) is an abstract subtype of `Number`.
"""
kw"abstract type", kw"abstract"

"""
    module

`module` declares a [`Module`](@ref), which is a separate global variable workspace. Within a
module, you can control which names from other modules are visible (via importing), and
specify which of your names are intended to be public (via exporting).
Modules allow you to create top-level definitions without worrying about name conflicts
when your code is used together with somebody else’s.
See the [manual section about modules](@ref modules) for more details.

# Examples
```julia
module Foo
import Base.show
export MyType, foo

struct MyType
    x
end

bar(x) = 2x
foo(a::MyType) = bar(a.x) + 1
show(io::IO, a::MyType) = print(io, "MyType \$(a.x)")
end
```
"""
kw"module"

"""
    __init__

The `__init__()` function in a module executes immediately *after* the module is loaded at
runtime for the first time. It is called once, after all other statements in the module
have been executed. Because it is called after fully importing the module, `__init__`
functions of submodules will be executed first. Two typical uses of `__init__` are calling
runtime initialization functions of external C libraries and initializing global constants
that involve pointers returned by external libraries.
See the [manual section about modules](@ref modules) for more details.

# Examples
```julia
const foo_data_ptr = Ref{Ptr{Cvoid}}(0)
function __init__()
    ccall((:foo_init, :libfoo), Cvoid, ())
    foo_data_ptr[] = ccall((:foo_data, :libfoo), Ptr{Cvoid}, ())
    nothing
end
```
"""
kw"__init__"

"""
    baremodule

`baremodule` declares a module that does not contain `using Base` or local definitions of
[`eval`](@ref Base.MainInclude.eval) and [`include`](@ref Base.include). It does still import `Core`. In other words,

```julia
module Mod

...

end
```

is equivalent to

```julia
baremodule Mod

using Base

eval(x) = Core.eval(Mod, x)
include(p) = Base.include(Mod, p)

...

end
```
"""
kw"baremodule"

"""
    primitive type

`primitive type` declares a concrete type whose data consists only of a series of bits. Classic
examples of primitive types are integers and floating-point values. Some example built-in
primitive type declarations:

```julia
primitive type Char 32 end
primitive type Bool <: Integer 8 end
```
The number after the name indicates how many bits of storage the type requires. Currently,
only sizes that are multiples of 8 bits are supported.
The [`Bool`](@ref) declaration shows how a primitive type can be optionally
declared to be a subtype of some supertype.
"""
kw"primitive type"

"""
    macro

`macro` defines a method for inserting generated code into a program.
A macro maps a sequence of argument expressions to a returned expression, and the
resulting expression is substituted directly into the program at the point where
the macro is invoked.
Macros are a way to run generated code without calling [`eval`](@ref Base.MainInclude.eval),
since the generated code instead simply becomes part of the surrounding program.
Macro arguments may include expressions, literal values, and symbols. Macros can be defined for
variable number of arguments (varargs), but do not accept keyword arguments.
Every macro also implicitly gets passed the arguments `__source__`, which contains the line number
and file name the macro is called from, and `__module__`, which is the module the macro is expanded
in.

See the manual section on [Metaprogramming](@ref) for more information about how to write a macro.

# Examples
```jldoctest
julia> macro sayhello(name)
           return :( println("Hello, ", \$name, "!") )
       end
@sayhello (macro with 1 method)

julia> @sayhello "Charlie"
Hello, Charlie!

julia> macro saylots(x...)
           return :( println("Say: ", \$(x...)) )
       end
@saylots (macro with 1 method)

julia> @saylots "hey " "there " "friend"
Say: hey there friend
```
"""
kw"macro"

"""
    __module__

The argument `__module__` is only visible inside the macro, and it provides information
(in the form of a `Module` object) about the expansion context of the macro invocation.
See the manual section on [Macro invocation](@ref) for more information.
"""
kw"__module__"

"""
    __source__

The argument `__source__` is only visible inside the macro, and it provides information
(in the form of a `LineNumberNode` object) about the parser location of the `@` sign from
the macro invocation. See the manual section on [Macro invocation](@ref) for more information.
"""
kw"__source__"

"""
    local

`local` introduces a new local variable.
See the [manual section on variable scoping](@ref scope-of-variables) for more information.

# Examples
```jldoctest
julia> function foo(n)
           x = 0
           for i = 1:n
               local x # introduce a loop-local x
               x = i
           end
           x
       end
foo (generic function with 1 method)

julia> foo(10)
0
```
"""
kw"local"

"""
    global

`global x` makes `x` in the current scope and its inner scopes refer to the global
variable of that name.
See the [manual section on variable scoping](@ref scope-of-variables) for more information.

# Examples
```jldoctest
julia> z = 3
3

julia> function foo()
           global z = 6 # use the z variable defined outside foo
       end
foo (generic function with 1 method)

julia> foo()
6

julia> z
6
```
"""
kw"global"

"""
    for outer

Reuse an existing local variable for iteration in a `for` loop.

See the [manual section on variable scoping](@ref scope-of-variables) for more information.

See also [`for`](@ref).


# Examples
```jldoctest
julia> function f()
           i = 0
           for i = 1:3
               # empty
           end
           return i
       end;

julia> f()
0
```

```jldoctest
julia> function f()
           i = 0
           for outer i = 1:3
               # empty
           end
           return i
       end;

julia> f()
3
```

```jldoctest
julia> i = 0 # global variable
       for outer i = 1:3
       end
ERROR: syntax: no outer local variable declaration exists for "for outer"
[...]
```
"""
kw"outer"

"""
    ' '

A pair of single-quote characters delimit a [`Char`](@ref) (that is, character) literal.

# Examples
```jldoctest
julia> 'j'
'j': ASCII/Unicode U+006A (category Ll: Letter, lowercase)
```
"""
kw"''"

"""
    =

`=` is the assignment operator.
* For variable `a` and expression `b`, `a = b` makes `a` refer to the value of `b`.
* For functions `f(x)`, `f(x) = x` defines a new function constant `f`, or adds a new method to `f` if `f` is already defined; this usage is equivalent to `function f(x); x; end`.
* `a[i] = v` calls [`setindex!`](@ref)`(a,v,i)`.
* `a.b = c` calls [`setproperty!`](@ref)`(a,:b,c)`.
* Inside a function call, `f(a=b)` passes `b` as the value of keyword argument `a`.
* Inside parentheses with commas, `(a=1,)` constructs a [`NamedTuple`](@ref).

# Examples
Assigning `a` to `b` does not create a copy of `b`; instead use [`copy`](@ref) or [`deepcopy`](@ref).

```jldoctest
julia> b = [1]; a = b; b[1] = 2; a
1-element Array{Int64, 1}:
 2

julia> b = [1]; a = copy(b); b[1] = 2; a
1-element Array{Int64, 1}:
 1

```
Collections passed to functions are also not copied. Functions can modify (mutate) the contents of the objects their arguments refer to. (The names of functions which do this are conventionally suffixed with '!'.)
```jldoctest
julia> function f!(x); x[:] .+= 1; end
f! (generic function with 1 method)

julia> a = [1]; f!(a); a
1-element Array{Int64, 1}:
 2

```
Assignment can operate on multiple variables in parallel, taking values from an iterable:
```jldoctest
julia> a, b = 4, 5
(4, 5)

julia> a, b = 1:3
1:3

julia> a, b
(1, 2)

```
Assignment can operate on multiple variables in series, and will return the value of the right-hand-most expression:
```jldoctest
julia> a = [1]; b = [2]; c = [3]; a = b = c
1-element Array{Int64, 1}:
 3

julia> b[1] = 2; a, b, c
([2], [2], [2])

```
Assignment at out-of-bounds indices does not grow a collection. If the collection is a [`Vector`](@ref) it can instead be grown with [`push!`](@ref) or [`append!`](@ref).
```jldoctest
julia> a = [1, 1]; a[3] = 2
ERROR: BoundsError: attempt to access 2-element Array{Int64, 1} at index [3]
[...]

julia> push!(a, 2, 3)
4-element Array{Int64, 1}:
 1
 1
 2
 3

```
Assigning `[]` does not eliminate elements from a collection; instead use [`filter!`](@ref).
```jldoctest
julia> a = collect(1:3); a[a .<= 1] = []
ERROR: DimensionMismatch: tried to assign 0 elements to 1 destinations
[...]

julia> filter!(x -> x > 1, a) # in-place & thus more efficient than a = a[a .> 1]
2-element Array{Int64, 1}:
 2
 3

```
"""
kw"="

"""
    .=

Perform broadcasted assignment. The right-side argument is expanded as in
[`broadcast`](@ref) and then assigned into the left-side argument in-place.
Fuses with other dotted operators in the same expression; i.e. the whole
assignment expression is converted into a single loop.

`A .= B` is similar to `broadcast!(identity, A, B)`.

# Examples
```jldoctest
julia> A = zeros(4, 4); B = [1, 2, 3, 4];

julia> A .= B
4×4 Array{Float64, 2}:
 1.0  1.0  1.0  1.0
 2.0  2.0  2.0  2.0
 3.0  3.0  3.0  3.0
 4.0  4.0  4.0  4.0

julia> A
4×4 Array{Float64, 2}:
 1.0  1.0  1.0  1.0
 2.0  2.0  2.0  2.0
 3.0  3.0  3.0  3.0
 4.0  4.0  4.0  4.0
```
"""
kw".="

"""
    .

The dot operator is used to access fields or properties of objects and access
variables defined inside modules.

In general, `a.b` calls `getproperty(a, :b)` (see [`getproperty`](@ref Base.getproperty)).

# Examples
```jldoctest
julia> z = 1 + 2im; z.im
2

julia> Iterators.product
product (generic function with 1 method)
```
"""
kw"."

"""
    let

`let` blocks create a new hard scope and optionally introduce new local bindings.

Just like the [other scope constructs](@ref man-scope-table), `let` blocks define
the block of code where newly introduced local variables are accessible.
Additionally, the syntax has a special meaning for comma-separated assignments
and variable names that may optionally appear on the same line as the `let`:

```julia
let var1 = value1, var2, var3 = value3
    code
end
```

The variables introduced on this line are local to the `let` block and the assignments are
evaluated in order, with each right-hand side evaluated in the scope
without considering the name on the left-hand side. Therefore it makes
sense to write something like `let x = x`, since the two `x` variables are distinct with
the left-hand side locally shadowing the `x` from the outer scope. This can even
be a useful idiom as new local variables are freshly created each time local scopes
are entered, but this is only observable in the case of variables that outlive their
scope via closures.  A `let` variable without an assignment, such as `var2` in the
example above, declares a new local variable that is not yet bound to a value.

By contrast, [`begin`](@ref) blocks also group multiple expressions together but do
not introduce scope or have the special assignment syntax.

### Examples

In the function below, there is a single `x` that is iteratively updated three times by the `map`.
The closures returned all reference that one `x` at its final value:

```jldoctest
julia> function test_outer_x()
           x = 0
           map(1:3) do _
               x += 1
               return ()->x
           end
       end
test_outer_x (generic function with 1 method)

julia> [f() for f in test_outer_x()]
3-element Vector{Int64}:
 3
 3
 3
```

If, however, we add a `let` block that introduces a _new_ local variable we will end up
with three distinct variables being captured (one at each iteration) even though we
chose to use (shadow) the same name.

```jldoctest
julia> function test_let_x()
           x = 0
           map(1:3) do _
               x += 1
               let x = x
                   return ()->x
               end
           end
       end
test_let_x (generic function with 1 method)

julia> [f() for f in test_let_x()]
3-element Vector{Int64}:
 1
 2
 3
```

All scope constructs that introduce new local variables behave this way
when repeatedly run; the distinctive feature of `let` is its ability
to succinctly declare new `local`s that may shadow outer variables of the same
name. For example, directly using the argument of the `do` function similarly
captures three distinct variables:

```jldoctest
julia> function test_do_x()
           map(1:3) do x
               return ()->x
           end
       end
test_do_x (generic function with 1 method)

julia> [f() for f in test_do_x()]
3-element Vector{Int64}:
 1
 2
 3
```


"""
kw"let"

"""
    quote

`quote` creates multiple expression objects in a block without using the explicit
[`Expr`](@ref) constructor. For example:

```julia
ex = quote
    x = 1
    y = 2
    x + y
end
```
Unlike the other means of quoting, `:( ... )`, this form introduces `QuoteNode` elements
to the expression tree, which must be considered when directly manipulating the tree.
For other purposes, `:( ... )` and `quote .. end` blocks are treated identically.
"""
kw"quote"

"""
    @

The at sign followed by a macro name marks a macro call. Macros provide the
ability to include generated code in the final body of a program. A macro maps
a tuple of arguments, expressed as space-separated expressions or a
function-call-like argument list, to a returned *expression*. The resulting
expression is compiled directly into the surrounding code. See
[Metaprogramming](@ref man-macros) for more details and examples.
"""
kw"@"

"""
    {}

Curly braces are used to specify [type parameters](@ref man-parametric-types).

Type parameters allow a single type declaration to introduce a whole family of
new types — one for each possible combination of parameter values. For example,
the [`Set`](@ref) type describes many possible types of sets; it uses one type
parameter to describe the type of the elements it contains. The specific _parameterized_
types `Set{Float64}` and `Set{Int64}` describe two _concrete_ types: both are
subtypes ([`<:`](@ref)) of `Set`, but the former has `Float64` elements and the latter
has `Int64` elements.
"""
kw"{", kw"{}", kw"}"

"""
    []

Square braces are used for [indexing](@ref man-array-indexing), [indexed assignment](@ref man-indexed-assignment),
[array literals](@ref man-array-literals), and [array comprehensions](@ref man-comprehensions).
"""
kw"[", kw"[]", kw"]"

"""
    ()

Parentheses are used to group expressions, call functions, and construct [tuples](@ref Tuple) and [named tuples](@ref NamedTuple).
"""
kw"(", kw"()", kw")"

"""
    #

The number sign (or hash) character is used to begin a single-line comment.
"""
kw"#"

"""
    #= =#

A multi-line comment begins with `#=` and ends with `=#`, and may be nested.
"""
kw"#=", kw"=#"

"""
    ;

Semicolons are used as statement separators and mark the beginning of keyword arguments in function declarations or calls.
"""
kw";"

"""
    Expr(head::Symbol, args...)

A type representing compound expressions in parsed julia code (ASTs).
Each expression consists of a `head` `Symbol` identifying which kind of
expression it is (e.g. a call, for loop, conditional statement, etc.),
and subexpressions (e.g. the arguments of a call).
The subexpressions are stored in a `Vector{Any}` field called `args`.

See the manual chapter on [Metaprogramming](@ref) and the developer
documentation [Julia ASTs](@ref).

# Examples
```jldoctest
julia> Expr(:call, :+, 1, 2)
:(1 + 2)

julia> dump(:(a ? b : c))
Expr
  head: Symbol if
  args: Array{Any}((3,))
    1: Symbol a
    2: Symbol b
    3: Symbol c
```
"""
Expr

"""
    :expr

Quote an expression `expr`, returning the abstract syntax tree (AST) of `expr`.
The AST may be of type `Expr`, `Symbol`, or a literal value.
The syntax `:identifier` evaluates to a `Symbol`.

See also: [`Expr`](@ref), [`Symbol`](@ref), [`Meta.parse`](@ref)

# Examples
```jldoctest
julia> expr = :(a = b + 2*x)
:(a = b + 2x)

julia> sym = :some_identifier
:some_identifier

julia> value = :0xff
0xff

julia> typeof((expr, sym, value))
Tuple{Expr, Symbol, UInt8}
```
"""
(:)

"""
    \$

Interpolation operator for interpolating into e.g. [strings](@ref string-interpolation)
and [expressions](@ref man-expression-interpolation).

# Examples
```jldoctest
julia> name = "Joe"
"Joe"

julia> "My name is \$name."
"My name is Joe."
```
"""
kw"$"

"""
    const

`const` is used to declare global variables whose values will not change. In almost all code
(and particularly performance sensitive code) global variables should be declared
constant in this way.

```julia
const x = 5
```

Multiple variables can be declared within a single `const`:
```julia
const y, z = 7, 11
```

Note that `const` only applies to one `=` operation, therefore `const x = y = 1`
declares `x` to be constant but not `y`. On the other hand, `const x = const y = 1`
declares both `x` and `y` constant.

Note that "constant-ness" does not extend into mutable containers; only the
association between a variable and its value is constant.
If `x` is an array or dictionary (for example) you can still modify, add, or remove elements.

In some cases changing the value of a `const` variable gives a warning instead of
an error.
However, this can produce unpredictable behavior or corrupt the state of your program,
and so should be avoided.
This feature is intended only for convenience during interactive use.
"""
kw"const"

"""
    function

Functions are defined with the `function` keyword:

```julia
function add(a, b)
    return a + b
end
```
Or the short form notation:

```julia
add(a, b) = a + b
```

The use of the [`return`](@ref) keyword is exactly the same as in other languages,
but is often optional. A function without an explicit `return` statement will return
the last expression in the function body.
"""
kw"function"

"""
    x -> y

Create an anonymous function mapping argument(s) `x` to the function body `y`.

```jldoctest
julia> f = x -> x^2 + 2x - 1
#1 (generic function with 1 method)

julia> f(2)
7
```

Anonymous functions can also be defined for multiple arguments.
```jldoctest
julia> g = (x,y) -> x^2 + y^2
#2 (generic function with 1 method)

julia> g(2,3)
13
```

See the manual section on [anonymous functions](@ref man-anonymous-functions) for more details.
"""
kw"->"

"""
    return

`return x` causes the enclosing function to exit early, passing the given value `x`
back to its caller. `return` by itself with no value is equivalent to `return nothing`
(see [`nothing`](@ref)).

```julia
function compare(a, b)
    a == b && return "equal to"
    a < b ? "less than" : "greater than"
end
```
In general you can place a `return` statement anywhere within a function body, including
within deeply nested loops or conditionals, but be careful with `do` blocks. For
example:

```julia
function test1(xs)
    for x in xs
        iseven(x) && return 2x
    end
end

function test2(xs)
    map(xs) do x
        iseven(x) && return 2x
        x
    end
end
```
In the first example, the return breaks out of `test1` as soon as it hits
an even number, so `test1([5,6,7])` returns `12`.

You might expect the second example to behave the same way, but in fact the `return`
there only breaks out of the *inner* function (inside the `do` block) and gives a value
back to `map`. `test2([5,6,7])` then returns `[5,12,7]`.

When used in a top-level expression (i.e. outside any function), `return` causes
the entire current top-level expression to terminate early.
"""
kw"return"

"""
    if/elseif/else

`if`/`elseif`/`else` performs conditional evaluation, which allows portions of code to
be evaluated or not evaluated depending on the value of a boolean expression. Here is
the anatomy of the `if`/`elseif`/`else` conditional syntax:

```julia
if x < y
    println("x is less than y")
elseif x > y
    println("x is greater than y")
else
    println("x is equal to y")
end
```
If the condition expression `x < y` is true, then the corresponding block is evaluated;
otherwise the condition expression `x > y` is evaluated, and if it is true, the
corresponding block is evaluated; if neither expression is true, the `else` block is
evaluated. The `elseif` and `else` blocks are optional, and as many `elseif` blocks as
desired can be used.

In contrast to some other languages conditions must be of type `Bool`. It does not
suffice for conditions to be convertible to `Bool`.
```jldoctest
julia> if 1 end
ERROR: TypeError: non-boolean (Int64) used in boolean context
```
"""
kw"if", kw"elseif", kw"else"

"""
    a ? b : c

Short form for conditionals; read "if `a`, evaluate `b` otherwise evaluate `c`".
Also known as the [ternary operator](https://en.wikipedia.org/wiki/%3F:).

This syntax is equivalent to `if a; b else c end`, but is often used to
emphasize the value `b`-or-`c` which is being used as part of a larger
expression, rather than the side effects that evaluating `b` or `c` may have.

See the manual section on [control flow](@ref man-conditional-evaluation) for more details.

# Examples
```
julia> x = 1; y = 2;

julia> x > y ? println("x is larger") : println("y is larger")
y is larger
```
"""
kw"?", kw"?:"

"""
    for

`for` loops repeatedly evaluate a block of statements while
iterating over a sequence of values.

The iteration variable is always a new variable, even if a variable of the same name
exists in the enclosing scope.
Use [`outer`](@ref) to reuse an existing local variable for iteration.

# Examples
```jldoctest
julia> for i in [1, 4, 0]
           println(i)
       end
1
4
0
```
"""
kw"for"

"""
    while

`while` loops repeatedly evaluate a conditional expression, and continue evaluating the
body of the while loop as long as the expression remains true. If the condition
expression is false when the while loop is first reached, the body is never evaluated.

# Examples
```jldoctest
julia> i = 1
1

julia> while i < 5
           println(i)
           global i += 1
       end
1
2
3
4
```
"""
kw"while"

"""
    end

`end` marks the conclusion of a block of expressions, for example
[`module`](@ref), [`struct`](@ref), [`mutable struct`](@ref),
[`begin`](@ref), [`let`](@ref), [`for`](@ref) etc.

`end` may also be used when indexing to represent the last index of a
collection or the last index of a dimension of an array.

# Examples
```jldoctest
julia> A = [1 2; 3 4]
2×2 Array{Int64, 2}:
 1  2
 3  4

julia> A[end, :]
2-element Array{Int64, 1}:
 3
 4
```
"""
kw"end"

"""
    try/catch

A `try`/`catch` statement allows intercepting errors (exceptions) thrown
by [`throw`](@ref) so that program execution can continue.
For example, the following code attempts to write a file, but warns the user
and proceeds instead of terminating execution if the file cannot be written:

```julia
try
    open("/danger", "w") do f
        println(f, "Hello")
    end
catch
    @warn "Could not write file."
end
```

or, when the file cannot be read into a variable:

```julia
lines = try
    open("/danger", "r") do f
        readlines(f)
    end
catch
    @warn "File not found."
end
```

The syntax `catch e` (where `e` is any variable) assigns the thrown
exception object to the given variable within the `catch` block.

The power of the `try`/`catch` construct lies in the ability to unwind a deeply
nested computation immediately to a much higher level in the stack of calling functions.
"""
kw"try", kw"catch"

"""
    finally

Run some code when a given block of code exits, regardless
of how it exits. For example, here is how we can guarantee that an opened file is
closed:

```julia
f = open("file")
try
    operate_on_file(f)
finally
    close(f)
end
```

When control leaves the [`try`](@ref) block (for example, due to a [`return`](@ref), or just finishing
normally), [`close(f)`](@ref) will be executed. If the `try` block exits due to an exception,
the exception will continue propagating. A `catch` block may be combined with `try` and
`finally` as well. In this case the `finally` block will run after `catch` has handled
the error.
"""
kw"finally"

"""
    break

Break out of a loop immediately.

# Examples
```jldoctest
julia> i = 0
0

julia> while true
           global i += 1
           i > 5 && break
           println(i)
       end
1
2
3
4
5
```
"""
kw"break"

"""
    continue

Skip the rest of the current loop iteration.

# Examples
```jldoctest
julia> for i = 1:6
           iseven(i) && continue
           println(i)
       end
1
3
5
```
"""
kw"continue"

"""
    do

Create an anonymous function and pass it as the first argument to
a function call.
For example:

```julia
map(1:10) do x
    2x
end
```

is equivalent to `map(x->2x, 1:10)`.

Use multiple arguments like so:

```julia
map(1:10, 11:20) do x, y
    x + y
end
```
"""
kw"do"

"""
    ...

The "splat" operator, `...`, represents a sequence of arguments.
`...` can be used in function definitions, to indicate that the function
accepts an arbitrary number of arguments.
`...` can also be used to apply a function to a sequence of arguments.

# Examples
```jldoctest
julia> add(xs...) = reduce(+, xs)
add (generic function with 1 method)

julia> add(1, 2, 3, 4, 5)
15

julia> add([1, 2, 3]...)
6

julia> add(7, 1:100..., 1000:1100...)
111107
```
"""
kw"..."

"""
    ;

`;` has a similar role in Julia as in many C-like languages, and is used to delimit the
end of the previous statement.

`;` is not necessary at the end of a line, but can be used to
separate statements on a single line or to join statements into a single expression.

Adding `;` at the end of a line in the REPL will suppress printing the result of that expression.

In function declarations, and optionally in calls, `;` separates regular arguments from keywords.

In array literals, arguments separated by semicolons have their contents
concatenated together. A separator made of a single `;` concatenates vertically
(i.e. along the first dimension), `;;` concatenates horizontally (second
dimension), `;;;` concatenates along the third dimension, etc. Such a separator
can also be used in last position in the square brackets to add trailing
dimensions of length 1.

A `;` in first position inside of parentheses can be used to construct a named
tuple. The same `(; ...)` syntax on the left side of an assignment allows for
property destructuring.

In the standard REPL, typing `;` on an empty line will switch to shell mode.

# Examples
```jldoctest
julia> function foo()
           x = "Hello, "; x *= "World!"
           return x
       end
foo (generic function with 1 method)

julia> bar() = (x = "Hello, Mars!"; return x)
bar (generic function with 1 method)

julia> foo();

julia> bar()
"Hello, Mars!"

julia> function plot(x, y; style="solid", width=1, color="black")
           ###
       end

julia> A = [1 2; 3 4]
2×2 Matrix{Int64}:
 1  2
 3  4

julia> [1; 3;; 2; 4;;; 10*A]
2×2×2 Array{Int64, 3}:
[:, :, 1] =
 1  2
 3  4

[:, :, 2] =
 10  20
 30  40

julia> [2; 3;;;]
2×1×1 Array{Int64, 3}:
[:, :, 1] =
 2
 3

julia> nt = (; x=1) # without the ; or a trailing comma this would assign to x
(x = 1,)

julia> key = :a; c = 3;

julia> nt2 = (; key => 1, b=2, c, nt.x)
(a = 1, b = 2, c = 3, x = 1)

julia> (; b, x) = nt2; # set variables b and x using property destructuring

julia> b, x
(2, 1)

julia> ; # upon typing ;, the prompt changes (in place) to: shell>
shell> echo hello
hello
```
"""
kw";"

"""
    x && y

Short-circuiting boolean AND.

See also [`&`](@ref), the ternary operator `? :`, and the manual section on [control flow](@ref man-conditional-evaluation).

# Examples
```jldoctest
julia> x = 3;

julia> x > 1 && x < 10 && x isa Int
true

julia> x < 0 && error("expected positive x")
false
```
"""
kw"&&"

"""
    x || y

Short-circuiting boolean OR.

See also: [`|`](@ref), [`xor`](@ref), [`&&`](@ref).

# Examples
```jldoctest
julia> pi < 3 || ℯ < 3
true

julia> false || true || println("neither is true!")
true
```
"""
kw"||"

"""
    ccall((function_name, library), returntype, (argtype1, ...), argvalue1, ...)
    ccall(function_name, returntype, (argtype1, ...), argvalue1, ...)
    ccall(function_pointer, returntype, (argtype1, ...), argvalue1, ...)

Call a function in a C-exported shared library, specified by the tuple `(function_name, library)`,
where each component is either a string or symbol. Instead of specifying a library,
one can also use a `function_name` symbol or string, which is resolved in the current process.
Alternatively, `ccall` may also be used to call a function pointer `function_pointer`, such as one returned by `dlsym`.

Note that the argument type tuple must be a literal tuple, and not a tuple-valued
variable or expression.

Each `argvalue` to the `ccall` will be converted to the corresponding
`argtype`, by automatic insertion of calls to `unsafe_convert(argtype,
cconvert(argtype, argvalue))`. (See also the documentation for
[`unsafe_convert`](@ref Base.unsafe_convert) and [`cconvert`](@ref Base.cconvert) for further details.)
In most cases, this simply results in a call to `convert(argtype, argvalue)`.
"""
kw"ccall"

"""
    llvmcall(fun_ir::String, returntype, Tuple{argtype1, ...}, argvalue1, ...)
    llvmcall((mod_ir::String, entry_fn::String), returntype, Tuple{argtype1, ...}, argvalue1, ...)
    llvmcall((mod_bc::Vector{UInt8}, entry_fn::String), returntype, Tuple{argtype1, ...}, argvalue1, ...)

Call the LLVM code provided in the first argument. There are several ways to specify this
first argument:

- as a literal string, representing function-level IR (similar to an LLVM `define` block),
  with arguments are available as consecutive unnamed SSA variables (%0, %1, etc.);
- as a 2-element tuple, containing a string of module IR and a string representing the name
  of the entry-point function to call;
- as a 2-element tuple, but with the module provided as an `Vector{UInt8}` with bitcode.

Note that contrary to `ccall`, the argument types must be specified as a tuple type, and not
a tuple of types. All types, as well as the LLVM code, should be specified as literals, and
not as variables or expressions (it may be necessary to use `@eval` to generate these
literals).

See `test/llvmcall.jl` for usage examples.
"""
Core.Intrinsics.llvmcall

"""
    begin

`begin...end` denotes a block of code.

```julia
begin
    println("Hello, ")
    println("World!")
end
```

Usually `begin` will not be necessary, since keywords such as [`function`](@ref) and [`let`](@ref)
implicitly begin blocks of code. See also [`;`](@ref).

`begin` may also be used when indexing to represent the first index of a
collection or the first index of a dimension of an array.

# Examples
```jldoctest
julia> A = [1 2; 3 4]
2×2 Array{Int64,2}:
 1  2
 3  4

julia> A[begin, :]
2-element Array{Int64,1}:
 1
 2
```
"""
kw"begin"

"""
    struct

The most commonly used kind of type in Julia is a struct, specified as a name and a
set of fields.

```julia
struct Point
    x
    y
end
```

Fields can have type restrictions, which may be parameterized:

```julia
struct Point{X}
    x::X
    y::Float64
end
```

A struct can also declare an abstract super type via `<:` syntax:

```julia
struct Point <: AbstractPoint
    x
    y
end
```

`struct`s are immutable by default; an instance of one of these types cannot
be modified after construction. Use [`mutable struct`](@ref) instead to declare a
type whose instances can be modified.

See the manual section on [Composite Types](@ref) for more details,
such as how to define constructors.
"""
kw"struct"

"""
    mutable struct

`mutable struct` is similar to [`struct`](@ref), but additionally allows the
fields of the type to be set after construction. See the manual section on
[Composite Types](@ref) for more information.
"""
kw"mutable struct"

"""
    new, or new{A,B,...}

Special function available to inner constructors which creates a new object
of the type. The form new{A,B,...} explicitly specifies values of parameters for parametric types.
See the manual section on [Inner Constructor Methods](@ref man-inner-constructor-methods)
for more information.
"""
kw"new"

"""
    where

The `where` keyword creates a type that is an iterated union of other types, over all
values of some variable. For example `Vector{T} where T<:Real` includes all [`Vector`](@ref)s
where the element type is some kind of `Real` number.

The variable bound defaults to [`Any`](@ref) if it is omitted:

```julia
Vector{T} where T    # short for `where T<:Any`
```
Variables can also have lower bounds:

```julia
Vector{T} where T>:Int
Vector{T} where Int<:T<:Real
```
There is also a concise syntax for nested `where` expressions. For example, this:

```julia
Pair{T, S} where S<:Array{T} where T<:Number
```
can be shortened to:

```julia
Pair{T, S} where {T<:Number, S<:Array{T}}
```
This form is often found on method signatures.

Note that in this form, the variables are listed outermost-first. This matches the
order in which variables are substituted when a type is "applied" to parameter values
using the syntax `T{p1, p2, ...}`.
"""
kw"where"

"""
    var

The syntax `var"#example#"` refers to a variable named `Symbol("#example#")`,
even though `#example#` is not a valid Julia identifier name.

This can be useful for interoperability with programming languages which have
different rules for the construction of valid identifiers. For example, to
refer to the `R` variable `draw.segments`, you can use `var"draw.segments"` in
your Julia code.

It is also used to `show` julia source code which has gone through macro
hygiene or otherwise contains variable names which can't be parsed normally.

Note that this syntax requires parser support so it is expanded directly by the
parser rather than being implemented as a normal string macro `@var_str`.

!!! compat "Julia 1.3"
    This syntax requires at least Julia 1.3.

"""
kw"var\"name\"", kw"@var_str"

"""
    devnull

Used in a stream redirect to discard all data written to it. Essentially equivalent to
`/dev/null` on Unix or `NUL` on Windows. Usage:

```julia
run(pipeline(`cat test.txt`, devnull))
```
"""
devnull

# doc strings for code in boot.jl and built-ins

"""
    Nothing

A type with no fields that is the type of [`nothing`](@ref).

See also: [`isnothing`](@ref), [`Some`](@ref), [`Missing`](@ref).
"""
Nothing

"""
    nothing

The singleton instance of type [`Nothing`](@ref), used by convention when there is no value to return
(as in a C `void` function) or when a variable or field holds no value.

See also: [`isnothing`](@ref), [`something`](@ref), [`missing`](@ref).
"""
nothing

"""
    Core.TypeofBottom

The singleton type containing only the value `Union{}` (which represents the empty type).
"""
Core.TypeofBottom

"""
    Core.Type{T}

`Core.Type` is an abstract type which has all type objects as its instances.
The only instance of the singleton type `Core.Type{T}` is the object
`T`.

# Examples
```jldoctest
julia> isa(Type{Float64}, Type)
true

julia> isa(Float64, Type)
true

julia> isa(Real, Type{Float64})
false

julia> isa(Real, Type{Real})
true
```
"""
Core.Type

"""
    DataType <: Type{T}

`DataType` represents explicitly declared types that have names, explicitly
declared supertypes, and, optionally, parameters.  Every concrete value in the
system is an instance of some `DataType`.

# Examples
```jldoctest
julia> typeof(Real)
DataType

julia> typeof(Int)
DataType

julia> struct Point
           x::Int
           y
       end

julia> typeof(Point)
DataType
```
"""
Core.DataType

"""
    Function

Abstract type of all functions.

# Examples
```jldoctest
julia> isa(+, Function)
true

julia> typeof(sin)
typeof(sin) (singleton type of function sin, subtype of Function)

julia> ans <: Function
true
```
"""
Function

"""
    ReadOnlyMemoryError()

An operation tried to write to memory that is read-only.
"""
ReadOnlyMemoryError

"""
    ErrorException(msg)

Generic error type. The error message, in the `.msg` field, may provide more specific details.

# Examples
```jldoctest
julia> ex = ErrorException("I've done a bad thing");

julia> ex.msg
"I've done a bad thing"
```
"""
ErrorException

"""
    WrappedException(msg)

Generic type for `Exception`s wrapping another `Exception`, such as `LoadError` and
`InitError`. Those exceptions contain information about the root cause of an
exception. Subtypes define a field `error` containing the causing `Exception`.
"""
Core.WrappedException

"""
    UndefRefError()

The item or field is not defined for the given object.

# Examples
```jldoctest
julia> struct MyType
           a::Vector{Int}
           MyType() = new()
       end

julia> A = MyType()
MyType(#undef)

julia> A.a
ERROR: UndefRefError: access to undefined reference
Stacktrace:
[...]
```
"""
UndefRefError

"""
    Float32(x [, mode::RoundingMode])

Create a `Float32` from `x`. If `x` is not exactly representable then `mode` determines how
`x` is rounded.

# Examples
```jldoctest
julia> Float32(1/3, RoundDown)
0.3333333f0

julia> Float32(1/3, RoundUp)
0.33333334f0
```

See [`RoundingMode`](@ref) for available rounding modes.
"""
Float32(x)

"""
    Float64(x [, mode::RoundingMode])

Create a `Float64` from `x`. If `x` is not exactly representable then `mode` determines how
`x` is rounded.

# Examples
```jldoctest
julia> Float64(pi, RoundDown)
3.141592653589793

julia> Float64(pi, RoundUp)
3.1415926535897936
```

See [`RoundingMode`](@ref) for available rounding modes.
"""
Float64(x)

"""
    OutOfMemoryError()

An operation allocated too much memory for either the system or the garbage collector to
handle properly.
"""
OutOfMemoryError

"""
    BoundsError([a],[i])

An indexing operation into an array, `a`, tried to access an out-of-bounds element at index `i`.

# Examples
```jldoctest; filter = r"Stacktrace:(\\n \\[[0-9]+\\].*)*"
julia> A = fill(1.0, 7);

julia> A[8]
ERROR: BoundsError: attempt to access 7-element Vector{Float64} at index [8]


julia> B = fill(1.0, (2,3));

julia> B[2, 4]
ERROR: BoundsError: attempt to access 2×3 Matrix{Float64} at index [2, 4]


julia> B[9]
ERROR: BoundsError: attempt to access 2×3 Matrix{Float64} at index [9]

```
"""
BoundsError

"""
    InexactError(name::Symbol, T, val)

Cannot exactly convert `val` to type `T` in a method of function `name`.

# Examples
```jldoctest
julia> convert(Float64, 1+2im)
ERROR: InexactError: Float64(1 + 2im)
Stacktrace:
[...]
```
"""
InexactError

"""
    DomainError(val)
    DomainError(val, msg)

The argument `val` to a function or constructor is outside the valid domain.

# Examples
```jldoctest
julia> sqrt(-1)
ERROR: DomainError with -1.0:
sqrt was called with a negative real argument but will only return a complex result if called with a complex argument. Try sqrt(Complex(x)).
Stacktrace:
[...]
```
"""
DomainError

"""
    Task(func)

Create a `Task` (i.e. coroutine) to execute the given function `func` (which
must be callable with no arguments). The task exits when this function returns.
The task will run in the "world age" from the parent at construction when [`schedule`](@ref)d.

!!! warning
    By default tasks will have the sticky bit set to true `t.sticky`. This models the
    historic default for [`@async`](@ref). Sticky tasks can only be run on the worker thread
    they are first scheduled on. To obtain the behavior of [`Threads.@spawn`](@ref) set the sticky
    bit manually to `false`.

# Examples
```jldoctest
julia> a() = sum(i for i in 1:1000);

julia> b = Task(a);
```

In this example, `b` is a runnable `Task` that hasn't started yet.
"""
Task

"""
    StackOverflowError()

The function call grew beyond the size of the call stack. This usually happens when a call
recurses infinitely.
"""
StackOverflowError

"""
    nfields(x) -> Int

Get the number of fields in the given object.

# Examples
```jldoctest
julia> a = 1//2;

julia> nfields(a)
2

julia> b = 1
1

julia> nfields(b)
0

julia> ex = ErrorException("I've done a bad thing");

julia> nfields(ex)
1
```

In these examples, `a` is a [`Rational`](@ref), which has two fields.
`b` is an `Int`, which is a primitive bitstype with no fields at all.
`ex` is an [`ErrorException`](@ref), which has one field.
"""
nfields

"""
    UndefVarError(var::Symbol)

A symbol in the current scope is not defined.

# Examples
```jldoctest
julia> a
ERROR: UndefVarError: `a` not defined

julia> a = 1;

julia> a
1
```
"""
UndefVarError

"""
    UndefKeywordError(var::Symbol)

The required keyword argument `var` was not assigned in a function call.

# Examples
```jldoctest; filter = r"Stacktrace:(\\n \\[[0-9]+\\].*)*"
julia> function my_func(;my_arg)
           return my_arg + 1
       end
my_func (generic function with 1 method)

julia> my_func()
ERROR: UndefKeywordError: keyword argument `my_arg` not assigned
Stacktrace:
 [1] my_func() at ./REPL[1]:2
 [2] top-level scope at REPL[2]:1
```
"""
UndefKeywordError

"""
    OverflowError(msg)

The result of an expression is too large for the specified type and will cause a wraparound.
"""
OverflowError

"""
    TypeError(func::Symbol, context::AbstractString, expected::Type, got)

A type assertion failure, or calling an intrinsic function with an incorrect argument type.
"""
TypeError

"""
    InterruptException()

The process was stopped by a terminal interrupt (CTRL+C).

Note that, in Julia script started without `-i` (interactive) option,
`InterruptException` is not thrown by default.  Calling
[`Base.exit_on_sigint(false)`](@ref Base.exit_on_sigint) in the script
can recover the behavior of the REPL.  Alternatively, a Julia script
can be started with

```sh
julia -e "include(popfirst!(ARGS))" script.jl
```

to let `InterruptException` be thrown by CTRL+C during the execution.
"""
InterruptException

"""
    applicable(f, args...) -> Bool

Determine whether the given generic function has a method applicable to the given arguments.

See also [`hasmethod`](@ref).

# Examples
```jldoctest
julia> function f(x, y)
           x + y
       end;

julia> applicable(f, 1)
false

julia> applicable(f, 1, 2)
true
```
"""
applicable

"""
    invoke(f, argtypes::Type, args...; kwargs...)

Invoke a method for the given generic function `f` matching the specified types `argtypes` on the
specified arguments `args` and passing the keyword arguments `kwargs`. The arguments `args` must
conform with the specified types in `argtypes`, i.e. conversion is not automatically performed.
This method allows invoking a method other than the most specific matching method, which is useful
when the behavior of a more general definition is explicitly needed (often as part of the
implementation of a more specific method of the same function).

Be careful when using `invoke` for functions that you don't write.  What definition is used
for given `argtypes` is an implementation detail unless the function is explicitly states
that calling with certain `argtypes` is a part of public API.  For example, the change
between `f1` and `f2` in the example below is usually considered compatible because the
change is invisible by the caller with a normal (non-`invoke`) call.  However, the change is
visible if you use `invoke`.

# Examples
```jldoctest
julia> f(x::Real) = x^2;

julia> f(x::Integer) = 1 + invoke(f, Tuple{Real}, x);

julia> f(2)
5

julia> f1(::Integer) = Integer
       f1(::Real) = Real;

julia> f2(x::Real) = _f2(x)
       _f2(::Integer) = Integer
       _f2(_) = Real;

julia> f1(1)
Integer

julia> f2(1)
Integer

julia> invoke(f1, Tuple{Real}, 1)
Real

julia> invoke(f2, Tuple{Real}, 1)
Integer
```
"""
invoke

"""
    isa(x, type) -> Bool

Determine whether `x` is of the given `type`. Can also be used as an infix operator, e.g.
`x isa type`.

# Examples
```jldoctest
julia> isa(1, Int)
true

julia> isa(1, Matrix)
false

julia> isa(1, Char)
false

julia> isa(1, Number)
true

julia> 1 isa Number
true
```
"""
isa

"""
    DivideError()

Integer division was attempted with a denominator value of 0.

# Examples
```jldoctest
julia> 2/0
Inf

julia> div(2, 0)
ERROR: DivideError: integer division error
Stacktrace:
[...]
```
"""
DivideError

"""
    Number

Abstract supertype for all number types.
"""
Number

"""
    Real <: Number

Abstract supertype for all real numbers.
"""
Real

"""
    AbstractFloat <: Real

Abstract supertype for all floating point numbers.
"""
AbstractFloat

"""
    Integer <: Real

Abstract supertype for all integers.
"""
Integer

"""
    Signed <: Integer

Abstract supertype for all signed integers.
"""
Signed

"""
    Unsigned <: Integer

Abstract supertype for all unsigned integers.
"""
Unsigned

"""
    Bool <: Integer

Boolean type, containing the values `true` and `false`.

`Bool` is a kind of number: `false` is numerically
equal to `0` and `true` is numerically equal to `1`.
Moreover, `false` acts as a multiplicative "strong zero":

```jldoctest
julia> false == 0
true

julia> true == 1
true

julia> 0 * NaN
NaN

julia> false * NaN
0.0
```

See also: [`digits`](@ref), [`iszero`](@ref), [`NaN`](@ref).
"""
Bool

for (bit, sign, exp, frac) in ((16, 1, 5, 10), (32, 1, 8, 23), (64, 1, 11, 52))
    @eval begin
        """
            Float$($bit) <: AbstractFloat

        $($bit)-bit floating point number type (IEEE 754 standard).

        Binary format: $($sign) sign, $($exp) exponent, $($frac) fraction bits.
        """
        $(Symbol("Float", bit))
    end
end

for bit in (8, 16, 32, 64, 128)
    @eval begin
        """
            Int$($bit) <: Signed

        $($bit)-bit signed integer type.
        """
        $(Symbol("Int", bit))

        """
            UInt$($bit) <: Unsigned

        $($bit)-bit unsigned integer type.
        """
        $(Symbol("UInt", bit))
    end
end

"""
    Symbol

The type of object used to represent identifiers in parsed julia code (ASTs).
Also often used as a name or label to identify an entity (e.g. as a dictionary key).
`Symbol`s can be entered using the `:` quote operator:
```jldoctest
julia> :name
:name

julia> typeof(:name)
Symbol

julia> x = 42
42

julia> eval(:x)
42
```
`Symbol`s can also be constructed from strings or other values by calling the
constructor `Symbol(x...)`.

`Symbol`s are immutable and their implementation re-uses the same object for all `Symbol`s
with the same name.

Unlike strings, `Symbol`s are "atomic" or "scalar" entities that do not support
iteration over characters.
"""
Symbol

"""
    Symbol(x...) -> Symbol

Create a [`Symbol`](@ref) by concatenating the string representations of the arguments together.

# Examples
```jldoctest
julia> Symbol("my", "name")
:myname

julia> Symbol("day", 4)
:day4
```
"""
Symbol(x...)

"""
    tuple(xs...)

Construct a tuple of the given objects.

See also [`Tuple`](@ref), [`ntuple`](@ref), [`NamedTuple`](@ref).

# Examples
```jldoctest
julia> tuple(1, 'b', pi)
(1, 'b', π)

julia> ans === (1, 'b', π)
true

julia> Tuple(Real[1, 2, pi])  # takes a collection
(1, 2, π)
```
"""
tuple

"""
    getfield(value, name::Symbol, [order::Symbol])
    getfield(value, i::Int, [order::Symbol])

Extract a field from a composite `value` by name or position. Optionally, an
ordering can be defined for the operation. If the field was declared `@atomic`,
the specification is strongly recommended to be compatible with the stores to
that location. Otherwise, if not declared as `@atomic`, this parameter must be
`:not_atomic` if specified.
See also [`getproperty`](@ref Base.getproperty) and [`fieldnames`](@ref).

# Examples
```jldoctest
julia> a = 1//2
1//2

julia> getfield(a, :num)
1

julia> a.num
1

julia> getfield(a, 1)
1
```
"""
getfield

"""
    setfield!(value, name::Symbol, x, [order::Symbol])
    setfield!(value, i::Int, x, [order::Symbol])

Assign `x` to a named field in `value` of composite type. The `value` must be
mutable and `x` must be a subtype of `fieldtype(typeof(value), name)`.
Additionally, an ordering can be specified for this operation. If the field was
declared `@atomic`, this specification is mandatory. Otherwise, if not declared
as `@atomic`, it must be `:not_atomic` if specified.
See also [`setproperty!`](@ref Base.setproperty!).

# Examples
```jldoctest
julia> mutable struct MyMutableStruct
           field::Int
       end

julia> a = MyMutableStruct(1);

julia> setfield!(a, :field, 2);

julia> getfield(a, :field)
2

julia> a = 1//2
1//2

julia> setfield!(a, :num, 3);
ERROR: setfield!: immutable struct of type Rational cannot be changed
```
"""
setfield!

"""
    swapfield!(value, name::Symbol, x, [order::Symbol])
    swapfield!(value, i::Int, x, [order::Symbol])

These atomically perform the operations to simultaneously get and set a field:

    y = getfield(value, name)
    setfield!(value, name, x)
    return y
"""
swapfield!

"""
    modifyfield!(value, name::Symbol, op, x, [order::Symbol]) -> Pair
    modifyfield!(value, i::Int, op, x, [order::Symbol]) -> Pair

These atomically perform the operations to get and set a field after applying
the function `op`.

    y = getfield(value, name)
    z = op(y, x)
    setfield!(value, name, z)
    return y => z

If supported by the hardware (for example, atomic increment), this may be
optimized to the appropriate hardware instruction, otherwise it'll use a loop.
"""
modifyfield!

"""
    replacefield!(value, name::Symbol, expected, desired,
                  [success_order::Symbol, [fail_order::Symbol=success_order]) -> (; old, success::Bool)
    replacefield!(value, i::Int, expected, desired,
                  [success_order::Symbol, [fail_order::Symbol=success_order]) -> (; old, success::Bool)

These atomically perform the operations to get and conditionally set a field to
a given value.

    y = getfield(value, name, fail_order)
    ok = y === expected
    if ok
        setfield!(value, name, desired, success_order)
    end
    return (; old = y, success = ok)

If supported by the hardware, this may be optimized to the appropriate hardware
instruction, otherwise it'll use a loop.
"""
replacefield!

"""
    getglobal(module::Module, name::Symbol, [order::Symbol=:monotonic])

Retrieve the value of the binding `name` from the module `module`. Optionally, an
atomic ordering can be defined for the operation, otherwise it defaults to
monotonic.

While accessing module bindings using [`getfield`](@ref) is still supported to
maintain compatibility, using `getglobal` should always be preferred since
`getglobal` allows for control over atomic ordering (`getfield` is always
monotonic) and better signifies the code's intent both to the user as well as the
compiler.

Most users should not have to call this function directly -- The
[`getproperty`](@ref Base.getproperty) function or corresponding syntax (i.e.
`module.name`) should be preferred in all but few very specific use cases.

!!! compat "Julia 1.9"
    This function requires Julia 1.9 or later.

See also [`getproperty`](@ref Base.getproperty) and [`setglobal!`](@ref).

# Examples
```jldoctest
julia> a = 1
1

julia> module M
       a = 2
       end;

julia> getglobal(@__MODULE__, :a)
1

julia> getglobal(M, :a)
2
```
"""
getglobal

"""
    setglobal!(module::Module, name::Symbol, x, [order::Symbol=:monotonic])

Set or change the value of the binding `name` in the module `module` to `x`. No
type conversion is performed, so if a type has already been declared for the
binding, `x` must be of appropriate type or an error is thrown.

Additionally, an atomic ordering can be specified for this operation, otherwise it
defaults to monotonic.

Users will typically access this functionality through the
[`setproperty!`](@ref Base.setproperty!) function or corresponding syntax
(i.e. `module.name = x`) instead, so this is intended only for very specific use
cases.

!!! compat "Julia 1.9"
    This function requires Julia 1.9 or later.

See also [`setproperty!`](@ref Base.setproperty!) and [`getglobal`](@ref)

# Examples
```jldoctest
julia> module M end;

julia> M.a  # same as `getglobal(M, :a)`
ERROR: UndefVarError: `a` not defined

julia> setglobal!(M, :a, 1)
1

julia> M.a
1
```
"""
setglobal!

"""
    typeof(x)

Get the concrete type of `x`.

See also [`eltype`](@ref).

# Examples
```jldoctest
julia> a = 1//2;

julia> typeof(a)
Rational{Int64}

julia> M = [1 2; 3.5 4];

julia> typeof(M)
Matrix{Float64} (alias for Array{Float64, 2})
```
"""
typeof

"""
    isdefined(m::Module, s::Symbol, [order::Symbol])
    isdefined(object, s::Symbol, [order::Symbol])
    isdefined(object, index::Int, [order::Symbol])

Tests whether a global variable or object field is defined. The arguments can
be a module and a symbol or a composite object and field name (as a symbol) or
index. Optionally, an ordering can be defined for the operation. If the field
was declared `@atomic`, the specification is strongly recommended to be
compatible with the stores to that location. Otherwise, if not declared as
`@atomic`, this parameter must be `:not_atomic` if specified.

To test whether an array element is defined, use [`isassigned`](@ref) instead.

See also [`@isdefined`](@ref).

# Examples
```jldoctest
julia> isdefined(Base, :sum)
true

julia> isdefined(Base, :NonExistentMethod)
false

julia> a = 1//2;

julia> isdefined(a, 2)
true

julia> isdefined(a, 3)
false

julia> isdefined(a, :num)
true

julia> isdefined(a, :numerator)
false
```
"""
isdefined


"""
    Vector{T}(undef, n)

Construct an uninitialized [`Vector{T}`](@ref) of length `n`.

# Examples
```julia-repl
julia> Vector{Float64}(undef, 3)
3-element Array{Float64, 1}:
 6.90966e-310
 6.90966e-310
 6.90966e-310
```
"""
Vector{T}(::UndefInitializer, n)

"""
    Vector{T}(nothing, m)

Construct a [`Vector{T}`](@ref) of length `m`, initialized with
[`nothing`](@ref) entries. Element type `T` must be able to hold
these values, i.e. `Nothing <: T`.

# Examples
```jldoctest
julia> Vector{Union{Nothing, String}}(nothing, 2)
2-element Vector{Union{Nothing, String}}:
 nothing
 nothing
```
"""
Vector{T}(::Nothing, n)

"""
    Vector{T}(missing, m)

Construct a [`Vector{T}`](@ref) of length `m`, initialized with
[`missing`](@ref) entries. Element type `T` must be able to hold
these values, i.e. `Missing <: T`.

# Examples
```jldoctest
julia> Vector{Union{Missing, String}}(missing, 2)
2-element Vector{Union{Missing, String}}:
 missing
 missing
```
"""
Vector{T}(::Missing, n)

"""
    Matrix{T}(undef, m, n)

Construct an uninitialized [`Matrix{T}`](@ref) of size `m`×`n`.

# Examples
```julia-repl
julia> Matrix{Float64}(undef, 2, 3)
2×3 Array{Float64, 2}:
 2.36365e-314  2.28473e-314    5.0e-324
 2.26704e-314  2.26711e-314  NaN

julia> similar(ans, Int32, 2, 2)
2×2 Matrix{Int32}:
 490537216  1277177453
         1  1936748399
```
"""
Matrix{T}(::UndefInitializer, m, n)

"""
    Matrix{T}(nothing, m, n)

Construct a [`Matrix{T}`](@ref) of size `m`×`n`, initialized with
[`nothing`](@ref) entries. Element type `T` must be able to hold
these values, i.e. `Nothing <: T`.

# Examples
```jldoctest
julia> Matrix{Union{Nothing, String}}(nothing, 2, 3)
2×3 Matrix{Union{Nothing, String}}:
 nothing  nothing  nothing
 nothing  nothing  nothing
```
"""
Matrix{T}(::Nothing, m, n)

"""
    Matrix{T}(missing, m, n)

Construct a [`Matrix{T}`](@ref) of size `m`×`n`, initialized with
[`missing`](@ref) entries. Element type `T` must be able to hold
these values, i.e. `Missing <: T`.

# Examples
```jldoctest
julia> Matrix{Union{Missing, String}}(missing, 2, 3)
2×3 Matrix{Union{Missing, String}}:
 missing  missing  missing
 missing  missing  missing
```
"""
Matrix{T}(::Missing, m, n)

"""
    Array{T}(undef, dims)
    Array{T,N}(undef, dims)

Construct an uninitialized `N`-dimensional [`Array`](@ref)
containing elements of type `T`. `N` can either be supplied explicitly,
as in `Array{T,N}(undef, dims)`, or be determined by the length or number of `dims`.
`dims` may be a tuple or a series of integer arguments corresponding to the lengths
in each dimension. If the rank `N` is supplied explicitly, then it must
match the length or number of `dims`. Here [`undef`](@ref) is
the [`UndefInitializer`](@ref).

# Examples
```julia-repl
julia> A = Array{Float64, 2}(undef, 2, 3) # N given explicitly
2×3 Matrix{Float64}:
 6.90198e-310  6.90198e-310  6.90198e-310
 6.90198e-310  6.90198e-310  0.0

julia> B = Array{Float64}(undef, 4) # N determined by the input
4-element Vector{Float64}:
   2.360075077e-314
 NaN
   2.2671131793e-314
   2.299821756e-314

julia> similar(B, 2, 4, 1) # use typeof(B), and the given size
2×4×1 Array{Float64, 3}:
[:, :, 1] =
 2.26703e-314  2.26708e-314  0.0           2.80997e-314
 0.0           2.26703e-314  2.26708e-314  0.0
```
"""
Array{T,N}(::UndefInitializer, dims)

"""
    Array{T}(nothing, dims)
    Array{T,N}(nothing, dims)

Construct an `N`-dimensional [`Array`](@ref) containing elements of type `T`,
initialized with [`nothing`](@ref) entries. Element type `T` must be able
to hold these values, i.e. `Nothing <: T`.

# Examples
```jldoctest
julia> Array{Union{Nothing, String}}(nothing, 2)
2-element Vector{Union{Nothing, String}}:
 nothing
 nothing

julia> Array{Union{Nothing, Int}}(nothing, 2, 3)
2×3 Matrix{Union{Nothing, Int64}}:
 nothing  nothing  nothing
 nothing  nothing  nothing
```
"""
Array{T,N}(::Nothing, dims)


"""
    Array{T}(missing, dims)
    Array{T,N}(missing, dims)

Construct an `N`-dimensional [`Array`](@ref) containing elements of type `T`,
initialized with [`missing`](@ref) entries. Element type `T` must be able
to hold these values, i.e. `Missing <: T`.

# Examples
```jldoctest
julia> Array{Union{Missing, String}}(missing, 2)
2-element Vector{Union{Missing, String}}:
 missing
 missing

julia> Array{Union{Missing, Int}}(missing, 2, 3)
2×3 Matrix{Union{Missing, Int64}}:
 missing  missing  missing
 missing  missing  missing
```
"""
Array{T,N}(::Missing, dims)

"""
    UndefInitializer

Singleton type used in array initialization, indicating the array-constructor-caller
would like an uninitialized array. See also [`undef`](@ref),
an alias for `UndefInitializer()`.

# Examples
```julia-repl
julia> Array{Float64, 1}(UndefInitializer(), 3)
3-element Array{Float64, 1}:
 2.2752528595e-314
 2.202942107e-314
 2.275252907e-314
```
"""
UndefInitializer

"""
    undef

Alias for `UndefInitializer()`, which constructs an instance of the singleton type
[`UndefInitializer`](@ref), used in array initialization to indicate the
array-constructor-caller would like an uninitialized array.

See also: [`missing`](@ref), [`similar`](@ref).

# Examples
```julia-repl
julia> Array{Float64, 1}(undef, 3)
3-element Vector{Float64}:
 2.2752528595e-314
 2.202942107e-314
 2.275252907e-314
```
"""
undef

"""
    Ptr{T}()

Creates a null pointer to type `T`.
"""
Ptr{T}()

"""
    +(x, y...)

Addition operator. `x+y+z+...` calls this function with all arguments, i.e. `+(x, y, z, ...)`.

# Examples
```jldoctest
julia> 1 + 20 + 4
25

julia> +(1, 20, 4)
25
```
"""
(+)(x, y...)

"""
    -(x)

Unary minus operator.

See also: [`abs`](@ref), [`flipsign`](@ref).

# Examples
```jldoctest
julia> -1
-1

julia> -(2)
-2

julia> -[1 2; 3 4]
2×2 Matrix{Int64}:
 -1  -2
 -3  -4
```
"""
-(x)

"""
    -(x, y)

Subtraction operator.

# Examples
```jldoctest
julia> 2 - 3
-1

julia> -(2, 4.5)
-2.5
```
"""
-(x, y)

"""
    *(x, y...)

Multiplication operator. `x*y*z*...` calls this function with all arguments, i.e. `*(x, y, z, ...)`.

# Examples
```jldoctest
julia> 2 * 7 * 8
112

julia> *(2, 7, 8)
112
```
"""
(*)(x, y...)

"""
    /(x, y)

Right division operator: multiplication of `x` by the inverse of `y` on the right. Gives
floating-point results for integer arguments.

# Examples
```jldoctest
julia> 1/2
0.5

julia> 4/2
2.0

julia> 4.5/2
2.25
```
"""
/(x, y)

"""
    ArgumentError(msg)

The arguments passed to a function are invalid.
`msg` is a descriptive error message.
"""
ArgumentError

"""
    MethodError(f, args)

A method with the required type signature does not exist in the given generic function.
Alternatively, there is no unique most-specific method.
"""
MethodError

"""
    AssertionError([msg])

The asserted condition did not evaluate to `true`.
Optional argument `msg` is a descriptive error string.

# Examples
```jldoctest
julia> @assert false "this is not true"
ERROR: AssertionError: this is not true
```

`AssertionError` is usually thrown from [`@assert`](@ref).
"""
AssertionError

"""
    LoadError(file::AbstractString, line::Int, error)

An error occurred while [`include`](@ref Base.include)ing, [`require`](@ref Base.require)ing, or [`using`](@ref) a file. The error specifics
should be available in the `.error` field.

!!! compat "Julia 1.7"
    LoadErrors are no longer emitted by `@macroexpand`, `@macroexpand1`, and `macroexpand` as of Julia 1.7.
"""
LoadError

"""
    InitError(mod::Symbol, error)

An error occurred when running a module's `__init__` function. The actual error thrown is
available in the `.error` field.
"""
InitError

"""
    Any::DataType

`Any` is the union of all types. It has the defining property `isa(x, Any) == true` for any `x`. `Any` therefore
describes the entire universe of possible values. For example `Integer` is a subset of `Any` that includes `Int`,
`Int8`, and other integer types.
"""
Any

"""
    Union{}

`Union{}`, the empty [`Union`](@ref) of types, is the type that has no values. That is, it has the defining
property `isa(x, Union{}) == false` for any `x`. `Base.Bottom` is defined as its alias and the type of `Union{}`
is `Core.TypeofBottom`.

# Examples
```jldoctest
julia> isa(nothing, Union{})
false
```
"""
kw"Union{}", Base.Bottom

"""
    Union{Types...}

A type union is an abstract type which includes all instances of any of its argument types. The empty
union [`Union{}`](@ref) is the bottom type of Julia.

# Examples
```jldoctest
julia> IntOrString = Union{Int,AbstractString}
Union{Int64, AbstractString}

julia> 1 isa IntOrString
true

julia> "Hello!" isa IntOrString
true

julia> 1.0 isa IntOrString
false
```
"""
Union


"""
    UnionAll

A union of types over all values of a type parameter. `UnionAll` is used to describe parametric types
where the values of some parameters are not known.

# Examples
```jldoctest
julia> typeof(Vector)
UnionAll

julia> typeof(Vector{Int})
DataType
```
"""
UnionAll

"""
    ::

The `::` operator either asserts that a value has the given type, or declares that
a local variable or function return always has the given type.

Given `expression::T`, `expression` is first evaluated. If the result is of type
`T`, the value is simply returned. Otherwise, a [`TypeError`](@ref) is thrown.

In local scope, the syntax `local x::T` or `x::T = expression` declares that local variable
`x` always has type `T`. When a value is assigned to the variable, it will be
converted to type `T` by calling [`convert`](@ref).

In a method declaration, the syntax `function f(x)::T` causes any value returned by
the method to be converted to type `T`.

See the manual section on [Type Declarations](@ref).

# Examples
```jldoctest
julia> (1+2)::AbstractFloat
ERROR: TypeError: typeassert: expected AbstractFloat, got a value of type Int64

julia> (1+2)::Int
3

julia> let
           local x::Int
           x = 2.0
           x
       end
2
```
"""
kw"::"

"""
    Vararg{T,N}

The last parameter of a tuple type [`Tuple`](@ref) can be the special value `Vararg`, which denotes any
number of trailing elements. `Vararg{T,N}` corresponds to exactly `N` elements of type `T`. Finally
`Vararg{T}` corresponds to zero or more elements of type `T`. `Vararg` tuple types are used to represent the
arguments accepted by varargs methods (see the section on [Varargs Functions](@ref) in the manual.)

See also [`NTuple`](@ref).

# Examples
```jldoctest
julia> mytupletype = Tuple{AbstractString, Vararg{Int}}
Tuple{AbstractString, Vararg{Int64}}

julia> isa(("1",), mytupletype)
true

julia> isa(("1",1), mytupletype)
true

julia> isa(("1",1,2), mytupletype)
true

julia> isa(("1",1,2,3.0), mytupletype)
false
```
"""
Vararg

"""
    Tuple{Types...}

A tuple is a fixed-length container that can hold any values of different
types, but cannot be modified (it is immutable). The values can be accessed via
indexing. Tuple literals are written with commas and parentheses:

```jldoctest
julia> (1, 1+1)
(1, 2)

julia> (1,)
(1,)

julia> x = (0.0, "hello", 6*7)
(0.0, "hello", 42)

julia> x[2]
"hello"

julia> typeof(x)
Tuple{Float64, String, Int64}
```

A length-1 tuple must be written with a comma, `(1,)`, since `(1)` would just
be a parenthesized value. `()` represents the empty (length-0) tuple.

A tuple can be constructed from an iterator by using a `Tuple` type as constructor:

```jldoctest
julia> Tuple(["a", 1])
("a", 1)

julia> Tuple{String, Float64}(["a", 1])
("a", 1.0)
```

Tuple types are covariant in their parameters: `Tuple{Int}` is a subtype of `Tuple{Any}`. Therefore `Tuple{Any}`
is considered an abstract type, and tuple types are only concrete if their parameters are. Tuples do not have
field names; fields are only accessed by index.
Tuple types may have any number of parameters.

See the manual section on [Tuple Types](@ref).

See also [`Vararg`](@ref), [`NTuple`](@ref), [`ntuple`](@ref), [`tuple`](@ref), [`NamedTuple`](@ref).
"""
Tuple

"""
    NamedTuple{names}(args::Tuple)

Construct a named tuple with the given `names` (a tuple of Symbols) from a tuple of values.
"""
NamedTuple{names}(args::Tuple)

"""
    NamedTuple{names,T}(args::Tuple)

Construct a named tuple with the given `names` (a tuple of Symbols) and field types `T`
(a `Tuple` type) from a tuple of values.
"""
NamedTuple{names,T}(args::Tuple)

"""
    NamedTuple{names}(nt::NamedTuple)

Construct a named tuple by selecting fields in `names` (a tuple of Symbols) from
another named tuple.
"""
NamedTuple{names}(nt::NamedTuple)

"""
    NamedTuple(itr)

Construct a named tuple from an iterator of key-value pairs (where the keys must be
`Symbol`s). Equivalent to `(; itr...)`.

!!! compat "Julia 1.6"
    This method requires at least Julia 1.6.
"""
NamedTuple(itr)

"""
    typeassert(x, type)

Throw a [`TypeError`](@ref) unless `x isa type`.
The syntax `x::type` calls this function.

# Examples
```jldoctest
julia> typeassert(2.5, Int)
ERROR: TypeError: in typeassert, expected Int64, got a value of type Float64
Stacktrace:
[...]
```
"""
typeassert

"""
    getproperty(value, name::Symbol)
    getproperty(value, name::Symbol, order::Symbol)

The syntax `a.b` calls `getproperty(a, :b)`.
The syntax `@atomic order a.b` calls `getproperty(a, :b, :order)` and
the syntax `@atomic a.b` calls `getproperty(a, :b, :sequentially_consistent)`.

# Examples
```jldoctest
julia> struct MyType{T <: Number}
           x::T
       end

julia> function Base.getproperty(obj::MyType, sym::Symbol)
           if sym === :special
               return obj.x + 1
           else # fallback to getfield
               return getfield(obj, sym)
           end
       end

julia> obj = MyType(1);

julia> obj.special
2

julia> obj.x
1
```

One should overload `getproperty` only when necessary, as it can be confusing if
the behavior of the syntax `obj.f` is unusual.
Also note that using methods is often preferable. See also this style guide documentation
for more information: [Prefer exported methods over direct field access](@ref).

See also [`getfield`](@ref Core.getfield),
[`propertynames`](@ref Base.propertynames) and
[`setproperty!`](@ref Base.setproperty!).
"""
Base.getproperty

"""
    setproperty!(value, name::Symbol, x)
    setproperty!(value, name::Symbol, x, order::Symbol)

The syntax `a.b = c` calls `setproperty!(a, :b, c)`.
The syntax `@atomic order a.b = c` calls `setproperty!(a, :b, c, :order)`
and the syntax `@atomic a.b = c` calls `setproperty!(a, :b, c, :sequentially_consistent)`.

!!! compat "Julia 1.8"
    `setproperty!` on modules requires at least Julia 1.8.

See also [`setfield!`](@ref Core.setfield!),
[`propertynames`](@ref Base.propertynames) and
[`getproperty`](@ref Base.getproperty).
"""
Base.setproperty!

"""
    swapproperty!(x, f::Symbol, v, order::Symbol=:not_atomic)

The syntax `@atomic a.b, _ = c, a.b` returns `(c, swapproperty!(a, :b, c, :sequentially_consistent))`,
where there must be one `getproperty` expression common to both sides.

See also [`swapfield!`](@ref Core.swapfield!)
and [`setproperty!`](@ref Base.setproperty!).
"""
Base.swapproperty!

"""
    modifyproperty!(x, f::Symbol, op, v, order::Symbol=:not_atomic)

The syntax `@atomic op(x.f, v)` (and its equivalent `@atomic x.f op v`) returns
`modifyproperty!(x, :f, op, v, :sequentially_consistent)`, where the first argument
must be a `getproperty` expression and is modified atomically.

Invocation of `op(getproperty(x, f), v)` must return a value that can be stored in the field
`f` of the object `x` by default.  In particular, unlike the default behavior of
[`setproperty!`](@ref Base.setproperty!), the `convert` function is not called
automatically.

See also [`modifyfield!`](@ref Core.modifyfield!)
and [`setproperty!`](@ref Base.setproperty!).
"""
Base.modifyproperty!

"""
    replaceproperty!(x, f::Symbol, expected, desired, success_order::Symbol=:not_atomic, fail_order::Symbol=success_order)

Perform a compare-and-swap operation on `x.f` from `expected` to `desired`, per
egal. The syntax `@atomic_replace! x.f expected => desired` can be used instead
of the function call form.

See also [`replacefield!`](@ref Core.replacefield!)
and [`setproperty!`](@ref Base.setproperty!).
"""
Base.replaceproperty!


"""
    StridedArray{T, N}

A hard-coded [`Union`](@ref) of common array types that follow the [strided array interface](@ref man-interface-strided-arrays),
with elements of type `T` and `N` dimensions.

If `A` is a `StridedArray`, then its elements are stored in memory with offsets, which may
vary between dimensions but are constant within a dimension. For example, `A` could
have stride 2 in dimension 1, and stride 3 in dimension 2. Incrementing `A` along
dimension `d` jumps in memory by [`stride(A, d)`] slots. Strided arrays are
particularly important and useful because they can sometimes be passed directly
as pointers to foreign language libraries like BLAS.
"""
StridedArray

"""
    StridedVector{T}

One dimensional [`StridedArray`](@ref) with elements of type `T`.
"""
StridedVector

"""
    StridedMatrix{T}

Two dimensional [`StridedArray`](@ref) with elements of type `T`.
"""
StridedMatrix

"""
    StridedVecOrMat{T}

Union type of [`StridedVector`](@ref) and [`StridedMatrix`](@ref) with elements of type `T`.
"""
StridedVecOrMat

"""
    Module

A `Module` is a separate global variable workspace. See [`module`](@ref) and the [manual section about modules](@ref modules) for details.

    Module(name::Symbol=:anonymous, std_imports=true, default_names=true)

Return a module with the specified name. A `baremodule` corresponds to `Module(:ModuleName, false)`

An empty module containing no names at all can be created with `Module(:ModuleName, false, false)`.
This module will not import `Base` or `Core` and does not contain a reference to itself.
"""
Module

"""
    Core

`Core` is the module that contains all identifiers considered "built in" to the language, i.e. part of the core language and not libraries. Every module implicitly specifies `using Core`, since you can't do anything without those definitions.
"""
Core.Core

"""
    Main

`Main` is the top-level module, and Julia starts with `Main` set as the current module.  Variables defined at the prompt go in `Main`, and `varinfo` lists variables in `Main`.
```jldoctest
julia> @__MODULE__
Main
```
"""
Main.Main

"""
    Base

The base library of Julia. `Base` is a module that contains basic functionality (the contents of `base/`). All modules implicitly contain `using Base`, since this is needed in the vast majority of cases.
"""
Base.Base

"""
    QuoteNode

A quoted piece of code, that does not support interpolation. See the [manual section about QuoteNodes](@ref man-quote-node) for details.
"""
QuoteNode


"""
    "
`"` Is used to delimit string literals. A trailing `\\` can be used to continue a string literal on the next line.

# Examples

```jldoctest
julia> "Hello World!"
"Hello World!"

julia> "Hello World!\\n"
"Hello World!\\n"

julia> "Hello \\
        World"
"Hello World"
```

See also [`\"""`](@ref \"\"\").
"""
kw"\""

"""
    \"""
`\"""` is used to delimit string literals. Strings created by triple quotation marks can contain `"` characters without escaping and are dedented to the level of the least-indented line. This is useful for defining strings within code that is indented.

# Examples

```jldoctest
julia> \"""Hello World!\"""
"Hello World!"

julia> \"""Contains "quote" characters\"""
"Contains \\"quote\\" characters"

julia> \"""
         Hello,
         world.\"""
"Hello,\\nworld."
```

See also [`"`](@ref \")
"""
kw"\"\"\""

"""
Unsafe pointer operations are compatible with loading and storing pointers declared with
`_Atomic` and `std::atomic` type in C11 and C++23 respectively. An error may be thrown if
there is not support for atomically loading the Julia type `T`.

See also: [`unsafe_load`](@ref), [`unsafe_modify!`](@ref), [`unsafe_replace!`](@ref), [`unsafe_store!`](@ref), [`unsafe_swap!`](@ref)
"""
kw"atomic"

"""
    Base.donotdelete(args...)

This function prevents dead-code elimination (DCE) of itself and any arguments
passed to it, but is otherwise the lightest barrier possible. In particular,
it is not a GC safepoint, does model an observable heap effect, does not expand
to any code itself and may be re-ordered with respect to other side effects
(though the total number of executions may not change).

A useful model for this function is that it hashes all memory `reachable` from
args and escapes this information through some observable side-channel that does
not otherwise impact program behavior. Of course that's just a model. The
function does nothing and returns `nothing`.

This is intended for use in benchmarks that want to guarantee that `args` are
actually computed. (Otherwise DCE may see that the result of the benchmark is
unused and delete the entire benchmark code).

!!! note
    `donotdelete` does not affect constant folding. For example, in
    `donotdelete(1+1)`, no add instruction needs to be executed at runtime and
    the code is semantically equivalent to `donotdelete(2).`

# Examples

```julia
function loop()
    for i = 1:1000
        # The compiler must guarantee that there are 1000 program points (in the correct
        # order) at which the value of `i` is in a register, but has otherwise
        # total control over the program.
        donotdelete(i)
    end
end
```
"""
Base.donotdelete

"""
    Base.compilerbarrier(setting::Symbol, val)

This function puts a barrier at a specified compilation phase.
It is supposed to only influence the compilation behavior according to `setting`,
and its runtime semantics is just to return the second argument `val` (except that
this function will perform additional checks on `setting` in a case when `setting`
isn't known precisely at compile-time.)

Currently either of the following `setting`s is allowed:
- Barriers on abstract interpretation:
  * `:type`: the return type of this function call will be inferred as `Any` always
    (the strongest barrier on abstract interpretation)
  * `:const`: the return type of this function call will be inferred with widening
    constant information on `val`
  * `:conditional`: the return type of this function call will be inferred with widening
    conditional information on `val` (see the example below)
- Any barriers on optimization aren't implemented yet

!!! note
    This function is supposed to be used _with `setting` known precisely at compile-time_.
    Note that in a case when the `setting` isn't known precisely at compile-time, the compiler
    currently will put the most strongest barrier(s) rather than emitting a compile-time warning.

# Examples

```julia
julia> Base.return_types((Int,)) do a
           x = compilerbarrier(:type, a) # `x` won't be inferred as `x::Int`
           return x
       end |> only
Any

julia> Base.return_types() do
           x = compilerbarrier(:const, 42)
           if x == 42 # no constant information here, so inference also accounts for the else branch
               return x # but `x` is still inferred as `x::Int` at least here
           else
               return nothing
           end
       end |> only
Union{Nothing, Int64}

julia> Base.return_types((Union{Int,Nothing},)) do a
           if compilerbarrier(:conditional, isa(a, Int))
               # the conditional information `a::Int` isn't available here (leading to less accurate return type inference)
               return a
           else
               return nothing
           end
       end |> only
Union{Nothing, Int64}
```
"""
Base.compilerbarrier

"""
    Core.finalizer(f, o)

This builtin is an implementation detail of [`Base.finalizer`](@ref) and end-users
should use the latter instead.

# Differences from `Base.finalizer`

The interface of `Core.finalizer` is essentially the same as `Base.finalizer`,
but there are a number of small differences. They are documented here for
completeness only and (unlike `Base.finalizer`) have no stability guarantees.

The current differences are:
- `Core.finalizer` does not check for mutability of `o`. Attempting to register
  a finalizer for an immutable object is undefined behavior.
- The value `f` must be a Julia object. `Core.finalizer` does not support a
  raw C function pointer.
- `Core.finalizer` returns `nothing` rather than `o`.
"""
Core.finalizer

end
P   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/docs/Docs.jl+Z      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
    Docs

The `Docs` module provides the `@doc` macro which can be used to set and retrieve
documentation metadata for Julia objects.

Please see the manual section on [documentation](@ref man-documentation) for more
information.
"""
module Docs

@nospecialize # don't specialize on any arguments of the methods declared herein

"""
# Documentation

Functions, methods and types can be documented by placing a string before the definition:

    \"\"\"
    # The Foo Function
    `foo(x)`: Foo the living hell out of `x`.
    \"\"\"
    foo(x) = ...

The `@doc` macro can be used directly to both set and retrieve documentation / metadata.
The macro has special parsing so that the documented object may occur on the next line:

    @doc "blah"
    function foo() ...

By default, documentation is written as Markdown, but any object can be used as
the first argument.

## Documenting objects after they are defined
You can document an object after its definition by

    @doc "foo" function_to_doc
    @doc "bar" TypeToDoc

For macros, the syntax is `@doc "macro doc" :(Module.@macro)` or `@doc "macro doc"
:(string_macro"")` for string macros. Without the quote `:()` the expansion of the macro
will be documented.

## Retrieving Documentation
You can retrieve docs for functions, macros and other objects as follows:

    @doc foo
    @doc @time
    @doc md""

## Functions & Methods
Placing documentation before a method definition (e.g. `function foo() ...` or `foo() = ...`)
will cause that specific method to be documented, as opposed to the whole function. Method
docs are concatenated together in the order they were defined to provide docs for the
function.
"""
:(Core.@doc)

include("bindings.jl")

import .Base.Meta: quot, isexpr
import .Base: Callable, with_output_color
using .Base: RefValue, mapany
import ..CoreDocs: lazy_iterpolate

export doc

# Basic API / Storage

const modules = Module[]
const META    = gensym(:meta)
const METAType = IdDict{Any,Any}

function meta(m::Module; autoinit::Bool=true)
    if !isdefined(m, META) || getfield(m, META) === nothing
        autoinit ? initmeta(m) : return nothing
    end
    return getfield(m, META)::METAType
end

function initmeta(m::Module)
    if !isdefined(m, META) || getfield(m, META) === nothing
        Core.eval(m, :($META = $(METAType())))
        push!(modules, m)
    end
    nothing
end

function signature!(tv::Vector{Any}, expr::Expr)
    is_macrocall = isexpr(expr, :macrocall)
    if is_macrocall || isexpr(expr, :call)
        sig = :(Union{Tuple{}})
        first_arg = is_macrocall ? 3 : 2 # skip function arguments
        for arg in expr.args[first_arg:end]
            isexpr(arg, :parameters) && continue
            if isexpr(arg, :kw) # optional arg
                push!(sig.args, :(Tuple{$((sig.args[end]::Expr).args[2:end]...)}))
            end
            push!((sig.args[end]::Expr).args, argtype(arg))
        end
        if isexpr(expr.args[1], :curly) && isempty(tv)
            append!(tv, mapany(tvar, (expr.args[1]::Expr).args[2:end]))
        end
        for i = length(tv):-1:1
            push!(sig.args, :(Tuple{$((tv[i]::Expr).args[1])}))
        end
        for i = length(tv):-1:1
            sig = Expr(:where, sig, tv[i])
        end
        return sig
    elseif isexpr(expr, :where)
        append!(tv, mapany(tvar, expr.args[2:end]))
        return signature!(tv, expr.args[1])
    else
        return signature!(tv, expr.args[1])
    end
end
signature!(tv::Vector{Any}, @nospecialize(other)) = :(Union{})
signature(expr::Expr) = signature!([], expr)
signature(@nospecialize other) = signature!([], other)

function argtype(expr::Expr)
    isexpr(expr, :(::))  && return expr.args[end]
    isexpr(expr, :(...)) && return :(Vararg{$(argtype(expr.args[1]))})
    if isexpr(expr, :meta) && length(expr.args) == 2
        a1 = expr.args[1]
        if a1 === :nospecialize || a1 === :specialize
            return argtype(expr.args[2])
        end
    end
    return argtype(expr.args[1])
end
argtype(@nospecialize other) = :Any

tvar(x::Expr)   = x
tvar(s::Symbol) = :($s <: Any)

# Docsystem types.
# ================

"""
    Docs.DocStr

Stores the contents of a single docstring as well as related metadata.

Both the raw text, `.text`, and the parsed markdown, `.object`, are tracked by this type.
Parsing of the raw text is done lazily when a request is made to render the docstring,
which helps to reduce total precompiled image size.

The `.data` fields stores several values related to the docstring, such as: path,
linenumber, source code, and fielddocs.
"""
mutable struct DocStr
    text   :: Core.SimpleVector
    object :: Any
    data   :: Dict{Symbol, Any}
end

function docstr(binding::Binding, typesig = Union{})
    @nospecialize typesig
    for m in modules
        dict = meta(m; autoinit=false)
        isnothing(dict) && continue
        if haskey(dict, binding)
            docs = dict[binding].docs
            if haskey(docs, typesig)
                return docs[typesig]
            end
        end
    end
    error("could not find matching docstring for '$binding :: $typesig'.")
end
docstr(object, data = Dict{Symbol,Any}()) = _docstr(object, data)

_docstr(vec::Core.SimpleVector, data::Dict{Symbol,Any}) = DocStr(vec,            nothing, data)
_docstr(str::AbstractString,    data::Dict{Symbol,Any}) = DocStr(Core.svec(str), nothing, data)
_docstr(object,                 data::Dict{Symbol,Any}) = DocStr(Core.svec(),     object, data)

_docstr(doc::DocStr, data::Dict{Symbol,Any}) = (doc.data = merge(data, doc.data); doc)

macro ref(x)
    binding = bindingexpr(namify(x))
    typesig = signature(x)
    return esc(docexpr(__source__, __module__, binding, typesig))
end

docexpr(__source__, __module__, args...) = Expr(:call, docstr, args...)

"""
    MultiDoc

Stores a collection of docstrings for related objects, ie. a `Function`/`DataType` and
associated `Method` objects.

Each documented object in a `MultiDoc` is referred to by it's signature which is represented
by a `Union` of `Tuple` types. For example, the following `Method` definition

    f(x, y) = ...

is stored as `Tuple{Any, Any}` in the `MultiDoc` while

    f(x::T, y = ?) where {T} = ...

is stored as `Union{Tuple{T, Any}, Tuple{T}} where T`.

Note: The `Function`/`DataType` object's signature is always `Union{}`.
"""
mutable struct MultiDoc
    "Ordered (via definition order) vector of object signatures."
    order::Vector{Type}
    "Documentation for each object. Keys are signatures."
    docs::METAType

    MultiDoc() = new(Type[], METAType())
end

# Docstring registration.
# =======================

"""
    Docs.doc!(__module__, binding, str, sig)

Adds a new docstring `str` to the docsystem of `__module__` for `binding` and signature `sig`.
"""
function doc!(__module__::Module, b::Binding, str::DocStr, @nospecialize sig = Union{})
    # Module docstrings are in the module itself
    if defined(b)
        obj = resolve(b)
        if isa(obj, Module)
            __module__ = obj
        end
    end
    initmeta(__module__)
    m = get!(meta(__module__), b, MultiDoc())
    if haskey(m.docs, sig)
        # We allow for docstrings to be updated, but print a warning since it is possible
        # that over-writing a docstring *may* have been accidental.  The warning
        # is suppressed for symbols in Main (or current active module),
        # for interactive use (#23011).
        __module__ === Base.active_module() ||
            @warn "Replacing docs for `$b :: $sig` in module `$(__module__)`"
    else
        # The ordering of docstrings for each Binding is defined by the order in which they
        # are initially added. Replacing a specific docstring does not change it's ordering.
        push!(m.order, sig)
    end
    m.docs[sig] = str
    str.data[:binding] = b
    str.data[:typesig] = sig
    return b
end

# Docstring lookup.
# =================

"""
    getdoc(obj)
    getdoc(obj, sig)

Return a custom docstring object associated with the object `obj` and, optionally, the tuple
type signature `sig`. See `MultiDoc` docs for an explanation of the possible values of `sig`.

The returned object can either be a markdown object generated by `Markdown.parse` or some
other custom type used to display non-markdown formatted documentation.

A return value of `nothing` can be used to signify to the docsystem that no documentation
was found for `obj`, in which case the docsystem will fall back to searching for the
`Binding` associated with `obj` instead.
"""
function getdoc end

getdoc(@nospecialize(x), @nospecialize(sig)) = getdoc(x)
getdoc(@nospecialize(x)) = nothing

# Utilities.
# ==========

"""
`catdoc(xs...)`: Combine the documentation metadata `xs` into a single meta object.
"""
catdoc() = nothing
catdoc(xs...) = vcat(xs...)

const keywords = Dict{Symbol, DocStr}()

function unblock(@nospecialize ex)
    while isexpr(ex, :var"hygienic-scope")
        isexpr(ex.args[1], :escape) || break
        ex = ex.args[1].args[1]
    end
    isexpr(ex, :block) || return ex
    exs = filter(ex -> !(isa(ex, LineNumberNode) || isexpr(ex, :line)), ex.args)
    length(exs) == 1 || return ex
    return unblock(exs[1])
end

# peek through ex to figure out what kind of expression it may eventually act like
# but ignoring scopes and line numbers
function unescape(@nospecialize ex)
    ex = unblock(ex)
    while isexpr(ex, :escape) || isexpr(ex, :var"hygienic-scope")
       ex = unblock(ex.args[1])
    end
    return ex
end

uncurly(@nospecialize ex) = isexpr(ex, :curly) ? ex.args[1] : ex

namify(@nospecialize x) = astname(x, isexpr(x, :macro))::Union{Symbol,Expr,GlobalRef}

function astname(x::Expr, ismacro::Bool)
    head = x.head
    if head === :.
        ismacro ? macroname(x) : x
    elseif head === :call && isexpr(x.args[1], :(::))
        return astname((x.args[1]::Expr).args[end], ismacro)
    else
        n = isexpr(x, (:module, :struct)) ? 2 : 1
        astname(x.args[n], ismacro)
    end
end
astname(q::QuoteNode, ismacro::Bool) = astname(q.value, ismacro)
astname(s::Symbol, ismacro::Bool)    = ismacro ? macroname(s) : s
astname(@nospecialize(other), ismacro::Bool) = other

macroname(s::Symbol) = Symbol('@', s)
macroname(x::Expr)   = Expr(x.head, x.args[1], macroname(x.args[end].value))

isfield(@nospecialize x) = isexpr(x, :.) &&
    (isa(x.args[1], Symbol) || isfield(x.args[1])) &&
    (isa(x.args[2], QuoteNode) || isexpr(x.args[2], :quote))

# @doc expression builders.
# =========================

"""
    Docs.metadata(source, module, expr, ismodule)

Build a `Dict` expression containing metadata captured from the expression `expr`.

Fields that may be included in the returned `Dict`:

- `:path`:       Symbol representing the file where `expr` is defined.
- `:linenumber`: Linenumber where `expr` is defined.
- `:module`:     Module where the docstring is defined.
- `:fields`:     `Dict` of all field docs found in `expr`. Only for concrete types.
"""
function metadata(__source__, __module__, expr, ismodule)
    args = []
    # Filename and linenumber of the docstring.
    __file__ = isa(__source__.file, Symbol) ? String(__source__.file) : ""
    push!(args, Pair(:path, __file__))
    push!(args, Pair(:linenumber, __source__.line))
    # Module in which the docstring is defined.
    if ismodule # Module docs go inside the module with name `expr`
        push!(args, :($Pair(:module, $expr)))
    else
        push!(args, Pair(:module, __module__))
    end
    if isexpr(expr, :struct)
        # Field docs for concrete types.
        P = Pair{Symbol,Any}
        fields = P[]
        last_docstr = nothing
        for each in (expr.args[3]::Expr).args
            eachex = unescape(each)
            if isa(eachex, Symbol) || isexpr(eachex, :(::))
                # a field declaration
                if last_docstr !== nothing
                    push!(fields, P(namify(eachex::Union{Symbol,Expr}), last_docstr))
                    last_docstr = nothing
                end
            elseif isexpr(eachex, :function) || isexpr(eachex, :(=))
                break
            elseif isa(eachex, String) || isexpr(eachex, :string) || isexpr(eachex, :call) ||
                (isexpr(eachex, :macrocall) && eachex.args[1] === Symbol("@doc_str"))
                # forms that might be doc strings
                last_docstr = each
            end
        end
        dict = :($(Dict{Symbol,Any})($([(:($(P)($(quot(f)), $d)))::Expr for (f, d) in fields]...)))
        push!(args, :($(Pair)(:fields, $dict)))
    end
    return :($(Dict{Symbol,Any})($(args...)))
end

function keyworddoc(__source__, __module__, str, def::Base.BaseDocs.Keyword)
    @nospecialize str
    docstr = esc(docexpr(__source__, __module__, lazy_iterpolate(str), metadata(__source__, __module__, def, false)))
    return :($setindex!($(keywords), $docstr, $(esc(quot(def.name)))); nothing)
end

function objectdoc(__source__, __module__, str, def, expr, sig = :(Union{}))
    @nospecialize str def expr sig
    binding = esc(bindingexpr(namify(expr)))
    docstr  = esc(docexpr(__source__, __module__, lazy_iterpolate(str), metadata(__source__, __module__, expr, false)))
    # Note: we want to avoid introducing line number nodes here (issue #24468)
    return Expr(:block, esc(def), :($(doc!)($__module__, $binding, $docstr, $(esc(sig)))))
end

function calldoc(__source__, __module__, str, def::Expr)
    @nospecialize str
    args = callargs(def)
    if isempty(args) || all(validcall, args)
        objectdoc(__source__, __module__, str, nothing, def, signature(def))
    else
        docerror(def)
    end
end
callargs(ex::Expr) = isexpr(ex, :where) ? callargs(ex.args[1]) :
    isexpr(ex, :call) ? ex.args[2:end] : error("Invalid expression to callargs: $ex")
validcall(x) = isa(x, Symbol) || isexpr(x, (:(::), :..., :kw, :parameters))

function moduledoc(__source__, __module__, meta, def, def′::Expr)
    @nospecialize meta def
    name  = namify(def′)
    docex = Expr(:call, doc!, name, bindingexpr(name),
        docexpr(__source__, name, lazy_iterpolate(meta), metadata(__source__, __module__, name, true)))
    if def === nothing
        esc(:(Core.eval($name, $(quot(docex)))))
    else
        def = unblock(def)
        block = def.args[3].args
        if !def.args[1]
            pushfirst!(block, :(import Base: @doc))
        end
        push!(block, docex)
        esc(Expr(:toplevel, def))
    end
end

# Shares a single doc, `meta`, between several expressions from the tuple expression `ex`.
function multidoc(__source__, __module__, meta, ex::Expr, define::Bool)
    @nospecialize meta
    out = Expr(:block)
    str = docexpr(__source__, __module__, lazy_iterpolate(meta), metadata(__source__, __module__, ex, false))
    ref = RefValue{DocStr}()
    first = true
    for arg in ex.args
        # The first `arg` to be documented needs to also create the docstring for the group
        # (after doing the action defined by the argument).
        # Subsequent `arg`s just need `ref` to be able to find the docstring without having
        # to create an entirely new one each.
        if first
            first = false
            docstr = :($getindex($setindex!($(ref), $str)))
        else
            docstr = :($getindex($(ref)))
        end
        push!(out.args, docm(__source__, __module__, docstr, arg, define))
    end
    return out
end

"""
    @__doc__(ex)

Low-level macro used to mark expressions returned by a macro that should be documented. If
more than one expression is marked then the same docstring is applied to each expression.

    macro example(f)
        quote
            \$(f)() = 0
            @__doc__ \$(f)(x) = 1
            \$(f)(x, y) = 2
        end |> esc
    end

`@__doc__` has no effect when a macro that uses it is not documented.
"""
:(Core.@__doc__)

function __doc__!(source, mod, meta, def, define::Bool)
    @nospecialize source mod meta def
    # Two cases must be handled here to avoid redefining all definitions contained in `def`:
    if define
        # `def` has not been defined yet (this is the common case, i.e. when not generating
        # the Base image). We just need to convert each `@__doc__` marker to an `@doc`.
        finddoc(def) do each
            each.head = :macrocall
            each.args = Any[Symbol("@doc"), source, mod, nothing, meta, each.args[end], define]
        end
    else
        # `def` has already been defined during Base image gen so we just need to find and
        # document any subexpressions marked with `@__doc__`.
        docs  = []
        found = finddoc(def) do each
            push!(docs, :(@doc($source, $mod, $meta, $(each.args[end]), $define)))
        end
        # If any subexpressions have been documented then replace the entire expression with
        # just those documented subexpressions to avoid redefining any definitions.
        if found
            def.head = :toplevel
            def.args = docs
        end
        found
    end
end
# Walk expression tree `def` and call `λ` when any `@__doc__` markers are found. Returns
# `true` to signify that at least one `@__doc__` has been found, and `false` otherwise.
function finddoc(λ, def::Expr)
    if isexpr(def, :block, 2) && isexpr(def.args[1], :meta, 1) && (def.args[1]::Expr).args[1] === :doc
        # Found the macroexpansion of an `@__doc__` expression.
        λ(def)
        true
    else
        found = false
        for each in def.args
            found |= finddoc(λ, each)
        end
        found
    end
end
finddoc(λ, @nospecialize def) = false

# Predicates and helpers for `docm` expression selection:

const FUNC_HEADS    = [:function, :macro, :(=)]
const BINDING_HEADS = [:const, :global, :(=)]
# For the special `:@mac` / `:(Base.@mac)` syntax for documenting a macro after definition.
isquotedmacrocall(@nospecialize x) =
    isexpr(x, :copyast, 1) &&
    isa(x.args[1], QuoteNode) &&
    isexpr(x.args[1].value, :macrocall, 2)
# Simple expressions / atoms the may be documented.
isbasicdoc(@nospecialize x) = isexpr(x, :.) || isa(x, Union{QuoteNode, Symbol})
is_signature(@nospecialize x) = isexpr(x, :call) || (isexpr(x, :(::), 2) && isexpr(x.args[1], :call)) || isexpr(x, :where)

function docm(source::LineNumberNode, mod::Module, ex)
    @nospecialize ex
    if isexpr(ex, :->) && length(ex.args) > 1
        return docm(source, mod, ex.args...)
    elseif isassigned(Base.REPL_MODULE_REF)
        # TODO: this is a shim to continue to allow `@doc` for looking up docstrings
        REPL = Base.REPL_MODULE_REF[]
        return REPL.lookup_doc(ex)
    end
    return nothing
end
# Drop incorrect line numbers produced by nested macro calls.
docm(source::LineNumberNode, mod::Module, _, _, x...) = docm(source, mod, x...)

# iscallexpr checks if an expression is a :call expression. The call expression may be
# also part of a :where expression, so it unwraps the :where layers until it reaches the
# "actual" expression
iscallexpr(ex::Expr) = isexpr(ex, :where) ? iscallexpr(ex.args[1]) : isexpr(ex, :call)
iscallexpr(ex) = false

function docm(source::LineNumberNode, mod::Module, meta, ex, define::Bool = true)
    @nospecialize meta ex
    # Some documented expressions may be decorated with macro calls which obscure the actual
    # expression. Expand the macro calls and remove extra blocks.
    x = unblock(macroexpand(mod, ex))
    # Don't try to redefine expressions. This is only needed for `Base` img gen since
    # otherwise calling `loaddocs` would redefine all documented functions and types.
    def = define ? x : nothing
    if isa(x, GlobalRef) && (x::GlobalRef).mod == mod
        x = (x::GlobalRef).name
    end

    # Keywords using the `@kw_str` macro in `base/docs/basedocs.jl`.
    #
    #   "..."
    #   kw"if", kw"else"
    #
    doc =
    isa(x, Base.BaseDocs.Keyword) ? keyworddoc(source, mod, meta, x) :

    # Method / macro definitions and "call" syntax.
    #
    #   function f(...) ... end
    #   f(...) = ...
    #   macro m(...) end
    #   function f end
    #   f(...)
    #
    # Including if the "call" expression is wrapped in "where" expression(s) (#32960), i.e.
    #
    #   f(::T) where T
    #   f(::T, ::U) where T where U
    #
    isexpr(x, FUNC_HEADS) && is_signature((x::Expr).args[1]) ? objectdoc(source, mod, meta, def, x::Expr, signature(x::Expr)) :
    isexpr(x, [:function, :macro])  && !isexpr((x::Expr).args[1], :call) ? objectdoc(source, mod, meta, def, x::Expr) :
    iscallexpr(x) ? calldoc(source, mod, meta, x::Expr) :

    # Type definitions.
    #
    #   struct T ... end
    #   abstract type T end
    #   primitive type T N end
    #
    isexpr(x, [:struct, :abstract, :primitive]) ? objectdoc(source, mod, meta, def, x::Expr) :

    # "Bindings". Names that resolve to objects with different names, ie.
    #
    #   const T = S
    #   T = S
    #   global T = S
    #
    isexpr(x, BINDING_HEADS) && !isexpr((x::Expr).args[1], :call) ? objectdoc(source, mod, meta, def, x::Expr) :

    # Quoted macrocall syntax. `:@time` / `:(Base.@time)`.
    isquotedmacrocall(x) ? objectdoc(source, mod, meta, def, x) :
    # Modules and baremodules.
    isexpr(x, :module) ? moduledoc(source, mod, meta, def, x::Expr) :
    # Document several expressions with the same docstring. `a, b, c`.
    isexpr(x, :tuple) ? multidoc(source, mod, meta, x::Expr, define) :
    # Errors generated by calling `macroexpand` are passed back to the call site.
    isexpr(x, :error) ? esc(x) :
    # When documenting macro-generated code we look for embedded `@__doc__` calls.
    __doc__!(source, mod, meta, x, define) ? esc(x) :
    # Any "basic" expression such as a bare function or module name or numeric literal.
    isbasicdoc(x) ? objectdoc(source, mod, meta, nothing, x) :

    # All other expressions are undocumentable and should be handled on a case-by-case basis
    # with `@__doc__`. Unbound string literals are also undocumentable since they cannot be
    # retrieved from the module's metadata `IdDict` without a reference to the string.
    docerror(ex)

    return doc
end

function docerror(@nospecialize ex)
    txt = """
    cannot document the following expression:

    $(isa(ex, AbstractString) ? repr(ex) : ex)"""
    if isexpr(ex, :macrocall)
        txt *= "\n\n'$(ex.args[1])' not documentable. See 'Base.@__doc__' docs for details."
    end
    return :($(error)($txt, "\n"))
end

include("utils.jl")

# Swap out the bootstrap macro with the real one.
Core.atdoc!(docm)

function loaddocs(docs::Vector{Core.SimpleVector})
    for (mod, ex, str, file, line) in docs
        data = Dict{Symbol,Any}(:path => string(file), :linenumber => line)
        doc = docstr(str, data)
        lno = LineNumberNode(line, file)
        docstring = docm(lno, mod, doc, ex, false) # expand the real @doc macro now
        Core.eval(mod, Expr(:var"hygienic-scope", docstring, Docs, lno))
    end
    empty!(docs)
    nothing
end

function formatdoc end
function parsedoc end
function apropos end
function doc end

end
T   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/docs/bindings.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

export @var

struct Binding
    mod::Module
    var::Symbol

    function Binding(m::Module, v::Symbol)
        # Normalise the binding module for module symbols so that:
        #   Binding(Base, :Base) === Binding(Main, :Base)
        m = nameof(m) === v ? parentmodule(m) : m
        new(Base.binding_module(m, v), v)
    end
end

bindingexpr(x) = Expr(:call, Binding, splitexpr(x)...)

defined(b::Binding) = isdefined(b.mod, b.var)
resolve(b::Binding) = getfield(b.mod, b.var)

function splitexpr(x::Expr)
    isexpr(x, :macrocall) ? splitexpr(x.args[1]) :
    isexpr(x, :.)         ? (x.args[1], x.args[2]) :
    error("Invalid @var syntax `$x`.")
end
splitexpr(s::Symbol) = Expr(:macrocall, getfield(Base, Symbol("@__MODULE__")), nothing), quot(s)
splitexpr(r::GlobalRef) = r.mod, quot(r.name)
splitexpr(other)     = error("Invalid @var syntax `$other`.")

macro var(x)
    esc(bindingexpr(x))
end

function Base.show(io::IO, b::Binding)
    if b.mod === Base.active_module()
        print(io, b.var)
    else
        print(io, b.mod, '.', Base.isoperator(b.var) ? ":" : "", b.var)
    end
end

aliasof(b::Binding)     = defined(b) ? (a = aliasof(resolve(b), b); defined(a) ? a : b) : b
aliasof(d::DataType, b) = Binding(d.name.module, d.name.name)
aliasof(λ::Function, b) = (m = typeof(λ).name.mt; Binding(m.module, m.name))
aliasof(m::Module,   b) = Binding(m, nameof(m))
aliasof(other,       b) = b
Q   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/base/docs/utils.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

# Text / HTML objects

import .Base: print, show, ==, hash

export HTML, @html_str

export HTML, Text

"""
`HTML(s)`: Create an object that renders `s` as html.

    HTML("<div>foo</div>")

You can also use a stream for large amounts of data:

    HTML() do io
      println(io, "<div>foo</div>")
    end

!!! warning
    `HTML` is currently exported to maintain
    backwards compatibility, but this export
    is deprecated. It is recommended to use
    this type as `Docs.HTML` or to explicitly
    import it from `Docs`.
"""
mutable struct HTML{T}
    content::T
end

function HTML(xs...)
    HTML() do io
        for x in xs
            print(io, x)
        end
    end
end

show(io::IO, ::MIME"text/html", h::HTML) = print(io, h.content)
show(io::IO, ::MIME"text/html", h::HTML{<:Function}) = h.content(io)

"""
    @html_str -> Docs.HTML

Create an `HTML` object from a literal string.

# Examples
```jldoctest
julia> html"Julia"
HTML{String}("Julia")
```
"""
macro html_str(s)
    :(HTML($s))
end

function catdoc(xs::HTML...)
    HTML() do io
        for x in xs
            show(io, MIME"text/html"(), x)
        end
    end
end

export Text, @text_str

"""
`Text(s)`: Create an object that renders `s` as plain text.

    Text("foo")

You can also use a stream for large amounts of data:

    Text() do io
      println(io, "foo")
    end

!!! warning
    `Text` is currently exported to maintain
    backwards compatibility, but this export
    is deprecated. It is recommended to use
    this type as `Docs.Text` or to explicitly
    import it from `Docs`.
"""
mutable struct Text{T}
    content::T
end

print(io::IO, t::Text) = print(io, t.content)
print(io::IO, t::Text{<:Function}) = t.content(io)
show(io::IO, t::Text) = print(io, t)

==(t1::T, t2::T) where {T<:Union{HTML,Text}} = t1.content == t2.content
hash(t::T, h::UInt) where {T<:Union{HTML,Text}} = hash(T, hash(t.content, h))

"""
    @text_str -> Docs.Text

Create a `Text` object from a literal string.

# Examples
```jldoctest
julia> text"Julia"
Julia
```
"""
macro text_str(s)
    :(Text($s))
end

function catdoc(xs::Text...)
    Text() do io
        for x in xs
            show(io, MIME"text/plain"(), x)
        end
    end
end
t   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/ArgTools/src/ArgTools.jl*      module ArgTools

export
    arg_read,  ArgRead,  arg_readers,
    arg_write, ArgWrite, arg_writers,
    arg_isdir, arg_mkdir, @arg_test

import Base: AbstractCmd, CmdRedirect, Process

if isdefined(Base.Filesystem, :prepare_for_deletion)
    using Base.Filesystem: prepare_for_deletion
else
    function prepare_for_deletion(path::AbstractString)
        try prepare_for_deletion_core(path)
        catch
        end
    end
    function prepare_for_deletion_core(path::AbstractString)
        isdir(path) || return
        chmod(path, filemode(path) | 0o333)
        for name in readdir(path)
            path′ = joinpath(path, name)
            prepare_for_deletion_core(path′)
        end
    end
end

const nolock_docstring = """
Note: when opening a file, ArgTools will pass `lock = false` to the file `open(...)` call.
Therefore, the object returned by this function should not be used from multiple threads.
This restriction may be relaxed in the future, which would not break any working code.
"""

if VERSION ≥ v"1.5"
    open_nolock(args...; kws...) = open(args...; kws..., lock=false)
else
    open_nolock(args...; kws...) = open(args...; kws...)
end

## main API ##

"""
    ArgRead = Union{AbstractString, AbstractCmd, IO}

The `ArgRead` types is a union of the types that the `arg_read` function knows
how to convert into readable IO handles. See [`arg_read`](@ref) for details.
"""
const ArgRead = Union{AbstractString, AbstractCmd, IO}

"""
    ArgWrite = Union{AbstractString, AbstractCmd, IO}

The `ArgWrite` types is a union of the types that the `arg_write` function knows
how to convert into writeable IO handles, except for `Nothing` which `arg_write`
handles by generating a temporary file. See [`arg_write`](@ref) for details.
"""
const ArgWrite = Union{AbstractString, AbstractCmd, IO}

"""
    arg_read(f::Function, arg::ArgRead) -> f(arg_io)

The `arg_read` function accepts an argument `arg` that can be any of these:

- `AbstractString`: a file path to be opened for reading
- `AbstractCmd`: a command to be run, reading from its standard output
- `IO`: an open IO handle to be read from

Whether the body returns normally or throws an error, a path which is opened
will be closed before returning from `arg_read` and an `IO` handle will be
flushed but not closed before returning from `arg_read`.

$(nolock_docstring)
"""
arg_read(f::Function, arg::AbstractString) = open_nolock(f, arg)
arg_read(f::Function, arg::ArgRead) = open(f, arg)
arg_read(f::Function, arg::IO) = f(arg)

"""
    arg_write(f::Function, arg::ArgWrite) -> arg
    arg_write(f::Function, arg::Nothing) -> tempname()

The `arg_read` function accepts an argument `arg` that can be any of these:

- `AbstractString`: a file path to be opened for writing
- `AbstractCmd`: a command to be run, writing to its standard input
- `IO`: an open IO handle to be written to
- `Nothing`: a temporary path should be written to

If the body returns normally, a path that is opened will be closed upon
completion; an IO handle argument is left open but flushed before return. If the
argument is `nothing` then a temporary path is opened for writing and closed
open completion and the path is returned from `arg_write`. In all other cases,
`arg` itself is returned. This is a useful pattern since you can consistently
return whatever was written, whether an argument was passed or not.

If there is an error during the evaluation of the body, a path that is opened by
`arg_write` for writing will be deleted, whether it's passed in as a string or a
temporary path generated when `arg` is `nothing`.

$(nolock_docstring)
"""
function arg_write(f::Function, arg::AbstractString)
    try open_nolock(f, arg, write=true)
    catch
        rm(arg, force=true)
        rethrow()
    end
    return arg
end

function arg_write(f::Function, arg::AbstractCmd)
    open(f, arg, write=true)
    return arg
end

function arg_write(f::Function, arg::Nothing)
    @static if VERSION ≥ v"1.5"
        file = tempname()
        io = open_nolock(file, write=true)
    else
        file, io = mktemp()
    end
    try f(io)
    catch
        close(io)
        rm(file, force=true)
        rethrow()
    end
    close(io)
    return file
end

function arg_write(f::Function, arg::IO)
    try f(arg)
    finally
        flush(arg)
    end
    return arg
end

"""
    arg_isdir(f::Function, arg::AbstractString) -> f(arg)

The `arg_isdir` function takes `arg` which must be the path to an existing
directory (an error is raised otherwise) and passes that path to `f` finally
returning the result of `f(arg)`. This is definitely the least useful tool
offered by `ArgTools` and mostly exists for symmetry with `arg_mkdir` and to
give consistent error messages.
"""
function arg_isdir(f::Function, arg::AbstractString)
    isdir(arg) || error("arg_isdir: $(repr(arg)) not a directory")
    return f(arg)
end

"""
    arg_mkdir(f::Function, arg::AbstractString) -> arg
    arg_mkdir(f::Function, arg::Nothing) -> mktempdir()

The `arg_mkdir` function takes `arg` which must either be one of:

- a path to an already existing empty directory,
- a non-existent path which can be created as a directory, or
- `nothing` in which case a temporary directory is created.

In all cases the path to the directory is returned. If an error occurs during
`f(arg)`, the directory is returned to its original state: if it already existed
but was empty, it will be emptied; if it did not exist it will be deleted.
"""
function arg_mkdir(f::Function, arg::Union{AbstractString, Nothing})
    existed = false
    if arg === nothing
        arg = mktempdir()
    else
        st = stat(arg)
        if !ispath(st)
            mkdir(arg)
        elseif !isdir(st)
            error("arg_mkdir: $(repr(arg)) not a directory")
        else
            isempty(readdir(arg)) ||
                error("arg_mkdir: $(repr(arg)) directory not empty")
            existed = true
        end
    end
    try f(arg)
    catch
        if existed
            for name in readdir(arg)
                path = joinpath(arg, name)
                prepare_for_deletion(path)
                rm(path, force=true, recursive=true)
            end
        else
            prepare_for_deletion(arg)
            rm(arg, force=true, recursive=true)
        end
        rethrow()
    end
    return arg
end

## test utilities ##

const ARG_READERS = [
    String      => path -> f -> f(path)
    Cmd         => path -> f -> f(`cat $path`)
    CmdRedirect => path -> f -> f(pipeline(path, `cat`))
    IOStream    => path -> f -> open(f, path)
    Process     => path -> f -> open(f, `cat $path`)
]

const ARG_WRITERS = [
    String      => path -> f -> f(path)
    Cmd         => path -> f -> f(`tee $path`)
    CmdRedirect => path -> f -> f(pipeline(`cat`, path))
    IOStream    => path -> f -> open(f, path, write=true)
    Process     => path -> f -> open(f, pipeline(`cat`, path), write=true)
]

@assert all(t <: ArgRead  for t in map(first, ARG_READERS))
@assert all(t <: ArgWrite for t in map(first, ARG_WRITERS))

"""
    arg_readers(arg :: AbstractString, [ type = ArgRead ]) do arg::Function
        ## pre-test setup ##
        @arg_test arg begin
            arg :: ArgRead
            ## test using `arg` ##
        end
        ## post-test cleanup ##
    end

The `arg_readers` function takes a path to be read and a single-argument do
block, which is invoked once for each test reader type that `arg_read` can
handle. If the optional `type` argument is given then the do block is only
invoked for readers that produce arguments of that type.

The `arg` passed to the do block is not the argument value itself, because some
of test argument types need to be initialized and finalized for each test case.
Consider an open file handle argument: once you've used it for one test, you
can't use it again; you need to close it and open the file again for the next
test. This function `arg` can be converted into an `ArgRead` instance using
`@arg_test arg begin ... end`.
"""
function arg_readers(
    body::Function,
    path::AbstractString,
    type::Type = ArgRead,
)
    for (t, reader) in ARG_READERS
        t <: type || continue
        body(reader(path))
    end
end

"""
    arg_writers([ type = ArgWrite ]) do path::String, arg::Function
        ## pre-test setup ##
        @arg_test arg begin
            arg :: ArgWrite
            ## test using `arg` ##
        end
        ## post-test cleanup ##
    end

The `arg_writers` function takes a do block, which is invoked once for each test
writer type that `arg_write` can handle with a temporary (non-existent) `path`
and `arg` which can be converted into various writable argument types which
write to `path`. If the optional `type` argument is given then the do block is
only invoked for writers that produce arguments of that type.

The `arg` passed to the do block is not the argument value itself, because some
of test argument types need to be initialized and finalized for each test case.
Consider an open file handle argument: once you've used it for one test, you
can't use it again; you need to close it and open the file again for the next
test. This function `arg` can be converted into an `ArgWrite` instance using
`@arg_test arg begin ... end`.

There is also an `arg_writers` method that takes a path name like `arg_readers`:

    arg_writers(path::AbstractString, [ type = ArgWrite ]) do arg::Function
        ## pre-test setup ##
        @arg_test arg begin
            # here `arg :: ArgWrite`
            ## test using `arg` ##
        end
        ## post-test cleanup ##
    end

This method is useful if you need to specify `path` instead of using path name
generated by `tempname()`. Since `path` is passed from outside of `arg_writers`,
the path is not an argument to the do block in this form.
"""
function arg_writers(
    body::Function,
    type::Type = ArgWrite,
)
    for (t, writer) in ARG_WRITERS
        t <: type || continue
        path = tempname()
        try body(path, writer(path))
        finally
            rm(path, force=true)
        end
    end
end

function arg_writers(
    body::Function,
    path::AbstractString,
    type::Type = ArgWrite,
)
    for (t, writer) in ARG_WRITERS
        t <: type || continue
        body(writer(path))
    end
end

"""
    @arg_test arg1 arg2 ... body

The `@arg_test` macro is used to convert `arg` functions provided by
`arg_readers` and `arg_writers` into actual argument values. When you write
`@arg_test arg body` it is equivalent to `arg(arg -> body)`.
"""
macro arg_test(args...)
    arg_test(args...)
end

function arg_test(var::Symbol, args...)
    var = esc(var)
    body = arg_test(args...)
    :($var($var -> $body))
end

arg_test(ex::Expr) = esc(ex)

end # module
v   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Artifacts/src/Artifacts.jl@w      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
Artifacts.jl is a Julia module that is used for managing and accessing
artifacts in Julia packages. Artifacts are containers for
platform-specific binaries, datasets, text, or any other kind of data
that would be convenient to place within an immutable, life-cycled datastore.
"""
module Artifacts

import Base: get, SHA1
using Base.BinaryPlatforms, Base.TOML

export artifact_exists, artifact_path, artifact_meta, artifact_hash,
       select_downloadable_artifacts, find_artifacts_toml, @artifact_str

"""
    parse_toml(path::String)

Uses Base.TOML to parse a TOML file. Do not mutate the returned dictionary.
"""
function parse_toml(path::String)
    # Uses the caching mechanics for toml files in Base
    Base.parsed_toml(path)
end

# keep in sync with Base.project_names and Base.manifest_names
const artifact_names = ("JuliaArtifacts.toml", "Artifacts.toml")

const ARTIFACTS_DIR_OVERRIDE = Ref{Union{String,Nothing}}(nothing)
"""
    with_artifacts_directory(f::Function, artifacts_dir::String)

Helper function to allow temporarily changing the artifact installation and search
directory.  When this is set, no other directory will be searched for artifacts, and new
artifacts will be installed within this directory.  Similarly, removing an artifact will
only effect the given artifact directory.  To layer artifact installation locations, use
the typical Julia depot path mechanism.
"""
function with_artifacts_directory(f::Function, artifacts_dir::String)
    try
        ARTIFACTS_DIR_OVERRIDE[] = artifacts_dir
        f()
    finally
        ARTIFACTS_DIR_OVERRIDE[] = nothing
    end
end

"""
    artifacts_dirs(args...)

Return a list of paths joined into all possible artifacts directories, as dictated by the
current set of depot paths and the current artifact directory override via the method
`with_artifacts_dir()`.
"""
function artifacts_dirs(args...)
    if ARTIFACTS_DIR_OVERRIDE[] === nothing
        return String[abspath(depot, "artifacts", args...) for depot in Base.DEPOT_PATH]
    else
        # If we've been given an override, use _only_ that directory.
        return String[abspath(ARTIFACTS_DIR_OVERRIDE[]::String, args...)]
    end
end

# Recursive function, let's not make this a closure because it then has to
# be boxed.
function parse_mapping(mapping::String, name::String, override_file::String)
    if !isabspath(mapping) && !isempty(mapping)
        mapping = tryparse(Base.SHA1, mapping)
        if mapping === nothing
            @error("Invalid override in '$(override_file)': entry '$(name)' must map to an absolute path or SHA1 hash!")
        end
    end
    return mapping
end
function parse_mapping(mapping::Dict, name::String, override_file::String)
    return Dict(k => parse_mapping(v, name, override_file) for (k, v) in mapping)
end
# Fallthrough for invalid Overrides.toml files
parse_mapping(mapping, name::String, override_file::String) = nothing

"""
    ARTIFACT_OVERRIDES

Artifact locations can be overridden by writing `Overrides.toml` files within the artifact
directories of Pkg depots.  For example, in the default depot `~/.julia`, one may create
a `~/.julia/artifacts/Overrides.toml` file with the following contents:

    78f35e74ff113f02274ce60dab6e92b4546ef806 = "/path/to/replacement"
    c76f8cda85f83a06d17de6c57aabf9e294eb2537 = "fb886e813a4aed4147d5979fcdf27457d20aa35d"

    [d57dbccd-ca19-4d82-b9b8-9d660942965b]
    c_simple = "/path/to/c_simple_dir"
    libfoo = "fb886e813a4aed4147d5979fcdf27457d20aa35d""

This file defines four overrides; two which override specific artifacts identified
through their content hashes, two which override artifacts based on their bound names
within a particular package's UUID.  In both cases, there are two different targets of
the override: overriding to an on-disk location through an absolute path, and
overriding to another artifact by its content-hash.
"""
const ARTIFACT_OVERRIDES = Ref{Union{Dict{Symbol,Any},Nothing}}(nothing)
function load_overrides(;force::Bool = false)::Dict{Symbol, Any}
    if ARTIFACT_OVERRIDES[] !== nothing && !force
        return ARTIFACT_OVERRIDES[]
    end

    # We organize our artifact location overrides into two camps:
    #  - overrides per UUID with artifact names mapped to a new location
    #  - overrides per hash, mapped to a new location.
    #
    # Overrides per UUID/bound name are intercepted upon Artifacts.toml load, and new
    # entries within the "hash" overrides are generated on-the-fly.  Thus, all redirects
    # mechanistically happen through the "hash" overrides.
    overrides = Dict{Symbol,Any}(
        # Overrides by UUID
        :UUID => Dict{Base.UUID,Dict{String,Union{String,SHA1}}}(),

        # Overrides by hash
        :hash => Dict{SHA1,Union{String,SHA1}}(),
    )

    for override_file in reverse(artifacts_dirs("Overrides.toml"))
        !isfile(override_file) && continue

        # Load the toml file
        depot_override_dict = parse_toml(override_file)

        for (k, mapping) in depot_override_dict
            # First, parse the mapping. Is it an absolute path, a valid SHA1-hash, or neither?
            mapping = parse_mapping(mapping, k, override_file)
            if mapping === nothing
                @error("Invalid override in '$(override_file)': failed to parse entry `$(k)`")
                continue
            end

            # Next, determine if this is a hash override or a UUID/name override
            if isa(mapping, String) || isa(mapping, SHA1)
                # if this mapping is a direct mapping (e.g. a String), store it as a hash override
                local hash_str
                hash = tryparse(Base.SHA1, k)
                if hash === nothing
                    @error("Invalid override in '$(override_file)': Invalid SHA1 hash '$(k)'")
                    continue
                end

                # If this mapping is the empty string, un-override it
                if mapping == ""
                    delete!(overrides[:hash], hash)
                else
                    overrides[:hash][hash] = mapping
                end
            elseif isa(mapping, Dict)
                # Convert `k` into a uuid
                uuid = tryparse(Base.UUID, k)
                if uuid === nothing
                    @error("Invalid override in '$(override_file)': Invalid UUID '$(k)'")
                    continue
                end

                # If this mapping is itself a dict, store it as a set of UUID/artifact name overrides
                ovruuid = overrides[:UUID]::Dict{Base.UUID,Dict{String,Union{String,SHA1}}}
                if !haskey(ovruuid, uuid)
                    ovruuid[uuid] = Dict{String,Union{String,SHA1}}()
                end

                # For each name in the mapping, update appropriately
                for (name, override_value) in mapping
                    # If the mapping for this name is the empty string, un-override it
                    if override_value == ""
                        delete!(ovruuid[uuid], name)
                    else
                        # Otherwise, store it!
                        ovruuid[uuid][name] = override_value
                    end
                end
            else
                @error("Invalid override in '$(override_file)': unknown mapping type for '$(k)': $(typeof(mapping))")
            end
        end
    end

    ARTIFACT_OVERRIDES[] = overrides
    return overrides
end

# Helpers to map an override to an actual path
map_override_path(x::AbstractString) = String(x)::String
map_override_path(x::SHA1) = artifact_path(x)
map_override_path(x::Nothing) = nothing

"""
    query_override(hash::SHA1; overrides::Dict = load_overrides())

Query the loaded `<DEPOT>/artifacts/Overrides.toml` settings for artifacts that should be
redirected to a particular path or another content-hash.
"""
function query_override(hash::SHA1; overrides::Dict{Symbol,Any} = load_overrides())
    return map_override_path(get(overrides[:hash], hash, nothing))
end
function query_override(pkg::Base.UUID, artifact_name::String; overrides::Dict{Symbol,Any} = load_overrides())
    if haskey(overrides[:UUID], pkg)
        return map_override_path(get(overrides[:UUID][pkg], artifact_name, nothing))
    end
    return nothing
end

"""
    artifact_paths(hash::SHA1; honor_overrides::Bool=true)

Return all possible paths for an artifact given the current list of depots as returned
by `Pkg.depots()`.  All, some or none of these paths may exist on disk.
"""
function artifact_paths(hash::SHA1; honor_overrides::Bool=true)
    # First, check to see if we've got an override:
    if honor_overrides
        override = query_override(hash)
        if override !== nothing
            return [override]
        end
    end

    return artifacts_dirs(bytes2hex(hash.bytes))
end

"""
    artifact_path(hash::SHA1; honor_overrides::Bool=true)

Given an artifact (identified by SHA1 git tree hash), return its installation path.  If
the artifact does not exist, returns the location it would be installed to.

!!! compat "Julia 1.3"
    This function requires at least Julia 1.3.
"""
function artifact_path(hash::SHA1; honor_overrides::Bool=true)
    # Get all possible paths (rooted in all depots)
    possible_paths = artifact_paths(hash; honor_overrides=honor_overrides)

    # Find the first path that exists and return it
    for p in possible_paths
        if isdir(p)
            return p
        end
    end

    # If none exist, then just return the one that would exist within `depots1()`.
    return first(possible_paths)
end

"""
    artifact_exists(hash::SHA1; honor_overrides::Bool=true)

Return whether or not the given artifact (identified by its sha1 git tree hash) exists
on-disk.  Note that it is possible that the given artifact exists in multiple locations
(e.g. within multiple depots).

!!! compat "Julia 1.3"
    This function requires at least Julia 1.3.
"""
function artifact_exists(hash::SHA1; honor_overrides::Bool=true)
    return any(isdir, artifact_paths(hash; honor_overrides=honor_overrides))
end

"""
    unpack_platform(entry::Dict, name::String, artifacts_toml::String)

Given an `entry` for the artifact named `name`, located within the file `artifacts_toml`,
returns the `Platform` object that this entry specifies.  Returns `nothing` on error.
"""
function unpack_platform(entry::Dict{String,Any}, name::String,
                         artifacts_toml::String)::Union{Nothing,Platform}
    if !haskey(entry, "os")
        @error("Invalid artifacts file at '$(artifacts_toml)': platform-specific artifact entry '$name' missing 'os' key")
        return nothing
    end

    if !haskey(entry, "arch")
        @error("Invalid artifacts file at '$(artifacts_toml)': platform-specific artifact entry '$name' missing 'arch' key")
        return nothing
    end

    # Collect all String-valued mappings in `entry` and use them as tags
    tags = Dict{String, String}()
    for (k, v) in entry
        if v isa String
            tags[k] = v
        end
    end
    # Removing some known entries that shouldn't be passed through `tags`
    delete!(tags, "os")
    delete!(tags, "arch")
    delete!(tags, "git-tree-sha1")
    return Platform(entry["arch"], entry["os"], tags)
end

function pack_platform!(meta::Dict, p::AbstractPlatform)
    for (k, v) in tags(p)
        if v !== nothing
            meta[k] = v
        end
    end
    return meta
end

"""
    load_artifacts_toml(artifacts_toml::String;
                        pkg_uuid::Union{UUID,Nothing}=nothing)

Loads an `(Julia)Artifacts.toml` file from disk.  If `pkg_uuid` is set to the `UUID` of the
owning package, UUID/name overrides stored in a depot `Overrides.toml` will be resolved.
"""
function load_artifacts_toml(artifacts_toml::String;
                             pkg_uuid::Union{Base.UUID,Nothing} = nothing)
    artifact_dict = parse_toml(artifacts_toml)

    # Process overrides for this `pkg_uuid`
    process_overrides(artifact_dict, pkg_uuid)
    return artifact_dict
end

"""
    process_overrides(artifact_dict::Dict, pkg_uuid::Base.UUID)

When loading an `Artifacts.toml` file, we must check `Overrides.toml` files to see if any
of the artifacts within it have been overridden by UUID.  If they have, we honor the
overrides by inspecting the hashes of the targeted artifacts, then overriding them to
point to the given override, punting the actual redirection off to the hash-based
override system.  This does not modify the `artifact_dict` object, it merely dynamically
adds more hash-based overrides as `Artifacts.toml` files that are overridden are loaded.
"""
function process_overrides(artifact_dict::Dict, pkg_uuid::Base.UUID)
    # Insert just-in-time hash overrides by looking up the names of anything we need to
    # override for this UUID, and inserting new overrides for those hashes.
    overrides = load_overrides()
    if haskey(overrides[:UUID], pkg_uuid)
        pkg_overrides = overrides[:UUID][pkg_uuid]::Dict{String, <:Any}

        for name in keys(artifact_dict)
            # Skip names that we're not overriding
            if !haskey(pkg_overrides, name)
                continue
            end

            # If we've got a platform-specific friend, override all hashes:
            if isa(artifact_dict[name], Array)
                for entry in artifact_dict[name]
                    hash = SHA1(entry["git-tree-sha1"])
                    overrides[:hash][hash] = overrides[:UUID][pkg_uuid][name]
                end
            elseif isa(artifact_dict[name], Dict)
                hash = SHA1(artifact_dict[name]["git-tree-sha1"])
                overrides[:hash][hash] = overrides[:UUID][pkg_uuid][name]
            end
        end
    end
    return artifact_dict
end

# If someone tries to call process_overrides() with `nothing`, do exactly that
process_overrides(artifact_dict::Dict, pkg_uuid::Nothing) = nothing

"""
    artifact_meta(name::String, artifacts_toml::String;
                  platform::AbstractPlatform = HostPlatform(),
                  pkg_uuid::Union{Base.UUID,Nothing}=nothing)

Get metadata about a given artifact (identified by name) stored within the given
`(Julia)Artifacts.toml` file.  If the artifact is platform-specific, use `platform` to choose the
most appropriate mapping.  If none is found, return `nothing`.

!!! compat "Julia 1.3"
    This function requires at least Julia 1.3.
"""
function artifact_meta(name::String, artifacts_toml::String;
                       platform::AbstractPlatform = HostPlatform(),
                       pkg_uuid::Union{Base.UUID,Nothing}=nothing)
    if !isfile(artifacts_toml)
        return nothing
    end

    # Parse the toml of the artifacts_toml file
    artifact_dict = load_artifacts_toml(artifacts_toml; pkg_uuid=pkg_uuid)
    return artifact_meta(name, artifact_dict, artifacts_toml; platform=platform)
end

function artifact_meta(name::String, artifact_dict::Dict, artifacts_toml::String;
                       platform::AbstractPlatform = HostPlatform())
    if !haskey(artifact_dict, name)
        return nothing
    end
    meta = artifact_dict[name]

    # If it's an array, find the entry that best matches our current platform
    if isa(meta, Vector)
        dl_dict = Dict{AbstractPlatform,Dict{String,Any}}()
        for x in meta
            x::Dict{String}
            dl_dict[unpack_platform(x, name, artifacts_toml)] = x
        end
        meta = select_platform(dl_dict, platform)
    # If it's NOT a dict, complain
    elseif !isa(meta, Dict)
        @error("Invalid artifacts file at $(artifacts_toml): artifact '$name' malformed, must be array or dict!")
        return nothing
    end

    # This is such a no-no, we are going to call it out right here, right now.
    if meta !== nothing && !haskey(meta, "git-tree-sha1")
        @error("Invalid artifacts file at $(artifacts_toml): artifact '$name' contains no `git-tree-sha1`!")
        return nothing
    end

    # Return the full meta-dict.
    return meta
end

"""
    artifact_hash(name::String, artifacts_toml::String;
                  platform::AbstractPlatform = HostPlatform())

Thin wrapper around `artifact_meta()` to return the hash of the specified, platform-
collapsed artifact.  Returns `nothing` if no mapping can be found.

!!! compat "Julia 1.3"
    This function requires at least Julia 1.3.
"""
function artifact_hash(name::String, artifacts_toml::String;
                       platform::AbstractPlatform = HostPlatform(),
                       pkg_uuid::Union{Base.UUID,Nothing}=nothing)::Union{Nothing, SHA1}
    meta = artifact_meta(name, artifacts_toml; platform=platform)
    if meta === nothing
        return nothing
    end

    return SHA1(meta["git-tree-sha1"])
end

function select_downloadable_artifacts(artifact_dict::Dict, artifacts_toml::String;
                                       platform::AbstractPlatform = HostPlatform(),
                                       pkg_uuid::Union{Nothing,Base.UUID} = nothing,
                                       include_lazy::Bool = false)
    artifacts = Dict{String,Any}()
    for name in keys(artifact_dict)
        # Get the metadata about this name for the requested platform
        meta = artifact_meta(name, artifact_dict, artifacts_toml; platform=platform)

        # If there are no instances of this name for the desired platform, skip it
        # Also skip if there's no `download` stanza (e.g. it's only a local artifact)
        # or if it's lazy and we're not explicitly looking for lazy artifacts.
        if meta === nothing || !haskey(meta, "download") || (get(meta, "lazy", false) && !include_lazy)
            continue
        end

        # Else, welcome it into the meta-fold
        artifacts[name] = meta
    end
    return artifacts
end

"""
    select_downloadable_artifacts(artifacts_toml::String;
                                  platform = HostPlatform,
                                  include_lazy = false,
                                  pkg_uuid = nothing)

Return a dictionary where every entry is an artifact from the given `Artifacts.toml`
that should be downloaded for the requested platform.  Lazy artifacts are included if
`include_lazy` is set.
"""
function select_downloadable_artifacts(artifacts_toml::String;
                                       platform::AbstractPlatform = HostPlatform(),
                                       include_lazy::Bool = false,
                                       pkg_uuid::Union{Nothing,Base.UUID} = nothing)
    if !isfile(artifacts_toml)
        return Dict{String,Any}()
    end
    artifact_dict = load_artifacts_toml(artifacts_toml; pkg_uuid=pkg_uuid)
    return select_downloadable_artifacts(artifact_dict, artifacts_toml; platform, pkg_uuid, include_lazy)
end


"""
    find_artifacts_toml(path::String)

Given the path to a `.jl` file, (such as the one returned by `__source__.file` in a macro
context), find the `(Julia)Artifacts.toml` that is contained within the containing project (if it
exists), otherwise return `nothing`.

!!! compat "Julia 1.3"
    This function requires at least Julia 1.3.
"""
function find_artifacts_toml(path::String)
    if !isdir(path)
        path = dirname(path)
    end

    # Run until we hit the root directory.
    while dirname(path) != path
        for f in artifact_names
            artifacts_toml_path = joinpath(path, f)
            if isfile(artifacts_toml_path)
                return abspath(artifacts_toml_path)
            end
        end

        # Does a `(Julia)Project.toml` file exist here, in the absence of an Artifacts.toml?
        # If so, stop the search as we've probably hit the top-level of this package,
        # and we don't want to escape out into the larger filesystem.
        for f in Base.project_names
            if isfile(joinpath(path, f))
                return nothing
            end
        end

        # Move up a directory
        path = dirname(path)
    end

    # We never found anything, just return `nothing`
    return nothing
end

# We do this to avoid doing the `joinpath()` work if we don't have to, and also to
# avoid a trailing slash due to `joinpath()`'s habit of including one when the last
# argument is the empty string.
function jointail(dir, tail)
    if !isempty(tail)
        return joinpath(dir, tail)
    else
        return dir
    end
end

function _artifact_str(__module__, artifacts_toml, name, path_tail, artifact_dict, hash, platform, @nospecialize(lazyartifacts))
    moduleroot = Base.moduleroot(__module__)
    if haskey(Base.module_keys, moduleroot)
        # Process overrides for this UUID, if we know what it is
        process_overrides(artifact_dict, Base.module_keys[moduleroot].uuid)
    end

    # If the artifact exists, we're in the happy path and we can immediately
    # return the path to the artifact:
    dirs = artifact_paths(hash; honor_overrides=true)
    for dir in dirs
        if isdir(dir)
            return jointail(dir, path_tail)
        end
    end

    # If not, try determining what went wrong:
    meta = artifact_meta(name, artifact_dict, artifacts_toml; platform)
    if meta !== nothing && get(meta, "lazy", false)
        if lazyartifacts isa Module && isdefined(lazyartifacts, :ensure_artifact_installed)
            if nameof(lazyartifacts) in (:Pkg, :Artifacts)
                Base.depwarn("using Pkg instead of using LazyArtifacts is deprecated", :var"@artifact_str", force=true)
            end
            return jointail(lazyartifacts.ensure_artifact_installed(string(name), meta, artifacts_toml; platform), path_tail)
        end
        error("Artifact $(repr(name)) is a lazy artifact; package developers must call `using LazyArtifacts` in $(__module__) before using lazy artifacts.")
    end

    path_str = if length(dirs) == 1
        "path \"$(first(dirs))\". "
    else
        string("paths:\n", join("  " .* contractuser.(dirs), '\n'), '\n')
    end

    suggestion_str = if query_override(hash) !== nothing
        "Check that your `Overrides.toml` file is correct (https://pkgdocs.julialang.org/v1/artifacts/#Overriding-artifact-locations)."
    else
        "Try `using Pkg; Pkg.instantiate()` to re-install all missing resources if the artifact is part of a package \
         or call `Pkg.ensure_artifact_installed` (https://pkgdocs.julialang.org/v1/api/#Pkg.Artifacts.ensure_artifact_installed) if not."
    end

    error("Artifact $(repr(name)) was not found by looking in the $(path_str)$suggestion_str")
end

raw"""
    split_artifact_slash(name::String)

Splits an artifact indexing string by path delimiters, isolates the first path element,
returning that and the `joinpath()` of the remaining arguments.  This normalizes all path
separators to the native path separator for the current platform.  Examples:

# Examples
```jldoctest; setup = :(using Artifacts: split_artifact_slash)
julia> split_artifact_slash("Foo")
("Foo", "")

julia> ret = split_artifact_slash("Foo/bar/baz.so");

julia> if Sys.iswindows()
            ret == ("Foo", "bar\\baz.so")
       else
            ret == ("Foo", "bar/baz.so")
       end
true

julia> ret = split_artifact_slash("Foo\\bar\\baz.so");

julia> if Sys.iswindows()
            ret == ("Foo", "bar\\baz.so")
       else
            ret == ("Foo", "bar/baz.so")
       end
true
```
"""
function split_artifact_slash(name::String)
    split_name = split(name, r"(/|\\)")
    if length(split_name) == 1
        return (split_name[1], "")
    else
        return (split_name[1], joinpath(split_name[2:end]...))
    end
end

"""
    artifact_slash_lookup(name::String, atifact_dict::Dict,
                          artifacts_toml::String, platform::Platform)

Return `artifact_name`, `artifact_path_tail`, and `hash` by looking the results up in
the given `artifacts_toml`, first extracting the name and path tail from the given `name`
to support slash-indexing within the given artifact.
"""
function artifact_slash_lookup(name::String, artifact_dict::Dict,
                               artifacts_toml::String, platform::Platform)
    artifact_name, artifact_path_tail = split_artifact_slash(name)

    meta = artifact_meta(artifact_name, artifact_dict, artifacts_toml; platform)
    if meta === nothing
        error("Cannot locate artifact '$(name)' for $(triplet(platform)) in '$(artifacts_toml)'")
    end
    hash = SHA1(meta["git-tree-sha1"])
    return artifact_name, artifact_path_tail, hash
end

"""
    macro artifact_str(name)

Return the on-disk path to an artifact. Automatically looks the artifact up by
name in the project's `(Julia)Artifacts.toml` file. Throws an error on if the
requested artifact is not present. If run in the REPL, searches for the toml
file starting in the current directory, see `find_artifacts_toml()` for more.

If the artifact is marked "lazy" and the package has `using LazyArtifacts`
defined, the artifact will be downloaded on-demand with `Pkg` the first time
this macro tries to compute the path. The files will then be left installed
locally for later.

If `name` contains a forward or backward slash, all elements after the first slash will
be taken to be path names indexing into the artifact, allowing for an easy one-liner to
access a single file/directory within an artifact.  Example:

    ffmpeg_path = @artifact"FFMPEG/bin/ffmpeg"

!!! compat "Julia 1.3"
    This macro requires at least Julia 1.3.

!!! compat "Julia 1.6"
    Slash-indexing requires at least Julia 1.6.
"""
macro artifact_str(name, platform=nothing)
    # Find Artifacts.toml file we're going to load from
    srcfile = string(__source__.file)
    if ((isinteractive() && startswith(srcfile, "REPL[")) || (!isinteractive() && srcfile == "none")) && !isfile(srcfile)
        srcfile = pwd()
    end
    local artifacts_toml = find_artifacts_toml(srcfile)
    if artifacts_toml === nothing
        error(string(
            "Cannot locate '(Julia)Artifacts.toml' file when attempting to use artifact '",
            name,
            "' in '",
            __module__,
            "'",
        ))
    end

    # Load Artifacts.toml at compile time, so that we don't have to use `__source__.file`
    # at runtime, which gets stale if the `.ji` file is relocated.
    local artifact_dict = load_artifacts_toml(artifacts_toml)

    # Invalidate calling .ji file if Artifacts.toml file changes
    Base.include_dependency(artifacts_toml)

    # Check if the user has provided `LazyArtifacts`, and thus supports lazy artifacts
    # If not, check to see if `Pkg` or `Pkg.Artifacts` has been imported.
    lazyartifacts = nothing
    for module_name in (:LazyArtifacts, :Pkg, :Artifacts)
        if isdefined(__module__, module_name)
            lazyartifacts = GlobalRef(__module__, module_name)
            break
        end
    end

    # If `name` is a constant, (and we're using the default `Platform`) we can actually load
    # and parse the `Artifacts.toml` file now, saving the work from runtime.
    if isa(name, AbstractString) && platform === nothing
        # To support slash-indexing, we need to split the artifact name from the path tail:
        platform = HostPlatform()
        artifact_name, artifact_path_tail, hash = artifact_slash_lookup(name, artifact_dict, artifacts_toml, platform)
        return quote
            Base.invokelatest(_artifact_str, $(__module__), $(artifacts_toml), $(artifact_name), $(artifact_path_tail), $(artifact_dict), $(hash), $(platform), $(lazyartifacts))::String
        end
    else
        if platform === nothing
            platform = :($(HostPlatform)())
        end
        return quote
            local platform = $(esc(platform))
            local artifact_name, artifact_path_tail, hash = artifact_slash_lookup($(esc(name)), $(artifact_dict), $(artifacts_toml), platform)
            Base.invokelatest(_artifact_str, $(__module__), $(artifacts_toml), artifact_name, artifact_path_tail, $(artifact_dict), hash, platform, $(lazyartifacts))::String
        end
    end
end

# Support `AbstractString`s, but avoid compilers needing to track backedges for callers
# of these functions in case a user defines a new type that is `<: AbstractString`
with_artifacts_directory(f::Function, artifacts_dir::AbstractString) =
    with_artifacts_directory(f, String(artifacts_dir)::String)
query_override(pkg::Base.UUID, artifact_name::AbstractString; overrides::Dict=load_overrides()) =
    query_override(pkg, String(artifact_name)::String; overrides=convert(Dict{Symbol, Any}, overrides))
unpack_platform(entry::Dict, name::AbstractString, artifacts_toml::AbstractString) =
    unpack_platform(convert(Dict{String, Any}, entry), String(name)::String, String(artifacts_toml)::String)
load_artifacts_toml(artifacts_toml::AbstractString; kwargs...) =
    load_artifacts_toml(String(artifacts_toml)::String; kwargs...)
artifact_meta(name::AbstractString, artifacts_toml::AbstractString; kwargs...) =
    artifact_meta(String(name)::String, String(artifacts_toml)::String; kwargs...)
artifact_meta(name::AbstractString, artifact_dict::Dict, artifacts_toml::AbstractString; kwargs...) =
    artifact_meta(String(name)::String, artifact_dict, String(artifacts_toml)::String; kwargs...)
artifact_hash(name::AbstractString, artifacts_toml::AbstractString; kwargs...) =
    artifact_hash(String(name)::String, String(artifacts_toml)::String; kwargs...)
select_downloadable_artifacts(artifact_dict::Dict, artifacts_toml::AbstractString; kwargs...) =
    select_downloadable_artifacts(artifact_dict, String(artifacts_toml)::String, kwargs...)
select_downloadable_artifacts(artifacts_toml::AbstractString; kwargs...) =
    select_downloadable_artifacts(String(artifacts_toml)::String, kwargs...)
find_artifacts_toml(path::AbstractString) =
    find_artifacts_toml(String(path)::String)
split_artifact_slash(name::AbstractString) =
    split_artifact_slash(String(name)::String)
artifact_slash_lookup(name::AbstractString, artifact_dict::Dict, artifacts_toml::AbstractString) =
    artifact_slash_lookup(String(name)::String, artifact_dict, String(artifacts_toml)::String)

# Precompilation to reduce latency
precompile(load_artifacts_toml, (String,))
precompile(NamedTuple{(:pkg_uuid,)}, (Tuple{Base.UUID},))
precompile(Core.kwfunc(load_artifacts_toml), (NamedTuple{(:pkg_uuid,), Tuple{Base.UUID}}, typeof(load_artifacts_toml), String))
precompile(parse_mapping, (String, String, String))
precompile(parse_mapping, (Dict{String, Any}, String, String))


end # module Artifacts
p   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Base64/src/Base64.jls      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
    Base64

Functionality for [base64 encoding and decoding](https://en.wikipedia.org/wiki/Base64),
a method to represent binary data using text, common on the web.
"""
module Base64

using Base: require_one_based_indexing

export
    Base64EncodePipe,
    base64encode,
    Base64DecodePipe,
    base64decode,
    stringmime

# Base64EncodePipe is a pipe-like IO object, which converts into base64 data
# sent to a stream. (You must close the pipe to complete the encode, separate
# from closing the target stream).  We also have a function base64encode(f,
# args...) which works like sprint except that it produces base64-encoded data,
# along with base64encode(args...)  which is equivalent to base64encode(write,
# args...), to return base64 strings.  A Base64DecodePipe object can be used to
# decode base64-encoded data read from a stream , while function base64decode is
# useful for decoding strings

include("buffer.jl")
include("encode.jl")
include("decode.jl")

"""
    stringmime(mime, x; context=nothing)

Return an `AbstractString` containing the representation of `x` in the
requested `mime` type. This is similar to [`repr(mime, x)`](@ref) except
that binary data is base64-encoded as an ASCII string.

The optional keyword argument `context` can be set to `:key=>value` pair
or an `IO` or [`IOContext`](@ref) object whose attributes are used for the I/O
stream passed to [`show`](@ref).
"""
stringmime(m::MIME, x; context=nothing) = istextmime(m) ? Base.Multimedia._textrepr(m, x, context) : _binstringmime(m, x, context)
stringmime(m::AbstractString, x; context=nothing) = stringmime(MIME(m), x; context=context)

_binstringmime(m::MIME, x, context) = Base64.base64encode(show, m, x; context=context)
_binstringmime(m::MIME, x::Vector{UInt8}, context) = Base64.base64encode(write, x; context=context)

end
p   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Base64/src/buffer.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

# Data buffer for pipes.
mutable struct Buffer
    data::Vector{UInt8}
    ptr::Ptr{UInt8}
    size::Int

    function Buffer(bufsize)
        data = Vector{UInt8}(undef, bufsize)
        return new(data, pointer(data), 0)
    end
end

Base.empty!(buffer::Buffer) = buffer.size = 0
Base.getindex(buffer::Buffer, i::Integer) = unsafe_load(buffer.ptr, i)
Base.setindex!(buffer::Buffer, v::UInt8, i::Integer) = unsafe_store!(buffer.ptr, v, i)
Base.firstindex(buffer::Buffer) = 1
Base.lastindex(buffer::Buffer) = buffer.size
Base.pointer(buffer::Buffer) = buffer.ptr
capacity(buffer::Buffer) = Int(pointer(buffer.data, lastindex(buffer.data) + 1) - buffer.ptr)

function consumed!(buffer::Buffer, n::Integer)
    @assert n ≤ buffer.size
    buffer.ptr += n
    buffer.size -= n
end

function read_to_buffer(io::IO, buffer::Buffer)
    offset = buffer.ptr - pointer(buffer.data)
    copyto!(buffer.data, 1, buffer.data, offset + 1, buffer.size)
    buffer.ptr = pointer(buffer.data)
    if !eof(io)
        n = min(bytesavailable(io), capacity(buffer) - buffer.size)
        unsafe_read(io, buffer.ptr + buffer.size, n)
        buffer.size += n
    end
    return
end
p   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Base64/src/encode.jlb      # This file is a part of Julia. License is MIT: https://julialang.org/license

# Generate encode table.
const BASE64_ENCODE = [UInt8(x) for x in append!(['A':'Z'; 'a':'z'; '0':'9'], ['+', '/'])]
encode(x::UInt8) = @inbounds return BASE64_ENCODE[(x & 0x3f) + 1]
encodepadding()  = UInt8('=')

"""
    Base64EncodePipe(ostream)

Return a new write-only I/O stream, which converts any bytes written to it into
base64-encoded ASCII bytes written to `ostream`.  Calling [`close`](@ref) on the
`Base64EncodePipe` stream is necessary to complete the encoding (but does not
close `ostream`).

# Examples
```jldoctest
julia> io = IOBuffer();

julia> iob64_encode = Base64EncodePipe(io);

julia> write(iob64_encode, "Hello!")
6

julia> close(iob64_encode);

julia> str = String(take!(io))
"SGVsbG8h"

julia> String(base64decode(str))
"Hello!"
```
"""
struct Base64EncodePipe <: IO
    io::IO
    buffer::Buffer

    function Base64EncodePipe(io::IO)
        # The buffer size must be at least 3.
        buffer = Buffer(512)
        pipe = new(io, buffer)
        finalizer(_ -> close(pipe), buffer)
        return pipe
    end
end

Base.isreadable(::Base64EncodePipe) = false
Base.iswritable(pipe::Base64EncodePipe) = iswritable(pipe.io)

function Base.unsafe_write(pipe::Base64EncodePipe, ptr::Ptr{UInt8}, n::UInt)::Int
    buffer = pipe.buffer
    m = buffer.size
    b1, b2, b3, k = loadtriplet!(buffer, ptr, n)
    @assert k ≥ m
    p = ptr + k - m
    if k < 3
        if k == 1
            buffer[1] = b1
            buffer.size = 1
        elseif k == 2
            buffer[1] = b1
            buffer[2] = b2
            buffer.size = 2
        end
        return p - ptr
    end
    @assert buffer.size == 0

    i = 0
    p_end = ptr + n
    while true
        buffer[i+1] = encode(b1 >> 2          )
        buffer[i+2] = encode(b1 << 4 | b2 >> 4)
        buffer[i+3] = encode(b2 << 2 | b3 >> 6)
        buffer[i+4] = encode(          b3     )
        i += 4
        if p + 2 < p_end
            b1 = unsafe_load(p, 1)
            b2 = unsafe_load(p, 2)
            b3 = unsafe_load(p, 3)
            p += 3
        else
            break
        end
        if i + 4 > capacity(buffer)
            unsafe_write(pipe.io, pointer(buffer), i)
            i = 0
        end
    end
    if i > 0
        unsafe_write(pipe.io, pointer(buffer), i)
    end

    while p < p_end
        buffer[buffer.size+=1] = unsafe_load(p)
        p += 1
    end
    return p - ptr
end

function Base.write(pipe::Base64EncodePipe, x::UInt8)
    buffer = pipe.buffer
    buffer[buffer.size+=1] = x
    if buffer.size == 3
        unsafe_write(pipe, C_NULL, 0)
    end
    return 1
end

function Base.close(pipe::Base64EncodePipe)
    b1, b2, b3, k = loadtriplet!(pipe.buffer, Ptr{UInt8}(C_NULL), UInt(0))
    if k == 0
        # no leftover and padding
    elseif k == 1
        write(pipe.io,
              encode(b1 >> 2),
              encode(b1 << 4),
              encodepadding(),
              encodepadding())
    elseif k == 2
        write(pipe.io,
              encode(          b1 >> 2),
              encode(b1 << 4 | b2 >> 4),
              encode(b2 << 2          ),
              encodepadding())
    else
        @assert k == 3
        write(pipe.io,
              encode(b1 >> 2          ),
              encode(b1 << 4 | b2 >> 4),
              encode(b2 << 2 | b3 >> 6),
              encode(          b3     ))
    end
    return nothing
end

# Load three bytes from buffer and ptr.
function loadtriplet!(buffer::Buffer, ptr::Ptr{UInt8}, n::UInt)
    b1 = b2 = b3 = 0x00
    if buffer.size == 0
        if n == 0
            k = 0
        elseif n == 1
            b1 = unsafe_load(ptr, 1)
            k = 1
        elseif n == 2
            b1 = unsafe_load(ptr, 1)
            b2 = unsafe_load(ptr, 2)
            k = 2
        else
            b1 = unsafe_load(ptr, 1)
            b2 = unsafe_load(ptr, 2)
            b3 = unsafe_load(ptr, 3)
            k = 3
        end
    elseif buffer.size == 1
        b1 = buffer[1]
        if n == 0
            k = 1
        elseif n == 1
            b2 = unsafe_load(ptr, 1)
            k = 2
        else
            b2 = unsafe_load(ptr, 1)
            b3 = unsafe_load(ptr, 2)
            k = 3
        end
    elseif buffer.size == 2
        b1 = buffer[1]
        b2 = buffer[2]
        if n == 0
            k = 2
        else
            b3 = unsafe_load(ptr, 1)
            k = 3
        end
    else
        @assert buffer.size == 3
        b1 = buffer[1]
        b2 = buffer[2]
        b3 = buffer[3]
        k = 3
    end
    empty!(buffer)
    return b1, b2, b3, k
end

"""
    base64encode(writefunc, args...; context=nothing)
    base64encode(args...; context=nothing)

Given a [`write`](@ref)-like function `writefunc`, which takes an I/O stream as
its first argument, `base64encode(writefunc, args...)` calls `writefunc` to
write `args...` to a base64-encoded string, and returns the string.
`base64encode(args...)` is equivalent to `base64encode(write, args...)`: it
converts its arguments into bytes using the standard [`write`](@ref) functions
and returns the base64-encoded string.

The optional keyword argument `context` can be set to `:key=>value` pair
or an `IO` or [`IOContext`](@ref) object whose attributes are used for the I/O
stream passed to `writefunc` or `write`.

See also [`base64decode`](@ref).
"""
function base64encode(f::Function, args...; context=nothing)
    s = IOBuffer()
    b = Base64EncodePipe(s)
    if context === nothing
        f(b, args...)
    else
        f(IOContext(b, context), args...)
    end
    close(b)
    return String(take!(s))
end
base64encode(args...; context=nothing) = base64encode(write, args...; context=context)
p   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Base64/src/decode.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

# Generate decode table.
const BASE64_CODE_END = 0x40
const BASE64_CODE_PAD = 0x41
const BASE64_CODE_IGN = 0x42
const BASE64_DECODE = fill(BASE64_CODE_IGN, 256)
for (i, c) in enumerate(BASE64_ENCODE)
    BASE64_DECODE[Int(c)+1] = UInt8(i - 1)
end
BASE64_DECODE[Int(encodepadding())+1] = BASE64_CODE_PAD
decode(x::UInt8) = @inbounds return BASE64_DECODE[x + 1]

"""
    Base64DecodePipe(istream)

Return a new read-only I/O stream, which decodes base64-encoded data read from
`istream`.

# Examples
```jldoctest
julia> io = IOBuffer();

julia> iob64_decode = Base64DecodePipe(io);

julia> write(io, "SGVsbG8h")
8

julia> seekstart(io);

julia> String(read(iob64_decode))
"Hello!"
```
"""
struct Base64DecodePipe <: IO
    io::IO
    buffer::Buffer
    rest::Vector{UInt8}

    function Base64DecodePipe(io::IO)
        buffer = Buffer(512)
        return new(io, buffer, UInt8[])
    end
end

Base.isreadable(pipe::Base64DecodePipe) = !isempty(pipe.rest) || isreadable(pipe.io)
Base.iswritable(::Base64DecodePipe) = false

function Base.unsafe_read(pipe::Base64DecodePipe, ptr::Ptr{UInt8}, n::UInt)
    p = read_until_end(pipe, ptr, n)
    if p < ptr + n
        throw(EOFError())
    end
    return nothing
end

# Read and decode as much data as possible.
function read_until_end(pipe::Base64DecodePipe, ptr::Ptr{UInt8}, n::UInt)
    p = ptr
    p_end = ptr + n
    while !isempty(pipe.rest) && p < p_end
        unsafe_store!(p, popfirst!(pipe.rest))
        p += 1
    end

    buffer = pipe.buffer
    i = 0
    b1 = b2 = b3 = b4 = BASE64_CODE_IGN
    while true
        if b1 < 0x40 && b2 < 0x40 && b3 < 0x40 && b4 < 0x40 && p + 2 < p_end
            # fast path to decode
            unsafe_store!(p    , b1 << 2 | b2 >> 4)
            unsafe_store!(p + 1, b2 << 4 | b3 >> 2)
            unsafe_store!(p + 2, b3 << 6 | b4     )
            p += 3
        else
            i, p, ended = decode_slow(b1, b2, b3, b4, buffer, i, pipe.io, p, p_end - p, pipe.rest)
            if ended
                break
            end
        end
        if p < p_end
            if i + 4 ≤ lastindex(buffer)
                b1 = decode(buffer[i+1])
                b2 = decode(buffer[i+2])
                b3 = decode(buffer[i+3])
                b4 = decode(buffer[i+4])
                i += 4
            else
                consumed!(buffer, i)
                read_to_buffer(pipe.io, buffer)
                i = 0
                b1 = b2 = b3 = b4 = BASE64_CODE_IGN
            end
        else
            break
        end
    end
    consumed!(buffer, i)

    return p
end

function Base.read(pipe::Base64DecodePipe, ::Type{UInt8})
    if isempty(pipe.rest)
        unsafe_read(pipe, convert(Ptr{UInt8}, C_NULL), 0)
        if isempty(pipe.rest)
            throw(EOFError())
        end
    end
    return popfirst!(pipe.rest)
end

function Base.readbytes!(pipe::Base64DecodePipe, data::AbstractVector{UInt8}, nb::Integer=length(data))
    require_one_based_indexing(data)
    filled::Int = 0
    while filled < nb && !eof(pipe)
        if length(data) == filled
            resize!(data, min(length(data) * 2, nb))
        end
        p = pointer(data, filled + 1)
        p_end = read_until_end(pipe, p, UInt(min(length(data), nb) - filled))
        filled += p_end - p
    end
    resize!(data, filled)
    return filled
end

Base.eof(pipe::Base64DecodePipe) = isempty(pipe.rest) && eof(pipe.io)::Bool
Base.close(pipe::Base64DecodePipe) = nothing

# Decode data from (b1, b2, b3, b5, buffer, input) into (ptr, rest).
function decode_slow(b1, b2, b3, b4, buffer, i, input, ptr, n, rest)
    # Skip ignore code.
    while true
        if b1 == BASE64_CODE_IGN
            b1, b2, b3 = b2, b3, b4
        elseif b2 == BASE64_CODE_IGN
            b2, b3 = b3, b4
        elseif b3 == BASE64_CODE_IGN
            b3 = b4
        elseif b4 == BASE64_CODE_IGN
            # pass
        else
            break
        end
        if i + 1 ≤ lastindex(buffer)
            b4 = decode(buffer[i+=1])
        elseif !eof(input)
            b4 = decode(read(input, UInt8))
        else
            b4 = BASE64_CODE_END
        end
    end

    # Check the decoded quadruplet.
    k = 0
    if b1 < 0x40 && b2 < 0x40 && b3 < 0x40 && b4 < 0x40
        k = 3
    elseif b1 < 0x40 && b2 < 0x40 && b3 < 0x40 && (b4 == BASE64_CODE_PAD || b4 == BASE64_CODE_END)
        b4 = 0x00
        k = 2
    elseif b1 < 0x40 && b2 < 0x40 && (b3 == BASE64_CODE_PAD || b3 == BASE64_CODE_END) && (b4 == BASE64_CODE_PAD || b4 == BASE64_CODE_END)
        b3 = b4 = 0x00
        k = 1
    elseif b1 == b2 == b3 == b4 == BASE64_CODE_END
        b1 = b2 = b3 = b4 = 0x00
    else
        throw(ArgumentError("malformed base64 sequence"))
    end

    # Write output.
    p::Ptr{UInt8} = ptr
    p_end = ptr + n
    function output(b)
        if p < p_end
            unsafe_store!(p, b)
            p += 1
        else
            push!(rest, b)
        end
    end
    k ≥ 1 && output(b1 << 2 | b2 >> 4)
    k ≥ 2 && output(b2 << 4 | b3 >> 2)
    k ≥ 3 && output(b3 << 6 | b4     )

    return i, p, k == 0
end

"""
    base64decode(string)

Decode the base64-encoded `string` and returns a `Vector{UInt8}` of the decoded
bytes.

See also [`base64encode`](@ref).

# Examples
```jldoctest
julia> b = base64decode("SGVsbG8h")
6-element Vector{UInt8}:
 0x48
 0x65
 0x6c
 0x6c
 0x6f
 0x21

julia> String(b)
"Hello!"
```
"""
function base64decode(s)
    b = IOBuffer(s)
    try
        return read(Base64DecodePipe(b))
    finally
        close(b)
    end
end
p   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/CRC32c/src/CRC32c.jl*      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
Standard library module for computing the CRC-32c checksum.

See [`CRC32c.crc32c`](@ref) for more information.
"""
module CRC32c

import Base.FastContiguousSubArray

export crc32c

"""
    crc32c(data, crc::UInt32=0x00000000)

Compute the CRC-32c checksum of the given `data`, which can be
an `Array{UInt8}`, a contiguous subarray thereof, or a `String`.  Optionally, you can pass
a starting `crc` integer to be mixed in with the checksum.  The `crc` parameter
can be used to compute a checksum on data divided into chunks: performing
`crc32c(data2, crc32c(data1))` is equivalent to the checksum of `[data1; data2]`.
(Technically, a little-endian checksum is computed.)

There is also a method `crc32c(io, nb, crc)` to checksum `nb` bytes from
a stream `io`, or `crc32c(io, crc)` to checksum all the remaining bytes.
Hence you can do [`open(crc32c, filename)`](@ref) to checksum an entire file,
or `crc32c(seekstart(buf))` to checksum an [`IOBuffer`](@ref) without
calling [`take!`](@ref).

For a `String`, note that the result is specific to the UTF-8 encoding
(a different checksum would be obtained from a different Unicode encoding).
To checksum an `a::Array` of some other bitstype, you can do `crc32c(reinterpret(UInt8,a))`,
but note that the result may be endian-dependent.
"""
function crc32c end


crc32c(a::Union{Array{UInt8},FastContiguousSubArray{UInt8,N,<:Array{UInt8}} where N}, crc::UInt32=0x00000000) = Base._crc32c(a, crc)
crc32c(s::Union{String, SubString{String}}, crc::UInt32=0x00000000) = Base._crc32c(s, crc)

"""
    crc32c(io::IO, [nb::Integer,] crc::UInt32=0x00000000)

Read up to `nb` bytes from `io` and return the CRC-32c checksum, optionally
mixed with a starting `crc` integer.  If `nb` is not supplied, then
`io` will be read until the end of the stream.
"""
crc32c(io::IO, nb::Integer, crc::UInt32=0x00000000) = Base._crc32c(io, nb, crc)
crc32c(io::IO, crc::UInt32=0x00000000) = Base._crc32c(io, crc)
crc32c(io::IOStream, crc::UInt32=0x00000000) = Base._crc32c(io, crc)

end
|   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/FileWatching/src/FileWatching.jl�s      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
Utilities for monitoring files and file descriptors for events.
"""
module FileWatching

export
    # one-shot API (returns results):
    watch_file, # efficient for small numbers of files
    watch_folder, # efficient for large numbers of files
    unwatch_folder,
    poll_file, # very inefficient alternative to above
    poll_fd, # very efficient, unrelated to above
    # continuous API (returns objects):
    FileMonitor,
    FolderMonitor,
    PollingFileWatcher,
    FDWatcher,
    # pidfile:
    mkpidlock,
    trymkpidlock

import Base: @handle_as, wait, close, eventloop, notify_error, IOError,
    _sizeof_uv_poll, _sizeof_uv_fs_poll, _sizeof_uv_fs_event, _uv_hook_close, uv_error, _UVError,
    iolock_begin, iolock_end, associate_julia_struct, disassociate_julia_struct,
    preserve_handle, unpreserve_handle, isreadable, iswritable, isopen,
    |, getproperty, propertynames
import Base.Filesystem.StatStruct
if Sys.iswindows()
    import Base.WindowsRawSocket
end


# libuv file watching event flags
const UV_RENAME = Int32(1)
const UV_CHANGE = Int32(2)
struct FileEvent
    renamed::Bool
    changed::Bool
    timedout::Bool
    FileEvent(r::Bool, c::Bool, t::Bool) = new(r, c, t)
end
FileEvent() = FileEvent(false, false, true)
FileEvent(flags::Integer) = FileEvent((flags & UV_RENAME) != 0,
                                      (flags & UV_CHANGE) != 0,
                                      false)
|(a::FileEvent, b::FileEvent) =
    FileEvent(a.renamed | b.renamed,
              a.changed | b.changed,
              a.timedout | b.timedout)

# libuv file descriptor event flags
const UV_READABLE = Int32(1)
const UV_WRITABLE = Int32(2)
const UV_DISCONNECT = Int32(4)
const UV_PRIORITIZED = Int32(8)
struct FDEvent
    events::Int32
    FDEvent(flags::Integer=0) = new(flags)
end

FDEvent(r::Bool, w::Bool, d::Bool, t::Bool) = FDEvent((UV_READABLE * r) | (UV_WRITABLE * w) | (UV_DISCONNECT * d)) # deprecated method

function getproperty(f::FDEvent, field::Symbol)
    events = getfield(f, :events)
    field === :readable && return (events & UV_READABLE) != 0
    field === :writable && return (events & UV_WRITABLE) != 0
    field === :disconnect && return (events & UV_DISCONNECT) != 0
    field === :prioritized && return (events & UV_PRIORITIZED) != 0
    field === :timedout && return events == 0
    field === :events && return Int(events)
    getfield(f, field)::Union{}
end
propertynames(f::FDEvent) = (:readable, :writable, :disconnect, :prioritized, :timedout, :events)

isreadable(f::FDEvent) = f.readable
iswritable(f::FDEvent) = f.writable
|(a::FDEvent, b::FDEvent) = FDEvent(getfield(a, :events) | getfield(b, :events))

mutable struct FileMonitor
    @atomic handle::Ptr{Cvoid}
    file::String
    notify::Base.ThreadSynchronizer
    events::Int32
    active::Bool
    FileMonitor(file::AbstractString) = FileMonitor(String(file))
    function FileMonitor(file::String)
        handle = Libc.malloc(_sizeof_uv_fs_event)
        this = new(handle, file, Base.ThreadSynchronizer(), 0, false)
        associate_julia_struct(handle, this)
        iolock_begin()
        err = ccall(:uv_fs_event_init, Cint, (Ptr{Cvoid}, Ptr{Cvoid}), eventloop(), handle)
        if err != 0
            Libc.free(handle)
            throw(_UVError("FileMonitor", err))
        end
        iolock_end()
        finalizer(uvfinalize, this)
        return this
    end
end

mutable struct FolderMonitor
    @atomic handle::Ptr{Cvoid}
    # notify::Channel{Any} # eltype = Union{Pair{String, FileEvent}, IOError}
    notify::Base.ThreadSynchronizer
    channel::Vector{Any} # eltype = Pair{String, FileEvent}
    FolderMonitor(folder::AbstractString) = FolderMonitor(String(folder))
    function FolderMonitor(folder::String)
        handle = Libc.malloc(_sizeof_uv_fs_event)
        this = new(handle, Base.ThreadSynchronizer(), [])
        associate_julia_struct(handle, this)
        iolock_begin()
        err = ccall(:uv_fs_event_init, Cint, (Ptr{Cvoid}, Ptr{Cvoid}), eventloop(), handle)
        if err != 0
            Libc.free(handle)
            throw(_UVError("FolderMonitor", err))
        end
        finalizer(uvfinalize, this)
        uv_error("FolderMonitor (start)",
                 ccall(:uv_fs_event_start, Int32, (Ptr{Cvoid}, Ptr{Cvoid}, Cstring, Int32),
                       handle, uv_jl_fseventscb_folder::Ptr{Cvoid}, folder, 0))
        iolock_end()
        return this
    end
end

mutable struct PollingFileWatcher
    @atomic handle::Ptr{Cvoid}
    file::String
    interval::UInt32
    notify::Base.ThreadSynchronizer
    active::Bool
    curr_error::Int32
    curr_stat::StatStruct
    PollingFileWatcher(file::AbstractString, interval::Float64=5.007) = PollingFileWatcher(String(file), interval)
    function PollingFileWatcher(file::String, interval::Float64=5.007) # same default as nodejs
        handle = Libc.malloc(_sizeof_uv_fs_poll)
        this = new(handle, file, round(UInt32, interval * 1000), Base.ThreadSynchronizer(), false, 0, StatStruct())
        associate_julia_struct(handle, this)
        iolock_begin()
        err = ccall(:uv_fs_poll_init, Int32, (Ptr{Cvoid}, Ptr{Cvoid}), eventloop(), handle)
        if err != 0
            Libc.free(handle)
            throw(_UVError("PollingFileWatcher", err))
        end
        finalizer(uvfinalize, this)
        iolock_end()
        return this
    end
end

mutable struct _FDWatcher
    @atomic handle::Ptr{Cvoid}
    fdnum::Int # this is NOT the file descriptor
    refcount::Tuple{Int, Int}
    notify::Base.ThreadSynchronizer
    events::Int32
    active::Tuple{Bool, Bool}

    let FDWatchers = Vector{Any}() # n.b.: this structure and the refcount are protected by the iolock
        global _FDWatcher, uvfinalize
        @static if Sys.isunix()
            _FDWatcher(fd::RawFD, mask::FDEvent) = _FDWatcher(fd, mask.readable, mask.writable)
            function _FDWatcher(fd::RawFD, readable::Bool, writable::Bool)
                if !readable && !writable
                    throw(ArgumentError("must specify at least one of readable or writable to create a FDWatcher"))
                end
                fdnum = Core.Intrinsics.bitcast(Int32, fd) + 1
                iolock_begin()
                if fdnum > length(FDWatchers)
                    old_len = length(FDWatchers)
                    resize!(FDWatchers, fdnum)
                    FDWatchers[(old_len + 1):fdnum] .= nothing
                elseif FDWatchers[fdnum] !== nothing
                    this = FDWatchers[fdnum]::_FDWatcher
                    this.refcount = (this.refcount[1] + Int(readable), this.refcount[2] + Int(writable))
                    iolock_end()
                    return this
                end
                if ccall(:jl_uv_unix_fd_is_watched, Int32, (RawFD, Ptr{Cvoid}, Ptr{Cvoid}), fd, C_NULL, eventloop()) == 1
                    throw(ArgumentError("$(fd) is already being watched by libuv"))
                end

                handle = Libc.malloc(_sizeof_uv_poll)
                this = new(
                    handle,
                    fdnum,
                    (Int(readable), Int(writable)),
                    Base.ThreadSynchronizer(),
                    Int32(0),
                    (false, false))
                associate_julia_struct(handle, this)
                err = ccall(:uv_poll_init, Int32, (Ptr{Cvoid}, Ptr{Cvoid}, RawFD), eventloop(), handle, fd)
                if err != 0
                    Libc.free(handle)
                    throw(_UVError("FDWatcher", err))
                end
                finalizer(uvfinalize, this)
                FDWatchers[fdnum] = this
                iolock_end()
                return this
            end
        end

        function uvfinalize(t::_FDWatcher)
            iolock_begin()
            lock(t.notify)
            try
                if t.handle != C_NULL
                    disassociate_julia_struct(t)
                    ccall(:jl_close_uv, Cvoid, (Ptr{Cvoid},), t.handle)
                    @atomic :monotonic t.handle = C_NULL
                end
                t.refcount = (0, 0)
                t.active = (false, false)
                @static if Sys.isunix()
                    if FDWatchers[t.fdnum] === t
                        FDWatchers[t.fdnum] = nothing
                    end
                end
                notify(t.notify, Int32(0))
            finally
                unlock(t.notify)
            end
            iolock_end()
            nothing
        end
    end

    @static if Sys.iswindows()
        _FDWatcher(fd::RawFD, mask::FDEvent) = _FDWatcher(fd, mask.readable, mask.writable)
        function _FDWatcher(fd::RawFD, readable::Bool, writable::Bool)
            handle = Libc._get_osfhandle(fd)
            return _FDWatcher(handle, readable, writable)
        end
        _FDWatcher(fd::WindowsRawSocket, mask::FDEvent) = _FDWatcher(fd, mask.readable, mask.writable)
        function _FDWatcher(fd::WindowsRawSocket, readable::Bool, writable::Bool)
            if !readable && !writable
                throw(ArgumentError("must specify at least one of readable or writable to create a FDWatcher"))
            end

            handle = Libc.malloc(_sizeof_uv_poll)
            this = new(
                handle,
                0,
                (Int(readable), Int(writable)),
                Base.ThreadSynchronizer(),
                0,
                (false, false))
            associate_julia_struct(handle, this)
            iolock_begin()
            err = ccall(:uv_poll_init, Int32, (Ptr{Cvoid},  Ptr{Cvoid}, WindowsRawSocket),
                                               eventloop(), handle,     fd)
            iolock_end()
            if err != 0
                Libc.free(handle)
                throw(_UVError("FDWatcher", err))
            end
            finalizer(uvfinalize, this)
            return this
        end
    end
end

mutable struct FDWatcher
    # WARNING: make sure `close` has been manually called on this watcher before closing / destroying `fd`
    watcher::_FDWatcher
    mask::FDEvent
    function FDWatcher(fd::RawFD, readable::Bool, writable::Bool)
        return FDWatcher(fd, FDEvent(readable, writable, false, false))
    end
    function FDWatcher(fd::RawFD, mask::FDEvent)
        this = new(_FDWatcher(fd, mask), mask)
        finalizer(close, this)
        return this
    end
    @static if Sys.iswindows()
        function FDWatcher(fd::WindowsRawSocket, readable::Bool, writable::Bool)
            return FDWatcher(fd, FDEvent(readable, writable, false, false))
        end
        function FDWatcher(fd::WindowsRawSocket, mask::FDEvent)
            this = new(_FDWatcher(fd, mask), mask)
            finalizer(close, this)
            return this
        end
    end
end

function getproperty(fdw::FDWatcher, s::Symbol)
    # support deprecated field names
    s === :readable && return fdw.mask.readable
    s === :writable && return fdw.mask.writable
    return getfield(fdw, s)
end


close(t::_FDWatcher, mask::FDEvent) = close(t, mask.readable, mask.writable)
function close(t::_FDWatcher, readable::Bool, writable::Bool)
    iolock_begin()
    if t.refcount != (0, 0)
        t.refcount = (t.refcount[1] - Int(readable), t.refcount[2] - Int(writable))
    end
    if t.refcount == (0, 0)
        uvfinalize(t)
    else
        @lock t.notify notify(t.notify, Int32(0))
    end
    iolock_end()
    nothing
end

function close(t::FDWatcher)
    mask = t.mask
    t.mask = FDEvent()
    close(t.watcher, mask)
end

function uvfinalize(uv::Union{FileMonitor, FolderMonitor, PollingFileWatcher})
    iolock_begin()
    if uv.handle != C_NULL
        disassociate_julia_struct(uv) # close (and free) without notify
        ccall(:jl_close_uv, Cvoid, (Ptr{Cvoid},), uv.handle)
    end
    iolock_end()
end

function close(t::Union{FileMonitor, FolderMonitor, PollingFileWatcher})
    iolock_begin()
    if t.handle != C_NULL
        ccall(:jl_close_uv, Cvoid, (Ptr{Cvoid},), t.handle)
    end
    iolock_end()
end

function _uv_hook_close(uv::_FDWatcher)
    # fyi: jl_atexit_hook can cause this to get called too
    Libc.free(@atomicswap :monotonic uv.handle = C_NULL)
    uvfinalize(uv)
    nothing
end

function _uv_hook_close(uv::PollingFileWatcher)
    lock(uv.notify)
    try
        uv.active = false
        Libc.free(@atomicswap :monotonic uv.handle = C_NULL)
        notify(uv.notify, StatStruct())
    finally
        unlock(uv.notify)
    end
    nothing
end

function _uv_hook_close(uv::FileMonitor)
    lock(uv.notify)
    try
        uv.active = false
        Libc.free(@atomicswap :monotonic uv.handle = C_NULL)
        notify(uv.notify, FileEvent())
    finally
        unlock(uv.notify)
    end
    nothing
end

function _uv_hook_close(uv::FolderMonitor)
    lock(uv.notify)
    try
        Libc.free(@atomicswap :monotonic uv.handle = C_NULL)
        notify_error(uv.notify, EOFError())
    finally
        unlock(uv.notify)
    end
    nothing
end

isopen(fm::FileMonitor) = fm.handle != C_NULL
isopen(fm::FolderMonitor) = fm.handle != C_NULL
isopen(pfw::PollingFileWatcher) = pfw.handle != C_NULL
isopen(pfw::_FDWatcher) = pfw.refcount != (0, 0)
isopen(pfw::FDWatcher) = !pfw.mask.timedout

function uv_fseventscb_file(handle::Ptr{Cvoid}, filename::Ptr, events::Int32, status::Int32)
    t = @handle_as handle FileMonitor
    lock(t.notify)
    try
        if status != 0
            notify_error(t.notify, _UVError("FileMonitor", status))
        else
            t.events |= events
            notify(t.notify, FileEvent(events))
        end
    finally
        unlock(t.notify)
    end
    nothing
end

function uv_fseventscb_folder(handle::Ptr{Cvoid}, filename::Ptr, events::Int32, status::Int32)
    t = @handle_as handle FolderMonitor
    lock(t.notify)
    try
        if status != 0
            notify_error(t.notify, _UVError("FolderMonitor", status))
        else
            fname = (filename == C_NULL) ? "" : unsafe_string(convert(Cstring, filename))
            push!(t.channel, fname => FileEvent(events))
            notify(t.notify)
        end
    finally
        unlock(t.notify)
    end
    nothing
end

function uv_pollcb(handle::Ptr{Cvoid}, status::Int32, events::Int32)
    t = @handle_as handle _FDWatcher
    lock(t.notify)
    try
        if status != 0
            notify_error(t.notify, _UVError("FDWatcher", status))
        else
            t.events |= events
            if t.active[1] || t.active[2]
                if isempty(t.notify)
                    # if we keep hearing about events when nobody appears to be listening,
                    # stop the poll to save cycles
                    t.active = (false, false)
                    ccall(:uv_poll_stop, Int32, (Ptr{Cvoid},), t.handle)
                end
            end
            notify(t.notify, events)
        end
    finally
        unlock(t.notify)
    end
    nothing
end

function uv_fspollcb(handle::Ptr{Cvoid}, status::Int32, prev::Ptr, curr::Ptr)
    t = @handle_as handle PollingFileWatcher
    old_status = t.curr_error
    t.curr_error = status
    if status == 0
        t.curr_stat = StatStruct(convert(Ptr{UInt8}, curr))
    end
    if status == 0 || status != old_status
        prev_stat = StatStruct(convert(Ptr{UInt8}, prev))
        lock(t.notify)
        try
            notify(t.notify, prev_stat)
        finally
            unlock(t.notify)
        end
    end
    nothing
end

function __init__()
    global uv_jl_pollcb = @cfunction(uv_pollcb, Cvoid, (Ptr{Cvoid}, Cint, Cint))
    global uv_jl_fspollcb = @cfunction(uv_fspollcb, Cvoid, (Ptr{Cvoid}, Cint, Ptr{Cvoid}, Ptr{Cvoid}))
    global uv_jl_fseventscb_file = @cfunction(uv_fseventscb_file, Cvoid, (Ptr{Cvoid}, Ptr{Int8}, Int32, Int32))
    global uv_jl_fseventscb_folder = @cfunction(uv_fseventscb_folder, Cvoid, (Ptr{Cvoid}, Ptr{Int8}, Int32, Int32))

    Base.mkpidlock_hook = mkpidlock
    Base.trymkpidlock_hook = trymkpidlock
    Base.parse_pidfile_hook = Pidfile.parse_pidfile

    nothing
end

function start_watching(t::_FDWatcher)
    iolock_begin()
    t.handle == C_NULL && throw(ArgumentError("FDWatcher is closed"))
    readable = t.refcount[1] > 0
    writable = t.refcount[2] > 0
    if t.active[1] != readable || t.active[2] != writable
        # make sure the READABLE / WRITEABLE state is updated
        uv_error("FDWatcher (start)",
                 ccall(:uv_poll_start, Int32, (Ptr{Cvoid}, Int32, Ptr{Cvoid}),
                       t.handle,
                       (readable ? UV_READABLE : 0) | (writable ? UV_WRITABLE : 0),
                       uv_jl_pollcb::Ptr{Cvoid}))
        t.active = (readable, writable)
    end
    iolock_end()
    nothing
end

function start_watching(t::PollingFileWatcher)
    iolock_begin()
    t.handle == C_NULL && throw(ArgumentError("PollingFileWatcher is closed"))
    if !t.active
        uv_error("PollingFileWatcher (start)",
                 ccall(:uv_fs_poll_start, Int32, (Ptr{Cvoid}, Ptr{Cvoid}, Cstring, UInt32),
                       t.handle, uv_jl_fspollcb::Ptr{Cvoid}, t.file, t.interval))
        t.active = true
    end
    iolock_end()
    nothing
end

function stop_watching(t::PollingFileWatcher)
    iolock_begin()
    lock(t.notify)
    try
        if t.active && isempty(t.notify)
            t.active = false
            uv_error("PollingFileWatcher (stop)",
                     ccall(:uv_fs_poll_stop, Int32, (Ptr{Cvoid},), t.handle))
        end
    finally
        unlock(t.notify)
    end
    iolock_end()
    nothing
end

function start_watching(t::FileMonitor)
    iolock_begin()
    t.handle == C_NULL && throw(ArgumentError("FileMonitor is closed"))
    if !t.active
        uv_error("FileMonitor (start)",
                 ccall(:uv_fs_event_start, Int32, (Ptr{Cvoid}, Ptr{Cvoid}, Cstring, Int32),
                       t.handle, uv_jl_fseventscb_file::Ptr{Cvoid}, t.file, 0))
        t.active = true
    end
    iolock_end()
    nothing
end

function stop_watching(t::FileMonitor)
    iolock_begin()
    lock(t.notify)
    try
        if t.active && isempty(t.notify)
            t.active = false
            uv_error("FileMonitor (stop)",
                     ccall(:uv_fs_event_stop, Int32, (Ptr{Cvoid},), t.handle))
        end
    finally
        unlock(t.notify)
    end
    iolock_end()
    nothing
end

# n.b. this _wait may return spuriously early with a timedout event
function _wait(fdw::_FDWatcher, mask::FDEvent)
    iolock_begin()
    preserve_handle(fdw)
    lock(fdw.notify)
    try
        events = FDEvent(fdw.events & mask.events)
        if !isopen(fdw) # !open
            throw(EOFError())
        elseif events.timedout
            start_watching(fdw) # make sure the poll is active
            iolock_end()
            return FDEvent(wait(fdw.notify)::Int32)
        else
            iolock_end()
            return events
        end
    finally
        unlock(fdw.notify)
        unpreserve_handle(fdw)
    end
end

function wait(fdw::_FDWatcher; readable=true, writable=true)
    return wait(fdw, FDEvent(readable, writable, false, false))
end
function wait(fdw::_FDWatcher, mask::FDEvent)
    while true
        mask.timedout && return mask
        events = _wait(fdw, mask)
        if !events.timedout
            @lock fdw.notify fdw.events &= ~events.events
            return events
        end
    end
end

function wait(fdw::FDWatcher)
    isopen(fdw) || throw(EOFError())
    while true
        events = GC.@preserve fdw _wait(fdw.watcher, fdw.mask)
        isopen(fdw) || throw(EOFError())
        if !events.timedout
            @lock fdw.watcher.notify fdw.watcher.events &= ~events.events
            return events
        end
    end
end

function wait(socket::RawFD; readable=false, writable=false)
    return wait(socket, FDEvent(readable, writable, false, false))
end
function wait(fd::RawFD, mask::FDEvent)
    fdw = _FDWatcher(fd, mask)
    try
        return wait(fdw, mask)
    finally
        close(fdw, mask)
    end
end


if Sys.iswindows()
    function wait(socket::WindowsRawSocket; readable=false, writable=false)
        return wait(socket, FDEvent(readable, writable, false, false))
    end
    function wait(socket::WindowsRawSocket, mask::FDEvent)
        fdw = _FDWatcher(socket, mask)
        try
            return wait(fdw, mask)
        finally
            close(fdw, mask)
        end
    end
end

function wait(pfw::PollingFileWatcher)
    iolock_begin()
    preserve_handle(pfw)
    lock(pfw.notify)
    local prevstat
    try
        start_watching(pfw)
        iolock_end()
        prevstat = wait(pfw.notify)::StatStruct
        unlock(pfw.notify)
        iolock_begin()
        lock(pfw.notify)
    finally
        unlock(pfw.notify)
        unpreserve_handle(pfw)
    end
    stop_watching(pfw)
    iolock_end()
    if pfw.handle == C_NULL
        return prevstat, EOFError()
    elseif pfw.curr_error != 0
        return prevstat, _UVError("PollingFileWatcher", pfw.curr_error)
    else
        return prevstat, pfw.curr_stat
    end
end

function wait(m::FileMonitor)
    iolock_begin()
    preserve_handle(m)
    lock(m.notify)
    local events
    try
        start_watching(m)
        iolock_end()
        events = wait(m.notify)::FileEvent
        events |= FileEvent(m.events)
        m.events = 0
        unlock(m.notify)
        iolock_begin()
        lock(m.notify)
    finally
        unlock(m.notify)
        unpreserve_handle(m)
    end
    stop_watching(m)
    iolock_end()
    return events
end

function wait(m::FolderMonitor)
    m.handle == C_NULL && throw(EOFError())
    preserve_handle(m)
    lock(m.notify)
    evt = try
            m.handle == C_NULL && throw(EOFError())
            while isempty(m.channel)
                wait(m.notify)
            end
            popfirst!(m.channel)
        finally
            unlock(m.notify)
            unpreserve_handle(m)
        end
    return evt::Pair{String, FileEvent}
end


"""
    poll_fd(fd, timeout_s::Real=-1; readable=false, writable=false)

Monitor a file descriptor `fd` for changes in the read or write availability, and with a
timeout given by `timeout_s` seconds.

The keyword arguments determine which of read and/or write status should be monitored; at
least one of them must be set to `true`.

The returned value is an object with boolean fields `readable`, `writable`, and `timedout`,
giving the result of the polling.
"""
function poll_fd(s::Union{RawFD, Sys.iswindows() ? WindowsRawSocket : Union{}}, timeout_s::Real=-1; readable=false, writable=false)
    mask = FDEvent(readable, writable, false, false)
    mask.timedout && return mask
    fdw = _FDWatcher(s, mask)
    local timer
    # we need this flag to explicitly track whether we call `close` already, to update the internal refcount correctly
    timedout = false # TODO: make this atomic
    try
        if timeout_s >= 0
            # delay creating the timer until shortly before we start the poll wait
            timer = Timer(timeout_s) do t
                timedout && return
                timedout = true
                close(fdw, mask)
            end
            try
                while true
                    events = _wait(fdw, mask)
                    if timedout || !events.timedout
                        @lock fdw.notify fdw.events &= ~events.events
                        return events
                    end
                end
            catch ex
                ex isa EOFError() || rethrow()
                return FDEvent()
            end
        else
            return wait(fdw, mask)
        end
    finally
        if @isdefined(timer)
            if !timedout
                timedout = true
                close(timer)
                close(fdw, mask)
            end
        else
            close(fdw, mask)
        end
    end
end

"""
    watch_file(path::AbstractString, timeout_s::Real=-1)

Watch file or directory `path` for changes until a change occurs or `timeout_s` seconds have
elapsed. This function does not poll the file system and instead uses platform-specific
functionality to receive notifications from the operating system (e.g. via inotify on Linux).
See the NodeJS documentation linked below for details.

The returned value is an object with boolean fields `renamed`, `changed`, and `timedout`,
giving the result of watching the file.

This behavior of this function varies slightly across platforms. See
<https://nodejs.org/api/fs.html#fs_caveats> for more detailed information.
"""
function watch_file(s::String, timeout_s::Float64=-1.0)
    fm = FileMonitor(s)
    local timer
    try
        if timeout_s >= 0
            timer = Timer(timeout_s) do t
                close(fm)
            end
        end
        return wait(fm)
    finally
        close(fm)
        @isdefined(timer) && close(timer)
    end
end
watch_file(s::AbstractString, timeout_s::Real=-1) = watch_file(String(s), Float64(timeout_s))

"""
    watch_folder(path::AbstractString, timeout_s::Real=-1)

Watches a file or directory `path` for changes until a change has occurred or `timeout_s`
seconds have elapsed. This function does not poll the file system and instead uses platform-specific
functionality to receive notifications from the operating system (e.g. via inotify on Linux).
See the NodeJS documentation linked below for details.

This will continuing tracking changes for `path` in the background until
`unwatch_folder` is called on the same `path`.

The returned value is an pair where the first field is the name of the changed file (if available)
and the second field is an object with boolean fields `renamed`, `changed`, and `timedout`,
giving the event.

This behavior of this function varies slightly across platforms. See
<https://nodejs.org/api/fs.html#fs_caveats> for more detailed information.
"""
watch_folder(s::AbstractString, timeout_s::Real=-1) = watch_folder(String(s), timeout_s)
function watch_folder(s::String, timeout_s::Real=-1)
    fm = get!(watched_folders, s) do
        return FolderMonitor(s)
    end
    local timer
    if timeout_s >= 0
        @lock fm.notify isempty(fm.channel) || return popfirst!(fm.channel)
        if timeout_s <= 0.010
            # for very small timeouts, we can just sleep for the whole timeout-interval
            (timeout_s == 0) ? yield() : sleep(timeout_s)
            @lock fm.notify isempty(fm.channel) || return popfirst!(fm.channel)
            return "" => FileEvent() # timeout
        else
            timer = Timer(timeout_s) do t
                @lock fm.notify notify(fm.notify)
            end
        end
    end
    # inline a copy of `wait` with added support for checking timer
    fm.handle == C_NULL && throw(EOFError())
    preserve_handle(fm)
    lock(fm.notify)
    evt = try
            fm.handle == C_NULL && throw(EOFError())
            while isempty(fm.channel)
                if @isdefined(timer)
                    isopen(timer) || return "" => FileEvent() # timeout
                end
                wait(fm.notify)
            end
            popfirst!(fm.channel)
        finally
            unlock(fm.notify)
            unpreserve_handle(fm)
            @isdefined(timer) && close(timer)
        end
    return evt::Pair{String, FileEvent}
end

"""
    unwatch_folder(path::AbstractString)

Stop background tracking of changes for `path`.
It is not recommended to do this while another task is waiting for
`watch_folder` to return on the same path, as the result may be unpredictable.
"""
unwatch_folder(s::AbstractString) = unwatch_folder(String(s))
function unwatch_folder(s::String)
    fm = pop!(watched_folders, s, nothing)
    fm === nothing || close(fm)
    nothing
end

const watched_folders = Dict{String, FolderMonitor}()

"""
    poll_file(path::AbstractString, interval_s::Real=5.007, timeout_s::Real=-1) -> (previous::StatStruct, current)

Monitor a file for changes by polling every `interval_s` seconds until a change occurs or
`timeout_s` seconds have elapsed. The `interval_s` should be a long period; the default is
5.007 seconds.

Returns a pair of status objects `(previous, current)` when a change is detected.
The `previous` status is always a `StatStruct`, but it may have all of the fields zeroed
(indicating the file didn't previously exist, or wasn't previously accessible).

The `current` status object may be a `StatStruct`, an `EOFError` (indicating the timeout elapsed),
or some other `Exception` subtype (if the `stat` operation failed - for example, if the path does not exist).

To determine when a file was modified, compare `current isa StatStruct && mtime(prev) != mtime(current)` to detect
notification of changes. However, using [`watch_file`](@ref) for this operation is preferred, since
it is more reliable and efficient, although in some situations it may not be available.
"""
function poll_file(s::AbstractString, interval_seconds::Real=5.007, timeout_s::Real=-1)
    pfw = PollingFileWatcher(s, Float64(interval_seconds))
    local timer
    try
        if timeout_s >= 0
            timer = Timer(timeout_s) do t
                close(pfw)
            end
        end
        statdiff = wait(pfw)
        if isa(statdiff[2], IOError)
            # file didn't initially exist, continue watching for it to be created (or the error to change)
            statdiff = wait(pfw)
        end
        return statdiff
    finally
        close(pfw)
        @isdefined(timer) && close(timer)
    end
end

include("pidfile.jl")
import .Pidfile: mkpidlock, trymkpidlock

end
w   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/FileWatching/src/pidfile.jl�+      module Pidfile


export mkpidlock, trymkpidlock

using Base:
    IOError, UV_EEXIST, UV_ESRCH,
    Process

using Base.Libc: rand

using Base.Filesystem:
    File, open, JL_O_CREAT, JL_O_RDWR, JL_O_RDONLY, JL_O_EXCL,
    rename, samefile, path_separator

using ..FileWatching: watch_file
using Base.Sys: iswindows

"""
    mkpidlock([f::Function], at::String, [pid::Cint, proc::Process]; kwopts...)

Create a pidfile lock for the path "at" for the current process
or the process identified by pid or proc. Can take a function to execute once locked,
for usage in `do` blocks, after which the lock will be automatically closed. If the lock fails
and `wait` is false, then an error is thrown.

The lock will be released by either `close`, a `finalizer`, or shortly after `proc` exits.
Make sure the return value is live through the end of the critical section of
your program, so the `finalizer` does not reclaim it early.

Optional keyword arguments:
 - `mode`: file access mode (modified by the process umask). Defaults to world-readable.
 - `poll_interval`: Specify the maximum time to between attempts (if `watch_file` doesn't work)
 - `stale_age`: Delete an existing pidfile (ignoring the lock) if it is older than this many seconds, based on its mtime.
     The file won't be deleted until 5x longer than this if the pid in the file appears that it may be valid.
     Or 25x longer if `refresh` is overridden to 0 to disable lock refreshing.
     By default this is disabled (`stale_age` = 0), but a typical recommended value would be about 3-5x an
     estimated normal completion time.
 - `refresh`: Keeps a lock from becoming stale by updating the mtime every interval of time that passes.
     By default, this is set to `stale_age/2`, which is the recommended value.
 - `wait`: If true, block until we get the lock, if false, raise error if lock fails.
"""
function mkpidlock end

"""
    trymkpidlock([f::Function], at::String, [pid::Cint, proc::Process]; kwopts...)

Like `mkpidlock` except returns `false` instead of waiting if the file is already locked.

!!! compat "Julia 1.10"
    This function requires at least Julia 1.10.

"""
function trymkpidlock end

# mutable only because we want to add a finalizer
mutable struct LockMonitor
    const path::String
    const fd::File
    const update::Union{Nothing,Timer}

    global function mkpidlock(at::String, pid::Cint; stale_age::Real=0, refresh::Real=stale_age/2, kwopts...)
        local lock
        atdir, atname = splitdir(at)
        isempty(atdir) && (atdir = pwd())
        at = realpath(atdir) * path_separator * atname
        fd = open_exclusive(at; stale_age, refresh, kwopts...)
        update = nothing
        try
            write_pidfile(fd, pid)
            if refresh > 0
                # N.b.: to ensure our finalizer works we are careful to capture
                # `fd` here instead of `lock`.
                update = Timer(t -> isopen(t) && touch(fd), refresh; interval=refresh)
            end
            lock = new(at, fd, update)
            finalizer(close, lock)
        catch ex
            tryrmopenfile(at)
            close(fd)
            rethrow(ex)
        end
        return lock
    end
end

mkpidlock(at::String; kwopts...) = mkpidlock(at, getpid(); kwopts...)
mkpidlock(f::Function, at::String; kwopts...) = mkpidlock(f, at, getpid(); kwopts...)

function mkpidlock(f::Function, at::String, pid::Cint; kwopts...)
    lock = mkpidlock(at, pid; kwopts...)
    try
        return f()
    finally
        close(lock)
    end
end

function mkpidlock(at::String, proc::Process; kwopts...)
    lock = mkpidlock(at, getpid(proc); kwopts...)
    closer = @async begin
        wait(proc)
        close(lock)
    end
    isdefined(Base, :errormonitor) && Base.errormonitor(closer)
    return lock
end

function trymkpidlock(args...; kwargs...)
    try
        mkpidlock(args...; kwargs..., wait=false)
    catch ex
        if ex isa PidlockedError
            return false
        else
            rethrow()
        end
    end
end

"""
    Base.touch(::Pidfile.LockMonitor)

Update the `mtime` on the lock, to indicate it is still fresh.

See also the `refresh` keyword in the [`mkpidlock`](@ref) constructor.
"""
Base.touch(lock::LockMonitor) = (touch(lock.fd); lock)

"""
    write_pidfile(io, pid)

Write our pidfile format to an open IO descriptor.
"""
function write_pidfile(io::IO, pid::Cint)
    print(io, "$pid $(gethostname())")
end

"""
    parse_pidfile(file::Union{IO, String}) => (pid, hostname, age)

Attempt to parse our pidfile format,
replaced an element with (0, "", 0.0), respectively, for any read that failed.
"""
function parse_pidfile(io::IO)
    fields = split(read(io, String), ' ', limit = 2)
    pid = tryparse(Cuint, fields[1])
    pid === nothing && (pid = Cuint(0))
    hostname = (length(fields) == 2) ? fields[2] : ""
    when = mtime(io)
    age = time() - when
    return (pid, hostname, age)
end

function parse_pidfile(path::String)
    try
        existing = open(path, JL_O_RDONLY)
        try
            return parse_pidfile(existing)
        finally
            close(existing)
        end
    catch ex
        isa(ex, EOFError) || isa(ex, IOError) || rethrow(ex)
        return (Cuint(0), "", 0.0)
    end
end

"""
    isvalidpid(hostname::String, pid::Cuint) :: Bool

Attempt to conservatively estimate whether pid is a valid process id.
"""
function isvalidpid(hostname::AbstractString, pid::Cuint)
    # can't inspect remote hosts
    (hostname == "" || hostname == gethostname()) || return true
    # pid < 0 is never valid (must be a parser error or different OS),
    # and would have a completely different meaning when passed to kill
    !iswindows() && pid > typemax(Cint) && return false
    # (similarly for pid 0)
    pid == 0 && return false
    # see if the process id exists by querying kill without sending a signal
    # and checking if it returned ESRCH (no such process)
    return ccall(:uv_kill, Cint, (Cuint, Cint), pid, 0) != UV_ESRCH
end

"""
    stale_pidfile(path::String, stale_age::Real, refresh::Real) :: Bool

Helper function for `open_exclusive` for deciding if a pidfile is stale.
"""
function stale_pidfile(path::String, stale_age::Real, refresh::Real)
    pid, hostname, age = parse_pidfile(path)
    age < -stale_age && @warn "filesystem time skew detected" path=path
    longer_factor = refresh == 0 ? 25 : 5
    if age > stale_age
        if (age > stale_age * longer_factor) || !isvalidpid(hostname, pid)
            return true
        end
    end
    return false
end

"""
    tryopen_exclusive(path::String, mode::Integer = 0o444) :: Union{Void, File}

Try to create a new file for read-write advisory-exclusive access,
return nothing if it already exists.
"""
function tryopen_exclusive(path::String, mode::Integer = 0o444)
    try
        return open(path, JL_O_RDWR | JL_O_CREAT | JL_O_EXCL, mode)
    catch ex
        (isa(ex, IOError) && ex.code == UV_EEXIST) || rethrow(ex)
    end
    return nothing
end

struct PidlockedError <: Exception
    msg::AbstractString
end

"""
    open_exclusive(path::String; mode, poll_interval, wait, stale_age, refresh) :: File

Create a new a file for read-write advisory-exclusive access.
If `wait` is `false` then error out if the lock files exist
otherwise block until we get the lock.

For a description of the keyword arguments, see [`mkpidlock`](@ref).
"""
function open_exclusive(path::String;
                        mode::Integer = 0o444 #= read-only =#,
                        poll_interval::Real = 10 #= seconds =#,
                        wait::Bool = true #= return on failure if false =#,
                        stale_age::Real = 0 #= disabled =#,
                        refresh::Real = stale_age/2)
    # fast-path: just try to open it
    file = tryopen_exclusive(path, mode)
    file === nothing || return file
    if !wait
        if file === nothing && stale_age > 0
            if stale_age > 0 && stale_pidfile(path, stale_age, refresh)
                @warn "attempting to remove probably stale pidfile" path=path
                tryrmopenfile(path)
            end
            file = tryopen_exclusive(path, mode)
        end
        if file === nothing
            throw(PidlockedError("Failed to get pidfile lock for $(repr(path))."))
        else
            return file
        end
    end
    # fall-back: wait for the lock

    while true
        # start the file-watcher prior to checking for the pidfile existence
        t = @async try
            watch_file(path, poll_interval)
        catch ex
            isa(ex, IOError) || rethrow(ex)
            sleep(poll_interval) # if the watch failed, convert to just doing a sleep
        end
        # now try again to create it
        file = tryopen_exclusive(path, mode)
        file === nothing || return file
        Base.wait(t) # sleep for a bit before trying again
        if stale_age > 0 && stale_pidfile(path, stale_age, refresh)
            # if the file seems stale, try to remove it before attempting again
            # set stale_age to zero so we won't attempt again, even if the attempt fails
            stale_age -= stale_age
            @warn "attempting to remove probably stale pidfile" path=path
            tryrmopenfile(path)
        end
    end
end

function _rand_filename(len::Int=4) # modified from Base.Libc
    slug = Base.StringVector(len)
    chars = b"0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"
    for i = 1:len
        slug[i] = chars[(Libc.rand() % length(chars)) + 1]
    end
    return String(slug)
end

function tryrmopenfile(path::String)
    # Deleting open file on Windows is a bit hard
    # if we want to reuse the name immediately after:
    # we need to first rename it, then delete it.
    if Sys.iswindows()
        try
            local rmpath
            rmdir, rmname = splitdir(path)
            while true
                rmpath = string(rmdir, isempty(rmdir) ? "" : path_separator,
                    "\$", _rand_filename(), rmname, ".deleted")
                ispath(rmpath) || break
            end
            rename(path, rmpath)
            path = rmpath
        catch ex
            isa(ex, IOError) || rethrow(ex)
        end
    end
    return try
        rm(path)
        true
    catch ex
        isa(ex, IOError) || rethrow(ex)
        ex
    end
end

"""
    close(lock::LockMonitor)

Release a pidfile lock.
"""
function Base.close(lock::LockMonitor)
    update = lock.update
    update === nothing || close(update)
    isopen(lock.fd) || return false
    removed = false
    path = lock.path
    pathstat = try
            # Windows sometimes likes to return EACCES here,
            # if the path is in the process of being deleted
            stat(path)
        catch ex
            ex isa IOError || rethrow()
            removed = ex
            nothing
        end
    if pathstat !== nothing && samefile(stat(lock.fd), pathstat)
        # try not to delete someone else's lock
        removed = tryrmopenfile(path)
    end
    close(lock.fd)
    havelock = removed === true
    havelock || @warn "failed to remove pidfile on close" path=path removed=removed
    return havelock
end

end # module
n   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Libdl/src/Libdl.jlh      # This file is a part of Julia. License is MIT: https://julialang.org/license

module Libdl
# Just re-export Base.Libc.Libdl:
export DL_LOAD_PATH, RTLD_DEEPBIND, RTLD_FIRST, RTLD_GLOBAL, RTLD_LAZY, RTLD_LOCAL,
    RTLD_NODELETE, RTLD_NOLOAD, RTLD_NOW, dlclose, dlopen, dlopen_e, dlsym, dlsym_e,
    dlpath, find_library, dlext, dllist

import Base.Libc.Libdl: DL_LOAD_PATH, RTLD_DEEPBIND, RTLD_FIRST, RTLD_GLOBAL, RTLD_LAZY, RTLD_LOCAL,
                        RTLD_NODELETE, RTLD_NOLOAD, RTLD_NOW, dlclose, dlopen, dlopen_e, dlsym, dlsym_e,
                        dlpath, find_library, dlext, dllist

end # module
r   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Logging/src/Logging.jlM      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
Utilities for capturing, filtering and presenting streams of log events.
Normally you don't need to import `Logging` to create log events; for this
the standard logging macros such as `@info` are already exported by `Base`
and available by default.
"""
module Logging

# Import the CoreLogging implementation into Logging as new const bindings.
# Doing it this way (rather than with import) makes these symbols accessible to
# tab completion.
for sym in [
    :LogLevel, :BelowMinLevel, :AboveMaxLevel,
    :AbstractLogger,
    :NullLogger,
    :handle_message, :shouldlog, :min_enabled_level, :catch_exceptions,
    Symbol("@debug"),
    Symbol("@info"),
    Symbol("@warn"),
    Symbol("@error"),
    Symbol("@logmsg"),
    :with_logger,
    :current_logger,
    :global_logger,
    :disable_logging,
    :SimpleLogger]
    @eval const $sym = Base.CoreLogging.$sym
end

# LogLevel aliases (re-)documented here (JuliaLang/julia#40978)
"""
    Debug

Alias for [`LogLevel(-1000)`](@ref LogLevel).
"""
const Debug = Base.CoreLogging.Debug
"""
    Info

Alias for [`LogLevel(0)`](@ref LogLevel).
"""
const Info = Base.CoreLogging.Info
"""
    Warn

Alias for [`LogLevel(1000)`](@ref LogLevel).
"""
const Warn = Base.CoreLogging.Warn
"""
    Error

Alias for [`LogLevel(2000)`](@ref LogLevel).
"""
const Error = Base.CoreLogging.Error

using Base.CoreLogging:
    closed_stream

export
    AbstractLogger,
    LogLevel,
    NullLogger,
    @debug,
    @info,
    @warn,
    @error,
    @logmsg,
    with_logger,
    current_logger,
    global_logger,
    disable_logging,
    SimpleLogger,
    ConsoleLogger,
    BelowMinLevel,
    Debug,
    Info,
    Warn,
    Error,
    AboveMaxLevel

include("ConsoleLogger.jl")

# The following are also part of the public API, but not exported:
#
# 1. Log levels:
#   BelowMinLevel, Debug, Info, Warn, Error, AboveMaxLevel,
#
# 2. AbstractLogger message related functions:
#  handle_message, shouldlog, min_enabled_level, catch_exceptions,

function __init__()
    global_logger(ConsoleLogger())
end

end
x   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Logging/src/ConsoleLogger.jlF      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
    ConsoleLogger([stream,] min_level=Info; meta_formatter=default_metafmt,
                  show_limited=true, right_justify=0)

Logger with formatting optimized for readability in a text console, for example
interactive work with the Julia REPL.

Log levels less than `min_level` are filtered out.

Message formatting can be controlled by setting keyword arguments:

* `meta_formatter` is a function which takes the log event metadata
  `(level, _module, group, id, file, line)` and returns a color (as would be
  passed to printstyled), prefix and suffix for the log message.  The
  default is to prefix with the log level and a suffix containing the module,
  file and line location.
* `show_limited` limits the printing of large data structures to something
  which can fit on the screen by setting the `:limit` `IOContext` key during
  formatting.
* `right_justify` is the integer column which log metadata is right justified
  at. The default is zero (metadata goes on its own line).
"""
struct ConsoleLogger <: AbstractLogger
    stream::IO
    min_level::LogLevel
    meta_formatter
    show_limited::Bool
    right_justify::Int
    message_limits::Dict{Any,Int}
end
function ConsoleLogger(stream::IO, min_level=Info;
                       meta_formatter=default_metafmt, show_limited=true,
                       right_justify=0)
    ConsoleLogger(stream, min_level, meta_formatter,
                  show_limited, right_justify, Dict{Any,Int}())
end
function ConsoleLogger(min_level=Info;
                       meta_formatter=default_metafmt, show_limited=true,
                       right_justify=0)
    ConsoleLogger(closed_stream, min_level, meta_formatter,
                  show_limited, right_justify, Dict{Any,Int}())
end


shouldlog(logger::ConsoleLogger, level, _module, group, id) =
    get(logger.message_limits, id, 1) > 0

min_enabled_level(logger::ConsoleLogger) = logger.min_level

# Formatting of values in key value pairs
showvalue(io, msg) = show(io, "text/plain", msg)
function showvalue(io, e::Tuple{Exception,Any})
    ex,bt = e
    showerror(io, ex, bt; backtrace = bt!==nothing)
end
showvalue(io, ex::Exception) = showerror(io, ex)

function default_logcolor(level::LogLevel)
    level < Info  ? Base.debug_color() :
    level < Warn  ? Base.info_color()  :
    level < Error ? Base.warn_color()  :
                    Base.error_color()
end

function default_metafmt(level::LogLevel, _module, group, id, file, line)
    @nospecialize
    color = default_logcolor(level)
    prefix = string(level == Warn ? "Warning" : string(level), ':')
    suffix::String = ""
    Info <= level < Warn && return color, prefix, suffix
    _module !== nothing && (suffix *= string(_module)::String)
    if file !== nothing
        _module !== nothing && (suffix *= " ")
        suffix *= contractuser(file)::String
        if line !== nothing
            suffix *= ":$(isa(line, UnitRange) ? "$(first(line))-$(last(line))" : line)"
        end
    end
    !isempty(suffix) && (suffix = "@ " * suffix)
    return color, prefix, suffix
end

# Length of a string as it will appear in the terminal (after ANSI color codes
# are removed)
function termlength(str)
    N = 0
    in_esc = false
    for c in str
        if in_esc
            if c == 'm'
                in_esc = false
            end
        else
            if c == '\e'
                in_esc = true
            else
                N += 1
            end
        end
    end
    return N
end

function handle_message(logger::ConsoleLogger, level::LogLevel, message, _module, group, id,
                        filepath, line; kwargs...)
    @nospecialize
    hasmaxlog = haskey(kwargs, :maxlog) ? 1 : 0
    maxlog = get(kwargs, :maxlog, nothing)
    if maxlog isa Core.BuiltinInts
        remaining = get!(logger.message_limits, id, Int(maxlog)::Int)
        logger.message_limits[id] = remaining - 1
        remaining > 0 || return
    end

    # Generate a text representation of the message and all key value pairs,
    # split into lines.
    msglines = [(indent=0, msg=l) for l in split(chomp(convert(String, string(message))::String), '\n')]
    stream::IO = logger.stream
    if !(isopen(stream)::Bool)
        stream = stderr
    end
    dsize = displaysize(stream)::Tuple{Int,Int}
    nkwargs = length(kwargs)::Int
    if nkwargs > hasmaxlog
        valbuf = IOBuffer()
        rows_per_value = max(1, dsize[1] ÷ (nkwargs + 1 - hasmaxlog))
        valio = IOContext(IOContext(valbuf, stream),
                          :displaysize => (rows_per_value, dsize[2] - 5),
                          :limit => logger.show_limited)
        for (key, val) in kwargs
            key === :maxlog && continue
            showvalue(valio, val)
            vallines = split(String(take!(valbuf)), '\n')
            if length(vallines) == 1
                push!(msglines, (indent=2, msg=SubString("$key = $(vallines[1])")))
            else
                push!(msglines, (indent=2, msg=SubString("$key =")))
                append!(msglines, ((indent=3, msg=line) for line in vallines))
            end
        end
    end

    # Format lines as text with appropriate indentation and with a box
    # decoration on the left.
    color, prefix, suffix = logger.meta_formatter(level, _module, group, id, filepath, line)::Tuple{Union{Symbol,Int},String,String}
    minsuffixpad = 2
    buf = IOBuffer()
    iob = IOContext(buf, stream)
    nonpadwidth = 2 + (isempty(prefix) || length(msglines) > 1 ? 0 : length(prefix)+1) +
                  msglines[end].indent + termlength(msglines[end].msg) +
                  (isempty(suffix) ? 0 : length(suffix)+minsuffixpad)
    justify_width = min(logger.right_justify, dsize[2])
    if nonpadwidth > justify_width && !isempty(suffix)
        push!(msglines, (indent=0, msg=SubString("")))
        minsuffixpad = 0
        nonpadwidth = 2 + length(suffix)
    end
    for (i, (indent, msg)) in enumerate(msglines)
        boxstr = length(msglines) == 1 ? "[ " :
                 i == 1                ? "┌ " :
                 i < length(msglines)  ? "│ " :
                                         "└ "
        printstyled(iob, boxstr, bold=true, color=color)
        if i == 1 && !isempty(prefix)
            printstyled(iob, prefix, " ", bold=true, color=color)
        end
        print(iob, " "^indent, msg)
        if i == length(msglines) && !isempty(suffix)
            npad = max(0, justify_width - nonpadwidth) + minsuffixpad
            print(iob, " "^npad)
            printstyled(iob, suffix, color=:light_black)
        end
        println(iob)
    end

    write(stream, take!(buf))
    nothing
end
l   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Mmap/src/Mmap.jlG@      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
Low level module for mmap (memory mapping of files).
"""
module Mmap

import Base: OS_HANDLE, INVALID_OS_HANDLE

export mmap

const PAGESIZE = Int(Sys.isunix() ? ccall(:jl_getpagesize, Clong, ()) : ccall(:jl_getallocationgranularity, Clong, ()))

# for mmaps not backed by files
mutable struct Anonymous <: IO
    name::String
    readonly::Bool
    create::Bool
end

"""
    Mmap.Anonymous(name::AbstractString="", readonly::Bool=false, create::Bool=true)

Create an `IO`-like object for creating zeroed-out mmapped-memory that is not tied to a file
for use in [`mmap`](@ref mmap). Used by `SharedArray` for creating shared memory arrays.

# Examples
```jldoctest
julia> using Mmap

julia> anon = Mmap.Anonymous();

julia> isreadable(anon)
true

julia> iswritable(anon)
true

julia> isopen(anon)
true
```
"""
Anonymous() = Anonymous("",false,true)

Base.isopen(::Anonymous) = true
Base.isreadable(::Anonymous) = true
Base.iswritable(a::Anonymous) = !a.readonly

# const used for zeroed, anonymous memory
gethandle(io::Anonymous) = INVALID_OS_HANDLE

# platform-specific mmap utilities
if Sys.isunix()

const PROT_READ     = Cint(1)
const PROT_WRITE    = Cint(2)
const MAP_SHARED    = Cint(1)
const MAP_PRIVATE   = Cint(2)
const MAP_ANONYMOUS = Cint(Sys.isbsd() ? 0x1000 : 0x20)
const F_GETFL       = Cint(3)

gethandle(io::IO) = RawFD(fd(io))

# Determine a stream's read/write mode, and return prot & flags appropriate for mmap
function settings(s::RawFD, shared::Bool)
    flags = shared ? MAP_SHARED : MAP_PRIVATE
    if s == INVALID_OS_HANDLE
        flags |= MAP_ANONYMOUS
        prot = PROT_READ | PROT_WRITE
    else
        mode = ccall(:fcntl, Cint, (RawFD, Cint, Cint...), s, F_GETFL)
        systemerror("fcntl F_GETFL", mode == -1)
        mode = mode & 3
        prot = (mode == 0) ? PROT_READ : ((mode == 1) ? PROT_WRITE : (PROT_READ | PROT_WRITE))
        if prot & PROT_READ == 0
            throw(ArgumentError("mmap requires read permissions on the file (open with \"r+\" mode to override)"))
        end
    end
    return prot, flags, (prot & PROT_WRITE) > 0
end

# Before mapping, grow the file to sufficient size
# Note: a few mappable streams do not support lseek. When Julia
# supports structures in ccall, switch to fstat.
grow!(::Anonymous,o::Integer,l::Integer) = return
function grow!(io::IO, offset::Integer, len::Integer)
    pos = position(io)
    filelen = filesize(io)
    if filelen < offset + len
        failure = ccall(:jl_ftruncate, Cint, (Cint, Int64), fd(io), offset+len)
        Base.systemerror(:ftruncate, failure != 0)
    end
    seek(io, pos)
    return
end

elseif Sys.iswindows()

const DWORD = Culong

const PAGE_READONLY          = DWORD(0x02)
const PAGE_READWRITE         = DWORD(0x04)
const PAGE_WRITECOPY         = DWORD(0x08)
const PAGE_EXECUTE_READ      = DWORD(0x20)
const PAGE_EXECUTE_READWRITE = DWORD(0x40)
const PAGE_EXECUTE_WRITECOPY = DWORD(0x80)
const FILE_MAP_COPY          = DWORD(0x01)
const FILE_MAP_WRITE         = DWORD(0x02)
const FILE_MAP_READ          = DWORD(0x04)
const FILE_MAP_EXECUTE       = DWORD(0x20)

function gethandle(io::IO)
    handle = Libc._get_osfhandle(RawFD(fd(io)))
    Base.windowserror(:mmap, handle == INVALID_OS_HANDLE)
    return handle
end

settings(sh::Anonymous) = sh.name, sh.readonly, sh.create
settings(io::IO) = Ptr{Cwchar_t}(0), isreadonly(io), true

else
    error("mmap not defined for this OS")
end # os-test

# core implementation of mmap

"""
    mmap(io::Union{IOStream,AbstractString,Mmap.AnonymousMmap}[, type::Type{Array{T,N}}, dims, offset]; grow::Bool=true, shared::Bool=true)
    mmap(type::Type{Array{T,N}}, dims)

Create an `Array` whose values are linked to a file, using memory-mapping. This provides a
convenient way of working with data too large to fit in the computer's memory.

The type is an `Array{T,N}` with a bits-type element of `T` and dimension `N` that
determines how the bytes of the array are interpreted. Note that the file must be stored in
binary format, and no format conversions are possible (this is a limitation of operating
systems, not Julia).

`dims` is a tuple or single [`Integer`](@ref) specifying the size or length of the array.

The file is passed via the stream argument, either as an open [`IOStream`](@ref) or filename string.
When you initialize the stream, use `"r"` for a "read-only" array, and `"w+"` to create a
new array used to write values to disk.

If no `type` argument is specified, the default is `Vector{UInt8}`.

Optionally, you can specify an offset (in bytes) if, for example, you want to skip over a
header in the file. The default value for the offset is the current stream position for an
`IOStream`.

The `grow` keyword argument specifies whether the disk file should be grown to accommodate
the requested size of array (if the total file size is < requested array size). Write
privileges are required to grow the file.

The `shared` keyword argument specifies whether the resulting `Array` and changes made to it
will be visible to other processes mapping the same file.

For example, the following code

```julia
# Create a file for mmapping
# (you could alternatively use mmap to do this step, too)
using Mmap
A = rand(1:20, 5, 30)
s = open("/tmp/mmap.bin", "w+")
# We'll write the dimensions of the array as the first two Ints in the file
write(s, size(A,1))
write(s, size(A,2))
# Now write the data
write(s, A)
close(s)

# Test by reading it back in
s = open("/tmp/mmap.bin")   # default is read-only
m = read(s, Int)
n = read(s, Int)
A2 = mmap(s, Matrix{Int}, (m,n))
```

creates a `m`-by-`n` `Matrix{Int}`, linked to the file associated with stream `s`.

A more portable file would need to encode the word size -- 32 bit or 64 bit -- and endianness
information in the header. In practice, consider encoding binary data using standard formats
like HDF5 (which can be used with memory-mapping).
"""
function mmap(io::IO,
              ::Type{Array{T,N}}=Vector{UInt8},
              dims::NTuple{N,Integer}=(div(filesize(io)-position(io),sizeof(T)),),
              offset::Integer=position(io); grow::Bool=true, shared::Bool=true) where {T,N}
    # check inputs
    isopen(io) || throw(ArgumentError("$io must be open to mmap"))
    isbitstype(T)  || throw(ArgumentError("unable to mmap $T; must satisfy isbitstype(T) == true"))

    len = sizeof(T)
    for l in dims
        len, overflow = Base.Checked.mul_with_overflow(promote(len, l)...)
        overflow && throw(ArgumentError("requested size prod($((sizeof(T), dims...))) too large, would overflow typeof(size(T)) == $(typeof(len))"))
    end
    len >= 0 || throw(ArgumentError("requested size must be ≥ 0, got $len"))
    len == 0 && return Array{T}(undef, ntuple(x->0,Val(N)))
    len < typemax(Int) - PAGESIZE || throw(ArgumentError("requested size must be < $(typemax(Int)-PAGESIZE), got $len"))

    offset >= 0 || throw(ArgumentError("requested offset must be ≥ 0, got $offset"))

    # shift `offset` to start of page boundary
    offset_page::Int64 = div(offset, PAGESIZE) * PAGESIZE
    # add (offset - offset_page) to `len` to get total length of memory-mapped region
    mmaplen = (offset - offset_page) + len

    file_desc = gethandle(io)
    szfile = convert(Csize_t, len + offset)
    requestedSizeLarger = false
    if !(io isa Mmap.Anonymous)
        @static if !Sys.isapple()
            requestedSizeLarger = szfile > filesize(io)
        end
    end
    # platform-specific mmapping
    @static if Sys.isunix()
        prot, flags, iswrite = settings(file_desc, shared)
        if requestedSizeLarger
            if iswrite
                if grow
                    grow!(io, offset, len)
                else
                    throw(ArgumentError("requested size $szfile larger than file size $(filesize(io)), but requested not to grow"))
                end
            else
                throw(ArgumentError("unable to increase file size to $szfile due to read-only permissions"))
            end
        end
        @static if Sys.isapple()
            iswrite && grow && grow!(io, offset, len)
        end
        # mmap the file
        ptr = ccall(:jl_mmap, Ptr{Cvoid}, (Ptr{Cvoid}, Csize_t, Cint, Cint, RawFD, Int64),
            C_NULL, mmaplen, prot, flags, file_desc, offset_page)
        systemerror("memory mapping failed", reinterpret(Int, ptr) == -1)
    else
        name, readonly, create = settings(io)
        if requestedSizeLarger
            if readonly
                throw(ArgumentError("unable to increase file size to $szfile due to read-only permissions"))
            elseif !grow
                throw(ArgumentError("requested size $szfile larger than file size $(filesize(io)), but requested not to grow"))
            end
        end
        handle = create ? ccall(:CreateFileMappingW, stdcall, Ptr{Cvoid}, (OS_HANDLE, Ptr{Cvoid}, DWORD, DWORD, DWORD, Cwstring),
                                file_desc, C_NULL, readonly ? PAGE_READONLY : PAGE_READWRITE, szfile >> 32, szfile & typemax(UInt32), name) :
                          ccall(:OpenFileMappingW, stdcall, Ptr{Cvoid}, (DWORD, Cint, Cwstring),
                                readonly ? FILE_MAP_READ : FILE_MAP_WRITE, true, name)
        Base.windowserror(:mmap, handle == C_NULL)
        ptr = ccall(:MapViewOfFile, stdcall, Ptr{Cvoid}, (Ptr{Cvoid}, DWORD, DWORD, DWORD, Csize_t),
                    handle, readonly ? FILE_MAP_READ : FILE_MAP_WRITE, offset_page >> 32, offset_page & typemax(UInt32), mmaplen)
        Base.windowserror(:mmap, ptr == C_NULL)
    end # os-test
    # convert mmapped region to Julia Array at `ptr + (offset - offset_page)` since file was mapped at offset_page
    A = unsafe_wrap(Array, convert(Ptr{T}, UInt(ptr) + UInt(offset - offset_page)), dims)
    finalizer(A) do x
        @static if Sys.isunix()
            systemerror("munmap",  ccall(:munmap, Cint, (Ptr{Cvoid}, Int), ptr, mmaplen) != 0)
        else
            status = ccall(:UnmapViewOfFile, stdcall, Cint, (Ptr{Cvoid},), ptr)!=0
            status |= ccall(:CloseHandle, stdcall, Cint, (Ptr{Cvoid},), handle)!=0
            Base.windowserror(:UnmapViewOfFile, status == 0)
        end
    end
    return A
end

mmap(file::AbstractString,
     ::Type{T}=Vector{UInt8},
     dims::NTuple{N,Integer}=(div(filesize(file),sizeof(eltype(T))),),
     offset::Integer=Int64(0); grow::Bool=true, shared::Bool=true) where {T<:Array,N} =
    open(io->mmap(io, T, dims, offset; grow=grow, shared=shared), file, isfile(file) ? "r" : "w+")::Array{eltype(T),N}

# using a length argument instead of dims
mmap(io::IO, ::Type{T}, len::Integer, offset::Integer=position(io); grow::Bool=true, shared::Bool=true) where {T<:Array} =
    mmap(io, T, (len,), offset; grow=grow, shared=shared)
mmap(file::AbstractString, ::Type{T}, len::Integer, offset::Integer=Int64(0); grow::Bool=true, shared::Bool=true) where {T<:Array} =
    open(io->mmap(io, T, (len,), offset; grow=grow, shared=shared), file, isfile(file) ? "r" : "w+")::Vector{eltype(T)}

# constructors for non-file-backed (anonymous) mmaps
mmap(::Type{T}, dims::NTuple{N,Integer}; shared::Bool=true) where {T<:Array,N} = mmap(Anonymous(), T, dims, Int64(0); shared=shared)
mmap(::Type{T}, i::Integer...; shared::Bool=true) where {T<:Array} = mmap(Anonymous(), T, convert(Tuple{Vararg{Int}},i), Int64(0); shared=shared)

"""
    mmap(io, BitArray, [dims, offset])

Create a [`BitArray`](@ref) whose values are linked to a file, using memory-mapping; it has the same
purpose, works in the same way, and has the same arguments, as [`mmap`](@ref mmap), but
the byte representation is different.

# Examples
```jldoctest
julia> using Mmap

julia> io = open("mmap.bin", "w+");

julia> B = mmap(io, BitArray, (25,30000));

julia> B[3, 4000] = true;

julia> Mmap.sync!(B);

julia> close(io);

julia> io = open("mmap.bin", "r+");

julia> C = mmap(io, BitArray, (25,30000));

julia> C[3, 4000]
true

julia> C[2, 4000]
false

julia> close(io)

julia> rm("mmap.bin")
```
This creates a 25-by-30000 `BitArray`, linked to the file associated with stream `io`.
"""
function mmap(io::IOStream, ::Type{<:BitArray}, dims::NTuple{N,Integer},
              offset::Int64=position(io); grow::Bool=true, shared::Bool=true) where N
    n = prod(dims)
    nc = Base.num_bit_chunks(n)
    chunks = mmap(io, Vector{UInt64}, (nc,), offset; grow=grow, shared=shared)
    if !isreadonly(io)
        chunks[end] &= Base._msk_end(n)
    else
        if chunks[end] != chunks[end] & Base._msk_end(n)
            throw(ArgumentError("the given file does not contain a valid BitArray of size $(join(dims, 'x')) (open with \"r+\" mode to override)"))
        end
    end
    B = BitArray{N}(undef, ntuple(i->0,Val(N))...)
    B.chunks = chunks
    B.len = n
    if N != 1
        B.dims = dims
    end
    return B
end

mmap(file::AbstractString, ::Type{T}, dims::NTuple{N,Integer}, offset::Integer=Int64(0);grow::Bool=true, shared::Bool=true) where {T<:BitArray,N} =
    open(io->mmap(io, T, dims, offset; grow=grow, shared=shared), file, isfile(file) ? "r" : "w+")::BitArray{N}

# using a length argument instead of dims
mmap(io::IO, ::Type{T}, len::Integer, offset::Integer=position(io); grow::Bool=true, shared::Bool=true) where {T<:BitArray} =
    mmap(io, T, (len,), offset; grow=grow, shared=shared)
mmap(file::AbstractString, ::Type{T}, len::Integer, offset::Integer=Int64(0); grow::Bool=true, shared::Bool=true) where {T<:BitArray} =
    open(io->mmap(io, T, (len,), offset; grow=grow, shared=shared), file, isfile(file) ? "r" : "w+")::BitVector

# constructors for non-file-backed (anonymous) mmaps
mmap(::Type{T}, dims::NTuple{N,Integer}; shared::Bool=true) where {T<:BitArray,N} = mmap(Anonymous(), T, dims, Int64(0); shared=shared)
mmap(::Type{T}, i::Integer...; shared::Bool=true) where {T<:BitArray} = mmap(Anonymous(), T, convert(Tuple{Vararg{Int}},i), Int64(0); shared=shared)

# msync flags for unix
const MS_ASYNC = 1
const MS_INVALIDATE = 2
const MS_SYNC = 4

"""
    Mmap.sync!(array)

Forces synchronization between the in-memory version of a memory-mapped `Array` or
[`BitArray`](@ref) and the on-disk version.
"""
function sync!(m::Array, flags::Integer=MS_SYNC)
    offset = rem(UInt(pointer(m)), PAGESIZE)
    ptr = pointer(m) - offset
    mmaplen = sizeof(m) + offset
    GC.@preserve m @static if Sys.isunix()
        systemerror("msync",
                    ccall(:msync, Cint, (Ptr{Cvoid}, Csize_t, Cint), ptr, mmaplen, flags) != 0)
    else
        Base.windowserror(:FlushViewOfFile,
            ccall(:FlushViewOfFile, stdcall, Cint, (Ptr{Cvoid}, Csize_t), ptr, mmaplen) == 0)
    end
end
sync!(B::BitArray, flags::Integer=MS_SYNC) = sync!(B.chunks, flags)

@static if Sys.isunix()
const MADV_NORMAL = 0
const MADV_RANDOM = 1
const MADV_SEQUENTIAL = 2
const MADV_WILLNEED = 3
const MADV_DONTNEED = 4
if Sys.islinux()
    const MADV_FREE = 8
    const MADV_REMOVE = 9
    const MADV_DONTFORK = 10
    const MADV_DOFORK = 11
    const MADV_MERGEABLE = 12
    const MADV_UNMERGEABLE = 13
    const MADV_HUGEPAGE = 14
    const MADV_NOHUGEPAGE = 15
    const MADV_DONTDUMP = 16
    const MADV_DODUMP = 17
    const MADV_WIPEONFORK = 18
    const MADV_KEEPONFORK = 19
    const MADV_COLD = 20
    const MADV_PAGEOUT = 21
    const MADV_HWPOISON = 100
    const MADV_SOFT_OFFLINE = 101
elseif Sys.isapple()
    const MADV_FREE = 5
elseif Sys.isfreebsd() || Sys.isdragonfly()
    const MADV_FREE = 5
    const MADV_NOSYNC = 6
    const MADV_AUTOSYNC = 7
    const MADV_NOCORE = 8
    const MADV_CORE = 9
    if Sys.isfreebsd()
        const MADV_PROTECT = 10
    else
        const MADV_INVAL = 10
        const MADV_SETMAP = 11
    end
elseif Sys.isopenbsd() || Sys.isnetbsd()
    const MADV_SPACEAVAIL = 5
    const MADV_FREE = 6
end

"""
    Mmap.madvise!(array, flag::Integer = Mmap.MADV_NORMAL)

Advises the kernel on the intended usage of the memory-mapped `array`, with the intent
`flag` being one of the available `MADV_*` constants.
"""
function madvise!(m::Array, flag::Integer=MADV_NORMAL)
    offset = rem(UInt(pointer(m)), PAGESIZE)
    ptr = pointer(m) - offset
    mmaplen = sizeof(m) + offset
    GC.@preserve m begin
        systemerror("madvise",
                    ccall(:madvise, Cint, (Ptr{Cvoid}, Csize_t, Cint), ptr, mmaplen, flag) != 0)
    end
end
madvise!(B::BitArray, flag::Integer=MADV_NORMAL) = madvise!(B.chunks, flag)
end # Sys.isunix()

end # module
�   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/NetworkOptions/src/NetworkOptions.jl�       module NetworkOptions

include("ca_roots.jl")
include("ssh_options.jl")
include("verify_host.jl")

function __init__()
    SYSTEM_CA_ROOTS[] = nothing
    BUNDLED_KNOWN_HOSTS_FILE[] = nothing
    empty!(ENV_HOST_PATTERN_CACHE)
end

end # module
z   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/NetworkOptions/src/ca_roots.jl�      export ca_roots, ca_roots_path

"""
    ca_roots() :: Union{Nothing, String}

The `ca_roots()` function tells the caller where, if anywhere, to find a file or
directory of PEM-encoded certificate authority roots. By default, on systems
like Windows and macOS where the built-in TLS engines know how to verify hosts
using the system's built-in certificate verification mechanism, this function
will return `nothing`. On classic UNIX systems (excluding macOS), root
certificates are typically stored in a file in `/etc`: the common places for the
current UNIX system will be searched and if one of these paths exists, it will
be returned; if none of these typical root certificate paths exist, then the
path to the set of root certificates that are bundled with Julia is returned.

The default value returned by `ca_roots()` may be overridden by setting the
`JULIA_SSL_CA_ROOTS_PATH`, `SSL_CERT_DIR`, or `SSL_CERT_FILE` environment
variables, in which case this function will always return the value of the first
of these variables that is set (whether the path exists or not). If
`JULIA_SSL_CA_ROOTS_PATH` is set to the empty string, then the other variables
are ignored (as if unset); if the other variables are set to the empty string,
they behave is if they are not set.
"""
ca_roots()::Union{Nothing,String} = _ca_roots(true)

"""
    ca_roots_path() :: String

The `ca_roots_path()` function is similar to the `ca_roots()` function except
that it always returns a path to a file or directory of PEM-encoded certificate
authority roots. When called on a system like Windows or macOS, where system
root certificates are not stored in the file system, it will currently return
the path to the set of root certificates that are bundled with Julia. (In the
future, this function may instead extract the root certificates from the system
and save them to a file whose path would be returned.)

If it is possible to configure a library that uses TLS to use the system
certificates that is generally preferable: i.e. it is better to use
`ca_roots()` which returns `nothing` to indicate that the system certs should be
used. The `ca_roots_path()` function should only be used when configuring
libraries which _require_ a path to a file or directory for root certificates.

The default value returned by `ca_roots_path()` may be overridden by setting the
`JULIA_SSL_CA_ROOTS_PATH`, `SSL_CERT_DIR`, or `SSL_CERT_FILE` environment
variables, in which case this function will always return the value of the first
of these variables that is set (whether the path exists or not). If
`JULIA_SSL_CA_ROOTS_PATH` is set to the empty string, then the other variables
are ignored (as if unset); if the other variables are set to the empty string,
they behave is if they are not set.
"""
ca_roots_path()::String = _ca_roots(false)

# NOTE: this has to be a function not a constant since the
# value of Sys.BINDIR changes from build time to run time.
bundled_ca_roots() =
    normpath(Sys.BINDIR::String, "..", "share", "julia", "cert.pem")

const LINUX_CA_ROOTS = [
    "/etc/ssl/cert.pem"                                 # Alpine Linux
    "/etc/ssl/ca-bundle.pem"                            # OpenSUSE
    "/etc/ssl/ca-certificates.pem"                      # OpenSUSE
    "/etc/ssl/certs/ca-bundle.crt"                      # Debian/Ubuntu/Gentoo etc.
    "/etc/ssl/certs/ca-certificates.crt"                # Debian/Ubuntu/Gentoo etc.
    "/etc/pki/ca-trust/extracted/pem/tls-ca-bundle.pem" # CentOS/RHEL 7
    "/etc/pki/tls/certs/ca-bundle.crt"                  # Fedora/RHEL 6
    "/etc/pki/tls/certs/ca-certificates.crt"            # Fedora/RHEL 6
    "/etc/pki/tls/cacert.pem"                           # OpenELEC
]

const BSD_CA_ROOTS = [
    "/etc/ssl/cert.pem"                                 # OpenBSD
    "/usr/local/share/certs/ca-root-nss.crt"            # FreeBSD
    "/usr/local/etc/ssl/cert.pem"                       # FreeBSD
]

const SYSTEM_CA_ROOTS_LOCK = ReentrantLock()
const SYSTEM_CA_ROOTS = Ref{Union{Nothing, String}}(nothing)

const BEGIN_CERT_REGULAR = "-----BEGIN CERTIFICATE-----"
const BEGIN_CERT_OPENSSL = "-----BEGIN TRUSTED CERTIFICATE-----"
const OPENSSL_WARNING = """
NetworkOptions could only find OpenSSL-specific TLS certificates which cannot be used by MbedTLS. Please open an issue at https://github.com/JuliaLang/NetworkOptions.jl/issues with details about your system, especially where generic non-OpenSSL certificates can be found. See https://stackoverflow.com/questions/55447752/what-does-begin-trusted-certificate-in-a-certificate-mean for more details.
""" |> split |> text -> join(text, " ")

function system_ca_roots()
    lock(SYSTEM_CA_ROOTS_LOCK) do
        SYSTEM_CA_ROOTS[] !== nothing && return # from lock()
        search_path = Sys.islinux() ? LINUX_CA_ROOTS :
            Sys.isbsd() && !Sys.isapple() ? BSD_CA_ROOTS : String[]
        openssl_only = false
        for path in search_path
            ispath(path) || continue
            for line in eachline(path)
                if line == BEGIN_CERT_REGULAR
                    SYSTEM_CA_ROOTS[] = path
                    return # from lock()
                elseif line == BEGIN_CERT_OPENSSL
                    openssl_only = true
                end
            end
        end
        # warn if we:
        #  1. did not find any regular certs
        #  2. did find OpenSSL-only certs
        openssl_only && @warn OPENSSL_WARNING
        # TODO: extract system certs on Windows & macOS
        SYSTEM_CA_ROOTS[] = bundled_ca_roots()
    end
    return SYSTEM_CA_ROOTS[]
end

const CA_ROOTS_VARS = [
    "JULIA_SSL_CA_ROOTS_PATH"
    "SSL_CERT_DIR"
    "SSL_CERT_FILE"
]

function _ca_roots(allow_nothing::Bool)
    for var in CA_ROOTS_VARS
        path = get(ENV, var, nothing)
        if path == "" && startswith(var, "JULIA_")
            break # ignore other vars
        end
        if !isempty(something(path, ""))
            return path
        end
    end
    if Sys.iswindows() || Sys.isapple()
        allow_nothing && return # use system certs
    end
    return system_ca_roots()
end
}   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/NetworkOptions/src/ssh_options.jl�      export
    ssh_dir,
    ssh_key_pass,
    ssh_key_name,
    ssh_key_path,
    ssh_pub_key_path,
    ssh_known_hosts_files,
    ssh_known_hosts_file

"""
    ssh_dir() :: String

The `ssh_dir()` function returns the location of the directory where the `ssh`
program keeps/looks for configuration files. By default this is `~/.ssh` but
this can be overridden by setting the environment variable `SSH_DIR`.
"""
ssh_dir() = get(ENV, "SSH_DIR", joinpath(homedir(), ".ssh"))

"""
    ssh_key_pass() :: String

The `ssh_key_pass()` function returns the value of the environment variable
`SSH_KEY_PASS` if it is set or `nothing` if it is not set. In the future, this
may be able to find a password by other means, such as secure system storage, so
packages that need a password to decrypt an SSH private key should use this API
instead of directly checking the environment variable so that they gain such
capabilities automatically when they are added.
"""
ssh_key_pass() = get(ENV, "SSH_KEY_PASS", nothing)

"""
    ssh_key_name() :: String

The `ssh_key_name()` function returns the base name of key files that SSH should
use for when establishing a connection. There is usually no reason that this
function should be called directly and libraries should generally use the
`ssh_key_path` and `ssh_pub_key_path` functions to get full paths. If the
environment variable `SSH_KEY_NAME` is set then this function returns that;
otherwise it returns `id_rsa` by default.
"""
ssh_key_name() = get(ENV, "SSH_KEY_NAME", "id_rsa")

"""
    ssh_key_path() :: String

The `ssh_key_path()` function returns the path of the SSH private key file that
should be used for SSH connections. If the `SSH_KEY_PATH` environment variable
is set then it will return that value. Otherwise it defaults to returning

    joinpath(ssh_dir(), ssh_key_name())

This default value in turn depends on the `SSH_DIR` and `SSH_KEY_NAME`
environment variables.
"""
function ssh_key_path()
    key_path = get(ENV, "SSH_KEY_PATH", "")
    !isempty(key_path) && return key_path
    return joinpath(ssh_dir(), ssh_key_name())
end

"""
    ssh_pub_key_path() :: String

The `ssh_pub_key_path()` function returns the path of the SSH public key file
that should be used for SSH connections. If the `SSH_PUB_KEY_PATH` environment
variable is set then it will return that value. If that isn't set but
`SSH_KEY_PATH` is set, it will return that path with the `.pub` suffix appended.
If neither is set, it defaults to returning

    joinpath(ssh_dir(), ssh_key_name() * ".pub")

This default value in turn depends on the `SSH_DIR` and `SSH_KEY_NAME`
environment variables.
"""
function ssh_pub_key_path()
    pub_key_path = get(ENV, "SSH_PUB_KEY_PATH", "")
    !isempty(pub_key_path) && return pub_key_path
    key_path = get(ENV, "SSH_KEY_PATH", "")
    !isempty(key_path) && return "$key_path.pub"
    return joinpath(ssh_dir(), ssh_key_name() * ".pub")
end

"""
    ssh_known_hosts_files() :: Vector{String}

The `ssh_known_hosts_files()` function returns a vector of paths of SSH known
hosts files that should be used when establishing the identities of remote
servers for SSH connections. By default this function returns

    [joinpath(ssh_dir(), "known_hosts"), bundled_known_hosts]

where `bundled_known_hosts` is the path of a copy of a known hosts file that is
bundled with this package (containing known hosts keys for `github.com` and
`gitlab.com`). If the environment variable `SSH_KNOWN_HOSTS_FILES` is set,
however, then its value is split into paths on the `:` character (or on `;` on
Windows) and this vector of paths is returned instead. If any component of this
vector is empty, it is expanded to the default known hosts paths.

Packages that use `ssh_known_hosts_files()` should ideally look for matching
entries by comparing the host name and key types, considering the first entry in
any of the files which matches to be the definitive identity of the host. If the
caller cannot compare the key type (e.g. because it has been hashes) then it
must approximate the above algorithm by looking for all matching entries for a
host in each file: if a file has any entries for a host then one of them must
match; the caller should only continue to search further known hosts files if
there are no entries for the host in question in an earlier file.
"""
function ssh_known_hosts_files()
    bundled = bundled_known_hosts()
    default = joinpath(ssh_dir(), "known_hosts")
    value = get(ENV, "SSH_KNOWN_HOSTS_FILES", nothing)
    value === nothing && return [default, bundled]
    isempty(value) && return String[]
    paths = String[]
    for path in split(value, Sys.iswindows() ? ';' : ':')
        if !isempty(path)
            path in paths || push!(paths, path)
        else
            default in paths || push!(paths, default)
            bundled in paths || push!(paths, bundled)
        end
    end
    return paths
end

"""
    ssh_known_hosts_file() :: String

The `ssh_known_hosts_file()` function returns a single path of an SSH known
hosts file that should be used when establishing the identities of remote
servers for SSH connections. It returns the first path returned by
`ssh_known_hosts_files` that actually exists. Callers who can look in more than
one known hosts file should use `ssh_known_hosts_files` instead and look for
host matches in all the files returned as described in that function's docs.
"""
function ssh_known_hosts_file()
    files = ssh_known_hosts_files()
    for file in files
        ispath(file) && return file
    end
    return !isempty(files) ? files[1] :
        isfile("/dev/null") ? "/dev/null" : tempname()
end

## helper functions

const BUNDLED_KNOWN_HOSTS_LOCK = ReentrantLock()
const BUNDLED_KNOWN_HOSTS_FILE = Ref{Union{Nothing, String}}(nothing)

function bundled_known_hosts()
    lock(BUNDLED_KNOWN_HOSTS_LOCK) do
        file = BUNDLED_KNOWN_HOSTS_FILE[]
        if file === nothing
            file, io = mktemp()
            BUNDLED_KNOWN_HOSTS_FILE[] = file
            write(io, BUNDLED_KNOWN_HOSTS)
            close(io)
        end
        return file::String
    end
end

const BUNDLED_KNOWN_HOSTS = """
github.com ecdsa-sha2-nistp256 AAAAE2VjZHNhLXNoYTItbmlzdHAyNTYAAAAIbmlzdHAyNTYAAABBBEmKSENjQEezOmxkZMy7opKgwFB9nkt5YRrYMjNuG5N87uRgg6CLrbo5wAdT/y6v0mKV0U2w0WZ2YB/++Tpockg=
github.com ssh-ed25519 AAAAC3NzaC1lZDI1NTE5AAAAIOMqqnkVzrm0SdG6UOoqKLsabgH5C9okWi0dh2l9GKJl
github.com ssh-rsa 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
gitlab.com ecdsa-sha2-nistp256 AAAAE2VjZHNhLXNoYTItbmlzdHAyNTYAAAAIbmlzdHAyNTYAAABBBFSMqzJeV9rUzU4kWitGjeR4PWSa29SPqJ1fVkhtj3Hw9xjLVXVYrU9QlYWrOLXBpQ6KWjbjTDTdDkoohFzgbEY=
gitlab.com ssh-ed25519 AAAAC3NzaC1lZDI1NTE5AAAAIAfuCHKVTjquxvt6CM6tdG4SLp1Btn/nOeHHE5UOzRdf
gitlab.com ssh-rsa AAAAB3NzaC1yc2EAAAADAQABAAABAQCsj2bNKTBSpIYDEGk9KxsGh3mySTRgMtXL583qmBpzeQ+jqCMRgBqB98u3z++J1sKlXHWfM9dyhSevkMwSbhoR8XIq/U0tCNyokEi/ueaBMCvbcTHhO7FcwzY92WK4Yt0aGROY5qX2UKSeOvuP4D6TPqKF1onrSzH9bx9XUf2lEdWT/ia1NEKjunUqu1xOB/StKDHMoX4/OKyIzuS0q/T1zOATthvasJFoPrAjkohTyaDUz2LN5JoH839hViyEG82yB+MjcFV5MU3N1l1QL3cVUCh93xSaua1N85qivl+siMkPGbO5xR/En4iEY6K2XPASUEMaieWVNTRCtJ4S8H+9
"""
}   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/NetworkOptions/src/verify_host.jlD      export verify_host

"""
    verify_host(url::AbstractString, [transport::AbstractString]) :: Bool

The `verify_host` function tells the caller whether the identity of a host
should be verified when communicating over secure transports like TLS or SSH.
The `url` argument may be:

1. a proper URL staring with `proto://`
2. an `ssh`-style bare host name or host name prefixed with `user@`
3. an `scp`-style host as above, followed by `:` and a path location

In each case the host name part is parsed out and the decision about whether to
verify or not is made based solely on the host name, not anything else about the
input URL. In particular, the protocol of the URL does not matter (more below).

The `transport` argument indicates the kind of transport that the query is
about. The currently known values are `SSL`/`ssl` (alias `TLS`/`tls`) and `SSH`/`ssh`.
If the transport is omitted, the query will return `true` only if the host name should
not be verified regardless of transport.

The host name is matched against the host patterns in the relevant environment
variables depending on whether `transport` is supplied and what its value is:

- `JULIA_NO_VERIFY_HOSTS` — hosts that should not be verified for any transport
- `JULIA_SSL_NO_VERIFY_HOSTS` — hosts that should not be verified for SSL/TLS
- `JULIA_SSH_NO_VERIFY_HOSTS` — hosts that should not be verified for SSH
- `JULIA_ALWAYS_VERIFY_HOSTS` — hosts that should always be verified

The values of each of these variables is a comma-separated list of host name
patterns with the following syntax — each pattern is split on `.` into parts and
each part must one of:

1. A literal domain name component consisting of one or more ASCII letter,
   digit, hyphen or underscore (technically not part of a legal host name, but
   sometimes used). A literal domain name component matches only itself.
2. A `**`, which matches zero or more domain name components.
3. A `*`, which match any one domain name component.

When matching a host name against a pattern list in one of these variables, the
host name is split on `.` into components and that sequence of words is matched
against the pattern: a literal pattern matches exactly one host name component
with that value; a `*` pattern matches exactly one host name component with any
value; a `**` pattern matches any number of host name components. For example:

- `**` matches any host name
- `**.org` matches any host name in the `.org` top-level domain
- `example.com` matches only the exact host name `example.com`
- `*.example.com` matches `api.example.com` but not `example.com` or
  `v1.api.example.com`
- `**.example.com` matches any domain under `example.com`, including
  `example.com` itself, `api.example.com` and `v1.api.example.com`
"""
function verify_host(
    url :: AbstractString,
    tr :: Union{AbstractString, Nothing} = nothing,
)
    host = url_host(url)
    env_host_pattern_match("JULIA_ALWAYS_VERIFY_HOSTS", host) && return true
    env_host_pattern_match("JULIA_NO_VERIFY_HOSTS", host) && return false
    tr === nothing && return true
    return if tr == "SSL" || tr == "ssl" || tr == "TLS" || tr == "tls"
        !env_host_pattern_match("JULIA_SSL_NO_VERIFY_HOSTS", host)
    elseif tr == "SSH" || tr == "ssh"
        !env_host_pattern_match("JULIA_SSH_NO_VERIFY_HOSTS", host)
    else
        true # do verify
    end
end

function url_host(url::AbstractString)
    m = match(r"^(?:[a-z]+)://(?:[^@/]+@)?([-\w\.]+)"ai, url)
    m !== nothing && return m.captures[1]
    m = match(r"^(?:[-\w\.]+@)?([-\w\.]+)(?:$|:)"a, url)
    m !== nothing && return m.captures[1]
    return nothing # couldn't parse
end

const MATCH_ANY_RE = r""
const MATCH_NONE_RE = r"$.^"

# TODO: What to do when `env_host_pattern_regex` returns `nothing`?
env_host_pattern_match(var::AbstractString, host::AbstractString) =
    occursin(env_host_pattern_regex(var)::Regex, host)
env_host_pattern_match(var::AbstractString, host::Nothing) =
    env_host_pattern_regex(var) === MATCH_ANY_RE

const ENV_HOST_PATTERN_LOCK = ReentrantLock()
const ENV_HOST_PATTERN_CACHE = Dict{String,Tuple{String,Regex}}()

function env_host_pattern_regex(var::AbstractString)
    lock(ENV_HOST_PATTERN_LOCK) do
        value = get(ENV, var, nothing)
        if value === nothing
            delete!(ENV_HOST_PATTERN_CACHE, var)
            return MATCH_NONE_RE
        end
        old_value, regex = get(ENV_HOST_PATTERN_CACHE, var, (nothing, nothing))
        old_value == value && return regex
        regex = host_pattern_regex(value, var)
        ENV_HOST_PATTERN_CACHE[var] = (value, regex)
        return regex
    end
end

if !@isdefined(contains)
    contains(needle) = haystack -> occursin(needle, haystack)
end

function host_pattern_regex(value::AbstractString, var::AbstractString="")
    match_any = false
    patterns = Vector{String}[]
    for pattern in split(value, r"\s*,\s*", keepempty=false)
        match_any |= pattern == "**"
        parts = split(pattern, '.')
        # emit warning but ignore any pattern we don't recognize;
        # this allows adding syntax without breaking old versions
        if !all(contains(r"^([-\w]+|\*\*?)$"a), parts)
            in = isempty(var) ? "" : " in ENV[$(repr(var))]"
            @warn("bad host pattern$in: $(repr(pattern))")
            continue
        end
        push!(patterns, parts)
    end
    match_any && return MATCH_ANY_RE
    isempty(patterns) && return MATCH_NONE_RE
    regex = ""
    for parts in patterns
        re = ""
        for (i, part) in enumerate(parts)
            re *= if i < length(parts)
                part == "*"  ? "[-\\w]+\\." :
                part == "**" ? "(?:[-\\w]+\\.)*" : "$part\\."
            else
                part == "*"  ? "[-\\w]+" :
                part == "**" ? "(?:[-\\w]+\\.)*[-\\w]+" : part
            end
        end
        regex = isempty(regex) ? re : "$regex|$re"
    end
    return Regex("^(?:$regex)\$", "ai")
end
j   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/SHA/src/SHA.jl      """
    SHA

The SHA module provides hashing functionality for SHA1, SHA2 and SHA3 algorithms.

They are implemented as both pure functions for hashing single pieces of data,
or a stateful context which can be updated with the `update!` function and
finalized with `digest!`.

```julia-repl
julia> sha1(b"some data")
20-element Vector{UInt8}:
 0xba
 0xf3
    ⋮
 0xe3
 0x56


julia> ctx = SHA1_CTX()
SHA1 hash state

julia> update!(ctx, b"some data")
0x0000000000000009

julia> digest!(ctx)
20-element Vector{UInt8}:
 0xba
 0xf3
    ⋮
 0xe3
 0x56
"""
module SHA

# Export convenience functions, context types, update!() and digest!() functions
export sha1, SHA1_CTX, update!, digest!
export sha224, sha256, sha384, sha512
export sha2_224, sha2_256, sha2_384, sha2_512
export sha3_224, sha3_256, sha3_384, sha3_512
export SHA224_CTX, SHA256_CTX, SHA384_CTX, SHA512_CTX
export SHA2_224_CTX, SHA2_256_CTX, SHA2_384_CTX, SHA2_512_CTX
export SHA3_224_CTX, SHA3_256_CTX, SHA3_384_CTX, SHA3_512_CTX
export HMAC_CTX, hmac_sha1
export hmac_sha224, hmac_sha256, hmac_sha384, hmac_sha512
export hmac_sha2_224, hmac_sha2_256, hmac_sha2_384, hmac_sha2_512
export hmac_sha3_224, hmac_sha3_256, hmac_sha3_384, hmac_sha3_512

# data to be hashed:
const AbstractBytes = Union{AbstractVector{UInt8},NTuple{N,UInt8} where N}

include("constants.jl")
include("types.jl")
include("base_functions.jl")
include("sha1.jl")
include("sha2.jl")
include("sha3.jl")
include("common.jl")
include("hmac.jl")

# Create data types and convenience functions for each hash implemented
for (f, ctx) in [(:sha1, :SHA1_CTX),
                 (:sha224, :SHA224_CTX),
                 (:sha256, :SHA256_CTX),
                 (:sha384, :SHA384_CTX),
                 (:sha512, :SHA512_CTX),
                 (:sha2_224, :SHA2_224_CTX),
                 (:sha2_256, :SHA2_256_CTX),
                 (:sha2_384, :SHA2_384_CTX),
                 (:sha2_512, :SHA2_512_CTX),
                 (:sha3_224, :SHA3_224_CTX),
                 (:sha3_256, :SHA3_256_CTX),
                 (:sha3_384, :SHA3_384_CTX),
                 (:sha3_512, :SHA3_512_CTX),]
    g = Symbol(:hmac_, f)

    @eval begin
        # Our basic function is to process arrays of bytes
        """
            $($f)(data)

        Hash data using the `$($f)` algorithm and return the resulting digest.
        See also [`$($ctx)`](@ref).
        """
        function $f(data::AbstractBytes)
            ctx = $ctx()
            update!(ctx, data)
            return digest!(ctx)
        end

        """
            $($g)(key, data)

        Hash data using the `$($f)` algorithm using the passed key.
        See also [`HMAC_CTX`](@ref).
        """
        function $g(key::Vector{UInt8}, data::AbstractBytes)
            ctx = HMAC_CTX($ctx(), key)
            update!(ctx, data)
            return digest!(ctx)
        end

        # AbstractStrings are a pretty handy thing to be able to crunch through
        $f(str::AbstractString) = $f(String(str)) # always crunch UTF-8 repr
        $f(str::String) = $f(codeunits(str))
        $g(key::Vector{UInt8}, str::AbstractString) = $g(key, String(str))
        $g(key::Vector{UInt8}, str::String) = $g(key, codeunits(str))

        """
            $($f)(io::IO)

        Hash data from io using `$($f)` algorithm.
        """
        function $f(io::IO, chunk_size=4*1024)
            ctx = $ctx()
            buff = Vector{UInt8}(undef, chunk_size)
            while !eof(io)
                num_read = readbytes!(io, buff)
                update!(ctx, buff, num_read)
            end
            return digest!(ctx)
        end

        """
            $($g)(key, io::IO)

        Hash data from `io` with the passed key using `$($f)` algorithm.
        """
        function $g(key::Vector{UInt8}, io::IO, chunk_size=4*1024)
            ctx = HMAC_CTX($ctx(), key)
            buff = Vector{UInt8}(undef, chunk_size)
            while !eof(io)
                num_read = readbytes!(io, buff)
                update!(ctx, buff, num_read)
            end
            return digest!(ctx)
        end
    end
end

end #module SHA
p   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/SHA/src/constants.jl�      # SHA initial hash values and constants

# Hash constant words K for SHA1
const K1 = UInt32[
    0x5a827999, 0x6ed9eba1, 0x8f1bbcdc, 0xca62c1d6
]

# Initial hash value H for SHA1
const SHA1_initial_hash_value = UInt32[
    0x67452301, 0xefcdab89, 0x98badcfe, 0x10325476, 0xc3d2e1f0
]


# Hash constant words K for SHA-256:
const K256 = (
    0x428a2f98, 0x71374491, 0xb5c0fbcf, 0xe9b5dba5,
    0x3956c25b, 0x59f111f1, 0x923f82a4, 0xab1c5ed5,
    0xd807aa98, 0x12835b01, 0x243185be, 0x550c7dc3,
    0x72be5d74, 0x80deb1fe, 0x9bdc06a7, 0xc19bf174,
    0xe49b69c1, 0xefbe4786, 0x0fc19dc6, 0x240ca1cc,
    0x2de92c6f, 0x4a7484aa, 0x5cb0a9dc, 0x76f988da,
    0x983e5152, 0xa831c66d, 0xb00327c8, 0xbf597fc7,
    0xc6e00bf3, 0xd5a79147, 0x06ca6351, 0x14292967,
    0x27b70a85, 0x2e1b2138, 0x4d2c6dfc, 0x53380d13,
    0x650a7354, 0x766a0abb, 0x81c2c92e, 0x92722c85,
    0xa2bfe8a1, 0xa81a664b, 0xc24b8b70, 0xc76c51a3,
    0xd192e819, 0xd6990624, 0xf40e3585, 0x106aa070,
    0x19a4c116, 0x1e376c08, 0x2748774c, 0x34b0bcb5,
    0x391c0cb3, 0x4ed8aa4a, 0x5b9cca4f, 0x682e6ff3,
    0x748f82ee, 0x78a5636f, 0x84c87814, 0x8cc70208,
    0x90befffa, 0xa4506ceb, 0xbef9a3f7, 0xc67178f2
)

# Initial hash value H for SHA-224:
const SHA2_224_initial_hash_value = UInt32[
    0xc1059ed8, 0x367cd507, 0x3070dd17, 0xf70e5939,
    0xffc00b31, 0x68581511, 0x64f98fa7, 0xbefa4fa4
]


const SHA2_256_initial_hash_value = UInt32[
    0x6a09e667, 0xbb67ae85, 0x3c6ef372, 0xa54ff53a,
    0x510e527f, 0x9b05688c, 0x1f83d9ab, 0x5be0cd19
]

# Hash constant words K for SHA-384 and SHA-512:
const K512 = (
    0x428a2f98d728ae22, 0x7137449123ef65cd,
    0xb5c0fbcfec4d3b2f, 0xe9b5dba58189dbbc,
    0x3956c25bf348b538, 0x59f111f1b605d019,
    0x923f82a4af194f9b, 0xab1c5ed5da6d8118,
    0xd807aa98a3030242, 0x12835b0145706fbe,
    0x243185be4ee4b28c, 0x550c7dc3d5ffb4e2,
    0x72be5d74f27b896f, 0x80deb1fe3b1696b1,
    0x9bdc06a725c71235, 0xc19bf174cf692694,
    0xe49b69c19ef14ad2, 0xefbe4786384f25e3,
    0x0fc19dc68b8cd5b5, 0x240ca1cc77ac9c65,
    0x2de92c6f592b0275, 0x4a7484aa6ea6e483,
    0x5cb0a9dcbd41fbd4, 0x76f988da831153b5,
    0x983e5152ee66dfab, 0xa831c66d2db43210,
    0xb00327c898fb213f, 0xbf597fc7beef0ee4,
    0xc6e00bf33da88fc2, 0xd5a79147930aa725,
    0x06ca6351e003826f, 0x142929670a0e6e70,
    0x27b70a8546d22ffc, 0x2e1b21385c26c926,
    0x4d2c6dfc5ac42aed, 0x53380d139d95b3df,
    0x650a73548baf63de, 0x766a0abb3c77b2a8,
    0x81c2c92e47edaee6, 0x92722c851482353b,
    0xa2bfe8a14cf10364, 0xa81a664bbc423001,
    0xc24b8b70d0f89791, 0xc76c51a30654be30,
    0xd192e819d6ef5218, 0xd69906245565a910,
    0xf40e35855771202a, 0x106aa07032bbd1b8,
    0x19a4c116b8d2d0c8, 0x1e376c085141ab53,
    0x2748774cdf8eeb99, 0x34b0bcb5e19b48a8,
    0x391c0cb3c5c95a63, 0x4ed8aa4ae3418acb,
    0x5b9cca4f7763e373, 0x682e6ff3d6b2b8a3,
    0x748f82ee5defb2fc, 0x78a5636f43172f60,
    0x84c87814a1f0ab72, 0x8cc702081a6439ec,
    0x90befffa23631e28, 0xa4506cebde82bde9,
    0xbef9a3f7b2c67915, 0xc67178f2e372532b,
    0xca273eceea26619c, 0xd186b8c721c0c207,
    0xeada7dd6cde0eb1e, 0xf57d4f7fee6ed178,
    0x06f067aa72176fba, 0x0a637dc5a2c898a6,
    0x113f9804bef90dae, 0x1b710b35131c471b,
    0x28db77f523047d84, 0x32caab7b40c72493,
    0x3c9ebe0a15c9bebc, 0x431d67c49c100d4c,
    0x4cc5d4becb3e42b6, 0x597f299cfc657e2a,
    0x5fcb6fab3ad6faec, 0x6c44198c4a475817
)

# Initial hash value H for SHA-384
const SHA2_384_initial_hash_value = UInt64[
    0xcbbb9d5dc1059ed8, 0x629a292a367cd507,
    0x9159015a3070dd17, 0x152fecd8f70e5939,
    0x67332667ffc00b31, 0x8eb44a8768581511,
    0xdb0c2e0d64f98fa7, 0x47b5481dbefa4fa4
]

# Initial hash value H for SHA-512
const SHA2_512_initial_hash_value = UInt64[
    0x6a09e667f3bcc908, 0xbb67ae8584caa73b,
    0x3c6ef372fe94f82b, 0xa54ff53a5f1d36f1,
    0x510e527fade682d1, 0x9b05688c2b3e6c1f,
    0x1f83d9abfb41bd6b, 0x5be0cd19137e2179
]

# Round constants for SHA3 rounds
const SHA3_ROUND_CONSTS = UInt64[
    0x0000000000000001, 0x0000000000008082, 0x800000000000808a,
    0x8000000080008000, 0x000000000000808b, 0x0000000080000001,
    0x8000000080008081, 0x8000000000008009, 0x000000000000008a,
    0x0000000000000088, 0x0000000080008009, 0x000000008000000a,
    0x000000008000808b, 0x800000000000008b, 0x8000000000008089,
    0x8000000000008003, 0x8000000000008002, 0x8000000000000080,
    0x000000000000800a, 0x800000008000000a, 0x8000000080008081,
    0x8000000000008080, 0x0000000080000001, 0x8000000080008008
]

# Rotation constants for SHA3 rounds
const SHA3_ROTC = UInt64[
    1,  3,  6,  10, 15, 21, 28, 36, 45, 55, 2,  14,
    27, 41, 56, 8,  25, 43, 62, 18, 39, 61, 20, 44
]

# Permutation indices for SHA3 rounds (+1'ed so as to work with julia's 1-based indexing)
const SHA3_PILN = Int[
    11, 8,  12, 18, 19, 4, 6,  17, 9,  22, 25, 5,
    16, 24, 20, 14, 13, 3, 21, 15, 23, 10,  7,  2
]
l   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/SHA/src/types.jl�      # Type hierarchy to aid in splitting up of SHA2 algorithms
# as SHA224/256 are similar, and SHA-384/512 are similar
abstract type SHA_CTX end
abstract type SHA2_CTX <: SHA_CTX end
abstract type SHA3_CTX <: SHA_CTX end
import Base: copy

# We derive SHA1_CTX straight from SHA_CTX since it doesn't have a
# family of types like SHA2 or SHA3 do
mutable struct SHA1_CTX <: SHA_CTX
    state::Array{UInt32,1}
    bytecount::UInt64
    buffer::Array{UInt8,1}
    W::Array{UInt32,1}
    used::Bool
end

# SHA2 224/256/384/512-bit Context Structures
mutable struct SHA2_224_CTX <: SHA2_CTX
    state::Array{UInt32,1}
    bytecount::UInt64
    buffer::Array{UInt8,1}
    used::Bool
end

mutable struct SHA2_256_CTX <: SHA2_CTX
    state::Array{UInt32,1}
    bytecount::UInt64
    buffer::Array{UInt8,1}
    used::Bool
end

mutable struct SHA2_384_CTX <: SHA2_CTX
    state::Array{UInt64,1}
    bytecount::UInt128
    buffer::Array{UInt8,1}
    used::Bool
end

mutable struct SHA2_512_CTX <: SHA2_CTX
    state::Array{UInt64,1}
    bytecount::UInt128
    buffer::Array{UInt8,1}
    used::Bool
end

function Base.getproperty(ctx::SHA2_CTX, fieldname::Symbol)
    if fieldname === :state
        return getfield(ctx, :state)::Union{Vector{UInt32},Vector{UInt64}}
    elseif fieldname === :bytecount
        return getfield(ctx, :bytecount)::Union{UInt64,UInt128}
    elseif fieldname === :buffer
        return getfield(ctx, :buffer)::Vector{UInt8}
    elseif fieldname === :W
        return getfield(ctx, :W)::Vector{UInt32}
    elseif fieldname === :used
        return getfield(ctx, :used)::Bool
    else
        error("SHA2_CTX has no field ", fieldname)
    end
end


# Typealias common nicknames for SHA2 family of functions
const SHA224_CTX = SHA2_224_CTX
const SHA256_CTX = SHA2_256_CTX
const SHA384_CTX = SHA2_384_CTX
const SHA512_CTX = SHA2_512_CTX


# SHA3 224/256/384/512-bit context structures
mutable struct SHA3_224_CTX <: SHA3_CTX
    state::Array{UInt64,1}
    bytecount::UInt128
    buffer::Array{UInt8,1}
    bc::Array{UInt64,1}
    used::Bool
end
mutable struct SHA3_256_CTX <: SHA3_CTX
    state::Array{UInt64,1}
    bytecount::UInt128
    buffer::Array{UInt8,1}
    bc::Array{UInt64,1}
    used::Bool
end
mutable struct SHA3_384_CTX <: SHA3_CTX
    state::Array{UInt64,1}
    bytecount::UInt128
    buffer::Array{UInt8,1}
    bc::Array{UInt64,1}
    used::Bool
end
mutable struct SHA3_512_CTX <: SHA3_CTX
    state::Array{UInt64,1}
    bytecount::UInt128
    buffer::Array{UInt8,1}
    bc::Array{UInt64,1}
    used::Bool
end

function Base.getproperty(ctx::SHA3_CTX, fieldname::Symbol)
    if fieldname === :state
        return getfield(ctx, :state)::Vector{UInt64}
    elseif fieldname === :bytecount
        return getfield(ctx, :bytecount)::UInt128
    elseif fieldname === :buffer
        return getfield(ctx, :buffer)::Vector{UInt8}
    elseif fieldname === :bc
        return getfield(ctx, :bc)::Vector{UInt64}
    elseif fieldname === :used
        return getfield(ctx, :used)::Bool
    else
        error("type ", typeof(ctx), " has no field ", fieldname)
    end
end

# Define constants via functions so as not to bloat context objects.  Yay dispatch!

# Digest lengths for SHA1, SHA2 and SHA3.  This is easy to figure out from the typename
digestlen(::Type{SHA1_CTX}) = 20
digestlen(::Type{SHA2_224_CTX}) = 28
digestlen(::Type{SHA3_224_CTX}) = 28
digestlen(::Type{SHA2_256_CTX}) = 32
digestlen(::Type{SHA3_256_CTX}) = 32
digestlen(::Type{SHA2_384_CTX}) = 48
digestlen(::Type{SHA3_384_CTX}) = 48
digestlen(::Type{SHA2_512_CTX}) = 64
digestlen(::Type{SHA3_512_CTX}) = 64

# SHA1 and SHA2 have differing element types for the internal state objects
state_type(::Type{SHA1_CTX}) = UInt32
state_type(::Type{SHA2_224_CTX}) = UInt32
state_type(::Type{SHA2_256_CTX}) = UInt32
state_type(::Type{SHA2_384_CTX}) = UInt64
state_type(::Type{SHA2_512_CTX}) = UInt64
state_type(::Type{SHA3_CTX}) = UInt64

# blocklen is the number of bytes of data processed by the transform!() function at once
blocklen(::Type{SHA1_CTX}) = UInt64(64)
blocklen(::Type{SHA2_224_CTX}) = UInt64(64)
blocklen(::Type{SHA2_256_CTX}) = UInt64(64)
blocklen(::Type{SHA2_384_CTX}) = UInt64(128)
blocklen(::Type{SHA2_512_CTX}) = UInt64(128)

blocklen(::Type{SHA3_224_CTX}) = UInt64(25*8 - 2*digestlen(SHA3_224_CTX))
blocklen(::Type{SHA3_256_CTX}) = UInt64(25*8 - 2*digestlen(SHA3_256_CTX))
blocklen(::Type{SHA3_384_CTX}) = UInt64(25*8 - 2*digestlen(SHA3_384_CTX))
blocklen(::Type{SHA3_512_CTX}) = UInt64(25*8 - 2*digestlen(SHA3_512_CTX))


# short_blocklen is the size of a block minus the width of bytecount
short_blocklen(::Type{T}) where {T<:SHA_CTX} = blocklen(T) - 2*sizeof(state_type(T))

# Once the "blocklen" methods are defined, we can define our outer constructors for SHA types:

"""
    SHA2_224_CTX()

Construct an empty SHA2_224 context.
"""
SHA2_224_CTX() = SHA2_224_CTX(copy(SHA2_224_initial_hash_value), 0, zeros(UInt8, blocklen(SHA2_224_CTX)), false)
"""
    SHA2_256_CTX()

Construct an empty SHA2_256 context.
"""
SHA2_256_CTX() = SHA2_256_CTX(copy(SHA2_256_initial_hash_value), 0, zeros(UInt8, blocklen(SHA2_256_CTX)), false)
"""
    SHA2_384()

Construct an empty SHA2_384 context.
"""
SHA2_384_CTX() = SHA2_384_CTX(copy(SHA2_384_initial_hash_value), 0, zeros(UInt8, blocklen(SHA2_384_CTX)), false)
"""
    SHA2_512_CTX()

Construct an empty SHA2_512 context.
"""
SHA2_512_CTX() = SHA2_512_CTX(copy(SHA2_512_initial_hash_value), 0, zeros(UInt8, blocklen(SHA2_512_CTX)), false)

"""
    SHA3_224_CTX()

Construct an empty SHA3_224 context.
"""
SHA3_224_CTX() = SHA3_224_CTX(zeros(UInt64, 25), 0, zeros(UInt8, blocklen(SHA3_224_CTX)), Vector{UInt64}(undef, 5), false)
"""
    SHA3_256_CTX()

Construct an empty SHA3_256 context.
"""
SHA3_256_CTX() = SHA3_256_CTX(zeros(UInt64, 25), 0, zeros(UInt8, blocklen(SHA3_256_CTX)), Vector{UInt64}(undef, 5), false)
"""
    SHA3_384_CTX()

Construct an empty SHA3_384 context.
"""
SHA3_384_CTX() = SHA3_384_CTX(zeros(UInt64, 25), 0, zeros(UInt8, blocklen(SHA3_384_CTX)), Vector{UInt64}(undef, 5), false)
"""
    SHA3_512_CTX()

Construct an empty SHA3_512 context.
"""
SHA3_512_CTX() = SHA3_512_CTX(zeros(UInt64, 25), 0, zeros(UInt8, blocklen(SHA3_512_CTX)), Vector{UInt64}(undef, 5), false)

# Nickname'd outer constructor methods for SHA2
const SHA224_CTX = SHA2_224_CTX
const SHA256_CTX = SHA2_256_CTX
const SHA384_CTX = SHA2_384_CTX
const SHA512_CTX = SHA2_512_CTX

# SHA1 is special; he needs extra workspace
"""
    SHA1_CTX()

Construct an empty SHA1 context.
"""
SHA1_CTX() = SHA1_CTX(copy(SHA1_initial_hash_value), 0, zeros(UInt8, blocklen(SHA1_CTX)), Vector{UInt32}(undef, 80), false)


# Copy functions
copy(ctx::T) where {T<:SHA1_CTX} = T(copy(ctx.state), ctx.bytecount, copy(ctx.buffer), copy(ctx.W), ctx.used)
copy(ctx::T) where {T<:SHA2_CTX} = T(copy(ctx.state), ctx.bytecount, copy(ctx.buffer), ctx.used)
copy(ctx::T) where {T<:SHA3_CTX} = T(copy(ctx.state), ctx.bytecount, copy(ctx.buffer), Vector{UInt64}(undef, 5), ctx.used)


# Make printing these types a little friendlier
import Base.show
show(io::IO, ::SHA1_CTX) = print(io, "SHA1 hash state")
show(io::IO, ::SHA2_224_CTX) = print(io, "SHA2 224-bit hash state")
show(io::IO, ::SHA2_256_CTX) = print(io, "SHA2 256-bit hash state")
show(io::IO, ::SHA2_384_CTX) = print(io, "SHA2 384-bit hash state")
show(io::IO, ::SHA2_512_CTX) = print(io, "SHA2 512-bit hash state")
show(io::IO, ::SHA3_224_CTX) = print(io, "SHA3 224-bit hash state")
show(io::IO, ::SHA3_256_CTX) = print(io, "SHA3 256-bit hash state")
show(io::IO, ::SHA3_384_CTX) = print(io, "SHA3 384-bit hash state")
show(io::IO, ::SHA3_512_CTX) = print(io, "SHA3 512-bit hash state")


# use our types to define a method to get a pointer to the state buffer
buffer_pointer(ctx::T) where {T<:SHA_CTX} = Ptr{state_type(T)}(pointer(ctx.buffer))
u   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/SHA/src/base_functions.jl.      # THE SIX LOGICAL FUNCTIONS
#
# Bit shifting and rotation (used by the six SHA-XYZ logical functions:
#
#   NOTE:  The naming of R and S appears backwards here (R is a SHIFT and
#   S is a ROTATION) because the SHA2-256/384/512 description document
#   (see http://csrc.nist.gov/cryptval/shs/sha256-384-512.pdf) uses this
#   same "backwards" definition.

# 32-bit Rotate-right (equivalent to S32 in SHA-256) and rotate-left
rrot(b,x,width) = ((x >> b) | (x << (width - b)))
lrot(b,x,width) = ((x << b) | (x >> (width - b)))

# Shift-right (used in SHA-256, SHA-384, and SHA-512):
R(b,x)   = (x >> b)
# 32-bit Rotate-right (used in SHA-256):
S32(b,x) = rrot(b,x,32)
# 64-bit Rotate-right (used in SHA-384 and SHA-512):
S64(b,x) = rrot(b,x,64)
# 64-bit Rotate-left (used in SHA3)
L64(b,x) = lrot(b,x,64)

# Two of six logical functions used in SHA-256, SHA-384, and SHA-512:
Ch(x,y,z)  = ((x & y) ⊻ (~x & z))
Maj(x,y,z) = ((x & y) ⊻ (x & z) ⊻ (y & z))

# Four of six logical functions used in SHA-256:
Sigma0_256(x) = (S32(2,  UInt32(x)) ⊻ S32(13, UInt32(x)) ⊻ S32(22, UInt32(x)))
Sigma1_256(x) = (S32(6,  UInt32(x)) ⊻ S32(11, UInt32(x)) ⊻ S32(25, UInt32(x)))
sigma0_256(x) = (S32(7,  UInt32(x)) ⊻ S32(18, UInt32(x)) ⊻ R(3 ,   UInt32(x)))
sigma1_256(x) = (S32(17, UInt32(x)) ⊻ S32(19, UInt32(x)) ⊻ R(10,   UInt32(x)))

# Four of six logical functions used in SHA-384 and SHA-512:
Sigma0_512(x) = (S64(28, UInt64(x)) ⊻ S64(34, UInt64(x)) ⊻ S64(39, UInt64(x)))
Sigma1_512(x) = (S64(14, UInt64(x)) ⊻ S64(18, UInt64(x)) ⊻ S64(41, UInt64(x)))
sigma0_512(x) = (S64( 1, UInt64(x)) ⊻ S64( 8, UInt64(x)) ⊻ R( 7,   UInt64(x)))
sigma1_512(x) = (S64(19, UInt64(x)) ⊻ S64(61, UInt64(x)) ⊻ R( 6,   UInt64(x)))

# Let's be able to bswap arrays of these types as well
bswap!(x::Vector{<:Integer}) = map!(bswap, x, x)
k   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/SHA/src/sha1.jl�	      # Nonlinear functions, in order to encourage inlining, these sadly are not an array of lambdas
function Round0(b,c,d)
    return UInt32((b & c) | (~b & d))
end

function Round1And3(b,c,d)
    return UInt32(b ⊻ c ⊻ d)
end

function Round2(b,c,d)
    return UInt32((b & c) | (b & d) | (c & d))
end

function transform!(context::SHA1_CTX)
    # Buffer is 16 elements long, we expand to 80
    pbuf = buffer_pointer(context)
    for i in 1:16
        context.W[i] = bswap(unsafe_load(pbuf, i))
    end

    # First round of expansions
    for i in 17:32
        @inbounds begin
            context.W[i] = lrot(1, context.W[i-3] ⊻ context.W[i-8] ⊻ context.W[i-14] ⊻ context.W[i-16], 32)
        end
    end

    # Second round of expansions (possibly 4-way SIMD-able)
    for i in 33:80
        @inbounds begin
            context.W[i] = lrot(2, context.W[i-6] ⊻ context.W[i-16] ⊻ context.W[i-28] ⊻ context.W[i-32], 32)
        end
    end

    # Initialize registers with the previous intermediate values (our state)
    a = context.state[1]
    b = context.state[2]
    c = context.state[3]
    d = context.state[4]
    e = context.state[5]

    # Run our rounds, manually separated into the four rounds, unfortunately using an array of lambdas
    # really kills performance and causes a huge number of allocations, so we make it easy on the compiler
    for i = 1:20
        @inbounds begin
            temp = UInt32(lrot(5, a, 32) + Round0(b,c,d) + e + context.W[i] + K1[1])
            e = d
            d = c
            c = lrot(30, b, 32)
            b = a
            a = temp
        end
    end

    for i = 21:40
        @inbounds begin
            temp = UInt32(lrot(5, a, 32) + Round1And3(b,c,d) + e + context.W[i] + K1[2])
            e = d
            d = c
            c = lrot(30, b, 32)
            b = a
            a = temp
        end
    end

    for i = 41:60
        @inbounds begin
            temp = UInt32(lrot(5, a, 32) + Round2(b,c,d) + e + context.W[i] + K1[3])
            e = d
            d = c
            c = lrot(30, b, 32)
            b = a
            a = temp
        end
    end

    for i = 61:80
        @inbounds begin
            temp = UInt32(lrot(5, a, 32) + Round1And3(b,c,d) + e + context.W[i] + K1[4])
            e = d
            d = c
            c = lrot(30, b, 32)
            b = a
            a = temp
        end
    end

    context.state[1] += a
    context.state[2] += b
    context.state[3] += c
    context.state[4] += d
    context.state[5] += e
end
k   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/SHA/src/sha2.jl�      macro R1_16(j, T)

    ww = (:a, :b, :c, :d, :e, :f, :g, :h)

    a = ww[((81 - j) % 8) + 1]
    b = ww[((82 - j) % 8) + 1]
    c = ww[((83 - j) % 8) + 1]
    d = ww[((84 - j) % 8) + 1]
    e = ww[((85 - j) % 8) + 1]
    f = ww[((86 - j) % 8) + 1]
    g = ww[((87 - j) % 8) + 1]
    h = ww[((88 - j) % 8) + 1]

    if T == 512
        Sigma0 = :Sigma0_512
        Sigma1 = :Sigma1_512
        K = :K512
    elseif T == 256
        Sigma0 = :Sigma0_256
        Sigma1 = :Sigma1_256
        K = :K256
    end

    return esc(quote
        # We byteswap every input byte
        v = bswap(unsafe_load(pbuf, $j))
        unsafe_store!(pbuf, v, $j)

        # Apply the SHA-256 compression function to update a..h
        T1 = $h + $Sigma1($e) + Ch($e, $f, $g) + $K[$j] + v
        $h = $Sigma0($a) + Maj($a, $b, $c)
        $d += T1
        $h += T1
    end)
end

macro R17_80(j, T)

    ww = (:a, :b, :c, :d, :e, :f, :g, :h)

    a = ww[((81 - j) % 8) + 1]
    b = ww[((82 - j) % 8) + 1]
    c = ww[((83 - j) % 8) + 1]
    d = ww[((84 - j) % 8) + 1]
    e = ww[((85 - j) % 8) + 1]
    f = ww[((86 - j) % 8) + 1]
    g = ww[((87 - j) % 8) + 1]
    h = ww[((88 - j) % 8) + 1]

    if T == 512
        Sigma0 = :Sigma0_512
        Sigma1 = :Sigma1_512
        sigma0 = :sigma0_512
        sigma1 = :sigma1_512
        K = :K512
    elseif T == 256
        Sigma0 = :Sigma0_256
        Sigma1 = :Sigma1_256
        sigma0 = :sigma0_256
        sigma1 = :sigma1_256
        K = :K256
    end

    return esc(quote
        s0 = unsafe_load(pbuf, mod1($j + 1, 16))
        s0 = $sigma0(s0)
        s1 = unsafe_load(pbuf, mod1($j + 14, 16))
        s1 = $sigma1(s1)

        # Apply the SHA-256 compression function to update a..h
        v = unsafe_load(pbuf, mod1($j, 16)) + s1 + unsafe_load(pbuf, mod1($j + 9, 16)) + s0
        unsafe_store!(pbuf, v, mod1($j, 16))
        T1 = $h + $Sigma1($e) + Ch($e, $f, $g) + $K[$j] + v
        $h = $Sigma0($a) + Maj($a, $b, $c)
        $d += T1
        $h += T1
    end)
end

macro R_init(T)
    expr = :()
    for i in 1:16
        expr = :($expr; @R1_16($i, $T))
    end
    return esc(expr)
end

macro R_end(T)

    if T == 256
        n_rounds = 64
    elseif T == 512
        n_rounds = 80
    end

    expr = :()
    for i in 17:n_rounds
        expr = :($expr; @R17_80($i, $T))
    end

    return esc(expr)
end

@generated function transform!(context::Union{SHA2_224_CTX, SHA2_256_CTX,
                                              SHA2_384_CTX, SHA2_512_CTX})
    if context <: Union{SHA2_224_CTX,SHA2_256_CTX}
        T = 256
    elseif context <: Union{SHA2_384_CTX,SHA2_512_CTX}
        T = 512
    end

    return quote
        pbuf = buffer_pointer(context)
        # Initialize registers with the previous intermediate values (our state)
        a, b, c, d, e, f, g, h = context.state

        # Initial Rounds
        @R_init($T)

        # Other Rounds
        @R_end($T)

        # Compute the current intermediate hash value
        @inbounds begin
            context.state[1] += a
            context.state[2] += b
            context.state[3] += c
            context.state[4] += d
            context.state[5] += e
            context.state[6] += f
            context.state[7] += g
            context.state[8] += h
        end
    end
end
k   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/SHA/src/sha3.jl�	      function transform!(context::T) where {T<:SHA3_CTX}
    # First, update state with buffer
    pbuf = Ptr{eltype(context.state)}(pointer(context.buffer))
    for idx in 1:div(blocklen(T),8)
        context.state[idx] = context.state[idx] ⊻ unsafe_load(pbuf, idx)
    end
    bc = context.bc
    state = context.state

    # We always assume 24 rounds
    @inbounds for round in 0:23
        # Theta function
        for i in 1:5
            bc[i] = state[i] ⊻ state[i + 5] ⊻ state[i + 10] ⊻ state[i + 15] ⊻ state[i + 20]
        end

        for i in 0:4
            temp = bc[rem(i + 4, 5) + 1] ⊻ L64(1, bc[rem(i + 1, 5) + 1])
            j = 0
            while j <= 20
                state[Int(i + j + 1)] = state[i + j + 1] ⊻ temp
                j += 5
            end
        end

        # Rho Pi
        temp = state[2]
        for i in 1:24
            j = SHA3_PILN[i]
            bc[1] = state[j]
            state[j] = L64(SHA3_ROTC[i], temp)
            temp = bc[1]
        end

        # Chi
        j = 0
        while j <= 20
            for i in 1:5
                bc[i] = state[i + j]
            end
            for i in 0:4
                state[j + i + 1] = state[j + i + 1] ⊻ (~bc[rem(i + 1, 5) + 1] & bc[rem(i + 2, 5) + 1])
            end
            j += 5
        end

        # Iota
        state[1] = state[1] ⊻ SHA3_ROUND_CONSTS[round+1]
    end

    return context.state
end


# Finalize data in the buffer, append total bitlength, and return our precious hash!
function digest!(context::T) where {T<:SHA3_CTX}
    if !context.used
        usedspace = context.bytecount % blocklen(T)
        # If we have anything in the buffer still, pad and transform that data
        if usedspace < blocklen(T) - 1
            # Begin padding with a 0x06
            context.buffer[usedspace+1] = 0x06
            # Fill with zeros up until the last byte
            context.buffer[usedspace+2:end-1] .= 0x00
            # Finish it off with a 0x80
            context.buffer[end] = 0x80
        else
            # Otherwise, we have to add on a whole new buffer just for the zeros and 0x80
            context.buffer[end] = 0x06
            transform!(context)

            context.buffer[1:end-1] .= 0x0
            context.buffer[end] = 0x80
        end

        # Final transform:
        transform!(context)
        context.used = true
    end

    # Return the digest
    return reinterpret(UInt8, context.state)[1:digestlen(T)]
end
m   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/SHA/src/common.jl      # Common update and digest functions which work across SHA1 and SHA2

# update! takes in variable-length data, buffering it into blocklen()-sized pieces,
# calling transform!() when necessary to update the internal hash state.
"""
    update!(context, data[, datalen])

Update the SHA context with the bytes in data. See also [`digest!`](@ref) for
finalizing the hash.

# Examples
```julia-repl
julia> ctx = SHA1_CTX()
SHA1 hash state

julia> update!(ctx, b"data to to be hashed")
```
"""
function update!(context::T, data::U, datalen=length(data)) where {T<:SHA_CTX, U<:AbstractBytes}
    context.used && error("Cannot update CTX after `digest!` has been called on it")
    # We need to do all our arithmetic in the proper bitwidth
    UIntXXX = typeof(context.bytecount)

    # Process as many complete blocks as possible
    0 ≤ datalen ≤ length(data) || throw(BoundsError(data, firstindex(data)+datalen-1))
    len = convert(UIntXXX, datalen)
    data_idx = convert(UIntXXX, firstindex(data)-1)
    usedspace = context.bytecount % blocklen(T)
    while len - data_idx + usedspace >= blocklen(T)
        # Fill up as much of the buffer as we can with the data given us
        copyto!(context.buffer, usedspace + 1, data, data_idx + 1, blocklen(T) - usedspace)

        transform!(context)
        context.bytecount += blocklen(T) - usedspace
        data_idx += blocklen(T) - usedspace
        usedspace = convert(UIntXXX, 0)
    end

    # There is less than a complete block left, but we need to save the leftovers into context.buffer:
    if len > data_idx
        copyto!(context.buffer, usedspace + 1, data, data_idx + 1, len - data_idx)
        context.bytecount += len - data_idx
    end
end

# Pad the remainder leaving space for the bitcount
function pad_remainder!(context::T) where T<:SHA_CTX
    usedspace = context.bytecount % blocklen(T)
    # If we have anything in the buffer still, pad and transform that data
    if usedspace > 0
        # Begin padding with a 1 bit:
        context.buffer[usedspace+1] = 0x80
        usedspace += 1

        # If we have room for the bitcount, then pad up to the short blocklen
        if usedspace <= short_blocklen(T)
            for i = 1:(short_blocklen(T) - usedspace)
                context.buffer[usedspace + i] = 0x0
            end
        else
            # Otherwise, pad out this entire block, transform it, then pad up to short blocklen
            for i = 1:(blocklen(T) - usedspace)
                context.buffer[usedspace + i] = 0x0
            end
            transform!(context)
            for i = 1:short_blocklen(T)
                context.buffer[i] = 0x0
            end
        end
    else
        # If we don't have anything in the buffer, pad an entire shortbuffer
        context.buffer[1] = 0x80
        for i = 2:short_blocklen(T)
            context.buffer[i] = 0x0
        end
    end
end


# Clear out any saved data in the buffer, append total bitlength, and return our precious hash!
# Note: SHA3_CTX has a more specialised method
"""
    digest!(context)

Finalize the SHA context and return the hash as array of bytes (Array{Uint8, 1}).
Updating the context after calling `digest!` on it will error.

# Examples
```julia-repl
julia> ctx = SHA1_CTX()
SHA1 hash state

julia> update!(ctx, b"data to to be hashed")

julia> digest!(ctx)
20-element Array{UInt8,1}:
 0x83
 0xe4
 ⋮
 0x89
 0xf5

julia> update!(ctx, b"more data")
ERROR: Cannot update CTX after `digest!` has been called on it
[...]
```
"""
function digest!(context::T) where T<:SHA_CTX
    if !context.used
        pad_remainder!(context)
        # Store the length of the input data (in bits) at the end of the padding
        bitcount_idx = div(short_blocklen(T), sizeof(context.bytecount)) + 1
        pbuf = Ptr{typeof(context.bytecount)}(pointer(context.buffer))
        unsafe_store!(pbuf, bswap(context.bytecount * 8), bitcount_idx)

        # Final transform:
        transform!(context)
        bswap!(context.state)
        context.used = true
    end

    # Return the digest
    return reinterpret(UInt8, context.state)[1:digestlen(T)]
end
k   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/SHA/src/hmac.jl}      """
    HMAC_CTX(ctx::CTX, key::Vector{UInt8}) where {CTX<:SHA_CTX}

Construct an empty HMAC_CTX context.
"""
struct HMAC_CTX{CTX<:SHA_CTX}
    context::CTX
    outer::Vector{UInt8}

    function HMAC_CTX(ctx::CTX, key::Vector{UInt8}, blocksize::Integer=blocklen(CTX)) where CTX
        if length(key) > blocksize
            _ctx = CTX()
            update!(_ctx, key)
            key = digest!(_ctx)
        end

        pad = blocksize - length(key)

        if pad > 0
            key = [key; fill(0x00, pad)]
        end

        update!(ctx, key .⊻ 0x36)
        new{CTX}(ctx, key .⊻ 0x5c)
    end
end

function update!(ctx::HMAC_CTX, data, datalen=length(data))
    update!(ctx.context, data, datalen)
end

function digest!(ctx::HMAC_CTX{CTX}) where CTX
    digest = digest!(ctx.context)
    _ctx = CTX()
    update!(_ctx, ctx.outer)
    update!(_ctx, digest)
    digest!(_ctx)
end
~   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Serialization/src/Serialization.jlP�      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
Provide serialization of Julia objects via the functions
* [`serialize`](@ref)
* [`deserialize`](@ref)
"""
module Serialization

import Base: GMP, Bottom, unsafe_convert, uncompressed_ast
import Core: svec, SimpleVector
using Base: unaliascopy, unwrap_unionall, require_one_based_indexing, ntupleany
using Core.IR

export serialize, deserialize, AbstractSerializer, Serializer

abstract type AbstractSerializer end

mutable struct Serializer{I<:IO} <: AbstractSerializer
    io::I
    counter::Int
    table::IdDict{Any,Any}
    pending_refs::Vector{Int}
    known_object_data::Dict{UInt64,Any}
    version::Int
    Serializer{I}(io::I) where I<:IO = new(io, 0, IdDict(), Int[], Dict{UInt64,Any}(), ser_version)
end

Serializer(io::IO) = Serializer{typeof(io)}(io)

## serializing values ##

const n_int_literals = 33
const n_reserved_slots = 24
const n_reserved_tags = 8

const TAGS = Any[
    Symbol, Int8, UInt8, Int16, UInt16, Int32, UInt32, Int64, UInt64, Int128, UInt128,
    Float16, Float32, Float64, Char, DataType, Union, UnionAll, Core.TypeName, Tuple,
    Array, Expr, LineNumberNode, :__LabelNode__, GotoNode, QuoteNode, CodeInfo, TypeVar,
    Core.Box, Core.MethodInstance, Module, Task, String, SimpleVector, Method,
    GlobalRef, SlotNumber, Const, NewvarNode, SSAValue,

    # dummy entries for tags that don't correspond directly to types
    Symbol, # UNDEFREF_TAG
    Symbol, # BACKREF_TAG
    Symbol, # LONGBACKREF_TAG
    Symbol, # SHORTBACKREF_TAG
    Symbol, # LONGTUPLE_TAG
    Symbol, # LONGSYMBOL_TAG
    Symbol, # LONGEXPR_TAG
    Symbol, # LONGSTRING_TAG
    Symbol, # SHORTINT64_TAG
    Symbol, # FULL_DATATYPE_TAG
    Symbol, # WRAPPER_DATATYPE_TAG
    Symbol, # OBJECT_TAG
    Symbol, # REF_OBJECT_TAG
    Symbol, # FULL_GLOBALREF_TAG
    Symbol, # HEADER_TAG
    Symbol, # IDDICT_TAG
    Symbol, # SHARED_REF_TAG
    ReturnNode, GotoIfNot,
    fill(Symbol, n_reserved_tags)...,

    (), Bool, Any, Bottom, Core.TypeofBottom, Type, svec(), Tuple{}, false, true, nothing,
    :Any, :Array, :TypeVar, :Box, :Tuple, :Ptr, :return, :call, Symbol("::"), :Function,
    :(=), :(==), :(===), :gotoifnot, :A, :B, :C, :M, :N, :T, :S, :X, :Y, :a, :b, :c, :d, :e, :f,
    :g, :h, :i, :j, :k, :l, :m, :n, :o, :p, :q, :r, :s, :t, :u, :v, :w, :x, :y, :z, :add_int,
    :sub_int, :mul_int, :add_float, :sub_float, :new, :mul_float, :bitcast, :start, :done, :next,
    :indexed_iterate, :getfield, :meta, :eq_int, :slt_int, :sle_int, :ne_int, :push_loc, :pop_loc,
    :pop, :arrayset, :arrayref, :apply_type, :inbounds, :getindex, :setindex!, :Core, :!, :+,
    :Base, :static_parameter, :convert, :colon, Symbol("#self#"), Symbol("#temp#"), :tuple, Symbol(""),

    fill(:_reserved_, n_reserved_slots)...,

    (Int32(0):Int32(n_int_literals-1))...,
    (Int64(0):Int64(n_int_literals-1))...
]

const NTAGS = length(TAGS)
@assert NTAGS == 255

const ser_version = 24 # do not make changes without bumping the version #!

format_version(::AbstractSerializer) = ser_version
format_version(s::Serializer) = s.version

function sertag(@nospecialize(v))
    # NOTE: we use jl_value_ptr directly since we know at least one of the arguments
    # in the comparison below is a singleton.
    ptr = ccall(:jl_value_ptr, Ptr{Cvoid}, (Any,), v)
    ptags = convert(Ptr{Ptr{Cvoid}}, pointer(TAGS))
    # note: constant ints & reserved slots never returned here
    @inbounds for i in 1:(NTAGS-(n_reserved_slots+2*n_int_literals))
        ptr == unsafe_load(ptags,i) && return i%Int32
    end
    return Int32(-1)
end
desertag(i::Int32) = @inbounds(TAGS[i])

# tags >= this just represent themselves, their whole representation is 1 byte
const VALUE_TAGS = sertag(())
const ZERO32_TAG = Int32(NTAGS-(2*n_int_literals-1))
const ZERO64_TAG = Int64(NTAGS-(n_int_literals-1))
const TRUE_TAG = sertag(true)
const FALSE_TAG = sertag(false)
const EMPTYTUPLE_TAG = sertag(())
const TUPLE_TAG = sertag(Tuple)
const SIMPLEVECTOR_TAG = sertag(SimpleVector)
const SYMBOL_TAG = sertag(Symbol)
const INT8_TAG = sertag(Int8)
const ARRAY_TAG = findfirst(==(Array), TAGS)%Int32
const EXPR_TAG = sertag(Expr)
const MODULE_TAG = sertag(Module)
const METHODINSTANCE_TAG = sertag(Core.MethodInstance)
const METHOD_TAG = sertag(Method)
const TASK_TAG = sertag(Task)
const DATATYPE_TAG = sertag(DataType)
const TYPENAME_TAG = sertag(Core.TypeName)
const INT32_TAG = sertag(Int32)
const INT64_TAG = sertag(Int64)
const GLOBALREF_TAG = sertag(GlobalRef)
const BOTTOM_TAG = sertag(Bottom)
const UNIONALL_TAG = sertag(UnionAll)
const STRING_TAG = sertag(String)
const o0 = sertag(SSAValue)
const UNDEFREF_TAG         = Int32(o0+1)
const BACKREF_TAG          = Int32(o0+2)
const LONGBACKREF_TAG      = Int32(o0+3)
const SHORTBACKREF_TAG     = Int32(o0+4)
const LONGTUPLE_TAG        = Int32(o0+5)
const LONGSYMBOL_TAG       = Int32(o0+6)
const LONGEXPR_TAG         = Int32(o0+7)
const LONGSTRING_TAG       = Int32(o0+8)
const SHORTINT64_TAG       = Int32(o0+9)
const FULL_DATATYPE_TAG    = Int32(o0+10)
const WRAPPER_DATATYPE_TAG = Int32(o0+11)
const OBJECT_TAG           = Int32(o0+12)
const REF_OBJECT_TAG       = Int32(o0+13)
const FULL_GLOBALREF_TAG   = Int32(o0+14)
const HEADER_TAG           = Int32(o0+15)
const IDDICT_TAG           = Int32(o0+16)
const SHARED_REF_TAG       = Int32(o0+17)

writetag(s::IO, tag) = (write(s, UInt8(tag)); nothing)

function write_as_tag(s::IO, tag)
    tag < VALUE_TAGS && write(s, UInt8(0))
    write(s, UInt8(tag))
    nothing
end

# cycle handling
function serialize_cycle(s::AbstractSerializer, @nospecialize(x))
    offs = get(s.table, x, -1)::Int
    if offs != -1
        if offs <= typemax(UInt16)
            writetag(s.io, SHORTBACKREF_TAG)
            write(s.io, UInt16(offs))
        elseif offs <= typemax(Int32)
            writetag(s.io, BACKREF_TAG)
            write(s.io, Int32(offs))
        else
            writetag(s.io, LONGBACKREF_TAG)
            write(s.io, Int64(offs))
        end
        return true
    end
    s.table[x] = s.counter
    s.counter += 1
    return false
end

function serialize_cycle_header(s::AbstractSerializer, @nospecialize(x))
    serialize_cycle(s, x) && return true
    serialize_type(s, typeof(x), true)
    return false
end

function reset_state(s::AbstractSerializer)
    s.counter = 0
    empty!(s.table)
    empty!(s.pending_refs)
    s
end

serialize(s::AbstractSerializer, x::Bool) = x ? writetag(s.io, TRUE_TAG) :
                                                writetag(s.io, FALSE_TAG)

serialize(s::AbstractSerializer, p::Ptr) = serialize_any(s, oftype(p, C_NULL))

serialize(s::AbstractSerializer, ::Tuple{}) = writetag(s.io, EMPTYTUPLE_TAG)

function serialize(s::AbstractSerializer, t::Tuple)
    l = length(t)
    if l <= NTAGS
        writetag(s.io, TUPLE_TAG)
        write(s.io, UInt8(l))
    else
        writetag(s.io, LONGTUPLE_TAG)
        write(s.io, Int32(l))
    end
    for x in t
        serialize(s, x)
    end
end

function serialize(s::AbstractSerializer, v::SimpleVector)
    writetag(s.io, SIMPLEVECTOR_TAG)
    write(s.io, Int32(length(v)))
    for x in v
        serialize(s, x)
    end
end

function serialize(s::AbstractSerializer, x::Symbol)
    tag = sertag(x)
    if tag > 0
        return write_as_tag(s.io, tag)
    end
    pname = unsafe_convert(Ptr{UInt8}, x)
    len = Int(ccall(:strlen, Csize_t, (Cstring,), pname))
    if len > 7
        serialize_cycle(s, x) && return
    end
    if len <= NTAGS
        writetag(s.io, SYMBOL_TAG)
        write(s.io, UInt8(len))
    else
        writetag(s.io, LONGSYMBOL_TAG)
        write(s.io, Int32(len))
    end
    unsafe_write(s.io, pname, len)
    nothing
end

function serialize_array_data(s::IO, a)
    require_one_based_indexing(a)
    isempty(a) && return 0
    if eltype(a) === Bool
        last = a[1]::Bool
        count = 1
        for i = 2:length(a)
            if a[i]::Bool != last || count == 127
                write(s, UInt8((UInt8(last) << 7) | count))
                last = a[i]::Bool
                count = 1
            else
                count += 1
            end
        end
        write(s, UInt8((UInt8(last) << 7) | count))
    else
        write(s, a)
    end
end

function serialize(s::AbstractSerializer, a::Array)
    serialize_cycle(s, a) && return
    elty = eltype(a)
    writetag(s.io, ARRAY_TAG)
    if elty !== UInt8
        serialize(s, elty)
    end
    if ndims(a) != 1
        serialize(s, size(a))
    else
        serialize(s, length(a))
    end
    if isbitstype(elty)
        serialize_array_data(s.io, a)
    else
        sizehint!(s.table, div(length(a),4))  # prepare for lots of pointers
        @inbounds for i in eachindex(a)
            if isassigned(a, i)
                serialize(s, a[i])
            else
                writetag(s.io, UNDEFREF_TAG)
            end
        end
    end
end

function serialize(s::AbstractSerializer, a::SubArray{T,N,A}) where {T,N,A<:Array}
    # SubArray's copy only selects the relevant data (and reduces the size) but does not
    # preserve the type of the argument. This internal function does both:
    b = unaliascopy(a)
    serialize_any(s, b)
end

function serialize(s::AbstractSerializer, ss::String)
    len = sizeof(ss)
    if len > 7
        serialize_cycle(s, ss) && return
        writetag(s.io, SHARED_REF_TAG)
    end
    if len <= NTAGS
        writetag(s.io, STRING_TAG)
        write(s.io, UInt8(len))
    else
        writetag(s.io, LONGSTRING_TAG)
        write(s.io, Int64(len))
    end
    write(s.io, ss)
    nothing
end

function serialize(s::AbstractSerializer, ss::SubString{String})
    # avoid saving a copy of the parent string, keeping the type of ss
    serialize_any(s, SubString(String(ss)))
end

# Don't serialize the pointers
function serialize(s::AbstractSerializer, r::Regex)
    serialize_type(s, typeof(r))
    serialize(s, r.pattern)
    serialize(s, r.compile_options)
    serialize(s, r.match_options)
end

function serialize(s::AbstractSerializer, n::BigInt)
    serialize_type(s, BigInt)
    serialize(s, string(n, base = 62))
end

function serialize(s::AbstractSerializer, ex::Expr)
    serialize_cycle(s, ex) && return
    l = length(ex.args)
    if l <= NTAGS
        writetag(s.io, EXPR_TAG)
        write(s.io, UInt8(l))
    else
        writetag(s.io, LONGEXPR_TAG)
        write(s.io, Int32(l))
    end
    serialize(s, ex.head)
    for a in ex.args
        serialize(s, a)
    end
end

function serialize_dict_data(s::AbstractSerializer, d::AbstractDict)
    write(s.io, Int32(length(d)))
    for (k,v) in d
        serialize(s, k)
        serialize(s, v)
    end
end

function serialize(s::AbstractSerializer, d::Dict)
    serialize_cycle_header(s, d) && return
    serialize_dict_data(s, d)
end

function serialize(s::AbstractSerializer, d::IdDict)
    serialize_cycle(s, d) && return
    writetag(s.io, IDDICT_TAG)
    serialize_type_data(s, typeof(d))
    serialize_dict_data(s, d)
end

function serialize_mod_names(s::AbstractSerializer, m::Module)
    p = parentmodule(m)
    if p === m || m === Base
        key = Base.root_module_key(m)
        uuid = key.uuid
        serialize(s, uuid === nothing ? nothing : uuid.value)
        serialize(s, Symbol(key.name))
    else
        serialize_mod_names(s, p)
        serialize(s, nameof(m))
    end
end

function serialize(s::AbstractSerializer, m::Module)
    writetag(s.io, MODULE_TAG)
    serialize_mod_names(s, m)
    writetag(s.io, EMPTYTUPLE_TAG)
end

# TODO: make this bidirectional, so objects can be sent back via the same key
const object_numbers = WeakKeyDict()
const obj_number_salt = Ref{UInt64}(0)
function object_number(s::AbstractSerializer, @nospecialize(l))
    global obj_number_salt, object_numbers
    if haskey(object_numbers, l)
        return object_numbers[l]
    end
    ln = obj_number_salt[]
    object_numbers[l] = ln
    obj_number_salt[] += 1
    return ln::UInt64
end

lookup_object_number(s::AbstractSerializer, n::UInt64) = nothing

remember_object(s::AbstractSerializer, @nospecialize(o), n::UInt64) = nothing

function lookup_object_number(s::Serializer, n::UInt64)
    return get(s.known_object_data, n, nothing)
end

function remember_object(s::Serializer, @nospecialize(o), n::UInt64)
    s.known_object_data[n] = o
    return nothing
end

function serialize(s::AbstractSerializer, meth::Method)
    serialize_cycle(s, meth) && return
    writetag(s.io, METHOD_TAG)
    write(s.io, object_number(s, meth))
    serialize(s, meth.module)
    serialize(s, meth.name)
    serialize(s, meth.file)
    serialize(s, meth.line)
    serialize(s, meth.sig)
    serialize(s, meth.slot_syms)
    serialize(s, meth.nargs)
    serialize(s, meth.isva)
    serialize(s, meth.is_for_opaque_closure)
    serialize(s, meth.nospecializeinfer)
    serialize(s, meth.constprop)
    serialize(s, meth.purity)
    if isdefined(meth, :source)
        serialize(s, Base._uncompressed_ast(meth, meth.source))
    else
        serialize(s, nothing)
    end
    if isdefined(meth, :generator)
        serialize(s, meth.generator)
    else
        serialize(s, nothing)
    end
    if isdefined(meth, :recursion_relation)
        serialize(s, method.recursion_relation)
    else
        serialize(s, nothing)
    end
    if isdefined(meth, :external_mt)
        error("cannot serialize Method objects with external method tables")
    end
    nothing
end

function serialize(s::AbstractSerializer, linfo::Core.MethodInstance)
    serialize_cycle(s, linfo) && return
    writetag(s.io, METHODINSTANCE_TAG)
    if isdefined(linfo, :uninferred)
        serialize(s, linfo.uninferred)
    else
        writetag(s.io, UNDEFREF_TAG)
    end
    serialize(s, nothing)  # for backwards compat
    serialize(s, linfo.sparam_vals)
    serialize(s, Any)  # for backwards compat
    serialize(s, linfo.specTypes)
    serialize(s, linfo.def)
    nothing
end

function serialize(s::AbstractSerializer, t::Task)
    serialize_cycle(s, t) && return
    if istaskstarted(t) && !istaskdone(t)
        error("cannot serialize a running Task")
    end
    writetag(s.io, TASK_TAG)
    serialize(s, t.code)
    serialize(s, t.storage)
    serialize(s, t.state)
    if t._isexception && (stk = Base.current_exceptions(t); !isempty(stk))
        # the exception stack field is hidden inside the task, so if there
        # is any information there make a CapturedException from it instead.
        # TODO: Handle full exception chain, not just the first one.
        serialize(s, CapturedException(stk[1].exception, stk[1].backtrace))
    else
        serialize(s, t.result)
    end
    serialize(s, t._isexception)
end

function serialize(s::AbstractSerializer, g::GlobalRef)
    if (g.mod === __deserialized_types__ ) ||
        (g.mod === Main && isdefined(g.mod, g.name) && isconst(g.mod, g.name))

        v = getglobal(g.mod, g.name)
        unw = unwrap_unionall(v)
        if isa(unw,DataType) && v === unw.name.wrapper && should_send_whole_type(s, unw)
            # handle references to types in Main by sending the whole type.
            # needed to be able to send nested functions (#15451).
            writetag(s.io, FULL_GLOBALREF_TAG)
            serialize(s, v)
            return
        end
    end
    writetag(s.io, GLOBALREF_TAG)
    serialize(s, g.mod)
    serialize(s, g.name)
end

function serialize(s::AbstractSerializer, t::Core.TypeName)
    serialize_cycle(s, t) && return
    writetag(s.io, TYPENAME_TAG)
    write(s.io, object_number(s, t))
    serialize_typename(s, t)
end

function serialize_typename(s::AbstractSerializer, t::Core.TypeName)
    serialize(s, t.name)
    serialize(s, t.names)
    primary = unwrap_unionall(t.wrapper)
    serialize(s, primary.super)
    serialize(s, primary.parameters)
    serialize(s, primary.types)
    serialize(s, isdefined(primary, :instance))
    serialize(s, t.flags & 0x1 == 0x1) # .abstract
    serialize(s, t.flags & 0x2 == 0x2) # .mutable
    serialize(s, Int32(length(primary.types) - t.n_uninitialized))
    serialize(s, t.max_methods)
    if isdefined(t, :mt) && t.mt !== Symbol.name.mt
        serialize(s, t.mt.name)
        serialize(s, collect(Base.MethodList(t.mt)))
        serialize(s, t.mt.max_args)
        kws = collect(methods(Core.kwcall, (Any, t.wrapper, Vararg)))
        if isempty(kws)
            writetag(s.io, UNDEFREF_TAG)
        else
            serialize(s, kws)
        end
    else
        writetag(s.io, UNDEFREF_TAG)
    end
    nothing
end

# decide whether to send all data for a type (instead of just its name)
function should_send_whole_type(s, t::DataType)
    tn = t.name
    if isdefined(tn, :mt)
        # TODO improve somehow
        # send whole type for anonymous functions in Main
        name = tn.mt.name
        mod = tn.module
        isanonfunction = mod === Main && # only Main
            t.super === Function && # only Functions
            unsafe_load(unsafe_convert(Ptr{UInt8}, tn.name)) == UInt8('#') && # hidden type
            (!isdefined(mod, name) || t != typeof(getglobal(mod, name))) # XXX: 95% accurate test for this being an inner function
            # TODO: more accurate test? (tn.name !== "#" name)
        #TODO: iskw = startswith(tn.name, "#kw#") && ???
        #TODO: iskw && return send-as-kwftype
        return mod === __deserialized_types__ || isanonfunction
    end
    return false
end

function serialize_type_data(s, @nospecialize(t::DataType))
    whole = should_send_whole_type(s, t)
    iswrapper = (t === unwrap_unionall(t.name.wrapper))
    if whole && iswrapper
        writetag(s.io, WRAPPER_DATATYPE_TAG)
        serialize(s, t.name)
        return
    end
    serialize_cycle(s, t) && return
    if whole
        writetag(s.io, FULL_DATATYPE_TAG)
        serialize(s, t.name)
    else
        writetag(s.io, DATATYPE_TAG)
        serialize(s, nameof(t))
        serialize(s, parentmodule(t))
    end
    if !isempty(t.parameters)
        if iswrapper
            write(s.io, Int32(0))
        else
            write(s.io, Int32(length(t.parameters)))
            for p in t.parameters
                serialize(s, p)
            end
        end
    end
    nothing
end

function serialize(s::AbstractSerializer, t::DataType)
    tag = sertag(t)
    tag > 0 && return write_as_tag(s.io, tag)
    if t === Tuple
        # `sertag` is not able to find types === to `Tuple` because they
        # will not have been hash-consed. Plus `serialize_type_data` does not
        # handle this case correctly, since Tuple{} != Tuple. `Tuple` is the
        # only type with this property. issue #15849
        return write_as_tag(s.io, TUPLE_TAG)
    end
    serialize_type_data(s, t)
end

function serialize_type(s::AbstractSerializer, @nospecialize(t::DataType), ref::Bool = false)
    tag = sertag(t)
    tag > 0 && return writetag(s.io, tag)
    writetag(s.io, ref ? REF_OBJECT_TAG : OBJECT_TAG)
    serialize_type_data(s, t)
end

function serialize(s::AbstractSerializer, n::Int32)
    if 0 <= n <= (n_int_literals-1)
        write(s.io, UInt8(ZERO32_TAG+n))
    else
        writetag(s.io, INT32_TAG)
        write(s.io, n)
    end
    nothing
end

function serialize(s::AbstractSerializer, n::Int64)
    if 0 <= n <= (n_int_literals-1)
        write(s.io, UInt8(ZERO64_TAG+n))
    elseif typemin(Int32) <= n <= typemax(Int32)
        writetag(s.io, SHORTINT64_TAG)
        write(s.io, Int32(n))
    else
        writetag(s.io, INT64_TAG)
        write(s.io, n)
    end
    nothing
end

for i in 0:13
    tag = Int32(INT8_TAG + i)
    ty = TAGS[tag]
    (ty === Int32 || ty === Int64) && continue
    @eval serialize(s::AbstractSerializer, n::$ty) = (writetag(s.io, $tag); write(s.io, n); nothing)
end

serialize(s::AbstractSerializer, ::Type{Bottom}) = write_as_tag(s.io, BOTTOM_TAG)

function serialize(s::AbstractSerializer, u::UnionAll)
    writetag(s.io, UNIONALL_TAG)
    n = 0; t = u
    while isa(t, UnionAll)
        t = t.body
        n += 1
    end
    if isa(t, DataType) && t === unwrap_unionall(t.name.wrapper)
        write(s.io, UInt8(1))
        write(s.io, Int16(n))
        serialize(s, t)
    else
        write(s.io, UInt8(0))
        serialize(s, u.var)
        serialize(s, u.body)
    end
end

serialize(s::AbstractSerializer, @nospecialize(x)) = serialize_any(s, x)

function serialize_any(s::AbstractSerializer, @nospecialize(x))
    tag = sertag(x)
    if tag > 0
        return write_as_tag(s.io, tag)
    end
    t = typeof(x)::DataType
    if isprimitivetype(t)
        serialize_type(s, t)
        write(s.io, x)
    else
        if ismutable(x)
            serialize_cycle(s, x) && return
            serialize_type(s, t, true)
        else
            serialize_type(s, t, false)
        end
        nf = nfields(x)
        for i in 1:nf
            if isdefined(x, i)
                serialize(s, getfield(x, i))
            else
                writetag(s.io, UNDEFREF_TAG)
            end
        end
    end
    nothing
end

"""
    Serialization.writeheader(s::AbstractSerializer)

Write an identifying header to the specified serializer. The header consists of
8 bytes as follows:

| Offset | Description                                     |
|:-------|:------------------------------------------------|
|   0    | tag byte (0x37)                                 |
|   1-2  | signature bytes "JL"                            |
|   3    | protocol version                                |
|   4    | bits 0-1: endianness: 0 = little, 1 = big       |
|   4    | bits 2-3: platform: 0 = 32-bit, 1 = 64-bit      |
|   5-7  | reserved                                        |
"""
function writeheader(s::AbstractSerializer)
    io = s.io
    writetag(io, HEADER_TAG)
    write(io, "JL")  # magic bytes
    write(io, UInt8(ser_version))
    endianness = (ENDIAN_BOM == 0x04030201 ? 0 :
                  ENDIAN_BOM == 0x01020304 ? 1 :
                  error("unsupported endianness in serializer"))
    machine = (sizeof(Int) == 4 ? 0 :
               sizeof(Int) == 8 ? 1 :
               error("unsupported word size in serializer"))
    write(io, UInt8(endianness) | (UInt8(machine) << 2))
    write(io, [0x00,0x00,0x00]) # 3 reserved bytes
    nothing
end

function readheader(s::AbstractSerializer)
    # Tag already read
    io = s.io
    m1 = read(io, UInt8)
    m2 = read(io, UInt8)
    if m1 != UInt8('J') || m2 != UInt8('L')
        error("Unsupported serialization format (got header magic bytes $m1 $m2)")
    end
    version    = read(io, UInt8)
    flags      = read(io, UInt8)
    reserved1  = read(io, UInt8)
    reserved2  = read(io, UInt8)
    reserved3  = read(io, UInt8)
    endianflag = flags & 0x3
    wordflag   = (flags >> 2) & 0x3
    wordsize = wordflag == 0 ? 4 :
               wordflag == 1 ? 8 :
               error("Unknown word size flag in header")
    endian_bom = endianflag == 0 ? 0x04030201 :
                 endianflag == 1 ? 0x01020304 :
                 error("Unknown endianness flag in header")
    # Check protocol compatibility.
    endian_bom == ENDIAN_BOM  || error("Serialized byte order mismatch ($(repr(endian_bom)))")
    # We don't check wordsize == sizeof(Int) here, as Int is encoded concretely
    # as Int32 or Int64, which should be enough to correctly deserialize a range
    # of data structures between Julia versions.
    if version > ser_version
        error("""Cannot read stream serialized with a newer version of Julia.
                 Got data version $version > current version $ser_version""")
    end
    s.version = version
    return
end

"""
    serialize(stream::IO, value)

Write an arbitrary value to a stream in an opaque format, such that it can be read back by
[`deserialize`](@ref). The read-back value will be as identical as possible to the original,
but note that `Ptr` values are serialized as all-zero bit patterns (`NULL`).

An 8-byte identifying header is written to the stream first. To avoid writing the header,
construct a `Serializer` and use it as the first argument to `serialize` instead.
See also [`Serialization.writeheader`](@ref).

The data format can change in minor (1.x) Julia releases, but files written by prior 1.x
versions will remain readable. The main exception to this is when the definition of a
type in an external package changes. If that occurs, it may be necessary to specify
an explicit compatible version of the affected package in your environment.
Renaming functions, even private functions, inside packages can also put existing files
out of sync. Anonymous functions require special care: because their names are automatically
generated, minor code changes can cause them to be renamed.
Serializing anonymous functions should be avoided in files intended for long-term storage.

In some cases, the word size (32- or 64-bit) of the reading and writing machines must match.
In rarer cases the OS or architecture must also match, for example when using packages
that contain platform-dependent code.
"""
function serialize(s::IO, x)
    ss = Serializer(s)
    writeheader(ss)
    serialize(ss, x)
end

"""
    serialize(filename::AbstractString, value)

Open a file and serialize the given value to it.

!!! compat "Julia 1.1"
    This method is available as of Julia 1.1.
"""
serialize(filename::AbstractString, x) = open(io->serialize(io, x), filename, "w")

## deserializing values ##

"""
    deserialize(stream)

Read a value written by [`serialize`](@ref). `deserialize` assumes the binary data read from
`stream` is correct and has been serialized by a compatible implementation of [`serialize`](@ref).
`deserialize` is designed for simplicity and performance, and so does not validate
the data read. Malformed data can result in process termination. The caller must ensure
the integrity and correctness of data read from `stream`.
"""
deserialize(s::IO) = deserialize(Serializer(s))

"""
    deserialize(filename::AbstractString)

Open a file and deserialize its contents.

!!! compat "Julia 1.1"
    This method is available as of Julia 1.1.
"""
deserialize(filename::AbstractString) = open(deserialize, filename)

function deserialize(s::AbstractSerializer)
    handle_deserialize(s, Int32(read(s.io, UInt8)::UInt8))
end

function deserialize_cycle(s::AbstractSerializer, @nospecialize(x))
    slot = pop!(s.pending_refs)
    s.table[slot] = x
    nothing
end

# optimized version of:
#     slot = s.counter; s.counter += 1
#     push!(s.pending_refs, slot)
#     slot = pop!(s.pending_refs)
#     s.table[slot] = x
function resolve_ref_immediately(s::AbstractSerializer, @nospecialize(x))
    s.table[s.counter] = x
    s.counter += 1
    nothing
end

function gettable(s::AbstractSerializer, id::Int)
    get(s.table, id) do
        errmsg = """Inconsistent Serializer state when deserializing.
            Attempt to access internal table with key $id failed.

            This might occur if the Serializer contexts when serializing and deserializing are inconsistent.
            In particular, if multiple serialize calls use the same Serializer object then
            the corresponding deserialize calls should also use the same Serializer object.
        """
        error(errmsg)
    end
end

# deserialize_ is an internal function to dispatch on the tag
# describing the serialized representation. the number of
# representations is fixed, so deserialize_ does not get extended.
function handle_deserialize(s::AbstractSerializer, b::Int32)
    if b == 0
        return desertag(Int32(read(s.io, UInt8)::UInt8))
    end
    if b >= VALUE_TAGS
        return desertag(b)
    elseif b == TUPLE_TAG
        return deserialize_tuple(s, Int(read(s.io, UInt8)::UInt8))
    elseif b == SHORTBACKREF_TAG
        id = read(s.io, UInt16)::UInt16
        return gettable(s, Int(id))
    elseif b == BACKREF_TAG
        id = read(s.io, Int32)::Int32
        return gettable(s, Int(id))
    elseif b == ARRAY_TAG
        return deserialize_array(s)
    elseif b == DATATYPE_TAG
        return deserialize_datatype(s, false)
    elseif b == FULL_DATATYPE_TAG
        return deserialize_datatype(s, true)
    elseif b == WRAPPER_DATATYPE_TAG
        tname = deserialize(s)::Core.TypeName
        return unwrap_unionall(tname.wrapper)
    elseif b == OBJECT_TAG
        t = deserialize(s)
        if t === Missing
            return missing
        end
        return deserialize(s, t)
    elseif b == REF_OBJECT_TAG
        slot = s.counter; s.counter += 1
        push!(s.pending_refs, slot)
        t = deserialize(s)
        return deserialize(s, t)
    elseif b == SHARED_REF_TAG
        slot = s.counter; s.counter += 1
        obj = deserialize(s)
        s.table[slot] = obj
        return obj
    elseif b == SYMBOL_TAG
        return deserialize_symbol(s, Int(read(s.io, UInt8)::UInt8))
    elseif b == SHORTINT64_TAG
        return Int64(read(s.io, Int32)::Int32)
    elseif b == EXPR_TAG
        return deserialize_expr(s, Int(read(s.io, UInt8)::UInt8))
    elseif b == MODULE_TAG
        return deserialize_module(s)
    elseif b == STRING_TAG
        return deserialize_string(s, Int(read(s.io, UInt8)::UInt8))
    elseif b == LONGSTRING_TAG
        return deserialize_string(s, Int(read(s.io, Int64)::Int64))
    elseif b == SIMPLEVECTOR_TAG
        return deserialize_svec(s)
    elseif b == GLOBALREF_TAG
        return GlobalRef(deserialize(s)::Module, deserialize(s)::Symbol)
    elseif b == FULL_GLOBALREF_TAG
        ty = deserialize(s)
        tn = unwrap_unionall(ty).name
        return GlobalRef(tn.module, tn.name)
    elseif b == LONGTUPLE_TAG
        return deserialize_tuple(s, Int(read(s.io, Int32)::Int32))
    elseif b == LONGEXPR_TAG
        return deserialize_expr(s, Int(read(s.io, Int32)::Int32))
    elseif b == LONGBACKREF_TAG
        id = read(s.io, Int64)::Int64
        return gettable(s, Int(id))
    elseif b == LONGSYMBOL_TAG
        return deserialize_symbol(s, Int(read(s.io, Int32)::Int32))
    elseif b == HEADER_TAG
        readheader(s)
        return deserialize(s)
    elseif b == INT8_TAG
        return read(s.io, Int8)
    elseif b == INT8_TAG+1
        return read(s.io, UInt8)
    elseif b == INT8_TAG+2
        return read(s.io, Int16)
    elseif b == INT8_TAG+3
        return read(s.io, UInt16)
    elseif b == INT32_TAG
        return read(s.io, Int32)
    elseif b == INT8_TAG+5
        return read(s.io, UInt32)
    elseif b == INT64_TAG
        return read(s.io, Int64)
    elseif b == INT8_TAG+7
        return read(s.io, UInt64)
    elseif b == INT8_TAG+8
        return read(s.io, Int128)
    elseif b == INT8_TAG+9
        return read(s.io, UInt128)
    elseif b == INT8_TAG+10
        return read(s.io, Float16)
    elseif b == INT8_TAG+11
        return read(s.io, Float32)
    elseif b == INT8_TAG+12
        return read(s.io, Float64)
    elseif b == INT8_TAG+13
        return read(s.io, Char)
    elseif b == IDDICT_TAG
        slot = s.counter; s.counter += 1
        push!(s.pending_refs, slot)
        t = deserialize(s)
        return deserialize_dict(s, t)
    end
    t = desertag(b)::DataType
    if ismutabletype(t) && length(t.types) > 0  # manual specialization of fieldcount
        slot = s.counter; s.counter += 1
        push!(s.pending_refs, slot)
    end
    return deserialize(s, t)
end

function deserialize_symbol(s::AbstractSerializer, len::Int)
    str = Base._string_n(len)
    unsafe_read(s.io, pointer(str), len)
    sym = Symbol(str)
    if len > 7
        resolve_ref_immediately(s, sym)
    end
    return sym
end

deserialize_tuple(s::AbstractSerializer, len) = ntupleany(i->deserialize(s), len)

function deserialize_svec(s::AbstractSerializer)
    n = read(s.io, Int32)
    svec(Any[ deserialize(s) for i=1:n ]...)
end

function deserialize_module(s::AbstractSerializer)
    mkey = deserialize(s)
    if isa(mkey, Tuple)
        # old version, TODO: remove
        if mkey === ()
            return Main
        end
        m = Base.root_module(mkey[1])
        for i = 2:length(mkey)
            m = getglobal(m, mkey[i])::Module
        end
    else
        name = String(deserialize(s)::Symbol)
        pkg = (mkey === nothing) ? Base.PkgId(name) : Base.PkgId(Base.UUID(mkey), name)
        m = Base.root_module(pkg)
        mname = deserialize(s)
        while mname !== ()
            m = getglobal(m, mname)::Module
            mname = deserialize(s)
        end
    end
    return m
end

function deserialize(s::AbstractSerializer, ::Type{Method})
    lnumber = read(s.io, UInt64)
    meth = lookup_object_number(s, lnumber)
    if meth !== nothing
        meth = meth::Method
        makenew = false
    else
        meth = ccall(:jl_new_method_uninit, Ref{Method}, (Any,), Main)
        makenew = true
    end
    deserialize_cycle(s, meth)
    mod = deserialize(s)::Module
    name = deserialize(s)::Symbol
    file = deserialize(s)::Symbol
    line = deserialize(s)::Int32
    sig = deserialize(s)::Type
    syms = deserialize(s)
    if syms isa SimpleVector
        # < v1.2
        _ambig = deserialize(s)
    else
        slot_syms = syms::String
    end
    nargs = deserialize(s)::Int32
    isva = deserialize(s)::Bool
    is_for_opaque_closure = false
    nospecializeinfer = false
    constprop = purity = 0x00
    template_or_is_opaque = deserialize(s)
    if isa(template_or_is_opaque, Bool)
        is_for_opaque_closure = template_or_is_opaque
        if format_version(s) >= 24
            nospecializeinfer = deserialize(s)::Bool
        end
        if format_version(s) >= 14
            constprop = deserialize(s)::UInt8
        end
        if format_version(s) >= 17
            purity = deserialize(s)::UInt8
        end
        template = deserialize(s)
    else
        template = template_or_is_opaque
    end
    generator = deserialize(s)
    recursion_relation = nothing
    if format_version(s) >= 15
        recursion_relation = deserialize(s)
    end
    if makenew
        meth.module = mod
        meth.name = name
        meth.file = file
        meth.line = line
        meth.sig = sig
        meth.nargs = nargs
        meth.isva = isva
        meth.is_for_opaque_closure = is_for_opaque_closure
        meth.nospecializeinfer = nospecializeinfer
        meth.constprop = constprop
        meth.purity = purity
        if template !== nothing
            # TODO: compress template
            meth.source = template::CodeInfo
            if !@isdefined(slot_syms)
                slot_syms = ccall(:jl_compress_argnames, Ref{String}, (Any,), meth.source.slotnames)
            end
        end
        meth.slot_syms = slot_syms
        if generator !== nothing
            meth.generator = generator
        end
        if recursion_relation !== nothing
            meth.recursion_relation = recursion_relation
        end
        if !is_for_opaque_closure
            mt = ccall(:jl_method_table_for, Any, (Any,), sig)
            if mt !== nothing && nothing === ccall(:jl_methtable_lookup, Any, (Any, Any, UInt), mt, sig, typemax(UInt))
                ccall(:jl_method_table_insert, Cvoid, (Any, Any, Ptr{Cvoid}), mt, meth, C_NULL)
            end
        end
        remember_object(s, meth, lnumber)
    end
    return meth
end

function deserialize(s::AbstractSerializer, ::Type{Core.MethodInstance})
    linfo = ccall(:jl_new_method_instance_uninit, Ref{Core.MethodInstance}, (Ptr{Cvoid},), C_NULL)
    deserialize_cycle(s, linfo)
    tag = Int32(read(s.io, UInt8)::UInt8)
    if tag != UNDEFREF_TAG
        setfield!(linfo, :uninferred, handle_deserialize(s, tag)::CodeInfo, :monotonic)
    end
    tag = Int32(read(s.io, UInt8)::UInt8)
    if tag != UNDEFREF_TAG
        # for reading files prior to v1.2
        handle_deserialize(s, tag)
    end
    linfo.sparam_vals = deserialize(s)::SimpleVector
    _rettype = deserialize(s)  # for backwards compat
    linfo.specTypes = deserialize(s)
    linfo.def = deserialize(s)
    return linfo
end

function deserialize(s::AbstractSerializer, ::Type{Core.LineInfoNode})
    mod = deserialize(s)
    if mod isa Module
        method = deserialize(s)
    else
        # files post v1.2 and pre v1.6 are broken
        method = mod
        mod = Main
    end
    return Core.LineInfoNode(mod, method, deserialize(s)::Symbol, Int32(deserialize(s)::Union{Int32, Int}), Int32(deserialize(s)::Union{Int32, Int}))
end

function deserialize(s::AbstractSerializer, ::Type{PhiNode})
    edges = deserialize(s)
    if edges isa Vector{Any}
        edges = Vector{Int32}(edges)
    end
    values = deserialize(s)::Vector{Any}
    return PhiNode(edges, values)
end

function deserialize(s::AbstractSerializer, ::Type{CodeInfo})
    ci = ccall(:jl_new_code_info_uninit, Ref{CodeInfo}, ())
    deserialize_cycle(s, ci)
    code = deserialize(s)::Vector{Any}
    ci.code = code
    # allow older-style IR with return and gotoifnot Exprs
    for i in 1:length(code)
        stmt = code[i]
        if isa(stmt, Expr)
            ex = stmt::Expr
            if ex.head === :return
                code[i] = ReturnNode(isempty(ex.args) ? nothing : ex.args[1])
            elseif ex.head === :gotoifnot
                code[i] = GotoIfNot(ex.args[1], ex.args[2])
            end
        end
    end
    ci.codelocs = deserialize(s)::Vector{Int32}
    _x = deserialize(s)
    if _x isa Array || _x isa Int
        pre_12 = false
        ci.ssavaluetypes = _x
    else
        pre_12 = true
        # < v1.2
        ci.method_for_inference_limit_heuristics = _x
        ci.ssavaluetypes = deserialize(s)
        ci.linetable = deserialize(s)
    end
    ssaflags = deserialize(s)
    if length(ssaflags) ≠ length(code)
        # make sure the length of `ssaflags` matches that of `code`
        # so that the latest inference doesn't throw on IRs serialized from old versions
        ssaflags = UInt8[0x00 for _ in 1:length(code)]
    end
    ci.ssaflags = ssaflags
    if pre_12
        ci.slotflags = deserialize(s)
    else
        ci.method_for_inference_limit_heuristics = deserialize(s)
        ci.linetable = deserialize(s)
    end
    ci.slotnames = deserialize(s)
    if !pre_12
        ci.slotflags = deserialize(s)
        ci.slottypes = deserialize(s)
        ci.rettype = deserialize(s)
        ci.parent = deserialize(s)
        world_or_edges = deserialize(s)
        pre_13 = isa(world_or_edges, Integer)
        if pre_13
            ci.min_world = world_or_edges
        else
            ci.edges = world_or_edges
            ci.min_world = reinterpret(UInt, deserialize(s))
            ci.max_world = reinterpret(UInt, deserialize(s))
        end
    end
    ci.inferred = deserialize(s)
    if format_version(s) < 22
        inlining_cost = deserialize(s)
        if isa(inlining_cost, Bool)
            Core.Compiler.set_inlineable!(ci, inlining_cost)
        else
            ci.inlining_cost = inlining_cost
        end
    end
    ci.propagate_inbounds = deserialize(s)
    if format_version(s) < 23
        deserialize(s) # `pure` field has been removed
    end
    if format_version(s) >= 20
        ci.has_fcall = deserialize(s)
    end
    if format_version(s) >= 24
        ci.nospecializeinfer = deserialize(s)::Bool
    end
    if format_version(s) >= 21
        ci.inlining = deserialize(s)::UInt8
    end
    if format_version(s) >= 14
        ci.constprop = deserialize(s)::UInt8
    end
    if format_version(s) >= 17
        ci.purity = deserialize(s)::UInt8
    end
    if format_version(s) >= 22
        ci.inlining_cost = deserialize(s)::UInt16
    end
    return ci
end

if Int === Int64
const OtherInt = Int32
else
const OtherInt = Int64
end

function deserialize_array(s::AbstractSerializer)
    slot = s.counter; s.counter += 1
    d1 = deserialize(s)
    if isa(d1, Type)
        elty = d1
        d1 = deserialize(s)
    else
        elty = UInt8
    end
    if isa(d1, Int32) || isa(d1, Int64)
        if elty !== Bool && isbitstype(elty)
            a = Vector{elty}(undef, d1)
            s.table[slot] = a
            return read!(s.io, a)
        end
        dims = (Int(d1),)
    elseif d1 isa Dims
        dims = d1::Dims
    else
        dims = convert(Dims, d1::Tuple{Vararg{OtherInt}})::Dims
    end
    if isbitstype(elty)
        n = prod(dims)::Int
        if elty === Bool && n > 0
            A = Array{Bool, length(dims)}(undef, dims)
            i = 1
            while i <= n
                b = read(s.io, UInt8)::UInt8
                v = (b >> 7) != 0
                count = b & 0x7f
                nxt = i + count
                while i < nxt
                    A[i] = v
                    i += 1
                end
            end
        else
            A = read!(s.io, Array{elty}(undef, dims))
        end
        s.table[slot] = A
        return A
    end
    A = Array{elty, length(dims)}(undef, dims)
    s.table[slot] = A
    sizehint!(s.table, s.counter + div(length(A)::Int,4))
    deserialize_fillarray!(A, s)
    return A
end

function deserialize_fillarray!(A::Array{T}, s::AbstractSerializer) where {T}
    for i = eachindex(A)
        tag = Int32(read(s.io, UInt8)::UInt8)
        if tag != UNDEFREF_TAG
            @inbounds A[i] = handle_deserialize(s, tag)
        end
    end
    return A
end

function deserialize_expr(s::AbstractSerializer, len)
    e = Expr(:temp)
    resolve_ref_immediately(s, e)
    e.head = deserialize(s)::Symbol
    e.args = Any[ deserialize(s) for i = 1:len ]
    e
end

module __deserialized_types__ end

function deserialize(s::AbstractSerializer, ::Type{Core.TypeName})
    number = read(s.io, UInt64)
    return deserialize_typename(s, number)
end

function deserialize_typename(s::AbstractSerializer, number)
    name = deserialize(s)::Symbol
    tn = lookup_object_number(s, number)
    if tn !== nothing
        makenew = false
    else
        # reuse the same name for the type, if possible, for nicer debugging
        tn_name = isdefined(__deserialized_types__, name) ? gensym() : name
        tn = ccall(:jl_new_typename_in, Any, (Any, Any, Cint, Cint),
                   tn_name, __deserialized_types__, false, false)
        makenew = true
    end
    tn = tn::Core.TypeName
    remember_object(s, tn, number)
    deserialize_cycle(s, tn)

    names = deserialize(s)::SimpleVector
    super = deserialize(s)::Type
    parameters = deserialize(s)::SimpleVector
    types = deserialize(s)::SimpleVector
    attrs = Core.svec()
    has_instance = deserialize(s)::Bool
    abstr = deserialize(s)::Bool
    mutabl = deserialize(s)::Bool
    ninitialized = deserialize(s)::Int32
    maxm = format_version(s) >= 18 ? deserialize(s)::UInt8 : UInt8(0)

    if makenew
        # TODO: there's an unhanded cycle in the dependency graph at this point:
        # while deserializing super and/or types, we may have encountered
        # tn.wrapper and throw UndefRefException before we get to this point
        ndt = ccall(:jl_new_datatype, Any, (Any, Any, Any, Any, Any, Any, Any, Cint, Cint, Cint),
                    tn, tn.module, super, parameters, names, types, attrs,
                    abstr, mutabl, ninitialized)
        @assert tn == ndt.name
        ccall(:jl_set_const, Cvoid, (Any, Any, Any), tn.module, tn.name, tn.wrapper)
        ty = tn.wrapper
        tn.max_methods = maxm
        if has_instance
            ty = ty::DataType
            if !Base.issingletontype(ty)
                singleton = ccall(:jl_new_struct, Any, (Any, Any...), ty)
                # use setfield! directly to avoid `fieldtype` lowering expecting to see a Singleton object already on ty
                ccall(:jl_set_nth_field, Cvoid, (Any, Csize_t, Any), ty, Base.fieldindex(DataType, :instance)-1, singleton)
            end
        end
    end

    tag = Int32(read(s.io, UInt8)::UInt8)
    if tag != UNDEFREF_TAG
        mtname = handle_deserialize(s, tag)
        defs = deserialize(s)
        maxa = deserialize(s)::Int
        if makenew
            mt = ccall(:jl_new_method_table, Any, (Any, Any), name, tn.module)
            if !isempty(parameters)
                mt.offs = 0
            end
            mt.name = mtname
            setfield!(mt, :max_args, maxa, :monotonic)
            ccall(:jl_set_nth_field, Cvoid, (Any, Csize_t, Any), tn, Base.fieldindex(Core.TypeName, :mt)-1, mt)
            for def in defs
                if isdefined(def, :sig)
                    ccall(:jl_method_table_insert, Cvoid, (Any, Any, Ptr{Cvoid}), mt, def, C_NULL)
                end
            end
        end
        tag = Int32(read(s.io, UInt8)::UInt8)
        if tag != UNDEFREF_TAG
            kws = handle_deserialize(s, tag)
            if makenew
                if kws isa Vector{Method}
                    for def in kws
                        kwmt = typeof(Core.kwcall).name.mt
                        ccall(:jl_method_table_insert, Cvoid, (Any, Any, Ptr{Cvoid}), mt, def, C_NULL)
                    end
                else
                    # old object format -- try to forward from old to new
                    @eval Core.kwcall(kwargs::NamedTuple, f::$ty, args...) = $kws(kwargs, f, args...)
                end
            end
        end
    elseif makenew
        mt = Symbol.name.mt
        ccall(:jl_set_nth_field, Cvoid, (Any, Csize_t, Any), tn, Base.fieldindex(Core.TypeName, :mt)-1, mt)
    end
    return tn
end

function deserialize_datatype(s::AbstractSerializer, full::Bool)
    slot = s.counter; s.counter += 1
    if full
        tname = deserialize(s)::Core.TypeName
        ty = tname.wrapper
    else
        name = deserialize(s)::Symbol
        mod = deserialize(s)::Module
        ty = getglobal(mod, name)
    end
    if isa(ty,DataType) && isempty(ty.parameters)
        t = ty
    else
        np = Int(read(s.io, Int32)::Int32)
        if np == 0
            t = unwrap_unionall(ty)
        elseif ty === Tuple
            # note np==0 has its own tag
            if np == 1
                t = Tuple{deserialize(s)}
            elseif np == 2
                t = Tuple{deserialize(s), deserialize(s)}
            elseif np == 3
                t = Tuple{deserialize(s), deserialize(s), deserialize(s)}
            elseif np == 4
                t = Tuple{deserialize(s), deserialize(s), deserialize(s), deserialize(s)}
            else
                t = Tuple{Any[ deserialize(s) for i=1:np ]...}
            end
        else
            t = ty
            for i = 1:np
                t = t{deserialize(s)}
            end
        end
    end
    s.table[slot] = t
    return t
end

function deserialize(s::AbstractSerializer, ::Type{UnionAll})
    form = read(s.io, UInt8)
    if form == 0
        var = deserialize(s)
        body = deserialize(s)
        return UnionAll(var, body)
    else
        n = read(s.io, Int16)
        t = deserialize(s)::DataType
        w = t.name.wrapper
        k = 0
        while isa(w, UnionAll)
            w = w.body
            k += 1
        end
        w = t.name.wrapper
        k -= n
        while k > 0
            w = w.body
            k -= 1
        end
        return w
    end
end

function deserialize(s::AbstractSerializer, ::Type{Task})
    t = Task(()->nothing)
    deserialize_cycle(s, t)
    t.code = deserialize(s)
    t.storage = deserialize(s)
    state = deserialize(s)
    if state === :runnable
        t._state = Base.task_state_runnable
    elseif state === :done
        t._state = Base.task_state_done
    elseif state === :failed
        t._state = Base.task_state_failed
    else
        @assert false
    end
    t.result = deserialize(s)
    exc = deserialize(s)
    if exc === nothing
        t._isexception = false
    elseif exc isa Bool
        t._isexception = exc
    else
        t._isexception = true
        t.result = exc
    end
    t
end

function deserialize_string(s::AbstractSerializer, len::Int)
    out = ccall(:jl_alloc_string, Ref{String}, (Csize_t,), len)
    unsafe_read(s.io, pointer(out), len)
    return out
end

# default DataType deserializer
function deserialize(s::AbstractSerializer, t::DataType)
    nf = length(t.types)
    if isprimitivetype(t)
        return read(s.io, t)
    elseif ismutabletype(t)
        x = ccall(:jl_new_struct_uninit, Any, (Any,), t)
        deserialize_cycle(s, x)
        for i in 1:nf
            tag = Int32(read(s.io, UInt8)::UInt8)
            if tag != UNDEFREF_TAG
                ccall(:jl_set_nth_field, Cvoid, (Any, Csize_t, Any), x, i-1, handle_deserialize(s, tag))
            end
        end
        return x
    elseif nf == 0
        return ccall(:jl_new_struct_uninit, Any, (Any,), t)
    else
        na = nf
        vflds = Vector{Any}(undef, nf)
        for i in 1:nf
            tag = Int32(read(s.io, UInt8)::UInt8)
            if tag != UNDEFREF_TAG
                f = handle_deserialize(s, tag)
                na >= i && (vflds[i] = f)
            else
                na >= i && (na = i - 1) # rest of tail must be undefined values
            end
        end
        return ccall(:jl_new_structv, Any, (Any, Ptr{Any}, UInt32), t, vflds, na)
    end
end

function deserialize_dict(s::AbstractSerializer, T::Type{<:AbstractDict})
    n = read(s.io, Int32)
    t = T(); sizehint!(t, n)
    deserialize_cycle(s, t)
    for i = 1:n
        k = deserialize(s)
        v = deserialize(s)
        t[k] = v
    end
    return t
end

function deserialize(s::AbstractSerializer, T::Type{Dict{K,V}}) where {K,V}
    return deserialize_dict(s, T)
end

deserialize(s::AbstractSerializer, ::Type{BigInt}) = parse(BigInt, deserialize(s), base = 62)

function deserialize(s::AbstractSerializer, t::Type{Regex})
    pattern = deserialize(s)
    compile_options = deserialize(s)
    match_options = deserialize(s)
    return Regex(pattern, compile_options, match_options)
end

## StackTraces

# provide a custom serializer that skips attempting to serialize the `outer_linfo`
# which is likely to contain complex references, types, and module references
# that may not exist on the receiver end
function serialize(s::AbstractSerializer, frame::Base.StackTraces.StackFrame)
    serialize_type(s, typeof(frame))
    serialize(s, frame.func)
    serialize(s, frame.file)
    write(s.io, frame.line)
    write(s.io, frame.from_c)
    write(s.io, frame.inlined)
    write(s.io, frame.pointer)
    nothing
end

function deserialize(s::AbstractSerializer, ::Type{Base.StackTraces.StackFrame})
    func = deserialize(s)
    file = deserialize(s)
    line = read(s.io, Int)
    from_c = read(s.io, Bool)
    inlined = read(s.io, Bool)
    pointer = read(s.io, UInt64)
    return Base.StackTraces.StackFrame(func, file, line, nothing, from_c, inlined, pointer)
end

function serialize(s::AbstractSerializer, lock::Base.AbstractLock)
    # assert_havelock(lock)
    serialize_cycle_header(s, lock)
    nothing
end

function deserialize(s::AbstractSerializer, ::Type{T}) where T<:Base.AbstractLock
    lock = T()
    deserialize_cycle(s, lock)
    return lock
end

function serialize(s::AbstractSerializer, cond::Base.GenericCondition)
    serialize_cycle_header(s, cond) && return
    serialize(s, cond.lock)
    nothing
end

function deserialize(s::AbstractSerializer, ::Type{T}) where T<:Base.GenericCondition
    lock = deserialize(s)
    cond = T(lock)
    deserialize_cycle(s, cond)
    return cond
end

serialize(s::AbstractSerializer, l::LazyString) =
    invoke(serialize, Tuple{AbstractSerializer,Any}, s, Base._LazyString((), string(l)))

end
r   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Sockets/src/Sockets.jl�p      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
Support for sockets. Provides [`IPAddr`](@ref) and subtypes, [`TCPSocket`](@ref), and [`UDPSocket`](@ref).
"""
module Sockets

export
    accept,
    bind,
    connect,
    getaddrinfo,
    getalladdrinfo,
    getnameinfo,
    getipaddr,
    getipaddrs,
    islinklocaladdr,
    getpeername,
    getsockname,
    listen,
    listenany,
    recv,
    recvfrom,
    send,
    join_multicast_group,
    leave_multicast_group,
    TCPSocket,
    UDPSocket,
    @ip_str,
    IPAddr,
    IPv4,
    IPv6

import Base: isless, show, print, parse, bind, convert, isreadable, iswritable, alloc_buf_hook, _uv_hook_close

using Base: LibuvStream, LibuvServer, PipeEndpoint, @handle_as, uv_error, associate_julia_struct, uvfinalize,
    notify_error, uv_req_data, uv_req_set_data, preserve_handle, unpreserve_handle, _UVError, IOError,
    eventloop, StatusUninit, StatusInit, StatusConnecting, StatusOpen, StatusClosing, StatusClosed, StatusActive,
    preserve_handle, unpreserve_handle, iolock_begin, iolock_end,
    uv_status_string, check_open, OS_HANDLE, RawFD,
    UV_EINVAL, UV_ENOMEM, UV_ENOBUFS, UV_EAGAIN, UV_ECONNABORTED, UV_EADDRINUSE, UV_EACCES, UV_EADDRNOTAVAIL,
    UV_EAI_ADDRFAMILY, UV_EAI_AGAIN, UV_EAI_BADFLAGS,
    UV_EAI_BADHINTS, UV_EAI_CANCELED, UV_EAI_FAIL,
    UV_EAI_FAMILY, UV_EAI_NODATA, UV_EAI_NONAME,
    UV_EAI_OVERFLOW, UV_EAI_PROTOCOL, UV_EAI_SERVICE,
    UV_EAI_SOCKTYPE, UV_EAI_MEMORY

include("IPAddr.jl")
include("addrinfo.jl")

"""
    TCPSocket(; delay=true)

Open a TCP socket using libuv. If `delay` is true, libuv delays creation of the
socket's file descriptor till the first [`bind`](@ref) call. `TCPSocket` has various
fields to denote the state of the socket as well as its send/receive buffers.
"""
mutable struct TCPSocket <: LibuvStream
    handle::Ptr{Cvoid}
    status::Int
    buffer::IOBuffer
    cond::Base.ThreadSynchronizer
    readerror::Any
    sendbuf::Union{IOBuffer, Nothing}
    lock::ReentrantLock # advisory lock
    throttle::Int

    function TCPSocket(handle::Ptr{Cvoid}, status)
        tcp = new(
                handle,
                status,
                PipeBuffer(),
                Base.ThreadSynchronizer(),
                nothing,
                nothing,
                ReentrantLock(),
                Base.DEFAULT_READ_BUFFER_SZ)
        associate_julia_struct(tcp.handle, tcp)
        finalizer(uvfinalize, tcp)
        return tcp
    end
end

# kw arg "delay": if true, libuv delays creation of the socket fd till the first bind call
function TCPSocket(; delay=true)
    tcp = TCPSocket(Libc.malloc(Base._sizeof_uv_tcp), StatusUninit)
    af_spec = delay ? 0 : 2   # AF_UNSPEC is 0, AF_INET is 2
    iolock_begin()
    err = ccall(:uv_tcp_init_ex, Cint, (Ptr{Cvoid}, Ptr{Cvoid}, Cuint),
                eventloop(), tcp.handle, af_spec)
    uv_error("failed to create tcp socket", err)
    tcp.status = StatusInit
    iolock_end()
    return tcp
end

function TCPSocket(fd::OS_HANDLE)
    tcp = TCPSocket()
    iolock_begin()
    err = ccall(:uv_tcp_open, Int32, (Ptr{Cvoid}, OS_HANDLE), tcp.handle, fd)
    uv_error("tcp_open", err)
    tcp.status = StatusOpen
    iolock_end()
    return tcp
end
if OS_HANDLE != RawFD
    TCPSocket(fd::RawFD) = TCPSocket(Libc._get_osfhandle(fd))
end


mutable struct TCPServer <: LibuvServer
    handle::Ptr{Cvoid}
    status::Int
    cond::Base.ThreadSynchronizer

    function TCPServer(handle::Ptr{Cvoid}, status)
        tcp = new(
            handle,
            status,
            Base.ThreadSynchronizer())
        associate_julia_struct(tcp.handle, tcp)
        finalizer(uvfinalize, tcp)
        return tcp
    end
end

# Keyword arg "delay": if true, libuv delays creation of socket fd till bind.
# It can be set to false if there is a need to set socket options before
# further calls to `bind` and `listen`, e.g. `SO_REUSEPORT`.
function TCPServer(; delay=true)
    tcp = TCPServer(Libc.malloc(Base._sizeof_uv_tcp), StatusUninit)
    af_spec = delay ? 0 : 2   # AF_UNSPEC is 0, AF_INET is 2
    iolock_begin()
    err = ccall(:uv_tcp_init_ex, Cint, (Ptr{Cvoid}, Ptr{Cvoid}, Cuint),
                eventloop(), tcp.handle, af_spec)
    uv_error("failed to create tcp server", err)
    tcp.status = StatusInit
    iolock_end()
    return tcp
end

"""
    accept(server[, client])

Accepts a connection on the given server and returns a connection to the client. An
uninitialized client stream may be provided, in which case it will be used instead of
creating a new stream.
"""
accept(server::TCPServer) = accept(server, TCPSocket())

function accept(callback, server::LibuvServer)
    task = @async try
            while true
                client = accept(server)
                callback(client)
            end
        catch ex
            # accept below may explicitly throw UV_ECONNABORTED:
            # filter that out since we expect that error
            if !(ex isa IOError && ex.code == UV_ECONNABORTED) || isopen(server)
                rethrow()
            end
        end
    return task # caller is responsible for checking for errors
end


# UDP
"""
    UDPSocket()

Open a UDP socket using libuv. `UDPSocket` has various
fields to denote the state of the socket.
"""
mutable struct UDPSocket <: LibuvStream
    handle::Ptr{Cvoid}
    status::Int
    recvnotify::Base.ThreadSynchronizer
    cond::Base.ThreadSynchronizer

    function UDPSocket(handle::Ptr{Cvoid}, status)
        cond = Base.ThreadSynchronizer()
        udp = new(handle, status, Base.ThreadSynchronizer(cond.lock), cond)
        associate_julia_struct(udp.handle, udp)
        finalizer(uvfinalize, udp)
        return udp
    end
end
function UDPSocket()
    this = UDPSocket(Libc.malloc(Base._sizeof_uv_udp), StatusUninit)
    iolock_begin()
    err = ccall(:uv_udp_init, Cint, (Ptr{Cvoid}, Ptr{Cvoid}),
                eventloop(), this.handle)
    uv_error("failed to create udp socket", err)
    this.status = StatusInit
    iolock_end()
    return this
end

show(io::IO, stream::UDPSocket) = print(io, typeof(stream), "(", uv_status_string(stream), ")")

function _uv_hook_close(sock::UDPSocket)
    lock(sock.cond)
    try
        sock.status = StatusClosed
        notify(sock.cond)
        notify_error(sock.recvnotify, EOFError())
    finally
        unlock(sock.cond)
    end
    nothing
end

# Disables dual stack mode.
const UV_TCP_IPV6ONLY = 1

# Disables dual stack mode. Only available when using ipv6 binf
const UV_UDP_IPV6ONLY = 1

# Indicates message was truncated because read buffer was too small. The
# remainder was discarded by the OS.
const UV_UDP_PARTIAL = 2

# Indicates if SO_REUSEADDR will be set when binding the handle in uv_udp_bind. This sets
# the SO_REUSEPORT socket flag on the BSDs and OS X. On other Unix platforms, it sets the
# SO_REUSEADDR flag. What that means is that multiple threads or processes can bind to the
# same address without error (provided they all set the flag) but only the last one to bind
# will receive any traffic, in effect "stealing" the port from the previous listener.
const UV_UDP_REUSEADDR = 4

##

function _bind(sock::Union{TCPServer, TCPSocket}, host::Union{IPv4, IPv6}, port::UInt16, flags::UInt32=UInt32(0))
    host_in = Ref(hton(host.host))
    return ccall(:jl_tcp_bind, Int32, (Ptr{Cvoid}, UInt16, Ptr{Cvoid}, Cuint, Cint),
            sock, hton(port), host_in, flags, host isa IPv6)
end

function _bind(sock::UDPSocket, host::Union{IPv4, IPv6}, port::UInt16, flags::UInt32=UInt32(0))
    host_in = Ref(hton(host.host))
    return ccall(:jl_udp_bind, Int32, (Ptr{Cvoid}, UInt16, Ptr{Cvoid}, Cuint, Cint),
            sock, hton(port), host_in, flags, host isa IPv6)
end

"""
    bind(socket::Union{TCPServer, UDPSocket, TCPSocket}, host::IPAddr, port::Integer; ipv6only=false, reuseaddr=false, kws...)

Bind `socket` to the given `host:port`. Note that `0.0.0.0` will listen on all devices.

* The `ipv6only` parameter disables dual stack mode. If `ipv6only=true`, only an IPv6 stack is created.
* If `reuseaddr=true`, multiple threads or processes can bind to the same address without error
  if they all set `reuseaddr=true`, but only the last to bind will receive any traffic.
"""
function bind(sock::Union{TCPServer, UDPSocket, TCPSocket}, host::IPAddr, port::Integer; ipv6only = false, reuseaddr = false, kws...)
    if sock.status != StatusInit
        error("$(typeof(sock)) is not in initialization state")
    end
    flags = 0
    if isa(host, IPv6) && ipv6only
        flags |= isa(sock, UDPSocket) ? UV_UDP_IPV6ONLY : UV_TCP_IPV6ONLY
    end
    if isa(sock, UDPSocket) && reuseaddr
        flags |= UV_UDP_REUSEADDR
    end
    iolock_begin()
    err = _bind(sock, host, UInt16(port), UInt32(flags))
    if err < 0
        iolock_end()
        if err != UV_EADDRINUSE && err != UV_EACCES && err != UV_EADDRNOTAVAIL
            #TODO: this codepath is not currently tested
            throw(_UVError("bind", err))
        else
            return false
        end
    end
    if isa(sock, TCPServer) || isa(sock, UDPSocket)
        sock.status = StatusOpen
    end
    isa(sock, UDPSocket) && setopt(sock; kws...)
    iolock_end()
    return true
end

bind(sock::TCPServer, addr::InetAddr) = bind(sock, addr.host, addr.port)

"""
    setopt(sock::UDPSocket; multicast_loop=nothing, multicast_ttl=nothing, enable_broadcast=nothing, ttl=nothing)

Set UDP socket options.

* `multicast_loop`: loopback for multicast packets (default: `true`).
* `multicast_ttl`: TTL for multicast packets (default: `nothing`).
* `enable_broadcast`: flag must be set to `true` if socket will be used for broadcast
  messages, or else the UDP system will return an access error (default: `false`).
* `ttl`: Time-to-live of packets sent on the socket (default: `nothing`).
"""
function setopt(sock::UDPSocket; multicast_loop=nothing, multicast_ttl=nothing, enable_broadcast=nothing, ttl=nothing)
    iolock_begin()
    if sock.status == StatusUninit
        error("Cannot set options on uninitialized socket")
    end
    if multicast_loop !== nothing
        uv_error("multicast_loop", ccall(:uv_udp_set_multicast_loop, Cint, (Ptr{Cvoid}, Cint), sock.handle, multicast_loop) < 0)
    end
    if multicast_ttl !== nothing
        uv_error("multicast_ttl", ccall(:uv_udp_set_multicast_ttl, Cint, (Ptr{Cvoid}, Cint), sock.handle, multicast_ttl))
    end
    if enable_broadcast !== nothing
        uv_error("enable_broadcast", ccall(:uv_udp_set_broadcast, Cint, (Ptr{Cvoid}, Cint), sock.handle, enable_broadcast))
    end
    if ttl !== nothing
        uv_error("ttl", ccall(:uv_udp_set_ttl, Cint, (Ptr{Cvoid}, Cint), sock.handle, ttl))
    end
    iolock_end()
    nothing
end

"""
    recv(socket::UDPSocket)

Read a UDP packet from the specified socket, and return the bytes received. This call blocks.
"""
function recv(sock::UDPSocket)
    addr, data = recvfrom(sock)
    return data
end

function uv_recvcb end

"""
    recvfrom(socket::UDPSocket) -> (host_port, data)

Read a UDP packet from the specified socket, returning a tuple of `(host_port, data)`, where
`host_port` will be an InetAddr{IPv4} or InetAddr{IPv6}, as appropriate.

!!! compat "Julia 1.3"
    Prior to Julia version 1.3, the first returned value was an address (`IPAddr`).
    In version 1.3 it was changed to an `InetAddr`.
"""
function recvfrom(sock::UDPSocket)
    iolock_begin()
    # If the socket has not been bound, it will be bound implicitly to ::0 and a random port
    if sock.status != StatusInit && sock.status != StatusOpen && sock.status != StatusActive
        error("UDPSocket is not initialized and open")
    end
    if ccall(:uv_is_active, Cint, (Ptr{Cvoid},), sock.handle) == 0
        err = ccall(:uv_udp_recv_start, Cint, (Ptr{Cvoid}, Ptr{Cvoid}, Ptr{Cvoid}),
                    sock,
                    @cfunction(Base.uv_alloc_buf, Cvoid, (Ptr{Cvoid}, Csize_t, Ptr{Cvoid})),
                    @cfunction(uv_recvcb, Cvoid, (Ptr{Cvoid}, Cssize_t, Ptr{Cvoid}, Ptr{Cvoid}, Cuint)))
        uv_error("recv_start", err)
    end
    sock.status = StatusActive
    lock(sock.recvnotify)
    iolock_end()
    try
        From = Union{InetAddr{IPv4}, InetAddr{IPv6}}
        Data = Vector{UInt8}
        from, data = wait(sock.recvnotify)::Tuple{From, Data}
        return (from, data)
    finally
        unlock(sock.recvnotify)
    end
end

alloc_buf_hook(sock::UDPSocket, size::UInt) = (Libc.malloc(size), Int(size)) # size is always 64k from libuv

function uv_recvcb(handle::Ptr{Cvoid}, nread::Cssize_t, buf::Ptr{Cvoid}, addr::Ptr{Cvoid}, flags::Cuint)
    sock = @handle_as handle UDPSocket
    lock(sock.recvnotify)
    try
        buf_addr = ccall(:jl_uv_buf_base, Ptr{UInt8}, (Ptr{Cvoid},), buf)
        if nread == 0 && addr == C_NULL
            Libc.free(buf_addr)
        elseif nread < 0
            Libc.free(buf_addr)
            notify_error(sock.recvnotify, _UVError("recv", nread))
        elseif flags & UV_UDP_PARTIAL > 0
            Libc.free(buf_addr)
            notify_error(sock.recvnotify, "Partial message received")
        else
            buf_size = Int(ccall(:jl_uv_buf_len, Csize_t, (Ptr{Cvoid},), buf))
            if buf_size - nread < 16384 # waste at most 16k (note: buf_size is currently always 64k)
                buf = unsafe_wrap(Array, buf_addr, nread, own=true)
            else
                buf = Vector{UInt8}(undef, nread)
                GC.@preserve buf unsafe_copyto!(pointer(buf), buf_addr, nread)
                Libc.free(buf_addr)
            end
            # need to check the address type in order to convert to a Julia IPAddr
            host = IPv4(0)
            port = UInt16(0)
            if ccall(:jl_sockaddr_is_ip4, Cint, (Ptr{Cvoid},), addr) == 1
                host = IPv4(ntoh(ccall(:jl_sockaddr_host4, UInt32, (Ptr{Cvoid},), addr)))
                port = ntoh(ccall(:jl_sockaddr_port4, UInt16, (Ptr{Cvoid},), addr))
            elseif ccall(:jl_sockaddr_is_ip6, Cint, (Ptr{Cvoid},), addr) == 1
                tmp = Ref{UInt128}(0)
                scope_id = ccall(:jl_sockaddr_host6, UInt32, (Ptr{Cvoid}, Ptr{UInt128}), addr, tmp)
                host = IPv6(ntoh(tmp[]))
                port = ntoh(ccall(:jl_sockaddr_port6, UInt16, (Ptr{Cvoid},), addr))
            end
            from = InetAddr(host, port)
            notify(sock.recvnotify, (from, buf), all=false)
        end
        if sock.status == StatusActive && isempty(sock.recvnotify)
            sock.status = StatusOpen
            ccall(:uv_udp_recv_stop, Cint, (Ptr{Cvoid},), sock)
        end
    finally
        unlock(sock.recvnotify)
    end
    nothing
end

function _send_async(sock::UDPSocket, ipaddr::Union{IPv4, IPv6}, port::UInt16, buf)
    req = Libc.malloc(Base._sizeof_uv_udp_send)
    uv_req_set_data(req, C_NULL) # in case we get interrupted before arriving at the wait call
    host_in = Ref(hton(ipaddr.host))
    err = ccall(:jl_udp_send, Cint, (Ptr{Cvoid}, Ptr{Cvoid}, UInt16, Ptr{Cvoid}, Ptr{UInt8}, Csize_t, Ptr{Cvoid}, Cint),
                req, sock, hton(port), host_in, buf, sizeof(buf),
                @cfunction(Base.uv_writecb_task, Cvoid, (Ptr{Cvoid}, Cint)),
                ipaddr isa IPv6)
    if err < 0
        Libc.free(req)
        uv_error("send", err)
    end
    return req
end

"""
    send(socket::UDPSocket, host::IPAddr, port::Integer, msg)

Send `msg` over `socket` to `host:port`.
"""
function send(sock::UDPSocket, ipaddr::IPAddr, port::Integer, msg)
    # If the socket has not been bound, it will be bound implicitly to ::0 and a random port
    iolock_begin()
    if sock.status != StatusInit && sock.status != StatusOpen && sock.status != StatusActive
        error("UDPSocket is not initialized and open")
    end
    uvw = _send_async(sock, ipaddr, UInt16(port), msg)
    ct = current_task()
    preserve_handle(ct)
    Base.sigatomic_begin()
    uv_req_set_data(uvw, ct)
    iolock_end()
    status = try
        Base.sigatomic_end()
        wait()::Cint
    finally
        Base.sigatomic_end()
        iolock_begin()
        ct.queue === nothing || list_deletefirst!(ct.queue, ct)
        if uv_req_data(uvw) != C_NULL
            # uvw is still alive,
            # so make sure we won't get spurious notifications later
            uv_req_set_data(uvw, C_NULL)
        else
            # done with uvw
            Libc.free(uvw)
        end
        iolock_end()
        unpreserve_handle(ct)
    end
    uv_error("send", status)
    nothing
end


#from `connect`
function uv_connectcb(conn::Ptr{Cvoid}, status::Cint)
    hand = ccall(:jl_uv_connect_handle, Ptr{Cvoid}, (Ptr{Cvoid},), conn)
    sock = @handle_as hand LibuvStream
    lock(sock.cond)
    try
        if status >= 0 # success
            if !(sock.status == StatusClosed || sock.status == StatusClosing)
                sock.status = StatusOpen
            end
        else
            sock.readerror = _UVError("connect", status) # TODO: perhaps we should not reuse readerror for this
            if !(sock.status == StatusClosed || sock.status == StatusClosing)
                ccall(:jl_forceclose_uv, Cvoid, (Ptr{Cvoid},), hand)
                sock.status = StatusClosing
            end
        end
        notify(sock.cond)
    finally
        unlock(sock.cond)
    end
    Libc.free(conn)
    nothing
end

function connect!(sock::TCPSocket, host::Union{IPv4, IPv6}, port::Integer)
    iolock_begin()
    if sock.status != StatusInit
        error("TCPSocket is not in initialization state")
    end
    if !(0 <= port <= typemax(UInt16))
        throw(ArgumentError("port out of range, must be 0 ≤ port ≤ 65535, got $port"))
    end
    host_in = Ref(hton(host.host))
    uv_error("connect", ccall(:jl_tcp_connect, Int32, (Ptr{Cvoid}, Ptr{Cvoid}, UInt16, Ptr{Cvoid}, Cint),
                              sock, host_in, hton(UInt16(port)), @cfunction(uv_connectcb, Cvoid, (Ptr{Cvoid}, Cint)),
                              host isa IPv6))
    sock.status = StatusConnecting
    iolock_end()
    nothing
end

connect!(sock::TCPSocket, addr::InetAddr) = connect!(sock, addr.host, addr.port)

function wait_connected(x::LibuvStream)
    iolock_begin()
    check_open(x)
    isopen(x) || x.readerror === nothing || throw(x.readerror)
    preserve_handle(x)
    lock(x.cond)
    try
        while x.status == StatusConnecting
            iolock_end()
            wait(x.cond)
            unlock(x.cond)
            iolock_begin()
            lock(x.cond)
        end
        isopen(x) || x.readerror === nothing || throw(x.readerror)
    finally
        unlock(x.cond)
        unpreserve_handle(x)
    end
    iolock_end()
    nothing
end

# Default Host to localhost

"""
    connect([host], port::Integer) -> TCPSocket

Connect to the host `host` on port `port`.
"""
connect(sock::TCPSocket, port::Integer) = connect(sock, localhost, port)
connect(port::Integer) = connect(localhost, port)

# Valid connect signatures for TCP
connect(host::AbstractString, port::Integer) = connect(TCPSocket(), host, port)
connect(addr::IPAddr, port::Integer) = connect(TCPSocket(), addr, port)
connect(addr::InetAddr) = connect(TCPSocket(), addr)

function connect!(sock::TCPSocket, host::AbstractString, port::Integer)
    if sock.status != StatusInit
        error("TCPSocket is not in initialization state")
    end
    ipaddr = getaddrinfo(host)
    connect!(sock, ipaddr, port)
    return sock
end

function connect(sock::LibuvStream, args...)
    connect!(sock, args...)
    wait_connected(sock)
    return sock
end

"""
    nagle(socket::Union{TCPServer, TCPSocket}, enable::Bool)

Enables or disables Nagle's algorithm on a given TCP server or socket.

!!! compat "Julia 1.3"
    This function requires Julia 1.3 or later.
"""
function nagle(sock::Union{TCPServer, TCPSocket}, enable::Bool)
    # disable or enable Nagle's algorithm on all OSes
    iolock_begin()
    check_open(sock)
    err = ccall(:uv_tcp_nodelay, Cint, (Ptr{Cvoid}, Cint), sock.handle, Cint(!enable))
    # TODO: check err
    iolock_end()
    return err
end

"""
    quickack(socket::Union{TCPServer, TCPSocket}, enable::Bool)

On Linux systems, the TCP_QUICKACK is disabled or enabled on `socket`.
"""
function quickack(sock::Union{TCPServer, TCPSocket}, enable::Bool)
    iolock_begin()
    check_open(sock)
    @static if Sys.islinux()
        # tcp_quickack is a linux only option
        if ccall(:jl_tcp_quickack, Cint, (Ptr{Cvoid}, Cint), sock.handle, Cint(enable)) < 0
            @warn "Networking unoptimized ( Error enabling TCP_QUICKACK : $(Libc.strerror(Libc.errno())) )" maxlog=1
        end
    end
    iolock_end()
    nothing
end


##

const BACKLOG_DEFAULT = 511

"""
    listen([addr, ]port::Integer; backlog::Integer=BACKLOG_DEFAULT) -> TCPServer

Listen on port on the address specified by `addr`.
By default this listens on `localhost` only.
To listen on all interfaces pass `IPv4(0)` or `IPv6(0)` as appropriate.
`backlog` determines how many connections can be pending (not having
called [`accept`](@ref)) before the server will begin to
reject them. The default value of `backlog` is 511.
"""
function listen(addr; backlog::Integer=BACKLOG_DEFAULT)
    sock = TCPServer()
    bind(sock, addr) || error("cannot bind to port; may already be in use or access denied")
    listen(sock; backlog=backlog)
    return sock
end
listen(port::Integer; backlog::Integer=BACKLOG_DEFAULT) = listen(localhost, port; backlog=backlog)
listen(host::IPAddr, port::Integer; backlog::Integer=BACKLOG_DEFAULT) = listen(InetAddr(host, port); backlog=backlog)

function listen(sock::LibuvServer; backlog::Integer=BACKLOG_DEFAULT)
    uv_error("listen", trylisten(sock; backlog=backlog))
    return sock
end

# from `listen`
function uv_connectioncb(stream::Ptr{Cvoid}, status::Cint)
    sock = @handle_as stream LibuvServer
    lock(sock.cond)
    try
        if status >= 0
            notify(sock.cond)
        else
            notify_error(sock.cond, _UVError("connection", status))
        end
    finally
        unlock(sock.cond)
    end
    nothing
end

function trylisten(sock::LibuvServer; backlog::Integer=BACKLOG_DEFAULT)
    iolock_begin()
    check_open(sock)
    err = ccall(:uv_listen, Cint, (Ptr{Cvoid}, Cint, Ptr{Cvoid}),
                sock, backlog, @cfunction(uv_connectioncb, Cvoid, (Ptr{Cvoid}, Cint)))
    sock.status = StatusActive
    iolock_end()
    return err
end

##

function accept_nonblock(server::TCPServer, client::TCPSocket)
    iolock_begin()
    if client.status != StatusInit
        error("client TCPSocket is not in initialization state")
    end
    err = ccall(:uv_accept, Int32, (Ptr{Cvoid}, Ptr{Cvoid}), server.handle, client.handle)
    if err == 0
        client.status = StatusOpen
    end
    iolock_end()
    return err
end

function accept_nonblock(server::TCPServer)
    client = TCPSocket()
    uv_error("accept", accept_nonblock(server, client))
    return client
end

function accept(server::LibuvServer, client::LibuvStream)
    iolock_begin()
    if server.status != StatusActive && server.status != StatusClosing && server.status != StatusClosed
        throw(ArgumentError("server not connected, make sure \"listen\" has been called"))
    end
    while isopen(server)
        err = accept_nonblock(server, client)
        if err == 0
            iolock_end()
            return client
        elseif err != UV_EAGAIN
            uv_error("accept", err)
        end
        preserve_handle(server)
        lock(server.cond)
        iolock_end()
        try
            wait(server.cond)
        finally
            unlock(server.cond)
            unpreserve_handle(server)
        end
        iolock_begin()
    end
    uv_error("accept", UV_ECONNABORTED)
    nothing
end

## Utility functions

const localhost = ip"127.0.0.1"

"""
    listenany([host::IPAddr,] port_hint; backlog::Integer=BACKLOG_DEFAULT) -> (UInt16, TCPServer)

Create a `TCPServer` on any port, using hint as a starting point. Returns a tuple of the
actual port that the server was created on and the server itself.
The backlog argument defines the maximum length to which the queue of pending connections for sockfd may grow.
"""
function listenany(host::IPAddr, default_port; backlog::Integer=BACKLOG_DEFAULT)
    addr = InetAddr(host, default_port)
    while true
        sock = TCPServer()
        if bind(sock, addr) && trylisten(sock; backlog) == 0
            if default_port == 0
                _addr, port = getsockname(sock)
                return (port, sock)
            end
            return (addr.port, sock)
        end
        close(sock)
        addr = InetAddr(addr.host, addr.port + UInt16(1))
        if addr.port == default_port
            error("no ports available")
        end
    end
end

listenany(default_port; backlog::Integer=BACKLOG_DEFAULT) = listenany(localhost, default_port; backlog)

function udp_set_membership(sock::UDPSocket, group_addr::String,
                            interface_addr::Union{Nothing, String}, operation)
    if interface_addr === nothing
        interface_addr = C_NULL
    end
    r = ccall(:uv_udp_set_membership, Cint,
              (Ptr{Cvoid}, Cstring, Cstring, Cint),
              sock.handle, group_addr, interface_addr, operation)
    uv_error("uv_udp_set_membership", r)
    return
end

"""
    join_multicast_group(sock::UDPSocket, group_addr, interface_addr = nothing)

Join a socket to a particular multicast group defined by `group_addr`.
If `interface_addr` is given, specifies a particular interface for multi-homed
systems.  Use `leave_multicast_group()` to disable reception of a group.
"""
function join_multicast_group(sock::UDPSocket, group_addr::String,
                              interface_addr::Union{Nothing, String} = nothing)
    return udp_set_membership(sock, group_addr, interface_addr, 1)
end
function join_multicast_group(sock::UDPSocket, group_addr::IPAddr,
                              interface_addr::Union{Nothing, IPAddr} = nothing)
    if interface_addr !== nothing
        interface_addr = string(interface_addr)
    end
    return join_multicast_group(sock, string(group_addr), interface_addr)
end

"""
    leave_multicast_group(sock::UDPSocket, group_addr, interface_addr = nothing)

Remove a socket from  a particular multicast group defined by `group_addr`.
If `interface_addr` is given, specifies a particular interface for multi-homed
systems.  Use `join_multicast_group()` to enable reception of a group.
"""
function leave_multicast_group(sock::UDPSocket, group_addr::String,
                               interface_addr::Union{Nothing, String} = nothing)
    return udp_set_membership(sock, group_addr, interface_addr, 0)
end
function leave_multicast_group(sock::UDPSocket, group_addr::IPAddr,
                               interface_addr::Union{Nothing, IPAddr} = nothing)
    if interface_addr !== nothing
        interface_addr = string(interface_addr)
    end
    return leave_multicast_group(sock, string(group_addr), interface_addr)
end

"""
    getsockname(sock::Union{TCPServer, TCPSocket}) -> (IPAddr, UInt16)

Get the IP address and port that the given socket is bound to.
"""
getsockname(sock::Union{TCPSocket, TCPServer}) = _sockname(sock, true)


"""
    getpeername(sock::TCPSocket) -> (IPAddr, UInt16)

Get the IP address and port of the remote endpoint that the given
socket is connected to. Valid only for connected TCP sockets.
"""
getpeername(sock::TCPSocket) = _sockname(sock, false)

function _sockname(sock, self=true)
    sock.status == StatusInit || check_open(sock)
    rport = Ref{Cushort}(0)
    raddress = zeros(UInt8, 16)
    rfamily = Ref{Cuint}(0)

    iolock_begin()
    if self
        r = ccall(:jl_tcp_getsockname, Int32,
                (Ptr{Cvoid}, Ref{Cushort}, Ptr{Cvoid}, Ref{Cuint}),
                sock.handle, rport, raddress, rfamily)
    else
        r = ccall(:jl_tcp_getpeername, Int32,
                (Ptr{Cvoid}, Ref{Cushort}, Ptr{Cvoid}, Ref{Cuint}),
                sock.handle, rport, raddress, rfamily)
    end
    iolock_end()
    uv_error("cannot obtain socket name", r)
    port = ntoh(rport[])
    af_inet6 = @static if Sys.iswindows() # AF_INET6 in <sys/socket.h>
        23
    elseif Sys.isapple()
        30
    elseif Sys.KERNEL ∈ (:FreeBSD, :DragonFly)
        28
    elseif Sys.KERNEL ∈ (:NetBSD, :OpenBSD)
        24
    else
        10
    end

    if rfamily[] == 2 # AF_INET
        addrv4 = raddress[1:4]
        naddr = ntoh(unsafe_load(Ptr{Cuint}(pointer(addrv4)), 1))
        addr = IPv4(naddr)
    elseif rfamily[] == af_inet6
        naddr = ntoh(unsafe_load(Ptr{UInt128}(pointer(raddress)), 1))
        addr = IPv6(naddr)
    else
        error(string("unsupported address family: ", rfamily[]))
    end
    return addr, port
end

# domain sockets

include("PipeServer.jl")

end
q   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Sockets/src/IPAddr.jl^"      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
    IPAddr

Abstract supertype for IP addresses. [`IPv4`](@ref) and [`IPv6`](@ref) are subtypes of this.
"""
abstract type IPAddr end

Base.isless(a::T, b::T) where {T<:IPAddr} = isless(a.host, b.host)
(dt::Type{<:Integer})(ip::IPAddr) = dt(ip.host)::dt

# Allow IP addresses to broadcast as unwrapped scalars
Base.Broadcast.broadcastable(ip::IPAddr) = Ref(ip)

struct IPv4 <: IPAddr
    host::UInt32
    IPv4(host::UInt32) = new(host)
    IPv4(a::UInt8,b::UInt8,c::UInt8,d::UInt8) = new(UInt32(a)<<24|
                                                    UInt32(b)<<16|
                                                    UInt32(c)<<8|
                                                    d)
    function IPv4(a::Integer,b::Integer,c::Integer,d::Integer)
        if !(0<=a<=255 && 0<=b<=255 && 0<=c<=255 && 0<=d<=255)
            throw(ArgumentError("IPv4 field out of range (must be 0-255)"))
        end
        IPv4(UInt8(a),UInt8(b),UInt8(c),UInt8(d))
    end
end

"""
    IPv4(host::Integer) -> IPv4

Return an IPv4 object from ip address `host` formatted as an [`Integer`](@ref).

# Examples
```jldoctest
julia> IPv4(3223256218)
ip"192.30.252.154"
```
"""
function IPv4(host::Integer)
    if host < 0
        throw(ArgumentError("IPv4 address must be positive"))
    elseif typemax(typeof(host)) > typemax(UInt32) && host > typemax(UInt32)
        throw(ArgumentError("IPv4 address must fit within 32 bits"))
    else
        return IPv4(UInt32(host))
    end
end

# constructor: ("1.2.3.4")
IPv4(str::AbstractString) = parse(IPv4, str)

show(io::IO,ip::IPv4) = print(io,"ip\"",ip,"\"")
print(io::IO,ip::IPv4) = print(io,string((ip.host&(0xFF000000))>>24),".",
                                  string((ip.host&(0xFF0000))>>16),".",
                                  string((ip.host&(0xFF00))>>8),".",
                                  string(ip.host&0xFF))

struct IPv6 <: IPAddr
    host::UInt128
    IPv6(host::UInt128) = new(host)
    IPv6(a::UInt16,b::UInt16,c::UInt16,d::UInt16,
     e::UInt16,f::UInt16,g::UInt16,h::UInt16) = new(UInt128(a)<<(7*16)|
                            UInt128(b)<<(6*16)|
                            UInt128(c)<<(5*16)|
                            UInt128(d)<<(4*16)|
                            UInt128(e)<<(3*16)|
                            UInt128(f)<<(2*16)|
                            UInt128(g)<<(1*16)|
                            h)
    function IPv6(a::Integer,b::Integer,c::Integer,d::Integer,
          e::Integer,f::Integer,g::Integer,h::Integer)
        if !(0<=a<=0xFFFF && 0<=b<=0xFFFF && 0<=c<=0xFFFF && 0<=d<=0xFFFF &&
             0<=e<=0xFFFF && 0<=f<=0xFFFF && 0<=g<=0xFFFF && 0<=h<=0xFFFF)
            throw(ArgumentError("IPv6 field out of range (must be 0-65535)"))
        end
        IPv6(UInt16(a),UInt16(b),UInt16(c),UInt16(d),
             UInt16(e),UInt16(f),UInt16(g),UInt16(h))
    end
end

"""
    IPv6(host::Integer) -> IPv6

Return an IPv6 object from ip address `host` formatted as an [`Integer`](@ref).

# Examples
```jldoctest
julia> IPv6(3223256218)
ip"::c01e:fc9a"
```
"""
function IPv6(host::Integer)
    if host < 0
        throw(ArgumentError("IPv6 address must be positive"))
        # We allow passing bigger integer types, but need to be careful to avoid overflow
        # Let's hope promotion rules are sensible
    elseif typemax(typeof(host)) > typemax(UInt128) && host > typemax(UInt128)
        throw(ArgumentError("IPv6 address must fit within 128 bits"))
    else
        return IPv6(UInt128(host))
    end
end

IPv6(str::AbstractString) = parse(IPv6, str)

# Suppress leading '0's and "0x"
print_ipv6_field(io,field::UInt16) = print(io,string(field, base = 16))

print_ipv6_field(io,ip,i) = print_ipv6_field(io,ipv6_field(ip,i))
function ipv6_field(ip::IPv6,i)
    if i < 0 || i > 7
        throw(BoundsError())
    end
    UInt16((ip.host&(UInt128(0xFFFF)<<(i*16))) >> (i*16))
end

show(io::IO, ip::IPv6) = print(io,"ip\"",ip,"\"")
# RFC 5952 compliant show function
# http://tools.ietf.org/html/rfc5952
function print(io::IO,ip::IPv6)
    i = 8
    m = 0
    longest_sub_i = -1
    while i!=0
        i-=1
        field = ipv6_field(ip,i)
        if field == 0 && longest_sub_i == -1
            # Find longest subsequence of 0
            longest_sub_i,j,m,c = i,i,1,1
            while j != 0
                j-=1
                if ipv6_field(ip,j) == 0
                    c += 1
                else
                    c = 0
                end
                if c > m
                    if j+c != longest_sub_i+1
                        longest_sub_i = j+c-1
                    end
                    m = c
                end
            end
            # Prevent single 0 from contracting to :: as required
            if m == 1
                longest_sub_i = 9
            end
        end
        if i == longest_sub_i
            print(io,":")
            i -= m-1
            if i == 0
                print(io,":")
                break
            end
        else
            if i != 7
                print(io,":")
            end
            print_ipv6_field(io,field)
        end
    end
end

# Parsing

const ipv4_leading_zero_error = """
Leading zeros in IPv4 addresses are disallowed due to ambiguity.
If the address is in octal or hexadecimal, convert it to decimal, otherwise remove the leading zero.
"""

function parse(::Type{IPv4}, str::AbstractString)
    fields = split(str,'.')
    i = 1
    ret = 0
    for f in fields
        if isempty(f)
            throw(ArgumentError("empty field in IPv4 address"))
        end
        if length(f) > 1 && f[1] == '0'
            throw(ArgumentError(ipv4_leading_zero_error))
        else
            r = parse(Int, f, base = 10)
        end
        if i != length(fields)
            if r < 0 || r > 255
                throw(ArgumentError("IPv4 field out of range (must be 0-255)"))
            end
            ret |= UInt32(r) << ((4-i)*8)
        else
            if r > ((UInt64(1)<<((5-length(fields))*8))-1)
                throw(ArgumentError("IPv4 field too large"))
            end
            ret |= r
        end
        i+=1
    end
    IPv4(ret)
end

function parseipv6fields(fields,num_fields)
    if length(fields) > num_fields
        throw(ArgumentError("too many fields in IPv6 address"))
    end
    cf = 7
    ret = UInt128(0)
    for f in fields
        if isempty(f)
            # ::abc:... and ..:abc::
            if cf != 7 && cf != 0
                cf -= num_fields-length(fields)
            end
            cf -= 1
            continue
        end
        ret |= UInt128(parse(Int, f, base = 16))<<(cf*16)
        cf -= 1
    end
    ret
end
parseipv6fields(fields) = parseipv6fields(fields,8)

function parse(::Type{IPv6}, str::AbstractString)
    fields = split(str,':')
    if length(fields) > 8
        throw(ArgumentError("too many fields in IPv6 address"))
    elseif length(fields) == 8
        return IPv6(parseipv6fields(fields))
    elseif in('.',fields[end])
        return IPv6((parseipv6fields(fields[1:(end-1)],6))
            | parse(IPv4, fields[end]).host )
    else
        return IPv6(parseipv6fields(fields))
    end
end

#
# This supports IP addresses in the common dot (IPv4) or colon (IPv6)
# separated formats. Most other common formats use a standard integer encoding
# of the appropriate size and should use the appropriate constructor
#

function parse(::Type{IPAddr}, str::AbstractString)
    if ':' in str
        return parse(IPv6, str)
    else
        return parse(IPv4, str)
    end
end

"""
    @ip_str str -> IPAddr

Parse `str` as an IP address.

# Examples
```jldoctest
julia> ip"127.0.0.1"
ip"127.0.0.1"

julia> @ip_str "2001:db8:0:0:0:0:2:1"
ip"2001:db8::2:1"
```
"""
macro ip_str(str)
    return parse(IPAddr, str)
end

struct InetAddr{T<:IPAddr}
    host::T
    port::UInt16
end

"""
    InetAddr(ip::IPAddr, port) -> InetAddr

Return an `InetAddr` object from ip address `ip` and port number `port`.

# Examples
```jldoctest
julia> Sockets.InetAddr(ip"127.0.0.1", 8000)
Sockets.InetAddr{IPv4}(ip"127.0.0.1", 8000)
```
"""
InetAddr(ip::IPAddr, port) = InetAddr{typeof(ip)}(ip, port)

"""
    InetAddr(str::AbstractString, port) -> InetAddr

Return an `InetAddr` object from ip address `str` formatted as [`AbstractString`](@ref)
and port number `port`.

!!! compat "Julia 1.3"
    This constructor requires at least Julia 1.3.

# Examples
```jldoctest
julia> Sockets.InetAddr("127.0.0.1", 8000)
Sockets.InetAddr{IPv4}(ip"127.0.0.1", 8000)
```
"""
InetAddr(str::AbstractString, port) = InetAddr(parse(IPAddr, str), port)

function show(io::IO, addr::InetAddr)
    show(io, typeof(addr))
    print(io, "(")
    show(io, addr.host)
    print(io, ", ", Int(addr.port), ")")
end
s   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Sockets/src/addrinfo.jl�.      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
    DNSError

The type of exception thrown when an error occurs in DNS lookup.
The `host` field indicates the host URL string.
The `code` field indicates the error code based on libuv.
"""
struct DNSError <: Exception
    host::String
    code::Int32
end

function show(io::IO, err::DNSError)
    print(io, "DNSError: ", err.host, ", ", Base.struverror(err.code),
                                      " (", Base.uverrorname(err.code), ")")
end

function uv_getaddrinfocb(req::Ptr{Cvoid}, status::Cint, addrinfo::Ptr{Cvoid})
    data = uv_req_data(req)
    if data != C_NULL
        t = unsafe_pointer_to_objref(data)::Task
        uv_req_set_data(req, C_NULL)
        if status != 0 || addrinfo == C_NULL
            schedule(t, _UVError("getaddrinfo", status))
        else
            freeaddrinfo = addrinfo
            addrs = IPAddr[]
            while addrinfo != C_NULL
                sockaddr = ccall(:jl_sockaddr_from_addrinfo, Ptr{Cvoid}, (Ptr{Cvoid},), addrinfo)
                if ccall(:jl_sockaddr_is_ip4, Int32, (Ptr{Cvoid},), sockaddr) == 1
                    ip4addr = ccall(:jl_sockaddr_host4, UInt32, (Ptr{Cvoid},), sockaddr)
                    push!(addrs, IPv4(ntoh(ip4addr)))
                elseif ccall(:jl_sockaddr_is_ip6, Int32, (Ptr{Cvoid},), sockaddr) == 1
                    ip6addr = Ref{UInt128}()
                    scope_id = ccall(:jl_sockaddr_host6, UInt32, (Ptr{Cvoid}, Ptr{UInt128}), sockaddr, ip6addr)
                    push!(addrs, IPv6(ntoh(ip6addr[])))
                end
                addrinfo = ccall(:jl_next_from_addrinfo, Ptr{Cvoid}, (Ptr{Cvoid},), addrinfo)
            end
            ccall(:uv_freeaddrinfo, Cvoid, (Ptr{Cvoid},), freeaddrinfo)
            schedule(t, addrs)
        end
    else
        # no owner for this req, safe to just free it
        Libc.free(req)
    end
    nothing
end

"""
    getalladdrinfo(host::AbstractString) -> Vector{IPAddr}

Gets all of the IP addresses of the `host`.
Uses the operating system's underlying `getaddrinfo` implementation, which may do a DNS lookup.

# Example
```julia-repl
julia> getalladdrinfo("google.com")
2-element Array{IPAddr,1}:
 ip"172.217.6.174"
 ip"2607:f8b0:4000:804::200e"
```
"""
function getalladdrinfo(host::String)
    req = Libc.malloc(Base._sizeof_uv_getaddrinfo)
    uv_req_set_data(req, C_NULL) # in case we get interrupted before arriving at the wait call
    iolock_begin()
    status = ccall(:jl_getaddrinfo, Int32, (Ptr{Cvoid}, Ptr{Cvoid}, Cstring, Ptr{Cvoid}, Ptr{Cvoid}),
                   eventloop(), req, host, #=service=#C_NULL,
                   @cfunction(uv_getaddrinfocb, Cvoid, (Ptr{Cvoid}, Cint, Ptr{Cvoid})))
    if status < 0
        Libc.free(req)
        if status == UV_EINVAL
            throw(ArgumentError("Invalid getaddrinfo argument"))
        elseif status == UV_ENOMEM || status == UV_ENOBUFS
            throw(OutOfMemoryError())
        end
        uv_error("getaddrinfo", status)
    end
    ct = current_task()
    preserve_handle(ct)
    Base.sigatomic_begin()
    uv_req_set_data(req, ct)
    iolock_end()
    r = try
        Base.sigatomic_end()
        wait()
    finally
        Base.sigatomic_end()
        iolock_begin()
        ct.queue === nothing || list_deletefirst!(ct.queue, ct)
        if uv_req_data(req) != C_NULL
            # req is still alive,
            # so make sure we don't get spurious notifications later
            uv_req_set_data(req, C_NULL)
            ccall(:uv_cancel, Int32, (Ptr{Cvoid},), req) # try to let libuv know we don't care anymore
        else
            # done with req
            Libc.free(req)
        end
        iolock_end()
        unpreserve_handle(ct)
    end
    if isa(r, IOError)
        code = r.code
        if code in (UV_EAI_ADDRFAMILY, UV_EAI_AGAIN, UV_EAI_BADFLAGS,
                    UV_EAI_BADHINTS, UV_EAI_CANCELED, UV_EAI_FAIL,
                    UV_EAI_FAMILY, UV_EAI_NODATA, UV_EAI_NONAME,
                    UV_EAI_OVERFLOW, UV_EAI_PROTOCOL, UV_EAI_SERVICE,
                    UV_EAI_SOCKTYPE)
            throw(DNSError(host, code))
        elseif code == UV_EAI_MEMORY
            throw(OutOfMemoryError())
        else
            throw(r)
        end
    end
    return r::Vector{IPAddr}
end
getalladdrinfo(host::AbstractString) = getalladdrinfo(String(host))

"""
    getaddrinfo(host::AbstractString, IPAddr=IPv4) -> IPAddr

Gets the first IP address of the `host` of the specified `IPAddr` type.
Uses the operating system's underlying getaddrinfo implementation, which may do a DNS lookup.
"""
function getaddrinfo(host::String, T::Type{<:IPAddr})
    addrs = getalladdrinfo(host)
    for addr in addrs
        if addr isa T
            return addr
        end
    end
    throw(DNSError(host, UV_EAI_NONAME))
end
getaddrinfo(host::AbstractString, T::Type{<:IPAddr}) = getaddrinfo(String(host), T)
function getaddrinfo(host::AbstractString)
    addrs = getalladdrinfo(String(host))
    if !isempty(addrs)
        return addrs[begin]::Union{IPv4,IPv6}
    end
    throw(DNSError(host, UV_EAI_NONAME))
end

function uv_getnameinfocb(req::Ptr{Cvoid}, status::Cint, hostname::Cstring, service::Cstring)
    data = uv_req_data(req)
    if data != C_NULL
        t = unsafe_pointer_to_objref(data)::Task
        uv_req_set_data(req, C_NULL)
        if status != 0
            schedule(t, _UVError("getnameinfo", status))
        else
            schedule(t, unsafe_string(hostname))
        end
    else
        # no owner for this req, safe to just free it
        Libc.free(req)
    end
    nothing
end

"""
    getnameinfo(host::IPAddr) -> String

Performs a reverse-lookup for IP address to return a hostname and service
using the operating system's underlying `getnameinfo` implementation.

# Examples
```julia-repl
julia> getnameinfo(IPv4("8.8.8.8"))
"google-public-dns-a.google.com"
```
"""
function getnameinfo(address::Union{IPv4, IPv6})
    req = Libc.malloc(Base._sizeof_uv_getnameinfo)
    uv_req_set_data(req, C_NULL) # in case we get interrupted before arriving at the wait call
    port = hton(UInt16(0))
    flags = 0
    uvcb = @cfunction(uv_getnameinfocb, Cvoid, (Ptr{Cvoid}, Cint, Cstring, Cstring))
    status = UV_EINVAL
    host_in = Ref(hton(address.host))
    iolock_begin()
    status = ccall(:jl_getnameinfo, Int32, (Ptr{Cvoid}, Ptr{Cvoid}, Ptr{Cvoid}, UInt16, Cint, Ptr{Cvoid}, Cint),
                   eventloop(), req, host_in, port, flags, uvcb, address isa IPv6)
    if status < 0
        Libc.free(req)
        if status == UV_EINVAL
            throw(ArgumentError("Invalid getnameinfo argument"))
        elseif status == UV_ENOMEM || status == UV_ENOBUFS
            throw(OutOfMemoryError())
        end
        uv_error("getnameinfo", status)
    end
    ct = current_task()
    preserve_handle(ct)
    Base.sigatomic_begin()
    uv_req_set_data(req, ct)
    iolock_end()
    r = try
        Base.sigatomic_end()
        wait()
    finally
        Base.sigatomic_end()
        iolock_begin()
        ct.queue === nothing || list_deletefirst!(ct.queue, ct)
        if uv_req_data(req) != C_NULL
            # req is still alive,
            # so make sure we don't get spurious notifications later
            uv_req_set_data(req, C_NULL)
            ccall(:uv_cancel, Int32, (Ptr{Cvoid},), req) # try to let libuv know we don't care anymore
        else
            # done with req
            Libc.free(req)
        end
        iolock_end()
        unpreserve_handle(ct)
    end
    if isa(r, IOError)
        code = r.code
        if code in (UV_EAI_ADDRFAMILY, UV_EAI_AGAIN, UV_EAI_BADFLAGS,
                    UV_EAI_BADHINTS, UV_EAI_CANCELED, UV_EAI_FAIL,
                    UV_EAI_FAMILY, UV_EAI_NODATA, UV_EAI_NONAME,
                    UV_EAI_OVERFLOW, UV_EAI_PROTOCOL, UV_EAI_SERVICE,
                    UV_EAI_SOCKTYPE)
            throw(DNSError(repr(address), code))
        elseif code == UV_EAI_MEMORY
            throw(OutOfMemoryError())
        else
            throw(r)
        end
    end
    return r::String
end

const _sizeof_uv_interface_address = ccall(:jl_uv_sizeof_interface_address,Int32,())

"""
    getipaddr() -> IPAddr

Get an IP address of the local machine, preferring IPv4 over IPv6. Throws if no
addresses are available.

    getipaddr(addr_type::Type{T}) where T<:IPAddr -> T

Get an IP address of the local machine of the specified type. Throws if no
addresses of the specified type are available.

This function is a backwards-compatibility wrapper around [`getipaddrs`](@ref).
New applications should use [`getipaddrs`](@ref) instead.

# Examples
```julia-repl
julia> getipaddr()
ip"192.168.1.28"

julia> getipaddr(IPv6)
ip"fe80::9731:35af:e1c5:6e49"
```

See also [`getipaddrs`](@ref).
"""
function getipaddr(addr_type::Type{T}) where T<:IPAddr
    addrs = getipaddrs(addr_type)

    if length(addrs) == 0
        error("No networking interface available")
    end

    # Prefer the first IPv4 address
    i = something(findfirst(ip -> ip isa IPv4, addrs), 1)
    return addrs[i]
end
getipaddr() = getipaddr(IPv4)


"""
    getipaddrs(addr_type::Type{T}=IPAddr; loopback::Bool=false) where T<:IPAddr -> Vector{T}

Get the IP addresses of the local machine.

Setting the optional `addr_type` parameter to `IPv4` or `IPv6` causes only addresses of that type to be returned.

The `loopback` keyword argument dictates whether loopback addresses (e.g. `ip"127.0.0.1"`, `ip"::1"`) are included.

!!! compat "Julia 1.2"
    This function is available as of Julia 1.2.

# Examples
```julia-repl
julia> getipaddrs()
5-element Array{IPAddr,1}:
 ip"198.51.100.17"
 ip"203.0.113.2"
 ip"2001:db8:8:4:445e:5fff:fe5d:5500"
 ip"2001:db8:8:4:c164:402e:7e3c:3668"
 ip"fe80::445e:5fff:fe5d:5500"

julia> getipaddrs(IPv6)
3-element Array{IPv6,1}:
 ip"2001:db8:8:4:445e:5fff:fe5d:5500"
 ip"2001:db8:8:4:c164:402e:7e3c:3668"
 ip"fe80::445e:5fff:fe5d:5500"
```

See also [`islinklocaladdr`](@ref).
"""
function getipaddrs(addr_type::Type{T}=IPAddr; loopback::Bool=false) where T<:IPAddr
    addresses = T[]
    addr_ref = Ref{Ptr{UInt8}}(C_NULL)
    count_ref = Ref{Int32}(1)
    lo_present = false
    err = ccall(:jl_uv_interface_addresses, Int32, (Ref{Ptr{UInt8}}, Ref{Int32}), addr_ref, count_ref)
    uv_error("getlocalip", err)
    addr, count = addr_ref[], count_ref[]
    for i = 0:(count-1)
        current_addr = addr + i*_sizeof_uv_interface_address
        if 1 == ccall(:jl_uv_interface_address_is_internal, Int32, (Ptr{UInt8},), current_addr)
            lo_present = true
            if !loopback
                continue
            end
        end
        sockaddr = ccall(:jl_uv_interface_address_sockaddr, Ptr{Cvoid}, (Ptr{UInt8},), current_addr)
        if IPv4 <: T && ccall(:jl_sockaddr_is_ip4, Int32, (Ptr{Cvoid},), sockaddr) == 1
            push!(addresses, IPv4(ntoh(ccall(:jl_sockaddr_host4, UInt32, (Ptr{Cvoid},), sockaddr))))
        elseif IPv6 <: T && ccall(:jl_sockaddr_is_ip6, Int32, (Ptr{Cvoid},), sockaddr) == 1
            addr6 = Ref{UInt128}()
            scope_id = ccall(:jl_sockaddr_host6, UInt32, (Ptr{Cvoid}, Ref{UInt128},), sockaddr, addr6)
            push!(addresses, IPv6(ntoh(addr6[])))
        end
    end
    ccall(:uv_free_interface_addresses, Cvoid, (Ptr{UInt8}, Int32), addr, count)
    return addresses
end

"""
    islinklocaladdr(addr::IPAddr)

Tests if an IP address is a link-local address. Link-local addresses
are not guaranteed to be unique beyond their network segment,
therefore routers do not forward them. Link-local addresses are from
the address blocks `169.254.0.0/16` or `fe80::/10`.

# Example
```julia
filter(!islinklocaladdr, getipaddrs())
```
"""
function islinklocaladdr(addr::IPv4)
    # RFC 3927
    return (addr.host &
            0xFFFF0000) ==
            0xA9FE0000
end
function islinklocaladdr(addr::IPv6)
    # RFC 4291
    return (addr.host &
            0xFFC00000000000000000000000000000) ==
            0xFE800000000000000000000000000000
end
u   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Sockets/src/PipeServer.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

mutable struct PipeServer <: LibuvServer
    handle::Ptr{Cvoid}
    status::Int
    cond::Base.ThreadSynchronizer
    function PipeServer(handle::Ptr{Cvoid}, status)
        p = new(handle,
                status,
                Base.ThreadSynchronizer())
        associate_julia_struct(p.handle, p)
        finalizer(uvfinalize, p)
        return p
    end
end

function PipeServer()
    pipe = PipeServer(Libc.malloc(Base._sizeof_uv_named_pipe), StatusUninit)
    iolock_begin()
    err = ccall(:uv_pipe_init, Cint, (Ptr{Cvoid}, Ptr{Cvoid}, Cint), eventloop(), pipe.handle, 0)
    uv_error("failed to create pipe server", err)
    pipe.status = StatusInit
    iolock_end()
    return pipe
end

## server functions ##

accept(server::PipeServer) = accept(server, PipeEndpoint())

function accept_nonblock(server::PipeServer, client::PipeEndpoint)
    iolock_begin()
    if client.status != StatusInit
        error("client is already in use or has been closed")
    end
    err = ccall(:uv_accept, Int32, (Ptr{Cvoid}, Ptr{Cvoid}), server.handle, client.handle)
    if err == 0
        client.status = StatusOpen
    end
    iolock_end()
    return err
end

function accept_nonblock(server::PipeServer)
    client = PipeEndpoint()
    uv_error("accept", accept_nonblock(server, client) != 0)
    return client
end

function bind(server::PipeServer, name::AbstractString)
    iolock_begin()
    @assert server.status == StatusInit
    err = ccall(:uv_pipe_bind, Int32, (Ptr{Cvoid}, Cstring),
                server, name)
    if err != 0
        iolock_end()
        if err != UV_EADDRINUSE && err != UV_EACCES
            #TODO: this codepath is currently not tested
            throw(_UVError("bind", err))
        else
            return false
        end
    end
    server.status = StatusOpen
    iolock_end()
    return true
end

"""
    listen(path::AbstractString) -> PipeServer

Create and listen on a named pipe / UNIX domain socket.

!!! note
    Path length on Unix is limited to somewhere between 92 and 108 bytes (cf. `man unix`).
"""
function listen(path::AbstractString)
    sock = PipeServer()
    bind(sock, path) || throw(ArgumentError("could not listen on path $path"))
    return listen(sock)
end

function connect!(sock::PipeEndpoint, path::AbstractString)
    iolock_begin()
    @assert sock.status == StatusInit
    req = Libc.malloc(Base._sizeof_uv_connect)
    uv_req_set_data(req, C_NULL)
    ccall(:uv_pipe_connect, Cvoid, (Ptr{Cvoid}, Ptr{Cvoid}, Cstring, Ptr{Cvoid}), req, sock.handle, path,
          @cfunction(uv_connectcb, Cvoid, (Ptr{Cvoid}, Cint)))
    sock.status = StatusConnecting
    iolock_end()
    return sock
end

"""
    connect(path::AbstractString) -> PipeEndpoint

Connect to the named pipe / UNIX domain socket at `path`.

!!! note
    Path length on Unix is limited to somewhere between 92 and 108 bytes (cf. `man unix`).
"""
connect(path::AbstractString) = connect(PipeEndpoint(), path)
r   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Unicode/src/Unicode.jlT5      # This file is a part of Julia. License is MIT: https://julialang.org/license

module Unicode

export graphemes, isequal_normalized

"""
    Unicode.julia_chartransform(c::Union{Char,Integer})

Map the Unicode character (`Char`) or codepoint (`Integer`) `c` to the corresponding
"equivalent" character or codepoint, respectively, according to the custom equivalence
used within the Julia parser (in addition to NFC normalization).

For example, `'µ'` (U+00B5 micro) is treated as equivalent to `'μ'` (U+03BC mu) by
Julia's parser, so `julia_chartransform` performs this transformation while leaving
other characters unchanged:
```jldoctest
julia> Unicode.julia_chartransform('\u00B5')
'μ': Unicode U+03BC (category Ll: Letter, lowercase)

julia> Unicode.julia_chartransform('x')
'x': ASCII/Unicode U+0078 (category Ll: Letter, lowercase)
```

`julia_chartransform` is mainly useful for passing to the [`Unicode.normalize`](@ref)
function in order to mimic the normalization used by the Julia parser:
```jldoctest
julia> s = "\u00B5o\u0308"
"µö"

julia> s2 = Unicode.normalize(s, compose=true, stable=true, chartransform=Unicode.julia_chartransform)
"μö"

julia> collect(s2)
2-element Vector{Char}:
 'μ': Unicode U+03BC (category Ll: Letter, lowercase)
 'ö': Unicode U+00F6 (category Ll: Letter, lowercase)

julia> s2 == string(Meta.parse(s))
true
```

!!! compat "Julia 1.8"
    This function was introduced in Julia 1.8.
"""
function julia_chartransform end
julia_chartransform(codepoint::UInt32) = get(Base.Unicode._julia_charmap, codepoint, codepoint)
julia_chartransform(codepoint::Integer) = julia_chartransform(UInt32(codepoint))
julia_chartransform(char::Char) = Char(julia_chartransform(UInt32(char)))

"""
    Unicode.normalize(s::AbstractString; keywords...)
    Unicode.normalize(s::AbstractString, normalform::Symbol)

Normalize the string `s`. By default, canonical composition (`compose=true`) is performed without ensuring
Unicode versioning stability (`compat=false`), which produces the shortest possible equivalent string
but may introduce composition characters not present in earlier Unicode versions.

Alternatively, one of the four "normal forms" of the Unicode standard can be specified:
`normalform` can be `:NFC`, `:NFD`, `:NFKC`, or `:NFKD`.  Normal forms C
(canonical composition) and D (canonical decomposition) convert different visually identical
representations of the same abstract string into a single canonical form, with form C being
more compact.  Normal forms KC and KD additionally canonicalize "compatibility equivalents":
they convert characters that are abstractly similar but visually distinct into a single
canonical choice (e.g. they expand ligatures into the individual characters), with form KC
being more compact.

Alternatively, finer control and additional transformations may be obtained by calling
`Unicode.normalize(s; keywords...)`, where any number of the following boolean keywords
options (which all default to `false` except for `compose`) are specified:

* `compose=false`: do not perform canonical composition
* `decompose=true`: do canonical decomposition instead of canonical composition
  (`compose=true` is ignored if present)
* `compat=true`: compatibility equivalents are canonicalized
* `casefold=true`: perform Unicode case folding, e.g. for case-insensitive string comparison
* `newline2lf=true`, `newline2ls=true`, or `newline2ps=true`: convert various newline
  sequences (LF, CRLF, CR, NEL) into a linefeed (LF), line-separation (LS), or
  paragraph-separation (PS) character, respectively
* `stripmark=true`: strip diacritical marks (e.g. accents)
* `stripignore=true`: strip Unicode's "default ignorable" characters (e.g. the soft hyphen
  or the left-to-right marker)
* `stripcc=true`: strip control characters; horizontal tabs and form feeds are converted to
  spaces; newlines are also converted to spaces unless a newline-conversion flag was
  specified
* `rejectna=true`: throw an error if unassigned code points are found
* `stable=true`: enforce Unicode versioning stability (never introduce characters missing from earlier Unicode versions)

You can also use the `chartransform` keyword (which defaults to `identity`) to pass an arbitrary
*function* mapping `Integer` codepoints to codepoints, which is is called on each
character in `s` as it is processed, in order to perform arbitrary additional normalizations.
For example, by passing `chartransform=Unicode.julia_chartransform`, you can apply a few Julia-specific
character normalizations that are performed by Julia when parsing identifiers (in addition to
NFC normalization: `compose=true, stable=true`).

For example, NFKC corresponds to the options `compose=true, compat=true, stable=true`.

# Examples
```jldoctest
julia> "é" == Unicode.normalize("é") #LHS: Unicode U+00e9, RHS: U+0065 & U+0301
true

julia> "μ" == Unicode.normalize("µ", compat=true) #LHS: Unicode U+03bc, RHS: Unicode U+00b5
true

julia> Unicode.normalize("JuLiA", casefold=true)
"julia"

julia> Unicode.normalize("JúLiA", stripmark=true)
"JuLiA"
```

!!! compat "Julia 1.8"
    The `chartransform` keyword argument requires Julia 1.8.
"""
function normalize end
normalize(s::AbstractString, nf::Symbol) = Base.Unicode.normalize(s, nf)
normalize(s::AbstractString; kwargs...) = Base.Unicode.normalize(s; kwargs...)

"""
    Unicode.isassigned(c) -> Bool

Return `true` if the given char or integer is an assigned Unicode code point.

# Examples
```jldoctest
julia> Unicode.isassigned(101)
true

julia> Unicode.isassigned('\\x01')
true
```
"""
isassigned(c) = Base.Unicode.isassigned(c)

"""
    graphemes(s::AbstractString) -> GraphemeIterator

Return an iterator over substrings of `s` that correspond to the extended graphemes in the
string, as defined by Unicode UAX #29. (Roughly, these are what users would perceive as
single characters, even though they may contain more than one codepoint; for example a
letter combined with an accent mark is a single grapheme.)
"""
graphemes(s::AbstractString) = Base.Unicode.GraphemeIterator{typeof(s)}(s)

"""
    graphemes(s::AbstractString, m:n) -> SubString

Returns a [`SubString`](@ref) of `s` consisting of the `m`-th
through `n`-th graphemes of the string `s`, where the second
argument `m:n` is an integer-valued [`AbstractUnitRange`](@ref).

Loosely speaking, this corresponds to the `m:n`-th user-perceived
"characters" in the string.  For example:

```jldoctest
julia> s = graphemes("exposé", 3:6)
"posé"

julia> collect(s)
5-element Vector{Char}:
 'p': ASCII/Unicode U+0070 (category Ll: Letter, lowercase)
 'o': ASCII/Unicode U+006F (category Ll: Letter, lowercase)
 's': ASCII/Unicode U+0073 (category Ll: Letter, lowercase)
 'e': ASCII/Unicode U+0065 (category Ll: Letter, lowercase)
 '́': Unicode U+0301 (category Mn: Mark, nonspacing)
```
This consists of the 3rd to *7th* codepoints ([`Char`](@ref)s) in `"exposé"`,
because the grapheme `"é"` is actually *two* Unicode codepoints
(an `'e'` followed by an acute-accent combining character U+0301).

Because finding grapheme boundaries requires iteration over the
string contents, the `graphemes(s, m:n)` function requires time
proportional to the length of the string (number of codepoints)
before the end of the substring.

!!! compat "Julia 1.9"
    The `m:n` argument of `graphemes` requires Julia 1.9.
"""
function graphemes(s::AbstractString, r::AbstractUnitRange{<:Integer})
    m, n = Int(first(r)), Int(last(r))
    m > 0 || throw(ArgumentError("starting index $m is not ≥ 1"))
    n < m && return @view s[1:0]
    c0 = eltype(s)(0x00000000)
    state = Ref{Int32}(0)
    count = 0
    i, iprev, ilast = 1, 1, lastindex(s)
    # find the start of the m-th grapheme
    while i ≤ ilast && count < m
        @inbounds c = s[i]
        count += Base.Unicode.isgraphemebreak!(state, c0, c)
        c0 = c
        i, iprev = nextind(s, i), i
    end
    start = iprev
    count < m && throw(BoundsError(s, i))
    # find the end of the n-th grapheme
    while i ≤ ilast
        @inbounds c = s[i]
        count += Base.Unicode.isgraphemebreak!(state, c0, c)
        count > n && break
        c0 = c
        i, iprev = nextind(s, i), i
    end
    count < n && throw(BoundsError(s, i))
    return @view s[start:iprev]
end

using Base.Unicode: utf8proc_error, UTF8PROC_DECOMPOSE, UTF8PROC_CASEFOLD, UTF8PROC_STRIPMARK

function _decompose_char!(codepoint::Union{Integer,Char}, dest::Vector{UInt32}, offset::Integer, options::Integer)
    ret = GC.@preserve dest @ccall utf8proc_decompose_char(codepoint::UInt32, pointer(dest, 1+offset)::Ptr{UInt32}, (length(dest)-offset)::Int, options::Cint, C_NULL::Ptr{Cint})::Int
    ret < 0 && utf8proc_error(ret)
    return ret
end

# would be good to have higher-level accessor functions in utf8proc.  alternatively,
# we could mirror the whole utf8proc_property_t struct in Julia, but that is annoying
# because of the bitfields.
combining_class(uc::Integer) =
    0x000301 ≤ uc ≤ 0x10ffff ? unsafe_load(ccall(:utf8proc_get_property, Ptr{UInt16}, (UInt32,), uc), 2) : 0x0000
combining_class(c::AbstractChar) = ismalformed(c) ? 0x0000 : combining_class(UInt32(c))

"""
    isequal_normalized(s1::AbstractString, s2::AbstractString; casefold=false, stripmark=false, chartransform=identity)

Return whether `s1` and `s2` are canonically equivalent Unicode strings.   If `casefold=true`,
ignores case (performs Unicode case-folding); if `stripmark=true`, strips diacritical marks
and other combining characters.

As with [`Unicode.normalize`](@ref), you can also pass an arbitrary
function via the `chartransform` keyword (mapping `Integer` codepoints to codepoints)
to perform custom normalizations, such as [`Unicode.julia_chartransform`](@ref).

!!! compat "Julia 1.8"
    The `isequal_normalized` function was added in Julia 1.8.

# Examples

For example, the string `"noël"` can be constructed in two canonically equivalent ways
in Unicode, depending on whether `"ë"` is formed from a single codepoint U+00EB or
from the ASCII character `'e'` followed by the U+0308 combining-diaeresis character.

```jldoctest
julia> s1 = "no\u00EBl"
"noël"

julia> s2 = "noe\u0308l"
"noël"

julia> s1 == s2
false

julia> isequal_normalized(s1, s2)
true

julia> isequal_normalized(s1, "noel", stripmark=true)
true

julia> isequal_normalized(s1, "NOËL", casefold=true)
true
```
"""
isequal_normalized(s1::AbstractString, s2::AbstractString; casefold::Bool=false, stripmark::Bool=false, chartransform=identity) =
    _isequal_normalized!(s1, s2, Vector{UInt32}(undef, 4), Vector{UInt32}(undef, 4), chartransform; casefold, stripmark)

# like isequal_normalized, but takes pre-allocated codepoint buffers as arguments, and chartransform is a positional argument
function _isequal_normalized!(s1::AbstractString, s2::AbstractString,
                              d1::Vector{UInt32}, d2::Vector{UInt32}, chartransform::F=identity;
                              casefold::Bool=false, stripmark::Bool=false) where {F}
    function decompose_next_chars!(state, d, options, s)
        local n
        offset = 0
        @inbounds while true
            # read a char and decompose it to d
            c = chartransform(UInt32(state[1]))
            state = iterate(s, state[2])
            if c < 0x80 # fast path for common ASCII case
                n = 1 + offset
                n > length(d) && resize!(d, 2n)
                d[n] = casefold ? (0x41 ≤ c ≤ 0x5A ? c+0x20 : c) : c
                break # ASCII characters are all zero combining class
            else
                while true
                    n = _decompose_char!(c, d, offset, options) + offset
                    if n > length(d)
                        resize!(d, 2n)
                        continue
                    end
                    break
                end
            end

            # decomposed chars must be sorted in ascending order of combining class,
            # which means we need to keep fetching chars until we get to non-combining
            (iszero(combining_class(d[n])) || isnothing(state)) && break # non-combining
            offset = n
        end

        # sort by combining class
        if n < 32 # almost always true
            for j1 = 2:n # insertion sort
                cc = combining_class(d[j1])
                iszero(cc) && continue # don't re-order non-combiners
                for j2 = j1:-1:2
                    combining_class(d[j2-1]) ≤ cc && break
                    d[j2-1], d[j2] = d[j2], d[j2-1]
                end
            end
        else # avoid n^2 complexity in crazy large-n case
            j = 1
            @views while j < n
                j₀ = j + something(findnext(iszero ∘ combining_class, d[j+1:n], 1), n+1-j)
                sort!(d[j:j₀-1], by=combining_class)
                j = j₀
            end
        end

        # split return statement to help type inference:
        return state === nothing ? (1, n, nothing) : (1, n, state)
    end
    options = UTF8PROC_DECOMPOSE
    casefold && (options |= UTF8PROC_CASEFOLD)
    stripmark && (options |= UTF8PROC_STRIPMARK)
    i1,i2 = iterate(s1),iterate(s2)
    n1 = n2 = 0 # lengths of codepoint buffers
    j1 = j2 = 1 # indices in d1, d2
    while true
        if j1 > n1
            i1 === nothing && return i2 === nothing && j2 > n2
            j1, n1, i1 = decompose_next_chars!(i1, d1, options, s1)
        end
        if j2 > n2
            i2 === nothing && return false
            j2, n2, i2 = decompose_next_chars!(i2, d2, options, s2)
        end
        d1[j1] == d2[j2] || return false
        j1 += 1; j2 += 1
    end
end

end
~   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LinearAlgebra/src/LinearAlgebra.jl�P      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
Linear algebra module. Provides array arithmetic,
matrix factorizations and other linear algebra related
functionality.
"""
module LinearAlgebra

import Base: \, /, *, ^, +, -, ==
import Base: USE_BLAS64, abs, acos, acosh, acot, acoth, acsc, acsch, adjoint, asec, asech,
    asin, asinh, atan, atanh, axes, big, broadcast, ceil, cis, collect, conj, convert, copy,
    copyto!, copymutable, cos, cosh, cot, coth, csc, csch, eltype, exp, fill!, floor,
    getindex, hcat, getproperty, imag, inv, isapprox, isequal, isone, iszero, IndexStyle,
    kron, kron!, length, log, map, ndims, one, oneunit, parent, permutedims,
    power_by_squaring, promote_rule, real, sec, sech, setindex!, show, similar, sin,
    sincos, sinh, size, sqrt, strides, stride, tan, tanh, transpose, trunc, typed_hcat,
    vec, view, zero
using Base: IndexLinear, promote_eltype, promote_op, promote_typeof, print_matrix,
    @propagate_inbounds, reduce, typed_hvcat, typed_vcat, require_one_based_indexing,
    splat
using Base.Broadcast: Broadcasted, broadcasted
using Base.PermutedDimsArrays: CommutativeOps
using OpenBLAS_jll
using libblastrampoline_jll
import Libdl

export
# Modules
    LAPACK,
    BLAS,

# Types
    Adjoint,
    Transpose,
    SymTridiagonal,
    Tridiagonal,
    Bidiagonal,
    Factorization,
    BunchKaufman,
    Cholesky,
    CholeskyPivoted,
    ColumnNorm,
    Eigen,
    GeneralizedEigen,
    GeneralizedSVD,
    GeneralizedSchur,
    Hessenberg,
    LU,
    LDLt,
    NoPivot,
    RowNonZero,
    QR,
    QRPivoted,
    LQ,
    Schur,
    SVD,
    Hermitian,
    RowMaximum,
    Symmetric,
    LowerTriangular,
    UpperTriangular,
    UnitLowerTriangular,
    UnitUpperTriangular,
    UpperHessenberg,
    Diagonal,
    UniformScaling,

# Functions
    axpy!,
    axpby!,
    bunchkaufman,
    bunchkaufman!,
    cholesky,
    cholesky!,
    cond,
    condskeel,
    copyto!,
    copy_transpose!,
    cross,
    adjoint,
    adjoint!,
    det,
    diag,
    diagind,
    diagm,
    dot,
    eigen,
    eigen!,
    eigmax,
    eigmin,
    eigvals,
    eigvals!,
    eigvecs,
    factorize,
    givens,
    hermitianpart,
    hermitianpart!,
    hessenberg,
    hessenberg!,
    isdiag,
    ishermitian,
    isposdef,
    isposdef!,
    issuccess,
    issymmetric,
    istril,
    istriu,
    kron,
    kron!,
    ldiv!,
    ldlt!,
    ldlt,
    logabsdet,
    logdet,
    lowrankdowndate,
    lowrankdowndate!,
    lowrankupdate,
    lowrankupdate!,
    lu,
    lu!,
    lyap,
    mul!,
    lmul!,
    rmul!,
    norm,
    normalize,
    normalize!,
    nullspace,
    ordschur!,
    ordschur,
    pinv,
    qr,
    qr!,
    lq,
    lq!,
    opnorm,
    rank,
    rdiv!,
    reflect!,
    rotate!,
    schur,
    schur!,
    svd,
    svd!,
    svdvals!,
    svdvals,
    sylvester,
    tr,
    transpose,
    transpose!,
    tril,
    triu,
    tril!,
    triu!,

# Operators
    \,
    /,

# Constants
    I

const BlasFloat = Union{Float64,Float32,ComplexF64,ComplexF32}
const BlasReal = Union{Float64,Float32}
const BlasComplex = Union{ComplexF64,ComplexF32}

if USE_BLAS64
    const BlasInt = Int64
else
    const BlasInt = Int32
end


abstract type Algorithm end
struct DivideAndConquer <: Algorithm end
struct QRIteration <: Algorithm end

abstract type PivotingStrategy end
struct NoPivot <: PivotingStrategy end
struct RowNonZero <: PivotingStrategy end
struct RowMaximum <: PivotingStrategy end
struct ColumnNorm <: PivotingStrategy end

# Check that stride of matrix/vector is 1
# Writing like this to avoid splatting penalty when called with multiple arguments,
# see PR 16416
"""
    stride1(A) -> Int

Return the distance between successive array elements
in dimension 1 in units of element size.

# Examples
```jldoctest
julia> A = [1,2,3,4]
4-element Vector{Int64}:
 1
 2
 3
 4

julia> LinearAlgebra.stride1(A)
1

julia> B = view(A, 2:2:4)
2-element view(::Vector{Int64}, 2:2:4) with eltype Int64:
 2
 4

julia> LinearAlgebra.stride1(B)
2
```
"""
stride1(x) = stride(x,1)
stride1(x::Array) = 1
stride1(x::DenseArray) = stride(x, 1)::Int

@inline chkstride1(A...) = _chkstride1(true, A...)
@noinline _chkstride1(ok::Bool) = ok || error("matrix does not have contiguous columns")
@inline _chkstride1(ok::Bool, A, B...) = _chkstride1(ok & (stride1(A) == 1), B...)

"""
    LinearAlgebra.checksquare(A)

Check that a matrix is square, then return its common dimension.
For multiple arguments, return a vector.

# Examples
```jldoctest
julia> A = fill(1, (4,4)); B = fill(1, (5,5));

julia> LinearAlgebra.checksquare(A, B)
2-element Vector{Int64}:
 4
 5
```
"""
function checksquare(A)
    m,n = size(A)
    m == n || throw(DimensionMismatch("matrix is not square: dimensions are $(size(A))"))
    m
end

function checksquare(A...)
    sizes = Int[]
    for a in A
        size(a,1)==size(a,2) || throw(DimensionMismatch("matrix is not square: dimensions are $(size(a))"))
        push!(sizes, size(a,1))
    end
    return sizes
end

function char_uplo(uplo::Symbol)
    if uplo === :U
        return 'U'
    elseif uplo === :L
        return 'L'
    else
        throw_uplo()
    end
end

function sym_uplo(uplo::Char)
    if uplo == 'U'
        return :U
    elseif uplo == 'L'
        return :L
    else
        throw_uplo()
    end
end

@noinline throw_uplo() = throw(ArgumentError("uplo argument must be either :U (upper) or :L (lower)"))

"""
    ldiv!(Y, A, B) -> Y

Compute `A \\ B` in-place and store the result in `Y`, returning the result.

The argument `A` should *not* be a matrix.  Rather, instead of matrices it should be a
factorization object (e.g. produced by [`factorize`](@ref) or [`cholesky`](@ref)).
The reason for this is that factorization itself is both expensive and typically allocates memory
(although it can also be done in-place via, e.g., [`lu!`](@ref)),
and performance-critical situations requiring `ldiv!` usually also require fine-grained
control over the factorization of `A`.

!!! note
    Certain structured matrix types, such as `Diagonal` and `UpperTriangular`, are permitted, as
    these are already in a factorized form

# Examples
```jldoctest
julia> A = [1 2.2 4; 3.1 0.2 3; 4 1 2];

julia> X = [1; 2.5; 3];

julia> Y = zero(X);

julia> ldiv!(Y, qr(A), X);

julia> Y
3-element Vector{Float64}:
  0.7128099173553719
 -0.051652892561983674
  0.10020661157024757

julia> A\\X
3-element Vector{Float64}:
  0.7128099173553719
 -0.05165289256198333
  0.10020661157024785
```
"""
ldiv!(Y, A, B)

"""
    ldiv!(A, B)

Compute `A \\ B` in-place and overwriting `B` to store the result.

The argument `A` should *not* be a matrix.  Rather, instead of matrices it should be a
factorization object (e.g. produced by [`factorize`](@ref) or [`cholesky`](@ref)).
The reason for this is that factorization itself is both expensive and typically allocates memory
(although it can also be done in-place via, e.g., [`lu!`](@ref)),
and performance-critical situations requiring `ldiv!` usually also require fine-grained
control over the factorization of `A`.

!!! note
    Certain structured matrix types, such as `Diagonal` and `UpperTriangular`, are permitted, as
    these are already in a factorized form

# Examples
```jldoctest
julia> A = [1 2.2 4; 3.1 0.2 3; 4 1 2];

julia> X = [1; 2.5; 3];

julia> Y = copy(X);

julia> ldiv!(qr(A), X);

julia> X
3-element Vector{Float64}:
  0.7128099173553719
 -0.051652892561983674
  0.10020661157024757

julia> A\\Y
3-element Vector{Float64}:
  0.7128099173553719
 -0.05165289256198333
  0.10020661157024785
```
"""
ldiv!(A, B)


"""
    rdiv!(A, B)

Compute `A / B` in-place and overwriting `A` to store the result.

The argument `B` should *not* be a matrix.  Rather, instead of matrices it should be a
factorization object (e.g. produced by [`factorize`](@ref) or [`cholesky`](@ref)).
The reason for this is that factorization itself is both expensive and typically allocates memory
(although it can also be done in-place via, e.g., [`lu!`](@ref)),
and performance-critical situations requiring `rdiv!` usually also require fine-grained
control over the factorization of `B`.

!!! note
    Certain structured matrix types, such as `Diagonal` and `UpperTriangular`, are permitted, as
    these are already in a factorized form
"""
rdiv!(A, B)

"""
    copy_oftype(A, T)

Creates a copy of `A` with eltype `T`. No assertions about mutability of the result are
made. When `eltype(A) == T`, then this calls `copy(A)` which may be overloaded for custom
array types. Otherwise, this calls `convert(AbstractArray{T}, A)`.
"""
copy_oftype(A::AbstractArray{T}, ::Type{T}) where {T} = copy(A)
copy_oftype(A::AbstractArray{T,N}, ::Type{S}) where {T,N,S} = convert(AbstractArray{S,N}, A)

"""
    copymutable_oftype(A, T)

Copy `A` to a mutable array with eltype `T` based on `similar(A, T)`.

The resulting matrix typically has similar algebraic structure as `A`. For
example, supplying a tridiagonal matrix results in another tridiagonal matrix.
In general, the type of the output corresponds to that of `similar(A, T)`.

In LinearAlgebra, mutable copies (of some desired eltype) are created to be passed
to in-place algorithms (such as `ldiv!`, `rdiv!`, `lu!` and so on). If the specific
algorithm is known to preserve the algebraic structure, use `copymutable_oftype`.
If the algorithm is known to return a dense matrix (or some wrapper backed by a dense
matrix), then use `copy_similar`.

See also: `Base.copymutable`, `copy_similar`.
"""
copymutable_oftype(A::AbstractArray, ::Type{S}) where {S} = copyto!(similar(A, S), A)

"""
    copy_similar(A, T)

Copy `A` to a mutable array with eltype `T` based on `similar(A, T, size(A))`.

Compared to `copymutable_oftype`, the result can be more flexible. In general, the type
of the output corresponds to that of the three-argument method `similar(A, T, size(A))`.

See also: `copymutable_oftype`.
"""
copy_similar(A::AbstractArray, ::Type{T}) where {T} = copyto!(similar(A, T, size(A)), A)


include("adjtrans.jl")
include("transpose.jl")

include("exceptions.jl")
include("generic.jl")

include("blas.jl")
include("matmul.jl")
include("lapack.jl")

include("dense.jl")
include("tridiag.jl")
include("triangular.jl")

include("factorization.jl")
include("eigen.jl")
include("svd.jl")
include("symmetric.jl")
include("cholesky.jl")
include("lu.jl")
include("bunchkaufman.jl")
include("diagonal.jl")
include("symmetriceigen.jl")
include("bidiag.jl")
include("uniformscaling.jl")
include("qr.jl")
include("lq.jl")
include("hessenberg.jl")
include("abstractq.jl")
include("givens.jl")
include("special.jl")
include("bitarray.jl")
include("ldlt.jl")
include("schur.jl")
include("structuredbroadcast.jl")
include("deprecated.jl")

const ⋅ = dot
const × = cross
export ⋅, ×

wrapper_char(::AbstractArray) = 'N'
wrapper_char(::Adjoint) = 'C'
wrapper_char(::Adjoint{<:Real}) = 'T'
wrapper_char(::Transpose) = 'T'
wrapper_char(A::Hermitian) = A.uplo == 'U' ? 'H' : 'h'
wrapper_char(A::Hermitian{<:Real}) = A.uplo == 'U' ? 'S' : 's'
wrapper_char(A::Symmetric) = A.uplo == 'U' ? 'S' : 's'

Base.@constprop :aggressive function wrap(A::AbstractVecOrMat, tA::AbstractChar)
    if tA == 'N'
        return A
    elseif tA == 'T'
        return transpose(A)
    elseif tA == 'C'
        return adjoint(A)
    elseif tA == 'H'
        return Hermitian(A, :U)
    elseif tA == 'h'
        return Hermitian(A, :L)
    elseif tA == 'S'
        return Symmetric(A, :U)
    else # tA == 's'
        return Symmetric(A, :L)
    end
end

_unwrap(A::AbstractVecOrMat) = A

## convenience methods
## return only the solution of a least squares problem while avoiding promoting
## vectors to matrices.
_cut_B(x::AbstractVector, r::UnitRange) = length(x)  > length(r) ? x[r]   : x
_cut_B(X::AbstractMatrix, r::UnitRange) = size(X, 1) > length(r) ? X[r,:] : X

# SymTridiagonal ev can be the same length as dv, but the last element is
# ignored. However, some methods can fail if they read the entire ev
# rather than just the meaningful elements. This is a helper function
# for getting only the meaningful elements of ev. See #41089
_evview(S::SymTridiagonal) = @view S.ev[begin:begin + length(S.dv) - 2]

## append right hand side with zeros if necessary
_zeros(::Type{T}, b::AbstractVector, n::Integer) where {T} = zeros(T, max(length(b), n))
_zeros(::Type{T}, B::AbstractMatrix, n::Integer) where {T} = zeros(T, max(size(B, 1), n), size(B, 2))

# convert to Vector, if necessary
_makevector(x::Vector) = x
_makevector(x::AbstractVector) = Vector(x)

# append a zero element / drop the last element
_pushzero(A) = (B = similar(A, length(A)+1); @inbounds B[begin:end-1] .= A; @inbounds B[end] = zero(eltype(B)); B)
_droplast!(A) = deleteat!(A, lastindex(A))

# some trait like this would be cool
# onedefined(::Type{T}) where {T} = hasmethod(one, (T,))
# but we are actually asking for oneunit(T), that is, however, defined for generic T as
# `T(one(T))`, so the question is equivalent for whether one(T) is defined
onedefined(::Type) = false
onedefined(::Type{<:Number}) = true

# initialize return array for op(A, B)
_init_eltype(::typeof(*), ::Type{TA}, ::Type{TB}) where {TA,TB} =
    (onedefined(TA) && onedefined(TB)) ?
        typeof(matprod(oneunit(TA), oneunit(TB))) :
        promote_op(matprod, TA, TB)
_init_eltype(op, ::Type{TA}, ::Type{TB}) where {TA,TB} =
    (onedefined(TA) && onedefined(TB)) ?
        typeof(op(oneunit(TA), oneunit(TB))) :
        promote_op(op, TA, TB)
_initarray(op, ::Type{TA}, ::Type{TB}, C) where {TA,TB} =
    similar(C, _init_eltype(op, TA, TB), size(C))

# General fallback definition for handling under- and overdetermined system as well as square problems
# While this definition is pretty general, it does e.g. promote to common element type of lhs and rhs
# which is required by LAPACK but not SuiteSparse which allows real-complex solves in some cases. Hence,
# we restrict this method to only the LAPACK factorizations in LinearAlgebra.
# The definition is put here since it explicitly references all the Factorization structs so it has
# to be located after all the files that define the structs.
const LAPACKFactorizations{T,S} = Union{
    BunchKaufman{T,S},
    Cholesky{T,S},
    LQ{T,S},
    LU{T,S},
    QR{T,S},
    QRCompactWY{T,S},
    QRPivoted{T,S},
    SVD{T,<:Real,S}}

(\)(F::LAPACKFactorizations, B::AbstractVecOrMat) = ldiv(F, B)
(\)(F::AdjointFactorization{<:Any,<:LAPACKFactorizations}, B::AbstractVecOrMat) = ldiv(F, B)
(\)(F::TransposeFactorization{<:Any,<:LU}, B::AbstractVecOrMat) = ldiv(F, B)

function ldiv(F::Factorization, B::AbstractVecOrMat)
    require_one_based_indexing(B)
    m, n = size(F)
    if m != size(B, 1)
        throw(DimensionMismatch("arguments must have the same number of rows"))
    end

    TFB = typeof(oneunit(eltype(B)) / oneunit(eltype(F)))
    FF = Factorization{TFB}(F)

    # For wide problem we (often) compute a minimum norm solution. The solution
    # is larger than the right hand side so we use size(F, 2).
    BB = _zeros(TFB, B, n)

    if n > size(B, 1)
        # Underdetermined
        copyto!(view(BB, 1:m, :), B)
    else
        copyto!(BB, B)
    end

    ldiv!(FF, BB)

    # For tall problems, we compute a least squares solution so only part
    # of the rhs should be returned from \ while ldiv! uses (and returns)
    # the complete rhs
    return _cut_B(BB, 1:n)
end
# disambiguate
(\)(F::LAPACKFactorizations{T}, B::VecOrMat{Complex{T}}) where {T<:BlasReal} =
    @invoke \(F::Factorization{T}, B::VecOrMat{Complex{T}})
(\)(F::AdjointFactorization{T,<:LAPACKFactorizations}, B::VecOrMat{Complex{T}}) where {T<:BlasReal} =
    ldiv(F, B)
(\)(F::TransposeFactorization{T,<:LU}, B::VecOrMat{Complex{T}}) where {T<:BlasReal} =
    ldiv(F, B)

"""
    LinearAlgebra.peakflops(n::Integer=4096; eltype::DataType=Float64, ntrials::Integer=3, parallel::Bool=false)

`peakflops` computes the peak flop rate of the computer by using double precision
[`gemm!`](@ref LinearAlgebra.BLAS.gemm!). By default, if no arguments are specified, it
multiplies two `Float64` matrices of size `n x n`, where `n = 4096`. If the underlying BLAS is using
multiple threads, higher flop rates are realized. The number of BLAS threads can be set with
[`BLAS.set_num_threads(n)`](@ref).

If the keyword argument `eltype` is provided, `peakflops` will construct matrices with elements
of type `eltype` for calculating the peak flop rate.

By default, `peakflops` will use the best timing from 3 trials. If the `ntrials` keyword argument
is provided, `peakflops` will use those many trials for picking the best timing.

If the keyword argument `parallel` is set to `true`, `peakflops` is run in parallel on all
the worker processors. The flop rate of the entire parallel computer is returned. When
running in parallel, only 1 BLAS thread is used. The argument `n` still refers to the size
of the problem that is solved on each processor.

!!! compat "Julia 1.1"
    This function requires at least Julia 1.1. In Julia 1.0 it is available from
    the standard library `InteractiveUtils`.
"""
function peakflops(n::Integer=4096; eltype::DataType=Float64, ntrials::Integer=3, parallel::Bool=false)
    t = zeros(Float64, ntrials)
    for i=1:ntrials
        a = ones(eltype,n,n)
        t[i] = @elapsed a2 = a*a
        @assert a2[1,1] == n
    end

    if parallel
        let Distributed = Base.require(Base.PkgId(
                Base.UUID((0x8ba89e20_285c_5b6f, 0x9357_94700520ee1b)), "Distributed"))
            nworkers = @invokelatest Distributed.nworkers()
            results = @invokelatest Distributed.pmap(peakflops, fill(n, nworkers))
            return sum(results)
        end
    else
        return 2*Float64(n)^3 / minimum(t)
    end
end


function versioninfo(io::IO=stdout)
    indent = "  "
    config = BLAS.get_config()
    build_flags = join(string.(config.build_flags), ", ")
    println(io, "BLAS: ", BLAS.libblastrampoline, " (", build_flags, ")")
    for lib in config.loaded_libs
        interface = uppercase(string(lib.interface))
        println(io, indent, "--> ", lib.libname, " (", interface, ")")
    end
    println(io, "Threading:")
    println(io, indent, "Threads.threadpoolsize() = ", Threads.threadpoolsize())
    println(io, indent, "Threads.maxthreadid() = ", Base.Threads.maxthreadid())
    println(io, indent, "LinearAlgebra.BLAS.get_num_threads() = ", BLAS.get_num_threads())
    println(io, "Relevant environment variables:")
    env_var_names = [
        "JULIA_NUM_THREADS",
        "MKL_DYNAMIC",
        "MKL_NUM_THREADS",
         # OpenBLAS has a hierarchy of environment variables for setting the
         # number of threads, see
         # https://github.com/xianyi/OpenBLAS/blob/c43ec53bdd00d9423fc609d7b7ecb35e7bf41b85/README.md#setting-the-number-of-threads-using-environment-variables
        ("OPENBLAS_NUM_THREADS", "GOTO_NUM_THREADS", "OMP_NUM_THREADS"),
    ]
    printed_at_least_one_env_var = false
    print_var(io, indent, name) = println(io, indent, name, " = ", ENV[name])
    for name in env_var_names
        if name isa Tuple
            # If `name` is a Tuple, then find the first environment which is
            # defined, and disregard the following ones.
            for nm in name
                if haskey(ENV, nm)
                    print_var(io, indent, nm)
                    printed_at_least_one_env_var = true
                    break
                end
            end
        else
            if haskey(ENV, name)
                print_var(io, indent, name)
                printed_at_least_one_env_var = true
            end
        end
    end
    if !printed_at_least_one_env_var
        println(io, indent, "[none]")
    end
    return nothing
end

function __init__()
    try
        BLAS.lbt_forward(OpenBLAS_jll.libopenblas_path; clear=true)
        BLAS.check()
    catch ex
        Base.showerror_nostdio(ex, "WARNING: Error during initialization of module LinearAlgebra")
    end
    # register a hook to disable BLAS threading
    Base.at_disable_library_threading(() -> BLAS.set_num_threads(1))

    # https://github.com/xianyi/OpenBLAS/blob/c43ec53bdd00d9423fc609d7b7ecb35e7bf41b85/README.md#setting-the-number-of-threads-using-environment-variables
    if !haskey(ENV, "OPENBLAS_NUM_THREADS") && !haskey(ENV, "GOTO_NUM_THREADS") && !haskey(ENV, "OMP_NUM_THREADS")
        @static if Sys.isapple() && Base.BinaryPlatforms.arch(Base.BinaryPlatforms.HostPlatform()) == "aarch64"
            BLAS.set_num_threads(max(1, Sys.CPU_THREADS))
        else
            BLAS.set_num_threads(max(1, Sys.CPU_THREADS ÷ 2))
        end
    end
end

end # module LinearAlgebra
|   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/OpenBLAS_jll/src/OpenBLAS_jll.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

## dummy stub for https://github.com/JuliaBinaryWrappers/OpenBLAS_jll.jl
baremodule OpenBLAS_jll
using Base, Libdl, Base.BinaryPlatforms

# We are explicitly NOT loading this at runtime, as it contains `libgomp`
# which conflicts with `libiomp5`, breaking things like MKL.  In the future,
# we hope to transition to a JLL interface that provides a more granular
# interface than eagerly dlopen'ing all libraries provided in the JLL
# which will eliminate issues like this, where we avoid loading a JLL
# because we don't want to load a library that we don't even use yet.
# using CompilerSupportLibraries_jll
# Because of this however, we have to manually load the libraries we
# _do_ care about, namely libgfortran
Base.Experimental.@compiler_options compile=min optimize=0 infer=false

const PATH_list = String[]
const LIBPATH_list = String[]

export libopenblas

# These get calculated in __init__()
const PATH = Ref("")
const LIBPATH = Ref("")
artifact_dir::String = ""
libopenblas_handle::Ptr{Cvoid} = C_NULL
libopenblas_path::String = ""

if Base.USE_BLAS64
    const libsuffix = "64_"
else
    const libsuffix = ""
end

if Sys.iswindows()
    const libopenblas = "libopenblas$(libsuffix).dll"
    const _libgfortran = string("libgfortran-", libgfortran_version(HostPlatform()).major, ".dll")
elseif Sys.isapple()
    const libopenblas = "@rpath/libopenblas$(libsuffix).dylib"
    const _libgfortran = string("@rpath/", "libgfortran.", libgfortran_version(HostPlatform()).major, ".dylib")
else
    const libopenblas = "libopenblas$(libsuffix).so"
    const _libgfortran = string("libgfortran.so.", libgfortran_version(HostPlatform()).major)
end

function __init__()
    # make sure OpenBLAS does not set CPU affinity (#1070, #9639)
    if !haskey(ENV, "OPENBLAS_MAIN_FREE")
        ENV["OPENBLAS_MAIN_FREE"] = "1"
    end

    # Ensure that OpenBLAS does not grab a huge amount of memory at first,
    # since it instantly allocates scratch buffer space for the number of
    # threads it thinks it needs to use.
    # X-ref: https://github.com/xianyi/OpenBLAS/blob/c43ec53bdd00d9423fc609d7b7ecb35e7bf41b85/README.md#setting-the-number-of-threads-using-environment-variables
    # X-ref: https://github.com/JuliaLang/julia/issues/45434
    if !haskey(ENV, "OPENBLAS_NUM_THREADS") &&
       !haskey(ENV, "GOTO_NUM_THREADS") &&
       !haskey(ENV, "OMP_NUM_THREADS")
        # We set this to `1` here, and then LinearAlgebra will update
        # to the true value in its `__init__()` function.
        ENV["OPENBLAS_DEFAULT_NUM_THREADS"] = "1"
    end

    # As mentioned above, we are sneaking this in here so that we don't have to
    # depend on CSL_jll and load _all_ of its libraries.
    dlopen(_libgfortran)

    global libopenblas_handle = dlopen(libopenblas)
    global libopenblas_path = dlpath(libopenblas_handle)
    global artifact_dir = dirname(Sys.BINDIR)
    LIBPATH[] = dirname(libopenblas_path)
    push!(LIBPATH_list, LIBPATH[])
end

# JLLWrappers API compatibility shims.  Note that not all of these will really make sense.
# For instance, `find_artifact_dir()` won't actually be the artifact directory, because
# there isn't one.  It instead returns the overall Julia prefix.
is_available() = true
find_artifact_dir() = artifact_dir
dev_jll() = error("stdlib JLLs cannot be dev'ed")
best_wrapper = nothing
get_libopenblas_path() = libopenblas_path

end  # module OpenBLAS_jll
�   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/libblastrampoline_jll/src/libblastrampoline_jll.jl      # This file is a part of Julia. License is MIT: https://julialang.org/license

## dummy stub for https://github.com/JuliaBinaryWrappers/libblastrampoline_jll.jl

baremodule libblastrampoline_jll
using Base, Libdl
Base.Experimental.@compiler_options compile=min optimize=0 infer=false

const PATH_list = String[]
const LIBPATH_list = String[]

export libblastrampoline

# These get calculated in __init__()
const PATH = Ref("")
const LIBPATH = Ref("")
artifact_dir::String = ""
libblastrampoline_handle::Ptr{Cvoid} = C_NULL
libblastrampoline_path::String = ""

# NOTE: keep in sync with `Base.libblas_name` and `Base.liblapack_name`.
const libblastrampoline = if Sys.iswindows()
    "libblastrampoline-5.dll"
elseif Sys.isapple()
    "@rpath/libblastrampoline.5.dylib"
else
    "libblastrampoline.so.5"
end

function __init__()
    global libblastrampoline_handle = dlopen(libblastrampoline)
    global libblastrampoline_path = dlpath(libblastrampoline_handle)
    global artifact_dir = dirname(Sys.BINDIR)
    LIBPATH[] = dirname(libblastrampoline_path)
    push!(LIBPATH_list, LIBPATH[])
end

# JLLWrappers API compatibility shims.  Note that not all of these will really make sense.
# For instance, `find_artifact_dir()` won't actually be the artifact directory, because
# there isn't one.  It instead returns the overall Julia prefix.
is_available() = true
find_artifact_dir() = artifact_dir
dev_jll() = error("stdlib JLLs cannot be dev'ed")
best_wrapper = nothing
get_libblastrampoline_path() = libblastrampoline_path

end  # module libblastrampoline_jll
y   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LinearAlgebra/src/adjtrans.jl�O      # This file is a part of Julia. License is MIT: https://julialang.org/license

### basic definitions (types, aliases, constructors, abstractarray interface, sundry similar)

# note that Adjoint and Transpose must be able to wrap not only vectors and matrices
# but also factorizations, rotations, and other linear algebra objects, including
# user-defined such objects. so do not restrict the wrapped type.
"""
    Adjoint

Lazy wrapper type for an adjoint view of the underlying linear algebra object,
usually an `AbstractVector`/`AbstractMatrix`.
Usually, the `Adjoint` constructor should not be called directly, use [`adjoint`](@ref)
instead. To materialize the view use [`copy`](@ref).

This type is intended for linear algebra usage - for general data manipulation see
[`permutedims`](@ref Base.permutedims).

# Examples
```jldoctest
julia> A = [3+2im 9+2im; 0 0]
2×2 Matrix{Complex{Int64}}:
 3+2im  9+2im
 0+0im  0+0im

julia> Adjoint(A)
2×2 adjoint(::Matrix{Complex{Int64}}) with eltype Complex{Int64}:
 3-2im  0+0im
 9-2im  0+0im
```
"""
struct Adjoint{T,S} <: AbstractMatrix{T}
    parent::S
end
"""
    Transpose

Lazy wrapper type for a transpose view of the underlying linear algebra object,
usually an `AbstractVector`/`AbstractMatrix`.
Usually, the `Transpose` constructor should not be called directly, use [`transpose`](@ref)
instead. To materialize the view use [`copy`](@ref).

This type is intended for linear algebra usage - for general data manipulation see
[`permutedims`](@ref Base.permutedims).

# Examples
```jldoctest
julia> A = [2 3; 0 0]
2×2 Matrix{Int64}:
 2  3
 0  0

julia> Transpose(A)
2×2 transpose(::Matrix{Int64}) with eltype Int64:
 2  0
 3  0
```
"""
struct Transpose{T,S} <: AbstractMatrix{T}
    parent::S
end

# basic outer constructors
Adjoint(A) = Adjoint{Base.promote_op(adjoint,eltype(A)),typeof(A)}(A)
Transpose(A) = Transpose{Base.promote_op(transpose,eltype(A)),typeof(A)}(A)

"""
    inplace_adj_or_trans(::AbstractArray) -> adjoint!|transpose!|copyto!
    inplace_adj_or_trans(::Type{<:AbstractArray}) -> adjoint!|transpose!|copyto!

Return [`adjoint!`](@ref) from an `Adjoint` type or object and
[`transpose!`](@ref) from a `Transpose` type or object. Otherwise,
return [`copyto!`](@ref). Note that `Adjoint` and `Transpose` have
to be the outer-most wrapper object for a non-`identity` function to be
returned.
"""
inplace_adj_or_trans(::T) where {T <: AbstractArray} = inplace_adj_or_trans(T)
inplace_adj_or_trans(::Type{<:AbstractArray}) = copyto!
inplace_adj_or_trans(::Type{<:Adjoint}) = adjoint!
inplace_adj_or_trans(::Type{<:Transpose}) = transpose!

# unwraps Adjoint, Transpose, Symmetric, Hermitian
_unwrap(A::Adjoint)   = parent(A)
_unwrap(A::Transpose) = parent(A)

# unwraps Adjoint and Transpose only
_unwrap_at(A) = A
_unwrap_at(A::Adjoint)   = parent(A)
_unwrap_at(A::Transpose) = parent(A)

Base.dataids(A::Union{Adjoint, Transpose}) = Base.dataids(A.parent)
Base.unaliascopy(A::Union{Adjoint,Transpose}) = typeof(A)(Base.unaliascopy(A.parent))

# wrapping lowercase quasi-constructors
"""
    A'
    adjoint(A)

Lazy adjoint (conjugate transposition). Note that `adjoint` is applied recursively to
elements.

For number types, `adjoint` returns the complex conjugate, and therefore it is equivalent to
the identity function for real numbers.

This operation is intended for linear algebra usage - for general data manipulation see
[`permutedims`](@ref Base.permutedims).

# Examples
```jldoctest
julia> A = [3+2im 9+2im; 0  0]
2×2 Matrix{Complex{Int64}}:
 3+2im  9+2im
 0+0im  0+0im

julia> B = A' # equivalently adjoint(A)
2×2 adjoint(::Matrix{Complex{Int64}}) with eltype Complex{Int64}:
 3-2im  0+0im
 9-2im  0+0im

julia> B isa Adjoint
true

julia> adjoint(B) === A # the adjoint of an adjoint unwraps the parent
true

julia> Adjoint(B) # however, the constructor always wraps its argument
2×2 adjoint(adjoint(::Matrix{Complex{Int64}})) with eltype Complex{Int64}:
 3+2im  9+2im
 0+0im  0+0im

julia> B[1,2] = 4 + 5im; # modifying B will modify A automatically

julia> A
2×2 Matrix{Complex{Int64}}:
 3+2im  9+2im
 4-5im  0+0im
```

For real matrices, the `adjoint` operation is equivalent to a `transpose`.

```jldoctest
julia> A = reshape([x for x in 1:4], 2, 2)
2×2 Matrix{Int64}:
 1  3
 2  4

julia> A'
2×2 adjoint(::Matrix{Int64}) with eltype Int64:
 1  2
 3  4

julia> adjoint(A) == transpose(A)
true
```

The adjoint of an `AbstractVector` is a row-vector:
```jldoctest
julia> x = [3, 4im]
2-element Vector{Complex{Int64}}:
 3 + 0im
 0 + 4im

julia> x'
1×2 adjoint(::Vector{Complex{Int64}}) with eltype Complex{Int64}:
 3+0im  0-4im

julia> x'x # compute the dot product, equivalently x' * x
25 + 0im
```

For a matrix of matrices, the individual blocks are recursively operated on:
```jldoctest
julia> A = reshape([x + im*x for x in 1:4], 2, 2)
2×2 Matrix{Complex{Int64}}:
 1+1im  3+3im
 2+2im  4+4im

julia> C = reshape([A, 2A, 3A, 4A], 2, 2)
2×2 Matrix{Matrix{Complex{Int64}}}:
 [1+1im 3+3im; 2+2im 4+4im]  [3+3im 9+9im; 6+6im 12+12im]
 [2+2im 6+6im; 4+4im 8+8im]  [4+4im 12+12im; 8+8im 16+16im]

julia> C'
2×2 adjoint(::Matrix{Matrix{Complex{Int64}}}) with eltype Adjoint{Complex{Int64}, Matrix{Complex{Int64}}}:
 [1-1im 2-2im; 3-3im 4-4im]    [2-2im 4-4im; 6-6im 8-8im]
 [3-3im 6-6im; 9-9im 12-12im]  [4-4im 8-8im; 12-12im 16-16im]
```
"""
adjoint(A::AbstractVecOrMat) = Adjoint(A)

"""
    transpose(A)

Lazy transpose. Mutating the returned object should appropriately mutate `A`. Often,
but not always, yields `Transpose(A)`, where `Transpose` is a lazy transpose wrapper. Note
that this operation is recursive.

This operation is intended for linear algebra usage - for general data manipulation see
[`permutedims`](@ref Base.permutedims), which is non-recursive.

# Examples
```jldoctest
julia> A = [3 2; 0 0]
2×2 Matrix{Int64}:
 3  2
 0  0

julia> B = transpose(A)
2×2 transpose(::Matrix{Int64}) with eltype Int64:
 3  0
 2  0

julia> B isa Transpose
true

julia> transpose(B) === A # the transpose of a transpose unwraps the parent
true

julia> Transpose(B) # however, the constructor always wraps its argument
2×2 transpose(transpose(::Matrix{Int64})) with eltype Int64:
 3  2
 0  0

julia> B[1,2] = 4; # modifying B will modify A automatically

julia> A
2×2 Matrix{Int64}:
 3  2
 4  0
```

For complex matrices, the `adjoint` operation is equivalent to a conjugate-transpose.
```jldoctest
julia> A = reshape([Complex(x, x) for x in 1:4], 2, 2)
2×2 Matrix{Complex{Int64}}:
 1+1im  3+3im
 2+2im  4+4im

julia> adjoint(A) == conj(transpose(A))
true
```

The `transpose` of an `AbstractVector` is a row-vector:
```jldoctest
julia> v = [1,2,3]
3-element Vector{Int64}:
 1
 2
 3

julia> transpose(v) # returns a row-vector
1×3 transpose(::Vector{Int64}) with eltype Int64:
 1  2  3

julia> transpose(v) * v # compute the dot product
14
```

For a matrix of matrices, the individual blocks are recursively operated on:
```jldoctest
julia> C = [1 3; 2 4]
2×2 Matrix{Int64}:
 1  3
 2  4

julia> D = reshape([C, 2C, 3C, 4C], 2, 2) # construct a block matrix
2×2 Matrix{Matrix{Int64}}:
 [1 3; 2 4]  [3 9; 6 12]
 [2 6; 4 8]  [4 12; 8 16]

julia> transpose(D) # blocks are recursively transposed
2×2 transpose(::Matrix{Matrix{Int64}}) with eltype Transpose{Int64, Matrix{Int64}}:
 [1 2; 3 4]   [2 4; 6 8]
 [3 6; 9 12]  [4 8; 12 16]
```
"""
transpose(A::AbstractVecOrMat) = Transpose(A)

# unwrapping lowercase quasi-constructors
adjoint(A::Adjoint) = A.parent
transpose(A::Transpose) = A.parent
adjoint(A::Transpose{<:Real}) = A.parent
transpose(A::Adjoint{<:Real}) = A.parent

# printing
function Base.showarg(io::IO, v::Adjoint, toplevel)
    print(io, "adjoint(")
    Base.showarg(io, parent(v), false)
    print(io, ')')
    toplevel && print(io, " with eltype ", eltype(v))
    return nothing
end
function Base.showarg(io::IO, v::Transpose, toplevel)
    print(io, "transpose(")
    Base.showarg(io, parent(v), false)
    print(io, ')')
    toplevel && print(io, " with eltype ", eltype(v))
    return nothing
end

# some aliases for internal convenience use
const AdjOrTrans{T,S} = Union{Adjoint{T,S},Transpose{T,S}} where {T,S}
const AdjointAbsVec{T} = Adjoint{T,<:AbstractVector}
const AdjointAbsMat{T} = Adjoint{T,<:AbstractMatrix}
const TransposeAbsVec{T} = Transpose{T,<:AbstractVector}
const TransposeAbsMat{T} = Transpose{T,<:AbstractMatrix}
const AdjOrTransAbsVec{T} = AdjOrTrans{T,<:AbstractVector}
const AdjOrTransAbsMat{T} = AdjOrTrans{T,<:AbstractMatrix}

# for internal use below
wrapperop(_) = identity
wrapperop(::Adjoint) = adjoint
wrapperop(::Transpose) = transpose

# the following fallbacks can be removed if Adjoint/Transpose are restricted to AbstractVecOrMat
size(A::AdjOrTrans) = reverse(size(A.parent))
axes(A::AdjOrTrans) = reverse(axes(A.parent))
# AbstractArray interface, basic definitions
length(A::AdjOrTrans) = length(A.parent)
size(v::AdjOrTransAbsVec) = (1, length(v.parent))
size(A::AdjOrTransAbsMat) = reverse(size(A.parent))
axes(v::AdjOrTransAbsVec) = (Base.OneTo(1), axes(v.parent)...)
axes(A::AdjOrTransAbsMat) = reverse(axes(A.parent))
IndexStyle(::Type{<:AdjOrTransAbsVec}) = IndexLinear()
IndexStyle(::Type{<:AdjOrTransAbsMat}) = IndexCartesian()
@propagate_inbounds Base.isassigned(v::AdjOrTransAbsVec, i::Int) = isassigned(v.parent, i-1+first(axes(v.parent)[1]))
@propagate_inbounds Base.isassigned(v::AdjOrTransAbsMat, i::Int, j::Int) = isassigned(v.parent, j, i)
@propagate_inbounds getindex(v::AdjOrTransAbsVec{T}, i::Int) where {T} = wrapperop(v)(v.parent[i-1+first(axes(v.parent)[1])])::T
@propagate_inbounds getindex(A::AdjOrTransAbsMat{T}, i::Int, j::Int) where {T} = wrapperop(A)(A.parent[j, i])::T
@propagate_inbounds setindex!(v::AdjOrTransAbsVec, x, i::Int) = (setindex!(v.parent, wrapperop(v)(x), i-1+first(axes(v.parent)[1])); v)
@propagate_inbounds setindex!(A::AdjOrTransAbsMat, x, i::Int, j::Int) = (setindex!(A.parent, wrapperop(A)(x), j, i); A)
# AbstractArray interface, additional definitions to retain wrapper over vectors where appropriate
@propagate_inbounds getindex(v::AdjOrTransAbsVec, ::Colon, is::AbstractArray{Int}) = wrapperop(v)(v.parent[is])
@propagate_inbounds getindex(v::AdjOrTransAbsVec, ::Colon, ::Colon) = wrapperop(v)(v.parent[:])

# conversion of underlying storage
convert(::Type{Adjoint{T,S}}, A::Adjoint) where {T,S} = Adjoint{T,S}(convert(S, A.parent))::Adjoint{T,S}
convert(::Type{Transpose{T,S}}, A::Transpose) where {T,S} = Transpose{T,S}(convert(S, A.parent))::Transpose{T,S}

# Strides and pointer for transposed strided arrays — but only if the elements are actually stored in memory
Base.strides(A::Adjoint{<:Real, <:AbstractVector}) = (stride(A.parent, 2), stride(A.parent, 1))
Base.strides(A::Transpose{<:Any, <:AbstractVector}) = (stride(A.parent, 2), stride(A.parent, 1))
# For matrices it's slightly faster to use reverse and avoid calling stride twice
Base.strides(A::Adjoint{<:Real, <:AbstractMatrix}) = reverse(strides(A.parent))
Base.strides(A::Transpose{<:Any, <:AbstractMatrix}) = reverse(strides(A.parent))

Base.unsafe_convert(::Type{Ptr{T}}, A::Adjoint{<:Real, <:AbstractVecOrMat}) where {T} = Base.unsafe_convert(Ptr{T}, A.parent)
Base.unsafe_convert(::Type{Ptr{T}}, A::Transpose{<:Any, <:AbstractVecOrMat}) where {T} = Base.unsafe_convert(Ptr{T}, A.parent)

Base.elsize(::Type{<:Adjoint{<:Real, P}}) where {P<:AbstractVecOrMat} = Base.elsize(P)
Base.elsize(::Type{<:Transpose{<:Any, P}}) where {P<:AbstractVecOrMat} = Base.elsize(P)

# for vectors, the semantics of the wrapped and unwrapped types differ
# so attempt to maintain both the parent and wrapper type insofar as possible
similar(A::AdjOrTransAbsVec) = wrapperop(A)(similar(A.parent))
similar(A::AdjOrTransAbsVec, ::Type{T}) where {T} = wrapperop(A)(similar(A.parent, Base.promote_op(wrapperop(A), T)))
# for matrices, the semantics of the wrapped and unwrapped types are generally the same
# and as you are allocating with similar anyway, you might as well get something unwrapped
similar(A::AdjOrTrans) = similar(A.parent, eltype(A), axes(A))
similar(A::AdjOrTrans, ::Type{T}) where {T} = similar(A.parent, T, axes(A))
similar(A::AdjOrTrans, ::Type{T}, dims::Dims{N}) where {T,N} = similar(A.parent, T, dims)

# AbstractMatrix{T} constructor for adjtrans vector: preserve wrapped type
AbstractMatrix{T}(A::AdjOrTransAbsVec) where {T} = wrapperop(A)(AbstractVector{T}(A.parent))

# sundry basic definitions
parent(A::AdjOrTrans) = A.parent
vec(v::TransposeAbsVec{<:Number}) = parent(v)
vec(v::AdjointAbsVec{<:Real}) = parent(v)

### concatenation
# preserve Adjoint/Transpose wrapper around vectors
# to retain the associated semantics post-concatenation
hcat(avs::Union{Number,AdjointAbsVec}...) = _adjoint_hcat(avs...)
hcat(tvs::Union{Number,TransposeAbsVec}...) = _transpose_hcat(tvs...)
_adjoint_hcat(avs::Union{Number,AdjointAbsVec}...) = adjoint(vcat(map(adjoint, avs)...))
_transpose_hcat(tvs::Union{Number,TransposeAbsVec}...) = transpose(vcat(map(transpose, tvs)...))
typed_hcat(::Type{T}, avs::Union{Number,AdjointAbsVec}...) where {T} = adjoint(typed_vcat(T, map(adjoint, avs)...))
typed_hcat(::Type{T}, tvs::Union{Number,TransposeAbsVec}...) where {T} = transpose(typed_vcat(T, map(transpose, tvs)...))
# otherwise-redundant definitions necessary to prevent hitting the concat methods in LinearAlgebra/special.jl
hcat(avs::Adjoint{<:Any,<:Vector}...) = _adjoint_hcat(avs...)
hcat(tvs::Transpose{<:Any,<:Vector}...) = _transpose_hcat(tvs...)
hcat(avs::Adjoint{T,Vector{T}}...) where {T} = _adjoint_hcat(avs...)
hcat(tvs::Transpose{T,Vector{T}}...) where {T} = _transpose_hcat(tvs...)
# TODO unify and allow mixed combinations


### higher order functions
# preserve Adjoint/Transpose wrapper around vectors
# to retain the associated semantics post-map/broadcast
#
# note that the caller's operation f operates in the domain of the wrapped vectors' entries.
# hence the adjoint->f->adjoint shenanigans applied to the parent vectors' entries.
map(f, avs::AdjointAbsVec...) = adjoint(map((xs...) -> adjoint(f(adjoint.(xs)...)), parent.(avs)...))
map(f, tvs::TransposeAbsVec...) = transpose(map((xs...) -> transpose(f(transpose.(xs)...)), parent.(tvs)...))
quasiparentt(x) = parent(x); quasiparentt(x::Number) = x # to handle numbers in the defs below
quasiparenta(x) = parent(x); quasiparenta(x::Number) = conj(x) # to handle numbers in the defs below
broadcast(f, avs::Union{Number,AdjointAbsVec}...) = adjoint(broadcast((xs...) -> adjoint(f(adjoint.(xs)...)), quasiparenta.(avs)...))
broadcast(f, tvs::Union{Number,TransposeAbsVec}...) = transpose(broadcast((xs...) -> transpose(f(transpose.(xs)...)), quasiparentt.(tvs)...))
# Hack to preserve behavior after #32122; this needs to be done with a broadcast style instead to support dotted fusion
Broadcast.broadcast_preserving_zero_d(f, avs::Union{Number,AdjointAbsVec}...) = adjoint(broadcast((xs...) -> adjoint(f(adjoint.(xs)...)), quasiparenta.(avs)...))
Broadcast.broadcast_preserving_zero_d(f, tvs::Union{Number,TransposeAbsVec}...) = transpose(broadcast((xs...) -> transpose(f(transpose.(xs)...)), quasiparentt.(tvs)...))
# TODO unify and allow mixed combinations with a broadcast style


### reductions
# faster to sum the Array than to work through the wrapper (but only in commutative reduction ops as in Base/permuteddimsarray.jl)
Base._mapreduce_dim(f, op::CommutativeOps, init::Base._InitialValue, A::Transpose, dims::Colon) =
    Base._mapreduce_dim(f∘transpose, op, init, parent(A), dims)
Base._mapreduce_dim(f, op::CommutativeOps, init::Base._InitialValue, A::Adjoint, dims::Colon) =
    Base._mapreduce_dim(f∘adjoint, op, init, parent(A), dims)
# in prod, use fast path only in the commutative case to avoid surprises
Base._mapreduce_dim(f::typeof(identity), op::Union{typeof(*),typeof(Base.mul_prod)}, init::Base._InitialValue, A::Transpose{<:Union{Real,Complex}}, dims::Colon) =
    Base._mapreduce_dim(f∘transpose, op, init, parent(A), dims)
Base._mapreduce_dim(f::typeof(identity), op::Union{typeof(*),typeof(Base.mul_prod)}, init::Base._InitialValue, A::Adjoint{<:Union{Real,Complex}}, dims::Colon) =
    Base._mapreduce_dim(f∘adjoint, op, init, parent(A), dims)
# count allows for optimization only if the parent array has Bool eltype
Base._count(::typeof(identity), A::Transpose{Bool}, ::Colon, init) = Base._count(identity, parent(A), :, init)
Base._count(::typeof(identity), A::Adjoint{Bool}, ::Colon, init) = Base._count(identity, parent(A), :, init)
Base._any(f, A::Transpose, ::Colon) = Base._any(f∘transpose, parent(A), :)
Base._any(f, A::Adjoint, ::Colon) = Base._any(f∘adjoint, parent(A), :)
Base._all(f, A::Transpose, ::Colon) = Base._all(f∘transpose, parent(A), :)
Base._all(f, A::Adjoint, ::Colon) = Base._all(f∘adjoint, parent(A), :)
# sum(A'; dims)
Base.mapreducedim!(f, op::CommutativeOps, B::AbstractArray, A::TransposeAbsMat) =
    (Base.mapreducedim!(f∘transpose, op, switch_dim12(B), parent(A)); B)
Base.mapreducedim!(f, op::CommutativeOps, B::AbstractArray, A::AdjointAbsMat) =
    (Base.mapreducedim!(f∘adjoint, op, switch_dim12(B), parent(A)); B)
Base.mapreducedim!(f::typeof(identity), op::Union{typeof(*),typeof(Base.mul_prod)}, B::AbstractArray, A::TransposeAbsMat{<:Union{Real,Complex}}) =
    (Base.mapreducedim!(f∘transpose, op, switch_dim12(B), parent(A)); B)
Base.mapreducedim!(f::typeof(identity), op::Union{typeof(*),typeof(Base.mul_prod)}, B::AbstractArray, A::AdjointAbsMat{<:Union{Real,Complex}}) =
    (Base.mapreducedim!(f∘adjoint, op, switch_dim12(B), parent(A)); B)

switch_dim12(B::AbstractVector) = permutedims(B)
switch_dim12(B::AbstractVector{<:Number}) = transpose(B) # avoid allocs due to permutedims
switch_dim12(B::AbstractArray{<:Any,0}) = B
switch_dim12(B::AbstractArray) = PermutedDimsArray(B, (2, 1, ntuple(Base.Fix1(+,2), ndims(B) - 2)...))

### linear algebra

(-)(A::Adjoint)   = Adjoint(  -A.parent)
(-)(A::Transpose) = Transpose(-A.parent)

tr(A::Adjoint) = adjoint(tr(parent(A)))
tr(A::Transpose) = transpose(tr(parent(A)))

## multiplication *

function _dot_nonrecursive(u, v)
    lu = length(u)
    if lu != length(v)
        throw(DimensionMismatch("first array has length $(lu) which does not match the length of the second, $(length(v))."))
    end
    if lu == 0
        zero(eltype(u)) * zero(eltype(v))
    else
        sum(uu*vv for (uu, vv) in zip(u, v))
    end
end

# Adjoint/Transpose-vector * vector
*(u::AdjointAbsVec{<:Number}, v::AbstractVector{<:Number}) = dot(u.parent, v)
*(u::TransposeAbsVec{T}, v::AbstractVector{T}) where {T<:Real} = dot(u.parent, v)
*(u::AdjOrTransAbsVec, v::AbstractVector) = _dot_nonrecursive(u, v)


# vector * Adjoint/Transpose-vector
*(u::AbstractVector, v::AdjOrTransAbsVec) = broadcast(*, u, v)
# Adjoint/Transpose-vector * Adjoint/Transpose-vector
# (necessary for disambiguation with fallback methods in linalg/matmul)
*(u::AdjointAbsVec, v::AdjointAbsVec) = throw(MethodError(*, (u, v)))
*(u::TransposeAbsVec, v::TransposeAbsVec) = throw(MethodError(*, (u, v)))

# AdjOrTransAbsVec{<:Any,<:AdjOrTransAbsVec} is a lazy conj vectors
# We need to expand the combinations to avoid ambiguities
(*)(u::TransposeAbsVec, v::AdjointAbsVec{<:Any,<:TransposeAbsVec}) = _dot_nonrecursive(u, v)
(*)(u::AdjointAbsVec,   v::AdjointAbsVec{<:Any,<:TransposeAbsVec}) = _dot_nonrecursive(u, v)
(*)(u::TransposeAbsVec, v::TransposeAbsVec{<:Any,<:AdjointAbsVec}) = _dot_nonrecursive(u, v)
(*)(u::AdjointAbsVec,   v::TransposeAbsVec{<:Any,<:AdjointAbsVec}) = _dot_nonrecursive(u, v)

## pseudoinversion
pinv(v::AdjointAbsVec, tol::Real = 0) = pinv(v.parent, tol).parent
pinv(v::TransposeAbsVec, tol::Real = 0) = pinv(conj(v.parent)).parent


## left-division \
\(u::AdjOrTransAbsVec, v::AdjOrTransAbsVec) = pinv(u) * v


## right-division /
/(u::AdjointAbsVec, A::AbstractMatrix) = adjoint(adjoint(A) \ u.parent)
/(u::TransposeAbsVec, A::AbstractMatrix) = transpose(transpose(A) \ u.parent)
/(u::AdjointAbsVec, A::TransposeAbsMat) = adjoint(conj(A.parent) \ u.parent) # technically should be adjoint(copy(adjoint(copy(A))) \ u.parent)
/(u::TransposeAbsVec, A::AdjointAbsMat) = transpose(conj(A.parent) \ u.parent) # technically should be transpose(copy(transpose(copy(A))) \ u.parent)

## complex conjugate
conj(A::Transpose) = adjoint(A.parent)
conj(A::Adjoint) = transpose(A.parent)

## structured matrix methods ##
function Base.replace_in_print_matrix(A::AdjOrTrans,i::Integer,j::Integer,s::AbstractString)
    Base.replace_in_print_matrix(parent(A), j, i, s)
end
z   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LinearAlgebra/src/transpose.jl
      # This file is a part of Julia. License is MIT: https://julialang.org/license

adjoint(a::AbstractArray) = error("adjoint not defined for $(typeof(a)). Consider using `permutedims` for higher-dimensional arrays.")
transpose(a::AbstractArray) = error("transpose not defined for $(typeof(a)). Consider using `permutedims` for higher-dimensional arrays.")

## Matrix transposition ##

"""
    transpose!(dest,src)

Transpose array `src` and store the result in the preallocated array `dest`, which should
have a size corresponding to `(size(src,2),size(src,1))`. No in-place transposition is
supported and unexpected results will happen if `src` and `dest` have overlapping memory
regions.

# Examples
```jldoctest
julia> A = [3+2im 9+2im; 8+7im  4+6im]
2×2 Matrix{Complex{Int64}}:
 3+2im  9+2im
 8+7im  4+6im

julia> B = zeros(Complex{Int64}, 2, 2)
2×2 Matrix{Complex{Int64}}:
 0+0im  0+0im
 0+0im  0+0im

julia> transpose!(B, A);

julia> B
2×2 Matrix{Complex{Int64}}:
 3+2im  8+7im
 9+2im  4+6im

julia> A
2×2 Matrix{Complex{Int64}}:
 3+2im  9+2im
 8+7im  4+6im
```
"""
transpose!(B::AbstractMatrix, A::AbstractMatrix) = transpose_f!(transpose, B, A)

"""
    adjoint!(dest,src)

Conjugate transpose array `src` and store the result in the preallocated array `dest`, which
should have a size corresponding to `(size(src,2),size(src,1))`. No in-place transposition
is supported and unexpected results will happen if `src` and `dest` have overlapping memory
regions.

# Examples
```jldoctest
julia> A = [3+2im 9+2im; 8+7im  4+6im]
2×2 Matrix{Complex{Int64}}:
 3+2im  9+2im
 8+7im  4+6im

julia> B = zeros(Complex{Int64}, 2, 2)
2×2 Matrix{Complex{Int64}}:
 0+0im  0+0im
 0+0im  0+0im

julia> adjoint!(B, A);

julia> B
2×2 Matrix{Complex{Int64}}:
 3-2im  8-7im
 9-2im  4-6im

julia> A
2×2 Matrix{Complex{Int64}}:
 3+2im  9+2im
 8+7im  4+6im
```
"""
adjoint!(B::AbstractMatrix, A::AbstractMatrix) = transpose_f!(adjoint, B, A)
function transpose!(B::AbstractVector, A::AbstractMatrix)
    axes(B,1) == axes(A,2) && axes(A,1) == 1:1 || throw(DimensionMismatch("transpose"))
    copyto!(B, A)
end
function transpose!(B::AbstractMatrix, A::AbstractVector)
    axes(B,2) == axes(A,1) && axes(B,1) == 1:1 || throw(DimensionMismatch("transpose"))
    copyto!(B, A)
end
function adjoint!(B::AbstractVector, A::AbstractMatrix)
    axes(B,1) == axes(A,2) && axes(A,1) == 1:1 || throw(DimensionMismatch("transpose"))
    ccopy!(B, A)
end
function adjoint!(B::AbstractMatrix, A::AbstractVector)
    axes(B,2) == axes(A,1) && axes(B,1) == 1:1 || throw(DimensionMismatch("transpose"))
    ccopy!(B, A)
end

const transposebaselength=64
function transpose_f!(f, B::AbstractMatrix, A::AbstractMatrix)
    inds = axes(A)
    axes(B,1) == inds[2] && axes(B,2) == inds[1] || throw(DimensionMismatch(string(f)))

    m, n = length(inds[1]), length(inds[2])
    if m*n<=4*transposebaselength
        @inbounds begin
            for j = inds[2]
                for i = inds[1]
                    B[j,i] = f(A[i,j])
                end
            end
        end
    else
        transposeblock!(f,B,A,m,n,first(inds[1])-1,first(inds[2])-1)
    end
    return B
end
function transposeblock!(f, B::AbstractMatrix, A::AbstractMatrix, m::Int, n::Int, offseti::Int, offsetj::Int)
    if m*n<=transposebaselength
        @inbounds begin
            for j = offsetj .+ (1:n)
                for i = offseti .+ (1:m)
                    B[j,i] = f(A[i,j])
                end
            end
        end
    elseif m>n
        newm=m>>1
        transposeblock!(f,B,A,newm,n,offseti,offsetj)
        transposeblock!(f,B,A,m-newm,n,offseti+newm,offsetj)
    else
        newn=n>>1
        transposeblock!(f,B,A,m,newn,offseti,offsetj)
        transposeblock!(f,B,A,m,n-newn,offseti,offsetj+newn)
    end
    return B
end

function ccopy!(B, A)
    RB, RA = eachindex(B), eachindex(A)
    if RB == RA
        for i = RB
            B[i] = adjoint(A[i])
        end
    else
        for (i,j) = zip(RB, RA)
            B[i] = adjoint(A[j])
        end
    end
    return B
end

"""
    copy(A::Transpose)
    copy(A::Adjoint)

Eagerly evaluate the lazy matrix transpose/adjoint.
Note that the transposition is applied recursively to elements.

This operation is intended for linear algebra usage - for general data manipulation see
[`permutedims`](@ref Base.permutedims), which is non-recursive.

# Examples
```jldoctest
julia> A = [1 2im; -3im 4]
2×2 Matrix{Complex{Int64}}:
 1+0im  0+2im
 0-3im  4+0im

julia> T = transpose(A)
2×2 transpose(::Matrix{Complex{Int64}}) with eltype Complex{Int64}:
 1+0im  0-3im
 0+2im  4+0im

julia> copy(T)
2×2 Matrix{Complex{Int64}}:
 1+0im  0-3im
 0+2im  4+0im
```
"""
copy(::Union{Transpose,Adjoint})

Base.copy(A::TransposeAbsMat) = transpose!(similar(A.parent, reverse(axes(A.parent))), A.parent)
Base.copy(A::AdjointAbsMat) = adjoint!(similar(A.parent, reverse(axes(A.parent))), A.parent)

function copy_transpose!(B::AbstractVecOrMat, ir_dest::AbstractRange{Int}, jr_dest::AbstractRange{Int},
                         A::AbstractVecOrMat, ir_src::AbstractRange{Int}, jr_src::AbstractRange{Int})
    if length(ir_dest) != length(jr_src)
        throw(ArgumentError(LazyString("source and destination must have same size (got ",
                                   length(jr_src)," and ",length(ir_dest),")")))
    end
    if length(jr_dest) != length(ir_src)
        throw(ArgumentError(LazyString("source and destination must have same size (got ",
                                   length(ir_src)," and ",length(jr_dest),")")))
    end
    @boundscheck checkbounds(B, ir_dest, jr_dest)
    @boundscheck checkbounds(A, ir_src, jr_src)
    idest = first(ir_dest)
    for jsrc in jr_src
        jdest = first(jr_dest)
        for isrc in ir_src
            B[idest,jdest] = A[isrc,jsrc]
            jdest += step(jr_dest)
        end
        idest += step(ir_dest)
    end
    return B
end

function copy_similar(A::AdjointAbsMat, ::Type{T}) where {T}
    C = similar(A, T, size(A))
    adjoint!(C, parent(A))
end
function copy_similar(A::TransposeAbsMat, ::Type{T}) where {T}
    C = similar(A, T, size(A))
    transpose!(C, parent(A))
end
{   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LinearAlgebra/src/exceptions.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

export LAPACKException,
       SingularException,
       PosDefException,
       RankDeficientException,
       ZeroPivotException

struct LAPACKException <: Exception
    info::BlasInt
end

"""
    SingularException

Exception thrown when the input matrix has one or more zero-valued eigenvalues, and is not invertible.
A linear solve involving such a matrix cannot be computed.
The `info` field indicates the location of (one of) the singular value(s).
"""
struct SingularException <: Exception
    info::BlasInt
end

"""
    PosDefException

Exception thrown when the input matrix was not [positive definite](https://en.wikipedia.org/wiki/Definiteness_of_a_matrix).
Some linear algebra functions and factorizations are only applicable to positive definite matrices.
The `info` field indicates the location of (one of) the eigenvalue(s) which is (are) less than/equal to 0.
"""
struct PosDefException <: Exception
    info::BlasInt
end
function Base.showerror(io::IO, ex::PosDefException)
    print(io, "PosDefException: matrix is not ")
    if ex.info == -1
        print(io, "Hermitian")
    else
        print(io, "positive definite")
    end
    print(io, "; Cholesky factorization failed.")
end

struct RankDeficientException <: Exception
    info::BlasInt
end

"""
    ZeroPivotException <: Exception

Exception thrown when a matrix factorization/solve encounters a zero in a pivot (diagonal)
position and cannot proceed.  This may *not* mean that the matrix is singular:
it may be fruitful to switch to a different factorization such as pivoted LU
that can re-order variables to eliminate spurious zero pivots.
The `info` field indicates the location of (one of) the zero pivot(s).
"""
struct ZeroPivotException <: Exception
    info::BlasInt
end
function Base.showerror(io::IO, ex::ZeroPivotException)
    print(io, "ZeroPivotException: factorization encountered one or more zero pivots. Consider switching to a pivoted LU factorization.")
end
x   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LinearAlgebra/src/generic.jlJ�      # This file is a part of Julia. License is MIT: https://julialang.org/license

## linalg.jl: Some generic Linear Algebra definitions

# Elements of `out` may not be defined (e.g., for `BigFloat`). To make
# `mul!(out, A, B)` work for such cases, `out .*ₛ beta` short-circuits
# `out * beta`.  Using `broadcasted` to avoid the multiplication
# inside this function.
function *ₛ end
Broadcast.broadcasted(::typeof(*ₛ), out, beta) =
    iszero(beta::Number) ? false : broadcasted(*, out, beta)

"""
    MulAddMul(alpha, beta)

A callable for operating short-circuiting version of `x * alpha + y * beta`.

# Examples
```jldoctest
julia> using LinearAlgebra: MulAddMul

julia> _add = MulAddMul(1, 0);

julia> _add(123, nothing)
123

julia> MulAddMul(12, 34)(56, 78) == 56 * 12 + 78 * 34
true
```
"""
struct MulAddMul{ais1, bis0, TA, TB}
    alpha::TA
    beta::TB
end

@inline function MulAddMul(alpha::TA, beta::TB) where {TA,TB}
    if isone(alpha)
        if iszero(beta)
            return MulAddMul{true,true,TA,TB}(alpha, beta)
        else
            return MulAddMul{true,false,TA,TB}(alpha, beta)
        end
    else
        if iszero(beta)
            return MulAddMul{false,true,TA,TB}(alpha, beta)
        else
            return MulAddMul{false,false,TA,TB}(alpha, beta)
        end
    end
end

MulAddMul() = MulAddMul{true,true,Bool,Bool}(true, false)

@inline (::MulAddMul{true})(x) = x
@inline (p::MulAddMul{false})(x) = x * p.alpha
@inline (::MulAddMul{true, true})(x, _) = x
@inline (p::MulAddMul{false, true})(x, _) = x * p.alpha
@inline (p::MulAddMul{true, false})(x, y) = x + y * p.beta
@inline (p::MulAddMul{false, false})(x, y) = x * p.alpha + y * p.beta

"""
    _modify!(_add::MulAddMul, x, C, idx)

Short-circuiting version of `C[idx] = _add(x, C[idx])`.

Short-circuiting the indexing `C[idx]` is necessary for avoiding `UndefRefError`
when mutating an array of non-primitive numbers such as `BigFloat`.

# Examples
```jldoctest
julia> using LinearAlgebra: MulAddMul, _modify!

julia> _add = MulAddMul(1, 0);
       C = Vector{BigFloat}(undef, 1);

julia> _modify!(_add, 123, C, 1)

julia> C
1-element Vector{BigFloat}:
 123.0
```
"""
@inline @propagate_inbounds function _modify!(p::MulAddMul{ais1, bis0},
                                              x, C, idx′) where {ais1, bis0}
    # `idx′` may be an integer, a tuple of integer, or a `CartesianIndex`.
    #  Let `CartesianIndex` constructor normalize them so that it can be
    # used uniformly.  It also acts as a workaround for performance penalty
    # of splatting a number (#29114):
    idx = CartesianIndex(idx′)
    if bis0
        C[idx] = p(x)
    else
        C[idx] = p(x, C[idx])
    end
    return
end

@inline function _rmul_or_fill!(C::AbstractArray, beta::Number)
    if isempty(C)
        return C
    end
    if iszero(beta)
        fill!(C, zero(eltype(C)))
    else
        rmul!(C, beta)
    end
    return C
end


function generic_mul!(C::AbstractArray, X::AbstractArray, s::Number, _add::MulAddMul)
    if length(C) != length(X)
        throw(DimensionMismatch("first array has length $(length(C)) which does not match the length of the second, $(length(X))."))
    end
    for (IC, IX) in zip(eachindex(C), eachindex(X))
        @inbounds _modify!(_add, X[IX] * s, C, IC)
    end
    C
end

function generic_mul!(C::AbstractArray, s::Number, X::AbstractArray, _add::MulAddMul)
    if length(C) != length(X)
        throw(DimensionMismatch("first array has length $(length(C)) which does not
match the length of the second, $(length(X))."))
    end
    for (IC, IX) in zip(eachindex(C), eachindex(X))
        @inbounds _modify!(_add, s * X[IX], C, IC)
    end
    C
end

@inline function mul!(C::AbstractArray, s::Number, X::AbstractArray, alpha::Number, beta::Number)
    if axes(C) == axes(X)
        C .= (s .* X) .*ₛ alpha .+ C .*ₛ beta
    else
        generic_mul!(C, s, X, MulAddMul(alpha, beta))
    end
    return C
end
@inline function mul!(C::AbstractArray, X::AbstractArray, s::Number, alpha::Number, beta::Number)
    if axes(C) == axes(X)
        C .= (X .* s) .*ₛ alpha .+ C .*ₛ beta
    else
        generic_mul!(C, X, s, MulAddMul(alpha, beta))
    end
    return C
end

# For better performance when input and output are the same array
# See https://github.com/JuliaLang/julia/issues/8415#issuecomment-56608729
"""
    rmul!(A::AbstractArray, b::Number)

Scale an array `A` by a scalar `b` overwriting `A` in-place.  Use
[`lmul!`](@ref) to multiply scalar from left.  The scaling operation
respects the semantics of the multiplication [`*`](@ref) between an
element of `A` and `b`.  In particular, this also applies to
multiplication involving non-finite numbers such as `NaN` and `±Inf`.

!!! compat "Julia 1.1"
    Prior to Julia 1.1, `NaN` and `±Inf` entries in `A` were treated
    inconsistently.

# Examples
```jldoctest
julia> A = [1 2; 3 4]
2×2 Matrix{Int64}:
 1  2
 3  4

julia> rmul!(A, 2)
2×2 Matrix{Int64}:
 2  4
 6  8

julia> rmul!([NaN], 0.0)
1-element Vector{Float64}:
 NaN
```
"""
function rmul!(X::AbstractArray, s::Number)
    @simd for I in eachindex(X)
        @inbounds X[I] *= s
    end
    X
end


"""
    lmul!(a::Number, B::AbstractArray)

Scale an array `B` by a scalar `a` overwriting `B` in-place.  Use
[`rmul!`](@ref) to multiply scalar from right.  The scaling operation
respects the semantics of the multiplication [`*`](@ref) between `a`
and an element of `B`.  In particular, this also applies to
multiplication involving non-finite numbers such as `NaN` and `±Inf`.

!!! compat "Julia 1.1"
    Prior to Julia 1.1, `NaN` and `±Inf` entries in `B` were treated
    inconsistently.

# Examples
```jldoctest
julia> B = [1 2; 3 4]
2×2 Matrix{Int64}:
 1  2
 3  4

julia> lmul!(2, B)
2×2 Matrix{Int64}:
 2  4
 6  8

julia> lmul!(0.0, [Inf])
1-element Vector{Float64}:
 NaN
```
"""
function lmul!(s::Number, X::AbstractArray)
    @simd for I in eachindex(X)
        @inbounds X[I] = s*X[I]
    end
    X
end

"""
    rdiv!(A::AbstractArray, b::Number)

Divide each entry in an array `A` by a scalar `b` overwriting `A`
in-place.  Use [`ldiv!`](@ref) to divide scalar from left.

# Examples
```jldoctest
julia> A = [1.0 2.0; 3.0 4.0]
2×2 Matrix{Float64}:
 1.0  2.0
 3.0  4.0

julia> rdiv!(A, 2.0)
2×2 Matrix{Float64}:
 0.5  1.0
 1.5  2.0
```
"""
function rdiv!(X::AbstractArray, s::Number)
    @simd for I in eachindex(X)
        @inbounds X[I] /= s
    end
    X
end

"""
    ldiv!(a::Number, B::AbstractArray)

Divide each entry in an array `B` by a scalar `a` overwriting `B`
in-place.  Use [`rdiv!`](@ref) to divide scalar from right.

# Examples
```jldoctest
julia> B = [1.0 2.0; 3.0 4.0]
2×2 Matrix{Float64}:
 1.0  2.0
 3.0  4.0

julia> ldiv!(2.0, B)
2×2 Matrix{Float64}:
 0.5  1.0
 1.5  2.0
```
"""
function ldiv!(s::Number, X::AbstractArray)
    @simd for I in eachindex(X)
        @inbounds X[I] = s\X[I]
    end
    X
end
ldiv!(Y::AbstractArray, s::Number, X::AbstractArray) = Y .= s .\ X

# Generic fallback. This assumes that B and Y have the same sizes.
ldiv!(Y::AbstractArray, A::AbstractMatrix, B::AbstractArray) = ldiv!(A, copyto!(Y, B))


"""
    cross(x, y)
    ×(x,y)

Compute the cross product of two 3-vectors.

# Examples
```jldoctest
julia> a = [0;1;0]
3-element Vector{Int64}:
 0
 1
 0

julia> b = [0;0;1]
3-element Vector{Int64}:
 0
 0
 1

julia> cross(a,b)
3-element Vector{Int64}:
 1
 0
 0
```
"""
function cross(a::AbstractVector, b::AbstractVector)
    if !(length(a) == length(b) == 3)
        throw(DimensionMismatch("cross product is only defined for vectors of length 3"))
    end
    a1, a2, a3 = a
    b1, b2, b3 = b
    [a2*b3-a3*b2, a3*b1-a1*b3, a1*b2-a2*b1]
end

"""
    triu(M)

Upper triangle of a matrix.

# Examples
```jldoctest
julia> a = fill(1.0, (4,4))
4×4 Matrix{Float64}:
 1.0  1.0  1.0  1.0
 1.0  1.0  1.0  1.0
 1.0  1.0  1.0  1.0
 1.0  1.0  1.0  1.0

julia> triu(a)
4×4 Matrix{Float64}:
 1.0  1.0  1.0  1.0
 0.0  1.0  1.0  1.0
 0.0  0.0  1.0  1.0
 0.0  0.0  0.0  1.0
```
"""
triu(M::AbstractMatrix) = triu!(copy(M))

"""
    tril(M)

Lower triangle of a matrix.

# Examples
```jldoctest
julia> a = fill(1.0, (4,4))
4×4 Matrix{Float64}:
 1.0  1.0  1.0  1.0
 1.0  1.0  1.0  1.0
 1.0  1.0  1.0  1.0
 1.0  1.0  1.0  1.0

julia> tril(a)
4×4 Matrix{Float64}:
 1.0  0.0  0.0  0.0
 1.0  1.0  0.0  0.0
 1.0  1.0  1.0  0.0
 1.0  1.0  1.0  1.0
```
"""
tril(M::AbstractMatrix) = tril!(copy(M))

"""
    triu(M, k::Integer)

Return the upper triangle of `M` starting from the `k`th superdiagonal.

# Examples
```jldoctest
julia> a = fill(1.0, (4,4))
4×4 Matrix{Float64}:
 1.0  1.0  1.0  1.0
 1.0  1.0  1.0  1.0
 1.0  1.0  1.0  1.0
 1.0  1.0  1.0  1.0

julia> triu(a,3)
4×4 Matrix{Float64}:
 0.0  0.0  0.0  1.0
 0.0  0.0  0.0  0.0
 0.0  0.0  0.0  0.0
 0.0  0.0  0.0  0.0

julia> triu(a,-3)
4×4 Matrix{Float64}:
 1.0  1.0  1.0  1.0
 1.0  1.0  1.0  1.0
 1.0  1.0  1.0  1.0
 1.0  1.0  1.0  1.0
```
"""
triu(M::AbstractMatrix,k::Integer) = triu!(copy(M),k)

"""
    tril(M, k::Integer)

Return the lower triangle of `M` starting from the `k`th superdiagonal.

# Examples
```jldoctest
julia> a = fill(1.0, (4,4))
4×4 Matrix{Float64}:
 1.0  1.0  1.0  1.0
 1.0  1.0  1.0  1.0
 1.0  1.0  1.0  1.0
 1.0  1.0  1.0  1.0

julia> tril(a,3)
4×4 Matrix{Float64}:
 1.0  1.0  1.0  1.0
 1.0  1.0  1.0  1.0
 1.0  1.0  1.0  1.0
 1.0  1.0  1.0  1.0

julia> tril(a,-3)
4×4 Matrix{Float64}:
 0.0  0.0  0.0  0.0
 0.0  0.0  0.0  0.0
 0.0  0.0  0.0  0.0
 1.0  0.0  0.0  0.0
```
"""
tril(M::AbstractMatrix,k::Integer) = tril!(copy(M),k)

"""
    triu!(M)

Upper triangle of a matrix, overwriting `M` in the process.
See also [`triu`](@ref).
"""
triu!(M::AbstractMatrix) = triu!(M,0)

"""
    tril!(M)

Lower triangle of a matrix, overwriting `M` in the process.
See also [`tril`](@ref).
"""
tril!(M::AbstractMatrix) = tril!(M,0)

diag(A::AbstractVector) = throw(ArgumentError("use diagm instead of diag to construct a diagonal matrix"))

###########################################################################################
# Dot products and norms

# special cases of norm; note that they don't need to handle isempty(x)
generic_normMinusInf(x) = float(mapreduce(norm, min, x))

generic_normInf(x) = float(mapreduce(norm, max, x))

generic_norm1(x) = mapreduce(float ∘ norm, +, x)

# faster computation of norm(x)^2, avoiding overflow for integers
norm_sqr(x) = norm(x)^2
norm_sqr(x::Number) = abs2(x)
norm_sqr(x::Union{T,Complex{T},Rational{T}}) where {T<:Integer} = abs2(float(x))

function generic_norm2(x)
    maxabs = normInf(x)
    (ismissing(maxabs) || iszero(maxabs) || isinf(maxabs)) && return maxabs
    (v, s) = iterate(x)::Tuple
    T = typeof(maxabs)
    if isfinite(length(x)*maxabs*maxabs) && !iszero(maxabs*maxabs) # Scaling not necessary
        sum::promote_type(Float64, T) = norm_sqr(v)
        while true
            y = iterate(x, s)
            y === nothing && break
            (v, s) = y
            sum += norm_sqr(v)
        end
        ismissing(sum) && return missing
        return convert(T, sqrt(sum))
    else
        sum = abs2(norm(v)/maxabs)
        while true
            y = iterate(x, s)
            y === nothing && break
            (v, s) = y
            sum += (norm(v)/maxabs)^2
        end
        ismissing(sum) && return missing
        return convert(T, maxabs*sqrt(sum))
    end
end

# Compute L_p norm ‖x‖ₚ = sum(abs(x).^p)^(1/p)
# (Not technically a "norm" for p < 1.)
function generic_normp(x, p)
    (v, s) = iterate(x)::Tuple
    if p > 1 || p < -1 # might need to rescale to avoid overflow
        maxabs = p > 1 ? normInf(x) : normMinusInf(x)
        (ismissing(maxabs) || iszero(maxabs) || isinf(maxabs)) && return maxabs
        T = typeof(maxabs)
    else
        T = typeof(float(norm(v)))
    end
    spp::promote_type(Float64, T) = p
    if -1 <= p <= 1 || (isfinite(length(x)*maxabs^spp) && !iszero(maxabs^spp)) # scaling not necessary
        sum::promote_type(Float64, T) = norm(v)^spp
        while true
            y = iterate(x, s)
            y === nothing && break
            (v, s) = y
            ismissing(v) && return missing
            sum += norm(v)^spp
        end
        return convert(T, sum^inv(spp))
    else # rescaling
        sum = (norm(v)/maxabs)^spp
        ismissing(sum) && return missing
        while true
            y = iterate(x, s)
            y === nothing && break
            (v, s) = y
            ismissing(v) && return missing
            sum += (norm(v)/maxabs)^spp
        end
        return convert(T, maxabs*sum^inv(spp))
    end
end

normMinusInf(x) = generic_normMinusInf(x)
normInf(x) = generic_normInf(x)
norm1(x) = generic_norm1(x)
norm2(x) = generic_norm2(x)
normp(x, p) = generic_normp(x, p)


"""
    norm(A, p::Real=2)

For any iterable container `A` (including arrays of any dimension) of numbers (or any
element type for which `norm` is defined), compute the `p`-norm (defaulting to `p=2`) as if
`A` were a vector of the corresponding length.

The `p`-norm is defined as
```math
\\|A\\|_p = \\left( \\sum_{i=1}^n | a_i | ^p \\right)^{1/p}
```
with ``a_i`` the entries of ``A``, ``| a_i |`` the [`norm`](@ref) of ``a_i``, and
``n`` the length of ``A``. Since the `p`-norm is computed using the [`norm`](@ref)s
of the entries of `A`, the `p`-norm of a vector of vectors is not compatible with
the interpretation of it as a block vector in general if `p != 2`.

`p` can assume any numeric value (even though not all values produce a
mathematically valid vector norm). In particular, `norm(A, Inf)` returns the largest value
in `abs.(A)`, whereas `norm(A, -Inf)` returns the smallest. If `A` is a matrix and `p=2`,
then this is equivalent to the Frobenius norm.

The second argument `p` is not necessarily a part of the interface for `norm`, i.e. a custom
type may only implement `norm(A)` without second argument.

Use [`opnorm`](@ref) to compute the operator norm of a matrix.

# Examples
```jldoctest
julia> v = [3, -2, 6]
3-element Vector{Int64}:
  3
 -2
  6

julia> norm(v)
7.0

julia> norm(v, 1)
11.0

julia> norm(v, Inf)
6.0

julia> norm([1 2 3; 4 5 6; 7 8 9])
16.881943016134134

julia> norm([1 2 3 4 5 6 7 8 9])
16.881943016134134

julia> norm(1:9)
16.881943016134134

julia> norm(hcat(v,v), 1) == norm(vcat(v,v), 1) != norm([v,v], 1)
true

julia> norm(hcat(v,v), 2) == norm(vcat(v,v), 2) == norm([v,v], 2)
true

julia> norm(hcat(v,v), Inf) == norm(vcat(v,v), Inf) != norm([v,v], Inf)
true
```
"""
function norm(itr, p::Real=2)
    isempty(itr) && return float(norm(zero(eltype(itr))))
    if p == 2
        return norm2(itr)
    elseif p == 1
        return norm1(itr)
    elseif p == Inf
        return normInf(itr)
    elseif p == 0
        return typeof(float(norm(first(itr))))(count(!iszero, itr))
    elseif p == -Inf
        return normMinusInf(itr)
    else
        normp(itr, p)
    end
end

"""
    norm(x::Number, p::Real=2)

For numbers, return ``\\left( |x|^p \\right)^{1/p}``.

# Examples
```jldoctest
julia> norm(2, 1)
2.0

julia> norm(-2, 1)
2.0

julia> norm(2, 2)
2.0

julia> norm(-2, 2)
2.0

julia> norm(2, Inf)
2.0

julia> norm(-2, Inf)
2.0
```
"""
@inline function norm(x::Number, p::Real=2)
    afx = abs(float(x))
    if p == 0
        if iszero(x)
            return zero(afx)
        elseif !isnan(x)
            return oneunit(afx)
        else
            return afx
        end
    else
        return afx
    end
end
norm(::Missing, p::Real=2) = missing

# special cases of opnorm
function opnorm1(A::AbstractMatrix{T}) where T
    require_one_based_indexing(A)
    m, n = size(A)
    Tnorm = typeof(float(real(zero(T))))
    Tsum = promote_type(Float64, Tnorm)
    nrm::Tsum = 0
    @inbounds begin
        for j = 1:n
            nrmj::Tsum = 0
            for i = 1:m
                nrmj += norm(A[i,j])
            end
            nrm = max(nrm,nrmj)
        end
    end
    return convert(Tnorm, nrm)
end

function opnorm2(A::AbstractMatrix{T}) where T
    require_one_based_indexing(A)
    m,n = size(A)
    Tnorm = typeof(float(real(zero(T))))
    if m == 0 || n == 0 return zero(Tnorm) end
    if m == 1 || n == 1 return norm2(A) end
    return svdvals(A)[1]
end

function opnormInf(A::AbstractMatrix{T}) where T
    require_one_based_indexing(A)
    m,n = size(A)
    Tnorm = typeof(float(real(zero(T))))
    Tsum = promote_type(Float64, Tnorm)
    nrm::Tsum = 0
    @inbounds begin
        for i = 1:m
            nrmi::Tsum = 0
            for j = 1:n
                nrmi += norm(A[i,j])
            end
            nrm = max(nrm,nrmi)
        end
    end
    return convert(Tnorm, nrm)
end


"""
    opnorm(A::AbstractMatrix, p::Real=2)

Compute the operator norm (or matrix norm) induced by the vector `p`-norm,
where valid values of `p` are `1`, `2`, or `Inf`. (Note that for sparse matrices,
`p=2` is currently not implemented.) Use [`norm`](@ref) to compute the Frobenius
norm.

When `p=1`, the operator norm is the maximum absolute column sum of `A`:
```math
\\|A\\|_1 = \\max_{1 ≤ j ≤ n} \\sum_{i=1}^m | a_{ij} |
```
with ``a_{ij}`` the entries of ``A``, and ``m`` and ``n`` its dimensions.

When `p=2`, the operator norm is the spectral norm, equal to the largest
singular value of `A`.

When `p=Inf`, the operator norm is the maximum absolute row sum of `A`:
```math
\\|A\\|_\\infty = \\max_{1 ≤ i ≤ m} \\sum _{j=1}^n | a_{ij} |
```

# Examples
```jldoctest
julia> A = [1 -2 -3; 2 3 -1]
2×3 Matrix{Int64}:
 1  -2  -3
 2   3  -1

julia> opnorm(A, Inf)
6.0

julia> opnorm(A, 1)
5.0
```
"""
function opnorm(A::AbstractMatrix, p::Real=2)
    if p == 2
        return opnorm2(A)
    elseif p == 1
        return opnorm1(A)
    elseif p == Inf
        return opnormInf(A)
    else
        throw(ArgumentError("invalid p-norm p=$p. Valid: 1, 2, Inf"))
    end
end

"""
    opnorm(x::Number, p::Real=2)

For numbers, return ``\\left( |x|^p \\right)^{1/p}``.
This is equivalent to [`norm`](@ref).
"""
@inline opnorm(x::Number, p::Real=2) = norm(x, p)

"""
    opnorm(A::Adjoint{<:Any,<:AbstracVector}, q::Real=2)
    opnorm(A::Transpose{<:Any,<:AbstracVector}, q::Real=2)

For Adjoint/Transpose-wrapped vectors, return the operator ``q``-norm of `A`, which is
equivalent to the `p`-norm with value `p = q/(q-1)`. They coincide at `p = q = 2`.
Use [`norm`](@ref) to compute the `p` norm of `A` as a vector.

The difference in norm between a vector space and its dual arises to preserve
the relationship between duality and the dot product, and the result is
consistent with the operator `p`-norm of a `1 × n` matrix.

# Examples
```jldoctest
julia> v = [1; im];

julia> vc = v';

julia> opnorm(vc, 1)
1.0

julia> norm(vc, 1)
2.0

julia> norm(v, 1)
2.0

julia> opnorm(vc, 2)
1.4142135623730951

julia> norm(vc, 2)
1.4142135623730951

julia> norm(v, 2)
1.4142135623730951

julia> opnorm(vc, Inf)
2.0

julia> norm(vc, Inf)
1.0

julia> norm(v, Inf)
1.0
```
"""
opnorm(v::TransposeAbsVec, q::Real) = q == Inf ? norm(v.parent, 1) : norm(v.parent, q/(q-1))
opnorm(v::AdjointAbsVec, q::Real) = q == Inf ? norm(conj(v.parent), 1) : norm(conj(v.parent), q/(q-1))
opnorm(v::AdjointAbsVec) = norm(conj(v.parent))
opnorm(v::TransposeAbsVec) = norm(v.parent)

norm(v::AdjOrTrans, p::Real) = norm(v.parent, p)

"""
    dot(x, y)
    x ⋅ y

Compute the dot product between two vectors. For complex vectors, the first
vector is conjugated.

`dot` also works on arbitrary iterable objects, including arrays of any dimension,
as long as `dot` is defined on the elements.

`dot` is semantically equivalent to `sum(dot(vx,vy) for (vx,vy) in zip(x, y))`,
with the added restriction that the arguments must have equal lengths.

`x ⋅ y` (where `⋅` can be typed by tab-completing `\\cdot` in the REPL) is a synonym for
`dot(x, y)`.

# Examples
```jldoctest
julia> dot([1; 1], [2; 3])
5

julia> dot([im; im], [1; 1])
0 - 2im

julia> dot(1:5, 2:6)
70

julia> x = fill(2., (5,5));

julia> y = fill(3., (5,5));

julia> dot(x, y)
150.0
```
"""
function dot end

function dot(x, y) # arbitrary iterables
    ix = iterate(x)
    iy = iterate(y)
    if ix === nothing
        if iy !== nothing
            throw(DimensionMismatch("x and y are of different lengths!"))
        end
        return dot(zero(eltype(x)), zero(eltype(y)))
    end
    if iy === nothing
        throw(DimensionMismatch("x and y are of different lengths!"))
    end
    (vx, xs) = ix
    (vy, ys) = iy
    s = dot(vx, vy)
    while true
        ix = iterate(x, xs)
        iy = iterate(y, ys)
        ix === nothing && break
        iy === nothing && break
        (vx, xs), (vy, ys) = ix, iy
        s += dot(vx, vy)
    end
    if !(iy === nothing && ix === nothing)
        throw(DimensionMismatch("x and y are of different lengths!"))
    end
    return s
end

dot(x::Number, y::Number) = conj(x) * y

function dot(x::AbstractArray, y::AbstractArray)
    lx = length(x)
    if lx != length(y)
        throw(DimensionMismatch("first array has length $(lx) which does not match the length of the second, $(length(y))."))
    end
    if lx == 0
        return dot(zero(eltype(x)), zero(eltype(y)))
    end
    s = zero(dot(first(x), first(y)))
    for (Ix, Iy) in zip(eachindex(x), eachindex(y))
        @inbounds s += dot(x[Ix], y[Iy])
    end
    s
end

function dot(x::Adjoint{<:Union{Real,Complex}}, y::Adjoint{<:Union{Real,Complex}})
    return conj(dot(parent(x), parent(y)))
end
dot(x::Transpose, y::Transpose) = dot(parent(x), parent(y))

"""
    dot(x, A, y)

Compute the generalized dot product `dot(x, A*y)` between two vectors `x` and `y`,
without storing the intermediate result of `A*y`. As for the two-argument
[`dot(_,_)`](@ref), this acts recursively. Moreover, for complex vectors, the
first vector is conjugated.

!!! compat "Julia 1.4"
    Three-argument `dot` requires at least Julia 1.4.

# Examples
```jldoctest
julia> dot([1; 1], [1 2; 3 4], [2; 3])
26

julia> dot(1:5, reshape(1:25, 5, 5), 2:6)
4850

julia> ⋅(1:5, reshape(1:25, 5, 5), 2:6) == dot(1:5, reshape(1:25, 5, 5), 2:6)
true
```
"""
dot(x, A, y) = dot(x, A*y) # generic fallback for cases that are not covered by specialized methods

function dot(x::AbstractVector, A::AbstractMatrix, y::AbstractVector)
    (axes(x)..., axes(y)...) == axes(A) || throw(DimensionMismatch())
    T = typeof(dot(first(x), first(A), first(y)))
    s = zero(T)
    i₁ = first(eachindex(x))
    x₁ = first(x)
    @inbounds for j in eachindex(y)
        yj = y[j]
        if !iszero(yj)
            temp = zero(adjoint(A[i₁,j]) * x₁)
            @simd for i in eachindex(x)
                temp += adjoint(A[i,j]) * x[i]
            end
            s += dot(temp, yj)
        end
    end
    return s
end
dot(x::AbstractVector, adjA::Adjoint, y::AbstractVector) = adjoint(dot(y, adjA.parent, x))
dot(x::AbstractVector, transA::Transpose{<:Real}, y::AbstractVector) = adjoint(dot(y, transA.parent, x))

###########################################################################################

"""
    rank(A::AbstractMatrix; atol::Real=0, rtol::Real=atol>0 ? 0 : n*ϵ)
    rank(A::AbstractMatrix, rtol::Real)

Compute the numerical rank of a matrix by counting how many outputs of
`svdvals(A)` are greater than `max(atol, rtol*σ₁)` where `σ₁` is `A`'s largest
calculated singular value. `atol` and `rtol` are the absolute and relative
tolerances, respectively. The default relative tolerance is `n*ϵ`, where `n`
is the size of the smallest dimension of `A`, and `ϵ` is the [`eps`](@ref) of
the element type of `A`.

!!! note
    Numerical rank can be a sensitive and imprecise characterization of
    ill-conditioned matrices with singular values that are close to the threshold
    tolerance `max(atol, rtol*σ₁)`. In such cases, slight perturbations to the
    singular-value computation or to the matrix can change the result of `rank`
    by pushing one or more singular values across the threshold. These variations
    can even occur due to changes in floating-point errors between different Julia
    versions, architectures, compilers, or operating systems.

!!! compat "Julia 1.1"
    The `atol` and `rtol` keyword arguments requires at least Julia 1.1.
    In Julia 1.0 `rtol` is available as a positional argument, but this
    will be deprecated in Julia 2.0.

# Examples
```jldoctest
julia> rank(Matrix(I, 3, 3))
3

julia> rank(diagm(0 => [1, 0, 2]))
2

julia> rank(diagm(0 => [1, 0.001, 2]), rtol=0.1)
2

julia> rank(diagm(0 => [1, 0.001, 2]), rtol=0.00001)
3

julia> rank(diagm(0 => [1, 0.001, 2]), atol=1.5)
1
```
"""
function rank(A::AbstractMatrix; atol::Real = 0.0, rtol::Real = (min(size(A)...)*eps(real(float(one(eltype(A))))))*iszero(atol))
    isempty(A) && return 0 # 0-dimensional case
    s = svdvals(A)
    tol = max(atol, rtol*s[1])
    count(>(tol), s)
end
rank(x::Union{Number,AbstractVector}) = iszero(x) ? 0 : 1

"""
    tr(M)

Matrix trace. Sums the diagonal elements of `M`.

# Examples
```jldoctest
julia> A = [1 2; 3 4]
2×2 Matrix{Int64}:
 1  2
 3  4

julia> tr(A)
5
```
"""
function tr(A::AbstractMatrix)
    checksquare(A)
    sum(diag(A))
end
tr(x::Number) = x

#kron(a::AbstractVector, b::AbstractVector)
#kron(a::AbstractMatrix{T}, b::AbstractMatrix{S}) where {T,S}

#det(a::AbstractMatrix)

"""
    inv(M)

Matrix inverse. Computes matrix `N` such that
`M * N = I`, where `I` is the identity matrix.
Computed by solving the left-division
`N = M \\ I`.

# Examples
```jldoctest
julia> M = [2 5; 1 3]
2×2 Matrix{Int64}:
 2  5
 1  3

julia> N = inv(M)
2×2 Matrix{Float64}:
  3.0  -5.0
 -1.0   2.0

julia> M*N == N*M == Matrix(I, 2, 2)
true
```
"""
function inv(A::AbstractMatrix{T}) where T
    n = checksquare(A)
    S = typeof(zero(T)/one(T))      # dimensionful
    S0 = typeof(zero(T)/oneunit(T)) # dimensionless
    dest = Matrix{S0}(I, n, n)
    ldiv!(factorize(convert(AbstractMatrix{S}, A)), dest)
end
inv(A::Adjoint) = adjoint(inv(parent(A)))
inv(A::Transpose) = transpose(inv(parent(A)))

pinv(v::AbstractVector{T}, tol::Real = real(zero(T))) where {T<:Real} = _vectorpinv(transpose, v, tol)
pinv(v::AbstractVector{T}, tol::Real = real(zero(T))) where {T<:Complex} = _vectorpinv(adjoint, v, tol)
pinv(v::AbstractVector{T}, tol::Real = real(zero(T))) where {T} = _vectorpinv(adjoint, v, tol)
function _vectorpinv(dualfn::Tf, v::AbstractVector{Tv}, tol) where {Tv,Tf}
    res = dualfn(similar(v, typeof(zero(Tv) / (abs2(one(Tv)) + abs2(one(Tv))))))
    den = sum(abs2, v)
    # as tol is the threshold relative to the maximum singular value, for a vector with
    # single singular value σ=√den, σ ≦ tol*σ is equivalent to den=0 ∨ tol≥1
    if iszero(den) || tol >= one(tol)
        fill!(res, zero(eltype(res)))
    else
        res .= dualfn(v) ./ den
    end
    return res
end

# this method is just an optimization: literal negative powers of A are
# already turned by literal_pow into powers of inv(A), but for A^-1 this
# would turn into inv(A)^1 = copy(inv(A)), which makes an extra copy.
@inline Base.literal_pow(::typeof(^), A::AbstractMatrix, ::Val{-1}) = inv(A)

"""
    \\(A, B)

Matrix division using a polyalgorithm. For input matrices `A` and `B`, the result `X` is
such that `A*X == B` when `A` is square. The solver that is used depends upon the structure
of `A`.  If `A` is upper or lower triangular (or diagonal), no factorization of `A` is
required and the system is solved with either forward or backward substitution.
For non-triangular square matrices, an LU factorization is used.

For rectangular `A` the result is the minimum-norm least squares solution computed by a
pivoted QR factorization of `A` and a rank estimate of `A` based on the R factor.

When `A` is sparse, a similar polyalgorithm is used. For indefinite matrices, the `LDLt`
factorization does not use pivoting during the numerical factorization and therefore the
procedure can fail even for invertible matrices.

See also: [`factorize`](@ref), [`pinv`](@ref).

# Examples
```jldoctest
julia> A = [1 0; 1 -2]; B = [32; -4];

julia> X = A \\ B
2-element Vector{Float64}:
 32.0
 18.0

julia> A * X == B
true
```
"""
function (\)(A::AbstractMatrix, B::AbstractVecOrMat)
    require_one_based_indexing(A, B)
    m, n = size(A)
    if m == n
        if istril(A)
            if istriu(A)
                return Diagonal(A) \ B
            else
                return LowerTriangular(A) \ B
            end
        end
        if istriu(A)
            return UpperTriangular(A) \ B
        end
        return lu(A) \ B
    end
    return qr(A, ColumnNorm()) \ B
end

(\)(a::AbstractVector, b::AbstractArray) = pinv(a) * b
"""
    A / B

Matrix right-division: `A / B` is equivalent to `(B' \\ A')'` where [`\\`](@ref) is the left-division operator.
For square matrices, the result `X` is such that `A == X*B`.

See also: [`rdiv!`](@ref).

# Examples
```jldoctest
julia> A = Float64[1 4 5; 3 9 2]; B = Float64[1 4 2; 3 4 2; 8 7 1];

julia> X = A / B
2×3 Matrix{Float64}:
 -0.65   3.75  -1.2
  3.25  -2.75   1.0

julia> isapprox(A, X*B)
true

julia> isapprox(X, A*pinv(B))
true
```
"""
function (/)(A::AbstractVecOrMat, B::AbstractVecOrMat)
    size(A,2) != size(B,2) && throw(DimensionMismatch("Both inputs should have the same number of columns"))
    return copy(adjoint(adjoint(B) \ adjoint(A)))
end

cond(x::Number) = iszero(x) ? Inf : 1.0
cond(x::Number, p) = cond(x)

#Skeel condition numbers
condskeel(A::AbstractMatrix, p::Real=Inf) = opnorm(abs.(inv(A))*abs.(A), p)

"""
    condskeel(M, [x, p::Real=Inf])

```math
\\kappa_S(M, p) = \\left\\Vert \\left\\vert M \\right\\vert \\left\\vert M^{-1} \\right\\vert \\right\\Vert_p \\\\
\\kappa_S(M, x, p) = \\frac{\\left\\Vert \\left\\vert M \\right\\vert \\left\\vert M^{-1} \\right\\vert \\left\\vert x \\right\\vert \\right\\Vert_p}{\\left \\Vert x \\right \\Vert_p}
```

Skeel condition number ``\\kappa_S`` of the matrix `M`, optionally with respect to the
vector `x`, as computed using the operator `p`-norm. ``\\left\\vert M \\right\\vert``
denotes the matrix of (entry wise) absolute values of ``M``;
``\\left\\vert M \\right\\vert_{ij} = \\left\\vert M_{ij} \\right\\vert``.
Valid values for `p` are `1`, `2` and `Inf` (default).

This quantity is also known in the literature as the Bauer condition number, relative
condition number, or componentwise relative condition number.
"""
function condskeel(A::AbstractMatrix, x::AbstractVector, p::Real=Inf)
    norm(abs.(inv(A))*(abs.(A)*abs.(x)), p) / norm(x, p)
end

issymmetric(A::AbstractMatrix{<:Real}) = ishermitian(A)

"""
    issymmetric(A) -> Bool

Test whether a matrix is symmetric.

# Examples
```jldoctest
julia> a = [1 2; 2 -1]
2×2 Matrix{Int64}:
 1   2
 2  -1

julia> issymmetric(a)
true

julia> b = [1 im; -im 1]
2×2 Matrix{Complex{Int64}}:
 1+0im  0+1im
 0-1im  1+0im

julia> issymmetric(b)
false
```
"""
function issymmetric(A::AbstractMatrix)
    indsm, indsn = axes(A)
    if indsm != indsn
        return false
    end
    for i = first(indsn):last(indsn), j = (i):last(indsn)
        if A[i,j] != transpose(A[j,i])
            return false
        end
    end
    return true
end

issymmetric(x::Number) = x == x

"""
    ishermitian(A) -> Bool

Test whether a matrix is Hermitian.

# Examples
```jldoctest
julia> a = [1 2; 2 -1]
2×2 Matrix{Int64}:
 1   2
 2  -1

julia> ishermitian(a)
true

julia> b = [1 im; -im 1]
2×2 Matrix{Complex{Int64}}:
 1+0im  0+1im
 0-1im  1+0im

julia> ishermitian(b)
true
```
"""
function ishermitian(A::AbstractMatrix)
    indsm, indsn = axes(A)
    if indsm != indsn
        return false
    end
    for i = indsn, j = i:last(indsn)
        if A[i,j] != adjoint(A[j,i])
            return false
        end
    end
    return true
end

ishermitian(x::Number) = (x == conj(x))

"""
    istriu(A::AbstractMatrix, k::Integer = 0) -> Bool

Test whether `A` is upper triangular starting from the `k`th superdiagonal.

# Examples
```jldoctest
julia> a = [1 2; 2 -1]
2×2 Matrix{Int64}:
 1   2
 2  -1

julia> istriu(a)
false

julia> istriu(a, -1)
true

julia> b = [1 im; 0 -1]
2×2 Matrix{Complex{Int64}}:
 1+0im   0+1im
 0+0im  -1+0im

julia> istriu(b)
true

julia> istriu(b, 1)
false
```
"""
function istriu(A::AbstractMatrix, k::Integer = 0)
    require_one_based_indexing(A)
    return _istriu(A, k)
end
istriu(x::Number) = true

@inline function _istriu(A::AbstractMatrix, k)
    m, n = size(A)
    for j in 1:min(n, m + k - 1)
        all(iszero, view(A, max(1, j - k + 1):m, j)) || return false
    end
    return true
end

"""
    istril(A::AbstractMatrix, k::Integer = 0) -> Bool

Test whether `A` is lower triangular starting from the `k`th superdiagonal.

# Examples
```jldoctest
julia> a = [1 2; 2 -1]
2×2 Matrix{Int64}:
 1   2
 2  -1

julia> istril(a)
false

julia> istril(a, 1)
true

julia> b = [1 0; -im -1]
2×2 Matrix{Complex{Int64}}:
 1+0im   0+0im
 0-1im  -1+0im

julia> istril(b)
true

julia> istril(b, -1)
false
```
"""
function istril(A::AbstractMatrix, k::Integer = 0)
    require_one_based_indexing(A)
    return _istril(A, k)
end
istril(x::Number) = true

@inline function _istril(A::AbstractMatrix, k)
    m, n = size(A)
    for j in max(1, k + 2):n
        all(iszero, view(A, 1:min(j - k - 1, m), j)) || return false
    end
    return true
end

"""
    isbanded(A::AbstractMatrix, kl::Integer, ku::Integer) -> Bool

Test whether `A` is banded with lower bandwidth starting from the `kl`th superdiagonal
and upper bandwidth extending through the `ku`th superdiagonal.

# Examples
```jldoctest
julia> a = [1 2; 2 -1]
2×2 Matrix{Int64}:
 1   2
 2  -1

julia> LinearAlgebra.isbanded(a, 0, 0)
false

julia> LinearAlgebra.isbanded(a, -1, 1)
true

julia> b = [1 0; -im -1] # lower bidiagonal
2×2 Matrix{Complex{Int64}}:
 1+0im   0+0im
 0-1im  -1+0im

julia> LinearAlgebra.isbanded(b, 0, 0)
false

julia> LinearAlgebra.isbanded(b, -1, 0)
true
```
"""
isbanded(A::AbstractMatrix, kl::Integer, ku::Integer) = istriu(A, kl) && istril(A, ku)

"""
    isdiag(A) -> Bool

Test whether a matrix is diagonal in the sense that `iszero(A[i,j])` is true unless `i == j`.
Note that it is not necessary for `A` to be square;
if you would also like to check that, you need to check that `size(A, 1) == size(A, 2)`.

# Examples
```jldoctest
julia> a = [1 2; 2 -1]
2×2 Matrix{Int64}:
 1   2
 2  -1

julia> isdiag(a)
false

julia> b = [im 0; 0 -im]
2×2 Matrix{Complex{Int64}}:
 0+1im  0+0im
 0+0im  0-1im

julia> isdiag(b)
true

julia> c = [1 0 0; 0 2 0]
2×3 Matrix{Int64}:
 1  0  0
 0  2  0

julia> isdiag(c)
true

julia> d = [1 0 0; 0 2 3]
2×3 Matrix{Int64}:
 1  0  0
 0  2  3

julia> isdiag(d)
false
```
"""
isdiag(A::AbstractMatrix) = isbanded(A, 0, 0)
isdiag(x::Number) = true

"""
    axpy!(α, x::AbstractArray, y::AbstractArray)

Overwrite `y` with `x * α + y` and return `y`.
If `x` and `y` have the same axes, it's equivalent with `y .+= x .* a`.

# Examples
```jldoctest
julia> x = [1; 2; 3];

julia> y = [4; 5; 6];

julia> axpy!(2, x, y)
3-element Vector{Int64}:
  6
  9
 12
```
"""
function axpy!(α, x::AbstractArray, y::AbstractArray)
    n = length(x)
    if n != length(y)
        throw(DimensionMismatch("x has length $n, but y has length $(length(y))"))
    end
    iszero(α) && return y
    for (IY, IX) in zip(eachindex(y), eachindex(x))
        @inbounds y[IY] += x[IX]*α
    end
    return y
end

function axpy!(α, x::AbstractArray, rx::AbstractArray{<:Integer}, y::AbstractArray, ry::AbstractArray{<:Integer})
    if length(rx) != length(ry)
        throw(DimensionMismatch("rx has length $(length(rx)), but ry has length $(length(ry))"))
    elseif !checkindex(Bool, eachindex(IndexLinear(), x), rx)
        throw(BoundsError(x, rx))
    elseif !checkindex(Bool, eachindex(IndexLinear(), y), ry)
        throw(BoundsError(y, ry))
    end
    iszero(α) && return y
    for (IY, IX) in zip(eachindex(ry), eachindex(rx))
        @inbounds y[ry[IY]] += x[rx[IX]]*α
    end
    return y
end

"""
    axpby!(α, x::AbstractArray, β, y::AbstractArray)

Overwrite `y` with `x * α + y * β` and return `y`.
If `x` and `y` have the same axes, it's equivalent with `y .= x .* a .+ y .* β`.

# Examples
```jldoctest
julia> x = [1; 2; 3];

julia> y = [4; 5; 6];

julia> axpby!(2, x, 2, y)
3-element Vector{Int64}:
 10
 14
 18
```
"""
function axpby!(α, x::AbstractArray, β, y::AbstractArray)
    if length(x) != length(y)
        throw(DimensionMismatch("x has length $(length(x)), but y has length $(length(y))"))
    end
    iszero(α) && isone(β) && return y
    for (IX, IY) in zip(eachindex(x), eachindex(y))
        @inbounds y[IY] = x[IX]*α + y[IY]*β
    end
    y
end

DenseLike{T} = Union{DenseArray{T}, Base.StridedReshapedArray{T}, Base.StridedReinterpretArray{T}}
StridedVecLike{T} = Union{DenseLike{T}, Base.FastSubArray{T,<:Any,<:DenseLike{T}}}
axpy!(α::Number, x::StridedVecLike{T}, y::StridedVecLike{T}) where {T<:BlasFloat} = BLAS.axpy!(α, x, y)
axpby!(α::Number, x::StridedVecLike{T}, β::Number, y::StridedVecLike{T}) where {T<:BlasFloat} = BLAS.axpby!(α, x, β, y)
function axpy!(α::Number,
    x::StridedVecLike{T}, rx::AbstractRange{<:Integer},
    y::StridedVecLike{T}, ry::AbstractRange{<:Integer},
) where {T<:BlasFloat}
    if Base.has_offset_axes(rx, ry)
        return @invoke axpy!(α,
            x::AbstractArray, rx::AbstractArray{<:Integer},
            y::AbstractArray, ry::AbstractArray{<:Integer},
        )
    end
    @views BLAS.axpy!(α, x[rx], y[ry])
    return y
end

"""
    rotate!(x, y, c, s)

Overwrite `x` with `c*x + s*y` and `y` with `-conj(s)*x + c*y`.
Returns `x` and `y`.

!!! compat "Julia 1.5"
    `rotate!` requires at least Julia 1.5.
"""
function rotate!(x::AbstractVector, y::AbstractVector, c, s)
    require_one_based_indexing(x, y)
    n = length(x)
    if n != length(y)
        throw(DimensionMismatch("x has length $(length(x)), but y has length $(length(y))"))
    end
    @inbounds for i = 1:n
        xi, yi = x[i], y[i]
        x[i] =       c *xi + s*yi
        y[i] = -conj(s)*xi + c*yi
    end
    return x, y
end

"""
    reflect!(x, y, c, s)

Overwrite `x` with `c*x + s*y` and `y` with `conj(s)*x - c*y`.
Returns `x` and `y`.

!!! compat "Julia 1.5"
    `reflect!` requires at least Julia 1.5.
"""
function reflect!(x::AbstractVector, y::AbstractVector, c, s)
    require_one_based_indexing(x, y)
    n = length(x)
    if n != length(y)
        throw(DimensionMismatch("x has length $(length(x)), but y has length $(length(y))"))
    end
    @inbounds for i = 1:n
        xi, yi = x[i], y[i]
        x[i] =      c *xi + s*yi
        y[i] = conj(s)*xi - c*yi
    end
    return x, y
end

# Elementary reflection similar to LAPACK. The reflector is not Hermitian but
# ensures that tridiagonalization of Hermitian matrices become real. See lawn72
@inline function reflector!(x::AbstractVector{T}) where {T}
    require_one_based_indexing(x)
    n = length(x)
    n == 0 && return zero(eltype(x))
    @inbounds begin
        ξ1 = x[1]
        normu = norm(x)
        if iszero(normu)
            return zero(ξ1/normu)
        end
        ν = T(copysign(normu, real(ξ1)))
        ξ1 += ν
        x[1] = -ν
        for i = 2:n
            x[i] /= ξ1
        end
    end
    ξ1/ν
end

"""
    reflectorApply!(x, τ, A)

Multiplies `A` in-place by a Householder reflection on the left. It is equivalent to `A .= (I - τ*[1; x] * [1; x]')*A`.
"""
@inline function reflectorApply!(x::AbstractVector, τ::Number, A::AbstractVecOrMat)
    require_one_based_indexing(x)
    m, n = size(A, 1), size(A, 2)
    if length(x) != m
        throw(DimensionMismatch("reflector has length $(length(x)), which must match the first dimension of matrix A, $m"))
    end
    m == 0 && return A
    @inbounds for j = 1:n
        Aj, xj = view(A, 2:m, j), view(x, 2:m)
        vAj = conj(τ)*(A[1, j] + dot(xj, Aj))
        A[1, j] -= vAj
        axpy!(-vAj, xj, Aj)
    end
    return A
end

"""
    det(M)

Matrix determinant.

See also: [`logdet`](@ref) and [`logabsdet`](@ref).

# Examples
```jldoctest
julia> M = [1 0; 2 2]
2×2 Matrix{Int64}:
 1  0
 2  2

julia> det(M)
2.0
```
"""
function det(A::AbstractMatrix{T}) where {T}
    if istriu(A) || istril(A)
        S = promote_type(T, typeof((one(T)*zero(T) + zero(T))/one(T)))
        return convert(S, det(UpperTriangular(A)))
    end
    return det(lu(A; check = false))
end
det(x::Number) = x

# Resolve Issue #40128
det(A::AbstractMatrix{BigInt}) = det_bareiss(A)

"""
    logabsdet(M)

Log of absolute value of matrix determinant. Equivalent to
`(log(abs(det(M))), sign(det(M)))`, but may provide increased accuracy and/or speed.

# Examples
```jldoctest
julia> A = [-1. 0.; 0. 1.]
2×2 Matrix{Float64}:
 -1.0  0.0
  0.0  1.0

julia> det(A)
-1.0

julia> logabsdet(A)
(0.0, -1.0)

julia> B = [2. 0.; 0. 1.]
2×2 Matrix{Float64}:
 2.0  0.0
 0.0  1.0

julia> det(B)
2.0

julia> logabsdet(B)
(0.6931471805599453, 1.0)
```
"""
logabsdet(A::AbstractMatrix) = logabsdet(lu(A, check=false))

logabsdet(a::Number) = log(abs(a)), sign(a)

"""
    logdet(M)

Log of matrix determinant. Equivalent to `log(det(M))`, but may provide
increased accuracy and/or speed.

# Examples
```jldoctest
julia> M = [1 0; 2 2]
2×2 Matrix{Int64}:
 1  0
 2  2

julia> logdet(M)
0.6931471805599453

julia> logdet(Matrix(I, 3, 3))
0.0
```
"""
function logdet(A::AbstractMatrix)
    d,s = logabsdet(A)
    return d + log(s)
end

logdet(A) = log(det(A))

const NumberArray{T<:Number} = AbstractArray{T}

exactdiv(a, b) = a/b
exactdiv(a::Integer, b::Integer) = div(a, b)

"""
    det_bareiss!(M)

Calculates the determinant of a matrix using the
[Bareiss Algorithm](https://en.wikipedia.org/wiki/Bareiss_algorithm) using
inplace operations.

# Examples
```jldoctest
julia> M = [1 0; 2 2]
2×2 Matrix{Int64}:
 1  0
 2  2

julia> LinearAlgebra.det_bareiss!(M)
2
```
"""
function det_bareiss!(M)
    n = checksquare(M)
    sign, prev = Int8(1), one(eltype(M))
    for i in 1:n-1
        if iszero(M[i,i]) # swap with another col to make nonzero
            swapto = findfirst(!iszero, @view M[i,i+1:end])
            isnothing(swapto) && return zero(prev)
            sign = -sign
            Base.swapcols!(M, i, i + swapto)
        end
        for k in i+1:n, j in i+1:n
            M[j,k] = exactdiv(M[j,k]*M[i,i] - M[j,i]*M[i,k], prev)
        end
        prev = M[i,i]
    end
    return sign * M[end,end]
end
"""
    LinearAlgebra.det_bareiss(M)

Calculates the determinant of a matrix using the
[Bareiss Algorithm](https://en.wikipedia.org/wiki/Bareiss_algorithm).
Also refer to [`det_bareiss!`](@ref).
"""
det_bareiss(M) = det_bareiss!(copy(M))


"""
    promote_leaf_eltypes(itr)

For an (possibly nested) iterable object `itr`, promote the types of leaf
elements.  Equivalent to `promote_type(typeof(leaf1), typeof(leaf2), ...)`.
Currently supports only numeric leaf elements.

# Examples
```jldoctest
julia> a = [[1,2, [3,4]], 5.0, [6im, [7.0, 8.0]]]
3-element Vector{Any}:
  Any[1, 2, [3, 4]]
 5.0
  Any[0 + 6im, [7.0, 8.0]]

julia> LinearAlgebra.promote_leaf_eltypes(a)
ComplexF64 (alias for Complex{Float64})
```
"""
promote_leaf_eltypes(x::Union{AbstractArray{T},Tuple{T,Vararg{T}}}) where {T<:Number} = T
promote_leaf_eltypes(x::Union{AbstractArray{T},Tuple{T,Vararg{T}}}) where {T<:NumberArray} = eltype(T)
promote_leaf_eltypes(x::T) where {T} = T
promote_leaf_eltypes(x::Union{AbstractArray,Tuple}) = mapreduce(promote_leaf_eltypes, promote_type, x; init=Bool)

# isapprox: approximate equality of arrays [like isapprox(Number,Number)]
# Supports nested arrays; e.g., for `a = [[1,2, [3,4]], 5.0, [6im, [7.0, 8.0]]]`
# `a ≈ a` is `true`.
function isapprox(x::AbstractArray, y::AbstractArray;
    atol::Real=0,
    rtol::Real=Base.rtoldefault(promote_leaf_eltypes(x),promote_leaf_eltypes(y),atol),
    nans::Bool=false, norm::Function=norm)
    d = norm(x - y)
    if isfinite(d)
        return iszero(rtol) ? d <= atol : d <= max(atol, rtol*max(norm(x), norm(y)))
    else
        # Fall back to a component-wise approximate comparison
        # (mapreduce instead of all for greater generality [#44893])
        return mapreduce((a, b) -> isapprox(a, b; rtol=rtol, atol=atol, nans=nans), &, x, y)
    end
end

"""
    normalize!(a::AbstractArray, p::Real=2)

Normalize the array `a` in-place so that its `p`-norm equals unity,
i.e. `norm(a, p) == 1`.
See also [`normalize`](@ref) and [`norm`](@ref).
"""
function normalize!(a::AbstractArray, p::Real=2)
    nrm = norm(a, p)
    __normalize!(a, nrm)
end

@inline function __normalize!(a::AbstractArray, nrm)
    # The largest positive floating point number whose inverse is less than infinity
    δ = inv(prevfloat(typemax(nrm)))
    if nrm ≥ δ # Safe to multiply with inverse
        invnrm = inv(nrm)
        rmul!(a, invnrm)
    else # scale elements to avoid overflow
        εδ = eps(one(nrm))/δ
        rmul!(a, εδ)
        rmul!(a, inv(nrm*εδ))
    end
    return a
end

"""
    normalize(a, p::Real=2)

Normalize `a` so that its `p`-norm equals unity,
i.e. `norm(a, p) == 1`. For scalars, this is similar to sign(a),
except normalize(0) = NaN.
See also [`normalize!`](@ref), [`norm`](@ref), and [`sign`](@ref).

# Examples
```jldoctest
julia> a = [1,2,4];

julia> b = normalize(a)
3-element Vector{Float64}:
 0.2182178902359924
 0.4364357804719848
 0.8728715609439696

julia> norm(b)
1.0

julia> c = normalize(a, 1)
3-element Vector{Float64}:
 0.14285714285714285
 0.2857142857142857
 0.5714285714285714

julia> norm(c, 1)
1.0

julia> a = [1 2 4 ; 1 2 4]
2×3 Matrix{Int64}:
 1  2  4
 1  2  4

julia> norm(a)
6.48074069840786

julia> normalize(a)
2×3 Matrix{Float64}:
 0.154303  0.308607  0.617213
 0.154303  0.308607  0.617213

julia> normalize(3, 1)
1.0

julia> normalize(-8, 1)
-1.0

julia> normalize(0, 1)
NaN
```
"""
function normalize(a::AbstractArray, p::Real = 2)
    nrm = norm(a, p)
    if !isempty(a)
        aa = copymutable_oftype(a, typeof(first(a)/nrm))
        return __normalize!(aa, nrm)
    else
        T = typeof(zero(eltype(a))/nrm)
        return T[]
    end
end

normalize(x) = x / norm(x)
normalize(x, p::Real) = x / norm(x, p)
u   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LinearAlgebra/src/blas.jl�9     # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
Interface to BLAS subroutines.
"""
module BLAS

import Base: copyto!
using Base: require_one_based_indexing, USE_BLAS64

export
# Note: `xFUNC_NAME` is a placeholder for not exported BLAS functions
#   ref: http://www.netlib.org/blas/blasqr.pdf
# Level 1
    # xROTG
    # xROTMG
    rot!,
    # xROTM
    # xSWAP
    scal!,
    scal,
    blascopy!,
    # xAXPY!,
    # xAXPBY!,
    # xDOT
    dotc,
    dotu,
    # xxDOT
    nrm2,
    asum,
    iamax,
# Level 2
    gemv!,
    gemv,
    gbmv!,
    gbmv,
    hemv!,
    hemv,
    # xHBMV
    hpmv!,
    symv!,
    symv,
    sbmv!,
    sbmv,
    spmv!,
    trmv!,
    trmv,
    # xTBMV
    # xTPMV
    trsv!,
    trsv,
    # xTBSV
    # xTPSV
    ger!,
    # xGERU
    # xGERC
    her!,
    # xHPR
    # xHER2
    # xHPR2
    syr!,
    spr!,
    # xSYR2
    # xSPR2
# Level 3
    gemm!,
    gemm,
    symm!,
    symm,
    hemm!,
    hemm,
    syrk!,
    syrk,
    herk!,
    herk,
    syr2k!,
    syr2k,
    her2k!,
    her2k,
    trmm!,
    trmm,
    trsm!,
    trsm

using ..LinearAlgebra: libblastrampoline, BlasReal, BlasComplex, BlasFloat, BlasInt, DimensionMismatch, checksquare, stride1, chkstride1

include("lbt.jl")

# Legacy bindings that some packages (such as NNlib.jl) use.
# We maintain these for backwards-compatibility but new packages
# should not look at these, instead preferring to parse the output
# of BLAS.get_config()
const libblas = libblastrampoline
const liblapack = libblastrampoline

vendor() = :lbt

"""
    get_config()

Return an object representing the current `libblastrampoline` configuration.

!!! compat "Julia 1.7"
    `get_config()` requires at least Julia 1.7.
"""
get_config() = lbt_get_config()

if USE_BLAS64
    macro blasfunc(x)
        return Expr(:quote, Symbol(x, "64_"))
    end
else
    macro blasfunc(x)
        return Expr(:quote, x)
    end
end

_tryparse_env_int(key) = tryparse(Int, get(ENV, key, ""))


"""
    set_num_threads(n::Integer)
    set_num_threads(::Nothing)

Set the number of threads the BLAS library should use equal to `n::Integer`.

Also accepts `nothing`, in which case julia tries to guess the default number of threads.
Passing `nothing` is discouraged and mainly exists for historical reasons.
"""
set_num_threads(nt::Integer)::Nothing = lbt_set_num_threads(Int32(nt))
function set_num_threads(::Nothing)
    nt = something(
        _tryparse_env_int("OPENBLAS_NUM_THREADS"),
        _tryparse_env_int("OMP_NUM_THREADS"),
        _tryparse_env_int("VECLIB_MAXIMUM_THREADS"),
        max(1, Sys.CPU_THREADS ÷ 2),
    )
    return set_num_threads(nt)
end

"""
    get_num_threads()

Get the number of threads the BLAS library is using.

!!! compat "Julia 1.6"
    `get_num_threads` requires at least Julia 1.6.
"""
get_num_threads()::Int = lbt_get_num_threads()

function check()
    # TODO: once we have bitfields of the BLAS functions that are actually forwarded,
    # ensure that we have a complete set here (warning on an incomplete BLAS implementation)
    config = get_config()

    # Ensure that one of our loaded libraries satisfies our interface requirement
    interface = USE_BLAS64 ? :ilp64 : :lp64
    if !any(lib.interface == interface for lib in config.loaded_libs)
        interfacestr = uppercase(string(interface))
        @error("No loaded BLAS libraries were built with $(interfacestr) support")
        println("Quitting.")
        exit()
    end
end

"Check that upper/lower (for special matrices) is correctly specified"
function chkuplo(uplo::AbstractChar)
    if !(uplo == 'U' || uplo == 'L')
        throw(ArgumentError(lazy"uplo argument must be 'U' (upper) or 'L' (lower), got $uplo"))
    end
    uplo
end

# Level 1
# A help function to pick the pointer and inc for 1d like inputs.
@inline function vec_pointer_stride(x::AbstractArray, stride0check = nothing)
    Base._checkcontiguous(Bool, x) && return pointer(x), 1 # simplify runtime check when possible
    st, ptr = checkedstride(x), pointer(x)
    isnothing(stride0check) || (st == 0 && throw(stride0check))
    ptr += min(st, 0) * sizeof(eltype(x)) * (length(x) - 1)
    ptr, st
end
function checkedstride(x::AbstractArray)
    szs::Dims = size(x)
    sts::Dims = strides(x)
    _, st, n = Base.merge_adjacent_dim(szs, sts)
    n === ndims(x) && return st
    throw(ArgumentError("only support vector like inputs"))
end
## copy

"""
    blascopy!(n, X, incx, Y, incy)

Copy `n` elements of array `X` with stride `incx` to array `Y` with stride `incy`. Returns `Y`.
"""
function blascopy! end

for (fname, elty) in ((:dcopy_,:Float64),
                      (:scopy_,:Float32),
                      (:zcopy_,:ComplexF64),
                      (:ccopy_,:ComplexF32))
    @eval begin
        # SUBROUTINE DCOPY(N,DX,INCX,DY,INCY)
        function blascopy!(n::Integer, DX::Union{Ptr{$elty},AbstractArray{$elty}}, incx::Integer, DY::Union{Ptr{$elty},AbstractArray{$elty}}, incy::Integer)
            ccall((@blasfunc($fname), libblastrampoline), Cvoid,
                (Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}),
                 n, DX, incx, DY, incy)
            DY
        end
    end
end


## rot

"""
    rot!(n, X, incx, Y, incy, c, s)

Overwrite `X` with `c*X + s*Y` and `Y` with `-conj(s)*X + c*Y` for the first `n` elements of array `X` with stride `incx` and
first `n` elements of array `Y` with stride `incy`. Returns `X` and `Y`.

!!! compat "Julia 1.5"
    `rot!` requires at least Julia 1.5.
"""
function rot! end

for (fname, elty, cty, sty, lib) in ((:drot_, :Float64, :Float64, :Float64, libblastrampoline),
                                     (:srot_, :Float32, :Float32, :Float32, libblastrampoline),
                                     (:zdrot_, :ComplexF64, :Float64, :Float64, libblastrampoline),
                                     (:csrot_, :ComplexF32, :Float32, :Float32, libblastrampoline),
                                     (:zrot_, :ComplexF64, :Float64, :ComplexF64, libblastrampoline),
                                     (:crot_, :ComplexF32, :Float32, :ComplexF32, libblastrampoline))
    @eval begin
        # SUBROUTINE DROT(N,DX,INCX,DY,INCY,C,S)
        function rot!(n::Integer, DX::Union{Ptr{$elty},AbstractArray{$elty}}, incx::Integer, DY::Union{Ptr{$elty},AbstractArray{$elty}}, incy::Integer, C::$cty, S::$sty)
            ccall((@blasfunc($fname), $lib), Cvoid,
                (Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ref{$cty}, Ref{$sty}),
                 n, DX, incx, DY, incy, C, S)
            DX, DY
        end
    end
end

## scal

"""
    scal!(n, a, X, incx)
    scal!(a, X)

Overwrite `X` with `a*X` for the first `n` elements of array `X` with stride `incx`. Returns `X`.

If `n` and `incx` are not provided, `length(X)` and `stride(X,1)` are used.
"""
function scal! end

"""
    scal(n, a, X, incx)
    scal(a, X)

Return `X` scaled by `a` for the first `n` elements of array `X` with stride `incx`.

If `n` and `incx` are not provided, `length(X)` and `stride(X,1)` are used.
"""
function scal end

for (fname, elty) in ((:dscal_,:Float64),
                      (:sscal_,:Float32),
                      (:zscal_,:ComplexF64),
                      (:cscal_,:ComplexF32))
    @eval begin
        # SUBROUTINE DSCAL(N,DA,DX,INCX)
        function scal!(n::Integer, DA::$elty, DX::Union{Ptr{$elty},AbstractArray{$elty}}, incx::Integer)
            ccall((@blasfunc($fname), libblastrampoline), Cvoid,
                  (Ref{BlasInt}, Ref{$elty}, Ptr{$elty}, Ref{BlasInt}),
                  n, DA, DX, incx)
            DX
        end

        function scal!(DA::$elty, DX::AbstractArray{$elty})
            p, st = vec_pointer_stride(DX, ArgumentError("dest vector with 0 stride is not allowed"))
            GC.@preserve DX scal!(length(DX), DA, p, abs(st))
            DX
        end
    end
end
scal(n, DA, DX, incx) = scal!(n, DA, copy(DX), incx)
scal(DA, DX) = scal!(DA, copy(DX))

## dot

"""
    dot(n, X, incx, Y, incy)

Dot product of two vectors consisting of `n` elements of array `X` with stride `incx` and
`n` elements of array `Y` with stride `incy`.

# Examples
```jldoctest
julia> BLAS.dot(10, fill(1.0, 10), 1, fill(1.0, 20), 2)
10.0
```
"""
function dot end

"""
    dotc(n, X, incx, U, incy)

Dot function for two complex vectors, consisting of `n` elements of array `X`
with stride `incx` and `n` elements of array `U` with stride `incy`,
conjugating the first vector.

# Examples
```jldoctest
julia> BLAS.dotc(10, fill(1.0im, 10), 1, fill(1.0+im, 20), 2)
10.0 - 10.0im
```
"""
function dotc end

"""
    dotu(n, X, incx, Y, incy)

Dot function for two complex vectors consisting of `n` elements of array `X`
with stride `incx` and `n` elements of array `Y` with stride `incy`.

# Examples
```jldoctest
julia> BLAS.dotu(10, fill(1.0im, 10), 1, fill(1.0+im, 20), 2)
-10.0 + 10.0im
```
"""
function dotu end

for (fname, elty) in ((:cblas_ddot,:Float64),
                      (:cblas_sdot,:Float32))
    @eval begin
                #       DOUBLE PRECISION FUNCTION DDOT(N,DX,INCX,DY,INCY)
                # *     .. Scalar Arguments ..
                #       INTEGER INCX,INCY,N
                # *     ..
                # *     .. Array Arguments ..
                #       DOUBLE PRECISION DX(*),DY(*)
        function dot(n::Integer, DX::Union{Ptr{$elty},AbstractArray{$elty}}, incx::Integer, DY::Union{Ptr{$elty},AbstractArray{$elty}}, incy::Integer)
            ccall((@blasfunc($fname), libblastrampoline), $elty,
                (BlasInt, Ptr{$elty}, BlasInt, Ptr{$elty}, BlasInt),
                 n, DX, incx, DY, incy)
        end
    end
end
for (fname, elty) in ((:cblas_zdotc_sub,:ComplexF64),
                      (:cblas_cdotc_sub,:ComplexF32))
    @eval begin
                #       DOUBLE PRECISION FUNCTION DDOT(N,DX,INCX,DY,INCY)
                # *     .. Scalar Arguments ..
                #       INTEGER INCX,INCY,N
                # *     ..
                # *     .. Array Arguments ..
                #       DOUBLE PRECISION DX(*),DY(*)
        function dotc(n::Integer, DX::Union{Ptr{$elty},AbstractArray{$elty}}, incx::Integer, DY::Union{Ptr{$elty},AbstractArray{$elty}}, incy::Integer)
            result = Ref{$elty}()
            ccall((@blasfunc($fname), libblastrampoline), Cvoid,
                (BlasInt, Ptr{$elty}, BlasInt, Ptr{$elty}, BlasInt, Ptr{$elty}),
                 n, DX, incx, DY, incy, result)
            result[]
        end
    end
end
for (fname, elty) in ((:cblas_zdotu_sub,:ComplexF64),
                      (:cblas_cdotu_sub,:ComplexF32))
    @eval begin
                #       DOUBLE PRECISION FUNCTION DDOT(N,DX,INCX,DY,INCY)
                # *     .. Scalar Arguments ..
                #       INTEGER INCX,INCY,N
                # *     ..
                # *     .. Array Arguments ..
                #       DOUBLE PRECISION DX(*),DY(*)
        function dotu(n::Integer, DX::Union{Ptr{$elty},AbstractArray{$elty}}, incx::Integer, DY::Union{Ptr{$elty},AbstractArray{$elty}}, incy::Integer)
            result = Ref{$elty}()
            ccall((@blasfunc($fname), libblastrampoline), Cvoid,
                (BlasInt, Ptr{$elty}, BlasInt, Ptr{$elty}, BlasInt, Ptr{$elty}),
                 n, DX, incx, DY, incy, result)
            result[]
        end
    end
end

for (elty, f) in ((Float32, :dot), (Float64, :dot),
                  (ComplexF32, :dotc), (ComplexF64, :dotc),
                  (ComplexF32, :dotu), (ComplexF64, :dotu))
    @eval begin
        function $f(x::AbstractArray{$elty}, y::AbstractArray{$elty})
            n, m = length(x), length(y)
            n == m || throw(DimensionMismatch(lazy"dot product arguments have lengths $n and $m"))
            GC.@preserve x y $f(n, vec_pointer_stride(x)..., vec_pointer_stride(y)...)
        end
    end
end

## nrm2

"""
    nrm2(n, X, incx)

2-norm of a vector consisting of `n` elements of array `X` with stride `incx`.

# Examples
```jldoctest
julia> BLAS.nrm2(4, fill(1.0, 8), 2)
2.0

julia> BLAS.nrm2(1, fill(1.0, 8), 2)
1.0
```
"""
function nrm2 end

for (fname, elty, ret_type) in ((:dnrm2_,:Float64,:Float64),
                                (:snrm2_,:Float32,:Float32),
                                (:dznrm2_,:ComplexF64,:Float64),
                                (:scnrm2_,:ComplexF32,:Float32))
    @eval begin
        # SUBROUTINE DNRM2(N,X,INCX)
        function nrm2(n::Integer, X::Union{Ptr{$elty},AbstractArray{$elty}}, incx::Integer)
            ccall((@blasfunc($fname), libblastrampoline), $ret_type,
                (Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}),
                 n, X, incx)
        end
    end
end
# openblas returns 0 for negative stride
function nrm2(x::AbstractArray)
    p, st = vec_pointer_stride(x, ArgumentError("input vector with 0 stride is not allowed"))
    GC.@preserve x nrm2(length(x), p, abs(st))
end

## asum

"""
    asum(n, X, incx)

Sum of the magnitudes of the first `n` elements of array `X` with stride `incx`.

For a real array, the magnitude is the absolute value. For a complex array, the
magnitude is the sum of the absolute value of the real part and the absolute value
of the imaginary part.

# Examples
```jldoctest
julia> BLAS.asum(5, fill(1.0im, 10), 2)
5.0

julia> BLAS.asum(2, fill(1.0im, 10), 5)
2.0
```
"""
function asum end

for (fname, elty, ret_type) in ((:dasum_,:Float64,:Float64),
                                (:sasum_,:Float32,:Float32),
                                (:dzasum_,:ComplexF64,:Float64),
                                (:scasum_,:ComplexF32,:Float32))
    @eval begin
        # SUBROUTINE ASUM(N, X, INCX)
        function asum(n::Integer, X::Union{Ptr{$elty},AbstractArray{$elty}}, incx::Integer)
            ccall((@blasfunc($fname), libblastrampoline), $ret_type,
                (Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}),
                 n, X, incx)
        end
    end
end
function asum(x::AbstractArray)
    p, st = vec_pointer_stride(x, ArgumentError("input vector with 0 stride is not allowed"))
    GC.@preserve x asum(length(x), p, abs(st))
end

## axpy

"""
    axpy!(a, X, Y)

Overwrite `Y` with `X*a + Y`, where `a` is a scalar. Return `Y`.

# Examples
```jldoctest
julia> x = [1.; 2; 3];

julia> y = [4. ;; 5 ;; 6];

julia> BLAS.axpy!(2, x, y)
1×3 Matrix{Float64}:
 6.0  9.0  12.0
```
"""
function axpy! end

for (fname, elty) in ((:daxpy_,:Float64),
                      (:saxpy_,:Float32),
                      (:zaxpy_,:ComplexF64),
                      (:caxpy_,:ComplexF32))
    @eval begin
                # SUBROUTINE DAXPY(N,DA,DX,INCX,DY,INCY)
                # DY <- DA*DX + DY
                #*     .. Scalar Arguments ..
                #      DOUBLE PRECISION DA
                #      INTEGER INCX,INCY,N
                #*     .. Array Arguments ..
                #      DOUBLE PRECISION DX(*),DY(*)
        function axpy!(n::Integer, alpha::($elty), dx::Union{Ptr{$elty}, AbstractArray{$elty}}, incx::Integer, dy::Union{Ptr{$elty}, AbstractArray{$elty}}, incy::Integer)
            ccall((@blasfunc($fname), libblastrampoline), Cvoid,
                (Ref{BlasInt}, Ref{$elty}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}),
                 n, alpha, dx, incx, dy, incy)
            dy
        end
    end
end

function axpy!(alpha::Number, x::AbstractArray{T}, y::AbstractArray{T}) where T<:BlasFloat
    if length(x) != length(y)
        throw(DimensionMismatch(lazy"x has length $(length(x)), but y has length $(length(y))"))
    end
    GC.@preserve x y axpy!(length(x), T(alpha), vec_pointer_stride(x)...,
        vec_pointer_stride(y, ArgumentError("dest vector with 0 stride is not allowed"))...)
    y
end

function axpy!(alpha::Number, x::Array{T}, rx::AbstractRange{Ti},
               y::Array{T}, ry::AbstractRange{Ti}) where {T<:BlasFloat,Ti<:Integer}
    if length(rx) != length(ry)
        throw(DimensionMismatch("ranges of differing lengths"))
    end
    if minimum(rx) < 1 || maximum(rx) > length(x)
        throw(ArgumentError(lazy"range out of bounds for x, of length $(length(x))"))
    end
    if minimum(ry) < 1 || maximum(ry) > length(y)
        throw(ArgumentError(lazy"range out of bounds for y, of length $(length(y))"))
    end
    GC.@preserve x y axpy!(
        length(rx),
        T(alpha),
        pointer(x, minimum(rx)),
        step(rx),
        pointer(y, minimum(ry)),
        step(ry))

    return y
end

"""
    axpby!(a, X, b, Y)

Overwrite `Y` with `X*a + Y*b`, where `a` and `b` are scalars. Return `Y`.

# Examples
```jldoctest
julia> x = [1., 2, 3];

julia> y = [4., 5, 6];

julia> BLAS.axpby!(2., x, 3., y)
3-element Vector{Float64}:
 14.0
 19.0
 24.0
```
"""
function axpby! end

for (fname, elty) in ((:daxpby_,:Float64), (:saxpby_,:Float32),
                      (:zaxpby_,:ComplexF64), (:caxpby_,:ComplexF32))
    @eval begin
        # SUBROUTINE DAXPBY(N,DA,DX,INCX,DB,DY,INCY)
        # DY <- DA*DX + DB*DY
        #*     .. Scalar Arguments ..
        #      DOUBLE PRECISION DA,DB
        #      INTEGER INCX,INCY,N
        #*     .. Array Arguments ..
        #      DOUBLE PRECISION DX(*),DY(*)
        function axpby!(n::Integer, alpha::($elty), dx::Union{Ptr{$elty},
                        AbstractArray{$elty}}, incx::Integer, beta::($elty),
                        dy::Union{Ptr{$elty}, AbstractArray{$elty}}, incy::Integer)
            ccall((@blasfunc($fname), libblastrampoline), Cvoid, (Ref{BlasInt}, Ref{$elty}, Ptr{$elty},
                Ref{BlasInt}, Ref{$elty}, Ptr{$elty}, Ref{BlasInt}),
                n, alpha, dx, incx, beta, dy, incy)
            dy
        end
    end
end

function axpby!(alpha::Number, x::AbstractArray{T}, beta::Number, y::AbstractArray{T}) where T<:BlasFloat
    require_one_based_indexing(x, y)
    if length(x) != length(y)
        throw(DimensionMismatch(lazy"x has length $(length(x)), but y has length $(length(y))"))
    end
    GC.@preserve x y axpby!(length(x), T(alpha), vec_pointer_stride(x)..., T(beta),
        vec_pointer_stride(y, ArgumentError("dest vector with 0 stride is not allowed"))...)
    y
end

## iamax
for (fname, elty) in ((:idamax_,:Float64),
                      (:isamax_,:Float32),
                      (:izamax_,:ComplexF64),
                      (:icamax_,:ComplexF32))
    @eval begin
        function iamax(n::Integer, dx::Union{Ptr{$elty}, AbstractArray{$elty}}, incx::Integer)
            ccall((@blasfunc($fname), libblastrampoline),BlasInt,
                (Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}),
                n, dx, incx)
        end
    end
end
function iamax(dx::AbstractArray)
    p, st = vec_pointer_stride(dx)
    st <= 0 && return BlasInt(0)
    iamax(length(dx), p, st)
end

"""
    iamax(n, dx, incx)
    iamax(dx)

Find the index of the element of `dx` with the maximum absolute value. `n` is the length of `dx`, and `incx` is the
stride. If `n` and `incx` are not provided, they assume default values of `n=length(dx)` and `incx=stride1(dx)`.
"""
iamax

# Level 2
## mv
### gemv
for (fname, elty) in ((:dgemv_,:Float64),
                      (:sgemv_,:Float32),
                      (:zgemv_,:ComplexF64),
                      (:cgemv_,:ComplexF32))
    @eval begin
             #SUBROUTINE DGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
             #*     .. Scalar Arguments ..
             #      DOUBLE PRECISION ALPHA,BETA
             #      INTEGER INCX,INCY,LDA,M,N
             #      CHARACTER TRANS
             #*     .. Array Arguments ..
             #      DOUBLE PRECISION A(LDA,*),X(*),Y(*)
        function gemv!(trans::AbstractChar, alpha::Union{($elty), Bool},
                       A::AbstractVecOrMat{$elty}, X::AbstractVector{$elty},
                       beta::Union{($elty), Bool}, Y::AbstractVector{$elty})
            require_one_based_indexing(A, X, Y)
            m,n = size(A,1),size(A,2)
            if trans == 'N' && (length(X) != n || length(Y) != m)
                throw(DimensionMismatch(lazy"A has dimensions $(size(A)), X has length $(length(X)) and Y has length $(length(Y))"))
            elseif trans == 'C' && (length(X) != m || length(Y) != n)
                throw(DimensionMismatch(lazy"the adjoint of A has dimensions $n, $m, X has length $(length(X)) and Y has length $(length(Y))"))
            elseif trans == 'T' && (length(X) != m || length(Y) != n)
                throw(DimensionMismatch(lazy"the transpose of A has dimensions $n, $m, X has length $(length(X)) and Y has length $(length(Y))"))
            end
            chkstride1(A)
            lda = stride(A,2)
            pX, sX = vec_pointer_stride(X, ArgumentError("input vector with 0 stride is not allowed"))
            pY, sY = vec_pointer_stride(Y, ArgumentError("dest vector with 0 stride is not allowed"))
            pA = pointer(A)
            if lda < 0
                pA += (size(A, 2) - 1) * lda * sizeof($elty)
                lda = -lda
                trans == 'N' ? (sX = -sX) : (sY = -sY)
            end
            lda >= size(A,1) || size(A,2) <= 1 || error("when `size(A,2) > 1`, `abs(stride(A,2))` must be at least `size(A,1)`")
            lda = max(1, size(A,1), lda)
            GC.@preserve A X Y ccall((@blasfunc($fname), libblastrampoline), Cvoid,
                (Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt}, Ref{$elty},
                 Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                 Ref{$elty}, Ptr{$elty}, Ref{BlasInt}, Clong),
                 trans, size(A,1), size(A,2), alpha,
                 pA, lda, pX, sX,
                 beta, pY, sY, 1)
            Y
        end
        function gemv(trans::AbstractChar, alpha::($elty), A::AbstractMatrix{$elty}, X::AbstractVector{$elty})
            gemv!(trans, alpha, A, X, zero($elty), similar(X, $elty, size(A, (trans == 'N' ? 1 : 2))))
        end
        function gemv(trans::AbstractChar, A::AbstractMatrix{$elty}, X::AbstractVector{$elty})
            gemv!(trans, one($elty), A, X, zero($elty), similar(X, $elty, size(A, (trans == 'N' ? 1 : 2))))
        end
    end
end

"""
    gemv!(tA, alpha, A, x, beta, y)

Update the vector `y` as `alpha*A*x + beta*y` or `alpha*A'x + beta*y`
according to [`tA`](@ref stdlib-blas-trans).
`alpha` and `beta` are scalars. Return the updated `y`.
"""
gemv!

"""
    gemv(tA, alpha, A, x)

Return `alpha*A*x` or `alpha*A'x` according to [`tA`](@ref stdlib-blas-trans).
`alpha` is a scalar.
"""
gemv(tA, alpha, A, x)

"""
    gemv(tA, A, x)

Return `A*x` or `A'x` according to [`tA`](@ref stdlib-blas-trans).
"""
gemv(tA, A, x)

### (GB) general banded matrix-vector multiplication

"""
    gbmv!(trans, m, kl, ku, alpha, A, x, beta, y)

Update vector `y` as `alpha*A*x + beta*y` or `alpha*A'*x + beta*y` according to [`trans`](@ref stdlib-blas-trans).
The matrix `A` is a general band matrix of dimension `m` by `size(A,2)` with `kl`
sub-diagonals and `ku` super-diagonals. `alpha` and `beta` are scalars. Return the updated `y`.
"""
function gbmv! end

"""
    gbmv(trans, m, kl, ku, alpha, A, x)

Return `alpha*A*x` or `alpha*A'*x` according to [`trans`](@ref stdlib-blas-trans).
The matrix `A` is a general band matrix of dimension `m` by `size(A,2)` with `kl` sub-diagonals and `ku`
super-diagonals, and `alpha` is a scalar.
"""
function gbmv end

for (fname, elty) in ((:dgbmv_,:Float64),
                      (:sgbmv_,:Float32),
                      (:zgbmv_,:ComplexF64),
                      (:cgbmv_,:ComplexF32))
    @eval begin
             # SUBROUTINE DGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
             # *     .. Scalar Arguments ..
             #       DOUBLE PRECISION ALPHA,BETA
             #       INTEGER INCX,INCY,KL,KU,LDA,M,N
             #       CHARACTER TRANS
             # *     .. Array Arguments ..
             #       DOUBLE PRECISION A(LDA,*),X(*),Y(*)
        function gbmv!(trans::AbstractChar, m::Integer, kl::Integer, ku::Integer,
                       alpha::Union{($elty), Bool}, A::AbstractMatrix{$elty},
                       x::AbstractVector{$elty}, beta::Union{($elty), Bool},
                       y::AbstractVector{$elty})
            require_one_based_indexing(A, x, y)
            chkstride1(A)
            px, stx = vec_pointer_stride(x, ArgumentError("input vector with 0 stride is not allowed"))
            py, sty = vec_pointer_stride(y, ArgumentError("dest vector with 0 stride is not allowed"))
            GC.@preserve x y ccall((@blasfunc($fname), libblastrampoline), Cvoid,
                (Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt}, Ref{BlasInt},
                 Ref{BlasInt}, Ref{$elty}, Ptr{$elty}, Ref{BlasInt},
                 Ptr{$elty}, Ref{BlasInt}, Ref{$elty}, Ptr{$elty},
                 Ref{BlasInt}, Clong),
                 trans, m, size(A,2), kl,
                 ku, alpha, A, max(1,stride(A,2)),
                 px, stx, beta, py, sty, 1)
            y
        end
        function gbmv(trans::AbstractChar, m::Integer, kl::Integer, ku::Integer, alpha::($elty), A::AbstractMatrix{$elty}, x::AbstractVector{$elty})
            n = size(A,2)
            leny = trans == 'N' ? m : n
            gbmv!(trans, m, kl, ku, alpha, A, x, zero($elty), similar(x, $elty, leny))
        end
        function gbmv(trans::AbstractChar, m::Integer, kl::Integer, ku::Integer, A::AbstractMatrix{$elty}, x::AbstractVector{$elty})
            gbmv(trans, m, kl, ku, one($elty), A, x)
        end
    end
end

### symv

"""
    symv!(ul, alpha, A, x, beta, y)

Update the vector `y` as `alpha*A*x + beta*y`. `A` is assumed to be symmetric.
Only the [`ul`](@ref stdlib-blas-uplo) triangle of `A` is used.
`alpha` and `beta` are scalars. Return the updated `y`.
"""
function symv! end

for (fname, elty, lib) in ((:dsymv_,:Float64,libblastrampoline),
                           (:ssymv_,:Float32,libblastrampoline),
                           (:zsymv_,:ComplexF64,libblastrampoline),
                           (:csymv_,:ComplexF32,libblastrampoline))
    # Note that the complex symv are not BLAS but auiliary functions in LAPACK
    @eval begin
             #      SUBROUTINE DSYMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
             #     .. Scalar Arguments ..
             #      DOUBLE PRECISION ALPHA,BETA
             #      INTEGER INCX,INCY,LDA,N
             #      CHARACTER UPLO
             #     .. Array Arguments ..
             #      DOUBLE PRECISION A(LDA,*),X(*),Y(*)
        function symv!(uplo::AbstractChar, alpha::Union{($elty), Bool},
                       A::AbstractMatrix{$elty}, x::AbstractVector{$elty},
                       beta::Union{($elty), Bool}, y::AbstractVector{$elty})
            chkuplo(uplo)
            require_one_based_indexing(A, x, y)
            m, n = size(A)
            if m != n
                throw(DimensionMismatch(lazy"matrix A is $m by $n but must be square"))
            end
            if n != length(x)
                throw(DimensionMismatch(lazy"A has size $(size(A)), and x has length $(length(x))"))
            end
            if m != length(y)
                throw(DimensionMismatch(lazy"A has size $(size(A)), and y has length $(length(y))"))
            end
            chkstride1(A)
            px, stx = vec_pointer_stride(x, ArgumentError("input vector with 0 stride is not allowed"))
            py, sty = vec_pointer_stride(y, ArgumentError("dest vector with 0 stride is not allowed"))
            GC.@preserve x y ccall((@blasfunc($fname), $lib), Cvoid,
                (Ref{UInt8}, Ref{BlasInt}, Ref{$elty}, Ptr{$elty},
                 Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ref{$elty},
                 Ptr{$elty}, Ref{BlasInt}, Clong),
                 uplo, n, alpha, A,
                 max(1,stride(A,2)), px, stx, beta,
                 py, sty, 1)
            y
        end
        function symv(uplo::AbstractChar, alpha::($elty), A::AbstractMatrix{$elty}, x::AbstractVector{$elty})
                symv!(uplo, alpha, A, x, zero($elty), similar(x))
        end
        function symv(uplo::AbstractChar, A::AbstractMatrix{$elty}, x::AbstractVector{$elty})
            symv(uplo, one($elty), A, x)
        end
    end
end

"""
    symv(ul, alpha, A, x)

Return `alpha*A*x`. `A` is assumed to be symmetric.
Only the [`ul`](@ref stdlib-blas-uplo) triangle of `A` is used.
`alpha` is a scalar.
"""
symv(ul, alpha, A, x)

"""
    symv(ul, A, x)

Return `A*x`. `A` is assumed to be symmetric.
Only the [`ul`](@ref stdlib-blas-uplo) triangle of `A` is used.
"""
symv(ul, A, x)

### hemv
"""
    hemv!(ul, alpha, A, x, beta, y)

Update the vector `y` as `alpha*A*x + beta*y`. `A` is assumed to be Hermitian.
Only the [`ul`](@ref stdlib-blas-uplo) triangle of `A` is used.
`alpha` and `beta` are scalars. Return the updated `y`.
"""
function hemv! end

for (fname, elty) in ((:zhemv_,:ComplexF64),
                      (:chemv_,:ComplexF32))
    @eval begin
        function hemv!(uplo::AbstractChar, α::Union{$elty, Bool}, A::AbstractMatrix{$elty}, x::AbstractVector{$elty}, β::Union{$elty, Bool}, y::AbstractVector{$elty})
            chkuplo(uplo)
            require_one_based_indexing(A, x, y)
            m, n = size(A)
            if m != n
                throw(DimensionMismatch(lazy"matrix A is $m by $n but must be square"))
            end
            if n != length(x)
                throw(DimensionMismatch(lazy"A has size $(size(A)), and x has length $(length(x))"))
            end
            if m != length(y)
                throw(DimensionMismatch(lazy"A has size $(size(A)), and y has length $(length(y))"))
            end
            chkstride1(A)
            lda = max(1, stride(A, 2))
            px, stx = vec_pointer_stride(x, ArgumentError("input vector with 0 stride is not allowed"))
            py, sty = vec_pointer_stride(y, ArgumentError("dest vector with 0 stride is not allowed"))
            GC.@preserve x y ccall((@blasfunc($fname), libblastrampoline), Cvoid,
                (Ref{UInt8}, Ref{BlasInt}, Ref{$elty}, Ptr{$elty},
                 Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ref{$elty},
                 Ptr{$elty}, Ref{BlasInt}, Clong),
                uplo, n, α, A,
                lda, px, stx, β,
                py, sty, 1)
            y
        end
        function hemv(uplo::AbstractChar, α::($elty), A::AbstractMatrix{$elty}, x::AbstractVector{$elty})
            hemv!(uplo, α, A, x, zero($elty), similar(x))
        end
        function hemv(uplo::AbstractChar, A::AbstractMatrix{$elty}, x::AbstractVector{$elty})
            hemv(uplo, one($elty), A, x)
        end
    end
end

"""
    hemv(ul, alpha, A, x)

Return `alpha*A*x`. `A` is assumed to be Hermitian.
Only the [`ul`](@ref stdlib-blas-uplo) triangle of `A` is used.
`alpha` is a scalar.
"""
hemv(ul, alpha, A, x)

"""
    hemv(ul, A, x)

Return `A*x`. `A` is assumed to be Hermitian.
Only the [`ul`](@ref stdlib-blas-uplo) triangle of `A` is used.
"""
hemv(ul, A, x)

### hpmv!, (HP) Hermitian packed matrix-vector operation defined as y := alpha*A*x + beta*y.
for (fname, elty) in ((:zhpmv_, :ComplexF64),
                      (:chpmv_, :ComplexF32))
    @eval begin
        # SUBROUTINE ZHPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY)
        # Y <- ALPHA*AP*X + BETA*Y
        # *     .. Scalar Arguments ..
        #       DOUBLE PRECISION ALPHA,BETA
        #       INTEGER INCX,INCY,N
        #       CHARACTER UPLO
        # *     .. Array Arguments ..
        #       DOUBLE PRECISION A(N,N),X(N),Y(N)
        function hpmv!(uplo::AbstractChar,
                       n::Integer,
                       α::$elty,
                       AP::Union{Ptr{$elty}, AbstractArray{$elty}},
                       x::Union{Ptr{$elty}, AbstractArray{$elty}},
                       incx::Integer,
                       β::$elty,
                       y::Union{Ptr{$elty}, AbstractArray{$elty}},
                       incy::Integer)

            ccall((@blasfunc($fname), libblastrampoline), Cvoid,
                  (Ref{UInt8},     # uplo,
                   Ref{BlasInt},   # n,
                   Ref{$elty},     # α,
                   Ptr{$elty},     # AP,
                   Ptr{$elty},     # x,
                   Ref{BlasInt},   # incx,
                   Ref{$elty},     # β,
                   Ptr{$elty},     # y, output
                   Ref{BlasInt},   # incy
                   Clong),         # length of uplo
                  uplo,
                  n,
                  α,
                  AP,
                  x,
                  incx,
                  β,
                  y,
                  incy,
                  1)
            return y
        end
    end
end

function hpmv!(uplo::AbstractChar,
               α::Number, AP::AbstractArray{T}, x::AbstractArray{T},
               β::Number, y::AbstractArray{T}) where {T <: BlasComplex}
    require_one_based_indexing(AP, x, y)
    N = length(x)
    if N != length(y)
        throw(DimensionMismatch(lazy"x has length $(N), but y has length $(length(y))"))
    end
    if 2*length(AP) < N*(N + 1)
        throw(DimensionMismatch(lazy"Packed hermitian matrix A has size smaller than length(x) = $(N)."))
    end
    chkstride1(AP)
    px, stx = vec_pointer_stride(x, ArgumentError("input vector with 0 stride is not allowed"))
    py, sty = vec_pointer_stride(y, ArgumentError("dest vector with 0 stride is not allowed"))
    GC.@preserve x y hpmv!(uplo, N, T(α), AP, px, stx, T(β), py, sty)
    y
end

"""
    hpmv!(uplo, α, AP, x, β, y)

Update vector `y` as `α*A*x + β*y`, where `A` is a Hermitian matrix provided
in packed format `AP`.

With `uplo = 'U'`, the array AP must contain the upper triangular part of the
Hermitian matrix packed sequentially, column by column, so that `AP[1]`
contains `A[1, 1]`, `AP[2]` and `AP[3]` contain `A[1, 2]` and `A[2, 2]`
respectively, and so on.

With `uplo = 'L'`, the array AP must contain the lower triangular part of the
Hermitian matrix packed sequentially, column by column, so that `AP[1]`
contains `A[1, 1]`, `AP[2]` and `AP[3]` contain `A[2, 1]` and `A[3, 1]`
respectively, and so on.

The scalar inputs `α` and `β` must be complex or real numbers.

The array inputs `x`, `y` and `AP` must all be of `ComplexF32` or `ComplexF64` type.

Return the updated `y`.

!!! compat "Julia 1.5"
    `hpmv!` requires at least Julia 1.5.
"""
hpmv!

### sbmv, (SB) symmetric banded matrix-vector multiplication
for (fname, elty) in ((:dsbmv_,:Float64),
                      (:ssbmv_,:Float32))
    @eval begin
             #       SUBROUTINE DSBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
             # *     .. Scalar Arguments ..
             #       DOUBLE PRECISION ALPHA,BETA
             #       INTEGER INCX,INCY,K,LDA,N
             #       CHARACTER UPLO
             # *     .. Array Arguments ..
             #       DOUBLE PRECISION A(LDA,*),X(*),Y(*)
        function sbmv!(uplo::AbstractChar, k::Integer, alpha::($elty), A::AbstractMatrix{$elty}, x::AbstractVector{$elty}, beta::($elty), y::AbstractVector{$elty})
            chkuplo(uplo)
            require_one_based_indexing(A, x, y)
            chkstride1(A)
            px, stx = vec_pointer_stride(x, ArgumentError("input vector with 0 stride is not allowed"))
            py, sty = vec_pointer_stride(y, ArgumentError("dest vector with 0 stride is not allowed"))
            GC.@preserve x y ccall((@blasfunc($fname), libblastrampoline), Cvoid,
                (Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt}, Ref{$elty},
                 Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                 Ref{$elty}, Ptr{$elty}, Ref{BlasInt}, Clong),
                 uplo, size(A,2), k, alpha,
                 A, max(1,stride(A,2)), px, stx,
                 beta, py, sty, 1)
            y
        end
        function sbmv(uplo::AbstractChar, k::Integer, alpha::($elty), A::AbstractMatrix{$elty}, x::AbstractVector{$elty})
            n = size(A,2)
            sbmv!(uplo, k, alpha, A, x, zero($elty), similar(x, $elty, n))
        end
        function sbmv(uplo::AbstractChar, k::Integer, A::AbstractMatrix{$elty}, x::AbstractVector{$elty})
            sbmv(uplo, k, one($elty), A, x)
        end
    end
end

"""
    sbmv(uplo, k, alpha, A, x)

Return `alpha*A*x` where `A` is a symmetric band matrix of order `size(A,2)` with `k`
super-diagonals stored in the argument `A`.
Only the [`uplo`](@ref stdlib-blas-uplo) triangle of `A` is used.
"""
sbmv(uplo, k, alpha, A, x)

"""
    sbmv(uplo, k, A, x)

Return `A*x` where `A` is a symmetric band matrix of order `size(A,2)` with `k`
super-diagonals stored in the argument `A`.
Only the [`uplo`](@ref stdlib-blas-uplo) triangle of `A` is used.
"""
sbmv(uplo, k, A, x)

"""
    sbmv!(uplo, k, alpha, A, x, beta, y)

Update vector `y` as `alpha*A*x + beta*y` where `A` is a symmetric band matrix of order
`size(A,2)` with `k` super-diagonals stored in the argument `A`. The storage layout for `A`
is described the reference BLAS module, level-2 BLAS at
<http://www.netlib.org/lapack/explore-html/>.
Only the [`uplo`](@ref stdlib-blas-uplo) triangle of `A` is used.

Return the updated `y`.
"""
sbmv!

### spmv!, (SP) symmetric packed matrix-vector operation defined as y := alpha*A*x + beta*y.
for (fname, elty) in ((:dspmv_, :Float64),
                      (:sspmv_, :Float32))
    @eval begin
        # SUBROUTINE DSPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY)
        # Y <- ALPHA*AP*X + BETA*Y
        # *     .. Scalar Arguments ..
        #       DOUBLE PRECISION ALPHA,BETA
        #       INTEGER INCX,INCY,N
        #       CHARACTER UPLO
        # *     .. Array Arguments ..
        #       DOUBLE PRECISION A(N,N),X(N),Y(N)
        function spmv!(uplo::AbstractChar,
                       n::Integer,
                       α::$elty,
                       AP::Union{Ptr{$elty}, AbstractArray{$elty}},
                       x::Union{Ptr{$elty}, AbstractArray{$elty}},
                       incx::Integer,
                       β::$elty,
                       y::Union{Ptr{$elty}, AbstractArray{$elty}},
                       incy::Integer)

            ccall((@blasfunc($fname), libblastrampoline), Cvoid,
                  (Ref{UInt8},     # uplo,
                   Ref{BlasInt},   # n,
                   Ref{$elty},     # α,
                   Ptr{$elty},     # AP,
                   Ptr{$elty},     # x,
                   Ref{BlasInt},   # incx,
                   Ref{$elty},     # β,
                   Ptr{$elty},     # y, out
                   Ref{BlasInt},   # incy
                   Clong),         # length of uplo
                  uplo,
                  n,
                  α,
                  AP,
                  x,
                  incx,
                  β,
                  y,
                  incy,
                  1)
            return y
        end
    end
end

function spmv!(uplo::AbstractChar,
               α::Real, AP::AbstractArray{T}, x::AbstractArray{T},
               β::Real, y::AbstractArray{T}) where {T <: BlasReal}
    require_one_based_indexing(AP, x, y)
    N = length(x)
    if N != length(y)
        throw(DimensionMismatch(lazy"x has length $(N), but y has length $(length(y))"))
    end
    if 2*length(AP) < N*(N + 1)
        throw(DimensionMismatch(lazy"Packed symmetric matrix A has size smaller than length(x) = $(N)."))
    end
    chkstride1(AP)
    px, stx = vec_pointer_stride(x, ArgumentError("input vector with 0 stride is not allowed"))
    py, sty = vec_pointer_stride(y, ArgumentError("dest vector with 0 stride is not allowed"))
    GC.@preserve x y spmv!(uplo, N, T(α), AP, px, stx, T(β), py, sty)
    y
end

"""
    spmv!(uplo, α, AP, x, β, y)

Update vector `y` as `α*A*x + β*y`, where `A` is a symmetric matrix provided
in packed format `AP`.

With `uplo = 'U'`, the array AP must contain the upper triangular part of the
symmetric matrix packed sequentially, column by column, so that `AP[1]`
contains `A[1, 1]`, `AP[2]` and `AP[3]` contain `A[1, 2]` and `A[2, 2]`
respectively, and so on.

With `uplo = 'L'`, the array AP must contain the lower triangular part of the
symmetric matrix packed sequentially, column by column, so that `AP[1]`
contains `A[1, 1]`, `AP[2]` and `AP[3]` contain `A[2, 1]` and `A[3, 1]`
respectively, and so on.

The scalar inputs `α` and `β` must be real.

The array inputs `x`, `y` and `AP` must all be of `Float32` or `Float64` type.

Return the updated `y`.

!!! compat "Julia 1.5"
    `spmv!` requires at least Julia 1.5.
"""
spmv!

### spr!, (SP) symmetric packed matrix-vector operation defined as A := alpha*x*x' + A
for (fname, elty) in ((:dspr_, :Float64),
                      (:sspr_, :Float32))
    @eval begin
        function spr!(uplo::AbstractChar,
                      n::Integer,
                      α::$elty,
                      x::Union{Ptr{$elty}, AbstractArray{$elty}},
                      incx::Integer,
                      AP::Union{Ptr{$elty}, AbstractArray{$elty}})

            ccall((@blasfunc($fname), libblastrampoline), Cvoid,
                  (Ref{UInt8},     # uplo,
                   Ref{BlasInt},   # n,
                   Ref{$elty},     # α,
                   Ptr{$elty},     # x,
                   Ref{BlasInt},   # incx,
                   Ptr{$elty},     # AP,
                   Clong),         # length of uplo
                  uplo,
                  n,
                  α,
                  x,
                  incx,
                  AP,
                  1)
            return AP
        end
    end
end

function spr!(uplo::AbstractChar,
              α::Real, x::AbstractArray{T},
              AP::AbstractArray{T}) where {T <: BlasReal}
    chkuplo(uplo)
    require_one_based_indexing(AP, x)
    N = length(x)
    if 2*length(AP) < N*(N + 1)
        throw(DimensionMismatch(lazy"Packed symmetric matrix A has size smaller than length(x) = $(N)."))
    end
    chkstride1(AP)
    px, stx = vec_pointer_stride(x, ArgumentError("input vector with 0 stride is not allowed"))
    return GC.@preserve x spr!(uplo, N, T(α), px, stx , AP)
end

"""
    spr!(uplo, α, x, AP)

Update matrix `A` as `A+α*x*x'`, where `A` is a symmetric matrix provided
in packed format `AP` and `x` is a vector.

With `uplo = 'U'`, the array AP must contain the upper triangular part of the
symmetric matrix packed sequentially, column by column, so that `AP[1]`
contains `A[1, 1]`, `AP[2]` and `AP[3]` contain `A[1, 2]` and `A[2, 2]`
respectively, and so on.

With `uplo = 'L'`, the array AP must contain the lower triangular part of the
symmetric matrix packed sequentially, column by column, so that `AP[1]`
contains `A[1, 1]`, `AP[2]` and `AP[3]` contain `A[2, 1]` and `A[3, 1]`
respectively, and so on.

The scalar input `α` must be real.

The array inputs `x` and `AP` must all be of `Float32` or `Float64` type.
Return the updated `AP`.

!!! compat "Julia 1.8"
    `spr!` requires at least Julia 1.8.
"""
spr!

### hbmv, (HB) Hermitian banded matrix-vector multiplication
for (fname, elty) in ((:zhbmv_,:ComplexF64),
                      (:chbmv_,:ComplexF32))
    @eval begin
             #       SUBROUTINE ZHBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
             # *     .. Scalar Arguments ..
             #       DOUBLE PRECISION ALPHA,BETA
             #       INTEGER INCX,INCY,K,LDA,N
             #       CHARACTER UPLO
             # *     .. Array Arguments ..
             #       DOUBLE PRECISION A(LDA,*),X(*),Y(*)
        function hbmv!(uplo::AbstractChar, k::Integer, alpha::($elty), A::AbstractMatrix{$elty}, x::AbstractVector{$elty}, beta::($elty), y::AbstractVector{$elty})
            chkuplo(uplo)
            require_one_based_indexing(A, x, y)
            chkstride1(A)
            px, stx = vec_pointer_stride(x, ArgumentError("input vector with 0 stride is not allowed"))
            py, sty = vec_pointer_stride(y, ArgumentError("dest vector with 0 stride is not allowed"))
            GC.@preserve x y ccall((@blasfunc($fname), libblastrampoline), Cvoid,
                (Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt}, Ref{$elty},
                 Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                 Ref{$elty}, Ptr{$elty}, Ref{BlasInt}, Clong),
                 uplo, size(A,2), k, alpha,
                 A, max(1,stride(A,2)), px, stx,
                 beta, py, sty, 1)
            y
        end
        function hbmv(uplo::AbstractChar, k::Integer, alpha::($elty), A::AbstractMatrix{$elty}, x::AbstractVector{$elty})
            n = size(A,2)
            hbmv!(uplo, k, alpha, A, x, zero($elty), similar(x, $elty, n))
        end
        function hbmv(uplo::AbstractChar, k::Integer, A::AbstractMatrix{$elty}, x::AbstractVector{$elty})
            hbmv(uplo, k, one($elty), A, x)
        end
    end
end

### trmv, Triangular matrix-vector multiplication

"""
    trmv(ul, tA, dA, A, b)

Return `op(A)*b`, where `op` is determined by [`tA`](@ref stdlib-blas-trans).
Only the [`ul`](@ref stdlib-blas-uplo) triangle of `A` is used.
[`dA`](@ref stdlib-blas-diag) determines if the diagonal values are read or
are assumed to be all ones.
"""
function trmv end

"""
    trmv!(ul, tA, dA, A, b)

Return `op(A)*b`, where `op` is determined by [`tA`](@ref stdlib-blas-trans).
Only the [`ul`](@ref stdlib-blas-uplo) triangle of `A` is used.
[`dA`](@ref stdlib-blas-diag) determines if the diagonal values are read or
are assumed to be all ones.
The multiplication occurs in-place on `b`.
"""
function trmv! end

for (fname, elty) in ((:dtrmv_,:Float64),
                        (:strmv_,:Float32),
                        (:ztrmv_,:ComplexF64),
                        (:ctrmv_,:ComplexF32))
    @eval begin
                #       SUBROUTINE DTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
                # *     .. Scalar Arguments ..
                #       INTEGER INCX,LDA,N
                #       CHARACTER DIAG,TRANS,UPLO
                # *     .. Array Arguments ..
                #       DOUBLE PRECISION A(LDA,*),X(*)
        function trmv!(uplo::AbstractChar, trans::AbstractChar, diag::AbstractChar, A::AbstractMatrix{$elty}, x::AbstractVector{$elty})
            chkuplo(uplo)
            require_one_based_indexing(A, x)
            n = checksquare(A)
            if n != length(x)
                throw(DimensionMismatch(lazy"A has size ($n,$n), x has length $(length(x))"))
            end
            chkstride1(A)
            px, stx = vec_pointer_stride(x, ArgumentError("input vector with 0 stride is not allowed"))
            GC.@preserve x ccall((@blasfunc($fname), libblastrampoline), Cvoid,
                (Ref{UInt8}, Ref{UInt8}, Ref{UInt8}, Ref{BlasInt},
                 Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                 Clong, Clong, Clong),
                 uplo, trans, diag, n,
                 A, max(1,stride(A,2)), px, stx, 1, 1, 1)
            x
        end
        function trmv(uplo::AbstractChar, trans::AbstractChar, diag::AbstractChar, A::AbstractMatrix{$elty}, x::AbstractVector{$elty})
            trmv!(uplo, trans, diag, A, copy(x))
        end
    end
end

### trsv, Triangular matrix-vector solve

"""
    trsv!(ul, tA, dA, A, b)

Overwrite `b` with the solution to `A*x = b` or one of the other two variants determined by
[`tA`](@ref stdlib-blas-trans) and [`ul`](@ref stdlib-blas-uplo).
[`dA`](@ref stdlib-blas-diag) determines if the diagonal values are read or
are assumed to be all ones.
Return the updated `b`.
"""
function trsv! end

"""
    trsv(ul, tA, dA, A, b)

Return the solution to `A*x = b` or one of the other two variants determined by
[`tA`](@ref stdlib-blas-trans) and [`ul`](@ref stdlib-blas-uplo).
[`dA`](@ref stdlib-blas-diag) determines if the diagonal values are read or
are assumed to be all ones.
"""
function trsv end

for (fname, elty) in ((:dtrsv_,:Float64),
                        (:strsv_,:Float32),
                        (:ztrsv_,:ComplexF64),
                        (:ctrsv_,:ComplexF32))
    @eval begin
                #       SUBROUTINE DTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
                #       .. Scalar Arguments ..
                #       INTEGER INCX,LDA,N
                #       CHARACTER DIAG,TRANS,UPLO
                #       .. Array Arguments ..
                #       DOUBLE PRECISION A(LDA,*),X(*)
        function trsv!(uplo::AbstractChar, trans::AbstractChar, diag::AbstractChar, A::AbstractMatrix{$elty}, x::AbstractVector{$elty})
            chkuplo(uplo)
            require_one_based_indexing(A, x)
            n = checksquare(A)
            if n != length(x)
                throw(DimensionMismatch(lazy"size of A is $n != length(x) = $(length(x))"))
            end
            chkstride1(A)
            px, stx = vec_pointer_stride(x, ArgumentError("input vector with 0 stride is not allowed"))
            GC.@preserve x ccall((@blasfunc($fname), libblastrampoline), Cvoid,
                (Ref{UInt8}, Ref{UInt8}, Ref{UInt8}, Ref{BlasInt},
                 Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                 Clong, Clong, Clong),
                 uplo, trans, diag, n,
                 A, max(1,stride(A,2)), px, stx, 1, 1, 1)
            x
        end
        function trsv(uplo::AbstractChar, trans::AbstractChar, diag::AbstractChar, A::AbstractMatrix{$elty}, x::AbstractVector{$elty})
            trsv!(uplo, trans, diag, A, copy(x))
        end
    end
end

### ger

"""
    ger!(alpha, x, y, A)

Rank-1 update of the matrix `A` with vectors `x` and `y` as `alpha*x*y' + A`.
"""
function ger! end

for (fname, elty) in ((:dger_,:Float64),
                      (:sger_,:Float32),
                      (:zgerc_,:ComplexF64),
                      (:cgerc_,:ComplexF32))
    @eval begin
        function ger!(α::$elty, x::AbstractVector{$elty}, y::AbstractVector{$elty}, A::AbstractMatrix{$elty})
            require_one_based_indexing(A, x, y)
            m, n = size(A)
            if m != length(x) || n != length(y)
                throw(DimensionMismatch(lazy"A has size ($m,$n), x has length $(length(x)), y has length $(length(y))"))
            end
            px, stx = vec_pointer_stride(x, ArgumentError("input vector with 0 stride is not allowed"))
            py, sty = vec_pointer_stride(y, ArgumentError("input vector with 0 stride is not allowed"))
            GC.@preserve x y ccall((@blasfunc($fname), libblastrampoline), Cvoid,
                (Ref{BlasInt}, Ref{BlasInt}, Ref{$elty}, Ptr{$elty},
                 Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty},
                 Ref{BlasInt}),
                 m, n, α, px, stx, py, sty, A, max(1,stride(A,2)))
            A
        end
    end
end

### syr

"""
    syr!(uplo, alpha, x, A)

Rank-1 update of the symmetric matrix `A` with vector `x` as `alpha*x*transpose(x) + A`.
[`uplo`](@ref stdlib-blas-uplo) controls which triangle of `A` is updated. Returns `A`.
"""
function syr! end

for (fname, elty, lib) in ((:dsyr_,:Float64,libblastrampoline),
                           (:ssyr_,:Float32,libblastrampoline),
                           (:zsyr_,:ComplexF64,libblastrampoline),
                           (:csyr_,:ComplexF32,libblastrampoline))
    @eval begin
        function syr!(uplo::AbstractChar, α::$elty, x::AbstractVector{$elty}, A::AbstractMatrix{$elty})
            chkuplo(uplo)
            require_one_based_indexing(A, x)
            n = checksquare(A)
            if length(x) != n
                throw(DimensionMismatch(lazy"A has size ($n,$n), x has length $(length(x))"))
            end
            px, stx = vec_pointer_stride(x, ArgumentError("input vector with 0 stride is not allowed"))
            GC.@preserve x ccall((@blasfunc($fname), $lib), Cvoid,
                (Ref{UInt8}, Ref{BlasInt}, Ref{$elty}, Ptr{$elty},
                 Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}),
                 uplo, n, α, px, stx, A, max(1,stride(A, 2)))
            A
        end
    end
end

### her

"""
    her!(uplo, alpha, x, A)

Methods for complex arrays only. Rank-1 update of the Hermitian matrix `A` with vector `x`
as `alpha*x*x' + A`.
[`uplo`](@ref stdlib-blas-uplo) controls which triangle of `A` is updated. Returns `A`.
"""
function her! end

for (fname, elty, relty) in ((:zher_,:ComplexF64, :Float64),
                             (:cher_,:ComplexF32, :Float32))
    @eval begin
        function her!(uplo::AbstractChar, α::$relty, x::AbstractVector{$elty}, A::AbstractMatrix{$elty})
            chkuplo(uplo)
            require_one_based_indexing(A, x)
            n = checksquare(A)
            if length(x) != n
                throw(DimensionMismatch(lazy"A has size ($n,$n), x has length $(length(x))"))
            end
            px, stx = vec_pointer_stride(x, ArgumentError("input vector with 0 stride is not allowed"))
            GC.@preserve x ccall((@blasfunc($fname), libblastrampoline), Cvoid,
                (Ref{UInt8}, Ref{BlasInt}, Ref{$relty}, Ptr{$elty},
                 Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Clong),
                 uplo, n, α, px, stx, A, max(1,stride(A,2)), 1)
            A
        end
    end
end

# Level 3
## (GE) general matrix-matrix multiplication

"""
    gemm!(tA, tB, alpha, A, B, beta, C)

Update `C` as `alpha*A*B + beta*C` or the other three variants according to
[`tA`](@ref stdlib-blas-trans) and `tB`. Return the updated `C`.
"""
function gemm! end

for (gemm, elty) in
        ((:dgemm_,:Float64),
         (:sgemm_,:Float32),
         (:zgemm_,:ComplexF64),
         (:cgemm_,:ComplexF32))
    @eval begin
             # SUBROUTINE DGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
             # *     .. Scalar Arguments ..
             #       DOUBLE PRECISION ALPHA,BETA
             #       INTEGER K,LDA,LDB,LDC,M,N
             #       CHARACTER TRANSA,TRANSB
             # *     .. Array Arguments ..
             #       DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*)
        function gemm!(transA::AbstractChar, transB::AbstractChar,
                       alpha::Union{($elty), Bool},
                       A::AbstractVecOrMat{$elty}, B::AbstractVecOrMat{$elty},
                       beta::Union{($elty), Bool},
                       C::AbstractVecOrMat{$elty})
#           if any([stride(A,1), stride(B,1), stride(C,1)] .!= 1)
#               error("gemm!: BLAS module requires contiguous matrix columns")
#           end  # should this be checked on every call?
            require_one_based_indexing(A, B, C)
            m = size(A, transA == 'N' ? 1 : 2)
            ka = size(A, transA == 'N' ? 2 : 1)
            kb = size(B, transB == 'N' ? 1 : 2)
            n = size(B, transB == 'N' ? 2 : 1)
            if ka != kb || m != size(C,1) || n != size(C,2)
                throw(DimensionMismatch(lazy"A has size ($m,$ka), B has size ($kb,$n), C has size $(size(C))"))
            end
            chkstride1(A)
            chkstride1(B)
            chkstride1(C)
            ccall((@blasfunc($gemm), libblastrampoline), Cvoid,
                (Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt},
                 Ref{BlasInt}, Ref{$elty}, Ptr{$elty}, Ref{BlasInt},
                 Ptr{$elty}, Ref{BlasInt}, Ref{$elty}, Ptr{$elty},
                 Ref{BlasInt}, Clong, Clong),
                 transA, transB, m, n,
                 ka, alpha, A, max(1,stride(A,2)),
                 B, max(1,stride(B,2)), beta, C,
                 max(1,stride(C,2)), 1, 1)
            C
        end
        function gemm(transA::AbstractChar, transB::AbstractChar, alpha::($elty), A::AbstractMatrix{$elty}, B::AbstractMatrix{$elty})
            gemm!(transA, transB, alpha, A, B, zero($elty), similar(B, $elty, (size(A, transA == 'N' ? 1 : 2), size(B, transB == 'N' ? 2 : 1))))
        end
        function gemm(transA::AbstractChar, transB::AbstractChar, A::AbstractMatrix{$elty}, B::AbstractMatrix{$elty})
            gemm(transA, transB, one($elty), A, B)
        end
    end
end

"""
    gemm(tA, tB, alpha, A, B)

Return `alpha*A*B` or the other three variants according to [`tA`](@ref stdlib-blas-trans) and `tB`.
"""
gemm(tA, tB, alpha, A, B)

"""
    gemm(tA, tB, A, B)

Return `A*B` or the other three variants according to [`tA`](@ref stdlib-blas-trans) and `tB`.
"""
gemm(tA, tB, A, B)


## (SY) symmetric matrix-matrix and matrix-vector multiplication
for (mfname, elty) in ((:dsymm_,:Float64),
                       (:ssymm_,:Float32),
                       (:zsymm_,:ComplexF64),
                       (:csymm_,:ComplexF32))
    @eval begin
             #     SUBROUTINE DSYMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
             #     .. Scalar Arguments ..
             #     DOUBLE PRECISION ALPHA,BETA
             #     INTEGER LDA,LDB,LDC,M,N
             #     CHARACTER SIDE,UPLO
             #     .. Array Arguments ..
             #     DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*)
        function symm!(side::AbstractChar, uplo::AbstractChar, alpha::Union{($elty), Bool},
                       A::AbstractMatrix{$elty}, B::AbstractMatrix{$elty},
                       beta::Union{($elty), Bool}, C::AbstractMatrix{$elty})
            chkuplo(uplo)
            require_one_based_indexing(A, B, C)
            m, n = size(C)
            j = checksquare(A)
            M, N = size(B)
            if side == 'L'
                if j != m
                    throw(DimensionMismatch(lazy"A has first dimension $j but needs to match first dimension of C, $m"))
                end
                if N != n
                    throw(DimensionMismatch(lazy"B has second dimension $N but needs to match second dimension of C, $n"))
                end
                if j != M
                    throw(DimensionMismatch(lazy"A has second dimension $j but needs to match first dimension of B, $M"))
                end
            else
                if j != n
                    throw(DimensionMismatch(lazy"B has second dimension $j but needs to match second dimension of C, $n"))
                end
                if N != j
                    throw(DimensionMismatch(lazy"A has second dimension $N but needs to match first dimension of B, $j"))
                end
                if M != m
                    throw(DimensionMismatch(lazy"A has first dimension $M but needs to match first dimension of C, $m"))
                end
            end
            chkstride1(A)
            chkstride1(B)
            chkstride1(C)
            ccall((@blasfunc($mfname), libblastrampoline), Cvoid,
                (Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt},
                 Ref{$elty}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty},
                 Ref{BlasInt}, Ref{$elty}, Ptr{$elty}, Ref{BlasInt},
                 Clong, Clong),
                 side, uplo, m, n,
                 alpha, A, max(1,stride(A,2)), B,
                 max(1,stride(B,2)), beta, C, max(1,stride(C,2)),
                 1, 1)
            C
        end
        function symm(side::AbstractChar, uplo::AbstractChar, alpha::($elty), A::AbstractMatrix{$elty}, B::AbstractMatrix{$elty})
            symm!(side, uplo, alpha, A, B, zero($elty), similar(B))
        end
        function symm(side::AbstractChar, uplo::AbstractChar, A::AbstractMatrix{$elty}, B::AbstractMatrix{$elty})
            symm(side, uplo, one($elty), A, B)
        end
    end
end

"""
    symm(side, ul, alpha, A, B)

Return `alpha*A*B` or `alpha*B*A` according to [`side`](@ref stdlib-blas-side).
`A` is assumed to be symmetric. Only
the [`ul`](@ref stdlib-blas-uplo) triangle of `A` is used.
"""
symm(side, ul, alpha, A, B)

"""
    symm(side, ul, A, B)

Return `A*B` or `B*A` according to [`side`](@ref stdlib-blas-side).
`A` is assumed to be symmetric. Only the [`ul`](@ref stdlib-blas-uplo)
triangle of `A` is used.
"""
symm(side, ul, A, B)

"""
    symm!(side, ul, alpha, A, B, beta, C)

Update `C` as `alpha*A*B + beta*C` or `alpha*B*A + beta*C` according to [`side`](@ref stdlib-blas-side).
`A` is assumed to be symmetric. Only the [`ul`](@ref stdlib-blas-uplo) triangle of
`A` is used. Return the updated `C`.
"""
symm!

## (HE) Hermitian matrix-matrix and matrix-vector multiplication
for (mfname, elty) in ((:zhemm_,:ComplexF64),
                       (:chemm_,:ComplexF32))
    @eval begin
             #     SUBROUTINE DHEMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
             #     .. Scalar Arguments ..
             #     DOUBLE PRECISION ALPHA,BETA
             #     INTEGER LDA,LDB,LDC,M,N
             #     CHARACTER SIDE,UPLO
             #     .. Array Arguments ..
             #     DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*)
        function hemm!(side::AbstractChar, uplo::AbstractChar, alpha::Union{($elty), Bool},
                       A::AbstractMatrix{$elty}, B::AbstractMatrix{$elty},
                       beta::Union{($elty), Bool}, C::AbstractMatrix{$elty})
            chkuplo(uplo)
            require_one_based_indexing(A, B, C)
            m, n = size(C)
            j = checksquare(A)
            M, N = size(B)
            if side == 'L'
                if j != m
                    throw(DimensionMismatch(lazy"A has first dimension $j but needs to match first dimension of C, $m"))
                end
                if N != n
                    throw(DimensionMismatch(lazy"B has second dimension $N but needs to match second dimension of C, $n"))
                end
                if j != M
                    throw(DimensionMismatch(lazy"A has second dimension $j but needs to match first dimension of B, $M"))
                end
            else
                if j != n
                    throw(DimensionMismatch(lazy"B has second dimension $j but needs to match second dimension of C, $n"))
                end
                if N != j
                    throw(DimensionMismatch(lazy"A has second dimension $N but needs to match first dimension of B, $j"))
                end
                if M != m
                    throw(DimensionMismatch(lazy"A has first dimension $M but needs to match first dimension of C, $m"))
                end
            end
            chkstride1(A)
            chkstride1(B)
            chkstride1(C)
            ccall((@blasfunc($mfname), libblastrampoline), Cvoid,
                (Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt},
                 Ref{$elty}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty},
                 Ref{BlasInt}, Ref{$elty}, Ptr{$elty}, Ref{BlasInt},
                 Clong, Clong),
                 side, uplo, m, n,
                 alpha, A, max(1,stride(A,2)), B,
                 max(1,stride(B,2)), beta, C, max(1,stride(C,2)),
                 1, 1)
            C
        end
        function hemm(side::AbstractChar, uplo::AbstractChar, alpha::($elty), A::AbstractMatrix{$elty}, B::AbstractMatrix{$elty})
            hemm!(side, uplo, alpha, A, B, zero($elty), similar(B))
        end
        function hemm(side::AbstractChar, uplo::AbstractChar, A::AbstractMatrix{$elty}, B::AbstractMatrix{$elty})
            hemm(side, uplo, one($elty), A, B)
        end
    end
end

"""
    hemm(side, ul, alpha, A, B)

Return `alpha*A*B` or `alpha*B*A` according to [`side`](@ref stdlib-blas-side).
`A` is assumed to be Hermitian. Only the [`ul`](@ref stdlib-blas-uplo) triangle
of `A` is used.
"""
hemm(side, ul, alpha, A, B)

"""
    hemm(side, ul, A, B)

Return `A*B` or `B*A` according to [`side`](@ref stdlib-blas-side). `A` is assumed
to be Hermitian. Only the [`ul`](@ref stdlib-blas-uplo) triangle of `A` is used.
"""
hemm(side, ul, A, B)

"""
    hemm!(side, ul, alpha, A, B, beta, C)

Update `C` as `alpha*A*B + beta*C` or `alpha*B*A + beta*C` according to
[`side`](@ref stdlib-blas-side). `A` is assumed to be Hermitian. Only the
[`ul`](@ref stdlib-blas-uplo) triangle of `A` is used. Return the updated `C`.
"""
hemm!

## syrk

"""
    syrk!(uplo, trans, alpha, A, beta, C)

Rank-k update of the symmetric matrix `C` as `alpha*A*transpose(A) + beta*C` or
`alpha*transpose(A)*A + beta*C` according to [`trans`](@ref stdlib-blas-trans).
Only the [`uplo`](@ref stdlib-blas-uplo) triangle of `C` is used. Return `C`.
"""
function syrk! end

"""
    syrk(uplo, trans, alpha, A)

Return either the upper triangle or the lower triangle of `A`,
according to [`uplo`](@ref stdlib-blas-uplo),
of `alpha*A*transpose(A)` or `alpha*transpose(A)*A`,
according to [`trans`](@ref stdlib-blas-trans).
"""
function syrk end

for (fname, elty) in ((:dsyrk_,:Float64),
                      (:ssyrk_,:Float32),
                      (:zsyrk_,:ComplexF64),
                      (:csyrk_,:ComplexF32))
    @eval begin
        # SUBROUTINE DSYRK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC)
        # *     .. Scalar Arguments ..
        #       REAL ALPHA,BETA
        #       INTEGER K,LDA,LDC,N
        #       CHARACTER TRANS,UPLO
        # *     .. Array Arguments ..
        #       REAL A(LDA,*),C(LDC,*)
        function syrk!(uplo::AbstractChar, trans::AbstractChar,
                      alpha::Union{($elty), Bool}, A::AbstractVecOrMat{$elty},
                      beta::Union{($elty), Bool}, C::AbstractMatrix{$elty})
            chkuplo(uplo)
            require_one_based_indexing(A, C)
            n = checksquare(C)
            nn = size(A, trans == 'N' ? 1 : 2)
            if nn != n throw(DimensionMismatch(lazy"C has size ($n,$n), corresponding dimension of A is $nn")) end
            k  = size(A, trans == 'N' ? 2 : 1)
            chkstride1(A)
            chkstride1(C)
            ccall((@blasfunc($fname), libblastrampoline), Cvoid,
                  (Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt},
                   Ref{$elty}, Ptr{$elty}, Ref{BlasInt}, Ref{$elty},
                   Ptr{$elty}, Ref{BlasInt}, Clong, Clong),
                  uplo, trans, n, k,
                  alpha, A, max(1,stride(A,2)), beta,
                  C, max(1,stride(C,2)), 1, 1)
            C
        end
    end
end
function syrk(uplo::AbstractChar, trans::AbstractChar, alpha::Number, A::AbstractVecOrMat)
    T = eltype(A)
    n = size(A, trans == 'N' ? 1 : 2)
    syrk!(uplo, trans, convert(T,alpha), A, zero(T), similar(A, T, (n, n)))
end
syrk(uplo::AbstractChar, trans::AbstractChar, A::AbstractVecOrMat) = syrk(uplo, trans, one(eltype(A)), A)

"""
    herk!(uplo, trans, alpha, A, beta, C)

Methods for complex arrays only. Rank-k update of the Hermitian matrix `C` as
`alpha*A*A' + beta*C` or `alpha*A'*A + beta*C` according to [`trans`](@ref stdlib-blas-trans).
Only the [`uplo`](@ref stdlib-blas-uplo) triangle of `C` is updated. Returns `C`.
"""
function herk! end

"""
    herk(uplo, trans, alpha, A)

Methods for complex arrays only. Returns the [`uplo`](@ref stdlib-blas-uplo)
triangle of `alpha*A*A'` or `alpha*A'*A`, according to [`trans`](@ref stdlib-blas-trans).
"""
function herk end

for (fname, elty, relty) in ((:zherk_, :ComplexF64, :Float64),
                             (:cherk_, :ComplexF32, :Float32))
    @eval begin
        # SUBROUTINE CHERK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC)
        # *     .. Scalar Arguments ..
        #       REAL ALPHA,BETA
        #       INTEGER K,LDA,LDC,N
        #       CHARACTER TRANS,UPLO
        # *     ..
        # *     .. Array Arguments ..
        #       COMPLEX A(LDA,*),C(LDC,*)
        function herk!(uplo::AbstractChar, trans::AbstractChar,
                        α::Union{$relty, Bool}, A::AbstractVecOrMat{$elty},
                        β::Union{$relty, Bool}, C::AbstractMatrix{$elty})
            chkuplo(uplo)
            require_one_based_indexing(A, C)
            n = checksquare(C)
            nn = size(A, trans == 'N' ? 1 : 2)
            if nn != n
                throw(DimensionMismatch(lazy"the matrix to update has dimension $n but the implied dimension of the update is $(size(A, trans == 'N' ? 1 : 2))"))
            end
            chkstride1(A)
            chkstride1(C)
            k  = size(A, trans == 'N' ? 2 : 1)
            ccall((@blasfunc($fname), libblastrampoline), Cvoid,
                    (Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt},
                    Ref{$relty}, Ptr{$elty}, Ref{BlasInt}, Ref{$relty},
                    Ptr{$elty}, Ref{BlasInt}, Clong, Clong),
                    uplo, trans, n, k,
                    α, A, max(1,stride(A,2)), β,
                    C, max(1,stride(C,2)), 1, 1)
            C
        end
        function herk(uplo::AbstractChar, trans::AbstractChar, α::$relty, A::AbstractVecOrMat{$elty})
            n = size(A, trans == 'N' ? 1 : 2)
            herk!(uplo, trans, α, A, zero($relty), similar(A, (n,n)))
        end
        herk(uplo::AbstractChar, trans::AbstractChar, A::AbstractVecOrMat{$elty}) = herk(uplo, trans, one($relty), A)
    end
end

## syr2k
for (fname, elty) in ((:dsyr2k_,:Float64),
                      (:ssyr2k_,:Float32),
                      (:zsyr2k_,:ComplexF64),
                      (:csyr2k_,:ComplexF32))
    @eval begin
            #       SUBROUTINE DSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
            #
            #       .. Scalar Arguments ..
            #       REAL PRECISION ALPHA,BETA
            #       INTEGER K,LDA,LDB,LDC,N
            #       CHARACTER TRANS,UPLO
            #       ..
            #       .. Array Arguments ..
            #       REAL PRECISION A(LDA,*),B(LDB,*),C(LDC,*)
        function syr2k!(uplo::AbstractChar, trans::AbstractChar,
                        alpha::($elty), A::AbstractVecOrMat{$elty}, B::AbstractVecOrMat{$elty},
                        beta::($elty), C::AbstractMatrix{$elty})
            chkuplo(uplo)
            require_one_based_indexing(A, B, C)
            n = checksquare(C)
            nn = size(A, trans == 'N' ? 1 : 2)
            if nn != n throw(DimensionMismatch(lazy"C has size ($n,$n), corresponding dimension of A is $nn")) end
            k  = size(A, trans == 'N' ? 2 : 1)
            chkstride1(A)
            chkstride1(B)
            chkstride1(C)
            ccall((@blasfunc($fname), libblastrampoline), Cvoid,
                (Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt},
                 Ref{$elty}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ref{$elty},
                 Ptr{$elty}, Ref{BlasInt}, Clong, Clong),
                 uplo, trans, n, k,
                 alpha, A, max(1,stride(A,2)), B, max(1,stride(B,2)), beta,
                 C, max(1,stride(C,2)), 1, 1)
            C
        end
    end
end

"""
    syr2k!(uplo, trans, alpha, A, B, beta, C)

Rank-2k update of the symmetric matrix `C` as
`alpha*A*transpose(B) + alpha*B*transpose(A) + beta*C` or
`alpha*transpose(A)*B + alpha*transpose(B)*A + beta*C`
according to [`trans`](@ref stdlib-blas-trans).
Only the [`uplo`](@ref stdlib-blas-uplo) triangle of `C` is used. Returns `C`.
"""
function syr2k! end

"""
    syr2k(uplo, trans, alpha, A, B)

Returns the [`uplo`](@ref stdlib-blas-uplo) triangle of
`alpha*A*transpose(B) + alpha*B*transpose(A)` or
`alpha*transpose(A)*B + alpha*transpose(B)*A`,
according to [`trans`](@ref stdlib-blas-trans).
"""
function syr2k(uplo::AbstractChar, trans::AbstractChar, alpha::Number, A::AbstractVecOrMat, B::AbstractVecOrMat)
    T = eltype(A)
    n = size(A, trans == 'N' ? 1 : 2)
    syr2k!(uplo, trans, convert(T,alpha), A, B, zero(T), similar(A, T, (n, n)))
end
"""
    syr2k(uplo, trans, A, B)

Return the [`uplo`](@ref stdlib-blas-uplo) triangle of `A*transpose(B) + B*transpose(A)`
or `transpose(A)*B + transpose(B)*A`, according to [`trans`](@ref stdlib-blas-trans).
"""
syr2k(uplo::AbstractChar, trans::AbstractChar, A::AbstractVecOrMat, B::AbstractVecOrMat) = syr2k(uplo, trans, one(eltype(A)), A, B)

for (fname, elty1, elty2) in ((:zher2k_,:ComplexF64,:Float64), (:cher2k_,:ComplexF32,:Float32))
    @eval begin
        # SUBROUTINE CHER2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
        #
        #       .. Scalar Arguments ..
        #       COMPLEX ALPHA
        #       REAL BETA
        #       INTEGER K,LDA,LDB,LDC,N
        #       CHARACTER TRANS,UPLO
        #       ..
        #       .. Array Arguments ..
        #       COMPLEX A(LDA,*),B(LDB,*),C(LDC,*)
        function her2k!(uplo::AbstractChar, trans::AbstractChar, alpha::($elty1),
                        A::AbstractVecOrMat{$elty1}, B::AbstractVecOrMat{$elty1},
                        beta::($elty2), C::AbstractMatrix{$elty1})
            chkuplo(uplo)
            require_one_based_indexing(A, B, C)
            n = checksquare(C)
            nn = size(A, trans == 'N' ? 1 : 2)
            if nn != n throw(DimensionMismatch(lazy"C has size ($n,$n), corresponding dimension of A is $nn")) end
            chkstride1(A)
            chkstride1(B)
            chkstride1(C)
            k  = size(A, trans == 'N' ? 2 : 1)
            ccall((@blasfunc($fname), libblastrampoline), Cvoid,
                    (Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt},
                    Ref{$elty1}, Ptr{$elty1}, Ref{BlasInt}, Ptr{$elty1}, Ref{BlasInt},
                    Ref{$elty2},  Ptr{$elty1}, Ref{BlasInt}, Clong, Clong),
                    uplo, trans, n, k,
                    alpha, A, max(1,stride(A,2)), B, max(1,stride(B,2)),
                    beta, C, max(1,stride(C,2)), 1, 1)
            C
        end
        function her2k(uplo::AbstractChar, trans::AbstractChar, alpha::($elty1), A::AbstractVecOrMat{$elty1}, B::AbstractVecOrMat{$elty1})
            n = size(A, trans == 'N' ? 1 : 2)
            her2k!(uplo, trans, alpha, A, B, zero($elty2), similar(A, $elty1, (n,n)))
        end
        her2k(uplo::AbstractChar, trans::AbstractChar, A::AbstractVecOrMat{$elty1}, B::AbstractVecOrMat{$elty1}) =
            her2k(uplo, trans, one($elty1), A, B)
    end
end

"""
    her2k!(uplo, trans, alpha, A, B, beta, C)

Rank-2k update of the Hermitian matrix `C` as
`alpha*A*B' + alpha*B*A' + beta*C` or `alpha*A'*B + alpha*B'*A + beta*C`
according to [`trans`](@ref stdlib-blas-trans). The scalar `beta` has to be real.
Only the [`uplo`](@ref stdlib-blas-uplo) triangle of `C` is used. Return `C`.
"""
function her2k! end

"""
    her2k(uplo, trans, alpha, A, B)

Return the [`uplo`](@ref stdlib-blas-uplo) triangle of `alpha*A*B' + alpha*B*A'`
or `alpha*A'*B + alpha*B'*A`, according to [`trans`](@ref stdlib-blas-trans).
"""
her2k(uplo, trans, alpha, A, B)

"""
    her2k(uplo, trans, A, B)

Return the [`uplo`](@ref stdlib-blas-uplo) triangle of `A*B' + B*A'`
or `A'*B + B'*A`, according to [`trans`](@ref stdlib-blas-trans).
"""
her2k(uplo, trans, A, B)

## (TR) Triangular matrix and vector multiplication and solution

"""
    trmm!(side, ul, tA, dA, alpha, A, B)

Update `B` as `alpha*A*B` or one of the other three variants determined by
[`side`](@ref stdlib-blas-side) and [`tA`](@ref stdlib-blas-trans).
Only the [`ul`](@ref stdlib-blas-uplo) triangle of `A` is used.
[`dA`](@ref stdlib-blas-diag) determines if the diagonal values are read or
are assumed to be all ones.
Return the updated `B`.
"""
function trmm! end

"""
    trmm(side, ul, tA, dA, alpha, A, B)

Return `alpha*A*B` or one of the other three variants determined by
[`side`](@ref stdlib-blas-side) and [`tA`](@ref stdlib-blas-trans).
Only the [`ul`](@ref stdlib-blas-uplo) triangle of `A` is used.
[`dA`](@ref stdlib-blas-diag) determines if the diagonal values are read or
are assumed to be all ones.
"""
function trmm end

"""
    trsm!(side, ul, tA, dA, alpha, A, B)

Overwrite `B` with the solution to `A*X = alpha*B` or one of the other three variants
determined by [`side`](@ref stdlib-blas-side) and [`tA`](@ref stdlib-blas-trans).
Only the [`ul`](@ref stdlib-blas-uplo) triangle of `A` is used.
[`dA`](@ref stdlib-blas-diag) determines if the diagonal values are read or
are assumed to be all ones.
Returns the updated `B`.
"""
function trsm! end

"""
    trsm(side, ul, tA, dA, alpha, A, B)

Return the solution to `A*X = alpha*B` or one of the other three variants determined by
determined by [`side`](@ref stdlib-blas-side) and [`tA`](@ref stdlib-blas-trans).
Only the [`ul`](@ref stdlib-blas-uplo) triangle of `A` is used.
[`dA`](@ref stdlib-blas-diag) determines if the diagonal values are read or
are assumed to be all ones.
"""
function trsm end

for (mmname, smname, elty) in
        ((:dtrmm_,:dtrsm_,:Float64),
         (:strmm_,:strsm_,:Float32),
         (:ztrmm_,:ztrsm_,:ComplexF64),
         (:ctrmm_,:ctrsm_,:ComplexF32))
    @eval begin
        #       SUBROUTINE DTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
        # *     .. Scalar Arguments ..
        #       DOUBLE PRECISION ALPHA
        #       INTEGER LDA,LDB,M,N
        #       CHARACTER DIAG,SIDE,TRANSA,UPLO
        # *     .. Array Arguments ..
        #       DOUBLE PRECISION A(LDA,*),B(LDB,*)
        function trmm!(side::AbstractChar, uplo::AbstractChar, transa::AbstractChar, diag::AbstractChar, alpha::Number,
                       A::AbstractMatrix{$elty}, B::AbstractMatrix{$elty})
            chkuplo(uplo)
            require_one_based_indexing(A, B)
            m, n = size(B)
            nA = checksquare(A)
            if nA != (side == 'L' ? m : n)
                throw(DimensionMismatch(lazy"size of A, $(size(A)), doesn't match $side size of B with dims, $(size(B))"))
            end
            chkstride1(A)
            chkstride1(B)
            ccall((@blasfunc($mmname), libblastrampoline), Cvoid,
                  (Ref{UInt8}, Ref{UInt8}, Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt},
                   Ref{$elty}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                   Clong, Clong, Clong, Clong),
                  side, uplo, transa, diag, m, n,
                  alpha, A, max(1,stride(A,2)), B, max(1,stride(B,2)),
                  1, 1, 1, 1)
            B
        end
        function trmm(side::AbstractChar, uplo::AbstractChar, transa::AbstractChar, diag::AbstractChar,
                      alpha::$elty, A::AbstractMatrix{$elty}, B::AbstractMatrix{$elty})
            trmm!(side, uplo, transa, diag, alpha, A, copy(B))
        end
        #       SUBROUTINE DTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
        # *     .. Scalar Arguments ..
        #       DOUBLE PRECISION ALPHA
        #       INTEGER LDA,LDB,M,N
        #       CHARACTER DIAG,SIDE,TRANSA,UPLO
        # *     .. Array Arguments ..
        #       DOUBLE PRECISION A(LDA,*),B(LDB,*)
        function trsm!(side::AbstractChar, uplo::AbstractChar, transa::AbstractChar, diag::AbstractChar,
                       alpha::$elty, A::AbstractMatrix{$elty}, B::AbstractMatrix{$elty})
            chkuplo(uplo)
            require_one_based_indexing(A, B)
            m, n = size(B)
            k = checksquare(A)
            if k != (side == 'L' ? m : n)
                throw(DimensionMismatch(lazy"size of A is ($k,$k), size of B is ($m,$n), side is $side, and transa='$transa'"))
            end
            chkstride1(A)
            chkstride1(B)
            ccall((@blasfunc($smname), libblastrampoline), Cvoid,
                   (Ref{UInt8}, Ref{UInt8}, Ref{UInt8}, Ref{UInt8},
                    Ref{BlasInt}, Ref{BlasInt}, Ref{$elty}, Ptr{$elty},
                    Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                    Clong, Clong, Clong, Clong),
                   side, uplo, transa, diag,
                   m, n, alpha, A,
                   max(1,stride(A,2)), B, max(1,stride(B,2)),
                   1, 1, 1, 1)
            B
        end
        function trsm(side::AbstractChar, uplo::AbstractChar, transa::AbstractChar, diag::AbstractChar, alpha::$elty, A::AbstractMatrix{$elty}, B::AbstractMatrix{$elty})
            trsm!(side, uplo, transa, diag, alpha, A, copy(B))
        end
    end
end

end # module

function copyto!(dest::Array{T}, rdest::AbstractRange{Ti},
                 src::Array{T}, rsrc::AbstractRange{Ti}) where {T<:BlasFloat,Ti<:Integer}
    if minimum(rdest) < 1 || maximum(rdest) > length(dest)
        throw(ArgumentError(lazy"range out of bounds for dest, of length $(length(dest))"))
    end
    if minimum(rsrc) < 1 || maximum(rsrc) > length(src)
        throw(ArgumentError(lazy"range out of bounds for src, of length $(length(src))"))
    end
    if length(rdest) != length(rsrc)
        throw(DimensionMismatch(lazy"ranges must be of the same length"))
    end
    GC.@preserve src dest BLAS.blascopy!(
        length(rsrc),
        pointer(src, minimum(rsrc)),
        step(rsrc),
        pointer(dest, minimum(rdest)),
        step(rdest))

    return dest
end
t   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LinearAlgebra/src/lbt.jlP+      # This file is a part of Julia. License is MIT: https://julialang.org/license

## This file contains libblastrampoline-specific APIs

# Keep these in sync with `src/libblastrampoline_internal.h`
struct lbt_library_info_t
    libname::Cstring
    handle::Ptr{Cvoid}
    suffix::Cstring
    active_forwards::Ptr{UInt8}
    interface::Int32
    complex_retstyle::Int32
    f2c::Int32
    cblas::Int32
end
const LBT_INTERFACE_LP64    = 32
const LBT_INTERFACE_ILP64   = 64
const LBT_INTERFACE_UNKNOWN = -1
const LBT_INTERFACE_MAP = Dict(
    LBT_INTERFACE_LP64    => :lp64,
    LBT_INTERFACE_ILP64   => :ilp64,
    LBT_INTERFACE_UNKNOWN => :unknown,
)
const LBT_INV_INTERFACE_MAP = Dict(v => k for (k, v) in LBT_INTERFACE_MAP)

const LBT_F2C_PLAIN         =  0
const LBT_F2C_REQUIRED      =  1
const LBT_F2C_UNKNOWN       = -1
const LBT_F2C_MAP = Dict(
    LBT_F2C_PLAIN    => :plain,
    LBT_F2C_REQUIRED => :required,
    LBT_F2C_UNKNOWN  => :unknown,
)
const LBT_INV_F2C_MAP = Dict(v => k for (k, v) in LBT_F2C_MAP)

const LBT_COMPLEX_RETSTYLE_NORMAL   =  0
const LBT_COMPLEX_RETSTYLE_ARGUMENT =  1
const LBT_COMPLEX_RETSTYLE_UNKNOWN  = -1
const LBT_COMPLEX_RETSTYLE_MAP = Dict(
    LBT_COMPLEX_RETSTYLE_NORMAL   => :normal,
    LBT_COMPLEX_RETSTYLE_ARGUMENT => :argument,
    LBT_COMPLEX_RETSTYLE_UNKNOWN  => :unknown,
)
const LBT_INV_COMPLEX_RETSTYLE_MAP = Dict(v => k for (k, v) in LBT_COMPLEX_RETSTYLE_MAP)

const LBT_CBLAS_CONFORMANT =  0
const LBT_CBLAS_DIVERGENT  =  1
const LBT_CBLAS_UNKNOWN    = -1
const LBT_CBLAS_MAP = Dict(
    LBT_CBLAS_CONFORMANT => :conformant,
    LBT_CBLAS_DIVERGENT  => :divergent,
    LBT_CBLAS_UNKNOWN    => :unknown,
)
const LBT_INV_CBLAS_MAP = Dict(v => k for (k, v) in LBT_CBLAS_MAP)

struct LBTLibraryInfo
    libname::String
    handle::Ptr{Cvoid}
    suffix::String
    active_forwards::Vector{UInt8}
    interface::Symbol
    complex_retstyle::Symbol
    f2c::Symbol
    cblas::Symbol

    function LBTLibraryInfo(lib_info::lbt_library_info_t, num_exported_symbols::UInt32)
        return new(
            unsafe_string(lib_info.libname),
            lib_info.handle,
            unsafe_string(lib_info.suffix),
            unsafe_wrap(Vector{UInt8}, lib_info.active_forwards, div(num_exported_symbols,8)+1),
            LBT_INTERFACE_MAP[lib_info.interface],
            LBT_COMPLEX_RETSTYLE_MAP[lib_info.complex_retstyle],
            LBT_F2C_MAP[lib_info.f2c],
            LBT_CBLAS_MAP[lib_info.cblas],
        )
    end
end

struct lbt_config_t
    loaded_libs::Ptr{Ptr{lbt_library_info_t}}
    build_flags::UInt32
    exported_symbols::Ptr{Cstring}
    num_exported_symbols::UInt32
end
const LBT_BUILDFLAGS_DEEPBINDLESS     = 0x01
const LBT_BUILDFLAGS_F2C_CAPABLE      = 0x02
const LBT_BUILDFLAGS_CBLAS_DIVERGENCE = 0x04
const LBT_BUILDFLAGS_COMPLEX_RETSTYLE = 0x08
const LBT_BUILDFLAGS_SYMBOL_TRIMMING  = 0x10
const LBT_BUILDFLAGS_MAP = Dict(
    LBT_BUILDFLAGS_DEEPBINDLESS => :deepbindless,
    LBT_BUILDFLAGS_F2C_CAPABLE => :f2c_capable,
    LBT_BUILDFLAGS_CBLAS_DIVERGENCE => :cblas_divergence,
    LBT_BUILDFLAGS_COMPLEX_RETSTYLE => :complex_retstyle,
    LBT_BUILDFLAGS_SYMBOL_TRIMMING  => :symbol_trimming,
)

struct LBTConfig
    loaded_libs::Vector{LBTLibraryInfo}
    build_flags::Vector{Symbol}
    exported_symbols::Vector{String}

    function LBTConfig(config::lbt_config_t)
        # Decode OR'ed flags into a list of names
        build_flag_names = Symbol[]
        for (flag, name) in LBT_BUILDFLAGS_MAP
            if config.build_flags & flag != 0x00
                push!(build_flag_names, name)
            end
        end

        # Load all exported symbol names
        exported_symbols = String[]
        for sym_idx in 1:config.num_exported_symbols
            str_ptr = unsafe_load(config.exported_symbols, sym_idx)
            if str_ptr != C_NULL
                push!(exported_symbols, unsafe_string(str_ptr))
            else
                @error("NULL string in lbt_config.exported_symbols[$(sym_idx)]")
            end
        end

        # Unpack library info structures
        libs = LBTLibraryInfo[]
        idx = 1
        lib_ptr = unsafe_load(config.loaded_libs, idx)
        while lib_ptr != C_NULL
            push!(libs, LBTLibraryInfo(unsafe_load(lib_ptr), config.num_exported_symbols))

            idx += 1
            lib_ptr = unsafe_load(config.loaded_libs, idx)
        end
        return new(
            libs,
            build_flag_names,
            exported_symbols,
        )
    end
end

Base.show(io::IO, lbt::LBTLibraryInfo) = print(io, "LBTLibraryInfo(", basename(lbt.libname), ", ", lbt.interface, ")")
function Base.show(io::IO, mime::MIME{Symbol("text/plain")}, lbt::LBTLibraryInfo)
    summary(io, lbt); println(io)
    println(io, "├ Library: ", basename(lbt.libname))
    println(io, "├ Interface: ", lbt.interface)
    println(io, "├ Complex return style: ", lbt.complex_retstyle)
    println(io, "├ F2C: ", lbt.f2c)
      print(io, "└ CBLAS: ", lbt.cblas)
end

function Base.show(io::IO, lbt::LBTConfig)
    if length(lbt.loaded_libs) <= 3
        print(io, "LBTConfig(")
        gen = (string("[", uppercase(string(l.interface)), "] ",
            basename(l.libname)) for l in lbt.loaded_libs)
        print(io, join(gen, ", "))
        print(io, ")")
    else
        print(io, "LBTConfig(...)")
    end
end
function Base.show(io::IO, mime::MIME{Symbol("text/plain")}, lbt::LBTConfig)
    summary(io, lbt); println(io)
    println(io, "Libraries: ")
    for (i,l) in enumerate(lbt.loaded_libs)
        char = i == length(lbt.loaded_libs) ? "└" : "├"
        interface_str = if l.interface === :ilp64
            "ILP64"
        elseif l.interface === :lp64
            " LP64"
        else
            "UNKWN"
        end
        print(io, char, " [", interface_str,"] ", basename(l.libname))
        i !== length(lbt.loaded_libs) && println()
    end
end

mutable struct ConfigCache
    @atomic config::Union{Nothing,LBTConfig}
    lock::ReentrantLock
end

# In the event that users want to call `lbt_get_config()` multiple times (e.g. for
# runtime checks of which BLAS vendor is providing a symbol), let's cache the value
# and clear it only when someone calls something that would cause it to change.
const _CACHED_CONFIG = ConfigCache(nothing, ReentrantLock())

function lbt_get_config()
    config = @atomic :acquire _CACHED_CONFIG.config
    config === nothing || return config
    return lock(_CACHED_CONFIG.lock) do
        local config = @atomic :monotonic _CACHED_CONFIG.config
        config === nothing || return config
        config_ptr = ccall((:lbt_get_config, libblastrampoline), Ptr{lbt_config_t}, ())
        @atomic :release _CACHED_CONFIG.config = LBTConfig(unsafe_load(config_ptr))
    end
end

function _clear_config_with(f)
    lock(_CACHED_CONFIG.lock) do
        @atomic :release _CACHED_CONFIG.config = nothing
        f()
    end
end

function lbt_get_num_threads()
    return ccall((:lbt_get_num_threads, libblastrampoline), Int32, ())
end

function lbt_set_num_threads(nthreads)
    return ccall((:lbt_set_num_threads, libblastrampoline), Cvoid, (Int32,), nthreads)
end

function lbt_forward(path::AbstractString; clear::Bool = false, verbose::Bool = false, suffix_hint::Union{String,Nothing} = nothing)
    _clear_config_with() do
        return ccall((:lbt_forward, libblastrampoline), Int32, (Cstring, Int32, Int32, Cstring),
                     path, clear ? 1 : 0, verbose ? 1 : 0, something(suffix_hint, C_NULL))
    end
end

function lbt_set_default_func(addr)
    _clear_config_with() do
        return ccall((:lbt_set_default_func, libblastrampoline), Cvoid, (Ptr{Cvoid},), addr)
    end
end

function lbt_get_default_func()
    return ccall((:lbt_get_default_func, libblastrampoline), Ptr{Cvoid}, ())
end

"""
    lbt_find_backing_library(symbol_name, interface; config::LBTConfig = lbt_get_config())

Return the `LBTLibraryInfo` that represents the backing library for the given symbol
exported from libblastrampoline.  This allows us to discover which library will service
a particular BLAS call from Julia code.  This method returns `nothing` if either of the
following conditions are met:

 * No loaded library exports the desired symbol (the default function will be called)
 * The symbol was set via `lbt_set_forward()`, which does not track library provenance.

If the given `symbol_name` is not contained within the list of exported symbols, an
`ArgumentError` will be thrown.
"""
function lbt_find_backing_library(symbol_name, interface::Symbol;
                                  config::LBTConfig = lbt_get_config())
    if interface ∉ (:ilp64, :lp64)
        throw(ArgumentError("Invalid interface specification: '$(interface)'"))
    end
    symbol_idx = findfirst(s -> s == symbol_name, config.exported_symbols)
    if symbol_idx === nothing
        throw(ArgumentError("Invalid exported symbol name '$(symbol_name)'"))
    end
    # Convert to zero-indexed
    symbol_idx -= 1

    forward_byte_offset = div(symbol_idx, 8)
    forward_byte_mask = 1 << mod(symbol_idx, 8)
    for lib in filter(l -> l.interface == interface, config.loaded_libs)
        if lib.active_forwards[forward_byte_offset+1] & forward_byte_mask != 0x00
            return lib
        end
    end

    # No backing library was found
    return nothing
end


## NOTE: Manually setting forwards is referred to as the 'footgun API'.  It allows truly
## bizarre and complex setups to be created.  If you run into strange errors while using
## it, the first thing you should ask yourself is whether you've set things up properly.
function lbt_set_forward(symbol_name, addr, interface,
                         complex_retstyle = LBT_COMPLEX_RETSTYLE_NORMAL,
                         f2c = LBT_F2C_PLAIN; verbose::Bool = false)
    _clear_config_with() do
        return ccall(
            (:lbt_set_forward, libblastrampoline),
            Int32,
            (Cstring, Ptr{Cvoid}, Int32, Int32, Int32, Int32),
            string(symbol_name),
            addr,
            Int32(interface),
            Int32(complex_retstyle),
            Int32(f2c),
            verbose ? Int32(1) : Int32(0),
        )
    end
end
function lbt_set_forward(symbol_name, addr, interface::Symbol,
                         complex_retstyle::Symbol = :normal,
                         f2c::Symbol = :plain; kwargs...)
    return lbt_set_forward(symbol_name, addr,
                           LBT_INV_INTERFACE_MAP[interface],
                           LBT_INV_COMPLEX_RETSTYLE_MAP[complex_retstyle],
                           LBT_INV_F2C_MAP[f2c];
                           kwargs...)
end

function lbt_get_forward(symbol_name, interface, f2c = LBT_F2C_PLAIN)
    return ccall(
        (:lbt_get_forward, libblastrampoline),
        Ptr{Cvoid},
        (Cstring, Int32, Int32),
        string(symbol_name),
        Int32(interface),
        Int32(f2c),
    )
end
function lbt_get_forward(symbol_name, interface::Symbol, f2c::Symbol = :plain)
    return lbt_get_forward(symbol_name, LBT_INV_INTERFACE_MAP[interface], LBT_INV_F2C_MAP[f2c])
end
w   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LinearAlgebra/src/matmul.jlm�      # This file is a part of Julia. License is MIT: https://julialang.org/license

# matmul.jl: Everything to do with dense matrix multiplication

# Matrix-matrix multiplication

AdjOrTransStridedMat{T} = Union{Adjoint{<:Any, <:StridedMatrix{T}}, Transpose{<:Any, <:StridedMatrix{T}}}
StridedMaybeAdjOrTransMat{T} = Union{StridedMatrix{T}, Adjoint{<:Any, <:StridedMatrix{T}}, Transpose{<:Any, <:StridedMatrix{T}}}
StridedMaybeAdjOrTransVecOrMat{T} = Union{StridedVecOrMat{T}, AdjOrTrans{<:Any, <:StridedVecOrMat{T}}}

matprod(x, y) = x*y + x*y

# dot products

dot(x::StridedVecLike{T}, y::StridedVecLike{T}) where {T<:BlasReal} = BLAS.dot(x, y)
dot(x::StridedVecLike{T}, y::StridedVecLike{T}) where {T<:BlasComplex} = BLAS.dotc(x, y)

function dot(x::Vector{T}, rx::AbstractRange{TI}, y::Vector{T}, ry::AbstractRange{TI}) where {T<:BlasReal,TI<:Integer}
    if length(rx) != length(ry)
        throw(DimensionMismatch(lazy"length of rx, $(length(rx)), does not equal length of ry, $(length(ry))"))
    end
    if minimum(rx) < 1 || maximum(rx) > length(x)
        throw(BoundsError(x, rx))
    end
    if minimum(ry) < 1 || maximum(ry) > length(y)
        throw(BoundsError(y, ry))
    end
    GC.@preserve x y BLAS.dot(length(rx), pointer(x)+(first(rx)-1)*sizeof(T), step(rx), pointer(y)+(first(ry)-1)*sizeof(T), step(ry))
end

function dot(x::Vector{T}, rx::AbstractRange{TI}, y::Vector{T}, ry::AbstractRange{TI}) where {T<:BlasComplex,TI<:Integer}
    if length(rx) != length(ry)
        throw(DimensionMismatch(lazy"length of rx, $(length(rx)), does not equal length of ry, $(length(ry))"))
    end
    if minimum(rx) < 1 || maximum(rx) > length(x)
        throw(BoundsError(x, rx))
    end
    if minimum(ry) < 1 || maximum(ry) > length(y)
        throw(BoundsError(y, ry))
    end
    GC.@preserve x y BLAS.dotc(length(rx), pointer(x)+(first(rx)-1)*sizeof(T), step(rx), pointer(y)+(first(ry)-1)*sizeof(T), step(ry))
end

function *(transx::Transpose{<:Any,<:StridedVector{T}}, y::StridedVector{T}) where {T<:BlasComplex}
    x = transx.parent
    return BLAS.dotu(x, y)
end

# Matrix-vector multiplication
function (*)(A::StridedMaybeAdjOrTransMat{T}, x::StridedVector{S}) where {T<:BlasFloat,S<:Real}
    TS = promote_op(matprod, T, S)
    y = isconcretetype(TS) ? convert(AbstractVector{TS}, x) : x
    mul!(similar(x, TS, size(A,1)), A, y)
end
function (*)(A::AbstractMatrix{T}, x::AbstractVector{S}) where {T,S}
    TS = promote_op(matprod, T, S)
    mul!(similar(x, TS, axes(A,1)), A, x)
end

# these will throw a DimensionMismatch unless B has 1 row (or 1 col for transposed case):
(*)(a::AbstractVector, tB::TransposeAbsMat) = reshape(a, length(a), 1) * tB
(*)(a::AbstractVector, adjB::AdjointAbsMat) = reshape(a, length(a), 1) * adjB
(*)(a::AbstractVector, B::AbstractMatrix) = reshape(a, length(a), 1) * B

@inline mul!(y::AbstractVector, A::AbstractVecOrMat, x::AbstractVector,
                alpha::Number, beta::Number) =
    generic_matvecmul!(y, wrapper_char(A), _unwrap(A), x, MulAddMul(alpha, beta))
# BLAS cases
# equal eltypes
@inline generic_matvecmul!(y::StridedVector{T}, tA, A::StridedVecOrMat{T}, x::StridedVector{T},
                _add::MulAddMul=MulAddMul()) where {T<:BlasFloat} =
    gemv!(y, tA, A, x, _add.alpha, _add.beta)
# Real (possibly transposed) matrix times complex vector.
# Multiply the matrix with the real and imaginary parts separately
@inline generic_matvecmul!(y::StridedVector{Complex{T}}, tA, A::StridedVecOrMat{T}, x::StridedVector{Complex{T}},
                _add::MulAddMul=MulAddMul()) where {T<:BlasReal} =
    gemv!(y, tA, A, x, _add.alpha, _add.beta)
# Complex matrix times real vector.
# Reinterpret the matrix as a real matrix and do real matvec computation.
# works only in cooperation with BLAS when A is untransposed (tA == 'N')
# but that check is included in gemv! anyway
@inline generic_matvecmul!(y::StridedVector{Complex{T}}, tA, A::StridedVecOrMat{Complex{T}}, x::StridedVector{T},
                _add::MulAddMul=MulAddMul()) where {T<:BlasReal} =
    gemv!(y, tA, A, x, _add.alpha, _add.beta)

# Vector-Matrix multiplication
(*)(x::AdjointAbsVec,   A::AbstractMatrix) = (A'*x')'
(*)(x::TransposeAbsVec, A::AbstractMatrix) = transpose(transpose(A)*transpose(x))

# Matrix-matrix multiplication
"""
    *(A::AbstractMatrix, B::AbstractMatrix)

Matrix multiplication.

# Examples
```jldoctest
julia> [1 1; 0 1] * [1 0; 1 1]
2×2 Matrix{Int64}:
 2  1
 1  1
```
"""
function (*)(A::AbstractMatrix, B::AbstractMatrix)
    TS = promote_op(matprod, eltype(A), eltype(B))
    mul!(similar(B, TS, (size(A, 1), size(B, 2))), A, B)
end
# optimization for dispatching to BLAS, e.g. *(::Matrix{Float32}, ::Matrix{Float64})
# but avoiding the case *(::Matrix{<:BlasComplex}, ::Matrix{<:BlasReal})
# which is better handled by reinterpreting rather than promotion
function (*)(A::StridedMaybeAdjOrTransMat{<:BlasReal}, B::StridedMaybeAdjOrTransMat{<:BlasReal})
    TS = promote_type(eltype(A), eltype(B))
    mul!(similar(B, TS, (size(A, 1), size(B, 2))),
         wrapperop(A)(convert(AbstractArray{TS}, _unwrap(A))),
         wrapperop(B)(convert(AbstractArray{TS}, _unwrap(B))))
end
function (*)(A::StridedMaybeAdjOrTransMat{<:BlasComplex}, B::StridedMaybeAdjOrTransMat{<:BlasComplex})
    TS = promote_type(eltype(A), eltype(B))
    mul!(similar(B, TS, (size(A, 1), size(B, 2))),
         wrapperop(A)(convert(AbstractArray{TS}, _unwrap(A))),
         wrapperop(B)(convert(AbstractArray{TS}, _unwrap(B))))
end

# Complex Matrix times real matrix: We use that it is generally faster to reinterpret the
# first matrix as a real matrix and carry out real matrix matrix multiply
function (*)(A::StridedMatrix{<:BlasComplex}, B::StridedMaybeAdjOrTransMat{<:BlasReal})
    TS = promote_type(eltype(A), eltype(B))
    mul!(similar(B, TS, (size(A, 1), size(B, 2))),
         convert(AbstractArray{TS}, A),
         wrapperop(B)(convert(AbstractArray{real(TS)}, _unwrap(B))))
end
function (*)(A::AdjOrTransStridedMat{<:BlasComplex}, B::StridedMaybeAdjOrTransMat{<:BlasReal})
    TS = promote_type(eltype(A), eltype(B))
    mul!(similar(B, TS, (size(A, 1), size(B, 2))),
         copymutable_oftype(A, TS), # remove AdjOrTrans to use reinterpret trick below
         wrapperop(B)(convert(AbstractArray{real(TS)}, _unwrap(B))))
end
# the following case doesn't seem to benefit from the translation A*B = (B' * A')'
function (*)(A::StridedMatrix{<:BlasReal}, B::StridedMatrix{<:BlasComplex})
    temp = real(B)
    R = A * temp
    temp .= imag.(B)
    I = A * temp
    Complex.(R, I)
end
(*)(A::AdjOrTransStridedMat{<:BlasReal}, B::StridedMatrix{<:BlasComplex}) = copy(transpose(transpose(B) * parent(A)))
(*)(A::StridedMaybeAdjOrTransMat{<:BlasReal}, B::AdjOrTransStridedMat{<:BlasComplex}) = copy(wrapperop(B)(parent(B) * transpose(A)))

"""
    muladd(A, y, z)

Combined multiply-add, `A*y .+ z`, for matrix-matrix or matrix-vector multiplication.
The result is always the same size as `A*y`, but `z` may be smaller, or a scalar.

!!! compat "Julia 1.6"
     These methods require Julia 1.6 or later.

# Examples
```jldoctest
julia> A=[1.0 2.0; 3.0 4.0]; B=[1.0 1.0; 1.0 1.0]; z=[0, 100];

julia> muladd(A, B, z)
2×2 Matrix{Float64}:
   3.0    3.0
 107.0  107.0
```
"""
function Base.muladd(A::AbstractMatrix, y::AbstractVecOrMat, z::Union{Number, AbstractArray})
    Ay = A * y
    for d in 1:ndims(Ay)
        # Same error as Ay .+= z would give, to match StridedMatrix method:
        size(z,d) > size(Ay,d) && throw(DimensionMismatch("array could not be broadcast to match destination"))
    end
    for d in ndims(Ay)+1:ndims(z)
        # Similar error to what Ay + z would give, to match (Any,Any,Any) method:
        size(z,d) > 1 && throw(DimensionMismatch(string("dimensions must match: z has dims ",
            axes(z), ", must have singleton at dim ", d)))
    end
    Ay .+ z
end

function Base.muladd(u::AbstractVector, v::AdjOrTransAbsVec, z::Union{Number, AbstractArray})
    if size(z,1) > length(u) || size(z,2) > length(v)
        # Same error as (u*v) .+= z:
        throw(DimensionMismatch("array could not be broadcast to match destination"))
    end
    for d in 3:ndims(z)
        # Similar error to (u*v) + z:
        size(z,d) > 1 && throw(DimensionMismatch(string("dimensions must match: z has dims ",
            axes(z), ", must have singleton at dim ", d)))
    end
    (u .* v) .+ z
end

Base.muladd(x::AdjointAbsVec, A::AbstractMatrix, z::Union{Number, AbstractVecOrMat}) =
    muladd(A', x', z')'
Base.muladd(x::TransposeAbsVec, A::AbstractMatrix, z::Union{Number, AbstractVecOrMat}) =
    transpose(muladd(transpose(A), transpose(x), transpose(z)))

function Base.muladd(A::StridedMaybeAdjOrTransMat{<:Number}, y::AbstractVector{<:Number}, z::Union{Number, AbstractVector})
    T = promote_type(eltype(A), eltype(y), eltype(z))
    C = similar(A, T, axes(A,1))
    C .= z
    mul!(C, A, y, true, true)
end

function Base.muladd(A::StridedMaybeAdjOrTransMat{<:Number}, B::StridedMaybeAdjOrTransMat{<:Number}, z::Union{Number, AbstractVecOrMat})
    T = promote_type(eltype(A), eltype(B), eltype(z))
    C = similar(A, T, axes(A,1), axes(B,2))
    C .= z
    mul!(C, A, B, true, true)
end

"""
    mul!(Y, A, B) -> Y

Calculates the matrix-matrix or matrix-vector product ``AB`` and stores the result in `Y`,
overwriting the existing value of `Y`. Note that `Y` must not be aliased with either `A` or
`B`.

# Examples
```jldoctest
julia> A=[1.0 2.0; 3.0 4.0]; B=[1.0 1.0; 1.0 1.0]; Y = similar(B); mul!(Y, A, B);

julia> Y
2×2 Matrix{Float64}:
 3.0  3.0
 7.0  7.0
```

# Implementation
For custom matrix and vector types, it is recommended to implement
5-argument `mul!` rather than implementing 3-argument `mul!` directly
if possible.
"""
@inline function mul!(C, A, B)
    return mul!(C, A, B, true, false)
end

"""
    mul!(C, A, B, α, β) -> C

Combined inplace matrix-matrix or matrix-vector multiply-add ``A B α + C β``.
The result is stored in `C` by overwriting it.  Note that `C` must not be
aliased with either `A` or `B`.

!!! compat "Julia 1.3"
    Five-argument `mul!` requires at least Julia 1.3.

# Examples
```jldoctest
julia> A=[1.0 2.0; 3.0 4.0]; B=[1.0 1.0; 1.0 1.0]; C=[1.0 2.0; 3.0 4.0];

julia> mul!(C, A, B, 100.0, 10.0) === C
true

julia> C
2×2 Matrix{Float64}:
 310.0  320.0
 730.0  740.0
```
"""
@inline mul!(C::AbstractMatrix, A::AbstractVecOrMat, B::AbstractVecOrMat, α::Number, β::Number) =
    generic_matmatmul!(
        C,
        wrapper_char(A),
        wrapper_char(B),
        _unwrap(A),
        _unwrap(B),
        MulAddMul(α, β)
    )

"""
    rmul!(A, B)

Calculate the matrix-matrix product ``AB``, overwriting `A`, and return the result.
Here, `B` must be of special matrix type, like, e.g., [`Diagonal`](@ref),
[`UpperTriangular`](@ref) or [`LowerTriangular`](@ref), or of some orthogonal type,
see [`QR`](@ref).

# Examples
```jldoctest
julia> A = [0 1; 1 0];

julia> B = UpperTriangular([1 2; 0 3]);

julia> rmul!(A, B);

julia> A
2×2 Matrix{Int64}:
 0  3
 1  2

julia> A = [1.0 2.0; 3.0 4.0];

julia> F = qr([0 1; -1 0]);

julia> rmul!(A, F.Q)
2×2 Matrix{Float64}:
 2.0  1.0
 4.0  3.0
```
"""
rmul!(A, B)

"""
    lmul!(A, B)

Calculate the matrix-matrix product ``AB``, overwriting `B`, and return the result.
Here, `A` must be of special matrix type, like, e.g., [`Diagonal`](@ref),
[`UpperTriangular`](@ref) or [`LowerTriangular`](@ref), or of some orthogonal type,
see [`QR`](@ref).

# Examples
```jldoctest
julia> B = [0 1; 1 0];

julia> A = UpperTriangular([1 2; 0 3]);

julia> lmul!(A, B);

julia> B
2×2 Matrix{Int64}:
 2  1
 3  0

julia> B = [1.0 2.0; 3.0 4.0];

julia> F = qr([0 1; -1 0]);

julia> lmul!(F.Q, B)
2×2 Matrix{Float64}:
 3.0  4.0
 1.0  2.0
```
"""
lmul!(A, B)

# THE one big BLAS dispatch
@inline function generic_matmatmul!(C::StridedMatrix{T}, tA, tB, A::StridedVecOrMat{T}, B::StridedVecOrMat{T},
                                    _add::MulAddMul=MulAddMul()) where {T<:BlasFloat}
    if all(in(('N', 'T', 'C')), (tA, tB))
        if tA == 'T' && tB == 'N' && A === B
            return syrk_wrapper!(C, 'T', A, _add)
        elseif tA == 'N' && tB == 'T' && A === B
            return syrk_wrapper!(C, 'N', A, _add)
        elseif tA == 'C' && tB == 'N' && A === B
            return herk_wrapper!(C, 'C', A, _add)
        elseif tA == 'N' && tB == 'C' && A === B
            return herk_wrapper!(C, 'N', A, _add)
        else
            return gemm_wrapper!(C, tA, tB, A, B, _add)
        end
    end
    alpha, beta = promote(_add.alpha, _add.beta, zero(T))
    if alpha isa Union{Bool,T} && beta isa Union{Bool,T}
        if (tA == 'S' || tA == 's') && tB == 'N'
            return BLAS.symm!('L', tA == 'S' ? 'U' : 'L', alpha, A, B, beta, C)
        elseif (tB == 'S' || tB == 's') && tA == 'N'
            return BLAS.symm!('R', tB == 'S' ? 'U' : 'L', alpha, B, A, beta, C)
        elseif (tA == 'H' || tA == 'h') && tB == 'N'
            return BLAS.hemm!('L', tA == 'H' ? 'U' : 'L', alpha, A, B, beta, C)
        elseif (tB == 'H' || tB == 'h') && tA == 'N'
            return BLAS.hemm!('R', tB == 'H' ? 'U' : 'L', alpha, B, A, beta, C)
        end
    end
    return _generic_matmatmul!(C, 'N', 'N', wrap(A, tA), wrap(B, tB), _add)
end

# Complex matrix times (transposed) real matrix. Reinterpret the first matrix to real for efficiency.
@inline function generic_matmatmul!(C::StridedVecOrMat{Complex{T}}, tA, tB, A::StridedVecOrMat{Complex{T}}, B::StridedVecOrMat{T},
                    _add::MulAddMul=MulAddMul()) where {T<:BlasReal}
    if all(in(('N', 'T', 'C')), (tA, tB))
        gemm_wrapper!(C, tA, tB, A, B, _add)
    else
        _generic_matmatmul!(C, 'N', 'N', wrap(A, tA), wrap(B, tB), _add)
    end
end


# Supporting functions for matrix multiplication

# copy transposed(adjoint) of upper(lower) side-diagonals. Optionally include diagonal.
@inline function copytri!(A::AbstractMatrix, uplo::AbstractChar, conjugate::Bool=false, diag::Bool=false)
    n = checksquare(A)
    off = diag ? 0 : 1
    if uplo == 'U'
        for i = 1:n, j = (i+off):n
            A[j,i] = conjugate ? adjoint(A[i,j]) : transpose(A[i,j])
        end
    elseif uplo == 'L'
        for i = 1:n, j = (i+off):n
            A[i,j] = conjugate ? adjoint(A[j,i]) : transpose(A[j,i])
        end
    else
        throw(ArgumentError(lazy"uplo argument must be 'U' (upper) or 'L' (lower), got $uplo"))
    end
    A
end

function gemv!(y::StridedVector{T}, tA::AbstractChar, A::StridedVecOrMat{T}, x::StridedVector{T},
               α::Number=true, β::Number=false) where {T<:BlasFloat}
    mA, nA = lapack_size(tA, A)
    nA != length(x) &&
        throw(DimensionMismatch(lazy"second dimension of A, $nA, does not match length of x, $(length(x))"))
    mA != length(y) &&
        throw(DimensionMismatch(lazy"first dimension of A, $mA, does not match length of y, $(length(y))"))
    mA == 0 && return y
    nA == 0 && return _rmul_or_fill!(y, β)
    alpha, beta = promote(α, β, zero(T))
    if alpha isa Union{Bool,T} && beta isa Union{Bool,T} &&
        stride(A, 1) == 1 && abs(stride(A, 2)) >= size(A, 1) &&
        !iszero(stride(x, 1)) && # We only check input's stride here.
        if tA in ('N', 'T', 'C')
            return BLAS.gemv!(tA, alpha, A, x, beta, y)
        elseif tA in ('S', 's')
            return BLAS.symv!(tA == 'S' ? 'U' : 'L', alpha, A, x, beta, y)
        elseif tA in ('H', 'h')
            return BLAS.hemv!(tA == 'H' ? 'U' : 'L', alpha, A, x, beta, y)
        end
    end
    if tA in ('S', 's', 'H', 'h')
        # re-wrap again and use plain ('N') matvec mul algorithm,
        # because _generic_matvecmul! can't handle the HermOrSym cases specifically
        return _generic_matvecmul!(y, 'N', wrap(A, tA), x, MulAddMul(α, β))
    else
        return _generic_matvecmul!(y, tA, A, x, MulAddMul(α, β))
    end
end

function gemv!(y::StridedVector{Complex{T}}, tA::AbstractChar, A::StridedVecOrMat{Complex{T}}, x::StridedVector{T},
    α::Number = true, β::Number = false) where {T<:BlasReal}
    mA, nA = lapack_size(tA, A)
    nA != length(x) &&
        throw(DimensionMismatch(lazy"second dimension of A, $nA, does not match length of x, $(length(x))"))
    mA != length(y) &&
        throw(DimensionMismatch(lazy"first dimension of A, $mA, does not match length of y, $(length(y))"))
    mA == 0 && return y
    nA == 0 && return _rmul_or_fill!(y, β)
    alpha, beta = promote(α, β, zero(T))
    if alpha isa Union{Bool,T} && beta isa Union{Bool,T} &&
        stride(A, 1) == 1 && abs(stride(A, 2)) >= size(A, 1) &&
        stride(y, 1) == 1 && tA == 'N' && # reinterpret-based optimization is valid only for contiguous `y`
        !iszero(stride(x, 1))
        BLAS.gemv!(tA, alpha, reinterpret(T, A), x, beta, reinterpret(T, y))
        return y
    else
        Anew, ta = tA in ('S', 's', 'H', 'h') ? (wrap(A, tA), 'N') : (A, tA)
        return _generic_matvecmul!(y, ta, Anew, x, MulAddMul(α, β))
    end
end

function gemv!(y::StridedVector{Complex{T}}, tA::AbstractChar, A::StridedVecOrMat{T}, x::StridedVector{Complex{T}},
    α::Number = true, β::Number = false) where {T<:BlasFloat}
    mA, nA = lapack_size(tA, A)
    nA != length(x) &&
        throw(DimensionMismatch(lazy"second dimension of A, $nA, does not match length of x, $(length(x))"))
    mA != length(y) &&
        throw(DimensionMismatch(lazy"first dimension of A, $mA, does not match length of y, $(length(y))"))
    mA == 0 && return y
    nA == 0 && return _rmul_or_fill!(y, β)
    alpha, beta = promote(α, β, zero(T))
    @views if alpha isa Union{Bool,T} && beta isa Union{Bool,T} &&
        stride(A, 1) == 1 && abs(stride(A, 2)) >= size(A, 1) &&
        !iszero(stride(x, 1)) && tA in ('N', 'T', 'C')
        xfl = reinterpret(reshape, T, x) # Use reshape here.
        yfl = reinterpret(reshape, T, y)
        BLAS.gemv!(tA, alpha, A, xfl[1, :], beta, yfl[1, :])
        BLAS.gemv!(tA, alpha, A, xfl[2, :], beta, yfl[2, :])
        return y
    elseif tA in ('S', 's', 'H', 'h')
        # re-wrap again and use plain ('N') matvec mul algorithm,
        # because _generic_matvecmul! can't handle the HermOrSym cases specifically
        return _generic_matvecmul!(y, 'N', wrap(A, tA), x, MulAddMul(α, β))
    else
        return _generic_matvecmul!(y, tA, A, x, MulAddMul(α, β))
    end
end

function syrk_wrapper!(C::StridedMatrix{T}, tA::AbstractChar, A::StridedVecOrMat{T},
        _add = MulAddMul()) where {T<:BlasFloat}
    nC = checksquare(C)
    if tA == 'T'
        (nA, mA) = size(A,1), size(A,2)
        tAt = 'N'
    else
        (mA, nA) = size(A,1), size(A,2)
        tAt = 'T'
    end
    if nC != mA
        throw(DimensionMismatch(lazy"output matrix has size: $(nC), but should have size $(mA)"))
    end
    if mA == 0 || nA == 0 || iszero(_add.alpha)
        return _rmul_or_fill!(C, _add.beta)
    end
    if mA == 2 && nA == 2
        return matmul2x2!(C, tA, tAt, A, A, _add)
    end
    if mA == 3 && nA == 3
        return matmul3x3!(C, tA, tAt, A, A, _add)
    end

    # BLAS.syrk! only updates symmetric C
    # alternatively, make non-zero β a show-stopper for BLAS.syrk!
    if iszero(_add.beta) || issymmetric(C)
        alpha, beta = promote(_add.alpha, _add.beta, zero(T))
        if (alpha isa Union{Bool,T} &&
            beta isa Union{Bool,T} &&
            stride(A, 1) == stride(C, 1) == 1 &&
            stride(A, 2) >= size(A, 1) &&
            stride(C, 2) >= size(C, 1))
            return copytri!(BLAS.syrk!('U', tA, alpha, A, beta, C), 'U')
        end
    end
    return gemm_wrapper!(C, tA, tAt, A, A, _add)
end

function herk_wrapper!(C::Union{StridedMatrix{T}, StridedMatrix{Complex{T}}}, tA::AbstractChar, A::Union{StridedVecOrMat{T}, StridedVecOrMat{Complex{T}}},
        _add = MulAddMul()) where {T<:BlasReal}
    nC = checksquare(C)
    if tA == 'C'
        (nA, mA) = size(A,1), size(A,2)
        tAt = 'N'
    else
        (mA, nA) = size(A,1), size(A,2)
        tAt = 'C'
    end
    if nC != mA
        throw(DimensionMismatch(lazy"output matrix has size: $(nC), but should have size $(mA)"))
    end
    if mA == 0 || nA == 0 || iszero(_add.alpha)
        return _rmul_or_fill!(C, _add.beta)
    end
    if mA == 2 && nA == 2
        return matmul2x2!(C, tA, tAt, A, A, _add)
    end
    if mA == 3 && nA == 3
        return matmul3x3!(C, tA, tAt, A, A, _add)
    end

    # Result array does not need to be initialized as long as beta==0
    #    C = Matrix{T}(undef, mA, mA)

    if iszero(_add.beta) || issymmetric(C)
        alpha, beta = promote(_add.alpha, _add.beta, zero(T))
        if (alpha isa Union{Bool,T} &&
            beta isa Union{Bool,T} &&
            stride(A, 1) == stride(C, 1) == 1 &&
            stride(A, 2) >= size(A, 1) &&
            stride(C, 2) >= size(C, 1))
            return copytri!(BLAS.herk!('U', tA, alpha, A, beta, C), 'U', true)
        end
    end
    return gemm_wrapper!(C, tA, tAt, A, A, _add)
end

function gemm_wrapper(tA::AbstractChar, tB::AbstractChar,
                      A::StridedVecOrMat{T},
                      B::StridedVecOrMat{T}) where {T<:BlasFloat}
    mA, nA = lapack_size(tA, A)
    mB, nB = lapack_size(tB, B)
    C = similar(B, T, mA, nB)
    if all(in(('N', 'T', 'C')), (tA, tB))
        gemm_wrapper!(C, tA, tB, A, B)
    else
        _generic_matmatmul!(C, 'N', 'N', wrap(A, tA), wrap(B, tB), _add)
    end
end

function gemm_wrapper!(C::StridedVecOrMat{T}, tA::AbstractChar, tB::AbstractChar,
                       A::StridedVecOrMat{T}, B::StridedVecOrMat{T},
                       _add = MulAddMul()) where {T<:BlasFloat}
    mA, nA = lapack_size(tA, A)
    mB, nB = lapack_size(tB, B)

    if nA != mB
        throw(DimensionMismatch(lazy"A has dimensions ($mA,$nA) but B has dimensions ($mB,$nB)"))
    end

    if C === A || B === C
        throw(ArgumentError("output matrix must not be aliased with input matrix"))
    end

    if mA == 0 || nA == 0 || nB == 0 || iszero(_add.alpha)
        if size(C) != (mA, nB)
            throw(DimensionMismatch(lazy"C has dimensions $(size(C)), should have ($mA,$nB)"))
        end
        return _rmul_or_fill!(C, _add.beta)
    end

    if mA == 2 && nA == 2 && nB == 2
        return matmul2x2!(C, tA, tB, A, B, _add)
    end
    if mA == 3 && nA == 3 && nB == 3
        return matmul3x3!(C, tA, tB, A, B, _add)
    end

    alpha, beta = promote(_add.alpha, _add.beta, zero(T))
    if (alpha isa Union{Bool,T} &&
        beta isa Union{Bool,T} &&
        stride(A, 1) == stride(B, 1) == stride(C, 1) == 1 &&
        stride(A, 2) >= size(A, 1) &&
        stride(B, 2) >= size(B, 1) &&
        stride(C, 2) >= size(C, 1))
        return BLAS.gemm!(tA, tB, alpha, A, B, beta, C)
    end
    _generic_matmatmul!(C, tA, tB, A, B, _add)
end

function gemm_wrapper!(C::StridedVecOrMat{Complex{T}}, tA::AbstractChar, tB::AbstractChar,
                       A::StridedVecOrMat{Complex{T}}, B::StridedVecOrMat{T},
                       _add = MulAddMul()) where {T<:BlasReal}
    mA, nA = lapack_size(tA, A)
    mB, nB = lapack_size(tB, B)

    if nA != mB
        throw(DimensionMismatch(lazy"A has dimensions ($mA,$nA) but B has dimensions ($mB,$nB)"))
    end

    if C === A || B === C
        throw(ArgumentError("output matrix must not be aliased with input matrix"))
    end

    if mA == 0 || nA == 0 || nB == 0 || iszero(_add.alpha)
        if size(C) != (mA, nB)
            throw(DimensionMismatch(lazy"C has dimensions $(size(C)), should have ($mA,$nB)"))
        end
        return _rmul_or_fill!(C, _add.beta)
    end

    if mA == 2 && nA == 2 && nB == 2
        return matmul2x2!(C, tA, tB, A, B, _add)
    end
    if mA == 3 && nA == 3 && nB == 3
        return matmul3x3!(C, tA, tB, A, B, _add)
    end

    alpha, beta = promote(_add.alpha, _add.beta, zero(T))

    # Make-sure reinterpret-based optimization is BLAS-compatible.
    if (alpha isa Union{Bool,T} &&
        beta isa Union{Bool,T} &&
        stride(A, 1) == stride(B, 1) == stride(C, 1) == 1 &&
        stride(A, 2) >= size(A, 1) &&
        stride(B, 2) >= size(B, 1) &&
        stride(C, 2) >= size(C, 1) && tA == 'N')
        BLAS.gemm!(tA, tB, alpha, reinterpret(T, A), B, beta, reinterpret(T, C))
        return C
    end
    _generic_matmatmul!(C, tA, tB, A, B, _add)
end

# blas.jl defines matmul for floats; other integer and mixed precision
# cases are handled here

lapack_size(t::AbstractChar, M::AbstractVecOrMat) = (size(M, t=='N' ? 1 : 2), size(M, t=='N' ? 2 : 1))

function copyto!(B::AbstractVecOrMat, ir_dest::AbstractUnitRange{Int}, jr_dest::AbstractUnitRange{Int}, tM::AbstractChar, M::AbstractVecOrMat, ir_src::AbstractUnitRange{Int}, jr_src::AbstractUnitRange{Int})
    if tM == 'N'
        copyto!(B, ir_dest, jr_dest, M, ir_src, jr_src)
    else
        LinearAlgebra.copy_transpose!(B, ir_dest, jr_dest, M, jr_src, ir_src)
        tM == 'C' && conj!(@view B[ir_dest, jr_dest])
    end
    B
end

function copy_transpose!(B::AbstractMatrix, ir_dest::AbstractUnitRange{Int}, jr_dest::AbstractUnitRange{Int}, tM::AbstractChar, M::AbstractVecOrMat, ir_src::AbstractUnitRange{Int}, jr_src::AbstractUnitRange{Int})
    if tM == 'N'
        LinearAlgebra.copy_transpose!(B, ir_dest, jr_dest, M, ir_src, jr_src)
    else
        copyto!(B, ir_dest, jr_dest, M, jr_src, ir_src)
        tM == 'C' && conj!(@view B[ir_dest, jr_dest])
    end
    B
end

# TODO: It will be faster for large matrices to convert to float,
# call BLAS, and convert back to required type.

# NOTE: the generic version is also called as fallback for
#       strides != 1 cases

@inline function generic_matvecmul!(C::AbstractVector, tA, A::AbstractVecOrMat, B::AbstractVector,
                                    _add::MulAddMul = MulAddMul())
    Anew, ta = tA in ('S', 's', 'H', 'h') ? (wrap(A, tA), 'N') : (A, tA)
    return _generic_matvecmul!(C, ta, Anew, B, _add)
end

function _generic_matvecmul!(C::AbstractVector, tA, A::AbstractVecOrMat, B::AbstractVector,
                            _add::MulAddMul = MulAddMul())
    require_one_based_indexing(C, A, B)
    @assert tA in ('N', 'T', 'C')
    mB = length(B)
    mA, nA = lapack_size(tA, A)
    if mB != nA
        throw(DimensionMismatch(lazy"matrix A has dimensions ($mA,$nA), vector B has length $mB"))
    end
    if mA != length(C)
        throw(DimensionMismatch(lazy"result C has length $(length(C)), needs length $mA"))
    end

    Astride = size(A, 1)

    @inbounds begin
    if tA == 'T'  # fastest case
        if nA == 0
            for k = 1:mA
                _modify!(_add, false, C, k)
            end
        else
            for k = 1:mA
                aoffs = (k-1)*Astride
                s = zero(A[aoffs + 1]*B[1] + A[aoffs + 1]*B[1])
                for i = 1:nA
                    s += transpose(A[aoffs+i]) * B[i]
                end
                _modify!(_add, s, C, k)
            end
        end
    elseif tA == 'C'
        if nA == 0
            for k = 1:mA
                _modify!(_add, false, C, k)
            end
        else
            for k = 1:mA
                aoffs = (k-1)*Astride
                s = zero(A[aoffs + 1]*B[1] + A[aoffs + 1]*B[1])
                for i = 1:nA
                    s += A[aoffs + i]'B[i]
                end
                _modify!(_add, s, C, k)
            end
        end
    else # tA == 'N'
        for i = 1:mA
            if !iszero(_add.beta)
                C[i] *= _add.beta
            elseif mB == 0
                C[i] = false
            else
                C[i] = zero(A[i]*B[1] + A[i]*B[1])
            end
        end
        for k = 1:mB
            aoffs = (k-1)*Astride
            b = _add(B[k])
            for i = 1:mA
                C[i] += A[aoffs + i] * b
            end
        end
    end
    end # @inbounds
    C
end

function generic_matmatmul(tA, tB, A::AbstractVecOrMat{T}, B::AbstractMatrix{S}) where {T,S}
    mA, nA = lapack_size(tA, A)
    mB, nB = lapack_size(tB, B)
    C = similar(B, promote_op(matprod, T, S), mA, nB)
    generic_matmatmul!(C, tA, tB, A, B)
end

const tilebufsize = 10800  # Approximately 32k/3

function generic_matmatmul!(C::AbstractVecOrMat, tA, tB, A::AbstractVecOrMat, B::AbstractVecOrMat, _add::MulAddMul)
    mA, nA = lapack_size(tA, A)
    mB, nB = lapack_size(tB, B)
    mC, nC = size(C)

    if iszero(_add.alpha)
        return _rmul_or_fill!(C, _add.beta)
    end
    if mA == nA == mB == nB == mC == nC == 2
        return matmul2x2!(C, tA, tB, A, B, _add)
    end
    if mA == nA == mB == nB == mC == nC == 3
        return matmul3x3!(C, tA, tB, A, B, _add)
    end
    A, tA = tA in ('H', 'h', 'S', 's') ? (wrap(A, tA), 'N') : (A, tA)
    B, tB = tB in ('H', 'h', 'S', 's') ? (wrap(B, tB), 'N') : (B, tB)
    _generic_matmatmul!(C, tA, tB, A, B, _add)
end

function _generic_matmatmul!(C::AbstractVecOrMat{R}, tA, tB, A::AbstractVecOrMat{T}, B::AbstractVecOrMat{S},
                             _add::MulAddMul) where {T,S,R}
    @assert tA in ('N', 'T', 'C') && tB in ('N', 'T', 'C')
    require_one_based_indexing(C, A, B)

    mA, nA = lapack_size(tA, A)
    mB, nB = lapack_size(tB, B)
    if mB != nA
        throw(DimensionMismatch(lazy"matrix A has dimensions ($mA,$nA), matrix B has dimensions ($mB,$nB)"))
    end
    if size(C,1) != mA || size(C,2) != nB
        throw(DimensionMismatch(lazy"result C has dimensions $(size(C)), needs ($mA,$nB)"))
    end

    if iszero(_add.alpha) || isempty(A) || isempty(B)
        return _rmul_or_fill!(C, _add.beta)
    end

    tile_size = 0
    if isbitstype(R) && isbitstype(T) && isbitstype(S) && (tA == 'N' || tB != 'N')
        tile_size = floor(Int, sqrt(tilebufsize / max(sizeof(R), sizeof(S), sizeof(T), 1)))
    end
    @inbounds begin
    if tile_size > 0
        sz = (tile_size, tile_size)
        Atile = Array{T}(undef, sz)
        Btile = Array{S}(undef, sz)

        z1 = zero(A[1, 1]*B[1, 1] + A[1, 1]*B[1, 1])
        z = convert(promote_type(typeof(z1), R), z1)

        if mA < tile_size && nA < tile_size && nB < tile_size
            copy_transpose!(Atile, 1:nA, 1:mA, tA, A, 1:mA, 1:nA)
            copyto!(Btile, 1:mB, 1:nB, tB, B, 1:mB, 1:nB)
            for j = 1:nB
                boff = (j-1)*tile_size
                for i = 1:mA
                    aoff = (i-1)*tile_size
                    s = z
                    for k = 1:nA
                        s += Atile[aoff+k] * Btile[boff+k]
                    end
                    _modify!(_add, s, C, (i,j))
                end
            end
        else
            Ctile = Array{R}(undef, sz)
            for jb = 1:tile_size:nB
                jlim = min(jb+tile_size-1,nB)
                jlen = jlim-jb+1
                for ib = 1:tile_size:mA
                    ilim = min(ib+tile_size-1,mA)
                    ilen = ilim-ib+1
                    fill!(Ctile, z)
                    for kb = 1:tile_size:nA
                        klim = min(kb+tile_size-1,mB)
                        klen = klim-kb+1
                        copy_transpose!(Atile, 1:klen, 1:ilen, tA, A, ib:ilim, kb:klim)
                        copyto!(Btile, 1:klen, 1:jlen, tB, B, kb:klim, jb:jlim)
                        for j=1:jlen
                            bcoff = (j-1)*tile_size
                            for i = 1:ilen
                                aoff = (i-1)*tile_size
                                s = z
                                for k = 1:klen
                                    s += Atile[aoff+k] * Btile[bcoff+k]
                                end
                                Ctile[bcoff+i] += s
                            end
                        end
                    end
                    if isone(_add.alpha) && iszero(_add.beta)
                        copyto!(C, ib:ilim, jb:jlim, Ctile, 1:ilen, 1:jlen)
                    else
                        C[ib:ilim, jb:jlim] .= @views _add.(Ctile[1:ilen, 1:jlen], C[ib:ilim, jb:jlim])
                    end
                end
            end
        end
    else
        # Multiplication for non-plain-data uses the naive algorithm
        if tA == 'N'
            if tB == 'N'
                for i = 1:mA, j = 1:nB
                    z2 = zero(A[i, 1]*B[1, j] + A[i, 1]*B[1, j])
                    Ctmp = convert(promote_type(R, typeof(z2)), z2)
                    for k = 1:nA
                        Ctmp += A[i, k]*B[k, j]
                    end
                    _modify!(_add, Ctmp, C, (i,j))
                end
            elseif tB == 'T'
                for i = 1:mA, j = 1:nB
                    z2 = zero(A[i, 1]*transpose(B[j, 1]) + A[i, 1]*transpose(B[j, 1]))
                    Ctmp = convert(promote_type(R, typeof(z2)), z2)
                    for k = 1:nA
                        Ctmp += A[i, k] * transpose(B[j, k])
                    end
                    _modify!(_add, Ctmp, C, (i,j))
                end
            else
                for i = 1:mA, j = 1:nB
                    z2 = zero(A[i, 1]*B[j, 1]' + A[i, 1]*B[j, 1]')
                    Ctmp = convert(promote_type(R, typeof(z2)), z2)
                    for k = 1:nA
                        Ctmp += A[i, k]*B[j, k]'
                    end
                    _modify!(_add, Ctmp, C, (i,j))
                end
            end
        elseif tA == 'T'
            if tB == 'N'
                for i = 1:mA, j = 1:nB
                    z2 = zero(transpose(A[1, i])*B[1, j] + transpose(A[1, i])*B[1, j])
                    Ctmp = convert(promote_type(R, typeof(z2)), z2)
                    for k = 1:nA
                        Ctmp += transpose(A[k, i]) * B[k, j]
                    end
                    _modify!(_add, Ctmp, C, (i,j))
                end
            elseif tB == 'T'
                for i = 1:mA, j = 1:nB
                    z2 = zero(transpose(A[1, i])*transpose(B[j, 1]) + transpose(A[1, i])*transpose(B[j, 1]))
                    Ctmp = convert(promote_type(R, typeof(z2)), z2)
                    for k = 1:nA
                        Ctmp += transpose(A[k, i]) * transpose(B[j, k])
                    end
                    _modify!(_add, Ctmp, C, (i,j))
                end
            else
                for i = 1:mA, j = 1:nB
                    z2 = zero(transpose(A[1, i])*B[j, 1]' + transpose(A[1, i])*B[j, 1]')
                    Ctmp = convert(promote_type(R, typeof(z2)), z2)
                    for k = 1:nA
                        Ctmp += transpose(A[k, i]) * adjoint(B[j, k])
                    end
                    _modify!(_add, Ctmp, C, (i,j))
                end
            end
        else
            if tB == 'N'
                for i = 1:mA, j = 1:nB
                    z2 = zero(A[1, i]'*B[1, j] + A[1, i]'*B[1, j])
                    Ctmp = convert(promote_type(R, typeof(z2)), z2)
                    for k = 1:nA
                        Ctmp += A[k, i]'B[k, j]
                    end
                    _modify!(_add, Ctmp, C, (i,j))
                end
            elseif tB == 'T'
                for i = 1:mA, j = 1:nB
                    z2 = zero(A[1, i]'*transpose(B[j, 1]) + A[1, i]'*transpose(B[j, 1]))
                    Ctmp = convert(promote_type(R, typeof(z2)), z2)
                    for k = 1:nA
                        Ctmp += adjoint(A[k, i]) * transpose(B[j, k])
                    end
                    _modify!(_add, Ctmp, C, (i,j))
                end
            else
                for i = 1:mA, j = 1:nB
                    z2 = zero(A[1, i]'*B[j, 1]' + A[1, i]'*B[j, 1]')
                    Ctmp = convert(promote_type(R, typeof(z2)), z2)
                    for k = 1:nA
                        Ctmp += A[k, i]'B[j, k]'
                    end
                    _modify!(_add, Ctmp, C, (i,j))
                end
            end
        end
    end
    end # @inbounds
    C
end


# multiply 2x2 matrices
function matmul2x2(tA, tB, A::AbstractMatrix{T}, B::AbstractMatrix{S}) where {T,S}
    matmul2x2!(similar(B, promote_op(matprod, T, S), 2, 2), tA, tB, A, B)
end

function matmul2x2!(C::AbstractMatrix, tA, tB, A::AbstractMatrix, B::AbstractMatrix,
                    _add::MulAddMul = MulAddMul())
    require_one_based_indexing(C, A, B)
    if !(size(A) == size(B) == size(C) == (2,2))
        throw(DimensionMismatch(lazy"A has size $(size(A)), B has size $(size(B)), C has size $(size(C))"))
    end
    @inbounds begin
    if tA == 'N'
        A11 = A[1,1]; A12 = A[1,2]; A21 = A[2,1]; A22 = A[2,2]
    elseif tA == 'T'
        # TODO making these lazy could improve perf
        A11 = copy(transpose(A[1,1])); A12 = copy(transpose(A[2,1]))
        A21 = copy(transpose(A[1,2])); A22 = copy(transpose(A[2,2]))
    elseif tA == 'C'
        # TODO making these lazy could improve perf
        A11 = copy(A[1,1]'); A12 = copy(A[2,1]')
        A21 = copy(A[1,2]'); A22 = copy(A[2,2]')
    elseif tA == 'S'
        A11 = symmetric(A[1,1], :U); A12 = A[1,2]
        A21 = copy(transpose(A[1,2])); A22 = symmetric(A[2,2], :U)
    elseif tA == 's'
        A11 = symmetric(A[1,1], :L); A12 = copy(transpose(A[2,1]))
        A21 = A[2,1]; A22 = symmetric(A[2,2], :L)
    elseif tA == 'H'
        A11 = hermitian(A[1,1], :U); A12 = A[1,2]
        A21 = copy(adjoint(A[1,2])); A22 = hermitian(A[2,2], :U)
    else # if tA == 'h'
        A11 = hermitian(A[1,1], :L); A12 = copy(adjoint(A[2,1]))
        A21 = A[2,1]; A22 = hermitian(A[2,2], :L)
    end
    if tB == 'N'
        B11 = B[1,1]; B12 = B[1,2];
        B21 = B[2,1]; B22 = B[2,2]
    elseif tB == 'T'
        # TODO making these lazy could improve perf
        B11 = copy(transpose(B[1,1])); B12 = copy(transpose(B[2,1]))
        B21 = copy(transpose(B[1,2])); B22 = copy(transpose(B[2,2]))
    elseif tB == 'C'
        # TODO making these lazy could improve perf
        B11 = copy(B[1,1]'); B12 = copy(B[2,1]')
        B21 = copy(B[1,2]'); B22 = copy(B[2,2]')
    elseif tB == 'S'
        B11 = symmetric(B[1,1], :U); B12 = B[1,2]
        B21 = copy(transpose(B[1,2])); B22 = symmetric(B[2,2], :U)
    elseif tB == 's'
        B11 = symmetric(B[1,1], :L); B12 = copy(transpose(B[2,1]))
        B21 = B[2,1]; B22 = symmetric(B[2,2], :L)
    elseif tB == 'H'
        B11 = hermitian(B[1,1], :U); B12 = B[1,2]
        B21 = copy(adjoint(B[1,2])); B22 = hermitian(B[2,2], :U)
    else # if tB == 'h'
        B11 = hermitian(B[1,1], :L); B12 = copy(adjoint(B[2,1]))
        B21 = B[2,1]; B22 = hermitian(B[2,2], :L)
    end
    _modify!(_add, A11*B11 + A12*B21, C, (1,1))
    _modify!(_add, A11*B12 + A12*B22, C, (1,2))
    _modify!(_add, A21*B11 + A22*B21, C, (2,1))
    _modify!(_add, A21*B12 + A22*B22, C, (2,2))
    end # inbounds
    C
end

# Multiply 3x3 matrices
function matmul3x3(tA, tB, A::AbstractMatrix{T}, B::AbstractMatrix{S}) where {T,S}
    matmul3x3!(similar(B, promote_op(matprod, T, S), 3, 3), tA, tB, A, B)
end

function matmul3x3!(C::AbstractMatrix, tA, tB, A::AbstractMatrix, B::AbstractMatrix,
                    _add::MulAddMul = MulAddMul())
    require_one_based_indexing(C, A, B)
    if !(size(A) == size(B) == size(C) == (3,3))
        throw(DimensionMismatch(lazy"A has size $(size(A)), B has size $(size(B)), C has size $(size(C))"))
    end
    @inbounds begin
    if tA == 'N'
        A11 = A[1,1]; A12 = A[1,2]; A13 = A[1,3]
        A21 = A[2,1]; A22 = A[2,2]; A23 = A[2,3]
        A31 = A[3,1]; A32 = A[3,2]; A33 = A[3,3]
    elseif tA == 'T'
        # TODO making these lazy could improve perf
        A11 = copy(transpose(A[1,1])); A12 = copy(transpose(A[2,1])); A13 = copy(transpose(A[3,1]))
        A21 = copy(transpose(A[1,2])); A22 = copy(transpose(A[2,2])); A23 = copy(transpose(A[3,2]))
        A31 = copy(transpose(A[1,3])); A32 = copy(transpose(A[2,3])); A33 = copy(transpose(A[3,3]))
    elseif tA == 'C'
        # TODO making these lazy could improve perf
        A11 = copy(A[1,1]'); A12 = copy(A[2,1]'); A13 = copy(A[3,1]')
        A21 = copy(A[1,2]'); A22 = copy(A[2,2]'); A23 = copy(A[3,2]')
        A31 = copy(A[1,3]'); A32 = copy(A[2,3]'); A33 = copy(A[3,3]')
    elseif tA == 'S'
        A11 = symmetric(A[1,1], :U); A12 = A[1,2]; A13 = A[1,3]
        A21 = copy(transpose(A[1,2])); A22 = symmetric(A[2,2], :U); A23 = A[2,3]
        A31 = copy(transpose(A[1,3])); A32 = copy(transpose(A[2,3])); A33 = symmetric(A[3,3], :U)
    elseif tA == 's'
        A11 = symmetric(A[1,1], :L); A12 = copy(transpose(A[2,1])); A13 = copy(transpose(A[3,1]))
        A21 = A[2,1]; A22 = symmetric(A[2,2], :L); A23 = copy(transpose(A[3,2]))
        A31 = A[3,1]; A32 = A[3,2]; A33 = symmetric(A[3,3], :L)
    elseif tA == 'H'
        A11 = hermitian(A[1,1], :U); A12 = A[1,2]; A13 = A[1,3]
        A21 = copy(adjoint(A[1,2])); A22 = hermitian(A[2,2], :U); A23 = A[2,3]
        A31 = copy(adjoint(A[1,3])); A32 = copy(adjoint(A[2,3])); A33 = hermitian(A[3,3], :U)
    else # if tA == 'h'
        A11 = hermitian(A[1,1], :L); A12 = copy(adjoint(A[2,1])); A13 = copy(adjoint(A[3,1]))
        A21 = A[2,1]; A22 = hermitian(A[2,2], :L); A23 = copy(adjoint(A[3,2]))
        A31 = A[3,1]; A32 = A[3,2]; A33 = hermitian(A[3,3], :L)
    end

    if tB == 'N'
        B11 = B[1,1]; B12 = B[1,2]; B13 = B[1,3]
        B21 = B[2,1]; B22 = B[2,2]; B23 = B[2,3]
        B31 = B[3,1]; B32 = B[3,2]; B33 = B[3,3]
    elseif tB == 'T'
        # TODO making these lazy could improve perf
        B11 = copy(transpose(B[1,1])); B12 = copy(transpose(B[2,1])); B13 = copy(transpose(B[3,1]))
        B21 = copy(transpose(B[1,2])); B22 = copy(transpose(B[2,2])); B23 = copy(transpose(B[3,2]))
        B31 = copy(transpose(B[1,3])); B32 = copy(transpose(B[2,3])); B33 = copy(transpose(B[3,3]))
    elseif tB == 'C'
        # TODO making these lazy could improve perf
        B11 = copy(B[1,1]'); B12 = copy(B[2,1]'); B13 = copy(B[3,1]')
        B21 = copy(B[1,2]'); B22 = copy(B[2,2]'); B23 = copy(B[3,2]')
        B31 = copy(B[1,3]'); B32 = copy(B[2,3]'); B33 = copy(B[3,3]')
    elseif tB == 'S'
        B11 = symmetric(B[1,1], :U); B12 = B[1,2]; B13 = B[1,3]
        B21 = copy(transpose(B[1,2])); B22 = symmetric(B[2,2], :U); B23 = B[2,3]
        B31 = copy(transpose(B[1,3])); B32 = copy(transpose(B[2,3])); B33 = symmetric(B[3,3], :U)
    elseif tB == 's'
        B11 = symmetric(B[1,1], :L); B12 = copy(transpose(B[2,1])); B13 = copy(transpose(B[3,1]))
        B21 = B[2,1]; B22 = symmetric(B[2,2], :L); B23 = copy(transpose(B[3,2]))
        B31 = B[3,1]; B32 = B[3,2]; B33 = symmetric(B[3,3], :L)
    elseif tB == 'H'
        B11 = hermitian(B[1,1], :U); B12 = B[1,2]; B13 = B[1,3]
        B21 = copy(adjoint(B[1,2])); B22 = hermitian(B[2,2], :U); B23 = B[2,3]
        B31 = copy(adjoint(B[1,3])); B32 = copy(adjoint(B[2,3])); B33 = hermitian(B[3,3], :U)
    else # if tB == 'h'
        B11 = hermitian(B[1,1], :L); B12 = copy(adjoint(B[2,1])); B13 = copy(adjoint(B[3,1]))
        B21 = B[2,1]; B22 = hermitian(B[2,2], :L); B23 = copy(adjoint(B[3,2]))
        B31 = B[3,1]; B32 = B[3,2]; B33 = hermitian(B[3,3], :L)
    end

    _modify!(_add, A11*B11 + A12*B21 + A13*B31, C, (1,1))
    _modify!(_add, A11*B12 + A12*B22 + A13*B32, C, (1,2))
    _modify!(_add, A11*B13 + A12*B23 + A13*B33, C, (1,3))

    _modify!(_add, A21*B11 + A22*B21 + A23*B31, C, (2,1))
    _modify!(_add, A21*B12 + A22*B22 + A23*B32, C, (2,2))
    _modify!(_add, A21*B13 + A22*B23 + A23*B33, C, (2,3))

    _modify!(_add, A31*B11 + A32*B21 + A33*B31, C, (3,1))
    _modify!(_add, A31*B12 + A32*B22 + A33*B32, C, (3,2))
    _modify!(_add, A31*B13 + A32*B23 + A33*B33, C, (3,3))
    end # inbounds
    C
end

const RealOrComplex = Union{Real,Complex}

# Three-argument *
"""
    *(A, B::AbstractMatrix, C)
    A * B * C * D

Chained multiplication of 3 or 4 matrices is done in the most efficient sequence,
based on the sizes of the arrays. That is, the number of scalar multiplications needed
for `(A * B) * C` (with 3 dense matrices) is compared to that for `A * (B * C)`
to choose which of these to execute.

If the last factor is a vector, or the first a transposed vector, then it is efficient
to deal with these first. In particular `x' * B * y` means `(x' * B) * y`
for an ordinary column-major `B::Matrix`. Unlike `dot(x, B, y)`, this
allocates an intermediate array.

If the first or last factor is a number, this will be fused with the matrix
multiplication, using 5-arg [`mul!`](@ref).

See also [`muladd`](@ref), [`dot`](@ref).

!!! compat "Julia 1.7"
    These optimisations require at least Julia 1.7.
"""
*(A::AbstractMatrix, B::AbstractMatrix, x::AbstractVector) = A * (B*x)

*(tu::AdjOrTransAbsVec, B::AbstractMatrix, v::AbstractVector) = (tu*B) * v
*(tu::AdjOrTransAbsVec, B::AdjOrTransAbsMat, v::AbstractVector) = tu * (B*v)

*(A::AbstractMatrix, x::AbstractVector, γ::Number) = mat_vec_scalar(A,x,γ)
*(A::AbstractMatrix, B::AbstractMatrix, γ::Number) = mat_mat_scalar(A,B,γ)
*(α::RealOrComplex, B::AbstractMatrix{<:RealOrComplex}, C::AbstractVector{<:RealOrComplex}) =
    mat_vec_scalar(B,C,α)
*(α::RealOrComplex, B::AbstractMatrix{<:RealOrComplex}, C::AbstractMatrix{<:RealOrComplex}) =
    mat_mat_scalar(B,C,α)

*(α::Number, u::AbstractVector, tv::AdjOrTransAbsVec) = broadcast(*, α, u, tv)
*(u::AbstractVector, tv::AdjOrTransAbsVec, γ::Number) = broadcast(*, u, tv, γ)
*(u::AbstractVector, tv::AdjOrTransAbsVec, C::AbstractMatrix) = u * (tv*C)

*(A::AbstractMatrix, B::AbstractMatrix, C::AbstractMatrix) = _tri_matmul(A,B,C)
*(tv::AdjOrTransAbsVec, B::AbstractMatrix, C::AbstractMatrix) = (tv*B) * C

function _tri_matmul(A,B,C,δ=nothing)
    n,m = size(A)
    # m,k == size(B)
    k,l = size(C)
    costAB_C = n*m*k + n*k*l  # multiplications, allocations n*k + n*l
    costA_BC = m*k*l + n*m*l  #                              m*l + n*l
    if costA_BC < costAB_C
        isnothing(δ) ? A * (B*C) : A * mat_mat_scalar(B,C,δ)
    else
        isnothing(δ) ? (A*B) * C : mat_mat_scalar(A*B, C, δ)
    end
end

# Fast path for two arrays * one scalar is opt-in, via mat_vec_scalar and mat_mat_scalar.

mat_vec_scalar(A, x, γ) = A * (x * γ)  # fallback
mat_vec_scalar(A::StridedMaybeAdjOrTransMat, x::StridedVector, γ) = _mat_vec_scalar(A, x, γ)
mat_vec_scalar(A::AdjOrTransAbsVec, x::StridedVector, γ) = (A * x) * γ

function _mat_vec_scalar(A, x, γ)
    T = promote_type(eltype(A), eltype(x), typeof(γ))
    C = similar(A, T, axes(A,1))
    mul!(C, A, x, γ, false)
end

mat_mat_scalar(A, B, γ) = (A*B) * γ # fallback
mat_mat_scalar(A::StridedMaybeAdjOrTransMat, B::StridedMaybeAdjOrTransMat, γ) =
    _mat_mat_scalar(A, B, γ)

function _mat_mat_scalar(A, B, γ)
    T = promote_type(eltype(A), eltype(B), typeof(γ))
    C = similar(A, T, axes(A,1), axes(B,2))
    mul!(C, A, B, γ, false)
end

mat_mat_scalar(A::AdjointAbsVec, B, γ) = (γ' * (A * B)')' # preserving order, adjoint reverses
mat_mat_scalar(A::AdjointAbsVec{<:RealOrComplex}, B::StridedMaybeAdjOrTransMat{<:RealOrComplex}, γ::RealOrComplex) =
    mat_vec_scalar(B', A', γ')'

mat_mat_scalar(A::TransposeAbsVec, B, γ) = transpose(γ * transpose(A * B))
mat_mat_scalar(A::TransposeAbsVec{<:RealOrComplex}, B::StridedMaybeAdjOrTransMat{<:RealOrComplex}, γ::RealOrComplex) =
    transpose(mat_vec_scalar(transpose(B), transpose(A), γ))


# Four-argument *, by type
*(α::Number, β::Number, C::AbstractMatrix, x::AbstractVector) = (α*β) * C * x
*(α::Number, β::Number, C::AbstractMatrix, D::AbstractMatrix) = (α*β) * C * D
*(α::Number, B::AbstractMatrix, C::AbstractMatrix, x::AbstractVector) = α * B * (C*x)
*(α::Number, vt::AdjOrTransAbsVec, C::AbstractMatrix, x::AbstractVector) = α * (vt*C*x)
*(α::RealOrComplex, vt::AdjOrTransAbsVec{<:RealOrComplex}, C::AbstractMatrix{<:RealOrComplex}, D::AbstractMatrix{<:RealOrComplex}) =
    (α*vt*C) * D # solves an ambiguity

*(A::AbstractMatrix, x::AbstractVector, γ::Number, δ::Number) = A * x * (γ*δ)
*(A::AbstractMatrix, B::AbstractMatrix, γ::Number, δ::Number) = A * B * (γ*δ)
*(A::AbstractMatrix, B::AbstractMatrix, x::AbstractVector, δ::Number, ) = A * (B*x*δ)
*(vt::AdjOrTransAbsVec, B::AbstractMatrix, x::AbstractVector, δ::Number) = (vt*B*x) * δ
*(vt::AdjOrTransAbsVec, B::AbstractMatrix, C::AbstractMatrix, δ::Number) = (vt*B) * C * δ

*(A::AbstractMatrix, B::AbstractMatrix, C::AbstractMatrix, x::AbstractVector) = A * B * (C*x)
*(vt::AdjOrTransAbsVec, B::AbstractMatrix, C::AbstractMatrix, D::AbstractMatrix) = (vt*B) * C * D
*(vt::AdjOrTransAbsVec, B::AbstractMatrix, C::AbstractMatrix, x::AbstractVector) = vt * B * (C*x)

# Four-argument *, by size
*(A::AbstractMatrix, B::AbstractMatrix, C::AbstractMatrix, δ::Number) = _tri_matmul(A,B,C,δ)
*(α::RealOrComplex, B::AbstractMatrix{<:RealOrComplex}, C::AbstractMatrix{<:RealOrComplex}, D::AbstractMatrix{<:RealOrComplex}) =
    _tri_matmul(B,C,D,α)
*(A::AbstractMatrix, B::AbstractMatrix, C::AbstractMatrix, D::AbstractMatrix) =
    _quad_matmul(A,B,C,D)

function _quad_matmul(A,B,C,D)
    c1 = _mul_cost((A,B),(C,D))
    c2 = _mul_cost(((A,B),C),D)
    c3 = _mul_cost(A,(B,(C,D)))
    c4 = _mul_cost((A,(B,C)),D)
    c5 = _mul_cost(A,((B,C),D))
    cmin = min(c1,c2,c3,c4,c5)
    if c1 == cmin
        (A*B) * (C*D)
    elseif c2 == cmin
        ((A*B) * C) * D
    elseif c3 == cmin
        A * (B * (C*D))
    elseif c4 == cmin
        (A * (B*C)) * D
    else
        A * ((B*C) * D)
    end
end
@inline _mul_cost(A::AbstractMatrix) = 0
@inline _mul_cost((A,B)::Tuple) = _mul_cost(A,B)
@inline _mul_cost(A,B) = _mul_cost(A) + _mul_cost(B) + *(_mul_sizes(A)..., last(_mul_sizes(B)))
@inline _mul_sizes(A::AbstractMatrix) = size(A)
@inline _mul_sizes((A,B)::Tuple) = first(_mul_sizes(A)), last(_mul_sizes(B))
w   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LinearAlgebra/src/lapack.jlk�     # This file is a part of Julia. License is MIT: https://julialang.org/license

module LAPACK
@doc """
Interfaces to LAPACK subroutines.
""" LAPACK

using ..LinearAlgebra.BLAS: @blasfunc, chkuplo

using ..LinearAlgebra: libblastrampoline, BlasFloat, BlasInt, LAPACKException, DimensionMismatch,
    SingularException, PosDefException, chkstride1, checksquare,triu, tril, dot

using Base: iszero, require_one_based_indexing


# Legacy binding maintained for backwards-compatibility but new packages
# should not look at this, instead preferring to parse the output
# of BLAS.get_config()
const liblapack = libblastrampoline

#Generic LAPACK error handlers
"""
Handle only negative LAPACK error codes

*NOTE* use only if the positive error code is useful.
"""
function chkargsok(ret::BlasInt)
    if ret < 0
        throw(ArgumentError("invalid argument #$(-ret) to LAPACK call"))
    end
end

"Handle all nonzero info codes"
function chklapackerror(ret::BlasInt)
    if ret == 0
        return
    elseif ret < 0
        throw(ArgumentError("invalid argument #$(-ret) to LAPACK call"))
    else # ret > 0
        throw(LAPACKException(ret))
    end
end

function chknonsingular(ret::BlasInt)
    if ret > 0
        throw(SingularException(ret))
    end
end

function chkposdef(ret::BlasInt)
    if ret > 0
        throw(PosDefException(ret))
    end
end

"Check that {c}transpose is correctly specified"
function chktrans(trans::AbstractChar)
    if !(trans == 'N' || trans == 'C' || trans == 'T')
        throw(ArgumentError("trans argument must be 'N' (no transpose), 'T' (transpose), or 'C' (conjugate transpose), got $trans"))
    end
    trans
end

"Check that left/right hand side multiply is correctly specified"
function chkside(side::AbstractChar)
    if !(side == 'L' || side == 'R')
        throw(ArgumentError("side argument must be 'L' (left hand multiply) or 'R' (right hand multiply), got $side"))
    end
    side
end

"Check that unit diagonal flag is correctly specified"
function chkdiag(diag::AbstractChar)
    if !(diag == 'U' || diag =='N')
        throw(ArgumentError("diag argument must be 'U' (unit diagonal) or 'N' (non-unit diagonal), got $diag"))
    end
    diag
end

subsetrows(X::AbstractVector, Y::AbstractArray, k) = Y[1:k]
subsetrows(X::AbstractMatrix, Y::AbstractArray, k) = Y[1:k, :]

function chkfinite(A::AbstractMatrix)
    for a in A
        if !isfinite(a)
            throw(ArgumentError("matrix contains Infs or NaNs"))
        end
    end
    return true
end

function chkuplofinite(A::AbstractMatrix, uplo::AbstractChar)
    require_one_based_indexing(A)
    m, n = size(A)
    if uplo == 'U'
        @inbounds for j in 1:n, i in 1:j
            if !isfinite(A[i,j])
                throw(ArgumentError("matrix contains Infs or NaNs"))
            end
        end
    else
        @inbounds for j in 1:n, i in j:m
            if !isfinite(A[i,j])
                throw(ArgumentError("matrix contains Infs or NaNs"))
            end
        end
    end
end

# LAPACK version number
function version()
    major = Ref{BlasInt}(0)
    minor = Ref{BlasInt}(0)
    patch = Ref{BlasInt}(0)
    ccall((@blasfunc(ilaver_), libblastrampoline), Cvoid,
          (Ptr{BlasInt}, Ptr{BlasInt}, Ptr{BlasInt}),
          major, minor, patch)
    return VersionNumber(major[], minor[], patch[])
end

# (GB) general banded matrices, LU decomposition and solver
for (gbtrf, gbtrs, elty) in
    ((:dgbtrf_,:dgbtrs_,:Float64),
     (:sgbtrf_,:sgbtrs_,:Float32),
     (:zgbtrf_,:zgbtrs_,:ComplexF64),
     (:cgbtrf_,:cgbtrs_,:ComplexF32))
    @eval begin
        # SUBROUTINE DGBTRF( M, N, KL, KU, AB, LDAB, IPIV, INFO )
        # *     .. Scalar Arguments ..
        #       INTEGER            INFO, KL, KU, LDAB, M, N
        # *     .. Array Arguments ..
        #       INTEGER            IPIV( * )
        #       DOUBLE PRECISION   AB( LDAB, * )
        function gbtrf!(kl::Integer, ku::Integer, m::Integer, AB::AbstractMatrix{$elty})
            require_one_based_indexing(AB)
            chkstride1(AB)
            n    = size(AB, 2)
            mnmn = min(m, n)
            ipiv = similar(AB, BlasInt, mnmn)
            info = Ref{BlasInt}()
            ccall((@blasfunc($gbtrf), libblastrampoline), Cvoid,
                  (Ref{BlasInt}, Ref{BlasInt}, Ref{BlasInt}, Ref{BlasInt},
                   Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}, Ptr{BlasInt}),
                  m, n, kl, ku, AB, max(1,stride(AB,2)), ipiv, info)
            chklapackerror(info[])
            AB, ipiv
        end

        # SUBROUTINE DGBTRS( TRANS, N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO)
        # *     .. Scalar Arguments ..
        #       CHARACTER          TRANS
        #       INTEGER            INFO, KL, KU, LDAB, LDB, N, NRHS
        # *     .. Array Arguments ..
        #       INTEGER            IPIV( * )
        #       DOUBLE PRECISION   AB( LDAB, * ), B( LDB, * )
        function gbtrs!(trans::AbstractChar, kl::Integer, ku::Integer, m::Integer,
                        AB::AbstractMatrix{$elty}, ipiv::AbstractVector{BlasInt},
                        B::AbstractVecOrMat{$elty})
            require_one_based_indexing(AB, B)
            chkstride1(AB, B, ipiv)
            chktrans(trans)
            info = Ref{BlasInt}()
            n    = size(AB,2)
            if m != n || m != size(B,1)
                throw(DimensionMismatch("matrix AB has dimensions $(size(AB)), but right hand side matrix B has dimensions $(size(B))"))
            end
            ccall((@blasfunc($gbtrs), libblastrampoline), Cvoid,
                  (Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt}, Ref{BlasInt}, Ref{BlasInt},
                   Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                   Ptr{BlasInt}, Clong),
                  trans, n, kl, ku, size(B,2), AB, max(1,stride(AB,2)), ipiv,
                  B, max(1,stride(B,2)), info, 1)
            chklapackerror(info[])
            B
        end
    end
end

"""
    gbtrf!(kl, ku, m, AB) -> (AB, ipiv)

Compute the LU factorization of a banded matrix `AB`. `kl` is the first
subdiagonal containing a nonzero band, `ku` is the last superdiagonal
containing one, and `m` is the first dimension of the matrix `AB`. Returns
the LU factorization in-place and `ipiv`, the vector of pivots used.
"""
gbtrf!(kl::Integer, ku::Integer, m::Integer, AB::AbstractMatrix)

"""
    gbtrs!(trans, kl, ku, m, AB, ipiv, B)

Solve the equation `AB * X = B`. `trans` determines the orientation of `AB`. It may
be `N` (no transpose), `T` (transpose), or `C` (conjugate transpose). `kl` is the
first subdiagonal containing a nonzero band, `ku` is the last superdiagonal
containing one, and `m` is the first dimension of the matrix `AB`. `ipiv` is the vector
of pivots returned from `gbtrf!`. Returns the vector or matrix `X`, overwriting `B` in-place.
"""
gbtrs!(trans::AbstractChar, kl::Integer, ku::Integer, m::Integer, AB::AbstractMatrix, ipiv::AbstractVector{BlasInt}, B::AbstractVecOrMat)

## (GE) general matrices: balancing and back-transforming
for (gebal, gebak, elty, relty) in
    ((:dgebal_, :dgebak_, :Float64, :Float64),
     (:sgebal_, :sgebak_, :Float32, :Float32),
     (:zgebal_, :zgebak_, :ComplexF64, :Float64),
     (:cgebal_, :cgebak_, :ComplexF32, :Float32))
    @eval begin
        #     SUBROUTINE DGEBAL( JOB, N, A, LDA, ILO, IHI, SCALE, INFO )
        #*     .. Scalar Arguments ..
        #      CHARACTER          JOB
        #      INTEGER            IHI, ILP, INFO, LDA, N
        #     .. Array Arguments ..
        #      DOUBLE PRECISION   A( LDA, * ), SCALE( * )
        function gebal!(job::AbstractChar, A::AbstractMatrix{$elty})
            chkstride1(A)
            n = checksquare(A)
            chkfinite(A) # balancing routines don't support NaNs and Infs
            ihi = Ref{BlasInt}()
            ilo = Ref{BlasInt}()
            scale = similar(A, $relty, n)
            info = Ref{BlasInt}()
            ccall((@blasfunc($gebal), libblastrampoline), Cvoid,
                  (Ref{UInt8}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                   Ptr{BlasInt}, Ptr{BlasInt}, Ptr{$relty}, Ptr{BlasInt}, Clong),
                  job, n, A, max(1,stride(A,2)), ilo, ihi, scale, info, 1)
            chklapackerror(info[])
            ilo[], ihi[], scale
        end

        #     SUBROUTINE DGEBAK( JOB, SIDE, N, ILO, IHI, SCALE, M, V, LDV, INFO )
        #*     .. Scalar Arguments ..
        #      CHARACTER          JOB, SIDE
        #      INTEGER            IHI, ILP, INFO, LDV, M, N
        #     .. Array Arguments ..
        #      DOUBLE PRECISION   SCALE( * ), V( LDV, * )
        function gebak!(job::AbstractChar, side::AbstractChar,
                        ilo::BlasInt, ihi::BlasInt, scale::AbstractVector{$relty},
                        V::AbstractMatrix{$elty})
            require_one_based_indexing(scale, V)
            chkstride1(scale, V)
            chkside(side)
            chkfinite(V) # balancing routines don't support NaNs and Infs
            n = checksquare(V)
            info = Ref{BlasInt}()
            ccall((@blasfunc($gebak), libblastrampoline), Cvoid,
                  (Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt}, Ref{BlasInt},
                   Ptr{$relty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt},
                   Clong, Clong),
                  job, side, size(V,1), ilo, ihi, scale, n, V, max(1,stride(V,2)), info,
                  1, 1)
            chklapackerror(info[])
            V
        end
    end
end

"""
    gebal!(job, A) -> (ilo, ihi, scale)

Balance the matrix `A` before computing its eigensystem or Schur factorization.
`job` can be one of `N` (`A` will not be permuted or scaled), `P` (`A` will only
be permuted), `S` (`A` will only be scaled), or `B` (`A` will be both permuted
and scaled). Modifies `A` in-place and returns `ilo`, `ihi`, and `scale`. If
permuting was turned on, `A[i,j] = 0` if `j > i` and `1 < j < ilo` or `j > ihi`.
`scale` contains information about the scaling/permutations performed.
"""
gebal!(job::AbstractChar, A::AbstractMatrix)

"""
    gebak!(job, side, ilo, ihi, scale, V)

Transform the eigenvectors `V` of a matrix balanced using `gebal!` to
the unscaled/unpermuted eigenvectors of the original matrix. Modifies `V`
in-place. `side` can be `L` (left eigenvectors are transformed) or `R`
(right eigenvectors are transformed).
"""
gebak!(job::AbstractChar, side::AbstractChar, ilo::BlasInt, ihi::BlasInt, scale::AbstractVector, V::AbstractMatrix)

# (GE) general matrices, direct decompositions
#
# These mutating functions take as arguments all the values they
# return, even if the value of the function does not depend on them
# (e.g. the tau argument).  This is so that a factorization can be
# updated in place.  The condensed mutating functions, usually a
# function of A only, are defined after this block.
for (gebrd, gelqf, geqlf, geqrf, geqp3, geqrt, geqrt3, gerqf, getrf, elty, relty) in
    ((:dgebrd_,:dgelqf_,:dgeqlf_,:dgeqrf_,:dgeqp3_,:dgeqrt_,:dgeqrt3_,:dgerqf_,:dgetrf_,:Float64,:Float64),
     (:sgebrd_,:sgelqf_,:sgeqlf_,:sgeqrf_,:sgeqp3_,:sgeqrt_,:sgeqrt3_,:sgerqf_,:sgetrf_,:Float32,:Float32),
     (:zgebrd_,:zgelqf_,:zgeqlf_,:zgeqrf_,:zgeqp3_,:zgeqrt_,:zgeqrt3_,:zgerqf_,:zgetrf_,:ComplexF64,:Float64),
     (:cgebrd_,:cgelqf_,:cgeqlf_,:cgeqrf_,:cgeqp3_,:cgeqrt_,:cgeqrt3_,:cgerqf_,:cgetrf_,:ComplexF32,:Float32))
    @eval begin
        # SUBROUTINE DGEBRD( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, LWORK,
        #                    INFO )
        # .. Scalar Arguments ..
        # INTEGER            INFO, LDA, LWORK, M, N
        # .. Array Arguments ..
        #  DOUBLE PRECISION   A( LDA, * ), D( * ), E( * ), TAUP( * ),
        #           TAUQ( * ), WORK( * )
        function gebrd!(A::AbstractMatrix{$elty})
            require_one_based_indexing(A)
            chkstride1(A)
            m, n  = size(A)
            k     = min(m, n)
            d     = similar(A, $relty, k)
            e     = similar(A, $relty, k)
            tauq  = similar(A, $elty, k)
            taup  = similar(A, $elty, k)
            work  = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            info  = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($gebrd), libblastrampoline), Cvoid,
                    (Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                     Ptr{$relty}, Ptr{$relty}, Ptr{$elty}, Ptr{$elty},
                     Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}),
                     m, n, A, max(1,stride(A,2)),
                     d, e, tauq, taup,
                     work, lwork, info)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            A, d, e, tauq, taup
        end

        # SUBROUTINE DGELQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
        # *     .. Scalar Arguments ..
        #       INTEGER            INFO, LDA, LWORK, M, N
        # *     .. Array Arguments ..
        #       DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
        function gelqf!(A::AbstractMatrix{$elty}, tau::AbstractVector{$elty})
            require_one_based_indexing(A, tau)
            chkstride1(A,tau)
            m     = BlasInt(size(A, 1))
            n     = BlasInt(size(A, 2))
            lda   = BlasInt(max(1,stride(A, 2)))
            if length(tau) != min(m,n)
                throw(DimensionMismatch("tau has length $(length(tau)), but needs length $(min(m,n))"))
            end
            lwork = BlasInt(-1)
            work  = Vector{$elty}(undef, 1)
            info  = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($gelqf), libblastrampoline), Cvoid,
                      (Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                       Ptr{$elty}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}),
                      m, n, A, lda, tau, work, lwork, info)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            A, tau
        end

        # SUBROUTINE DGEQLF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
        # *     .. Scalar Arguments ..
        #       INTEGER            INFO, LDA, LWORK, M, N
        # *     .. Array Arguments ..
        #       DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
        function geqlf!(A::AbstractMatrix{$elty}, tau::AbstractVector{$elty})
            require_one_based_indexing(A, tau)
            chkstride1(A,tau)
            m     = BlasInt(size(A, 1))
            n     = BlasInt(size(A, 2))
            lda   = BlasInt(max(1,stride(A, 2)))
            if length(tau) != min(m,n)
                throw(DimensionMismatch("tau has length $(length(tau)), but needs length $(min(m,n))"))
            end
            lwork = BlasInt(-1)
            work  = Vector{$elty}(undef, 1)
            info  = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($geqlf), libblastrampoline), Cvoid,
                      (Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                       Ptr{$elty}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}),
                      m, n, A, lda, tau, work, lwork, info)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            A, tau
        end

        # SUBROUTINE DGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, INFO )
        # *     .. Scalar Arguments ..
        #       INTEGER            INFO, LDA, LWORK, M, N
        # *     .. Array Arguments ..
        #       INTEGER            JPVT( * )
        #       DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
        function geqp3!(A::AbstractMatrix{$elty}, jpvt::AbstractVector{BlasInt}, tau::AbstractVector{$elty})
            require_one_based_indexing(A, jpvt, tau)
            chkstride1(A,jpvt,tau)
            m,n = size(A)
            if length(tau) != min(m,n)
                throw(DimensionMismatch("tau has length $(length(tau)), but needs length $(min(m,n))"))
            end
            if length(jpvt) != n
                throw(DimensionMismatch("jpvt has length $(length(jpvt)), but needs length $n"))
            end
            lda = stride(A,2)
            if lda == 0
                return A, tau, jpvt
            end # Early exit
            work  = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            cmplx = eltype(A)<:Complex
            if cmplx
                rwork = Vector{$relty}(undef, 2n)
            end
            info = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                if cmplx
                    ccall((@blasfunc($geqp3), libblastrampoline), Cvoid,
                          (Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                           Ptr{BlasInt}, Ptr{$elty}, Ptr{$elty}, Ref{BlasInt},
                           Ptr{$relty}, Ptr{BlasInt}),
                          m, n, A, lda,
                          jpvt, tau, work, lwork,
                          rwork, info)
                else
                    ccall((@blasfunc($geqp3), libblastrampoline), Cvoid,
                          (Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                           Ptr{BlasInt}, Ptr{$elty}, Ptr{$elty}, Ref{BlasInt},
                           Ptr{BlasInt}),
                          m, n, A, lda,
                          jpvt, tau, work,
                          lwork, info)
                end
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            return A, tau, jpvt
        end

        function geqrt!(A::AbstractMatrix{$elty}, T::AbstractMatrix{$elty})
            require_one_based_indexing(A, T)
            chkstride1(A)
            m, n = size(A)
            minmn = min(m, n)
            nb = size(T, 1)
            if nb > minmn
                throw(ArgumentError("block size $nb > $minmn too large"))
            end
            lda = max(1, stride(A,2))
            work = Vector{$elty}(undef, nb*n)
            if n > 0
                info = Ref{BlasInt}()
                ccall((@blasfunc($geqrt), libblastrampoline), Cvoid,
                    (Ref{BlasInt}, Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty},
                     Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty},
                     Ptr{BlasInt}),
                     m, n, nb, A,
                     lda, T, max(1,stride(T,2)), work,
                     info)
                chklapackerror(info[])
            end
            A, T
        end

        function geqrt3!(A::AbstractMatrix{$elty}, T::AbstractMatrix{$elty})
            require_one_based_indexing(A, T)
            chkstride1(A)
            chkstride1(T)
            m, n = size(A)
            p, q = size(T)
            if m < n
                throw(DimensionMismatch("input matrix A has dimensions ($m,$n), but should have more rows than columns"))
            end
            if p != n || q != n
                throw(DimensionMismatch("block reflector T has dimensions ($p,$q), but should have dimensions ($n,$n)"))
            end
            if n > 0
                info = Ref{BlasInt}()
                ccall((@blasfunc($geqrt3), libblastrampoline), Cvoid,
                    (Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                     Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}),
                     m, n, A, max(1, stride(A, 2)),
                     T, max(1,stride(T,2)), info)
                chklapackerror(info[])
            end
            A, T
        end

        ## geqrfp! - positive elements on diagonal of R - not defined yet
        # SUBROUTINE DGEQRFP( M, N, A, LDA, TAU, WORK, LWORK, INFO )
        # *     .. Scalar Arguments ..
        #       INTEGER            INFO, LDA, LWORK, M, N
        # *     .. Array Arguments ..
        #       DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
        function geqrf!(A::AbstractMatrix{$elty}, tau::AbstractVector{$elty})
            require_one_based_indexing(A, tau)
            chkstride1(A,tau)
            m, n  = size(A)
            if length(tau) != min(m,n)
                throw(DimensionMismatch("tau has length $(length(tau)), but needs length $(min(m,n))"))
            end
            work  = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            info  = Ref{BlasInt}()
            for i = 1:2                # first call returns lwork as work[1]
                ccall((@blasfunc($geqrf), libblastrampoline), Cvoid,
                      (Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                       Ptr{$elty}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}),
                      m, n, A, max(1,stride(A,2)), tau, work, lwork, info)
                chklapackerror(info[])
                if i == 1
                    lwork = max(BlasInt(1),BlasInt(real(work[1])))
                    resize!(work, lwork)
                end
            end
            A, tau
        end

        # SUBROUTINE DGERQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
        # *     .. Scalar Arguments ..
        #       INTEGER            INFO, LDA, LWORK, M, N
        # *     .. Array Arguments ..
        #       DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
        function gerqf!(A::AbstractMatrix{$elty},tau::AbstractVector{$elty})
            require_one_based_indexing(A, tau)
            chkstride1(A,tau)
            m, n  = size(A)
            if length(tau) != min(m,n)
                throw(DimensionMismatch("tau has length $(length(tau)), but needs length $(min(m,n))"))
            end
            lwork = BlasInt(-1)
            work  = Vector{$elty}(undef, 1)
            info  = Ref{BlasInt}()
            for i = 1:2                # first call returns lwork as work[1]
                ccall((@blasfunc($gerqf), libblastrampoline), Cvoid,
                      (Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                       Ptr{$elty}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}),
                      m, n, A, max(1,stride(A,2)), tau, work, lwork, info)
                chklapackerror(info[])
                if i == 1
                    lwork = max(BlasInt(m), BlasInt(real(work[1])))
                    resize!(work, lwork)
                end
            end
            A, tau
        end

        # SUBROUTINE DGETRF( M, N, A, LDA, IPIV, INFO )
        # *     .. Scalar Arguments ..
        #       INTEGER            INFO, LDA, M, N
        # *     .. Array Arguments ..
        #       INTEGER            IPIV( * )
        #       DOUBLE PRECISION   A( LDA, * )
        function getrf!(A::AbstractMatrix{$elty}; check = true)
            require_one_based_indexing(A)
            check && chkfinite(A)
            chkstride1(A)
            m, n = size(A)
            lda  = max(1,stride(A, 2))
            ipiv = similar(A, BlasInt, min(m,n))
            info = Ref{BlasInt}()
            ccall((@blasfunc($getrf), libblastrampoline), Cvoid,
                  (Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty},
                   Ref{BlasInt}, Ptr{BlasInt}, Ptr{BlasInt}),
                  m, n, A, lda, ipiv, info)
            chkargsok(info[])
            A, ipiv, info[] #Error code is stored in LU factorization type
        end
    end
end

"""
    gebrd!(A) -> (A, d, e, tauq, taup)

Reduce `A` in-place to bidiagonal form `A = QBP'`. Returns `A`, containing the
bidiagonal matrix `B`; `d`, containing the diagonal elements of `B`; `e`,
containing the off-diagonal elements of `B`; `tauq`, containing the
elementary reflectors representing `Q`; and `taup`, containing the
elementary reflectors representing `P`.
"""
gebrd!(A::AbstractMatrix)

"""
    gelqf!(A, tau)

Compute the `LQ` factorization of `A`, `A = LQ`. `tau` contains scalars
which parameterize the elementary reflectors of the factorization. `tau`
must have length greater than or equal to the smallest dimension of `A`.

Returns
`A` and `tau` modified in-place.
"""
gelqf!(A::AbstractMatrix, tau::AbstractVector)

"""
    geqlf!(A, tau)

Compute the `QL` factorization of `A`, `A = QL`. `tau` contains scalars
which parameterize the elementary reflectors of the factorization. `tau`
must have length greater than or equal to the smallest dimension of `A`.

Returns `A` and `tau` modified in-place.
"""
geqlf!(A::AbstractMatrix, tau::AbstractVector)

"""
    geqp3!(A, [jpvt, tau]) -> (A, tau, jpvt)

Compute the pivoted `QR` factorization of `A`, `AP = QR` using BLAS level 3.
`P` is a pivoting matrix, represented by `jpvt`. `tau` stores the elementary
reflectors. The arguments `jpvt` and `tau` are optional and allow
for passing preallocated arrays. When passed, `jpvt` must have length greater
than or equal to `n` if `A` is an `(m x n)` matrix and `tau` must have length
greater than or equal to the smallest dimension of `A`.

`A`, `jpvt`, and `tau` are modified in-place.
"""
geqp3!(A::AbstractMatrix, jpvt::AbstractVector{BlasInt}, tau::AbstractVector)

function geqp3!(A::AbstractMatrix{<:BlasFloat}, jpvt::AbstractVector{BlasInt})
    m, n = size(A)
    geqp3!(A, jpvt, similar(A, min(m, n)))
end

function geqp3!(A::AbstractMatrix{<:BlasFloat})
    m, n = size(A)
    geqp3!(A, zeros(BlasInt, n), similar(A, min(m, n)))
end

"""
    geqrt!(A, T)

Compute the blocked `QR` factorization of `A`, `A = QR`. `T` contains upper
triangular block reflectors which parameterize the elementary reflectors of
the factorization. The first dimension of `T` sets the block size and it must
be between 1 and `n`. The second dimension of `T` must equal the smallest
dimension of `A`.

Returns `A` and `T` modified in-place.
"""
geqrt!(A::AbstractMatrix, T::AbstractMatrix)

"""
    geqrt3!(A, T)

Recursively computes the blocked `QR` factorization of `A`, `A = QR`. `T`
contains upper triangular block reflectors which parameterize the
elementary reflectors of the factorization.  The first dimension of `T` sets the
block size and it must be between 1 and `n`. The second dimension of `T` must
equal the smallest dimension of `A`.

Returns `A` and `T` modified in-place.
"""
geqrt3!(A::AbstractMatrix, T::AbstractMatrix)

"""
    geqrf!(A, tau)

Compute the `QR` factorization of `A`, `A = QR`. `tau` contains scalars
which parameterize the elementary reflectors of the factorization. `tau`
must have length greater than or equal to the smallest dimension of `A`.

Returns `A` and `tau` modified in-place.
"""
geqrf!(A::AbstractMatrix, tau::AbstractVector)

"""
    gerqf!(A, tau)

Compute the `RQ` factorization of `A`, `A = RQ`. `tau` contains scalars
which parameterize the elementary reflectors of the factorization. `tau`
must have length greater than or equal to the smallest dimension of `A`.

Returns `A` and `tau` modified in-place.
"""
gerqf!(A::AbstractMatrix, tau::AbstractVector)

"""
    getrf!(A) -> (A, ipiv, info)

Compute the pivoted `LU` factorization of `A`, `A = LU`.

Returns `A`, modified in-place, `ipiv`, the pivoting information, and an `info`
code which indicates success (`info = 0`), a singular value in `U`
(`info = i`, in which case `U[i,i]` is singular), or an error code (`info < 0`).
"""
getrf!(A::AbstractMatrix, tau::AbstractVector)

"""
    gelqf!(A) -> (A, tau)

Compute the `LQ` factorization of `A`, `A = LQ`.

Returns `A`, modified in-place, and `tau`, which contains scalars
which parameterize the elementary reflectors of the factorization.
"""
gelqf!(A::AbstractMatrix{<:BlasFloat}) = ((m,n) = size(A); gelqf!(A, similar(A, min(m, n))))

"""
    geqlf!(A) -> (A, tau)

Compute the `QL` factorization of `A`, `A = QL`.

Returns `A`, modified in-place, and `tau`, which contains scalars
which parameterize the elementary reflectors of the factorization.
"""
geqlf!(A::AbstractMatrix{<:BlasFloat}) = ((m,n) = size(A); geqlf!(A, similar(A, min(m, n))))

"""
    geqrt!(A, nb) -> (A, T)

Compute the blocked `QR` factorization of `A`, `A = QR`. `nb` sets the block size
and it must be between 1 and `n`, the second dimension of `A`.

Returns `A`, modified in-place, and `T`, which contains upper
triangular block reflectors which parameterize the elementary reflectors of
the factorization.
"""
geqrt!(A::AbstractMatrix{<:BlasFloat}, nb::Integer) = geqrt!(A, similar(A, nb, minimum(size(A))))

"""
    geqrt3!(A) -> (A, T)

Recursively computes the blocked `QR` factorization of `A`, `A = QR`.

Returns `A`, modified in-place, and `T`, which contains upper triangular block
reflectors which parameterize the elementary reflectors of the factorization.
"""
geqrt3!(A::AbstractMatrix{<:BlasFloat}) = (n = size(A, 2); geqrt3!(A, similar(A, n, n)))

"""
    geqrf!(A) -> (A, tau)

Compute the `QR` factorization of `A`, `A = QR`.

Returns `A`, modified in-place, and `tau`, which contains scalars
which parameterize the elementary reflectors of the factorization.
"""
geqrf!(A::AbstractMatrix{<:BlasFloat}) = ((m,n) = size(A); geqrf!(A, similar(A, min(m, n))))

"""
    gerqf!(A) -> (A, tau)

Compute the `RQ` factorization of `A`, `A = RQ`.

Returns `A`, modified in-place, and `tau`, which contains scalars
which parameterize the elementary reflectors of the factorization.
"""
gerqf!(A::AbstractMatrix{<:BlasFloat}) = ((m,n) = size(A); gerqf!(A, similar(A, min(m, n))))

## Tools to compute and apply elementary reflectors
for (larfg, elty) in
    ((:dlarfg_, Float64),
     (:slarfg_, Float32),
     (:zlarfg_, ComplexF64),
     (:clarfg_, ComplexF32))
    @eval begin
        #        .. Scalar Arguments ..
        #        INTEGER            incx, n
        #        DOUBLE PRECISION   alpha, tau
        #        ..
        #        .. Array Arguments ..
        #        DOUBLE PRECISION   x( * )
        function larfg!(x::AbstractVector{$elty})
            N    = BlasInt(length(x))
            α    = Ref{$elty}(x[1])
            incx = BlasInt(1)
            τ    = Ref{$elty}(0)
            ccall((@blasfunc($larfg), libblastrampoline), Cvoid,
                (Ref{BlasInt}, Ref{$elty}, Ptr{$elty}, Ref{BlasInt}, Ref{$elty}),
                N, α, pointer(x, 2), incx, τ)
            @inbounds x[1] = one($elty)
            return τ[]
        end
    end
end

for (larf, elty) in
    ((:dlarf_, Float64),
     (:slarf_, Float32),
     (:zlarf_, ComplexF64),
     (:clarf_, ComplexF32))
    @eval begin
        #        .. Scalar Arguments ..
        #        CHARACTER          side
        #        INTEGER            incv, ldc, m, n
        #        DOUBLE PRECISION   tau
        #        ..
        #        .. Array Arguments ..
        #        DOUBLE PRECISION   c( ldc, * ), v( * ), work( * )
        function larf!(side::AbstractChar, v::AbstractVector{$elty},
                       τ::$elty, C::AbstractMatrix{$elty}, work::AbstractVector{$elty})
            m, n = size(C)
            chkside(side)
            ldc = max(1, stride(C, 2))
            l = side == 'L' ? n : m
            incv  = BlasInt(1)
            ccall((@blasfunc($larf), libblastrampoline), Cvoid,
                (Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                 Ref{$elty}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Clong),
                side, m, n, v, incv,
                τ, C, ldc, work, 1)
            return C
        end

        function larf!(side::AbstractChar, v::AbstractVector{$elty},
                       τ::$elty, C::AbstractMatrix{$elty})
            m, n = size(C)
            chkside(side)
            lwork = side == 'L' ? n : m
            return larf!(side, v, τ, C, Vector{$elty}(undef,lwork))
        end
    end
end

## Complete orthogonaliztion tools
for (tzrzf, ormrz, elty) in
    ((:dtzrzf_,:dormrz_,:Float64),
     (:stzrzf_,:sormrz_,:Float32),
     (:ztzrzf_,:zunmrz_,:ComplexF64),
     (:ctzrzf_,:cunmrz_,:ComplexF32))
    @eval begin
         #       SUBROUTINE ZTZRZF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
         #
         #       .. Scalar Arguments ..
         #       INTEGER            INFO, LDA, LWORK, M, N
         #       ..
         #       .. Array Arguments ..
         #       COMPLEX*16         A( LDA, * ), TAU( * ), WORK( * )
        function tzrzf!(A::AbstractMatrix{$elty})
            require_one_based_indexing(A)
            chkstride1(A)
            m, n = size(A)
            if n < m
                throw(DimensionMismatch("input matrix A has dimensions ($m,$n), but cannot have fewer columns than rows"))
            end
            lda = max(1, stride(A,2))
            tau = similar(A, $elty, m)
            work  = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            info  = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($tzrzf), libblastrampoline), Cvoid,
                    (Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                     Ptr{$elty}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}),
                    m, n, A, lda,
                    tau, work, lwork, info)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            A, tau
        end

        #       SUBROUTINE ZUNMRZ( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
        #                          WORK, LWORK, INFO )
        #
        #       .. Scalar Arguments ..
        #       CHARACTER          SIDE, TRANS
        #       INTEGER            INFO, K, L, LDA, LDC, LWORK, M, N
        #       ..
        #       .. Array Arguments ..
        #       COMPLEX*16         A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
        function ormrz!(side::AbstractChar, trans::AbstractChar, A::AbstractMatrix{$elty},
                        tau::AbstractVector{$elty}, C::AbstractMatrix{$elty})
            require_one_based_indexing(A, tau, C)
            chktrans(trans)
            chkside(side)
            chkstride1(A, tau, C)
            m, n = size(C)
            k = length(tau)
            l = size(A, 2) - size(A, 1)
            lda = max(1, stride(A,2))
            ldc = max(1, stride(C,2))
            work  = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            info  = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($ormrz), libblastrampoline), Cvoid,
                    (Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt},
                     Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                     Ptr{$elty}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty},
                     Ref{BlasInt}, Ptr{BlasInt}, Clong, Clong),
                    side, trans, m, n,
                    k, l, A, lda,
                    tau, C, ldc, work,
                    lwork, info, 1, 1)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            C
        end
    end
end

"""
    ormrz!(side, trans, A, tau, C)

Multiplies the matrix `C` by `Q` from the transformation supplied by
`tzrzf!`. Depending on `side` or `trans` the multiplication can be
left-sided (`side = L, Q*C`) or right-sided (`side = R, C*Q`) and `Q`
can be unmodified (`trans = N`), transposed (`trans = T`), or conjugate
transposed (`trans = C`). Returns matrix `C` which is modified in-place
with the result of the multiplication.
"""
ormrz!(side::AbstractChar, trans::AbstractChar, A::AbstractMatrix, tau::AbstractVector, C::AbstractMatrix)

"""
    tzrzf!(A) -> (A, tau)

Transforms the upper trapezoidal matrix `A` to upper triangular form in-place.
Returns `A` and `tau`, the scalar parameters for the elementary reflectors
of the transformation.
"""
tzrzf!(A::AbstractMatrix)

## (GE) general matrices, solvers with factorization, solver and inverse
for (gels, gesv, getrs, getri, elty) in
    ((:dgels_,:dgesv_,:dgetrs_,:dgetri_,:Float64),
     (:sgels_,:sgesv_,:sgetrs_,:sgetri_,:Float32),
     (:zgels_,:zgesv_,:zgetrs_,:zgetri_,:ComplexF64),
     (:cgels_,:cgesv_,:cgetrs_,:cgetri_,:ComplexF32))
    @eval begin
        #      SUBROUTINE DGELS( TRANS, M, N, NRHS, A, LDA, B, LDB, WORK, LWORK,INFO)
        # *     .. Scalar Arguments ..
        #       CHARACTER          TRANS
        #       INTEGER            INFO, LDA, LDB, LWORK, M, N, NRHS
        function gels!(trans::AbstractChar, A::AbstractMatrix{$elty}, B::AbstractVecOrMat{$elty})
            require_one_based_indexing(A, B)
            chktrans(trans)
            chkstride1(A, B)
            btrn  = trans == 'T'
            m, n  = size(A)
            if size(B,1) != (btrn ? n : m)
                throw(DimensionMismatch("matrix A has dimensions ($m,$n), transposed: $btrn, but leading dimension of B is $(size(B,1))"))
            end
            info  = Ref{BlasInt}()
            work  = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($gels), libblastrampoline), Cvoid,
                      (Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt}, Ref{BlasInt},
                       Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                       Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}, Clong),
                      (btrn ? 'T' : 'N'), m, n, size(B,2), A, max(1,stride(A,2)),
                      B, max(1,stride(B,2)), work, lwork, info, 1)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            k   = min(m, n)
            F   = m < n ? tril(A[1:k, 1:k]) : triu(A[1:k, 1:k])
            ssr = Vector{$elty}(undef, size(B, 2))
            for i = 1:size(B,2)
                x = zero($elty)
                for j = k+1:size(B,1)
                    x += abs2(B[j,i])
                end
                ssr[i] = x
            end
            F, subsetrows(B, B, k), ssr
        end

        # SUBROUTINE DGESV( N, NRHS, A, LDA, IPIV, B, LDB, INFO )
        # *     .. Scalar Arguments ..
        #       INTEGER            INFO, LDA, LDB, N, NRHS
        # *     ..
        # *     .. Array Arguments ..
        #       INTEGER            IPIV( * )
        #       DOUBLE PRECISION   A( LDA, * ), B( LDB, * )
        function gesv!(A::AbstractMatrix{$elty}, B::AbstractVecOrMat{$elty})
            require_one_based_indexing(A, B)
            chkstride1(A, B)
            n = checksquare(A)
            if size(B,1) != n
                throw(DimensionMismatch("B has leading dimension $(size(B,1)), but needs $n"))
            end
            ipiv = similar(A, BlasInt, n)
            info = Ref{BlasInt}()
            ccall((@blasfunc($gesv), libblastrampoline), Cvoid,
                  (Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt},
                   Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}),
                  n, size(B,2), A, max(1,stride(A,2)), ipiv, B, max(1,stride(B,2)), info)
            chklapackerror(info[])
            B, A, ipiv
        end

        #     SUBROUTINE DGETRS( TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
        #*     .. Scalar Arguments ..
        #      CHARACTER          TRANS
        #      INTEGER            INFO, LDA, LDB, N, NRHS
        #     .. Array Arguments ..
        #      INTEGER            IPIV( * )
        #      DOUBLE PRECISION   A( LDA, * ), B( LDB, * )
        function getrs!(trans::AbstractChar, A::AbstractMatrix{$elty}, ipiv::AbstractVector{BlasInt}, B::AbstractVecOrMat{$elty})
            require_one_based_indexing(A, ipiv, B)
            chktrans(trans)
            chkstride1(A, B, ipiv)
            n = checksquare(A)
            if n != size(B, 1)
                throw(DimensionMismatch("B has leading dimension $(size(B,1)), but needs $n"))
            end
            if n != length(ipiv)
                throw(DimensionMismatch("ipiv has length $(length(ipiv)), but needs to be $n"))
            end
            nrhs = size(B, 2)
            info = Ref{BlasInt}()
            ccall((@blasfunc($getrs), libblastrampoline), Cvoid,
                  (Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                   Ptr{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}, Clong),
                  trans, n, size(B,2), A, max(1,stride(A,2)), ipiv, B, max(1,stride(B,2)), info, 1)
            chklapackerror(info[])
            B
        end

        #     SUBROUTINE DGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO )
        #*     .. Scalar Arguments ..
        #      INTEGER            INFO, LDA, LWORK, N
        #*     .. Array Arguments ..
        #      INTEGER            IPIV( * )
        #      DOUBLE PRECISION   A( LDA, * ), WORK( * )
        function getri!(A::AbstractMatrix{$elty}, ipiv::AbstractVector{BlasInt})
            require_one_based_indexing(A, ipiv)
            chkstride1(A, ipiv)
            n = checksquare(A)
            if n != length(ipiv)
                throw(DimensionMismatch("ipiv has length $(length(ipiv)), but needs $n"))
            end
            lda = max(1,stride(A, 2))
            lwork = BlasInt(-1)
            work  = Vector{$elty}(undef, 1)
            info  = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($getri), libblastrampoline), Cvoid,
                      (Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt},
                       Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}),
                      n, A, lda, ipiv, work, lwork, info)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            A
        end
    end
end

"""
    gels!(trans, A, B) -> (F, B, ssr)

Solves the linear equation `A * X = B`, `transpose(A) * X = B`, or `adjoint(A) * X = B` using
a QR or LQ factorization. Modifies the matrix/vector `B` in place with the
solution. `A` is overwritten with its `QR` or `LQ` factorization. `trans`
may be one of `N` (no modification), `T` (transpose), or `C` (conjugate
transpose). `gels!` searches for the minimum norm/least squares solution.
`A` may be under or over determined. The solution is returned in `B`.
"""
gels!(trans::AbstractChar, A::AbstractMatrix, B::AbstractVecOrMat)

"""
    gesv!(A, B) -> (B, A, ipiv)

Solves the linear equation `A * X = B` where `A` is a square matrix using
the `LU` factorization of `A`. `A` is overwritten with its `LU`
factorization and `B` is overwritten with the solution `X`. `ipiv` contains the
pivoting information for the `LU` factorization of `A`.
"""
gesv!(A::AbstractMatrix, B::AbstractVecOrMat)

"""
    getrs!(trans, A, ipiv, B)

Solves the linear equation `A * X = B`, `transpose(A) * X = B`, or `adjoint(A) * X = B` for
square `A`. Modifies the matrix/vector `B` in place with the solution. `A`
is the `LU` factorization from `getrf!`, with `ipiv` the pivoting
information. `trans` may be one of `N` (no modification), `T` (transpose),
or `C` (conjugate transpose).
"""
getrs!(trans::AbstractChar, A::AbstractMatrix, ipiv::AbstractVector{BlasInt}, B::AbstractVecOrMat)

"""
    getri!(A, ipiv)

Computes the inverse of `A`, using its `LU` factorization found by
`getrf!`. `ipiv` is the pivot information output and `A`
contains the `LU` factorization of `getrf!`. `A` is overwritten with
its inverse.
"""
getri!(A::AbstractMatrix, ipiv::AbstractVector{BlasInt})

for (gesvx, elty) in
    ((:dgesvx_,:Float64),
     (:sgesvx_,:Float32))
    @eval begin
        #     SUBROUTINE DGESVX( FACT, TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV,
        #                        EQUED, R, C, B, LDB, X, LDX, RCOND, FERR, BERR,
        #                        WORK, IWORK, INFO )
        #
        #     .. Scalar Arguments ..
        #     CHARACTER          EQUED, FACT, TRANS
        #     INTEGER            INFO, LDA, LDAF, LDB, LDX, N, NRHS
        #     DOUBLE PRECISION   RCOND
        #     ..
        #     .. Array Arguments ..
        #     INTEGER            IPIV( * ), IWORK( * )
        #     DOUBLE PRECISION   A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
        #    $                   BERR( * ), C( * ), FERR( * ), R( * ),
        #    $                   WORK( * ), X( LDX, *
        #
        function gesvx!(fact::AbstractChar, trans::AbstractChar, A::AbstractMatrix{$elty},
                        AF::AbstractMatrix{$elty}, ipiv::AbstractVector{BlasInt}, equed::AbstractChar,
                        R::AbstractVector{$elty}, C::AbstractVector{$elty}, B::AbstractVecOrMat{$elty})
            require_one_based_indexing(A, AF, ipiv, R, C, B)
            chktrans(trans)
            chkstride1(ipiv, R, C, B)
            n    = checksquare(A)
            lda  = stride(A,2)
            n    = checksquare(AF)
            ldaf = stride(AF,2)
            nrhs = size(B,2)
            ldb  = stride(B,2)
            rcond = Ref{$elty}()
            ferr  = similar(A, $elty, nrhs)
            berr  = similar(A, $elty, nrhs)
            work  = Vector{$elty}(undef, 4n)
            iwork = Vector{BlasInt}(undef, n)
            info  = Ref{BlasInt}()
            X = similar(A, $elty, n, nrhs)
            ccall((@blasfunc($gesvx), libblastrampoline), Cvoid,
              (Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt},
               Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt},
               Ref{UInt8}, Ptr{$elty}, Ptr{$elty}, Ptr{$elty}, Ref{BlasInt},
               Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ptr{$elty}, Ptr{$elty},
               Ptr{$elty}, Ptr{BlasInt}, Ptr{BlasInt}, Clong, Clong, Clong),
              fact, trans, n, nrhs, A, lda, AF, ldaf, ipiv, equed, R, C, B,
              ldb, X, n, rcond, ferr, berr, work, iwork, info, 1, 1, 1)
            chklapackerror(info[])
            if info[] == n + 1
                @warn "Matrix is singular to working precision"
            else
                chknonsingular(info[])
            end
            #WORK(1) contains the reciprocal pivot growth factor norm(A)/norm(U)
            X, equed, R, C, B, rcond[], ferr, berr, work[1]
        end

        function gesvx!(A::AbstractMatrix{$elty}, B::AbstractVecOrMat{$elty})
            n = size(A,1)
            X, equed, R, C, B, rcond, ferr, berr, rpgf =
                gesvx!('N', 'N', A,
                       similar(A, $elty, n, n),
                       similar(A, BlasInt, n),
                       'N',
                       similar(A, $elty, n),
                       similar(A, $elty, n),
                       B)
            X, rcond, ferr, berr, rpgf
        end
    end
end
for (gesvx, elty, relty) in
    ((:zgesvx_,:ComplexF64,:Float64),
     (:cgesvx_,:ComplexF32 ,:Float32))
    @eval begin
        #     SUBROUTINE ZGESVX( FACT, TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV,
        #                        EQUED, R, C, B, LDB, X, LDX, RCOND, FERR, BERR,
        #                        WORK, RWORK, INFO )
        #
        #     .. Scalar Arguments ..
        #     CHARACTER          EQUED, FACT, TRANS
        #     INTEGER            INFO, LDA, LDAF, LDB, LDX, N, NRHS
        #     DOUBLE PRECISION   RCOND
        #     ..
        #     .. Array Arguments ..
        #     INTEGER            IPIV( * )
        #     DOUBLE PRECISION   BERR( * ), C( * ), FERR( * ), R( * ),
        #    $                   RWORK( * )
        #     COMPLEX*16         A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
        #    $                   WORK( * ), X( LDX, * )
        function gesvx!(fact::AbstractChar, trans::AbstractChar, A::AbstractMatrix{$elty},
                        AF::AbstractMatrix{$elty}, ipiv::AbstractVector{BlasInt}, equed::AbstractChar,
                        R::AbstractVector{$relty}, C::AbstractVector{$relty}, B::AbstractVecOrMat{$elty})
            require_one_based_indexing(A, AF, ipiv, R, C, B)
            chktrans(trans)
            chkstride1(A, AF, ipiv, R, C, B)
            n   = checksquare(A)
            lda = stride(A,2)
            n   = checksquare(AF)
            ldaf = stride(AF,2)
            nrhs = size(B,2)
            ldb = stride(B,2)
            rcond = Ref{$relty}()
            ferr  = similar(A, $relty, nrhs)
            berr  = similar(A, $relty, nrhs)
            work  = Vector{$elty}(undef, 2n)
            rwork = Vector{$relty}(undef, 2n)
            info  = Ref{BlasInt}()
            X = similar(A, $elty, n, nrhs)
            ccall((@blasfunc($gesvx), libblastrampoline), Cvoid,
              (Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt},
               Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt},
               Ref{UInt8}, Ptr{$relty}, Ptr{$relty}, Ptr{$elty}, Ref{BlasInt},
               Ptr{$elty}, Ref{BlasInt}, Ptr{$relty}, Ptr{$relty}, Ptr{$relty},
               Ptr{$elty}, Ptr{$relty}, Ptr{BlasInt}, Clong, Clong, Clong),
              fact, trans, n, nrhs, A, lda, AF, ldaf, ipiv, equed, R, C, B,
              ldb, X, n, rcond, ferr, berr, work, rwork, info, 1, 1, 1)
            chklapackerror(info[])
            if info[] == n + 1
                @warn "Matrix is singular to working precision"
            else
                chknonsingular(info[])
            end
            #RWORK(1) contains the reciprocal pivot growth factor norm(A)/norm(U)
            X, equed, R, C, B, rcond[], ferr, berr, rwork[1]
        end

        #Wrapper for the no-equilibration, no-transpose calculation
        function gesvx!(A::AbstractMatrix{$elty}, B::AbstractVecOrMat{$elty})
            n = size(A,1)
            X, equed, R, C, B, rcond, ferr, berr, rpgf =
                gesvx!('N', 'N', A,
                       similar(A, $elty, n, n),
                       similar(A, BlasInt, n),
                       'N',
                       similar(A, $relty, n),
                       similar(A, $relty, n),
                       B)
            X, rcond, ferr, berr, rpgf
        end
    end
end

"""
    gesvx!(fact, trans, A, AF, ipiv, equed, R, C, B) -> (X, equed, R, C, B, rcond, ferr, berr, work)

Solves the linear equation `A * X = B` (`trans = N`), `transpose(A) * X = B`
(`trans = T`), or `adjoint(A) * X = B` (`trans = C`) using the `LU` factorization
of `A`. `fact` may be `E`, in which case `A` will be equilibrated and copied
to `AF`; `F`, in which case `AF` and `ipiv` from a previous `LU` factorization
are inputs; or `N`, in which case `A` will be copied to `AF` and then
factored. If `fact = F`, `equed` may be `N`, meaning `A` has not been
equilibrated; `R`, meaning `A` was multiplied by `Diagonal(R)` from the left;
`C`, meaning `A` was multiplied by `Diagonal(C)` from the right; or `B`, meaning
`A` was multiplied by `Diagonal(R)` from the left and `Diagonal(C)` from the right.
If `fact = F` and `equed = R` or `B` the elements of `R` must all be positive.
If `fact = F` and `equed = C` or `B` the elements of `C` must all be positive.

Returns the solution `X`; `equed`, which is an output if `fact` is not `N`,
and describes the equilibration that was performed; `R`, the row equilibration
diagonal; `C`, the column equilibration diagonal; `B`, which may be overwritten
with its equilibrated form `Diagonal(R)*B` (if `trans = N` and `equed = R,B`) or
`Diagonal(C)*B` (if `trans = T,C` and `equed = C,B`); `rcond`, the reciprocal
condition number of `A` after equilbrating; `ferr`, the forward error bound for
each solution vector in `X`; `berr`, the forward error bound for each solution
vector in `X`; and `work`, the reciprocal pivot growth factor.
"""
gesvx!(fact::AbstractChar, trans::AbstractChar, A::AbstractMatrix, AF::AbstractMatrix,
    ipiv::AbstractVector{BlasInt}, equed::AbstractChar, R::AbstractVector, C::AbstractVector, B::AbstractVecOrMat)

"""
    gesvx!(A, B)

The no-equilibration, no-transpose simplification of `gesvx!`.
"""
gesvx!(A::AbstractMatrix, B::AbstractVecOrMat)

for (gelsd, gelsy, elty) in
    ((:dgelsd_,:dgelsy_,:Float64),
     (:sgelsd_,:sgelsy_,:Float32))
    @eval begin
        # SUBROUTINE DGELSD( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK,
        #      $                   WORK, LWORK, IWORK, INFO )
        # *     .. Scalar Arguments ..
        #       INTEGER            INFO, LDA, LDB, LWORK, M, N, NRHS, RANK
        #       DOUBLE PRECISION   RCOND
        # *     ..
        # *     .. Array Arguments ..
        #       INTEGER            IWORK( * )
        #       DOUBLE PRECISION   A( LDA, * ), B( LDB, * ), S( * ), WORK( * )
        function gelsd!(A::AbstractMatrix{$elty}, B::AbstractVecOrMat{$elty}, rcond::Real=-one($elty))
            require_one_based_indexing(A, B)
            chkstride1(A, B)
            m, n  = size(A)
            if size(B, 1) != m
                throw(DimensionMismatch("B has leading dimension $(size(B,1)) but needs $m"))
            end
            newB = [B; zeros($elty, max(0, n - size(B, 1)), size(B, 2))]
            s     = similar(A, $elty, min(m, n))
            rnk   = Ref{BlasInt}()
            info  = Ref{BlasInt}()
            work  = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            iwork = Vector{BlasInt}(undef, 1)
            for i = 1:2  # first call returns lwork as work[1] and iwork length as iwork[1]
                ccall((@blasfunc($gelsd), libblastrampoline), Cvoid,
                      (Ref{BlasInt}, Ref{BlasInt}, Ref{BlasInt},
                       Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                       Ptr{$elty}, Ref{$elty}, Ref{BlasInt}, Ptr{$elty},
                       Ref{BlasInt}, Ptr{BlasInt}, Ptr{BlasInt}),
                      m, n, size(B,2),
                      A, max(1,stride(A,2)), newB, max(1,stride(B,2),n),
                      s, $elty(rcond), rnk, work,
                      lwork, iwork, info)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                    resize!(iwork, iwork[1])
                end
            end
            subsetrows(B, newB, n), rnk[]
        end

        #       SUBROUTINE DGELSY( M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK,
        #      $                   WORK, LWORK, INFO )
        # *     .. Scalar Arguments ..
        #       INTEGER            INFO, LDA, LDB, LWORK, M, N, NRHS, RANK
        #       DOUBLE PRECISION   RCOND
        # *     ..
        # *     .. Array Arguments ..
        #       INTEGER            JPVT( * )
        #       DOUBLE PRECISION   A( LDA, * ), B( LDB, * ), WORK( * )
        function gelsy!(A::AbstractMatrix{$elty}, B::AbstractVecOrMat{$elty}, rcond::Real=eps($elty))
            require_one_based_indexing(A, B)
            chkstride1(A)
            m = size(A, 1)
            n = size(A, 2)
            nrhs = size(B, 2)
            if size(B, 1) != m
                throw(DimensionMismatch("B has leading dimension $(size(B,1)) but needs $m"))
            end
            newB = [B; zeros($elty, max(0, n - size(B, 1)), size(B, 2))]
            lda = max(1, stride(A,2))
            ldb = max(1, stride(newB,2))
            jpvt = zeros(BlasInt, n)
            rnk = Ref{BlasInt}()
            work = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            info = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($gelsy), libblastrampoline), Cvoid,
                    (Ref{BlasInt}, Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty},
                     Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt},
                     Ref{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                     Ptr{BlasInt}),
                    m, n, nrhs, A,
                    lda, newB, ldb, jpvt,
                    $elty(rcond), rnk, work, lwork,
                    info)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(work[1])
                    resize!(work, lwork)
                end
            end
            subsetrows(B, newB, n), rnk[]
        end
    end
end

for (gelsd, gelsy, elty, relty) in
    ((:zgelsd_,:zgelsy_,:ComplexF64,:Float64),
     (:cgelsd_,:cgelsy_,:ComplexF32,:Float32))
    @eval begin
        # SUBROUTINE ZGELSD( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK,
        #      $                   WORK, LWORK, RWORK, IWORK, INFO )
        # *     .. Scalar Arguments ..
        #       INTEGER            INFO, LDA, LDB, LWORK, M, N, NRHS, RANK
        #       DOUBLE PRECISION   RCOND
        # *     ..
        # *     .. Array Arguments ..
        #       INTEGER            IWORK( * )
        #       DOUBLE PRECISION   RWORK( * ), S( * )
        #       COMPLEX*16         A( LDA, * ), B( LDB, * ), WORK( * )
        function gelsd!(A::AbstractMatrix{$elty}, B::AbstractVecOrMat{$elty}, rcond::Real=-one($relty))
            require_one_based_indexing(A, B)
            chkstride1(A, B)
            m, n  = size(A)
            if size(B, 1) != m
                throw(DimensionMismatch("B has leading dimension $(size(B,1)) but needs $m"))
            end
            newB = [B; zeros($elty, max(0, n - size(B, 1)), size(B, 2))]
            s     = similar(A, $relty, min(m, n))
            rnk   = Ref{BlasInt}()
            info  = Ref{BlasInt}()
            work  = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            rwork = Vector{$relty}(undef, 1)
            iwork = Vector{BlasInt}(undef, 1)
            for i = 1:2  # first call returns lwork as work[1], rwork length as rwork[1] and iwork length as iwork[1]
                ccall((@blasfunc($gelsd), libblastrampoline), Cvoid,
                      (Ref{BlasInt}, Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty},
                       Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{$relty},
                       Ref{$relty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                       Ptr{$relty}, Ref{BlasInt}, Ref{BlasInt}),
                      m, n, size(B,2), A,
                      max(1,stride(A,2)), newB, max(1,stride(B,2),n), s,
                      $relty(rcond), rnk, work, lwork,
                      rwork, iwork, info)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                    resize!(rwork, BlasInt(rwork[1]))
                    resize!(iwork, iwork[1])
                end
            end
            subsetrows(B, newB, n), rnk[]
        end

        #       SUBROUTINE ZGELSY( M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK,
        #      $                   WORK, LWORK, RWORK, INFO )
        # *     .. Scalar Arguments ..
        #       INTEGER            INFO, LDA, LDB, LWORK, M, N, NRHS, RANK
        #       DOUBLE PRECISION   RCOND
        # *     ..
        # *     .. Array Arguments ..
        #       INTEGER            JPVT( * )
        #       DOUBLE PRECISION   RWORK( * )
        #       COMPLEX*16         A( LDA, * ), B( LDB, * ), WORK( * )
        function gelsy!(A::AbstractMatrix{$elty}, B::AbstractVecOrMat{$elty}, rcond::Real=eps($relty))
            require_one_based_indexing(A, B)
            chkstride1(A, B)
            m, n = size(A)
            nrhs = size(B, 2)
            if size(B, 1) != m
                throw(DimensionMismatch("B has leading dimension $(size(B,1)) but needs $m"))
            end
            newB = [B; zeros($elty, max(0, n - size(B, 1)), size(B, 2))]
            lda = max(1, m)
            ldb = max(1, m, n)
            jpvt = zeros(BlasInt, n)
            rnk = Ref{BlasInt}(1)
            work = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            rwork = Vector{$relty}(undef, 2n)
            info = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($gelsy), libblastrampoline), Cvoid,
                    (Ref{BlasInt}, Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty},
                     Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt},
                     Ref{$relty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                     Ptr{$relty}, Ptr{BlasInt}),
                    m, n, nrhs, A,
                    lda, newB, ldb, jpvt,
                    $relty(rcond), rnk, work, lwork,
                    rwork, info)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            subsetrows(B, newB, n), rnk[]
        end
    end
end

"""
    gelsd!(A, B, rcond) -> (B, rnk)

Computes the least norm solution of `A * X = B` by finding the `SVD`
factorization of `A`, then dividing-and-conquering the problem. `B`
is overwritten with the solution `X`. Singular values below `rcond`
will be treated as zero. Returns the solution in `B` and the effective rank
of `A` in `rnk`.
"""
gelsd!(A::AbstractMatrix, B::AbstractVecOrMat, rcond::Real)

"""
    gelsy!(A, B, rcond) -> (B, rnk)

Computes the least norm solution of `A * X = B` by finding the full `QR`
factorization of `A`, then dividing-and-conquering the problem. `B`
is overwritten with the solution `X`. Singular values below `rcond`
will be treated as zero. Returns the solution in `B` and the effective rank
of `A` in `rnk`.
"""
gelsy!(A::AbstractMatrix, B::AbstractVecOrMat, rcond::Real)

for (gglse, elty) in ((:dgglse_, :Float64),
                      (:sgglse_, :Float32),
                      (:zgglse_, :ComplexF64),
                      (:cgglse_, :ComplexF32))
    @eval begin
        # SUBROUTINE DGGLSE( M, N, P, A, LDA, B, LDB, C, D, X, WORK, LWORK,
        #      $                   INFO )
        # *     .. Scalar Arguments ..
        #       INTEGER            INFO, LDA, LDB, LWORK, M, N, P
        # *     ..
        # *     .. Array Arguments ..
        #       DOUBLE PRECISION   A( LDA, * ), B( LDB, * ), C( * ), D( * ),
        #      $                   WORK( * ), X( * )
        function gglse!(A::AbstractMatrix{$elty}, c::AbstractVector{$elty},
                        B::AbstractMatrix{$elty}, d::AbstractVector{$elty})
            require_one_based_indexing(A, c, B, d)
            chkstride1(A, c, B, d)
            m, n = size(A)
            p = size(B, 1)
            if size(B, 2) != n
                throw(DimensionMismatch("B has second dimension $(size(B,2)), needs $n"))
            end
            if length(c) != m
                throw(DimensionMismatch("c has length $(length(c)), needs $m"))
            end
            if length(d) != p
                throw(DimensionMismatch("d has length $(length(d)), needs $p"))
            end
            X = zeros($elty, n)
            info  = Ref{BlasInt}()
            work  = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($gglse), libblastrampoline), Cvoid,
                      (Ref{BlasInt}, Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty},
                       Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty},
                       Ptr{$elty}, Ptr{$elty}, Ptr{$elty}, Ref{BlasInt},
                       Ptr{BlasInt}),
                      m, n, p, A, max(1,stride(A,2)), B, max(1,stride(B,2)), c, d, X,
                      work, lwork, info)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            X, dot(view(c, n - p + 1:m), view(c, n - p + 1:m))
        end
    end
end

"""
    gglse!(A, c, B, d) -> (X,res)

Solves the equation `A * x = c` where `x` is subject to the equality
constraint `B * x = d`. Uses the formula `||c - A*x||^2 = 0` to solve.
Returns `X` and the residual sum-of-squares.
"""
gglse!(A::AbstractMatrix, c::AbstractVector, B::AbstractMatrix, d::AbstractVector)

# (GE) general matrices eigenvalue-eigenvector and singular value decompositions
for (geev, gesvd, gesdd, ggsvd, elty, relty) in
    ((:dgeev_,:dgesvd_,:dgesdd_,:dggsvd_,:Float64,:Float64),
     (:sgeev_,:sgesvd_,:sgesdd_,:sggsvd_,:Float32,:Float32),
     (:zgeev_,:zgesvd_,:zgesdd_,:zggsvd_,:ComplexF64,:Float64),
     (:cgeev_,:cgesvd_,:cgesdd_,:cggsvd_,:ComplexF32,:Float32))
    @eval begin
        #      SUBROUTINE DGEEV( JOBVL, JOBVR, N, A, LDA, WR, WI, VL, LDVL, VR,
        #      $                  LDVR, WORK, LWORK, INFO )
        # *     .. Scalar Arguments ..
        #       CHARACTER          JOBVL, JOBVR
        #       INTEGER            INFO, LDA, LDVL, LDVR, LWORK, N
        # *     .. Array Arguments ..
        #       DOUBLE PRECISION   A( LDA, * ), VL( LDVL, * ), VR( LDVR, * ),
        #      $                   WI( * ), WORK( * ), WR( * )
        function geev!(jobvl::AbstractChar, jobvr::AbstractChar, A::AbstractMatrix{$elty})
            chkstride1(A)
            n = checksquare(A)
            chkfinite(A) # balancing routines don't support NaNs and Infs
            lvecs = jobvl == 'V'
            rvecs = jobvr == 'V'
            VL    = similar(A, $elty, (n, lvecs ? n : 0))
            VR    = similar(A, $elty, (n, rvecs ? n : 0))
            cmplx = eltype(A) <: Complex
            if cmplx
                W     = similar(A, $elty, n)
                rwork = similar(A, $relty, 2n)
            else
                WR    = similar(A, $elty, n)
                WI    = similar(A, $elty, n)
            end
            work  = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            info  = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                if cmplx
                    ccall((@blasfunc($geev), libblastrampoline), Cvoid,
                          (Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ptr{$elty},
                           Ref{BlasInt}, Ptr{$elty}, Ptr{$elty}, Ref{BlasInt},
                           Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                           Ptr{$relty}, Ptr{BlasInt}, Clong, Clong),
                          jobvl, jobvr, n, A, max(1,stride(A,2)), W, VL, n, VR, n,
                          work, lwork, rwork, info, 1, 1)
                else
                    ccall((@blasfunc($geev), libblastrampoline), Cvoid,
                          (Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ptr{$elty},
                           Ref{BlasInt}, Ptr{$elty}, Ptr{$elty}, Ptr{$elty},
                           Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty},
                           Ref{BlasInt}, Ptr{BlasInt}, Clong, Clong),
                          jobvl, jobvr, n, A, max(1,stride(A,2)), WR, WI, VL, n,
                          VR, n, work, lwork, info, 1, 1)
                end
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            cmplx ? (W, VL, VR) : (WR, WI, VL, VR)
        end

        #    SUBROUTINE DGESDD( JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK,
        #                   LWORK, IWORK, INFO )
        #*     .. Scalar Arguments ..
        #      CHARACTER          JOBZ
        #      INTEGER            INFO, LDA, LDU, LDVT, LWORK, M, N
        #*     ..
        #*     .. Array Arguments ..
        #      INTEGER            IWORK( * )
        #      DOUBLE PRECISION   A( LDA, * ), S( * ), U( LDU, * ),
        #                        VT( LDVT, * ), WORK( * )
        function gesdd!(job::AbstractChar, A::AbstractMatrix{$elty})
            require_one_based_indexing(A)
            chkstride1(A)
            m, n   = size(A)
            minmn  = min(m, n)
            if job == 'A'
                U  = similar(A, $elty, (m, m))
                VT = similar(A, $elty, (n, n))
            elseif job == 'S'
                U  = similar(A, $elty, (m, minmn))
                VT = similar(A, $elty, (minmn, n))
            elseif job == 'O'
                U  = similar(A, $elty, (m, m >= n ? 0 : m))
                VT = similar(A, $elty, (n, m >= n ? n : 0))
            else
                U  = similar(A, $elty, (m, 0))
                VT = similar(A, $elty, (n, 0))
            end
            work   = Vector{$elty}(undef, 1)
            lwork  = BlasInt(-1)
            S      = similar(A, $relty, minmn)
            cmplx  = eltype(A)<:Complex
            if cmplx
                rwork = Vector{$relty}(undef, job == 'N' ? 7*minmn : minmn*max(5*minmn+7, 2*max(m,n)+2*minmn+1))
            end
            iwork  = Vector{BlasInt}(undef, 8*minmn)
            info   = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                if cmplx
                    ccall((@blasfunc($gesdd), libblastrampoline), Cvoid,
                          (Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty},
                           Ref{BlasInt}, Ptr{$relty}, Ptr{$elty}, Ref{BlasInt},
                           Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                           Ptr{$relty}, Ptr{BlasInt}, Ptr{BlasInt}, Clong),
                          job, m, n, A, max(1,stride(A,2)), S, U, max(1,stride(U,2)), VT, max(1,stride(VT,2)),
                          work, lwork, rwork, iwork, info, 1)
                else
                    ccall((@blasfunc($gesdd), libblastrampoline), Cvoid,
                          (Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty},
                           Ref{BlasInt}, Ptr{$elty}, Ptr{$elty}, Ref{BlasInt},
                           Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                           Ptr{BlasInt}, Ptr{BlasInt}, Clong),
                          job, m, n, A, max(1,stride(A,2)), S, U, max(1,stride(U,2)), VT, max(1,stride(VT,2)),
                          work, lwork, iwork, info, 1)
                end
                chklapackerror(info[])
                if i == 1
                    # Work around issue with truncated Float32 representation of lwork in
                    # sgesdd by using nextfloat. See
                    # http://icl.cs.utk.edu/lapack-forum/viewtopic.php?f=13&t=4587&p=11036&hilit=sgesdd#p11036
                    # and
                    # https://github.com/scipy/scipy/issues/5401
                    lwork = round(BlasInt, nextfloat(real(work[1])))
                    resize!(work, lwork)
                end
            end
            if job == 'O'
                if m >= n
                    return (A, S, VT)
                else
                    # ()__
                    # ||::Z__
                    # ||::|:::Z____
                    # ||::|:::|====|
                    # ||==|===|====|
                    # ||""|===|====|
                    # ||  `"""|====|
                    # ||      `""""`
                    return (U, S, A)
                end
            end
            return (U, S, VT)
        end

        # SUBROUTINE DGESVD( JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, INFO )
        # *     .. Scalar Arguments ..
        #       CHARACTER          JOBU, JOBVT
        #       INTEGER            INFO, LDA, LDU, LDVT, LWORK, M, N
        # *     .. Array Arguments ..
        #       DOUBLE PRECISION   A( LDA, * ), S( * ), U( LDU, * ),
        #      $                   VT( LDVT, * ), WORK( * )
        function gesvd!(jobu::AbstractChar, jobvt::AbstractChar, A::AbstractMatrix{$elty})
            require_one_based_indexing(A)
            chkstride1(A)
            m, n   = size(A)
            minmn  = min(m, n)
            S      = similar(A, $relty, minmn)
            U      = similar(A, $elty, jobu  == 'A' ? (m, m) : (jobu  == 'S' ? (m, minmn) : (m, 0)))
            VT     = similar(A, $elty, jobvt == 'A' ? (n, n) : (jobvt == 'S' ? (minmn, n) : (n, 0)))
            work   = Vector{$elty}(undef, 1)
            cmplx  = eltype(A) <: Complex
            if cmplx
                rwork = Vector{$relty}(undef, 5minmn)
            end
            lwork  = BlasInt(-1)
            info   = Ref{BlasInt}()
            for i in 1:2  # first call returns lwork as work[1]
                if cmplx
                    ccall((@blasfunc($gesvd), libblastrampoline), Cvoid,
                          (Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt},
                           Ptr{$elty}, Ref{BlasInt}, Ptr{$relty}, Ptr{$elty},
                           Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty},
                           Ref{BlasInt}, Ptr{$relty}, Ptr{BlasInt}, Clong, Clong),
                          jobu, jobvt, m, n, A, max(1,stride(A,2)), S, U, max(1,stride(U,2)), VT, max(1,stride(VT,2)),
                          work, lwork, rwork, info, 1, 1)
                else
                    ccall((@blasfunc($gesvd), libblastrampoline), Cvoid,
                          (Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt},
                           Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ptr{$elty},
                           Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty},
                           Ref{BlasInt}, Ptr{BlasInt}, Clong, Clong),
                          jobu, jobvt, m, n, A, max(1,stride(A,2)), S, U, max(1,stride(U,2)), VT, max(1,stride(VT,2)),
                          work, lwork, info, 1, 1)
                end
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            if jobu == 'O'
                return (A, S, VT)
            elseif jobvt == 'O'
                    # =============|===========|()
                                   # # # #::::::
                                   # # # #::::::
                                   # # # #::::::
                                   # # # #::::::
                                   # # # # # # #
                                   # # # # # # #
                                   # # # # # # #
                return (U, S, A)   # # # # # # #
            else                   # # # # # # #
                return (U, S, VT)  # # # # # # #

            end
        end

        #       SUBROUTINE ZGGSVD( JOBU, JOBV, JOBQ, M, N, P, K, L, A, LDA, B,
        #      $                   LDB, ALPHA, BETA, U, LDU, V, LDV, Q, LDQ, WORK,
        #      $                   RWORK, IWORK, INFO )
        # *     .. Scalar Arguments ..
        #       CHARACTER          JOBQ, JOBU, JOBV
        #       INTEGER            INFO, K, L, LDA, LDB, LDQ, LDU, LDV, M, N, P
        # *     ..
        # *     .. Array Arguments ..
        #       INTEGER            IWORK( * )
        #       DOUBLE PRECISION   ALPHA( * ), BETA( * ), RWORK( * )
        #       COMPLEX*16         A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
        #      $                   U( LDU, * ), V( LDV, * ), WORK( * )
        function ggsvd!(jobu::AbstractChar, jobv::AbstractChar, jobq::AbstractChar, A::AbstractMatrix{$elty}, B::AbstractMatrix{$elty})
            require_one_based_indexing(A, B)
            chkstride1(A, B)
            m, n = size(A)
            if size(B, 2) != n
                throw(DimensionMismatch("B has second dimension $(size(B,2)) but needs $n"))
            end
            p = size(B, 1)
            k = Vector{BlasInt}(undef, 1)
            l = Vector{BlasInt}(undef, 1)
            lda = max(1,stride(A, 2))
            ldb = max(1,stride(B, 2))
            alpha = similar(A, $relty, n)
            beta = similar(A, $relty, n)
            ldu = max(1, m)
            U = jobu == 'U' ? similar(A, $elty, ldu, m) : similar(A, $elty, 0)
            ldv = max(1, p)
            V = jobv == 'V' ? similar(A, $elty, ldv, p) : similar(A, $elty, 0)
            ldq = max(1, n)
            Q = jobq == 'Q' ? similar(A, $elty, ldq, n) : similar(A, $elty, 0)
            work = Vector{$elty}(undef, max(3n, m, p) + n)
            cmplx = eltype(A) <: Complex
            if cmplx
                rwork = Vector{$relty}(undef, 2n)
            end
            iwork = Vector{BlasInt}(undef, n)
            info = Ref{BlasInt}()
            if cmplx
                ccall((@blasfunc($ggsvd), libblastrampoline), Cvoid,
                    (Ref{UInt8}, Ref{UInt8}, Ref{UInt8}, Ref{BlasInt},
                    Ref{BlasInt}, Ref{BlasInt}, Ptr{BlasInt}, Ptr{BlasInt},
                    Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                    Ptr{$relty}, Ptr{$relty}, Ptr{$elty}, Ref{BlasInt},
                    Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                    Ptr{$elty}, Ptr{$relty}, Ptr{BlasInt}, Ptr{BlasInt},
                    Clong, Clong, Clong),
                    jobu, jobv, jobq, m,
                    n, p, k, l,
                    A, lda, B, ldb,
                    alpha, beta, U, ldu,
                    V, ldv, Q, ldq,
                    work, rwork, iwork, info,
                    1, 1, 1)
            else
                ccall((@blasfunc($ggsvd), libblastrampoline), Cvoid,
                    (Ref{UInt8}, Ref{UInt8}, Ref{UInt8}, Ref{BlasInt},
                    Ref{BlasInt}, Ref{BlasInt}, Ptr{BlasInt}, Ptr{BlasInt},
                    Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                    Ptr{$relty}, Ptr{$relty}, Ptr{$elty}, Ref{BlasInt},
                    Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                    Ptr{$elty}, Ptr{BlasInt}, Ptr{BlasInt},
                    Clong, Clong, Clong),
                    jobu, jobv, jobq, m,
                    n, p, k, l,
                    A, lda, B, ldb,
                    alpha, beta, U, ldu,
                    V, ldv, Q, ldq,
                    work, iwork, info,
                    1, 1, 1)
            end
            chklapackerror(info[])
            if m - k[1] - l[1] >= 0
                R = triu(A[1:k[1] + l[1],n - k[1] - l[1] + 1:n])
            else
                R = triu([A[1:m, n - k[1] - l[1] + 1:n]; B[m - k[1] + 1:l[1], n - k[1] - l[1] + 1:n]])
            end
            U, V, Q, alpha, beta, k[1], l[1], R
        end
    end
end

"""
    geev!(jobvl, jobvr, A) -> (W, VL, VR)

Finds the eigensystem of `A`. If `jobvl = N`, the left eigenvectors of
`A` aren't computed. If `jobvr = N`, the right eigenvectors of `A`
aren't computed. If `jobvl = V` or `jobvr = V`, the corresponding
eigenvectors are computed. Returns the eigenvalues in `W`, the right
eigenvectors in `VR`, and the left eigenvectors in `VL`.
"""
geev!(jobvl::AbstractChar, jobvr::AbstractChar, A::AbstractMatrix)

"""
    gesdd!(job, A) -> (U, S, VT)

Finds the singular value decomposition of `A`, `A = U * S * V'`,
using a divide and conquer approach. If `job = A`, all the columns of `U` and
the rows of `V'` are computed. If `job = N`, no columns of `U` or rows of `V'`
are computed. If `job = O`, `A` is overwritten with the columns of (thin) `U`
and the rows of (thin) `V'`. If `job = S`, the columns of (thin) `U` and the
rows of (thin) `V'` are computed and returned separately.
"""
gesdd!(job::AbstractChar, A::AbstractMatrix)

"""
    gesvd!(jobu, jobvt, A) -> (U, S, VT)

Finds the singular value decomposition of `A`, `A = U * S * V'`.
If `jobu = A`, all the columns of `U` are computed. If `jobvt = A` all the rows
of `V'` are computed. If `jobu = N`, no columns of `U` are computed. If
`jobvt = N` no rows of `V'` are computed. If `jobu = O`, `A` is overwritten with
the columns of (thin) `U`. If `jobvt = O`, `A` is overwritten with the rows
of (thin) `V'`. If `jobu = S`, the columns of (thin) `U` are computed
and returned separately. If `jobvt = S` the rows of (thin) `V'` are
computed and returned separately. `jobu` and `jobvt` can't both be `O`.

Returns `U`, `S`, and `Vt`, where `S` are the singular values of `A`.
"""
gesvd!(jobu::AbstractChar, jobvt::AbstractChar, A::AbstractMatrix)

"""
    ggsvd!(jobu, jobv, jobq, A, B) -> (U, V, Q, alpha, beta, k, l, R)

Finds the generalized singular value decomposition of `A` and `B`, `U'*A*Q = D1*R`
and `V'*B*Q = D2*R`. `D1` has `alpha` on its diagonal and `D2` has `beta` on its
diagonal. If `jobu = U`, the orthogonal/unitary matrix `U` is computed. If
`jobv = V` the orthogonal/unitary matrix `V` is computed. If `jobq = Q`,
the orthogonal/unitary matrix `Q` is computed. If `jobu`, `jobv` or `jobq` is
`N`, that matrix is not computed. This function is only available in LAPACK
versions prior to 3.6.0.
"""
ggsvd!(jobu::AbstractChar, jobv::AbstractChar, jobq::AbstractChar, A::AbstractMatrix, B::AbstractMatrix)


for (f, elty) in ((:dggsvd3_, :Float64),
                  (:sggsvd3_, :Float32))
    @eval begin
        function ggsvd3!(jobu::AbstractChar, jobv::AbstractChar, jobq::AbstractChar, A::AbstractMatrix{$elty}, B::AbstractMatrix{$elty})
            require_one_based_indexing(A, B)
            chkstride1(A, B)
            m, n = size(A)
            if size(B, 2) != n
                throw(DimensionMismatch("B has second dimension $(size(B,2)) but needs $n"))
            end
            p = size(B, 1)
            k = Ref{BlasInt}()
            l = Ref{BlasInt}()
            lda = max(1, stride(A, 2))
            ldb = max(1, stride(B, 2))
            alpha = similar(A, $elty, n)
            beta = similar(A, $elty, n)
            ldu = max(1, m)
            U = jobu == 'U' ? similar(A, $elty, ldu, m) : similar(A, $elty, 0)
            ldv = max(1, p)
            V = jobv == 'V' ? similar(A, $elty, ldv, p) : similar(A, $elty, 0)
            ldq = max(1, n)
            Q = jobq == 'Q' ? similar(A, $elty, ldq, n) : similar(A, $elty, 0)
            work = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            iwork = Vector{BlasInt}(undef, n)
            info = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($f), libblastrampoline), Cvoid,
                    (Ref{UInt8}, Ref{UInt8}, Ref{UInt8}, Ref{BlasInt},
                    Ref{BlasInt}, Ref{BlasInt}, Ref{BlasInt}, Ref{BlasInt},
                    Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                    Ptr{$elty}, Ptr{$elty}, Ptr{$elty}, Ref{BlasInt},
                    Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                    Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}, Ref{BlasInt},
                    Clong, Clong, Clong),
                    jobu, jobv, jobq, m,
                    n, p, k, l,
                    A, lda, B, ldb,
                    alpha, beta, U, ldu,
                    V, ldv, Q, ldq,
                    work, lwork, iwork, info,
                    1, 1, 1)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(work[1])
                    resize!(work, lwork)
                end
            end
            if m - k[] - l[] >= 0
                R = triu(A[1:k[] + l[],n - k[] - l[] + 1:n])
            else
                R = triu([A[1:m, n - k[] - l[] + 1:n]; B[m - k[] + 1:l[], n - k[] - l[] + 1:n]])
            end
            return U, V, Q, alpha, beta, k[], l[], R
        end
    end
end

for (f, elty, relty) in ((:zggsvd3_, :ComplexF64, :Float64),
                         (:cggsvd3_, :ComplexF32, :Float32))
    @eval begin
        function ggsvd3!(jobu::AbstractChar, jobv::AbstractChar, jobq::AbstractChar, A::AbstractMatrix{$elty}, B::AbstractMatrix{$elty})
            require_one_based_indexing(A, B)
            chkstride1(A, B)
            m, n = size(A)
            if size(B, 2) != n
                throw(DimensionMismatch("B has second dimension $(size(B,2)) but needs $n"))
            end
            p = size(B, 1)
            k = Vector{BlasInt}(undef, 1)
            l = Vector{BlasInt}(undef, 1)
            lda = max(1,stride(A, 2))
            ldb = max(1,stride(B, 2))
            alpha = similar(A, $relty, n)
            beta = similar(A, $relty, n)
            ldu = max(1, m)
            U = jobu == 'U' ? similar(A, $elty, ldu, m) : similar(A, $elty, 0)
            ldv = max(1, p)
            V = jobv == 'V' ? similar(A, $elty, ldv, p) : similar(A, $elty, 0)
            ldq = max(1, n)
            Q = jobq == 'Q' ? similar(A, $elty, ldq, n) : similar(A, $elty, 0)
            work = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            rwork = Vector{$relty}(undef, 2n)
            iwork = Vector{BlasInt}(undef, n)
            info = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($f), libblastrampoline), Cvoid,
                    (Ref{UInt8}, Ref{UInt8}, Ref{UInt8}, Ref{BlasInt},
                    Ref{BlasInt}, Ref{BlasInt}, Ptr{BlasInt}, Ptr{BlasInt},
                    Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                    Ptr{$relty}, Ptr{$relty}, Ptr{$elty}, Ref{BlasInt},
                    Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                    Ptr{$elty}, Ref{BlasInt}, Ptr{$relty}, Ptr{BlasInt},
                    Ptr{BlasInt}, Clong, Clong, Clong),
                    jobu, jobv, jobq, m,
                    n, p, k, l,
                    A, lda, B, ldb,
                    alpha, beta, U, ldu,
                    V, ldv, Q, ldq,
                    work, lwork, rwork, iwork,
                    info, 1, 1, 1)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(work[1])
                    resize!(work, lwork)
                end
            end
            if m - k[1] - l[1] >= 0
                R = triu(A[1:k[1] + l[1],n - k[1] - l[1] + 1:n])
            else
                R = triu([A[1:m, n - k[1] - l[1] + 1:n]; B[m - k[1] + 1:l[1], n - k[1] - l[1] + 1:n]])
            end
            return U, V, Q, alpha, beta, k[1], l[1], R
        end
    end
end

"""
    ggsvd3!(jobu, jobv, jobq, A, B) -> (U, V, Q, alpha, beta, k, l, R)

Finds the generalized singular value decomposition of `A` and `B`, `U'*A*Q = D1*R`
and `V'*B*Q = D2*R`. `D1` has `alpha` on its diagonal and `D2` has `beta` on its
diagonal. If `jobu = U`, the orthogonal/unitary matrix `U` is computed. If
`jobv = V` the orthogonal/unitary matrix `V` is computed. If `jobq = Q`,
the orthogonal/unitary matrix `Q` is computed. If `jobu`, `jobv`, or `jobq` is
`N`, that matrix is not computed. This function requires LAPACK 3.6.0.
"""
ggsvd3!

## Expert driver and generalized eigenvalue problem
for (geevx, ggev, ggev3, elty) in
    ((:dgeevx_,:dggev_,:dggev3_,:Float64),
     (:sgeevx_,:sggev_,:sggev3_,:Float32))
    @eval begin
        #     SUBROUTINE DGEEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, WR, WI,
        #                          VL, LDVL, VR, LDVR, ILO, IHI, SCALE, ABNRM,
        #                          RCONDE, RCONDV, WORK, LWORK, IWORK, INFO )
        #
        #       .. Scalar Arguments ..
        #       CHARACTER          BALANC, JOBVL, JOBVR, SENSE
        #       INTEGER            IHI, ILO, INFO, LDA, LDVL, LDVR, LWORK, N
        #       DOUBLE PRECISION   ABNRM
        #       ..
        #       .. Array Arguments ..
        #       INTEGER            IWORK( * )
        #       DOUBLE PRECISION   A( LDA, * ), RCONDE( * ), RCONDV( * ),
        #      $                   SCALE( * ), VL( LDVL, * ), VR( LDVR, * ),
        #      $                   WI( * ), WORK( * ), WR( * )
        function geevx!(balanc::AbstractChar, jobvl::AbstractChar, jobvr::AbstractChar, sense::AbstractChar, A::AbstractMatrix{$elty})
            n = checksquare(A)
            chkfinite(A) # balancing routines don't support NaNs and Infs
            lda = max(1,stride(A,2))
            wr = similar(A, $elty, n)
            wi = similar(A, $elty, n)
            if balanc ∉ ['N', 'P', 'S', 'B']
                throw(ArgumentError("balanc must be 'N', 'P', 'S', or 'B', but $balanc was passed"))
            end
            ldvl = 0
            if jobvl == 'V'
                ldvl = n
            elseif jobvl == 'N'
                ldvl = 0
            else
                throw(ArgumentError("jobvl must be 'V' or 'N', but $jobvl was passed"))
            end
            VL = similar(A, $elty, ldvl, n)
            ldvr = 0
            if jobvr == 'V'
                ldvr = n
            elseif jobvr == 'N'
                ldvr = 0
            else
                throw(ArgumentError("jobvr must be 'V' or 'N', but $jobvr was passed"))
            end
            VR = similar(A, $elty, ldvr, n)
            ilo = Ref{BlasInt}()
            ihi = Ref{BlasInt}()
            scale = similar(A, $elty, n)
            abnrm = Ref{$elty}()
            rconde = similar(A, $elty, n)
            rcondv = similar(A, $elty, n)
            work = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            iworksize = 0
            if sense == 'N' || sense == 'E'
                iworksize = 0
            elseif sense == 'V' || sense == 'B'
                iworksize = 2*n - 2
            else
                throw(ArgumentError("sense must be 'N', 'E', 'V' or 'B', but $sense was passed"))
            end
            iwork = Vector{BlasInt}(undef, iworksize)
            info = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($geevx), libblastrampoline), Cvoid,
                      (Ref{UInt8}, Ref{UInt8}, Ref{UInt8}, Ref{UInt8},
                       Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty},
                       Ptr{$elty}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty},
                       Ref{BlasInt}, Ptr{BlasInt}, Ptr{BlasInt}, Ptr{$elty},
                       Ptr{$elty}, Ptr{$elty}, Ptr{$elty}, Ptr{$elty},
                       Ref{BlasInt}, Ptr{BlasInt}, Ref{BlasInt},
                       Clong, Clong, Clong, Clong),
                       balanc, jobvl, jobvr, sense,
                       n, A, lda, wr,
                       wi, VL, max(1,ldvl), VR,
                       max(1,ldvr), ilo, ihi, scale,
                       abnrm, rconde, rcondv, work,
                       lwork, iwork, info,
                       1, 1, 1, 1)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(work[1])
                    resize!(work, lwork)
                end
            end
            A, wr, wi, VL, VR, ilo[], ihi[], scale, abnrm[], rconde, rcondv
        end

        #       SUBROUTINE DGGEV( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHAR, ALPHAI,
        #      $                  BETA, VL, LDVL, VR, LDVR, WORK, LWORK, INFO )
        # *     .. Scalar Arguments ..
        #       CHARACTER          JOBVL, JOBVR
        #       INTEGER            INFO, LDA, LDB, LDVL, LDVR, LWORK, N
        # *     ..
        # *     .. Array Arguments ..
        #       DOUBLE PRECISION   A( LDA, * ), ALPHAI( * ), ALPHAR( * ),
        #      $                   B( LDB, * ), BETA( * ), VL( LDVL, * ),
        #      $                   VR( LDVR, * ), WORK( * )
        function ggev!(jobvl::AbstractChar, jobvr::AbstractChar, A::AbstractMatrix{$elty}, B::AbstractMatrix{$elty})
            require_one_based_indexing(A, B)
            chkstride1(A,B)
            n, m = checksquare(A,B)
            if n != m
                throw(DimensionMismatch("A has dimensions $(size(A)), and B has dimensions $(size(B)), but A and B must have the same size"))
            end
            lda = max(1, stride(A, 2))
            ldb = max(1, stride(B, 2))
            alphar = similar(A, $elty, n)
            alphai = similar(A, $elty, n)
            beta = similar(A, $elty, n)
            ldvl = 0
            if jobvl == 'V'
                ldvl = n
            elseif jobvl == 'N'
                ldvl = 1
            else
                throw(ArgumentError("jobvl must be 'V' or 'N', but $jobvl was passed"))
            end
            vl = similar(A, $elty, ldvl, n)
            ldvr = 0
            if jobvr == 'V'
                ldvr = n
            elseif jobvr == 'N'
                ldvr = 1
            else
                throw(ArgumentError("jobvr must be 'V' or 'N', but $jobvr was passed"))
            end
            vr = similar(A, $elty, ldvr, n)
            work = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            info = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($ggev), libblastrampoline), Cvoid,
                    (Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ptr{$elty},
                     Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty},
                     Ptr{$elty}, Ptr{$elty}, Ptr{$elty}, Ref{BlasInt},
                     Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                     Ref{BlasInt}, Clong, Clong),
                    jobvl, jobvr, n, A,
                    lda, B, ldb, alphar,
                    alphai, beta, vl, ldvl,
                    vr, ldvr, work, lwork,
                    info, 1, 1)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(work[1])
                    resize!(work, lwork)
                end
            end
            alphar, alphai, beta, vl, vr
        end

        #       SUBROUTINE DGGEV3( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHAR, ALPHAI,
        #      $                   BETA, VL, LDVL, VR, LDVR, WORK, LWORK, INFO )
        # *     .. Scalar Arguments ..
        #       CHARACTER          JOBVL, JOBVR
        #       INTEGER            INFO, LDA, LDB, LDVL, LDVR, LWORK, N
        # *     ..
        # *     .. Array Arguments ..
        #       DOUBLE PRECISION   A( LDA, * ), ALPHAI( * ), ALPHAR( * ),
        #      $                   B( LDB, * ), BETA( * ), VL( LDVL, * ),
        #      $                   VR( LDVR, * ), WORK( * )
        function ggev3!(jobvl::AbstractChar, jobvr::AbstractChar, A::AbstractMatrix{$elty}, B::AbstractMatrix{$elty})
            require_one_based_indexing(A, B)
            chkstride1(A,B)
            n, m = checksquare(A,B)
            if n != m
                throw(DimensionMismatch("A has dimensions $(size(A)), and B has dimensions $(size(B)), but A and B must have the same size"))
            end
            lda = max(1, stride(A, 2))
            ldb = max(1, stride(B, 2))
            alphar = similar(A, $elty, n)
            alphai = similar(A, $elty, n)
            beta = similar(A, $elty, n)
            ldvl = 0
            if jobvl == 'V'
                ldvl = n
            elseif jobvl == 'N'
                ldvl = 1
            else
                throw(ArgumentError("jobvl must be 'V' or 'N', but $jobvl was passed"))
            end
            vl = similar(A, $elty, ldvl, n)
            ldvr = 0
            if jobvr == 'V'
                ldvr = n
            elseif jobvr == 'N'
                ldvr = 1
            else
                throw(ArgumentError("jobvr must be 'V' or 'N', but $jobvr was passed"))
            end
            vr = similar(A, $elty, ldvr, n)
            work = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            info = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($ggev3), libblastrampoline), Cvoid,
                    (Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ptr{$elty},
                     Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty},
                     Ptr{$elty}, Ptr{$elty}, Ptr{$elty}, Ref{BlasInt},
                     Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                     Ref{BlasInt}, Clong, Clong),
                    jobvl, jobvr, n, A,
                    lda, B, ldb, alphar,
                    alphai, beta, vl, ldvl,
                    vr, ldvr, work, lwork,
                    info, 1, 1)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(work[1])
                    resize!(work, lwork)
                end
            end
            alphar, alphai, beta, vl, vr
        end
    end
end

for (geevx, ggev, ggev3, elty, relty) in
    ((:zgeevx_,:zggev_,:zggev3_,:ComplexF64,:Float64),
     (:cgeevx_,:cggev_,:cggev3_,:ComplexF32,:Float32))
    @eval begin
        #     SUBROUTINE ZGEEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, W, VL,
        #                          LDVL, VR, LDVR, ILO, IHI, SCALE, ABNRM, RCONDE,
        #                          RCONDV, WORK, LWORK, RWORK, INFO )
        #
        #       .. Scalar Arguments ..
        #       CHARACTER          BALANC, JOBVL, JOBVR, SENSE
        #       INTEGER            IHI, ILO, INFO, LDA, LDVL, LDVR, LWORK, N
        #       DOUBLE PRECISION   ABNRM
        #       ..
        #       .. Array Arguments ..
        #       DOUBLE PRECISION   RCONDE( * ), RCONDV( * ), RWORK( * ),
        #      $                   SCALE( * )
        #       COMPLEX*16         A( LDA, * ), VL( LDVL, * ), VR( LDVR, * ),
        #      $                   W( * ), WORK( * )
        function geevx!(balanc::AbstractChar, jobvl::AbstractChar, jobvr::AbstractChar, sense::AbstractChar, A::AbstractMatrix{$elty})
            n = checksquare(A)
            chkfinite(A) # balancing routines don't support NaNs and Infs
            lda = max(1,stride(A,2))
            w = similar(A, $elty, n)
            if balanc ∉ ['N', 'P', 'S', 'B']
                throw(ArgumentError("balanc must be 'N', 'P', 'S', or 'B', but $balanc was passed"))
            end
            ldvl = 0
            if jobvl == 'V'
                ldvl = n
            elseif jobvl == 'N'
                ldvl = 0
            else
                throw(ArgumentError("jobvl must be 'V' or 'N', but $jobvl was passed"))
            end
            VL = similar(A, $elty, ldvl, n)
            ldvr = 0
            if jobvr == 'V'
                ldvr = n
            elseif jobvr == 'N'
                ldvr = 0
            else
                throw(ArgumentError("jobvr must be 'V' or 'N', but $jobvr was passed"))
            end
            if sense ∉ ['N','E','V','B']
                throw(ArgumentError("sense must be 'N', 'E', 'V' or 'B', but $sense was passed"))
            end
            VR = similar(A, $elty, ldvr, n)
            ilo = Ref{BlasInt}()
            ihi = Ref{BlasInt}()
            scale = similar(A, $relty, n)
            abnrm = Ref{$relty}()
            rconde = similar(A, $relty, n)
            rcondv = similar(A, $relty, n)
            work = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            rwork = Vector{$relty}(undef, 2n)
            info = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($geevx), libblastrampoline), Cvoid,
                      (Ref{UInt8}, Ref{UInt8}, Ref{UInt8}, Ref{UInt8},
                       Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty},
                       Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                       Ptr{BlasInt}, Ptr{BlasInt}, Ptr{$relty}, Ptr{$relty},
                       Ptr{$relty}, Ptr{$relty}, Ptr{$elty}, Ref{BlasInt},
                       Ptr{$relty}, Ref{BlasInt}, Clong, Clong, Clong, Clong),
                       balanc, jobvl, jobvr, sense,
                       n, A, lda, w,
                       VL, max(1,ldvl), VR, max(1,ldvr),
                       ilo, ihi, scale, abnrm,
                       rconde, rcondv, work, lwork,
                       rwork, info, 1, 1, 1, 1)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(work[1])
                    resize!(work, lwork)
                end
            end
            A, w, VL, VR, ilo[], ihi[], scale, abnrm[], rconde, rcondv
        end

        # SUBROUTINE ZGGEV( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA,
        #      $                  VL, LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO )
        # *     .. Scalar Arguments ..
        #       CHARACTER          JOBVL, JOBVR
        #       INTEGER            INFO, LDA, LDB, LDVL, LDVR, LWORK, N
        # *     ..
        # *     .. Array Arguments ..
        #       DOUBLE PRECISION   RWORK( * )
        #       COMPLEX*16         A( LDA, * ), ALPHA( * ), B( LDB, * ),
        #      $                   BETA( * ), VL( LDVL, * ), VR( LDVR, * ),
        #      $                   WORK( * )
        function ggev!(jobvl::AbstractChar, jobvr::AbstractChar, A::AbstractMatrix{$elty}, B::AbstractMatrix{$elty})
            require_one_based_indexing(A, B)
            chkstride1(A, B)
            n, m = checksquare(A, B)
            if n != m
                throw(DimensionMismatch("A has dimensions $(size(A)), and B has dimensions $(size(B)), but A and B must have the same size"))
            end
            lda = max(1, stride(A, 2))
            ldb = max(1, stride(B, 2))
            alpha = similar(A, $elty, n)
            beta = similar(A, $elty, n)
            ldvl = 0
            if jobvl == 'V'
                ldvl = n
            elseif jobvl == 'N'
                ldvl = 1
            else
                throw(ArgumentError("jobvl must be 'V' or 'N', but $jobvl was passed"))
            end
            vl = similar(A, $elty, ldvl, n)
            ldvr = 0
            if jobvr == 'V'
                ldvr = n
            elseif jobvr == 'N'
                ldvr = 1
            else
                throw(ArgumentError("jobvr must be 'V' or 'N', but $jobvr was passed"))
            end
            vr = similar(A, $elty, ldvr, n)
            work = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            rwork = Vector{$relty}(undef, 8n)
            info = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($ggev), libblastrampoline), Cvoid,
                    (Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ptr{$elty},
                     Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty},
                     Ptr{$elty}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty},
                     Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{$relty},
                     Ref{BlasInt}, Clong, Clong),
                    jobvl, jobvr, n, A,
                    lda, B, ldb, alpha,
                    beta, vl, ldvl, vr,
                    ldvr, work, lwork, rwork,
                    info, 1, 1)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(work[1])
                    resize!(work, lwork)
                end
            end
            alpha, beta, vl, vr
        end

        # SUBROUTINE ZGGEV3( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA,
        #      $                  VL, LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO )
        # *     .. Scalar Arguments ..
        #       CHARACTER          JOBVL, JOBVR
        #       INTEGER            INFO, LDA, LDB, LDVL, LDVR, LWORK, N
        # *     ..
        # *     .. Array Arguments ..
        #       DOUBLE PRECISION   RWORK( * )
        #       COMPLEX*16         A( LDA, * ), ALPHA( * ), B( LDB, * ),
        #      $                   BETA( * ), VL( LDVL, * ), VR( LDVR, * ),
        #      $                   WORK( * )
        function ggev3!(jobvl::AbstractChar, jobvr::AbstractChar, A::AbstractMatrix{$elty}, B::AbstractMatrix{$elty})
            require_one_based_indexing(A, B)
            chkstride1(A, B)
            n, m = checksquare(A, B)
            if n != m
                throw(DimensionMismatch("A has dimensions $(size(A)), and B has dimensions $(size(B)), but A and B must have the same size"))
            end
            lda = max(1, stride(A, 2))
            ldb = max(1, stride(B, 2))
            alpha = similar(A, $elty, n)
            beta = similar(A, $elty, n)
            ldvl = 0
            if jobvl == 'V'
                ldvl = n
            elseif jobvl == 'N'
                ldvl = 1
            else
                throw(ArgumentError("jobvl must be 'V' or 'N', but $jobvl was passed"))
            end
            vl = similar(A, $elty, ldvl, n)
            ldvr = 0
            if jobvr == 'V'
                ldvr = n
            elseif jobvr == 'N'
                ldvr = 1
            else
                throw(ArgumentError("jobvr must be 'V' or 'N', but $jobvr was passed"))
            end
            vr = similar(A, $elty, ldvr, n)
            work = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            rwork = Vector{$relty}(undef, 8n)
            info = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($ggev3), libblastrampoline), Cvoid,
                    (Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ptr{$elty},
                     Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty},
                     Ptr{$elty}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty},
                     Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{$relty},
                     Ref{BlasInt}, Clong, Clong),
                    jobvl, jobvr, n, A,
                    lda, B, ldb, alpha,
                    beta, vl, ldvl, vr,
                    ldvr, work, lwork, rwork,
                    info, 1, 1)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(work[1])
                    resize!(work, lwork)
                end
            end
            alpha, beta, vl, vr
        end
    end
end

"""
    geevx!(balanc, jobvl, jobvr, sense, A) -> (A, w, VL, VR, ilo, ihi, scale, abnrm, rconde, rcondv)

Finds the eigensystem of `A` with matrix balancing. If `jobvl = N`, the
left eigenvectors of `A` aren't computed. If `jobvr = N`, the right
eigenvectors of `A` aren't computed. If `jobvl = V` or `jobvr = V`, the
corresponding eigenvectors are computed. If `balanc = N`, no balancing is
performed. If `balanc = P`, `A` is permuted but not scaled. If
`balanc = S`, `A` is scaled but not permuted. If `balanc = B`, `A` is
permuted and scaled. If `sense = N`, no reciprocal condition numbers are
computed. If `sense = E`, reciprocal condition numbers are computed for
the eigenvalues only. If `sense = V`, reciprocal condition numbers are
computed for the right eigenvectors only. If `sense = B`, reciprocal
condition numbers are computed for the right eigenvectors and the
eigenvectors. If `sense = E,B`, the right and left eigenvectors must be
computed.
"""
geevx!(balanc::AbstractChar, jobvl::AbstractChar, jobvr::AbstractChar, sense::AbstractChar, A::AbstractMatrix)

"""
    ggev!(jobvl, jobvr, A, B) -> (alpha, beta, vl, vr)

Finds the generalized eigendecomposition of `A` and `B`. If `jobvl = N`,
the left eigenvectors aren't computed. If `jobvr = N`, the right
eigenvectors aren't computed. If `jobvl = V` or `jobvr = V`, the
corresponding eigenvectors are computed.
"""
ggev!(jobvl::AbstractChar, jobvr::AbstractChar, A::AbstractMatrix, B::AbstractMatrix)

"""
    ggev3!(jobvl, jobvr, A, B) -> (alpha, beta, vl, vr)

Finds the generalized eigendecomposition of `A` and `B` using a blocked
algorithm. If `jobvl = N`, the left eigenvectors aren't computed. If
`jobvr = N`, the right eigenvectors aren't computed. If `jobvl = V` or
`jobvr = V`, the corresponding eigenvectors are computed.  This function
requires LAPACK 3.6.0.
"""
ggev3!(jobvl::AbstractChar, jobvr::AbstractChar, A::AbstractMatrix, B::AbstractMatrix)

# One step incremental condition estimation of max/min singular values
for (laic1, elty) in
    ((:dlaic1_,:Float64),
     (:slaic1_,:Float32))
    @eval begin
        #  SUBROUTINE DLAIC1( JOB, J, X, SEST, W, GAMMA, SESTPR, S, C )
        #
        #  .. Scalar Arguments ..
        #  INTEGER            J, JOB
        #  DOUBLE PRECISION   C, GAMMA, S, SEST, SESTPR
        #  ..
        #  .. Array Arguments ..
        #  DOUBLE PRECISION   W( J ), X( J )
        function laic1!(job::Integer, x::AbstractVector{$elty},
                        sest::$elty, w::AbstractVector{$elty}, gamma::$elty)
            require_one_based_indexing(x, w)
            j = length(x)
            if j != length(w)
                throw(DimensionMismatch("vectors must have same length, but length of x is $j and length of w is $(length(w))"))
            end
            sestpr = Vector{$elty}(undef, 1)
            s = Vector{$elty}(undef, 1)
            c = Vector{$elty}(undef, 1)
            ccall((@blasfunc($laic1), libblastrampoline), Cvoid,
                (Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty}, Ref{$elty},
                 Ptr{$elty}, Ref{$elty}, Ptr{$elty}, Ptr{$elty},
                 Ptr{$elty}),
                job, j, x, sest,
                w, gamma, sestpr, s,
                c)
            sestpr[1], s[1], c[1]
        end
    end
end
for (laic1, elty, relty) in
    ((:zlaic1_,:ComplexF64,:Float64),
     (:claic1_,:ComplexF32,:Float32))
    @eval begin
       #  SUBROUTINE ZLAIC1( JOB, J, X, SEST, W, GAMMA, SESTPR, S, C )
       #
       #  .. Scalar Arguments ..
       #  INTEGER            J, JOB
       #  DOUBLE PRECISION   SEST, SESTPR
       #  COMPLEX*16         C, GAMMA, S
       #  ..
       #  .. Array Arguments ..
       #  COMPLEX*16         W( J ), X( J )
        function laic1!(job::Integer, x::AbstractVector{$elty},
                        sest::$relty, w::AbstractVector{$elty}, gamma::$elty)
            require_one_based_indexing(x, w)
            j = length(x)
            if j != length(w)
                throw(DimensionMismatch("vectors must have same length, but length of x is $j and length of w is $(length(w))"))
            end
            sestpr = Vector{$relty}(undef, 1)
            s = Vector{$elty}(undef, 1)
            c = Vector{$elty}(undef, 1)
            ccall((@blasfunc($laic1), libblastrampoline), Cvoid,
                (Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty}, Ref{$relty},
                 Ptr{$elty}, Ref{$elty}, Ptr{$relty}, Ptr{$elty},
                 Ptr{$elty}),
                job, j, x, sest,
                w, gamma, sestpr, s,
                c)
            sestpr[1], s[1], c[1]
        end
    end
end

# (GT) General tridiagonal, decomposition, solver and direct solver
for (gtsv, gttrf, gttrs, elty) in
    ((:dgtsv_,:dgttrf_,:dgttrs_,:Float64),
     (:sgtsv_,:sgttrf_,:sgttrs_,:Float32),
     (:zgtsv_,:zgttrf_,:zgttrs_,:ComplexF64),
     (:cgtsv_,:cgttrf_,:cgttrs_,:ComplexF32))
    @eval begin
        #       SUBROUTINE DGTSV( N, NRHS, DL, D, DU, B, LDB, INFO )
        #       .. Scalar Arguments ..
        #       INTEGER            INFO, LDB, N, NRHS
        #       .. Array Arguments ..
        #       DOUBLE PRECISION   B( LDB, * ), D( * ), DL( * ), DU( * )
        function gtsv!(dl::AbstractVector{$elty}, d::AbstractVector{$elty}, du::AbstractVector{$elty},
                       B::AbstractVecOrMat{$elty})
            require_one_based_indexing(dl, d, du, B)
            chkstride1(B, dl, d, du)
            n = length(d)
            if !(n >= length(dl) >= n - 1)
                throw(DimensionMismatch("subdiagonal has length $(length(dl)), but should be $n or $(n - 1)"))
            end
            if !(n >= length(du) >= n - 1)
                throw(DimensionMismatch("superdiagonal has length $(length(du)), but should be $n or $(n - 1)"))
            end
            if n != size(B,1)
                throw(DimensionMismatch("B has leading dimension $(size(B,1)), but should have $n"))
            end
            if n == 0
                return B # Early exit if possible
            end
            info = Ref{BlasInt}()
            ccall((@blasfunc($gtsv), libblastrampoline), Cvoid,
                  (Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty}, Ptr{$elty}, Ptr{$elty},
                   Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}),
                  n, size(B,2), dl, d, du, B, max(1,stride(B,2)), info)
            chklapackerror(info[])
            B
        end

        #       SUBROUTINE DGTTRF( N, DL, D, DU, DU2, IPIV, INFO )
        #       .. Scalar Arguments ..
        #       INTEGER            INFO, N
        #       .. Array Arguments ..
        #       INTEGER            IPIV( * )
        #       DOUBLE PRECISION   D( * ), DL( * ), DU( * ), DU2( * )
        function gttrf!(dl::AbstractVector{$elty}, d::AbstractVector{$elty}, du::AbstractVector{$elty})
            require_one_based_indexing(dl, d, du)
            chkstride1(dl,d,du)
            n    = length(d)
            if length(dl) != n - 1
                throw(DimensionMismatch("subdiagonal has length $(length(dl)), but should be $(n - 1)"))
            end
            if length(du) != n - 1
                throw(DimensionMismatch("superdiagonal has length $(length(du)), but should be $(n - 1)"))
            end
            du2  = similar(d, $elty, n-2)
            ipiv = similar(d, BlasInt, n)
            info = Ref{BlasInt}()
            ccall((@blasfunc($gttrf), libblastrampoline), Cvoid,
                  (Ref{BlasInt}, Ptr{$elty}, Ptr{$elty}, Ptr{$elty}, Ptr{$elty},
                   Ptr{BlasInt}, Ptr{BlasInt}),
                  n, dl, d, du, du2, ipiv, info)
            chklapackerror(info[])
            dl, d, du, du2, ipiv
        end

        #       SUBROUTINE DGTTRS( TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB, INFO )
        #       .. Scalar Arguments ..
        #       CHARACTER          TRANS
        #       INTEGER            INFO, LDB, N, NRHS
        #       .. Array Arguments ..
        #       INTEGER            IPIV( * )
        #       DOUBLE PRECISION   B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
        function gttrs!(trans::AbstractChar, dl::AbstractVector{$elty}, d::AbstractVector{$elty},
                        du::AbstractVector{$elty}, du2::AbstractVector{$elty}, ipiv::AbstractVector{BlasInt},
                        B::AbstractVecOrMat{$elty})
            require_one_based_indexing(dl, d, du, du2, ipiv, B)
            chktrans(trans)
            chkstride1(B, ipiv, dl, d, du, du2)
            n = length(d)
            if length(dl) != n - 1
                throw(DimensionMismatch("subdiagonal has length $(length(dl)), but should be $(n - 1)"))
            end
            if length(du) != n - 1
                throw(DimensionMismatch("superdiagonal has length $(length(du)), but should be $(n - 1)"))
            end
            if n != size(B,1)
                throw(DimensionMismatch("B has leading dimension $(size(B,1)), but should have $n"))
            end
            info = Ref{BlasInt}()
            ccall((@blasfunc($gttrs), libblastrampoline), Cvoid,
                   (Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt},
                    Ptr{$elty}, Ptr{$elty}, Ptr{$elty}, Ptr{$elty},
                    Ptr{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}, Clong),
                   trans, n, size(B,2), dl, d, du, du2, ipiv, B, max(1,stride(B,2)), info, 1)
            chklapackerror(info[])
            B
         end
    end
end

"""
    gtsv!(dl, d, du, B)

Solves the equation `A * X = B` where `A` is a tridiagonal matrix with
`dl` on the subdiagonal, `d` on the diagonal, and `du` on the
superdiagonal.

Overwrites `B` with the solution `X` and returns it.
"""
gtsv!(dl::AbstractVector, d::AbstractVector, du::AbstractVector, B::AbstractVecOrMat)

"""
    gttrf!(dl, d, du) -> (dl, d, du, du2, ipiv)

Finds the `LU` factorization of a tridiagonal matrix with `dl` on the
subdiagonal, `d` on the diagonal, and `du` on the superdiagonal.

Modifies `dl`, `d`, and `du` in-place and returns them and the second
superdiagonal `du2` and the pivoting vector `ipiv`.
"""
gttrf!(dl::AbstractVector, d::AbstractVector, du::AbstractVector)

"""
    gttrs!(trans, dl, d, du, du2, ipiv, B)

Solves the equation `A * X = B` (`trans = N`), `transpose(A) * X = B` (`trans = T`),
or `adjoint(A) * X = B` (`trans = C`) using the `LU` factorization computed by
`gttrf!`. `B` is overwritten with the solution `X`.
"""
gttrs!(trans::AbstractChar, dl::AbstractVector, d::AbstractVector, du::AbstractVector, du2::AbstractVector,
       ipiv::AbstractVector{BlasInt}, B::AbstractVecOrMat)

## (OR) orthogonal (or UN, unitary) matrices, extractors and multiplication
for (orglq, orgqr, orgql, orgrq, ormlq, ormqr, ormql, ormrq, gemqrt, elty) in
    ((:dorglq_,:dorgqr_,:dorgql_,:dorgrq_,:dormlq_,:dormqr_,:dormql_,:dormrq_,:dgemqrt_,:Float64),
     (:sorglq_,:sorgqr_,:sorgql_,:sorgrq_,:sormlq_,:sormqr_,:sormql_,:sormrq_,:sgemqrt_,:Float32),
     (:zunglq_,:zungqr_,:zungql_,:zungrq_,:zunmlq_,:zunmqr_,:zunmql_,:zunmrq_,:zgemqrt_,:ComplexF64),
     (:cunglq_,:cungqr_,:cungql_,:cungrq_,:cunmlq_,:cunmqr_,:cunmql_,:cunmrq_,:cgemqrt_,:ComplexF32))
    @eval begin
        # SUBROUTINE DORGLQ( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
        # *     .. Scalar Arguments ..
        #       INTEGER            INFO, K, LDA, LWORK, M, N
        # *     .. Array Arguments ..
        #       DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
        function orglq!(A::AbstractMatrix{$elty}, tau::AbstractVector{$elty}, k::Integer = length(tau))
            require_one_based_indexing(A, tau)
            chkstride1(A,tau)
            n = size(A, 2)
            m = min(n, size(A, 1))
            if k > m
                throw(DimensionMismatch("invalid number of reflectors: k = $k should be <= m = $m"))
            end
            work  = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            info  = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($orglq), libblastrampoline), Cvoid,
                      (Ref{BlasInt}, Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty},
                       Ref{BlasInt}, Ptr{$elty}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}),
                      m, n, k, A, max(1,stride(A,2)), tau, work, lwork, info)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            if m < size(A,1)
                A[1:m,:]
            else
                A
            end
        end

        # SUBROUTINE DORGQR( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
        # *     .. Scalar Arguments ..
        #       INTEGER            INFO, K, LDA, LWORK, M, N
        # *     .. Array Arguments ..
        #       DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
        function orgqr!(A::AbstractMatrix{$elty}, tau::AbstractVector{$elty}, k::Integer = length(tau))
            require_one_based_indexing(A, tau)
            chkstride1(A,tau)
            m = size(A, 1)
            n = min(m, size(A, 2))
            if k > n
                throw(DimensionMismatch("invalid number of reflectors: k = $k should be <= n = $n"))
            end
            work  = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            info  = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($orgqr), libblastrampoline), Cvoid,
                      (Ref{BlasInt}, Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty},
                       Ref{BlasInt}, Ptr{$elty}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}),
                      m, n, k, A,
                      max(1,stride(A,2)), tau, work, lwork,
                      info)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            if n < size(A,2)
                A[:,1:n]
            else
                A
            end
        end

        # SUBROUTINE DORGQL( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
        # *     .. Scalar Arguments ..
        #       INTEGER            INFO, K, LDA, LWORK, M, N
        # *     .. Array Arguments ..
        #       DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
        function orgql!(A::AbstractMatrix{$elty}, tau::AbstractVector{$elty}, k::Integer = length(tau))
            require_one_based_indexing(A, tau)
            chkstride1(A,tau)
            m = size(A, 1)
            n = min(m, size(A, 2))
            if k > n
                throw(DimensionMismatch("invalid number of reflectors: k = $k should be <= n = $n"))
            end
            work  = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            info  = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($orgql), libblastrampoline), Cvoid,
                      (Ref{BlasInt}, Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty},
                       Ref{BlasInt}, Ptr{$elty}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}),
                      m, n, k, A,
                      max(1,stride(A,2)), tau, work, lwork,
                      info)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            if n < size(A,2)
                A[:,1:n]
            else
                A
            end
        end

        # SUBROUTINE DORGRQ( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
        # *     .. Scalar Arguments ..
        #       INTEGER            INFO, K, LDA, LWORK, M, N
        # *     .. Array Arguments ..
        #       DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
        function orgrq!(A::AbstractMatrix{$elty}, tau::AbstractVector{$elty}, k::Integer = length(tau))
            require_one_based_indexing(A, tau)
            chkstride1(A,tau)
            m, n = size(A)
            if n < m
                throw(DimensionMismatch("input matrix A has dimensions ($m,$n), but cannot have fewer columns than rows"))
            end
            if k > n
                throw(DimensionMismatch("invalid number of reflectors: k = $k should be <= n = $n"))
            end
            work  = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            info  = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($orgrq), libblastrampoline), Cvoid,
                      (Ref{BlasInt}, Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty},
                       Ref{BlasInt}, Ptr{$elty}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}),
                      m, n, k, A,
                      max(1,stride(A,2)), tau, work, lwork,
                      info)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            A
        end

        #      SUBROUTINE DORMLQ( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
        #                         WORK, LWORK, INFO )
        #      .. Scalar Arguments ..
        #      CHARACTER          SIDE, TRANS
        #      INTEGER            INFO, K, LDA, LDC, LWORK, M, N
        #      .. Array Arguments ..
        #      DOUBLE PRECISION   A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
        function ormlq!(side::AbstractChar, trans::AbstractChar, A::AbstractMatrix{$elty},
                        tau::AbstractVector{$elty}, C::AbstractVecOrMat{$elty})
            require_one_based_indexing(A, tau, C)
            chktrans(trans)
            chkside(side)
            chkstride1(A, C, tau)
            m,n = ndims(C) == 2 ? size(C) : (size(C, 1), 1)
            nA = size(A, 2)
            k   = length(tau)
            if side == 'L' && m != nA
                throw(DimensionMismatch("for a left-sided multiplication, the first dimension of C, $m, must equal the second dimension of A, $nA"))
            end
            if side == 'R' && n != nA
                throw(DimensionMismatch("for a right-sided multiplication, the second dimension of C, $n, must equal the second dimension of A, $nA"))
            end
            if side == 'L' && k > m
                throw(DimensionMismatch("invalid number of reflectors: k = $k should be <= m = $m"))
            end
            if side == 'R' && k > n
                throw(DimensionMismatch("invalid number of reflectors: k = $k should be <= n = $n"))
            end
            work  = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            info  = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($ormlq), libblastrampoline), Cvoid,
                      (Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt}, Ref{BlasInt},
                       Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ptr{$elty}, Ref{BlasInt},
                       Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}, Clong, Clong),
                      side, trans, m, n, k, A, max(1,stride(A,2)), tau,
                      C, max(1,stride(C,2)), work, lwork, info, 1, 1)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            C
        end

        #      SUBROUTINE DORMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
        #                         WORK, INFO )
        #      .. Scalar Arguments ..
        #      CHARACTER          SIDE, TRANS
        #      INTEGER            INFO, K, LDA, LDC, M, N
        #      .. Array Arguments ..
        #      DOUBLE PRECISION   A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
        function ormqr!(side::AbstractChar, trans::AbstractChar, A::AbstractMatrix{$elty},
                        tau::AbstractVector{$elty}, C::AbstractVecOrMat{$elty})
            require_one_based_indexing(A, tau, C)
            chktrans(trans)
            chkside(side)
            chkstride1(A, C, tau)
            m,n = ndims(C) == 2 ? size(C) : (size(C, 1), 1)
            mA  = size(A, 1)
            k   = length(tau)
            if side == 'L' && m != mA
                throw(DimensionMismatch("for a left-sided multiplication, the first dimension of C, $m, must equal the second dimension of A, $mA"))
            end
            if side == 'R' && n != mA
                throw(DimensionMismatch("for a right-sided multiplication, the second dimension of C, $m, must equal the second dimension of A, $mA"))
            end
            if side == 'L' && k > m
                throw(DimensionMismatch("invalid number of reflectors: k = $k should be <= m = $m"))
            end
            if side == 'R' && k > n
                throw(DimensionMismatch("invalid number of reflectors: k = $k should be <= n = $n"))
            end
            work  = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            info  = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($ormqr), libblastrampoline), Cvoid,
                      (Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt},
                       Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty},
                       Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                       Ptr{BlasInt}, Clong, Clong),
                      side, trans, m, n,
                      k, A, max(1,stride(A,2)), tau,
                      C, max(1, stride(C,2)), work, lwork,
                      info, 1, 1)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            C
        end

        #      SUBROUTINE DORMQL( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
        #                         WORK, INFO )
        #      .. Scalar Arguments ..
        #      CHARACTER          SIDE, TRANS
        #      INTEGER            INFO, K, LDA, LDC, M, N
        #      .. Array Arguments ..
        #      DOUBLE PRECISION   A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
        function ormql!(side::AbstractChar, trans::AbstractChar, A::AbstractMatrix{$elty},
                        tau::AbstractVector{$elty}, C::AbstractVecOrMat{$elty})
            require_one_based_indexing(A, tau, C)
            chktrans(trans)
            chkside(side)
            chkstride1(A, C, tau)
            m,n = ndims(C) == 2 ? size(C) : (size(C, 1), 1)
            mA  = size(A, 1)
            k   = length(tau)
            if side == 'L' && m != mA
                throw(DimensionMismatch("for a left-sided multiplication, the first dimension of C, $m, must equal the second dimension of A, $mA"))
            end
            if side == 'R' && n != mA
                throw(DimensionMismatch("for a right-sided multiplication, the second dimension of C, $m, must equal the second dimension of A, $mA"))
            end
            if side == 'L' && k > m
                throw(DimensionMismatch("invalid number of reflectors: k = $k should be <= m = $m"))
            end
            if side == 'R' && k > n
                throw(DimensionMismatch("invalid number of reflectors: k = $k should be <= n = $n"))
            end
            work  = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            info  = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($ormql), libblastrampoline), Cvoid,
                      (Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt},
                       Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty},
                       Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                       Ptr{BlasInt}, Clong, Clong),
                      side, trans, m, n,
                      k, A, max(1,stride(A,2)), tau,
                      C, max(1, stride(C,2)), work, lwork,
                      info, 1, 1)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            C
        end

        #      SUBROUTINE DORMRQ( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
        #                         WORK, LWORK, INFO )
        #      .. Scalar Arguments ..
        #      CHARACTER          SIDE, TRANS
        #      INTEGER            INFO, K, LDA, LDC, LWORK, M, N
        #      .. Array Arguments ..
        #      DOUBLE PRECISION   A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
        function ormrq!(side::AbstractChar, trans::AbstractChar, A::AbstractMatrix{$elty},
                        tau::AbstractVector{$elty}, C::AbstractVecOrMat{$elty})
            require_one_based_indexing(A, tau, C)
            chktrans(trans)
            chkside(side)
            chkstride1(A, C, tau)
            m,n = ndims(C) == 2 ? size(C) : (size(C, 1), 1)
            nA  = size(A, 2)
            k   = length(tau)
            if side == 'L' && m != nA
                throw(DimensionMismatch("for a left-sided multiplication, the first dimension of C, $m, must equal the second dimension of A, $nA"))
            end
            if side == 'R' && n != nA
                throw(DimensionMismatch("for a right-sided multiplication, the second dimension of C, $m, must equal the second dimension of A, $nA"))
            end
            if side == 'L' && k > m
                throw(DimensionMismatch("invalid number of reflectors: k = $k should be <= m = $m"))
            end
            if side == 'R' && k > n
                throw(DimensionMismatch("invalid number of reflectors: k = $k should be <= n = $n"))
            end
            work  = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            info  = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($ormrq), libblastrampoline), Cvoid,
                      (Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt}, Ref{BlasInt},
                       Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ptr{$elty}, Ref{BlasInt},
                       Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}, Clong, Clong),
                      side, trans, m, n, k, A, max(1,stride(A,2)), tau,
                      C, max(1,stride(C,2)), work, lwork, info, 1, 1)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            C
        end

        function gemqrt!(side::AbstractChar, trans::AbstractChar, V::AbstractMatrix{$elty}, T::AbstractMatrix{$elty}, C::AbstractVecOrMat{$elty})
            require_one_based_indexing(V, T, C)
            chktrans(trans)
            chkside(side)
            chkstride1(V, T, C)
            m,n = ndims(C) == 2 ? size(C) : (size(C, 1), 1)
            nb, k = size(T)
            if k == 0
                return C
            end
            if side == 'L'
                if !(0 <= k <= m)
                    throw(DimensionMismatch("wrong value for k = $k: must be between 0 and $m"))
                end
                if m != size(V,1)
                    throw(DimensionMismatch("first dimensions of C, $m, and V, $(size(V,1)) must match"))
                end
                ldv = stride(V,2)
                if ldv < max(1, m)
                    throw(DimensionMismatch("Q and C don't fit! The stride of V, $ldv, is too small"))
                end
                wss = n*k
            elseif side == 'R'
                if !(0 <= k <= n)
                    throw(DimensionMismatch("wrong value for k = $k: must be between 0 and $n"))
                end
                if n != size(V,1)
                    throw(DimensionMismatch("second dimension of C, $n, and first dimension of V, $(size(V,1)) must match"))
                end
                ldv = stride(V,2)
                if ldv < max(1, n)
                    throw(DimensionMismatch("Q and C don't fit! The stride of V, $ldv, is too small"))
                end
                wss = m*k
            end
            if !(1 <= nb <= k)
                throw(DimensionMismatch("wrong value for nb = $nb, which must be between 1 and $k"))
            end
            ldc = stride(C, 2)
            work = Vector{$elty}(undef, wss)
            info = Ref{BlasInt}()
            ccall((@blasfunc($gemqrt), libblastrampoline), Cvoid,
                (Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt},
                 Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                 Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                 Ptr{$elty}, Ptr{BlasInt}, Clong, Clong),
                side, trans, m, n,
                k, nb, V, ldv,
                T, max(1,stride(T,2)), C, max(1,ldc),
                work, info, 1, 1)
            chklapackerror(info[])
            return C
        end
    end
end

"""
    orglq!(A, tau, k = length(tau))

Explicitly finds the matrix `Q` of a `LQ` factorization after calling
`gelqf!` on `A`. Uses the output of `gelqf!`. `A` is overwritten by `Q`.
"""
orglq!(A::AbstractMatrix, tau::AbstractVector, k::Integer = length(tau))

"""
    orgqr!(A, tau, k = length(tau))

Explicitly finds the matrix `Q` of a `QR` factorization after calling
`geqrf!` on `A`. Uses the output of `geqrf!`. `A` is overwritten by `Q`.
"""
orgqr!(A::AbstractMatrix, tau::AbstractVector, k::Integer = length(tau))

"""
    orgql!(A, tau, k = length(tau))

Explicitly finds the matrix `Q` of a `QL` factorization after calling
`geqlf!` on `A`. Uses the output of `geqlf!`. `A` is overwritten by `Q`.
"""
orgql!(A::AbstractMatrix, tau::AbstractVector, k::Integer = length(tau))

"""
    orgrq!(A, tau, k = length(tau))

Explicitly finds the matrix `Q` of a `RQ` factorization after calling
`gerqf!` on `A`. Uses the output of `gerqf!`. `A` is overwritten by `Q`.
"""
orgrq!(A::AbstractMatrix, tau::AbstractVector, k::Integer = length(tau))

"""
    ormlq!(side, trans, A, tau, C)

Computes `Q * C` (`trans = N`), `transpose(Q) * C` (`trans = T`), `adjoint(Q) * C`
(`trans = C`) for `side = L` or the equivalent right-sided multiplication
for `side = R` using `Q` from a `LQ` factorization of `A` computed using
`gelqf!`. `C` is overwritten.
"""
ormlq!(side::AbstractChar, trans::AbstractChar, A::AbstractMatrix, tau::AbstractVector, C::AbstractVecOrMat)

"""
    ormqr!(side, trans, A, tau, C)

Computes `Q * C` (`trans = N`), `transpose(Q) * C` (`trans = T`), `adjoint(Q) * C`
(`trans = C`) for `side = L` or the equivalent right-sided multiplication
for `side = R` using `Q` from a `QR` factorization of `A` computed using
`geqrf!`. `C` is overwritten.
"""
ormqr!(side::AbstractChar, trans::AbstractChar, A::AbstractMatrix, tau::AbstractVector, C::AbstractVecOrMat)

"""
    ormql!(side, trans, A, tau, C)

Computes `Q * C` (`trans = N`), `transpose(Q) * C` (`trans = T`), `adjoint(Q) * C`
(`trans = C`) for `side = L` or the equivalent right-sided multiplication
for `side = R` using `Q` from a `QL` factorization of `A` computed using
`geqlf!`. `C` is overwritten.
"""
ormql!(side::AbstractChar, trans::AbstractChar, A::AbstractMatrix, tau::AbstractVector, C::AbstractVecOrMat)

"""
    ormrq!(side, trans, A, tau, C)

Computes `Q * C` (`trans = N`), `transpose(Q) * C` (`trans = T`), `adjoint(Q) * C`
(`trans = C`) for `side = L` or the equivalent right-sided multiplication
for `side = R` using `Q` from a `RQ` factorization of `A` computed using
`gerqf!`. `C` is overwritten.
"""
ormrq!(side::AbstractChar, trans::AbstractChar, A::AbstractMatrix, tau::AbstractVector, C::AbstractVecOrMat)

"""
    gemqrt!(side, trans, V, T, C)

Computes `Q * C` (`trans = N`), `transpose(Q) * C` (`trans = T`), `adjoint(Q) * C`
(`trans = C`) for `side = L` or the equivalent right-sided multiplication
for `side = R` using `Q` from a `QR` factorization of `A` computed using
`geqrt!`. `C` is overwritten.
"""
gemqrt!(side::AbstractChar, trans::AbstractChar, V::AbstractMatrix, T::AbstractMatrix, C::AbstractVecOrMat)

# (PO) positive-definite symmetric matrices,
for (posv, potrf, potri, potrs, pstrf, elty, rtyp) in
    ((:dposv_,:dpotrf_,:dpotri_,:dpotrs_,:dpstrf_,:Float64,:Float64),
     (:sposv_,:spotrf_,:spotri_,:spotrs_,:spstrf_,:Float32,:Float32),
     (:zposv_,:zpotrf_,:zpotri_,:zpotrs_,:zpstrf_,:ComplexF64,:Float64),
     (:cposv_,:cpotrf_,:cpotri_,:cpotrs_,:cpstrf_,:ComplexF32,:Float32))
    @eval begin
        #     SUBROUTINE DPOSV( UPLO, N, NRHS, A, LDA, B, LDB, INFO )
        #*     .. Scalar Arguments ..
        #      CHARACTER          UPLO
        #      INTEGER            INFO, LDA, LDB, N, NRHS
        #     .. Array Arguments ..
        #      DOUBLE PRECISION   A( LDA, * ), B( LDB, * )
        function posv!(uplo::AbstractChar, A::AbstractMatrix{$elty}, B::AbstractVecOrMat{$elty})
            require_one_based_indexing(A, B)
            chkstride1(A, B)
            n = checksquare(A)
            chkuplo(uplo)
            if size(B,1) != n
                throw(DimensionMismatch("first dimension of B, $(size(B,1)), and size of A, ($n,$n), must match!"))
            end
            info = Ref{BlasInt}()
            ccall((@blasfunc($posv), libblastrampoline), Cvoid,
                  (Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                   Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}, Clong),
                  uplo, n, size(B,2), A, max(1,stride(A,2)), B, max(1,stride(B,2)), info, 1)
            chkargsok(info[])
            chkposdef(info[])
            A, B
        end

        # SUBROUTINE DPOTRF( UPLO, N, A, LDA, INFO )
        # *     .. Scalar Arguments ..
        #       CHARACTER          UPLO
        #       INTEGER            INFO, LDA, N
        # *     .. Array Arguments ..
        #       DOUBLE PRECISION   A( LDA, * )
        function potrf!(uplo::AbstractChar, A::AbstractMatrix{$elty})
            require_one_based_indexing(A)
            chkstride1(A)
            checksquare(A)
            chkuplo(uplo)
            lda = max(1,stride(A,2))
            if lda == 0
                return A, 0
            end
            info = Ref{BlasInt}()
            ccall((@blasfunc($potrf), libblastrampoline), Cvoid,
                  (Ref{UInt8}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}, Clong),
                  uplo, size(A,1), A, lda, info, 1)
            chkargsok(info[])
            #info[] > 0 means the leading minor of order info[] is not positive definite
            #ordinarily, throw Exception here, but return error code here
            #this simplifies isposdef! and factorize
            return A, info[] # info stored in Cholesky
        end

        #       SUBROUTINE DPOTRI( UPLO, N, A, LDA, INFO )
        #       .. Scalar Arguments ..
        #       CHARACTER          UPLO
        #       INTEGER            INFO, LDA, N
        #       .. Array Arguments ..
        #       DOUBLE PRECISION   A( LDA, * )
        function potri!(uplo::AbstractChar, A::AbstractMatrix{$elty})
            require_one_based_indexing(A)
            chkstride1(A)
            chkuplo(uplo)
            info = Ref{BlasInt}()
            ccall((@blasfunc($potri), libblastrampoline), Cvoid,
                  (Ref{UInt8}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}, Clong),
                  uplo, size(A,1), A, max(1,stride(A,2)), info, 1)
            chkargsok(info[])
            chknonsingular(info[])
            A
        end

        #     SUBROUTINE DPOTRS( UPLO, N, NRHS, A, LDA, B, LDB, INFO )
        #     .. Scalar Arguments ..
        #      CHARACTER          UPLO
        #      INTEGER            INFO, LDA, LDB, N, NRHS
        #     .. Array Arguments ..
        #      DOUBLE PRECISION   A( LDA, * ), B( LDB, * )
        function potrs!(uplo::AbstractChar, A::AbstractMatrix{$elty}, B::AbstractVecOrMat{$elty})
            require_one_based_indexing(A, B)
            chkstride1(A, B)
            n = checksquare(A)
            chkuplo(uplo)
            nrhs = size(B,2)
            if size(B,1) != n
                throw(DimensionMismatch("first dimension of B, $(size(B,1)), and size of A, ($n,$n), must match!"))
            end
            lda = max(1,stride(A,2))
            if lda == 0 || nrhs == 0
                return B
            end
            ldb = max(1,stride(B,2))
            info = Ref{BlasInt}()
            ccall((@blasfunc($potrs), libblastrampoline), Cvoid,
                  (Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty},
                    Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}, Clong),
                   uplo, n, nrhs, A,
                   lda, B, ldb, info, 1)
            chklapackerror(info[])
            return B
        end

        #       SUBROUTINE DPSTRF( UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO )
        #       .. Scalar Arguments ..
        #       DOUBLE PRECISION   TOL
        #       INTEGER            INFO, LDA, N, RANK
        #       CHARACTER          UPLO
        #       .. Array Arguments ..
        #       DOUBLE PRECISION   A( LDA, * ), WORK( 2*N )
        #       INTEGER            PIV( N )
        function pstrf!(uplo::AbstractChar, A::AbstractMatrix{$elty}, tol::Real)
            chkstride1(A)
            n = checksquare(A)
            chkuplo(uplo)
            piv  = similar(A, BlasInt, n)
            rank = Vector{BlasInt}(undef, 1)
            work = Vector{$rtyp}(undef, 2n)
            info = Ref{BlasInt}()
            ccall((@blasfunc($pstrf), libblastrampoline), Cvoid,
                  (Ref{UInt8}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt},
                   Ptr{BlasInt}, Ref{$rtyp}, Ptr{$rtyp}, Ptr{BlasInt}, Clong),
                  uplo, n, A, max(1,stride(A,2)), piv, rank, tol, work, info, 1)
            chkargsok(info[])
            A, piv, rank[1], info[] #Stored in CholeskyPivoted
        end
    end
end

"""
    posv!(uplo, A, B) -> (A, B)

Finds the solution to `A * X = B` where `A` is a symmetric or Hermitian
positive definite matrix. If `uplo = U` the upper Cholesky decomposition
of `A` is computed. If `uplo = L` the lower Cholesky decomposition of `A`
is computed. `A` is overwritten by its Cholesky decomposition. `B` is
overwritten with the solution `X`.
"""
posv!(uplo::AbstractChar, A::AbstractMatrix, B::AbstractVecOrMat)

"""
    potrf!(uplo, A)

Computes the Cholesky (upper if `uplo = U`, lower if `uplo = L`)
decomposition of positive-definite matrix `A`. `A` is overwritten and
returned with an info code.
"""
potrf!(uplo::AbstractChar, A::AbstractMatrix)

"""
    potri!(uplo, A)

Computes the inverse of positive-definite matrix `A` after calling
`potrf!` to find its (upper if `uplo = U`, lower if `uplo = L`) Cholesky
decomposition.

`A` is overwritten by its inverse and returned.
"""
potri!(uplo::AbstractChar, A::AbstractMatrix)

"""
    potrs!(uplo, A, B)

Finds the solution to `A * X = B` where `A` is a symmetric or Hermitian
positive definite matrix whose Cholesky decomposition was computed by
`potrf!`. If `uplo = U` the upper Cholesky decomposition of `A` was
computed. If `uplo = L` the lower Cholesky decomposition of `A` was
computed. `B` is overwritten with the solution `X`.
"""
potrs!(uplo::AbstractChar, A::AbstractMatrix, B::AbstractVecOrMat)

"""
    pstrf!(uplo, A, tol) -> (A, piv, rank, info)

Computes the (upper if `uplo = U`, lower if `uplo = L`) pivoted Cholesky
decomposition of positive-definite matrix `A` with a user-set tolerance
`tol`. `A` is overwritten by its Cholesky decomposition.

Returns `A`, the pivots `piv`, the rank of `A`, and an `info` code. If `info = 0`,
the factorization succeeded. If `info = i > 0 `, then `A` is indefinite or
rank-deficient.
"""
pstrf!(uplo::AbstractChar, A::AbstractMatrix, tol::Real)

# (PT) positive-definite, symmetric, tri-diagonal matrices
# Direct solvers for general tridiagonal and symmetric positive-definite tridiagonal
for (ptsv, pttrf, elty, relty) in
    ((:dptsv_,:dpttrf_,:Float64,:Float64),
     (:sptsv_,:spttrf_,:Float32,:Float32),
     (:zptsv_,:zpttrf_,:ComplexF64,:Float64),
     (:cptsv_,:cpttrf_,:ComplexF32,:Float32))
    @eval begin
        #       SUBROUTINE DPTSV( N, NRHS, D, E, B, LDB, INFO )
        #       .. Scalar Arguments ..
        #       INTEGER            INFO, LDB, N, NRHS
        #       .. Array Arguments ..
        #       DOUBLE PRECISION   B( LDB, * ), D( * ), E( * )
        function ptsv!(D::AbstractVector{$relty}, E::AbstractVector{$elty}, B::AbstractVecOrMat{$elty})
            require_one_based_indexing(D, E, B)
            chkstride1(B, D, E)
            n = length(D)
            if length(E) != n - 1
                throw(DimensionMismatch("E has length $(length(E)), but needs $(n - 1)"))
            end
            if n != size(B,1)
                throw(DimensionMismatch("B has first dimension $(size(B,1)) but needs $n"))
            end
            info = Ref{BlasInt}()
            ccall((@blasfunc($ptsv), libblastrampoline), Cvoid,
                  (Ref{BlasInt}, Ref{BlasInt}, Ptr{$relty}, Ptr{$elty},
                   Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}),
                  n, size(B,2), D, E, B, max(1,stride(B,2)), info)
            chklapackerror(info[])
            B
        end

        #       SUBROUTINE DPTTRF( N, D, E, INFO )
        #       .. Scalar Arguments ..
        #       INTEGER            INFO, N
        #       .. Array Arguments ..
        #       DOUBLE PRECISION   D( * ), E( * )
        function pttrf!(D::AbstractVector{$relty}, E::AbstractVector{$elty})
            require_one_based_indexing(D, E)
            chkstride1(D, E)
            n = length(D)
            if length(E) != n - 1
                throw(DimensionMismatch("E has length $(length(E)), but needs $(n - 1)"))
            end
            info = Ref{BlasInt}()
            ccall((@blasfunc($pttrf), libblastrampoline), Cvoid,
                  (Ref{BlasInt}, Ptr{$relty}, Ptr{$elty}, Ptr{BlasInt}),
                  n, D, E, info)
            chklapackerror(info[])
            D, E
        end
    end
end

"""
    ptsv!(D, E, B)

Solves `A * X = B` for positive-definite tridiagonal `A`. `D` is the
diagonal of `A` and `E` is the off-diagonal. `B` is overwritten with the
solution `X` and returned.
"""
ptsv!(D::AbstractVector, E::AbstractVector, B::AbstractVecOrMat)

"""
    pttrf!(D, E)

Computes the LDLt factorization of a positive-definite tridiagonal matrix
with `D` as diagonal and `E` as off-diagonal. `D` and `E` are overwritten
and returned.
"""
pttrf!(D::AbstractVector, E::AbstractVector)

for (pttrs, elty, relty) in
    ((:dpttrs_,:Float64,:Float64),
     (:spttrs_,:Float32,:Float32))
    @eval begin
        #       SUBROUTINE DPTTRS( N, NRHS, D, E, B, LDB, INFO )
        #       .. Scalar Arguments ..
        #       INTEGER            INFO, LDB, N, NRHS
        #       .. Array Arguments ..
        #       DOUBLE PRECISION   B( LDB, * ), D( * ), E( * )
        function pttrs!(D::AbstractVector{$relty}, E::AbstractVector{$elty}, B::AbstractVecOrMat{$elty})
            require_one_based_indexing(D, E, B)
            chkstride1(B, D, E)
            n = length(D)
            if length(E) != n - 1
                throw(DimensionMismatch("E has length $(length(E)), but needs $(n - 1)"))
            end
            if n != size(B,1)
                throw(DimensionMismatch("B has first dimension $(size(B,1)) but needs $n"))
            end
            info = Ref{BlasInt}()
            ccall((@blasfunc($pttrs), libblastrampoline), Cvoid,
                  (Ref{BlasInt}, Ref{BlasInt}, Ptr{$relty}, Ptr{$elty},
                   Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}),
                  n, size(B,2), D, E, B, max(1,stride(B,2)), info)
            chklapackerror(info[])
            B
        end
    end
end

for (pttrs, elty, relty) in
    ((:zpttrs_,:ComplexF64,:Float64),
     (:cpttrs_,:ComplexF32,:Float32))
    @eval begin
        #       SUBROUTINE ZPTTRS( UPLO, N, NRHS, D, E, B, LDB, INFO )
        # *     .. Scalar Arguments ..
        #       CHARACTER          UPLO
        #       INTEGER            INFO, LDB, N, NRHS
        # *     ..
        # *     .. Array Arguments ..
        #       DOUBLE PRECISION   D( * )
        #       COMPLEX*16         B( LDB, * ), E( * )
        function pttrs!(uplo::AbstractChar, D::AbstractVector{$relty}, E::AbstractVector{$elty}, B::AbstractVecOrMat{$elty})
            require_one_based_indexing(D, E, B)
            chkstride1(B, D, E)
            chkuplo(uplo)
            n = length(D)
            if length(E) != n - 1
                throw(DimensionMismatch("E has length $(length(E)), but needs $(n - 1)"))
            end
            if n != size(B,1)
                throw(DimensionMismatch("B has first dimension $(size(B,1)) but needs $n"))
            end
            info = Ref{BlasInt}()
            ccall((@blasfunc($pttrs), libblastrampoline), Cvoid,
                  (Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt}, Ptr{$relty}, Ptr{$elty},
                   Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}, Clong),
                  uplo, n, size(B,2), D, E, B, max(1,stride(B,2)), info, 1)
            chklapackerror(info[])
            B
        end
    end
end

"""
    pttrs!(D, E, B)

Solves `A * X = B` for positive-definite tridiagonal `A` with diagonal
`D` and off-diagonal `E` after computing `A`'s LDLt factorization using
`pttrf!`. `B` is overwritten with the solution `X`.
"""
pttrs!(D::AbstractVector, E::AbstractVector, B::AbstractVecOrMat)

## (TR) triangular matrices: solver and inverse
for (trtri, trtrs, elty) in
    ((:dtrtri_,:dtrtrs_,:Float64),
     (:strtri_,:strtrs_,:Float32),
     (:ztrtri_,:ztrtrs_,:ComplexF64),
     (:ctrtri_,:ctrtrs_,:ComplexF32))
    @eval begin
        #     SUBROUTINE DTRTRI( UPLO, DIAG, N, A, LDA, INFO )
        #*     .. Scalar Arguments ..
        #      CHARACTER          DIAG, UPLO
        #      INTEGER            INFO, LDA, N
        #     .. Array Arguments ..
        #      DOUBLE PRECISION   A( LDA, * )
        function trtri!(uplo::AbstractChar, diag::AbstractChar, A::AbstractMatrix{$elty})
            chkstride1(A)
            n = checksquare(A)
            chkuplo(uplo)
            chkdiag(diag)
            lda = max(1,stride(A, 2))
            info = Ref{BlasInt}()
            ccall((@blasfunc($trtri), libblastrampoline), Cvoid,
                  (Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                   Ptr{BlasInt}, Clong, Clong),
                  uplo, diag, n, A, lda, info, 1, 1)
            chklapackerror(info[])
            A
        end

        #      SUBROUTINE DTRTRS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, INFO )
        # *     .. Scalar Arguments ..
        #       CHARACTER          DIAG, TRANS, UPLO
        #       INTEGER            INFO, LDA, LDB, N, NRHS
        # *     .. Array Arguments ..
        #       DOUBLE PRECISION   A( LDA, * ), B( LDB, * )
        function trtrs!(uplo::AbstractChar, trans::AbstractChar, diag::AbstractChar,
                        A::AbstractMatrix{$elty}, B::AbstractVecOrMat{$elty})
            require_one_based_indexing(A, B)
            chktrans(trans)
            chkdiag(diag)
            chkstride1(A)
            n = checksquare(A)
            chkuplo(uplo)
            if n != size(B,1)
                throw(DimensionMismatch("B has first dimension $(size(B,1)) but needs $n"))
            end
            info = Ref{BlasInt}()
            ccall((@blasfunc($trtrs), libblastrampoline), Cvoid,
                  (Ref{UInt8}, Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt},
                   Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt},
                   Clong, Clong, Clong),
                  uplo, trans, diag, n, size(B,2), A, max(1,stride(A,2)),
                  B, max(1,stride(B,2)), info,
                  1, 1, 1)
            chklapackerror(info[])
            B
        end
    end
end

"""
    trtri!(uplo, diag, A)

Finds the inverse of (upper if `uplo = U`, lower if `uplo = L`)
triangular matrix `A`. If `diag = N`, `A` has non-unit diagonal elements.
If `diag = U`, all diagonal elements of `A` are one. `A` is overwritten
with its inverse.
"""
trtri!(uplo::AbstractChar, diag::AbstractChar, A::AbstractMatrix)

"""
    trtrs!(uplo, trans, diag, A, B)

Solves `A * X = B` (`trans = N`), `transpose(A) * X = B` (`trans = T`), or
`adjoint(A) * X = B` (`trans = C`) for (upper if `uplo = U`, lower if `uplo = L`)
triangular matrix `A`. If `diag = N`, `A` has non-unit diagonal elements.
If `diag = U`, all diagonal elements of `A` are one. `B` is overwritten
with the solution `X`.
"""
trtrs!(uplo::AbstractChar, trans::AbstractChar, diag::AbstractChar, A::AbstractMatrix, B::AbstractVecOrMat)

#Eigenvector computation and condition number estimation
for (trcon, trevc, trrfs, elty) in
    ((:dtrcon_,:dtrevc_,:dtrrfs_,:Float64),
     (:strcon_,:strevc_,:strrfs_,:Float32))
    @eval begin
        # SUBROUTINE DTRCON( NORM, UPLO, DIAG, N, A, LDA, RCOND, WORK,
        #                  IWORK, INFO )
        # .. Scalar Arguments ..
        # CHARACTER          DIAG, NORM, UPLO
        # INTEGER            INFO, LDA, N
        # DOUBLE PRECISION   RCOND
        # .. Array Arguments ..
        # INTEGER            IWORK( * )
        # DOUBLE PRECISION   A( LDA, * ), WORK( * )
        function trcon!(norm::AbstractChar, uplo::AbstractChar, diag::AbstractChar, A::AbstractMatrix{$elty})
            chkstride1(A)
            chkdiag(diag)
            n = checksquare(A)
            chkuplo(uplo)
            rcond = Ref{$elty}()
            work  = Vector{$elty}(undef, 3n)
            iwork = Vector{BlasInt}(undef, n)
            info  = Ref{BlasInt}()
            ccall((@blasfunc($trcon), libblastrampoline), Cvoid,
                  (Ref{UInt8}, Ref{UInt8}, Ref{UInt8}, Ref{BlasInt},
                   Ptr{$elty}, Ref{BlasInt}, Ref{$elty}, Ptr{$elty}, Ptr{BlasInt}, Ptr{BlasInt},
                   Clong, Clong, Clong),
                  norm, uplo, diag, n,
                  A, max(1,stride(A,2)), rcond, work, iwork, info,
                  1, 1, 1)
            chklapackerror(info[])
            rcond[]
        end

        # SUBROUTINE DTREVC( SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR,
        #                    LDVR, MM, M, WORK, INFO )
        #
        # .. Scalar Arguments ..
        # CHARACTER          HOWMNY, SIDE
        # INTEGER            INFO, LDT, LDVL, LDVR, M, MM, N
        # ..
        # .. Array Arguments ..
        # LOGICAL            SELECT( * )
        # DOUBLE PRECISION   T( LDT, * ), VL( LDVL, * ), VR( LDVR, * ),
        #$                   WORK( * )
        function trevc!(side::AbstractChar, howmny::AbstractChar, select::AbstractVector{BlasInt}, T::AbstractMatrix{$elty},
                        VL::AbstractMatrix{$elty} = similar(T),
                        VR::AbstractMatrix{$elty} = similar(T))
            require_one_based_indexing(select, T, VL, VR)
            # Extract
            if side ∉ ['L','R','B']
                throw(ArgumentError("side argument must be 'L' (left eigenvectors), 'R' (right eigenvectors), or 'B' (both), got $side"))
            end
            n, mm = checksquare(T), size(VL, 2)
            ldt, ldvl, ldvr = stride(T, 2), stride(VL, 2), stride(VR, 2)

            # Check
            chkstride1(T, select, VL, VR)

            # Allocate
            m = Ref{BlasInt}()
            work = Vector{$elty}(undef, 3n)
            info = Ref{BlasInt}()

            ccall((@blasfunc($trevc), libblastrampoline), Cvoid,
                (Ref{UInt8}, Ref{UInt8}, Ptr{BlasInt}, Ref{BlasInt},
                 Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                 Ptr{$elty}, Ref{BlasInt}, Ref{BlasInt}, Ptr{BlasInt},
                 Ptr{$elty}, Ptr{BlasInt}, Clong, Clong),
                side, howmny, select, n,
                T, ldt, VL, ldvl,
                VR, ldvr, mm, m,
                work, info, 1, 1)
            chklapackerror(info[])

            #Decide what exactly to return
            if howmny == 'S' #compute selected eigenvectors
                if side == 'L' #left eigenvectors only
                    return select, VL[:,1:m[]]
                elseif side == 'R' #right eigenvectors only
                    return select, VR[:,1:m[]]
                else #side == 'B' #both eigenvectors
                    return select, VL[:,1:m[]], VR[:,1:m[]]
                end
            else #compute all eigenvectors
                if side == 'L' #left eigenvectors only
                    return VL[:,1:m[]]
                elseif side == 'R' #right eigenvectors only
                    return VR[:,1:m[]]
                else #side == 'B' #both eigenvectors
                    return VL[:,1:m[]], VR[:,1:m[]]
                end
            end
        end

        # SUBROUTINE DTRRFS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, X,
        #                    LDX, FERR, BERR, WORK, IWORK, INFO )
        # .. Scalar Arguments ..
        # CHARACTER          DIAG, TRANS, UPLO
        # INTEGER            INFO, LDA, LDB, LDX, N, NRHS
        # .. Array Arguments ..
        # INTEGER            IWORK( * )
        # DOUBLE PRECISION   A( LDA, * ), B( LDB, * ), BERR( * ), FERR( * ),
        #$                   WORK( * ), X( LDX, * )
        function trrfs!(uplo::AbstractChar, trans::AbstractChar, diag::AbstractChar,
                A::AbstractMatrix{$elty}, B::AbstractVecOrMat{$elty}, X::AbstractVecOrMat{$elty},
                Ferr::AbstractVector{$elty} = similar(B, $elty, size(B,2)),
                Berr::AbstractVector{$elty} = similar(B, $elty, size(B,2)))
            require_one_based_indexing(A, B, X, Ferr, Berr)
            chkstride1(A, B, X, Ferr, Berr)
            chktrans(trans)
            chkuplo(uplo)
            chkdiag(diag)
            n = size(A,2)
            nrhs = size(B,2)
            if nrhs != size(X,2)
                throw(DimensionMismatch("second dimensions of B, $nrhs, and X, $(size(X,2)), must match"))
            end
            work = Vector{$elty}(undef, 3n)
            iwork = Vector{BlasInt}(undef, n)
            info = Ref{BlasInt}()
            ccall((@blasfunc($trrfs), libblastrampoline), Cvoid,
                (Ref{UInt8}, Ref{UInt8}, Ref{UInt8}, Ref{BlasInt},
                 Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                 Ptr{$elty}, Ptr{$elty}, Ptr{$elty}, Ptr{BlasInt}, Ptr{BlasInt}, Clong, Clong, Clong),
                uplo, trans, diag, n,
                nrhs, A, max(1,stride(A,2)), B, max(1,stride(B,2)), X, max(1,stride(X,2)),
                Ferr, Berr, work, iwork, info, 1, 1, 1)
            chklapackerror(info[])
            Ferr, Berr
        end
    end
end

for (trcon, trevc, trrfs, elty, relty) in
    ((:ztrcon_,:ztrevc_,:ztrrfs_,:ComplexF64,:Float64),
     (:ctrcon_,:ctrevc_,:ctrrfs_,:ComplexF32, :Float32))
    @eval begin
        # SUBROUTINE ZTRCON( NORM, UPLO, DIAG, N, A, LDA, RCOND, WORK,
        #                   RWORK, INFO )
        # .. Scalar Arguments ..
        # CHARACTER          DIAG, NORM, UPLO
        # INTEGER            INFO, LDA, N
        # DOUBLE PRECISION   RCOND
        # .. Array Arguments ..
        # DOUBLE PRECISION   RWORK( * )
        # COMPLEX*16         A( LDA, * ), WORK( * )
        function trcon!(norm::AbstractChar, uplo::AbstractChar, diag::AbstractChar, A::AbstractMatrix{$elty})
            chkstride1(A)
            n = checksquare(A)
            chkuplo(uplo)
            chkdiag(diag)
            rcond = Ref{$relty}(1)
            work  = Vector{$elty}(undef, 2n)
            rwork = Vector{$relty}(undef, n)
            info  = Ref{BlasInt}()
            ccall((@blasfunc($trcon), libblastrampoline), Cvoid,
                  (Ref{UInt8}, Ref{UInt8}, Ref{UInt8}, Ref{BlasInt},
                   Ptr{$elty}, Ref{BlasInt}, Ref{$relty}, Ptr{$elty}, Ptr{$relty}, Ptr{BlasInt},
                   Clong, Clong, Clong),
                  norm, uplo, diag, n,
                  A, max(1,stride(A,2)), rcond, work, rwork, info,
                  1, 1, 1)
            chklapackerror(info[])
            rcond[]
        end

        # SUBROUTINE ZTREVC( SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR,
        #                    LDVR, MM, M, WORK, RWORK, INFO )
        #
        # .. Scalar Arguments ..
        # CHARACTER          HOWMNY, SIDE
        # INTEGER            INFO, LDT, LDVL, LDVR, M, MM, N
        # ..
        # .. Array Arguments ..
        # LOGICAL            SELECT( * )
        # DOUBLE PRECISION   RWORK( * )
        # COMPLEX*16         T( LDT, * ), VL( LDVL, * ), VR( LDVR, * ),
        #$                   WORK( * )
        function trevc!(side::AbstractChar, howmny::AbstractChar, select::AbstractVector{BlasInt}, T::AbstractMatrix{$elty},
                        VL::AbstractMatrix{$elty} = similar(T),
                        VR::AbstractMatrix{$elty} = similar(T))
            require_one_based_indexing(select, T, VL, VR)
            # Extract
            n, mm = checksquare(T), size(VL, 2)
            ldt, ldvl, ldvr = stride(T, 2), stride(VL, 2), stride(VR, 2)

            # Check
            chkstride1(T, select, VL, VR)
            if side ∉ ['L','R','B']
                throw(ArgumentError("side argument must be 'L' (left eigenvectors), 'R' (right eigenvectors), or 'B' (both), got $side"))
            end

            # Allocate
            m = Ref{BlasInt}()
            work = Vector{$elty}(undef, 2n)
            rwork = Vector{$relty}(undef, n)
            info = Ref{BlasInt}()
            ccall((@blasfunc($trevc), libblastrampoline), Cvoid,
                (Ref{UInt8}, Ref{UInt8}, Ptr{BlasInt}, Ref{BlasInt},
                 Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                 Ptr{$elty}, Ref{BlasInt}, Ref{BlasInt}, Ptr{BlasInt},
                 Ptr{$elty}, Ptr{$relty}, Ptr{BlasInt}, Clong, Clong),
                side, howmny, select, n,
                T, ldt, VL, ldvl,
                VR, ldvr, mm, m,
                work, rwork, info, 1, 1)
            chklapackerror(info[])

            #Decide what exactly to return
            if howmny == 'S' #compute selected eigenvectors
                if side == 'L' #left eigenvectors only
                    return select, VL[:,1:m[]]
                elseif side == 'R' #right eigenvectors only
                    return select, VR[:,1:m[]]
                else #side=='B' #both eigenvectors
                    return select, VL[:,1:m[]], VR[:,1:m[]]
                end
            else #compute all eigenvectors
                if side == 'L' #left eigenvectors only
                    return VL[:,1:m[]]
                elseif side == 'R' #right eigenvectors only
                    return VR[:,1:m[]]
                else #side=='B' #both eigenvectors
                    return VL[:,1:m[]], VR[:,1:m[]]
                end
            end
        end

        # SUBROUTINE ZTRRFS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, X,
        #                    LDX, FERR, BERR, WORK, IWORK, INFO )
        # .. Scalar Arguments ..
        # CHARACTER          DIAG, TRANS, UPLO
        # INTEGER            INFO, LDA, LDB, LDX, N, NRHS
        # .. Array Arguments ..
        # INTEGER            IWORK( * )
        # DOUBLE PRECISION   A( LDA, * ), B( LDB, * ), BERR( * ), FERR( * ),
        #$                   WORK( * ), X( LDX, * )
        function trrfs!(uplo::AbstractChar, trans::AbstractChar, diag::AbstractChar,
                        A::AbstractMatrix{$elty}, B::AbstractVecOrMat{$elty}, X::AbstractVecOrMat{$elty},
                        Ferr::AbstractVector{$relty} = similar(B, $relty, size(B,2)),
                        Berr::AbstractVector{$relty} = similar(B, $relty, size(B,2)))
            require_one_based_indexing(A, B, X, Ferr, Berr)
            chkstride1(A, B, X, Ferr, Berr)
            chktrans(trans)
            chkuplo(uplo)
            chkdiag(diag)
            n = size(A,2)
            nrhs = size(B,2)
            if nrhs != size(X,2)
                throw(DimensionMismatch("second dimensions of B, $nrhs, and X, $(size(X,2)), must match"))
            end
            work  = Vector{$elty}(undef, 2n)
            rwork = Vector{$relty}(undef, n)
            info  = Ref{BlasInt}()
            ccall((@blasfunc($trrfs), libblastrampoline), Cvoid,
                (Ref{UInt8}, Ref{UInt8}, Ref{UInt8}, Ref{BlasInt},
                 Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                 Ptr{$relty}, Ptr{$relty}, Ptr{$elty}, Ptr{$relty}, Ptr{BlasInt}, Clong, Clong, Clong),
                uplo, trans, diag, n,
                nrhs, A, max(1,stride(A,2)), B, max(1,stride(B,2)), X, max(1,stride(X,2)),
                Ferr, Berr, work, rwork, info, 1, 1, 1)
            chklapackerror(info[])
            Ferr, Berr
        end
    end
end

"""
    trcon!(norm, uplo, diag, A)

Finds the reciprocal condition number of (upper if `uplo = U`, lower if
`uplo = L`) triangular matrix `A`. If `diag = N`, `A` has non-unit
diagonal elements. If `diag = U`, all diagonal elements of `A` are one.
If `norm = I`, the condition number is found in the infinity norm. If
`norm = O` or `1`, the condition number is found in the one norm.
"""
trcon!(norm::AbstractChar, uplo::AbstractChar, diag::AbstractChar, A::AbstractMatrix)

"""
    trevc!(side, howmny, select, T, VL = similar(T), VR = similar(T))

Finds the eigensystem of an upper triangular matrix `T`. If `side = R`,
the right eigenvectors are computed. If `side = L`, the left
eigenvectors are computed. If `side = B`, both sets are computed. If
`howmny = A`, all eigenvectors are found. If `howmny = B`, all
eigenvectors are found and backtransformed using `VL` and `VR`. If
`howmny = S`, only the eigenvectors corresponding to the values in
`select` are computed.
"""
trevc!(side::AbstractChar, howmny::AbstractChar, select::AbstractVector{BlasInt}, T::AbstractMatrix,
        VL::AbstractMatrix = similar(T), VR::AbstractMatrix = similar(T))

"""
    trrfs!(uplo, trans, diag, A, B, X, Ferr, Berr) -> (Ferr, Berr)

Estimates the error in the solution to `A * X = B` (`trans = N`),
`transpose(A) * X = B` (`trans = T`), `adjoint(A) * X = B` (`trans = C`) for `side = L`,
or the equivalent equations a right-handed `side = R` `X * A` after
computing `X` using `trtrs!`. If `uplo = U`, `A` is upper triangular.
If `uplo = L`, `A` is lower triangular. If `diag = N`, `A` has non-unit
diagonal elements. If `diag = U`, all diagonal elements of `A` are one.
`Ferr` and `Berr` are optional inputs. `Ferr` is the forward error and
`Berr` is the backward error, each component-wise.
"""
trrfs!(uplo::AbstractChar, trans::AbstractChar, diag::AbstractChar, A::AbstractMatrix, B::AbstractVecOrMat,
       X::AbstractVecOrMat, Ferr::AbstractVector, Berr::AbstractVector)

## (ST) Symmetric tridiagonal - eigendecomposition
for (stev, stebz, stegr, stein, elty) in
    ((:dstev_,:dstebz_,:dstegr_,:dstein_,:Float64),
     (:sstev_,:sstebz_,:sstegr_,:sstein_,:Float32)
#     , (:zstev_,:ComplexF64)  Need to rewrite for ZHEEV, rwork, etc.
#     , (:cstev_,:ComplexF32)
     )
    @eval begin
        function stev!(job::AbstractChar, dv::AbstractVector{$elty}, ev::AbstractVector{$elty})
            require_one_based_indexing(dv, ev)
            chkstride1(dv, ev)
            n = length(dv)
            if length(ev) != n - 1 && length(ev) != n
                throw(DimensionMismatch("ev has length $(length(ev)) but needs one less than or equal to dv's length, $n)"))
            end
            Zmat = similar(dv, $elty, (n, job != 'N' ? n : 0))
            work = Vector{$elty}(undef, max(1, 2n-2))
            info = Ref{BlasInt}()
            ccall((@blasfunc($stev), libblastrampoline), Cvoid,
                  (Ref{UInt8}, Ref{BlasInt}, Ptr{$elty}, Ptr{$elty}, Ptr{$elty},
                   Ref{BlasInt}, Ptr{$elty}, Ptr{BlasInt}, Clong),
                  job, n, dv, ev, Zmat, n, work, info, 1)
            chklapackerror(info[])
            dv, Zmat
        end

        #*  DSTEBZ computes the eigenvalues of a symmetric tridiagonal
        #*  matrix T.  The user may ask for all eigenvalues, all eigenvalues
        #*  in the half-open interval (VL, VU], or the IL-th through IU-th
        #*  eigenvalues.
        function stebz!(range::AbstractChar, order::AbstractChar, vl::$elty, vu::$elty, il::Integer, iu::Integer, abstol::Real, dv::AbstractVector{$elty}, ev::AbstractVector{$elty})
            require_one_based_indexing(dv, ev)
            chkstride1(dv, ev)
            n = length(dv)
            if length(ev) != n - 1
                throw(DimensionMismatch("ev has length $(length(ev)) but needs one less than dv's length, $n)"))
            end
            m = Ref{BlasInt}()
            nsplit = Vector{BlasInt}(undef, 1)
            w = similar(dv, $elty, n)
            tmp = 0.0
            iblock = similar(dv, BlasInt,n)
            isplit = similar(dv, BlasInt,n)
            work = Vector{$elty}(undef, 4*n)
            iwork = Vector{BlasInt}(undef, 3*n)
            info = Ref{BlasInt}()
            ccall((@blasfunc($stebz), libblastrampoline), Cvoid,
                (Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ref{$elty},
                Ref{$elty}, Ref{BlasInt}, Ref{BlasInt}, Ref{$elty},
                Ptr{$elty}, Ptr{$elty}, Ptr{BlasInt}, Ptr{BlasInt},
                Ptr{$elty}, Ptr{BlasInt}, Ptr{BlasInt}, Ptr{$elty},
                Ptr{BlasInt}, Ptr{BlasInt}, Clong, Clong),
                range, order, n, vl,
                vu, il, iu, abstol,
                dv, ev, m, nsplit,
                w, iblock, isplit, work,
                iwork, info, 1, 1)
            chklapackerror(info[])
            w[1:m[]], iblock[1:m[]], isplit[1:nsplit[1]]
        end

        function stegr!(jobz::AbstractChar, range::AbstractChar, dv::AbstractVector{$elty}, ev::AbstractVector{$elty}, vl::Real, vu::Real, il::Integer, iu::Integer)
            require_one_based_indexing(dv, ev)
            chkstride1(dv, ev)
            n = length(dv)
            ne = length(ev)
            if ne == n - 1
                eev = [ev; zero($elty)]
            elseif ne == n
                eev = copy(ev)
                eev[n] = zero($elty)
            else
                throw(DimensionMismatch("ev has length $ne but needs one less than or equal to dv's length, $n)"))
            end

            abstol = Vector{$elty}(undef, 1)
            m = Ref{BlasInt}()
            w = similar(dv, $elty, n)
            ldz = jobz == 'N' ? 1 : n
            Z = similar(dv, $elty, ldz, range == 'I' ? iu-il+1 : n)
            isuppz = similar(dv, BlasInt, 2*size(Z, 2))
            work = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            iwork = Vector{BlasInt}(undef, 1)
            liwork = BlasInt(-1)
            info = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1] and liwork as iwork[1]
                ccall((@blasfunc($stegr), libblastrampoline), Cvoid,
                    (Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ptr{$elty},
                    Ptr{$elty}, Ref{$elty}, Ref{$elty}, Ref{BlasInt},
                    Ref{BlasInt}, Ptr{$elty}, Ptr{BlasInt}, Ptr{$elty},
                    Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}, Ptr{$elty},
                    Ref{BlasInt}, Ptr{BlasInt}, Ref{BlasInt}, Ptr{BlasInt},
                    Clong, Clong),
                    jobz, range, n, dv,
                    eev, vl, vu, il,
                    iu, abstol, m, w,
                    Z, ldz, isuppz, work,
                    lwork, iwork, liwork, info,
                    1, 1)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(work[1])
                    resize!(work, lwork)
                    liwork = iwork[1]
                    resize!(iwork, liwork)
                end
            end
            m[] == length(w) ? w : w[1:m[]], m[] == size(Z, 2) ? Z : Z[:,1:m[]]
        end

        function stein!(dv::AbstractVector{$elty}, ev_in::AbstractVector{$elty}, w_in::AbstractVector{$elty}, iblock_in::AbstractVector{BlasInt}, isplit_in::AbstractVector{BlasInt})
            require_one_based_indexing(dv, ev_in, w_in, iblock_in, isplit_in)
            chkstride1(dv, ev_in, w_in, iblock_in, isplit_in)
            n = length(dv)
            ne = length(ev_in)
            if ne == n - 1
                ev = [ev_in; zero($elty)]
            elseif ne == n
                ev = copy(ev_in)
                ev[n] = zero($elty)
            else
                throw(DimensionMismatch("ev_in has length $ne but needs one less than or equal to dv's length, $n)"))
            end
            ldz = n #Leading dimension
            #Number of eigenvalues to find
            if !(1 <= length(w_in) <= n)
                throw(DimensionMismatch("w_in has length $(length(w_in)), but needs to be between 1 and $n"))
            end
            m = length(w_in)
            #If iblock and isplit are invalid input, assume worst-case block partitioning,
            # i.e. set the block scheme to be the entire matrix
            iblock = similar(dv, BlasInt,n)
            isplit = similar(dv, BlasInt,n)
            w = similar(dv, $elty,n)
            if length(iblock_in) < m #Not enough block specifications
                iblock[1:m] = fill(BlasInt(1), m)
                w[1:m] = sort(w_in)
            else
                iblock[1:m] = iblock_in
                w[1:m] = w_in #Assume user has sorted the eigenvalues properly
            end
            if length(isplit_in) < 1 #Not enough block specifications
                isplit[1] = n
            else
                isplit[1:length(isplit_in)] = isplit_in
            end
            z = similar(dv, $elty,(n,m))
            work  = Vector{$elty}(undef, 5*n)
            iwork = Vector{BlasInt}(undef, n)
            ifail = Vector{BlasInt}(undef, m)
            info  = Ref{BlasInt}()
            ccall((@blasfunc($stein), libblastrampoline), Cvoid,
                (Ref{BlasInt}, Ptr{$elty}, Ptr{$elty}, Ref{BlasInt},
                Ptr{$elty}, Ptr{BlasInt}, Ptr{BlasInt}, Ptr{$elty},
                Ref{BlasInt}, Ptr{$elty}, Ptr{BlasInt}, Ptr{BlasInt},
                Ptr{BlasInt}),
                n, dv, ev, m, w, iblock, isplit, z, ldz, work, iwork, ifail, info)
            chklapackerror(info[])
            if any(ifail .!= 0)
                # TODO: better error message / type
                error("failed to converge eigenvectors:\n$(findall(!iszero, ifail))")
            end
            z
        end
    end
end
stegr!(jobz::AbstractChar, dv::AbstractVector, ev::AbstractVector) = stegr!(jobz, 'A', dv, ev, 0.0, 0.0, 0, 0)

# Allow user to skip specification of iblock and isplit
stein!(dv::AbstractVector, ev::AbstractVector, w_in::AbstractVector) = stein!(dv, ev, w_in, zeros(BlasInt,0), zeros(BlasInt,0))
# Allow user to specify just one eigenvector to get in stein!
stein!(dv::AbstractVector, ev::AbstractVector, eval::Real) = stein!(dv, ev, [eval], zeros(BlasInt,0), zeros(BlasInt,0))

"""
    stev!(job, dv, ev) -> (dv, Zmat)

Computes the eigensystem for a symmetric tridiagonal matrix with `dv` as
diagonal and `ev` as off-diagonal. If `job = N` only the eigenvalues are
found and returned in `dv`. If `job = V` then the eigenvectors are also found
and returned in `Zmat`.
"""
stev!(job::AbstractChar, dv::AbstractVector, ev::AbstractVector)

"""
    stebz!(range, order, vl, vu, il, iu, abstol, dv, ev) -> (dv, iblock, isplit)

Computes the eigenvalues for a symmetric tridiagonal matrix with `dv` as
diagonal and `ev` as off-diagonal. If `range = A`, all the eigenvalues
are found. If `range = V`, the eigenvalues in the half-open interval
`(vl, vu]` are found. If `range = I`, the eigenvalues with indices between
`il` and `iu` are found. If `order = B`, eigvalues are ordered within a
block. If `order = E`, they are ordered across all the blocks.
`abstol` can be set as a tolerance for convergence.
"""
stebz!(range::AbstractChar, order::AbstractChar, vl, vu, il::Integer, iu::Integer, abstol::Real, dv::AbstractVector, ev::AbstractVector)

"""
    stegr!(jobz, range, dv, ev, vl, vu, il, iu) -> (w, Z)

Computes the eigenvalues (`jobz = N`) or eigenvalues and eigenvectors
(`jobz = V`) for a symmetric tridiagonal matrix with `dv` as diagonal
and `ev` as off-diagonal. If `range = A`, all the eigenvalues
are found. If `range = V`, the eigenvalues in the half-open interval
`(vl, vu]` are found. If `range = I`, the eigenvalues with indices between
`il` and `iu` are found. The eigenvalues are returned in `w` and the eigenvectors
in `Z`.
"""
stegr!(jobz::AbstractChar, range::AbstractChar, dv::AbstractVector, ev::AbstractVector, vl::Real, vu::Real, il::Integer, iu::Integer)

"""
    stein!(dv, ev_in, w_in, iblock_in, isplit_in)

Computes the eigenvectors for a symmetric tridiagonal matrix with `dv`
as diagonal and `ev_in` as off-diagonal. `w_in` specifies the input
eigenvalues for which to find corresponding eigenvectors. `iblock_in`
specifies the submatrices corresponding to the eigenvalues in `w_in`.
`isplit_in` specifies the splitting points between the submatrix blocks.
"""
stein!(dv::AbstractVector, ev_in::AbstractVector, w_in::AbstractVector, iblock_in::AbstractVector{BlasInt}, isplit_in::AbstractVector{BlasInt})

## (SY) symmetric real matrices - Bunch-Kaufman decomposition,
## solvers (direct and factored) and inverse.
for (syconv, sysv, sytrf, sytri, sytrs, elty) in
    ((:dsyconv_,:dsysv_,:dsytrf_,:dsytri_,:dsytrs_,:Float64),
     (:ssyconv_,:ssysv_,:ssytrf_,:ssytri_,:ssytrs_,:Float32))
    @eval begin
        #       SUBROUTINE DSYCONV( UPLO, WAY, N, A, LDA, IPIV, WORK, INFO )
        # *     .. Scalar Arguments ..
        #       CHARACTER          UPLO, WAY
        #       INTEGER            INFO, LDA, N
        # *     .. Array Arguments ..
        #       INTEGER            IPIV( * )
        #       DOUBLE PRECISION   A( LDA, * ), WORK( * )
        function syconv!(uplo::AbstractChar, A::AbstractMatrix{$elty}, ipiv::AbstractVector{BlasInt})
            chkstride1(A, ipiv)
            n = checksquare(A)
            chkuplo(uplo)
            work = Vector{$elty}(undef, n)
            info = Ref{BlasInt}()
            ccall((@blasfunc($syconv), libblastrampoline), Cvoid,
                  (Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                   Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt}, Clong, Clong),
                  uplo, 'C', n, A, max(1,stride(A,2)), ipiv, work, info, 1, 1)
            chklapackerror(info[])
            A, work
        end

        #       SUBROUTINE DSYSV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
        #                         LWORK, INFO )
        #       .. Scalar Arguments ..
        #       CHARACTER          UPLO
        #       INTEGER            INFO, LDA, LDB, LWORK, N, NRHS
        #       .. Array Arguments ..
        #       INTEGER            IPIV( * )
        #       DOUBLE PRECISION   A( LDA, * ), B( LDB, * ), WORK( * )
        function sysv!(uplo::AbstractChar, A::AbstractMatrix{$elty}, B::AbstractVecOrMat{$elty})
            require_one_based_indexing(A, B)
            chkstride1(A,B)
            n = checksquare(A)
            chkuplo(uplo)
            if n != size(B,1)
                throw(DimensionMismatch("B has first dimension $(size(B,1)), but needs $n"))
            end
            ipiv  = similar(A, BlasInt, n)
            work  = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            info  = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($sysv), libblastrampoline), Cvoid,
                      (Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt},
                       Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}, Clong),
                      uplo, n, size(B,2), A, max(1,stride(A,2)), ipiv, B, max(1,stride(B,2)),
                      work, lwork, info,  1)
                chkargsok(info[])
                chknonsingular(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            B, A, ipiv
        end

        #       SUBROUTINE DSYTRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
        # *     .. Scalar Arguments ..
        #       CHARACTER          UPLO
        #       INTEGER            INFO, LDA, LWORK, N
        # *     .. Array Arguments ..
        #       INTEGER            IPIV( * )
        #       DOUBLE PRECISION   A( LDA, * ), WORK( * )
        function sytrf!(uplo::AbstractChar, A::AbstractMatrix{$elty})
            chkstride1(A)
            n = checksquare(A)
            chkuplo(uplo)
            ipiv  = similar(A, BlasInt, n)
            if n == 0
                return A, ipiv, zero(BlasInt)
            end
            work  = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            info  = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($sytrf), libblastrampoline), Cvoid,
                      (Ref{UInt8}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                       Ptr{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}, Clong),
                      uplo, n, A, stride(A,2), ipiv, work, lwork, info, 1)
                chkargsok(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            return A, ipiv, info[]
        end

        #       SUBROUTINE DSYTRI2( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
        # *     .. Scalar Arguments ..
        #       CHARACTER          UPLO
        #       INTEGER            INFO, LDA, LWORK, N
        # *     .. Array Arguments ..
        #       INTEGER            IPIV( * )
        #       DOUBLE PRECISION   A( LDA, * ), WORK( * )
#         function sytri!(uplo::AbstractChar, A::AbstractMatrix{$elty}, ipiv::Vector{BlasInt})
#             chkstride1(A)
#             n = checksquare(A)
#             chkuplo(uplo)
#             work  = Vector{$elty}(undef, 1)
#             lwork = BlasInt(-1)
#             info  = Ref{BlasInt}()
#             for i in 1:2
#                 ccall((@blasfunc($sytri), libblastrampoline), Cvoid,
#                       (Ptr{UInt8}, Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt},
#                        Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt}, Ptr{BlasInt}, Clong),
#                       &uplo, &n, A, &max(1,stride(A,2)), ipiv, work, &lwork, info, 1)
#                 @assertargsok
#                 chknonsingular(info[])
#                 if lwork < 0
#                     lwork = BlasInt(real(work[1]))
#                     work = Vector{$elty}(undef, lwork)
#                 end
#             end
#             A
#         end

        #      SUBROUTINE DSYTRI( UPLO, N, A, LDA, IPIV, WORK, INFO )
        #     .. Scalar Arguments ..
        #      CHARACTER          UPLO
        #      INTEGER            INFO, LDA, N
        #     .. Array Arguments ..
        #      INTEGER            IPIV( * )
        #      DOUBLE PRECISION   A( LDA, * ), WORK( * )
        function sytri!(uplo::AbstractChar, A::AbstractMatrix{$elty}, ipiv::AbstractVector{BlasInt})
            chkstride1(A, ipiv)
            n = checksquare(A)
            chkuplo(uplo)
            work = Vector{$elty}(undef, n)
            info = Ref{BlasInt}()
            ccall((@blasfunc($sytri), libblastrampoline), Cvoid,
                  (Ref{UInt8}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                   Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt}, Clong),
                  uplo, n, A, max(1,stride(A,2)), ipiv, work, info, 1)
            chkargsok(info[])
            chknonsingular(info[])
            A
        end

        #       SUBROUTINE DSYTRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
        #
        #       .. Scalar Arguments ..
        #       CHARACTER          UPLO
        #       INTEGER            INFO, LDA, LDB, N, NRHS
        #       .. Array Arguments ..
        #       INTEGER            IPIV( * )
        #       DOUBLE PRECISION   A( LDA, * ), B( LDB, * )
        function sytrs!(uplo::AbstractChar, A::AbstractMatrix{$elty},
                       ipiv::AbstractVector{BlasInt}, B::AbstractVecOrMat{$elty})
            require_one_based_indexing(A, ipiv, B)
            chkstride1(A,B,ipiv)
            n = checksquare(A)
            chkuplo(uplo)
            if n != size(B,1)
                throw(DimensionMismatch("B has first dimension $(size(B,1)), but needs $n"))
            end
            info = Ref{BlasInt}()
            ccall((@blasfunc($sytrs), libblastrampoline), Cvoid,
                  (Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                   Ptr{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}, Clong),
                  uplo, n, size(B,2), A, max(1,stride(A,2)), ipiv, B, max(1,stride(B,2)), info, 1)
            chklapackerror(info[])
            B
        end
    end
end

# Rook-pivoting variants of symmetric-matrix algorithms
for (sysv, sytrf, sytri, sytrs, syconvf, elty) in
    ((:dsysv_rook_,:dsytrf_rook_,:dsytri_rook_,:dsytrs_rook_,:dsyconvf_rook_,:Float64),
     (:ssysv_rook_,:ssytrf_rook_,:ssytri_rook_,:ssytrs_rook_,:ssyconvf_rook_,:Float32))
    @eval begin
        #       SUBROUTINE DSYSV_ROOK(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
        #                             LWORK, INFO )
        #       .. Scalar Arguments ..
        #       CHARACTER          UPLO
        #       INTEGER            INFO, LDA, LDB, LWORK, N, NRHS
        #       .. Array Arguments ..
        #       INTEGER            IPIV( * )
        #       DOUBLE PRECISION   A( LDA, * ), B( LDB, * ), WORK( * )
        function sysv_rook!(uplo::AbstractChar, A::AbstractMatrix{$elty}, B::AbstractVecOrMat{$elty})
            require_one_based_indexing(A, B)
            chkstride1(A,B)
            n = checksquare(A)
            chkuplo(uplo)
            if n != size(B,1)
                throw(DimensionMismatch("B has first dimension $(size(B,1)), but needs $n"))
            end
            ipiv  = similar(A, BlasInt, n)
            work  = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            info  = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($sysv), libblastrampoline), Cvoid,
                      (Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt},
                       Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}, Clong),
                      uplo, n, size(B,2), A, max(1,stride(A,2)), ipiv, B, max(1,stride(B,2)),
                      work, lwork, info, 1)
                chkargsok(info[])
                chknonsingular(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            B, A, ipiv
        end

        #       SUBROUTINE DSYTRF_ROOK(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
        # *     .. Scalar Arguments ..
        #       CHARACTER          UPLO
        #       INTEGER            INFO, LDA, LWORK, N
        # *     .. Array Arguments ..
        #       INTEGER            IPIV( * )
        #       DOUBLE PRECISION   A( LDA, * ), WORK( * )
        function sytrf_rook!(uplo::AbstractChar, A::AbstractMatrix{$elty})
            chkstride1(A)
            n = checksquare(A)
            chkuplo(uplo)
            ipiv  = similar(A, BlasInt, n)
            if n == 0
                return A, ipiv, zero(BlasInt)
            end
            work  = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            info  = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($sytrf), libblastrampoline), Cvoid,
                      (Ref{UInt8}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                       Ptr{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}, Clong),
                      uplo, n, A, stride(A,2), ipiv, work, lwork, info, 1)
                chkargsok(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            return A, ipiv, info[]
        end

        #      SUBROUTINE DSYTRI_ROOK( UPLO, N, A, LDA, IPIV, WORK, INFO )
        #     .. Scalar Arguments ..
        #      CHARACTER          UPLO
        #      INTEGER            INFO, LDA, N
        #     .. Array Arguments ..
        #      INTEGER            IPIV( * )
        #      DOUBLE PRECISION   A( LDA, * ), WORK( * )
        function sytri_rook!(uplo::AbstractChar, A::AbstractMatrix{$elty}, ipiv::AbstractVector{BlasInt})
            chkstride1(A, ipiv)
            n = checksquare(A)
            chkuplo(uplo)
            work = Vector{$elty}(undef, n)
            info = Ref{BlasInt}()
            ccall((@blasfunc($sytri), libblastrampoline), Cvoid,
                  (Ref{UInt8}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                   Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt}, Clong),
                  uplo, n, A, max(1,stride(A,2)), ipiv, work, info, 1)
            chkargsok(info[])
            chknonsingular(info[])
            A
        end

        #       SUBROUTINE DSYTRS_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
        #
        #       .. Scalar Arguments ..
        #       CHARACTER          UPLO
        #       INTEGER            INFO, LDA, LDB, N, NRHS
        #       .. Array Arguments ..
        #       INTEGER            IPIV( * )
        #       DOUBLE PRECISION   A( LDA, * ), B( LDB, * )
        function sytrs_rook!(uplo::AbstractChar, A::AbstractMatrix{$elty},
                       ipiv::AbstractVector{BlasInt}, B::AbstractVecOrMat{$elty})
            require_one_based_indexing(A, ipiv, B)
            chkstride1(A,B,ipiv)
            n = checksquare(A)
            chkuplo(uplo)
            if n != size(B,1)
                throw(DimensionMismatch("B has first dimension $(size(B,1)), but needs $n"))
            end
            info = Ref{BlasInt}()
            ccall((@blasfunc($sytrs), libblastrampoline), Cvoid,
                  (Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                   Ptr{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}, Clong),
                  uplo, n, size(B,2), A, max(1,stride(A,2)), ipiv, B, max(1,stride(B,2)), info, 1)
            chklapackerror(info[])
            B
        end

        # SUBROUTINE DSYCONVF_ROOK( UPLO, WAY, N, A, LDA, IPIV, E, INFO )
        #
        # .. Scalar Arguments ..
        # CHARACTER          UPLO, WAY
        # INTEGER            INFO, LDA, N
        # ..
        # .. Array Arguments ..
        # INTEGER            IPIV( * )
        # DOUBLE PRECISION   A( LDA, * ), E( * )
        function syconvf_rook!(uplo::AbstractChar, way::AbstractChar,
                                A::AbstractMatrix{$elty}, ipiv::AbstractVector{BlasInt},
                                e::AbstractVector{$elty} = Vector{$elty}(undef, length(ipiv)))
            require_one_based_indexing(A, ipiv, e)
            # extract
            n = checksquare(A)
            lda = max(1, stride(A, 2))

            # check
            chkuplo(uplo)
            if way != 'C' && way != 'R'
                throw(ArgumentError("way must be C or R"))
            end
            if length(ipiv) != n
                throw(ArgumentError("length of pivot vector was $(length(ipiv)) but should have been $n"))
            end
            if length(e) != n
                throw(ArgumentError("length of e vector was $(length(e)) but should have been $n"))
            end

            # allocate
            info = Ref{BlasInt}()

            ccall((@blasfunc($syconvf), libblastrampoline), Cvoid,
                (Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ptr{$elty},
                 Ref{BlasInt}, Ptr{$elty}, Ptr{BlasInt}, Ptr{BlasInt},
                 Clong, Clong),
                uplo, way, n, A,
                lda, e, ipiv, info,
                1, 1)

            chklapackerror(info[])
            return A, e
        end
    end
end

## (SY) hermitian matrices - eigendecomposition, Bunch-Kaufman decomposition,
## solvers (direct and factored) and inverse.
for (syconv, hesv, hetrf, hetri, hetrs, elty, relty) in
    ((:zsyconv_,:zhesv_,:zhetrf_,:zhetri_,:zhetrs_,:ComplexF64, :Float64),
     (:csyconv_,:chesv_,:chetrf_,:chetri_,:chetrs_,:ComplexF32, :Float32))
    @eval begin
       #   SUBROUTINE ZSYCONV( UPLO, WAY, N, A, LDA, IPIV, WORK, INFO )
       #
       #        .. Scalar Arguments ..
       #        CHARACTER          UPLO, WAY
       #        INTEGER            INFO, LDA, N
       #        ..
       #        .. Array Arguments ..
       #        INTEGER            IPIV( * )
       #        COMPLEX*16         A( LDA, * ), WORK( * )
        function syconv!(uplo::AbstractChar, A::AbstractMatrix{$elty}, ipiv::AbstractVector{BlasInt})
            chkstride1(A,ipiv)
            n = checksquare(A)
            chkuplo(uplo)
            work = Vector{$elty}(undef, n)
            info = Ref{BlasInt}()
            ccall((@blasfunc($syconv), libblastrampoline), Cvoid,
                  (Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                   Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt}, Clong, Clong),
                  uplo, 'C', n, A, max(1,stride(A,2)), ipiv, work, info, 1, 1)
            chklapackerror(info[])
            A, work
        end

        #       SUBROUTINE ZHESV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
        # *     .. Scalar Arguments ..
        #       CHARACTER          UPLO
        #       INTEGER            INFO, LDA, LDB, LWORK, N, NRHS
        # *     ..
        # *     .. Array Arguments ..
        #       INTEGER            IPIV( * )
        #       COMPLEX*16         A( LDA, * ), B( LDB, * ), WORK( * )
        function hesv!(uplo::AbstractChar, A::AbstractMatrix{$elty}, B::AbstractVecOrMat{$elty})
            require_one_based_indexing(A, B)
            chkstride1(A,B)
            n = checksquare(A)
            chkuplo(uplo)
            if n != size(B,1)
                throw(DimensionMismatch("B has first dimension $(size(B,1)), but needs $n"))
            end
            ipiv  = similar(A, BlasInt, n)
            work  = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            info  = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($hesv), libblastrampoline), Cvoid,
                      (Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt},
                       Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}, Clong),
                      uplo, n, size(B,2), A, max(1,stride(A,2)), ipiv, B, max(1,stride(B,2)),
                      work, lwork, info, 1)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            B, A, ipiv
        end

        #       SUBROUTINE ZHETRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
        # *     .. Scalar Arguments ..
        #       CHARACTER          UPLO
        #       INTEGER            INFO, LDA, LWORK, N
        # *     ..
        # *     .. Array Arguments ..
        #       INTEGER            IPIV( * )
        #       COMPLEX*16         A( LDA, * ), WORK( * )
        function hetrf!(uplo::AbstractChar, A::AbstractMatrix{$elty})
            chkstride1(A)
            n = checksquare(A)
            chkuplo(uplo)
            ipiv  = similar(A, BlasInt, n)
            work  = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            info  = Ref{BlasInt}()
            for i in 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($hetrf), libblastrampoline), Cvoid,
                      (Ref{UInt8}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                       Ptr{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}, Clong),
                      uplo, n, A, max(1,stride(A,2)), ipiv, work, lwork, info, 1)
                chkargsok(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            A, ipiv, info[]
        end

#       SUBROUTINE ZHETRI2( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
# *     .. Scalar Arguments ..
#       CHARACTER          UPLO
#       INTEGER            INFO, LDA, LWORK, N
# *     ..
# *     .. Array Arguments ..
#       INTEGER            IPIV( * )
#       COMPLEX*16         A( LDA, * ), WORK( * )
#         function hetri!(uplo::AbstractChar, A::AbstractMatrix{$elty}, ipiv::Vector{BlasInt})
#             chkstride1(A)
#             n = checksquare(A)
#             chkuplo(uplo)
#             work  = Vector{$elty}(undef, 1)
#             lwork = BlasInt(-1)
#             info  = Ref{BlasInt}()
#             for i in 1:2
#                 ccall((@blasfunc($hetri), libblastrampoline), Cvoid,
#                       (Ptr{UInt8}, Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt},
#                        Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt}, Ptr{BlasInt}, Clong),
#                       &uplo, &n, A, &max(1,stride(A,2)), ipiv, work, &lwork, info, 1)
#                 chklapackerror(info[])
#                 if lwork < 0
#                     lwork = BlasInt(real(work[1]))
#                     work = Vector{$elty}(undef, lwork)
#                 end
#             end
#             A
#         end


        #       SUBROUTINE ZHETRI( UPLO, N, A, LDA, IPIV, WORK, INFO )
        # *     .. Scalar Arguments ..
        #       CHARACTER          UPLO
        #       INTEGER            INFO, LDA, N
        # *     ..
        # *     .. Array Arguments ..
        #       INTEGER            IPIV( * )
        #       COMPLEX*16         A( LDA, * ), WORK( * )
        function hetri!(uplo::AbstractChar, A::AbstractMatrix{$elty}, ipiv::AbstractVector{BlasInt})
            chkstride1(A, ipiv)
            n = checksquare(A)
            chkuplo(uplo)
            work = Vector{$elty}(undef, n)
            info = Ref{BlasInt}()
            ccall((@blasfunc($hetri), libblastrampoline), Cvoid,
                  (Ref{UInt8}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                   Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt}, Clong),
                  uplo, n, A, max(1,stride(A,2)), ipiv, work, info, 1)
            chklapackerror(info[])
            A
        end

        #       SUBROUTINE ZHETRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
        # *     .. Scalar Arguments ..
        #       CHARACTER          UPLO
        #       INTEGER            INFO, LDA, LDB, N, NRHS
        # *     ..
        # *     .. Array Arguments ..
        #       INTEGER            IPIV( * )
        #       COMPLEX*16         A( LDA, * ), B( LDB, * )
        function hetrs!(uplo::AbstractChar, A::AbstractMatrix{$elty},
                       ipiv::AbstractVector{BlasInt}, B::AbstractVecOrMat{$elty})
            require_one_based_indexing(A, ipiv, B)
            chkstride1(A,B,ipiv)
            n = checksquare(A)
            if n != size(B,1)
                throw(DimensionMismatch("B has first dimension $(size(B,1)), but needs $n"))
            end
            info = Ref{BlasInt}()
            ccall((@blasfunc($hetrs), libblastrampoline), Cvoid,
                  (Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                   Ptr{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}, Clong),
                  uplo, n, size(B,2), A, max(1,stride(A,2)), ipiv, B, max(1,stride(B,2)), info, 1)
            chklapackerror(info[])
            B
        end
    end
end

for (hesv, hetrf, hetri, hetrs, elty, relty) in
    ((:zhesv_rook_,:zhetrf_rook_,:zhetri_rook_,:zhetrs_rook_,:ComplexF64, :Float64),
     (:chesv_rook_,:chetrf_rook_,:chetri_rook_,:chetrs_rook_,:ComplexF32, :Float32))
    @eval begin
        #       SUBROUTINE ZHESV_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
        # *     .. Scalar Arguments ..
        #       CHARACTER          UPLO
        #       INTEGER            INFO, LDA, LDB, LWORK, N, NRHS
        # *     ..
        # *     .. Array Arguments ..
        #       INTEGER            IPIV( * )
        #       COMPLEX*16         A( LDA, * ), B( LDB, * ), WORK( * )
        function hesv_rook!(uplo::AbstractChar, A::AbstractMatrix{$elty}, B::AbstractVecOrMat{$elty})
            require_one_based_indexing(A, B)
            chkstride1(A,B)
            n = checksquare(A)
            chkuplo(uplo)
            if n != size(B,1)
                throw(DimensionMismatch("B has first dimension $(size(B,1)), but needs $n"))
            end
            ipiv  = similar(A, BlasInt, n)
            work  = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            info  = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($hesv), libblastrampoline), Cvoid,
                      (Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt},
                       Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}, Clong),
                      uplo, n, size(B,2), A, max(1,stride(A,2)), ipiv, B, max(1,stride(B,2)),
                      work, lwork, info, 1)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            B, A, ipiv
        end

        #       SUBROUTINE ZHETRF_ROOK( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
        # *     .. Scalar Arguments ..
        #       CHARACTER          UPLO
        #       INTEGER            INFO, LDA, LWORK, N
        # *     ..
        # *     .. Array Arguments ..
        #       INTEGER            IPIV( * )
        #       COMPLEX*16         A( LDA, * ), WORK( * )
        function hetrf_rook!(uplo::AbstractChar, A::AbstractMatrix{$elty})
            chkstride1(A)
            n = checksquare(A)
            chkuplo(uplo)
            ipiv  = similar(A, BlasInt, n)
            work  = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            info  = Ref{BlasInt}()
            for i in 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($hetrf), libblastrampoline), Cvoid,
                      (Ref{UInt8}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                       Ptr{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}, Clong),
                      uplo, n, A, max(1,stride(A,2)), ipiv, work, lwork, info, 1)
                chkargsok(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            A, ipiv, info[]
        end

        #       SUBROUTINE ZHETRI_ROOK( UPLO, N, A, LDA, IPIV, WORK, INFO )
        # *     .. Scalar Arguments ..
        #       CHARACTER          UPLO
        #       INTEGER            INFO, LDA, N
        # *     ..
        # *     .. Array Arguments ..
        #       INTEGER            IPIV( * )
        #       COMPLEX*16         A( LDA, * ), WORK( * )
        function hetri_rook!(uplo::AbstractChar, A::AbstractMatrix{$elty}, ipiv::AbstractVector{BlasInt})
            chkstride1(A,ipiv)
            n = checksquare(A)
            chkuplo(uplo)
            work = Vector{$elty}(undef, n)
            info = Ref{BlasInt}()
            ccall((@blasfunc($hetri), libblastrampoline), Cvoid,
                  (Ref{UInt8}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                   Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt}, Clong),
                  uplo, n, A, max(1,stride(A,2)), ipiv, work, info, 1)
            chklapackerror(info[])
            A
        end

        #       SUBROUTINE ZHETRS_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
        # *     .. Scalar Arguments ..
        #       CHARACTER          UPLO
        #       INTEGER            INFO, LDA, LDB, N, NRHS
        # *     ..
        # *     .. Array Arguments ..
        #       INTEGER            IPIV( * )
        #       COMPLEX*16         A( LDA, * ), B( LDB, * )
        function hetrs_rook!(uplo::AbstractChar, A::AbstractMatrix{$elty},
                             ipiv::AbstractVector{BlasInt}, B::AbstractVecOrMat{$elty})
            require_one_based_indexing(A, ipiv, B)
            chkstride1(A,B,ipiv)
            n = checksquare(A)
            if n != size(B,1)
                throw(DimensionMismatch("B has first dimension $(size(B,1)), but needs $n"))
            end
            info = Ref{BlasInt}()
            ccall((@blasfunc($hetrs), libblastrampoline), Cvoid,
                  (Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                   Ptr{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}, Clong),
                  uplo, n, size(B,2), A, max(1,stride(A,2)), ipiv, B, max(1,stride(B,2)), info, 1)
            chklapackerror(info[])
            B
        end
    end
end

for (sysv, sytrf, sytri, sytrs, elty, relty) in
    ((:zsysv_,:zsytrf_,:zsytri_,:zsytrs_,:ComplexF64, :Float64),
     (:csysv_,:csytrf_,:csytri_,:csytrs_,:ComplexF32, :Float32))
    @eval begin
        #       SUBROUTINE ZSYSV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
        #      $                  LWORK, INFO )
        # *     .. Scalar Arguments ..
        #       CHARACTER          UPLO
        #       INTEGER            INFO, LDA, LDB, LWORK, N, NRHS
        # *     ..
        # *     .. Array Arguments ..
        #       INTEGER            IPIV( * )
        #       COMPLEX*16         A( LDA, * ), B( LDB, * ), WORK( * )
        function sysv!(uplo::AbstractChar, A::AbstractMatrix{$elty}, B::AbstractVecOrMat{$elty})
            require_one_based_indexing(A, B)
            chkstride1(A,B)
            n = checksquare(A)
            chkuplo(uplo)
            if n != size(B,1)
                throw(DimensionMismatch("B has first dimension $(size(B,1)), but needs $n"))
            end
            ipiv  = similar(A, BlasInt, n)
            work  = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            info  = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($sysv), libblastrampoline), Cvoid,
                      (Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt},
                       Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}, Clong),
                      uplo, n, size(B,2), A, max(1,stride(A,2)), ipiv, B, max(1,stride(B,2)),
                      work, lwork, info, 1)
                chkargsok(info[])
                chknonsingular(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            B, A, ipiv
        end

        #       SUBROUTINE ZSYTRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
        # *     .. Scalar Arguments ..
        #       CHARACTER          UPLO
        #       INTEGER            INFO, LDA, LWORK, N
        # *     ..
        # *     .. Array Arguments ..
        #       INTEGER            IPIV( * )
        #       COMPLEX*16         A( LDA, * ), WORK( * )
        function sytrf!(uplo::AbstractChar, A::AbstractMatrix{$elty})
            chkstride1(A)
            n = checksquare(A)
            chkuplo(uplo)
            ipiv = similar(A, BlasInt, n)
            if n == 0
                return A, ipiv, zero(BlasInt)
            end
            work  = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            info  = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($sytrf), libblastrampoline), Cvoid,
                      (Ref{UInt8}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                       Ptr{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}, Clong),
                      uplo, n, A, max(1,stride(A,2)), ipiv, work, lwork, info, 1)
                chkargsok(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            A, ipiv, info[]
        end

#       SUBROUTINE ZSYTRI2( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
# *     .. Scalar Arguments ..
#       CHARACTER          UPLO
#       INTEGER            INFO, LDA, LWORK, N
# *     ..
# *     .. Array Arguments ..
#       INTEGER            IPIV( * )
#       COMPLEX*16         A( LDA, * ), WORK( * )
#         function sytri!(uplo::AbstractChar, A::AbstractMatrix{$elty}, ipiv::Vector{BlasInt})
#             chkstride1(A)
#             n = checksquare(A)
#             chkuplo(uplo)
#             work  = Vector{$elty}(undef, 1)
#             lwork = BlasInt(-1)
#             info  = Ref{BlasInt}()
#             for i in 1:2
#                 ccall((@blasfunc($sytri), libblastrampoline), Cvoid,
#                       (Ptr{UInt8}, Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt},
#                        Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt}, Ptr{BlasInt}, Clong),
#                       &uplo, &n, A, &max(1,stride(A,2)), ipiv, work, &lwork, info, 1)
#                 chklapackerror(info[])
#                 if lwork < 0
#                     lwork = BlasInt(real(work[1]))
#                     work = Vector{$elty}(undef, lwork)
#                 end
#             end
#             A
#         end

        #       SUBROUTINE ZSYTRI( UPLO, N, A, LDA, IPIV, WORK, INFO )
        # *     .. Scalar Arguments ..
        #       CHARACTER          UPLO
        #       INTEGER            INFO, LDA, N
        # *     ..
        # *     .. Array Arguments ..
        #       INTEGER            IPIV( * )
        #       COMPLEX*16         A( LDA, * ), WORK( * )
        function sytri!(uplo::AbstractChar, A::AbstractMatrix{$elty}, ipiv::AbstractVector{BlasInt})
            chkstride1(A, ipiv)
            n = checksquare(A)
            chkuplo(uplo)
            work = Vector{$elty}(undef, n)
            info = Ref{BlasInt}()
            ccall((@blasfunc($sytri), libblastrampoline), Cvoid,
                  (Ref{UInt8}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                   Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt}, Clong),
                  uplo, n, A, max(1,stride(A,2)), ipiv, work, info, 1)
            chklapackerror(info[])
            A
        end

        #       SUBROUTINE ZSYTRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
        # *     .. Scalar Arguments ..
        #       CHARACTER          UPLO
        #       INTEGER            INFO, LDA, LDB, N, NRHS
        # *     ..
        # *     .. Array Arguments ..
        #       INTEGER            IPIV( * )
        #       COMPLEX*16         A( LDA, * ), B( LDB, * )
        function sytrs!(uplo::AbstractChar, A::AbstractMatrix{$elty},
                       ipiv::AbstractVector{BlasInt}, B::AbstractVecOrMat{$elty})
            require_one_based_indexing(A, ipiv, B)
            chkstride1(A,B,ipiv)
            n = checksquare(A)
            chkuplo(uplo)
            if n != size(B,1)
                throw(DimensionMismatch("B has first dimension $(size(B,1)), but needs $n"))
            end
            info = Ref{BlasInt}()
            ccall((@blasfunc($sytrs), libblastrampoline), Cvoid,
                  (Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                   Ptr{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}, Clong),
                  uplo, n, size(B,2), A, max(1,stride(A,2)), ipiv, B, max(1,stride(B,2)), info,  1)
            chklapackerror(info[])
            B
        end
    end
end

for (sysv, sytrf, sytri, sytrs, syconvf, elty, relty) in
    ((:zsysv_rook_,:zsytrf_rook_,:zsytri_rook_,:zsytrs_rook_,:zsyconvf_rook_,:ComplexF64, :Float64),
     (:csysv_rook_,:csytrf_rook_,:csytri_rook_,:csytrs_rook_,:csyconvf_rook_,:ComplexF32, :Float32))
    @eval begin
        #       SUBROUTINE ZSYSV_ROOK(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
        #      $                      LWORK, INFO )
        # *     .. Scalar Arguments ..
        #       CHARACTER          UPLO
        #       INTEGER            INFO, LDA, LDB, LWORK, N, NRHS
        # *     ..
        # *     .. Array Arguments ..
        #       INTEGER            IPIV( * )
        #       COMPLEX*16         A( LDA, * ), B( LDB, * ), WORK( * )
        function sysv_rook!(uplo::AbstractChar, A::AbstractMatrix{$elty}, B::AbstractVecOrMat{$elty})
            require_one_based_indexing(A, B)
            chkstride1(A,B)
            n = checksquare(A)
            chkuplo(uplo)
            if n != size(B,1)
                throw(DimensionMismatch("B has first dimension $(size(B,1)), but needs $n"))
            end
            ipiv  = similar(A, BlasInt, n)
            work  = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            info  = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($sysv), libblastrampoline), Cvoid,
                      (Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt},
                       Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}, Clong),
                      uplo, n, size(B,2), A, max(1,stride(A,2)), ipiv, B, max(1,stride(B,2)),
                      work, lwork, info, 1)
                chkargsok(info[])
                chknonsingular(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            B, A, ipiv
        end

        #       SUBROUTINE ZSYTRF_ROOK( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
        # *     .. Scalar Arguments ..
        #       CHARACTER          UPLO
        #       INTEGER            INFO, LDA, LWORK, N
        # *     ..
        # *     .. Array Arguments ..
        #       INTEGER            IPIV( * )
        #       COMPLEX*16         A( LDA, * ), WORK( * )
        function sytrf_rook!(uplo::AbstractChar, A::AbstractMatrix{$elty})
            chkstride1(A)
            n = checksquare(A)
            chkuplo(uplo)
            ipiv = similar(A, BlasInt, n)
            if n == 0
                return A, ipiv, zero(BlasInt)
            end
            work  = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            info  = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($sytrf), libblastrampoline), Cvoid,
                      (Ref{UInt8}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                       Ptr{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}, Clong),
                      uplo, n, A, max(1,stride(A,2)), ipiv, work, lwork, info, 1)
                chkargsok(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            A, ipiv, info[]
        end

        #       SUBROUTINE ZSYTRI_ROOK( UPLO, N, A, LDA, IPIV, WORK, INFO )
        # *     .. Scalar Arguments ..
        #       CHARACTER          UPLO
        #       INTEGER            INFO, LDA, N
        # *     ..
        # *     .. Array Arguments ..
        #       INTEGER            IPIV( * )
        #       COMPLEX*16         A( LDA, * ), WORK( * )
        function sytri_rook!(uplo::AbstractChar, A::AbstractMatrix{$elty}, ipiv::AbstractVector{BlasInt})
            chkstride1(A, ipiv)
            n = checksquare(A)
            chkuplo(uplo)
            work = Vector{$elty}(undef, n)
            info = Ref{BlasInt}()
            ccall((@blasfunc($sytri), libblastrampoline), Cvoid,
                  (Ref{UInt8}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                   Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt}, Clong),
                  uplo, n, A, max(1,stride(A,2)), ipiv, work, info, 1)
            chklapackerror(info[])
            A
        end

        #       SUBROUTINE ZSYTRS_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
        # *     .. Scalar Arguments ..
        #       CHARACTER          UPLO
        #       INTEGER            INFO, LDA, LDB, N, NRHS
        # *     ..
        # *     .. Array Arguments ..
        #       INTEGER            IPIV( * )
        #       COMPLEX*16         A( LDA, * ), B( LDB, * )
        function sytrs_rook!(uplo::AbstractChar, A::AbstractMatrix{$elty},
                             ipiv::AbstractVector{BlasInt}, B::AbstractVecOrMat{$elty})
            require_one_based_indexing(A, ipiv, B)
            chkstride1(A,B,ipiv)
            n = checksquare(A)
            chkuplo(uplo)
            if n != size(B,1)
                throw(DimensionMismatch("B has first dimension $(size(B,1)), but needs $n"))
            end
            info = Ref{BlasInt}()
            ccall((@blasfunc($sytrs), libblastrampoline), Cvoid,
                  (Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                   Ptr{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}, Clong),
                  uplo, n, size(B,2), A, max(1,stride(A,2)), ipiv, B, max(1,stride(B,2)), info, 1)
            chklapackerror(info[])
            B
        end

        # SUBROUTINE ZSYCONVF_ROOK( UPLO, WAY, N, A, LDA, IPIV, E, INFO )
        #
        # .. Scalar Arguments ..
        # CHARACTER          UPLO, WAY
        # INTEGER            INFO, LDA, N
        # ..
        # .. Array Arguments ..
        # INTEGER            IPIV( * )
        # COMPLEX*16         A( LDA, * ), E( * )
        function syconvf_rook!(uplo::AbstractChar, way::AbstractChar,
                                A::AbstractMatrix{$elty}, ipiv::AbstractVector{BlasInt},
                                e::AbstractVector{$elty} = Vector{$elty}(undef, length(ipiv)))
            require_one_based_indexing(A, ipiv, e)
            chkstride1(A, ipiv, e)

            # extract
            n   = checksquare(A)
            lda = stride(A, 2)

            # check
            chkuplo(uplo)
            if way != 'C' && way != 'R'
                throw(ArgumentError("way must be 'C' or 'R'"))
            end
            if length(ipiv) != n
                throw(ArgumentError("length of pivot vector was $(length(ipiv)) but should have been $n"))
            end
            if length(e) != n
                throw(ArgumentError("length of e vector was $(length(e)) but should have been $n"))
            end

            # allocate
            info = Ref{BlasInt}()

            ccall((@blasfunc($syconvf), libblastrampoline), Cvoid,
                (Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ptr{$elty},
                 Ref{BlasInt}, Ptr{$elty}, Ptr{BlasInt}, Ptr{BlasInt},
                 Clong, Clong),
                uplo, way, n, A,
                max(1, lda), e, ipiv, info,
                1, 1)

            chklapackerror(info[])
            return A, e
        end
    end
end

"""
    syconv!(uplo, A, ipiv) -> (A, work)

Converts a symmetric matrix `A` (which has been factorized into a
triangular matrix) into two matrices `L` and `D`. If `uplo = U`, `A`
is upper triangular. If `uplo = L`, it is lower triangular. `ipiv` is
the pivot vector from the triangular factorization. `A` is overwritten
by `L` and `D`.
"""
syconv!(uplo::AbstractChar, A::AbstractMatrix, ipiv::AbstractVector{BlasInt})

"""
    sysv!(uplo, A, B) -> (B, A, ipiv)

Finds the solution to `A * X = B` for symmetric matrix `A`. If `uplo = U`,
the upper half of `A` is stored. If `uplo = L`, the lower half is stored.
`B` is overwritten by the solution `X`. `A` is overwritten by its
Bunch-Kaufman factorization. `ipiv` contains pivoting information about the
factorization.
"""
sysv!(uplo::AbstractChar, A::AbstractMatrix, B::AbstractVecOrMat)

"""
    sytrf!(uplo, A) -> (A, ipiv, info)

Computes the Bunch-Kaufman factorization of a symmetric matrix `A`. If
`uplo = U`, the upper half of `A` is stored. If `uplo = L`, the lower
half is stored.

Returns `A`, overwritten by the factorization, a pivot vector `ipiv`, and
the error code `info` which is a non-negative integer. If `info` is positive
the matrix is singular and the diagonal part of the factorization is exactly
zero at position `info`.
"""
sytrf!(uplo::AbstractChar, A::AbstractMatrix)

"""
    sytri!(uplo, A, ipiv)

Computes the inverse of a symmetric matrix `A` using the results of
`sytrf!`. If `uplo = U`, the upper half of `A` is stored. If `uplo = L`,
the lower half is stored. `A` is overwritten by its inverse.
"""
sytri!(uplo::AbstractChar, A::AbstractMatrix, ipiv::AbstractVector{BlasInt})

"""
    sytrs!(uplo, A, ipiv, B)

Solves the equation `A * X = B` for a symmetric matrix `A` using the
results of `sytrf!`. If `uplo = U`, the upper half of `A` is stored.
If `uplo = L`, the lower half is stored. `B` is overwritten by the
solution `X`.
"""
sytrs!(uplo::AbstractChar, A::AbstractMatrix, ipiv::AbstractVector{BlasInt}, B::AbstractVecOrMat)


"""
    hesv!(uplo, A, B) -> (B, A, ipiv)

Finds the solution to `A * X = B` for Hermitian matrix `A`. If `uplo = U`,
the upper half of `A` is stored. If `uplo = L`, the lower half is stored.
`B` is overwritten by the solution `X`. `A` is overwritten by its
Bunch-Kaufman factorization. `ipiv` contains pivoting information about the
factorization.
"""
hesv!(uplo::AbstractChar, A::AbstractMatrix, B::AbstractVecOrMat)

"""
    hetrf!(uplo, A) -> (A, ipiv, info)

Computes the Bunch-Kaufman factorization of a Hermitian matrix `A`. If
`uplo = U`, the upper half of `A` is stored. If `uplo = L`, the lower
half is stored.

Returns `A`, overwritten by the factorization, a pivot vector `ipiv`, and
the error code `info` which is a non-negative integer. If `info` is positive
the matrix is singular and the diagonal part of the factorization is exactly
zero at position `info`.
"""
hetrf!(uplo::AbstractChar, A::AbstractMatrix)

"""
    hetri!(uplo, A, ipiv)

Computes the inverse of a Hermitian matrix `A` using the results of
`sytrf!`. If `uplo = U`, the upper half of `A` is stored. If `uplo = L`,
the lower half is stored. `A` is overwritten by its inverse.
"""
hetri!(uplo::AbstractChar, A::AbstractMatrix, ipiv::AbstractVector{BlasInt})

"""
    hetrs!(uplo, A, ipiv, B)

Solves the equation `A * X = B` for a Hermitian matrix `A` using the
results of `sytrf!`. If `uplo = U`, the upper half of `A` is stored.
If `uplo = L`, the lower half is stored. `B` is overwritten by the
solution `X`.
"""
hetrs!(uplo::AbstractChar, A::AbstractMatrix, ipiv::AbstractVector{BlasInt}, B::AbstractVecOrMat)

# Symmetric (real) eigensolvers
for (syev, syevr, syevd, sygvd, elty) in
    ((:dsyev_,:dsyevr_,:dsyevd_,:dsygvd_,:Float64),
     (:ssyev_,:ssyevr_,:ssyevd_,:ssygvd_,:Float32))
    @eval begin
        #       SUBROUTINE DSYEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, INFO )
        # *     .. Scalar Arguments ..
        #       CHARACTER          JOBZ, UPLO
        #       INTEGER            INFO, LDA, LWORK, N
        # *     .. Array Arguments ..
        #       DOUBLE PRECISION   A( LDA, * ), W( * ), WORK( * )
        function syev!(jobz::AbstractChar, uplo::AbstractChar, A::AbstractMatrix{$elty})
            chkstride1(A)
            n = checksquare(A)
            W     = similar(A, $elty, n)
            work  = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            info  = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($syev), libblastrampoline), Cvoid,
                      (Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                      Ptr{$elty}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}, Clong, Clong),
                      jobz, uplo, n, A, max(1,stride(A,2)), W, work, lwork, info, 1, 1)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            jobz == 'V' ? (W, A) : W
        end

        #       SUBROUTINE DSYEVR( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU,
        #      $                   ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK,
        #      $                   IWORK, LIWORK, INFO )
        # *     .. Scalar Arguments ..
        #       CHARACTER          JOBZ, RANGE, UPLO
        #       INTEGER            IL, INFO, IU, LDA, LDZ, LIWORK, LWORK, M, N
        #       DOUBLE PRECISION   ABSTOL, VL, VU
        # *     ..
        # *     .. Array Arguments ..
        #       INTEGER            ISUPPZ( * ), IWORK( * )
        #       DOUBLE PRECISION   A( LDA, * ), W( * ), WORK( * ), Z( LDZ, * )
        function syevr!(jobz::AbstractChar, range::AbstractChar, uplo::AbstractChar, A::AbstractMatrix{$elty},
                        vl::AbstractFloat, vu::AbstractFloat, il::Integer, iu::Integer, abstol::AbstractFloat)
            chkstride1(A)
            n = checksquare(A)
            chkuplofinite(A, uplo)
            if range == 'I' && !(1 <= il <= iu <= n)
                throw(ArgumentError("illegal choice of eigenvalue indices (il = $il, iu = $iu), which must be between 1 and n = $n"))
            end
            if range == 'V' && vl >= vu
                throw(ArgumentError("lower boundary, $vl, must be less than upper boundary, $vu"))
            end
            lda = stride(A,2)
            m = Ref{BlasInt}()
            W = similar(A, $elty, n)
            ldz = n
            if jobz == 'N'
                Z = similar(A, $elty, ldz, 0)
            elseif jobz == 'V'
                Z = similar(A, $elty, ldz, n)
            end
            isuppz = similar(A, BlasInt, 2*n)
            work   = Vector{$elty}(undef, 1)
            lwork  = BlasInt(-1)
            iwork  = Vector{BlasInt}(undef, 1)
            liwork = BlasInt(-1)
            info   = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1] and liwork as iwork[1]
                ccall((@blasfunc($syevr), libblastrampoline), Cvoid,
                    (Ref{UInt8}, Ref{UInt8}, Ref{UInt8}, Ref{BlasInt},
                        Ptr{$elty}, Ref{BlasInt}, Ref{$elty}, Ref{$elty},
                        Ref{BlasInt}, Ref{BlasInt}, Ref{$elty}, Ptr{BlasInt},
                        Ptr{$elty}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt},
                        Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}, Ref{BlasInt},
                        Ptr{BlasInt}, Clong, Clong, Clong),
                    jobz, range, uplo, n,
                    A, max(1,lda), vl, vu,
                    il, iu, abstol, m,
                    W, Z, max(1,ldz), isuppz,
                    work, lwork, iwork, liwork,
                    info, 1, 1, 1)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                    liwork = iwork[1]
                    resize!(iwork, liwork)
                end
            end
            W[1:m[]], Z[:,1:(jobz == 'V' ? m[] : 0)]
        end
        syevr!(jobz::AbstractChar, A::AbstractMatrix{$elty}) =
            syevr!(jobz, 'A', 'U', A, 0.0, 0.0, 0, 0, -1.0)

        #       SUBROUTINE DSYEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK,
        #      $                   IWORK, LIWORK, INFO )
        # *     .. Scalar Arguments ..
        #       CHARACTER          JOBZ, UPLO
        #       INTEGER            INFO, LDA, LIWORK, LWORK, N
        # *     ..
        # *     .. Array Arguments ..
        #       INTEGER            IWORK( * )
        #       DOUBLE PRECISION   A( LDA, * ), W( * ), WORK( * )
        function syevd!(jobz::AbstractChar, uplo::AbstractChar, A::AbstractMatrix{$elty})
            chkstride1(A)
            n = checksquare(A)
            chkuplofinite(A, uplo)
            lda = stride(A,2)
            m = Ref{BlasInt}()
            W = similar(A, $elty, n)
            work   = Vector{$elty}(undef, 1)
            lwork  = BlasInt(-1)
            iwork  = Vector{BlasInt}(undef, 1)
            liwork = BlasInt(-1)
            info   = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1] and liwork as iwork[1]
                ccall((@blasfunc($syevd), libblastrampoline), Cvoid,
                    (Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                        Ptr{$elty}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}, Ref{BlasInt},
                        Ptr{BlasInt}, Clong, Clong),
                    jobz, uplo, n, A, max(1,lda),
                    W, work, lwork, iwork, liwork,
                    info, 1, 1)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                    liwork = iwork[1]
                    resize!(iwork, liwork)
                end
            end
            jobz == 'V' ? (W, A) : W
        end

        # Generalized eigenproblem
        #           SUBROUTINE DSYGVD( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
        #      $                   LWORK, IWORK, LIWORK, INFO )
        # *     .. Scalar Arguments ..
        #       CHARACTER          JOBZ, UPLO
        #       INTEGER            INFO, ITYPE, LDA, LDB, LIWORK, LWORK, N
        # *     ..
        # *     .. Array Arguments ..
        #       INTEGER            IWORK( * )
        #       DOUBLE PRECISION   A( LDA, * ), B( LDB, * ), W( * ), WORK( * )
        function sygvd!(itype::Integer, jobz::AbstractChar, uplo::AbstractChar, A::AbstractMatrix{$elty}, B::AbstractMatrix{$elty})
            chkstride1(A, B)
            n, m = checksquare(A, B)
            if n != m
                throw(DimensionMismatch("dimensions of A, ($n,$n), and B, ($m,$m), must match"))
            end
            lda = max(1, stride(A, 2))
            ldb = max(1, stride(B, 2))
            w = similar(A, $elty, n)
            work = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            iwork = Vector{BlasInt}(undef, 1)
            liwork = BlasInt(-1)
            info = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1] and liwork as iwork[1]
                ccall((@blasfunc($sygvd), libblastrampoline), Cvoid,
                    (Ref{BlasInt}, Ref{UInt8}, Ref{UInt8}, Ref{BlasInt},
                     Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                     Ptr{$elty}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt},
                     Ref{BlasInt}, Ptr{BlasInt}, Clong, Clong),
                    itype, jobz, uplo, n,
                    A, lda, B, ldb,
                    w, work, lwork, iwork,
                    liwork, info, 1, 1)
                chkargsok(info[])
                if i == 1
                    lwork = BlasInt(work[1])
                    resize!(work, lwork)
                    liwork = iwork[1]
                    resize!(iwork, liwork)
                end
            end
            chkposdef(info[])
            w, A, B
        end
    end
end
# Hermitian eigensolvers
for (syev, syevr, syevd, sygvd, elty, relty) in
    ((:zheev_,:zheevr_,:zheevd_,:zhegvd_,:ComplexF64,:Float64),
     (:cheev_,:cheevr_,:cheevd_,:chegvd_,:ComplexF32,:Float32))
    @eval begin
        # SUBROUTINE ZHEEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, INFO )
        # *     .. Scalar Arguments ..
        #       CHARACTER          JOBZ, UPLO
        #       INTEGER            INFO, LDA, LWORK, N
        # *     ..
        # *     .. Array Arguments ..
        #       DOUBLE PRECISION   RWORK( * ), W( * )
        #       COMPLEX*16         A( LDA, * ), WORK( * )
        function syev!(jobz::AbstractChar, uplo::AbstractChar, A::AbstractMatrix{$elty})
            chkstride1(A)
            chkuplofinite(A, uplo)
            n = checksquare(A)
            W     = similar(A, $relty, n)
            work  = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            rwork = Vector{$relty}(undef, max(1, 3n-2))
            info  = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($syev), libblastrampoline), Cvoid,
                      (Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                      Ptr{$relty}, Ptr{$elty}, Ref{BlasInt}, Ptr{$relty}, Ptr{BlasInt},
                      Clong, Clong),
                      jobz, uplo, n, A, stride(A,2), W, work, lwork, rwork, info,
                      1, 1)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            jobz == 'V' ? (W, A) : W
        end

        #       SUBROUTINE ZHEEVR( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU,
        #      $                   ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK,
        #      $                   RWORK, LRWORK, IWORK, LIWORK, INFO )
        # *     .. Scalar Arguments ..
        #       CHARACTER          JOBZ, RANGE, UPLO
        #       INTEGER            IL, INFO, IU, LDA, LDZ, LIWORK, LRWORK, LWORK,
        #      $                   M, N
        #       DOUBLE PRECISION   ABSTOL, VL, VU
        # *     ..
        # *     .. Array Arguments ..
        #       INTEGER            ISUPPZ( * ), IWORK( * )
        #       DOUBLE PRECISION   RWORK( * ), W( * )
        #       COMPLEX*16         A( LDA, * ), WORK( * ), Z( LDZ, * )
        function syevr!(jobz::AbstractChar, range::AbstractChar, uplo::AbstractChar, A::AbstractMatrix{$elty},
                        vl::AbstractFloat, vu::AbstractFloat, il::Integer, iu::Integer, abstol::AbstractFloat)
            chkstride1(A)
            chkuplofinite(A, uplo)
            n = checksquare(A)
            if range == 'I' && !(1 <= il <= iu <= n)
                throw(ArgumentError("illegal choice of eigenvalue indices (il = $il, iu=$iu), which must be between 1 and n = $n"))
            end
            if range == 'V' && vl >= vu
                throw(ArgumentError("lower boundary, $vl, must be less than upper boundary, $vu"))
            end
            lda = max(1,stride(A,2))
            m = Ref{BlasInt}()
            W = similar(A, $relty, n)
            if jobz == 'N'
                ldz = 1
                Z = similar(A, $elty, ldz, 0)
            elseif jobz == 'V'
                ldz = n
                Z = similar(A, $elty, ldz, n)
            end
            isuppz = similar(A, BlasInt, 2*n)
            work   = Vector{$elty}(undef, 1)
            lwork  = BlasInt(-1)
            rwork  = Vector{$relty}(undef, 1)
            lrwork = BlasInt(-1)
            iwork  = Vector{BlasInt}(undef, 1)
            liwork = BlasInt(-1)
            info   = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1], lrwork as rwork[1] and liwork as iwork[1]
                ccall((@blasfunc($syevr), libblastrampoline), Cvoid,
                      (Ref{UInt8}, Ref{UInt8}, Ref{UInt8}, Ref{BlasInt},
                       Ptr{$elty}, Ref{BlasInt}, Ref{$elty}, Ref{$elty},
                       Ref{BlasInt}, Ref{BlasInt}, Ref{$elty}, Ptr{BlasInt},
                       Ptr{$relty}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt},
                       Ptr{$elty}, Ref{BlasInt}, Ptr{$relty}, Ref{BlasInt},
                       Ptr{BlasInt}, Ref{BlasInt}, Ptr{BlasInt},
                       Clong, Clong, Clong),
                      jobz, range, uplo, n,
                      A, lda, vl, vu,
                      il, iu, abstol, m,
                      W, Z, ldz, isuppz,
                      work, lwork, rwork, lrwork,
                      iwork, liwork, info,
                      1, 1, 1)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                    lrwork = BlasInt(rwork[1])
                    resize!(rwork, lrwork)
                    liwork = iwork[1]
                    resize!(iwork, liwork)
                end
            end
            W[1:m[]], Z[:,1:(jobz == 'V' ? m[] : 0)]
        end
        syevr!(jobz::AbstractChar, A::AbstractMatrix{$elty}) =
            syevr!(jobz, 'A', 'U', A, 0.0, 0.0, 0, 0, -1.0)

        #       SUBROUTINE ZHEEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK,
        #      $                   LRWORK, IWORK, LIWORK, INFO )
        # *     .. Scalar Arguments ..
        #       CHARACTER          JOBZ, UPLO
        #       INTEGER            INFO, LDA, LIWORK, LRWORK, LWORK, N
        # *     ..
        # *     .. Array Arguments ..
        #       INTEGER            IWORK( * )
        #       DOUBLE PRECISION   RWORK( * )
        #       COMPLEX*16         A( LDA, * ), WORK( * )
        function syevd!(jobz::AbstractChar, uplo::AbstractChar, A::AbstractMatrix{$elty})
            chkstride1(A)
            chkuplofinite(A, uplo)
            n = checksquare(A)
            lda = max(1, stride(A,2))
            m = Ref{BlasInt}()
            W = similar(A, $relty, n)
            work   = Vector{$elty}(undef, 1)
            lwork  = BlasInt(-1)
            rwork  = Vector{$relty}(undef, 1)
            lrwork = BlasInt(-1)
            iwork  = Vector{BlasInt}(undef, 1)
            liwork = BlasInt(-1)
            info   = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1], lrwork as rwork[1] and liwork as iwork[1]
                ccall((@blasfunc($syevd), liblapack), Cvoid,
                    (Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                    Ptr{$relty}, Ptr{$elty}, Ref{BlasInt}, Ptr{$relty}, Ref{BlasInt},
                    Ptr{BlasInt}, Ref{BlasInt}, Ptr{BlasInt}, Clong, Clong),
                    jobz, uplo, n, A, stride(A,2),
                    W, work, lwork, rwork, lrwork,
                    iwork, liwork, info, 1, 1)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                    lrwork = BlasInt(rwork[1])
                    resize!(rwork, lrwork)
                    liwork = iwork[1]
                    resize!(iwork, liwork)
                end
            end
            jobz == 'V' ? (W, A) : W
        end

        #       SUBROUTINE ZHEGVD( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
        #      $                   LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )
        # *     .. Scalar Arguments ..
        #       CHARACTER          JOBZ, UPLO
        #       INTEGER            INFO, ITYPE, LDA, LDB, LIWORK, LRWORK, LWORK, N
        # *     ..
        # *     .. Array Arguments ..
        #       INTEGER            IWORK( * )
        #       DOUBLE PRECISION   RWORK( * ), W( * )
        #       COMPLEX*16         A( LDA, * ), B( LDB, * ), WORK( * )
        function sygvd!(itype::Integer, jobz::AbstractChar, uplo::AbstractChar, A::AbstractMatrix{$elty}, B::AbstractMatrix{$elty})
            chkstride1(A, B)
            chkuplofinite(A, uplo)
            chkuplofinite(B, uplo)
            n, m = checksquare(A, B)
            if n != m
                throw(DimensionMismatch("dimensions of A, ($n,$n), and B, ($m,$m), must match"))
            end
            lda = max(1, stride(A, 2))
            ldb = max(1, stride(B, 2))
            w = similar(A, $relty, n)
            work = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            iwork = Vector{BlasInt}(undef, 1)
            liwork = BlasInt(-1)
            rwork = Vector{$relty}(undef, 1)
            lrwork = BlasInt(-1)
            info = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1], lrwork as rwork[1] and liwork as iwork[1]
                ccall((@blasfunc($sygvd), libblastrampoline), Cvoid,
                    (Ref{BlasInt}, Ref{UInt8}, Ref{UInt8}, Ref{BlasInt},
                     Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                     Ptr{$relty}, Ptr{$elty}, Ref{BlasInt}, Ptr{$relty},
                     Ref{BlasInt}, Ptr{BlasInt}, Ref{BlasInt}, Ptr{BlasInt},
                     Clong, Clong),
                    itype, jobz, uplo, n,
                    A, lda, B, ldb,
                    w, work, lwork, rwork,
                    lrwork, iwork, liwork, info,
                    1, 1)
                chkargsok(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                    liwork = iwork[1]
                    resize!(iwork, liwork)
                    lrwork = BlasInt(rwork[1])
                    resize!(rwork, lrwork)
                end
            end
            chkposdef(info[])
            w, A, B
        end
    end
end

"""
    syev!(jobz, uplo, A)

Finds the eigenvalues (`jobz = N`) or eigenvalues and eigenvectors
(`jobz = V`) of a symmetric matrix `A`. If `uplo = U`, the upper triangle
of `A` is used. If `uplo = L`, the lower triangle of `A` is used.
"""
syev!(jobz::AbstractChar, uplo::AbstractChar, A::AbstractMatrix)

"""
    syevr!(jobz, range, uplo, A, vl, vu, il, iu, abstol) -> (W, Z)

Finds the eigenvalues (`jobz = N`) or eigenvalues and eigenvectors
(`jobz = V`) of a symmetric matrix `A`. If `uplo = U`, the upper triangle
of `A` is used. If `uplo = L`, the lower triangle of `A` is used. If
`range = A`, all the eigenvalues are found. If `range = V`, the
eigenvalues in the half-open interval `(vl, vu]` are found.
If `range = I`, the eigenvalues with indices between `il` and `iu` are
found. `abstol` can be set as a tolerance for convergence.

The eigenvalues are returned in `W` and the eigenvectors in `Z`.
"""
syevr!(jobz::AbstractChar, range::AbstractChar, uplo::AbstractChar, A::AbstractMatrix,
       vl::AbstractFloat, vu::AbstractFloat, il::Integer, iu::Integer, abstol::AbstractFloat)

"""
    syevd!(jobz, uplo, A)

Finds the eigenvalues (`jobz = N`) or eigenvalues and eigenvectors
(`jobz = V`) of a symmetric matrix `A`. If `uplo = U`, the upper triangle
of `A` is used. If `uplo = L`, the lower triangle of `A` is used.

Use the divide-and-conquer method, instead of the QR iteration used by
`syev!` or multiple relatively robust representations used by `syevr!`.
See James W. Demmel et al, SIAM J. Sci. Comput. 30, 3, 1508 (2008) for
a comparison of the accuracy and performatce of different methods.
"""
syevd!(jobz::AbstractChar, uplo::AbstractChar, A::AbstractMatrix)

"""
    sygvd!(itype, jobz, uplo, A, B) -> (w, A, B)

Finds the generalized eigenvalues (`jobz = N`) or eigenvalues and
eigenvectors (`jobz = V`) of a symmetric matrix `A` and symmetric
positive-definite matrix `B`. If `uplo = U`, the upper triangles
of `A` and `B` are used. If `uplo = L`, the lower triangles of `A` and
`B` are used. If `itype = 1`, the problem to solve is
`A * x = lambda * B * x`. If `itype = 2`, the problem to solve is
`A * B * x = lambda * x`. If `itype = 3`, the problem to solve is
`B * A * x = lambda * x`.
"""
sygvd!(itype::Integer, jobz::AbstractChar, uplo::AbstractChar, A::AbstractMatrix, B::AbstractMatrix)

## (BD) Bidiagonal matrices - singular value decomposition
for (bdsqr, relty, elty) in
    ((:dbdsqr_,:Float64,:Float64),
     (:sbdsqr_,:Float32,:Float32),
     (:zbdsqr_,:Float64,:ComplexF64),
     (:cbdsqr_,:Float32,:ComplexF32))
    @eval begin
        function bdsqr!(uplo::AbstractChar, d::AbstractVector{$relty}, e_::AbstractVector{$relty},
                        Vt::AbstractMatrix{$elty}, U::AbstractMatrix{$elty}, C::AbstractMatrix{$elty})
            require_one_based_indexing(d, e_, Vt, U, C)
            chkstride1(d, e_, Vt, U, C)
            # Extract number
            n = length(d)
            ncvt, nru, ncc = size(Vt, 2), size(U, 1), size(C, 2)
            ldvt, ldu, ldc = max(1, stride(Vt,2)), max(1, stride(U, 2)), max(1, stride(C,2))
            # Do checks
            chkuplo(uplo)
            if length(e_) != n - 1
                throw(DimensionMismatch("off-diagonal has length $(length(e_)) but should have length $(n - 1)"))
            end
            if ncvt > 0 && ldvt < n
                throw(DimensionMismatch("leading dimension of Vt, $ldvt, must be at least $n"))
            end
            if ldu < nru
                throw(DimensionMismatch("leading dimension of U, $ldu, must be at least $nru"))
            end
            if size(U, 2) != n
                throw(DimensionMismatch("U must have $n columns but has $(size(U, 2))"))
            end
            if ncc > 0 && ldc < n
                throw(DimensionMismatch("leading dimension of C, $ldc, must be at least $n"))
            end
            # Allocate
            work = Vector{$relty}(undef, 4n)
            info = Ref{BlasInt}()
            ccall((@blasfunc($bdsqr), libblastrampoline), Cvoid,
                (Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt}, Ref{BlasInt},
                 Ref{BlasInt}, Ptr{$relty}, Ptr{$relty}, Ptr{$elty},
                 Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty},
                 Ref{BlasInt}, Ptr{$relty}, Ptr{BlasInt}, Clong),
                uplo, n, ncvt, nru,
                ncc, d, e_, Vt,
                ldvt, U, ldu, C,
                ldc, work, info, 1)
            chklapackerror(info[])
            d, Vt, U, C #singular values in descending order, P**T * VT, U * Q, Q**T * C
        end
    end
end

"""
    bdsqr!(uplo, d, e_, Vt, U, C) -> (d, Vt, U, C)

Computes the singular value decomposition of a bidiagonal matrix with
`d` on the diagonal and `e_` on the off-diagonal. If `uplo = U`, `e_` is
the superdiagonal. If `uplo = L`, `e_` is the subdiagonal. Can optionally also
compute the product `Q' * C`.

Returns the singular values in `d`, and the matrix `C` overwritten with `Q' * C`.
"""
bdsqr!(uplo::AbstractChar, d::AbstractVector, e_::AbstractVector, Vt::AbstractMatrix, U::AbstractMatrix, C::AbstractMatrix)

#Defined only for real types
for (bdsdc, elty) in
    ((:dbdsdc_,:Float64),
     (:sbdsdc_,:Float32))
    @eval begin
        #*  DBDSDC computes the singular value decomposition (SVD) of a real
        #*  N-by-N (upper or lower) bidiagonal matrix B:  B = U * S * VT,
        #*  using a divide and conquer method
        #*     .. Scalar Arguments ..
        #      CHARACTER          COMPQ, UPLO
        #      INTEGER            INFO, LDU, LDVT, N
        #*     ..
        #*     .. Array Arguments ..
        #      INTEGER            IQ( * ), IWORK( * )
        #      DOUBLE PRECISION   D( * ), E( * ), Q( * ), U( LDU, * ),
        #     $                   VT( LDVT, * ), WORK( * )
        function bdsdc!(uplo::AbstractChar, compq::AbstractChar, d::AbstractVector{$elty}, e_::AbstractVector{$elty})
            require_one_based_indexing(d, e_)
            chkstride1(d, e_)
            n, ldiq, ldq, ldu, ldvt = length(d), 1, 1, 1, 1
            chkuplo(uplo)
            if compq == 'N'
                lwork = 6*n
            elseif compq == 'P'
                @warn "COMPQ='P' is not tested"
                #TODO turn this into an actual LAPACK call
                #smlsiz=ilaenv(9, $elty === :Float64 ? 'dbdsqr' : 'sbdsqr', string(uplo, compq), n,n,n,n)
                smlsiz=100 #For now, completely overkill
                ldq = n*(11+2*smlsiz+8*round(Int,log((n/(smlsiz+1)))/log(2)))
                ldiq = n*(3+3*round(Int,log(n/(smlsiz+1))/log(2)))
                lwork = 6*n
            elseif compq == 'I'
                ldvt=ldu=max(1, n)
                lwork=3*n^2 + 4*n
            else
                throw(ArgumentError("COMPQ argument must be 'N', 'P' or 'I', got $(repr(compq))"))
            end
            u  = similar(d, $elty, (ldu,  n))
            vt = similar(d, $elty, (ldvt, n))
            q  = similar(d, $elty, ldq)
            iq = similar(d, BlasInt, ldiq)
            work  = Vector{$elty}(undef, lwork)
            iwork = Vector{BlasInt}(undef, 8n)
            info  = Ref{BlasInt}()
            ccall((@blasfunc($bdsdc), libblastrampoline), Cvoid,
               (Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ptr{$elty}, Ptr{$elty},
                Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                Ptr{$elty}, Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt}, Ptr{BlasInt},
                Clong, Clong),
                uplo, compq, n, d, e_,
                u, ldu, vt, ldvt,
                q, iq, work, iwork, info,
                1, 1)
            chklapackerror(info[])
            d, e_, u, vt, q, iq
        end
    end
end

"""
    bdsdc!(uplo, compq, d, e_) -> (d, e, u, vt, q, iq)

Computes the singular value decomposition of a bidiagonal matrix with `d` on the
diagonal and `e_` on the off-diagonal using a divide and conqueq method.
If `uplo = U`, `e_` is the superdiagonal. If `uplo = L`, `e_` is the subdiagonal.
If `compq = N`, only the singular values are found. If `compq = I`, the singular
values and vectors are found. If `compq = P`, the singular values
and vectors are found in compact form. Only works for real types.

Returns the singular values in `d`, and if `compq = P`, the compact singular
vectors in `iq`.
"""
bdsdc!(uplo::AbstractChar, compq::AbstractChar, d::AbstractVector, e_::AbstractVector)

for (gecon, elty) in
    ((:dgecon_,:Float64),
     (:sgecon_,:Float32))
    @eval begin
        #  SUBROUTINE DGECON( NORM, N, A, LDA, ANORM, RCOND, WORK, IWORK,
        #      $                   INFO )
        # *     .. Scalar Arguments ..
        #       CHARACTER          NORM
        #       INTEGER            INFO, LDA, N
        #       DOUBLE PRECISION   ANORM, RCOND
        # *     ..
        # *     .. Array Arguments ..
        #       INTEGER            IWORK( * )
        #       DOUBLE PRECISION   A( LDA, * ), WORK( * )
        function gecon!(normtype::AbstractChar, A::AbstractMatrix{$elty}, anorm::$elty)
            chkstride1(A)
            n = checksquare(A)
            lda = max(1, stride(A, 2))
            rcond = Ref{$elty}()
            work = Vector{$elty}(undef, 4n)
            iwork = Vector{BlasInt}(undef, n)
            info = Ref{BlasInt}()
            ccall((@blasfunc($gecon), libblastrampoline), Cvoid,
                  (Ref{UInt8}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                   Ref{$elty}, Ref{$elty}, Ptr{$elty}, Ptr{BlasInt},
                   Ptr{BlasInt}, Clong),
                  normtype, n, A, lda, anorm, rcond, work, iwork,
                  info, 1)
            chklapackerror(info[])
            rcond[]
        end
    end
end

for (gecon, elty, relty) in
    ((:zgecon_,:ComplexF64,:Float64),
     (:cgecon_,:ComplexF32,:Float32))
    @eval begin
        #       SUBROUTINE ZGECON( NORM, N, A, LDA, ANORM, RCOND, WORK, RWORK,
        #      $                   INFO )
        # *     .. Scalar Arguments ..
        #       CHARACTER          NORM
        #       INTEGER            INFO, LDA, N
        #       DOUBLE PRECISION   ANORM, RCOND
        # *     ..
        # *     .. Array Arguments ..
        #       DOUBLE PRECISION   RWORK( * )
        #       COMPLEX*16         A( LDA, * ), WORK( * )
        function gecon!(normtype::AbstractChar, A::AbstractMatrix{$elty}, anorm::$relty)
            chkstride1(A)
            n = checksquare(A)
            lda = max(1, stride(A, 2))
            rcond = Ref{$relty}()
            work = Vector{$elty}(undef, 2n)
            rwork = Vector{$relty}(undef, 2n)
            info = Ref{BlasInt}()
            ccall((@blasfunc($gecon), libblastrampoline), Cvoid,
                  (Ref{UInt8}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                   Ref{$relty}, Ref{$relty}, Ptr{$elty}, Ptr{$relty},
                   Ptr{BlasInt}, Clong),
                  normtype, n, A, lda, anorm, rcond, work, rwork,
                  info, 1)
            chklapackerror(info[])
            rcond[]
        end
    end
end

"""
    gecon!(normtype, A, anorm)

Finds the reciprocal condition number of matrix `A`. If `normtype = I`,
the condition number is found in the infinity norm. If `normtype = O` or
`1`, the condition number is found in the one norm. `A` must be the
result of `getrf!` and `anorm` is the norm of `A` in the relevant norm.
"""
gecon!(normtype::AbstractChar, A::AbstractMatrix, anorm)

for (gehrd, elty) in
    ((:dgehrd_,:Float64),
     (:sgehrd_,:Float32),
     (:zgehrd_,:ComplexF64),
     (:cgehrd_,:ComplexF32))
    @eval begin

        #                 .. Scalar Arguments ..
        #       INTEGER            IHI, ILO, INFO, LDA, LWORK, N
        # *     ..
        # *     .. Array Arguments ..
        #       DOUBLE PRECISION  A( LDA, * ), TAU( * ), WORK( * )
        function gehrd!(ilo::Integer, ihi::Integer, A::AbstractMatrix{$elty})
            chkstride1(A)
            n = checksquare(A)
            chkfinite(A) # balancing routines don't support NaNs and Infs
            tau = similar(A, $elty, max(0,n - 1))
            work = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            info = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($gehrd), libblastrampoline), Cvoid,
                    (Ref{BlasInt}, Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty},
                     Ref{BlasInt}, Ptr{$elty}, Ptr{$elty}, Ref{BlasInt},
                     Ptr{BlasInt}),
                    n, ilo, ihi, A,
                    max(1, stride(A, 2)), tau, work, lwork,
                    info)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            A, tau
        end
    end
end
gehrd!(A::AbstractMatrix) = gehrd!(1, size(A, 1), A)

"""
    gehrd!(ilo, ihi, A) -> (A, tau)

Converts a matrix `A` to Hessenberg form. If `A` is balanced with `gebal!`
then `ilo` and `ihi` are the outputs of `gebal!`. Otherwise they should be
`ilo = 1` and `ihi = size(A,2)`. `tau` contains the elementary reflectors of
the factorization.
"""
gehrd!(ilo::Integer, ihi::Integer, A::AbstractMatrix)

for (orghr, elty) in
    ((:dorghr_,:Float64),
     (:sorghr_,:Float32),
     (:zunghr_,:ComplexF64),
     (:cunghr_,:ComplexF32))
    @eval begin
        # *     .. Scalar Arguments ..
        #       INTEGER            IHI, ILO, INFO, LDA, LWORK, N
        # *     ..
        # *     .. Array Arguments ..
        #       DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
        function orghr!(ilo::Integer, ihi::Integer, A::AbstractMatrix{$elty}, tau::AbstractVector{$elty})
            require_one_based_indexing(A, tau)
            chkstride1(A, tau)
            n = checksquare(A)
            if n - length(tau) != 1
                throw(DimensionMismatch("tau has length $(length(tau)), needs $(n - 1)"))
            end
            work = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            info = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($orghr), libblastrampoline), Cvoid,
                    (Ref{BlasInt}, Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty},
                     Ref{BlasInt}, Ptr{$elty}, Ptr{$elty}, Ref{BlasInt},
                     Ptr{BlasInt}),
                    n, ilo, ihi, A,
                    max(1, stride(A, 2)), tau, work, lwork,
                    info)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            A
        end
    end
end

"""
    orghr!(ilo, ihi, A, tau)

Explicitly finds `Q`, the orthogonal/unitary matrix from `gehrd!`. `ilo`,
`ihi`, `A`, and `tau` must correspond to the input/output to `gehrd!`.
"""
orghr!(ilo::Integer, ihi::Integer, A::AbstractMatrix, tau::AbstractVector)

for (ormhr, elty) in
    ((:dormhr_,:Float64),
     (:sormhr_,:Float32),
     (:zunmhr_,:ComplexF64),
     (:cunmhr_,:ComplexF32))
    @eval begin
        # .. Scalar Arguments ..
        # CHARACTER          side, trans
        # INTEGER            ihi, ilo, info, lda, ldc, lwork, m, n
        # ..
        # .. Array Arguments ..
        # DOUBLE PRECISION   a( lda, * ), c( ldc, * ), tau( * ), work( * )
        function ormhr!(side::AbstractChar, trans::AbstractChar, ilo::Integer, ihi::Integer, A::AbstractMatrix{$elty},
            tau::AbstractVector{$elty}, C::AbstractVecOrMat{$elty})

            require_one_based_indexing(A, tau, C)
            chkstride1(A, tau, C)
            n = checksquare(A)
            mC, nC = size(C, 1), size(C, 2)

            if n - length(tau) != 1
                throw(DimensionMismatch("tau has length $(length(tau)), needs $(n - 1)"))
            end
            if (side == 'L' && mC != n) || (side == 'R' && nC != n)
                throw(DimensionMismatch("A and C matrices are not conformable"))
            end

            work = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            info = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($ormhr), libblastrampoline), Cvoid,
                    (Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt},
                     Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                     Ptr{$elty}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty},
                     Ref{BlasInt}, Ptr{BlasInt}, Clong, Clong),
                    side, trans, mC, nC,
                    ilo, ihi, A, max(1, stride(A, 2)),
                    tau, C, max(1, stride(C, 2)), work,
                    lwork, info, 1, 1)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            C
        end
    end
end

for (hseqr, elty) in
    ((:zhseqr_,:ComplexF64),
     (:chseqr_,:ComplexF32))
    @eval begin
        # *     .. Scalar Arguments ..
        #       CHARACTER          JOB, COMPZ
        #       INTEGER            N, ILO, IHI, LWORK, LDH, LDZ, INFO
        # *     ..
        # *     .. Array Arguments ..
        #       COMPLEX*16         H( LDH, * ), Z( LDZ, * ), WORK( * )
        function hseqr!(job::AbstractChar, compz::AbstractChar, ilo::Integer, ihi::Integer,
                        H::AbstractMatrix{$elty}, Z::AbstractMatrix{$elty})
            require_one_based_indexing(H, Z)
            chkstride1(H)
            n = checksquare(H)
            checksquare(Z) == n || throw(DimensionMismatch())
            ldh = max(1, stride(H, 2))
            ldz = max(1, stride(Z, 2))
            w = similar(H, $elty, n)
            work = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            info = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($hseqr), libblastrampoline), Cvoid,
                    (Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt},
                    Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty},
                    Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                    Ptr{BlasInt}),
                    job, compz, n, ilo, ihi,
                    H, ldh, w, Z, ldz, work,
                    lwork, info)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            H, Z, w
        end
    end
end

for (hseqr, elty) in
    ((:dhseqr_,:Float64),
     (:shseqr_,:Float32))
    @eval begin
        # *     .. Scalar Arguments ..
        #       CHARACTER          JOB, COMPZ
        #       INTEGER            N, ILO, IHI, LWORK, LDH, LDZ, INFO
        # *     ..
        # *     .. Array Arguments ..
        #       COMPLEX*16         H( LDH, * ), Z( LDZ, * ), WORK( * )
        function hseqr!(job::AbstractChar, compz::AbstractChar, ilo::Integer, ihi::Integer,
                        H::AbstractMatrix{$elty}, Z::AbstractMatrix{$elty})
            require_one_based_indexing(H, Z)
            chkstride1(H)
            n = checksquare(H)
            checksquare(Z) == n || throw(DimensionMismatch())
            ldh = max(1, stride(H, 2))
            ldz = max(1, stride(Z, 2))
            wr = similar(H, $elty, n)
            wi = similar(H, $elty, n)
            work = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            info = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($hseqr), libblastrampoline), Cvoid,
                    (Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt},
                    Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ptr{$elty},
                    Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                    Ptr{BlasInt}),
                    job, compz, n, ilo, ihi,
                    H, ldh, wr, wi, Z, ldz, work,
                    lwork, info)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            H, Z, complex.(wr, wi)
        end
    end
end
hseqr!(H::StridedMatrix{T}, Z::StridedMatrix{T}) where {T<:BlasFloat} = hseqr!('S', 'V', 1, size(H, 1), H, Z)
hseqr!(H::StridedMatrix{T}) where {T<:BlasFloat} = hseqr!('S', 'I', 1, size(H, 1), H, similar(H))

"""
    hseqr!(job, compz, ilo, ihi, H, Z) -> (H, Z, w)

Computes all eigenvalues and (optionally) the Schur factorization of a matrix
reduced to Hessenberg form. If `H` is balanced with `gebal!`
then `ilo` and `ihi` are the outputs of `gebal!`. Otherwise they should be
`ilo = 1` and `ihi = size(H,2)`. `tau` contains the elementary reflectors of
the factorization.
"""
hseqr!(job::AbstractChar, compz::AbstractChar, ilo::Integer, ihi::Integer, H::AbstractMatrix, Z::AbstractMatrix)

for (hetrd, elty) in
    ((:dsytrd_,Float64),
     (:ssytrd_,Float32),
     (:zhetrd_,ComplexF64),
     (:chetrd_,ComplexF32))
    relty = real(elty)
    @eval begin

        #                 .. Scalar Arguments ..
        #       CHARACTER          UPLO
        #       INTEGER            INFO, LDA, LWORK, N
        # *     ..
        # *     .. Array Arguments ..
        #       DOUBLE PRECISION  A( LDA, * ), D( * ), E( * ), TAU( * ), WORK( * )
        function hetrd!(uplo::AbstractChar, A::AbstractMatrix{$elty})
            chkstride1(A)
            n = checksquare(A)
            chkuplo(uplo)
            chkfinite(A) # balancing routines don't support NaNs and Infs
            tau = similar(A, $elty, max(0,n - 1))
            d = Vector{$relty}(undef, n)
            e = Vector{$relty}(undef, max(0,n - 1))
            work = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            info = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($hetrd), libblastrampoline), Cvoid,
                    (Ref{UInt8}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                    Ptr{$relty}, Ptr{$relty},
                    Ptr{$elty}, Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}, Clong),
                    uplo, n, A, max(1, stride(A, 2)), d, e, tau, work, lwork, info, 1)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            A, tau, d, e
        end
    end
end

"""
    hetrd!(uplo, A) -> (A, tau, d, e)

Converts a Hermitian matrix `A` to real-symmetric tridiagonal Hessenberg form.
If `uplo = U`, the upper half of `A` is stored; if `uplo = L`, the lower half is stored.
`tau` contains the elementary reflectors of the factorization, `d` contains the
diagonal and `e` contains the upper/lower diagonal.
"""
hetrd!(uplo::AbstractChar, A::AbstractMatrix)

for (orgtr, elty) in
    ((:dorgtr_,:Float64),
     (:sorgtr_,:Float32),
     (:zungtr_,:ComplexF64),
     (:cungtr_,:ComplexF32))
    @eval begin
        # *     .. Scalar Arguments ..
        #       CHARACTER          UPLO
        #       INTEGER            INFO, LDA, LWORK, N
        # *     ..
        # *     .. Array Arguments ..
        #       DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
        function orgtr!(uplo::AbstractChar, A::AbstractMatrix{$elty}, tau::AbstractVector{$elty})
            require_one_based_indexing(A, tau)
            chkstride1(A, tau)
            n = checksquare(A)
            if n - length(tau) != 1
                throw(DimensionMismatch("tau has length $(length(tau)), needs $(n - 1)"))
            end
            chkuplo(uplo)
            work = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            info = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($orgtr), libblastrampoline), Cvoid,
                    (Ref{UInt8}, Ref{BlasInt}, Ptr{$elty},
                     Ref{BlasInt}, Ptr{$elty}, Ptr{$elty}, Ref{BlasInt},
                     Ptr{BlasInt}, Clong),
                    uplo, n, A,
                    max(1, stride(A, 2)), tau, work, lwork,
                    info, 1)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            A
        end
    end
end

"""
    orgtr!(uplo, A, tau)

Explicitly finds `Q`, the orthogonal/unitary matrix from `hetrd!`. `uplo`,
`A`, and `tau` must correspond to the input/output to `hetrd!`.
"""
orgtr!(uplo::AbstractChar, A::AbstractMatrix, tau::AbstractVector)

for (ormtr, elty) in
    ((:dormtr_,:Float64),
     (:sormtr_,:Float32),
     (:zunmtr_,:ComplexF64),
     (:cunmtr_,:ComplexF32))
    @eval begin
        # .. Scalar Arguments ..
        # CHARACTER          side, trans, uplo
        # INTEGER            info, lda, ldc, lwork, m, n
        # ..
        # .. Array Arguments ..
        # DOUBLE PRECISION   a( lda, * ), c( ldc, * ), tau( * ), work( * )
        function ormtr!(side::AbstractChar, uplo::AbstractChar, trans::AbstractChar, A::AbstractMatrix{$elty},
                        tau::AbstractVector{$elty}, C::AbstractVecOrMat{$elty})

            require_one_based_indexing(A, tau, C)
            chkstride1(A, tau, C)
            n = checksquare(A)
            chkuplo(uplo)
            mC, nC = size(C, 1), size(C, 2)

            if n - length(tau) != 1
                throw(DimensionMismatch("tau has length $(length(tau)), needs $(n - 1)"))
            end
            if (side == 'L' && mC != n) || (side == 'R' && nC != n)
                throw(DimensionMismatch("A and C matrices are not conformable"))
            end

            work = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            info = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($ormtr), libblastrampoline), Cvoid,
                    (Ref{UInt8}, Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt},
                     Ptr{$elty}, Ref{BlasInt},
                     Ptr{$elty}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty},
                     Ref{BlasInt}, Ptr{BlasInt}, Clong, Clong, Clong),
                    side, uplo, trans, mC, nC,
                    A, max(1, stride(A, 2)),
                    tau, C, max(1, stride(C, 2)), work,
                    lwork, info, 1, 1, 1)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            C
        end
    end
end

for (gees, gges, gges3, elty) in
    ((:dgees_,:dgges_,:dgges3_,:Float64),
     (:sgees_,:sgges_,:sgges3_,:Float32))
    @eval begin
        #     .. Scalar Arguments ..
        #     CHARACTER          JOBVS, SORT
        #     INTEGER            INFO, LDA, LDVS, LWORK, N, SDIM
        #     ..
        #     .. Array Arguments ..
        #     LOGICAL            BWORK( * )
        #     DOUBLE PRECISION   A( LDA, * ), VS( LDVS, * ), WI( * ), WORK( * ),
        #    $                   WR( * )
        function gees!(jobvs::AbstractChar, A::AbstractMatrix{$elty})
            require_one_based_indexing(A)
            chkstride1(A)
            n     = checksquare(A)
            sdim  = Vector{BlasInt}(undef, 1)
            wr    = similar(A, $elty, n)
            wi    = similar(A, $elty, n)
            vs    = similar(A, $elty, jobvs == 'V' ? n : 0, n)
            ldvs  = max(size(vs, 1), 1)
            work  = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            info  = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($gees), libblastrampoline), Cvoid,
                    (Ref{UInt8}, Ref{UInt8}, Ptr{Cvoid}, Ref{BlasInt},
                        Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}, Ptr{$elty},
                        Ptr{$elty}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty},
                        Ref{BlasInt}, Ptr{Cvoid}, Ref{BlasInt}, Clong, Clong),
                    jobvs, 'N', C_NULL, n,
                        A, max(1, stride(A, 2)), sdim, wr,
                        wi, vs, ldvs, work,
                        lwork, C_NULL, info, 1, 1)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            A, vs, iszero(wi) ? wr : complex.(wr, wi)
        end

        # *     .. Scalar Arguments ..
        #       CHARACTER          JOBVSL, JOBVSR, SORT
        #       INTEGER            INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N, SDIM
        # *     ..
        # *     .. Array Arguments ..
        #       LOGICAL            BWORK( * )
        #       DOUBLE PRECISION   A( LDA, * ), ALPHAI( * ), ALPHAR( * ),
        #      $                   B( LDB, * ), BETA( * ), VSL( LDVSL, * ),
        #      $                   VSR( LDVSR, * ), WORK( * )
        function gges!(jobvsl::AbstractChar, jobvsr::AbstractChar, A::AbstractMatrix{$elty}, B::AbstractMatrix{$elty})
            chkstride1(A, B)
            n, m = checksquare(A, B)
            if n != m
                throw(DimensionMismatch("dimensions of A, ($n,$n), and B, ($m,$m), must match"))
            end
            sdim = BlasInt(0)
            alphar = similar(A, $elty, n)
            alphai = similar(A, $elty, n)
            beta = similar(A, $elty, n)
            ldvsl = jobvsl == 'V' ? max(1, n) : 1
            vsl = similar(A, $elty, ldvsl, n)
            ldvsr = jobvsr == 'V' ? max(1, n) : 1
            vsr = similar(A, $elty, ldvsr, n)
            work = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            info = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($gges), libblastrampoline), Cvoid,
                    (Ref{UInt8}, Ref{UInt8}, Ref{UInt8}, Ptr{Cvoid},
                        Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty},
                        Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty}, Ptr{$elty},
                        Ptr{$elty}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty},
                        Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{Cvoid},
                        Ref{BlasInt}, Clong, Clong, Clong),
                    jobvsl, jobvsr, 'N', C_NULL,
                    n, A, max(1,stride(A, 2)), B,
                    max(1,stride(B, 2)), sdim, alphar, alphai,
                    beta, vsl, ldvsl, vsr,
                    ldvsr, work, lwork, C_NULL,
                    info, 1, 1, 1)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            A, B, complex.(alphar, alphai), beta, vsl[1:(jobvsl == 'V' ? n : 0),:], vsr[1:(jobvsr == 'V' ? n : 0),:]
        end

        # *     .. Scalar Arguments ..
        #       CHARACTER          JOBVSL, JOBVSR, SORT
        #       INTEGER            INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N, SDIM
        # *     ..
        # *     .. Array Arguments ..
        #       LOGICAL            BWORK( * )
        #       DOUBLE PRECISION   A( LDA, * ), ALPHAI( * ), ALPHAR( * ),
        #      $                   B( LDB, * ), BETA( * ), VSL( LDVSL, * ),
        #      $                   VSR( LDVSR, * ), WORK( * )
        function gges3!(jobvsl::AbstractChar, jobvsr::AbstractChar, A::AbstractMatrix{$elty}, B::AbstractMatrix{$elty})
            chkstride1(A, B)
            n, m = checksquare(A, B)
            if n != m
                throw(DimensionMismatch("dimensions of A, ($n,$n), and B, ($m,$m), must match"))
            end
            sdim = BlasInt(0)
            alphar = similar(A, $elty, n)
            alphai = similar(A, $elty, n)
            beta = similar(A, $elty, n)
            ldvsl = jobvsl == 'V' ? max(1, n) : 1
            vsl = similar(A, $elty, ldvsl, n)
            ldvsr = jobvsr == 'V' ? max(1, n) : 1
            vsr = similar(A, $elty, ldvsr, n)
            work = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            info = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($gges3), libblastrampoline), Cvoid,
                    (Ref{UInt8}, Ref{UInt8}, Ref{UInt8}, Ptr{Cvoid},
                        Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty},
                        Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty}, Ptr{$elty},
                        Ptr{$elty}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty},
                        Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{Cvoid},
                        Ref{BlasInt}, Clong, Clong, Clong),
                    jobvsl, jobvsr, 'N', C_NULL,
                    n, A, max(1,stride(A, 2)), B,
                    max(1,stride(B, 2)), sdim, alphar, alphai,
                    beta, vsl, ldvsl, vsr,
                    ldvsr, work, lwork, C_NULL,
                    info, 1, 1, 1)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            A, B, complex.(alphar, alphai), beta, vsl[1:(jobvsl == 'V' ? n : 0),:], vsr[1:(jobvsr == 'V' ? n : 0),:]
        end
    end
end

for (gees, gges, gges3, elty, relty) in
    ((:zgees_,:zgges_,:zgges3_,:ComplexF64,:Float64),
     (:cgees_,:cgges_,:cgges3_,:ComplexF32,:Float32))
    @eval begin
        # *     .. Scalar Arguments ..
        #       CHARACTER          JOBVS, SORT
        #       INTEGER            INFO, LDA, LDVS, LWORK, N, SDIM
        # *     ..
        # *     .. Array Arguments ..
        #       LOGICAL            BWORK( * )
        #       DOUBLE PRECISION   RWORK( * )
        #       COMPLEX*16         A( LDA, * ), VS( LDVS, * ), W( * ), WORK( * )
        function gees!(jobvs::AbstractChar, A::AbstractMatrix{$elty})
            require_one_based_indexing(A)
            chkstride1(A)
            n     = checksquare(A)
            sort  = 'N'
            sdim  = BlasInt(0)
            w     = similar(A, $elty, n)
            vs    = similar(A, $elty, jobvs == 'V' ? n : 1, n)
            ldvs  = max(size(vs, 1), 1)
            work  = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            rwork = Vector{$relty}(undef, n)
            info  = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($gees), libblastrampoline), Cvoid,
                    (Ref{UInt8}, Ref{UInt8}, Ptr{Cvoid}, Ref{BlasInt},
                        Ptr{$elty}, Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty},
                        Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                        Ptr{$relty}, Ptr{Cvoid}, Ref{BlasInt}, Clong, Clong),
                    jobvs, sort, C_NULL, n,
                        A, max(1, stride(A, 2)), sdim, w,
                        vs, ldvs, work, lwork,
                        rwork, C_NULL, info, 1, 1)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            A, vs, w
        end

        # *     .. Scalar Arguments ..
        #       CHARACTER          JOBVSL, JOBVSR, SORT
        #       INTEGER            INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N, SDIM
        # *     ..
        # *     .. Array Arguments ..
        #       LOGICAL            BWORK( * )
        #       DOUBLE PRECISION   RWORK( * )
        #       COMPLEX*16         A( LDA, * ), ALPHA( * ), B( LDB, * ),
        #      $                   BETA( * ), VSL( LDVSL, * ), VSR( LDVSR, * ),
        #      $                   WORK( * )
        function gges!(jobvsl::AbstractChar, jobvsr::AbstractChar, A::AbstractMatrix{$elty}, B::AbstractMatrix{$elty})
            chkstride1(A, B)
            n, m = checksquare(A, B)
            if n != m
                throw(DimensionMismatch("dimensions of A, ($n,$n), and B, ($m,$m), must match"))
            end
            sdim = BlasInt(0)
            alpha = similar(A, $elty, n)
            beta = similar(A, $elty, n)
            ldvsl = jobvsl == 'V' ? max(1, n) : 1
            vsl = similar(A, $elty, ldvsl, n)
            ldvsr = jobvsr == 'V' ? max(1, n) : 1
            vsr = similar(A, $elty, ldvsr, n)
            work = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            rwork = Vector{$relty}(undef, 8n)
            info = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($gges), libblastrampoline), Cvoid,
                    (Ref{UInt8}, Ref{UInt8}, Ref{UInt8}, Ptr{Cvoid},
                        Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty},
                        Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty}, Ptr{$elty},
                        Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                        Ptr{$elty}, Ref{BlasInt}, Ptr{$relty}, Ptr{Cvoid},
                        Ref{BlasInt}, Clong, Clong, Clong),
                    jobvsl, jobvsr, 'N', C_NULL,
                    n, A, max(1, stride(A, 2)), B,
                    max(1, stride(B, 2)), sdim, alpha, beta,
                    vsl, ldvsl, vsr, ldvsr,
                    work, lwork, rwork, C_NULL,
                    info, 1, 1, 1)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            A, B, alpha, beta, vsl[1:(jobvsl == 'V' ? n : 0),:], vsr[1:(jobvsr == 'V' ? n : 0),:]
        end

        # *     .. Scalar Arguments ..
        #       CHARACTER          JOBVSL, JOBVSR, SORT
        #       INTEGER            INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N, SDIM
        # *     ..
        # *     .. Array Arguments ..
        #       LOGICAL            BWORK( * )
        #       DOUBLE PRECISION   RWORK( * )
        #       COMPLEX*16         A( LDA, * ), ALPHA( * ), B( LDB, * ),
        #      $                   BETA( * ), VSL( LDVSL, * ), VSR( LDVSR, * ),
        #      $                   WORK( * )
        function gges3!(jobvsl::AbstractChar, jobvsr::AbstractChar, A::AbstractMatrix{$elty}, B::AbstractMatrix{$elty})
            chkstride1(A, B)
            n, m = checksquare(A, B)
            if n != m
                throw(DimensionMismatch("dimensions of A, ($n,$n), and B, ($m,$m), must match"))
            end
            sdim = BlasInt(0)
            alpha = similar(A, $elty, n)
            beta = similar(A, $elty, n)
            ldvsl = jobvsl == 'V' ? max(1, n) : 1
            vsl = similar(A, $elty, ldvsl, n)
            ldvsr = jobvsr == 'V' ? max(1, n) : 1
            vsr = similar(A, $elty, ldvsr, n)
            work = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            rwork = Vector{$relty}(undef, 8n)
            info = Ref{BlasInt}()
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($gges3), libblastrampoline), Cvoid,
                    (Ref{UInt8}, Ref{UInt8}, Ref{UInt8}, Ptr{Cvoid},
                        Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty},
                        Ref{BlasInt}, Ref{BlasInt}, Ptr{$elty}, Ptr{$elty},
                        Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                        Ptr{$elty}, Ref{BlasInt}, Ptr{$relty}, Ptr{Cvoid},
                        Ref{BlasInt}, Clong, Clong, Clong),
                    jobvsl, jobvsr, 'N', C_NULL,
                    n, A, max(1, stride(A, 2)), B,
                    max(1, stride(B, 2)), sdim, alpha, beta,
                    vsl, ldvsl, vsr, ldvsr,
                    work, lwork, rwork, C_NULL,
                    info, 1, 1, 1)
                chklapackerror(info[])
                if i == 1
                    lwork = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            A, B, alpha, beta, vsl[1:(jobvsl == 'V' ? n : 0),:], vsr[1:(jobvsr == 'V' ? n : 0),:]
        end
    end
end

"""
    gees!(jobvs, A) -> (A, vs, w)

Computes the eigenvalues (`jobvs = N`) or the eigenvalues and Schur
vectors (`jobvs = V`) of matrix `A`. `A` is overwritten by its Schur form.

Returns `A`, `vs` containing the Schur vectors, and `w`, containing the
eigenvalues.
"""
gees!(jobvs::AbstractChar, A::AbstractMatrix)


"""
    gges!(jobvsl, jobvsr, A, B) -> (A, B, alpha, beta, vsl, vsr)

Computes the generalized eigenvalues, generalized Schur form, left Schur
vectors (`jobsvl = V`), or right Schur vectors (`jobvsr = V`) of `A` and
`B`.

The generalized eigenvalues are returned in `alpha` and `beta`. The left Schur
vectors are returned in `vsl` and the right Schur vectors are returned in `vsr`.
"""
gges!(jobvsl::AbstractChar, jobvsr::AbstractChar, A::AbstractMatrix, B::AbstractMatrix)

"""
    gges3!(jobvsl, jobvsr, A, B) -> (A, B, alpha, beta, vsl, vsr)

Computes the generalized eigenvalues, generalized Schur form, left Schur
vectors (`jobsvl = V`), or right Schur vectors (`jobvsr = V`) of `A` and
`B` using a blocked algorithm. This function requires LAPACK 3.6.0.

The generalized eigenvalues are returned in `alpha` and `beta`. The left Schur
vectors are returned in `vsl` and the right Schur vectors are returned in `vsr`.
"""
gges3!(jobvsl::AbstractChar, jobvsr::AbstractChar, A::AbstractMatrix, B::AbstractMatrix)

for (trexc, trsen, tgsen, elty) in
    ((:dtrexc_, :dtrsen_, :dtgsen_, :Float64),
     (:strexc_, :strsen_, :stgsen_, :Float32))
    @eval begin
        # *     .. Scalar Arguments ..
        #       CHARACTER          COMPQ
        #       INTEGER            IFST, ILST, INFO, LDQ, LDT, N
        # *     ..
        # *     .. Array Arguments ..
        #       DOUBLE PRECISION   Q( LDQ, * ), T( LDT, * ), WORK( * )
        function trexc!(compq::AbstractChar, ifst::BlasInt, ilst::BlasInt, T::AbstractMatrix{$elty}, Q::AbstractMatrix{$elty})
            chkstride1(T, Q)
            n = checksquare(T)
            ldt = max(1, stride(T, 2))
            ldq = max(1, stride(Q, 2))
            work = Vector{$elty}(undef, n)
            info = Ref{BlasInt}()
            ccall((@blasfunc($trexc), libblastrampoline), Cvoid,
                  (Ref{UInt8},  Ref{BlasInt},
                   Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                   Ref{BlasInt}, Ref{BlasInt},
                   Ptr{$elty}, Ptr{BlasInt}, Clong),
                  compq, n,
                  T, ldt, Q, ldq,
                  ifst, ilst,
                  work, info, 1)
            chklapackerror(info[])
            T, Q
        end
        trexc!(ifst::BlasInt, ilst::BlasInt, T::AbstractMatrix{$elty}, Q::AbstractMatrix{$elty}) =
            trexc!('V', ifst, ilst, T, Q)

        # *     .. Scalar Arguments ..
        #       CHARACTER          COMPQ, JOB
        #       INTEGER            INFO, LDQ, LDT, LIWORK, LWORK, M, N
        #       DOUBLE PRECISION   S, SEP
        # *     ..
        # *     .. Array Arguments ..
        #       LOGICAL            SELECT( * )
        #       INTEGER            IWORK( * )
        #       DOUBLE PRECISION   Q( LDQ, * ), T( LDT, * ), WI( * ), WORK( * ), WR( * )
        function trsen!(job::AbstractChar, compq::AbstractChar, select::AbstractVector{BlasInt},
                        T::AbstractMatrix{$elty}, Q::AbstractMatrix{$elty})
            chkstride1(T, Q, select)
            n = checksquare(T)
            ldt = max(1, stride(T, 2))
            ldq = max(1, stride(Q, 2))
            wr = similar(T, $elty, n)
            wi = similar(T, $elty, n)
            m = sum(select)
            work = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            iwork = Vector{BlasInt}(undef, 1)
            liwork = BlasInt(-1)
            info = Ref{BlasInt}()
            select = convert(Array{BlasInt}, select)
            s = Ref{$elty}(zero($elty))
            sep = Ref{$elty}(zero($elty))
            for i = 1:2  # first call returns lwork as work[1] and liwork as iwork[1]
                ccall((@blasfunc($trsen), libblastrampoline), Cvoid,
                    (Ref{UInt8}, Ref{UInt8}, Ptr{BlasInt}, Ref{BlasInt},
                    Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                    Ptr{$elty}, Ptr{$elty}, Ref{BlasInt}, Ref{$elty}, Ref{$elty},
                    Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}, Ref{BlasInt},
                    Ptr{BlasInt}, Clong, Clong),
                    job, compq, select, n,
                    T, ldt, Q, ldq,
                    wr, wi, m, s, sep,
                    work, lwork, iwork, liwork,
                    info, 1, 1)
                chklapackerror(info[])
                if i == 1 # only estimated optimal lwork, liwork
                    lwork  = BlasInt(real(work[1]))
                    resize!(work, lwork)
                    liwork = BlasInt(real(iwork[1]))
                    resize!(iwork, liwork)
                end
            end
            T, Q, iszero(wi) ? wr : complex.(wr, wi), s[], sep[]
        end
        trsen!(select::AbstractVector{BlasInt}, T::AbstractMatrix{$elty}, Q::AbstractMatrix{$elty}) =
            trsen!('N', 'V', select, T, Q)

        #        .. Scalar Arguments ..
        #        LOGICAL            WANTQ, WANTZ
        #        INTEGER            IJOB, INFO, LDA, LDB, LDQ, LDZ, LIWORK, LWORK,
        #       $                   M, N
        #        DOUBLE PRECISION   PL, PR
        #        ..
        #        .. Array Arguments ..
        #        LOGICAL            SELECT( * )
        #        INTEGER            IWORK( * )
        #        DOUBLE PRECISION   A( LDA, * ), ALPHAI( * ), ALPHAR( * ),
        #       $                   B( LDB, * ), BETA( * ), DIF( * ), Q( LDQ, * ),
        #       $                   WORK( * ), Z( LDZ, * )
        #        ..
        function tgsen!(select::AbstractVector{BlasInt}, S::AbstractMatrix{$elty}, T::AbstractMatrix{$elty},
                        Q::AbstractMatrix{$elty}, Z::AbstractMatrix{$elty})
            chkstride1(select, S, T, Q, Z)
            n, nt, nq, nz = checksquare(S, T, Q, Z)
            if n != nt
                throw(DimensionMismatch("dimensions of S, ($n,$n), and T, ($nt,$nt), must match"))
            end
            if n != nq
                throw(DimensionMismatch("dimensions of S, ($n,$n), and Q, ($nq,$nq), must match"))
            end
            if n != nz
                throw(DimensionMismatch("dimensions of S, ($n,$n), and Z, ($nz,$nz), must match"))
            end
            lds = max(1, stride(S, 2))
            ldt = max(1, stride(T, 2))
            ldq = max(1, stride(Q, 2))
            ldz = max(1, stride(Z, 2))
            m = sum(select)
            alphai = similar(T, $elty, n)
            alphar = similar(T, $elty, n)
            beta = similar(T, $elty, n)
            lwork = BlasInt(-1)
            work = Vector{$elty}(undef, 1)
            liwork = BlasInt(-1)
            iwork = Vector{BlasInt}(undef, 1)
            info = Ref{BlasInt}()
            select = convert(Array{BlasInt}, select)
            for i = 1:2  # first call returns lwork as work[1] and liwork as iwork[1]
                ccall((@blasfunc($tgsen), libblastrampoline), Cvoid,
                       (Ref{BlasInt}, Ref{BlasInt}, Ref{BlasInt}, Ptr{BlasInt},
                        Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty},
                        Ref{BlasInt}, Ptr{$elty}, Ptr{$elty}, Ptr{$elty},
                        Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                        Ref{BlasInt}, Ptr{Cvoid}, Ptr{Cvoid}, Ptr{Cvoid},
                        Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}, Ref{BlasInt},
                        Ptr{BlasInt}),
                    0, 1, 1, select,
                    n, S, lds, T,
                    ldt, alphar, alphai, beta,
                    Q, ldq, Z, ldz,
                    m, C_NULL, C_NULL, C_NULL,
                    work, lwork, iwork, liwork,
                    info)
                chklapackerror(info[])
                if i == 1 # only estimated optimal lwork, liwork
                    lwork  = BlasInt(real(work[1]))
                    resize!(work, lwork)
                    liwork = BlasInt(real(iwork[1]))
                    resize!(iwork, liwork)
                end
            end
            S, T, complex.(alphar, alphai), beta, Q, Z
        end
    end
end

for (trexc, trsen, tgsen, elty, relty) in
    ((:ztrexc_, :ztrsen_, :ztgsen_, :ComplexF64, :Float64),
     (:ctrexc_, :ctrsen_, :ctgsen_, :ComplexF32, :Float32))
    @eval begin
        #      .. Scalar Arguments ..
        #      CHARACTER          COMPQ
        #      INTEGER            IFST, ILST, INFO, LDQ, LDT, N
        #      ..
        #      .. Array Arguments ..
        #      DOUBLE PRECISION   Q( LDQ, * ), T( LDT, * ), WORK( * )
        function trexc!(compq::AbstractChar, ifst::BlasInt, ilst::BlasInt, T::AbstractMatrix{$elty}, Q::AbstractMatrix{$elty})
            chkstride1(T, Q)
            n = checksquare(T)
            ldt = max(1, stride(T, 2))
            ldq = max(1, stride(Q, 2))
            info = Ref{BlasInt}()
            ccall((@blasfunc($trexc), libblastrampoline), Cvoid,
                  (Ref{UInt8},  Ref{BlasInt},
                   Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                   Ref{BlasInt}, Ref{BlasInt},
                   Ptr{BlasInt}, Clong),
                  compq, n,
                  T, ldt, Q, ldq,
                  ifst, ilst,
                  info,  1)
            chklapackerror(info[])
            T, Q
        end
        trexc!(ifst::BlasInt, ilst::BlasInt, T::AbstractMatrix{$elty}, Q::AbstractMatrix{$elty}) =
            trexc!('V', ifst, ilst, T, Q)

        #      .. Scalar Arguments ..
        #      CHARACTER          COMPQ, JOB
        #      INTEGER            INFO, LDQ, LDT, LWORK, M, N
        #      DOUBLE PRECISION   S, SEP
        #      ..
        #      .. Array Arguments ..
        #      LOGICAL            SELECT( * )
        #      COMPLEX            Q( LDQ, * ), T( LDT, * ), W( * ), WORK( * )
        function trsen!(job::AbstractChar, compq::AbstractChar, select::AbstractVector{BlasInt},
                        T::AbstractMatrix{$elty}, Q::AbstractMatrix{$elty})
            chkstride1(select, T, Q)
            n = checksquare(T)
            ldt = max(1, stride(T, 2))
            ldq = max(1, stride(Q, 2))
            w = similar(T, $elty, n)
            m = sum(select)
            work = Vector{$elty}(undef, 1)
            lwork = BlasInt(-1)
            info = Ref{BlasInt}()
            select = convert(Array{BlasInt}, select)
            s = Ref{$relty}(zero($relty))
            sep = Ref{$relty}(zero($relty))
            for i = 1:2  # first call returns lwork as work[1]
                ccall((@blasfunc($trsen), libblastrampoline), Cvoid,
                    (Ref{UInt8}, Ref{UInt8}, Ptr{BlasInt}, Ref{BlasInt},
                    Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                    Ptr{$elty}, Ref{BlasInt}, Ref{$relty}, Ref{$relty},
                    Ptr{$elty}, Ref{BlasInt},
                    Ptr{BlasInt}, Clong, Clong),
                    job, compq, select, n,
                    T, ldt, Q, ldq,
                    w, m, s, sep,
                    work, lwork,
                    info, 1, 1)
                chklapackerror(info[])
                if i == 1 # only estimated optimal lwork, liwork
                    lwork  = BlasInt(real(work[1]))
                    resize!(work, lwork)
                end
            end
            T, Q, w, s[], sep[]
        end
        trsen!(select::AbstractVector{BlasInt}, T::AbstractMatrix{$elty}, Q::AbstractMatrix{$elty}) =
            trsen!('N', 'V', select, T, Q)

        #        .. Scalar Arguments ..
        #        LOGICAL            WANTQ, WANTZ
        #        INTEGER            IJOB, INFO, LDA, LDB, LDQ, LDZ, LIWORK, LWORK,
        #       $                   M, N
        #        DOUBLE PRECISION   PL, PR
        #        ..
        #        .. Array Arguments ..
        #        LOGICAL            SELECT( * )
        #        INTEGER            IWORK( * )
        #        DOUBLE PRECISION   DIF( * )
        #        COMPLEX*16         A( LDA, * ), ALPHA( * ), B( LDB, * ),
        #       $                   BETA( * ), Q( LDQ, * ), WORK( * ), Z( LDZ, * )
        #        ..
        function tgsen!(select::AbstractVector{BlasInt}, S::AbstractMatrix{$elty}, T::AbstractMatrix{$elty},
                        Q::AbstractMatrix{$elty}, Z::AbstractMatrix{$elty})
            chkstride1(select, S, T, Q, Z)
            n, nt, nq, nz = checksquare(S, T, Q, Z)
            if n != nt
                throw(DimensionMismatch("dimensions of S, ($n,$n), and T, ($nt,$nt), must match"))
            end
            if n != nq
                throw(DimensionMismatch("dimensions of S, ($n,$n), and Q, ($nq,$nq), must match"))
            end
            if n != nz
                throw(DimensionMismatch("dimensions of S, ($n,$n), and Z, ($nz,$nz), must match"))
            end
            lds = max(1, stride(S, 2))
            ldt = max(1, stride(T, 2))
            ldq = max(1, stride(Q, 2))
            ldz = max(1, stride(Z, 2))
            m = sum(select)
            alpha = similar(T, $elty, n)
            beta = similar(T, $elty, n)
            lwork = BlasInt(-1)
            work = Vector{$elty}(undef, 1)
            liwork = BlasInt(-1)
            iwork = Vector{BlasInt}(undef, 1)
            info = Ref{BlasInt}()
            select = convert(Array{BlasInt}, select)
            for i = 1:2  # first call returns lwork as work[1] and liwork as iwork[1]
                ccall((@blasfunc($tgsen), libblastrampoline), Cvoid,
                       (Ref{BlasInt}, Ref{BlasInt}, Ref{BlasInt}, Ptr{BlasInt},
                        Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty},
                        Ref{BlasInt}, Ptr{$elty}, Ptr{$elty},
                        Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                        Ref{BlasInt}, Ptr{Cvoid}, Ptr{Cvoid}, Ptr{Cvoid},
                        Ptr{$elty}, Ref{BlasInt}, Ptr{BlasInt}, Ref{BlasInt},
                        Ptr{BlasInt}),
                    0, 1, 1, select,
                    n, S, lds, T,
                    ldt, alpha, beta,
                    Q, ldq, Z, ldz,
                    m, C_NULL, C_NULL, C_NULL,
                    work, lwork, iwork, liwork,
                    info)
                chklapackerror(info[])
                if i == 1 # only estimated optimal lwork, liwork
                    lwork  = BlasInt(real(work[1]))
                    resize!(work, lwork)
                    liwork = BlasInt(real(iwork[1]))
                    resize!(iwork, liwork)
                end
            end
            S, T, alpha, beta, Q, Z
        end
    end
end

"""
    trexc!(compq, ifst, ilst, T, Q) -> (T, Q)
    trexc!(ifst, ilst, T, Q) -> (T, Q)

Reorder the Schur factorization `T` of a matrix, such that the diagonal block
of `T` with row index `ifst` is moved to row index `ilst`. If `compq = V`, the Schur
vectors `Q` are reordered. If `compq = N` they are not modified. The 4-arg method
calls the 5-arg method with `compq = V`.
"""
trexc!(compq::AbstractChar, ifst::BlasInt, ilst::BlasInt, T::AbstractMatrix, Q::AbstractMatrix)

"""
    trsen!(job, compq, select, T, Q) -> (T, Q, w, s, sep)
    trsen!(select, T, Q) -> (T, Q, w, s, sep)

Reorder the Schur factorization of a matrix and optionally finds reciprocal
condition numbers. If `job = N`, no condition numbers are found. If `job = E`,
only the condition number for this cluster of eigenvalues is found. If
`job = V`, only the condition number for the invariant subspace is found.
If `job = B` then the condition numbers for the cluster and subspace are
found. If `compq = V` the Schur vectors `Q` are updated. If `compq = N`
the Schur vectors are not modified. `select` determines which
eigenvalues are in the cluster. The 3-arg method calls the 5-arg method
with `job = N` and `compq = V`.

Returns `T`, `Q`, reordered eigenvalues in `w`, the condition number of the
cluster of eigenvalues `s`, and the condition number of the invariant subspace
`sep`.
"""
trsen!(compq::AbstractChar, job::AbstractChar, select::AbstractVector{BlasInt}, T::AbstractMatrix, Q::AbstractMatrix)

"""
    tgsen!(select, S, T, Q, Z) -> (S, T, alpha, beta, Q, Z)

Reorders the vectors of a generalized Schur decomposition. `select` specifies
the eigenvalues in each cluster.
"""
tgsen!(select::AbstractVector{BlasInt}, S::AbstractMatrix, T::AbstractMatrix, Q::AbstractMatrix, Z::AbstractMatrix)

for (fn, elty, relty) in ((:dtrsyl_, :Float64, :Float64),
                   (:strsyl_, :Float32, :Float32),
                   (:ztrsyl_, :ComplexF64, :Float64),
                   (:ctrsyl_, :ComplexF32, :Float32))
    @eval begin
        function trsyl!(transa::AbstractChar, transb::AbstractChar, A::AbstractMatrix{$elty},
                        B::AbstractMatrix{$elty}, C::AbstractMatrix{$elty}, isgn::Int=1)
            require_one_based_indexing(A, B, C)
            chkstride1(A, B, C)
            m, n = checksquare(A), checksquare(B)
            lda = max(1, stride(A, 2))
            ldb = max(1, stride(B, 2))
            m1, n1 = size(C)
            if m != m1 || n != n1
                throw(DimensionMismatch("dimensions of A, ($m,$n), and C, ($m1,$n1), must match"))
            end
            ldc = max(1, stride(C, 2))
            scale = Ref{$relty}()
            info  = Ref{BlasInt}()
            ccall((@blasfunc($fn), libblastrampoline), Cvoid,
                (Ref{UInt8}, Ref{UInt8}, Ref{BlasInt}, Ref{BlasInt}, Ref{BlasInt},
                 Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt},
                 Ptr{$relty}, Ptr{BlasInt}, Clong, Clong),
                transa, transb, isgn, m, n,
                A, lda, B, ldb, C, ldc,
                scale, info, 1, 1)
            chklapackerror(info[])
            C, scale[]
        end
    end
end

"""
    trsyl!(transa, transb, A, B, C, isgn=1) -> (C, scale)

Solves the Sylvester matrix equation `A * X +/- X * B = scale*C` where `A` and
`B` are both quasi-upper triangular. If `transa = N`, `A` is not modified.
If `transa = T`, `A` is transposed. If `transa = C`, `A` is conjugate
transposed. Similarly for `transb` and `B`. If `isgn = 1`, the equation
`A * X + X * B = scale * C` is solved. If `isgn = -1`, the equation
`A * X - X * B = scale * C` is solved.

Returns `X` (overwriting `C`) and `scale`.
"""
trsyl!(transa::AbstractChar, transb::AbstractChar, A::AbstractMatrix, B::AbstractMatrix, C::AbstractMatrix, isgn::Int=1)

end # module
v   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LinearAlgebra/src/dense.jl��      # This file is a part of Julia. License is MIT: https://julialang.org/license

# Linear algebra functions for dense matrices in column major format

## BLAS cutoff threshold constants

#TODO const DOT_CUTOFF = 128
const ASUM_CUTOFF = 32
const NRM2_CUTOFF = 32

# Generic cross-over constant based on benchmarking on a single thread with an i7 CPU @ 2.5GHz
# L1 cache: 32K, L2 cache: 256K, L3 cache: 6144K
# This constant should ideally be determined by the actual CPU cache size
const ISONE_CUTOFF = 2^21 # 2M

function isone(A::AbstractMatrix)
    m, n = size(A)
    m != n && return false # only square matrices can satisfy x == one(x)
    if sizeof(A) < ISONE_CUTOFF
        _isone_triacheck(A, m)
    else
        _isone_cachefriendly(A, m)
    end
end

@inline function _isone_triacheck(A::AbstractMatrix, m::Int)
    @inbounds for i in 1:m, j in i:m
        if i == j
            isone(A[i,i]) || return false
        else
            iszero(A[i,j]) && iszero(A[j,i]) || return false
        end
    end
    return true
end

# Inner loop over rows to be friendly to the CPU cache
@inline function _isone_cachefriendly(A::AbstractMatrix, m::Int)
    @inbounds for i in 1:m, j in 1:m
        if i == j
            isone(A[i,i]) || return false
        else
            iszero(A[j,i]) || return false
        end
    end
    return true
end


"""
    isposdef!(A) -> Bool

Test whether a matrix is positive definite (and Hermitian) by trying to perform a
Cholesky factorization of `A`, overwriting `A` in the process.
See also [`isposdef`](@ref).

# Examples
```jldoctest
julia> A = [1. 2.; 2. 50.];

julia> isposdef!(A)
true

julia> A
2×2 Matrix{Float64}:
 1.0  2.0
 2.0  6.78233
```
"""
isposdef!(A::AbstractMatrix) =
    ishermitian(A) && isposdef(cholesky!(Hermitian(A); check = false))

"""
    isposdef(A) -> Bool

Test whether a matrix is positive definite (and Hermitian) by trying to perform a
Cholesky factorization of `A`.

See also [`isposdef!`](@ref), [`cholesky`](@ref).

# Examples
```jldoctest
julia> A = [1 2; 2 50]
2×2 Matrix{Int64}:
 1   2
 2  50

julia> isposdef(A)
true
```
"""
isposdef(A::AbstractMatrix) =
    ishermitian(A) && isposdef(cholesky(Hermitian(A); check = false))
isposdef(x::Number) = imag(x)==0 && real(x) > 0

function norm(x::StridedVector{T}, rx::Union{UnitRange{TI},AbstractRange{TI}}) where {T<:BlasFloat,TI<:Integer}
    if minimum(rx) < 1 || maximum(rx) > length(x)
        throw(BoundsError(x, rx))
    end
    GC.@preserve x BLAS.nrm2(length(rx), pointer(x)+(first(rx)-1)*sizeof(T), step(rx))
end

norm1(x::Union{Array{T},StridedVector{T}}) where {T<:BlasReal} =
    length(x) < ASUM_CUTOFF ? generic_norm1(x) : BLAS.asum(x)

norm2(x::Union{Array{T},StridedVector{T}}) where {T<:BlasFloat} =
    length(x) < NRM2_CUTOFF ? generic_norm2(x) : BLAS.nrm2(x)

"""
    triu!(M, k::Integer)

Return the upper triangle of `M` starting from the `k`th superdiagonal,
overwriting `M` in the process.

# Examples
```jldoctest
julia> M = [1 2 3 4 5; 1 2 3 4 5; 1 2 3 4 5; 1 2 3 4 5; 1 2 3 4 5]
5×5 Matrix{Int64}:
 1  2  3  4  5
 1  2  3  4  5
 1  2  3  4  5
 1  2  3  4  5
 1  2  3  4  5

julia> triu!(M, 1)
5×5 Matrix{Int64}:
 0  2  3  4  5
 0  0  3  4  5
 0  0  0  4  5
 0  0  0  0  5
 0  0  0  0  0
```
"""
function triu!(M::AbstractMatrix, k::Integer)
    require_one_based_indexing(M)
    m, n = size(M)
    for j in 1:min(n, m + k)
        for i in max(1, j - k + 1):m
            M[i,j] = zero(M[i,j])
        end
    end
    M
end

triu(M::Matrix, k::Integer) = triu!(copy(M), k)

"""
    tril!(M, k::Integer)

Return the lower triangle of `M` starting from the `k`th superdiagonal, overwriting `M` in
the process.

# Examples
```jldoctest
julia> M = [1 2 3 4 5; 1 2 3 4 5; 1 2 3 4 5; 1 2 3 4 5; 1 2 3 4 5]
5×5 Matrix{Int64}:
 1  2  3  4  5
 1  2  3  4  5
 1  2  3  4  5
 1  2  3  4  5
 1  2  3  4  5

julia> tril!(M, 2)
5×5 Matrix{Int64}:
 1  2  3  0  0
 1  2  3  4  0
 1  2  3  4  5
 1  2  3  4  5
 1  2  3  4  5
```
"""
function tril!(M::AbstractMatrix, k::Integer)
    require_one_based_indexing(M)
    m, n = size(M)
    for j in max(1, k + 1):n
        @inbounds for i in 1:min(j - k - 1, m)
            M[i,j] = zero(M[i,j])
        end
    end
    M
end
tril(M::Matrix, k::Integer) = tril!(copy(M), k)

"""
    fillband!(A::AbstractMatrix, x, l, u)

Fill the band between diagonals `l` and `u` with the value `x`.
"""
function fillband!(A::AbstractMatrix{T}, x, l, u) where T
    require_one_based_indexing(A)
    m, n = size(A)
    xT = convert(T, x)
    for j in 1:n
        for i in max(1,j-u):min(m,j-l)
            @inbounds A[i, j] = xT
        end
    end
    return A
end

diagind(m::Integer, n::Integer, k::Integer=0) =
    k <= 0 ? range(1-k, step=m+1, length=min(m+k, n)) : range(k*m+1, step=m+1, length=min(m, n-k))

"""
    diagind(M, k::Integer=0)

An `AbstractRange` giving the indices of the `k`th diagonal of the matrix `M`.

See also: [`diag`](@ref), [`diagm`](@ref), [`Diagonal`](@ref).

# Examples
```jldoctest
julia> A = [1 2 3; 4 5 6; 7 8 9]
3×3 Matrix{Int64}:
 1  2  3
 4  5  6
 7  8  9

julia> diagind(A,-1)
2:4:6
```
"""
function diagind(A::AbstractMatrix, k::Integer=0)
    require_one_based_indexing(A)
    diagind(size(A,1), size(A,2), k)
end

"""
    diag(M, k::Integer=0)

The `k`th diagonal of a matrix, as a vector.

See also [`diagm`](@ref), [`diagind`](@ref), [`Diagonal`](@ref), [`isdiag`](@ref).

# Examples
```jldoctest
julia> A = [1 2 3; 4 5 6; 7 8 9]
3×3 Matrix{Int64}:
 1  2  3
 4  5  6
 7  8  9

julia> diag(A,1)
2-element Vector{Int64}:
 2
 6
```
"""
diag(A::AbstractMatrix, k::Integer=0) = A[diagind(A,k)]

"""
    diagm(kv::Pair{<:Integer,<:AbstractVector}...)
    diagm(m::Integer, n::Integer, kv::Pair{<:Integer,<:AbstractVector}...)

Construct a matrix from `Pair`s of diagonals and vectors.
Vector `kv.second` will be placed on the `kv.first` diagonal.
By default the matrix is square and its size is inferred
from `kv`, but a non-square size `m`×`n` (padded with zeros as needed)
can be specified by passing `m,n` as the first arguments.
For repeated diagonal indices `kv.first` the values in the corresponding
vectors `kv.second` will be added.

`diagm` constructs a full matrix; if you want storage-efficient
versions with fast arithmetic, see [`Diagonal`](@ref), [`Bidiagonal`](@ref)
[`Tridiagonal`](@ref) and [`SymTridiagonal`](@ref).

# Examples
```jldoctest
julia> diagm(1 => [1,2,3])
4×4 Matrix{Int64}:
 0  1  0  0
 0  0  2  0
 0  0  0  3
 0  0  0  0

julia> diagm(1 => [1,2,3], -1 => [4,5])
4×4 Matrix{Int64}:
 0  1  0  0
 4  0  2  0
 0  5  0  3
 0  0  0  0

julia> diagm(1 => [1,2,3], 1 => [1,2,3])
4×4 Matrix{Int64}:
 0  2  0  0
 0  0  4  0
 0  0  0  6
 0  0  0  0
```
"""
diagm(kv::Pair{<:Integer,<:AbstractVector}...) = _diagm(nothing, kv...)
diagm(m::Integer, n::Integer, kv::Pair{<:Integer,<:AbstractVector}...) = _diagm((Int(m),Int(n)), kv...)
function _diagm(size, kv::Pair{<:Integer,<:AbstractVector}...)
    A = diagm_container(size, kv...)
    for p in kv
        inds = diagind(A, p.first)
        for (i, val) in enumerate(p.second)
            A[inds[i]] += val
        end
    end
    return A
end
function diagm_size(size::Nothing, kv::Pair{<:Integer,<:AbstractVector}...)
    mnmax = mapreduce(x -> length(x.second) + abs(Int(x.first)), max, kv; init=0)
    return mnmax, mnmax
end
function diagm_size(size::Tuple{Int,Int}, kv::Pair{<:Integer,<:AbstractVector}...)
    mmax = mapreduce(x -> length(x.second) - min(0,Int(x.first)), max, kv; init=0)
    nmax = mapreduce(x -> length(x.second) + max(0,Int(x.first)), max, kv; init=0)
    m, n = size
    (m ≥ mmax && n ≥ nmax) || throw(DimensionMismatch("invalid size=$size"))
    return m, n
end
function diagm_container(size, kv::Pair{<:Integer,<:AbstractVector}...)
    T = promote_type(map(x -> eltype(x.second), kv)...)
    # For some type `T`, `zero(T)` is not a `T` and `zeros(T, ...)` fails.
    U = promote_type(T, typeof(zero(T)))
    return zeros(U, diagm_size(size, kv...)...)
end
diagm_container(size, kv::Pair{<:Integer,<:BitVector}...) =
    falses(diagm_size(size, kv...)...)

"""
    diagm(v::AbstractVector)
    diagm(m::Integer, n::Integer, v::AbstractVector)

Construct a matrix with elements of the vector as diagonal elements.
By default, the matrix is square and its size is given by
`length(v)`, but a non-square size `m`×`n` can be specified
by passing `m,n` as the first arguments.

# Examples
```jldoctest
julia> diagm([1,2,3])
3×3 Matrix{Int64}:
 1  0  0
 0  2  0
 0  0  3
```
"""
diagm(v::AbstractVector) = diagm(0 => v)
diagm(m::Integer, n::Integer, v::AbstractVector) = diagm(m, n, 0 => v)

function tr(A::Matrix{T}) where T
    n = checksquare(A)
    t = zero(T)
    @inbounds @simd for i in 1:n
        t += A[i,i]
    end
    t
end

_kronsize(A::AbstractMatrix, B::AbstractMatrix) = map(*, size(A), size(B))
_kronsize(A::AbstractMatrix, B::AbstractVector) = (size(A, 1)*length(B), size(A, 2))
_kronsize(A::AbstractVector, B::AbstractMatrix) = (length(A)*size(B, 1), size(B, 2))

"""
    kron!(C, A, B)

Computes the Kronecker product of `A` and `B` and stores the result in `C`,
overwriting the existing content of `C`. This is the in-place version of [`kron`](@ref).

!!! compat "Julia 1.6"
    This function requires Julia 1.6 or later.
"""
function kron!(C::AbstractVecOrMat, A::AbstractVecOrMat, B::AbstractVecOrMat)
    size(C) == _kronsize(A, B) || throw(DimensionMismatch("kron!"))
    _kron!(C, A, B)
end
function kron!(c::AbstractVector, a::AbstractVector, b::AbstractVector)
    length(c) == length(a) * length(b) || throw(DimensionMismatch("kron!"))
    m = firstindex(c)
    @inbounds for i in eachindex(a)
        ai = a[i]
        for k in eachindex(b)
            c[m] = ai*b[k]
            m += 1
        end
    end
    return c
end
kron!(c::AbstractVecOrMat, a::AbstractVecOrMat, b::Number) = mul!(c, a, b)
kron!(c::AbstractVecOrMat, a::Number, b::AbstractVecOrMat) = mul!(c, a, b)

function _kron!(C, A::AbstractMatrix, B::AbstractMatrix)
    m = firstindex(C)
    @inbounds for j in axes(A,2), l in axes(B,2), i in axes(A,1)
        Aij = A[i,j]
        for k in axes(B,1)
            C[m] = Aij*B[k,l]
            m += 1
        end
    end
    return C
end
function _kron!(C, A::AbstractMatrix, b::AbstractVector)
    m = firstindex(C)
    @inbounds for j in axes(A,2), i in axes(A,1)
        Aij = A[i,j]
        for k in eachindex(b)
            C[m] = Aij*b[k]
            m += 1
        end
    end
    return C
end
function _kron!(C, a::AbstractVector, B::AbstractMatrix)
    m = firstindex(C)
    @inbounds for l in axes(B,2), i in eachindex(a)
        ai = a[i]
        for k in axes(B,1)
            C[m] = ai*B[k,l]
            m += 1
        end
    end
    return C
end

"""
    kron(A, B)

Computes the Kronecker product of two vectors, matrices or numbers.

For real vectors `v` and `w`, the Kronecker product is related to the outer product by
`kron(v,w) == vec(w * transpose(v))` or
`w * transpose(v) == reshape(kron(v,w), (length(w), length(v)))`.
Note how the ordering of `v` and `w` differs on the left and right
of these expressions (due to column-major storage).
For complex vectors, the outer product `w * v'` also differs by conjugation of `v`.

# Examples
```jldoctest
julia> A = [1 2; 3 4]
2×2 Matrix{Int64}:
 1  2
 3  4

julia> B = [im 1; 1 -im]
2×2 Matrix{Complex{Int64}}:
 0+1im  1+0im
 1+0im  0-1im

julia> kron(A, B)
4×4 Matrix{Complex{Int64}}:
 0+1im  1+0im  0+2im  2+0im
 1+0im  0-1im  2+0im  0-2im
 0+3im  3+0im  0+4im  4+0im
 3+0im  0-3im  4+0im  0-4im

julia> v = [1, 2]; w = [3, 4, 5];

julia> w*transpose(v)
3×2 Matrix{Int64}:
 3   6
 4   8
 5  10

julia> reshape(kron(v,w), (length(w), length(v)))
3×2 Matrix{Int64}:
 3   6
 4   8
 5  10
```
"""
function kron(A::AbstractVecOrMat{T}, B::AbstractVecOrMat{S}) where {T,S}
    R = Matrix{promote_op(*,T,S)}(undef, _kronsize(A, B))
    return kron!(R, A, B)
end
function kron(a::AbstractVector{T}, b::AbstractVector{S}) where {T,S}
    c = Vector{promote_op(*,T,S)}(undef, length(a)*length(b))
    return kron!(c, a, b)
end
kron(a::Number, b::Union{Number, AbstractVecOrMat}) = a * b
kron(a::AbstractVecOrMat, b::Number) = a * b
kron(a::AdjointAbsVec, b::AdjointAbsVec) = adjoint(kron(adjoint(a), adjoint(b)))
kron(a::AdjOrTransAbsVec, b::AdjOrTransAbsVec) = transpose(kron(transpose(a), transpose(b)))

# Matrix power
(^)(A::AbstractMatrix, p::Integer) = p < 0 ? power_by_squaring(inv(A), -p) : power_by_squaring(A, p)
function (^)(A::AbstractMatrix{T}, p::Integer) where T<:Integer
    # make sure that e.g. [1 1;1 0]^big(3)
    # gets promotes in a similar way as 2^big(3)
    TT = promote_op(^, T, typeof(p))
    return power_by_squaring(convert(AbstractMatrix{TT}, A), p)
end
function integerpow(A::AbstractMatrix{T}, p) where T
    TT = promote_op(^, T, typeof(p))
    return (TT == T ? A : convert(AbstractMatrix{TT}, A))^Integer(p)
end
function schurpow(A::AbstractMatrix, p)
    if istriu(A)
        # Integer part
        retmat = A ^ floor(p)
        # Real part
        if p - floor(p) == 0.5
            # special case: A^0.5 === sqrt(A)
            retmat = retmat * sqrt(A)
        else
            retmat = retmat * powm!(UpperTriangular(float.(A)), real(p - floor(p)))
        end
    else
        S,Q,d = Schur{Complex}(schur(A))
        # Integer part
        R = S ^ floor(p)
        # Real part
        if p - floor(p) == 0.5
            # special case: A^0.5 === sqrt(A)
            R = R * sqrt(S)
        else
            R = R * powm!(UpperTriangular(float.(S)), real(p - floor(p)))
        end
        retmat = Q * R * Q'
    end

    # if A has nonpositive real eigenvalues, retmat is a nonprincipal matrix power.
    if isreal(retmat)
        return real(retmat)
    else
        return retmat
    end
end
function (^)(A::AbstractMatrix{T}, p::Real) where T
    n = checksquare(A)

    # Quicker return if A is diagonal
    if isdiag(A)
        TT = promote_op(^, T, typeof(p))
        retmat = copymutable_oftype(A, TT)
        for i in 1:n
            retmat[i, i] = retmat[i, i] ^ p
        end
        return retmat
    end

    # For integer powers, use power_by_squaring
    isinteger(p) && return integerpow(A, p)

    # If possible, use diagonalization
    if issymmetric(A)
        return (Symmetric(A)^p)
    end
    if ishermitian(A)
        return (Hermitian(A)^p)
    end

    # Otherwise, use Schur decomposition
    return schurpow(A, p)
end

"""
    ^(A::AbstractMatrix, p::Number)

Matrix power, equivalent to ``\\exp(p\\log(A))``

# Examples
```jldoctest
julia> [1 2; 0 3]^3
2×2 Matrix{Int64}:
 1  26
 0  27
```
"""
(^)(A::AbstractMatrix, p::Number) = exp(p*log(A))

# Matrix exponential

"""
    exp(A::AbstractMatrix)

Compute the matrix exponential of `A`, defined by

```math
e^A = \\sum_{n=0}^{\\infty} \\frac{A^n}{n!}.
```

For symmetric or Hermitian `A`, an eigendecomposition ([`eigen`](@ref)) is
used, otherwise the scaling and squaring algorithm (see [^H05]) is chosen.

[^H05]: Nicholas J. Higham, "The squaring and scaling method for the matrix exponential revisited", SIAM Journal on Matrix Analysis and Applications, 26(4), 2005, 1179-1193. [doi:10.1137/090768539](https://doi.org/10.1137/090768539)

# Examples
```jldoctest
julia> A = Matrix(1.0I, 2, 2)
2×2 Matrix{Float64}:
 1.0  0.0
 0.0  1.0

julia> exp(A)
2×2 Matrix{Float64}:
 2.71828  0.0
 0.0      2.71828
```
"""
exp(A::AbstractMatrix) = exp!(copy_similar(A, eigtype(eltype(A))))
exp(A::AdjointAbsMat) = adjoint(exp(parent(A)))
exp(A::TransposeAbsMat) = transpose(exp(parent(A)))

"""
    cis(A::AbstractMatrix)

More efficient method for `exp(im*A)` of square matrix `A`
(especially if `A` is `Hermitian` or real-`Symmetric`).

See also [`cispi`](@ref), [`sincos`](@ref), [`exp`](@ref).

!!! compat "Julia 1.7"
    Support for using `cis` with matrices was added in Julia 1.7.

# Examples
```jldoctest
julia> cis([π 0; 0 π]) ≈ -I
true
```
"""
cis(A::AbstractMatrix) = exp(im * A)  # fallback
cis(A::AbstractMatrix{<:Base.HWNumber}) = exp_maybe_inplace(float.(im .* A))

exp_maybe_inplace(A::StridedMatrix{<:Union{ComplexF32, ComplexF64}}) = exp!(A)
exp_maybe_inplace(A) = exp(A)

"""
    ^(b::Number, A::AbstractMatrix)

Matrix exponential, equivalent to ``\\exp(\\log(b)A)``.

!!! compat "Julia 1.1"
    Support for raising `Irrational` numbers (like `ℯ`)
    to a matrix was added in Julia 1.1.

# Examples
```jldoctest
julia> 2^[1 2; 0 3]
2×2 Matrix{Float64}:
 2.0  6.0
 0.0  8.0

julia> ℯ^[1 2; 0 3]
2×2 Matrix{Float64}:
 2.71828  17.3673
 0.0      20.0855
```
"""
Base.:^(b::Number, A::AbstractMatrix) = exp!(log(b)*A)
# method for ℯ to explicitly elide the log(b) multiplication
Base.:^(::Irrational{:ℯ}, A::AbstractMatrix) = exp(A)

## Destructive matrix exponential using algorithm from Higham, 2008,
## "Functions of Matrices: Theory and Computation", SIAM
function exp!(A::StridedMatrix{T}) where T<:BlasFloat
    n = checksquare(A)
    if ishermitian(A)
        return copytri!(parent(exp(Hermitian(A))), 'U', true)
    end
    ilo, ihi, scale = LAPACK.gebal!('B', A)    # modifies A
    nA   = opnorm(A, 1)
    ## For sufficiently small nA, use lower order Padé-Approximations
    if (nA <= 2.1)
        if nA > 0.95
            C = T[17643225600.,8821612800.,2075673600.,302702400.,
                     30270240.,   2162160.,    110880.,     3960.,
                           90.,         1.]
        elseif nA > 0.25
            C = T[17297280.,8648640.,1995840.,277200.,
                     25200.,   1512.,     56.,     1.]
        elseif nA > 0.015
            C = T[30240.,15120.,3360.,
                    420.,   30.,   1.]
        else
            C = T[120.,60.,12.,1.]
        end
        A2 = A * A
        # Compute U and V: Even/odd terms in Padé numerator & denom
        # Expansion of k=1 in for loop
        P = A2
        U = mul!(C[4]*P, true, C[2]*I, true, true) #U = C[2]*I + C[4]*P
        V = mul!(C[3]*P, true, C[1]*I, true, true) #V = C[1]*I + C[3]*P
        for k in 2:(div(length(C), 2) - 1)
            P *= A2
            mul!(U, C[2k + 2], P, true, true) # U += C[2k+2]*P
            mul!(V, C[2k + 1], P, true, true) # V += C[2k+1]*P
        end

        U = A * U

        # Padé approximant:  (V-U)\(V+U)
        tmp1, tmp2 = A, A2 # Reuse already allocated arrays
        tmp1 .= V .- U
        tmp2 .= V .+ U
        X = LAPACK.gesv!(tmp1, tmp2)[1]
    else
        s  = log2(nA/5.4)               # power of 2 later reversed by squaring
        if s > 0
            si = ceil(Int,s)
            A ./= convert(T,2^si)
        end
        CC = T[64764752532480000.,32382376266240000.,7771770303897600.,
                1187353796428800.,  129060195264000.,  10559470521600.,
                    670442572800.,      33522128640.,      1323241920.,
                        40840800.,           960960.,           16380.,
                             182.,                1.]
        A2 = A * A
        A4 = A2 * A2
        A6 = A2 * A4
        tmp1, tmp2 = similar(A6), similar(A6)

        # Allocation economical version of:
        # U  = A * (A6 * (CC[14].*A6 .+ CC[12].*A4 .+ CC[10].*A2) .+
        #           CC[8].*A6 .+ CC[6].*A4 .+ CC[4]*A2+CC[2]*I)
        tmp1 .= CC[14].*A6 .+ CC[12].*A4 .+ CC[10].*A2
        tmp2 .= CC[8].*A6 .+ CC[6].*A4 .+ CC[4].*A2
        mul!(tmp2, true,CC[2]*I, true, true) # tmp2 .+= CC[2]*I
        U = mul!(tmp2, A6, tmp1, true, true)
        U, tmp1 = mul!(tmp1, A, U), A # U = A * U0

        # Allocation economical version of:
        # V  = A6 * (CC[13].*A6 .+ CC[11].*A4 .+ CC[9].*A2) .+
        #           CC[7].*A6 .+ CC[5].*A4 .+ CC[3]*A2 .+ CC[1]*I
        tmp1 .= CC[13].*A6 .+ CC[11].*A4 .+ CC[9].*A2
        tmp2 .= CC[7].*A6 .+ CC[5].*A4 .+ CC[3].*A2
        mul!(tmp2, true, CC[1]*I, true, true) # tmp2 .+= CC[1]*I
        V = mul!(tmp2, A6, tmp1, true, true)

        tmp1 .= V .+ U
        tmp2 .= V .- U # tmp2 already contained V but this seems more readable
        X = LAPACK.gesv!(tmp2, tmp1)[1] # X now contains r_13 in Higham 2008

        if s > 0
            # Repeated squaring to compute X = r_13^(2^si)
            for t=1:si
                mul!(tmp2, X, X)
                X, tmp2 = tmp2, X
            end
        end
    end

    # Undo the balancing
    for j = ilo:ihi
        scj = scale[j]
        for i = 1:n
            X[j,i] *= scj
        end
        for i = 1:n
            X[i,j] /= scj
        end
    end

    if ilo > 1       # apply lower permutations in reverse order
        for j in (ilo-1):-1:1; rcswap!(j, Int(scale[j]), X) end
    end
    if ihi < n       # apply upper permutations in forward order
        for j in (ihi+1):n;    rcswap!(j, Int(scale[j]), X) end
    end
    X
end

## Swap rows i and j and columns i and j in X
function rcswap!(i::Integer, j::Integer, X::AbstractMatrix{<:Number})
    for k = 1:size(X,1)
        X[k,i], X[k,j] = X[k,j], X[k,i]
    end
    for k = 1:size(X,2)
        X[i,k], X[j,k] = X[j,k], X[i,k]
    end
end

"""
    log(A::AbstractMatrix)

If `A` has no negative real eigenvalue, compute the principal matrix logarithm of `A`, i.e.
the unique matrix ``X`` such that ``e^X = A`` and ``-\\pi < Im(\\lambda) < \\pi`` for all
the eigenvalues ``\\lambda`` of ``X``. If `A` has nonpositive eigenvalues, a nonprincipal
matrix function is returned whenever possible.

If `A` is symmetric or Hermitian, its eigendecomposition ([`eigen`](@ref)) is
used, if `A` is triangular an improved version of the inverse scaling and squaring method is
employed (see [^AH12] and [^AHR13]). If `A` is real with no negative eigenvalues, then
the real Schur form is computed. Otherwise, the complex Schur form is computed. Then
the upper (quasi-)triangular algorithm in [^AHR13] is used on the upper (quasi-)triangular
factor.

[^AH12]: Awad H. Al-Mohy and Nicholas J. Higham, "Improved inverse  scaling and squaring algorithms for the matrix logarithm", SIAM Journal on Scientific Computing, 34(4), 2012, C153-C169. [doi:10.1137/110852553](https://doi.org/10.1137/110852553)

[^AHR13]: Awad H. Al-Mohy, Nicholas J. Higham and Samuel D. Relton, "Computing the Fréchet derivative of the matrix logarithm and estimating the condition number", SIAM Journal on Scientific Computing, 35(4), 2013, C394-C410. [doi:10.1137/120885991](https://doi.org/10.1137/120885991)

# Examples
```jldoctest
julia> A = Matrix(2.7182818*I, 2, 2)
2×2 Matrix{Float64}:
 2.71828  0.0
 0.0      2.71828

julia> log(A)
2×2 Matrix{Float64}:
 1.0  0.0
 0.0  1.0
```
"""
function log(A::AbstractMatrix)
    # If possible, use diagonalization
    if ishermitian(A)
        logHermA = log(Hermitian(A))
        return ishermitian(logHermA) ? copytri!(parent(logHermA), 'U', true) : parent(logHermA)
    elseif istriu(A)
        return triu!(parent(log(UpperTriangular(A))))
    elseif isreal(A)
        SchurF = schur(real(A))
        if istriu(SchurF.T)
            logA = SchurF.Z * log(UpperTriangular(SchurF.T)) * SchurF.Z'
        else
            # real log exists whenever all eigenvalues are positive
            is_log_real = !any(x -> isreal(x) && real(x) ≤ 0, SchurF.values)
            if is_log_real
                logA = SchurF.Z * log_quasitriu(SchurF.T) * SchurF.Z'
            else
                SchurS = Schur{Complex}(SchurF)
                logA = SchurS.Z * log(UpperTriangular(SchurS.T)) * SchurS.Z'
            end
        end
        return eltype(A) <: Complex ? complex(logA) : logA
    else
        SchurF = schur(A)
        return SchurF.vectors * log(UpperTriangular(SchurF.T)) * SchurF.vectors'
    end
end

log(A::AdjointAbsMat) = adjoint(log(parent(A)))
log(A::TransposeAbsMat) = transpose(log(parent(A)))

"""
    sqrt(A::AbstractMatrix)

If `A` has no negative real eigenvalues, compute the principal matrix square root of `A`,
that is the unique matrix ``X`` with eigenvalues having positive real part such that
``X^2 = A``. Otherwise, a nonprincipal square root is returned.

If `A` is real-symmetric or Hermitian, its eigendecomposition ([`eigen`](@ref)) is
used to compute the square root.   For such matrices, eigenvalues λ that
appear to be slightly negative due to roundoff errors are treated as if they were zero.
More precisely, matrices with all eigenvalues `≥ -rtol*(max |λ|)` are treated as semidefinite
(yielding a Hermitian square root), with negative eigenvalues taken to be zero.
`rtol` is a keyword argument to `sqrt` (in the Hermitian/real-symmetric case only) that
defaults to machine precision scaled by `size(A,1)`.

Otherwise, the square root is determined by means of the
Björck-Hammarling method [^BH83], which computes the complex Schur form ([`schur`](@ref))
and then the complex square root of the triangular factor.
If a real square root exists, then an extension of this method [^H87] that computes the real
Schur form and then the real square root of the quasi-triangular factor is instead used.

[^BH83]:

    Åke Björck and Sven Hammarling, "A Schur method for the square root of a matrix",
    Linear Algebra and its Applications, 52-53, 1983, 127-140.
    [doi:10.1016/0024-3795(83)80010-X](https://doi.org/10.1016/0024-3795(83)80010-X)

[^H87]:

    Nicholas J. Higham, "Computing real square roots of a real matrix",
    Linear Algebra and its Applications, 88-89, 1987, 405-430.
    [doi:10.1016/0024-3795(87)90118-2](https://doi.org/10.1016/0024-3795(87)90118-2)

# Examples
```jldoctest
julia> A = [4 0; 0 4]
2×2 Matrix{Int64}:
 4  0
 0  4

julia> sqrt(A)
2×2 Matrix{Float64}:
 2.0  0.0
 0.0  2.0
```
"""
sqrt(::AbstractMatrix)

function sqrt(A::AbstractMatrix{T}) where {T<:Union{Real,Complex}}
    if checksquare(A) == 0
        return copy(A)
    elseif ishermitian(A)
        sqrtHermA = sqrt(Hermitian(A))
        return ishermitian(sqrtHermA) ? copytri!(parent(sqrtHermA), 'U', true) : parent(sqrtHermA)
    elseif istriu(A)
        return triu!(parent(sqrt(UpperTriangular(A))))
    elseif isreal(A)
        SchurF = schur(real(A))
        if istriu(SchurF.T)
            sqrtA = SchurF.Z * sqrt(UpperTriangular(SchurF.T)) * SchurF.Z'
        else
            # real sqrt exists whenever no eigenvalues are negative
            is_sqrt_real = !any(x -> isreal(x) && real(x) < 0, SchurF.values)
            # sqrt_quasitriu uses LAPACK functions for non-triu inputs
            if typeof(sqrt(zero(T))) <: BlasFloat && is_sqrt_real
                sqrtA = SchurF.Z * sqrt_quasitriu(SchurF.T) * SchurF.Z'
            else
                SchurS = Schur{Complex}(SchurF)
                sqrtA = SchurS.Z * sqrt(UpperTriangular(SchurS.T)) * SchurS.Z'
            end
        end
        return eltype(A) <: Complex ? complex(sqrtA) : sqrtA
    else
        SchurF = schur(A)
        return SchurF.vectors * sqrt(UpperTriangular(SchurF.T)) * SchurF.vectors'
    end
end

sqrt(A::AdjointAbsMat) = adjoint(sqrt(parent(A)))
sqrt(A::TransposeAbsMat) = transpose(sqrt(parent(A)))

function inv(A::StridedMatrix{T}) where T
    checksquare(A)
    if istriu(A)
        Ai = triu!(parent(inv(UpperTriangular(A))))
    elseif istril(A)
        Ai = tril!(parent(inv(LowerTriangular(A))))
    else
        Ai = inv!(lu(A))
        Ai = convert(typeof(parent(Ai)), Ai)
    end
    return Ai
end

"""
    cos(A::AbstractMatrix)

Compute the matrix cosine of a square matrix `A`.

If `A` is symmetric or Hermitian, its eigendecomposition ([`eigen`](@ref)) is used to
compute the cosine. Otherwise, the cosine is determined by calling [`exp`](@ref).

# Examples
```jldoctest
julia> cos(fill(1.0, (2,2)))
2×2 Matrix{Float64}:
  0.291927  -0.708073
 -0.708073   0.291927
```
"""
function cos(A::AbstractMatrix{<:Real})
    if issymmetric(A)
        return copytri!(parent(cos(Symmetric(A))), 'U')
    end
    T = complex(float(eltype(A)))
    return real(exp!(T.(im .* A)))
end
function cos(A::AbstractMatrix{<:Complex})
    if ishermitian(A)
        return copytri!(parent(cos(Hermitian(A))), 'U', true)
    end
    T = complex(float(eltype(A)))
    X = exp!(T.(im .* A))
    @. X = (X + $exp!(T(-im*A))) / 2
    return X
end

"""
    sin(A::AbstractMatrix)

Compute the matrix sine of a square matrix `A`.

If `A` is symmetric or Hermitian, its eigendecomposition ([`eigen`](@ref)) is used to
compute the sine. Otherwise, the sine is determined by calling [`exp`](@ref).

# Examples
```jldoctest
julia> sin(fill(1.0, (2,2)))
2×2 Matrix{Float64}:
 0.454649  0.454649
 0.454649  0.454649
```
"""
function sin(A::AbstractMatrix{<:Real})
    if issymmetric(A)
        return copytri!(parent(sin(Symmetric(A))), 'U')
    end
    T = complex(float(eltype(A)))
    return imag(exp!(T.(im .* A)))
end
function sin(A::AbstractMatrix{<:Complex})
    if ishermitian(A)
        return copytri!(parent(sin(Hermitian(A))), 'U', true)
    end
    T = complex(float(eltype(A)))
    X = exp!(T.(im .* A))
    Y = exp!(T.(.-im .* A))
    @inbounds for i in eachindex(X)
        x, y = X[i]/2, Y[i]/2
        X[i] = Complex(imag(x)-imag(y), real(y)-real(x))
    end
    return X
end

"""
    sincos(A::AbstractMatrix)

Compute the matrix sine and cosine of a square matrix `A`.

# Examples
```jldoctest
julia> S, C = sincos(fill(1.0, (2,2)));

julia> S
2×2 Matrix{Float64}:
 0.454649  0.454649
 0.454649  0.454649

julia> C
2×2 Matrix{Float64}:
  0.291927  -0.708073
 -0.708073   0.291927
```
"""
function sincos(A::AbstractMatrix{<:Real})
    if issymmetric(A)
        symsinA, symcosA = sincos(Symmetric(A))
        sinA = copytri!(parent(symsinA), 'U')
        cosA = copytri!(parent(symcosA), 'U')
        return sinA, cosA
    end
    T = complex(float(eltype(A)))
    c, s = reim(exp!(T.(im .* A)))
    return s, c
end
function sincos(A::AbstractMatrix{<:Complex})
    if ishermitian(A)
        hermsinA, hermcosA = sincos(Hermitian(A))
        sinA = copytri!(parent(hermsinA), 'U', true)
        cosA = copytri!(parent(hermcosA), 'U', true)
        return sinA, cosA
    end
    T = complex(float(eltype(A)))
    X = exp!(T.(im .* A))
    Y = exp!(T.(.-im .* A))
    @inbounds for i in eachindex(X)
        x, y = X[i]/2, Y[i]/2
        X[i] = Complex(imag(x)-imag(y), real(y)-real(x))
        Y[i] = x+y
    end
    return X, Y
end

"""
    tan(A::AbstractMatrix)

Compute the matrix tangent of a square matrix `A`.

If `A` is symmetric or Hermitian, its eigendecomposition ([`eigen`](@ref)) is used to
compute the tangent. Otherwise, the tangent is determined by calling [`exp`](@ref).

# Examples
```jldoctest
julia> tan(fill(1.0, (2,2)))
2×2 Matrix{Float64}:
 -1.09252  -1.09252
 -1.09252  -1.09252
```
"""
function tan(A::AbstractMatrix)
    if ishermitian(A)
        return copytri!(parent(tan(Hermitian(A))), 'U', true)
    end
    S, C = sincos(A)
    S /= C
    return S
end

"""
    cosh(A::AbstractMatrix)

Compute the matrix hyperbolic cosine of a square matrix `A`.
"""
function cosh(A::AbstractMatrix)
    if ishermitian(A)
        return copytri!(parent(cosh(Hermitian(A))), 'U', true)
    end
    X = exp(A)
    @. X = (X + $exp!(float(-A))) / 2
    return X
end

"""
    sinh(A::AbstractMatrix)

Compute the matrix hyperbolic sine of a square matrix `A`.
"""
function sinh(A::AbstractMatrix)
    if ishermitian(A)
        return copytri!(parent(sinh(Hermitian(A))), 'U', true)
    end
    X = exp(A)
    @. X = (X - $exp!(float(-A))) / 2
    return X
end

"""
    tanh(A::AbstractMatrix)

Compute the matrix hyperbolic tangent of a square matrix `A`.
"""
function tanh(A::AbstractMatrix)
    if ishermitian(A)
        return copytri!(parent(tanh(Hermitian(A))), 'U', true)
    end
    X = exp(A)
    Y = exp!(float.(.-A))
    @inbounds for i in eachindex(X)
        x, y = X[i], Y[i]
        X[i] = x - y
        Y[i] = x + y
    end
    X /= Y
    return X
end

"""
    acos(A::AbstractMatrix)

Compute the inverse matrix cosine of a square matrix `A`.

If `A` is symmetric or Hermitian, its eigendecomposition ([`eigen`](@ref)) is used to
compute the inverse cosine. Otherwise, the inverse cosine is determined by using
[`log`](@ref) and [`sqrt`](@ref).  For the theory and logarithmic formulas used to compute
this function, see [^AH16_1].

[^AH16_1]: Mary Aprahamian and Nicholas J. Higham, "Matrix Inverse Trigonometric and Inverse Hyperbolic Functions: Theory and Algorithms", MIMS EPrint: 2016.4. [https://doi.org/10.1137/16M1057577](https://doi.org/10.1137/16M1057577)

# Examples
```julia-repl
julia> acos(cos([0.5 0.1; -0.2 0.3]))
2×2 Matrix{ComplexF64}:
  0.5-8.32667e-17im  0.1+0.0im
 -0.2+2.63678e-16im  0.3-3.46945e-16im
```
"""
function acos(A::AbstractMatrix)
    if ishermitian(A)
        acosHermA = acos(Hermitian(A))
        return isa(acosHermA, Hermitian) ? copytri!(parent(acosHermA), 'U', true) : parent(acosHermA)
    end
    SchurF = Schur{Complex}(schur(A))
    U = UpperTriangular(SchurF.T)
    R = triu!(parent(-im * log(U + im * sqrt(I - U^2))))
    return SchurF.Z * R * SchurF.Z'
end

"""
    asin(A::AbstractMatrix)

Compute the inverse matrix sine of a square matrix `A`.

If `A` is symmetric or Hermitian, its eigendecomposition ([`eigen`](@ref)) is used to
compute the inverse sine. Otherwise, the inverse sine is determined by using [`log`](@ref)
and [`sqrt`](@ref).  For the theory and logarithmic formulas used to compute this function,
see [^AH16_2].

[^AH16_2]: Mary Aprahamian and Nicholas J. Higham, "Matrix Inverse Trigonometric and Inverse Hyperbolic Functions: Theory and Algorithms", MIMS EPrint: 2016.4. [https://doi.org/10.1137/16M1057577](https://doi.org/10.1137/16M1057577)

# Examples
```julia-repl
julia> asin(sin([0.5 0.1; -0.2 0.3]))
2×2 Matrix{ComplexF64}:
  0.5-4.16334e-17im  0.1-5.55112e-17im
 -0.2+9.71445e-17im  0.3-1.249e-16im
```
"""
function asin(A::AbstractMatrix)
    if ishermitian(A)
        asinHermA = asin(Hermitian(A))
        return isa(asinHermA, Hermitian) ? copytri!(parent(asinHermA), 'U', true) : parent(asinHermA)
    end
    SchurF = Schur{Complex}(schur(A))
    U = UpperTriangular(SchurF.T)
    R = triu!(parent(-im * log(im * U + sqrt(I - U^2))))
    return SchurF.Z * R * SchurF.Z'
end

"""
    atan(A::AbstractMatrix)

Compute the inverse matrix tangent of a square matrix `A`.

If `A` is symmetric or Hermitian, its eigendecomposition ([`eigen`](@ref)) is used to
compute the inverse tangent. Otherwise, the inverse tangent is determined by using
[`log`](@ref).  For the theory and logarithmic formulas used to compute this function, see
[^AH16_3].

[^AH16_3]: Mary Aprahamian and Nicholas J. Higham, "Matrix Inverse Trigonometric and Inverse Hyperbolic Functions: Theory and Algorithms", MIMS EPrint: 2016.4. [https://doi.org/10.1137/16M1057577](https://doi.org/10.1137/16M1057577)

# Examples
```julia-repl
julia> atan(tan([0.5 0.1; -0.2 0.3]))
2×2 Matrix{ComplexF64}:
  0.5+1.38778e-17im  0.1-2.77556e-17im
 -0.2+6.93889e-17im  0.3-4.16334e-17im
```
"""
function atan(A::AbstractMatrix)
    if ishermitian(A)
        return copytri!(parent(atan(Hermitian(A))), 'U', true)
    end
    SchurF = Schur{Complex}(schur(A))
    U = im * UpperTriangular(SchurF.T)
    R = triu!(parent(log((I + U) / (I - U)) / 2im))
    return SchurF.Z * R * SchurF.Z'
end

"""
    acosh(A::AbstractMatrix)

Compute the inverse hyperbolic matrix cosine of a square matrix `A`.  For the theory and
logarithmic formulas used to compute this function, see [^AH16_4].

[^AH16_4]: Mary Aprahamian and Nicholas J. Higham, "Matrix Inverse Trigonometric and Inverse Hyperbolic Functions: Theory and Algorithms", MIMS EPrint: 2016.4. [https://doi.org/10.1137/16M1057577](https://doi.org/10.1137/16M1057577)
"""
function acosh(A::AbstractMatrix)
    if ishermitian(A)
        acoshHermA = acosh(Hermitian(A))
        return isa(acoshHermA, Hermitian) ? copytri!(parent(acoshHermA), 'U', true) : parent(acoshHermA)
    end
    SchurF = Schur{Complex}(schur(A))
    U = UpperTriangular(SchurF.T)
    R = triu!(parent(log(U + sqrt(U - I) * sqrt(U + I))))
    return SchurF.Z * R * SchurF.Z'
end

"""
    asinh(A::AbstractMatrix)

Compute the inverse hyperbolic matrix sine of a square matrix `A`.  For the theory and
logarithmic formulas used to compute this function, see [^AH16_5].

[^AH16_5]: Mary Aprahamian and Nicholas J. Higham, "Matrix Inverse Trigonometric and Inverse Hyperbolic Functions: Theory and Algorithms", MIMS EPrint: 2016.4. [https://doi.org/10.1137/16M1057577](https://doi.org/10.1137/16M1057577)
"""
function asinh(A::AbstractMatrix)
    if ishermitian(A)
        return copytri!(parent(asinh(Hermitian(A))), 'U', true)
    end
    SchurF = Schur{Complex}(schur(A))
    U = UpperTriangular(SchurF.T)
    R = triu!(parent(log(U + sqrt(I + U^2))))
    return SchurF.Z * R * SchurF.Z'
end

"""
    atanh(A::AbstractMatrix)

Compute the inverse hyperbolic matrix tangent of a square matrix `A`.  For the theory and
logarithmic formulas used to compute this function, see [^AH16_6].

[^AH16_6]: Mary Aprahamian and Nicholas J. Higham, "Matrix Inverse Trigonometric and Inverse Hyperbolic Functions: Theory and Algorithms", MIMS EPrint: 2016.4. [https://doi.org/10.1137/16M1057577](https://doi.org/10.1137/16M1057577)
"""
function atanh(A::AbstractMatrix)
    if ishermitian(A)
        return copytri!(parent(atanh(Hermitian(A))), 'U', true)
    end
    SchurF = Schur{Complex}(schur(A))
    U = UpperTriangular(SchurF.T)
    R = triu!(parent(log((I + U) / (I - U)) / 2))
    return SchurF.Z * R * SchurF.Z'
end

for (finv, f, finvh, fh, fn) in ((:sec, :cos, :sech, :cosh, "secant"),
                                 (:csc, :sin, :csch, :sinh, "cosecant"),
                                 (:cot, :tan, :coth, :tanh, "cotangent"))
    name = string(finv)
    hname = string(finvh)
    @eval begin
        @doc """
            $($name)(A::AbstractMatrix)

        Compute the matrix $($fn) of a square matrix `A`.
        """ ($finv)(A::AbstractMatrix{T}) where {T} = inv(($f)(A))
        @doc """
            $($hname)(A::AbstractMatrix)

        Compute the matrix hyperbolic $($fn) of square matrix `A`.
        """ ($finvh)(A::AbstractMatrix{T}) where {T} = inv(($fh)(A))
    end
end

for (tfa, tfainv, hfa, hfainv, fn) in ((:asec, :acos, :asech, :acosh, "secant"),
                                       (:acsc, :asin, :acsch, :asinh, "cosecant"),
                                       (:acot, :atan, :acoth, :atanh, "cotangent"))
    tname = string(tfa)
    hname = string(hfa)
    @eval begin
        @doc """
            $($tname)(A::AbstractMatrix)
        Compute the inverse matrix $($fn) of `A`. """ ($tfa)(A::AbstractMatrix{T}) where {T} = ($tfainv)(inv(A))
        @doc """
            $($hname)(A::AbstractMatrix)
        Compute the inverse matrix hyperbolic $($fn) of `A`. """ ($hfa)(A::AbstractMatrix{T}) where {T} = ($hfainv)(inv(A))
    end
end

"""
    factorize(A)

Compute a convenient factorization of `A`, based upon the type of the input matrix.
`factorize` checks `A` to see if it is symmetric/triangular/etc. if `A` is passed
as a generic matrix. `factorize` checks every element of `A` to verify/rule out
each property. It will short-circuit as soon as it can rule out symmetry/triangular
structure. The return value can be reused for efficient solving of multiple
systems. For example: `A=factorize(A); x=A\\b; y=A\\C`.

| Properties of `A`          | type of factorization                          |
|:---------------------------|:-----------------------------------------------|
| Positive-definite          | Cholesky (see [`cholesky`](@ref))  |
| Dense Symmetric/Hermitian  | Bunch-Kaufman (see [`bunchkaufman`](@ref)) |
| Sparse Symmetric/Hermitian | LDLt (see [`ldlt`](@ref))      |
| Triangular                 | Triangular                                     |
| Diagonal                   | Diagonal                                       |
| Bidiagonal                 | Bidiagonal                                     |
| Tridiagonal                | LU (see [`lu`](@ref))            |
| Symmetric real tridiagonal | LDLt (see [`ldlt`](@ref))      |
| General square             | LU (see [`lu`](@ref))            |
| General non-square         | QR (see [`qr`](@ref))            |

If `factorize` is called on a Hermitian positive-definite matrix, for instance, then `factorize`
will return a Cholesky factorization.

# Examples
```jldoctest
julia> A = Array(Bidiagonal(fill(1.0, (5, 5)), :U))
5×5 Matrix{Float64}:
 1.0  1.0  0.0  0.0  0.0
 0.0  1.0  1.0  0.0  0.0
 0.0  0.0  1.0  1.0  0.0
 0.0  0.0  0.0  1.0  1.0
 0.0  0.0  0.0  0.0  1.0

julia> factorize(A) # factorize will check to see that A is already factorized
5×5 Bidiagonal{Float64, Vector{Float64}}:
 1.0  1.0   ⋅    ⋅    ⋅
  ⋅   1.0  1.0   ⋅    ⋅
  ⋅    ⋅   1.0  1.0   ⋅
  ⋅    ⋅    ⋅   1.0  1.0
  ⋅    ⋅    ⋅    ⋅   1.0
```
This returns a `5×5 Bidiagonal{Float64}`, which can now be passed to other linear algebra functions
(e.g. eigensolvers) which will use specialized methods for `Bidiagonal` types.
"""
function factorize(A::AbstractMatrix{T}) where T
    m, n = size(A)
    if m == n
        if m == 1 return A[1] end
        utri    = true
        utri1   = true
        herm    = true
        sym     = true
        for j = 1:n-1, i = j+1:m
            if utri1
                if A[i,j] != 0
                    utri1 = i == j + 1
                    utri = false
                end
            end
            if sym
                sym &= A[i,j] == A[j,i]
            end
            if herm
                herm &= A[i,j] == conj(A[j,i])
            end
            if !(utri1|herm|sym) break end
        end
        ltri = true
        ltri1 = true
        for j = 3:n, i = 1:j-2
            ltri1 &= A[i,j] == 0
            if !ltri1 break end
        end
        if ltri1
            for i = 1:n-1
                if A[i,i+1] != 0
                    ltri &= false
                    break
                end
            end
            if ltri
                if utri
                    return Diagonal(A)
                end
                if utri1
                    return Bidiagonal(diag(A), diag(A, -1), :L)
                end
                return LowerTriangular(A)
            end
            if utri
                return Bidiagonal(diag(A), diag(A, 1), :U)
            end
            if utri1
                # TODO: enable once a specialized, non-dense bunchkaufman method exists
                # if (herm & (T <: Complex)) | sym
                    # return bunchkaufman(SymTridiagonal(diag(A), diag(A, -1)))
                # end
                return lu(Tridiagonal(diag(A, -1), diag(A), diag(A, 1)))
            end
        end
        if utri
            return UpperTriangular(A)
        end
        if herm
            cf = cholesky(A; check = false)
            if cf.info == 0
                return cf
            else
                return factorize(Hermitian(A))
            end
        end
        if sym
            return factorize(Symmetric(A))
        end
        return lu(A)
    end
    qr(A, ColumnNorm())
end
factorize(A::Adjoint)   =   adjoint(factorize(parent(A)))
factorize(A::Transpose) = transpose(factorize(parent(A)))
factorize(a::Number)    = a # same as how factorize behaves on Diagonal types

## Moore-Penrose pseudoinverse

"""
    pinv(M; atol::Real=0, rtol::Real=atol>0 ? 0 : n*ϵ)
    pinv(M, rtol::Real) = pinv(M; rtol=rtol) # to be deprecated in Julia 2.0

Computes the Moore-Penrose pseudoinverse.

For matrices `M` with floating point elements, it is convenient to compute
the pseudoinverse by inverting only singular values greater than
`max(atol, rtol*σ₁)` where `σ₁` is the largest singular value of `M`.

The optimal choice of absolute (`atol`) and relative tolerance (`rtol`) varies
both with the value of `M` and the intended application of the pseudoinverse.
The default relative tolerance is `n*ϵ`, where `n` is the size of the smallest
dimension of `M`, and `ϵ` is the [`eps`](@ref) of the element type of `M`.

For inverting dense ill-conditioned matrices in a least-squares sense,
`rtol = sqrt(eps(real(float(oneunit(eltype(M))))))` is recommended.

For more information, see [^issue8859], [^B96], [^S84], [^KY88].

# Examples
```jldoctest
julia> M = [1.5 1.3; 1.2 1.9]
2×2 Matrix{Float64}:
 1.5  1.3
 1.2  1.9

julia> N = pinv(M)
2×2 Matrix{Float64}:
  1.47287   -1.00775
 -0.930233   1.16279

julia> M * N
2×2 Matrix{Float64}:
 1.0          -2.22045e-16
 4.44089e-16   1.0
```

[^issue8859]: Issue 8859, "Fix least squares", [https://github.com/JuliaLang/julia/pull/8859](https://github.com/JuliaLang/julia/pull/8859)

[^B96]: Åke Björck, "Numerical Methods for Least Squares Problems",  SIAM Press, Philadelphia, 1996, "Other Titles in Applied Mathematics", Vol. 51. [doi:10.1137/1.9781611971484](http://epubs.siam.org/doi/book/10.1137/1.9781611971484)

[^S84]: G. W. Stewart, "Rank Degeneracy", SIAM Journal on Scientific and Statistical Computing, 5(2), 1984, 403-413. [doi:10.1137/0905030](http://epubs.siam.org/doi/abs/10.1137/0905030)

[^KY88]: Konstantinos Konstantinides and Kung Yao, "Statistical analysis of effective singular values in matrix rank determination", IEEE Transactions on Acoustics, Speech and Signal Processing, 36(5), 1988, 757-763. [doi:10.1109/29.1585](https://doi.org/10.1109/29.1585)
"""
function pinv(A::AbstractMatrix{T}; atol::Real = 0.0, rtol::Real = (eps(real(float(oneunit(T))))*min(size(A)...))*iszero(atol)) where T
    m, n = size(A)
    Tout = typeof(zero(T)/sqrt(oneunit(T) + oneunit(T)))
    if m == 0 || n == 0
        return similar(A, Tout, (n, m))
    end
    if isdiag(A)
        indA = diagind(A)
        dA = view(A, indA)
        maxabsA = maximum(abs, dA)
        tol = max(rtol * maxabsA, atol)
        B = fill!(similar(A, Tout, (n, m)), 0)
        indB = diagind(B)
        B[indB] .= (x -> abs(x) > tol ? pinv(x) : zero(x)).(dA)
        return B
    end
    SVD         = svd(A)
    tol         = max(rtol*maximum(SVD.S), atol)
    Stype       = eltype(SVD.S)
    Sinv        = fill!(similar(A, Stype, length(SVD.S)), 0)
    index       = SVD.S .> tol
    Sinv[index] .= pinv.(view(SVD.S, index))
    return SVD.Vt' * (Diagonal(Sinv) * SVD.U')
end
function pinv(x::Number)
    xi = inv(x)
    return ifelse(isfinite(xi), xi, zero(xi))
end

## Basis for null space

"""
    nullspace(M; atol::Real=0, rtol::Real=atol>0 ? 0 : n*ϵ)
    nullspace(M, rtol::Real) = nullspace(M; rtol=rtol) # to be deprecated in Julia 2.0

Computes a basis for the nullspace of `M` by including the singular
vectors of `M` whose singular values have magnitudes smaller than `max(atol, rtol*σ₁)`,
where `σ₁` is `M`'s largest singular value.

By default, the relative tolerance `rtol` is `n*ϵ`, where `n`
is the size of the smallest dimension of `M`, and `ϵ` is the [`eps`](@ref) of
the element type of `M`.

# Examples
```jldoctest
julia> M = [1 0 0; 0 1 0; 0 0 0]
3×3 Matrix{Int64}:
 1  0  0
 0  1  0
 0  0  0

julia> nullspace(M)
3×1 Matrix{Float64}:
 0.0
 0.0
 1.0

julia> nullspace(M, rtol=3)
3×3 Matrix{Float64}:
 0.0  1.0  0.0
 1.0  0.0  0.0
 0.0  0.0  1.0

julia> nullspace(M, atol=0.95)
3×1 Matrix{Float64}:
 0.0
 0.0
 1.0
```
"""
function nullspace(A::AbstractVecOrMat; atol::Real = 0.0, rtol::Real = (min(size(A, 1), size(A, 2))*eps(real(float(oneunit(eltype(A))))))*iszero(atol))
    m, n = size(A, 1), size(A, 2)
    (m == 0 || n == 0) && return Matrix{eigtype(eltype(A))}(I, n, n)
    SVD = svd(A; full=true)
    tol = max(atol, SVD.S[1]*rtol)
    indstart = sum(s -> s .> tol, SVD.S) + 1
    return copy((@view SVD.Vt[indstart:end,:])')
end

"""
    cond(M, p::Real=2)

Condition number of the matrix `M`, computed using the operator `p`-norm. Valid values for
`p` are `1`, `2` (default), or `Inf`.
"""
function cond(A::AbstractMatrix, p::Real=2)
    if p == 2
        v = svdvals(A)
        maxv = maximum(v)
        return iszero(maxv) ? oftype(real(maxv), Inf) : maxv / minimum(v)
    elseif p == 1 || p == Inf
        checksquare(A)
        try
            Ainv = inv(A)
            return opnorm(A, p)*opnorm(Ainv, p)
        catch e
            if isa(e, LAPACKException) || isa(e, SingularException)
                return convert(float(real(eltype(A))), Inf)
            else
                rethrow()
            end
        end
    end
    throw(ArgumentError("p-norm must be 1, 2 or Inf, got $p"))
end

## Lyapunov and Sylvester equation

# AX + XB + C = 0

"""
    sylvester(A, B, C)

Computes the solution `X` to the Sylvester equation `AX + XB + C = 0`, where `A`, `B` and
`C` have compatible dimensions and `A` and `-B` have no eigenvalues with equal real part.

# Examples
```jldoctest
julia> A = [3. 4.; 5. 6]
2×2 Matrix{Float64}:
 3.0  4.0
 5.0  6.0

julia> B = [1. 1.; 1. 2.]
2×2 Matrix{Float64}:
 1.0  1.0
 1.0  2.0

julia> C = [1. 2.; -2. 1]
2×2 Matrix{Float64}:
  1.0  2.0
 -2.0  1.0

julia> X = sylvester(A, B, C)
2×2 Matrix{Float64}:
 -4.46667   1.93333
  3.73333  -1.8

julia> A*X + X*B ≈ -C
true
```
"""
function sylvester(A::AbstractMatrix, B::AbstractMatrix, C::AbstractMatrix)
    T = promote_type(float(eltype(A)), float(eltype(B)), float(eltype(C)))
    return sylvester(copy_similar(A, T), copy_similar(B, T), copy_similar(C, T))
end
function sylvester(A::AbstractMatrix{T}, B::AbstractMatrix{T}, C::AbstractMatrix{T}) where {T<:BlasFloat}
    RA, QA = schur(A)
    RB, QB = schur(B)
    D = QA' * C * QB
    D .= .-D
    Y, scale = LAPACK.trsyl!('N', 'N', RA, RB, D)
    rmul!(QA * Y * QB', inv(scale))
end

Base.@propagate_inbounds function _sylvester_2x1!(A, B, C)
    b = B[1]
    a21, a12 = A[2, 1], A[1, 2]
    m11 = b + A[1, 1]
    m22 = b + A[2, 2]
    d = m11 * m22 - a12 * a21
    c1, c2 = C
    C[1] = (a12 * c2 - m22 * c1) / d
    C[2] = (a21 * c1 - m11 * c2) / d
    return C
end
Base.@propagate_inbounds function _sylvester_1x2!(A, B, C)
    a = A[1]
    b21, b12 = B[2, 1], B[1, 2]
    m11 = a + B[1, 1]
    m22 = a + B[2, 2]
    d = m11 * m22 - b21 * b12
    c1, c2 = C
    C[1] = (b21 * c2 - m22 * c1) / d
    C[2] = (b12 * c1 - m11 * c2) / d
    return C
end
function _sylvester_2x2!(A, B, C)
    _, scale = LAPACK.trsyl!('N', 'N', A, B, C)
    rmul!(C, -inv(scale))
    return C
end

sylvester(a::Union{Real,Complex}, b::Union{Real,Complex}, c::Union{Real,Complex}) = -c / (a + b)

# AX + XA' + C = 0

"""
    lyap(A, C)

Computes the solution `X` to the continuous Lyapunov equation `AX + XA' + C = 0`, where no
eigenvalue of `A` has a zero real part and no two eigenvalues are negative complex
conjugates of each other.

# Examples
```jldoctest
julia> A = [3. 4.; 5. 6]
2×2 Matrix{Float64}:
 3.0  4.0
 5.0  6.0

julia> B = [1. 1.; 1. 2.]
2×2 Matrix{Float64}:
 1.0  1.0
 1.0  2.0

julia> X = lyap(A, B)
2×2 Matrix{Float64}:
  0.5  -0.5
 -0.5   0.25

julia> A*X + X*A' ≈ -B
true
```
"""
function lyap(A::AbstractMatrix, C::AbstractMatrix)
    T = promote_type(float(eltype(A)), float(eltype(C)))
    return lyap(copy_similar(A, T), copy_similar(C, T))
end
function lyap(A::AbstractMatrix{T}, C::AbstractMatrix{T}) where {T<:BlasFloat}
    R, Q = schur(A)
    D = Q' * C * Q
    D .= .-D
    Y, scale = LAPACK.trsyl!('N', T <: Complex ? 'C' : 'T', R, R, D)
    rmul!(Q * Y * Q', inv(scale))
end
lyap(a::Union{Real,Complex}, c::Union{Real,Complex}) = -c/(2real(a))
x   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LinearAlgebra/src/tridiag.jlwr      # This file is a part of Julia. License is MIT: https://julialang.org/license

#### Specialized matrix types ####

## (complex) symmetric tridiagonal matrices
struct SymTridiagonal{T, V<:AbstractVector{T}} <: AbstractMatrix{T}
    dv::V                        # diagonal
    ev::V                        # superdiagonal
    function SymTridiagonal{T, V}(dv, ev) where {T, V<:AbstractVector{T}}
        require_one_based_indexing(dv, ev)
        if !(length(dv) - 1 <= length(ev) <= length(dv))
            throw(DimensionMismatch("subdiagonal has wrong length. Has length $(length(ev)), but should be either $(length(dv) - 1) or $(length(dv))."))
        end
        new{T, V}(dv, ev)
    end
end

"""
    SymTridiagonal(dv::V, ev::V) where V <: AbstractVector

Construct a symmetric tridiagonal matrix from the diagonal (`dv`) and first
sub/super-diagonal (`ev`), respectively. The result is of type `SymTridiagonal`
and provides efficient specialized eigensolvers, but may be converted into a
regular matrix with [`convert(Array, _)`](@ref) (or `Array(_)` for short).

For `SymTridiagonal` block matrices, the elements of `dv` are symmetrized.
The argument `ev` is interpreted as the superdiagonal. Blocks from the
subdiagonal are (materialized) transpose of the corresponding superdiagonal blocks.

# Examples
```jldoctest
julia> dv = [1, 2, 3, 4]
4-element Vector{Int64}:
 1
 2
 3
 4

julia> ev = [7, 8, 9]
3-element Vector{Int64}:
 7
 8
 9

julia> SymTridiagonal(dv, ev)
4×4 SymTridiagonal{Int64, Vector{Int64}}:
 1  7  ⋅  ⋅
 7  2  8  ⋅
 ⋅  8  3  9
 ⋅  ⋅  9  4

julia> A = SymTridiagonal(fill([1 2; 3 4], 3), fill([1 2; 3 4], 2));

julia> A[1,1]
2×2 Symmetric{Int64, Matrix{Int64}}:
 1  2
 2  4

julia> A[1,2]
2×2 Matrix{Int64}:
 1  2
 3  4

julia> A[2,1]
2×2 Matrix{Int64}:
 1  3
 2  4
```
"""
SymTridiagonal(dv::V, ev::V) where {T,V<:AbstractVector{T}} = SymTridiagonal{T}(dv, ev)
SymTridiagonal{T}(dv::V, ev::V) where {T,V<:AbstractVector{T}} = SymTridiagonal{T,V}(dv, ev)
function SymTridiagonal{T}(dv::AbstractVector, ev::AbstractVector) where {T}
    SymTridiagonal(convert(AbstractVector{T}, dv)::AbstractVector{T},
                   convert(AbstractVector{T}, ev)::AbstractVector{T})
end

"""
    SymTridiagonal(A::AbstractMatrix)

Construct a symmetric tridiagonal matrix from the diagonal and first superdiagonal
of the symmetric matrix `A`.

# Examples
```jldoctest
julia> A = [1 2 3; 2 4 5; 3 5 6]
3×3 Matrix{Int64}:
 1  2  3
 2  4  5
 3  5  6

julia> SymTridiagonal(A)
3×3 SymTridiagonal{Int64, Vector{Int64}}:
 1  2  ⋅
 2  4  5
 ⋅  5  6

julia> B = reshape([[1 2; 2 3], [1 2; 3 4], [1 3; 2 4], [1 2; 2 3]], 2, 2);

julia> SymTridiagonal(B)
2×2 SymTridiagonal{Matrix{Int64}, Vector{Matrix{Int64}}}:
 [1 2; 2 3]  [1 3; 2 4]
 [1 2; 3 4]  [1 2; 2 3]
```
"""
function SymTridiagonal(A::AbstractMatrix)
    if (diag(A, 1) == transpose.(diag(A, -1))) && all(issymmetric.(diag(A, 0)))
        SymTridiagonal(diag(A, 0), diag(A, 1))
    else
        throw(ArgumentError("matrix is not symmetric; cannot convert to SymTridiagonal"))
    end
end

SymTridiagonal{T,V}(S::SymTridiagonal{T,V}) where {T,V<:AbstractVector{T}} = S
SymTridiagonal{T,V}(S::SymTridiagonal) where {T,V<:AbstractVector{T}} =
    SymTridiagonal(convert(V, S.dv)::V, convert(V, S.ev)::V)
SymTridiagonal{T}(S::SymTridiagonal{T}) where {T} = S
SymTridiagonal{T}(S::SymTridiagonal) where {T} =
    SymTridiagonal(convert(AbstractVector{T}, S.dv)::AbstractVector{T},
                   convert(AbstractVector{T}, S.ev)::AbstractVector{T})
SymTridiagonal(S::SymTridiagonal) = S

AbstractMatrix{T}(S::SymTridiagonal) where {T} =
    SymTridiagonal(convert(AbstractVector{T}, S.dv)::AbstractVector{T},
                   convert(AbstractVector{T}, S.ev)::AbstractVector{T})
function Matrix{T}(M::SymTridiagonal) where T
    n = size(M, 1)
    Mf = Matrix{T}(undef, n, n)
    n == 0 && return Mf
    n > 2 && fill!(Mf, zero(T))
    @inbounds for i = 1:n-1
        Mf[i,i] = symmetric(M.dv[i], :U)
        Mf[i+1,i] = transpose(M.ev[i])
        Mf[i,i+1] = M.ev[i]
    end
    Mf[n,n] = symmetric(M.dv[n], :U)
    return Mf
end
Matrix(M::SymTridiagonal{T}) where {T} = Matrix{promote_type(T, typeof(zero(T)))}(M)
Array(M::SymTridiagonal) = Matrix(M)

size(A::SymTridiagonal) = (length(A.dv), length(A.dv))
function size(A::SymTridiagonal, d::Integer)
    if d < 1
        throw(ArgumentError("dimension must be ≥ 1, got $d"))
    elseif d<=2
        return length(A.dv)
    else
        return 1
    end
end

similar(S::SymTridiagonal, ::Type{T}) where {T} = SymTridiagonal(similar(S.dv, T), similar(S.ev, T))
similar(S::SymTridiagonal, ::Type{T}, dims::Union{Dims{1},Dims{2}}) where {T} = similar(S.dv, T, dims)

copyto!(dest::SymTridiagonal, src::SymTridiagonal) =
    (copyto!(dest.dv, src.dv); copyto!(dest.ev, _evview(src)); dest)

#Elementary operations
for func in (:conj, :copy, :real, :imag)
    @eval ($func)(M::SymTridiagonal) = SymTridiagonal(($func)(M.dv), ($func)(M.ev))
end

transpose(S::SymTridiagonal) = S
adjoint(S::SymTridiagonal{<:Real}) = S
adjoint(S::SymTridiagonal) = Adjoint(S)
permutedims(S::SymTridiagonal) = S
function permutedims(S::SymTridiagonal, perm)
    Base.checkdims_perm(S, S, perm)
    NTuple{2}(perm) == (2, 1) ? permutedims(S) : S
end
Base.copy(S::Adjoint{<:Any,<:SymTridiagonal}) = SymTridiagonal(map(x -> copy.(adjoint.(x)), (S.parent.dv, S.parent.ev))...)

ishermitian(S::SymTridiagonal) = isreal(S.dv) && isreal(_evview(S))
issymmetric(S::SymTridiagonal) = true

tr(S::SymTridiagonal) = sum(S.dv)

function diag(M::SymTridiagonal{T}, n::Integer=0) where T<:Number
    # every branch call similar(..., ::Int) to make sure the
    # same vector type is returned independent of n
    absn = abs(n)
    if absn == 0
        return copyto!(similar(M.dv, length(M.dv)), M.dv)
    elseif absn == 1
        return copyto!(similar(M.ev, length(M.dv)-1), _evview(M))
    elseif absn <= size(M,1)
        return fill!(similar(M.dv, size(M,1)-absn), zero(T))
    else
        throw(ArgumentError(string("requested diagonal, $n, must be at least $(-size(M, 1)) ",
            "and at most $(size(M, 2)) for an $(size(M, 1))-by-$(size(M, 2)) matrix")))
    end
end
function diag(M::SymTridiagonal, n::Integer=0)
    # every branch call similar(..., ::Int) to make sure the
    # same vector type is returned independent of n
    if n == 0
        return copyto!(similar(M.dv, length(M.dv)), symmetric.(M.dv, :U))
    elseif n == 1
        return copyto!(similar(M.ev, length(M.dv)-1), _evview(M))
    elseif n == -1
        return copyto!(similar(M.ev, length(M.dv)-1), transpose.(_evview(M)))
    elseif n <= size(M,1)
        throw(ArgumentError("requested diagonal contains undefined zeros of an array type"))
    else
        throw(ArgumentError(string("requested diagonal, $n, must be at least $(-size(M, 1)) ",
            "and at most $(size(M, 2)) for an $(size(M, 1))-by-$(size(M, 2)) matrix")))
    end
end

+(A::SymTridiagonal, B::SymTridiagonal) = SymTridiagonal(A.dv+B.dv, _evview(A)+_evview(B))
-(A::SymTridiagonal, B::SymTridiagonal) = SymTridiagonal(A.dv-B.dv, _evview(A)-_evview(B))
-(A::SymTridiagonal) = SymTridiagonal(-A.dv, -A.ev)
*(A::SymTridiagonal, B::Number) = SymTridiagonal(A.dv*B, A.ev*B)
*(B::Number, A::SymTridiagonal) = SymTridiagonal(B*A.dv, B*A.ev)
/(A::SymTridiagonal, B::Number) = SymTridiagonal(A.dv/B, A.ev/B)
\(B::Number, A::SymTridiagonal) = SymTridiagonal(B\A.dv, B\A.ev)
==(A::SymTridiagonal{<:Number}, B::SymTridiagonal{<:Number}) =
    (A.dv == B.dv) && (_evview(A) == _evview(B))
==(A::SymTridiagonal, B::SymTridiagonal) =
    size(A) == size(B) && all(i -> A[i,i] == B[i,i], axes(A, 1)) && (_evview(A) == _evview(B))

function dot(x::AbstractVector, S::SymTridiagonal, y::AbstractVector)
    require_one_based_indexing(x, y)
    nx, ny = length(x), length(y)
    (nx == size(S, 1) == ny) || throw(DimensionMismatch("dot"))
    if nx ≤ 1
        nx == 0 && return dot(zero(eltype(x)), zero(eltype(S)), zero(eltype(y)))
        return dot(x[1], S.dv[1], y[1])
    end
    dv, ev = S.dv, S.ev
    @inbounds begin
        x₀ = x[1]
        x₊ = x[2]
        sub = transpose(ev[1])
        r = dot(adjoint(dv[1])*x₀ + adjoint(sub)*x₊, y[1])
        for j in 2:nx-1
            x₋, x₀, x₊ = x₀, x₊, x[j+1]
            sup, sub = transpose(sub), transpose(ev[j])
            r += dot(adjoint(sup)*x₋ + adjoint(dv[j])*x₀ + adjoint(sub)*x₊, y[j])
        end
        r += dot(adjoint(transpose(sub))*x₀ + adjoint(dv[nx])*x₊, y[nx])
    end
    return r
end

(\)(T::SymTridiagonal, B::AbstractVecOrMat) = ldlt(T)\B

# division with optional shift for use in shifted-Hessenberg solvers (hessenberg.jl):
ldiv!(A::SymTridiagonal, B::AbstractVecOrMat; shift::Number=false) = ldiv!(ldlt(A, shift=shift), B)
rdiv!(B::AbstractVecOrMat, A::SymTridiagonal; shift::Number=false) = rdiv!(B, ldlt(A, shift=shift))

eigen!(A::SymTridiagonal{<:BlasReal,<:StridedVector}) = Eigen(LAPACK.stegr!('V', A.dv, A.ev)...)
eigen(A::SymTridiagonal{T}) where T = eigen!(copymutable_oftype(A, eigtype(T)))

eigen!(A::SymTridiagonal{<:BlasReal,<:StridedVector}, irange::UnitRange) =
    Eigen(LAPACK.stegr!('V', 'I', A.dv, A.ev, 0.0, 0.0, irange.start, irange.stop)...)
eigen(A::SymTridiagonal{T}, irange::UnitRange) where T =
    eigen!(copymutable_oftype(A, eigtype(T)), irange)

eigen!(A::SymTridiagonal{<:BlasReal,<:StridedVector}, vl::Real, vu::Real) =
    Eigen(LAPACK.stegr!('V', 'V', A.dv, A.ev, vl, vu, 0, 0)...)
eigen(A::SymTridiagonal{T}, vl::Real, vu::Real) where T =
    eigen!(copymutable_oftype(A, eigtype(T)), vl, vu)

eigvals!(A::SymTridiagonal{<:BlasReal,<:StridedVector}) = LAPACK.stev!('N', A.dv, A.ev)[1]
eigvals(A::SymTridiagonal{T}) where T = eigvals!(copymutable_oftype(A, eigtype(T)))

eigvals!(A::SymTridiagonal{<:BlasReal,<:StridedVector}, irange::UnitRange) =
    LAPACK.stegr!('N', 'I', A.dv, A.ev, 0.0, 0.0, irange.start, irange.stop)[1]
eigvals(A::SymTridiagonal{T}, irange::UnitRange) where T =
    eigvals!(copymutable_oftype(A, eigtype(T)), irange)

eigvals!(A::SymTridiagonal{<:BlasReal,<:StridedVector}, vl::Real, vu::Real) =
    LAPACK.stegr!('N', 'V', A.dv, A.ev, vl, vu, 0, 0)[1]
eigvals(A::SymTridiagonal{T}, vl::Real, vu::Real) where T =
    eigvals!(copymutable_oftype(A, eigtype(T)), vl, vu)

#Computes largest and smallest eigenvalue
eigmax(A::SymTridiagonal) = eigvals(A, size(A, 1):size(A, 1))[1]
eigmin(A::SymTridiagonal) = eigvals(A, 1:1)[1]

#Compute selected eigenvectors only corresponding to particular eigenvalues
eigvecs(A::SymTridiagonal) = eigen(A).vectors

"""
    eigvecs(A::SymTridiagonal[, eigvals]) -> Matrix

Return a matrix `M` whose columns are the eigenvectors of `A`. (The `k`th eigenvector can
be obtained from the slice `M[:, k]`.)

If the optional vector of eigenvalues `eigvals` is specified, `eigvecs`
returns the specific corresponding eigenvectors.

# Examples
```jldoctest
julia> A = SymTridiagonal([1.; 2.; 1.], [2.; 3.])
3×3 SymTridiagonal{Float64, Vector{Float64}}:
 1.0  2.0   ⋅
 2.0  2.0  3.0
  ⋅   3.0  1.0

julia> eigvals(A)
3-element Vector{Float64}:
 -2.1400549446402604
  1.0000000000000002
  5.140054944640259

julia> eigvecs(A)
3×3 Matrix{Float64}:
  0.418304  -0.83205      0.364299
 -0.656749  -7.39009e-16  0.754109
  0.627457   0.5547       0.546448

julia> eigvecs(A, [1.])
3×1 Matrix{Float64}:
  0.8320502943378438
  4.263514128092366e-17
 -0.5547001962252291
```
"""
eigvecs(A::SymTridiagonal{<:BlasFloat,<:StridedVector}, eigvals::Vector{<:Real}) = LAPACK.stein!(A.dv, A.ev, eigvals)

function svdvals!(A::SymTridiagonal)
    vals = eigvals!(A)
    return sort!(map!(abs, vals, vals); rev=true)
end

# tril and triu

function istriu(M::SymTridiagonal, k::Integer=0)
    if k <= -1
        return true
    elseif k == 0
        return iszero(_evview(M))
    else # k >= 1
        return iszero(_evview(M)) && iszero(M.dv)
    end
end
istril(M::SymTridiagonal, k::Integer) = istriu(M, -k)
iszero(M::SymTridiagonal) =  iszero(_evview(M)) && iszero(M.dv)
isone(M::SymTridiagonal) =  iszero(_evview(M)) && all(isone, M.dv)
isdiag(M::SymTridiagonal) =  iszero(_evview(M))


function tril!(M::SymTridiagonal{T}, k::Integer=0) where T
    n = length(M.dv)
    if !(-n - 1 <= k <= n - 1)
        throw(ArgumentError(string("the requested diagonal, $k, must be at least ",
            "$(-n - 1) and at most $(n - 1) in an $n-by-$n matrix")))
    elseif k < -1
        fill!(M.ev, zero(T))
        fill!(M.dv, zero(T))
        return Tridiagonal(M.ev,M.dv,copy(M.ev))
    elseif k == -1
        fill!(M.dv, zero(T))
        return Tridiagonal(M.ev,M.dv,zero(M.ev))
    elseif k == 0
        return Tridiagonal(M.ev,M.dv,zero(M.ev))
    elseif k >= 1
        return Tridiagonal(M.ev,M.dv,copy(M.ev))
    end
end

function triu!(M::SymTridiagonal{T}, k::Integer=0) where T
    n = length(M.dv)
    if !(-n + 1 <= k <= n + 1)
        throw(ArgumentError(string("the requested diagonal, $k, must be at least ",
            "$(-n + 1) and at most $(n + 1) in an $n-by-$n matrix")))
    elseif k > 1
        fill!(M.ev, zero(T))
        fill!(M.dv, zero(T))
        return Tridiagonal(M.ev,M.dv,copy(M.ev))
    elseif k == 1
        fill!(M.dv, zero(T))
        return Tridiagonal(zero(M.ev),M.dv,M.ev)
    elseif k == 0
        return Tridiagonal(zero(M.ev),M.dv,M.ev)
    elseif k <= -1
        return Tridiagonal(M.ev,M.dv,copy(M.ev))
    end
end

###################
# Generic methods #
###################

## structured matrix methods ##
function Base.replace_in_print_matrix(A::SymTridiagonal, i::Integer, j::Integer, s::AbstractString)
    i==j-1||i==j||i==j+1 ? s : Base.replace_with_centered_mark(s)
end

# Implements the determinant using principal minors
# a, b, c are assumed to be the subdiagonal, diagonal, and superdiagonal of
# a tridiagonal matrix.
#Reference:
#    R. Usmani, "Inversion of a tridiagonal Jacobi matrix",
#    Linear Algebra and its Applications 212-213 (1994), pp.413-414
#    doi:10.1016/0024-3795(94)90414-6
function det_usmani(a::V, b::V, c::V, shift::Number=0) where {T,V<:AbstractVector{T}}
    require_one_based_indexing(a, b, c)
    n = length(b)
    θa = oneunit(T)+zero(shift)
    if n == 0
        return θa
    end
    θb = b[1]+shift
    for i in 2:n
        θb, θa = (b[i]+shift)*θb - a[i-1]*c[i-1]*θa, θb
    end
    return θb
end

# det with optional diagonal shift for use with shifted Hessenberg factorizations
det(A::SymTridiagonal; shift::Number=false) = det_usmani(A.ev, A.dv, A.ev, shift)
logabsdet(A::SymTridiagonal; shift::Number=false) = logabsdet(ldlt(A; shift=shift))

@inline function Base.isassigned(A::SymTridiagonal, i::Int, j::Int)
    @boundscheck checkbounds(Bool, A, i, j) || return false
    if i == j
        return @inbounds isassigned(A.dv, i)
    elseif i == j + 1
        return @inbounds isassigned(A.ev, j)
    elseif i + 1 == j
        return @inbounds isassigned(A.ev, i)
    else
        return true
    end
end

@inline function getindex(A::SymTridiagonal{T}, i::Integer, j::Integer) where T
    @boundscheck checkbounds(A, i, j)
    if i == j
        return symmetric((@inbounds A.dv[i]), :U)::symmetric_type(eltype(A.dv))
    elseif i == j + 1
        return copy(transpose(@inbounds A.ev[j])) # materialized for type stability
    elseif i + 1 == j
        return @inbounds A.ev[i]
    else
        return zero(T)
    end
end

@inline function setindex!(A::SymTridiagonal, x, i::Integer, j::Integer)
    @boundscheck checkbounds(A, i, j)
    if i == j
        @inbounds A.dv[i] = x
    else
        throw(ArgumentError("cannot set off-diagonal entry ($i, $j)"))
    end
    return x
end

## Tridiagonal matrices ##
struct Tridiagonal{T,V<:AbstractVector{T}} <: AbstractMatrix{T}
    dl::V    # sub-diagonal
    d::V     # diagonal
    du::V    # sup-diagonal
    du2::V   # supsup-diagonal for pivoting in LU
    function Tridiagonal{T,V}(dl, d, du) where {T,V<:AbstractVector{T}}
        require_one_based_indexing(dl, d, du)
        n = length(d)
        if (length(dl) != n-1 || length(du) != n-1) && !(length(d) == 0 && length(dl) == 0 && length(du) == 0)
            throw(ArgumentError(string("cannot construct Tridiagonal from incompatible ",
                "lengths of subdiagonal, diagonal and superdiagonal: ",
                "($(length(dl)), $(length(d)), $(length(du)))")))
        end
        new{T,V}(dl, d, du)
    end
    # constructor used in lu!
    function Tridiagonal{T,V}(dl, d, du, du2) where {T,V<:AbstractVector{T}}
        require_one_based_indexing(dl, d, du, du2)
        # length checks?
        new{T,V}(dl, d, du, du2)
    end
end

"""
    Tridiagonal(dl::V, d::V, du::V) where V <: AbstractVector

Construct a tridiagonal matrix from the first subdiagonal, diagonal, and first superdiagonal,
respectively. The result is of type `Tridiagonal` and provides efficient specialized linear
solvers, but may be converted into a regular matrix with
[`convert(Array, _)`](@ref) (or `Array(_)` for short).
The lengths of `dl` and `du` must be one less than the length of `d`.

# Examples
```jldoctest
julia> dl = [1, 2, 3];

julia> du = [4, 5, 6];

julia> d = [7, 8, 9, 0];

julia> Tridiagonal(dl, d, du)
4×4 Tridiagonal{Int64, Vector{Int64}}:
 7  4  ⋅  ⋅
 1  8  5  ⋅
 ⋅  2  9  6
 ⋅  ⋅  3  0
```
"""
Tridiagonal(dl::V, d::V, du::V) where {T,V<:AbstractVector{T}} = Tridiagonal{T,V}(dl, d, du)
Tridiagonal(dl::V, d::V, du::V, du2::V) where {T,V<:AbstractVector{T}} = Tridiagonal{T,V}(dl, d, du, du2)
function Tridiagonal{T}(dl::AbstractVector, d::AbstractVector, du::AbstractVector) where {T}
    Tridiagonal(map(x->convert(AbstractVector{T}, x), (dl, d, du))...)
end
function Tridiagonal{T,V}(A::Tridiagonal) where {T,V<:AbstractVector{T}}
    Tridiagonal{T,V}(A.dl, A.d, A.du)
end

"""
    Tridiagonal(A)

Construct a tridiagonal matrix from the first sub-diagonal,
diagonal and first super-diagonal of the matrix `A`.

# Examples
```jldoctest
julia> A = [1 2 3 4; 1 2 3 4; 1 2 3 4; 1 2 3 4]
4×4 Matrix{Int64}:
 1  2  3  4
 1  2  3  4
 1  2  3  4
 1  2  3  4

julia> Tridiagonal(A)
4×4 Tridiagonal{Int64, Vector{Int64}}:
 1  2  ⋅  ⋅
 1  2  3  ⋅
 ⋅  2  3  4
 ⋅  ⋅  3  4
```
"""
Tridiagonal(A::AbstractMatrix) = Tridiagonal(diag(A,-1), diag(A,0), diag(A,1))

Tridiagonal(A::Tridiagonal) = A
Tridiagonal{T}(A::Tridiagonal{T}) where {T} = A
function Tridiagonal{T}(A::Tridiagonal) where {T}
    dl, d, du = map(x->convert(AbstractVector{T}, x)::AbstractVector{T},
                    (A.dl, A.d, A.du))
    if isdefined(A, :du2)
        Tridiagonal(dl, d, du, convert(AbstractVector{T}, A.du2)::AbstractVector{T})
    else
        Tridiagonal(dl, d, du)
    end
end

size(M::Tridiagonal) = (length(M.d), length(M.d))
function size(M::Tridiagonal, d::Integer)
    if d < 1
        throw(ArgumentError("dimension d must be ≥ 1, got $d"))
    elseif d <= 2
        return length(M.d)
    else
        return 1
    end
end

function Matrix{T}(M::Tridiagonal) where {T}
    A = Matrix{T}(undef, size(M))
    n = length(M.d)
    n == 0 && return A
    n > 2 && fill!(A, zero(T))
    for i in 1:n-1
        A[i,i] = M.d[i]
        A[i+1,i] = M.dl[i]
        A[i,i+1] = M.du[i]
    end
    A[n,n] = M.d[n]
    A
end
Matrix(M::Tridiagonal{T}) where {T} = Matrix{promote_type(T, typeof(zero(T)))}(M)
Array(M::Tridiagonal) = Matrix(M)

similar(M::Tridiagonal, ::Type{T}) where {T} = Tridiagonal(similar(M.dl, T), similar(M.d, T), similar(M.du, T))
similar(M::Tridiagonal, ::Type{T}, dims::Union{Dims{1},Dims{2}}) where {T} = similar(M.d, T, dims)

# Operations on Tridiagonal matrices
copyto!(dest::Tridiagonal, src::Tridiagonal) = (copyto!(dest.dl, src.dl); copyto!(dest.d, src.d); copyto!(dest.du, src.du); dest)

#Elementary operations
for func in (:conj, :copy, :real, :imag)
    @eval function ($func)(M::Tridiagonal)
        Tridiagonal(($func)(M.dl), ($func)(M.d), ($func)(M.du))
    end
end

adjoint(S::Tridiagonal) = Adjoint(S)
transpose(S::Tridiagonal) = Transpose(S)
adjoint(S::Tridiagonal{<:Real}) = Tridiagonal(S.du, S.d, S.dl)
transpose(S::Tridiagonal{<:Number}) = Tridiagonal(S.du, S.d, S.dl)
permutedims(T::Tridiagonal) = Tridiagonal(T.du, T.d, T.dl)
function permutedims(T::Tridiagonal, perm)
    Base.checkdims_perm(T, T, perm)
    NTuple{2}(perm) == (2, 1) ? permutedims(T) : T
end
Base.copy(aS::Adjoint{<:Any,<:Tridiagonal}) = (S = aS.parent; Tridiagonal(map(x -> copy.(adjoint.(x)), (S.du, S.d, S.dl))...))
Base.copy(tS::Transpose{<:Any,<:Tridiagonal}) = (S = tS.parent; Tridiagonal(map(x -> copy.(transpose.(x)), (S.du, S.d, S.dl))...))

ishermitian(S::Tridiagonal) = all(ishermitian, S.d) && all(Iterators.map((x, y) -> x == y', S.du, S.dl))
issymmetric(S::Tridiagonal) = all(issymmetric, S.d) && all(Iterators.map((x, y) -> x == transpose(y), S.du, S.dl))

\(A::Adjoint{<:Any,<:Tridiagonal}, B::Adjoint{<:Any,<:AbstractVecOrMat}) = copy(A) \ B

function diag(M::Tridiagonal{T}, n::Integer=0) where T
    # every branch call similar(..., ::Int) to make sure the
    # same vector type is returned independent of n
    if n == 0
        return copyto!(similar(M.d, length(M.d)), M.d)
    elseif n == -1
        return copyto!(similar(M.dl, length(M.dl)), M.dl)
    elseif n == 1
        return copyto!(similar(M.du, length(M.du)), M.du)
    elseif abs(n) <= size(M,1)
        return fill!(similar(M.d, size(M,1)-abs(n)), zero(T))
    else
        throw(ArgumentError(string("requested diagonal, $n, must be at least $(-size(M, 1)) ",
            "and at most $(size(M, 2)) for an $(size(M, 1))-by-$(size(M, 2)) matrix")))
    end
end

@inline function Base.isassigned(A::Tridiagonal, i::Int, j::Int)
    @boundscheck checkbounds(Bool, A, i, j) || return false
    if i == j
        return @inbounds isassigned(A.d, i)
    elseif i == j + 1
        return @inbounds isassigned(A.dl, j)
    elseif i + 1 == j
        return @inbounds isassigned(A.du, i)
    else
        return true
    end
end

@inline function getindex(A::Tridiagonal{T}, i::Integer, j::Integer) where T
    @boundscheck checkbounds(A, i, j)
    if i == j
        return @inbounds A.d[i]
    elseif i == j + 1
        return @inbounds A.dl[j]
    elseif i + 1 == j
        return @inbounds A.du[i]
    else
        return zero(T)
    end
end

@inline function setindex!(A::Tridiagonal, x, i::Integer, j::Integer)
    @boundscheck checkbounds(A, i, j)
    if i == j
        @inbounds A.d[i] = x
    elseif i - j == 1
        @inbounds A.dl[j] = x
    elseif j - i == 1
        @inbounds A.du[i] = x
    elseif !iszero(x)
        throw(ArgumentError(string("cannot set entry ($i, $j) off ",
            "the tridiagonal band to a nonzero value ($x)")))
    end
    return x
end

## structured matrix methods ##
function Base.replace_in_print_matrix(A::Tridiagonal,i::Integer,j::Integer,s::AbstractString)
    i==j-1||i==j||i==j+1 ? s : Base.replace_with_centered_mark(s)
end


#tril and triu

iszero(M::Tridiagonal) = iszero(M.dl) && iszero(M.d) && iszero(M.du)
isone(M::Tridiagonal) = iszero(M.dl) && all(isone, M.d) && iszero(M.du)
function istriu(M::Tridiagonal, k::Integer=0)
    if k <= -1
        return true
    elseif k == 0
        return iszero(M.dl)
    elseif k == 1
        return iszero(M.dl) && iszero(M.d)
    else # k >= 2
        return iszero(M.dl) && iszero(M.d) && iszero(M.du)
    end
end
function istril(M::Tridiagonal, k::Integer=0)
    if k >= 1
        return true
    elseif k == 0
        return iszero(M.du)
    elseif k == -1
        return iszero(M.du) && iszero(M.d)
    else # k <= -2
        return iszero(M.du) && iszero(M.d) && iszero(M.dl)
    end
end
isdiag(M::Tridiagonal) = iszero(M.dl) && iszero(M.du)

function tril!(M::Tridiagonal{T}, k::Integer=0) where T
    n = length(M.d)
    if !(-n - 1 <= k <= n - 1)
        throw(ArgumentError(string("the requested diagonal, $k, must be at least ",
            "$(-n - 1) and at most $(n - 1) in an $n-by-$n matrix")))
    elseif k < -1
        fill!(M.dl, zero(T))
        fill!(M.d, zero(T))
        fill!(M.du, zero(T))
    elseif k == -1
        fill!(M.d, zero(T))
        fill!(M.du, zero(T))
    elseif k == 0
        fill!(M.du, zero(T))
    end
    return M
end

function triu!(M::Tridiagonal{T}, k::Integer=0) where T
    n = length(M.d)
    if !(-n + 1 <= k <= n + 1)
        throw(ArgumentError(string("the requested diagonal, $k, must be at least ",
            "$(-n + 1) and at most $(n + 1) in an $n-by-$n matrix")))
    elseif k > 1
        fill!(M.dl, zero(T))
        fill!(M.d, zero(T))
        fill!(M.du, zero(T))
    elseif k == 1
        fill!(M.dl, zero(T))
        fill!(M.d, zero(T))
    elseif k == 0
        fill!(M.dl, zero(T))
    end
    return M
end

tr(M::Tridiagonal) = sum(M.d)

###################
# Generic methods #
###################

+(A::Tridiagonal, B::Tridiagonal) = Tridiagonal(A.dl+B.dl, A.d+B.d, A.du+B.du)
-(A::Tridiagonal, B::Tridiagonal) = Tridiagonal(A.dl-B.dl, A.d-B.d, A.du-B.du)
-(A::Tridiagonal) = Tridiagonal(-A.dl, -A.d, -A.du)
*(A::Tridiagonal, B::Number) = Tridiagonal(A.dl*B, A.d*B, A.du*B)
*(B::Number, A::Tridiagonal) = Tridiagonal(B*A.dl, B*A.d, B*A.du)
/(A::Tridiagonal, B::Number) = Tridiagonal(A.dl/B, A.d/B, A.du/B)
\(B::Number, A::Tridiagonal) = Tridiagonal(B\A.dl, B\A.d, B\A.du)

==(A::Tridiagonal, B::Tridiagonal) = (A.dl==B.dl) && (A.d==B.d) && (A.du==B.du)
function ==(A::Tridiagonal, B::SymTridiagonal)
    iseq = all(Iterators.map((x, y) -> x == transpose(y), A.du, A.dl))
    iseq = iseq && A.du == _evview(B)
    iseq && all(Iterators.map((x, y) -> x == symmetric(y, :U), A.d, B.dv))
end
==(A::SymTridiagonal, B::Tridiagonal) = B == A

det(A::Tridiagonal) = det_usmani(A.dl, A.d, A.du)

AbstractMatrix{T}(M::Tridiagonal) where {T} = Tridiagonal{T}(M)
Tridiagonal{T}(M::SymTridiagonal{T}) where {T} = Tridiagonal(M)
function SymTridiagonal{T}(M::Tridiagonal) where T
    if issymmetric(M)
        return SymTridiagonal{T}(convert(AbstractVector{T},M.d), convert(AbstractVector{T},M.dl))
    else
        throw(ArgumentError("Tridiagonal is not symmetric, cannot convert to SymTridiagonal"))
    end
end

Base._sum(A::Tridiagonal, ::Colon) = sum(A.d) + sum(A.dl) + sum(A.du)
function Base._sum(A::SymTridiagonal, ::Colon)
    se = sum(_evview(A))
    symmetric(sum(A.dv), :U) + se + transpose(se)
end

function Base._sum(A::Tridiagonal, dims::Integer)
    res = Base.reducedim_initarray(A, dims, zero(eltype(A)))
    n = length(A.d)
    if n == 0
        return res
    elseif n == 1
        res[1] = A.d[1]
        return res
    end
    @inbounds begin
        if dims == 1
            res[1] = A.dl[1] + A.d[1]
            for i = 2:n-1
                res[i] = A.dl[i] + A.d[i] + A.du[i-1]
            end
            res[n] = A.d[n] + A.du[n-1]
        elseif dims == 2
            res[1] = A.d[1] + A.du[1]
            for i = 2:n-1
                res[i] = A.dl[i-1] + A.d[i] + A.du[i]
            end
            res[n] = A.dl[n-1] + A.d[n]
        elseif dims >= 3
            for i = 1:n-1
                res[i,i+1] = A.du[i]
                res[i,i]   = A.d[i]
                res[i+1,i] = A.dl[i]
            end
            res[n,n] = A.d[n]
        end
    end
    res
end

function Base._sum(A::SymTridiagonal, dims::Integer)
    res = Base.reducedim_initarray(A, dims, zero(eltype(A)))
    n = length(A.dv)
    if n == 0
        return res
    elseif n == 1
        res[1] = A.dv[1]
        return res
    end
    @inbounds begin
        if dims == 1
            res[1] = transpose(A.ev[1]) + symmetric(A.dv[1], :U)
            for i = 2:n-1
                res[i] = transpose(A.ev[i]) + symmetric(A.dv[i], :U) + A.ev[i-1]
            end
            res[n] = symmetric(A.dv[n], :U) + A.ev[n-1]
        elseif dims == 2
            res[1] = symmetric(A.dv[1], :U) + A.ev[1]
            for i = 2:n-1
                res[i] = transpose(A.ev[i-1]) + symmetric(A.dv[i], :U) + A.ev[i]
            end
            res[n] = transpose(A.ev[n-1]) + symmetric(A.dv[n], :U)
        elseif dims >= 3
            for i = 1:n-1
                res[i,i+1] = A.ev[i]
                res[i,i]   = symmetric(A.dv[i], :U)
                res[i+1,i] = transpose(A.ev[i])
            end
            res[n,n] = symmetric(A.dv[n], :U)
        end
    end
    res
end

function dot(x::AbstractVector, A::Tridiagonal, y::AbstractVector)
    require_one_based_indexing(x, y)
    nx, ny = length(x), length(y)
    (nx == size(A, 1) == ny) || throw(DimensionMismatch())
    if nx ≤ 1
        nx == 0 && return dot(zero(eltype(x)), zero(eltype(A)), zero(eltype(y)))
        return dot(x[1], A.d[1], y[1])
    end
    @inbounds begin
        x₀ = x[1]
        x₊ = x[2]
        dl, d, du = A.dl, A.d, A.du
        r = dot(adjoint(d[1])*x₀ + adjoint(dl[1])*x₊, y[1])
        for j in 2:nx-1
            x₋, x₀, x₊ = x₀, x₊, x[j+1]
            r += dot(adjoint(du[j-1])*x₋ + adjoint(d[j])*x₀ + adjoint(dl[j])*x₊, y[j])
        end
        r += dot(adjoint(du[nx-1])*x₀ + adjoint(d[nx])*x₊, y[nx])
    end
    return r
end

function cholesky(S::SymTridiagonal, ::NoPivot = NoPivot(); check::Bool = true)
    if !ishermitian(S)
        check && checkpositivedefinite(-1)
        return Cholesky(S, 'U', convert(BlasInt, -1))
    end
    T = choltype(eltype(S))
    cholesky!(Hermitian(Bidiagonal{T}(diag(S, 0), diag(S, 1), :U)), NoPivot(); check = check)
end
{   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LinearAlgebra/src/triangular.jl\     # This file is a part of Julia. License is MIT: https://julialang.org/license

## Triangular

# could be renamed to Triangular when that name has been fully deprecated
abstract type AbstractTriangular{T,S<:AbstractMatrix} <: AbstractMatrix{T} end

# First loop through all methods that don't need special care for upper/lower and unit diagonal
for t in (:LowerTriangular, :UnitLowerTriangular, :UpperTriangular,
          :UnitUpperTriangular)
    @eval begin
        struct $t{T,S<:AbstractMatrix{T}} <: AbstractTriangular{T,S}
            data::S

            function $t{T,S}(data) where {T,S<:AbstractMatrix{T}}
                require_one_based_indexing(data)
                checksquare(data)
                new{T,S}(data)
            end
        end
        $t(A::$t) = A
        $t{T}(A::$t{T}) where {T} = A
        function $t(A::AbstractMatrix)
            return $t{eltype(A), typeof(A)}(A)
        end
        function $t{T}(A::AbstractMatrix) where T
            $t(convert(AbstractMatrix{T}, A))
        end

        function $t{T}(A::$t) where T
            Anew = convert(AbstractMatrix{T}, A.data)
            $t(Anew)
        end
        Matrix(A::$t{T}) where {T} = Matrix{T}(A)

        AbstractMatrix{T}(A::$t) where {T} = $t{T}(A)

        size(A::$t, d) = size(A.data, d)
        size(A::$t) = size(A.data)

        # For A<:AbstractTriangular, similar(A[, neweltype]) should yield a matrix with the same
        # triangular type and underlying storage type as A. The following method covers these cases.
        similar(A::$t, ::Type{T}) where {T} = $t(similar(parent(A), T))
        # On the other hand, similar(A, [neweltype,] shape...) should yield a matrix of the underlying
        # storage type of A (not wrapped in a triangular type). The following method covers these cases.
        similar(A::$t, ::Type{T}, dims::Dims{N}) where {T,N} = similar(parent(A), T, dims)

        copy(A::$t) = $t(copy(A.data))

        real(A::$t{<:Real}) = A
        real(A::$t{<:Complex}) = (B = real(A.data); $t(B))
    end
end

similar(A::UpperTriangular{<:Any,<:Union{Adjoint{Ti}, Transpose{Ti}}}, ::Type{T}) where {T,Ti} =
    UpperTriangular(similar(parent(parent(A)), T))
similar(A::UnitUpperTriangular{<:Any,<:Union{Adjoint{Ti}, Transpose{Ti}}}, ::Type{T}) where {T,Ti} =
    UnitUpperTriangular(similar(parent(parent(A)), T))
similar(A::LowerTriangular{<:Any,<:Union{Adjoint{Ti}, Transpose{Ti}}}, ::Type{T}) where {T,Ti} =
    LowerTriangular(similar(parent(parent(A)), T))
similar(A::UnitLowerTriangular{<:Any,<:Union{Adjoint{Ti}, Transpose{Ti}}}, ::Type{T}) where {T,Ti} =
    UnitLowerTriangular(similar(parent(parent(A)), T))


"""
    LowerTriangular(A::AbstractMatrix)

Construct a `LowerTriangular` view of the matrix `A`.

# Examples
```jldoctest
julia> A = [1.0 2.0 3.0; 4.0 5.0 6.0; 7.0 8.0 9.0]
3×3 Matrix{Float64}:
 1.0  2.0  3.0
 4.0  5.0  6.0
 7.0  8.0  9.0

julia> LowerTriangular(A)
3×3 LowerTriangular{Float64, Matrix{Float64}}:
 1.0   ⋅    ⋅
 4.0  5.0   ⋅
 7.0  8.0  9.0
```
"""
LowerTriangular
"""
    UpperTriangular(A::AbstractMatrix)

Construct an `UpperTriangular` view of the matrix `A`.

# Examples
```jldoctest
julia> A = [1.0 2.0 3.0; 4.0 5.0 6.0; 7.0 8.0 9.0]
3×3 Matrix{Float64}:
 1.0  2.0  3.0
 4.0  5.0  6.0
 7.0  8.0  9.0

julia> UpperTriangular(A)
3×3 UpperTriangular{Float64, Matrix{Float64}}:
 1.0  2.0  3.0
  ⋅   5.0  6.0
  ⋅    ⋅   9.0
```
"""
UpperTriangular
"""
    UnitLowerTriangular(A::AbstractMatrix)

Construct a `UnitLowerTriangular` view of the matrix `A`.
Such a view has the [`oneunit`](@ref) of the [`eltype`](@ref)
of `A` on its diagonal.

# Examples
```jldoctest
julia> A = [1.0 2.0 3.0; 4.0 5.0 6.0; 7.0 8.0 9.0]
3×3 Matrix{Float64}:
 1.0  2.0  3.0
 4.0  5.0  6.0
 7.0  8.0  9.0

julia> UnitLowerTriangular(A)
3×3 UnitLowerTriangular{Float64, Matrix{Float64}}:
 1.0   ⋅    ⋅
 4.0  1.0   ⋅
 7.0  8.0  1.0
```
"""
UnitLowerTriangular
"""
    UnitUpperTriangular(A::AbstractMatrix)

Construct an `UnitUpperTriangular` view of the matrix `A`.
Such a view has the [`oneunit`](@ref) of the [`eltype`](@ref)
of `A` on its diagonal.

# Examples
```jldoctest
julia> A = [1.0 2.0 3.0; 4.0 5.0 6.0; 7.0 8.0 9.0]
3×3 Matrix{Float64}:
 1.0  2.0  3.0
 4.0  5.0  6.0
 7.0  8.0  9.0

julia> UnitUpperTriangular(A)
3×3 UnitUpperTriangular{Float64, Matrix{Float64}}:
 1.0  2.0  3.0
  ⋅   1.0  6.0
  ⋅    ⋅   1.0
```
"""
UnitUpperTriangular

const UpperOrUnitUpperTriangular{T,S} = Union{UpperTriangular{T,S}, UnitUpperTriangular{T,S}}
const LowerOrUnitLowerTriangular{T,S} = Union{LowerTriangular{T,S}, UnitLowerTriangular{T,S}}
const UpperOrLowerTriangular{T,S} = Union{UpperOrUnitUpperTriangular{T,S}, LowerOrUnitLowerTriangular{T,S}}

imag(A::UpperTriangular) = UpperTriangular(imag(A.data))
imag(A::LowerTriangular) = LowerTriangular(imag(A.data))
imag(A::UnitLowerTriangular) = LowerTriangular(tril!(imag(A.data),-1))
imag(A::UnitUpperTriangular) = UpperTriangular(triu!(imag(A.data),1))

Array(A::AbstractTriangular) = Matrix(A)
parent(A::UpperOrLowerTriangular) = A.data

# then handle all methods that requires specific handling of upper/lower and unit diagonal

function Matrix{T}(A::LowerTriangular) where T
    B = Matrix{T}(undef, size(A, 1), size(A, 1))
    copyto!(B, A.data)
    tril!(B)
    B
end
function Matrix{T}(A::UnitLowerTriangular) where T
    B = Matrix{T}(undef, size(A, 1), size(A, 1))
    copyto!(B, A.data)
    tril!(B)
    for i = 1:size(B,1)
        B[i,i] = oneunit(T)
    end
    B
end
function Matrix{T}(A::UpperTriangular) where T
    B = Matrix{T}(undef, size(A, 1), size(A, 1))
    copyto!(B, A.data)
    triu!(B)
    B
end
function Matrix{T}(A::UnitUpperTriangular) where T
    B = Matrix{T}(undef, size(A, 1), size(A, 1))
    copyto!(B, A.data)
    triu!(B)
    for i = 1:size(B,1)
        B[i,i] = oneunit(T)
    end
    B
end

function full!(A::LowerTriangular)
    B = A.data
    tril!(B)
    B
end
function full!(A::UnitLowerTriangular)
    B = A.data
    tril!(B)
    for i = 1:size(A,1)
        B[i,i] = oneunit(eltype(B))
    end
    B
end
function full!(A::UpperTriangular)
    B = A.data
    triu!(B)
    B
end
function full!(A::UnitUpperTriangular)
    B = A.data
    triu!(B)
    for i = 1:size(A,1)
        B[i,i] = oneunit(eltype(B))
    end
    B
end

Base.isassigned(A::UnitLowerTriangular, i::Int, j::Int) =
    i > j ? isassigned(A.data, i, j) : true
Base.isassigned(A::LowerTriangular, i::Int, j::Int) =
    i >= j ? isassigned(A.data, i, j) : true
Base.isassigned(A::UnitUpperTriangular, i::Int, j::Int) =
    i < j ? isassigned(A.data, i, j) : true
Base.isassigned(A::UpperTriangular, i::Int, j::Int) =
    i <= j ? isassigned(A.data, i, j) : true

getindex(A::UnitLowerTriangular{T}, i::Integer, j::Integer) where {T} =
    i > j ? A.data[i,j] : ifelse(i == j, oneunit(T), zero(T))
getindex(A::LowerTriangular, i::Integer, j::Integer) =
    i >= j ? A.data[i,j] : zero(A.data[j,i])
getindex(A::UnitUpperTriangular{T}, i::Integer, j::Integer) where {T} =
    i < j ? A.data[i,j] : ifelse(i == j, oneunit(T), zero(T))
getindex(A::UpperTriangular, i::Integer, j::Integer) =
    i <= j ? A.data[i,j] : zero(A.data[j,i])

function setindex!(A::UpperTriangular, x, i::Integer, j::Integer)
    if i > j
        iszero(x) || throw(ArgumentError("cannot set index in the lower triangular part " *
            "($i, $j) of an UpperTriangular matrix to a nonzero value ($x)"))
    else
        A.data[i,j] = x
    end
    return A
end

function setindex!(A::UnitUpperTriangular, x, i::Integer, j::Integer)
    if i > j
        iszero(x) || throw(ArgumentError("cannot set index in the lower triangular part " *
            "($i, $j) of a UnitUpperTriangular matrix to a nonzero value ($x)"))
    elseif i == j
        x == oneunit(x) || throw(ArgumentError("cannot set index on the diagonal ($i, $j) " *
            "of a UnitUpperTriangular matrix to a non-unit value ($x)"))
    else
        A.data[i,j] = x
    end
    return A
end

function setindex!(A::LowerTriangular, x, i::Integer, j::Integer)
    if i < j
        iszero(x) || throw(ArgumentError("cannot set index in the upper triangular part " *
            "($i, $j) of a LowerTriangular matrix to a nonzero value ($x)"))
    else
        A.data[i,j] = x
    end
    return A
end

function setindex!(A::UnitLowerTriangular, x, i::Integer, j::Integer)
    if i < j
        iszero(x) || throw(ArgumentError("cannot set index in the upper triangular part " *
            "($i, $j) of a UnitLowerTriangular matrix to a nonzero value ($x)"))
    elseif i == j
        x == oneunit(x) || throw(ArgumentError("cannot set index on the diagonal ($i, $j) " *
            "of a UnitLowerTriangular matrix to a non-unit value ($x)"))
    else
        A.data[i,j] = x
    end
    return A
end


## structured matrix methods ##
function Base.replace_in_print_matrix(A::Union{UpperTriangular,UnitUpperTriangular},
                                      i::Integer, j::Integer, s::AbstractString)
    return i <= j ? s : Base.replace_with_centered_mark(s)
end
function Base.replace_in_print_matrix(A::Union{LowerTriangular,UnitLowerTriangular},
                                      i::Integer, j::Integer, s::AbstractString)
    return i >= j ? s : Base.replace_with_centered_mark(s)
end

function istril(A::Union{LowerTriangular,UnitLowerTriangular}, k::Integer=0)
    k >= 0 && return true
    return _istril(A, k)
end
function istriu(A::Union{UpperTriangular,UnitUpperTriangular}, k::Integer=0)
    k <= 0 && return true
    return _istriu(A, k)
end
istril(A::Adjoint, k::Integer=0) = istriu(A.parent, -k)
istril(A::Transpose, k::Integer=0) = istriu(A.parent, -k)
istriu(A::Adjoint, k::Integer=0) = istril(A.parent, -k)
istriu(A::Transpose, k::Integer=0) = istril(A.parent, -k)

function tril!(A::UpperTriangular{T}, k::Integer=0) where {T}
    n = size(A,1)
    if k < 0
        fill!(A.data, zero(T))
        return A
    elseif k == 0
        for j in 1:n, i in 1:j-1
            A.data[i,j] = zero(T)
        end
        return A
    else
        return UpperTriangular(tril!(A.data,k))
    end
end
triu!(A::UpperTriangular, k::Integer=0) = UpperTriangular(triu!(A.data, k))

function tril!(A::UnitUpperTriangular{T}, k::Integer=0) where {T}
    n = size(A,1)
    if k < 0
        fill!(A.data, zero(T))
        return UpperTriangular(A.data)
    elseif k == 0
        fill!(A.data, zero(T))
        for i in diagind(A)
            A.data[i] = oneunit(T)
        end
        return UpperTriangular(A.data)
    else
        for i in diagind(A)
            A.data[i] = oneunit(T)
        end
        return UpperTriangular(tril!(A.data,k))
    end
end

function triu!(A::UnitUpperTriangular, k::Integer=0)
    for i in diagind(A)
        A.data[i] = oneunit(eltype(A))
    end
    return triu!(UpperTriangular(A.data), k)
end

function triu!(A::LowerTriangular{T}, k::Integer=0) where {T}
    n = size(A,1)
    if k > 0
        fill!(A.data, zero(T))
        return A
    elseif k == 0
        for j in 1:n, i in j+1:n
            A.data[i,j] = zero(T)
        end
        return A
    else
        return LowerTriangular(triu!(A.data, k))
    end
end

tril!(A::LowerTriangular, k::Integer=0) = LowerTriangular(tril!(A.data, k))

function triu!(A::UnitLowerTriangular{T}, k::Integer=0) where T
    n = size(A,1)
    if k > 0
        fill!(A.data, zero(T))
        return LowerTriangular(A.data)
    elseif k == 0
        fill!(A.data, zero(T))
        for i in diagind(A)
            A.data[i] = oneunit(T)
        end
        return LowerTriangular(A.data)
    else
        for i in diagind(A)
            A.data[i] = oneunit(T)
        end
        return LowerTriangular(triu!(A.data, k))
    end
end

function tril!(A::UnitLowerTriangular, k::Integer=0)
    for i in diagind(A)
        A.data[i] = oneunit(eltype(A))
    end
    return tril!(LowerTriangular(A.data), k)
end

adjoint(A::LowerTriangular) = UpperTriangular(adjoint(A.data))
adjoint(A::UpperTriangular) = LowerTriangular(adjoint(A.data))
adjoint(A::UnitLowerTriangular) = UnitUpperTriangular(adjoint(A.data))
adjoint(A::UnitUpperTriangular) = UnitLowerTriangular(adjoint(A.data))
transpose(A::LowerTriangular) = UpperTriangular(transpose(A.data))
transpose(A::UpperTriangular) = LowerTriangular(transpose(A.data))
transpose(A::UnitLowerTriangular) = UnitUpperTriangular(transpose(A.data))
transpose(A::UnitUpperTriangular) = UnitLowerTriangular(transpose(A.data))

transpose!(A::LowerTriangular) = UpperTriangular(copytri!(A.data, 'L', false, true))
transpose!(A::UnitLowerTriangular) = UnitUpperTriangular(copytri!(A.data, 'L', false, false))
transpose!(A::UpperTriangular) = LowerTriangular(copytri!(A.data, 'U', false, true))
transpose!(A::UnitUpperTriangular) = UnitLowerTriangular(copytri!(A.data, 'U', false, false))
adjoint!(A::LowerTriangular) = UpperTriangular(copytri!(A.data, 'L' , true, true))
adjoint!(A::UnitLowerTriangular) = UnitUpperTriangular(copytri!(A.data, 'L' , true, false))
adjoint!(A::UpperTriangular) = LowerTriangular(copytri!(A.data, 'U' , true, true))
adjoint!(A::UnitUpperTriangular) = UnitLowerTriangular(copytri!(A.data, 'U' , true, false))

diag(A::LowerTriangular) = diag(A.data)
diag(A::UnitLowerTriangular) = fill(oneunit(eltype(A)), size(A,1))
diag(A::UpperTriangular) = diag(A.data)
diag(A::UnitUpperTriangular) = fill(oneunit(eltype(A)), size(A,1))

# Unary operations
-(A::LowerTriangular) = LowerTriangular(-A.data)
-(A::UpperTriangular) = UpperTriangular(-A.data)
function -(A::UnitLowerTriangular)
    Anew = -A.data
    for i = 1:size(A, 1)
        Anew[i, i] = -A[i, i]
    end
    LowerTriangular(Anew)
end
function -(A::UnitUpperTriangular)
    Anew = -A.data
    for i = 1:size(A, 1)
        Anew[i, i] = -A[i, i]
    end
    UpperTriangular(Anew)
end

tr(A::LowerTriangular) = tr(A.data)
tr(A::UnitLowerTriangular) = size(A, 1) * oneunit(eltype(A))
tr(A::UpperTriangular) = tr(A.data)
tr(A::UnitUpperTriangular) = size(A, 1) * oneunit(eltype(A))

# copy and scale
function copyto!(A::T, B::T) where {T<:Union{UpperTriangular,UnitUpperTriangular}}
    n = size(B,1)
    for j = 1:n
        for i = 1:(isa(B, UnitUpperTriangular) ? j-1 : j)
            @inbounds A[i,j] = B[i,j]
        end
    end
    return A
end
function copyto!(A::T, B::T) where {T<:Union{LowerTriangular,UnitLowerTriangular}}
    n = size(B,1)
    for j = 1:n
        for i = (isa(B, UnitLowerTriangular) ? j+1 : j):n
            @inbounds A[i,j] = B[i,j]
        end
    end
    return A
end

# Define `mul!` for (Unit){Upper,Lower}Triangular matrices times a number.
# be permissive here and require compatibility later in _triscale!
@inline mul!(A::AbstractTriangular, B::AbstractTriangular, C::Number, alpha::Number, beta::Number) =
    _triscale!(A, B, C, MulAddMul(alpha, beta))
@inline mul!(A::AbstractTriangular, B::Number, C::AbstractTriangular, alpha::Number, beta::Number) =
    _triscale!(A, B, C, MulAddMul(alpha, beta))

function _triscale!(A::UpperTriangular, B::UpperTriangular, c::Number, _add)
    n = checksquare(B)
    iszero(_add.alpha) && return _rmul_or_fill!(A, _add.beta)
    for j = 1:n
        for i = 1:j
            @inbounds _modify!(_add, B.data[i,j] * c, A.data, (i,j))
        end
    end
    return A
end
function _triscale!(A::UpperTriangular, c::Number, B::UpperTriangular, _add)
    n = checksquare(B)
    iszero(_add.alpha) && return _rmul_or_fill!(A, _add.beta)
for j = 1:n
        for i = 1:j
            @inbounds _modify!(_add, c * B.data[i,j], A.data, (i,j))
        end
    end
    return A
end
function _triscale!(A::UpperOrUnitUpperTriangular, B::UnitUpperTriangular, c::Number, _add)
    n = checksquare(B)
    iszero(_add.alpha) && return _rmul_or_fill!(A, _add.beta)
    for j = 1:n
        @inbounds _modify!(_add, c, A, (j,j))
        for i = 1:(j - 1)
            @inbounds _modify!(_add, B.data[i,j] * c, A.data, (i,j))
        end
    end
    return A
end
function _triscale!(A::UpperOrUnitUpperTriangular, c::Number, B::UnitUpperTriangular, _add)
    n = checksquare(B)
    iszero(_add.alpha) && return _rmul_or_fill!(A, _add.beta)
    for j = 1:n
        @inbounds _modify!(_add, c, A, (j,j))
        for i = 1:(j - 1)
            @inbounds _modify!(_add, c * B.data[i,j], A.data, (i,j))
        end
    end
    return A
end
function _triscale!(A::LowerTriangular, B::LowerTriangular, c::Number, _add)
    n = checksquare(B)
    iszero(_add.alpha) && return _rmul_or_fill!(A, _add.beta)
    for j = 1:n
        for i = j:n
            @inbounds _modify!(_add, B.data[i,j] * c, A.data, (i,j))
        end
    end
    return A
end
function _triscale!(A::LowerTriangular, c::Number, B::LowerTriangular, _add)
    n = checksquare(B)
    iszero(_add.alpha) && return _rmul_or_fill!(A, _add.beta)
   for j = 1:n
        for i = j:n
            @inbounds _modify!(_add, c * B.data[i,j], A.data, (i,j))
        end
    end
    return A
end
function _triscale!(A::LowerOrUnitLowerTriangular, B::UnitLowerTriangular, c::Number, _add)
    n = checksquare(B)
    iszero(_add.alpha) && return _rmul_or_fill!(A, _add.beta)
    for j = 1:n
        @inbounds _modify!(_add, c, A, (j,j))
        for i = (j + 1):n
            @inbounds _modify!(_add, B.data[i,j] * c, A.data, (i,j))
        end
    end
    return A
end
function _triscale!(A::LowerOrUnitLowerTriangular, c::Number, B::UnitLowerTriangular, _add)
    n = checksquare(B)
    iszero(_add.alpha) && return _rmul_or_fill!(A, _add.beta)
    for j = 1:n
        @inbounds _modify!(_add, c, A, (j,j))
        for i = (j + 1):n
            @inbounds _modify!(_add, c * B.data[i,j], A.data, (i,j))
        end
    end
    return A
end

rmul!(A::UpperOrLowerTriangular, c::Number) = @inline _triscale!(A, A, c, MulAddMul())
lmul!(c::Number, A::UpperOrLowerTriangular) = @inline _triscale!(A, c, A, MulAddMul())

function dot(x::AbstractVector, A::UpperTriangular, y::AbstractVector)
    require_one_based_indexing(x, y)
    m = size(A, 1)
    (length(x) == m == length(y)) || throw(DimensionMismatch())
    if iszero(m)
        return dot(zero(eltype(x)), zero(eltype(A)), zero(eltype(y)))
    end
    x₁ = x[1]
    r = dot(x₁, A[1,1], y[1])
    @inbounds for j in 2:m
        yj = y[j]
        if !iszero(yj)
            temp = adjoint(A[1,j]) * x₁
            @simd for i in 2:j
                temp += adjoint(A[i,j]) * x[i]
            end
            r += dot(temp, yj)
        end
    end
    return r
end
function dot(x::AbstractVector, A::UnitUpperTriangular, y::AbstractVector)
    require_one_based_indexing(x, y)
    m = size(A, 1)
    (length(x) == m == length(y)) || throw(DimensionMismatch())
    if iszero(m)
        return dot(zero(eltype(x)), zero(eltype(A)), zero(eltype(y)))
    end
    x₁ = first(x)
    r = dot(x₁, y[1])
    @inbounds for j in 2:m
        yj = y[j]
        if !iszero(yj)
            temp = adjoint(A[1,j]) * x₁
            @simd for i in 2:j-1
                temp += adjoint(A[i,j]) * x[i]
            end
            r += dot(temp, yj)
            r += dot(x[j], yj)
        end
    end
    return r
end
function dot(x::AbstractVector, A::LowerTriangular, y::AbstractVector)
    require_one_based_indexing(x, y)
    m = size(A, 1)
    (length(x) == m == length(y)) || throw(DimensionMismatch())
    if iszero(m)
        return dot(zero(eltype(x)), zero(eltype(A)), zero(eltype(y)))
    end
    r = zero(typeof(dot(first(x), first(A), first(y))))
    @inbounds for j in 1:m
        yj = y[j]
        if !iszero(yj)
            temp = adjoint(A[j,j]) * x[j]
            @simd for i in j+1:m
                temp += adjoint(A[i,j]) * x[i]
            end
            r += dot(temp, yj)
        end
    end
    return r
end
function dot(x::AbstractVector, A::UnitLowerTriangular, y::AbstractVector)
    require_one_based_indexing(x, y)
    m = size(A, 1)
    (length(x) == m == length(y)) || throw(DimensionMismatch())
    if iszero(m)
        return dot(zero(eltype(x)), zero(eltype(A)), zero(eltype(y)))
    end
    r = zero(typeof(dot(first(x), first(y))))
    @inbounds for j in 1:m
        yj = y[j]
        if !iszero(yj)
            temp = x[j]
            @simd for i in j+1:m
                temp += adjoint(A[i,j]) * x[i]
            end
            r += dot(temp, yj)
        end
    end
    return r
end

fillstored!(A::LowerTriangular, x)     = (fillband!(A.data, x, 1-size(A,1), 0); A)
fillstored!(A::UnitLowerTriangular, x) = (fillband!(A.data, x, 1-size(A,1), -1); A)
fillstored!(A::UpperTriangular, x)     = (fillband!(A.data, x, 0, size(A,2)-1); A)
fillstored!(A::UnitUpperTriangular, x) = (fillband!(A.data, x, 1, size(A,2)-1); A)

# Binary operations
+(A::UpperTriangular, B::UpperTriangular) = UpperTriangular(A.data + B.data)
+(A::LowerTriangular, B::LowerTriangular) = LowerTriangular(A.data + B.data)
+(A::UpperTriangular, B::UnitUpperTriangular) = UpperTriangular(A.data + triu(B.data, 1) + I)
+(A::LowerTriangular, B::UnitLowerTriangular) = LowerTriangular(A.data + tril(B.data, -1) + I)
+(A::UnitUpperTriangular, B::UpperTriangular) = UpperTriangular(triu(A.data, 1) + B.data + I)
+(A::UnitLowerTriangular, B::LowerTriangular) = LowerTriangular(tril(A.data, -1) + B.data + I)
+(A::UnitUpperTriangular, B::UnitUpperTriangular) = UpperTriangular(triu(A.data, 1) + triu(B.data, 1) + 2I)
+(A::UnitLowerTriangular, B::UnitLowerTriangular) = LowerTriangular(tril(A.data, -1) + tril(B.data, -1) + 2I)
+(A::AbstractTriangular, B::AbstractTriangular) = copyto!(similar(parent(A)), A) + copyto!(similar(parent(B)), B)

-(A::UpperTriangular, B::UpperTriangular) = UpperTriangular(A.data - B.data)
-(A::LowerTriangular, B::LowerTriangular) = LowerTriangular(A.data - B.data)
-(A::UpperTriangular, B::UnitUpperTriangular) = UpperTriangular(A.data - triu(B.data, 1) - I)
-(A::LowerTriangular, B::UnitLowerTriangular) = LowerTriangular(A.data - tril(B.data, -1) - I)
-(A::UnitUpperTriangular, B::UpperTriangular) = UpperTriangular(triu(A.data, 1) - B.data + I)
-(A::UnitLowerTriangular, B::LowerTriangular) = LowerTriangular(tril(A.data, -1) - B.data + I)
-(A::UnitUpperTriangular, B::UnitUpperTriangular) = UpperTriangular(triu(A.data, 1) - triu(B.data, 1))
-(A::UnitLowerTriangular, B::UnitLowerTriangular) = LowerTriangular(tril(A.data, -1) - tril(B.data, -1))
-(A::AbstractTriangular, B::AbstractTriangular) = copyto!(similar(parent(A)), A) - copyto!(similar(parent(B)), B)

######################
# BlasFloat routines #
######################

# which triangle to use of the underlying data
uplo_char(::UpperOrUnitUpperTriangular) = 'U'
uplo_char(::LowerOrUnitLowerTriangular) = 'L'
uplo_char(::UpperOrUnitUpperTriangular{<:Any,<:AdjOrTrans}) = 'L'
uplo_char(::LowerOrUnitLowerTriangular{<:Any,<:AdjOrTrans}) = 'U'
uplo_char(::UpperOrUnitUpperTriangular{<:Any,<:Adjoint{<:Any,<:Transpose}}) = 'U'
uplo_char(::LowerOrUnitLowerTriangular{<:Any,<:Adjoint{<:Any,<:Transpose}}) = 'L'
uplo_char(::UpperOrUnitUpperTriangular{<:Any,<:Transpose{<:Any,<:Adjoint}}) = 'U'
uplo_char(::LowerOrUnitLowerTriangular{<:Any,<:Transpose{<:Any,<:Adjoint}}) = 'L'

isunit_char(::UpperTriangular) = 'N'
isunit_char(::UnitUpperTriangular) = 'U'
isunit_char(::LowerTriangular) = 'N'
isunit_char(::UnitLowerTriangular) = 'U'

lmul!(A::Tridiagonal, B::AbstractTriangular) = A*full!(B)
mul!(C::AbstractVecOrMat, A::AbstractTriangular, B::AbstractVector) = _trimul!(C, A, B)
mul!(C::AbstractMatrix, A::AbstractTriangular, B::AbstractMatrix) = _trimul!(C, A, B)
mul!(C::AbstractMatrix, A::AbstractMatrix, B::AbstractTriangular) = _trimul!(C, A, B)
mul!(C::AbstractMatrix, A::AbstractTriangular, B::AbstractTriangular) = _trimul!(C, A, B)

# generic fallback for AbstractTriangular matrices outside of the four subtypes provided here
_trimul!(C::AbstractVecOrMat, A::AbstractTriangular, B::AbstractVector) =
    lmul!(A, copyto!(C, B))
_trimul!(C::AbstractMatrix, A::AbstractTriangular, B::AbstractMatrix) =
    lmul!(A, inplace_adj_or_trans(B)(C, _unwrap_at(B)))
_trimul!(C::AbstractMatrix, A::AbstractMatrix, B::AbstractTriangular) =
    rmul!(inplace_adj_or_trans(A)(C, _unwrap_at(A)), B)
_trimul!(C::AbstractMatrix, A::AbstractTriangular, B::AbstractTriangular) =
    lmul!(A, copyto!(C, B))
# redirect for UpperOrLowerTriangular
_trimul!(C::AbstractVecOrMat, A::UpperOrLowerTriangular, B::AbstractVector) =
    generic_trimatmul!(C, uplo_char(A), isunit_char(A), wrapperop(parent(A)), _unwrap_at(parent(A)), B)
_trimul!(C::AbstractMatrix, A::UpperOrLowerTriangular, B::AbstractMatrix) =
    generic_trimatmul!(C, uplo_char(A), isunit_char(A), wrapperop(parent(A)), _unwrap_at(parent(A)), B)
_trimul!(C::AbstractMatrix, A::AbstractMatrix, B::UpperOrLowerTriangular) =
    generic_mattrimul!(C, uplo_char(B), isunit_char(B), wrapperop(parent(B)), A, _unwrap_at(parent(B)))
_trimul!(C::AbstractMatrix, A::UpperOrLowerTriangular, B::UpperOrLowerTriangular) =
    generic_trimatmul!(C, uplo_char(A), isunit_char(A), wrapperop(parent(A)), _unwrap_at(parent(A)), B)
# disambiguation with AbstractTriangular
_trimul!(C::AbstractMatrix, A::UpperOrLowerTriangular, B::AbstractTriangular) =
    generic_trimatmul!(C, uplo_char(A), isunit_char(A), wrapperop(parent(A)), _unwrap_at(parent(A)), B)
_trimul!(C::AbstractMatrix, A::AbstractTriangular, B::UpperOrLowerTriangular) =
    generic_mattrimul!(C, uplo_char(B), isunit_char(B), wrapperop(parent(B)), A, _unwrap_at(parent(B)))

lmul!(A::AbstractTriangular, B::AbstractVecOrMat) = @inline _trimul!(B, A, B)
rmul!(A::AbstractMatrix, B::AbstractTriangular)   = @inline _trimul!(A, A, B)


for TC in (:AbstractVector, :AbstractMatrix)
    @eval @inline function mul!(C::$TC, A::AbstractTriangular, B::AbstractVector, alpha::Number, beta::Number)
        if isone(alpha) && iszero(beta)
            return mul!(C, A, B)
        else
            return generic_matvecmul!(C, 'N', A, B, MulAddMul(alpha, beta))
        end
    end
end
for (TA, TB) in ((:AbstractTriangular, :AbstractMatrix),
                    (:AbstractMatrix, :AbstractTriangular),
                    (:AbstractTriangular, :AbstractTriangular)
                )
    @eval @inline function mul!(C::AbstractMatrix, A::$TA, B::$TB, alpha::Number, beta::Number)
        if isone(alpha) && iszero(beta)
            return mul!(C, A, B)
        else
            return generic_matmatmul!(C, 'N', 'N', A, B, MulAddMul(alpha, beta))
        end
    end
end

ldiv!(C::AbstractVecOrMat, A::AbstractTriangular, B::AbstractVecOrMat) = _ldiv!(C, A, B)
# generic fallback for AbstractTriangular, directs to 2-arg [l/r]div!
_ldiv!(C::AbstractVecOrMat, A::AbstractTriangular, B::AbstractVecOrMat) =
    ldiv!(A, inplace_adj_or_trans(B)(C, _unwrap_at(B)))
_rdiv!(C::AbstractMatrix, A::AbstractMatrix, B::AbstractTriangular) =
    rdiv!(inplace_adj_or_trans(A)(C, _unwrap_at(A)), B)
# redirect for UpperOrLowerTriangular to generic_*div!
_ldiv!(C::AbstractVecOrMat, A::UpperOrLowerTriangular, B::AbstractVecOrMat) =
    generic_trimatdiv!(C, uplo_char(A), isunit_char(A), wrapperop(parent(A)), _unwrap_at(parent(A)), B)
_rdiv!(C::AbstractMatrix, A::AbstractMatrix, B::UpperOrLowerTriangular) =
    generic_mattridiv!(C, uplo_char(B), isunit_char(B), wrapperop(parent(B)), A, _unwrap_at(parent(B)))

ldiv!(A::AbstractTriangular, B::AbstractVecOrMat) = @inline _ldiv!(B, A, B)
rdiv!(A::AbstractMatrix, B::AbstractTriangular)   = @inline _rdiv!(A, A, B)

# preserve triangular structure in in-place multiplication/division
for (cty, aty, bty) in ((:UpperTriangular, :UpperTriangular, :UpperTriangular),
                        (:UpperTriangular, :UpperTriangular, :UnitUpperTriangular),
                        (:UpperTriangular, :UnitUpperTriangular, :UpperTriangular),
                        (:UnitUpperTriangular, :UnitUpperTriangular, :UnitUpperTriangular),
                        (:LowerTriangular, :LowerTriangular, :LowerTriangular),
                        (:LowerTriangular, :LowerTriangular, :UnitLowerTriangular),
                        (:LowerTriangular, :UnitLowerTriangular, :LowerTriangular),
                        (:UnitLowerTriangular, :UnitLowerTriangular, :UnitLowerTriangular))
    @eval begin
        function _trimul!(C::$cty, A::$aty, B::$bty)
            _trimul!(parent(C), A, B)
            return C
        end
        function _ldiv!(C::$cty, A::$aty, B::$bty)
            _ldiv!(parent(C), A, B)
            return C
        end
        function _rdiv!(C::$cty, A::$aty, B::$bty)
            _rdiv!(parent(C), A, B)
            return C
        end
    end
end

for (t, uploc, isunitc) in ((:LowerTriangular, 'L', 'N'),
                            (:UnitLowerTriangular, 'L', 'U'),
                            (:UpperTriangular, 'U', 'N'),
                            (:UnitUpperTriangular, 'U', 'U'))
    @eval begin
        # Matrix inverse
        inv!(A::$t{T,S}) where {T<:BlasFloat,S<:StridedMatrix} =
            $t{T,S}(LAPACK.trtri!($uploc, $isunitc, A.data))

        function inv(A::$t{T}) where {T}
            S = typeof(inv(oneunit(T)))
            if S <: BlasFloat || S === T # i.e. A is unitless
                $t(ldiv!(convert(AbstractArray{S}, A), Matrix{S}(I, size(A))))
            else
                J = (one(T)*I)(size(A, 1))
                $t(ldiv!(similar(A, S, size(A)), A, J))
            end
        end

        # Error bounds for triangular solve
        errorbounds(A::$t{T,<:StridedMatrix}, X::StridedVecOrMat{T}, B::StridedVecOrMat{T}) where {T<:BlasFloat} =
            LAPACK.trrfs!($uploc, 'N', $isunitc, A.data, B, X)

        # Condition numbers
        function cond(A::$t{<:BlasFloat,<:StridedMatrix}, p::Real=2)
            checksquare(A)
            if p == 1
                return inv(LAPACK.trcon!('O', $uploc, $isunitc, A.data))
            elseif p == Inf
                return inv(LAPACK.trcon!('I', $uploc, $isunitc, A.data))
            else # use fallback
                return cond(copyto!(similar(parent(A)), A), p)
            end
        end
    end
end

# multiplication
generic_trimatmul!(c::StridedVector{T}, uploc, isunitc, tfun::Function, A::StridedMatrix{T}, b::AbstractVector{T}) where {T<:BlasFloat} =
    BLAS.trmv!(uploc, tfun === identity ? 'N' : tfun === transpose ? 'T' : 'C', isunitc, A, c === b ? c : copyto!(c, b))
generic_trimatmul!(C::StridedMatrix{T}, uploc, isunitc, tfun::Function, A::StridedMatrix{T}, B::AbstractMatrix{T}) where {T<:BlasFloat} =
    BLAS.trmm!('L', uploc, tfun === identity ? 'N' : tfun === transpose ? 'T' : 'C', isunitc, one(T), A, C === B ? C : copyto!(C, B))
generic_mattrimul!(C::StridedMatrix{T}, uploc, isunitc, tfun::Function, A::AbstractMatrix{T}, B::StridedMatrix{T}) where {T<:BlasFloat} =
    BLAS.trmm!('R', uploc, tfun === identity ? 'N' : tfun === transpose ? 'T' : 'C', isunitc, one(T), B, C === A ? C : copyto!(C, A))
# division
generic_trimatdiv!(C::StridedVecOrMat{T}, uploc, isunitc, tfun::Function, A::StridedMatrix{T}, B::AbstractVecOrMat{T}) where {T<:BlasFloat} =
    LAPACK.trtrs!(uploc, tfun === identity ? 'N' : tfun === transpose ? 'T' : 'C', isunitc, A, C === B ? C : copyto!(C, B))
generic_mattridiv!(C::StridedMatrix{T}, uploc, isunitc, tfun::Function, A::AbstractMatrix{T}, B::StridedMatrix{T}) where {T<:BlasFloat} =
    BLAS.trsm!('R', uploc, tfun === identity ? 'N' : tfun === transpose ? 'T' : 'C', isunitc, one(T), B, C === A ? C : copyto!(C, A))

errorbounds(A::AbstractTriangular{T,<:AbstractMatrix}, X::AbstractVecOrMat{T}, B::AbstractVecOrMat{T}) where {T<:Union{BigFloat,Complex{BigFloat}}} =
    error("not implemented yet! Please submit a pull request.")
function errorbounds(A::AbstractTriangular{TA,<:AbstractMatrix}, X::AbstractVecOrMat{TX}, B::AbstractVecOrMat{TB}) where {TA<:Number,TX<:Number,TB<:Number}
    TAXB = promote_type(TA, TB, TX, Float32)
    errorbounds(convert(AbstractMatrix{TAXB}, A), convert(AbstractArray{TAXB}, X), convert(AbstractArray{TAXB}, B))
end

# Eigensystems
## Notice that trecv works for quasi-triangular matrices and therefore the lower sub diagonal must be zeroed before calling the subroutine
function eigvecs(A::UpperTriangular{<:BlasFloat,<:StridedMatrix})
    LAPACK.trevc!('R', 'A', BlasInt[], triu!(A.data))
end
function eigvecs(A::UnitUpperTriangular{<:BlasFloat,<:StridedMatrix})
    for i = 1:size(A, 1)
        A.data[i,i] = 1
    end
    LAPACK.trevc!('R', 'A', BlasInt[], triu!(A.data))
end
function eigvecs(A::LowerTriangular{<:BlasFloat,<:StridedMatrix})
    LAPACK.trevc!('L', 'A', BlasInt[], copy(tril!(A.data)'))
end
function eigvecs(A::UnitLowerTriangular{<:BlasFloat,<:StridedMatrix})
    for i = 1:size(A, 1)
        A.data[i,i] = 1
    end
    LAPACK.trevc!('L', 'A', BlasInt[], copy(tril!(A.data)'))
end

####################
# Generic routines #
####################

for (t, unitt) in ((UpperTriangular, UnitUpperTriangular),
                   (LowerTriangular, UnitLowerTriangular))
    @eval begin
        (*)(A::$t, x::Number) = $t(A.data*x)

        function (*)(A::$unitt, x::Number)
            B = A.data*x
            for i = 1:size(A, 1)
                B[i,i] = x
            end
            $t(B)
        end

        (*)(x::Number, A::$t) = $t(x*A.data)

        function (*)(x::Number, A::$unitt)
            B = x*A.data
            for i = 1:size(A, 1)
                B[i,i] = x
            end
            $t(B)
        end

        (/)(A::$t, x::Number) = $t(A.data/x)

        function (/)(A::$unitt, x::Number)
            B = A.data/x
            invx = inv(x)
            for i = 1:size(A, 1)
                B[i,i] = invx
            end
            $t(B)
        end

        (\)(x::Number, A::$t) = $t(x\A.data)

        function (\)(x::Number, A::$unitt)
            B = x\A.data
            invx = inv(x)
            for i = 1:size(A, 1)
                B[i,i] = invx
            end
            $t(B)
        end
    end
end

## Generic triangular multiplication
function generic_trimatmul!(C::AbstractVecOrMat, uploc, isunitc, tfun::Function, A::AbstractMatrix, B::AbstractVecOrMat)
    require_one_based_indexing(C, A, B)
    m, n = size(B, 1), size(B, 2)
    N = size(A, 1)
    if m != N
        throw(DimensionMismatch("right hand side B needs first dimension of size $(size(A,1)), has size $m"))
    end
    mc, nc = size(C, 1), size(C, 2)
    if mc != N || nc != n
        throw(DimensionMismatch("output has dimensions ($mc,$nc), should have ($N,$n)"))
    end
    oA = oneunit(eltype(A))
    unit = isunitc == 'U'
    @inbounds if uploc == 'U'
        if tfun === identity
            for j in 1:n
                for i in 1:m
                    Cij = (unit ? oA : A[i,i]) * B[i,j]
                    for k in i + 1:m
                        Cij += A[i,k] * B[k,j]
                    end
                    C[i,j] = Cij
                end
            end
        else # tfun in (transpose, adjoint)
            for j in 1:n
                for i in m:-1:1
                    Cij = (unit ? oA : tfun(A[i,i])) * B[i,j]
                    for k in 1:i - 1
                        Cij += tfun(A[k,i]) * B[k,j]
                    end
                    C[i,j] = Cij
                end
            end
        end
    else # uploc == 'L'
        if tfun === identity
            for j in 1:n
                for i in m:-1:1
                    Cij = (unit ? oA : A[i,i]) * B[i,j]
                    for k in 1:i - 1
                        Cij += A[i,k] * B[k,j]
                    end
                    C[i,j] = Cij
                end
            end
        else # tfun in (transpose, adjoint)
            for j in 1:n
                for i in 1:m
                    Cij = (unit ? oA : tfun(A[i,i])) * B[i,j]
                    for k in i + 1:m
                        Cij += tfun(A[k,i]) * B[k,j]
                    end
                    C[i,j] = Cij
                end
            end
        end
    end
    return C
end
# conjugate cases
function generic_trimatmul!(C::AbstractVecOrMat, uploc, isunitc, ::Function, xA::AdjOrTrans, B::AbstractVecOrMat)
    A = parent(xA)
    require_one_based_indexing(C, A, B)
    m, n = size(B, 1), size(B, 2)
    N = size(A, 1)
    if m != N
        throw(DimensionMismatch("right hand side B needs first dimension of size $(size(A,1)), has size $m"))
    end
    mc, nc = size(C, 1), size(C, 2)
    if mc != N || nc != n
        throw(DimensionMismatch("output has dimensions ($mc,$nc), should have ($N,$n)"))
    end
    oA = oneunit(eltype(A))
    unit = isunitc == 'U'
    @inbounds if uploc == 'U'
        for j in 1:n
            for i in 1:m
                Cij = (unit ? oA : conj(A[i,i])) * B[i,j]
                for k in i + 1:m
                    Cij += conj(A[i,k]) * B[k,j]
                end
                C[i,j] = Cij
            end
        end
    else # uploc == 'L'
        for j in 1:n
            for i in m:-1:1
                Cij = (unit ? oA : conj(A[i,i])) * B[i,j]
                for k in 1:i - 1
                    Cij += conj(A[i,k]) * B[k,j]
                end
                C[i,j] = Cij
            end
        end
    end
    return C
end

function generic_mattrimul!(C::AbstractMatrix, uploc, isunitc, tfun::Function, A::AbstractMatrix, B::AbstractMatrix)
    require_one_based_indexing(C, A, B)
    m, n = size(A, 1), size(A, 2)
    N = size(B, 1)
    if n != N
        throw(DimensionMismatch("right hand side B needs first dimension of size $n, has size $N"))
    end
    mc, nc = size(C, 1), size(C, 2)
    if mc != m || nc != N
        throw(DimensionMismatch("output has dimensions ($mc,$nc), should have ($m,$N)"))
    end
    oB = oneunit(eltype(B))
    unit = isunitc == 'U'
    @inbounds if uploc == 'U'
        if tfun === identity
            for i in 1:m
                for j in n:-1:1
                    Cij = A[i,j] * (unit ? oB : B[j,j])
                    for k in 1:j - 1
                        Cij += A[i,k] * B[k,j]
                    end
                    C[i,j] = Cij
                end
            end
        else # tfun in (transpose, adjoint)
            for i in 1:m
                for j in 1:n
                    Cij = A[i,j] * (unit ? oB : tfun(B[j,j]))
                    for k in j + 1:n
                        Cij += A[i,k] * tfun(B[j,k])
                    end
                    C[i,j] = Cij
                end
            end
        end
    else # uploc == 'L'
        if tfun === identity
            for i in 1:m
                for j in 1:n
                    Cij = A[i,j] * (unit ? oB : B[j,j])
                    for k in j + 1:n
                        Cij += A[i,k] * B[k,j]
                    end
                    C[i,j] = Cij
                end
            end
        else # tfun in (transpose, adjoint)
            for i in 1:m
                for j in n:-1:1
                    Cij = A[i,j] * (unit ? oB : tfun(B[j,j]))
                    for k in 1:j - 1
                        Cij += A[i,k] * tfun(B[j,k])
                    end
                    C[i,j] = Cij
                end
            end
        end
    end
    return C
end
# conjugate cases
function generic_mattrimul!(C::AbstractMatrix, uploc, isunitc, ::Function, A::AbstractMatrix, xB::AdjOrTrans)
    B = parent(xB)
    require_one_based_indexing(C, A, B)
    m, n = size(A, 1), size(A, 2)
    N = size(B, 1)
    if n != N
        throw(DimensionMismatch("right hand side B needs first dimension of size $n, has size $N"))
    end
    mc, nc = size(C, 1), size(C, 2)
    if mc != m || nc != N
        throw(DimensionMismatch("output has dimensions ($mc,$nc), should have ($m,$N)"))
    end
    oB = oneunit(eltype(B))
    unit = isunitc == 'U'
    @inbounds if uploc == 'U'
        for i in 1:m
            for j in n:-1:1
                Cij = A[i,j] * (unit ? oB : conj(B[j,j]))
                for k in 1:j - 1
                    Cij += A[i,k] * conj(B[k,j])
                end
                C[i,j] = Cij
            end
        end
    else # uploc == 'L'
        for i in 1:m
            for j in 1:n
                Cij = A[i,j] * (unit ? oB : conj(B[j,j]))
                for k in j + 1:n
                    Cij += A[i,k] * conj(B[k,j])
                end
                C[i,j] = Cij
            end
        end
    end
    return C
end

#Generic solver using naive substitution

@inline _ustrip(a) = oneunit(a) \ a
@inline _ustrip(a::Union{AbstractFloat,Integer,Complex,Rational}) = a

# manually hoisting b[j] significantly improves performance as of Dec 2015
# manually eliding bounds checking significantly improves performance as of Dec 2015
# replacing repeated references to A.data[j,j] with [Ajj = A.data[j,j] and references to Ajj]
# does not significantly impact performance as of Dec 2015
# in the transpose and conjugate transpose naive substitution variants,
# accumulating in z rather than b[j,k] significantly improves performance as of Dec 2015
function generic_trimatdiv!(C::AbstractVecOrMat, uploc, isunitc, tfun::Function, A::AbstractMatrix, B::AbstractVecOrMat)
    require_one_based_indexing(C, A, B)
    mA, nA = size(A)
    m, n = size(B, 1), size(B,2)
    if nA != m
        throw(DimensionMismatch("second dimension of left hand side A, $nA, and first dimension of right hand side B, $m, must be equal"))
    end
    if size(C) != size(B)
        throw(DimensionMismatch("size of output, $(size(C)), does not match size of right hand side, $(size(B))"))
    end
    oA = oneunit(eltype(A))
    @inbounds if uploc == 'U'
        if isunitc == 'N'
            if tfun === identity
                for k in 1:n
                    amm = A[m,m]
                    iszero(amm) && throw(SingularException(m))
                    Cm = C[m,k] = amm \ B[m,k]
                    # fill C-column
                    for i in m-1:-1:1
                        C[i,k] = oA \ B[i,k] - _ustrip(A[i,m]) * Cm
                    end
                    for j in m-1:-1:1
                        ajj = A[j,j]
                        iszero(ajj) && throw(SingularException(j))
                        Cj = C[j,k] = _ustrip(ajj) \ C[j,k]
                        for i in j-1:-1:1
                            C[i,k] -= _ustrip(A[i,j]) * Cj
                        end
                    end
                end
            else # tfun in (adjoint, transpose)
                for k in 1:n
                    for j in 1:m
                        ajj = A[j,j]
                        iszero(ajj) && throw(SingularException(j))
                        Bj = B[j,k]
                        for i in 1:j-1
                            Bj -= tfun(A[i,j]) * C[i,k]
                        end
                        C[j,k] = tfun(ajj) \ Bj
                    end
                end
            end
        else # isunitc == 'U'
            if tfun === identity
                for k in 1:n
                    Cm = C[m,k] = oA \ B[m,k]
                    # fill C-column
                    for i in m-1:-1:1
                        C[i,k] = oA \ B[i,k] - _ustrip(A[i,m]) * Cm
                    end
                    for j in m-1:-1:1
                        Cj = C[j,k]
                        for i in 1:j-1
                            C[i,k] -= _ustrip(A[i,j]) * Cj
                        end
                    end
                end
            else # tfun in (adjoint, transpose)
                for k in 1:n
                    for j in 1:m
                        Bj = B[j,k]
                        for i in 1:j-1
                            Bj -= tfun(A[i,j]) * C[i,k]
                        end
                        C[j,k] = oA \ Bj
                    end
                end
            end
        end
    else # uploc == 'L'
        if isunitc == 'N'
            if tfun === identity
                for k in 1:n
                    a11 = A[1,1]
                    iszero(a11) && throw(SingularException(1))
                    C1 = C[1,k] = a11 \ B[1,k]
                    # fill C-column
                    for i in 2:m
                        C[i,k] = oA \ B[i,k] - _ustrip(A[i,1]) * C1
                    end
                    for j in 2:m
                        ajj = A[j,j]
                        iszero(ajj) && throw(SingularException(j))
                        Cj = C[j,k] = _ustrip(ajj) \ C[j,k]
                        for i in j+1:m
                            C[i,k] -= _ustrip(A[i,j]) * Cj
                        end
                    end
                end
            else # tfun in (adjoint, transpose)
                for k in 1:n
                    for j in m:-1:1
                        ajj = A[j,j]
                        iszero(ajj) && throw(SingularException(j))
                        Bj = B[j,k]
                        for i in j+1:m
                            Bj -= tfun(A[i,j]) * C[i,k]
                        end
                        C[j,k] = tfun(ajj) \ Bj
                    end
                end
            end
        else # isunitc == 'U'
            if tfun === identity
                for k in 1:n
                    C1 = C[1,k] = oA \ B[1,k]
                    # fill C-column
                    for i in 2:m
                        C[i,k] = oA \ B[i,k] - _ustrip(A[i,1]) * C1
                    end
                    for j in 2:m
                        Cj = C[j,k]
                        for i in j+1:m
                            C[i,k] -= _ustrip(A[i,j]) * Cj
                        end
                    end
                end
            else # tfun in (adjoint, transpose)
                for k in 1:n
                    for j in m:-1:1
                        Bj = B[j,k]
                        for i in j+1:m
                            Bj -= tfun(A[i,j]) * C[i,k]
                        end
                        C[j,k] = oA \ Bj
                    end
                end
            end
        end
    end
    return C
end
# conjugate cases
function generic_trimatdiv!(C::AbstractVecOrMat, uploc, isunitc, ::Function, xA::AdjOrTrans, B::AbstractVecOrMat)
    A = parent(xA)
    require_one_based_indexing(C, A, B)
    mA, nA = size(A)
    m, n = size(B, 1), size(B,2)
    if nA != m
        throw(DimensionMismatch("second dimension of left hand side A, $nA, and first dimension of right hand side B, $m, must be equal"))
    end
    if size(C) != size(B)
        throw(DimensionMismatch("size of output, $(size(C)), does not match size of right hand side, $(size(B))"))
    end
    oA = oneunit(eltype(A))
    @inbounds if uploc == 'U'
        if isunitc == 'N'
            for k in 1:n
                amm = conj(A[m,m])
                iszero(amm) && throw(SingularException(m))
                Cm = C[m,k] = amm \ B[m,k]
                # fill C-column
                for i in m-1:-1:1
                    C[i,k] = oA \ B[i,k] - _ustrip(conj(A[i,m])) * Cm
                end
                for j in m-1:-1:1
                    ajj = conj(A[j,j])
                    iszero(ajj) && throw(SingularException(j))
                    Cj = C[j,k] = _ustrip(ajj) \ C[j,k]
                    for i in j-1:-1:1
                        C[i,k] -= _ustrip(conj(A[i,j])) * Cj
                    end
                end
            end
        else # isunitc == 'U'
            for k in 1:n
                Cm = C[m,k] = oA \ B[m,k]
                # fill C-column
                for i in m-1:-1:1
                    C[i,k] = oA \ B[i,k] - _ustrip(conj(A[i,m])) * Cm
                end
                for j in m-1:-1:1
                    Cj = C[j,k]
                    for i in 1:j-1
                        C[i,k] -= _ustrip(conj(A[i,j])) * Cj
                    end
                end
            end
        end
    else # uploc == 'L'
        if isunitc == 'N'
            for k in 1:n
                a11 = conj(A[1,1])
                iszero(a11) && throw(SingularException(1))
                C1 = C[1,k] = a11 \ B[1,k]
                # fill C-column
                for i in 2:m
                    C[i,k] = oA \ B[i,k] - _ustrip(conj(A[i,1])) * C1
                end
                for j in 2:m
                    ajj = conj(A[j,j])
                    iszero(ajj) && throw(SingularException(j))
                    Cj = C[j,k] = _ustrip(ajj) \ C[j,k]
                    for i in j+1:m
                        C[i,k] -= _ustrip(conj(A[i,j])) * Cj
                    end
                end
            end
        else # isunitc == 'U'
            for k in 1:n
                C1 = C[1,k] = oA \ B[1,k]
                # fill C-column
                for i in 2:m
                    C[i,k] = oA \ B[i,k] - _ustrip(conj(A[i,1])) * C1
                end
                for j in 1:m
                    Cj = C[j,k]
                    for i in j+1:m
                        C[i,k] -= _ustrip(conj(A[i,j])) * Cj
                    end
                end
            end
        end
    end
    return C
end

function generic_mattridiv!(C::AbstractMatrix, uploc, isunitc, tfun::Function, A::AbstractMatrix, B::AbstractMatrix)
    require_one_based_indexing(C, A, B)
    m, n = size(A)
    if size(B, 1) != n
        throw(DimensionMismatch("right hand side B needs first dimension of size $n, has size $(size(B,1))"))
    end
    if size(C) != size(A)
        throw(DimensionMismatch("size of output, $(size(C)), does not match size of left hand side, $(size(A))"))
    end
    oB = oneunit(eltype(B))
    unit = isunitc == 'U'
    @inbounds if uploc == 'U'
        if tfun === identity
            for i in 1:m
                for j in 1:n
                    Aij = A[i,j]
                    for k in 1:j - 1
                        Aij -= C[i,k]*B[k,j]
                    end
                    unit || (iszero(B[j,j]) && throw(SingularException(j)))
                    C[i,j] = Aij / (unit ? oB : B[j,j])
                end
            end
        else # tfun in (adjoint, transpose)
            for i in 1:m
                for j in n:-1:1
                    Aij = A[i,j]
                    for k in j + 1:n
                        Aij -= C[i,k]*tfun(B[j,k])
                    end
                    unit || (iszero(B[j,j]) && throw(SingularException(j)))
                    C[i,j] = Aij / (unit ? oB : tfun(B[j,j]))
                end
            end
        end
    else # uploc == 'L'
        if tfun === identity
            for i in 1:m
                for j in n:-1:1
                    Aij = A[i,j]
                    for k in j + 1:n
                        Aij -= C[i,k]*B[k,j]
                    end
                    unit || (iszero(B[j,j]) && throw(SingularException(j)))
                    C[i,j] = Aij / (unit ? oB : B[j,j])
                end
            end
        else # tfun in (adjoint, transpose)
            for i in 1:m
                for j in 1:n
                    Aij = A[i,j]
                    for k in 1:j - 1
                        Aij -= C[i,k]*tfun(B[j,k])
                    end
                    unit || (iszero(B[j,j]) && throw(SingularException(j)))
                    C[i,j] = Aij / (unit ? oB : tfun(B[j,j]))
                end
            end
        end
    end
    return C
end
function generic_mattridiv!(C::AbstractMatrix, uploc, isunitc, ::Function, A::AbstractMatrix, xB::AdjOrTrans)
    B = parent(xB)
    require_one_based_indexing(C, A, B)
    m, n = size(A)
    if size(B, 1) != n
        throw(DimensionMismatch("right hand side B needs first dimension of size $n, has size $(size(B,1))"))
    end
    if size(C) != size(A)
        throw(DimensionMismatch("size of output, $(size(C)), does not match size of left hand side, $(size(A))"))
    end
    oB = oneunit(eltype(B))
    unit = isunitc == 'U'
    if uploc == 'U'
        @inbounds for i in 1:m
            for j in 1:n
                Aij = A[i,j]
                for k in 1:j - 1
                    Aij -= C[i,k]*conj(B[k,j])
                end
                unit || (iszero(B[j,j]) && throw(SingularException(j)))
                C[i,j] = Aij / (unit ? oB : conj(B[j,j]))
            end
        end
    else # uploc == 'L'
        @inbounds for i in 1:m
            for j in n:-1:1
                Aij = A[i,j]
                for k in j + 1:n
                    Aij -= C[i,k]*conj(B[k,j])
                end
                unit || (iszero(B[j,j]) && throw(SingularException(j)))
                C[i,j] = Aij / (unit ? oB : conj(B[j,j]))
            end
        end
    end
    return C
end

# these are needed because we don't keep track of left- and right-multiplication in tritrimul!
rmul!(A::UpperTriangular, B::UpperTriangular)     = UpperTriangular(rmul!(triu!(A.data), B))
rmul!(A::UpperTriangular, B::UnitUpperTriangular) = UpperTriangular(rmul!(triu!(A.data), B))
rmul!(A::LowerTriangular, B::LowerTriangular)     = LowerTriangular(rmul!(tril!(A.data), B))
rmul!(A::LowerTriangular, B::UnitLowerTriangular) = LowerTriangular(rmul!(tril!(A.data), B))

# Promotion
## Promotion methods in matmul don't apply to triangular multiplication since
## it is inplace. Hence we have to make very similar definitions, but without
## allocation of a result array. For multiplication and unit diagonal division
## the element type doesn't have to be stable under division whereas that is
## necessary in the general triangular solve problem.

_inner_type_promotion(op, ::Type{TA}, ::Type{TB}) where {TA<:Integer,TB<:Integer} =
    _init_eltype(*, TA, TB)
_inner_type_promotion(op, ::Type{TA}, ::Type{TB}) where {TA,TB} =
    _init_eltype(op, TA, TB)
## The general promotion methods
function *(A::AbstractTriangular, B::AbstractTriangular)
    TAB = _init_eltype(*, eltype(A), eltype(B))
    mul!(similar(B, TAB, size(B)), A, B)
end

for mat in (:AbstractVector, :AbstractMatrix)
    ### Multiplication with triangle to the left and hence rhs cannot be transposed.
    @eval function *(A::AbstractTriangular, B::$mat)
        require_one_based_indexing(B)
        TAB = _init_eltype(*, eltype(A), eltype(B))
        mul!(similar(B, TAB, size(B)), A, B)
    end
    ### Left division with triangle to the left hence rhs cannot be transposed. No quotients.
    @eval function \(A::Union{UnitUpperTriangular,UnitLowerTriangular}, B::$mat)
        require_one_based_indexing(B)
        TAB = _inner_type_promotion(\, eltype(A), eltype(B))
        ldiv!(similar(B, TAB, size(B)), A, B)
    end
    ### Left division with triangle to the left hence rhs cannot be transposed. Quotients.
    @eval function \(A::Union{UpperTriangular,LowerTriangular}, B::$mat)
        require_one_based_indexing(B)
        TAB = _init_eltype(\, eltype(A), eltype(B))
        ldiv!(similar(B, TAB, size(B)), A, B)
    end
    ### Right division with triangle to the right hence lhs cannot be transposed. No quotients.
    @eval function /(A::$mat, B::Union{UnitUpperTriangular, UnitLowerTriangular})
        require_one_based_indexing(A)
        TAB = _inner_type_promotion(/, eltype(A), eltype(B))
        _rdiv!(similar(A, TAB, size(A)), A, B)
    end
    ### Right division with triangle to the right hence lhs cannot be transposed. Quotients.
    @eval function /(A::$mat, B::Union{UpperTriangular,LowerTriangular})
        require_one_based_indexing(A)
        TAB = _init_eltype(/, eltype(A), eltype(B))
        _rdiv!(similar(A, TAB, size(A)), A, B)
    end
end
### Multiplication with triangle to the right and hence lhs cannot be transposed.
# Only for AbstractMatrix, hence outside the above loop.
function *(A::AbstractMatrix, B::AbstractTriangular)
    require_one_based_indexing(A)
    TAB = _init_eltype(*, eltype(A), eltype(B))
    mul!(similar(A, TAB, size(A)), A, B)
end
# ambiguity resolution with definitions in matmul.jl
*(v::AdjointAbsVec, A::AbstractTriangular) = adjoint(adjoint(A) * v.parent)
*(v::TransposeAbsVec, A::AbstractTriangular) = transpose(transpose(A) * v.parent)

## Some Triangular-Triangular cases. We might want to write tailored methods
## for these cases, but I'm not sure it is worth it.
for f in (:*, :\)
    @eval begin
        ($f)(A::LowerTriangular, B::LowerTriangular) =
            LowerTriangular(@invoke $f(A::LowerTriangular, B::AbstractMatrix))
        ($f)(A::LowerTriangular, B::UnitLowerTriangular) =
            LowerTriangular(@invoke $f(A::LowerTriangular, B::AbstractMatrix))
        ($f)(A::UnitLowerTriangular, B::LowerTriangular) =
            LowerTriangular(@invoke $f(A::UnitLowerTriangular, B::AbstractMatrix))
        ($f)(A::UnitLowerTriangular, B::UnitLowerTriangular) =
            UnitLowerTriangular(@invoke $f(A::UnitLowerTriangular, B::AbstractMatrix))
        ($f)(A::UpperTriangular, B::UpperTriangular) =
            UpperTriangular(@invoke $f(A::UpperTriangular, B::AbstractMatrix))
        ($f)(A::UpperTriangular, B::UnitUpperTriangular) =
            UpperTriangular(@invoke $f(A::UpperTriangular, B::AbstractMatrix))
        ($f)(A::UnitUpperTriangular, B::UpperTriangular) =
            UpperTriangular(@invoke $f(A::UnitUpperTriangular, B::AbstractMatrix))
        ($f)(A::UnitUpperTriangular, B::UnitUpperTriangular) =
            UnitUpperTriangular(@invoke $f(A::UnitUpperTriangular, B::AbstractMatrix))
    end
end
(/)(A::LowerTriangular, B::LowerTriangular) =
    LowerTriangular(@invoke /(A::AbstractMatrix, B::LowerTriangular))
(/)(A::LowerTriangular, B::UnitLowerTriangular) =
    LowerTriangular(@invoke /(A::AbstractMatrix, B::UnitLowerTriangular))
(/)(A::UnitLowerTriangular, B::LowerTriangular) =
    LowerTriangular(@invoke /(A::AbstractMatrix, B::LowerTriangular))
(/)(A::UnitLowerTriangular, B::UnitLowerTriangular) =
    UnitLowerTriangular(@invoke /(A::AbstractMatrix, B::UnitLowerTriangular))
(/)(A::UpperTriangular, B::UpperTriangular) =
    UpperTriangular(@invoke /(A::AbstractMatrix, B::UpperTriangular))
(/)(A::UpperTriangular, B::UnitUpperTriangular) =
    UpperTriangular(@invoke /(A::AbstractMatrix, B::UnitUpperTriangular))
(/)(A::UnitUpperTriangular, B::UpperTriangular) =
    UpperTriangular(@invoke /(A::AbstractMatrix, B::UpperTriangular))
(/)(A::UnitUpperTriangular, B::UnitUpperTriangular) =
    UnitUpperTriangular(@invoke /(A::AbstractMatrix, B::UnitUpperTriangular))

# Complex matrix power for upper triangular factor, see:
#   Higham and Lin, "A Schur-Padé algorithm for fractional powers of a Matrix",
#     SIAM J. Matrix Anal. & Appl., 32 (3), (2011) 1056–1078.
#   Higham and Lin, "An improved Schur-Padé algorithm for fractional powers of
#     a matrix and their Fréchet derivatives", SIAM. J. Matrix Anal. & Appl.,
#     34(3), (2013) 1341–1360.
function powm!(A0::UpperTriangular, p::Real)
    if abs(p) >= 1
        throw(ArgumentError("p must be a real number in (-1,1), got $p"))
    end

    normA0 = opnorm(A0, 1)
    rmul!(A0, 1/normA0)

    theta = [1.53e-5, 2.25e-3, 1.92e-2, 6.08e-2, 1.25e-1, 2.03e-1, 2.84e-1]
    n = checksquare(A0)

    A, m, s = invsquaring(A0, theta)
    A = I - A

    # Compute accurate diagonal of I - T
    sqrt_diag!(A0, A, s)
    for i = 1:n
        A[i, i] = -A[i, i]
    end
    # Compute the Padé approximant
    c = 0.5 * (p - m) / (2 * m - 1)
    triu!(A)
    S = c * A
    Stmp = similar(S)
    for j = m-1:-1:1
        j4 = 4 * j
        c = (-p - j) / (j4 + 2)
        for i = 1:n
            @inbounds S[i, i] = S[i, i] + 1
        end
        copyto!(Stmp, S)
        mul!(S, A, c)
        ldiv!(Stmp, S)

        c = (p - j) / (j4 - 2)
        for i = 1:n
            @inbounds S[i, i] = S[i, i] + 1
        end
        copyto!(Stmp, S)
        mul!(S, A, c)
        ldiv!(Stmp, S)
    end
    for i = 1:n
        S[i, i] = S[i, i] + 1
    end
    copyto!(Stmp, S)
    mul!(S, A, -p)
    ldiv!(Stmp, S)
    for i = 1:n
        @inbounds S[i, i] = S[i, i] + 1
    end

    blockpower!(A0, S, p/(2^s))
    for m = 1:s
        mul!(Stmp.data, S, S)
        copyto!(S, Stmp)
        blockpower!(A0, S, p/(2^(s-m)))
    end
    rmul!(S, normA0^p)
    return S
end
powm(A::LowerTriangular, p::Real) = copy(transpose(powm!(copy(transpose(A)), p::Real)))

# Complex matrix logarithm for the upper triangular factor, see:
#   Al-Mohy and Higham, "Improved inverse scaling and squaring algorithms for
#     the matrix logarithm", SIAM J. Sci. Comput., 34(4), (2012), pp. C153–C169.
#   Al-Mohy, Higham and Relton, "Computing the Frechet derivative of the matrix
#     logarithm and estimating the condition number", SIAM J. Sci. Comput.,
#     35(4), (2013), C394–C410.
#
# Based on the code available at http://eprints.ma.man.ac.uk/1851/02/logm.zip,
# Copyright (c) 2011, Awad H. Al-Mohy and Nicholas J. Higham
# Julia version relicensed with permission from original authors
log(A::UpperTriangular{T}) where {T<:BlasFloat} = log_quasitriu(A)
log(A::UnitUpperTriangular{T}) where {T<:BlasFloat} = log_quasitriu(A)
log(A::LowerTriangular) = copy(transpose(log(copy(transpose(A)))))
log(A::UnitLowerTriangular) = copy(transpose(log(copy(transpose(A)))))

function log_quasitriu(A0::AbstractMatrix{T}) where T<:BlasFloat
    # allocate real A if log(A) will be real and complex A otherwise
    n = checksquare(A0)
    if isreal(A0) && (!istriu(A0) || !any(x -> real(x) < zero(real(T)), diag(A0)))
        A = T <: Complex ? real(A0) : copy(A0)
    else
        A = T <: Complex ? copy(A0) : complex(A0)
    end
    if A0 isa UnitUpperTriangular
        A = UpperTriangular(parent(A))
        @inbounds for i in 1:n
            A[i,i] = 1
        end
    end
    Y0 = _log_quasitriu!(A0, A)
    # return complex result for complex input
    Y = T <: Complex ? complex(Y0) : Y0

    if A0 isa UpperTriangular || A0 isa UnitUpperTriangular
        return UpperTriangular(Y)
    else
        return Y
    end
end
# type-stable implementation of log_quasitriu
# A is a copy of A0 that is overwritten while computing the result. It has the same eltype
# as the result.
function _log_quasitriu!(A0, A)
    # Find Padé degree m and s while replacing A with A^(1/2^s)
    m, s = _find_params_log_quasitriu!(A)

    # Compute accurate superdiagonal of A
    _pow_superdiag_quasitriu!(A, A0, 0.5^s)

    # Compute accurate block diagonal of A
    _sqrt_pow_diag_quasitriu!(A, A0, s)

    # Get the Gauss-Legendre quadrature points and weights
    R = zeros(Float64, m, m)
    for i = 1:m - 1
        R[i,i+1] = i / sqrt((2 * i)^2 - 1)
        R[i+1,i] = R[i,i+1]
    end
    x,V = eigen(R)
    w = Vector{Float64}(undef, m)
    for i = 1:m
        x[i] = (x[i] + 1) / 2
        w[i] = V[1,i]^2
    end

    # Compute the Padé approximation
    t = eltype(A)
    n = size(A, 1)
    Y = zeros(t, n, n)
    B = similar(A)
    for k = 1:m
        B .= t(x[k]) .* A
        @inbounds for i in 1:n
            B[i,i] += 1
        end
        Y .+= t(w[k]) .* rdiv_quasitriu!(A, B)
    end

    # Scale back
    lmul!(2.0^s, Y)

    # Compute accurate diagonal and superdiagonal of log(A)
    _log_diag_quasitriu!(Y, A0)

    return Y
end

# Auxiliary functions for matrix logarithm and matrix power

# Find Padé degree m and s while replacing A with A^(1/2^s)
#   Al-Mohy and Higham, "Improved inverse scaling and squaring algorithms for
#     the matrix logarithm", SIAM J. Sci. Comput., 34(4), (2012), pp. C153–C169.
#   from Algorithm 4.1
function _find_params_log_quasitriu!(A)
    maxsqrt = 100
    theta = [1.586970738772063e-005,
         2.313807884242979e-003,
         1.938179313533253e-002,
         6.209171588994762e-002,
         1.276404810806775e-001,
         2.060962623452836e-001,
         2.879093714241194e-001]
    tmax = size(theta, 1)
    n = size(A, 1)
    p = 0
    m = 0

    # Find s0, the smallest s such that the ρ(triu(A)^(1/2^s) - I) ≤ theta[tmax], where ρ(X)
    # is the spectral radius of X
    d = complex.(@view(A[diagind(A)]))
    dm1 = d .- 1
    s = 0
    while norm(dm1, Inf) > theta[tmax] && s < maxsqrt
        d .= sqrt.(d)
        dm1 .= d .- 1
        s = s + 1
    end
    s0 = s

    # Compute repeated roots
    for k = 1:min(s, maxsqrt)
        _sqrt_quasitriu!(A isa UpperTriangular ? parent(A) : A, A)
    end

    # these three never needed at the same time, so reuse the same temporary
    AmI = AmI4 = AmI5 = A - I
    AmI2 = AmI * AmI
    AmI3 = AmI2 * AmI
    d2 = sqrt(opnorm(AmI2, 1))
    d3 = cbrt(opnorm(AmI3, 1))
    alpha2 = max(d2, d3)
    foundm = false
    if alpha2 <= theta[2]
        m = alpha2 <= theta[1] ? 1 : 2
        foundm = true
    end

    while !foundm
        more_sqrt = false
        mul!(AmI4, AmI2, AmI2)
        d4 = opnorm(AmI4, 1)^(1/4)
        alpha3 = max(d3, d4)
        if alpha3 <= theta[tmax]
            local j
            for outer j = 3:tmax
                if alpha3 <= theta[j]
                    break
                end
            end
            if j <= 6
                m = j
                break
            elseif alpha3 / 2 <= theta[5] && p < 2
                more_sqrt = true
                p = p + 1
           end
        end

        if !more_sqrt
            mul!(AmI5, AmI3, AmI2)
            d5 = opnorm(AmI5, 1)^(1/5)
            alpha4 = max(d4, d5)
            eta = min(alpha3, alpha4)
            if eta <= theta[tmax]
                j = 0
                for outer j = 6:tmax
                    if eta <= theta[j]
                        m = j
                        break
                    end
                end
                break
            end
        end

        if s == maxsqrt
            m = tmax
            break
        end
        _sqrt_quasitriu!(A isa UpperTriangular ? parent(A) : A, A)
        copyto!(AmI, A)
        for i in 1:n
            @inbounds AmI[i,i] -= 1
        end
        mul!(AmI2, AmI, AmI)
        mul!(AmI3, AmI2, AmI)
        d3 = cbrt(opnorm(AmI3, 1))
        s = s + 1
    end
    return m, s
end

# Compute accurate diagonal of A = A0^s - I
function sqrt_diag!(A0::UpperTriangular, A::UpperTriangular, s)
    n = checksquare(A0)
    T = eltype(A)
    @inbounds for i = 1:n
        a = complex(A0[i,i])
        A[i,i] = _sqrt_pow(a, s)
    end
end
# Compute accurate block diagonal of A = A0^s - I for upper quasi-triangular A0 produced
# by the Schur decomposition. Diagonal is made of 1x1 and 2x2 blocks.
# 2x2 blocks are real with non-negative conjugate pair eigenvalues
function _sqrt_pow_diag_quasitriu!(A, A0, s)
    n = checksquare(A0)
    t = typeof(sqrt(zero(eltype(A))))
    i = 1
    @inbounds while i < n
        if iszero(A0[i+1,i])  # 1x1 block
            A[i,i] = _sqrt_pow(t(A0[i,i]), s)
            i += 1
        else  # real 2x2 block
            @views _sqrt_pow_diag_block_2x2!(A[i:i+1,i:i+1], A0[i:i+1,i:i+1], s)
            i += 2
        end
    end
    if i == n  # last block is 1x1
        @inbounds A[n,n] = _sqrt_pow(t(A0[n,n]), s)
    end
    return A
end
# compute a^(1/2^s)-1
#   Al-Mohy, "A more accurate Briggs method for the logarithm",
#      Numer. Algorithms, 59, (2012), 393–402.
#   Algorithm 2
function _sqrt_pow(a::Number, s)
    T = typeof(sqrt(zero(a)))
    s == 0 && return T(a) - 1
    s0 = s
    if imag(a) >= 0 && real(a) <= 0 && !iszero(a)  # angle(a) ≥ π / 2
        a = sqrt(a)
        s0 = s - 1
    end
    z0 = a - 1
    a = sqrt(a)
    r = 1 + a
    for j = 1:s0-1
        a = sqrt(a)
        r = r * (1 + a)
    end
    return z0 / r
end
# compute A0 = A^(1/2^s)-I for 2x2 real matrices A and A0
# A has non-negative conjugate pair eigenvalues
# "Improved Inverse Scaling and Squaring Algorithms for the Matrix Logarithm"
# SIAM J. Sci. Comput., 34(4), (2012) C153–C169. doi: 10.1137/110852553
# Algorithm 5.1
Base.@propagate_inbounds function _sqrt_pow_diag_block_2x2!(A, A0, s)
    _sqrt_real_2x2!(A, A0)
    if isone(s)
        A[1,1] -= 1
        A[2,2] -= 1
    else
        # Z = A - I
        z11, z21, z12, z22 = A[1,1] - 1, A[2,1], A[1,2], A[2,2] - 1
        # A = sqrt(A)
        _sqrt_real_2x2!(A, A)
        # P = A + I
        p11, p21, p12, p22 = A[1,1] + 1, A[2,1], A[1,2], A[2,2] + 1
        for i in 1:(s - 2)
            # A = sqrt(A)
            _sqrt_real_2x2!(A, A)
            a11, a21, a12, a22 = A[1,1], A[2,1], A[1,2], A[2,2]
            # P += P * A
            r11 = p11*(1 + a11) + p12*a21
            r22 = p21*a12 + p22*(1 + a22)
            p21 = p21*(1 + a11) + p22*a21
            p12 = p11*a12 + p12*(1 + a22)
            p11 = r11
            p22 = r22
        end
        # A = Z / P
        c = inv(p11*p22 - p21*p12)
        A[1,1] = (p22*z11 - p21*z12) * c
        A[2,1] = (p22*z21 - p21*z22) * c
        A[1,2] = (p11*z12 - p12*z11) * c
        A[2,2] = (p11*z22 - p12*z21) * c
    end
    return A
end
# Compute accurate superdiagonal of A = A0^s - I for upper quasi-triangular A0 produced
# by a Schur decomposition.
# Higham and Lin, "A Schur–Padé Algorithm for Fractional Powers of a Matrix"
# SIAM J. Matrix Anal. Appl., 32(3), (2011), 1056–1078.
# Equation 5.6
# see also blockpower for when A0 is upper triangular
function _pow_superdiag_quasitriu!(A, A0, p)
    n = checksquare(A0)
    t = eltype(A)
    k = 1
    @inbounds while k < n
        if !iszero(A[k+1,k])
            k += 2
            continue
        end
        if !(k == n - 1 || iszero(A[k+2,k+1]))
            k += 3
            continue
        end
        Ak = t(A0[k,k])
        Akp1 = t(A0[k+1,k+1])

        Akp = Ak^p
        Akp1p = Akp1^p

        if Ak == Akp1
            A[k,k+1] = p * A0[k,k+1] * Ak^(p-1)
        elseif 2 * abs(Ak) < abs(Akp1) || 2 * abs(Akp1) < abs(Ak) || iszero(Akp1 + Ak)
            A[k,k+1] = A0[k,k+1] * (Akp1p - Akp) / (Akp1 - Ak)
        else
            logAk = log(Ak)
            logAkp1 = log(Akp1)
            z = (Akp1 - Ak)/(Akp1 + Ak)
            if abs(z) > 1
                A[k,k+1] = A0[k,k+1] * (Akp1p - Akp) / (Akp1 - Ak)
            else
                w = atanh(z) + im * pi * (unw(logAkp1-logAk) - unw(log1p(z)-log1p(-z)))
                dd = 2 * exp(p*(logAk+logAkp1)/2) * sinh(p*w) / (Akp1 - Ak);
                A[k,k+1] = A0[k,k+1] * dd
            end
        end
        k += 1
    end
end

# Compute accurate block diagonal and superdiagonal of A = log(A0) for upper
# quasi-triangular A0 produced by the Schur decomposition.
function _log_diag_quasitriu!(A, A0)
    n = checksquare(A0)
    t = eltype(A)
    k = 1
    @inbounds while k < n
        if iszero(A0[k+1,k])  # 1x1 block
            Ak = t(A0[k,k])
            logAk = log(Ak)
            A[k,k] = logAk
            if k < n - 2 && iszero(A0[k+2,k+1])
                Akp1 = t(A0[k+1,k+1])
                logAkp1 = log(Akp1)
                A[k+1,k+1] = logAkp1
                if Ak == Akp1
                    A[k,k+1] = A0[k,k+1] / Ak
                elseif 2 * abs(Ak) < abs(Akp1) || 2 * abs(Akp1) < abs(Ak) || iszero(Akp1 + Ak)
                    A[k,k+1] = A0[k,k+1] * (logAkp1 - logAk) / (Akp1 - Ak)
                else
                    z = (Akp1 - Ak)/(Akp1 + Ak)
                    if abs(z) > 1
                        A[k,k+1] = A0[k,k+1] * (logAkp1 - logAk) / (Akp1 - Ak)
                    else
                        w = atanh(z) + im * pi * (unw(logAkp1-logAk) - unw(log1p(z)-log1p(-z)))
                        A[k,k+1] = 2 * A0[k,k+1] * w / (Akp1 - Ak)
                    end
                end
                k += 2
            else
                k += 1
            end
        else  # real 2x2 block
            @views _log_diag_block_2x2!(A[k:k+1,k:k+1], A0[k:k+1,k:k+1])
            k += 2
        end
    end
    if k == n  # last 1x1 block
        @inbounds A[n,n] = log(t(A0[n,n]))
    end
    return A
end
# compute A0 = log(A) for 2x2 real matrices A and A0, where A0 is a diagonal 2x2 block
# produced by real Schur decomposition.
# Al-Mohy, Higham and Relton, "Computing the Frechet derivative of the matrix
# logarithm and estimating the condition number", SIAM J. Sci. Comput.,
# 35(4), (2013), C394–C410.
# Eq. 6.1
Base.@propagate_inbounds function _log_diag_block_2x2!(A, A0)
    a, b, c = A0[1,1], A0[1,2], A0[2,1]
    # avoid underflow/overflow for large/small b and c
    s = sqrt(abs(b)) * sqrt(abs(c))
    θ = atan(s, a)
    t = θ / s
    au = abs(a)
    if au > s
        a1 = log1p((s / au)^2) / 2 + log(au)
    else
        a1 = log1p((au / s)^2) / 2 + log(s)
    end
    A[1,1] = a1
    A[2,1] = c*t
    A[1,2] = b*t
    A[2,2] = a1
    return A
end

# Used only by powm at the moment
# Repeatedly compute the square roots of A so that in the end its
# eigenvalues are close enough to the positive real line
function invsquaring(A0::UpperTriangular, theta)
    require_one_based_indexing(theta)
    # assumes theta is in ascending order
    maxsqrt = 100
    tmax = size(theta, 1)
    n = checksquare(A0)
    A = complex(copy(A0))
    p = 0
    m = 0

    # Compute repeated roots
    d = complex(diag(A))
    dm1 = d .- 1
    s = 0
    while norm(dm1, Inf) > theta[tmax] && s < maxsqrt
        d .= sqrt.(d)
        dm1 .= d .- 1
        s = s + 1
    end
    s0 = s
    for k = 1:min(s, maxsqrt)
        A = sqrt(A)
    end

    AmI = A - I
    d2 = sqrt(opnorm(AmI^2, 1))
    d3 = cbrt(opnorm(AmI^3, 1))
    alpha2 = max(d2, d3)
    foundm = false
    if alpha2 <= theta[2]
        m = alpha2 <= theta[1] ? 1 : 2
        foundm = true
    end

    while !foundm
        more = false
        if s > s0
            d3 = cbrt(opnorm(AmI^3, 1))
        end
        d4 = opnorm(AmI^4, 1)^(1/4)
        alpha3 = max(d3, d4)
        if alpha3 <= theta[tmax]
            local j
            for outer j = 3:tmax
                if alpha3 <= theta[j]
                    break
                elseif alpha3 / 2 <= theta[5] && p < 2
                    more = true
                    p = p + 1
                end
            end
            if j <= 6
                m = j
                foundm = true
                break
            elseif alpha3 / 2 <= theta[5] && p < 2
                more = true
                p = p + 1
           end
        end

        if !more
            d5 = opnorm(AmI^5, 1)^(1/5)
            alpha4 = max(d4, d5)
            eta = min(alpha3, alpha4)
            if eta <= theta[tmax]
                j = 0
                for outer j = 6:tmax
                    if eta <= theta[j]
                        m = j
                        break
                    end
                    break
                end
            end
            if s == maxsqrt
                m = tmax
                break
            end
            A = sqrt(A)
            AmI = A - I
            s = s + 1
        end
    end

    # Compute accurate superdiagonal of T
    p = 1 / 2^s
    A = complex(A)
    blockpower!(A, A0, p)
    return A,m,s
end

# Compute accurate diagonal and superdiagonal of A = A0^p
function blockpower!(A::UpperTriangular, A0::UpperTriangular, p)
    n = checksquare(A0)
    @inbounds for k = 1:n-1
        Ak = complex(A0[k,k])
        Akp1 = complex(A0[k+1,k+1])

        Akp = Ak^p
        Akp1p = Akp1^p

        A[k,k] = Akp
        A[k+1,k+1] = Akp1p

        if Ak == Akp1
            A[k,k+1] = p * A0[k,k+1] * Ak^(p-1)
        elseif 2 * abs(Ak) < abs(Akp1) || 2 * abs(Akp1) < abs(Ak) || iszero(Akp1 + Ak)
            A[k,k+1] = A0[k,k+1] * (Akp1p - Akp) / (Akp1 - Ak)
        else
            logAk = log(Ak)
            logAkp1 = log(Akp1)
            z = (Akp1 - Ak)/(Akp1 + Ak)
            if abs(z) > 1
                A[k,k+1] = A0[k,k+1] * (Akp1p - Akp) / (Akp1 - Ak)
            else
                w = atanh(z) + im * pi * (unw(logAkp1-logAk) - unw(log1p(z)-log1p(-z)))
                dd = 2 * exp(p*(logAk+logAkp1)/2) * sinh(p*w) / (Akp1 - Ak);
                A[k,k+1] = A0[k,k+1] * dd
            end
        end
    end
end

# Unwinding number
unw(x::Real) = 0
unw(x::Number) = ceil((imag(x) - pi) / (2 * pi))

# compute A / B for upper quasi-triangular B, possibly overwriting B
function rdiv_quasitriu!(A, B)
    n = checksquare(A)
    AG = copy(A)
    # use Givens rotations to annihilate 2x2 blocks
    @inbounds for k in 1:(n-1)
        s = B[k+1,k]
        iszero(s) && continue  # 1x1 block
        G = first(givens(B[k+1,k+1], s, k, k+1))
        rmul!(B, G)
        rmul!(AG, G)
    end
    return rdiv!(AG, UpperTriangular(B))
end

# End of auxiliary functions for matrix logarithm and matrix power

sqrt(A::UpperTriangular) = sqrt_quasitriu(A)
function sqrt(A::UnitUpperTriangular{T}) where T
    B = A.data
    n = checksquare(B)
    t = typeof(sqrt(zero(T)))
    R = Matrix{t}(I, n, n)
    tt = typeof(oneunit(t)*oneunit(t))
    half = inv(R[1,1]+R[1,1]) # for general, algebraic cases. PR#20214
    @inbounds for j = 1:n
        for i = j-1:-1:1
            r::tt = B[i,j]
            @simd for k = i+1:j-1
                r -= R[i,k]*R[k,j]
            end
            iszero(r) || (R[i,j] = half*r)
        end
    end
    return UnitUpperTriangular(R)
end
sqrt(A::LowerTriangular) = copy(transpose(sqrt(copy(transpose(A)))))
sqrt(A::UnitLowerTriangular) = copy(transpose(sqrt(copy(transpose(A)))))

# Auxiliary functions for matrix square root

# square root of upper triangular or real upper quasitriangular matrix
function sqrt_quasitriu(A0; blockwidth = eltype(A0) <: Complex ? 512 : 256)
    n = checksquare(A0)
    T = eltype(A0)
    Tr = typeof(sqrt(real(zero(T))))
    Tc = typeof(sqrt(complex(zero(T))))
    if isreal(A0)
        is_sqrt_real = true
        if istriu(A0)
            for i in 1:n
                Aii = real(A0[i,i])
                if Aii < zero(Aii)
                    is_sqrt_real = false
                    break
                end
            end
        end
        if is_sqrt_real
            R = zeros(Tr, n, n)
            A = real(A0)
        else
            R = zeros(Tc, n, n)
            A = A0
        end
    else
        A = A0
        R = zeros(Tc, n, n)
    end
    _sqrt_quasitriu!(R, A; blockwidth=blockwidth, n=n)
    Rc = eltype(A0) <: Real ? R : complex(R)
    if A0 isa UpperTriangular
        return UpperTriangular(Rc)
    elseif A0 isa UnitUpperTriangular
        return UnitUpperTriangular(Rc)
    else
        return Rc
    end
end

# in-place recursive sqrt of upper quasi-triangular matrix A from
# Deadman E., Higham N.J., Ralha R. (2013) Blocked Schur Algorithms for Computing the Matrix
# Square Root. Applied Parallel and Scientific Computing. PARA 2012. Lecture Notes in
# Computer Science, vol 7782. https://doi.org/10.1007/978-3-642-36803-5_12
function _sqrt_quasitriu!(R, A; blockwidth=64, n=checksquare(A))
    if n ≤ blockwidth || !(eltype(R) <: BlasFloat) # base case, perform "point" algorithm
        _sqrt_quasitriu_block!(R, A)
    else  # compute blockwise recursion
        split = div(n, 2)
        iszero(A[split+1, split]) || (split += 1) # don't split 2x2 diagonal block
        r1 = 1:split
        r2 = (split + 1):n
        n1, n2 = split, n - split
        A11, A12, A22 = @views A[r1,r1], A[r1,r2], A[r2,r2]
        R11, R12, R22 = @views R[r1,r1], R[r1,r2], R[r2,r2]
        # solve diagonal blocks recursively
        _sqrt_quasitriu!(R11, A11; blockwidth=blockwidth, n=n1)
        _sqrt_quasitriu!(R22, A22; blockwidth=blockwidth, n=n2)
        # solve off-diagonal block
        R12 .= .- A12
        _sylvester_quasitriu!(R11, R22, R12; blockwidth=blockwidth, nA=n1, nB=n2, raise=false)
    end
    return R
end

function _sqrt_quasitriu_block!(R, A)
    _sqrt_quasitriu_diag_block!(R, A)
    _sqrt_quasitriu_offdiag_block!(R, A)
    return R
end

function _sqrt_quasitriu_diag_block!(R, A)
    n = size(R, 1)
    ta = eltype(R) <: Complex ? complex(eltype(A)) : eltype(A)
    i = 1
    @inbounds while i < n
        if iszero(A[i + 1, i])
            R[i, i] = sqrt(ta(A[i, i]))
            i += 1
        else
            # this branch is never reached when A is complex triangular
            @views _sqrt_real_2x2!(R[i:(i + 1), i:(i + 1)], A[i:(i + 1), i:(i + 1)])
            i += 2
        end
    end
    if i == n
        R[n, n] = sqrt(ta(A[n, n]))
    end
    return R
end

function _sqrt_quasitriu_offdiag_block!(R, A)
    n = size(R, 1)
    j = 1
    @inbounds while j ≤ n
        jsize_is_2 = j < n && !iszero(A[j + 1, j])
        i = j - 1
        while i > 0
            isize_is_2 = i > 1 && !iszero(A[i, i - 1])
            if isize_is_2
                if jsize_is_2
                    _sqrt_quasitriu_offdiag_block_2x2!(R, A, i - 1, j)
                else
                    _sqrt_quasitriu_offdiag_block_2x1!(R, A, i - 1, j)
                end
                i -= 2
            else
                if jsize_is_2
                    _sqrt_quasitriu_offdiag_block_1x2!(R, A, i, j)
                else
                    _sqrt_quasitriu_offdiag_block_1x1!(R, A, i, j)
                end
                i -= 1
            end
        end
        j += 2 - !jsize_is_2
    end
    return R
end

# real square root of 2x2 diagonal block of quasi-triangular matrix from real Schur
# decomposition. Eqs 6.8-6.9 and Algorithm 6.5 of
# Higham, 2008, "Functions of Matrices: Theory and Computation", SIAM.
Base.@propagate_inbounds function _sqrt_real_2x2!(R, A)
    # in the real Schur form, A[1, 1] == A[2, 2], and A[2, 1] * A[1, 2] < 0
    θ, a21, a12 = A[1, 1], A[2, 1], A[1, 2]
    # avoid overflow/underflow of μ
    # for real sqrt, |d| ≤ 2 max(|a12|,|a21|)
    μ = sqrt(abs(a12)) * sqrt(abs(a21))
    α = _real_sqrt(θ, μ)
    c = 2α
    R[1, 1] = α
    R[2, 1] = a21 / c
    R[1, 2] = a12 / c
    R[2, 2] = α
    return R
end

# real part of square root of θ+im*μ
@inline function _real_sqrt(θ, μ)
    t = sqrt((abs(θ) + hypot(θ, μ)) / 2)
    return θ ≥ 0 ? t : μ / 2t
end

Base.@propagate_inbounds function _sqrt_quasitriu_offdiag_block_1x1!(R, A, i, j)
    Rii = R[i, i]
    Rjj = R[j, j]
    iszero(Rii) && iszero(Rjj) && return R
    t = eltype(R)
    tt = typeof(zero(t)*zero(t))
    r = tt(-A[i, j])
    @simd for k in (i + 1):(j - 1)
        r += R[i, k] * R[k, j]
    end
    iszero(r) && return R
    R[i, j] = sylvester(Rii, Rjj, r)
    return R
end

Base.@propagate_inbounds function _sqrt_quasitriu_offdiag_block_1x2!(R, A, i, j)
    jrange = j:(j + 1)
    t = eltype(R)
    tt = typeof(zero(t)*zero(t))
    r1 = tt(-A[i, j])
    r2 = tt(-A[i, j + 1])
    @simd for k in (i + 1):(j - 1)
        rik = R[i, k]
        r1 += rik * R[k, j]
        r2 += rik * R[k, j + 1]
    end
    Rjj = @view R[jrange, jrange]
    Rij = @view R[i, jrange]
    Rij[1] = r1
    Rij[2] = r2
    _sylvester_1x2!(R[i, i], Rjj, Rij)
    return R
end

Base.@propagate_inbounds function _sqrt_quasitriu_offdiag_block_2x1!(R, A, i, j)
    irange = i:(i + 1)
    t = eltype(R)
    tt = typeof(zero(t)*zero(t))
    r1 = tt(-A[i, j])
    r2 = tt(-A[i + 1, j])
    @simd for k in (i + 2):(j - 1)
        rkj = R[k, j]
        r1 += R[i, k] * rkj
        r2 += R[i + 1, k] * rkj
    end
    Rii = @view R[irange, irange]
    Rij = @view R[irange, j]
    Rij[1] = r1
    Rij[2] = r2
    @views _sylvester_2x1!(Rii, R[j, j], Rij)
    return R
end

Base.@propagate_inbounds function _sqrt_quasitriu_offdiag_block_2x2!(R, A, i, j)
    irange = i:(i + 1)
    jrange = j:(j + 1)
    t = eltype(R)
    tt = typeof(zero(t)*zero(t))
    for i′ in irange, j′ in jrange
        Cij = tt(-A[i′, j′])
        @simd for k in (i + 2):(j - 1)
            Cij += R[i′, k] * R[k, j′]
        end
        R[i′, j′] = Cij
    end
    Rii = @view R[irange, irange]
    Rjj = @view R[jrange, jrange]
    Rij = @view R[irange, jrange]
    if !iszero(Rij) && !all(isnan, Rij)
        _sylvester_2x2!(Rii, Rjj, Rij)
    end
    return R
end

# solve Sylvester's equation AX + XB = -C using blockwise recursion until the dimension of
# A and B are no greater than blockwidth, based on Algorithm 1 from
# Jonsson I, Kågström B. Recursive blocked algorithms for solving triangular systems—
# Part I: one-sided and coupled Sylvester-type matrix equations. (2002) ACM Trans Math Softw.
# 28(4), https://doi.org/10.1145/592843.592845.
# specify raise=false to avoid breaking the recursion if a LAPACKException is thrown when
# computing one of the blocks.
function _sylvester_quasitriu!(A, B, C; blockwidth=64, nA=checksquare(A), nB=checksquare(B), raise=true)
    if 1 ≤ nA ≤ blockwidth && 1 ≤ nB ≤ blockwidth
        _sylvester_quasitriu_base!(A, B, C; raise=raise)
    elseif nA ≥ 2nB ≥ 2
        _sylvester_quasitriu_split1!(A, B, C; blockwidth=blockwidth, nA=nA, nB=nB, raise=raise)
    elseif nB ≥ 2nA ≥ 2
        _sylvester_quasitriu_split2!(A, B, C; blockwidth=blockwidth, nA=nA, nB=nB, raise=raise)
    else
        _sylvester_quasitriu_splitall!(A, B, C; blockwidth=blockwidth, nA=nA, nB=nB, raise=raise)
    end
    return C
end
function _sylvester_quasitriu_base!(A, B, C; raise=true)
    try
        _, scale = LAPACK.trsyl!('N', 'N', A, B, C)
        rmul!(C, -inv(scale))
    catch e
        if !(e isa LAPACKException) || raise
            throw(e)
        end
    end
    return C
end
function _sylvester_quasitriu_split1!(A, B, C; nA=checksquare(A), kwargs...)
    iA = div(nA, 2)
    iszero(A[iA + 1, iA]) || (iA += 1)  # don't split 2x2 diagonal block
    rA1, rA2 = 1:iA, (iA + 1):nA
    nA1, nA2 = iA, nA-iA
    A11, A12, A22 = @views A[rA1,rA1], A[rA1,rA2], A[rA2,rA2]
    C1, C2 = @views C[rA1,:], C[rA2,:]
    _sylvester_quasitriu!(A22, B, C2; nA=nA2, kwargs...)
    mul!(C1, A12, C2, true, true)
    _sylvester_quasitriu!(A11, B, C1; nA=nA1, kwargs...)
    return C
end
function _sylvester_quasitriu_split2!(A, B, C; nB=checksquare(B), kwargs...)
    iB = div(nB, 2)
    iszero(B[iB + 1, iB]) || (iB += 1)  # don't split 2x2 diagonal block
    rB1, rB2 = 1:iB, (iB + 1):nB
    nB1, nB2 = iB, nB-iB
    B11, B12, B22 = @views B[rB1,rB1], B[rB1,rB2], B[rB2,rB2]
    C1, C2 = @views C[:,rB1], C[:,rB2]
    _sylvester_quasitriu!(A, B11, C1; nB=nB1, kwargs...)
    mul!(C2, C1, B12, true, true)
    _sylvester_quasitriu!(A, B22, C2; nB=nB2, kwargs...)
    return C
end
function _sylvester_quasitriu_splitall!(A, B, C; nA=checksquare(A), nB=checksquare(B), kwargs...)
    iA = div(nA, 2)
    iszero(A[iA + 1, iA]) || (iA += 1)  # don't split 2x2 diagonal block
    iB = div(nB, 2)
    iszero(B[iB + 1, iB]) || (iB += 1)  # don't split 2x2 diagonal block
    rA1, rA2 = 1:iA, (iA + 1):nA
    nA1, nA2 = iA, nA-iA
    rB1, rB2 = 1:iB, (iB + 1):nB
    nB1, nB2 = iB, nB-iB
    A11, A12, A22 = @views A[rA1,rA1], A[rA1,rA2], A[rA2,rA2]
    B11, B12, B22 = @views B[rB1,rB1], B[rB1,rB2], B[rB2,rB2]
    C11, C21, C12, C22 = @views C[rA1,rB1], C[rA2,rB1], C[rA1,rB2], C[rA2,rB2]
    _sylvester_quasitriu!(A22, B11, C21; nA=nA2, nB=nB1, kwargs...)
    mul!(C11, A12, C21, true, true)
    _sylvester_quasitriu!(A11, B11, C11; nA=nA1, nB=nB1, kwargs...)
    mul!(C22, C21, B12, true, true)
    _sylvester_quasitriu!(A22, B22, C22; nA=nA2, nB=nB2, kwargs...)
    mul!(C12, A12, C22, true, true)
    mul!(C12, C11, B12, true, true)
    _sylvester_quasitriu!(A11, B22, C12; nA=nA1, nB=nB2, kwargs...)
    return C
end

# End of auxiliary functions for matrix square root

# Generic eigensystems
eigvals(A::AbstractTriangular) = diag(A)
function eigvecs(A::AbstractTriangular{T}) where T
    TT = promote_type(T, Float32)
    if TT <: BlasFloat
        return eigvecs(convert(AbstractMatrix{TT}, A))
    else
        throw(ArgumentError("eigvecs type $(typeof(A)) not supported. Please submit a pull request."))
    end
end
det(A::UnitUpperTriangular{T}) where {T} = one(T)
det(A::UnitLowerTriangular{T}) where {T} = one(T)
logdet(A::UnitUpperTriangular{T}) where {T} = zero(T)
logdet(A::UnitLowerTriangular{T}) where {T} = zero(T)
logabsdet(A::UnitUpperTriangular{T}) where {T} = zero(T), one(T)
logabsdet(A::UnitLowerTriangular{T}) where {T} = zero(T), one(T)
det(A::UpperTriangular) = prod(diag(A.data))
det(A::LowerTriangular) = prod(diag(A.data))
function logabsdet(A::Union{UpperTriangular{T},LowerTriangular{T}}) where T
    sgn = one(T)
    abs_det = zero(real(T))
    @inbounds for i in 1:size(A,1)
        diag_i = A.data[i,i]
        sgn *= sign(diag_i)
        abs_det += log(abs(diag_i))
    end
    return abs_det, sgn
end

eigen(A::AbstractTriangular) = Eigen(eigvals(A), eigvecs(A))

# Generic singular systems
for func in (:svd, :svd!, :svdvals)
    @eval begin
        ($func)(A::AbstractTriangular; kwargs...) = ($func)(copyto!(similar(parent(A)), A); kwargs...)
    end
end

factorize(A::AbstractTriangular) = A

# disambiguation methods: /(Adjoint of AbsVec, <:AbstractTriangular)
/(u::AdjointAbsVec, A::Union{LowerTriangular,UpperTriangular}) = adjoint(adjoint(A) \ u.parent)
/(u::AdjointAbsVec, A::Union{UnitLowerTriangular,UnitUpperTriangular}) = adjoint(adjoint(A) \ u.parent)
# disambiguation methods: /(Transpose of AbsVec, <:AbstractTriangular)
/(u::TransposeAbsVec, A::Union{LowerTriangular,UpperTriangular}) = transpose(transpose(A) \ u.parent)
/(u::TransposeAbsVec, A::Union{UnitLowerTriangular,UnitUpperTriangular}) = transpose(transpose(A) \ u.parent)
# disambiguation methods: /(Transpose of AbsVec, Adj/Trans of <:AbstractTriangular)
for (tritype, comptritype) in ((:LowerTriangular, :UpperTriangular),
                               (:UnitLowerTriangular, :UnitUpperTriangular),
                               (:UpperTriangular, :LowerTriangular),
                               (:UnitUpperTriangular, :UnitLowerTriangular))
    @eval /(u::TransposeAbsVec, A::$tritype{<:Any,<:Adjoint}) = transpose($comptritype(conj(parent(parent(A)))) \ u.parent)
    @eval /(u::TransposeAbsVec, A::$tritype{<:Any,<:Transpose}) = transpose(transpose(A) \ u.parent)
end
~   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LinearAlgebra/src/factorization.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

## Matrix factorizations and decompositions
"""
    LinearAlgebra.Factorization

Abstract type for [matrix factorizations](https://en.wikipedia.org/wiki/Matrix_decomposition)
a.k.a. matrix decompositions.
See [online documentation](@ref man-linalg-factorizations) for a list of available
matrix factorizations.
"""
abstract type Factorization{T} end

"""
    AdjointFactorization

Lazy wrapper type for the adjoint of the underlying `Factorization` object. Usually, the
`AdjointFactorization` constructor should not be called directly, use
[`adjoint(:: Factorization)`](@ref) instead.
"""
struct AdjointFactorization{T,S<:Factorization} <: Factorization{T}
    parent::S
end
AdjointFactorization(F::Factorization) =
    AdjointFactorization{Base.promote_op(adjoint,eltype(F)),typeof(F)}(F)

"""
    TransposeFactorization

Lazy wrapper type for the transpose of the underlying `Factorization` object. Usually, the
`TransposeFactorization` constructor should not be called directly, use
[`transpose(:: Factorization)`](@ref) instead.
"""
struct TransposeFactorization{T,S<:Factorization} <: Factorization{T}
    parent::S
end
TransposeFactorization(F::Factorization) =
    TransposeFactorization{Base.promote_op(adjoint,eltype(F)),typeof(F)}(F)

eltype(::Type{<:Factorization{T}}) where {T} = T
size(F::AdjointFactorization) = reverse(size(parent(F)))
size(F::TransposeFactorization) = reverse(size(parent(F)))
size(F::Union{AdjointFactorization,TransposeFactorization}, d::Integer) = d in (1, 2) ? size(F)[d] : 1
parent(F::Union{AdjointFactorization,TransposeFactorization}) = F.parent

"""
    adjoint(F::Factorization)

Lazy adjoint of the factorization `F`. By default, returns an
[`AdjointFactorization`](@ref) wrapper.
"""
adjoint(F::Factorization) = AdjointFactorization(F)
"""
    transpose(F::Factorization)

Lazy transpose of the factorization `F`. By default, returns a [`TransposeFactorization`](@ref),
except for `Factorization`s with real `eltype`, in which case returns an [`AdjointFactorization`](@ref).
"""
transpose(F::Factorization) = TransposeFactorization(F)
transpose(F::Factorization{<:Real}) = AdjointFactorization(F)
adjoint(F::AdjointFactorization) = F.parent
transpose(F::TransposeFactorization) = F.parent
transpose(F::AdjointFactorization{<:Real}) = F.parent
conj(A::TransposeFactorization) = adjoint(A.parent)
conj(A::AdjointFactorization) = transpose(A.parent)

checkpositivedefinite(info) = info == 0 || throw(PosDefException(info))
checknonsingular(info, ::RowMaximum) = info == 0 || throw(SingularException(info))
checknonsingular(info, ::RowNonZero) = info == 0 || throw(SingularException(info))
checknonsingular(info, ::NoPivot) = info == 0 || throw(ZeroPivotException(info))
checknonsingular(info) = checknonsingular(info, RowMaximum())

"""
    issuccess(F::Factorization)

Test that a factorization of a matrix succeeded.

!!! compat "Julia 1.6"
    `issuccess(::CholeskyPivoted)` requires Julia 1.6 or later.

```jldoctest
julia> F = cholesky([1 0; 0 1]);

julia> issuccess(F)
true

julia> F = lu([1 0; 0 0]; check = false);

julia> issuccess(F)
false
```
"""
issuccess(F::Factorization)

function logdet(F::Factorization)
    d, s = logabsdet(F)
    return d + log(s)
end

function det(F::Factorization)
    d, s = logabsdet(F)
    return exp(d)*s
end

convert(::Type{T}, f::T) where {T<:Factorization} = f
convert(::Type{T}, f::Factorization) where {T<:Factorization} = T(f)::T

convert(::Type{T}, f::Factorization) where {T<:AbstractArray} = T(f)::T

### General promotion rules
Factorization{T}(F::Factorization{T}) where {T} = F
# This no longer looks odd since the return _is_ a Factorization!
Factorization{T}(A::AdjointFactorization) where {T} =
    adjoint(Factorization{T}(parent(A)))
Factorization{T}(A::TransposeFactorization) where {T} =
    transpose(Factorization{T}(parent(A)))
inv(F::Factorization{T}) where {T} = (n = size(F, 1); ldiv!(F, Matrix{T}(I, n, n)))

Base.hash(F::Factorization, h::UInt) = mapreduce(f -> hash(getfield(F, f)), hash, 1:nfields(F); init=h)
Base.:(==)(  F::T, G::T) where {T<:Factorization} = all(f -> getfield(F, f) == getfield(G, f), 1:nfields(F))
Base.isequal(F::T, G::T) where {T<:Factorization} = all(f -> isequal(getfield(F, f), getfield(G, f)), 1:nfields(F))::Bool

function Base.show(io::IO, x::AdjointFactorization)
    print(io, "adjoint of ")
    show(io, parent(x))
end
function Base.show(io::IO, x::TransposeFactorization)
    print(io, "transpose of ")
    show(io, parent(x))
end
function Base.show(io::IO, ::MIME"text/plain", x::AdjointFactorization)
    print(io, "adjoint of ")
    show(io, MIME"text/plain"(), parent(x))
end
function Base.show(io::IO, ::MIME"text/plain", x::TransposeFactorization)
    print(io, "transpose of ")
    show(io, MIME"text/plain"(), parent(x))
end

function (\)(F::Factorization, B::AbstractVecOrMat)
    require_one_based_indexing(B)
    TFB = typeof(oneunit(eltype(F)) \ oneunit(eltype(B)))
    ldiv!(F, copy_similar(B, TFB))
end
(\)(F::TransposeFactorization, B::AbstractVecOrMat) = conj!(adjoint(F.parent) \ conj.(B))
# With a real lhs and complex rhs with the same precision, we can reinterpret
# the complex rhs as a real rhs with twice the number of columns or rows
function (\)(F::Factorization{T}, B::VecOrMat{Complex{T}}) where {T<:BlasReal}
    require_one_based_indexing(B)
    c2r = reshape(copy(transpose(reinterpret(T, reshape(B, (1, length(B)))))), size(B, 1), 2*size(B, 2))
    x = ldiv!(F, c2r)
    return reshape(copy(reinterpret(Complex{T}, copy(transpose(reshape(x, div(length(x), 2), 2))))), _ret_size(F, B))
end
# don't do the reinterpretation for [Adjoint/Transpose]Factorization
(\)(F::TransposeFactorization{T}, B::VecOrMat{Complex{T}}) where {T<:BlasReal} =
    conj!(adjoint(parent(F)) \ conj.(B))
(\)(F::AdjointFactorization{T}, B::VecOrMat{Complex{T}}) where {T<:BlasReal} =
    @invoke \(F::typeof(F), B::VecOrMat)

function ldiv!(Y::AbstractVector, A::Factorization, B::AbstractVector)
    require_one_based_indexing(Y, B)
    m, n = size(A)
    if m > n
        Bc = copy(B)
        ldiv!(A, Bc)
        return copyto!(Y, 1, Bc, 1, n)
    else
        return ldiv!(A, copyto!(Y, B))
    end
end
function ldiv!(Y::AbstractMatrix, A::Factorization, B::AbstractMatrix)
    require_one_based_indexing(Y, B)
    m, n = size(A)
    if m > n
        Bc = copy(B)
        ldiv!(A, Bc)
        return copyto!(Y, view(Bc, 1:n, :))
    else
        copyto!(view(Y, 1:m, :), view(B, 1:m, :))
        return ldiv!(A, Y)
    end
end

function (/)(B::AbstractMatrix, F::Factorization)
    require_one_based_indexing(B)
    TFB = typeof(oneunit(eltype(B)) / oneunit(eltype(F)))
    rdiv!(copy_similar(B, TFB), F)
end
# reinterpretation trick for complex lhs and real factorization
function (/)(B::Union{Matrix{Complex{T}},AdjOrTrans{Complex{T},Vector{Complex{T}}}}, F::Factorization{T}) where {T<:BlasReal}
    require_one_based_indexing(B)
    x = rdiv!(copy(reinterpret(T, B)), F)
    return copy(reinterpret(Complex{T}, x))
end
# don't do the reinterpretation for [Adjoint/Transpose]Factorization
(/)(B::Union{Matrix{Complex{T}},AdjOrTrans{Complex{T},Vector{Complex{T}}}}, F::TransposeFactorization{T}) where {T<:BlasReal} =
    @invoke /(B::AbstractMatrix, F::Factorization)
(/)(B::Matrix{Complex{T}}, F::AdjointFactorization{T}) where {T<:BlasReal} =
    @invoke /(B::AbstractMatrix, F::Factorization)
(/)(B::Adjoint{Complex{T},Vector{Complex{T}}}, F::AdjointFactorization{T}) where {T<:BlasReal} =
    (F' \ B')'
(/)(B::Transpose{Complex{T},Vector{Complex{T}}}, F::TransposeFactorization{T}) where {T<:BlasReal} =
    transpose(transpose(F) \ transpose(B))

rdiv!(B::AbstractMatrix, A::TransposeFactorization) = transpose(ldiv!(A.parent, transpose(B)))
rdiv!(B::AbstractMatrix, A::AdjointFactorization) = adjoint(ldiv!(A.parent, adjoint(B)))
v   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LinearAlgebra/src/eigen.jl}P      # This file is a part of Julia. License is MIT: https://julialang.org/license

# Eigendecomposition
"""
    Eigen <: Factorization

Matrix factorization type of the eigenvalue/spectral decomposition of a square
matrix `A`. This is the return type of [`eigen`](@ref), the corresponding matrix
factorization function.

If `F::Eigen` is the factorization object, the eigenvalues can be obtained via
`F.values` and the eigenvectors as the columns of the matrix `F.vectors`.
(The `k`th eigenvector can be obtained from the slice `F.vectors[:, k]`.)

Iterating the decomposition produces the components `F.values` and `F.vectors`.

# Examples
```jldoctest
julia> F = eigen([1.0 0.0 0.0; 0.0 3.0 0.0; 0.0 0.0 18.0])
Eigen{Float64, Float64, Matrix{Float64}, Vector{Float64}}
values:
3-element Vector{Float64}:
  1.0
  3.0
 18.0
vectors:
3×3 Matrix{Float64}:
 1.0  0.0  0.0
 0.0  1.0  0.0
 0.0  0.0  1.0

julia> F.values
3-element Vector{Float64}:
  1.0
  3.0
 18.0

julia> F.vectors
3×3 Matrix{Float64}:
 1.0  0.0  0.0
 0.0  1.0  0.0
 0.0  0.0  1.0

julia> vals, vecs = F; # destructuring via iteration

julia> vals == F.values && vecs == F.vectors
true
```
"""
struct Eigen{T,V,S<:AbstractMatrix,U<:AbstractVector} <: Factorization{T}
    values::U
    vectors::S
    Eigen{T,V,S,U}(values::AbstractVector{V}, vectors::AbstractMatrix{T}) where {T,V,S,U} =
        new(values, vectors)
end
Eigen(values::AbstractVector{V}, vectors::AbstractMatrix{T}) where {T,V} =
    Eigen{T,V,typeof(vectors),typeof(values)}(values, vectors)

# Generalized eigenvalue problem.
"""
    GeneralizedEigen <: Factorization

Matrix factorization type of the generalized eigenvalue/spectral decomposition of
`A` and `B`. This is the return type of [`eigen`](@ref), the corresponding
matrix factorization function, when called with two matrix arguments.

If `F::GeneralizedEigen` is the factorization object, the eigenvalues can be obtained via
`F.values` and the eigenvectors as the columns of the matrix `F.vectors`.
(The `k`th eigenvector can be obtained from the slice `F.vectors[:, k]`.)

Iterating the decomposition produces the components `F.values` and `F.vectors`.

# Examples
```jldoctest
julia> A = [1 0; 0 -1]
2×2 Matrix{Int64}:
 1   0
 0  -1

julia> B = [0 1; 1 0]
2×2 Matrix{Int64}:
 0  1
 1  0

julia> F = eigen(A, B)
GeneralizedEigen{ComplexF64, ComplexF64, Matrix{ComplexF64}, Vector{ComplexF64}}
values:
2-element Vector{ComplexF64}:
 0.0 - 1.0im
 0.0 + 1.0im
vectors:
2×2 Matrix{ComplexF64}:
  0.0+1.0im   0.0-1.0im
 -1.0+0.0im  -1.0-0.0im

julia> F.values
2-element Vector{ComplexF64}:
 0.0 - 1.0im
 0.0 + 1.0im

julia> F.vectors
2×2 Matrix{ComplexF64}:
  0.0+1.0im   0.0-1.0im
 -1.0+0.0im  -1.0-0.0im

julia> vals, vecs = F; # destructuring via iteration

julia> vals == F.values && vecs == F.vectors
true
```
"""
struct GeneralizedEigen{T,V,S<:AbstractMatrix,U<:AbstractVector} <: Factorization{T}
    values::U
    vectors::S
    GeneralizedEigen{T,V,S,U}(values::AbstractVector{V}, vectors::AbstractMatrix{T}) where {T,V,S,U} =
        new(values, vectors)
end
GeneralizedEigen(values::AbstractVector{V}, vectors::AbstractMatrix{T}) where {T,V} =
    GeneralizedEigen{T,V,typeof(vectors),typeof(values)}(values, vectors)

# iteration for destructuring into components
Base.iterate(S::Union{Eigen,GeneralizedEigen}) = (S.values, Val(:vectors))
Base.iterate(S::Union{Eigen,GeneralizedEigen}, ::Val{:vectors}) = (S.vectors, Val(:done))
Base.iterate(S::Union{Eigen,GeneralizedEigen}, ::Val{:done}) = nothing

isposdef(A::Union{Eigen,GeneralizedEigen}) = isreal(A.values) && all(x -> x > 0, A.values)

# pick a canonical ordering to avoid returning eigenvalues in "random" order
# as is the LAPACK default (for complex λ — LAPACK sorts by λ for the Hermitian/Symmetric case)
eigsortby(λ::Real) = λ
eigsortby(λ::Complex) = (real(λ),imag(λ))
function sorteig!(λ::AbstractVector, X::AbstractMatrix, sortby::Union{Function,Nothing}=eigsortby)
    if sortby !== nothing && !issorted(λ, by=sortby)
        p = sortperm(λ; alg=QuickSort, by=sortby)
        permute!(λ, p)
        Base.permutecols!!(X, p)
    end
    return λ, X
end
sorteig!(λ::AbstractVector, sortby::Union{Function,Nothing}=eigsortby) = sortby === nothing ? λ : sort!(λ, by=sortby)

"""
    eigen!(A; permute, scale, sortby)
    eigen!(A, B; sortby)

Same as [`eigen`](@ref), but saves space by overwriting the input `A` (and
`B`), instead of creating a copy.
"""
function eigen!(A::StridedMatrix{T}; permute::Bool=true, scale::Bool=true, sortby::Union{Function,Nothing}=eigsortby) where T<:BlasReal
    n = size(A, 2)
    n == 0 && return Eigen(zeros(T, 0), zeros(T, 0, 0))
    issymmetric(A) && return eigen!(Symmetric(A), sortby=sortby)
    A, WR, WI, VL, VR, _ = LAPACK.geevx!(permute ? (scale ? 'B' : 'P') : (scale ? 'S' : 'N'), 'N', 'V', 'N', A)
    iszero(WI) && return Eigen(sorteig!(WR, VR, sortby)...)
    evec = zeros(Complex{T}, n, n)
    j = 1
    while j <= n
        if WI[j] == 0
            evec[:,j] = view(VR, :, j)
        else
            for i = 1:n
                evec[i,j]   = VR[i,j] + im*VR[i,j+1]
                evec[i,j+1] = VR[i,j] - im*VR[i,j+1]
            end
            j += 1
        end
        j += 1
    end
    return Eigen(sorteig!(complex.(WR, WI), evec, sortby)...)
end

function eigen!(A::StridedMatrix{T}; permute::Bool=true, scale::Bool=true, sortby::Union{Function,Nothing}=eigsortby) where T<:BlasComplex
    n = size(A, 2)
    n == 0 && return Eigen(zeros(T, 0), zeros(T, 0, 0))
    ishermitian(A) && return eigen!(Hermitian(A), sortby=sortby)
    eval, evec = LAPACK.geevx!(permute ? (scale ? 'B' : 'P') : (scale ? 'S' : 'N'), 'N', 'V', 'N', A)[[2,4]]
    return Eigen(sorteig!(eval, evec, sortby)...)
end

"""
    eigen(A; permute::Bool=true, scale::Bool=true, sortby) -> Eigen

Compute the eigenvalue decomposition of `A`, returning an [`Eigen`](@ref) factorization object `F`
which contains the eigenvalues in `F.values` and the eigenvectors in the columns of the
matrix `F.vectors`. This corresponds to solving an eigenvalue problem of the form
`Ax =  λx`, where `A` is a matrix, `x` is an eigenvector, and `λ` is an eigenvalue.
(The `k`th eigenvector can be obtained from the slice `F.vectors[:, k]`.)

Iterating the decomposition produces the components `F.values` and `F.vectors`.

The following functions are available for `Eigen` objects: [`inv`](@ref), [`det`](@ref), and [`isposdef`](@ref).

For general nonsymmetric matrices it is possible to specify how the matrix is balanced
before the eigenvector calculation. The option `permute=true` permutes the matrix to become
closer to upper triangular, and `scale=true` scales the matrix by its diagonal elements to
make rows and columns more equal in norm. The default is `true` for both options.

By default, the eigenvalues and vectors are sorted lexicographically by `(real(λ),imag(λ))`.
A different comparison function `by(λ)` can be passed to `sortby`, or you can pass
`sortby=nothing` to leave the eigenvalues in an arbitrary order.   Some special matrix types
(e.g. [`Diagonal`](@ref) or [`SymTridiagonal`](@ref)) may implement their own sorting convention and not
accept a `sortby` keyword.

# Examples
```jldoctest
julia> F = eigen([1.0 0.0 0.0; 0.0 3.0 0.0; 0.0 0.0 18.0])
Eigen{Float64, Float64, Matrix{Float64}, Vector{Float64}}
values:
3-element Vector{Float64}:
  1.0
  3.0
 18.0
vectors:
3×3 Matrix{Float64}:
 1.0  0.0  0.0
 0.0  1.0  0.0
 0.0  0.0  1.0

julia> F.values
3-element Vector{Float64}:
  1.0
  3.0
 18.0

julia> F.vectors
3×3 Matrix{Float64}:
 1.0  0.0  0.0
 0.0  1.0  0.0
 0.0  0.0  1.0

julia> vals, vecs = F; # destructuring via iteration

julia> vals == F.values && vecs == F.vectors
true
```
"""
function eigen(A::AbstractMatrix{T}; permute::Bool=true, scale::Bool=true, sortby::Union{Function,Nothing}=eigsortby) where T
    isdiag(A) && return eigen(Diagonal{eigtype(T)}(diag(A)); sortby)
    ishermitian(A) && return eigen!(eigencopy_oftype(Hermitian(A), eigtype(T)); sortby)
    AA = eigencopy_oftype(A, eigtype(T))
    return eigen!(AA; permute, scale, sortby)
end
function eigen(A::AbstractMatrix{T}; permute::Bool=true, scale::Bool=true, sortby::Union{Function,Nothing}=eigsortby) where {T <: Union{Float16,Complex{Float16}}}
    isdiag(A) && return eigen(Diagonal{eigtype(T)}(diag(A)); sortby)
    E = if ishermitian(A)
        eigen!(eigencopy_oftype(Hermitian(A), eigtype(T)); sortby)
    else
        eigen!(eigencopy_oftype(A, eigtype(T)); permute, scale, sortby)
    end
    values = convert(AbstractVector{isreal(E.values) ? Float16 : Complex{Float16}}, E.values)
    vectors = convert(AbstractMatrix{isreal(E.vectors) ? Float16 : Complex{Float16}}, E.vectors)
    return Eigen(values, vectors)
end
eigen(x::Number) = Eigen([x], fill(one(x), 1, 1))

"""
    eigvecs(A; permute::Bool=true, scale::Bool=true, `sortby`) -> Matrix

Return a matrix `M` whose columns are the eigenvectors of `A`. (The `k`th eigenvector can
be obtained from the slice `M[:, k]`.) The `permute`, `scale`, and `sortby` keywords are the same as
for [`eigen`](@ref).

# Examples
```jldoctest
julia> eigvecs([1.0 0.0 0.0; 0.0 3.0 0.0; 0.0 0.0 18.0])
3×3 Matrix{Float64}:
 1.0  0.0  0.0
 0.0  1.0  0.0
 0.0  0.0  1.0
```
"""
eigvecs(A::Union{Number, AbstractMatrix}; kws...) =
    eigvecs(eigen(A; kws...))
eigvecs(F::Union{Eigen, GeneralizedEigen}) = F.vectors

eigvals(F::Union{Eigen, GeneralizedEigen}) = F.values

"""
    eigvals!(A; permute::Bool=true, scale::Bool=true, sortby) -> values

Same as [`eigvals`](@ref), but saves space by overwriting the input `A`, instead of creating a copy.
The `permute`, `scale`, and `sortby` keywords are the same as for [`eigen`](@ref).

!!! note
    The input matrix `A` will not contain its eigenvalues after `eigvals!` is
    called on it - `A` is used as a workspace.

# Examples
```jldoctest
julia> A = [1. 2.; 3. 4.]
2×2 Matrix{Float64}:
 1.0  2.0
 3.0  4.0

julia> eigvals!(A)
2-element Vector{Float64}:
 -0.3722813232690143
  5.372281323269014

julia> A
2×2 Matrix{Float64}:
 -0.372281  -1.0
  0.0        5.37228
```
"""
function eigvals!(A::StridedMatrix{<:BlasReal}; permute::Bool=true, scale::Bool=true, sortby::Union{Function,Nothing}=eigsortby)
    issymmetric(A) && return sorteig!(eigvals!(Symmetric(A)), sortby)
    _, valsre, valsim, _ = LAPACK.geevx!(permute ? (scale ? 'B' : 'P') : (scale ? 'S' : 'N'), 'N', 'N', 'N', A)
    return sorteig!(iszero(valsim) ? valsre : complex.(valsre, valsim), sortby)
end
function eigvals!(A::StridedMatrix{<:BlasComplex}; permute::Bool=true, scale::Bool=true, sortby::Union{Function,Nothing}=eigsortby)
    ishermitian(A) && return sorteig!(eigvals(Hermitian(A)), sortby)
    return sorteig!(LAPACK.geevx!(permute ? (scale ? 'B' : 'P') : (scale ? 'S' : 'N'), 'N', 'N', 'N', A)[2], sortby)
end

# promotion type to use for eigenvalues of a Matrix{T}
eigtype(T) = promote_type(Float32, typeof(zero(T)/sqrt(abs2(one(T)))))

"""
    eigvals(A; permute::Bool=true, scale::Bool=true, sortby) -> values

Return the eigenvalues of `A`.

For general non-symmetric matrices it is possible to specify how the matrix is balanced
before the eigenvalue calculation. The `permute`, `scale`, and `sortby` keywords are
the same as for [`eigen`](@ref).

# Examples
```jldoctest
julia> diag_matrix = [1 0; 0 4]
2×2 Matrix{Int64}:
 1  0
 0  4

julia> eigvals(diag_matrix)
2-element Vector{Float64}:
 1.0
 4.0
```
"""
eigvals(A::AbstractMatrix{T}; kws...) where T =
    eigvals!(eigencopy_oftype(A, eigtype(T)); kws...)

"""
For a scalar input, `eigvals` will return a scalar.

# Example
```jldoctest
julia> eigvals(-2)
-2
```
"""
eigvals(x::Number; kwargs...) = imag(x) == 0 ? real(x) : x

"""
    eigmax(A; permute::Bool=true, scale::Bool=true)

Return the largest eigenvalue of `A`.
The option `permute=true` permutes the matrix to become
closer to upper triangular, and `scale=true` scales the matrix by its diagonal elements to
make rows and columns more equal in norm.
Note that if the eigenvalues of `A` are complex,
this method will fail, since complex numbers cannot
be sorted.

# Examples
```jldoctest
julia> A = [0 im; -im 0]
2×2 Matrix{Complex{Int64}}:
 0+0im  0+1im
 0-1im  0+0im

julia> eigmax(A)
1.0

julia> A = [0 im; -1 0]
2×2 Matrix{Complex{Int64}}:
  0+0im  0+1im
 -1+0im  0+0im

julia> eigmax(A)
ERROR: DomainError with Complex{Int64}[0+0im 0+1im; -1+0im 0+0im]:
`A` cannot have complex eigenvalues.
Stacktrace:
[...]
```
"""
function eigmax(A::Union{Number, AbstractMatrix}; permute::Bool=true, scale::Bool=true)
    v = eigvals(A, permute = permute, scale = scale)
    if eltype(v)<:Complex
        throw(DomainError(A, "`A` cannot have complex eigenvalues."))
    end
    maximum(v)
end

"""
    eigmin(A; permute::Bool=true, scale::Bool=true)

Return the smallest eigenvalue of `A`.
The option `permute=true` permutes the matrix to become
closer to upper triangular, and `scale=true` scales the matrix by its diagonal elements to
make rows and columns more equal in norm.
Note that if the eigenvalues of `A` are complex,
this method will fail, since complex numbers cannot
be sorted.

# Examples
```jldoctest
julia> A = [0 im; -im 0]
2×2 Matrix{Complex{Int64}}:
 0+0im  0+1im
 0-1im  0+0im

julia> eigmin(A)
-1.0

julia> A = [0 im; -1 0]
2×2 Matrix{Complex{Int64}}:
  0+0im  0+1im
 -1+0im  0+0im

julia> eigmin(A)
ERROR: DomainError with Complex{Int64}[0+0im 0+1im; -1+0im 0+0im]:
`A` cannot have complex eigenvalues.
Stacktrace:
[...]
```
"""
function eigmin(A::Union{Number, AbstractMatrix};
                permute::Bool=true, scale::Bool=true)
    v = eigvals(A, permute = permute, scale = scale)
    if eltype(v)<:Complex
        throw(DomainError(A, "`A` cannot have complex eigenvalues."))
    end
    minimum(v)
end

inv(A::Eigen) = A.vectors * inv(Diagonal(A.values)) / A.vectors
det(A::Eigen) = prod(A.values)

# Generalized eigenproblem
function eigen!(A::StridedMatrix{T}, B::StridedMatrix{T}; sortby::Union{Function,Nothing}=eigsortby) where T<:BlasReal
    issymmetric(A) && isposdef(B) && return eigen!(Symmetric(A), Symmetric(B), sortby=sortby)
    n = size(A, 1)
    if LAPACK.version() < v"3.6.0"
        alphar, alphai, beta, _, vr = LAPACK.ggev!('N', 'V', A, B)
    else
        alphar, alphai, beta, _, vr = LAPACK.ggev3!('N', 'V', A, B)
    end
    iszero(alphai) && return GeneralizedEigen(sorteig!(alphar ./ beta, vr, sortby)...)

    vecs = zeros(Complex{T}, n, n)
    j = 1
    while j <= n
        if alphai[j] == 0
            vecs[:,j] = view(vr, :, j)
        else
            for i = 1:n
                vecs[i,j  ] = vr[i,j] + im*vr[i,j+1]
                vecs[i,j+1] = vr[i,j] - im*vr[i,j+1]
            end
            j += 1
        end
        j += 1
    end
    return GeneralizedEigen(sorteig!(complex.(alphar, alphai)./beta, vecs, sortby)...)
end

function eigen!(A::StridedMatrix{T}, B::StridedMatrix{T}; sortby::Union{Function,Nothing}=eigsortby) where T<:BlasComplex
    ishermitian(A) && isposdef(B) && return eigen!(Hermitian(A), Hermitian(B), sortby=sortby)
    if LAPACK.version() < v"3.6.0"
        alpha, beta, _, vr = LAPACK.ggev!('N', 'V', A, B)
    else
        alpha, beta, _, vr = LAPACK.ggev3!('N', 'V', A, B)
    end
    return GeneralizedEigen(sorteig!(alpha./beta, vr, sortby)...)
end

"""
    eigen(A, B; sortby) -> GeneralizedEigen

Compute the generalized eigenvalue decomposition of `A` and `B`, returning a
[`GeneralizedEigen`](@ref) factorization object `F` which contains the generalized eigenvalues in
`F.values` and the generalized eigenvectors in the columns of the matrix `F.vectors`.
This corresponds to solving a generalized eigenvalue problem of the form
`Ax =  λBx`, where `A, B` are matrices, `x` is an eigenvector, and `λ` is an eigenvalue.
(The `k`th generalized eigenvector can be obtained from the slice `F.vectors[:, k]`.)

Iterating the decomposition produces the components `F.values` and `F.vectors`.

By default, the eigenvalues and vectors are sorted lexicographically by `(real(λ),imag(λ))`.
A different comparison function `by(λ)` can be passed to `sortby`, or you can pass
`sortby=nothing` to leave the eigenvalues in an arbitrary order.

# Examples
```jldoctest
julia> A = [1 0; 0 -1]
2×2 Matrix{Int64}:
 1   0
 0  -1

julia> B = [0 1; 1 0]
2×2 Matrix{Int64}:
 0  1
 1  0

julia> F = eigen(A, B);

julia> F.values
2-element Vector{ComplexF64}:
 0.0 - 1.0im
 0.0 + 1.0im

julia> F.vectors
2×2 Matrix{ComplexF64}:
  0.0+1.0im   0.0-1.0im
 -1.0+0.0im  -1.0-0.0im

julia> vals, vecs = F; # destructuring via iteration

julia> vals == F.values && vecs == F.vectors
true
```
"""
function eigen(A::AbstractMatrix{TA}, B::AbstractMatrix{TB}; kws...) where {TA,TB}
    S = promote_type(eigtype(TA), TB)
    eigen!(copy_similar(A, S), copy_similar(B, S); kws...)
end
eigen(A::Number, B::Number) = eigen(fill(A,1,1), fill(B,1,1))

"""
    LinearAlgebra.eigencopy_oftype(A::AbstractMatrix, ::Type{S})

Creates a dense copy of `A` with eltype `S` by calling `copy_similar(A, S)`.
In the case of `Hermitian` or `Symmetric` matrices additionally retains the wrapper,
together with the `uplo` field.
"""
eigencopy_oftype(A, S) = copy_similar(A, S)

"""
    eigvals!(A, B; sortby) -> values

Same as [`eigvals`](@ref), but saves space by overwriting the input `A` (and `B`),
instead of creating copies.

!!! note
    The input matrices `A` and `B` will not contain their eigenvalues after
    `eigvals!` is called. They are used as workspaces.

# Examples
```jldoctest
julia> A = [1. 0.; 0. -1.]
2×2 Matrix{Float64}:
 1.0   0.0
 0.0  -1.0

julia> B = [0. 1.; 1. 0.]
2×2 Matrix{Float64}:
 0.0  1.0
 1.0  0.0

julia> eigvals!(A, B)
2-element Vector{ComplexF64}:
 0.0 - 1.0im
 0.0 + 1.0im

julia> A
2×2 Matrix{Float64}:
 -0.0  -1.0
  1.0  -0.0

julia> B
2×2 Matrix{Float64}:
 1.0  0.0
 0.0  1.0
```
"""
function eigvals!(A::StridedMatrix{T}, B::StridedMatrix{T}; sortby::Union{Function,Nothing}=eigsortby) where T<:BlasReal
    issymmetric(A) && isposdef(B) && return sorteig!(eigvals!(Symmetric(A), Symmetric(B)), sortby)
    if LAPACK.version() < v"3.6.0"
        alphar, alphai, beta, vl, vr = LAPACK.ggev!('N', 'N', A, B)
    else
        alphar, alphai, beta, vl, vr = LAPACK.ggev3!('N', 'N', A, B)
    end
    return sorteig!((iszero(alphai) ? alphar : complex.(alphar, alphai))./beta, sortby)
end
function eigvals!(A::StridedMatrix{T}, B::StridedMatrix{T}; sortby::Union{Function,Nothing}=eigsortby) where T<:BlasComplex
    ishermitian(A) && isposdef(B) && return sorteig!(eigvals!(Hermitian(A), Hermitian(B)), sortby)
    if LAPACK.version() < v"3.6.0"
        alpha, beta, vl, vr = LAPACK.ggev!('N', 'N', A, B)
    else
        alpha, beta, vl, vr = LAPACK.ggev3!('N', 'N', A, B)
    end
    return sorteig!(alpha./beta, sortby)
end

"""
    eigvals(A, B) -> values

Compute the generalized eigenvalues of `A` and `B`.

# Examples
```jldoctest
julia> A = [1 0; 0 -1]
2×2 Matrix{Int64}:
 1   0
 0  -1

julia> B = [0 1; 1 0]
2×2 Matrix{Int64}:
 0  1
 1  0

julia> eigvals(A,B)
2-element Vector{ComplexF64}:
 0.0 - 1.0im
 0.0 + 1.0im
```
"""
function eigvals(A::AbstractMatrix{TA}, B::AbstractMatrix{TB}; kws...) where {TA,TB}
    S = promote_type(eigtype(TA), TB)
    return eigvals!(copy_similar(A, S), copy_similar(B, S); kws...)
end

"""
    eigvecs(A, B) -> Matrix

Return a matrix `M` whose columns are the generalized eigenvectors of `A` and `B`. (The `k`th eigenvector can
be obtained from the slice `M[:, k]`.)

# Examples
```jldoctest
julia> A = [1 0; 0 -1]
2×2 Matrix{Int64}:
 1   0
 0  -1

julia> B = [0 1; 1 0]
2×2 Matrix{Int64}:
 0  1
 1  0

julia> eigvecs(A, B)
2×2 Matrix{ComplexF64}:
  0.0+1.0im   0.0-1.0im
 -1.0+0.0im  -1.0-0.0im
```
"""
eigvecs(A::AbstractMatrix, B::AbstractMatrix; kws...) = eigvecs(eigen(A, B; kws...))

function show(io::IO, mime::MIME{Symbol("text/plain")}, F::Union{Eigen,GeneralizedEigen})
    summary(io, F); println(io)
    println(io, "values:")
    show(io, mime, F.values)
    println(io, "\nvectors:")
    show(io, mime, F.vectors)
end

function Base.hash(F::Eigen, h::UInt)
    return hash(F.values, hash(F.vectors, hash(Eigen, h)))
end
function Base.:(==)(A::Eigen, B::Eigen)
    return A.values == B.values && A.vectors == B.vectors
end
function Base.isequal(A::Eigen, B::Eigen)
    return isequal(A.values, B.values) && isequal(A.vectors, B.vectors)
end

# Conversion methods

## Can we determine the source/result is Real?  This is not stored in the type Eigen
AbstractMatrix(F::Eigen) = F.vectors * Diagonal(F.values) / F.vectors
AbstractArray(F::Eigen) = AbstractMatrix(F)
Matrix(F::Eigen) = Array(AbstractArray(F))
Array(F::Eigen) = Matrix(F)
t   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LinearAlgebra/src/svd.jl�G      # This file is a part of Julia. License is MIT: https://julialang.org/license

# Singular Value Decomposition
"""
    SVD <: Factorization

Matrix factorization type of the singular value decomposition (SVD) of a matrix `A`.
This is the return type of [`svd(_)`](@ref), the corresponding matrix factorization function.

If `F::SVD` is the factorization object, `U`, `S`, `V` and `Vt` can be obtained
via `F.U`, `F.S`, `F.V` and `F.Vt`, such that `A = U * Diagonal(S) * Vt`.
The singular values in `S` are sorted in descending order.

Iterating the decomposition produces the components `U`, `S`, and `V`.

# Examples
```jldoctest
julia> A = [1. 0. 0. 0. 2.; 0. 0. 3. 0. 0.; 0. 0. 0. 0. 0.; 0. 2. 0. 0. 0.]
4×5 Matrix{Float64}:
 1.0  0.0  0.0  0.0  2.0
 0.0  0.0  3.0  0.0  0.0
 0.0  0.0  0.0  0.0  0.0
 0.0  2.0  0.0  0.0  0.0

julia> F = svd(A)
SVD{Float64, Float64, Matrix{Float64}, Vector{Float64}}
U factor:
4×4 Matrix{Float64}:
 0.0  1.0   0.0  0.0
 1.0  0.0   0.0  0.0
 0.0  0.0   0.0  1.0
 0.0  0.0  -1.0  0.0
singular values:
4-element Vector{Float64}:
 3.0
 2.23606797749979
 2.0
 0.0
Vt factor:
4×5 Matrix{Float64}:
 -0.0        0.0  1.0  -0.0  0.0
  0.447214   0.0  0.0   0.0  0.894427
  0.0       -1.0  0.0   0.0  0.0
  0.0        0.0  0.0   1.0  0.0

julia> F.U * Diagonal(F.S) * F.Vt
4×5 Matrix{Float64}:
 1.0  0.0  0.0  0.0  2.0
 0.0  0.0  3.0  0.0  0.0
 0.0  0.0  0.0  0.0  0.0
 0.0  2.0  0.0  0.0  0.0

julia> u, s, v = F; # destructuring via iteration

julia> u == F.U && s == F.S && v == F.V
true
```
"""
struct SVD{T,Tr,M<:AbstractArray{T},C<:AbstractVector{Tr}} <: Factorization{T}
    U::M
    S::C
    Vt::M
    function SVD{T,Tr,M,C}(U, S, Vt) where {T,Tr,M<:AbstractArray{T},C<:AbstractVector{Tr}}
        require_one_based_indexing(U, S, Vt)
        new{T,Tr,M,C}(U, S, Vt)
    end
end
SVD(U::AbstractArray{T}, S::AbstractVector{Tr}, Vt::AbstractArray{T}) where {T,Tr} =
    SVD{T,Tr,typeof(U),typeof(S)}(U, S, Vt)
SVD{T}(U::AbstractArray, S::AbstractVector{Tr}, Vt::AbstractArray) where {T,Tr} =
    SVD(convert(AbstractArray{T}, U),
        convert(AbstractVector{Tr}, S),
        convert(AbstractArray{T}, Vt))
# backwards-compatible constructors (remove with Julia 2.0)
@deprecate(SVD{T,Tr,M}(U::AbstractArray{T}, S::AbstractVector{Tr}, Vt::AbstractArray{T}) where {T,Tr,M},
           SVD{T,Tr,M,typeof(S)}(U, S, Vt))

SVD{T}(F::SVD) where {T} = SVD(
    convert(AbstractMatrix{T}, F.U),
    convert(AbstractVector{real(T)}, F.S),
    convert(AbstractMatrix{T}, F.Vt))
Factorization{T}(F::SVD) where {T} = SVD{T}(F)

# iteration for destructuring into components
Base.iterate(S::SVD) = (S.U, Val(:S))
Base.iterate(S::SVD, ::Val{:S}) = (S.S, Val(:V))
Base.iterate(S::SVD, ::Val{:V}) = (S.V, Val(:done))
Base.iterate(S::SVD, ::Val{:done}) = nothing


default_svd_alg(A) = DivideAndConquer()


"""
    svd!(A; full::Bool = false, alg::Algorithm = default_svd_alg(A)) -> SVD

`svd!` is the same as [`svd`](@ref), but saves space by
overwriting the input `A`, instead of creating a copy. See documentation of [`svd`](@ref) for details.
"""
function svd!(A::StridedMatrix{T}; full::Bool = false, alg::Algorithm = default_svd_alg(A)) where {T<:BlasFloat}
    m, n = size(A)
    if m == 0 || n == 0
        u, s, vt = (Matrix{T}(I, m, full ? m : n), real(zeros(T,0)), Matrix{T}(I, n, n))
    else
        u, s, vt = _svd!(A, full, alg)
    end
    SVD(u, s, vt)
end
function svd!(A::StridedVector{T}; full::Bool = false, alg::Algorithm = default_svd_alg(A)) where {T<:BlasFloat}
    m = length(A)
    normA = norm(A)
    if iszero(normA)
        return SVD(Matrix{T}(I, m, full ? m : 1), [normA], ones(T, 1, 1))
    elseif !full
        normalize!(A)
        return SVD(reshape(A, (m, 1)), [normA], ones(T, 1, 1))
    else
        u, s, vt = _svd!(reshape(A, (m, 1)), full, alg)
        return SVD(u, s, vt)
    end
end

_svd!(A::StridedMatrix{T}, full::Bool, alg::Algorithm) where {T<:BlasFloat} =
    throw(ArgumentError("Unsupported value for `alg` keyword."))
_svd!(A::StridedMatrix{T}, full::Bool, alg::DivideAndConquer) where {T<:BlasFloat} =
    LAPACK.gesdd!(full ? 'A' : 'S', A)
function _svd!(A::StridedMatrix{T}, full::Bool, alg::QRIteration) where {T<:BlasFloat}
    c = full ? 'A' : 'S'
    u, s, vt = LAPACK.gesvd!(c, c, A)
end


"""
    svd(A; full::Bool = false, alg::Algorithm = default_svd_alg(A)) -> SVD

Compute the singular value decomposition (SVD) of `A` and return an `SVD` object.

`U`, `S`, `V` and `Vt` can be obtained from the factorization `F` with `F.U`,
`F.S`, `F.V` and `F.Vt`, such that `A = U * Diagonal(S) * Vt`.
The algorithm produces `Vt` and hence `Vt` is more efficient to extract than `V`.
The singular values in `S` are sorted in descending order.

Iterating the decomposition produces the components `U`, `S`, and `V`.

If `full = false` (default), a "thin" SVD is returned. For an ``M
\\times N`` matrix `A`, in the full factorization `U` is ``M \\times M``
and `V` is ``N \\times N``, while in the thin factorization `U` is ``M
\\times K`` and `V` is ``N \\times K``, where ``K = \\min(M,N)`` is the
number of singular values.

If `alg = DivideAndConquer()` a divide-and-conquer algorithm is used to calculate the SVD.
Another (typically slower but more accurate) option is `alg = QRIteration()`.

!!! compat "Julia 1.3"
    The `alg` keyword argument requires Julia 1.3 or later.

# Examples
```jldoctest
julia> A = rand(4,3);

julia> F = svd(A); # Store the Factorization Object

julia> A ≈ F.U * Diagonal(F.S) * F.Vt
true

julia> U, S, V = F; # destructuring via iteration

julia> A ≈ U * Diagonal(S) * V'
true

julia> Uonly, = svd(A); # Store U only

julia> Uonly == U
true
```
"""
function svd(A::AbstractVecOrMat{T}; full::Bool = false, alg::Algorithm = default_svd_alg(A)) where {T}
    svd!(eigencopy_oftype(A, eigtype(T)), full = full, alg = alg)
end
function svd(A::AbstractVecOrMat{T}; full::Bool = false, alg::Algorithm = default_svd_alg(A)) where {T <: Union{Float16,Complex{Float16}}}
    A = svd!(eigencopy_oftype(A, eigtype(T)), full = full, alg = alg)
    return SVD{T}(A)
end
function svd(x::Number; full::Bool = false, alg::Algorithm = default_svd_alg(x))
    SVD(x == 0 ? fill(one(x), 1, 1) : fill(x/abs(x), 1, 1), [abs(x)], fill(one(x), 1, 1))
end
function svd(x::Integer; full::Bool = false, alg::Algorithm = default_svd_alg(x))
    svd(float(x), full = full, alg = alg)
end
function svd(A::Adjoint; full::Bool = false, alg::Algorithm = default_svd_alg(A))
    s = svd(A.parent, full = full, alg = alg)
    return SVD(s.Vt', s.S, s.U')
end
function svd(A::Transpose; full::Bool = false, alg::Algorithm = default_svd_alg(A))
    s = svd(A.parent, full = full, alg = alg)
    return SVD(transpose(s.Vt), s.S, transpose(s.U))
end

function getproperty(F::SVD, d::Symbol)
    if d === :V
        return getfield(F, :Vt)'
    else
        return getfield(F, d)
    end
end

Base.propertynames(F::SVD, private::Bool=false) =
    private ? (:V, fieldnames(typeof(F))...) : (:U, :S, :V, :Vt)

"""
    svdvals!(A)

Return the singular values of `A`, saving space by overwriting the input.
See also [`svdvals`](@ref) and [`svd`](@ref).
"""
svdvals!(A::StridedMatrix{T}) where {T<:BlasFloat} = isempty(A) ? zeros(real(T), 0) : LAPACK.gesdd!('N', A)[2]
svdvals!(A::StridedVector{T}) where {T<:BlasFloat} = svdvals!(reshape(A, (length(A), 1)))

"""
    svdvals(A)

Return the singular values of `A` in descending order.

# Examples
```jldoctest
julia> A = [1. 0. 0. 0. 2.; 0. 0. 3. 0. 0.; 0. 0. 0. 0. 0.; 0. 2. 0. 0. 0.]
4×5 Matrix{Float64}:
 1.0  0.0  0.0  0.0  2.0
 0.0  0.0  3.0  0.0  0.0
 0.0  0.0  0.0  0.0  0.0
 0.0  2.0  0.0  0.0  0.0

julia> svdvals(A)
4-element Vector{Float64}:
 3.0
 2.23606797749979
 2.0
 0.0
```
"""
svdvals(A::AbstractMatrix{T}) where {T} = svdvals!(eigencopy_oftype(A, eigtype(T)))
svdvals(A::AbstractVector{T}) where {T} = [convert(eigtype(T), norm(A))]
svdvals(x::Number) = abs(x)
svdvals(S::SVD{<:Any,T}) where {T} = (S.S)::Vector{T}

### SVD least squares ###
function ldiv!(A::SVD{T}, B::AbstractVecOrMat) where T
    m, n = size(A)
    k = searchsortedlast(A.S, eps(real(T))*A.S[1], rev=true)
    mul!(view(B, 1:n, :), view(A.Vt, 1:k, :)', view(A.S, 1:k) .\ (view(A.U, :, 1:k)' * _cut_B(B, 1:m)))
    return B
end

function inv(F::SVD{T}) where T
    @inbounds for i in eachindex(F.S)
        iszero(F.S[i]) && throw(SingularException(i))
    end
    k = searchsortedlast(F.S, eps(real(T))*F.S[1], rev=true)
    @views (F.S[1:k] .\ F.Vt[1:k, :])' * F.U[:,1:k]'
end

size(A::SVD, dim::Integer) = dim == 1 ? size(A.U, dim) : size(A.Vt, dim)
size(A::SVD) = (size(A, 1), size(A, 2))

function adjoint(F::SVD)
    return SVD(F.Vt', F.S, F.U')
end

function show(io::IO, mime::MIME{Symbol("text/plain")}, F::SVD{<:Any,<:Any,<:AbstractArray,<:AbstractVector})
    summary(io, F); println(io)
    println(io, "U factor:")
    show(io, mime, F.U)
    println(io, "\nsingular values:")
    show(io, mime, F.S)
    println(io, "\nVt factor:")
    show(io, mime, F.Vt)
end

# Generalized svd
"""
    GeneralizedSVD <: Factorization

Matrix factorization type of the generalized singular value decomposition (SVD)
of two matrices `A` and `B`, such that `A = F.U*F.D1*F.R0*F.Q'` and
`B = F.V*F.D2*F.R0*F.Q'`. This is the return type of [`svd(_, _)`](@ref), the
corresponding matrix factorization function.

For an M-by-N matrix `A` and P-by-N matrix `B`,

- `U` is a M-by-M orthogonal matrix,
- `V` is a P-by-P orthogonal matrix,
- `Q` is a N-by-N orthogonal matrix,
- `D1` is a M-by-(K+L) diagonal matrix with 1s in the first K entries,
- `D2` is a P-by-(K+L) matrix whose top right L-by-L block is diagonal,
- `R0` is a (K+L)-by-N matrix whose rightmost (K+L)-by-(K+L) block is
           nonsingular upper block triangular,

`K+L` is the effective numerical rank of the matrix `[A; B]`.

Iterating the decomposition produces the components `U`, `V`, `Q`, `D1`, `D2`, and `R0`.

The entries of `F.D1` and `F.D2` are related, as explained in the LAPACK
documentation for the
[generalized SVD](http://www.netlib.org/lapack/lug/node36.html) and the
[xGGSVD3](http://www.netlib.org/lapack/explore-html/d6/db3/dggsvd3_8f.html)
routine which is called underneath (in LAPACK 3.6.0 and newer).

# Examples
```jldoctest
julia> A = [1. 0.; 0. -1.]
2×2 Matrix{Float64}:
 1.0   0.0
 0.0  -1.0

julia> B = [0. 1.; 1. 0.]
2×2 Matrix{Float64}:
 0.0  1.0
 1.0  0.0

julia> F = svd(A, B)
GeneralizedSVD{Float64, Matrix{Float64}, Float64, Vector{Float64}}
U factor:
2×2 Matrix{Float64}:
 1.0  0.0
 0.0  1.0
V factor:
2×2 Matrix{Float64}:
 -0.0  -1.0
  1.0   0.0
Q factor:
2×2 Matrix{Float64}:
 1.0  0.0
 0.0  1.0
D1 factor:
2×2 Matrix{Float64}:
 0.707107  0.0
 0.0       0.707107
D2 factor:
2×2 Matrix{Float64}:
 0.707107  0.0
 0.0       0.707107
R0 factor:
2×2 Matrix{Float64}:
 1.41421   0.0
 0.0      -1.41421

julia> F.U*F.D1*F.R0*F.Q'
2×2 Matrix{Float64}:
 1.0   0.0
 0.0  -1.0

julia> F.V*F.D2*F.R0*F.Q'
2×2 Matrix{Float64}:
 -0.0  1.0
  1.0  0.0
```
"""
struct GeneralizedSVD{T,S<:AbstractMatrix,Tr,C<:AbstractVector{Tr}} <: Factorization{T}
    U::S
    V::S
    Q::S
    a::C
    b::C
    k::Int
    l::Int
    R::S
    function GeneralizedSVD{T,S,Tr,C}(U, V, Q, a, b, k, l, R) where {T,S<:AbstractMatrix{T},Tr,C<:AbstractVector{Tr}}
        new{T,S,Tr,C}(U, V, Q, a, b, k, l, R)
    end
end
GeneralizedSVD(U::AbstractMatrix{T}, V::AbstractMatrix{T}, Q::AbstractMatrix{T},
              a::AbstractVector{Tr}, b::AbstractVector{Tr}, k::Int, l::Int,
              R::AbstractMatrix{T}) where {T, Tr} =
    GeneralizedSVD{T,typeof(U),Tr,typeof(a)}(U, V, Q, a, b, k, l, R)
# backwards-compatible constructors (remove with Julia 2.0)
@deprecate(GeneralizedSVD{T,S}(U, V, Q, a, b, k, l, R) where {T, S},
           GeneralizedSVD{T,S,real(T),typeof(a)}(U, V, Q, a, b, k, l, R))

# iteration for destructuring into components
Base.iterate(S::GeneralizedSVD) = (S.U, Val(:V))
Base.iterate(S::GeneralizedSVD, ::Val{:V}) = (S.V, Val(:Q))
Base.iterate(S::GeneralizedSVD, ::Val{:Q}) = (S.Q, Val(:D1))
Base.iterate(S::GeneralizedSVD, ::Val{:D1}) = (S.D1, Val(:D2))
Base.iterate(S::GeneralizedSVD, ::Val{:D2}) = (S.D2, Val(:R0))
Base.iterate(S::GeneralizedSVD, ::Val{:R0}) = (S.R0, Val(:done))
Base.iterate(S::GeneralizedSVD, ::Val{:done}) = nothing

"""
    svd!(A, B) -> GeneralizedSVD

`svd!` is the same as [`svd`](@ref), but modifies the arguments
`A` and `B` in-place, instead of making copies. See documentation of [`svd`](@ref) for details.
"""
function svd!(A::StridedMatrix{T}, B::StridedMatrix{T}) where T<:BlasFloat
    # xggsvd3 replaced xggsvd in LAPACK 3.6.0
    if LAPACK.version() < v"3.6.0"
        U, V, Q, a, b, k, l, R = LAPACK.ggsvd!('U', 'V', 'Q', A, B)
    else
        U, V, Q, a, b, k, l, R = LAPACK.ggsvd3!('U', 'V', 'Q', A, B)
    end
    GeneralizedSVD(U, V, Q, a, b, Int(k), Int(l), R)
end
svd(A::AbstractMatrix{T}, B::AbstractMatrix{T}) where {T<:BlasFloat} =
    svd!(copy_similar(A, T), copy_similar(B, T))

"""

    svd(A, B) -> GeneralizedSVD

Compute the generalized SVD of `A` and `B`, returning a `GeneralizedSVD` factorization
object `F` such that `[A;B] = [F.U * F.D1; F.V * F.D2] * F.R0 * F.Q'`

- `U` is a M-by-M orthogonal matrix,
- `V` is a P-by-P orthogonal matrix,
- `Q` is a N-by-N orthogonal matrix,
- `D1` is a M-by-(K+L) diagonal matrix with 1s in the first K entries,
- `D2` is a P-by-(K+L) matrix whose top right L-by-L block is diagonal,
- `R0` is a (K+L)-by-N matrix whose rightmost (K+L)-by-(K+L) block is
           nonsingular upper block triangular,

`K+L` is the effective numerical rank of the matrix `[A; B]`.

Iterating the decomposition produces the components `U`, `V`, `Q`, `D1`, `D2`, and `R0`.

The generalized SVD is used in applications such as when one wants to compare how much belongs
to `A` vs. how much belongs to `B`, as in human vs yeast genome, or signal vs noise, or between
clusters vs within clusters. (See Edelman and Wang for discussion: https://arxiv.org/abs/1901.00485)

It decomposes `[A; B]` into `[UC; VS]H`, where `[UC; VS]` is a natural orthogonal basis for the
column space of `[A; B]`, and `H = RQ'` is a natural non-orthogonal basis for the rowspace of `[A;B]`,
where the top rows are most closely attributed to the `A` matrix, and the bottom to the `B` matrix.
The multi-cosine/sine matrices `C` and `S` provide a multi-measure of how much `A` vs how much `B`,
and `U` and `V` provide directions in which these are measured.

# Examples
```jldoctest
julia> A = randn(3,2); B=randn(4,2);

julia> F = svd(A, B);

julia> U,V,Q,C,S,R = F;

julia> H = R*Q';

julia> [A; B] ≈ [U*C; V*S]*H
true

julia> [A; B] ≈ [F.U*F.D1; F.V*F.D2]*F.R0*F.Q'
true

julia> Uonly, = svd(A,B);

julia> U == Uonly
true
```
"""
function svd(A::AbstractMatrix{TA}, B::AbstractMatrix{TB}) where {TA,TB}
    S = promote_type(eigtype(TA),TB)
    return svd!(copy_similar(A, S), copy_similar(B, S))
end
# This method can be heavily optimized but it is probably not critical
# and might introduce bugs or inconsistencies relative to the 1x1 matrix
# version
svd(x::Number, y::Number) = svd(fill(x, 1, 1), fill(y, 1, 1))

@inline function getproperty(F::GeneralizedSVD{T}, d::Symbol) where T
    Fa = getfield(F, :a)
    Fb = getfield(F, :b)
    Fk = getfield(F, :k)
    Fl = getfield(F, :l)
    FU = getfield(F, :U)
    FV = getfield(F, :V)
    FQ = getfield(F, :Q)
    FR = getfield(F, :R)
    if d === :alpha
        return Fa
    elseif d === :beta
        return Fb
    elseif d === :vals || d === :S
        return Fa[1:Fk + Fl] ./ Fb[1:Fk + Fl]
    elseif d === :D1
        m = size(FU, 1)
        if m - Fk - Fl >= 0
            return [Matrix{T}(I, Fk, Fk)  zeros(T, Fk, Fl)            ;
                    zeros(T, Fl, Fk)      Diagonal(Fa[Fk + 1:Fk + Fl]);
                    zeros(T, m - Fk - Fl, Fk + Fl)                    ]
        else
            return [Matrix{T}(I, m, Fk) [zeros(T, Fk, m - Fk); Diagonal(Fa[Fk + 1:m])] zeros(T, m, Fk + Fl - m)]
        end
    elseif d === :D2
        m = size(FU, 1)
        p = size(FV, 1)
        if m - Fk - Fl >= 0
            return [zeros(T, Fl, Fk) Diagonal(Fb[Fk + 1:Fk + Fl]); zeros(T, p - Fl, Fk + Fl)]
        else
            return [zeros(T, p, Fk) [Diagonal(Fb[Fk + 1:m]); zeros(T, Fk + p - m, m - Fk)] [zeros(T, m - Fk, Fk + Fl - m); Matrix{T}(I, Fk + p - m, Fk + Fl - m)]]
        end
    elseif d === :R0
        n = size(FQ, 1)
        return [zeros(T, Fk + Fl, n - Fk - Fl) FR]
    else
        getfield(F, d)
    end
end

Base.propertynames(F::GeneralizedSVD) =
    (:alpha, :beta, :vals, :S, :D1, :D2, :R0, fieldnames(typeof(F))...)

function show(io::IO, mime::MIME{Symbol("text/plain")}, F::GeneralizedSVD{<:Any,<:AbstractArray})
    summary(io, F); println(io)
    println(io, "U factor:")
    show(io, mime, F.U)
    println(io, "\nV factor:")
    show(io, mime, F.V)
    println(io, "\nQ factor:")
    show(io, mime, F.Q)
    println(io, "\nD1 factor:")
    show(io, mime, F.D1)
    println(io, "\nD2 factor:")
    show(io, mime, F.D2)
    println(io, "\nR0 factor:")
    show(io, mime, F.R0)
end

"""
    svdvals!(A, B)

Return the generalized singular values from the generalized singular value
decomposition of `A` and `B`, saving space by overwriting `A` and `B`.
See also [`svd`](@ref) and [`svdvals`](@ref).
"""
function svdvals!(A::StridedMatrix{T}, B::StridedMatrix{T}) where T<:BlasFloat
    # xggsvd3 replaced xggsvd in LAPACK 3.6.0
    if LAPACK.version() < v"3.6.0"
        _, _, _, a, b, k, l, _ = LAPACK.ggsvd!('N', 'N', 'N', A, B)
    else
        _, _, _, a, b, k, l, _ = LAPACK.ggsvd3!('N', 'N', 'N', A, B)
    end
    a[1:k + l] ./ b[1:k + l]
end

"""
    svdvals(A, B)

Return the generalized singular values from the generalized singular value
decomposition of `A` and `B`. See also [`svd`](@ref).

# Examples
```jldoctest
julia> A = [1. 0.; 0. -1.]
2×2 Matrix{Float64}:
 1.0   0.0
 0.0  -1.0

julia> B = [0. 1.; 1. 0.]
2×2 Matrix{Float64}:
 0.0  1.0
 1.0  0.0

julia> svdvals(A, B)
2-element Vector{Float64}:
 1.0
 1.0
```
"""
function svdvals(A::AbstractMatrix{TA}, B::AbstractMatrix{TB}) where {TA,TB}
    S = promote_type(eigtype(TA), TB)
    return svdvals!(copy_similar(A, S), copy_similar(B, S))
end
svdvals(x::Number, y::Number) = abs(x/y)

# Conversion
AbstractMatrix(F::SVD) = (F.U * Diagonal(F.S)) * F.Vt
AbstractArray(F::SVD) = AbstractMatrix(F)
Matrix(F::SVD) = Array(AbstractArray(F))
Array(F::SVD) = Matrix(F)
z   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LinearAlgebra/src/symmetric.jl�v      # This file is a part of Julia. License is MIT: https://julialang.org/license

# Symmetric and Hermitian matrices
struct Symmetric{T,S<:AbstractMatrix{<:T}} <: AbstractMatrix{T}
    data::S
    uplo::Char

    function Symmetric{T,S}(data, uplo::Char) where {T,S<:AbstractMatrix{<:T}}
        require_one_based_indexing(data)
        (uplo != 'U' && uplo != 'L') && throw_uplo()
        new{T,S}(data, uplo)
    end
end
"""
    Symmetric(A, uplo=:U)

Construct a `Symmetric` view of the upper (if `uplo = :U`) or lower (if `uplo = :L`)
triangle of the matrix `A`.

`Symmetric` views are mainly useful for real-symmetric matrices, for which
specialized algorithms (e.g. for eigenproblems) are enabled for `Symmetric` types.
More generally, see also [`Hermitian(A)`](@ref) for Hermitian matrices `A == A'`, which
is effectively equivalent to `Symmetric` for real matrices but is also useful for
complex matrices.  (Whereas complex `Symmetric` matrices are supported but have few
if any specialized algorithms.)

To compute the symmetric part of a real matrix, or more generally the Hermitian part `(A + A') / 2` of
a real or complex matrix `A`, use [`hermitianpart`](@ref).

# Examples
```jldoctest
julia> A = [1 2 3; 4 5 6; 7 8 9]
3×3 Matrix{Int64}:
 1  2  3
 4  5  6
 7  8  9

julia> Supper = Symmetric(A)
3×3 Symmetric{Int64, Matrix{Int64}}:
 1  2  3
 2  5  6
 3  6  9

julia> Slower = Symmetric(A, :L)
3×3 Symmetric{Int64, Matrix{Int64}}:
 1  4  7
 4  5  8
 7  8  9

julia> hermitianpart(A)
3×3 Hermitian{Float64, Matrix{Float64}}:
 1.0  3.0  5.0
 3.0  5.0  7.0
 5.0  7.0  9.0
```

Note that `Supper` will not be equal to `Slower` unless `A` is itself symmetric (e.g. if
`A == transpose(A)`).
"""
function Symmetric(A::AbstractMatrix, uplo::Symbol=:U)
    checksquare(A)
    return symmetric_type(typeof(A))(A, char_uplo(uplo))
end

"""
    symmetric(A, uplo=:U)

Construct a symmetric view of `A`. If `A` is a matrix, `uplo` controls whether the upper
(if `uplo = :U`) or lower (if `uplo = :L`) triangle of `A` is used to implicitly fill the
other one. If `A` is a `Number`, it is returned as is.

If a symmetric view of a matrix is to be constructed of which the elements are neither
matrices nor numbers, an appropriate method of `symmetric` has to be implemented. In that
case, `symmetric_type` has to be implemented, too.
"""
symmetric(A::AbstractMatrix, uplo::Symbol=:U) = Symmetric(A, uplo)
symmetric(A::Number, ::Symbol=:U) = A

"""
    symmetric_type(T::Type)

The type of the object returned by `symmetric(::T, ::Symbol)`. For matrices, this is an
appropriately typed `Symmetric`, for `Number`s, it is the original type. If `symmetric` is
implemented for a custom type, so should be `symmetric_type`, and vice versa.
"""
function symmetric_type(::Type{T}) where {S, T<:AbstractMatrix{S}}
    return Symmetric{Union{S, promote_op(transpose, S), symmetric_type(S)}, T}
end
function symmetric_type(::Type{T}) where {S<:Number, T<:AbstractMatrix{S}}
    return Symmetric{S, T}
end
function symmetric_type(::Type{T}) where {S<:AbstractMatrix, T<:AbstractMatrix{S}}
    return Symmetric{AbstractMatrix, T}
end
symmetric_type(::Type{T}) where {T<:Number} = T

struct Hermitian{T,S<:AbstractMatrix{<:T}} <: AbstractMatrix{T}
    data::S
    uplo::Char

    function Hermitian{T,S}(data, uplo::Char) where {T,S<:AbstractMatrix{<:T}}
        require_one_based_indexing(data)
        (uplo != 'U' && uplo != 'L') && throw_uplo()
        new{T,S}(data, uplo)
    end
end
"""
    Hermitian(A, uplo=:U)

Construct a `Hermitian` view of the upper (if `uplo = :U`) or lower (if `uplo = :L`)
triangle of the matrix `A`.

To compute the Hermitian part of `A`, use [`hermitianpart`](@ref).

# Examples
```jldoctest
julia> A = [1 2+2im 3-3im; 4 5 6-6im; 7 8+8im 9]
3×3 Matrix{Complex{Int64}}:
 1+0im  2+2im  3-3im
 4+0im  5+0im  6-6im
 7+0im  8+8im  9+0im

julia> Hupper = Hermitian(A)
3×3 Hermitian{Complex{Int64}, Matrix{Complex{Int64}}}:
 1+0im  2+2im  3-3im
 2-2im  5+0im  6-6im
 3+3im  6+6im  9+0im

julia> Hlower = Hermitian(A, :L)
3×3 Hermitian{Complex{Int64}, Matrix{Complex{Int64}}}:
 1+0im  4+0im  7+0im
 4+0im  5+0im  8-8im
 7+0im  8+8im  9+0im

julia> hermitianpart(A)
3×3 Hermitian{ComplexF64, Matrix{ComplexF64}}:
 1.0+0.0im  3.0+1.0im  5.0-1.5im
 3.0-1.0im  5.0+0.0im  7.0-7.0im
 5.0+1.5im  7.0+7.0im  9.0+0.0im
```

Note that `Hupper` will not be equal to `Hlower` unless `A` is itself Hermitian (e.g. if `A == adjoint(A)`).

All non-real parts of the diagonal will be ignored.

```julia
Hermitian(fill(complex(1,1), 1, 1)) == fill(1, 1, 1)
```
"""
function Hermitian(A::AbstractMatrix, uplo::Symbol=:U)
    n = checksquare(A)
    return hermitian_type(typeof(A))(A, char_uplo(uplo))
end

"""
    hermitian(A, uplo=:U)

Construct a hermitian view of `A`. If `A` is a matrix, `uplo` controls whether the upper
(if `uplo = :U`) or lower (if `uplo = :L`) triangle of `A` is used to implicitly fill the
other one. If `A` is a `Number`, its real part is returned converted back to the input
type.

If a hermitian view of a matrix is to be constructed of which the elements are neither
matrices nor numbers, an appropriate method of `hermitian` has to be implemented. In that
case, `hermitian_type` has to be implemented, too.
"""
hermitian(A::AbstractMatrix, uplo::Symbol=:U) = Hermitian(A, uplo)
hermitian(A::Number, ::Symbol=:U) = convert(typeof(A), real(A))

"""
    hermitian_type(T::Type)

The type of the object returned by `hermitian(::T, ::Symbol)`. For matrices, this is an
appropriately typed `Hermitian`, for `Number`s, it is the original type. If `hermitian` is
implemented for a custom type, so should be `hermitian_type`, and vice versa.
"""
function hermitian_type(::Type{T}) where {S, T<:AbstractMatrix{S}}
    return Hermitian{Union{S, promote_op(adjoint, S), hermitian_type(S)}, T}
end
function hermitian_type(::Type{T}) where {S<:Number, T<:AbstractMatrix{S}}
    return Hermitian{S, T}
end
function hermitian_type(::Type{T}) where {S<:AbstractMatrix, T<:AbstractMatrix{S}}
    return Hermitian{AbstractMatrix, T}
end
hermitian_type(::Type{T}) where {T<:Number} = T

_unwrap(A::Hermitian) = parent(A)
_unwrap(A::Symmetric) = parent(A)

for (S, H) in ((:Symmetric, :Hermitian), (:Hermitian, :Symmetric))
    @eval begin
        $S(A::$S) = A
        function $S(A::$S, uplo::Symbol)
            if A.uplo == char_uplo(uplo)
                return A
            else
                throw(ArgumentError("Cannot construct $($S); uplo doesn't match"))
            end
        end
        $S(A::$H) = $S(A, sym_uplo(A.uplo))
        function $S(A::$H, uplo::Symbol)
            if A.uplo == char_uplo(uplo)
                if $H === Hermitian && !(eltype(A) <: Real) &&
                    any(!isreal, A.data[i] for i in diagind(A.data))

                    throw(ArgumentError("Cannot construct $($S)($($H))); diagonal contains complex values"))
                end
                return $S(A.data, sym_uplo(A.uplo))
            else
                throw(ArgumentError("Cannot construct $($S); uplo doesn't match"))
            end
        end
    end
end

convert(::Type{T}, m::Union{Symmetric,Hermitian}) where {T<:Symmetric} = m isa T ? m : T(m)::T
convert(::Type{T}, m::Union{Symmetric,Hermitian}) where {T<:Hermitian} = m isa T ? m : T(m)::T

const HermOrSym{T,        S} = Union{Hermitian{T,S}, Symmetric{T,S}}
const RealHermSym{T<:Real,S} = Union{Hermitian{T,S}, Symmetric{T,S}}
const RealHermSymComplexHerm{T<:Real,S} = Union{Hermitian{T,S}, Symmetric{T,S}, Hermitian{Complex{T},S}}
const RealHermSymComplexSym{T<:Real,S} = Union{Hermitian{T,S}, Symmetric{T,S}, Symmetric{Complex{T},S}}

size(A::HermOrSym, d) = size(A.data, d)
size(A::HermOrSym) = size(A.data)
@inline function Base.isassigned(A::HermOrSym, i::Int, j::Int)
    @boundscheck checkbounds(Bool, A, i, j) || return false
    @inbounds if i == j || ((A.uplo == 'U') == (i < j))
        return isassigned(A.data, i, j)
    else
        return isassigned(A.data, j, i)
    end
end

@inline function getindex(A::Symmetric, i::Integer, j::Integer)
    @boundscheck checkbounds(A, i, j)
    @inbounds if i == j
        return symmetric(A.data[i, j], sym_uplo(A.uplo))::symmetric_type(eltype(A.data))
    elseif (A.uplo == 'U') == (i < j)
        return A.data[i, j]
    else
        return transpose(A.data[j, i])
    end
end
@inline function getindex(A::Hermitian, i::Integer, j::Integer)
    @boundscheck checkbounds(A, i, j)
    @inbounds if i == j
        return hermitian(A.data[i, j], sym_uplo(A.uplo))::hermitian_type(eltype(A.data))
    elseif (A.uplo == 'U') == (i < j)
        return A.data[i, j]
    else
        return adjoint(A.data[j, i])
    end
end

function setindex!(A::Symmetric, v, i::Integer, j::Integer)
    i == j || throw(ArgumentError("Cannot set a non-diagonal index in a symmetric matrix"))
    setindex!(A.data, v, i, j)
end

function setindex!(A::Hermitian, v, i::Integer, j::Integer)
    if i != j
        throw(ArgumentError("Cannot set a non-diagonal index in a Hermitian matrix"))
    elseif !isreal(v)
        throw(ArgumentError("Cannot set a diagonal entry in a Hermitian matrix to a nonreal value"))
    else
        setindex!(A.data, v, i, j)
    end
end

diag(A::Symmetric) = symmetric.(diag(parent(A)), sym_uplo(A.uplo))
diag(A::Hermitian) = hermitian.(diag(parent(A)), sym_uplo(A.uplo))

isdiag(A::HermOrSym) = isdiag(A.uplo == 'U' ? UpperTriangular(A.data) : LowerTriangular(A.data))

# For A<:Union{Symmetric,Hermitian}, similar(A[, neweltype]) should yield a matrix with the same
# symmetry type, uplo flag, and underlying storage type as A. The following methods cover these cases.
similar(A::Symmetric, ::Type{T}) where {T} = Symmetric(similar(parent(A), T), ifelse(A.uplo == 'U', :U, :L))
# If the Hermitian constructor's check ascertaining that the wrapped matrix's
# diagonal is strictly real is removed, the following method can be simplified.
function similar(A::Hermitian, ::Type{T}) where T
    B = similar(parent(A), T)
    for i in 1:size(B, 1) B[i, i] = 0 end
    return Hermitian(B, ifelse(A.uplo == 'U', :U, :L))
end
# On the other hand, similar(A, [neweltype,] shape...) should yield a matrix of the underlying
# storage type of A (not wrapped in a symmetry type). The following method covers these cases.
similar(A::Union{Symmetric,Hermitian}, ::Type{T}, dims::Dims{N}) where {T,N} = similar(parent(A), T, dims)

# Conversion
function Matrix(A::Symmetric)
    B = copytri!(convert(Matrix, copy(A.data)), A.uplo)
    for i = 1:size(A, 1)
        B[i,i] = symmetric(A[i,i], sym_uplo(A.uplo))::symmetric_type(eltype(A.data))
    end
    return B
end
function Matrix(A::Hermitian)
    B = copytri!(convert(Matrix, copy(A.data)), A.uplo, true)
    for i = 1:size(A, 1)
        B[i,i] = hermitian(A[i,i], sym_uplo(A.uplo))::hermitian_type(eltype(A.data))
    end
    return B
end
Array(A::Union{Symmetric,Hermitian}) = convert(Matrix, A)

parent(A::HermOrSym) = A.data
Symmetric{T,S}(A::Symmetric{T,S}) where {T,S<:AbstractMatrix{T}} = A
Symmetric{T,S}(A::Symmetric) where {T,S<:AbstractMatrix{T}} = Symmetric{T,S}(convert(S,A.data),A.uplo)
AbstractMatrix{T}(A::Symmetric) where {T} = Symmetric(convert(AbstractMatrix{T}, A.data), sym_uplo(A.uplo))
Hermitian{T,S}(A::Hermitian{T,S}) where {T,S<:AbstractMatrix{T}} = A
Hermitian{T,S}(A::Hermitian) where {T,S<:AbstractMatrix{T}} = Hermitian{T,S}(convert(S,A.data),A.uplo)
AbstractMatrix{T}(A::Hermitian) where {T} = Hermitian(convert(AbstractMatrix{T}, A.data), sym_uplo(A.uplo))

copy(A::Symmetric{T,S}) where {T,S} = (B = copy(A.data); Symmetric{T,typeof(B)}(B,A.uplo))
copy(A::Hermitian{T,S}) where {T,S} = (B = copy(A.data); Hermitian{T,typeof(B)}(B,A.uplo))

function copyto!(dest::Symmetric, src::Symmetric)
    if src.uplo == dest.uplo
        copyto!(dest.data, src.data)
    else
        transpose!(dest.data, src.data)
    end
    return dest
end

function copyto!(dest::Hermitian, src::Hermitian)
    if src.uplo == dest.uplo
        copyto!(dest.data, src.data)
    else
        adjoint!(dest.data, src.data)
    end
    return dest
end

# fill[stored]!
fill!(A::HermOrSym, x) = fillstored!(A, x)
function fillstored!(A::HermOrSym{T}, x) where T
    xT = convert(T, x)
    if isa(A, Hermitian)
        isreal(xT) || throw(ArgumentError("cannot fill Hermitian matrix with a nonreal value"))
    end
    if A.uplo == 'U'
        fillband!(A.data, xT, 0, size(A,2)-1)
    else # A.uplo == 'L'
        fillband!(A.data, xT, 1-size(A,1), 0)
    end
    return A
end

Base.isreal(A::HermOrSym{<:Real}) = true
function Base.isreal(A::HermOrSym)
    n = size(A, 1)
    @inbounds if A.uplo == 'U'
        for j in 1:n
            for i in 1:(j - (A isa Hermitian))
                if !isreal(A.data[i,j])
                    return false
                end
            end
        end
    else
        for j in 1:n
            for i in (j + (A isa Hermitian)):n
                if !isreal(A.data[i,j])
                    return false
                end
            end
        end
    end
    return true
end

ishermitian(A::Hermitian) = true
ishermitian(A::Symmetric{<:Real}) = true
ishermitian(A::Symmetric{<:Complex}) = isreal(A)
issymmetric(A::Hermitian{<:Real}) = true
issymmetric(A::Hermitian{<:Complex}) = isreal(A)
issymmetric(A::Symmetric) = true

adjoint(A::Hermitian) = A
transpose(A::Symmetric) = A
adjoint(A::Symmetric{<:Real}) = A
transpose(A::Hermitian{<:Real}) = A
adjoint(A::Symmetric) = Adjoint(A)
transpose(A::Hermitian) = Transpose(A)

real(A::Symmetric{<:Real}) = A
real(A::Hermitian{<:Real}) = A
real(A::Symmetric) = Symmetric(real(A.data), sym_uplo(A.uplo))
real(A::Hermitian) = Hermitian(real(A.data), sym_uplo(A.uplo))
imag(A::Symmetric) = Symmetric(imag(A.data), sym_uplo(A.uplo))

Base.copy(A::Adjoint{<:Any,<:Symmetric}) =
    Symmetric(copy(adjoint(A.parent.data)), ifelse(A.parent.uplo == 'U', :L, :U))
Base.copy(A::Transpose{<:Any,<:Hermitian}) =
    Hermitian(copy(transpose(A.parent.data)), ifelse(A.parent.uplo == 'U', :L, :U))

tr(A::Symmetric) = tr(A.data) # to avoid AbstractMatrix fallback (incl. allocations)
tr(A::Hermitian) = real(tr(A.data))

Base.conj(A::HermOrSym) = typeof(A)(conj(A.data), A.uplo)
Base.conj!(A::HermOrSym) = typeof(A)(conj!(A.data), A.uplo)

# tril/triu
function tril(A::Hermitian, k::Integer=0)
    if A.uplo == 'U' && k <= 0
        return tril!(copy(A.data'),k)
    elseif A.uplo == 'U' && k > 0
        return tril!(copy(A.data'),-1) + tril!(triu(A.data),k)
    elseif A.uplo == 'L' && k <= 0
        return tril(A.data,k)
    else
        return tril(A.data,-1) + tril!(triu!(copy(A.data')),k)
    end
end

function tril(A::Symmetric, k::Integer=0)
    if A.uplo == 'U' && k <= 0
        return tril!(copy(transpose(A.data)),k)
    elseif A.uplo == 'U' && k > 0
        return tril!(copy(transpose(A.data)),-1) + tril!(triu(A.data),k)
    elseif A.uplo == 'L' && k <= 0
        return tril(A.data,k)
    else
        return tril(A.data,-1) + tril!(triu!(copy(transpose(A.data))),k)
    end
end

function triu(A::Hermitian, k::Integer=0)
    if A.uplo == 'U' && k >= 0
        return triu(A.data,k)
    elseif A.uplo == 'U' && k < 0
        return triu(A.data,1) + triu!(tril!(copy(A.data')),k)
    elseif A.uplo == 'L' && k >= 0
        return triu!(copy(A.data'),k)
    else
        return triu!(copy(A.data'),1) + triu!(tril(A.data),k)
    end
end

function triu(A::Symmetric, k::Integer=0)
    if A.uplo == 'U' && k >= 0
        return triu(A.data,k)
    elseif A.uplo == 'U' && k < 0
        return triu(A.data,1) + triu!(tril!(copy(transpose(A.data))),k)
    elseif A.uplo == 'L' && k >= 0
        return triu!(copy(transpose(A.data)),k)
    else
        return triu!(copy(transpose(A.data)),1) + triu!(tril(A.data),k)
    end
end

for (T, trans, real) in [(:Symmetric, :transpose, :identity), (:(Hermitian{<:Union{Real,Complex}}), :adjoint, :real)]
    @eval begin
        function dot(A::$T, B::$T)
            n = size(A, 2)
            if n != size(B, 2)
                throw(DimensionMismatch("A has dimensions $(size(A)) but B has dimensions $(size(B))"))
            end

            dotprod = zero(dot(first(A), first(B)))
            @inbounds if A.uplo == 'U' && B.uplo == 'U'
                for j in 1:n
                    for i in 1:(j - 1)
                        dotprod += 2 * $real(dot(A.data[i, j], B.data[i, j]))
                    end
                    dotprod += dot(A[j, j], B[j, j])
                end
            elseif A.uplo == 'L' && B.uplo == 'L'
                for j in 1:n
                    dotprod += dot(A[j, j], B[j, j])
                    for i in (j + 1):n
                        dotprod += 2 * $real(dot(A.data[i, j], B.data[i, j]))
                    end
                end
            elseif A.uplo == 'U' && B.uplo == 'L'
                for j in 1:n
                    for i in 1:(j - 1)
                        dotprod += 2 * $real(dot(A.data[i, j], $trans(B.data[j, i])))
                    end
                    dotprod += dot(A[j, j], B[j, j])
                end
            else
                for j in 1:n
                    dotprod += dot(A[j, j], B[j, j])
                    for i in (j + 1):n
                        dotprod += 2 * $real(dot(A.data[i, j], $trans(B.data[j, i])))
                    end
                end
            end
            return dotprod
        end
    end
end

(-)(A::Symmetric) = Symmetric(-A.data, sym_uplo(A.uplo))
(-)(A::Hermitian) = Hermitian(-A.data, sym_uplo(A.uplo))

## Addition/subtraction
for f ∈ (:+, :-), (Wrapper, conjugation) ∈ ((:Hermitian, :adjoint), (:Symmetric, :transpose))
    @eval begin
        function $f(A::$Wrapper, B::$Wrapper)
            if A.uplo == B.uplo
                return $Wrapper($f(parent(A), parent(B)), sym_uplo(A.uplo))
            elseif A.uplo == 'U'
                return $Wrapper($f(parent(A), $conjugation(parent(B))), :U)
            else
                return $Wrapper($f($conjugation(parent(A)), parent(B)), :U)
            end
        end
    end
end

for f in (:+, :-)
    @eval begin
        $f(A::Hermitian, B::Symmetric{<:Real}) = $f(A, Hermitian(parent(B), sym_uplo(B.uplo)))
        $f(A::Symmetric{<:Real}, B::Hermitian) = $f(Hermitian(parent(A), sym_uplo(A.uplo)), B)
        $f(A::SymTridiagonal, B::Symmetric) = Symmetric($f(A, B.data), sym_uplo(B.uplo))
        $f(A::Symmetric, B::SymTridiagonal) = Symmetric($f(A.data, B), sym_uplo(A.uplo))
        $f(A::SymTridiagonal{<:Real}, B::Hermitian) = Hermitian($f(A, B.data), sym_uplo(B.uplo))
        $f(A::Hermitian, B::SymTridiagonal{<:Real}) = Hermitian($f(A.data, B), sym_uplo(A.uplo))
    end
end

*(A::HermOrSym, B::HermOrSym) = A * copyto!(similar(parent(B)), B)

function dot(x::AbstractVector, A::RealHermSymComplexHerm, y::AbstractVector)
    require_one_based_indexing(x, y)
    n = length(x)
    (n == length(y) == size(A, 1)) || throw(DimensionMismatch())
    data = A.data
    r = dot(zero(eltype(x)), zero(eltype(A)), zero(eltype(y)))
    iszero(n) && return r
    if A.uplo == 'U'
        @inbounds for j = 1:length(y)
            r += dot(x[j], real(data[j,j]), y[j])
            @simd for i = 1:j-1
                Aij = data[i,j]
                r += dot(x[i], Aij, y[j]) + dot(x[j], adjoint(Aij), y[i])
            end
        end
    else # A.uplo == 'L'
        @inbounds for j = 1:length(y)
            r += dot(x[j], real(data[j,j]), y[j])
            @simd for i = j+1:length(y)
                Aij = data[i,j]
                r += dot(x[i], Aij, y[j]) + dot(x[j], adjoint(Aij), y[i])
            end
        end
    end
    return r
end

# Scaling with Number
*(A::Symmetric, x::Number) = Symmetric(A.data*x, sym_uplo(A.uplo))
*(x::Number, A::Symmetric) = Symmetric(x*A.data, sym_uplo(A.uplo))
*(A::Hermitian, x::Real) = Hermitian(A.data*x, sym_uplo(A.uplo))
*(x::Real, A::Hermitian) = Hermitian(x*A.data, sym_uplo(A.uplo))
/(A::Symmetric, x::Number) = Symmetric(A.data/x, sym_uplo(A.uplo))
/(A::Hermitian, x::Real) = Hermitian(A.data/x, sym_uplo(A.uplo))

factorize(A::HermOrSym) = _factorize(A)
function _factorize(A::HermOrSym{T}; check::Bool=true) where T
    TT = typeof(sqrt(oneunit(T)))
    if isdiag(A)
        return Diagonal(A)
    elseif TT <: BlasFloat
        return bunchkaufman(A; check=check)
    else # fallback
        return lu(A; check=check)
    end
end

det(A::RealHermSymComplexHerm) = real(det(_factorize(A; check=false)))
det(A::Symmetric{<:Real}) = det(_factorize(A; check=false))
det(A::Symmetric) = det(_factorize(A; check=false))

\(A::HermOrSym, B::AbstractVector) = \(factorize(A), B)
# Bunch-Kaufman solves can not utilize BLAS-3 for multiple right hand sides
# so using LU is faster for AbstractMatrix right hand side
\(A::HermOrSym, B::AbstractMatrix) = \(isdiag(A) ? Diagonal(A) : lu(A), B)

function _inv(A::HermOrSym)
    n = checksquare(A)
    B = inv!(lu(A))
    conjugate = isa(A, Hermitian)
    # symmetrize
    if A.uplo == 'U' # add to upper triangle
        @inbounds for i = 1:n, j = i:n
            B[i,j] = conjugate ? (B[i,j] + conj(B[j,i])) / 2 : (B[i,j] + B[j,i]) / 2
        end
    else # A.uplo == 'L', add to lower triangle
        @inbounds for i = 1:n, j = i:n
            B[j,i] = conjugate ? (B[j,i] + conj(B[i,j])) / 2 : (B[j,i] + B[i,j]) / 2
        end
    end
    B
end
# StridedMatrix restriction seems necessary due to inv! call in _inv above
inv(A::Hermitian{<:Any,<:StridedMatrix}) = Hermitian(_inv(A), sym_uplo(A.uplo))
inv(A::Symmetric{<:Any,<:StridedMatrix}) = Symmetric(_inv(A), sym_uplo(A.uplo))

function svd(A::RealHermSymComplexHerm; full::Bool=false)
    vals, vecs = eigen(A)
    I = sortperm(vals; by=abs, rev=true)
    permute!(vals, I)
    Base.permutecols!!(vecs, I)         # left-singular vectors
    V = copy(vecs)                      # right-singular vectors
    # shifting -1 from singular values to right-singular vectors
    @inbounds for i = 1:length(vals)
        if vals[i] < 0
            vals[i] = -vals[i]
            for j = 1:size(V,1); V[j,i] = -V[j,i]; end
        end
    end
    return SVD(vecs, vals, V')
end

function svdvals!(A::RealHermSymComplexHerm)
    vals = eigvals!(A)
    for i = 1:length(vals)
        vals[i] = abs(vals[i])
    end
    return sort!(vals, rev = true)
end

# Matrix functions
^(A::Symmetric{<:Real}, p::Integer) = sympow(A, p)
^(A::Symmetric{<:Complex}, p::Integer) = sympow(A, p)
function sympow(A::Symmetric, p::Integer)
    if p < 0
        return Symmetric(Base.power_by_squaring(inv(A), -p))
    else
        return Symmetric(Base.power_by_squaring(A, p))
    end
end
function ^(A::Symmetric{<:Real}, p::Real)
    isinteger(p) && return integerpow(A, p)
    F = eigen(A)
    if all(λ -> λ ≥ 0, F.values)
        return Symmetric((F.vectors * Diagonal((F.values).^p)) * F.vectors')
    else
        return Symmetric((F.vectors * Diagonal((complex(F.values)).^p)) * F.vectors')
    end
end
function ^(A::Symmetric{<:Complex}, p::Real)
    isinteger(p) && return integerpow(A, p)
    return Symmetric(schurpow(A, p))
end
function ^(A::Hermitian, p::Integer)
    if p < 0
        retmat = Base.power_by_squaring(inv(A), -p)
    else
        retmat = Base.power_by_squaring(A, p)
    end
    for i = 1:size(A,1)
        retmat[i,i] = real(retmat[i,i])
    end
    return Hermitian(retmat)
end
function ^(A::Hermitian{T}, p::Real) where T
    isinteger(p) && return integerpow(A, p)
    F = eigen(A)
    if all(λ -> λ ≥ 0, F.values)
        retmat = (F.vectors * Diagonal((F.values).^p)) * F.vectors'
        if T <: Real
            return Hermitian(retmat)
        else
            for i = 1:size(A,1)
                retmat[i,i] = real(retmat[i,i])
            end
            return Hermitian(retmat)
        end
    else
        return (F.vectors * Diagonal((complex(F.values).^p))) * F.vectors'
    end
end

for func in (:exp, :cos, :sin, :tan, :cosh, :sinh, :tanh, :atan, :asinh, :atanh)
    @eval begin
        function ($func)(A::HermOrSym{<:Real})
            F = eigen(A)
            return Symmetric((F.vectors * Diagonal(($func).(F.values))) * F.vectors')
        end
        function ($func)(A::Hermitian{<:Complex})
            n = checksquare(A)
            F = eigen(A)
            retmat = (F.vectors * Diagonal(($func).(F.values))) * F.vectors'
            for i = 1:n
                retmat[i,i] = real(retmat[i,i])
            end
            return Hermitian(retmat)
        end
    end
end

function cis(A::Union{RealHermSymComplexHerm,SymTridiagonal{<:Real}})
    F = eigen(A)
    # The returned matrix is unitary, and is complex-symmetric for real A
    return F.vectors .* cis.(F.values') * F.vectors'
end

for func in (:acos, :asin)
    @eval begin
        function ($func)(A::HermOrSym{<:Real})
            F = eigen(A)
            if all(λ -> -1 ≤ λ ≤ 1, F.values)
                retmat = (F.vectors * Diagonal(($func).(F.values))) * F.vectors'
            else
                retmat = (F.vectors * Diagonal(($func).(complex.(F.values)))) * F.vectors'
            end
            return Symmetric(retmat)
        end
        function ($func)(A::Hermitian{<:Complex})
            n = checksquare(A)
            F = eigen(A)
            if all(λ -> -1 ≤ λ ≤ 1, F.values)
                retmat = (F.vectors * Diagonal(($func).(F.values))) * F.vectors'
                for i = 1:n
                    retmat[i,i] = real(retmat[i,i])
                end
                return Hermitian(retmat)
            else
                return (F.vectors * Diagonal(($func).(complex.(F.values)))) * F.vectors'
            end
        end
    end
end

function acosh(A::HermOrSym{<:Real})
    F = eigen(A)
    if all(λ -> λ ≥ 1, F.values)
        retmat = (F.vectors * Diagonal(acosh.(F.values))) * F.vectors'
    else
        retmat = (F.vectors * Diagonal(acosh.(complex.(F.values)))) * F.vectors'
    end
    return Symmetric(retmat)
end
function acosh(A::Hermitian{<:Complex})
    n = checksquare(A)
    F = eigen(A)
    if all(λ -> λ ≥ 1, F.values)
        retmat = (F.vectors * Diagonal(acosh.(F.values))) * F.vectors'
        for i = 1:n
            retmat[i,i] = real(retmat[i,i])
        end
        return Hermitian(retmat)
    else
        return (F.vectors * Diagonal(acosh.(complex.(F.values)))) * F.vectors'
    end
end

function sincos(A::HermOrSym{<:Real})
    n = checksquare(A)
    F = eigen(A)
    S, C = Diagonal(similar(A, (n,))), Diagonal(similar(A, (n,)))
    for i in 1:n
        S.diag[i], C.diag[i] = sincos(F.values[i])
    end
    return Symmetric((F.vectors * S) * F.vectors'), Symmetric((F.vectors * C) * F.vectors')
end
function sincos(A::Hermitian{<:Complex})
    n = checksquare(A)
    F = eigen(A)
    S, C = Diagonal(similar(A, (n,))), Diagonal(similar(A, (n,)))
    for i in 1:n
        S.diag[i], C.diag[i] = sincos(F.values[i])
    end
    retmatS, retmatC = (F.vectors * S) * F.vectors', (F.vectors * C) * F.vectors'
    for i = 1:n
        retmatS[i,i] = real(retmatS[i,i])
        retmatC[i,i] = real(retmatC[i,i])
    end
    return Hermitian(retmatS), Hermitian(retmatC)
end


for func in (:log, :sqrt)
    # sqrt has rtol arg to handle matrices that are semidefinite up to roundoff errors
    rtolarg = func === :sqrt ? Any[Expr(:kw, :(rtol::Real), :(eps(real(float(one(T))))*size(A,1)))] : Any[]
    rtolval = func === :sqrt ? :(-maximum(abs, F.values) * rtol) : 0
    @eval begin
        function ($func)(A::HermOrSym{T}; $(rtolarg...)) where {T<:Real}
            F = eigen(A)
            λ₀ = $rtolval # treat λ ≥ λ₀ as "zero" eigenvalues up to roundoff
            if all(λ -> λ ≥ λ₀, F.values)
                retmat = (F.vectors * Diagonal(($func).(max.(0, F.values)))) * F.vectors'
            else
                retmat = (F.vectors * Diagonal(($func).(complex.(F.values)))) * F.vectors'
            end
            return Symmetric(retmat)
        end

        function ($func)(A::Hermitian{T}; $(rtolarg...)) where {T<:Complex}
            n = checksquare(A)
            F = eigen(A)
            λ₀ = $rtolval # treat λ ≥ λ₀ as "zero" eigenvalues up to roundoff
            if all(λ -> λ ≥ λ₀, F.values)
                retmat = (F.vectors * Diagonal(($func).(max.(0, F.values)))) * F.vectors'
                for i = 1:n
                    retmat[i,i] = real(retmat[i,i])
                end
                return Hermitian(retmat)
            else
                retmat = (F.vectors * Diagonal(($func).(complex(F.values)))) * F.vectors'
                return retmat
            end
        end
    end
end

"""
    hermitianpart(A, uplo=:U) -> Hermitian

Return the Hermitian part of the square matrix `A`, defined as `(A + A') / 2`, as a
[`Hermitian`](@ref) matrix. For real matrices `A`, this is also known as the symmetric part
of `A`; it is also sometimes called the "operator real part". The optional argument `uplo` controls the corresponding argument of the
[`Hermitian`](@ref) view. For real matrices, the latter is equivalent to a
[`Symmetric`](@ref) view.

See also [`hermitianpart!`](@ref) for the corresponding in-place operation.

!!! compat "Julia 1.10"
    This function requires Julia 1.10 or later.
"""
hermitianpart(A::AbstractMatrix, uplo::Symbol=:U) = Hermitian(_hermitianpart(A), uplo)

"""
    hermitianpart!(A, uplo=:U) -> Hermitian

Overwrite the square matrix `A` in-place with its Hermitian part `(A + A') / 2`, and return
[`Hermitian(A, uplo)`](@ref). For real matrices `A`, this is also known as the symmetric
part of `A`.

See also [`hermitianpart`](@ref) for the corresponding out-of-place operation.

!!! compat "Julia 1.10"
    This function requires Julia 1.10 or later.
"""
hermitianpart!(A::AbstractMatrix, uplo::Symbol=:U) = Hermitian(_hermitianpart!(A), uplo)

_hermitianpart(A::AbstractMatrix) = _hermitianpart!(copy_similar(A, Base.promote_op(/, eltype(A), Int)))
_hermitianpart(a::Number) = real(a)

function _hermitianpart!(A::AbstractMatrix)
    require_one_based_indexing(A)
    n = checksquare(A)
    @inbounds for j in 1:n
        A[j, j] = _hermitianpart(A[j, j])
        for i in 1:j-1
            A[i, j] = val = (A[i, j] + adjoint(A[j, i])) / 2
            A[j, i] = adjoint(val)
        end
    end
    return A
end

## structured matrix printing ##
function Base.replace_in_print_matrix(A::HermOrSym,i::Integer,j::Integer,s::AbstractString)
    ijminmax = minmax(i, j)
    inds = A.uplo == 'U' ? ijminmax : reverse(ijminmax)
    Base.replace_in_print_matrix(parent(A), inds..., s)
end
y   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LinearAlgebra/src/cholesky.jl�n      # This file is a part of Julia. License is MIT: https://julialang.org/license

##########################
# Cholesky Factorization #
##########################

# The dispatch structure in the cholesky, and cholesky! methods is a bit
# complicated and some explanation is therefore provided in the following
#
# In the methods below, LAPACK is called when possible, i.e. StridedMatrices with Float32,
# Float64, ComplexF32, and ComplexF64 element types. For other element or
# matrix types, the unblocked Julia implementation in _chol! is used. For cholesky
# and cholesky! pivoting is supported through a RowMaximum() argument. A type argument is
# necessary for type stability since the output of cholesky and cholesky! is either
# Cholesky or CholeskyPivoted. The latter is only
# supported for the four LAPACK element types. For other types, e.g. BigFloats RowMaximum() will
# give an error. It is required that the input is Hermitian (including real symmetric) either
# through the Hermitian and Symmetric views or exact symmetric or Hermitian elements which
# is checked for and an error is thrown if the check fails.

# The internal structure is as follows
# - _chol! returns the factor and info without checking positive definiteness
# - cholesky/cholesky! returns Cholesky without checking positive definiteness

# FixMe? The dispatch below seems overly complicated. One simplification could be to
# merge the two Cholesky types into one. It would remove the need for Val completely but
# the cost would be extra unnecessary/unused fields for the unpivoted Cholesky and runtime
# checks of those fields before calls to LAPACK to check which version of the Cholesky
# factorization the type represents.
"""
    Cholesky <: Factorization

Matrix factorization type of the Cholesky factorization of a dense symmetric/Hermitian
positive definite matrix `A`. This is the return type of [`cholesky`](@ref),
the corresponding matrix factorization function.

The triangular Cholesky factor can be obtained from the factorization `F::Cholesky`
via `F.L` and `F.U`, where `A ≈ F.U' * F.U ≈ F.L * F.L'`.

The following functions are available for `Cholesky` objects: [`size`](@ref), [`\\`](@ref),
[`inv`](@ref), [`det`](@ref), [`logdet`](@ref) and [`isposdef`](@ref).

Iterating the decomposition produces the components `L` and `U`.

# Examples
```jldoctest
julia> A = [4. 12. -16.; 12. 37. -43.; -16. -43. 98.]
3×3 Matrix{Float64}:
   4.0   12.0  -16.0
  12.0   37.0  -43.0
 -16.0  -43.0   98.0

julia> C = cholesky(A)
Cholesky{Float64, Matrix{Float64}}
U factor:
3×3 UpperTriangular{Float64, Matrix{Float64}}:
 2.0  6.0  -8.0
  ⋅   1.0   5.0
  ⋅    ⋅    3.0

julia> C.U
3×3 UpperTriangular{Float64, Matrix{Float64}}:
 2.0  6.0  -8.0
  ⋅   1.0   5.0
  ⋅    ⋅    3.0

julia> C.L
3×3 LowerTriangular{Float64, Matrix{Float64}}:
  2.0   ⋅    ⋅
  6.0  1.0   ⋅
 -8.0  5.0  3.0

julia> C.L * C.U == A
true

julia> l, u = C; # destructuring via iteration

julia> l == C.L && u == C.U
true
```
"""
struct Cholesky{T,S<:AbstractMatrix} <: Factorization{T}
    factors::S
    uplo::Char
    info::BlasInt

    function Cholesky{T,S}(factors, uplo, info) where {T,S<:AbstractMatrix}
        require_one_based_indexing(factors)
        new(factors, uplo, info)
    end
end
Cholesky(A::AbstractMatrix{T}, uplo::Symbol, info::Integer) where {T} =
    Cholesky{T,typeof(A)}(A, char_uplo(uplo), info)
Cholesky(A::AbstractMatrix{T}, uplo::AbstractChar, info::Integer) where {T} =
    Cholesky{T,typeof(A)}(A, uplo, info)
Cholesky(U::UpperTriangular{T}) where {T} = Cholesky{T,typeof(U.data)}(U.data, 'U', 0)
Cholesky(L::LowerTriangular{T}) where {T} = Cholesky{T,typeof(L.data)}(L.data, 'L', 0)

# iteration for destructuring into components
Base.iterate(C::Cholesky) = (C.L, Val(:U))
Base.iterate(C::Cholesky, ::Val{:U}) = (C.U, Val(:done))
Base.iterate(C::Cholesky, ::Val{:done}) = nothing


"""
    CholeskyPivoted

Matrix factorization type of the pivoted Cholesky factorization of a dense symmetric/Hermitian
positive semi-definite matrix `A`. This is the return type of [`cholesky(_, ::RowMaximum)`](@ref),
the corresponding matrix factorization function.

The triangular Cholesky factor can be obtained from the factorization `F::CholeskyPivoted`
via `F.L` and `F.U`, and the permutation via `F.p`, where `A[F.p, F.p] ≈ Ur' * Ur ≈ Lr * Lr'`
with `Ur = F.U[1:F.rank, :]` and `Lr = F.L[:, 1:F.rank]`, or alternatively
`A ≈ Up' * Up ≈ Lp * Lp'` with `Up = F.U[1:F.rank, invperm(F.p)]` and
`Lp = F.L[invperm(F.p), 1:F.rank]`.

The following functions are available for `CholeskyPivoted` objects:
[`size`](@ref), [`\\`](@ref), [`inv`](@ref), [`det`](@ref), and [`rank`](@ref).

Iterating the decomposition produces the components `L` and `U`.

# Examples
```jldoctest
julia> X = [1.0, 2.0, 3.0, 4.0];

julia> A = X * X';

julia> C = cholesky(A, RowMaximum(), check = false)
CholeskyPivoted{Float64, Matrix{Float64}, Vector{Int64}}
U factor with rank 1:
4×4 UpperTriangular{Float64, Matrix{Float64}}:
 4.0  2.0  3.0  1.0
  ⋅   0.0  6.0  2.0
  ⋅    ⋅   9.0  3.0
  ⋅    ⋅    ⋅   1.0
permutation:
4-element Vector{Int64}:
 4
 2
 3
 1

julia> C.U[1:C.rank, :]' * C.U[1:C.rank, :] ≈ A[C.p, C.p]
true

julia> l, u = C; # destructuring via iteration

julia> l == C.L && u == C.U
true
```
"""
struct CholeskyPivoted{T,S<:AbstractMatrix,P<:AbstractVector{<:Integer}} <: Factorization{T}
    factors::S
    uplo::Char
    piv::P
    rank::BlasInt
    tol::Real
    info::BlasInt

    function CholeskyPivoted{T,S,P}(factors, uplo, piv, rank, tol, info) where {T,S<:AbstractMatrix,P<:AbstractVector}
        require_one_based_indexing(factors)
        new{T,S,P}(factors, uplo, piv, rank, tol, info)
    end
end
CholeskyPivoted(A::AbstractMatrix{T}, uplo::AbstractChar, piv::AbstractVector{<:Integer},
                rank::Integer, tol::Real, info::Integer) where T =
    CholeskyPivoted{T,typeof(A),typeof(piv)}(A, uplo, piv, rank, tol, info)
# backwards-compatible constructors (remove with Julia 2.0)
@deprecate(CholeskyPivoted{T,S}(factors, uplo, piv, rank, tol, info) where {T,S<:AbstractMatrix},
           CholeskyPivoted{T,S,typeof(piv)}(factors, uplo, piv, rank, tol, info), false)


# iteration for destructuring into components
Base.iterate(C::CholeskyPivoted) = (C.L, Val(:U))
Base.iterate(C::CholeskyPivoted, ::Val{:U}) = (C.U, Val(:done))
Base.iterate(C::CholeskyPivoted, ::Val{:done}) = nothing


# make a copy that allow inplace Cholesky factorization
choltype(A) = promote_type(typeof(sqrt(oneunit(eltype(A)))), Float32)
cholcopy(A::AbstractMatrix) = eigencopy_oftype(A, choltype(A))

# _chol!. Internal methods for calling unpivoted Cholesky
## BLAS/LAPACK element types
function _chol!(A::StridedMatrix{<:BlasFloat}, ::Type{UpperTriangular})
    C, info = LAPACK.potrf!('U', A)
    return UpperTriangular(C), info
end
function _chol!(A::StridedMatrix{<:BlasFloat}, ::Type{LowerTriangular})
    C, info = LAPACK.potrf!('L', A)
    return LowerTriangular(C), info
end

## Non BLAS/LAPACK element types (generic)
function _chol!(A::AbstractMatrix, ::Type{UpperTriangular})
    require_one_based_indexing(A)
    n = checksquare(A)
    realdiag = eltype(A) <: Complex
    @inbounds begin
        for k = 1:n
            Akk = realdiag ? real(A[k,k]) : A[k,k]
            for i = 1:k - 1
                Akk -= realdiag ? abs2(A[i,k]) : A[i,k]'A[i,k]
            end
            A[k,k] = Akk
            Akk, info = _chol!(Akk, UpperTriangular)
            if info != 0
                return UpperTriangular(A), convert(BlasInt, k)
            end
            A[k,k] = Akk
            AkkInv = inv(copy(Akk'))
            for j = k + 1:n
                for i = 1:k - 1
                    A[k,j] -= A[i,k]'A[i,j]
                end
                A[k,j] = AkkInv*A[k,j]
            end
        end
    end
    return UpperTriangular(A), convert(BlasInt, 0)
end
function _chol!(A::AbstractMatrix, ::Type{LowerTriangular})
    require_one_based_indexing(A)
    n = checksquare(A)
    realdiag = eltype(A) <: Complex
    @inbounds begin
        for k = 1:n
            Akk = realdiag ? real(A[k,k]) : A[k,k]
            for i = 1:k - 1
                Akk -= realdiag ? abs2(A[k,i]) : A[k,i]*A[k,i]'
            end
            A[k,k] = Akk
            Akk, info = _chol!(Akk, LowerTriangular)
            if info != 0
                return LowerTriangular(A), convert(BlasInt, k)
            end
            A[k,k] = Akk
            AkkInv = inv(Akk)
            for j = 1:k - 1
                @simd for i = k + 1:n
                    A[i,k] -= A[i,j]*A[k,j]'
                end
            end
            for i = k + 1:n
                A[i,k] *= AkkInv'
            end
        end
     end
    return LowerTriangular(A), convert(BlasInt, 0)
end

## Numbers
function _chol!(x::Number, _)
    rx = real(x)
    iszero(rx) && return (rx, convert(BlasInt, 1))
    rxr = sqrt(abs(rx))
    rval =  convert(promote_type(typeof(x), typeof(rxr)), rxr)
    return (rval, convert(BlasInt, rx != abs(x)))
end

## for StridedMatrices, check that matrix is symmetric/Hermitian

# cholesky!. Destructive methods for computing Cholesky factorization of real symmetric
# or Hermitian matrix
## No pivoting (default)
function cholesky!(A::RealHermSymComplexHerm, ::NoPivot = NoPivot(); check::Bool = true)
    C, info = _chol!(A.data, A.uplo == 'U' ? UpperTriangular : LowerTriangular)
    check && checkpositivedefinite(info)
    return Cholesky(C.data, A.uplo, info)
end

### for AbstractMatrix, check that matrix is symmetric/Hermitian
"""
    cholesky!(A::AbstractMatrix, NoPivot(); check = true) -> Cholesky

The same as [`cholesky`](@ref), but saves space by overwriting the input `A`,
instead of creating a copy. An [`InexactError`](@ref) exception is thrown if
the factorization produces a number not representable by the element type of
`A`, e.g. for integer types.

# Examples
```jldoctest
julia> A = [1 2; 2 50]
2×2 Matrix{Int64}:
 1   2
 2  50

julia> cholesky!(A)
ERROR: InexactError: Int64(6.782329983125268)
Stacktrace:
[...]
```
"""
function cholesky!(A::AbstractMatrix, ::NoPivot = NoPivot(); check::Bool = true)
    checksquare(A)
    if !ishermitian(A) # return with info = -1 if not Hermitian
        check && checkpositivedefinite(-1)
        return Cholesky(A, 'U', convert(BlasInt, -1))
    else
        return cholesky!(Hermitian(A), NoPivot(); check = check)
    end
end
@deprecate cholesky!(A::StridedMatrix, ::Val{false}; check::Bool = true) cholesky!(A, NoPivot(); check) false
@deprecate cholesky!(A::RealHermSymComplexHerm, ::Val{false}; check::Bool = true) cholesky!(A, NoPivot(); check) false

## With pivoting
### BLAS/LAPACK element types
function cholesky!(A::RealHermSymComplexHerm{<:BlasReal,<:StridedMatrix},
                   ::RowMaximum; tol = 0.0, check::Bool = true)
    AA, piv, rank, info = LAPACK.pstrf!(A.uplo, A.data, tol)
    C = CholeskyPivoted{eltype(AA),typeof(AA),typeof(piv)}(AA, A.uplo, piv, rank, tol, info)
    check && chkfullrank(C)
    return C
end
@deprecate cholesky!(A::RealHermSymComplexHerm{<:BlasReal,<:StridedMatrix}, ::Val{true}; kwargs...) cholesky!(A, RowMaximum(); kwargs...) false

### Non BLAS/LAPACK element types (generic). Since generic fallback for pivoted Cholesky
### is not implemented yet we throw an error
cholesky!(A::RealHermSymComplexHerm{<:Real}, ::RowMaximum; tol = 0.0, check::Bool = true) =
    throw(ArgumentError("generic pivoted Cholesky factorization is not implemented yet"))
@deprecate cholesky!(A::RealHermSymComplexHerm{<:Real}, ::Val{true}; kwargs...) cholesky!(A, RowMaximum(); kwargs...) false

### for AbstractMatrix, check that matrix is symmetric/Hermitian
"""
    cholesky!(A::AbstractMatrix, RowMaximum(); tol = 0.0, check = true) -> CholeskyPivoted

The same as [`cholesky`](@ref), but saves space by overwriting the input `A`,
instead of creating a copy. An [`InexactError`](@ref) exception is thrown if the
factorization produces a number not representable by the element type of `A`,
e.g. for integer types.
"""
function cholesky!(A::AbstractMatrix, ::RowMaximum; tol = 0.0, check::Bool = true)
    checksquare(A)
    if !ishermitian(A)
        C = CholeskyPivoted(A, 'U', Vector{BlasInt}(),convert(BlasInt, 1),
                            tol, convert(BlasInt, -1))
        check && chkfullrank(C)
        return C
    else
        return cholesky!(Hermitian(A), RowMaximum(); tol = tol, check = check)
    end
end
@deprecate cholesky!(A::StridedMatrix, ::Val{true}; kwargs...) cholesky!(A, RowMaximum(); kwargs...) false

# cholesky. Non-destructive methods for computing Cholesky factorization of real symmetric
# or Hermitian matrix
## No pivoting (default)
"""
    cholesky(A, NoPivot(); check = true) -> Cholesky

Compute the Cholesky factorization of a dense symmetric positive definite matrix `A`
and return a [`Cholesky`](@ref) factorization. The matrix `A` can either be a [`Symmetric`](@ref) or [`Hermitian`](@ref)
[`AbstractMatrix`](@ref) or a *perfectly* symmetric or Hermitian `AbstractMatrix`.

The triangular Cholesky factor can be obtained from the factorization `F` via `F.L` and `F.U`,
where `A ≈ F.U' * F.U ≈ F.L * F.L'`.

The following functions are available for `Cholesky` objects: [`size`](@ref), [`\\`](@ref),
[`inv`](@ref), [`det`](@ref), [`logdet`](@ref) and [`isposdef`](@ref).

If you have a matrix `A` that is slightly non-Hermitian due to roundoff errors in its construction,
wrap it in `Hermitian(A)` before passing it to `cholesky` in order to treat it as perfectly Hermitian.

When `check = true`, an error is thrown if the decomposition fails.
When `check = false`, responsibility for checking the decomposition's
validity (via [`issuccess`](@ref)) lies with the user.

# Examples
```jldoctest
julia> A = [4. 12. -16.; 12. 37. -43.; -16. -43. 98.]
3×3 Matrix{Float64}:
   4.0   12.0  -16.0
  12.0   37.0  -43.0
 -16.0  -43.0   98.0

julia> C = cholesky(A)
Cholesky{Float64, Matrix{Float64}}
U factor:
3×3 UpperTriangular{Float64, Matrix{Float64}}:
 2.0  6.0  -8.0
  ⋅   1.0   5.0
  ⋅    ⋅    3.0

julia> C.U
3×3 UpperTriangular{Float64, Matrix{Float64}}:
 2.0  6.0  -8.0
  ⋅   1.0   5.0
  ⋅    ⋅    3.0

julia> C.L
3×3 LowerTriangular{Float64, Matrix{Float64}}:
  2.0   ⋅    ⋅
  6.0  1.0   ⋅
 -8.0  5.0  3.0

julia> C.L * C.U == A
true
```
"""
cholesky(A::AbstractMatrix, ::NoPivot=NoPivot(); check::Bool = true) =
    cholesky!(cholcopy(A); check)
@deprecate cholesky(A::Union{StridedMatrix,RealHermSymComplexHerm{<:Real,<:StridedMatrix}}, ::Val{false}; check::Bool = true) cholesky(A, NoPivot(); check) false

function cholesky(A::AbstractMatrix{Float16}, ::NoPivot=NoPivot(); check::Bool = true)
    X = cholesky!(cholcopy(A); check = check)
    return Cholesky{Float16}(X)
end
@deprecate cholesky(A::Union{StridedMatrix{Float16},RealHermSymComplexHerm{Float16,<:StridedMatrix}}, ::Val{false}; check::Bool = true) cholesky(A, NoPivot(); check) false

## With pivoting
"""
    cholesky(A, RowMaximum(); tol = 0.0, check = true) -> CholeskyPivoted

Compute the pivoted Cholesky factorization of a dense symmetric positive semi-definite matrix `A`
and return a [`CholeskyPivoted`](@ref) factorization. The matrix `A` can either be a [`Symmetric`](@ref)
or [`Hermitian`](@ref) [`AbstractMatrix`](@ref) or a *perfectly* symmetric or Hermitian `AbstractMatrix`.

The triangular Cholesky factor can be obtained from the factorization `F` via `F.L` and `F.U`,
and the permutation via `F.p`, where `A[F.p, F.p] ≈ Ur' * Ur ≈ Lr * Lr'` with `Ur = F.U[1:F.rank, :]`
and `Lr = F.L[:, 1:F.rank]`, or alternatively `A ≈ Up' * Up ≈ Lp * Lp'` with
`Up = F.U[1:F.rank, invperm(F.p)]` and `Lp = F.L[invperm(F.p), 1:F.rank]`.

The following functions are available for `CholeskyPivoted` objects:
[`size`](@ref), [`\\`](@ref), [`inv`](@ref), [`det`](@ref), and [`rank`](@ref).

The argument `tol` determines the tolerance for determining the rank.
For negative values, the tolerance is the machine precision.

If you have a matrix `A` that is slightly non-Hermitian due to roundoff errors in its construction,
wrap it in `Hermitian(A)` before passing it to `cholesky` in order to treat it as perfectly Hermitian.

When `check = true`, an error is thrown if the decomposition fails.
When `check = false`, responsibility for checking the decomposition's
validity (via [`issuccess`](@ref)) lies with the user.

# Examples
```jldoctest
julia> X = [1.0, 2.0, 3.0, 4.0];

julia> A = X * X';

julia> C = cholesky(A, RowMaximum(), check = false)
CholeskyPivoted{Float64, Matrix{Float64}, Vector{Int64}}
U factor with rank 1:
4×4 UpperTriangular{Float64, Matrix{Float64}}:
 4.0  2.0  3.0  1.0
  ⋅   0.0  6.0  2.0
  ⋅    ⋅   9.0  3.0
  ⋅    ⋅    ⋅   1.0
permutation:
4-element Vector{Int64}:
 4
 2
 3
 1

julia> C.U[1:C.rank, :]' * C.U[1:C.rank, :] ≈ A[C.p, C.p]
true

julia> l, u = C; # destructuring via iteration

julia> l == C.L && u == C.U
true
```
"""
cholesky(A::AbstractMatrix, ::RowMaximum; tol = 0.0, check::Bool = true) =
    cholesky!(cholcopy(A), RowMaximum(); tol, check)
@deprecate cholesky(A::Union{StridedMatrix,RealHermSymComplexHerm{<:Real,<:StridedMatrix}}, ::Val{true}; tol = 0.0, check::Bool = true) cholesky(A, RowMaximum(); tol, check) false

function cholesky(A::AbstractMatrix{Float16}, ::RowMaximum; tol = 0.0, check::Bool = true)
    X = cholesky!(cholcopy(A), RowMaximum(); tol, check)
    return CholeskyPivoted{Float16}(X)
end

## Number
function cholesky(x::Number, uplo::Symbol=:U)
    C, info = _chol!(x, uplo)
    xf = fill(C, 1, 1)
    Cholesky(xf, uplo, info)
end


function Cholesky{T}(C::Cholesky) where T
    Cnew = convert(AbstractMatrix{T}, C.factors)
    Cholesky{T, typeof(Cnew)}(Cnew, C.uplo, C.info)
end
Factorization{T}(C::Cholesky{T}) where {T} = C
Factorization{T}(C::Cholesky) where {T} = Cholesky{T}(C)
CholeskyPivoted{T}(C::CholeskyPivoted{T}) where {T} = C
CholeskyPivoted{T}(C::CholeskyPivoted) where {T} =
    CholeskyPivoted(AbstractMatrix{T}(C.factors),C.uplo,C.piv,C.rank,C.tol,C.info)
Factorization{T}(C::CholeskyPivoted{T}) where {T} = C
Factorization{T}(C::CholeskyPivoted) where {T} = CholeskyPivoted{T}(C)

AbstractMatrix(C::Cholesky) = C.uplo == 'U' ? C.U'C.U : C.L*C.L'
AbstractArray(C::Cholesky) = AbstractMatrix(C)
Matrix(C::Cholesky) = Array(AbstractArray(C))
Array(C::Cholesky) = Matrix(C)

function AbstractMatrix(F::CholeskyPivoted)
    ip = invperm(F.p)
    U = F.U[1:F.rank,ip]
    U'U
end
AbstractArray(F::CholeskyPivoted) = AbstractMatrix(F)
Matrix(F::CholeskyPivoted) = Array(AbstractArray(F))
Array(F::CholeskyPivoted) = Matrix(F)

copy(C::Cholesky) = Cholesky(copy(C.factors), C.uplo, C.info)
copy(C::CholeskyPivoted) = CholeskyPivoted(copy(C.factors), C.uplo, C.piv, C.rank, C.tol, C.info)

size(C::Union{Cholesky, CholeskyPivoted}) = size(C.factors)
size(C::Union{Cholesky, CholeskyPivoted}, d::Integer) = size(C.factors, d)

function getproperty(C::Cholesky, d::Symbol)
    Cfactors = getfield(C, :factors)
    Cuplo    = getfield(C, :uplo)
    if d === :U
        return UpperTriangular(Cuplo === char_uplo(d) ? Cfactors : copy(Cfactors'))
    elseif d === :L
        return LowerTriangular(Cuplo === char_uplo(d) ? Cfactors : copy(Cfactors'))
    elseif d === :UL
        return (Cuplo === 'U' ? UpperTriangular(Cfactors) : LowerTriangular(Cfactors))
    else
        return getfield(C, d)
    end
end
Base.propertynames(F::Cholesky, private::Bool=false) =
    (:U, :L, :UL, (private ? fieldnames(typeof(F)) : ())...)

function getproperty(C::CholeskyPivoted{T}, d::Symbol) where {T}
    Cfactors = getfield(C, :factors)
    Cuplo    = getfield(C, :uplo)
    if d === :U
        return UpperTriangular(sym_uplo(Cuplo) == d ? Cfactors : copy(Cfactors'))
    elseif d === :L
        return LowerTriangular(sym_uplo(Cuplo) == d ? Cfactors : copy(Cfactors'))
    elseif d === :p
        return getfield(C, :piv)
    elseif d === :P
        n = size(C, 1)
        P = zeros(T, n, n)
        for i = 1:n
            P[getfield(C, :piv)[i], i] = one(T)
        end
        return P
    else
        return getfield(C, d)
    end
end
Base.propertynames(F::CholeskyPivoted, private::Bool=false) =
    (:U, :L, :p, :P, (private ? fieldnames(typeof(F)) : ())...)

issuccess(C::Union{Cholesky,CholeskyPivoted}) = C.info == 0

adjoint(C::Union{Cholesky,CholeskyPivoted}) = C

function show(io::IO, mime::MIME{Symbol("text/plain")}, C::Cholesky)
    if issuccess(C)
        summary(io, C); println(io)
        println(io, "$(C.uplo) factor:")
        show(io, mime, C.UL)
    else
        print(io, "Failed factorization of type $(typeof(C))")
    end
end

function show(io::IO, mime::MIME{Symbol("text/plain")}, C::CholeskyPivoted)
    summary(io, C); println(io)
    println(io, "$(C.uplo) factor with rank $(rank(C)):")
    show(io, mime, C.uplo == 'U' ? C.U : C.L)
    println(io, "\npermutation:")
    show(io, mime, C.p)
end

ldiv!(C::Cholesky{T,<:StridedMatrix}, B::StridedVecOrMat{T}) where {T<:BlasFloat} =
    LAPACK.potrs!(C.uplo, C.factors, B)

function ldiv!(C::Cholesky, B::AbstractVecOrMat)
    if C.uplo == 'L'
        return ldiv!(adjoint(LowerTriangular(C.factors)), ldiv!(LowerTriangular(C.factors), B))
    else
        return ldiv!(UpperTriangular(C.factors), ldiv!(adjoint(UpperTriangular(C.factors)), B))
    end
end

function ldiv!(C::CholeskyPivoted{T,<:StridedMatrix}, B::StridedVector{T}) where T<:BlasFloat
    invpermute!(LAPACK.potrs!(C.uplo, C.factors, permute!(B, C.piv)), C.piv)
end
function ldiv!(C::CholeskyPivoted{T,<:StridedMatrix}, B::StridedMatrix{T}) where T<:BlasFloat
    n = size(C, 1)
    for i=1:size(B, 2)
        permute!(view(B, 1:n, i), C.piv)
    end
    LAPACK.potrs!(C.uplo, C.factors, B)
    for i=1:size(B, 2)
        invpermute!(view(B, 1:n, i), C.piv)
    end
    B
end

function ldiv!(C::CholeskyPivoted, B::AbstractVector)
    if C.uplo == 'L'
        ldiv!(adjoint(LowerTriangular(C.factors)),
            ldiv!(LowerTriangular(C.factors), permute!(B, C.piv)))
    else
        ldiv!(UpperTriangular(C.factors),
            ldiv!(adjoint(UpperTriangular(C.factors)), permute!(B, C.piv)))
    end
    invpermute!(B, C.piv)
end

function ldiv!(C::CholeskyPivoted, B::AbstractMatrix)
    n = size(C, 1)
    for i in 1:size(B, 2)
        permute!(view(B, 1:n, i), C.piv)
    end
    if C.uplo == 'L'
        ldiv!(adjoint(LowerTriangular(C.factors)),
            ldiv!(LowerTriangular(C.factors), B))
    else
        ldiv!(UpperTriangular(C.factors),
            ldiv!(adjoint(UpperTriangular(C.factors)), B))
    end
    for i in 1:size(B, 2)
        invpermute!(view(B, 1:n, i), C.piv)
    end
    B
end

function rdiv!(B::AbstractMatrix, C::Cholesky)
    if C.uplo == 'L'
        return rdiv!(rdiv!(B, adjoint(LowerTriangular(C.factors))), LowerTriangular(C.factors))
    else
        return rdiv!(rdiv!(B, UpperTriangular(C.factors)), adjoint(UpperTriangular(C.factors)))
    end
end

function LinearAlgebra.rdiv!(B::AbstractMatrix, C::CholeskyPivoted)
    n = size(C, 2)
    for i in 1:size(B, 1)
        permute!(view(B, i, 1:n), C.piv)
    end
    if C.uplo == 'L'
        rdiv!(rdiv!(B, adjoint(LowerTriangular(C.factors))),
            LowerTriangular(C.factors))
    else
        rdiv!(rdiv!(B, UpperTriangular(C.factors)),
            adjoint(UpperTriangular(C.factors)))
    end
    for i in 1:size(B, 1)
        invpermute!(view(B, i, 1:n), C.piv)
    end
    B
end

isposdef(C::Union{Cholesky,CholeskyPivoted}) = C.info == 0

function det(C::Cholesky)
    dd = one(real(eltype(C)))
    @inbounds for i in 1:size(C.factors,1)
        dd *= real(C.factors[i,i])^2
    end
    return dd
end

function logdet(C::Cholesky)
    dd = zero(real(eltype(C)))
    @inbounds for i in 1:size(C.factors,1)
        dd += log(real(C.factors[i,i]))
    end
    dd + dd # instead of 2.0dd which can change the type
end

function det(C::CholeskyPivoted)
    if C.rank < size(C.factors, 1)
        return zero(real(eltype(C)))
    else
        dd = one(real(eltype(C)))
        for i in 1:size(C.factors,1)
            dd *= real(C.factors[i,i])^2
        end
        return dd
    end
end

function logdet(C::CholeskyPivoted)
    if C.rank < size(C.factors, 1)
        return real(eltype(C))(-Inf)
    else
        dd = zero(real(eltype(C)))
        for i in 1:size(C.factors,1)
            dd += log(real(C.factors[i,i]))
        end
        return dd + dd # instead of 2.0dd which can change the type
    end
end

logabsdet(C::Union{Cholesky, CholeskyPivoted}) = logdet(C), one(eltype(C)) # since C is p.s.d.

inv!(C::Cholesky{<:BlasFloat,<:StridedMatrix}) =
    copytri!(LAPACK.potri!(C.uplo, C.factors), C.uplo, true)

inv(C::Cholesky{<:BlasFloat,<:StridedMatrix}) = inv!(copy(C))

function inv(C::CholeskyPivoted{<:BlasFloat,<:StridedMatrix})
    ipiv = invperm(C.piv)
    copytri!(LAPACK.potri!(C.uplo, copy(C.factors)), C.uplo, true)[ipiv, ipiv]
end

function chkfullrank(C::CholeskyPivoted)
    if C.rank < size(C.factors, 1)
        throw(RankDeficientException(C.info))
    end
end

rank(C::CholeskyPivoted) = C.rank

"""
    lowrankupdate!(C::Cholesky, v::AbstractVector) -> CC::Cholesky

Update a Cholesky factorization `C` with the vector `v`. If `A = C.U'C.U` then
`CC = cholesky(C.U'C.U + v*v')` but the computation of `CC` only uses `O(n^2)`
operations. The input factorization `C` is updated in place such that on exit `C == CC`.
The vector `v` is destroyed during the computation.
"""
function lowrankupdate!(C::Cholesky, v::AbstractVector)
    A = C.factors
    n = length(v)
    if size(C, 1) != n
        throw(DimensionMismatch("updating vector must fit size of factorization"))
    end
    if C.uplo == 'U'
        conj!(v)
    end

    for i = 1:n

        # Compute Givens rotation
        c, s, r = givensAlgorithm(A[i,i], v[i])

        # Store new diagonal element
        A[i,i] = r

        # Update remaining elements in row/column
        if C.uplo == 'U'
            for j = i + 1:n
                Aij = A[i,j]
                vj  = v[j]
                A[i,j]  =   c*Aij + s*vj
                v[j]    = -s'*Aij + c*vj
            end
        else
            for j = i + 1:n
                Aji = A[j,i]
                vj  = v[j]
                A[j,i]  =   c*Aji + s*vj
                v[j]    = -s'*Aji + c*vj
            end
        end
    end
    return C
end

"""
    lowrankdowndate!(C::Cholesky, v::AbstractVector) -> CC::Cholesky

Downdate a Cholesky factorization `C` with the vector `v`. If `A = C.U'C.U` then
`CC = cholesky(C.U'C.U - v*v')` but the computation of `CC` only uses `O(n^2)`
operations. The input factorization `C` is updated in place such that on exit `C == CC`.
The vector `v` is destroyed during the computation.
"""
function lowrankdowndate!(C::Cholesky, v::AbstractVector)
    A = C.factors
    n = length(v)
    if size(C, 1) != n
        throw(DimensionMismatch("updating vector must fit size of factorization"))
    end
    if C.uplo == 'U'
        conj!(v)
    end

    for i = 1:n

        Aii = A[i,i]

        # Compute Givens rotation
        s = conj(v[i]/Aii)
        s2 = abs2(s)
        if s2 > 1
            throw(LinearAlgebra.PosDefException(i))
        end
        c = sqrt(1 - abs2(s))

        # Store new diagonal element
        A[i,i] = c*Aii

        # Update remaining elements in row/column
        if C.uplo == 'U'
            for j = i + 1:n
                vj = v[j]
                Aij = (A[i,j] - s*vj)/c
                A[i,j] = Aij
                v[j] = -s'*Aij + c*vj
            end
        else
            for j = i + 1:n
                vj = v[j]
                Aji = (A[j,i] - s*vj)/c
                A[j,i] = Aji
                v[j] = -s'*Aji + c*vj
            end
        end
    end
    return C
end

"""
    lowrankupdate(C::Cholesky, v::AbstractVector) -> CC::Cholesky

Update a Cholesky factorization `C` with the vector `v`. If `A = C.U'C.U`
then `CC = cholesky(C.U'C.U + v*v')` but the computation of `CC` only uses
`O(n^2)` operations.
"""
lowrankupdate(C::Cholesky, v::AbstractVector) = lowrankupdate!(copy(C), copy(v))

"""
    lowrankdowndate(C::Cholesky, v::AbstractVector) -> CC::Cholesky

Downdate a Cholesky factorization `C` with the vector `v`. If `A = C.U'C.U`
then `CC = cholesky(C.U'C.U - v*v')` but the computation of `CC` only uses
`O(n^2)` operations.
"""
lowrankdowndate(C::Cholesky, v::AbstractVector) = lowrankdowndate!(copy(C), copy(v))
s   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LinearAlgebra/src/lu.jl7_      # This file is a part of Julia. License is MIT: https://julialang.org/license

####################
# LU Factorization #
####################
"""
    LU <: Factorization

Matrix factorization type of the `LU` factorization of a square matrix `A`. This
is the return type of [`lu`](@ref), the corresponding matrix factorization function.

The individual components of the factorization `F::LU` can be accessed via [`getproperty`](@ref):

| Component | Description                              |
|:----------|:-----------------------------------------|
| `F.L`     | `L` (unit lower triangular) part of `LU` |
| `F.U`     | `U` (upper triangular) part of `LU`      |
| `F.p`     | (right) permutation `Vector`             |
| `F.P`     | (right) permutation `Matrix`             |

Iterating the factorization produces the components `F.L`, `F.U`, and `F.p`.

# Examples
```jldoctest
julia> A = [4 3; 6 3]
2×2 Matrix{Int64}:
 4  3
 6  3

julia> F = lu(A)
LU{Float64, Matrix{Float64}, Vector{Int64}}
L factor:
2×2 Matrix{Float64}:
 1.0       0.0
 0.666667  1.0
U factor:
2×2 Matrix{Float64}:
 6.0  3.0
 0.0  1.0

julia> F.L * F.U == A[F.p, :]
true

julia> l, u, p = lu(A); # destructuring via iteration

julia> l == F.L && u == F.U && p == F.p
true
```
"""
struct LU{T,S<:AbstractMatrix{T},P<:AbstractVector{<:Integer}} <: Factorization{T}
    factors::S
    ipiv::P
    info::BlasInt

    function LU{T,S,P}(factors, ipiv, info) where {T, S<:AbstractMatrix{T}, P<:AbstractVector{<:Integer}}
        require_one_based_indexing(factors)
        new{T,S,P}(factors, ipiv, info)
    end
end
LU(factors::AbstractMatrix{T}, ipiv::AbstractVector{<:Integer}, info::BlasInt) where {T} =
    LU{T,typeof(factors),typeof(ipiv)}(factors, ipiv, info)
LU{T}(factors::AbstractMatrix, ipiv::AbstractVector{<:Integer}, info::Integer) where {T} =
    LU(convert(AbstractMatrix{T}, factors), ipiv, BlasInt(info))
# backwards-compatible constructors (remove with Julia 2.0)
@deprecate(LU{T,S}(factors::AbstractMatrix{T}, ipiv::AbstractVector{<:Integer},
                   info::BlasInt) where {T,S},
           LU{T,S,typeof(ipiv)}(factors, ipiv, info), false)

# iteration for destructuring into components
Base.iterate(S::LU) = (S.L, Val(:U))
Base.iterate(S::LU, ::Val{:U}) = (S.U, Val(:p))
Base.iterate(S::LU, ::Val{:p}) = (S.p, Val(:done))
Base.iterate(S::LU, ::Val{:done}) = nothing

# LU prefers transpose over adjoint in the real case, override the generic fallback
adjoint(F::LU{<:Real}) = TransposeFactorization(F)
transpose(F::LU{<:Real}) = TransposeFactorization(F)

# the following method is meant to catch calls to lu!(A::LAPACKArray) without a pivoting stategy
lu!(A::StridedMatrix{<:BlasFloat}; check::Bool = true) = lu!(A, RowMaximum(); check=check)
function lu!(A::StridedMatrix{T}, ::RowMaximum; check::Bool = true) where {T<:BlasFloat}
    lpt = LAPACK.getrf!(A; check)
    check && checknonsingular(lpt[3])
    return LU{T,typeof(lpt[1]),typeof(lpt[2])}(lpt[1], lpt[2], lpt[3])
end
function lu!(A::HermOrSym{T}, pivot::Union{RowMaximum,NoPivot,RowNonZero} = lupivottype(T); check::Bool = true) where {T}
    copytri!(A.data, A.uplo, isa(A, Hermitian))
    lu!(A.data, pivot; check = check)
end
# for backward compatibility
# TODO: remove towards Julia v2
@deprecate lu!(A::Union{StridedMatrix,HermOrSym,Tridiagonal}, ::Val{true}; check::Bool = true) lu!(A, RowMaximum(); check=check)
@deprecate lu!(A::Union{StridedMatrix,HermOrSym,Tridiagonal}, ::Val{false}; check::Bool = true) lu!(A, NoPivot(); check=check)

"""
    lu!(A, pivot = RowMaximum(); check = true) -> LU

`lu!` is the same as [`lu`](@ref), but saves space by overwriting the
input `A`, instead of creating a copy. An [`InexactError`](@ref)
exception is thrown if the factorization produces a number not representable by the
element type of `A`, e.g. for integer types.

# Examples
```jldoctest
julia> A = [4. 3.; 6. 3.]
2×2 Matrix{Float64}:
 4.0  3.0
 6.0  3.0

julia> F = lu!(A)
LU{Float64, Matrix{Float64}, Vector{Int64}}
L factor:
2×2 Matrix{Float64}:
 1.0       0.0
 0.666667  1.0
U factor:
2×2 Matrix{Float64}:
 6.0  3.0
 0.0  1.0

julia> iA = [4 3; 6 3]
2×2 Matrix{Int64}:
 4  3
 6  3

julia> lu!(iA)
ERROR: InexactError: Int64(0.6666666666666666)
Stacktrace:
[...]
```
"""
lu!(A::AbstractMatrix, pivot::Union{RowMaximum,NoPivot,RowNonZero} = lupivottype(eltype(A)); check::Bool = true) =
    generic_lufact!(A, pivot; check = check)
function generic_lufact!(A::AbstractMatrix{T}, pivot::Union{RowMaximum,NoPivot,RowNonZero} = lupivottype(T);
                         check::Bool = true) where {T}
    check && LAPACK.chkfinite(A)
    # Extract values
    m, n = size(A)
    minmn = min(m,n)

    # Initialize variables
    info = 0
    ipiv = Vector{BlasInt}(undef, minmn)
    @inbounds begin
        for k = 1:minmn
            # find index max
            kp = k
            if pivot === RowMaximum() && k < m
                amax = abs(A[k, k])
                for i = k+1:m
                    absi = abs(A[i,k])
                    if absi > amax
                        kp = i
                        amax = absi
                    end
                end
            elseif pivot === RowNonZero()
                for i = k:m
                    if !iszero(A[i,k])
                        kp = i
                        break
                    end
                end
            end
            ipiv[k] = kp
            if !iszero(A[kp,k])
                if k != kp
                    # Interchange
                    for i = 1:n
                        tmp = A[k,i]
                        A[k,i] = A[kp,i]
                        A[kp,i] = tmp
                    end
                end
                # Scale first column
                Akkinv = inv(A[k,k])
                for i = k+1:m
                    A[i,k] *= Akkinv
                end
            elseif info == 0
                info = k
            end
            # Update the rest
            for j = k+1:n
                for i = k+1:m
                    A[i,j] -= A[i,k]*A[k,j]
                end
            end
        end
    end
    check && checknonsingular(info, pivot)
    return LU{T,typeof(A),typeof(ipiv)}(A, ipiv, convert(BlasInt, info))
end

function lutype(T::Type)
    # In generic_lufact!, the elements of the lower part of the matrix are
    # obtained using the division of two matrix elements. Hence their type can
    # be different (e.g. the division of two types with the same unit is a type
    # without unit).
    # The elements of the upper part are obtained by U - U * L
    # where U is an upper part element and L is a lower part element.
    # Therefore, the types LT, UT should be invariant under the map:
    # (LT, UT) -> begin
    #     L = oneunit(UT) / oneunit(UT)
    #     U = oneunit(UT) - oneunit(UT) * L
    #     typeof(L), typeof(U)
    # end
    # The following should handle most cases
    UT = typeof(oneunit(T) - oneunit(T) * (oneunit(T) / (oneunit(T) + zero(T))))
    LT = typeof(oneunit(UT) / oneunit(UT))
    S = promote_type(T, LT, UT)
end

lupivottype(::Type{T}) where {T} = RowMaximum()

# for all other types we must promote to a type which is stable under division
"""
    lu(A, pivot = RowMaximum(); check = true) -> F::LU

Compute the LU factorization of `A`.

When `check = true`, an error is thrown if the decomposition fails.
When `check = false`, responsibility for checking the decomposition's
validity (via [`issuccess`](@ref)) lies with the user.

In most cases, if `A` is a subtype `S` of `AbstractMatrix{T}` with an element
type `T` supporting `+`, `-`, `*` and `/`, the return type is `LU{T,S{T}}`.

In general, LU factorization involves a permutation of the rows of the matrix
(corresponding to the `F.p` output described below), known as "pivoting" (because it
corresponds to choosing which row contains the "pivot", the diagonal entry of `F.U`).
One of the following pivoting strategies can be selected via the optional `pivot` argument:

* `RowMaximum()` (default): the standard pivoting strategy; the pivot corresponds
  to the element of maximum absolute value among the remaining, to be factorized rows.
  This pivoting strategy requires the element type to also support [`abs`](@ref) and
  [`<`](@ref). (This is generally the only numerically stable option for floating-point
  matrices.)
* `RowNonZero()`: the pivot corresponds to the first non-zero element among the remaining,
  to be factorized rows.  (This corresponds to the typical choice in hand calculations, and
  is also useful for more general algebraic number types that support [`iszero`](@ref) but
  not `abs` or `<`.)
* `NoPivot()`: pivoting turned off (may fail if a zero entry is encountered).

The individual components of the factorization `F` can be accessed via [`getproperty`](@ref):

| Component | Description                         |
|:----------|:------------------------------------|
| `F.L`     | `L` (lower triangular) part of `LU` |
| `F.U`     | `U` (upper triangular) part of `LU` |
| `F.p`     | (right) permutation `Vector`        |
| `F.P`     | (right) permutation `Matrix`        |

Iterating the factorization produces the components `F.L`, `F.U`, and `F.p`.

The relationship between `F` and `A` is

`F.L*F.U == A[F.p, :]`

`F` further supports the following functions:

| Supported function               | `LU` | `LU{T,Tridiagonal{T}}` |
|:---------------------------------|:-----|:-----------------------|
| [`/`](@ref)                      | ✓    |                        |
| [`\\`](@ref)                     | ✓    | ✓                      |
| [`inv`](@ref)                    | ✓    | ✓                      |
| [`det`](@ref)                    | ✓    | ✓                      |
| [`logdet`](@ref)                 | ✓    | ✓                      |
| [`logabsdet`](@ref)              | ✓    | ✓                      |
| [`size`](@ref)                   | ✓    | ✓                      |

# Examples
```jldoctest
julia> A = [4 3; 6 3]
2×2 Matrix{Int64}:
 4  3
 6  3

julia> F = lu(A)
LU{Float64, Matrix{Float64}, Vector{Int64}}
L factor:
2×2 Matrix{Float64}:
 1.0       0.0
 0.666667  1.0
U factor:
2×2 Matrix{Float64}:
 6.0  3.0
 0.0  1.0

julia> F.L * F.U == A[F.p, :]
true

julia> l, u, p = lu(A); # destructuring via iteration

julia> l == F.L && u == F.U && p == F.p
true
```
"""
function lu(A::AbstractMatrix{T}, pivot::Union{RowMaximum,NoPivot,RowNonZero} = lupivottype(T); check::Bool = true) where {T}
    lu!(_lucopy(A, lutype(T)), pivot; check = check)
end
# TODO: remove for Julia v2.0
@deprecate lu(A::AbstractMatrix, ::Val{true}; check::Bool = true) lu(A, RowMaximum(); check=check)
@deprecate lu(A::AbstractMatrix, ::Val{false}; check::Bool = true) lu(A, NoPivot(); check=check)

_lucopy(A::AbstractMatrix, T) = copy_similar(A, T)
_lucopy(A::HermOrSym, T)      = copymutable_oftype(A, T)
_lucopy(A::Tridiagonal, T)    = copymutable_oftype(A, T)

lu(S::LU) = S
function lu(x::Number; check::Bool=true)
    info = x == 0 ? one(BlasInt) : zero(BlasInt)
    check && checknonsingular(info)
    return LU(fill(x, 1, 1), BlasInt[1], info)
end

function LU{T}(F::LU) where T
    M = convert(AbstractMatrix{T}, F.factors)
    LU{T,typeof(M),typeof(F.ipiv)}(M, F.ipiv, F.info)
end
LU{T,S,P}(F::LU) where {T,S,P} = LU{T,S,P}(convert(S, F.factors), convert(P, F.ipiv), F.info)
Factorization{T}(F::LU{T}) where {T} = F
Factorization{T}(F::LU) where {T} = LU{T}(F)

copy(A::LU{T,S,P}) where {T,S,P} = LU{T,S,P}(copy(A.factors), copy(A.ipiv), A.info)

size(A::LU)    = size(getfield(A, :factors))
size(A::LU, i::Integer) = size(getfield(A, :factors), i)

function ipiv2perm(v::AbstractVector{T}, maxi::Integer) where T
    require_one_based_indexing(v)
    p = T[1:maxi;]
    @inbounds for i in 1:length(v)
        p[i], p[v[i]] = p[v[i]], p[i]
    end
    return p
end

function getproperty(F::LU{T}, d::Symbol) where T
    m, n = size(F)
    if d === :L
        L = tril!(getfield(F, :factors)[1:m, 1:min(m,n)])
        for i = 1:min(m,n); L[i,i] = one(T); end
        return L
    elseif d === :U
        return triu!(getfield(F, :factors)[1:min(m,n), 1:n])
    elseif d === :p
        return ipiv2perm(getfield(F, :ipiv), m)
    elseif d === :P
        return Matrix{T}(I, m, m)[:,invperm(F.p)]
    else
        getfield(F, d)
    end
end

Base.propertynames(F::LU, private::Bool=false) =
    (:L, :U, :p, :P, (private ? fieldnames(typeof(F)) : ())...)

issuccess(F::LU) = F.info == 0

function show(io::IO, mime::MIME{Symbol("text/plain")}, F::LU)
    if issuccess(F)
        summary(io, F); println(io)
        println(io, "L factor:")
        show(io, mime, F.L)
        println(io, "\nU factor:")
        show(io, mime, F.U)
    else
        print(io, "Failed factorization of type $(typeof(F))")
    end
end

_apply_ipiv_rows!(A::LU, B::AbstractVecOrMat) = _ipiv_rows!(A, 1 : length(A.ipiv), B)
_apply_inverse_ipiv_rows!(A::LU, B::AbstractVecOrMat) = _ipiv_rows!(A, length(A.ipiv) : -1 : 1, B)

function _ipiv_rows!(A::LU, order::OrdinalRange, B::AbstractVecOrMat)
    for i = order
        if i != A.ipiv[i]
            _swap_rows!(B, i, A.ipiv[i])
        end
    end
    B
end

function _swap_rows!(B::AbstractVector, i::Integer, j::Integer)
    B[i], B[j] = B[j], B[i]
    B
end

function _swap_rows!(B::AbstractMatrix, i::Integer, j::Integer)
    for col = 1 : size(B, 2)
        B[i,col], B[j,col] = B[j,col], B[i,col]
    end
    B
end

_apply_ipiv_cols!(A::LU, B::AbstractVecOrMat) = _ipiv_cols!(A, 1 : length(A.ipiv), B)
_apply_inverse_ipiv_cols!(A::LU, B::AbstractVecOrMat) = _ipiv_cols!(A, length(A.ipiv) : -1 : 1, B)

function _ipiv_cols!(A::LU, order::OrdinalRange, B::AbstractVecOrMat)
    for i = order
        if i != A.ipiv[i]
            _swap_cols!(B, i, A.ipiv[i])
        end
    end
    B
end

function _swap_cols!(B::AbstractVector, i::Integer, j::Integer)
    _swap_rows!(B, i, j)
end

function _swap_cols!(B::AbstractMatrix, i::Integer, j::Integer)
    for row = 1 : size(B, 1)
        B[row,i], B[row,j] = B[row,j], B[row,i]
    end
    B
end

function rdiv!(A::AbstractVecOrMat, B::LU)
    rdiv!(rdiv!(A, UpperTriangular(B.factors)), UnitLowerTriangular(B.factors))
    _apply_inverse_ipiv_cols!(B, A)
end

ldiv!(A::LU{T,<:StridedMatrix}, B::StridedVecOrMat{T}) where {T<:BlasFloat} =
    LAPACK.getrs!('N', A.factors, A.ipiv, B)

function ldiv!(A::LU, B::AbstractVecOrMat)
    _apply_ipiv_rows!(A, B)
    ldiv!(UpperTriangular(A.factors), ldiv!(UnitLowerTriangular(A.factors), B))
end

ldiv!(transA::TransposeFactorization{T,<:LU{T,<:StridedMatrix}}, B::StridedVecOrMat{T}) where {T<:BlasFloat} =
    (A = transA.parent; LAPACK.getrs!('T', A.factors, A.ipiv, B))

function ldiv!(transA::TransposeFactorization{<:Any,<:LU}, B::AbstractVecOrMat)
    A = transA.parent
    ldiv!(transpose(UnitLowerTriangular(A.factors)), ldiv!(transpose(UpperTriangular(A.factors)), B))
    _apply_inverse_ipiv_rows!(A, B)
end

ldiv!(adjA::AdjointFactorization{T,<:LU{T,<:StridedMatrix}}, B::StridedVecOrMat{T}) where {T<:BlasComplex} =
    (A = adjA.parent; LAPACK.getrs!('C', A.factors, A.ipiv, B))

function ldiv!(adjA::AdjointFactorization{<:Any,<:LU}, B::AbstractVecOrMat)
    A = adjA.parent
    ldiv!(adjoint(UnitLowerTriangular(A.factors)), ldiv!(adjoint(UpperTriangular(A.factors)), B))
    _apply_inverse_ipiv_rows!(A, B)
end

(\)(A::AdjointFactorization{T,<:LU{T,<:StridedMatrix}}, B::Adjoint{T,<:StridedVecOrMat{T}}) where {T<:BlasComplex} =
    LAPACK.getrs!('C', A.parent.factors, A.parent.ipiv, copy(B))
(\)(A::TransposeFactorization{T,<:LU{T,<:StridedMatrix}}, B::Transpose{T,<:StridedVecOrMat{T}}) where {T<:BlasFloat} =
    LAPACK.getrs!('T', A.parent.factors, A.parent.ipiv, copy(B))

function det(F::LU{T}) where T
    n = checksquare(F)
    issuccess(F) || return zero(T)
    P = one(T)
    c = 0
    @inbounds for i = 1:n
        P *= F.factors[i,i]
        if F.ipiv[i] != i
            c += 1
        end
    end
    s = (isodd(c) ? -one(T) : one(T))
    return P * s
end

function logabsdet(F::LU{T}) where T  # return log(abs(det)) and sign(det)
    n = checksquare(F)
    issuccess(F) || return log(zero(real(T))), log(one(T))
    c = 0
    P = one(T)
    abs_det = zero(real(T))
    @inbounds for i = 1:n
        dg_ii = F.factors[i,i]
        P *= sign(dg_ii)
        if F.ipiv[i] != i
            c += 1
        end
        abs_det += log(abs(dg_ii))
    end
    s = ifelse(isodd(c), -one(real(T)), one(real(T))) * P
    abs_det, s
end

inv!(A::LU{<:BlasFloat,<:StridedMatrix}) =
    LAPACK.getri!(A.factors, A.ipiv)
inv!(A::LU{T,<:StridedMatrix}) where {T} =
    ldiv!(A.factors, copy(A), Matrix{T}(I, size(A, 1), size(A, 1)))
inv(A::LU{<:BlasFloat,<:StridedMatrix}) = inv!(copy(A))

# Tridiagonal

# See dgttrf.f
function lu!(A::Tridiagonal{T,V}, pivot::Union{RowMaximum,NoPivot} = RowMaximum(); check::Bool = true) where {T,V}
    # Extract values
    n = size(A, 1)

    # Initialize variables
    info = 0
    ipiv = Vector{BlasInt}(undef, n)
    dl = A.dl
    d = A.d
    du = A.du
    if dl === du
        throw(ArgumentError("off-diagonals of `A` must not alias"))
    end
    # Check if Tridiagonal matrix already has du2 for pivoting
    has_du2_defined = isdefined(A, :du2) && length(A.du2) == max(0, n-2)
    if has_du2_defined
        du2 = A.du2::V
    else
        du2 = similar(d, max(0, n-2))::V
    end
    fill!(du2, 0)

    @inbounds begin
        for i = 1:n
            ipiv[i] = i
        end
        for i = 1:n-2
            # pivot or not?
            if pivot === NoPivot() || abs(d[i]) >= abs(dl[i])
                # No interchange
                if d[i] != 0
                    fact = dl[i]/d[i]
                    dl[i] = fact
                    d[i+1] -= fact*du[i]
                    du2[i] = 0
                end
            else
                # Interchange
                fact = d[i]/dl[i]
                d[i] = dl[i]
                dl[i] = fact
                tmp = du[i]
                du[i] = d[i+1]
                d[i+1] = tmp - fact*d[i+1]
                du2[i] = du[i+1]
                du[i+1] = -fact*du[i+1]
                ipiv[i] = i+1
            end
        end
        if n > 1
            i = n-1
            if pivot === NoPivot() || abs(d[i]) >= abs(dl[i])
                if d[i] != 0
                    fact = dl[i]/d[i]
                    dl[i] = fact
                    d[i+1] -= fact*du[i]
                end
            else
                fact = d[i]/dl[i]
                d[i] = dl[i]
                dl[i] = fact
                tmp = du[i]
                du[i] = d[i+1]
                d[i+1] = tmp - fact*d[i+1]
                ipiv[i] = i+1
            end
        end
        # check for a zero on the diagonal of U
        for i = 1:n
            if d[i] == 0
                info = i
                break
            end
        end
    end
    B = has_du2_defined ? A : Tridiagonal{T,V}(dl, d, du, du2)
    check && checknonsingular(info, pivot)
    return LU{T,Tridiagonal{T,V},typeof(ipiv)}(B, ipiv, convert(BlasInt, info))
end

factorize(A::Tridiagonal) = lu(A)

function getproperty(F::LU{T,Tridiagonal{T,V}}, d::Symbol) where {T,V}
    m, n = size(F)
    if d === :L
        dl = getfield(getfield(F, :factors), :dl)
        L = Array(Bidiagonal(fill!(similar(dl, n), one(T)), dl, d))
        for i = 2:n
            tmp = L[getfield(F, :ipiv)[i], 1:i - 1]
            L[getfield(F, :ipiv)[i], 1:i - 1] = L[i, 1:i - 1]
            L[i, 1:i - 1] = tmp
        end
        return L
    elseif d === :U
        U = Array(Bidiagonal(getfield(getfield(F, :factors), :d), getfield(getfield(F, :factors), :du), d))
        for i = 1:n - 2
            U[i,i + 2] = getfield(getfield(F, :factors), :du2)[i]
        end
        return U
    elseif d === :p
        return ipiv2perm(getfield(F, :ipiv), m)
    elseif d === :P
        return Matrix{T}(I, m, m)[:,invperm(F.p)]
    end
    return getfield(F, d)
end

# See dgtts2.f
function ldiv!(A::LU{T,Tridiagonal{T,V}}, B::AbstractVecOrMat) where {T,V}
    require_one_based_indexing(B)
    n = size(A,1)
    if n != size(B,1)
        throw(DimensionMismatch("matrix has dimensions ($n,$n) but right hand side has $(size(B,1)) rows"))
    end
    nrhs = size(B,2)
    dl = A.factors.dl
    d = A.factors.d
    du = A.factors.du
    du2 = A.factors.du2
    ipiv = A.ipiv
    @inbounds begin
        for j = 1:nrhs
            for i = 1:n-1
                ip = ipiv[i]
                tmp = B[i+1-ip+i,j] - dl[i]*B[ip,j]
                B[i,j] = B[ip,j]
                B[i+1,j] = tmp
            end
            B[n,j] /= d[n]
            if n > 1
                B[n-1,j] = (B[n-1,j] - du[n-1]*B[n,j])/d[n-1]
            end
            for i = n-2:-1:1
                B[i,j] = (B[i,j] - du[i]*B[i+1,j] - du2[i]*B[i+2,j])/d[i]
            end
        end
    end
    return B
end

function ldiv!(transA::TransposeFactorization{<:Any,<:LU{T,Tridiagonal{T,V}}}, B::AbstractVecOrMat) where {T,V}
    require_one_based_indexing(B)
    A = transA.parent
    n = size(A,1)
    if n != size(B,1)
        throw(DimensionMismatch("matrix has dimensions ($n,$n) but right hand side has $(size(B,1)) rows"))
    end
    nrhs = size(B,2)
    dl = A.factors.dl
    d = A.factors.d
    du = A.factors.du
    du2 = A.factors.du2
    ipiv = A.ipiv
    @inbounds begin
        for j = 1:nrhs
            B[1,j] /= d[1]
            if n > 1
                B[2,j] = (B[2,j] - du[1]*B[1,j])/d[2]
            end
            for i = 3:n
                B[i,j] = (B[i,j] - du[i-1]*B[i-1,j] - du2[i-2]*B[i-2,j])/d[i]
            end
            for i = n-1:-1:1
                if ipiv[i] == i
                    B[i,j] = B[i,j] - dl[i]*B[i+1,j]
                else
                    tmp = B[i+1,j]
                    B[i+1,j] = B[i,j] - dl[i]*tmp
                    B[i,j] = tmp
                end
            end
        end
    end
    return B
end

# Ac_ldiv_B!(A::LU{T,Tridiagonal{T}}, B::AbstractVecOrMat) where {T<:Real} = At_ldiv_B!(A,B)
function ldiv!(adjA::AdjointFactorization{<:Any,<:LU{T,Tridiagonal{T,V}}}, B::AbstractVecOrMat) where {T,V}
    require_one_based_indexing(B)
    A = adjA.parent
    n = size(A,1)
    if n != size(B,1)
        throw(DimensionMismatch("matrix has dimensions ($n,$n) but right hand side has $(size(B,1)) rows"))
    end
    nrhs = size(B,2)
    dl = A.factors.dl
    d = A.factors.d
    du = A.factors.du
    du2 = A.factors.du2
    ipiv = A.ipiv
    @inbounds begin
        for j = 1:nrhs
            B[1,j] /= conj(d[1])
            if n > 1
                B[2,j] = (B[2,j] - conj(du[1])*B[1,j])/conj(d[2])
            end
            for i = 3:n
                B[i,j] = (B[i,j] - conj(du[i-1])*B[i-1,j] - conj(du2[i-2])*B[i-2,j])/conj(d[i])
            end
            for i = n-1:-1:1
                if ipiv[i] == i
                    B[i,j] = B[i,j] - conj(dl[i])*B[i+1,j]
                else
                    tmp = B[i+1,j]
                    B[i+1,j] = B[i,j] - conj(dl[i])*tmp
                    B[i,j] = tmp
                end
            end
        end
    end
    return B
end

rdiv!(B::AbstractMatrix, A::LU) = transpose(ldiv!(transpose(A), transpose(B)))

# Conversions
AbstractMatrix(F::LU) = (F.L * F.U)[invperm(F.p),:]
AbstractArray(F::LU) = AbstractMatrix(F)
Matrix(F::LU) = Array(AbstractArray(F))
Array(F::LU) = Matrix(F)

function Tridiagonal(F::LU{T,Tridiagonal{T,V}}) where {T,V}
    n = size(F, 1)

    dl  = copy(F.factors.dl)
    d   = copy(F.factors.d)
    du  = copy(F.factors.du)
    du2 = copy(F.factors.du2)

    for i = n - 1:-1:1
        li         = dl[i]
        dl[i]      = li*d[i]
        d[i + 1]  += li*du[i]
        if i < n - 1
            du[i + 1] += li*du2[i]
        end

        if F.ipiv[i] != i
            tmp   = dl[i]
            dl[i] = d[i]
            d[i]  = tmp

            tmp      = d[i + 1]
            d[i + 1] = du[i]
            du[i]    = tmp

            if i < n - 1
                tmp       = du[i + 1]
                du[i + 1] = du2[i]
                du2[i]    = tmp
            end
        end
    end
    return Tridiagonal(dl, d, du)
end
AbstractMatrix(F::LU{T,Tridiagonal{T,V}}) where {T,V} = Tridiagonal(F)
AbstractArray(F::LU{T,Tridiagonal{T,V}}) where {T,V} = AbstractMatrix(F)
Matrix(F::LU{T,Tridiagonal{T,V}}) where {T,V} = Array(AbstractArray(F))
Array(F::LU{T,Tridiagonal{T,V}}) where {T,V} = Matrix(F)
}   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LinearAlgebra/src/bunchkaufman.jl�2      # This file is a part of Julia. License is MIT: https://julialang.org/license

## Create an extractor that extracts the modified original matrix, e.g.
## LD for BunchKaufman, UL for CholeskyDense, LU for LUDense and
## define size methods for Factorization types using it.

"""
    BunchKaufman <: Factorization

Matrix factorization type of the Bunch-Kaufman factorization of a symmetric or
Hermitian matrix `A` as `P'UDU'P` or `P'LDL'P`, depending on whether the upper
(the default) or the lower triangle is stored in `A`. If `A` is complex symmetric
then `U'` and `L'` denote the unconjugated transposes, i.e. `transpose(U)` and
`transpose(L)`, respectively. This is the return type of [`bunchkaufman`](@ref),
the corresponding matrix factorization function.

If `S::BunchKaufman` is the factorization object, the components can be obtained
via `S.D`, `S.U` or `S.L` as appropriate given `S.uplo`, and `S.p`.

Iterating the decomposition produces the components `S.D`, `S.U` or `S.L`
as appropriate given `S.uplo`, and `S.p`.

# Examples
```jldoctest
julia> A = [1 2; 2 3]
2×2 Matrix{Int64}:
 1  2
 2  3

julia> S = bunchkaufman(A) # A gets wrapped internally by Symmetric(A)
BunchKaufman{Float64, Matrix{Float64}, Vector{Int64}}
D factor:
2×2 Tridiagonal{Float64, Vector{Float64}}:
 -0.333333  0.0
  0.0       3.0
U factor:
2×2 UnitUpperTriangular{Float64, Matrix{Float64}}:
 1.0  0.666667
  ⋅   1.0
permutation:
2-element Vector{Int64}:
 1
 2

julia> d, u, p = S; # destructuring via iteration

julia> d == S.D && u == S.U && p == S.p
true

julia> S = bunchkaufman(Symmetric(A, :L))
BunchKaufman{Float64, Matrix{Float64}, Vector{Int64}}
D factor:
2×2 Tridiagonal{Float64, Vector{Float64}}:
 3.0   0.0
 0.0  -0.333333
L factor:
2×2 UnitLowerTriangular{Float64, Matrix{Float64}}:
 1.0        ⋅
 0.666667  1.0
permutation:
2-element Vector{Int64}:
 2
 1
```
"""
struct BunchKaufman{T,S<:AbstractMatrix,P<:AbstractVector{<:Integer}} <: Factorization{T}
    LD::S
    ipiv::P
    uplo::Char
    symmetric::Bool
    rook::Bool
    info::BlasInt

    function BunchKaufman{T,S,P}(LD, ipiv, uplo, symmetric, rook, info) where {T,S<:AbstractMatrix,P<:AbstractVector}
        require_one_based_indexing(LD)
        new{T,S,P}(LD, ipiv, uplo, symmetric, rook, info)
    end
end
BunchKaufman(A::AbstractMatrix{T}, ipiv::AbstractVector{<:Integer}, uplo::AbstractChar,
             symmetric::Bool, rook::Bool, info::BlasInt) where {T} =
        BunchKaufman{T,typeof(A),typeof(ipiv)}(A, ipiv, uplo, symmetric, rook, info)
# backwards-compatible constructors (remove with Julia 2.0)
@deprecate(BunchKaufman{T,S}(LD, ipiv, uplo, symmetric, rook, info) where {T,S},
           BunchKaufman{T,S,typeof(ipiv)}(LD, ipiv, uplo, symmetric, rook, info), false)

# iteration for destructuring into components
Base.iterate(S::BunchKaufman) = (S.D, Val(:UL))
Base.iterate(S::BunchKaufman, ::Val{:UL}) = (S.uplo == 'L' ? S.L : S.U, Val(:p))
Base.iterate(S::BunchKaufman, ::Val{:p}) = (S.p, Val(:done))
Base.iterate(S::BunchKaufman, ::Val{:done}) = nothing


"""
    bunchkaufman!(A, rook::Bool=false; check = true) -> BunchKaufman

`bunchkaufman!` is the same as [`bunchkaufman`](@ref), but saves space by overwriting the
input `A`, instead of creating a copy.
"""
function bunchkaufman!(A::RealHermSymComplexSym{<:BlasReal,<:StridedMatrix},
                       rook::Bool = false; check::Bool = true)
    LD, ipiv, info = rook ? LAPACK.sytrf_rook!(A.uplo, A.data) : LAPACK.sytrf!(A.uplo, A.data)
    check && checknonsingular(info)
    BunchKaufman(LD, ipiv, A.uplo, true, rook, info)
end
function bunchkaufman!(A::Hermitian{<:BlasComplex,<:StridedMatrix},
                       rook::Bool = false; check::Bool = true)
    LD, ipiv, info = rook ? LAPACK.hetrf_rook!(A.uplo, A.data) : LAPACK.hetrf!(A.uplo, A.data)
    check && checknonsingular(info)
    BunchKaufman(LD, ipiv, A.uplo, false, rook, info)
end
function bunchkaufman!(A::StridedMatrix{<:BlasFloat}, rook::Bool = false; check::Bool = true)
    if ishermitian(A)
        return bunchkaufman!(Hermitian(A), rook; check = check)
    elseif issymmetric(A)
        return bunchkaufman!(Symmetric(A), rook; check = check)
    else
        throw(ArgumentError("Bunch-Kaufman decomposition is only valid for symmetric or Hermitian matrices"))
    end
end

"""
    bunchkaufman(A, rook::Bool=false; check = true) -> S::BunchKaufman

Compute the Bunch-Kaufman [^Bunch1977] factorization of a symmetric or
Hermitian matrix `A` as `P'*U*D*U'*P` or `P'*L*D*L'*P`, depending on
which triangle is stored in `A`, and return a [`BunchKaufman`](@ref) object.
Note that if `A` is complex symmetric then `U'` and `L'` denote
the unconjugated transposes, i.e. `transpose(U)` and `transpose(L)`.

Iterating the decomposition produces the components `S.D`, `S.U` or `S.L`
as appropriate given `S.uplo`, and `S.p`.

If `rook` is `true`, rook pivoting is used. If `rook` is false,
rook pivoting is not used.

When `check = true`, an error is thrown if the decomposition fails.
When `check = false`, responsibility for checking the decomposition's
validity (via [`issuccess`](@ref)) lies with the user.

The following functions are available for `BunchKaufman` objects:
[`size`](@ref), `\\`, [`inv`](@ref), [`issymmetric`](@ref),
[`ishermitian`](@ref), [`getindex`](@ref).

[^Bunch1977]: J R Bunch and L Kaufman, Some stable methods for calculating inertia and solving symmetric linear systems, Mathematics of Computation 31:137 (1977), 163-179. [url](http://www.ams.org/journals/mcom/1977-31-137/S0025-5718-1977-0428694-0/).

# Examples
```jldoctest
julia> A = [1 2; 2 3]
2×2 Matrix{Int64}:
 1  2
 2  3

julia> S = bunchkaufman(A) # A gets wrapped internally by Symmetric(A)
BunchKaufman{Float64, Matrix{Float64}, Vector{Int64}}
D factor:
2×2 Tridiagonal{Float64, Vector{Float64}}:
 -0.333333  0.0
  0.0       3.0
U factor:
2×2 UnitUpperTriangular{Float64, Matrix{Float64}}:
 1.0  0.666667
  ⋅   1.0
permutation:
2-element Vector{Int64}:
 1
 2

julia> d, u, p = S; # destructuring via iteration

julia> d == S.D && u == S.U && p == S.p
true

julia> S.U*S.D*S.U' - S.P*A*S.P'
2×2 Matrix{Float64}:
 0.0  0.0
 0.0  0.0

julia> S = bunchkaufman(Symmetric(A, :L))
BunchKaufman{Float64, Matrix{Float64}, Vector{Int64}}
D factor:
2×2 Tridiagonal{Float64, Vector{Float64}}:
 3.0   0.0
 0.0  -0.333333
L factor:
2×2 UnitLowerTriangular{Float64, Matrix{Float64}}:
 1.0        ⋅
 0.666667  1.0
permutation:
2-element Vector{Int64}:
 2
 1

julia> S.L*S.D*S.L' - A[S.p, S.p]
2×2 Matrix{Float64}:
 0.0  0.0
 0.0  0.0
```
"""
bunchkaufman(A::AbstractMatrix{T}, rook::Bool=false; check::Bool = true) where {T} =
    bunchkaufman!(eigencopy_oftype(A, typeof(sqrt(oneunit(T)))), rook; check = check)

BunchKaufman{T}(B::BunchKaufman) where {T} =
    BunchKaufman(convert(Matrix{T}, B.LD), B.ipiv, B.uplo, B.symmetric, B.rook, B.info)
Factorization{T}(B::BunchKaufman) where {T} = BunchKaufman{T}(B)

size(B::BunchKaufman) = size(getfield(B, :LD))
size(B::BunchKaufman, d::Integer) = size(getfield(B, :LD), d)
issymmetric(B::BunchKaufman) = B.symmetric
ishermitian(B::BunchKaufman{T}) where T = T<:Real || !B.symmetric

function _ipiv2perm_bk(v::AbstractVector{T}, maxi::Integer, uplo::AbstractChar, rook::Bool) where T
    require_one_based_indexing(v)
    p = T[1:maxi;]
    uploL = uplo == 'L'
    i = uploL ? 1 : maxi
    # if uplo == 'U' we construct the permutation backwards
    @inbounds while 1 <= i <= length(v)
        vi = v[i]
        if vi > 0 # the 1x1 blocks
            p[i], p[vi] = p[vi], p[i]
            i += uploL ? 1 : -1
        else # the 2x2 blocks
            if rook
                p[i], p[-vi] = p[-vi], p[i]
            end
            if uploL
                vp = rook ? -v[i+1] : -vi
                p[i + 1], p[vp] = p[vp], p[i + 1]
                i += 2
            else # 'U'
                vp = rook ? -v[i-1] : -vi
                p[i - 1], p[vp] = p[vp], p[i - 1]
                i -= 2
            end
        end
    end
    return p
end

function getproperty(B::BunchKaufman{T,<:StridedMatrix}, d::Symbol) where {T<:BlasFloat}
    n = size(B, 1)
    if d === :p
        return _ipiv2perm_bk(getfield(B, :ipiv), n, getfield(B, :uplo), B.rook)
    elseif d === :P
        return Matrix{T}(I, n, n)[:,invperm(B.p)]
    elseif d === :L || d === :U || d === :D
        if getfield(B, :rook)
            LUD, od = LAPACK.syconvf_rook!(getfield(B, :uplo), 'C', copy(getfield(B, :LD)), getfield(B, :ipiv))
        else
            LUD, od = LAPACK.syconv!(getfield(B, :uplo), copy(getfield(B, :LD)), getfield(B, :ipiv))
        end
        if d === :D
            if getfield(B, :uplo) == 'L'
                odl = od[1:n - 1]
                return Tridiagonal(odl, diag(LUD), getfield(B, :symmetric) ? odl : conj.(odl))
            else # 'U'
                odu = od[2:n]
                return Tridiagonal(getfield(B, :symmetric) ? odu : conj.(odu), diag(LUD), odu)
            end
        elseif d === :L
            if getfield(B, :uplo) == 'L'
                return UnitLowerTriangular(LUD)
            else
                throw(ArgumentError("factorization is U*D*transpose(U) but you requested L"))
            end
        else # :U
            if B.uplo == 'U'
                return UnitUpperTriangular(LUD)
            else
                throw(ArgumentError("factorization is L*D*transpose(L) but you requested U"))
            end
        end
    else
        getfield(B, d)
    end
end

Base.propertynames(B::BunchKaufman, private::Bool=false) =
    (:p, :P, :L, :U, :D, (private ? fieldnames(typeof(B)) : ())...)

issuccess(B::BunchKaufman) = B.info == 0

function adjoint(B::BunchKaufman)
    if ishermitian(B)
        return B
    else
        throw(ArgumentError("adjoint not implemented for complex symmetric matrices"))
    end
end

function Base.show(io::IO, mime::MIME{Symbol("text/plain")}, B::BunchKaufman)
    if issuccess(B)
        summary(io, B); println(io)
        println(io, "D factor:")
        show(io, mime, B.D)
        println(io, "\n$(B.uplo) factor:")
        show(io, mime, B.uplo == 'L' ? B.L : B.U)
        println(io, "\npermutation:")
        show(io, mime, B.p)
    else
        print(io, "Failed factorization of type $(typeof(B))")
    end
end

function inv(B::BunchKaufman{<:BlasReal,<:StridedMatrix})
    if B.rook
        copytri!(LAPACK.sytri_rook!(B.uplo, copy(B.LD), B.ipiv), B.uplo, true)
    else
        copytri!(LAPACK.sytri!(B.uplo, copy(B.LD), B.ipiv), B.uplo, true)
    end
end

function inv(B::BunchKaufman{<:BlasComplex,<:StridedMatrix})
    if issymmetric(B)
        if B.rook
            copytri!(LAPACK.sytri_rook!(B.uplo, copy(B.LD), B.ipiv), B.uplo)
        else
            copytri!(LAPACK.sytri!(B.uplo, copy(B.LD), B.ipiv), B.uplo)
        end
    else
        if B.rook
            copytri!(LAPACK.hetri_rook!(B.uplo, copy(B.LD), B.ipiv), B.uplo, true)
        else
            copytri!(LAPACK.hetri!(B.uplo, copy(B.LD), B.ipiv), B.uplo, true)
        end
    end
end

function ldiv!(B::BunchKaufman{T,<:StridedMatrix}, R::StridedVecOrMat{T}) where {T<:BlasReal}
    if B.rook
        LAPACK.sytrs_rook!(B.uplo, B.LD, B.ipiv, R)
    else
        LAPACK.sytrs!(B.uplo, B.LD, B.ipiv, R)
    end
end
function ldiv!(B::BunchKaufman{T,<:StridedMatrix}, R::StridedVecOrMat{T}) where {T<:BlasComplex}
    if B.rook
        if issymmetric(B)
            LAPACK.sytrs_rook!(B.uplo, B.LD, B.ipiv, R)
        else
            LAPACK.hetrs_rook!(B.uplo, B.LD, B.ipiv, R)
        end
    else
        if issymmetric(B)
            LAPACK.sytrs!(B.uplo, B.LD, B.ipiv, R)
        else
            LAPACK.hetrs!(B.uplo, B.LD, B.ipiv, R)
        end
    end
end

function logabsdet(F::BunchKaufman)
    M = F.LD
    p = F.ipiv
    n = size(F.LD, 1)

    if !issuccess(F)
        return eltype(F)(-Inf), zero(eltype(F))
    end
    s = one(real(eltype(F)))
    i = 1
    abs_det = zero(real(eltype(F)))
    while i <= n
        if p[i] > 0
            elm = M[i,i]
            s *= sign(elm)
            abs_det += log(abs(elm))
            i += 1
        else
            # 2x2 pivot case. Make sure not to square before the subtraction by scaling
            # with the off-diagonal element. This is safe because the off diagonal is
            # always large for 2x2 pivots.
            if F.uplo == 'U'
                elm = M[i, i + 1]*(M[i,i]/M[i, i + 1]*M[i + 1, i + 1] -
                    (issymmetric(F) ? M[i, i + 1] : conj(M[i, i + 1])))
                s *= sign(elm)
                abs_det += log(abs(elm))
            else
                elm = M[i + 1,i]*(M[i, i]/M[i + 1, i]*M[i + 1, i + 1] -
                    (issymmetric(F) ? M[i + 1, i] : conj(M[i + 1, i])))
                s *= sign(elm)
                abs_det += log(abs(elm))
            end
            i += 2
        end
    end
    return abs_det, s
end

## reconstruct the original matrix
## TODO: understand the procedure described at
## http://www.nag.com/numeric/FL/nagdoc_fl22/pdf/F07/f07mdf.pdf
y   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LinearAlgebra/src/diagonal.jl�x      # This file is a part of Julia. License is MIT: https://julialang.org/license

## Diagonal matrices

struct Diagonal{T,V<:AbstractVector{T}} <: AbstractMatrix{T}
    diag::V

    function Diagonal{T,V}(diag) where {T,V<:AbstractVector{T}}
        require_one_based_indexing(diag)
        new{T,V}(diag)
    end
end
Diagonal{T,V}(d::Diagonal) where {T,V<:AbstractVector{T}} = Diagonal{T,V}(d.diag)
Diagonal(v::AbstractVector{T}) where {T} = Diagonal{T,typeof(v)}(v)
Diagonal{T}(v::AbstractVector) where {T} = Diagonal(convert(AbstractVector{T}, v)::AbstractVector{T})

function Base.promote_rule(A::Type{<:Diagonal{<:Any,V}}, B::Type{<:Diagonal{<:Any,W}}) where {V,W}
    X = promote_type(V, W)
    T = eltype(X)
    isconcretetype(T) && return Diagonal{T,X}
    return typejoin(A, B)
end

"""
    Diagonal(V::AbstractVector)

Construct a lazy matrix with `V` as its diagonal.

See also [`UniformScaling`](@ref) for the lazy identity matrix `I`,
[`diagm`](@ref) to make a dense matrix, and [`diag`](@ref) to extract diagonal elements.

# Examples
```jldoctest
julia> d = Diagonal([1, 10, 100])
3×3 Diagonal{$Int, Vector{$Int}}:
 1   ⋅    ⋅
 ⋅  10    ⋅
 ⋅   ⋅  100

julia> diagm([7, 13])
2×2 Matrix{$Int}:
 7   0
 0  13

julia> ans + I
2×2 Matrix{Int64}:
 8   0
 0  14

julia> I(2)
2×2 Diagonal{Bool, Vector{Bool}}:
 1  ⋅
 ⋅  1
```

Note that a one-column matrix is not treated like a vector, but instead calls the
method `Diagonal(A::AbstractMatrix)` which extracts 1-element `diag(A)`:

```jldoctest
julia> A = transpose([7.0 13.0])
2×1 transpose(::Matrix{Float64}) with eltype Float64:
  7.0
 13.0

julia> Diagonal(A)
1×1 Diagonal{Float64, Vector{Float64}}:
 7.0
```
"""
Diagonal(V::AbstractVector)

"""
    Diagonal(A::AbstractMatrix)

Construct a matrix from the diagonal of `A`.

# Examples
```jldoctest
julia> A = permutedims(reshape(1:15, 5, 3))
3×5 Matrix{Int64}:
  1   2   3   4   5
  6   7   8   9  10
 11  12  13  14  15

julia> Diagonal(A)
3×3 Diagonal{$Int, Vector{$Int}}:
 1  ⋅   ⋅
 ⋅  7   ⋅
 ⋅  ⋅  13

julia> diag(A, 2)
3-element Vector{$Int}:
  3
  9
 15
```
"""
Diagonal(A::AbstractMatrix) = Diagonal(diag(A))
Diagonal{T}(A::AbstractMatrix) where T = Diagonal{T}(diag(A))
function convert(::Type{T}, A::AbstractMatrix) where T<:Diagonal
    checksquare(A)
    isdiag(A) ? T(A) : throw(InexactError(:convert, T, A))
end

Diagonal(D::Diagonal) = D
Diagonal{T}(D::Diagonal{T}) where {T} = D
Diagonal{T}(D::Diagonal) where {T} = Diagonal{T}(D.diag)

AbstractMatrix{T}(D::Diagonal) where {T} = Diagonal{T}(D)
Matrix(D::Diagonal{T}) where {T} = Matrix{promote_type(T, typeof(zero(T)))}(D)
Array(D::Diagonal{T}) where {T} = Matrix(D)
function Matrix{T}(D::Diagonal) where {T}
    n = size(D, 1)
    B = Matrix{T}(undef, n, n)
    n > 1 && fill!(B, zero(T))
    @inbounds for i in 1:n
        B[i,i] = D.diag[i]
    end
    return B
end

"""
    Diagonal{T}(undef, n)

Construct an uninitialized `Diagonal{T}` of length `n`. See `undef`.
"""
Diagonal{T}(::UndefInitializer, n::Integer) where T = Diagonal(Vector{T}(undef, n))

similar(D::Diagonal, ::Type{T}) where {T} = Diagonal(similar(D.diag, T))
similar(D::Diagonal, ::Type{T}, dims::Union{Dims{1},Dims{2}}) where {T} = similar(D.diag, T, dims)

copyto!(D1::Diagonal, D2::Diagonal) = (copyto!(D1.diag, D2.diag); D1)

size(D::Diagonal) = (n = length(D.diag); (n,n))

function size(D::Diagonal,d::Integer)
    if d<1
        throw(ArgumentError("dimension must be ≥ 1, got $d"))
    end
    return d<=2 ? length(D.diag) : 1
end

@inline function Base.isassigned(D::Diagonal, i::Int, j::Int)
    @boundscheck checkbounds(Bool, D, i, j) || return false
    if i == j
        @inbounds r = isassigned(D.diag, i)
    else
        r = true
    end
    r
end

@inline function getindex(D::Diagonal, i::Int, j::Int)
    @boundscheck checkbounds(D, i, j)
    if i == j
        @inbounds r = D.diag[i]
    else
        r = diagzero(D, i, j)
    end
    r
end
diagzero(::Diagonal{T}, i, j) where {T} = zero(T)
diagzero(D::Diagonal{<:AbstractMatrix{T}}, i, j) where {T} = zeros(T, size(D.diag[i], 1), size(D.diag[j], 2))

function setindex!(D::Diagonal, v, i::Int, j::Int)
    @boundscheck checkbounds(D, i, j)
    if i == j
        @inbounds D.diag[i] = v
    elseif !iszero(v)
        throw(ArgumentError("cannot set off-diagonal entry ($i, $j) to a nonzero value ($v)"))
    end
    return v
end


## structured matrix methods ##
function Base.replace_in_print_matrix(A::Diagonal,i::Integer,j::Integer,s::AbstractString)
    i==j ? s : Base.replace_with_centered_mark(s)
end

parent(D::Diagonal) = D.diag

ishermitian(D::Diagonal{<:Real}) = true
ishermitian(D::Diagonal{<:Number}) = isreal(D.diag)
ishermitian(D::Diagonal) = all(ishermitian, D.diag)
issymmetric(D::Diagonal{<:Number}) = true
issymmetric(D::Diagonal) = all(issymmetric, D.diag)
isposdef(D::Diagonal) = all(isposdef, D.diag)

factorize(D::Diagonal) = D

real(D::Diagonal) = Diagonal(real(D.diag))
imag(D::Diagonal) = Diagonal(imag(D.diag))

iszero(D::Diagonal) = all(iszero, D.diag)
isone(D::Diagonal) = all(isone, D.diag)
isdiag(D::Diagonal) = all(isdiag, D.diag)
isdiag(D::Diagonal{<:Number}) = true
istriu(D::Diagonal, k::Integer=0) = k <= 0 || iszero(D.diag) ? true : false
istril(D::Diagonal, k::Integer=0) = k >= 0 || iszero(D.diag) ? true : false
function triu!(D::Diagonal{T}, k::Integer=0) where T
    n = size(D,1)
    if !(-n + 1 <= k <= n + 1)
        throw(ArgumentError(string("the requested diagonal, $k, must be at least ",
            "$(-n + 1) and at most $(n + 1) in an $n-by-$n matrix")))
    elseif k > 0
        fill!(D.diag, zero(T))
    end
    return D
end

function tril!(D::Diagonal{T}, k::Integer=0) where T
    n = size(D,1)
    if !(-n - 1 <= k <= n - 1)
        throw(ArgumentError(string("the requested diagonal, $k, must be at least ",
            "$(-n - 1) and at most $(n - 1) in an $n-by-$n matrix")))
    elseif k < 0
        fill!(D.diag, zero(T))
    end
    return D
end

(==)(Da::Diagonal, Db::Diagonal) = Da.diag == Db.diag
(-)(A::Diagonal) = Diagonal(-A.diag)
(+)(Da::Diagonal, Db::Diagonal) = Diagonal(Da.diag + Db.diag)
(-)(Da::Diagonal, Db::Diagonal) = Diagonal(Da.diag - Db.diag)

for f in (:+, :-)
    @eval function $f(D::Diagonal, S::Symmetric)
        return Symmetric($f(D, S.data), sym_uplo(S.uplo))
    end
    @eval function $f(S::Symmetric, D::Diagonal)
        return Symmetric($f(S.data, D), sym_uplo(S.uplo))
    end
    @eval function $f(D::Diagonal{<:Real}, H::Hermitian)
        return Hermitian($f(D, H.data), sym_uplo(H.uplo))
    end
    @eval function $f(H::Hermitian, D::Diagonal{<:Real})
        return Hermitian($f(H.data, D), sym_uplo(H.uplo))
    end
end

(*)(x::Number, D::Diagonal) = Diagonal(x * D.diag)
(*)(D::Diagonal, x::Number) = Diagonal(D.diag * x)
(/)(D::Diagonal, x::Number) = Diagonal(D.diag / x)
(\)(x::Number, D::Diagonal) = Diagonal(x \ D.diag)
(^)(D::Diagonal, a::Number) = Diagonal(D.diag .^ a)
(^)(D::Diagonal, a::Real) = Diagonal(D.diag .^ a) # for disambiguation
(^)(D::Diagonal, a::Integer) = Diagonal(D.diag .^ a) # for disambiguation
Base.literal_pow(::typeof(^), D::Diagonal, valp::Val) =
    Diagonal(Base.literal_pow.(^, D.diag, valp)) # for speed
Base.literal_pow(::typeof(^), D::Diagonal, ::Val{-1}) = inv(D) # for disambiguation

function _muldiag_size_check(A, B)
    nA = size(A, 2)
    mB = size(B, 1)
    @noinline throw_dimerr(::AbstractMatrix, nA, mB) = throw(DimensionMismatch("second dimension of A, $nA, does not match first dimension of B, $mB"))
    @noinline throw_dimerr(::AbstractVector, nA, mB) = throw(DimensionMismatch("second dimension of D, $nA, does not match length of V, $mB"))
    nA == mB || throw_dimerr(B, nA, mB)
    return nothing
end
# the output matrix should have the same size as the non-diagonal input matrix or vector
@noinline throw_dimerr(szC, szA) = throw(DimensionMismatch("output matrix has size: $szC, but should have size $szA"))
_size_check_out(C, ::Diagonal, A) = _size_check_out(C, A)
_size_check_out(C, A, ::Diagonal) = _size_check_out(C, A)
_size_check_out(C, A::Diagonal, ::Diagonal) = _size_check_out(C, A)
function _size_check_out(C, A)
    szA = size(A)
    szC = size(C)
    szA == szC || throw_dimerr(szC, szA)
    return nothing
end
function _muldiag_size_check(C, A, B)
    _muldiag_size_check(A, B)
    _size_check_out(C, A, B)
end

function (*)(Da::Diagonal, Db::Diagonal)
    _muldiag_size_check(Da, Db)
    return Diagonal(Da.diag .* Db.diag)
end

function (*)(D::Diagonal, V::AbstractVector)
    _muldiag_size_check(D, V)
    return D.diag .* V
end

(*)(A::AbstractMatrix, D::Diagonal) =
    mul!(similar(A, promote_op(*, eltype(A), eltype(D.diag))), A, D)
(*)(A::HermOrSym, D::Diagonal) =
    mul!(similar(A, promote_op(*, eltype(A), eltype(D.diag)), size(A)), A, D)
(*)(D::Diagonal, A::AbstractMatrix) =
    mul!(similar(A, promote_op(*, eltype(A), eltype(D.diag))), D, A)
(*)(D::Diagonal, A::HermOrSym) =
    mul!(similar(A, promote_op(*, eltype(A), eltype(D.diag)), size(A)), D, A)

rmul!(A::AbstractMatrix, D::Diagonal) = @inline mul!(A, A, D)
lmul!(D::Diagonal, B::AbstractVecOrMat) = @inline mul!(B, D, B)

function (*)(A::AdjOrTransAbsMat, D::Diagonal)
    Ac = copy_similar(A, promote_op(*, eltype(A), eltype(D.diag)))
    rmul!(Ac, D)
end
function (*)(D::Diagonal, A::AdjOrTransAbsMat)
    Ac = copy_similar(A, promote_op(*, eltype(A), eltype(D.diag)))
    lmul!(D, Ac)
end

function __muldiag!(out, D::Diagonal, B, _add::MulAddMul{ais1,bis0}) where {ais1,bis0}
    require_one_based_indexing(out, B)
    alpha, beta = _add.alpha, _add.beta
    if iszero(alpha)
        _rmul_or_fill!(out, beta)
    else
        if bis0
            @inbounds for j in axes(B, 2)
                @simd for i in axes(B, 1)
                    out[i,j] = D.diag[i] * B[i,j] * alpha
                end
            end
        else
            @inbounds for j in axes(B, 2)
                @simd for i in axes(B, 1)
                    out[i,j] = D.diag[i] * B[i,j] * alpha + out[i,j] * beta
                end
            end
        end
    end
    return out
end
function __muldiag!(out, A, D::Diagonal, _add::MulAddMul{ais1,bis0}) where {ais1,bis0}
    require_one_based_indexing(out, A)
    alpha, beta = _add.alpha, _add.beta
    if iszero(alpha)
        _rmul_or_fill!(out, beta)
    else
        if bis0
            @inbounds for j in axes(A, 2)
                dja = D.diag[j] * alpha
                @simd for i in axes(A, 1)
                    out[i,j] = A[i,j] * dja
                end
            end
        else
            @inbounds for j in axes(A, 2)
                dja = D.diag[j] * alpha
                @simd for i in axes(A, 1)
                    out[i,j] = A[i,j] * dja + out[i,j] * beta
                end
            end
        end
    end
    return out
end
function __muldiag!(out::Diagonal, D1::Diagonal, D2::Diagonal, _add::MulAddMul{ais1,bis0}) where {ais1,bis0}
    d1 = D1.diag
    d2 = D2.diag
    alpha, beta = _add.alpha, _add.beta
    if iszero(alpha)
        _rmul_or_fill!(out.diag, beta)
    else
        if bis0
            @inbounds @simd for i in eachindex(out.diag)
                out.diag[i] = d1[i] * d2[i] * alpha
            end
        else
            @inbounds @simd for i in eachindex(out.diag)
                out.diag[i] = d1[i] * d2[i] * alpha + out.diag[i] * beta
            end
        end
    end
    return out
end
function __muldiag!(out, D1::Diagonal, D2::Diagonal, _add::MulAddMul{ais1,bis0}) where {ais1,bis0}
    require_one_based_indexing(out)
    alpha, beta = _add.alpha, _add.beta
    mA = size(D1, 1)
    d1 = D1.diag
    d2 = D2.diag
    _rmul_or_fill!(out, beta)
    if !iszero(alpha)
        @inbounds @simd for i in 1:mA
            out[i,i] += d1[i] * d2[i] * alpha
        end
    end
    return out
end

function _mul_diag!(out, A, B, _add)
    _muldiag_size_check(out, A, B)
    __muldiag!(out, A, B, _add)
    return out
end

_mul!(out::AbstractVecOrMat, D::Diagonal, V::AbstractVector, _add) =
    _mul_diag!(out, D, V, _add)
_mul!(out::AbstractMatrix, D::Diagonal, B::AbstractMatrix, _add) =
    _mul_diag!(out, D, B, _add)
_mul!(out::AbstractMatrix, A::AbstractMatrix, D::Diagonal, _add) =
    _mul_diag!(out, A, D, _add)
_mul!(C::Diagonal, Da::Diagonal, Db::Diagonal, _add) =
    _mul_diag!(C, Da, Db, _add)
_mul!(C::AbstractMatrix, Da::Diagonal, Db::Diagonal, _add) =
    _mul_diag!(C, Da, Db, _add)

function (*)(Da::Diagonal, A::AbstractMatrix, Db::Diagonal)
    _muldiag_size_check(Da, A)
    _muldiag_size_check(A, Db)
    return broadcast(*, Da.diag, A, permutedims(Db.diag))
end

function (*)(Da::Diagonal, Db::Diagonal, Dc::Diagonal)
    _muldiag_size_check(Da, Db)
    _muldiag_size_check(Db, Dc)
    return Diagonal(Da.diag .* Db.diag .* Dc.diag)
end

/(A::AbstractVecOrMat, D::Diagonal) = _rdiv!(similar(A, _init_eltype(/, eltype(A), eltype(D))), A, D)
/(A::HermOrSym, D::Diagonal) = _rdiv!(similar(A, _init_eltype(/, eltype(A), eltype(D)), size(A)), A, D)

rdiv!(A::AbstractVecOrMat, D::Diagonal) = @inline _rdiv!(A, A, D)
# avoid copy when possible via internal 3-arg backend
function _rdiv!(B::AbstractVecOrMat, A::AbstractVecOrMat, D::Diagonal)
    require_one_based_indexing(A)
    dd = D.diag
    m, n = size(A, 1), size(A, 2)
    if (k = length(dd)) != n
        throw(DimensionMismatch("left hand side has $n columns but D is $k by $k"))
    end
    @inbounds for j in 1:n
        ddj = dd[j]
        iszero(ddj) && throw(SingularException(j))
        for i in 1:m
            B[i, j] = A[i, j] / ddj
        end
    end
    B
end

function \(D::Diagonal, B::AbstractVector)
    j = findfirst(iszero, D.diag)
    isnothing(j) || throw(SingularException(j))
    return D.diag .\ B
end
\(D::Diagonal, B::AbstractMatrix) = ldiv!(similar(B, _init_eltype(\, eltype(D), eltype(B))), D, B)
\(D::Diagonal, B::HermOrSym) = ldiv!(similar(B, _init_eltype(\, eltype(D), eltype(B)), size(B)), D, B)

ldiv!(D::Diagonal, B::AbstractVecOrMat) = @inline ldiv!(B, D, B)
function ldiv!(B::AbstractVecOrMat, D::Diagonal, A::AbstractVecOrMat)
    require_one_based_indexing(A, B)
    dd = D.diag
    d = length(dd)
    m, n = size(A, 1), size(A, 2)
    m′, n′ = size(B, 1), size(B, 2)
    m == d || throw(DimensionMismatch("right hand side has $m rows but D is $d by $d"))
    (m, n) == (m′, n′) || throw(DimensionMismatch("expect output to be $m by $n, but got $m′ by $n′"))
    j = findfirst(iszero, D.diag)
    isnothing(j) || throw(SingularException(j))
    @inbounds for j = 1:n, i = 1:m
        B[i, j] = dd[i] \ A[i, j]
    end
    B
end

# Optimizations for \, / between Diagonals
\(D::Diagonal, B::Diagonal) = ldiv!(similar(B, promote_op(\, eltype(D), eltype(B))), D, B)
/(A::Diagonal, D::Diagonal) = _rdiv!(similar(A, promote_op(/, eltype(A), eltype(D))), A, D)
function _rdiv!(Dc::Diagonal, Db::Diagonal, Da::Diagonal)
    n, k = length(Db.diag), length(Da.diag)
    n == k || throw(DimensionMismatch("left hand side has $n columns but D is $k by $k"))
    j = findfirst(iszero, Da.diag)
    isnothing(j) || throw(SingularException(j))
    Dc.diag .= Db.diag ./ Da.diag
    Dc
end
ldiv!(Dc::Diagonal, Da::Diagonal, Db::Diagonal) = Diagonal(ldiv!(Dc.diag, Da, Db.diag))

# optimizations for (Sym)Tridiagonal and Diagonal
@propagate_inbounds _getudiag(T::Tridiagonal, i) = T.du[i]
@propagate_inbounds _getudiag(S::SymTridiagonal, i) = S.ev[i]
@propagate_inbounds _getdiag(T::Tridiagonal, i) = T.d[i]
@propagate_inbounds _getdiag(S::SymTridiagonal, i) = symmetric(S.dv[i], :U)::symmetric_type(eltype(S.dv))
@propagate_inbounds _getldiag(T::Tridiagonal, i) = T.dl[i]
@propagate_inbounds _getldiag(S::SymTridiagonal, i) = transpose(S.ev[i])

function (\)(D::Diagonal, S::SymTridiagonal)
    T = promote_op(\, eltype(D), eltype(S))
    du = similar(S.ev, T, max(length(S.dv)-1, 0))
    d  = similar(S.dv, T, length(S.dv))
    dl = similar(S.ev, T, max(length(S.dv)-1, 0))
    ldiv!(Tridiagonal(dl, d, du), D, S)
end
(\)(D::Diagonal, T::Tridiagonal) = ldiv!(similar(T, promote_op(\, eltype(D), eltype(T))), D, T)
function ldiv!(T::Tridiagonal, D::Diagonal, S::Union{SymTridiagonal,Tridiagonal})
    m = size(S, 1)
    dd = D.diag
    if (k = length(dd)) != m
        throw(DimensionMismatch("diagonal matrix is $k by $k but right hand side has $m rows"))
    end
    if length(T.d) != m
        throw(DimensionMismatch("target matrix size $(size(T)) does not match input matrix size $(size(S))"))
    end
    m == 0 && return T
    j = findfirst(iszero, dd)
    isnothing(j) || throw(SingularException(j))
    ddj = dd[1]
    T.d[1] = ddj \ _getdiag(S, 1)
    @inbounds if m > 1
        T.du[1] = ddj \ _getudiag(S, 1)
        for j in 2:m-1
            ddj = dd[j]
            T.dl[j-1] = ddj \ _getldiag(S, j-1)
            T.d[j]  = ddj \ _getdiag(S, j)
            T.du[j] = ddj \ _getudiag(S, j)
        end
        ddj = dd[m]
        T.dl[m-1] = ddj \ _getldiag(S, m-1)
        T.d[m] = ddj \ _getdiag(S, m)
    end
    return T
end

function (/)(S::SymTridiagonal, D::Diagonal)
    T = promote_op(\, eltype(D), eltype(S))
    du = similar(S.ev, T, max(length(S.dv)-1, 0))
    d  = similar(S.dv, T, length(S.dv))
    dl = similar(S.ev, T, max(length(S.dv)-1, 0))
    _rdiv!(Tridiagonal(dl, d, du), S, D)
end
(/)(T::Tridiagonal, D::Diagonal) = _rdiv!(similar(T, promote_op(/, eltype(T), eltype(D))), T, D)
function _rdiv!(T::Tridiagonal, S::Union{SymTridiagonal,Tridiagonal}, D::Diagonal)
    n = size(S, 2)
    dd = D.diag
    if (k = length(dd)) != n
        throw(DimensionMismatch("left hand side has $n columns but D is $k by $k"))
    end
    if length(T.d) != n
        throw(DimensionMismatch("target matrix size $(size(T)) does not match input matrix size $(size(S))"))
    end
    n == 0 && return T
    j = findfirst(iszero, dd)
    isnothing(j) || throw(SingularException(j))
    ddj = dd[1]
    T.d[1] = _getdiag(S, 1) / ddj
    @inbounds if n > 1
        T.dl[1] = _getldiag(S, 1) / ddj
        for j in 2:n-1
            ddj = dd[j]
            T.dl[j] = _getldiag(S, j) / ddj
            T.d[j] = _getdiag(S, j) / ddj
            T.du[j-1] = _getudiag(S, j-1) / ddj
        end
        ddj = dd[n]
        T.d[n] = _getdiag(S, n) / ddj
        T.du[n-1] = _getudiag(S, n-1) / ddj
    end
    return T
end

# Optimizations for [l/r]mul!, l/rdiv!, *, / and \ between Triangular and Diagonal.
# These functions are generally more efficient if we calculate the whole data field.
# The following code implements them in a unified pattern to avoid missing.
@inline function _setdiag!(data, f, diag, diag′ = nothing)
    @inbounds for i in 1:length(diag)
        data[i,i] = isnothing(diag′) ? f(diag[i]) : f(diag[i],diag′[i])
    end
    data
end
for Tri in (:UpperTriangular, :LowerTriangular)
    UTri = Symbol(:Unit, Tri)
    # 2 args
    for (fun, f) in zip((:*, :rmul!, :rdiv!, :/), (:identity, :identity, :inv, :inv))
        @eval $fun(A::$Tri, D::Diagonal) = $Tri($fun(A.data, D))
        @eval $fun(A::$UTri, D::Diagonal) = $Tri(_setdiag!($fun(A.data, D), $f, D.diag))
    end
    for (fun, f) in zip((:*, :lmul!, :ldiv!, :\), (:identity, :identity, :inv, :inv))
        @eval $fun(D::Diagonal, A::$Tri) = $Tri($fun(D, A.data))
        @eval $fun(D::Diagonal, A::$UTri) = $Tri(_setdiag!($fun(D, A.data), $f, D.diag))
    end
    # 3-arg ldiv!
    @eval ldiv!(C::$Tri, D::Diagonal, A::$Tri) = $Tri(ldiv!(C.data, D, A.data))
    @eval ldiv!(C::$Tri, D::Diagonal, A::$UTri) = $Tri(_setdiag!(ldiv!(C.data, D, A.data), inv, D.diag))
    # 3-arg mul! is disambiguated in special.jl
    # 5-arg mul!
    @eval _mul!(C::$Tri, D::Diagonal, A::$Tri, _add) = $Tri(mul!(C.data, D, A.data, _add.alpha, _add.beta))
    @eval function _mul!(C::$Tri, D::Diagonal, A::$UTri, _add::MulAddMul{ais1,bis0}) where {ais1,bis0}
        α, β = _add.alpha, _add.beta
        iszero(α) && return _rmul_or_fill!(C, β)
        diag′ = bis0 ? nothing : diag(C)
        data = mul!(C.data, D, A.data, α, β)
        $Tri(_setdiag!(data, _add, D.diag, diag′))
    end
    @eval _mul!(C::$Tri, A::$Tri, D::Diagonal, _add) = $Tri(mul!(C.data, A.data, D, _add.alpha, _add.beta))
    @eval function _mul!(C::$Tri, A::$UTri, D::Diagonal, _add::MulAddMul{ais1,bis0}) where {ais1,bis0}
        α, β = _add.alpha, _add.beta
        iszero(α) && return _rmul_or_fill!(C, β)
        diag′ = bis0 ? nothing : diag(C)
        data = mul!(C.data, A.data, D, α, β)
        $Tri(_setdiag!(data, _add, D.diag, diag′))
    end
end

@inline function kron!(C::AbstractMatrix, A::Diagonal, B::Diagonal)
    valA = A.diag; nA = length(valA)
    valB = B.diag; nB = length(valB)
    nC = checksquare(C)
    @boundscheck nC == nA*nB ||
        throw(DimensionMismatch("expect C to be a $(nA*nB)x$(nA*nB) matrix, got size $(nC)x$(nC)"))
    isempty(A) || isempty(B) || fill!(C, zero(A[1,1] * B[1,1]))
    @inbounds for i = 1:nA, j = 1:nB
        idx = (i-1)*nB+j
        C[idx, idx] = valA[i] * valB[j]
    end
    return C
end

kron(A::Diagonal, B::Diagonal) = Diagonal(kron(A.diag, B.diag))

function kron(A::Diagonal, B::SymTridiagonal)
    kdv = kron(diag(A), B.dv)
    # We don't need to drop the last element
    kev = kron(diag(A), _pushzero(_evview(B)))
    SymTridiagonal(kdv, kev)
end
function kron(A::Diagonal, B::Tridiagonal)
    # `_droplast!` is only guaranteed to work with `Vector`
    kd = _makevector(kron(diag(A), B.d))
    kdl = _droplast!(_makevector(kron(diag(A), _pushzero(B.dl))))
    kdu = _droplast!(_makevector(kron(diag(A), _pushzero(B.du))))
    Tridiagonal(kdl, kd, kdu)
end

@inline function kron!(C::AbstractMatrix, A::Diagonal, B::AbstractMatrix)
    require_one_based_indexing(B)
    (mA, nA) = size(A)
    (mB, nB) = size(B)
    (mC, nC) = size(C)
    @boundscheck (mC, nC) == (mA * mB, nA * nB) ||
        throw(DimensionMismatch("expect C to be a $(mA * mB)x$(nA * nB) matrix, got size $(mC)x$(nC)"))
    isempty(A) || isempty(B) || fill!(C, zero(A[1,1] * B[1,1]))
    m = 1
    @inbounds for j = 1:nA
        A_jj = A[j,j]
        for k = 1:nB
            for l = 1:mB
                C[m] = A_jj * B[l,k]
                m += 1
            end
            m += (nA - 1) * mB
        end
        m += mB
    end
    return C
end

@inline function kron!(C::AbstractMatrix, A::AbstractMatrix, B::Diagonal)
    require_one_based_indexing(A)
    (mA, nA) = size(A)
    (mB, nB) = size(B)
    (mC, nC) = size(C)
    @boundscheck (mC, nC) == (mA * mB, nA * nB) ||
        throw(DimensionMismatch("expect C to be a $(mA * mB)x$(nA * nB) matrix, got size $(mC)x$(nC)"))
    isempty(A) || isempty(B) || fill!(C, zero(A[1,1] * B[1,1]))
    m = 1
    @inbounds for j = 1:nA
        for l = 1:mB
            Bll = B[l,l]
            for k = 1:mA
                C[m] = A[k,j] * Bll
                m += nB
            end
            m += 1
        end
        m -= nB
    end
    return C
end

conj(D::Diagonal) = Diagonal(conj(D.diag))
transpose(D::Diagonal{<:Number}) = D
transpose(D::Diagonal) = Diagonal(transpose.(D.diag))
adjoint(D::Diagonal{<:Number}) = Diagonal(vec(adjoint(D.diag)))
adjoint(D::Diagonal{<:Number,<:Base.ReshapedArray{<:Number,1,<:Adjoint}}) = Diagonal(adjoint(parent(D.diag)))
adjoint(D::Diagonal) = Diagonal(adjoint.(D.diag))
permutedims(D::Diagonal) = D
permutedims(D::Diagonal, perm) = (Base.checkdims_perm(D, D, perm); D)

function diag(D::Diagonal{T}, k::Integer=0) where T
    # every branch call similar(..., ::Int) to make sure the
    # same vector type is returned independent of k
    if k == 0
        return copyto!(similar(D.diag, length(D.diag)), D.diag)
    elseif -size(D,1) <= k <= size(D,1)
        return fill!(similar(D.diag, size(D,1)-abs(k)), zero(T))
    else
        throw(ArgumentError(string("requested diagonal, $k, must be at least $(-size(D, 1)) ",
            "and at most $(size(D, 2)) for an $(size(D, 1))-by-$(size(D, 2)) matrix")))
    end
end
tr(D::Diagonal) = sum(tr, D.diag)
det(D::Diagonal) = prod(det, D.diag)
function logdet(D::Diagonal{<:Complex}) # make sure branch cut is correct
    z = sum(log, D.diag)
    complex(real(z), rem2pi(imag(z), RoundNearest))
end

# Matrix functions
for f in (:exp, :cis, :log, :sqrt,
          :cos, :sin, :tan, :csc, :sec, :cot,
          :cosh, :sinh, :tanh, :csch, :sech, :coth,
          :acos, :asin, :atan, :acsc, :asec, :acot,
          :acosh, :asinh, :atanh, :acsch, :asech, :acoth)
    @eval $f(D::Diagonal) = Diagonal($f.(D.diag))
end

function inv(D::Diagonal{T}) where T
    Di = similar(D.diag, typeof(inv(oneunit(T))))
    for i = 1:length(D.diag)
        if iszero(D.diag[i])
            throw(SingularException(i))
        end
        Di[i] = inv(D.diag[i])
    end
    Diagonal(Di)
end

function pinv(D::Diagonal{T}) where T
    Di = similar(D.diag, typeof(inv(oneunit(T))))
    for i = 1:length(D.diag)
        if !iszero(D.diag[i])
            invD = inv(D.diag[i])
            if isfinite(invD)
                Di[i] = invD
                continue
            end
        end
        # fallback
        Di[i] = zero(T)
    end
    Diagonal(Di)
end
function pinv(D::Diagonal{T}, tol::Real) where T
    Di = similar(D.diag, typeof(inv(oneunit(T))))
    if !isempty(D.diag)
        maxabsD = maximum(abs, D.diag)
        for i = 1:length(D.diag)
            if abs(D.diag[i]) > tol*maxabsD
                invD = inv(D.diag[i])
                if isfinite(invD)
                    Di[i] = invD
                    continue
                end
            end
            # fallback
            Di[i] = zero(T)
        end
    end
    Diagonal(Di)
end

#Eigensystem
eigvals(D::Diagonal{<:Number}; permute::Bool=true, scale::Bool=true) = copy(D.diag)
eigvals(D::Diagonal; permute::Bool=true, scale::Bool=true) =
    [eigvals(x) for x in D.diag] #For block matrices, etc.
eigvecs(D::Diagonal) = Matrix{eltype(D)}(I, size(D))
function eigen(D::Diagonal; permute::Bool=true, scale::Bool=true, sortby::Union{Function,Nothing}=nothing)
    if any(!isfinite, D.diag)
        throw(ArgumentError("matrix contains Infs or NaNs"))
    end
    Td = Base.promote_op(/, eltype(D), eltype(D))
    λ = eigvals(D)
    if !isnothing(sortby)
        p = sortperm(λ; alg=QuickSort, by=sortby)
        λ = λ[p]
        evecs = zeros(Td, size(D))
        @inbounds for i in eachindex(p)
            evecs[p[i],i] = one(Td)
        end
    else
        evecs = Matrix{Td}(I, size(D))
    end
    Eigen(λ, evecs)
end
function eigen(Da::Diagonal, Db::Diagonal; sortby::Union{Function,Nothing}=nothing)
    if any(!isfinite, Da.diag) || any(!isfinite, Db.diag)
        throw(ArgumentError("matrices contain Infs or NaNs"))
    end
    if any(iszero, Db.diag)
        throw(ArgumentError("right-hand side diagonal matrix is singular"))
    end
    return GeneralizedEigen(eigen(Db \ Da; sortby)...)
end
function eigen(A::AbstractMatrix, D::Diagonal; sortby::Union{Function,Nothing}=nothing)
    if any(iszero, D.diag)
        throw(ArgumentError("right-hand side diagonal matrix is singular"))
    end
    if size(A, 1) == size(A, 2) && isdiag(A)
        return eigen(Diagonal(A), D; sortby)
    elseif all(isposdef, D.diag)
        S = promote_type(eigtype(eltype(A)), eltype(D))
        return eigen(A, cholesky(Diagonal{S}(D)); sortby)
    else
        return eigen!(D \ A; sortby)
    end
end

#Singular system
svdvals(D::Diagonal{<:Number}) = sort!(abs.(D.diag), rev = true)
svdvals(D::Diagonal) = [svdvals(v) for v in D.diag]
function svd(D::Diagonal{T}) where {T<:Number}
    d = D.diag
    s = abs.(d)
    piv = sortperm(s, rev = true)
    S = s[piv]
    Td  = typeof(oneunit(T)/oneunit(T))
    U = zeros(Td, size(D))
    Vt = copy(U)
    for i in 1:length(d)
        j = piv[i]
        U[j,i] = d[j] / S[i]
        Vt[i,j] = one(Td)
    end
    return SVD(U, S, Vt)
end

# disambiguation methods: * and / of Diagonal and Adj/Trans AbsVec
*(u::AdjointAbsVec, D::Diagonal) = (D'u')'
*(u::TransposeAbsVec, D::Diagonal) = transpose(transpose(D) * transpose(u))
*(x::AdjointAbsVec,   D::Diagonal, y::AbstractVector) = _mapreduce_prod(*, x, D, y)
*(x::TransposeAbsVec, D::Diagonal, y::AbstractVector) = _mapreduce_prod(*, x, D, y)
/(u::AdjointAbsVec, D::Diagonal) = (D' \ u')'
/(u::TransposeAbsVec, D::Diagonal) = transpose(transpose(D) \ transpose(u))
# disambiguation methods: Call unoptimized version for user defined AbstractTriangular.
*(A::AbstractTriangular, D::Diagonal) = @invoke *(A::AbstractMatrix, D::Diagonal)
*(D::Diagonal, A::AbstractTriangular) = @invoke *(D::Diagonal, A::AbstractMatrix)

dot(x::AbstractVector, D::Diagonal, y::AbstractVector) = _mapreduce_prod(dot, x, D, y)

dot(A::Diagonal, B::Diagonal) = dot(A.diag, B.diag)
function dot(D::Diagonal, B::AbstractMatrix)
    size(D) == size(B) || throw(DimensionMismatch("Matrix sizes $(size(D)) and $(size(B)) differ"))
    return dot(D.diag, view(B, diagind(B)))
end

dot(A::AbstractMatrix, B::Diagonal) = conj(dot(B, A))

function _mapreduce_prod(f, x, D::Diagonal, y)
    if !(length(x) == length(D.diag) == length(y))
        throw(DimensionMismatch("x has length $(length(x)), D has size $(size(D)), and y has $(length(y))"))
    end
    if isempty(x) && isempty(D) && isempty(y)
        return zero(promote_op(f, eltype(x), eltype(D), eltype(y)))
    else
        return mapreduce(t -> f(t[1], t[2], t[3]), +, zip(x, D.diag, y))
    end
end

function cholesky!(A::Diagonal, ::NoPivot = NoPivot(); check::Bool = true)
    info = 0
    for (i, di) in enumerate(A.diag)
        if isreal(di) && real(di) > 0
            A.diag[i] = √di
        elseif check
            throw(PosDefException(i))
        else
            info = i
            break
        end
    end
    Cholesky(A, 'U', convert(BlasInt, info))
end
@deprecate cholesky!(A::Diagonal, ::Val{false}; check::Bool = true) cholesky!(A::Diagonal, NoPivot(); check) false
@deprecate cholesky(A::Diagonal, ::Val{false}; check::Bool = true) cholesky(A::Diagonal, NoPivot(); check) false

inv(C::Cholesky{<:Any,<:Diagonal}) = Diagonal(map(inv∘abs2, C.factors.diag))

cholcopy(A::Diagonal) = copymutable_oftype(A, choltype(A))
cholcopy(A::RealHermSymComplexHerm{<:Any,<:Diagonal}) = Diagonal(copy_similar(diag(A), choltype(A)))

function getproperty(C::Cholesky{<:Any,<:Diagonal}, d::Symbol)
    Cfactors = getfield(C, :factors)
    if d in (:U, :L, :UL)
        return Cfactors
    else
        return getfield(C, d)
    end
end

Base._sum(A::Diagonal, ::Colon) = sum(A.diag)
function Base._sum(A::Diagonal, dims::Integer)
    res = Base.reducedim_initarray(A, dims, zero(eltype(A)))
    if dims <= 2
        for i = 1:length(A.diag)
            @inbounds res[i] = A.diag[i]
        end
    else
        for i = 1:length(A.diag)
            @inbounds res[i,i] = A.diag[i]
        end
    end
    res
end

function logabsdet(A::Diagonal)
     mapreduce(x -> (log(abs(x)), sign(x)), ((d1, s1), (d2, s2)) -> (d1 + d2, s1 * s2),
               A.diag)
end

function Base.muladd(A::Diagonal, B::Diagonal, z::Diagonal)
    Diagonal(A.diag .* B.diag .+ z.diag)
end
   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LinearAlgebra/src/symmetriceigen.jl�#      # This file is a part of Julia. License is MIT: https://julialang.org/license

# preserve HermOrSym wrapper
eigencopy_oftype(A::Hermitian, S) = Hermitian(copy_similar(A, S), sym_uplo(A.uplo))
eigencopy_oftype(A::Symmetric, S) = Symmetric(copy_similar(A, S), sym_uplo(A.uplo))

# Eigensolvers for symmetric and Hermitian matrices
eigen!(A::RealHermSymComplexHerm{<:BlasReal,<:StridedMatrix}; sortby::Union{Function,Nothing}=nothing) =
    Eigen(sorteig!(LAPACK.syevr!('V', 'A', A.uplo, A.data, 0.0, 0.0, 0, 0, -1.0)..., sortby)...)

function eigen(A::RealHermSymComplexHerm; sortby::Union{Function,Nothing}=nothing)
    S = eigtype(eltype(A))
    eigen!(eigencopy_oftype(A, S), sortby=sortby)
end

eigen!(A::RealHermSymComplexHerm{<:BlasReal,<:StridedMatrix}, irange::UnitRange) =
    Eigen(LAPACK.syevr!('V', 'I', A.uplo, A.data, 0.0, 0.0, irange.start, irange.stop, -1.0)...)

"""
    eigen(A::Union{SymTridiagonal, Hermitian, Symmetric}, irange::UnitRange) -> Eigen

Compute the eigenvalue decomposition of `A`, returning an [`Eigen`](@ref) factorization object `F`
which contains the eigenvalues in `F.values` and the eigenvectors in the columns of the
matrix `F.vectors`. (The `k`th eigenvector can be obtained from the slice `F.vectors[:, k]`.)

Iterating the decomposition produces the components `F.values` and `F.vectors`.

The following functions are available for `Eigen` objects: [`inv`](@ref), [`det`](@ref), and [`isposdef`](@ref).

The [`UnitRange`](@ref) `irange` specifies indices of the sorted eigenvalues to search for.

!!! note
    If `irange` is not `1:n`, where `n` is the dimension of `A`, then the returned factorization
    will be a *truncated* factorization.
"""
function eigen(A::RealHermSymComplexHerm, irange::UnitRange)
    S = eigtype(eltype(A))
    eigen!(eigencopy_oftype(A, S), irange)
end

eigen!(A::RealHermSymComplexHerm{T,<:StridedMatrix}, vl::Real, vh::Real) where {T<:BlasReal} =
    Eigen(LAPACK.syevr!('V', 'V', A.uplo, A.data, convert(T, vl), convert(T, vh), 0, 0, -1.0)...)

"""
    eigen(A::Union{SymTridiagonal, Hermitian, Symmetric}, vl::Real, vu::Real) -> Eigen

Compute the eigenvalue decomposition of `A`, returning an [`Eigen`](@ref) factorization object `F`
which contains the eigenvalues in `F.values` and the eigenvectors in the columns of the
matrix `F.vectors`. (The `k`th eigenvector can be obtained from the slice `F.vectors[:, k]`.)

Iterating the decomposition produces the components `F.values` and `F.vectors`.

The following functions are available for `Eigen` objects: [`inv`](@ref), [`det`](@ref), and [`isposdef`](@ref).

`vl` is the lower bound of the window of eigenvalues to search for, and `vu` is the upper bound.

!!! note
    If [`vl`, `vu`] does not contain all eigenvalues of `A`, then the returned factorization
    will be a *truncated* factorization.
"""
function eigen(A::RealHermSymComplexHerm, vl::Real, vh::Real)
    S = eigtype(eltype(A))
    eigen!(eigencopy_oftype(A, S), vl, vh)
end

function eigvals!(A::RealHermSymComplexHerm{<:BlasReal,<:StridedMatrix}; sortby::Union{Function,Nothing}=nothing)
    vals = LAPACK.syevr!('N', 'A', A.uplo, A.data, 0.0, 0.0, 0, 0, -1.0)[1]
    !isnothing(sortby) && sort!(vals, by=sortby)
    return vals
end

function eigvals(A::RealHermSymComplexHerm; sortby::Union{Function,Nothing}=nothing)
    S = eigtype(eltype(A))
    eigvals!(eigencopy_oftype(A, S), sortby=sortby)
end

"""
    eigvals!(A::Union{SymTridiagonal, Hermitian, Symmetric}, irange::UnitRange) -> values

Same as [`eigvals`](@ref), but saves space by overwriting the input `A`, instead of creating a copy.
`irange` is a range of eigenvalue *indices* to search for - for instance, the 2nd to 8th eigenvalues.
"""
eigvals!(A::RealHermSymComplexHerm{<:BlasReal,<:StridedMatrix}, irange::UnitRange) =
    LAPACK.syevr!('N', 'I', A.uplo, A.data, 0.0, 0.0, irange.start, irange.stop, -1.0)[1]

"""
    eigvals(A::Union{SymTridiagonal, Hermitian, Symmetric}, irange::UnitRange) -> values

Return the eigenvalues of `A`. It is possible to calculate only a subset of the
eigenvalues by specifying a [`UnitRange`](@ref) `irange` covering indices of the sorted eigenvalues,
e.g. the 2nd to 8th eigenvalues.

# Examples
```jldoctest
julia> A = SymTridiagonal([1.; 2.; 1.], [2.; 3.])
3×3 SymTridiagonal{Float64, Vector{Float64}}:
 1.0  2.0   ⋅
 2.0  2.0  3.0
  ⋅   3.0  1.0

julia> eigvals(A, 2:2)
1-element Vector{Float64}:
 0.9999999999999996

julia> eigvals(A)
3-element Vector{Float64}:
 -2.1400549446402604
  1.0000000000000002
  5.140054944640259
```
"""
function eigvals(A::RealHermSymComplexHerm, irange::UnitRange)
    S = eigtype(eltype(A))
    eigvals!(eigencopy_oftype(A, S), irange)
end

"""
    eigvals!(A::Union{SymTridiagonal, Hermitian, Symmetric}, vl::Real, vu::Real) -> values

Same as [`eigvals`](@ref), but saves space by overwriting the input `A`, instead of creating a copy.
`vl` is the lower bound of the interval to search for eigenvalues, and `vu` is the upper bound.
"""
eigvals!(A::RealHermSymComplexHerm{T,<:StridedMatrix}, vl::Real, vh::Real) where {T<:BlasReal} =
    LAPACK.syevr!('N', 'V', A.uplo, A.data, convert(T, vl), convert(T, vh), 0, 0, -1.0)[1]

"""
    eigvals(A::Union{SymTridiagonal, Hermitian, Symmetric}, vl::Real, vu::Real) -> values

Return the eigenvalues of `A`. It is possible to calculate only a subset of the eigenvalues
by specifying a pair `vl` and `vu` for the lower and upper boundaries of the eigenvalues.

# Examples
```jldoctest
julia> A = SymTridiagonal([1.; 2.; 1.], [2.; 3.])
3×3 SymTridiagonal{Float64, Vector{Float64}}:
 1.0  2.0   ⋅
 2.0  2.0  3.0
  ⋅   3.0  1.0

julia> eigvals(A, -1, 2)
1-element Vector{Float64}:
 1.0000000000000009

julia> eigvals(A)
3-element Vector{Float64}:
 -2.1400549446402604
  1.0000000000000002
  5.140054944640259
```
"""
function eigvals(A::RealHermSymComplexHerm, vl::Real, vh::Real)
    S = eigtype(eltype(A))
    eigvals!(eigencopy_oftype(A, S), vl, vh)
end

eigmax(A::RealHermSymComplexHerm{<:Real}) = eigvals(A, size(A, 1):size(A, 1))[1]
eigmin(A::RealHermSymComplexHerm{<:Real}) = eigvals(A, 1:1)[1]

function eigen(A::HermOrSym{TA}, B::HermOrSym{TB}; kws...) where {TA,TB}
    S = promote_type(eigtype(TA), TB)
    return eigen!(eigencopy_oftype(A, S), eigencopy_oftype(B, S); kws...)
end

function eigen!(A::HermOrSym{T,S}, B::HermOrSym{T,S}; sortby::Union{Function,Nothing}=nothing) where {T<:BlasReal,S<:StridedMatrix}
    vals, vecs, _ = LAPACK.sygvd!(1, 'V', A.uplo, A.data, B.uplo == A.uplo ? B.data : copy(B.data'))
    GeneralizedEigen(sorteig!(vals, vecs, sortby)...)
end
function eigen!(A::Hermitian{T,S}, B::Hermitian{T,S}; sortby::Union{Function,Nothing}=nothing) where {T<:BlasComplex,S<:StridedMatrix}
    vals, vecs, _ = LAPACK.sygvd!(1, 'V', A.uplo, A.data, B.uplo == A.uplo ? B.data : copy(B.data'))
    GeneralizedEigen(sorteig!(vals, vecs, sortby)...)
end

function eigen(A::AbstractMatrix, C::Cholesky; sortby::Union{Function,Nothing}=nothing)
    if ishermitian(A)
        eigen!(eigencopy_oftype(Hermitian(A), eigtype(eltype(A))), C; sortby)
    else
        eigen!(copy_similar(A, eigtype(eltype(A))), C; sortby)
    end
end
function eigen!(A::AbstractMatrix, C::Cholesky; sortby::Union{Function,Nothing}=nothing)
    # Cholesky decomposition based eigenvalues and eigenvectors
    vals, w = eigen!(UtiAUi!(A, C.U))
    vecs = C.U \ w
    GeneralizedEigen(sorteig!(vals, vecs, sortby)...)
end

# Perform U' \ A / U in-place, where U::Union{UpperTriangular,Diagonal}
UtiAUi!(A, U) = _UtiAUi!(A, U)
UtiAUi!(A::Symmetric, U) = Symmetric(_UtiAUi!(copytri!(parent(A), A.uplo), U), sym_uplo(A.uplo))
UtiAUi!(A::Hermitian, U) = Hermitian(_UtiAUi!(copytri!(parent(A), A.uplo, true), U), sym_uplo(A.uplo))
_UtiAUi!(A, U) = rdiv!(ldiv!(U', A), U)

function eigvals(A::HermOrSym{TA}, B::HermOrSym{TB}; kws...) where {TA,TB}
    S = promote_type(eigtype(TA), TB)
    return eigvals!(eigencopy_oftype(A, S), eigencopy_oftype(B, S); kws...)
end

function eigvals!(A::HermOrSym{T,S}, B::HermOrSym{T,S}; sortby::Union{Function,Nothing}=nothing) where {T<:BlasReal,S<:StridedMatrix}
    vals = LAPACK.sygvd!(1, 'N', A.uplo, A.data, B.uplo == A.uplo ? B.data : copy(B.data'))[1]
    isnothing(sortby) || sort!(vals, by=sortby)
    return vals
end
function eigvals!(A::Hermitian{T,S}, B::Hermitian{T,S}; sortby::Union{Function,Nothing}=nothing) where {T<:BlasComplex,S<:StridedMatrix}
    vals = LAPACK.sygvd!(1, 'N', A.uplo, A.data, B.uplo == A.uplo ? B.data : copy(B.data'))[1]
    isnothing(sortby) || sort!(vals, by=sortby)
    return vals
end
eigvecs(A::HermOrSym) = eigvecs(eigen(A))

function eigvals(A::AbstractMatrix, C::Cholesky; sortby::Union{Function,Nothing}=nothing)
    if ishermitian(A)
        eigvals!(eigencopy_oftype(Hermitian(A), eigtype(eltype(A))), C; sortby)
    else
        eigvals!(copy_similar(A, eigtype(eltype(A))), C; sortby)
    end
end
function eigvals!(A::AbstractMatrix{T}, C::Cholesky{T, <:AbstractMatrix}; sortby::Union{Function,Nothing}=nothing) where {T<:Number}
    # Cholesky decomposition based eigenvalues
    return eigvals!(UtiAUi!(A, C.U); sortby)
end
w   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LinearAlgebra/src/bidiag.jl��      # This file is a part of Julia. License is MIT: https://julialang.org/license

# Bidiagonal matrices
struct Bidiagonal{T,V<:AbstractVector{T}} <: AbstractMatrix{T}
    dv::V      # diagonal
    ev::V      # sub/super diagonal
    uplo::Char # upper bidiagonal ('U') or lower ('L')
    function Bidiagonal{T,V}(dv, ev, uplo::AbstractChar) where {T,V<:AbstractVector{T}}
        require_one_based_indexing(dv, ev)
        if length(ev) != max(length(dv)-1, 0)
            throw(DimensionMismatch("length of diagonal vector is $(length(dv)), length of off-diagonal vector is $(length(ev))"))
        end
        (uplo != 'U' && uplo != 'L') && throw_uplo()
        new{T,V}(dv, ev, uplo)
    end
end
function Bidiagonal{T,V}(dv, ev, uplo::Symbol) where {T,V<:AbstractVector{T}}
    Bidiagonal{T,V}(dv, ev, char_uplo(uplo))
end
function Bidiagonal{T}(dv::AbstractVector, ev::AbstractVector, uplo::Union{Symbol,AbstractChar}) where {T}
    Bidiagonal(convert(AbstractVector{T}, dv)::AbstractVector{T},
               convert(AbstractVector{T}, ev)::AbstractVector{T},
               uplo)
end
function Bidiagonal{T,V}(A::Bidiagonal) where {T,V<:AbstractVector{T}}
    Bidiagonal{T,V}(A.dv, A.ev, A.uplo)
end

"""
    Bidiagonal(dv::V, ev::V, uplo::Symbol) where V <: AbstractVector

Constructs an upper (`uplo=:U`) or lower (`uplo=:L`) bidiagonal matrix using the
given diagonal (`dv`) and off-diagonal (`ev`) vectors. The result is of type `Bidiagonal`
and provides efficient specialized linear solvers, but may be converted into a regular
matrix with [`convert(Array, _)`](@ref) (or `Array(_)` for short). The length of `ev`
must be one less than the length of `dv`.

# Examples
```jldoctest
julia> dv = [1, 2, 3, 4]
4-element Vector{Int64}:
 1
 2
 3
 4

julia> ev = [7, 8, 9]
3-element Vector{Int64}:
 7
 8
 9

julia> Bu = Bidiagonal(dv, ev, :U) # ev is on the first superdiagonal
4×4 Bidiagonal{Int64, Vector{Int64}}:
 1  7  ⋅  ⋅
 ⋅  2  8  ⋅
 ⋅  ⋅  3  9
 ⋅  ⋅  ⋅  4

julia> Bl = Bidiagonal(dv, ev, :L) # ev is on the first subdiagonal
4×4 Bidiagonal{Int64, Vector{Int64}}:
 1  ⋅  ⋅  ⋅
 7  2  ⋅  ⋅
 ⋅  8  3  ⋅
 ⋅  ⋅  9  4
```
"""
function Bidiagonal(dv::V, ev::V, uplo::Symbol) where {T,V<:AbstractVector{T}}
    Bidiagonal{T,V}(dv, ev, uplo)
end
function Bidiagonal(dv::V, ev::V, uplo::AbstractChar) where {T,V<:AbstractVector{T}}
    Bidiagonal{T,V}(dv, ev, uplo)
end

#To allow Bidiagonal's where the "dv" is Vector{T} and "ev" Vector{S},
#where T and S can be promoted
function Bidiagonal(dv::Vector{T}, ev::Vector{S}, uplo::Symbol) where {T,S}
    TS = promote_type(T,S)
    return Bidiagonal{TS,Vector{TS}}(dv, ev, uplo)
end

"""
    Bidiagonal(A, uplo::Symbol)

Construct a `Bidiagonal` matrix from the main diagonal of `A` and
its first super- (if `uplo=:U`) or sub-diagonal (if `uplo=:L`).

# Examples
```jldoctest
julia> A = [1 1 1 1; 2 2 2 2; 3 3 3 3; 4 4 4 4]
4×4 Matrix{Int64}:
 1  1  1  1
 2  2  2  2
 3  3  3  3
 4  4  4  4

julia> Bidiagonal(A, :U) # contains the main diagonal and first superdiagonal of A
4×4 Bidiagonal{Int64, Vector{Int64}}:
 1  1  ⋅  ⋅
 ⋅  2  2  ⋅
 ⋅  ⋅  3  3
 ⋅  ⋅  ⋅  4

julia> Bidiagonal(A, :L) # contains the main diagonal and first subdiagonal of A
4×4 Bidiagonal{Int64, Vector{Int64}}:
 1  ⋅  ⋅  ⋅
 2  2  ⋅  ⋅
 ⋅  3  3  ⋅
 ⋅  ⋅  4  4
```
"""
function Bidiagonal(A::AbstractMatrix, uplo::Symbol)
    Bidiagonal(diag(A, 0), diag(A, uplo === :U ? 1 : -1), uplo)
end


Bidiagonal(A::Bidiagonal) = A
Bidiagonal{T}(A::Bidiagonal{T}) where {T} = A
Bidiagonal{T}(A::Bidiagonal) where {T} = Bidiagonal{T}(A.dv, A.ev, A.uplo)

bidiagzero(::Bidiagonal{T}, i, j) where {T} = zero(T)
function bidiagzero(A::Bidiagonal{<:AbstractMatrix}, i, j)
    Tel = eltype(eltype(A.dv))
    if i < j && A.uplo == 'U' #= top right zeros =#
        return zeros(Tel, size(A.ev[i], 1), size(A.ev[j-1], 2))
    elseif j < i && A.uplo == 'L' #= bottom left zeros =#
        return zeros(Tel, size(A.ev[i-1], 1), size(A.ev[j], 2))
    else
        return zeros(Tel, size(A.dv[i], 1), size(A.dv[j], 2))
    end
end

@inline function Base.isassigned(A::Bidiagonal, i::Int, j::Int)
    @boundscheck checkbounds(Bool, A, i, j) || return false
    if i == j
        return @inbounds isassigned(A.dv, i)
    elseif A.uplo == 'U' && (i == j - 1)
        return @inbounds isassigned(A.ev, i)
    elseif A.uplo == 'L' && (i == j + 1)
        return @inbounds isassigned(A.ev, j)
    else
        return true
    end
end

@inline function getindex(A::Bidiagonal{T}, i::Integer, j::Integer) where T
    @boundscheck checkbounds(A, i, j)
    if i == j
        return @inbounds A.dv[i]
    elseif A.uplo == 'U' && (i == j - 1)
        return @inbounds A.ev[i]
    elseif A.uplo == 'L' && (i == j + 1)
        return @inbounds A.ev[j]
    else
        return bidiagzero(A, i, j)
    end
end

@inline function setindex!(A::Bidiagonal, x, i::Integer, j::Integer)
    @boundscheck checkbounds(A, i, j)
    if i == j
        @inbounds A.dv[i] = x
    elseif A.uplo == 'U' && (i == j - 1)
        @inbounds A.ev[i] = x
    elseif A.uplo == 'L' && (i == j + 1)
        @inbounds A.ev[j] = x
    elseif !iszero(x)
        throw(ArgumentError(string("cannot set entry ($i, $j) off the ",
            "$(istriu(A) ? "upper" : "lower") bidiagonal band to a nonzero value ($x)")))
    end
    return x
end

## structured matrix methods ##
function Base.replace_in_print_matrix(A::Bidiagonal,i::Integer,j::Integer,s::AbstractString)
    if A.uplo == 'U'
        i==j || i==j-1 ? s : Base.replace_with_centered_mark(s)
    else
        i==j || i==j+1 ? s : Base.replace_with_centered_mark(s)
    end
end

#Converting from Bidiagonal to dense Matrix
function Matrix{T}(A::Bidiagonal) where T
    n = size(A, 1)
    B = Matrix{T}(undef, n, n)
    n == 0 && return B
    n > 1 && fill!(B, zero(T))
    @inbounds for i = 1:n - 1
        B[i,i] = A.dv[i]
        if A.uplo == 'U'
            B[i,i+1] = A.ev[i]
        else
            B[i+1,i] = A.ev[i]
        end
    end
    B[n,n] = A.dv[n]
    return B
end
Matrix(A::Bidiagonal{T}) where {T} = Matrix{promote_type(T, typeof(zero(T)))}(A)
Array(A::Bidiagonal) = Matrix(A)
promote_rule(::Type{Matrix{T}}, ::Type{<:Bidiagonal{S}}) where {T,S} =
    @isdefined(T) && @isdefined(S) ? Matrix{promote_type(T,S)} : Matrix
promote_rule(::Type{Matrix}, ::Type{<:Bidiagonal}) = Matrix

#Converting from Bidiagonal to Tridiagonal
function Tridiagonal{T}(A::Bidiagonal) where T
    dv = convert(AbstractVector{T}, A.dv)
    ev = convert(AbstractVector{T}, A.ev)
    z = fill!(similar(ev), zero(T))
    A.uplo == 'U' ? Tridiagonal(z, dv, ev) : Tridiagonal(ev, dv, z)
end
promote_rule(::Type{<:Tridiagonal{T}}, ::Type{<:Bidiagonal{S}}) where {T,S} =
    @isdefined(T) && @isdefined(S) ? Tridiagonal{promote_type(T,S)} : Tridiagonal
promote_rule(::Type{<:Tridiagonal}, ::Type{<:Bidiagonal}) = Tridiagonal

# When asked to convert Bidiagonal to AbstractMatrix{T}, preserve structure by converting to Bidiagonal{T} <: AbstractMatrix{T}
AbstractMatrix{T}(A::Bidiagonal) where {T} = convert(Bidiagonal{T}, A)

convert(::Type{T}, m::AbstractMatrix) where {T<:Bidiagonal} = m isa T ? m : T(m)::T

similar(B::Bidiagonal, ::Type{T}) where {T} = Bidiagonal(similar(B.dv, T), similar(B.ev, T), B.uplo)
similar(B::Bidiagonal, ::Type{T}, dims::Union{Dims{1},Dims{2}}) where {T} = similar(B.dv, T, dims)

tr(B::Bidiagonal) = sum(B.dv)

function kron(A::Diagonal, B::Bidiagonal)
    # `_droplast!` is only guaranteed to work with `Vector`
    kdv = _makevector(kron(diag(A), B.dv))
    kev = _droplast!(_makevector(kron(diag(A), _pushzero(B.ev))))
    Bidiagonal(kdv, kev, B.uplo)
end

###################
# LAPACK routines #
###################

#Singular values
svdvals!(M::Bidiagonal{<:BlasReal}) = LAPACK.bdsdc!(M.uplo, 'N', M.dv, M.ev)[1]
function svd!(M::Bidiagonal{<:BlasReal}; full::Bool = false)
    d, e, U, Vt, Q, iQ = LAPACK.bdsdc!(M.uplo, 'I', M.dv, M.ev)
    SVD(U, d, Vt)
end
function svd(M::Bidiagonal; kw...)
    svd!(copy(M), kw...)
end

####################
# Generic routines #
####################

function show(io::IO, M::Bidiagonal)
    # TODO: make this readable and one-line
    summary(io, M)
    print(io, ":\n diag:")
    print_matrix(io, (M.dv)')
    print(io, M.uplo == 'U' ? "\n super:" : "\n sub:")
    print_matrix(io, (M.ev)')
end

size(M::Bidiagonal) = (length(M.dv), length(M.dv))
function size(M::Bidiagonal, d::Integer)
    if d < 1
        throw(ArgumentError("dimension must be ≥ 1, got $d"))
    elseif d <= 2
        return length(M.dv)
    else
        return 1
    end
end

#Elementary operations
for func in (:conj, :copy, :real, :imag)
    @eval ($func)(M::Bidiagonal) = Bidiagonal(($func)(M.dv), ($func)(M.ev), M.uplo)
end

adjoint(B::Bidiagonal) = Adjoint(B)
transpose(B::Bidiagonal) = Transpose(B)
adjoint(B::Bidiagonal{<:Number}) = Bidiagonal(conj(B.dv), conj(B.ev), B.uplo == 'U' ? :L : :U)
transpose(B::Bidiagonal{<:Number}) = Bidiagonal(B.dv, B.ev, B.uplo == 'U' ? :L : :U)
permutedims(B::Bidiagonal) = Bidiagonal(B.dv, B.ev, B.uplo == 'U' ? 'L' : 'U')
function permutedims(B::Bidiagonal, perm)
    Base.checkdims_perm(B, B, perm)
    NTuple{2}(perm) == (2, 1) ? permutedims(B) : B
end
function Base.copy(aB::Adjoint{<:Any,<:Bidiagonal})
    B = aB.parent
    return Bidiagonal(map(x -> copy.(adjoint.(x)), (B.dv, B.ev))..., B.uplo == 'U' ? :L : :U)
end
function Base.copy(tB::Transpose{<:Any,<:Bidiagonal})
    B = tB.parent
    return Bidiagonal(map(x -> copy.(transpose.(x)), (B.dv, B.ev))..., B.uplo == 'U' ? :L : :U)
end

iszero(M::Bidiagonal) = iszero(M.dv) && iszero(M.ev)
isone(M::Bidiagonal) = all(isone, M.dv) && iszero(M.ev)
function istriu(M::Bidiagonal, k::Integer=0)
    if M.uplo == 'U'
        if k <= 0
            return true
        elseif k == 1
            return iszero(M.dv)
        else # k >= 2
            return iszero(M.dv) && iszero(M.ev)
        end
    else # M.uplo == 'L'
        if k <= -1
            return true
        elseif k == 0
            return iszero(M.ev)
        else # k >= 1
            return iszero(M.ev) && iszero(M.dv)
        end
    end
end
function istril(M::Bidiagonal, k::Integer=0)
    if M.uplo == 'U'
        if k >= 1
            return true
        elseif k == 0
            return iszero(M.ev)
        else # k <= -1
            return iszero(M.ev) && iszero(M.dv)
        end
    else # M.uplo == 'L'
        if k >= 0
            return true
        elseif k == -1
            return iszero(M.dv)
        else # k <= -2
            return iszero(M.dv) && iszero(M.ev)
        end
    end
end
isdiag(M::Bidiagonal) = iszero(M.ev)

function tril!(M::Bidiagonal{T}, k::Integer=0) where T
    n = length(M.dv)
    if !(-n - 1 <= k <= n - 1)
        throw(ArgumentError(string("the requested diagonal, $k, must be at least ",
            "$(-n - 1) and at most $(n - 1) in an $n-by-$n matrix")))
    elseif M.uplo == 'U' && k < 0
        fill!(M.dv, zero(T))
        fill!(M.ev, zero(T))
    elseif k < -1
        fill!(M.dv, zero(T))
        fill!(M.ev, zero(T))
    elseif M.uplo == 'U' && k == 0
        fill!(M.ev, zero(T))
    elseif M.uplo == 'L' && k == -1
        fill!(M.dv, zero(T))
    end
    return M
end

function triu!(M::Bidiagonal{T}, k::Integer=0) where T
    n = length(M.dv)
    if !(-n + 1 <= k <= n + 1)
        throw(ArgumentError(string("the requested diagonal, $k, must be at least",
            "$(-n + 1) and at most $(n + 1) in an $n-by-$n matrix")))
    elseif M.uplo == 'L' && k > 0
        fill!(M.dv, zero(T))
        fill!(M.ev, zero(T))
    elseif k > 1
        fill!(M.dv, zero(T))
        fill!(M.ev, zero(T))
    elseif M.uplo == 'L' && k == 0
        fill!(M.ev, zero(T))
    elseif M.uplo == 'U' && k == 1
        fill!(M.dv, zero(T))
    end
    return M
end

function diag(M::Bidiagonal{T}, n::Integer=0) where T
    # every branch call similar(..., ::Int) to make sure the
    # same vector type is returned independent of n
    if n == 0
        return copyto!(similar(M.dv, length(M.dv)), M.dv)
    elseif (n == 1 && M.uplo == 'U') ||  (n == -1 && M.uplo == 'L')
        return copyto!(similar(M.ev, length(M.ev)), M.ev)
    elseif -size(M,1) <= n <= size(M,1)
        return fill!(similar(M.dv, size(M,1)-abs(n)), zero(T))
    else
        throw(ArgumentError(string("requested diagonal, $n, must be at least $(-size(M, 1)) ",
            "and at most $(size(M, 2)) for an $(size(M, 1))-by-$(size(M, 2)) matrix")))
    end
end

function +(A::Bidiagonal, B::Bidiagonal)
    if A.uplo == B.uplo || length(A.dv) == 0
        Bidiagonal(A.dv+B.dv, A.ev+B.ev, A.uplo)
    else
        newdv = A.dv+B.dv
        Tridiagonal((A.uplo == 'U' ? (typeof(newdv)(B.ev), newdv, typeof(newdv)(A.ev)) : (typeof(newdv)(A.ev), newdv, typeof(newdv)(B.ev)))...)
    end
end

function -(A::Bidiagonal, B::Bidiagonal)
    if A.uplo == B.uplo || length(A.dv) == 0
        Bidiagonal(A.dv-B.dv, A.ev-B.ev, A.uplo)
    else
        newdv = A.dv-B.dv
        Tridiagonal((A.uplo == 'U' ? (typeof(newdv)(-B.ev), newdv, typeof(newdv)(A.ev)) : (typeof(newdv)(A.ev), newdv, typeof(newdv)(-B.ev)))...)
    end
end

-(A::Bidiagonal)=Bidiagonal(-A.dv,-A.ev,A.uplo)
*(A::Bidiagonal, B::Number) = Bidiagonal(A.dv*B, A.ev*B, A.uplo)
*(B::Number, A::Bidiagonal) = Bidiagonal(B*A.dv, B*A.ev, A.uplo)
/(A::Bidiagonal, B::Number) = Bidiagonal(A.dv/B, A.ev/B, A.uplo)
\(B::Number, A::Bidiagonal) = Bidiagonal(B\A.dv, B\A.ev, A.uplo)

function ==(A::Bidiagonal, B::Bidiagonal)
    if A.uplo == B.uplo
        return A.dv == B.dv && A.ev == B.ev
    else
        return iszero(A.ev) && iszero(B.ev) && A.dv == B.dv
    end
end

const BandedMatrix = Union{Bidiagonal,Diagonal,Tridiagonal,SymTridiagonal} # or BiDiTriSym
const BiTriSym = Union{Bidiagonal,Tridiagonal,SymTridiagonal}
const BiTri = Union{Bidiagonal,Tridiagonal}
@inline mul!(C::AbstractVector, A::BandedMatrix, B::AbstractVector, alpha::Number, beta::Number) = _mul!(C, A, B, MulAddMul(alpha, beta))
@inline mul!(C::AbstractMatrix, A::BandedMatrix, B::AbstractVector, alpha::Number, beta::Number) = _mul!(C, A, B, MulAddMul(alpha, beta))
@inline mul!(C::AbstractMatrix, A::BandedMatrix, B::AbstractMatrix, alpha::Number, beta::Number) = _mul!(C, A, B, MulAddMul(alpha, beta))
@inline mul!(C::AbstractMatrix, A::AbstractMatrix, B::BandedMatrix, alpha::Number, beta::Number) = _mul!(C, A, B, MulAddMul(alpha, beta))
@inline mul!(C::AbstractMatrix, A::BandedMatrix, B::BandedMatrix, alpha::Number, beta::Number) = _mul!(C, A, B, MulAddMul(alpha, beta))

function check_A_mul_B!_sizes(C, A, B)
    mA, nA = size(A)
    mB, nB = size(B)
    mC, nC = size(C)
    if mA != mC
        throw(DimensionMismatch("first dimension of A, $mA, and first dimension of output C, $mC, must match"))
    elseif nA != mB
        throw(DimensionMismatch("second dimension of A, $nA, and first dimension of B, $mB, must match"))
    elseif nB != nC
        throw(DimensionMismatch("second dimension of output C, $nC, and second dimension of B, $nB, must match"))
    end
end

# function to get the internally stored vectors for Bidiagonal and [Sym]Tridiagonal
# to avoid allocations in _mul! below (#24324, #24578)
_diag(A::Tridiagonal, k) = k == -1 ? A.dl : k == 0 ? A.d : A.du
_diag(A::SymTridiagonal, k) = k == 0 ? A.dv : A.ev
function _diag(A::Bidiagonal, k)
    if k == 0
        return A.dv
    elseif (A.uplo == 'L' && k == -1) || (A.uplo == 'U' && k == 1)
        return A.ev
    else
        return diag(A, k)
    end
end

function _mul!(C::AbstractMatrix, A::BiTriSym, B::BiTriSym, _add::MulAddMul = MulAddMul())
    check_A_mul_B!_sizes(C, A, B)
    n = size(A,1)
    n <= 3 && return mul!(C, Array(A), Array(B), _add.alpha, _add.beta)
    # We use `_rmul_or_fill!` instead of `_modify!` here since using
    # `_modify!` in the following loop will not update the
    # off-diagonal elements for non-zero beta.
    _rmul_or_fill!(C, _add.beta)
    iszero(_add.alpha) && return C
    Al = _diag(A, -1)
    Ad = _diag(A, 0)
    Au = _diag(A, 1)
    Bl = _diag(B, -1)
    Bd = _diag(B, 0)
    Bu = _diag(B, 1)
    @inbounds begin
        # first row of C
        C[1,1] += _add(A[1,1]*B[1,1] + A[1, 2]*B[2, 1])
        C[1,2] += _add(A[1,1]*B[1,2] + A[1,2]*B[2,2])
        C[1,3] += _add(A[1,2]*B[2,3])
        # second row of C
        C[2,1] += _add(A[2,1]*B[1,1] + A[2,2]*B[2,1])
        C[2,2] += _add(A[2,1]*B[1,2] + A[2,2]*B[2,2] + A[2,3]*B[3,2])
        C[2,3] += _add(A[2,2]*B[2,3] + A[2,3]*B[3,3])
        C[2,4] += _add(A[2,3]*B[3,4])
        for j in 3:n-2
            Ajj₋1   = Al[j-1]
            Ajj     = Ad[j]
            Ajj₊1   = Au[j]
            Bj₋1j₋2 = Bl[j-2]
            Bj₋1j₋1 = Bd[j-1]
            Bj₋1j   = Bu[j-1]
            Bjj₋1   = Bl[j-1]
            Bjj     = Bd[j]
            Bjj₊1   = Bu[j]
            Bj₊1j   = Bl[j]
            Bj₊1j₊1 = Bd[j+1]
            Bj₊1j₊2 = Bu[j+1]
            C[j,j-2]  += _add( Ajj₋1*Bj₋1j₋2)
            C[j, j-1] += _add(Ajj₋1*Bj₋1j₋1 + Ajj*Bjj₋1)
            C[j, j  ] += _add(Ajj₋1*Bj₋1j   + Ajj*Bjj       + Ajj₊1*Bj₊1j)
            C[j, j+1] += _add(Ajj  *Bjj₊1   + Ajj₊1*Bj₊1j₊1)
            C[j, j+2] += _add(Ajj₊1*Bj₊1j₊2)
        end
        # row before last of C
        C[n-1,n-3] += _add(A[n-1,n-2]*B[n-2,n-3])
        C[n-1,n-2] += _add(A[n-1,n-1]*B[n-1,n-2] + A[n-1,n-2]*B[n-2,n-2])
        C[n-1,n-1] += _add(A[n-1,n-2]*B[n-2,n-1] + A[n-1,n-1]*B[n-1,n-1] + A[n-1,n]*B[n,n-1])
        C[n-1,n  ] += _add(A[n-1,n-1]*B[n-1,n  ] + A[n-1,  n]*B[n  ,n  ])
        # last row of C
        C[n,n-2] += _add(A[n,n-1]*B[n-1,n-2])
        C[n,n-1] += _add(A[n,n-1]*B[n-1,n-1] + A[n,n]*B[n,n-1])
        C[n,n  ] += _add(A[n,n-1]*B[n-1,n  ] + A[n,n]*B[n,n  ])
    end # inbounds
    C
end

function _mul!(C::AbstractMatrix, A::BiTriSym, B::Diagonal, _add::MulAddMul = MulAddMul())
    require_one_based_indexing(C)
    check_A_mul_B!_sizes(C, A, B)
    n = size(A,1)
    iszero(n) && return C
    n <= 3 && return mul!(C, Array(A), Array(B), _add.alpha, _add.beta)
    _rmul_or_fill!(C, _add.beta)  # see the same use above
    iszero(_add.alpha) && return C
    Al = _diag(A, -1)
    Ad = _diag(A, 0)
    Au = _diag(A, 1)
    Bd = B.diag
    @inbounds begin
        # first row of C
        C[1,1] += _add(A[1,1]*B[1,1])
        C[1,2] += _add(A[1,2]*B[2,2])
        # second row of C
        C[2,1] += _add(A[2,1]*B[1,1])
        C[2,2] += _add(A[2,2]*B[2,2])
        C[2,3] += _add(A[2,3]*B[3,3])
        for j in 3:n-2
            C[j, j-1] += _add(Al[j-1]*Bd[j-1])
            C[j, j  ] += _add(Ad[j  ]*Bd[j  ])
            C[j, j+1] += _add(Au[j  ]*Bd[j+1])
        end
        # row before last of C
        C[n-1,n-2] += _add(A[n-1,n-2]*B[n-2,n-2])
        C[n-1,n-1] += _add(A[n-1,n-1]*B[n-1,n-1])
        C[n-1,n  ] += _add(A[n-1,  n]*B[n  ,n  ])
        # last row of C
        C[n,n-1] += _add(A[n,n-1]*B[n-1,n-1])
        C[n,n  ] += _add(A[n,n  ]*B[n,  n  ])
    end # inbounds
    C
end

function _mul!(C::AbstractVecOrMat, A::BiTriSym, B::AbstractVecOrMat, _add::MulAddMul = MulAddMul())
    require_one_based_indexing(C, B)
    nA = size(A,1)
    nB = size(B,2)
    if !(size(C,1) == size(B,1) == nA)
        throw(DimensionMismatch("A has first dimension $nA, B has $(size(B,1)), C has $(size(C,1)) but all must match"))
    end
    if size(C,2) != nB
        throw(DimensionMismatch("A has second dimension $nA, B has $(size(B,2)), C has $(size(C,2)) but all must match"))
    end
    iszero(nA) && return C
    iszero(_add.alpha) && return _rmul_or_fill!(C, _add.beta)
    nA <= 3 && return mul!(C, Array(A), Array(B), _add.alpha, _add.beta)
    l = _diag(A, -1)
    d = _diag(A, 0)
    u = _diag(A, 1)
    @inbounds begin
        for j = 1:nB
            b₀, b₊ = B[1, j], B[2, j]
            _modify!(_add, d[1]*b₀ + u[1]*b₊, C, (1, j))
            for i = 2:nA - 1
                b₋, b₀, b₊ = b₀, b₊, B[i + 1, j]
                _modify!(_add, l[i - 1]*b₋ + d[i]*b₀ + u[i]*b₊, C, (i, j))
            end
            _modify!(_add, l[nA - 1]*b₀ + d[nA]*b₊, C, (nA, j))
        end
    end
    C
end

function _mul!(C::AbstractMatrix, A::AbstractMatrix, B::BiTriSym, _add::MulAddMul = MulAddMul())
    require_one_based_indexing(C, A)
    check_A_mul_B!_sizes(C, A, B)
    iszero(_add.alpha) && return _rmul_or_fill!(C, _add.beta)
    n = size(A,1)
    m = size(B,2)
    if n <= 3 || m <= 1
        return mul!(C, Array(A), Array(B), _add.alpha, _add.beta)
    end
    Bl = _diag(B, -1)
    Bd = _diag(B, 0)
    Bu = _diag(B, 1)
    @inbounds begin
        # first and last column of C
        B11 = Bd[1]
        B21 = Bl[1]
        Bmm = Bd[m]
        Bm₋1m = Bu[m-1]
        for i in 1:n
            _modify!(_add, A[i,1] * B11 + A[i, 2] * B21, C, (i, 1))
            _modify!(_add, A[i, m-1] * Bm₋1m + A[i, m] * Bmm, C, (i, m))
        end
        # middle columns of C
        for j = 2:m-1
            Bj₋1j = Bu[j-1]
            Bjj = Bd[j]
            Bj₊1j = Bl[j]
            for i = 1:n
                _modify!(_add, A[i, j-1] * Bj₋1j + A[i, j]*Bjj + A[i, j+1] * Bj₊1j, C, (i, j))
            end
        end
    end # inbounds
    C
end

function _mul!(C::AbstractMatrix, A::Diagonal, B::BiTriSym, _add::MulAddMul = MulAddMul())
    require_one_based_indexing(C)
    check_A_mul_B!_sizes(C, A, B)
    n = size(A,1)
    n <= 3 && return mul!(C, Array(A), Array(B), _add.alpha, _add.beta)
    _rmul_or_fill!(C, _add.beta)  # see the same use above
    iszero(_add.alpha) && return C
    Ad = A.diag
    Bl = _diag(B, -1)
    Bd = _diag(B, 0)
    Bu = _diag(B, 1)
    @inbounds begin
        # first row of C
        C[1,1] += _add(A[1,1]*B[1,1])
        C[1,2] += _add(A[1,1]*B[1,2])
        # second row of C
        C[2,1] += _add(A[2,2]*B[2,1])
        C[2,2] += _add(A[2,2]*B[2,2])
        C[2,3] += _add(A[2,2]*B[2,3])
        for j in 3:n-2
            Ajj       = Ad[j]
            C[j, j-1] += _add(Ajj*Bl[j-1])
            C[j, j  ] += _add(Ajj*Bd[j])
            C[j, j+1] += _add(Ajj*Bu[j])
        end
        # row before last of C
        C[n-1,n-2] += _add(A[n-1,n-1]*B[n-1,n-2])
        C[n-1,n-1] += _add(A[n-1,n-1]*B[n-1,n-1])
        C[n-1,n  ] += _add(A[n-1,n-1]*B[n-1,n  ])
        # last row of C
        C[n,n-1] += _add(A[n,n]*B[n,n-1])
        C[n,n  ] += _add(A[n,n]*B[n,n  ])
    end # inbounds
    C
end

function *(A::UpperOrUnitUpperTriangular, B::Bidiagonal)
    TS = promote_op(matprod, eltype(A), eltype(B))
    C = mul!(similar(A, TS, size(A)), A, B)
    return B.uplo == 'U' ? UpperTriangular(C) : C
end

function *(A::LowerOrUnitLowerTriangular, B::Bidiagonal)
    TS = promote_op(matprod, eltype(A), eltype(B))
    C = mul!(similar(A, TS, size(A)), A, B)
    return B.uplo == 'L' ? LowerTriangular(C) : C
end

function *(A::Bidiagonal, B::UpperOrUnitUpperTriangular)
    TS = promote_op(matprod, eltype(A), eltype(B))
    C = mul!(similar(B, TS, size(B)), A, B)
    return A.uplo == 'U' ? UpperTriangular(C) : C
end

function *(A::Bidiagonal, B::LowerOrUnitLowerTriangular)
    TS = promote_op(matprod, eltype(A), eltype(B))
    C = mul!(similar(B, TS, size(B)), A, B)
    return A.uplo == 'L' ? LowerTriangular(C) : C
end

function *(A::Diagonal, B::SymTridiagonal)
    TS = promote_op(*, eltype(A), eltype(B))
    out = Tridiagonal(similar(A, TS, size(A, 1)-1), similar(A, TS, size(A, 1)), similar(A, TS, size(A, 1)-1))
    mul!(out, A, B)
end

function *(A::SymTridiagonal, B::Diagonal)
    TS = promote_op(*, eltype(A), eltype(B))
    out = Tridiagonal(similar(A, TS, size(A, 1)-1), similar(A, TS, size(A, 1)), similar(A, TS, size(A, 1)-1))
    mul!(out, A, B)
end

function dot(x::AbstractVector, B::Bidiagonal, y::AbstractVector)
    require_one_based_indexing(x, y)
    nx, ny = length(x), length(y)
    (nx == size(B, 1) == ny) || throw(DimensionMismatch())
    if nx ≤ 1
        nx == 0 && return dot(zero(eltype(x)), zero(eltype(B)), zero(eltype(y)))
        return dot(x[1], B.dv[1], y[1])
    end
    ev, dv = B.ev, B.dv
    @inbounds if B.uplo == 'U'
        x₀ = x[1]
        r = dot(x[1], dv[1], y[1])
        for j in 2:nx-1
            x₋, x₀ = x₀, x[j]
            r += dot(adjoint(ev[j-1])*x₋ + adjoint(dv[j])*x₀, y[j])
        end
        r += dot(adjoint(ev[nx-1])*x₀ + adjoint(dv[nx])*x[nx], y[nx])
        return r
    else # B.uplo == 'L'
        x₀ = x[1]
        x₊ = x[2]
        r = dot(adjoint(dv[1])*x₀ + adjoint(ev[1])*x₊, y[1])
        for j in 2:nx-1
            x₀, x₊ = x₊, x[j+1]
            r += dot(adjoint(dv[j])*x₀ + adjoint(ev[j])*x₊, y[j])
        end
        r += dot(x₊, dv[nx], y[nx])
        return r
    end
end

#Linear solvers
#Generic solver using naive substitution
ldiv!(A::Bidiagonal, b::AbstractVecOrMat) = @inline ldiv!(b, A, b)
function ldiv!(c::AbstractVecOrMat, A::Bidiagonal, b::AbstractVecOrMat)
    require_one_based_indexing(c, A, b)
    N = size(A, 2)
    mb, nb = size(b, 1), size(b, 2)
    if N != mb
        throw(DimensionMismatch("second dimension of A, $N, does not match first dimension of b, $mb"))
    end
    mc, nc = size(c, 1), size(c, 2)
    if mc != mb || nc != nb
        throw(DimensionMismatch("size of result, ($mc, $nc), does not match the size of b, ($mb, $nb)"))
    end

    if N == 0
        return copyto!(c, b)
    end

    zi = findfirst(iszero, A.dv)
    isnothing(zi) || throw(SingularException(zi))

    @inbounds for j in 1:nb
        if A.uplo == 'L' #do colwise forward substitution
            c[1,j] = bi1 = A.dv[1] \ b[1,j]
            for i in 2:N
                c[i,j] = bi1 = A.dv[i] \ (b[i,j] - A.ev[i - 1] * bi1)
            end
        else #do colwise backward substitution
            c[N,j] = bi1 = A.dv[N] \ b[N,j]
            for i in (N - 1):-1:1
                c[i,j] = bi1 = A.dv[i] \ (b[i,j] - A.ev[i] * bi1)
            end
        end
    end
    return c
end
ldiv!(A::AdjOrTrans{<:Any,<:Bidiagonal}, b::AbstractVecOrMat) = @inline ldiv!(b, A, b)
ldiv!(c::AbstractVecOrMat, A::AdjOrTrans{<:Any,<:Bidiagonal}, b::AbstractVecOrMat) =
    (t = wrapperop(A); _rdiv!(t(c), t(b), t(A)); return c)

### Generic promotion methods and fallbacks
\(A::Bidiagonal, B::AbstractVecOrMat) = ldiv!(_initarray(\, eltype(A), eltype(B), B), A, B)
\(xA::AdjOrTrans{<:Any,<:Bidiagonal}, B::AbstractVecOrMat) = copy(xA) \ B

### Triangular specializations
for tri in (:UpperTriangular, :UnitUpperTriangular)
    @eval function \(B::Bidiagonal, U::$tri)
        A = ldiv!(_initarray(\, eltype(B), eltype(U), U), B, U)
        return B.uplo == 'U' ? UpperTriangular(A) : A
    end
    @eval function \(U::$tri, B::Bidiagonal)
        A = ldiv!(_initarray(\, eltype(U), eltype(B), U), U, B)
        return B.uplo == 'U' ? UpperTriangular(A) : A
    end
end
for tri in (:LowerTriangular, :UnitLowerTriangular)
    @eval function \(B::Bidiagonal, L::$tri)
        A = ldiv!(_initarray(\, eltype(B), eltype(L), L), B, L)
        return B.uplo == 'L' ? LowerTriangular(A) : A
    end
    @eval function \(L::$tri, B::Bidiagonal)
        A = ldiv!(_initarray(\, eltype(L), eltype(B), L), L, B)
        return B.uplo == 'L' ? LowerTriangular(A) : A
    end
end

### Diagonal specialization
function \(B::Bidiagonal, D::Diagonal)
    A = ldiv!(_initarray(\, eltype(B), eltype(D), D), B, D)
    return B.uplo == 'U' ? UpperTriangular(A) : LowerTriangular(A)
end

function _rdiv!(C::AbstractMatrix, A::AbstractMatrix, B::Bidiagonal)
    require_one_based_indexing(C, A, B)
    m, n = size(A)
    if size(B, 1) != n
        throw(DimensionMismatch("right hand side B needs first dimension of size $n, has size $(size(B,1))"))
    end
    mc, nc = size(C)
    if mc != m || nc != n
        throw(DimensionMismatch("expect output to have size ($m, $n), but got ($mc, $nc)"))
    end

    zi = findfirst(iszero, B.dv)
    isnothing(zi) || throw(SingularException(zi))

    if B.uplo == 'L'
        diagB = B.dv[n]
        for i in 1:m
            C[i,n] = A[i,n] / diagB
        end
        for j in n-1:-1:1
            diagB = B.dv[j]
            offdiagB = B.ev[j]
            for i in 1:m
                C[i,j] = (A[i,j] - C[i,j+1]*offdiagB)/diagB
            end
        end
    else
        diagB = B.dv[1]
        for i in 1:m
            C[i,1] = A[i,1] / diagB
        end
        for j in 2:n
            diagB = B.dv[j]
            offdiagB = B.ev[j-1]
            for i = 1:m
                C[i,j] = (A[i,j] - C[i,j-1]*offdiagB)/diagB
            end
        end
    end
    C
end
rdiv!(A::AbstractMatrix, B::Bidiagonal) = @inline _rdiv!(A, A, B)
rdiv!(A::AbstractMatrix, B::AdjOrTrans{<:Any,<:Bidiagonal}) = @inline _rdiv!(A, A, B)
_rdiv!(C::AbstractMatrix, A::AbstractMatrix, B::AdjOrTrans{<:Any,<:Bidiagonal}) =
    (t = wrapperop(B); ldiv!(t(C), t(B), t(A)); return C)

/(A::AbstractMatrix, B::Bidiagonal) = _rdiv!(_initarray(/, eltype(A), eltype(B), A), A, B)

### Triangular specializations
for tri in (:UpperTriangular, :UnitUpperTriangular)
    @eval function /(U::$tri, B::Bidiagonal)
        A = _rdiv!(_initarray(/, eltype(U), eltype(B), U), U, B)
        return B.uplo == 'U' ? UpperTriangular(A) : A
    end
    @eval function /(B::Bidiagonal, U::$tri)
        A = _rdiv!(_initarray(/, eltype(B), eltype(U), U), B, U)
        return B.uplo == 'U' ? UpperTriangular(A) : A
    end
end
for tri in (:LowerTriangular, :UnitLowerTriangular)
    @eval function /(L::$tri, B::Bidiagonal)
        A = _rdiv!(_initarray(/, eltype(L), eltype(B), L), L, B)
        return B.uplo == 'L' ? LowerTriangular(A) : A
    end
    @eval function /(B::Bidiagonal, L::$tri)
        A = _rdiv!(_initarray(/, eltype(B), eltype(L), L), B, L)
        return B.uplo == 'L' ? LowerTriangular(A) : A
    end
end

### Diagonal specialization
function /(D::Diagonal, B::Bidiagonal)
    A = _rdiv!(_initarray(/, eltype(D), eltype(B), D), D, B)
    return B.uplo == 'U' ? UpperTriangular(A) : LowerTriangular(A)
end

/(A::AbstractMatrix, B::Transpose{<:Any,<:Bidiagonal}) = A / copy(B)
/(A::AbstractMatrix, B::Adjoint{<:Any,<:Bidiagonal}) = A / copy(B)
# disambiguation
/(A::AdjointAbsVec, B::Bidiagonal) = adjoint(adjoint(B) \ parent(A))
/(A::TransposeAbsVec, B::Bidiagonal) = transpose(transpose(B) \ parent(A))
/(A::AdjointAbsVec, B::Transpose{<:Any,<:Bidiagonal}) = adjoint(adjoint(B) \ parent(A))
/(A::TransposeAbsVec, B::Transpose{<:Any,<:Bidiagonal}) = transpose(transpose(B) \ parent(A))
/(A::AdjointAbsVec, B::Adjoint{<:Any,<:Bidiagonal}) = adjoint(adjoint(B) \ parent(A))
/(A::TransposeAbsVec, B::Adjoint{<:Any,<:Bidiagonal}) = transpose(transpose(B) \ parent(A))

factorize(A::Bidiagonal) = A
function inv(B::Bidiagonal{T}) where T
    n = size(B, 1)
    dest = zeros(typeof(inv(oneunit(T))), (n, n))
    ldiv!(dest, B, Diagonal{typeof(one(T)/one(T))}(I, n))
    return B.uplo == 'U' ? UpperTriangular(dest) : LowerTriangular(dest)
end

# Eigensystems
eigvals(M::Bidiagonal) = copy(M.dv)
function eigvecs(M::Bidiagonal{T}) where T
    n = length(M.dv)
    Q = Matrix{T}(undef, n,n)
    blks = [0; findall(iszero, M.ev); n]
    v = zeros(T, n)
    if M.uplo == 'U'
        for idx_block = 1:length(blks) - 1, i = blks[idx_block] + 1:blks[idx_block + 1] #index of eigenvector
            fill!(v, zero(T))
            v[blks[idx_block] + 1] = one(T)
            for j = blks[idx_block] + 1:i - 1 #Starting from j=i, eigenvector elements will be 0
                v[j+1] = (M.dv[i] - M.dv[j])/M.ev[j] * v[j]
            end
            c = norm(v)
            for j = 1:n
                Q[j, i] = v[j] / c
            end
        end
    else
        for idx_block = 1:length(blks) - 1, i = blks[idx_block + 1]:-1:blks[idx_block] + 1 #index of eigenvector
            fill!(v, zero(T))
            v[blks[idx_block+1]] = one(T)
            for j = (blks[idx_block+1] - 1):-1:max(1, (i - 1)) #Starting from j=i, eigenvector elements will be 0
                v[j] = (M.dv[i] - M.dv[j+1])/M.ev[j] * v[j+1]
            end
            c = norm(v)
            for j = 1:n
                Q[j, i] = v[j] / c
            end
        end
    end
    Q #Actually Triangular
end
eigen(M::Bidiagonal) = Eigen(eigvals(M), eigvecs(M))

Base._sum(A::Bidiagonal, ::Colon) = sum(A.dv) + sum(A.ev)
function Base._sum(A::Bidiagonal, dims::Integer)
    res = Base.reducedim_initarray(A, dims, zero(eltype(A)))
    n = length(A.dv)
    if n == 0
        # Just to be sure. This shouldn't happen since there is a check whether
        # length(A.dv) == length(A.ev) + 1 in the constructor.
        return res
    elseif n == 1
        res[1] = A.dv[1]
        return res
    end
    @inbounds begin
        if (dims == 1 && A.uplo == 'U') || (dims == 2 && A.uplo == 'L')
            res[1] = A.dv[1]
            for i = 2:length(A.dv)
                res[i] = A.ev[i-1] + A.dv[i]
            end
        elseif (dims == 1 && A.uplo == 'L') || (dims == 2 && A.uplo == 'U')
            for i = 1:length(A.dv)-1
                res[i] = A.ev[i] + A.dv[i]
            end
            res[end] = A.dv[end]
        elseif dims >= 3
            if A.uplo == 'U'
                for i = 1:length(A.dv)-1
                    res[i,i]   = A.dv[i]
                    res[i,i+1] = A.ev[i]
                end
            else
                for i = 1:length(A.dv)-1
                    res[i,i]   = A.dv[i]
                    res[i+1,i] = A.ev[i]
                end
            end
            res[end,end] = A.dv[end]
        end
    end
    res
end
   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LinearAlgebra/src/uniformscaling.jlR9      # This file is a part of Julia. License is MIT: https://julialang.org/license

import Base: copy, adjoint, getindex, show, transpose, one, zero, inv,
             hcat, vcat, hvcat, ^

"""
    UniformScaling{T<:Number}

Generically sized uniform scaling operator defined as a scalar times
the identity operator, `λ*I`. Although without an explicit `size`, it
acts similarly to a matrix in many cases and includes support for some
indexing. See also [`I`](@ref).

!!! compat "Julia 1.6"
     Indexing using ranges is available as of Julia 1.6.

# Examples
```jldoctest
julia> J = UniformScaling(2.)
UniformScaling{Float64}
2.0*I

julia> A = [1. 2.; 3. 4.]
2×2 Matrix{Float64}:
 1.0  2.0
 3.0  4.0

julia> J*A
2×2 Matrix{Float64}:
 2.0  4.0
 6.0  8.0

julia> J[1:2, 1:2]
2×2 Matrix{Float64}:
 2.0  0.0
 0.0  2.0
```
"""
struct UniformScaling{T<:Number}
    λ::T
end

"""
    I

An object of type [`UniformScaling`](@ref), representing an identity matrix of any size.

# Examples
```jldoctest
julia> fill(1, (5,6)) * I == fill(1, (5,6))
true

julia> [1 2im 3; 1im 2 3] * I
2×3 Matrix{Complex{Int64}}:
 1+0im  0+2im  3+0im
 0+1im  2+0im  3+0im
```
"""
const I = UniformScaling(true)

"""
    (I::UniformScaling)(n::Integer)

Construct a `Diagonal` matrix from a `UniformScaling`.

!!! compat "Julia 1.2"
     This method is available as of Julia 1.2.

# Examples
```jldoctest
julia> I(3)
3×3 Diagonal{Bool, Vector{Bool}}:
 1  ⋅  ⋅
 ⋅  1  ⋅
 ⋅  ⋅  1

julia> (0.7*I)(3)
3×3 Diagonal{Float64, Vector{Float64}}:
 0.7   ⋅    ⋅
  ⋅   0.7   ⋅
  ⋅    ⋅   0.7
```
"""
(I::UniformScaling)(n::Integer) = Diagonal(fill(I.λ, n))

eltype(::Type{UniformScaling{T}}) where {T} = T
ndims(J::UniformScaling) = 2
Base.has_offset_axes(::UniformScaling) = false
getindex(J::UniformScaling, i::Integer,j::Integer) = ifelse(i==j,J.λ,zero(J.λ))

getindex(J::UniformScaling, n::Integer, m::AbstractVector{<:Integer}) = getindex(J, m, n)
function getindex(J::UniformScaling{T}, n::AbstractVector{<:Integer}, m::Integer) where T
    v = zeros(T, axes(n))
    @inbounds for (i,ii) in pairs(n)
        if ii == m
            v[i] = J.λ
        end
    end
    return v
end

function getindex(J::UniformScaling{T}, n::AbstractVector{<:Integer}, m::AbstractVector{<:Integer}) where T
    A = zeros(T, axes(n)..., axes(m)...)
    @inbounds for (j,jj) in pairs(m), (i,ii) in pairs(n)
        if ii == jj
            A[i,j] = J.λ
        end
    end
    return A
end

function show(io::IO, ::MIME"text/plain", J::UniformScaling)
    s = "$(J.λ)"
    if occursin(r"\w+\s*[\+\-]\s*\w+", s)
        s = "($s)"
    end
    print(io, typeof(J), "\n$s*I")
end
copy(J::UniformScaling) = UniformScaling(J.λ)

Base.convert(::Type{UniformScaling{T}}, J::UniformScaling) where {T} = UniformScaling(convert(T, J.λ))::UniformScaling{T}

conj(J::UniformScaling) = UniformScaling(conj(J.λ))
real(J::UniformScaling) = UniformScaling(real(J.λ))
imag(J::UniformScaling) = UniformScaling(imag(J.λ))

transpose(J::UniformScaling) = J
adjoint(J::UniformScaling) = UniformScaling(conj(J.λ))

one(::Type{UniformScaling{T}}) where {T} = UniformScaling(one(T))
one(J::UniformScaling{T}) where {T} = one(UniformScaling{T})
oneunit(::Type{UniformScaling{T}}) where {T} = UniformScaling(oneunit(T))
oneunit(J::UniformScaling{T}) where {T} = oneunit(UniformScaling{T})
zero(::Type{UniformScaling{T}}) where {T} = UniformScaling(zero(T))
zero(J::UniformScaling{T}) where {T} = zero(UniformScaling{T})

isdiag(::UniformScaling) = true
istriu(::UniformScaling) = true
istril(::UniformScaling) = true
issymmetric(::UniformScaling) = true
ishermitian(J::UniformScaling) = isreal(J.λ)
isposdef(J::UniformScaling) = isposdef(J.λ)

(+)(J::UniformScaling, x::Number) = J.λ + x
(+)(x::Number, J::UniformScaling) = x + J.λ
(-)(J::UniformScaling, x::Number) = J.λ - x
(-)(x::Number, J::UniformScaling) = x - J.λ

(+)(J::UniformScaling)                      = UniformScaling(+J.λ)
(+)(J1::UniformScaling, J2::UniformScaling) = UniformScaling(J1.λ+J2.λ)
(+)(B::BitArray{2}, J::UniformScaling)      = Array(B) + J
(+)(J::UniformScaling, B::BitArray{2})      = J + Array(B)
(+)(J::UniformScaling, A::AbstractMatrix)   = A + J

(-)(J::UniformScaling)                      = UniformScaling(-J.λ)
(-)(J1::UniformScaling, J2::UniformScaling) = UniformScaling(J1.λ-J2.λ)
(-)(B::BitArray{2}, J::UniformScaling)      = Array(B) - J
(-)(J::UniformScaling, B::BitArray{2})      = J - Array(B)
(-)(A::AbstractMatrix, J::UniformScaling)   = A + (-J)

# matrix functions
for f in ( :exp,   :log,
           :expm1, :log1p,
           :sqrt,  :cbrt,
           :sin,   :cos,   :tan,
           :asin,  :acos,  :atan,
           :csc,   :sec,   :cot,
           :acsc,  :asec,  :acot,
           :sinh,  :cosh,  :tanh,
           :asinh, :acosh, :atanh,
           :csch,  :sech,  :coth,
           :acsch, :asech, :acoth )
    @eval Base.$f(J::UniformScaling) = UniformScaling($f(J.λ))
end

# Unit{Lower/Upper}Triangular matrices become {Lower/Upper}Triangular under
# addition with a UniformScaling
for (t1, t2) in ((:UnitUpperTriangular, :UpperTriangular),
                 (:UnitLowerTriangular, :LowerTriangular))
    @eval begin
        function (+)(UL::$t1, J::UniformScaling)
            ULnew = copymutable_oftype(UL.data, Base.promote_op(+, eltype(UL), typeof(J)))
            for i in axes(ULnew, 1)
                ULnew[i,i] = one(ULnew[i,i]) + J
            end
            return ($t2)(ULnew)
        end
    end
end

# Adding a complex UniformScaling to the diagonal of a Hermitian
# matrix breaks the hermiticity, if the UniformScaling is non-real.
# However, to preserve type stability, we do not special-case a
# UniformScaling{<:Complex} that happens to be real.
function (+)(A::Hermitian, J::UniformScaling{<:Complex})
    TS = Base.promote_op(+, eltype(A), typeof(J))
    B = copytri!(copymutable_oftype(parent(A), TS), A.uplo, true)
    for i in diagind(B)
        B[i] = A[i] + J
    end
    return B
end

function (-)(J::UniformScaling{<:Complex}, A::Hermitian)
    TS = Base.promote_op(+, eltype(A), typeof(J))
    B = copytri!(copymutable_oftype(parent(A), TS), A.uplo, true)
    B .= .-B
    for i in diagind(B)
        B[i] = J - A[i]
    end
    return B
end

function (+)(A::AbstractMatrix, J::UniformScaling)
    checksquare(A)
    B = copymutable_oftype(A, Base.promote_op(+, eltype(A), typeof(J)))
    for i in intersect(axes(A,1), axes(A,2))
        @inbounds B[i,i] += J
    end
    return B
end

function (-)(J::UniformScaling, A::AbstractMatrix)
    checksquare(A)
    B = convert(AbstractMatrix{Base.promote_op(+, eltype(A), typeof(J))}, -A)
    for i in intersect(axes(A,1), axes(A,2))
        @inbounds B[i,i] += J
    end
    return B
end

inv(J::UniformScaling) = UniformScaling(inv(J.λ))
opnorm(J::UniformScaling, p::Real=2) = opnorm(J.λ, p)

pinv(J::UniformScaling) = ifelse(iszero(J.λ),
                          UniformScaling(zero(inv(J.λ))),  # type stability
                          UniformScaling(inv(J.λ)))

function det(J::UniformScaling{T}) where T
    if isone(J.λ)
        one(T)
    elseif iszero(J.λ)
        zero(T)
    else
        throw(ArgumentError("Determinant of UniformScaling is only well-defined when λ = 0 or 1."))
    end
end

function tr(J::UniformScaling{T}) where T
    if iszero(J.λ)
        zero(T)
    else
        throw(ArgumentError("Trace of UniformScaling is only well-defined when λ = 0"))
    end
end

*(J1::UniformScaling, J2::UniformScaling) = UniformScaling(J1.λ*J2.λ)
*(B::BitArray{2}, J::UniformScaling) = *(Array(B), J::UniformScaling)
*(J::UniformScaling, B::BitArray{2}) = *(J::UniformScaling, Array(B))
*(A::AbstractMatrix, J::UniformScaling) = A*J.λ
*(v::AbstractVector, J::UniformScaling) = reshape(v, length(v), 1) * J
*(J::UniformScaling, A::AbstractVecOrMat) = J.λ*A
*(x::Number, J::UniformScaling) = UniformScaling(x*J.λ)
*(J::UniformScaling, x::Number) = UniformScaling(J.λ*x)

/(J1::UniformScaling, J2::UniformScaling) = J2.λ == 0 ? throw(SingularException(1)) : UniformScaling(J1.λ/J2.λ)
/(J::UniformScaling, A::AbstractMatrix) =
    (invA = inv(A); lmul!(J.λ, convert(AbstractMatrix{promote_type(eltype(J),eltype(invA))}, invA)))
/(A::AbstractMatrix, J::UniformScaling) = J.λ == 0 ? throw(SingularException(1)) : A/J.λ
/(v::AbstractVector, J::UniformScaling) = reshape(v, length(v), 1) / J

/(J::UniformScaling, x::Number) = UniformScaling(J.λ/x)

\(J1::UniformScaling, J2::UniformScaling) = J1.λ == 0 ? throw(SingularException(1)) : UniformScaling(J1.λ\J2.λ)
\(J::UniformScaling, A::AbstractVecOrMat) = J.λ == 0 ? throw(SingularException(1)) : J.λ\A
\(A::AbstractMatrix, J::UniformScaling) =
    (invA = inv(A); rmul!(convert(AbstractMatrix{promote_type(eltype(invA),eltype(J))}, invA), J.λ))
\(F::Factorization, J::UniformScaling) = F \ J(size(F,1))

\(x::Number, J::UniformScaling) = UniformScaling(x\J.λ)

@inline mul!(C::AbstractMatrix, A::AbstractMatrix, J::UniformScaling, alpha::Number, beta::Number) =
    mul!(C, A, J.λ, alpha, beta)
@inline mul!(C::AbstractVecOrMat, J::UniformScaling, B::AbstractVecOrMat, alpha::Number, beta::Number) =
    mul!(C, J.λ, B, alpha, beta)

function mul!(out::AbstractMatrix{T}, a::Number, B::UniformScaling, α::Number, β::Number) where {T}
    checksquare(out)
    if iszero(β)  # zero contribution of the out matrix
        fill!(out, zero(T))
    elseif !isone(β)
        rmul!(out, β)
    end
    s = convert(T, a*B.λ*α)
    if !iszero(s)
        @inbounds for i in diagind(out)
            out[i] += s
        end
    end
    return out
end
@inline mul!(out::AbstractMatrix, A::UniformScaling, b::Number, α::Number, β::Number)=
    mul!(out, A.λ, UniformScaling(b), α, β)
rmul!(A::AbstractMatrix, J::UniformScaling) = rmul!(A, J.λ)
lmul!(J::UniformScaling, B::AbstractVecOrMat) = lmul!(J.λ, B)
rdiv!(A::AbstractMatrix, J::UniformScaling) = rdiv!(A, J.λ)
ldiv!(J::UniformScaling, B::AbstractVecOrMat) = ldiv!(J.λ, B)
ldiv!(Y::AbstractVecOrMat, J::UniformScaling, B::AbstractVecOrMat) = (Y .= J.λ .\ B)

Broadcast.broadcasted(::typeof(*), x::Number,J::UniformScaling) = UniformScaling(x*J.λ)
Broadcast.broadcasted(::typeof(*), J::UniformScaling,x::Number) = UniformScaling(J.λ*x)

Broadcast.broadcasted(::typeof(/), J::UniformScaling,x::Number) = UniformScaling(J.λ/x)

Broadcast.broadcasted(::typeof(\), x::Number,J::UniformScaling) = UniformScaling(x\J.λ)

(^)(J::UniformScaling, x::Number) = UniformScaling((J.λ)^x)
Base.literal_pow(::typeof(^), J::UniformScaling, x::Val) = UniformScaling(Base.literal_pow(^, J.λ, x))

Broadcast.broadcasted(::typeof(^), J::UniformScaling, x::Number) = UniformScaling(J.λ^x)
function Broadcast.broadcasted(::typeof(Base.literal_pow), ::typeof(^), J::UniformScaling, x::Val)
    UniformScaling(Base.literal_pow(^, J.λ, x))
end

==(J1::UniformScaling,J2::UniformScaling) = (J1.λ == J2.λ)

## equality comparison with UniformScaling
==(J::UniformScaling, A::AbstractMatrix) = A == J
function ==(A::AbstractMatrix, J::UniformScaling)
    require_one_based_indexing(A)
    size(A, 1) == size(A, 2) || return false
    iszero(J.λ) && return iszero(A)
    isone(J.λ) && return isone(A)
    return A == J.λ*one(A)
end
function ==(A::StridedMatrix, J::UniformScaling)
    size(A, 1) == size(A, 2) || return false
    iszero(J.λ) && return iszero(A)
    isone(J.λ) && return isone(A)
    for j in axes(A, 2), i in axes(A, 1)
        ifelse(i == j, A[i, j] == J.λ, iszero(A[i, j])) || return false
    end
    return true
end

isequal(A::AbstractMatrix, J::UniformScaling) = false
isequal(J::UniformScaling, A::AbstractMatrix) = false

function isapprox(J1::UniformScaling{T}, J2::UniformScaling{S};
            atol::Real=0, rtol::Real=Base.rtoldefault(T,S,atol), nans::Bool=false) where {T<:Number,S<:Number}
    isapprox(J1.λ, J2.λ, rtol=rtol, atol=atol, nans=nans)
end
function isapprox(J::UniformScaling, A::AbstractMatrix;
                  atol::Real = 0,
                  rtol::Real = Base.rtoldefault(promote_leaf_eltypes(A), eltype(J), atol),
                  nans::Bool = false, norm::Function = norm)
    n = checksquare(A)
    normJ = norm === opnorm             ? abs(J.λ) :
            norm === LinearAlgebra.norm ? abs(J.λ) * sqrt(n) :
                                          norm(Diagonal(fill(J.λ, n)))
    return norm(A - J) <= max(atol, rtol * max(norm(A), normJ))
end
isapprox(A::AbstractMatrix, J::UniformScaling; kwargs...) = isapprox(J, A; kwargs...)

"""
    copyto!(dest::AbstractMatrix, src::UniformScaling)

Copies a [`UniformScaling`](@ref) onto a matrix.

!!! compat "Julia 1.1"
    In Julia 1.0 this method only supported a square destination matrix. Julia 1.1. added
    support for a rectangular matrix.
"""
function copyto!(A::AbstractMatrix, J::UniformScaling)
    require_one_based_indexing(A)
    fill!(A, 0)
    λ = J.λ
    for i = 1:min(size(A,1),size(A,2))
        @inbounds A[i,i] = λ
    end
    return A
end

function copyto!(A::Diagonal, J::UniformScaling)
    A.diag .= J.λ
    return A
end
function copyto!(A::Union{Bidiagonal, SymTridiagonal}, J::UniformScaling)
    A.ev .= 0
    A.dv .= J.λ
    return A
end
function copyto!(A::Tridiagonal, J::UniformScaling)
    A.dl .= 0
    A.du .= 0
    A.d .= J.λ
    return A
end

function cond(J::UniformScaling{T}) where T
    onereal = inv(one(real(J.λ)))
    return J.λ ≠ zero(T) ? onereal : oftype(onereal, Inf)
end

## Matrix construction from UniformScaling
function Matrix{T}(s::UniformScaling, dims::Dims{2}) where {T}
    A = zeros(T, dims)
    v = T(s.λ)
    for i in diagind(dims...)
        @inbounds A[i] = v
    end
    return A
end
Matrix{T}(s::UniformScaling, m::Integer, n::Integer) where {T} = Matrix{T}(s, Dims((m, n)))
Matrix(s::UniformScaling, m::Integer, n::Integer) = Matrix(s, Dims((m, n)))
Matrix(s::UniformScaling, dims::Dims{2}) = Matrix{eltype(s)}(s, dims)
Array{T}(s::UniformScaling, dims::Dims{2}) where {T} = Matrix{T}(s, dims)
Array{T}(s::UniformScaling, m::Integer, n::Integer) where {T} = Matrix{T}(s, m, n)
Array(s::UniformScaling, m::Integer, n::Integer) = Matrix(s, m, n)
Array(s::UniformScaling, dims::Dims{2}) = Matrix(s, dims)

dot(A::AbstractMatrix, J::UniformScaling) = dot(tr(A), J.λ)
dot(J::UniformScaling, A::AbstractMatrix) = dot(J.λ, tr(A))

dot(x::AbstractVector, J::UniformScaling, y::AbstractVector) = dot(x, J.λ, y)
dot(x::AbstractVector, a::Number, y::AbstractVector) = sum(t -> dot(t[1], a, t[2]), zip(x, y))
dot(x::AbstractVector, a::Union{Real,Complex}, y::AbstractVector) = a*dot(x, y)

# muladd
Base.muladd(A::UniformScaling, B::UniformScaling, z::UniformScaling) =
    UniformScaling(A.λ * B.λ + z.λ)
s   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LinearAlgebra/src/qr.jltk      # This file is a part of Julia. License is MIT: https://julialang.org/license

# QR Factorization
"""
    QR <: Factorization

A QR matrix factorization stored in a packed format, typically obtained from
[`qr`](@ref). If ``A`` is an `m`×`n` matrix, then

```math
A = Q R
```

where ``Q`` is an orthogonal/unitary matrix and ``R`` is upper triangular.
The matrix ``Q`` is stored as a sequence of Householder reflectors ``v_i``
and coefficients ``\\tau_i`` where:

```math
Q = \\prod_{i=1}^{\\min(m,n)} (I - \\tau_i v_i v_i^T).
```

Iterating the decomposition produces the components `Q` and `R`.

The object has two fields:

* `factors` is an `m`×`n` matrix.

  - The upper triangular part contains the elements of ``R``, that is `R =
    triu(F.factors)` for a `QR` object `F`.

  - The subdiagonal part contains the reflectors ``v_i`` stored in a packed format where
    ``v_i`` is the ``i``th column of the matrix `V = I + tril(F.factors, -1)`.

* `τ` is a vector  of length `min(m,n)` containing the coefficients ``\tau_i``.
"""
struct QR{T,S<:AbstractMatrix{T},C<:AbstractVector{T}} <: Factorization{T}
    factors::S
    τ::C

    function QR{T,S,C}(factors, τ) where {T,S<:AbstractMatrix{T},C<:AbstractVector{T}}
        require_one_based_indexing(factors)
        new{T,S,C}(factors, τ)
    end
end
QR(factors::AbstractMatrix{T}, τ::AbstractVector{T}) where {T} =
    QR{T,typeof(factors),typeof(τ)}(factors, τ)
QR{T}(factors::AbstractMatrix, τ::AbstractVector) where {T} =
    QR(convert(AbstractMatrix{T}, factors), convert(AbstractVector{T}, τ))
# backwards-compatible constructors (remove with Julia 2.0)
@deprecate(QR{T,S}(factors::AbstractMatrix{T}, τ::AbstractVector{T}) where {T,S},
           QR{T,S,typeof(τ)}(factors, τ), false)

# iteration for destructuring into components
Base.iterate(S::QR) = (S.Q, Val(:R))
Base.iterate(S::QR, ::Val{:R}) = (S.R, Val(:done))
Base.iterate(S::QR, ::Val{:done}) = nothing

# Note. For QRCompactWY factorization without pivoting, the WY representation based method introduced in LAPACK 3.4
"""
    QRCompactWY <: Factorization

A QR matrix factorization stored in a compact blocked format, typically obtained from
[`qr`](@ref). If ``A`` is an `m`×`n` matrix, then

```math
A = Q R
```

where ``Q`` is an orthogonal/unitary matrix and ``R`` is upper triangular. It is similar
to the [`QR`](@ref) format except that the orthogonal/unitary matrix ``Q`` is stored in
*Compact WY* format [^Schreiber1989].  For the block size ``n_b``, it is stored as
a `m`×`n` lower trapezoidal matrix ``V`` and a matrix ``T = (T_1 \\; T_2 \\; ... \\;
T_{b-1} \\; T_b')`` composed of ``b = \\lceil \\min(m,n) / n_b \\rceil`` upper triangular
matrices ``T_j`` of size ``n_b``×``n_b`` (``j = 1, ..., b-1``) and an upper trapezoidal
``n_b``×``\\min(m,n) - (b-1) n_b`` matrix ``T_b'`` (``j=b``) whose upper square part
denoted with ``T_b`` satisfying

```math
Q = \\prod_{i=1}^{\\min(m,n)} (I - \\tau_i v_i v_i^T)
= \\prod_{j=1}^{b} (I - V_j T_j V_j^T)
```

such that ``v_i`` is the ``i``th column of ``V``, ``\\tau_i`` is the ``i``th element
of `[diag(T_1); diag(T_2); …; diag(T_b)]`, and ``(V_1 \\; V_2 \\; ... \\; V_b)``
is the left `m`×`min(m, n)` block of ``V``.  When constructed using [`qr`](@ref),
the block size is given by ``n_b = \\min(m, n, 36)``.

Iterating the decomposition produces the components `Q` and `R`.

The object has two fields:

* `factors`, as in the [`QR`](@ref) type, is an `m`×`n` matrix.

  - The upper triangular part contains the elements of ``R``, that is `R =
    triu(F.factors)` for a `QR` object `F`.

  - The subdiagonal part contains the reflectors ``v_i`` stored in a packed format such
    that `V = I + tril(F.factors, -1)`.

* `T` is a ``n_b``-by-``\\min(m,n)`` matrix as described above. The subdiagonal elements
  for each triangular matrix ``T_j`` are ignored.

!!! note

    This format should not to be confused with the older *WY* representation
    [^Bischof1987].


[^Bischof1987]: C Bischof and C Van Loan, "The WY representation for products of Householder matrices", SIAM J Sci Stat Comput 8 (1987), s2-s13. [doi:10.1137/0908009](https://doi.org/10.1137/0908009)

[^Schreiber1989]: R Schreiber and C Van Loan, "A storage-efficient WY representation for products of Householder transformations", SIAM J Sci Stat Comput 10 (1989), 53-57. [doi:10.1137/0910005](https://doi.org/10.1137/0910005)
"""
struct QRCompactWY{S,M<:AbstractMatrix{S},C<:AbstractMatrix{S}} <: Factorization{S}
    factors::M
    T::C

    function QRCompactWY{S,M,C}(factors, T) where {S,M<:AbstractMatrix{S},C<:AbstractMatrix{S}}
        require_one_based_indexing(factors)
        new{S,M,C}(factors, T)
    end
end
QRCompactWY(factors::AbstractMatrix{S}, T::AbstractMatrix{S}) where {S} =
    QRCompactWY{S,typeof(factors),typeof(T)}(factors, T)
QRCompactWY{S}(factors::AbstractMatrix, T::AbstractMatrix) where {S} =
    QRCompactWY(convert(AbstractMatrix{S}, factors), convert(AbstractMatrix{S}, T))
# backwards-compatible constructors (remove with Julia 2.0)
@deprecate(QRCompactWY{S,M}(factors::AbstractMatrix{S}, T::AbstractMatrix{S}) where {S,M},
           QRCompactWY{S,M,typeof(T)}(factors, T), false)

# iteration for destructuring into components
Base.iterate(S::QRCompactWY) = (S.Q, Val(:R))
Base.iterate(S::QRCompactWY, ::Val{:R}) = (S.R, Val(:done))
Base.iterate(S::QRCompactWY, ::Val{:done}) = nothing

# returns upper triangular views of all non-undef values of `qr(A).T`:
#
# julia> sparse(qr(A).T .== qr(A).T)
# 36×100 SparseMatrixCSC{Bool, Int64} with 1767 stored entries:
# ⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
# ⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
# ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿
# ⠀⠀⠀⠀⠀⠂⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿
# ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⠐⠙⢿⣿⣿⣿⣿
# ⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⢙⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠙⢿⣿⣿
# ⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠄⠀⠙⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠙⢿
# ⠀⡀⠀⠀⠀⠀⠀⠀⠂⠒⠒⠀⠀⠀⠙⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀
# ⠀⠀⠀⠀⠀⠀⠀⠀⣈⡀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⢀⠀
#
function _triuppers_qr(T)
    blocksize, cols = size(T)
    return Iterators.map(0:div(cols - 1, blocksize)) do i
        n = min(blocksize, cols - i * blocksize)
        return UpperTriangular(view(T, 1:n, (1:n) .+ i * blocksize))
    end
end

function Base.hash(F::QRCompactWY, h::UInt)
    return hash(F.factors, foldr(hash, _triuppers_qr(F.T); init=hash(QRCompactWY, h)))
end
function Base.:(==)(A::QRCompactWY, B::QRCompactWY)
    return A.factors == B.factors && all(splat(==), zip(_triuppers_qr.((A.T, B.T))...))
end
function Base.isequal(A::QRCompactWY, B::QRCompactWY)
    return isequal(A.factors, B.factors) && all(zip(_triuppers_qr.((A.T, B.T))...)) do (a, b)
        isequal(a, b)::Bool
    end
end

"""
    QRPivoted <: Factorization

A QR matrix factorization with column pivoting in a packed format, typically obtained from
[`qr`](@ref). If ``A`` is an `m`×`n` matrix, then

```math
A P = Q R
```

where ``P`` is a permutation matrix, ``Q`` is an orthogonal/unitary matrix and ``R`` is
upper triangular. The matrix ``Q`` is stored as a sequence of Householder reflectors:

```math
Q = \\prod_{i=1}^{\\min(m,n)} (I - \\tau_i v_i v_i^T).
```

Iterating the decomposition produces the components `Q`, `R`, and `p`.

The object has three fields:

* `factors` is an `m`×`n` matrix.

  - The upper triangular part contains the elements of ``R``, that is `R =
    triu(F.factors)` for a `QR` object `F`.

  - The subdiagonal part contains the reflectors ``v_i`` stored in a packed format where
    ``v_i`` is the ``i``th column of the matrix `V = I + tril(F.factors, -1)`.

* `τ` is a vector of length `min(m,n)` containing the coefficients ``\tau_i``.

* `jpvt` is an integer vector of length `n` corresponding to the permutation ``P``.
"""
struct QRPivoted{T,S<:AbstractMatrix{T},C<:AbstractVector{T},P<:AbstractVector{<:Integer}} <: Factorization{T}
    factors::S
    τ::C
    jpvt::P

    function QRPivoted{T,S,C,P}(factors, τ, jpvt) where {T,S<:AbstractMatrix{T},C<:AbstractVector{T},P<:AbstractVector{<:Integer}}
        require_one_based_indexing(factors, τ, jpvt)
        new{T,S,C,P}(factors, τ, jpvt)
    end
end
QRPivoted(factors::AbstractMatrix{T}, τ::AbstractVector{T},
          jpvt::AbstractVector{<:Integer}) where {T} =
    QRPivoted{T,typeof(factors),typeof(τ),typeof(jpvt)}(factors, τ, jpvt)
QRPivoted{T}(factors::AbstractMatrix, τ::AbstractVector,
             jpvt::AbstractVector{<:Integer}) where {T} =
    QRPivoted(convert(AbstractMatrix{T}, factors), convert(AbstractVector{T}, τ), jpvt)
# backwards-compatible constructors (remove with Julia 2.0)
@deprecate(QRPivoted{T,S}(factors::AbstractMatrix{T}, τ::AbstractVector{T},
                          jpvt::AbstractVector{<:Integer}) where {T,S},
           QRPivoted{T,S,typeof(τ),typeof(jpvt)}(factors, τ, jpvt), false)

# iteration for destructuring into components
Base.iterate(S::QRPivoted) = (S.Q, Val(:R))
Base.iterate(S::QRPivoted, ::Val{:R}) = (S.R, Val(:p))
Base.iterate(S::QRPivoted, ::Val{:p}) = (S.p, Val(:done))
Base.iterate(S::QRPivoted, ::Val{:done}) = nothing

function qrfactUnblocked!(A::AbstractMatrix{T}) where {T}
    require_one_based_indexing(A)
    m, n = size(A)
    τ = zeros(T, min(m,n))
    for k = 1:min(m - 1 + !(T<:Real), n)
        x = view(A, k:m, k)
        τk = reflector!(x)
        τ[k] = τk
        reflectorApply!(x, τk, view(A, k:m, k + 1:n))
    end
    QR(A, τ)
end

# Find index for columns with largest two norm
function indmaxcolumn(A::AbstractMatrix)
    mm = norm(view(A, :, 1))
    ii = 1
    for i = 2:size(A, 2)
        mi = norm(view(A, :, i))
        if abs(mi) > mm
            mm = mi
            ii = i
        end
    end
    return ii
end

function qrfactPivotedUnblocked!(A::AbstractMatrix)
    m, n = size(A)
    piv = Vector(UnitRange{BlasInt}(1,n))
    τ = Vector{eltype(A)}(undef, min(m,n))
    for j = 1:min(m,n)

        # Find column with maximum norm in trailing submatrix
        jm = indmaxcolumn(view(A, j:m, j:n)) + j - 1

        if jm != j
            # Flip elements in pivoting vector
            tmpp = piv[jm]
            piv[jm] = piv[j]
            piv[j] = tmpp

            # Update matrix with
            for i = 1:m
                tmp = A[i,jm]
                A[i,jm] = A[i,j]
                A[i,j] = tmp
            end
        end

        # Compute reflector of columns j
        x = view(A, j:m, j)
        τj = reflector!(x)
        τ[j] = τj

        # Update trailing submatrix with reflector
        reflectorApply!(x, τj, view(A, j:m, j+1:n))
    end
    return QRPivoted{eltype(A), typeof(A), typeof(τ), typeof(piv)}(A, τ, piv)
end

# LAPACK version
qr!(A::StridedMatrix{<:BlasFloat}, ::NoPivot; blocksize=36) =
    QRCompactWY(LAPACK.geqrt!(A, min(min(size(A)...), blocksize))...)
qr!(A::StridedMatrix{<:BlasFloat}, ::ColumnNorm) = QRPivoted(LAPACK.geqp3!(A)...)

# Generic fallbacks

"""
    qr!(A, pivot = NoPivot(); blocksize)

`qr!` is the same as [`qr`](@ref) when `A` is a subtype of [`AbstractMatrix`](@ref),
but saves space by overwriting the input `A`, instead of creating a copy.
An [`InexactError`](@ref) exception is thrown if the factorization produces a number not
representable by the element type of `A`, e.g. for integer types.

!!! compat "Julia 1.4"
    The `blocksize` keyword argument requires Julia 1.4 or later.

# Examples
```jldoctest
julia> a = [1. 2.; 3. 4.]
2×2 Matrix{Float64}:
 1.0  2.0
 3.0  4.0

julia> qr!(a)
LinearAlgebra.QRCompactWY{Float64, Matrix{Float64}, Matrix{Float64}}
Q factor: 2×2 LinearAlgebra.QRCompactWYQ{Float64, Matrix{Float64}, Matrix{Float64}}
R factor:
2×2 Matrix{Float64}:
 -3.16228  -4.42719
  0.0      -0.632456

julia> a = [1 2; 3 4]
2×2 Matrix{Int64}:
 1  2
 3  4

julia> qr!(a)
ERROR: InexactError: Int64(3.1622776601683795)
Stacktrace:
[...]
```
"""
qr!(A::AbstractMatrix, ::NoPivot) = qrfactUnblocked!(A)
qr!(A::AbstractMatrix, ::ColumnNorm) = qrfactPivotedUnblocked!(A)
qr!(A::AbstractMatrix) = qr!(A, NoPivot())
# TODO: Remove in Julia v2.0
@deprecate qr!(A::AbstractMatrix, ::Val{true})  qr!(A, ColumnNorm())
@deprecate qr!(A::AbstractMatrix, ::Val{false}) qr!(A, NoPivot())

_qreltype(::Type{T}) where T = typeof(zero(T)/sqrt(abs2(one(T))))

"""
    qr(A, pivot = NoPivot(); blocksize) -> F

Compute the QR factorization of the matrix `A`: an orthogonal (or unitary if `A` is
complex-valued) matrix `Q`, and an upper triangular matrix `R` such that

```math
A = Q R
```

The returned object `F` stores the factorization in a packed format:

 - if `pivot == ColumnNorm()` then `F` is a [`QRPivoted`](@ref) object,

 - otherwise if the element type of `A` is a BLAS type ([`Float32`](@ref), [`Float64`](@ref),
   `ComplexF32` or `ComplexF64`), then `F` is a [`QRCompactWY`](@ref) object,

 - otherwise `F` is a [`QR`](@ref) object.

The individual components of the decomposition `F` can be retrieved via property accessors:

 - `F.Q`: the orthogonal/unitary matrix `Q`
 - `F.R`: the upper triangular matrix `R`
 - `F.p`: the permutation vector of the pivot ([`QRPivoted`](@ref) only)
 - `F.P`: the permutation matrix of the pivot ([`QRPivoted`](@ref) only)

Iterating the decomposition produces the components `Q`, `R`, and if extant `p`.

The following functions are available for the `QR` objects: [`inv`](@ref), [`size`](@ref),
and [`\\`](@ref). When `A` is rectangular, `\\` will return a least squares
solution and if the solution is not unique, the one with smallest norm is returned. When
`A` is not full rank, factorization with (column) pivoting is required to obtain a minimum
norm solution.

Multiplication with respect to either full/square or non-full/square `Q` is allowed, i.e. both `F.Q*F.R`
and `F.Q*A` are supported. A `Q` matrix can be converted into a regular matrix with
[`Matrix`](@ref). This operation returns the "thin" Q factor, i.e., if `A` is `m`×`n` with `m>=n`, then
`Matrix(F.Q)` yields an `m`×`n` matrix with orthonormal columns.  To retrieve the "full" Q factor, an
`m`×`m` orthogonal matrix, use `F.Q*I` or `collect(F.Q)`. If `m<=n`, then `Matrix(F.Q)` yields an `m`×`m`
orthogonal matrix.

The block size for QR decomposition can be specified by keyword argument
`blocksize :: Integer` when `pivot == NoPivot()` and `A isa StridedMatrix{<:BlasFloat}`.
It is ignored when `blocksize > minimum(size(A))`. See [`QRCompactWY`](@ref).

!!! compat "Julia 1.4"
    The `blocksize` keyword argument requires Julia 1.4 or later.

# Examples
```jldoctest
julia> A = [3.0 -6.0; 4.0 -8.0; 0.0 1.0]
3×2 Matrix{Float64}:
 3.0  -6.0
 4.0  -8.0
 0.0   1.0

julia> F = qr(A)
LinearAlgebra.QRCompactWY{Float64, Matrix{Float64}, Matrix{Float64}}
Q factor: 3×3 LinearAlgebra.QRCompactWYQ{Float64, Matrix{Float64}, Matrix{Float64}}
R factor:
2×2 Matrix{Float64}:
 -5.0  10.0
  0.0  -1.0

julia> F.Q * F.R == A
true
```

!!! note
    `qr` returns multiple types because LAPACK uses several representations
    that minimize the memory storage requirements of products of Householder
    elementary reflectors, so that the `Q` and `R` matrices can be stored
    compactly rather as two separate dense matrices.
"""
function qr(A::AbstractMatrix{T}, arg...; kwargs...) where T
    require_one_based_indexing(A)
    AA = copy_similar(A, _qreltype(T))
    return qr!(AA, arg...; kwargs...)
end
# TODO: remove in Julia v2.0
@deprecate qr(A::AbstractMatrix, ::Val{false}; kwargs...) qr(A, NoPivot(); kwargs...)
@deprecate qr(A::AbstractMatrix, ::Val{true}; kwargs...)  qr(A, ColumnNorm(); kwargs...)

qr(x::Number) = qr(fill(x,1,1))
function qr(v::AbstractVector)
    require_one_based_indexing(v)
    qr(reshape(v, (length(v), 1)))
end

# Conversions
QR{T}(A::QR) where {T} = QR(convert(AbstractMatrix{T}, A.factors), convert(Vector{T}, A.τ))
Factorization{T}(A::QR{T}) where {T} = A
Factorization{T}(A::QR) where {T} = QR{T}(A)
QRCompactWY{T}(A::QRCompactWY) where {T} = QRCompactWY(convert(AbstractMatrix{T}, A.factors), convert(AbstractMatrix{T}, A.T))
Factorization{T}(A::QRCompactWY{T}) where {T} = A
Factorization{T}(A::QRCompactWY) where {T} = QRCompactWY{T}(A)
AbstractMatrix(F::Union{QR,QRCompactWY}) = F.Q * F.R
AbstractArray(F::Union{QR,QRCompactWY}) = AbstractMatrix(F)
Matrix(F::Union{QR,QRCompactWY}) = Array(AbstractArray(F))
Array(F::Union{QR,QRCompactWY}) = Matrix(F)
QRPivoted{T}(A::QRPivoted) where {T} = QRPivoted(convert(AbstractMatrix{T}, A.factors), convert(Vector{T}, A.τ), A.jpvt)
Factorization{T}(A::QRPivoted{T}) where {T} = A
Factorization{T}(A::QRPivoted) where {T} = QRPivoted{T}(A)
AbstractMatrix(F::QRPivoted) = (F.Q * F.R)[:,invperm(F.p)]
AbstractArray(F::QRPivoted) = AbstractMatrix(F)
Matrix(F::QRPivoted) = Array(AbstractArray(F))
Array(F::QRPivoted) = Matrix(F)

function show(io::IO, mime::MIME{Symbol("text/plain")}, F::Union{QR, QRCompactWY, QRPivoted})
    summary(io, F); println(io)
    print(io, "Q factor: ")
    show(io, mime, F.Q)
    println(io, "\nR factor:")
    show(io, mime, F.R)
    if F isa QRPivoted
        println(io, "\npermutation:")
        show(io, mime, F.p)
    end
end

function getproperty(F::QR, d::Symbol)
    m, n = size(F)
    if d === :R
        return triu!(getfield(F, :factors)[1:min(m,n), 1:n])
    elseif d === :Q
        return QRPackedQ(getfield(F, :factors), F.τ)
    else
        getfield(F, d)
    end
end
function getproperty(F::QRCompactWY, d::Symbol)
    m, n = size(F)
    if d === :R
        return triu!(getfield(F, :factors)[1:min(m,n), 1:n])
    elseif d === :Q
        return QRCompactWYQ(getfield(F, :factors), F.T)
    else
        getfield(F, d)
    end
end
Base.propertynames(F::Union{QR,QRCompactWY}, private::Bool=false) =
    (:R, :Q, (private ? fieldnames(typeof(F)) : ())...)

function getproperty(F::QRPivoted{T}, d::Symbol) where T
    m, n = size(F)
    if d === :R
        return triu!(getfield(F, :factors)[1:min(m,n), 1:n])
    elseif d === :Q
        return QRPackedQ(getfield(F, :factors), F.τ)
    elseif d === :p
        return getfield(F, :jpvt)
    elseif d === :P
        p = F.p
        n = length(p)
        P = zeros(T, n, n)
        for i in 1:n
            P[p[i],i] = one(T)
        end
        return P
    else
        getfield(F, d)
    end
end
Base.propertynames(F::QRPivoted, private::Bool=false) =
    (:R, :Q, :p, :P, (private ? fieldnames(typeof(F)) : ())...)

transpose(F::Union{QR{<:Real},QRPivoted{<:Real},QRCompactWY{<:Real}}) = F'
transpose(::Union{QR,QRPivoted,QRCompactWY}) =
    throw(ArgumentError("transpose of QR decomposition is not supported, consider using adjoint"))

size(F::Union{QR,QRCompactWY,QRPivoted}) = size(getfield(F, :factors))
size(F::Union{QR,QRCompactWY,QRPivoted}, dim::Integer) = size(getfield(F, :factors), dim)


function ldiv!(A::QRCompactWY{T}, b::AbstractVector{T}) where {T}
    require_one_based_indexing(b)
    m, n = size(A)
    ldiv!(UpperTriangular(view(A.factors, 1:min(m,n), 1:n)), view(lmul!(adjoint(A.Q), b), 1:size(A, 2)))
    return b
end
function ldiv!(A::QRCompactWY{T}, B::AbstractMatrix{T}) where {T}
    require_one_based_indexing(B)
    m, n = size(A)
    ldiv!(UpperTriangular(view(A.factors, 1:min(m,n), 1:n)), view(lmul!(adjoint(A.Q), B), 1:size(A, 2), 1:size(B, 2)))
    return B
end

# Julia implementation similar to xgelsy
function ldiv!(A::QRPivoted{T,<:StridedMatrix}, B::AbstractMatrix{T}, rcond::Real) where {T<:BlasFloat}
    require_one_based_indexing(B)
    m, n = size(A)

    if m > size(B, 1) || n > size(B, 1)
        throw(DimensionMismatch("B has leading dimension $(size(B, 1)) but needs at least $(max(m, n))"))
    end

    if length(A.factors) == 0 || length(B) == 0
        return B, 0
    end

    @inbounds begin
        smin = smax = abs(A.factors[1])

        if smax == 0
            return fill!(B, 0), 0
        end

        mn = min(m, n)

        # allocate temporary work space
        tmp  = Vector{T}(undef, 2mn)
        wmin = view(tmp, 1:mn)
        wmax = view(tmp, mn+1:2mn)

        rnk = 1
        wmin[1] = 1
        wmax[1] = 1

        while rnk < mn
            i = rnk + 1

            smin, s1, c1 = LAPACK.laic1!(2, view(wmin, 1:rnk), smin, view(A.factors, 1:rnk, i), A.factors[i,i])
            smax, s2, c2 = LAPACK.laic1!(1, view(wmax, 1:rnk), smax, view(A.factors, 1:rnk, i), A.factors[i,i])

            if smax*rcond > smin
                break
            end

            for j in 1:rnk
                wmin[j] *= s1
                wmax[j] *= s2
            end
            wmin[i] = c1
            wmax[i] = c2

            rnk += 1
        end

        if rnk < n
            C, τ = LAPACK.tzrzf!(A.factors[1:rnk, :])
            work = vec(C)
        else
            C, τ = A.factors, A.τ
            work = resize!(tmp, n)
        end

        lmul!(adjoint(A.Q), view(B, 1:m, :))
        ldiv!(UpperTriangular(view(C, 1:rnk, 1:rnk)), view(B, 1:rnk, :))

        if rnk < n
            B[rnk+1:n,:] .= zero(T)
            LAPACK.ormrz!('L', T <: Complex ? 'C' : 'T', C, τ, view(B, 1:n, :))
        end

        for j in axes(B, 2)
            for i in 1:n
                work[A.p[i]] = B[i,j]
            end
            for i in 1:n
                B[i,j] = work[i]
            end
        end
    end

    return B, rnk
end

ldiv!(A::QRPivoted{T,<:StridedMatrix}, B::AbstractVector{T}) where {T<:BlasFloat} =
    vec(ldiv!(A, reshape(B, length(B), 1)))
ldiv!(A::QRPivoted{T,<:StridedMatrix}, B::AbstractMatrix{T}) where {T<:BlasFloat} =
    ldiv!(A, B, min(size(A)...)*eps(real(T)))[1]

function _wide_qr_ldiv!(A::QR{T}, B::AbstractMatrix{T}) where T
    m, n = size(A)
    minmn = min(m,n)
    mB, nB = size(B)
    lmul!(adjoint(A.Q), view(B, 1:m, :))
    R = A.R # makes a copy, used as a buffer below
    @inbounds begin
        if n > m # minimum norm solution
            τ = zeros(T,m)
            for k = m:-1:1 # Trapezoid to triangular by elementary operation
                x = view(R, k, [k; m + 1:n])
                τk = reflector!(x)
                τ[k] = conj(τk)
                for i = 1:k - 1
                    vRi = R[i,k]
                    for j = m + 1:n
                        vRi += R[i,j]*x[j - m + 1]'
                    end
                    vRi *= τk
                    R[i,k] -= vRi
                    for j = m + 1:n
                        R[i,j] -= vRi*x[j - m + 1]
                    end
                end
            end
        end
        ldiv!(UpperTriangular(view(R, :, 1:minmn)), view(B, 1:minmn, :))
        if n > m # Apply elementary transformation to solution
            B[m + 1:mB,1:nB] .= zero(T)
            for j = 1:nB
                for k = 1:m
                    vBj = B[k,j]'
                    for i = m + 1:n
                        vBj += B[i,j]'*R[k,i]'
                    end
                    vBj *= τ[k]
                    B[k,j] -= vBj'
                    for i = m + 1:n
                        B[i,j] -= R[k,i]'*vBj'
                    end
                end
            end
        end
    end
    return B
end


function ldiv!(A::QR{T}, B::AbstractMatrix{T}) where T
    m, n = size(A)
    m < n && return _wide_qr_ldiv!(A, B)

    lmul!(adjoint(A.Q), view(B, 1:m, :))
    R = A.factors
    ldiv!(UpperTriangular(view(R,1:n,:)), view(B, 1:n, :))
    return B
end
function ldiv!(A::QR, B::AbstractVector)
    ldiv!(A, reshape(B, length(B), 1))
    return B
end

function ldiv!(A::QRPivoted, b::AbstractVector)
    ldiv!(QR(A.factors,A.τ), b)
    b[1:size(A.factors, 2)] = view(b, 1:size(A.factors, 2))[invperm(A.jpvt)]
    b
end
function ldiv!(A::QRPivoted, B::AbstractMatrix)
    ldiv!(QR(A.factors, A.τ), B)
    B[1:size(A.factors, 2),:] = view(B, 1:size(A.factors, 2), :)[invperm(A.jpvt),:]
    B
end

function _apply_permutation!(F::QRPivoted, B::AbstractVecOrMat)
    # Apply permutation but only to the top part of the solution vector since
    # it's padded with zeros for underdetermined problems
    B[1:length(F.p), :] = B[F.p, :]
    return B
end
_apply_permutation!(::Factorization, B::AbstractVecOrMat) = B

function ldiv!(Fadj::AdjointFactorization{<:Any,<:Union{QR,QRCompactWY,QRPivoted}}, B::AbstractVecOrMat)
    require_one_based_indexing(B)
    m, n = size(Fadj)

    # We don't allow solutions overdetermined systems
    if m > n
        throw(DimensionMismatch("overdetermined systems are not supported"))
    end
    if n != size(B, 1)
        throw(DimensionMismatch("inputs should have the same number of rows"))
    end
    F = parent(Fadj)

    B = _apply_permutation!(F, B)

    # For underdetermined system, the triangular solve should only be applied to the top
    # part of B that contains the rhs. For square problems, the view corresponds to B itself
    ldiv!(LowerTriangular(adjoint(F.R)), view(B, 1:size(F.R, 2), :))
    lmul!(F.Q, B)

    return B
end

# With a real lhs and complex rhs with the same precision, we can reinterpret the complex
# rhs as a real rhs with twice the number of columns.

# convenience methods to compute the return size correctly for vectors and matrices
_ret_size(A::Factorization, b::AbstractVector) = (max(size(A, 2), length(b)),)
_ret_size(A::Factorization, B::AbstractMatrix) = (max(size(A, 2), size(B, 1)), size(B, 2))

function (\)(A::Union{QR{T},QRCompactWY{T},QRPivoted{T}}, BIn::VecOrMat{Complex{T}}) where T<:BlasReal
    require_one_based_indexing(BIn)
    m, n = size(A)
    m == size(BIn, 1) || throw(DimensionMismatch("left hand side has $m rows, but right hand side has $(size(BIn,1)) rows"))

# |z1|z3|  reinterpret  |x1|x2|x3|x4|  transpose  |x1|y1|  reshape  |x1|y1|x3|y3|
# |z2|z4|      ->       |y1|y2|y3|y4|     ->      |x2|y2|     ->    |x2|y2|x4|y4|
#                                                 |x3|y3|
#                                                 |x4|y4|
    B = reshape(copy(transpose(reinterpret(T, reshape(BIn, (1, length(BIn)))))), size(BIn, 1), 2*size(BIn, 2))

    X = _zeros(T, B, n)
    X[1:size(B, 1), :] = B

    ldiv!(A, X)

# |z1|z3|  reinterpret  |x1|x2|x3|x4|  transpose  |x1|y1|  reshape  |x1|y1|x3|y3|
# |z2|z4|      <-       |y1|y2|y3|y4|     <-      |x2|y2|     <-    |x2|y2|x4|y4|
#                                                 |x3|y3|
#                                                 |x4|y4|
    XX = reshape(collect(reinterpret(Complex{T}, copy(transpose(reshape(X, div(length(X), 2), 2))))), _ret_size(A, BIn))
    return _cut_B(XX, 1:n)
end

##TODO:  Add methods for rank(A::QRP{T}) and adjust the (\) method accordingly
##       Add rcond methods for Cholesky, LU, QR and QRP types
## Lower priority: Add LQ, QL and RQ factorizations

# FIXME! Should add balancing option through xgebal
s   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LinearAlgebra/src/lq.jlk      # This file is a part of Julia. License is MIT: https://julialang.org/license

# LQ Factorizations
"""
    LQ <: Factorization

Matrix factorization type of the `LQ` factorization of a matrix `A`. The `LQ`
decomposition is the [`QR`](@ref) decomposition of `transpose(A)`. This is the return
type of [`lq`](@ref), the corresponding matrix factorization function.

If `S::LQ` is the factorization object, the lower triangular component can be
obtained via `S.L`, and the orthogonal/unitary component via `S.Q`, such that
`A ≈ S.L*S.Q`.

Iterating the decomposition produces the components `S.L` and `S.Q`.

# Examples
```jldoctest
julia> A = [5. 7.; -2. -4.]
2×2 Matrix{Float64}:
  5.0   7.0
 -2.0  -4.0

julia> S = lq(A)
LQ{Float64, Matrix{Float64}, Vector{Float64}}
L factor:
2×2 Matrix{Float64}:
 -8.60233   0.0
  4.41741  -0.697486
Q factor: 2×2 LinearAlgebra.LQPackedQ{Float64, Matrix{Float64}, Vector{Float64}}

julia> S.L * S.Q
2×2 Matrix{Float64}:
  5.0   7.0
 -2.0  -4.0

julia> l, q = S; # destructuring via iteration

julia> l == S.L &&  q == S.Q
true
```
"""
struct LQ{T,S<:AbstractMatrix{T},C<:AbstractVector{T}} <: Factorization{T}
    factors::S
    τ::C

    function LQ{T,S,C}(factors, τ) where {T,S<:AbstractMatrix{T},C<:AbstractVector{T}}
        require_one_based_indexing(factors)
        new{T,S,C}(factors, τ)
    end
end
LQ(factors::AbstractMatrix{T}, τ::AbstractVector{T}) where {T} =
    LQ{T,typeof(factors),typeof(τ)}(factors, τ)
LQ{T}(factors::AbstractMatrix, τ::AbstractVector) where {T} =
    LQ(convert(AbstractMatrix{T}, factors), convert(AbstractVector{T}, τ))
# backwards-compatible constructors (remove with Julia 2.0)
@deprecate(LQ{T,S}(factors::AbstractMatrix{T}, τ::AbstractVector{T}) where {T,S},
           LQ{T,S,typeof(τ)}(factors, τ), false)

# iteration for destructuring into components
Base.iterate(S::LQ) = (S.L, Val(:Q))
Base.iterate(S::LQ, ::Val{:Q}) = (S.Q, Val(:done))
Base.iterate(S::LQ, ::Val{:done}) = nothing

"""
    lq!(A) -> LQ

Compute the [`LQ`](@ref) factorization of `A`, using the input
matrix as a workspace. See also [`lq`](@ref).
"""
lq!(A::StridedMatrix{<:BlasFloat}) = LQ(LAPACK.gelqf!(A)...)

"""
    lq(A) -> S::LQ

Compute the LQ decomposition of `A`. The decomposition's lower triangular
component can be obtained from the [`LQ`](@ref) object `S` via `S.L`, and the
orthogonal/unitary component via `S.Q`, such that `A ≈ S.L*S.Q`.

Iterating the decomposition produces the components `S.L` and `S.Q`.

The LQ decomposition is the QR decomposition of `transpose(A)`, and it is useful
in order to compute the minimum-norm solution `lq(A) \\ b` to an underdetermined
system of equations (`A` has more columns than rows, but has full row rank).

# Examples
```jldoctest
julia> A = [5. 7.; -2. -4.]
2×2 Matrix{Float64}:
  5.0   7.0
 -2.0  -4.0

julia> S = lq(A)
LQ{Float64, Matrix{Float64}, Vector{Float64}}
L factor:
2×2 Matrix{Float64}:
 -8.60233   0.0
  4.41741  -0.697486
Q factor: 2×2 LinearAlgebra.LQPackedQ{Float64, Matrix{Float64}, Vector{Float64}}

julia> S.L * S.Q
2×2 Matrix{Float64}:
  5.0   7.0
 -2.0  -4.0

julia> l, q = S; # destructuring via iteration

julia> l == S.L &&  q == S.Q
true
```
"""
lq(A::AbstractMatrix{T}) where {T} = lq!(copy_similar(A, lq_eltype(T)))
lq(x::Number) = lq!(fill(convert(lq_eltype(typeof(x)), x), 1, 1))

lq_eltype(::Type{T}) where {T} = typeof(zero(T) / sqrt(abs2(one(T))))

copy(A::LQ) = LQ(copy(A.factors), copy(A.τ))

LQ{T}(A::LQ) where {T} = LQ(convert(AbstractMatrix{T}, A.factors), convert(Vector{T}, A.τ))
Factorization{T}(A::LQ) where {T} = LQ{T}(A)

AbstractMatrix(A::LQ) = A.L*A.Q
AbstractArray(A::LQ) = AbstractMatrix(A)
Matrix(A::LQ) = Array(AbstractArray(A))
Array(A::LQ) = Matrix(A)

transpose(F::LQ{<:Real}) = F'
transpose(::LQ) =
    throw(ArgumentError("transpose of LQ decomposition is not supported, consider using adjoint"))

Base.copy(F::AdjointFactorization{T,<:LQ{T}}) where {T} =
    QR{T,typeof(F.parent.factors),typeof(F.parent.τ)}(copy(adjoint(F.parent.factors)), copy(F.parent.τ))

function getproperty(F::LQ, d::Symbol)
    m, n = size(F)
    if d === :L
        return tril!(getfield(F, :factors)[1:m, 1:min(m,n)])
    elseif d === :Q
        return LQPackedQ(getfield(F, :factors), getfield(F, :τ))
    else
        return getfield(F, d)
    end
end

Base.propertynames(F::LQ, private::Bool=false) =
    (:L, :Q, (private ? fieldnames(typeof(F)) : ())...)

# getindex(A::LQPackedQ, i::Integer, j::Integer) =
#     lmul!(A, setindex!(zeros(eltype(A), size(A, 2)), 1, j))[i]

function show(io::IO, mime::MIME{Symbol("text/plain")}, F::LQ)
    summary(io, F); println(io)
    println(io, "L factor:")
    show(io, mime, F.L)
    print(io, "\nQ factor: ")
    show(io, mime, F.Q)
end

size(F::LQ, dim::Integer) = size(getfield(F, :factors), dim)
size(F::LQ)               = size(getfield(F, :factors))

## Multiplication by LQ
function lmul!(A::LQ, B::AbstractVecOrMat)
    lmul!(LowerTriangular(A.L), view(lmul!(A.Q, B), 1:size(A,1), axes(B,2)))
    return B
end
function *(A::LQ{TA}, B::AbstractVecOrMat{TB}) where {TA,TB}
    TAB = promote_type(TA, TB)
    _cut_B(lmul!(convert(Factorization{TAB}, A), copy_similar(B, TAB)), 1:size(A,1))
end

# With a real lhs and complex rhs with the same precision, we can reinterpret
# the complex rhs as a real rhs with twice the number of columns
function (\)(F::LQ{T}, B::VecOrMat{Complex{T}}) where T<:BlasReal
    require_one_based_indexing(B)
    X = zeros(T, size(F,2), 2*size(B,2))
    X[1:size(B,1), 1:size(B,2)] .= real.(B)
    X[1:size(B,1), size(B,2)+1:size(X,2)] .= imag.(B)
    ldiv!(F, X)
    return reshape(copy(reinterpret(Complex{T}, copy(transpose(reshape(X, div(length(X), 2), 2))))),
                           isa(B, AbstractVector) ? (size(F,2),) : (size(F,2), size(B,2)))
end


function ldiv!(A::LQ, B::AbstractVecOrMat)
    require_one_based_indexing(B)
    m, n = size(A)
    m ≤ n || throw(DimensionMismatch("LQ solver does not support overdetermined systems (more rows than columns)"))

    ldiv!(LowerTriangular(A.L), view(B, 1:size(A,1), axes(B,2)))
    return lmul!(adjoint(A.Q), B)
end

function ldiv!(Fadj::AdjointFactorization{<:Any,<:LQ}, B::AbstractVecOrMat)
    require_one_based_indexing(B)
    m, n = size(Fadj)
    m >= n || throw(DimensionMismatch("solver does not support underdetermined systems (more columns than rows)"))

    F = parent(Fadj)
    lmul!(F.Q, B)
    ldiv!(UpperTriangular(adjoint(F.L)), view(B, 1:size(F,1), axes(B,2)))
    return B
end
{   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LinearAlgebra/src/hessenberg.jlqU      # This file is a part of Julia. License is MIT: https://julialang.org/license

######################################################################################
# Upper-Hessenberg matrices H+μI, analogous to the UpperTriangular type

"""
    UpperHessenberg(A::AbstractMatrix)

Construct an `UpperHessenberg` view of the matrix `A`.
Entries of `A` below the first subdiagonal are ignored.

!!! compat "Julia 1.3"
    This type was added in Julia 1.3.

Efficient algorithms are implemented for `H \\ b`, `det(H)`, and similar.

See also the [`hessenberg`](@ref) function to factor any matrix into a similar
upper-Hessenberg matrix.

If `F::Hessenberg` is the factorization object, the unitary matrix can be accessed
with `F.Q` and the Hessenberg matrix with `F.H`. When `Q` is extracted, the resulting
type is the `HessenbergQ` object, and may be converted to a regular matrix with
[`convert(Array, _)`](@ref) (or `Array(_)` for short).

Iterating the decomposition produces the factors `F.Q` and `F.H`.

# Examples
```jldoctest
julia> A = [1 2 3 4; 5 6 7 8; 9 10 11 12; 13 14 15 16]
4×4 Matrix{Int64}:
  1   2   3   4
  5   6   7   8
  9  10  11  12
 13  14  15  16

julia> UpperHessenberg(A)
4×4 UpperHessenberg{Int64, Matrix{Int64}}:
 1   2   3   4
 5   6   7   8
 ⋅  10  11  12
 ⋅   ⋅  15  16
```
"""
struct UpperHessenberg{T,S<:AbstractMatrix{T}} <: AbstractMatrix{T}
    data::S

    function UpperHessenberg{T,S}(data) where {T,S<:AbstractMatrix{T}}
        require_one_based_indexing(data)
        new{T,S}(data)
    end
end
UpperHessenberg(H::UpperHessenberg) = H
UpperHessenberg{T}(A::AbstractMatrix) where {T} = UpperHessenberg(convert(AbstractMatrix{T}, A))
UpperHessenberg{T}(H::UpperHessenberg) where {T} = UpperHessenberg{T}(H.data)
UpperHessenberg(A::AbstractMatrix) = UpperHessenberg{eltype(A),typeof(A)}(A)
Matrix(H::UpperHessenberg{T}) where {T} = Matrix{T}(H)
Array(H::UpperHessenberg) = Matrix(H)
size(H::UpperHessenberg, d) = size(H.data, d)
size(H::UpperHessenberg) = size(H.data)
parent(H::UpperHessenberg) = H.data

# similar behaves like UpperTriangular
similar(H::UpperHessenberg, ::Type{T}) where {T} = UpperHessenberg(similar(H.data, T))
similar(H::UpperHessenberg, ::Type{T}, dims::Dims{N}) where {T,N} = similar(H.data, T, dims)

AbstractMatrix{T}(H::UpperHessenberg) where {T} = UpperHessenberg(AbstractMatrix{T}(H.data))

copy(H::UpperHessenberg) = UpperHessenberg(copy(H.data))
real(H::UpperHessenberg{<:Real}) = H
real(H::UpperHessenberg{<:Complex}) = UpperHessenberg(triu!(real(H.data),-1))
imag(H::UpperHessenberg) = UpperHessenberg(triu!(imag(H.data),-1))

function istriu(A::UpperHessenberg, k::Integer=0)
    k <= -1 && return true
    return _istriu(A, k)
end

function Matrix{T}(H::UpperHessenberg) where T
    m,n = size(H)
    return triu!(copyto!(Matrix{T}(undef, m, n), H.data), -1)
end

Base.isassigned(H::UpperHessenberg, i::Int, j::Int) =
    i <= j+1 ? isassigned(H.data, i, j) : true

getindex(H::UpperHessenberg{T}, i::Integer, j::Integer) where {T} =
    i <= j+1 ? convert(T, H.data[i,j]) : zero(T)

function setindex!(A::UpperHessenberg, x, i::Integer, j::Integer)
    if i > j+1
        x == 0 || throw(ArgumentError("cannot set index in the lower triangular part " *
            "($i, $j) of an UpperHessenberg matrix to a nonzero value ($x)"))
    else
        A.data[i,j] = x
    end
    return A
end

function Base.replace_in_print_matrix(A::UpperHessenberg, i::Integer, j::Integer, s::AbstractString)
    return i <= j+1 ? s : Base.replace_with_centered_mark(s)
end

Base.copy(A::Adjoint{<:Any,<:UpperHessenberg}) = tril!(adjoint!(similar(A.parent.data), A.parent.data), 1)
Base.copy(A::Transpose{<:Any,<:UpperHessenberg}) = tril!(transpose!(similar(A.parent.data), A.parent.data), 1)

-(A::UpperHessenberg) = UpperHessenberg(-A.data)
rmul!(H::UpperHessenberg, x::Number) = (rmul!(H.data, x); H)
lmul!(x::Number, H::UpperHessenberg) = (lmul!(x, H.data); H)

fillstored!(H::UpperHessenberg, x) = (fillband!(H.data, x, -1, size(H,2)-1); H)

+(A::UpperHessenberg, B::UpperHessenberg) = UpperHessenberg(A.data+B.data)
-(A::UpperHessenberg, B::UpperHessenberg) = UpperHessenberg(A.data-B.data)

for T = (:UniformScaling, :Diagonal, :Bidiagonal, :Tridiagonal, :SymTridiagonal,
         :UpperTriangular, :UnitUpperTriangular)
    for op = (:+, :-)
        @eval begin
            $op(H::UpperHessenberg, x::$T) = UpperHessenberg($op(H.data, x))
            $op(x::$T, H::UpperHessenberg) = UpperHessenberg($op(x, H.data))
        end
    end
end

for T = (:Number, :UniformScaling, :Diagonal)
    @eval begin
        *(H::UpperHessenberg, x::$T) = UpperHessenberg(H.data * x)
        *(x::$T, H::UpperHessenberg) = UpperHessenberg(x * H.data)
        /(H::UpperHessenberg, x::$T) = UpperHessenberg(H.data / x)
        \(x::$T, H::UpperHessenberg) = UpperHessenberg(x \ H.data)
    end
end

function *(H::UpperHessenberg, U::UpperOrUnitUpperTriangular)
    HH = mul!(_initarray(*, eltype(H), eltype(U), H), H, U)
    UpperHessenberg(HH)
end
function *(U::UpperOrUnitUpperTriangular, H::UpperHessenberg)
    HH = mul!(_initarray(*, eltype(U), eltype(H), H), U, H)
    UpperHessenberg(HH)
end

function /(H::UpperHessenberg, U::UpperTriangular)
    HH = _rdiv!(_initarray(/, eltype(H), eltype(U), H), H, U)
    UpperHessenberg(HH)
end
function /(H::UpperHessenberg, U::UnitUpperTriangular)
    HH = _rdiv!(_initarray(/, eltype(H), eltype(U), H), H, U)
    UpperHessenberg(HH)
end

function \(U::UpperTriangular, H::UpperHessenberg)
    HH = ldiv!(_initarray(\, eltype(U), eltype(H), H), U, H)
    UpperHessenberg(HH)
end
function \(U::UnitUpperTriangular, H::UpperHessenberg)
    HH = ldiv!(_initarray(\, eltype(U), eltype(H), H), U, H)
    UpperHessenberg(HH)
end

# Solving (H+µI)x = b: we can do this in O(m²) time and O(m) memory
# (in-place in x) by the RQ algorithm from:
#
#    G. Henry, "The shifted Hessenberg system solve computation," Tech. Rep. 94–163,
#    Center for Appl. Math., Cornell University (1994).
#
# as reviewed in
#
#    C. Beattie et al., "A note on shifted Hessenberg systems and frequency
#    response computation," ACM Trans. Math. Soft. 38, pp. 12:6–12:16 (2011)
#
# (Note, however, that there is apparently a typo in Algorithm 1 of the
#  Beattie paper: the Givens rotation uses u(k), not H(k,k) - σ.)
#
# Essentially, it works by doing a Givens RQ factorization of H+µI from
# right to left, and doing backsubstitution *simultaneously*.

# solve (H+μI)X = B, storing result in B
function ldiv!(F::UpperHessenberg, B::AbstractVecOrMat; shift::Number=false)
    checksquare(F)
    m = size(F,1)
    m != size(B,1) && throw(DimensionMismatch("wrong right-hand-side # rows != $m"))
    require_one_based_indexing(B)
    n = size(B,2)
    H = F.data
    μ = shift
    u = Vector{typeof(zero(eltype(H))+μ)}(undef, m) # for last rotated col of H-μI
    copyto!(u, 1, H, m*(m-1)+1, m) # u .= H[:,m]
    u[m] += μ
    X = B # not a copy, just rename to match paper
    cs = Vector{Tuple{real(eltype(u)),eltype(u)}}(undef, length(u)) # store Givens rotations
    @inbounds for k = m:-1:2
        c, s, ρ = givensAlgorithm(u[k], H[k,k-1])
        cs[k] = (c, s)
        for i = 1:n
            X[k,i] /= ρ
            t₁ = s * X[k,i]; t₂ = c * X[k,i]
            @simd for j = 1:k-2
                X[j,i] -= u[j]*t₂ + H[j,k-1]*t₁
            end
            X[k-1,i] -= u[k-1]*t₂ + (H[k-1,k-1] + μ) * t₁
        end
        @simd for j = 1:k-2
            u[j] = H[j,k-1]*c - u[j]*s'
        end
        u[k-1] = (H[k-1,k-1] + μ) * c - u[k-1]*s'
    end
    for i = 1:n
        τ₁ = X[1,i] / u[1]
        @inbounds for j = 2:m
            τ₂ = X[j,i]
            c, s = cs[j]
            X[j-1,i] = c*τ₁ + s*τ₂
            τ₁ = c*τ₂ - s'τ₁
        end
        X[m,i] = τ₁
    end
    return X
end

# solve X(H+μI) = B, storing result in B
#
# Note: this can be derived from the Henry (1994) algorithm
# by transformation to F(Hᵀ+µI)F FXᵀ = FBᵀ, where
# F is the permutation matrix that reverses the order
# of rows/cols.  Essentially, we take the ldiv! algorithm,
# swap indices of H and X to transpose, and reverse the
# order of the H indices (or the order of the loops).
function rdiv!(B::AbstractMatrix, F::UpperHessenberg; shift::Number=false)
    checksquare(F)
    m = size(F,1)
    m != size(B,2) && throw(DimensionMismatch("wrong right-hand-side # cols != $m"))
    require_one_based_indexing(B)
    n = size(B,1)
    H = F.data
    μ = shift
    u = Vector{typeof(zero(eltype(H))+μ)}(undef, m) # for last rotated row of H-μI
    u .= @view H[1,:]
    u[1] += μ
    X = B # not a copy, just rename to match paper
    cs = Vector{Tuple{real(eltype(u)),eltype(u)}}(undef, length(u)) # store Givens rotations
    @inbounds for k = 1:m-1
        c, s, ρ = givensAlgorithm(u[k], H[k+1,k])
        cs[k] = (c, s)
        for i = 1:n
            X[i,k] /= ρ
            t₁ = s * X[i,k]; t₂ = c * X[i,k]
            @simd for j = k+2:m
                X[i,j] -= u[j]*t₂ + H[k+1,j]*t₁
            end
            X[i,k+1] -= u[k+1]*t₂ + (H[k+1,k+1] + μ) * t₁
        end
        @simd for j = k+2:m
            u[j] = H[k+1,j]*c - u[j]*s'
        end
        u[k+1] = (H[k+1,k+1] + μ) * c - u[k+1]*s'
    end
    for i = 1:n
        τ₁ = X[i,m] / u[m]
        @inbounds for j = m-1:-1:1
            τ₂ = X[i,j]
            c, s = cs[j]
            X[i,j+1] = c*τ₁ + s*τ₂
            τ₁ = c*τ₂ - s'τ₁
        end
        X[i,1] = τ₁
    end
    return X
end

# Hessenberg-matrix determinant formula for H+μI based on:
#
#    N. D. Cahill, J. R. D’Errico, D. A. Narayan, and J. Y. Narayan, "Fibonacci determinants,"
#    College Math. J. 33, pp. 221-225 (2003).
#
# as reviewed in Theorem 2.1 of:
#
#    K. Kaygisiz and A. Sahin, "Determinant and permanent of Hessenberg matrix and generalized Lucas polynomials,"
#    arXiv:1111.4067 (2011).
#
# Cost is O(m²) with O(m) storage.
function det(F::UpperHessenberg; shift::Number=false)
    checksquare(F)
    H = F.data
    m = size(H,1)
    μ = shift
    m == 0 && return one(zero(eltype(H)) + μ)
    determinant = H[1,1] + μ
    prevdeterminant = one(determinant)
    m == 1 && return determinant
    prods = Vector{typeof(determinant)}(undef, m-1) # temporary storage for partial products
    @inbounds for n = 2:m
        prods[n-1] = prevdeterminant
        prevdeterminant = determinant
        determinant *= H[n,n] + μ
        h = H[n,n-1]
        @simd for r = n-1:-2:2
            determinant -= H[r,n] * (prods[r] *= h) - H[r-1,n] * (prods[r-1] *= h)
        end
        if iseven(n)
            determinant -= H[1,n] * (prods[1] *= h)
        end
    end
    return determinant
end

# O(m²) log-determinant based on first doing Givens RQ to put H+μI into upper-triangular form and then
# taking the product of the diagonal entries.   The trick is that we only need O(m) temporary storage,
# because we don't need to store the whole Givens-rotated matrix, only the most recent column.
# We do RQ (column rotations) rather than QR (row rotations) for more consecutive memory access.
# (We could also use it for det instead of the Cahill algorithm above.  Cahill is slightly faster
#  for very small matrices where you are likely to use det, and also uses only ± and * so it can
#  be applied to Hessenberg matrices over other number fields.)
function logabsdet(F::UpperHessenberg; shift::Number=false)
    checksquare(F)
    H = F.data
    m = size(H,1)
    μ = shift
    P = one(zero(eltype(H)) + μ)
    logdeterminant = zero(real(P))
    m == 0 && return (logdeterminant, P)
    g = Vector{typeof(P)}(undef, m) # below, g is the k-th col of Givens-rotated H+μI matrix
    copyto!(g, 1, H, m*(m-1)+1, m) # g .= H[:,m]
    g[m] += μ
    @inbounds for k = m:-1:2
        c, s, ρ = givensAlgorithm(g[k], H[k,k-1])
        logdeterminant += log(abs(ρ))
        P *= sign(ρ)
        g[k-1] = c*(H[k-1,k-1] + μ) - s'*g[k-1]
        @simd for j = 1:k-2
            g[j] = c*H[j,k-1] - s'*g[j]
        end
    end
    logdeterminant += log(abs(g[1]))
    P *= sign(g[1])
    return (logdeterminant, P)
end

function dot(x::AbstractVector, H::UpperHessenberg, y::AbstractVector)
    require_one_based_indexing(x, y)
    m = size(H, 1)
    (length(x) == m == length(y)) || throw(DimensionMismatch())
    if iszero(m)
        return dot(zero(eltype(x)), zero(eltype(H)), zero(eltype(y)))
    end
    x₁ = x[1]
    r = dot(x₁, H[1,1], y[1])
    r += dot(x[2], H[2,1], y[1])
    @inbounds for j in 2:m-1
        yj = y[j]
        if !iszero(yj)
            temp = adjoint(H[1,j]) * x₁
            @simd for i in 2:j+1
                temp += adjoint(H[i,j]) * x[i]
            end
            r += dot(temp, yj)
        end
    end
    ym = y[m]
    if !iszero(ym)
        temp = adjoint(H[1,m]) * x₁
        @simd for i in 2:m
            temp += adjoint(H[i,m]) * x[i]
        end
        r += dot(temp, ym)
    end
    return r
end

######################################################################################
# Hessenberg factorizations Q(H+μI)Q' of A+μI:

"""
    Hessenberg <: Factorization

A `Hessenberg` object represents the Hessenberg factorization `QHQ'` of a square
matrix, or a shift `Q(H+μI)Q'` thereof, which is produced by the [`hessenberg`](@ref) function.
"""
struct Hessenberg{T,SH<:AbstractMatrix,S<:AbstractMatrix,W<:AbstractVector,V<:Number} <: Factorization{T}
    H::SH # UpperHessenberg or SymTridiagonal
    uplo::Char
    factors::S # reflector data in uplo triangle, may share data with H
    τ::W # more Q (reflector) data
    μ::V # diagonal shift for copy-free (F+μI) \ b solves and similar
end
Hessenberg(factors::AbstractMatrix, τ::AbstractVector, H::AbstractMatrix=UpperHessenberg(factors), uplo::AbstractChar='L'; μ::Number=false) =
    Hessenberg{typeof(zero(eltype(factors))+μ),typeof(H),typeof(factors),typeof(τ),typeof(μ)}(H, uplo, factors, τ, μ)
Hessenberg(F::Hessenberg) = F
Hessenberg(F::Hessenberg, μ::Number) = Hessenberg(F.factors, F.τ, F.H, F.uplo; μ=μ)

copy(F::Hessenberg{<:Any,<:UpperHessenberg}) = Hessenberg(copy(F.factors), copy(F.τ); μ=F.μ)
copy(F::Hessenberg{<:Any,<:SymTridiagonal}) = Hessenberg(copy(F.factors), copy(F.τ), copy(F.H), F.uplo; μ=F.μ)
size(F::Hessenberg, d::Integer) = size(F.H, d)
size(F::Hessenberg) = size(F.H)

transpose(F::Hessenberg{<:Real}) = F'
transpose(::Hessenberg) =
    throw(ArgumentError("transpose of Hessenberg decomposition is not supported, consider using adjoint"))

# iteration for destructuring into components
Base.iterate(S::Hessenberg) = (S.Q, Val(:H))
Base.iterate(S::Hessenberg, ::Val{:H}) = (S.H, Val(:μ))
Base.iterate(S::Hessenberg, ::Val{:μ}) = (S.μ, Val(:done))
Base.iterate(S::Hessenberg, ::Val{:done}) = nothing

hessenberg!(A::StridedMatrix{<:BlasFloat}) = Hessenberg(LAPACK.gehrd!(A)...)

function hessenberg!(A::Union{Symmetric{<:BlasReal,<:StridedMatrix},Hermitian{<:BlasFloat,<:StridedMatrix}})
    factors, τ, d, e = LAPACK.hetrd!(A.uplo, A.data)
    return Hessenberg(factors, τ, SymTridiagonal(d, e), A.uplo)
end

"""
    hessenberg!(A) -> Hessenberg

`hessenberg!` is the same as [`hessenberg`](@ref), but saves space by overwriting
the input `A`, instead of creating a copy.
"""
hessenberg!(A::AbstractMatrix)

"""
    hessenberg(A) -> Hessenberg

Compute the Hessenberg decomposition of `A` and return a `Hessenberg` object. If `F` is the
factorization object, the unitary matrix can be accessed with `F.Q` (of type `LinearAlgebra.HessenbergQ`)
and the Hessenberg matrix with `F.H` (of type [`UpperHessenberg`](@ref)), either of
which may be converted to a regular matrix with `Matrix(F.H)` or `Matrix(F.Q)`.

If `A` is [`Hermitian`](@ref) or real-[`Symmetric`](@ref), then the Hessenberg
decomposition produces a real-symmetric tridiagonal matrix and `F.H` is of type
[`SymTridiagonal`](@ref).

Note that the shifted factorization `A+μI = Q (H+μI) Q'` can be
constructed efficiently by `F + μ*I` using the [`UniformScaling`](@ref)
object [`I`](@ref), which creates a new `Hessenberg` object with shared storage
and a modified shift.   The shift of a given `F` is obtained by `F.μ`.
This is useful because multiple shifted solves `(F + μ*I) \\ b`
(for different `μ` and/or `b`) can be performed efficiently once `F` is created.

Iterating the decomposition produces the factors `F.Q, F.H, F.μ`.

# Examples
```jldoctest
julia> A = [4. 9. 7.; 4. 4. 1.; 4. 3. 2.]
3×3 Matrix{Float64}:
 4.0  9.0  7.0
 4.0  4.0  1.0
 4.0  3.0  2.0

julia> F = hessenberg(A)
Hessenberg{Float64, UpperHessenberg{Float64, Matrix{Float64}}, Matrix{Float64}, Vector{Float64}, Bool}
Q factor: 3×3 LinearAlgebra.HessenbergQ{Float64, Matrix{Float64}, Vector{Float64}, false}
H factor:
3×3 UpperHessenberg{Float64, Matrix{Float64}}:
  4.0      -11.3137       -1.41421
 -5.65685    5.0           2.0
   ⋅        -8.88178e-16   1.0

julia> F.Q * F.H * F.Q'
3×3 Matrix{Float64}:
 4.0  9.0  7.0
 4.0  4.0  1.0
 4.0  3.0  2.0

julia> q, h = F; # destructuring via iteration

julia> q == F.Q && h == F.H
true
```
"""
hessenberg(A::AbstractMatrix{T}) where T =
    hessenberg!(eigencopy_oftype(A, eigtype(T)))

function show(io::IO, mime::MIME"text/plain", F::Hessenberg)
    summary(io, F)
    if !iszero(F.μ)
        print("\nwith shift μI for μ = ", F.μ)
    end
    print(io, "\nQ factor: ")
    show(io, mime, F.Q)
    println(io, "\nH factor:")
    show(io, mime, F.H)
end

function getproperty(F::Hessenberg, d::Symbol)
    d === :Q && return HessenbergQ(F)
    return getfield(F, d)
end

Base.propertynames(F::Hessenberg, private::Bool=false) =
    (:Q, :H, :μ, (private ? (:τ, :factors, :uplo) : ())...)

AbstractArray(F::Hessenberg) = AbstractMatrix(F)
Matrix(F::Hessenberg) = Array(AbstractArray(F))
Array(F::Hessenberg) = Matrix(F)
function AbstractMatrix(F::Hessenberg)
    Q = F.Q
    A = rmul!(lmul!(Q, Matrix{eltype(Q)}(F.H)), Q')
    μ = F.μ
    if iszero(μ)
        return A
    elseif typeof(zero(eltype(A))+μ) <: eltype(A) # can shift A in-place
        for i = 1:size(A,1)
            @inbounds A[i,i] += μ
        end
        return A
    else
        return A + μ*I # allocate another matrix, e.g. if A is real and μ is complex
    end
end

# multiply x by the entries of M in the upper-k triangle, which contains
# the entries of the upper-Hessenberg matrix H for k=-1
function rmul_triu!(M::AbstractMatrix, x, k::Integer=0)
    require_one_based_indexing(M)
    m, n = size(M)
    for j = 1:n, i = 1:min(j-k,m)
        @inbounds M[i,j] *= x
    end
    return M
end
function lmul_triu!(x, M::AbstractMatrix, k::Integer=0)
    require_one_based_indexing(M)
    m, n = size(M)
    for j = 1:n, i = 1:min(j-k,m)
        @inbounds M[i,j] = x * M[i,j]
    end
    return M
end

# when H is UpperHessenberg, it shares data with F.factors
# multiply Hessenberg by scalar (but don't modify lower triangle of F.H.data)
rmul!(F::Hessenberg{<:Any,<:UpperHessenberg{T}}, x::T) where {T<:Number} = Hessenberg(rmul_triu!(F.factors, x, -1), F.τ; μ=F.μ*x)
lmul!(x::T, F::Hessenberg{<:Any,<:UpperHessenberg{T}}) where {T<:Number} = Hessenberg(lmul_triu!(x, F.factors, -1), F.τ; μ=x*F.μ)

rmul!(F::Hessenberg{<:Any,<:SymTridiagonal{T}}, x::T) where {T<:Number} = Hessenberg(F.factors, F.τ, SymTridiagonal(F.H.dv*x, F.H.ev*x), F.uplo; μ=F.μ*x)
lmul!(x::T, F::Hessenberg{<:Any,<:SymTridiagonal{T}}) where {T<:Number} = Hessenberg(F.factors, F.τ, SymTridiagonal(x*F.H.dv, x*F.H.ev), F.uplo; μ=x*F.μ)

# Promote F * x or x * F.  In general, we don't know how to do promotions
# that would change the element type of F.H, however.
function (*)(F::Hessenberg{<:Any,<:AbstractMatrix{T}}, x::S) where {T,S<:Number}
    TS = typeof(zero(T) * x)
    if TS === T
        return rmul!(copy(F), convert(T, x))
    else
        throw(MethodError(*, (F, x)))
    end
end
function (*)(x::S, F::Hessenberg{<:Any,<:AbstractMatrix{T}}) where {T,S<:Number}
    TS = typeof(zero(T) * x)
    if TS === T
        return lmul!(convert(T, x), copy(F))
    else
        throw(MethodError(*, (x, F)))
    end
end
-(F::Hessenberg) = F * -one(eltype(F.H))

# shift Hessenberg by λI
+(F::Hessenberg, J::UniformScaling) = Hessenberg(F, F.μ + J.λ)
+(J::UniformScaling, F::Hessenberg) = Hessenberg(F, J.λ + F.μ)
-(F::Hessenberg, J::UniformScaling) = Hessenberg(F, F.μ - J.λ)
-(J::UniformScaling, F::Hessenberg) = Hessenberg(-F, J.λ - F.μ)

function ldiv!(F::Hessenberg, B::AbstractVecOrMat)
    Q = F.Q
    if iszero(F.μ)
        return lmul!(Q, ldiv!(F.H, lmul!(Q', B)))
    else
        return lmul!(Q, ldiv!(F.H, lmul!(Q', B); shift=F.μ))
    end
end

function rdiv!(B::AbstractMatrix, F::Hessenberg)
    Q = F.Q
    return rmul!(rdiv!(rmul!(B, Q), F.H; shift=F.μ), Q')
end

# handle case of real H and complex μ — we need to work around the
# fact that we can't multiple a real F.Q by a complex matrix directly in LAPACK
function ldiv!(F::Hessenberg{<:Complex,<:Any,<:AbstractMatrix{<:Real}}, B::AbstractVecOrMat{<:Complex})
    Q = F.Q
    Br = lmul!(Q', real(B))
    Bi = lmul!(Q', imag(B))
    ldiv!(F.H, B .= Complex.(Br,Bi); shift=F.μ)
    Br .= real.(B); Bi .= imag.(B)
    Br = lmul!(Q, Br)
    Bi = lmul!(Q, Bi)
    return B .= Complex.(Br,Bi)
end
function rdiv!(B::AbstractVecOrMat{<:Complex}, F::Hessenberg{<:Complex,<:Any,<:AbstractMatrix{<:Real}})
    Q = F.Q
    Br = rmul!(real(B), Q)
    Bi = rmul!(imag(B), Q)
    rdiv!(B .= Complex.(Br,Bi), F.H; shift=F.μ)
    Br .= real.(B); Bi .= imag.(B)
    Br = rmul!(Br, Q')
    Bi = rmul!(Bi, Q')
    return B .= Complex.(Br,Bi)
end

ldiv!(F::AdjointFactorization{<:Any,<:Hessenberg}, B::AbstractVecOrMat) = rdiv!(B', F')'

det(F::Hessenberg) = det(F.H; shift=F.μ)
logabsdet(F::Hessenberg) = logabsdet(F.H; shift=F.μ)
function logdet(F::Hessenberg)
    d,s = logabsdet(F)
    return d + log(s)
end
z   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LinearAlgebra/src/abstractq.jld      # This file is a part of Julia. License is MIT: https://julialang.org/license

abstract type AbstractQ{T} end

struct AdjointQ{T,S<:AbstractQ{T}} <: AbstractQ{T}
    Q::S
end

parent(adjQ::AdjointQ) = adjQ.Q
eltype(::Type{<:AbstractQ{T}}) where {T} = T
Base.eltypeof(Q::AbstractQ) = eltype(Q)
ndims(::AbstractQ) = 2

# inversion/adjoint/transpose
inv(Q::AbstractQ) = Q'
adjoint(Q::AbstractQ) = AdjointQ(Q)
transpose(Q::AbstractQ{<:Real}) = AdjointQ(Q)
transpose(Q::AbstractQ) = error("transpose not implemented for $(typeof(Q)). Consider using adjoint instead of transpose.")
adjoint(adjQ::AdjointQ) = adjQ.Q

# promotion with AbstractMatrix, at least for equal eltypes
promote_rule(::Type{<:AbstractMatrix{T}}, ::Type{<:AbstractQ{T}}) where {T} =
    (@inline; Union{AbstractMatrix{T},AbstractQ{T}})

# conversion
# the following eltype promotion should be defined for each subtype `QType`
# convert(::Type{AbstractQ{T}}, Q::QType) where {T} = QType{T}(Q)
# and then care has to be taken that
# QType{T}(Q::QType{T}) where T = ...
# is implemented as a no-op

# the following conversion method ensures functionality when the above method is not defined
# (as for HessenbergQ), but no eltype conversion is required either (say, in multiplication)
convert(::Type{AbstractQ{T}}, Q::AbstractQ{T}) where {T} = Q
convert(::Type{AbstractQ{T}}, adjQ::AdjointQ{T}) where {T} = adjQ
convert(::Type{AbstractQ{T}}, adjQ::AdjointQ) where {T} = convert(AbstractQ{T}, adjQ.Q)'

# ... to matrix
collect(Q::AbstractQ) = copyto!(Matrix{eltype(Q)}(undef, size(Q)), Q)
Matrix{T}(Q::AbstractQ) where {T} = convert(Matrix{T}, Q*I) # generic fallback, yields square matrix
Matrix{T}(adjQ::AdjointQ{S}) where {T,S} = convert(Matrix{T}, lmul!(adjQ, Matrix{S}(I, size(adjQ))))
Matrix(Q::AbstractQ{T}) where {T} = Matrix{T}(Q)
Array{T}(Q::AbstractQ) where {T} = Matrix{T}(Q)
Array(Q::AbstractQ) = Matrix(Q)
convert(::Type{T}, Q::AbstractQ) where {T<:AbstractArray} = T(Q)
# legacy
@deprecate(convert(::Type{AbstractMatrix{T}}, Q::AbstractQ) where {T},
    convert(LinearAlgebra.AbstractQ{T}, Q))

function size(Q::AbstractQ, dim::Integer)
    if dim < 1
        throw(BoundsError())
    elseif dim <= 2 # && 1 <= dim
        return size(Q)[dim]
    else # 2 < dim
        return 1
    end
end
size(adjQ::AdjointQ) = reverse(size(adjQ.Q))

# comparison
(==)(Q::AbstractQ, A::AbstractMatrix) = lmul!(Q, Matrix{eltype(Q)}(I, size(A))) == A
(==)(A::AbstractMatrix, Q::AbstractQ) = Q == A
(==)(Q::AbstractQ, P::AbstractQ) = Matrix(Q) == Matrix(P)
isapprox(Q::AbstractQ, A::AbstractMatrix; kwargs...) =
    isapprox(lmul!(Q, Matrix{eltype(Q)}(I, size(A))), A, kwargs...)
isapprox(A::AbstractMatrix, Q::AbstractQ; kwargs...) = isapprox(Q, A, kwargs...)
isapprox(Q::AbstractQ, P::AbstractQ; kwargs...) = isapprox(Matrix(Q), Matrix(P), kwargs...)

# pseudo-array behaviour, required for indexing with `begin` or `end`
axes(Q::AbstractQ) = map(Base.oneto, size(Q))
axes(Q::AbstractQ, d::Integer) = d in (1, 2) ? axes(Q)[d] : Base.OneTo(1)

copymutable(Q::AbstractQ{T}) where {T} = lmul!(Q, Matrix{T}(I, size(Q)))
copy(Q::AbstractQ) = copymutable(Q)

# getindex
@inline function getindex(Q::AbstractQ, inds...)
    @boundscheck Base.checkbounds_indices(Bool, axes(Q), inds) || Base.throw_boundserror(Q, inds)
    return _getindex(Q, inds...)
end
@inline getindex(Q::AbstractQ, ::Colon) = copymutable(Q)[:]
@inline getindex(Q::AbstractQ, ::Colon, ::Colon) = copy(Q)

@inline _getindex(Q::AbstractQ, inds...) = @inbounds copymutable(Q)[inds...]
@inline function _getindex(Q::AbstractQ, ::Colon, J::AbstractVector{<:Integer})
    Y = zeros(eltype(Q), size(Q, 2), length(J))
    @inbounds for (i,j) in enumerate(J)
        Y[j,i] = oneunit(eltype(Q))
    end
    lmul!(Q, Y)
end
@inline _getindex(Q::AbstractQ, I::AbstractVector{Int}, J::AbstractVector{Int}) = @inbounds Q[:,J][I,:]
@inline function _getindex(Q::AbstractQ, ::Colon, j::Int)
    y = zeros(eltype(Q), size(Q, 2))
    y[j] = oneunit(eltype(Q))
    lmul!(Q, y)
end
@inline _getindex(Q::AbstractQ, i::Int, j::Int) = @inbounds Q[:,j][i]

# needed because AbstractQ does not subtype AbstractMatrix
qr(Q::AbstractQ{T}, arg...; kwargs...) where {T} = qr!(Matrix{_qreltype(T)}(Q), arg...; kwargs...)
lq(Q::AbstractQ{T}, arg...; kwargs...) where {T} = lq!(Matrix{lq_eltype(T)}(Q), arg...; kwargs...)
hessenberg(Q::AbstractQ{T}) where {T} = hessenberg!(Matrix{eigtype(T)}(Q))

# needed when used interchangeably with AbstractMatrix (analogous to views of ranges)
view(A::AbstractQ, I...) = getindex(A, I...)

# specialization avoiding the fallback using slow `getindex`
function copyto!(dest::AbstractMatrix, src::AbstractQ)
    copyto!(dest, I)
    lmul!(src, dest)
end
# needed to resolve method ambiguities
function copyto!(dest::PermutedDimsArray{T,2,perm}, src::AbstractQ) where {T,perm}
    if perm == (1, 2)
        copyto!(parent(dest), src)
    else
        @assert perm == (2, 1) # there are no other permutations of two indices
        if T <: Real
            copyto!(parent(dest), I)
            lmul!(src', parent(dest))
        else
            # LAPACK does not offer inplace lmul!(transpose(Q), B) for complex Q
            tmp = similar(parent(dest))
            copyto!(tmp, I)
            rmul!(tmp, src)
            permutedims!(parent(dest), tmp, (2, 1))
        end
    end
    return dest
end
# used in concatenations: Base.__cat_offset1!
Base._copy_or_fill!(A, inds, Q::AbstractQ) = (A[inds...] = collect(Q))
# overloads of helper functions
Base.cat_size(A::AbstractQ) = size(A)
Base.cat_size(A::AbstractQ, d) = size(A, d)
Base.cat_length(a::AbstractQ) = prod(size(a))
Base.cat_ndims(a::AbstractQ) = ndims(a)
Base.cat_indices(A::AbstractQ, d) = axes(A, d)
Base.cat_similar(A::AbstractQ, T::Type, shape::Tuple) = Array{T}(undef, shape)
Base.cat_similar(A::AbstractQ, T::Type, shape::Vector) = Array{T}(undef, shape...)

function show(io::IO, ::MIME{Symbol("text/plain")}, Q::AbstractQ)
    print(io, Base.dims2string(size(Q)), ' ', summary(Q))
end

# multiplication
# generically, treat AbstractQ like a matrix with its definite size
qsize_check(Q::AbstractQ, B::AbstractVecOrMat) =
    size(Q, 2) == size(B, 1) ||
        throw(DimensionMismatch("second dimension of Q, $(size(Q,2)), must coincide with first dimension of B, $(size(B,1))"))
qsize_check(A::AbstractVecOrMat, Q::AbstractQ) =
    size(A, 2) == size(Q, 1) ||
        throw(DimensionMismatch("second dimension of A, $(size(A,2)), must coincide with first dimension of Q, $(size(Q,1))"))
qsize_check(Q::AbstractQ, P::AbstractQ) =
    size(Q, 2) == size(P, 1) ||
        throw(DimensionMismatch("second dimension of A, $(size(Q,2)), must coincide with first dimension of B, $(size(P,1))"))

# mimic the AbstractArray fallback
*(Q::AbstractQ{<:Number}) = Q

(*)(Q::AbstractQ, J::UniformScaling) = Q*J.λ
function (*)(Q::AbstractQ, b::Number)
    T = promote_type(eltype(Q), typeof(b))
    lmul!(convert(AbstractQ{T}, Q), Matrix{T}(b*I, size(Q)))
end
function (*)(Q::AbstractQ, B::AbstractVector)
    T = promote_type(eltype(Q), eltype(B))
    qsize_check(Q, B)
    mul!(similar(B, T, size(Q, 1)), convert(AbstractQ{T}, Q), B)
end
function (*)(Q::AbstractQ, B::AbstractMatrix)
    T = promote_type(eltype(Q), eltype(B))
    qsize_check(Q, B)
    mul!(similar(B, T, (size(Q, 1), size(B, 2))), convert(AbstractQ{T}, Q), B)
end

(*)(J::UniformScaling, Q::AbstractQ) = J.λ*Q
function (*)(a::Number, Q::AbstractQ)
    T = promote_type(typeof(a), eltype(Q))
    rmul!(Matrix{T}(a*I, size(Q)), convert(AbstractQ{T}, Q))
end
function (*)(A::AbstractVector, Q::AbstractQ)
    T = promote_type(eltype(A), eltype(Q))
    qsize_check(A, Q)
    return mul!(similar(A, T, length(A)), A, convert(AbstractQ{T}, Q))
end
function (*)(A::AbstractMatrix, Q::AbstractQ)
    T = promote_type(eltype(A), eltype(Q))
    qsize_check(A, Q)
    return mul!(similar(A, T, (size(A, 1), size(Q, 2))), A, convert(AbstractQ{T}, Q))
end
(*)(u::AdjointAbsVec, Q::AbstractQ) = (Q'u')'

### Q*Q (including adjoints)
(*)(Q::AbstractQ, P::AbstractQ) = Q * (P*I)

### mul!
function mul!(C::AbstractVecOrMat{T}, Q::AbstractQ{T}, B::Union{AbstractVecOrMat,AbstractQ}) where {T}
    require_one_based_indexing(C, B)
    mB, nB = size(B, 1), size(B, 2)
    mC, nC = size(C, 1), size(C, 2)
    qsize_check(Q, B)
    nB != nC && throw(DimensionMismatch())
    if mB < mC
        inds = CartesianIndices(axes(B))
        copyto!(view(C, inds), B)
        C[CartesianIndices((mB+1:mC, axes(C, 2)))] .= zero(T)
        return lmul!(Q, C)
    else
        return lmul!(Q, copyto!(C, B))
    end
end
function mul!(C::AbstractVecOrMat{T}, A::AbstractVecOrMat, Q::AbstractQ{T}) where {T}
    require_one_based_indexing(C, A)
    mA, nA = size(A, 1), size(A, 2)
    mC, nC = size(C, 1), size(C, 2)
    mA != mC && throw(DimensionMismatch())
    qsize_check(A, Q)
    if nA < nC
        inds = CartesianIndices(axes(A))
        copyto!(view(C, inds), A)
        C[CartesianIndices((axes(C, 1), nA+1:nC))] .= zero(T)
        return rmul!(C, Q)
    else
        return rmul!(copyto!(C, A), Q)
    end
end

### division
\(Q::AbstractQ, A::AbstractVecOrMat) = Q'*A
/(A::AbstractVecOrMat, Q::AbstractQ) = A*Q'
ldiv!(Q::AbstractQ, A::AbstractVecOrMat) = lmul!(Q', A)
ldiv!(C::AbstractVecOrMat, Q::AbstractQ, A::AbstractVecOrMat) = mul!(C, Q', A)
rdiv!(A::AbstractVecOrMat, Q::AbstractQ) = rmul!(A, Q')

logabsdet(Q::AbstractQ) = (d = det(Q); return log(abs(d)), sign(d))
function logdet(A::AbstractQ)
    d, s = logabsdet(A)
    return d + log(s)
end

###########################################################
################ Q from QR decompositions #################
###########################################################

"""
    QRPackedQ <: LinearAlgebra.AbstractQ

The orthogonal/unitary ``Q`` matrix of a QR factorization stored in [`QR`](@ref) or
[`QRPivoted`](@ref) format.
"""
struct QRPackedQ{T,S<:AbstractMatrix{T},C<:AbstractVector{T}} <: AbstractQ{T}
    factors::S
    τ::C

    function QRPackedQ{T,S,C}(factors, τ) where {T,S<:AbstractMatrix{T},C<:AbstractVector{T}}
        require_one_based_indexing(factors, τ)
        new{T,S,C}(factors, τ)
    end
end
QRPackedQ(factors::AbstractMatrix{T}, τ::AbstractVector{T}) where {T} =
    QRPackedQ{T,typeof(factors),typeof(τ)}(factors, τ)
QRPackedQ{T}(factors::AbstractMatrix, τ::AbstractVector) where {T} =
    QRPackedQ(convert(AbstractMatrix{T}, factors), convert(AbstractVector{T}, τ))
# backwards-compatible constructors (remove with Julia 2.0)
@deprecate(QRPackedQ{T,S}(factors::AbstractMatrix{T}, τ::AbstractVector{T}) where {T,S},
           QRPackedQ{T,S,typeof(τ)}(factors, τ), false)

"""
    QRCompactWYQ <: LinearAlgebra.AbstractQ

The orthogonal/unitary ``Q`` matrix of a QR factorization stored in [`QRCompactWY`](@ref)
format.
"""
struct QRCompactWYQ{S, M<:AbstractMatrix{S}, C<:AbstractMatrix{S}} <: AbstractQ{S}
    factors::M
    T::C

    function QRCompactWYQ{S,M,C}(factors, T) where {S,M<:AbstractMatrix{S},C<:AbstractMatrix{S}}
        require_one_based_indexing(factors, T)
        new{S,M,C}(factors, T)
    end
end
QRCompactWYQ(factors::AbstractMatrix{S}, T::AbstractMatrix{S}) where {S} =
    QRCompactWYQ{S,typeof(factors),typeof(T)}(factors, T)
QRCompactWYQ{S}(factors::AbstractMatrix, T::AbstractMatrix) where {S} =
    QRCompactWYQ(convert(AbstractMatrix{S}, factors), convert(AbstractMatrix{S}, T))
# backwards-compatible constructors (remove with Julia 2.0)
@deprecate(QRCompactWYQ{S,M}(factors::AbstractMatrix{S}, T::AbstractMatrix{S}) where {S,M},
           QRCompactWYQ{S,M,typeof(T)}(factors, T), false)

QRPackedQ{T}(Q::QRPackedQ) where {T} = QRPackedQ(convert(AbstractMatrix{T}, Q.factors), convert(AbstractVector{T}, Q.τ))
QRCompactWYQ{S}(Q::QRCompactWYQ) where {S} = QRCompactWYQ(convert(AbstractMatrix{S}, Q.factors), convert(AbstractMatrix{S}, Q.T))

# override generic square fallback
Matrix{T}(Q::Union{QRCompactWYQ{S},QRPackedQ{S}}) where {T,S} =
    convert(Matrix{T}, lmul!(Q, Matrix{S}(I, size(Q, 1), min(size(Q.factors)...))))
Matrix(Q::Union{QRCompactWYQ{S},QRPackedQ{S}}) where {S} = Matrix{S}(Q)

convert(::Type{AbstractQ{T}}, Q::QRPackedQ) where {T} = QRPackedQ{T}(Q)
convert(::Type{AbstractQ{T}}, Q::QRCompactWYQ) where {T} = QRCompactWYQ{T}(Q)

size(Q::Union{QRCompactWYQ,QRPackedQ}, dim::Integer) =
    size(Q.factors, dim == 2 ? 1 : dim)
size(Q::Union{QRCompactWYQ,QRPackedQ}) = (n = size(Q.factors, 1); (n, n))

## Multiplication
### QB
lmul!(A::QRCompactWYQ{T,<:StridedMatrix}, B::StridedVecOrMat{T}) where {T<:BlasFloat} =
    LAPACK.gemqrt!('L', 'N', A.factors, A.T, B)
lmul!(A::QRPackedQ{T,<:StridedMatrix}, B::StridedVecOrMat{T}) where {T<:BlasFloat} =
    LAPACK.ormqr!('L', 'N', A.factors, A.τ, B)
function lmul!(A::QRPackedQ, B::AbstractVecOrMat)
    require_one_based_indexing(B)
    mA, nA = size(A.factors)
    mB, nB = size(B,1), size(B,2)
    if mA != mB
        throw(DimensionMismatch("matrix A has dimensions ($mA,$nA) but B has dimensions ($mB, $nB)"))
    end
    Afactors = A.factors
    @inbounds begin
        for k = min(mA,nA):-1:1
            for j = 1:nB
                vBj = B[k,j]
                for i = k+1:mB
                    vBj += conj(Afactors[i,k])*B[i,j]
                end
                vBj = A.τ[k]*vBj
                B[k,j] -= vBj
                for i = k+1:mB
                    B[i,j] -= Afactors[i,k]*vBj
                end
            end
        end
    end
    B
end

### QcB
lmul!(adjQ::AdjointQ{<:Any,<:QRCompactWYQ{T,<:StridedMatrix}}, B::StridedVecOrMat{T}) where {T<:BlasReal} =
    (Q = adjQ.Q; LAPACK.gemqrt!('L', 'T', Q.factors, Q.T, B))
lmul!(adjQ::AdjointQ{<:Any,<:QRCompactWYQ{T,<:StridedMatrix}}, B::StridedVecOrMat{T}) where {T<:BlasComplex} =
    (Q = adjQ.Q; LAPACK.gemqrt!('L', 'C', Q.factors, Q.T, B))
lmul!(adjQ::AdjointQ{<:Any,<:QRPackedQ{T,<:StridedMatrix}}, B::StridedVecOrMat{T}) where {T<:BlasReal} =
    (Q = adjQ.Q; LAPACK.ormqr!('L', 'T', Q.factors, Q.τ, B))
lmul!(adjQ::AdjointQ{<:Any,<:QRPackedQ{T,<:StridedMatrix}}, B::StridedVecOrMat{T}) where {T<:BlasComplex} =
    (Q = adjQ.Q; LAPACK.ormqr!('L', 'C', Q.factors, Q.τ, B))
function lmul!(adjA::AdjointQ{<:Any,<:QRPackedQ}, B::AbstractVecOrMat)
    require_one_based_indexing(B)
    A = adjA.Q
    mA, nA = size(A.factors)
    mB, nB = size(B,1), size(B,2)
    if mA != mB
        throw(DimensionMismatch("matrix A has dimensions ($mA,$nA) but B has dimensions ($mB, $nB)"))
    end
    Afactors = A.factors
    @inbounds begin
        for k = 1:min(mA,nA)
            for j = 1:nB
                vBj = B[k,j]
                for i = k+1:mB
                    vBj += conj(Afactors[i,k])*B[i,j]
                end
                vBj = conj(A.τ[k])*vBj
                B[k,j] -= vBj
                for i = k+1:mB
                    B[i,j] -= Afactors[i,k]*vBj
                end
            end
        end
    end
    B
end

### AQ
rmul!(A::StridedVecOrMat{T}, B::QRCompactWYQ{T,<:StridedMatrix}) where {T<:BlasFloat} =
    LAPACK.gemqrt!('R', 'N', B.factors, B.T, A)
rmul!(A::StridedVecOrMat{T}, B::QRPackedQ{T,<:StridedMatrix}) where {T<:BlasFloat} =
    LAPACK.ormqr!('R', 'N', B.factors, B.τ, A)
function rmul!(A::AbstractVecOrMat, Q::QRPackedQ)
    require_one_based_indexing(A)
    mQ, nQ = size(Q.factors)
    mA, nA = size(A,1), size(A,2)
    if nA != mQ
        throw(DimensionMismatch("matrix A has dimensions ($mA,$nA) but matrix Q has dimensions ($mQ, $nQ)"))
    end
    Qfactors = Q.factors
    @inbounds begin
        for k = 1:min(mQ,nQ)
            for i = 1:mA
                vAi = A[i,k]
                for j = k+1:mQ
                    vAi += A[i,j]*Qfactors[j,k]
                end
                vAi = vAi*Q.τ[k]
                A[i,k] -= vAi
                for j = k+1:nA
                    A[i,j] -= vAi*conj(Qfactors[j,k])
                end
            end
        end
    end
    A
end

### AQc
rmul!(A::StridedVecOrMat{T}, adjQ::AdjointQ{<:Any,<:QRCompactWYQ{T}}) where {T<:BlasReal} =
    (Q = adjQ.Q; LAPACK.gemqrt!('R', 'T', Q.factors, Q.T, A))
rmul!(A::StridedVecOrMat{T}, adjQ::AdjointQ{<:Any,<:QRCompactWYQ{T}}) where {T<:BlasComplex} =
    (Q = adjQ.Q; LAPACK.gemqrt!('R', 'C', Q.factors, Q.T, A))
rmul!(A::StridedVecOrMat{T}, adjQ::AdjointQ{<:Any,<:QRPackedQ{T}}) where {T<:BlasReal} =
    (Q = adjQ.Q; LAPACK.ormqr!('R', 'T', Q.factors, Q.τ, A))
rmul!(A::StridedVecOrMat{T}, adjQ::AdjointQ{<:Any,<:QRPackedQ{T}}) where {T<:BlasComplex} =
    (Q = adjQ.Q; LAPACK.ormqr!('R', 'C', Q.factors, Q.τ, A))
function rmul!(A::AbstractVecOrMat, adjQ::AdjointQ{<:Any,<:QRPackedQ})
    require_one_based_indexing(A)
    Q = adjQ.Q
    mQ, nQ = size(Q.factors)
    mA, nA = size(A,1), size(A,2)
    if nA != mQ
        throw(DimensionMismatch("matrix A has dimensions ($mA,$nA) but matrix Q has dimensions ($mQ, $nQ)"))
    end
    Qfactors = Q.factors
    @inbounds begin
        for k = min(mQ,nQ):-1:1
            for i = 1:mA
                vAi = A[i,k]
                for j = k+1:mQ
                    vAi += A[i,j]*Qfactors[j,k]
                end
                vAi = vAi*conj(Q.τ[k])
                A[i,k] -= vAi
                for j = k+1:nA
                    A[i,j] -= vAi*conj(Qfactors[j,k])
                end
            end
        end
    end
    A
end

det(Q::QRPackedQ) = _det_tau(Q.τ)
det(Q::QRCompactWYQ) =
    prod(i -> _det_tau(_diagview(Q.T[:, i:min(i + size(Q.T, 1), size(Q.T, 2))])),
         1:size(Q.T, 1):size(Q.T, 2))

_diagview(A) = @view A[diagind(A)]

# Compute `det` from the number of Householder reflections.  Handle
# the case `Q.τ` contains zeros.
_det_tau(τs::AbstractVector{<:Real}) =
    isodd(count(!iszero, τs)) ? -one(eltype(τs)) : one(eltype(τs))

# In complex case, we need to compute the non-unit eigenvalue `λ = 1 - c*τ`
# (where `c = v'v`) of each Householder reflector.  As we know that the
# reflector must have the determinant of 1, it must satisfy `abs2(λ) == 1`.
# Combining this with the constraint `c > 0`, it turns out that the eigenvalue
# (hence the determinant) can be computed as `λ = -sign(τ)^2`.
# See: https://github.com/JuliaLang/julia/pull/32887#issuecomment-521935716
_det_tau(τs) = prod(τ -> iszero(τ) ? one(τ) : -sign(τ)^2, τs)

###########################################################
######## Q from Hessenberg decomposition ##################
###########################################################

"""
    HessenbergQ <: AbstractQ

Given a [`Hessenberg`](@ref) factorization object `F`, `F.Q` returns
a `HessenbergQ` object, which is an implicit representation of the unitary
matrix `Q` in the Hessenberg factorization `QHQ'` represented by `F`.
This `F.Q` object can be efficiently multiplied by matrices or vectors,
and can be converted to an ordinary matrix type with `Matrix(F.Q)`.
"""
struct HessenbergQ{T,S<:AbstractMatrix,W<:AbstractVector,sym} <: AbstractQ{T}
    uplo::Char
    factors::S
    τ::W
    function HessenbergQ{T,S,W,sym}(uplo::AbstractChar, factors, τ) where {T,S<:AbstractMatrix,W<:AbstractVector,sym}
        new(uplo, factors, τ)
    end
end
HessenbergQ(F::Hessenberg{<:Any,<:UpperHessenberg,S,W}) where {S,W} = HessenbergQ{eltype(F.factors),S,W,false}(F.uplo, F.factors, F.τ)
HessenbergQ(F::Hessenberg{<:Any,<:SymTridiagonal,S,W}) where {S,W} = HessenbergQ{eltype(F.factors),S,W,true}(F.uplo, F.factors, F.τ)

size(Q::HessenbergQ, dim::Integer) = size(getfield(Q, :factors), dim == 2 ? 1 : dim)
size(Q::HessenbergQ) = size(Q, 1), size(Q, 2)

# HessenbergQ from LAPACK/BLAS (as opposed to Julia libraries like GenericLinearAlgebra)
const BlasHessenbergQ{T,sym} = HessenbergQ{T,<:StridedMatrix{T},<:StridedVector{T},sym} where {T<:BlasFloat,sym}

## reconstruct the original matrix
Matrix{T}(Q::BlasHessenbergQ{<:Any,false}) where {T} = convert(Matrix{T}, LAPACK.orghr!(1, size(Q.factors, 1), copy(Q.factors), Q.τ))
Matrix{T}(Q::BlasHessenbergQ{<:Any,true}) where {T} = convert(Matrix{T}, LAPACK.orgtr!(Q.uplo, copy(Q.factors), Q.τ))

lmul!(Q::BlasHessenbergQ{T,false}, X::StridedVecOrMat{T}) where {T<:BlasFloat} =
    LAPACK.ormhr!('L', 'N', 1, size(Q.factors, 1), Q.factors, Q.τ, X)
rmul!(X::StridedVecOrMat{T}, Q::BlasHessenbergQ{T,false}) where {T<:BlasFloat} =
    LAPACK.ormhr!('R', 'N', 1, size(Q.factors, 1), Q.factors, Q.τ, X)
lmul!(adjQ::AdjointQ{<:Any,<:BlasHessenbergQ{T,false}}, X::StridedVecOrMat{T}) where {T<:BlasFloat} =
    (Q = adjQ.Q; LAPACK.ormhr!('L', ifelse(T<:Real, 'T', 'C'), 1, size(Q.factors, 1), Q.factors, Q.τ, X))
rmul!(X::StridedVecOrMat{T}, adjQ::AdjointQ{<:Any,<:BlasHessenbergQ{T,false}}) where {T<:BlasFloat} =
    (Q = adjQ.Q; LAPACK.ormhr!('R', ifelse(T<:Real, 'T', 'C'), 1, size(Q.factors, 1), Q.factors, Q.τ, X))

lmul!(Q::BlasHessenbergQ{T,true}, X::StridedVecOrMat{T}) where {T<:BlasFloat} =
    LAPACK.ormtr!('L', Q.uplo, 'N', Q.factors, Q.τ, X)
rmul!(X::StridedVecOrMat{T}, Q::BlasHessenbergQ{T,true}) where {T<:BlasFloat} =
    LAPACK.ormtr!('R', Q.uplo, 'N', Q.factors, Q.τ, X)
lmul!(adjQ::AdjointQ{<:Any,<:BlasHessenbergQ{T,true}}, X::StridedVecOrMat{T}) where {T<:BlasFloat} =
    (Q = adjQ.Q; LAPACK.ormtr!('L', Q.uplo, ifelse(T<:Real, 'T', 'C'), Q.factors, Q.τ, X))
rmul!(X::StridedVecOrMat{T}, adjQ::AdjointQ{<:Any,<:BlasHessenbergQ{T,true}}) where {T<:BlasFloat} =
    (Q = adjQ.Q; LAPACK.ormtr!('R', Q.uplo, ifelse(T<:Real, 'T', 'C'), Q.factors, Q.τ, X))

lmul!(Q::HessenbergQ{T}, X::Adjoint{T,<:StridedVecOrMat{T}}) where {T} = rmul!(X', Q')'
rmul!(X::Adjoint{T,<:StridedVecOrMat{T}}, Q::HessenbergQ{T}) where {T} = lmul!(Q', X')'
lmul!(adjQ::AdjointQ{<:Any,<:HessenbergQ{T}}, X::Adjoint{T,<:StridedVecOrMat{T}}) where {T}  = rmul!(X', adjQ')'
rmul!(X::Adjoint{T,<:StridedVecOrMat{T}}, adjQ::AdjointQ{<:Any,<:HessenbergQ{T}}) where {T} = lmul!(adjQ', X')'

# flexible left-multiplication (and adjoint right-multiplication)
qsize_check(Q::Union{QRPackedQ,QRCompactWYQ,HessenbergQ}, B::AbstractVecOrMat) =
    size(B, 1) in size(Q.factors) ||
        throw(DimensionMismatch("first dimension of B, $(size(B,1)), must equal one of the dimensions of Q, $(size(Q.factors))"))
qsize_check(A::AbstractVecOrMat, adjQ::AdjointQ{<:Any,<:Union{QRPackedQ,QRCompactWYQ,HessenbergQ}}) =
    (Q = adjQ.Q; size(A, 2) in size(Q.factors) ||
        throw(DimensionMismatch("second dimension of A, $(size(A,2)), must equal one of the dimensions of Q, $(size(Q.factors))")))

det(Q::HessenbergQ) = _det_tau(Q.τ)

###########################################################
################ Q from LQ decomposition ##################
###########################################################

struct LQPackedQ{T,S<:AbstractMatrix{T},C<:AbstractVector{T}} <: AbstractQ{T}
    factors::S
    τ::C
end

LQPackedQ{T}(Q::LQPackedQ) where {T} = LQPackedQ(convert(AbstractMatrix{T}, Q.factors), convert(AbstractVector{T}, Q.τ))
@deprecate(AbstractMatrix{T}(Q::LQPackedQ) where {T},
    convert(AbstractQ{T}, Q),
    false)
Matrix{T}(A::LQPackedQ) where {T} = convert(Matrix{T}, LAPACK.orglq!(copy(A.factors), A.τ))
convert(::Type{AbstractQ{T}}, Q::LQPackedQ) where {T} = LQPackedQ{T}(Q)

# size(Q::LQPackedQ) yields the shape of Q's square form
size(Q::LQPackedQ) = (n = size(Q.factors, 2); return n, n)

## Multiplication
# out-of-place right application of LQPackedQs
#
# these methods: (1) check whether the applied-to matrix's (A's) appropriate dimension
# (columns for A_*, rows for Ac_*) matches the number of columns (nQ) of the LQPackedQ (Q),
# and if so effectively apply Q's square form to A without additional shenanigans; and
# (2) if the preceding dimensions do not match, check whether the appropriate dimension of
# A instead matches the number of rows of the matrix of which Q is a factor (i.e.
# size(Q.factors, 1)), and if so implicitly apply Q's truncated form to A by zero extending
# A as necessary for check (1) to pass (if possible) and then applying Q's square form

qsize_check(adjQ::AdjointQ{<:Any,<:LQPackedQ}, B::AbstractVecOrMat) =
    size(B, 1) in size(adjQ.Q.factors) ||
        throw(DimensionMismatch("first dimension of B, $(size(B,1)), must equal one of the dimensions of Q, $(size(adjQ.Q.factors))"))
qsize_check(A::AbstractVecOrMat, Q::LQPackedQ) =
    size(A, 2) in size(Q.factors) ||
        throw(DimensionMismatch("second dimension of A, $(size(A,2)), must equal one of the dimensions of Q, $(size(Q.factors))"))

# in-place right-application of LQPackedQs
# these methods require that the applied-to matrix's (A's) number of columns
# match the number of columns (nQ) of the LQPackedQ (Q) (necessary for in-place
# operation, and the underlying LAPACK routine (ormlq) treats the implicit Q
# as its (nQ-by-nQ) square form)
rmul!(A::StridedVecOrMat{T}, B::LQPackedQ{T}) where {T<:BlasFloat} =
    LAPACK.ormlq!('R', 'N', B.factors, B.τ, A)
rmul!(A::StridedVecOrMat{T}, adjB::AdjointQ{<:Any,<:LQPackedQ{T}}) where {T<:BlasReal} =
    (B = adjB.Q; LAPACK.ormlq!('R', 'T', B.factors, B.τ, A))
rmul!(A::StridedVecOrMat{T}, adjB::AdjointQ{<:Any,<:LQPackedQ{T}}) where {T<:BlasComplex} =
    (B = adjB.Q; LAPACK.ormlq!('R', 'C', B.factors, B.τ, A))

### QB / QcB
lmul!(A::LQPackedQ{T}, B::StridedVecOrMat{T}) where {T<:BlasFloat} = LAPACK.ormlq!('L','N',A.factors,A.τ,B)
lmul!(adjA::AdjointQ{<:Any,<:LQPackedQ{T}}, B::StridedVecOrMat{T}) where {T<:BlasReal} =
    (A = adjA.Q; LAPACK.ormlq!('L', 'T', A.factors, A.τ, B))
lmul!(adjA::AdjointQ{<:Any,<:LQPackedQ{T}}, B::StridedVecOrMat{T}) where {T<:BlasComplex} =
    (A = adjA.Q; LAPACK.ormlq!('L', 'C', A.factors, A.τ, B))

# In LQ factorization, `Q` is expressed as the product of the adjoint of the
# reflectors.  Thus, `det` has to be conjugated.
det(Q::LQPackedQ) = conj(_det_tau(Q.τ))
w   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LinearAlgebra/src/givens.jlp1      # This file is a part of Julia. License is MIT: https://julialang.org/license

# givensAlgorithm functions are derived from LAPACK, see below

abstract type AbstractRotation{T} end
struct AdjointRotation{T,S<:AbstractRotation{T}} <: AbstractRotation{T}
    R::S
end

transpose(R::AbstractRotation) = error("transpose not implemented for $(typeof(R)). Consider using adjoint instead of transpose.")

(*)(R::AbstractRotation, A::AbstractVector) = _rot_mul_vecormat(R, A)
(*)(R::AbstractRotation, A::AbstractMatrix) = _rot_mul_vecormat(R, A)
function _rot_mul_vecormat(R::AbstractRotation{T}, A::AbstractVecOrMat{S}) where {T,S}
    TS = typeof(zero(T)*zero(S) + zero(T)*zero(S))
    lmul!(convert(AbstractRotation{TS}, R), copy_similar(A, TS))
end

(*)(A::AbstractVector, R::AbstractRotation) = _vecormat_mul_rot(A, R)
(*)(A::AbstractMatrix, R::AbstractRotation) = _vecormat_mul_rot(A, R)
function _vecormat_mul_rot(A::AbstractVecOrMat{T}, R::AbstractRotation{S}) where {T,S}
    TS = typeof(zero(T)*zero(S) + zero(T)*zero(S))
    rmul!(copy_similar(A, TS), convert(AbstractRotation{TS}, R))
end

"""
    LinearAlgebra.Givens(i1,i2,c,s) -> G

A Givens rotation linear operator. The fields `c` and `s` represent the cosine and sine of
the rotation angle, respectively. The `Givens` type supports left multiplication `G*A` and
conjugated transpose right multiplication `A*G'`. The type doesn't have a `size` and can
therefore be multiplied with matrices of arbitrary size as long as `i2<=size(A,2)` for
`G*A` or `i2<=size(A,1)` for `A*G'`.

See also [`givens`](@ref).
"""
struct Givens{T} <: AbstractRotation{T}
    i1::Int
    i2::Int
    c::T
    s::T
end
struct Rotation{T} <: AbstractRotation{T}
    rotations::Vector{Givens{T}}
end

convert(::Type{T}, r::T) where {T<:AbstractRotation} = r
convert(::Type{T}, r::AbstractRotation) where {T<:AbstractRotation} = T(r)::T
convert(::Type{AbstractRotation{T}}, r::AdjointRotation) where {T} = convert(AbstractRotation{T}, r.R)'
convert(::Type{AbstractRotation{T}}, r::AdjointRotation{T}) where {T} = r

Givens(i1, i2, c, s) = Givens(i1, i2, promote(c, s)...)
Givens{T}(G::Givens{T}) where {T} = G
Givens{T}(G::Givens) where {T} = Givens(G.i1, G.i2, convert(T, G.c), convert(T, G.s))
Rotation{T}(R::Rotation{T}) where {T} = R
Rotation{T}(R::Rotation) where {T} = Rotation{T}([Givens{T}(g) for g in R.rotations])
AbstractRotation{T}(G::Givens) where {T} = Givens{T}(G)
AbstractRotation{T}(R::Rotation) where {T} = Rotation{T}(R)

adjoint(G::Givens) = Givens(G.i1, G.i2, G.c', -G.s)
adjoint(R::AbstractRotation) = AdjointRotation(R)
adjoint(adjR::AdjointRotation) = adjR.R

Base.copy(aR::AdjointRotation{T,Rotation{T}}) where {T} =
    Rotation{T}([r' for r in Iterators.reverse(aR.R.rotations)])

floatmin2(::Type{Float32}) = reinterpret(Float32, 0x26000000)
floatmin2(::Type{Float64}) = reinterpret(Float64, 0x21a0000000000000)
floatmin2(::Type{T}) where {T} = (twopar = 2one(T); twopar^trunc(Integer,log(floatmin(T)/eps(T))/log(twopar)/twopar))

# derived from LAPACK's dlartg
# Copyright:
# Univ. of Tennessee
# Univ. of California Berkeley
# Univ. of Colorado Denver
# NAG Ltd.
function givensAlgorithm(f::T, g::T) where T<:AbstractFloat
    onepar = one(T)
    twopar = 2one(T)
    T0 = typeof(onepar) # dimensionless
    zeropar = T0(zero(T)) # must be dimensionless

    # need both dimensionful and dimensionless versions of these:
    safmn2 = floatmin2(T0)
    safmn2u = floatmin2(T)
    safmx2 = one(T)/safmn2
    safmx2u = oneunit(T)/safmn2

    if g == 0
        cs = onepar
        sn = zeropar
        r = f
    elseif f == 0
        cs = zeropar
        sn = onepar
        r = g
    else
        f1 = f
        g1 = g
        scalepar = max(abs(f1), abs(g1))
        if scalepar >= safmx2u
            count = 0
            while true
                count += 1
                f1 *= safmn2
                g1 *= safmn2
                scalepar = max(abs(f1), abs(g1))
                if scalepar < safmx2u break end
            end
            r = sqrt(f1*f1 + g1*g1)
            cs = f1/r
            sn = g1/r
            for i = 1:count
                r *= safmx2
            end
        elseif scalepar <= safmn2u
            count = 0
            while true
                count += 1
                f1 *= safmx2
                g1 *= safmx2
                scalepar = max(abs(f1), abs(g1))
                if scalepar > safmn2u break end
            end
            r = sqrt(f1*f1 + g1*g1)
            cs = f1/r
            sn = g1/r
            for i = 1:count
                r *= safmn2
            end
        else
            r = sqrt(f1*f1 + g1*g1)
            cs = f1/r
            sn = g1/r
        end
        if abs(f) > abs(g) && cs < 0
            cs = -cs
            sn = -sn
            r = -r
        end
    end
    return cs, sn, r
end

# derived from LAPACK's zlartg
# Copyright:
# Univ. of Tennessee
# Univ. of California Berkeley
# Univ. of Colorado Denver
# NAG Ltd.
function givensAlgorithm(f::Complex{T}, g::Complex{T}) where T<:AbstractFloat
    twopar, onepar = 2one(T), one(T)
    T0 = typeof(onepar) # dimensionless
    zeropar = T0(zero(T)) # must be dimensionless
    czero = complex(zeropar)

    abs1(ff) = max(abs(real(ff)), abs(imag(ff)))
    safmin = floatmin(T0)
    safmn2 = floatmin2(T0)
    safmn2u = floatmin2(T)
    safmx2 = one(T)/safmn2
    safmx2u = oneunit(T)/safmn2
    scalepar = max(abs1(f), abs1(g))
    fs = f
    gs = g
    count = 0
    if scalepar >= safmx2u
        while true
            count += 1
            fs *= safmn2
            gs *= safmn2
            scalepar *= safmn2
            if scalepar < safmx2u break end
        end
    elseif scalepar <= safmn2u
        if g == 0
            cs = onepar
            sn = czero
            r = f
            return cs, sn, r
        end
        while true
            count -= 1
            fs *= safmx2
            gs *= safmx2
            scalepar *= safmx2
            if scalepar > safmn2u break end
        end
    end
    f2 = abs2(fs)
    g2 = abs2(gs)
    if f2 <= max(g2, oneunit(T))*safmin
        # This is a rare case: F is very small.
        if f == 0
            cs = zero(T)
            r = complex(hypot(real(g), imag(g)))
            # do complex/real division explicitly with two real divisions
            d = hypot(real(gs), imag(gs))
            sn = complex(real(gs)/d, -imag(gs)/d)
            return cs, sn, r
        end
        f2s = hypot(real(fs), imag(fs))
        # g2 and g2s are accurate
        # g2 is at least safmin, and g2s is at least safmn2
        g2s = sqrt(g2)
        # error in cs from underflow in f2s is at most
        # unfl / safmn2 .lt. sqrt(unfl*eps) .lt. eps
        # if max(g2,one)=g2, then f2 .lt. g2*safmin,
        # and so cs .lt. sqrt(safmin)
        # if max(g2,one)=one, then f2 .lt. safmin
        # and so cs .lt. sqrt(safmin)/safmn2 = sqrt(eps)
        # therefore, cs = f2s/g2s / sqrt( 1 + (f2s/g2s)**2 ) = f2s/g2s
        cs = f2s/g2s
        # make sure abs(ff) = 1
        # do complex/real division explicitly with 2 real divisions
        if abs1(f) > 1
            d = hypot(real(f), imag(f))
            ff = complex(real(f)/d, imag(f)/d)
        else
            dr = safmx2*real(f)
            di = safmx2*imag(f)
            d = hypot(dr, di)
            ff = complex(dr/d, di/d)
        end
        sn = ff*complex(real(gs)/g2s, -imag(gs)/g2s)
        r = cs*f + sn*g
    else
        # This is the most common case.
        # Neither F2 nor F2/G2 are less than SAFMIN
        # F2S cannot overflow, and it is accurate
        f2s = sqrt(onepar + g2/f2)
        # do the f2s(real)*fs(complex) multiply with two real multiplies
        r = complex(f2s*real(fs), f2s*imag(fs))
        cs = onepar/f2s
        d = f2 + g2
        # do complex/real division explicitly with two real divisions
        sn = complex(real(r)/d, imag(r)/d)
        sn *= conj(gs)
        if count != 0
            if count > 0
                for i = 1:count
                    r *= safmx2
                end
            else
                for i = 1:-count
                    r *= safmn2
                end
            end
        end
    end
    return cs, sn, r
end

# enable for unitful quantities
function givensAlgorithm(f::T, g::T) where T
    fs = f / oneunit(T)
    gs = g / oneunit(T)
    typeof(fs) === T && typeof(gs) === T &&
    !isa(fs, Union{AbstractFloat,Complex{<:AbstractFloat}}) &&
    throw(MethodError(givensAlgorithm, (fs, gs)))

    c, s, r = givensAlgorithm(fs, gs)
    return c, s, r * oneunit(T)
end

givensAlgorithm(f, g) = givensAlgorithm(promote(float(f), float(g))...)

"""

    givens(f::T, g::T, i1::Integer, i2::Integer) where {T} -> (G::Givens, r::T)

Computes the Givens rotation `G` and scalar `r` such that for any vector `x` where
```
x[i1] = f
x[i2] = g
```
the result of the multiplication
```
y = G*x
```
has the property that
```
y[i1] = r
y[i2] = 0
```

See also [`LinearAlgebra.Givens`](@ref).
"""
function givens(f::T, g::T, i1::Integer, i2::Integer) where T
    if i1 == i2
        throw(ArgumentError("Indices must be distinct."))
    end
    c, s, r = givensAlgorithm(f, g)
    if i1 > i2
        s = -conj(s)
        i1, i2 = i2, i1
    end
    Givens(i1, i2, c, s), r
end
"""
    givens(A::AbstractArray, i1::Integer, i2::Integer, j::Integer) -> (G::Givens, r)

Computes the Givens rotation `G` and scalar `r` such that the result of the multiplication
```
B = G*A
```
has the property that
```
B[i1,j] = r
B[i2,j] = 0
```

See also [`LinearAlgebra.Givens`](@ref).
"""
givens(A::AbstractMatrix, i1::Integer, i2::Integer, j::Integer) =
    givens(A[i1,j], A[i2,j], i1, i2)


"""
    givens(x::AbstractVector, i1::Integer, i2::Integer) -> (G::Givens, r)

Computes the Givens rotation `G` and scalar `r` such that the result of the multiplication
```
B = G*x
```
has the property that
```
B[i1] = r
B[i2] = 0
```

See also [`LinearAlgebra.Givens`](@ref).
"""
givens(x::AbstractVector, i1::Integer, i2::Integer) = givens(x[i1], x[i2], i1, i2)

function getindex(G::Givens, i::Integer, j::Integer)
    if i == j
        if i == G.i1 || i == G.i2
            G.c
        else
            oneunit(G.c)
        end
    elseif i == G.i1 && j == G.i2
        G.s
    elseif i == G.i2 && j == G.i1
        -conj(G.s)
    else
        zero(G.s)
    end
end

@inline function lmul!(G::Givens, A::AbstractVecOrMat)
    require_one_based_indexing(A)
    m, n = size(A, 1), size(A, 2)
    if G.i2 > m
        throw(DimensionMismatch("column indices for rotation are outside the matrix"))
    end
    @inbounds for i = 1:n
        a1, a2 = A[G.i1,i], A[G.i2,i]
        A[G.i1,i] =       G.c *a1 + G.s*a2
        A[G.i2,i] = -conj(G.s)*a1 + G.c*a2
    end
    return A
end
@inline function rmul!(A::AbstractMatrix, G::Givens)
    require_one_based_indexing(A)
    m, n = size(A, 1), size(A, 2)
    if G.i2 > n
        throw(DimensionMismatch("column indices for rotation are outside the matrix"))
    end
    @inbounds for i = 1:m
        a1, a2 = A[i,G.i1], A[i,G.i2]
        A[i,G.i1] = a1*G.c - a2*G.s'
        A[i,G.i2] = a1*G.s + a2*G.c
    end
    return A
end

function lmul!(G::Givens, R::Rotation)
    push!(R.rotations, G)
    return R
end
function rmul!(R::Rotation, G::Givens)
    pushfirst!(R.rotations, G)
    return R
end

function lmul!(R::Rotation, A::AbstractVecOrMat)
    @inbounds for i in eachindex(R.rotations)
        lmul!(R.rotations[i], A)
    end
    return A
end
function rmul!(A::AbstractMatrix, R::Rotation)
    @inbounds for i in eachindex(R.rotations)
        rmul!(A, R.rotations[i])
    end
    return A
end

function lmul!(adjR::AdjointRotation{<:Any,<:Rotation}, A::AbstractVecOrMat)
    R = adjR.R
    @inbounds for i in eachindex(R.rotations)
        lmul!(adjoint(R.rotations[i]), A)
    end
    return A
end
function rmul!(A::AbstractMatrix, adjR::AdjointRotation{<:Any,<:Rotation})
    R = adjR.R
    @inbounds for i in eachindex(R.rotations)
        rmul!(A, adjoint(R.rotations[i]))
    end
    return A
end

function *(G1::Givens{S}, G2::Givens{T}) where {S,T}
    TS = promote_type(T, S)
    Rotation{TS}([convert(AbstractRotation{TS}, G2), convert(AbstractRotation{TS}, G1)])
end
function *(G::Givens{T}, Gs::Givens{T}...) where {T}
    return Rotation([reverse(Gs)..., G])
end
function *(G::Givens{S}, R::Rotation{T}) where {S,T}
    TS = promote_type(T, S)
    Rotation(vcat(convert(AbstractRotation{TS}, R).rotations, convert(AbstractRotation{TS}, G)))
end
function *(R::Rotation{S}, G::Givens{T}) where {S,T}
    TS = promote_type(T, S)
    Rotation(vcat(convert(AbstractRotation{TS}, G), convert(AbstractRotation{TS}, R).rotations))
end
x   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LinearAlgebra/src/special.jlzM      # This file is a part of Julia. License is MIT: https://julialang.org/license

# Methods operating on different special matrix types

# Interconversion between special matrix types

# conversions from Diagonal to other special matrix types
Bidiagonal(A::Diagonal) = Bidiagonal(A.diag, fill!(similar(A.diag, length(A.diag)-1), 0), :U)
SymTridiagonal(A::Diagonal) = SymTridiagonal(A.diag, fill!(similar(A.diag, length(A.diag)-1), 0))
Tridiagonal(A::Diagonal) = Tridiagonal(fill!(similar(A.diag, length(A.diag)-1), 0), A.diag,
                                       fill!(similar(A.diag, length(A.diag)-1), 0))

# conversions from Bidiagonal to other special matrix types
Diagonal(A::Bidiagonal) = Diagonal(A.dv)
SymTridiagonal(A::Bidiagonal) =
    iszero(A.ev) ? SymTridiagonal(A.dv, A.ev) :
        throw(ArgumentError("matrix cannot be represented as SymTridiagonal"))
Tridiagonal(A::Bidiagonal) =
    Tridiagonal(A.uplo == 'U' ? fill!(similar(A.ev), 0) : A.ev, A.dv,
                A.uplo == 'U' ? A.ev : fill!(similar(A.ev), 0))

# conversions from SymTridiagonal to other special matrix types
Diagonal(A::SymTridiagonal) = Diagonal(A.dv)

# These can fail when ev has the same length as dv
# TODO: Revisit when a good solution for #42477 is found
Bidiagonal(A::SymTridiagonal) =
    iszero(A.ev) ? Bidiagonal(A.dv, A.ev, :U) :
        throw(ArgumentError("matrix cannot be represented as Bidiagonal"))
Tridiagonal(A::SymTridiagonal) =
    Tridiagonal(copy(A.ev), A.dv, A.ev)

# conversions from Tridiagonal to other special matrix types
Diagonal(A::Tridiagonal) = Diagonal(A.d)
Bidiagonal(A::Tridiagonal) =
    iszero(A.dl) ? Bidiagonal(A.d, A.du, :U) :
    iszero(A.du) ? Bidiagonal(A.d, A.dl, :L) :
        throw(ArgumentError("matrix cannot be represented as Bidiagonal"))

# conversions from AbstractTriangular to special matrix types
Bidiagonal(A::AbstractTriangular) =
    isbanded(A, 0, 1) ? Bidiagonal(diag(A, 0), diag(A,  1), :U) : # is upper bidiagonal
    isbanded(A, -1, 0) ? Bidiagonal(diag(A, 0), diag(A, -1), :L) : # is lower bidiagonal
        throw(ArgumentError("matrix cannot be represented as Bidiagonal"))

_lucopy(A::Bidiagonal, T) = copymutable_oftype(Tridiagonal(A), T)
_lucopy(A::Diagonal, T)   = copymutable_oftype(Tridiagonal(A), T)
function _lucopy(A::SymTridiagonal, T)
    du = copy_similar(_evview(A), T)
    dl = copy.(transpose.(du))
    d  = copy_similar(A.dv, T)
    return Tridiagonal(dl, d, du)
end

const ConvertibleSpecialMatrix = Union{Diagonal,Bidiagonal,SymTridiagonal,Tridiagonal,AbstractTriangular}
const PossibleTriangularMatrix = Union{Diagonal, Bidiagonal, AbstractTriangular}

convert(::Type{T}, m::ConvertibleSpecialMatrix) where {T<:Diagonal}       = m isa T ? m :
    isdiag(m) ? T(m)::T : throw(ArgumentError("matrix cannot be represented as Diagonal"))
convert(::Type{T}, m::ConvertibleSpecialMatrix) where {T<:SymTridiagonal} = m isa T ? m :
    issymmetric(m) && isbanded(m, -1, 1) ? T(m)::T : throw(ArgumentError("matrix cannot be represented as SymTridiagonal"))
convert(::Type{T}, m::ConvertibleSpecialMatrix) where {T<:Tridiagonal}    = m isa T ? m :
    isbanded(m, -1, 1) ? T(m)::T : throw(ArgumentError("matrix cannot be represented as Tridiagonal"))

convert(::Type{T}, m::Union{LowerTriangular,UnitLowerTriangular}) where {T<:LowerTriangular} = m isa T ? m : T(m)::T
convert(::Type{T}, m::Union{UpperTriangular,UnitUpperTriangular}) where {T<:UpperTriangular} = m isa T ? m : T(m)::T

convert(::Type{T}, m::PossibleTriangularMatrix) where {T<:LowerTriangular} = m isa T ? m :
    istril(m) ? T(m)::T : throw(ArgumentError("matrix cannot be represented as LowerTriangular"))
convert(::Type{T}, m::PossibleTriangularMatrix) where {T<:UpperTriangular} = m isa T ? m :
    istriu(m) ? T(m)::T : throw(ArgumentError("matrix cannot be represented as UpperTriangular"))

# Constructs two method definitions taking into account (assumed) commutativity
# e.g. @commutative f(x::S, y::T) where {S,T} = x+y is the same is defining
#     f(x::S, y::T) where {S,T} = x+y
#     f(y::T, x::S) where {S,T} = f(x, y)
macro commutative(myexpr)
    @assert Base.is_function_def(myexpr) # Make sure it is a function definition
    y = copy(myexpr.args[1].args[2:end])
    reverse!(y)
    reversed_call = Expr(:(=), Expr(:call,myexpr.args[1].args[1],y...), myexpr.args[1])
    esc(Expr(:block, myexpr, reversed_call))
end

for op in (:+, :-)
    for (matrixtype, uplo, converttype) in ((:UpperTriangular, 'U', :UpperTriangular),
                                            (:UnitUpperTriangular, 'U', :UpperTriangular),
                                            (:LowerTriangular, 'L', :LowerTriangular),
                                            (:UnitLowerTriangular, 'L', :LowerTriangular))
        @eval begin
            function ($op)(A::$matrixtype, B::Bidiagonal)
                if B.uplo == $uplo
                    ($op)(A, convert($converttype, B))
                else
                    ($op).(A, B)
                end
            end

            function ($op)(A::Bidiagonal, B::$matrixtype)
                if A.uplo == $uplo
                    ($op)(convert($converttype, A), B)
                else
                    ($op).(A, B)
                end
            end
        end
    end
end

# disambiguation between triangular and banded matrices, banded ones "dominate"
mul!(C::AbstractMatrix, A::AbstractTriangular, B::BandedMatrix) = _mul!(C, A, B, MulAddMul())
mul!(C::AbstractMatrix, A::BandedMatrix, B::AbstractTriangular) = _mul!(C, A, B, MulAddMul())
mul!(C::AbstractMatrix, A::AbstractTriangular, B::BandedMatrix, alpha::Number, beta::Number) =
    _mul!(C, A, B, MulAddMul(alpha, beta))
mul!(C::AbstractMatrix, A::BandedMatrix, B::AbstractTriangular, alpha::Number, beta::Number) =
    _mul!(C, A, B, MulAddMul(alpha, beta))

function *(H::UpperHessenberg, B::Bidiagonal)
    T = promote_op(matprod, eltype(H), eltype(B))
    A = mul!(similar(H, T, size(H)), H, B)
    return B.uplo == 'U' ? UpperHessenberg(A) : A
end
function *(B::Bidiagonal, H::UpperHessenberg)
    T = promote_op(matprod, eltype(B), eltype(H))
    A = mul!(similar(H, T, size(H)), B, H)
    return B.uplo == 'U' ? UpperHessenberg(A) : A
end

function /(H::UpperHessenberg, B::Bidiagonal)
    T = typeof(oneunit(eltype(H))/oneunit(eltype(B)))
    A = _rdiv!(similar(H, T, size(H)), H, B)
    return B.uplo == 'U' ? UpperHessenberg(A) : A
end

function \(B::Bidiagonal, H::UpperHessenberg)
    T = typeof(oneunit(eltype(B))\oneunit(eltype(H)))
    A = ldiv!(similar(H, T, size(H)), B, H)
    return B.uplo == 'U' ? UpperHessenberg(A) : A
end

# specialized +/- for structured matrices. If these are removed, it falls
# back to broadcasting which has ~2-10x speed regressions.
# For the other structure matrix pairs, broadcasting works well.

# For structured matrix types with different non-zero diagonals the underlying
# representations must be promoted to the same type.
# For example, in Diagonal + Bidiagonal only the main diagonal is touched so
# the off diagonal could be a different type after the operation resulting in
# an error. See issue #28994

@commutative function (+)(A::Bidiagonal, B::Diagonal)
    newdv = A.dv + B.diag
    Bidiagonal(newdv, typeof(newdv)(A.ev), A.uplo)
end

function (-)(A::Bidiagonal, B::Diagonal)
    newdv = A.dv - B.diag
    Bidiagonal(newdv, typeof(newdv)(A.ev), A.uplo)
end

function (-)(A::Diagonal, B::Bidiagonal)
    newdv = A.diag - B.dv
    Bidiagonal(newdv, typeof(newdv)(-B.ev), B.uplo)
end

@commutative function (+)(A::Diagonal, B::SymTridiagonal)
    newdv = A.diag + B.dv
    SymTridiagonal(A.diag + B.dv, typeof(newdv)(B.ev))
end

function (-)(A::Diagonal, B::SymTridiagonal)
    newdv = A.diag - B.dv
    SymTridiagonal(newdv, typeof(newdv)(-B.ev))
end

function (-)(A::SymTridiagonal, B::Diagonal)
    newdv = A.dv - B.diag
    SymTridiagonal(newdv, typeof(newdv)(A.ev))
end

# this set doesn't have the aforementioned problem

@commutative (+)(A::Tridiagonal, B::SymTridiagonal) = Tridiagonal(A.dl+_evview(B), A.d+B.dv, A.du+_evview(B))
-(A::Tridiagonal, B::SymTridiagonal) = Tridiagonal(A.dl-_evview(B), A.d-B.dv, A.du-_evview(B))
-(A::SymTridiagonal, B::Tridiagonal) = Tridiagonal(_evview(A)-B.dl, A.dv-B.d, _evview(A)-B.du)

@commutative function (+)(A::Diagonal, B::Tridiagonal)
    newdv = A.diag + B.d
    Tridiagonal(typeof(newdv)(B.dl), newdv, typeof(newdv)(B.du))
end

function (-)(A::Diagonal, B::Tridiagonal)
    newdv = A.diag - B.d
    Tridiagonal(typeof(newdv)(-B.dl), newdv, typeof(newdv)(-B.du))
end

function (-)(A::Tridiagonal, B::Diagonal)
    newdv = A.d - B.diag
    Tridiagonal(typeof(newdv)(A.dl), newdv, typeof(newdv)(A.du))
end

@commutative function (+)(A::Bidiagonal, B::Tridiagonal)
    newdv = A.dv + B.d
    Tridiagonal((A.uplo == 'U' ? (typeof(newdv)(B.dl), newdv, A.ev+B.du) : (A.ev+B.dl, newdv, typeof(newdv)(B.du)))...)
end

function (-)(A::Bidiagonal, B::Tridiagonal)
    newdv = A.dv - B.d
    Tridiagonal((A.uplo == 'U' ? (typeof(newdv)(-B.dl), newdv, A.ev-B.du) : (A.ev-B.dl, newdv, typeof(newdv)(-B.du)))...)
end

function (-)(A::Tridiagonal, B::Bidiagonal)
    newdv = A.d - B.dv
    Tridiagonal((B.uplo == 'U' ? (typeof(newdv)(A.dl), newdv, A.du-B.ev) : (A.dl-B.ev, newdv, typeof(newdv)(A.du)))...)
end

@commutative function (+)(A::Bidiagonal, B::SymTridiagonal)
    newdv = A.dv + B.dv
    Tridiagonal((A.uplo == 'U' ? (typeof(newdv)(_evview(B)), A.dv+B.dv, A.ev+_evview(B)) : (A.ev+_evview(B), A.dv+B.dv, typeof(newdv)(_evview(B))))...)
end

function (-)(A::Bidiagonal, B::SymTridiagonal)
    newdv = A.dv - B.dv
    Tridiagonal((A.uplo == 'U' ? (typeof(newdv)(-_evview(B)), newdv, A.ev-_evview(B)) : (A.ev-_evview(B), newdv, typeof(newdv)(-_evview(B))))...)
end

function (-)(A::SymTridiagonal, B::Bidiagonal)
    newdv = A.dv - B.dv
    Tridiagonal((B.uplo == 'U' ? (typeof(newdv)(_evview(A)), newdv, _evview(A)-B.ev) : (_evview(A)-B.ev, newdv, typeof(newdv)(_evview(A))))...)
end

@commutative function (+)(A::Tridiagonal, B::UniformScaling)
    newd = A.d .+ Ref(B)
    Tridiagonal(typeof(newd)(A.dl), newd, typeof(newd)(A.du))
end

@commutative function (+)(A::SymTridiagonal, B::UniformScaling)
    newdv = A.dv .+ Ref(B)
    SymTridiagonal(newdv, typeof(newdv)(A.ev))
end

@commutative function (+)(A::Bidiagonal, B::UniformScaling)
    newdv = A.dv .+ Ref(B)
    Bidiagonal(newdv, typeof(newdv)(A.ev), A.uplo)
end

@commutative function (+)(A::Diagonal, B::UniformScaling)
    Diagonal(A.diag .+ Ref(B))
end

# StructuredMatrix - UniformScaling = StructuredMatrix + (-UniformScaling) =>
# no need to define reversed order
function (-)(A::UniformScaling, B::Tridiagonal)
    d = Ref(A) .- B.d
    Tridiagonal(convert(typeof(d), -B.dl), d, convert(typeof(d), -B.du))
end
function (-)(A::UniformScaling, B::SymTridiagonal)
    dv = Ref(A) .- B.dv
    SymTridiagonal(dv, convert(typeof(dv), -B.ev))
end
function (-)(A::UniformScaling, B::Bidiagonal)
    dv = Ref(A) .- B.dv
    Bidiagonal(dv, convert(typeof(dv), -B.ev), B.uplo)
end
function (-)(A::UniformScaling, B::Diagonal)
    Diagonal(Ref(A) .- B.diag)
end

## Diagonal construction from UniformScaling
Diagonal{T}(s::UniformScaling, m::Integer) where {T} = Diagonal{T}(fill(T(s.λ), m))
Diagonal(s::UniformScaling, m::Integer) = Diagonal{eltype(s)}(s, m)

Base.muladd(A::Union{Diagonal, UniformScaling}, B::Union{Diagonal, UniformScaling}, z::Union{Diagonal, UniformScaling}) =
    Diagonal(_diag_or_value(A) .* _diag_or_value(B) .+ _diag_or_value(z))

_diag_or_value(A::Diagonal) = A.diag
_diag_or_value(A::UniformScaling) = A.λ

# fill[stored]! methods
fillstored!(A::Diagonal, x) = (fill!(A.diag, x); A)
fillstored!(A::Bidiagonal, x) = (fill!(A.dv, x); fill!(A.ev, x); A)
fillstored!(A::Tridiagonal, x) = (fill!(A.dl, x); fill!(A.d, x); fill!(A.du, x); A)
fillstored!(A::SymTridiagonal, x) = (fill!(A.dv, x); fill!(A.ev, x); A)

_small_enough(A::Union{Diagonal, Bidiagonal}) = size(A, 1) <= 1
_small_enough(A::Tridiagonal) = size(A, 1) <= 2
_small_enough(A::SymTridiagonal) = size(A, 1) <= 2

function fill!(A::Union{Diagonal,Bidiagonal,Tridiagonal,SymTridiagonal}, x)
    xT = convert(eltype(A), x)
    (iszero(xT) || _small_enough(A)) && return fillstored!(A, xT)
    throw(ArgumentError("array of type $(typeof(A)) and size $(size(A)) can
    not be filled with $x, since some of its entries are constrained."))
end

one(D::Diagonal) = Diagonal(one.(D.diag))
one(A::Bidiagonal{T}) where T = Bidiagonal(fill!(similar(A.dv, typeof(one(T))), one(T)), fill!(similar(A.ev, typeof(one(T))), zero(one(T))), A.uplo)
one(A::Tridiagonal{T}) where T = Tridiagonal(fill!(similar(A.du, typeof(one(T))), zero(one(T))), fill!(similar(A.d, typeof(one(T))), one(T)), fill!(similar(A.dl, typeof(one(T))), zero(one(T))))
one(A::SymTridiagonal{T}) where T = SymTridiagonal(fill!(similar(A.dv, typeof(one(T))), one(T)), fill!(similar(A.ev, typeof(one(T))), zero(one(T))))
for t in (:LowerTriangular, :UnitLowerTriangular, :UpperTriangular, :UnitUpperTriangular)
    @eval one(A::$t) = $t(one(parent(A)))
    @eval oneunit(A::$t) = $t(oneunit(parent(A)))
end

zero(D::Diagonal) = Diagonal(zero.(D.diag))
oneunit(D::Diagonal) = Diagonal(oneunit.(D.diag))

isdiag(A::HermOrSym{<:Any,<:Diagonal}) = isdiag(parent(A))
dot(x::AbstractVector, A::RealHermSymComplexSym{<:Real,<:Diagonal}, y::AbstractVector) =
    dot(x, A.data, y)

# equals and approx equals methods for structured matrices
# SymTridiagonal == Tridiagonal is already defined in tridiag.jl

==(A::Diagonal, B::Bidiagonal) = iszero(B.ev) && A.diag == B.dv
==(A::Diagonal, B::SymTridiagonal) = iszero(_evview(B)) && A.diag == B.dv
==(B::Bidiagonal, A::Diagonal) = A == B
==(A::Diagonal, B::Tridiagonal) = iszero(B.dl) && iszero(B.du) && A.diag == B.d
==(B::Tridiagonal, A::Diagonal) = A == B

function ==(A::Bidiagonal, B::Tridiagonal)
    if A.uplo == 'U'
        return iszero(B.dl) && A.dv == B.d && A.ev == B.du
    else
        return iszero(B.du) && A.dv == B.d && A.ev == B.dl
    end
end
==(B::Tridiagonal, A::Bidiagonal) = A == B

==(A::Bidiagonal, B::SymTridiagonal) = iszero(_evview(B)) && iszero(A.ev) && A.dv == B.dv
==(B::SymTridiagonal, A::Bidiagonal) = A == B

# TODO: remove these deprecations (used by SparseArrays in the past)
const _DenseConcatGroup = Union{}
const _SpecialArrays = Union{}

promote_to_array_type(::Tuple) = Matrix

# promote_to_arrays(n,k, T, A...) promotes any UniformScaling matrices
# in A to matrices of type T and sizes given by n[k:end].  n is an array
# so that the same promotion code can be used for hvcat.  We pass the type T
# so that we can re-use this code for sparse-matrix hcat etcetera.
promote_to_arrays_(n::Int, ::Type, a::Number) = a
promote_to_arrays_(n::Int, ::Type{Matrix}, J::UniformScaling{T}) where {T} = Matrix(J, n, n)
promote_to_arrays_(n::Int, ::Type, A::AbstractArray) = A
promote_to_arrays_(n::Int, ::Type, A::AbstractQ) = collect(A)
promote_to_arrays(n,k, ::Type) = ()
promote_to_arrays(n,k, ::Type{T}, A) where {T} = (promote_to_arrays_(n[k], T, A),)
promote_to_arrays(n,k, ::Type{T}, A, B) where {T} =
    (promote_to_arrays_(n[k], T, A), promote_to_arrays_(n[k+1], T, B))
promote_to_arrays(n,k, ::Type{T}, A, B, C) where {T} =
    (promote_to_arrays_(n[k], T, A), promote_to_arrays_(n[k+1], T, B), promote_to_arrays_(n[k+2], T, C))
promote_to_arrays(n,k, ::Type{T}, A, B, Cs...) where {T} =
    (promote_to_arrays_(n[k], T, A), promote_to_arrays_(n[k+1], T, B), promote_to_arrays(n,k+2, T, Cs...)...)

_us2number(A) = A
_us2number(J::UniformScaling) = J.λ

for (f, _f, dim, name) in ((:hcat, :_hcat, 1, "rows"), (:vcat, :_vcat, 2, "cols"))
    @eval begin
        @inline $f(A::Union{AbstractArray,AbstractQ,UniformScaling}...) = $_f(A...)
        # if there's a Number present, J::UniformScaling must be 1x1-dimensional
        @inline $f(A::Union{AbstractArray,AbstractQ,UniformScaling,Number}...) = $f(map(_us2number, A)...)
        function $_f(A::Union{AbstractArray,AbstractQ,UniformScaling,Number}...; array_type = promote_to_array_type(A))
            n = -1
            for a in A
                if !isa(a, UniformScaling)
                    require_one_based_indexing(a)
                    na = size(a,$dim)
                    n >= 0 && n != na &&
                        throw(DimensionMismatch(string("number of ", $name,
                            " of each array must match (got ", n, " and ", na, ")")))
                    n = na
                end
            end
            n == -1 && throw(ArgumentError($("$f of only UniformScaling objects cannot determine the matrix size")))
            return cat(promote_to_arrays(fill(n, length(A)), 1, array_type, A...)..., dims=Val(3-$dim))
        end
    end
end

hvcat(rows::Tuple{Vararg{Int}}, A::Union{AbstractArray,AbstractQ,UniformScaling}...) = _hvcat(rows, A...)
hvcat(rows::Tuple{Vararg{Int}}, A::Union{AbstractArray,AbstractQ,UniformScaling,Number}...) = _hvcat(rows, A...)
function _hvcat(rows::Tuple{Vararg{Int}}, A::Union{AbstractArray,AbstractQ,UniformScaling,Number}...; array_type = promote_to_array_type(A))
    require_one_based_indexing(A...)
    nr = length(rows)
    sum(rows) == length(A) || throw(ArgumentError("mismatch between row sizes and number of arguments"))
    n = fill(-1, length(A))
    needcols = false # whether we also need to infer some sizes from the column count
    j = 0
    for i = 1:nr # infer UniformScaling sizes from row counts, if possible:
        ni = -1 # number of rows in this block-row, -1 indicates unknown
        for k = 1:rows[i]
            if !isa(A[j+k], UniformScaling)
                na = size(A[j+k], 1)
                ni >= 0 && ni != na &&
                    throw(DimensionMismatch("mismatch in number of rows"))
                ni = na
            end
        end
        if ni >= 0
            for k = 1:rows[i]
                n[j+k] = ni
            end
        else # row consisted only of UniformScaling objects
            needcols = true
        end
        j += rows[i]
    end
    if needcols # some sizes still unknown, try to infer from column count
        nc = -1
        j = 0
        for i = 1:nr
            nci = 0
            rows[i] > 0 && n[j+1] == -1 && (j += rows[i]; continue)
            for k = 1:rows[i]
                nci += isa(A[j+k], UniformScaling) ? n[j+k] : size(A[j+k], 2)
            end
            nc >= 0 && nc != nci && throw(DimensionMismatch("mismatch in number of columns"))
            nc = nci
            j += rows[i]
        end
        nc == -1 && throw(ArgumentError("sizes of UniformScalings could not be inferred"))
        j = 0
        for i = 1:nr
            if rows[i] > 0 && n[j+1] == -1 # this row consists entirely of UniformScalings
                nci, r = divrem(nc, rows[i])
                r != 0 && throw(DimensionMismatch("indivisible UniformScaling sizes"))
                for k = 1:rows[i]
                    n[j+k] = nci
                end
            end
            j += rows[i]
        end
    end
    Amat = promote_to_arrays(n, 1, array_type, A...)
    # We have two methods for promote_to_array_type, one returning Matrix and
    # another one returning SparseMatrixCSC (in SparseArrays.jl). In the dense
    # case, we cannot call hvcat for the promoted UniformScalings because this
    # causes a stack overflow. In the sparse case, however, we cannot call
    # typed_hvcat because we need a sparse output.
    if array_type == Matrix
        return typed_hvcat(promote_eltype(Amat...), rows, Amat...)
    else
        return hvcat(rows, Amat...)
    end
end

# factorizations
function cholesky(S::RealHermSymComplexHerm{<:Real,<:SymTridiagonal}, ::NoPivot = NoPivot(); check::Bool = true)
    T = choltype(eltype(S))
    B = Bidiagonal{T}(diag(S, 0), diag(S, S.uplo == 'U' ? 1 : -1), sym_uplo(S.uplo))
    cholesky!(Hermitian(B, sym_uplo(S.uplo)), NoPivot(); check = check)
end
y   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LinearAlgebra/src/bitarray.jl2      # This file is a part of Julia. License is MIT: https://julialang.org/license

function dot(x::BitVector, y::BitVector)
    # simplest way to mimic Array dot behavior
    length(x) == length(y) || throw(DimensionMismatch())
    s = 0
    xc = x.chunks
    yc = y.chunks
    @inbounds for i = 1:length(xc)
        s += count_ones(xc[i] & yc[i])
    end
    s
end

## slower than the unpacked version, which is MUCH slower
#  than blas'd (this one saves storage though, keeping it commented
#  just in case)
#function aTb(A::BitMatrix, B::BitMatrix)
    #(mA, nA) = size(A)
    #(mB, nB) = size(B)
    #C = falses(nA, nB)
    #if mA != mB; throw(DimensionMismatch()) end
    #if mA == 0; return C; end
    #col_ch = num_bit_chunks(mA)
    ## TODO: avoid using aux chunks and copy (?)
    #aux_chunksA = zeros(UInt64, col_ch)
    #aux_chunksB = [zeros(UInt64, col_ch) for j=1:nB]
    #for j = 1:nB
        #Base.copy_chunks!(aux_chunksB[j], 1, B.chunks, (j-1)*mA+1, mA)
    #end
    #for i = 1:nA
        #Base.copy_chunks!(aux_chunksA, 1, A.chunks, (i-1)*mA+1, mA)
        #for j = 1:nB
            #for k = 1:col_ch
                ## TODO: improve
                #C[i, j] += count_ones(aux_chunksA[k] & aux_chunksB[j][k])
            #end
        #end
    #end
    #C
#end

#aCb(A::BitMatrix{T}, B::BitMatrix{S}) where {T,S} = aTb(A, B)

function triu(B::BitMatrix, k::Integer=0)
    m,n = size(B)
    if !(-m + 1 <= k <= n + 1)
        throw(ArgumentError(string("the requested diagonal, $k, must be at least",
            "$(-m + 1) and at most $(n + 1) in an $m-by-$n matrix")))
    end
    A = falses(m,n)
    Ac = A.chunks
    Bc = B.chunks
    for i = max(k+1,1):n
        j = clamp((i - 1) * m + 1, 1, i * m)
        Base.copy_chunks!(Ac, j, Bc, j, min(i-k, m))
    end
    A
end

function tril(B::BitMatrix, k::Integer=0)
    m,n = size(B)
    if !(-m - 1 <= k <= n - 1)
        throw(ArgumentError(string("the requested diagonal, $k, must be at least ",
            "$(-m - 1) and at most $(n - 1) in an $m-by-$n matrix")))
    end
    A = falses(m, n)
    Ac = A.chunks
    Bc = B.chunks
    for i = 1:min(n, m+k)
        j = clamp((i - 1) * m + i - k, 1, i * m)
        Base.copy_chunks!(Ac, j, Bc, j, max(m-i+k+1, 0))
    end
    A
end

## diag

function diag(B::BitMatrix)
    n = minimum(size(B))
    v = similar(B, n)
    for i = 1:n
        v[i] = B[i,i]
    end
    v
end

## norm and rank

svd(A::BitMatrix) = svd(float(A))
qr(A::BitMatrix) = qr(float(A))

## kron

@inline function kron!(R::BitVector, a::BitVector, b::BitVector)
    m = length(a)
    n = length(b)
    @boundscheck length(R) == n*m || throw(DimensionMismatch())
    Rc = R.chunks
    bc = b.chunks
    for j = 1:m
        a[j] && Base.copy_chunks!(Rc, (j-1)*n+1, bc, 1, n)
    end
    return R
end

function kron(a::BitVector, b::BitVector)
    m = length(a)
    n = length(b)
    R = falses(n * m)
    return @inbounds kron!(R, a, b)
end

function kron!(R::BitMatrix, a::BitMatrix, b::BitMatrix)
    mA,nA = size(a)
    mB,nB = size(b)
    @boundscheck size(R) == (mA*mB, nA*nB) || throw(DimensionMismatch())

    for i = 1:mA
        ri = (1:mB) .+ ((i-1)*mB)
        for j = 1:nA
            if a[i,j]
                rj = (1:nB) .+ ((j-1)*nB)
                R[ri,rj] = b
            end
        end
    end
    return R
end

function kron(a::BitMatrix, b::BitMatrix)
    mA,nA = size(a)
    mB,nB = size(b)
    R = falses(mA*mB, nA*nB)
    return @inbounds kron!(R, a, b)
end

## Structure query functions

issymmetric(A::BitMatrix) = size(A, 1)==size(A, 2) && count(!iszero, A - copy(A'))==0
ishermitian(A::BitMatrix) = issymmetric(A)

function nonzero_chunks(chunks::Vector{UInt64}, pos0::Int, pos1::Int)
    k0, l0 = Base.get_chunks_id(pos0)
    k1, l1 = Base.get_chunks_id(pos1)

    delta_k = k1 - k0

    z = UInt64(0)
    u = ~z
    if delta_k == 0
        msk_0 = (u << l0) & ~(u << l1 << 1)
    else
        msk_0 = (u << l0)
        msk_1 = ~(u << l1 << 1)
    end

    @inbounds begin
        (chunks[k0] & msk_0) == z || return true
        delta_k == 0 && return false
        for i = k0 + 1 : k1 - 1
            chunks[i] == z || return true
        end
        (chunks[k1] & msk_1)==z || return true
    end
    return false
end

function istriu(A::BitMatrix)
    m, n = size(A)
    for j = 1:min(n,m-1)
        stride = (j-1) * m
        nonzero_chunks(A.chunks, stride+j+1, stride+m) && return false
    end
    return true
end

function istril(A::BitMatrix)
    m, n = size(A)
    (m == 0 || n == 0) && return true
    for j = 2:n
        stride = (j-1) * m
        nonzero_chunks(A.chunks, stride+1, stride+min(j-1,m)) && return false
    end
    return true
end

# fast 8x8 bit transpose from Henry S. Warrens's "Hacker's Delight"
# http://www.hackersdelight.org/hdcodetxt/transpose8.c.txt
function transpose8x8(x::UInt64)
    y = x
    t = xor(y, y >>> 7) & 0x00aa00aa00aa00aa
    y = xor(y, t, t << 7)
    t = xor(y, y >>> 14) & 0x0000cccc0000cccc
    y = xor(y, t, t << 14)
    t = xor(y, y >>> 28) & 0x00000000f0f0f0f0
    return xor(y, t, t << 28)
end

function form_8x8_chunk(Bc::Vector{UInt64}, i1::Int, i2::Int, m::Int, cgap::Int, cinc::Int, nc::Int, msk8::UInt64)
    x = UInt64(0)

    k, l = Base.get_chunks_id(i1 + (i2 - 1) * m)
    r = 0
    for j = 1:8
        k > nc && break
        x |= ((Bc[k] >>> l) & msk8) << r
        if l + 8 >= 64 && nc > k
            r0 = 8 - Base._mod64(l + 8)
            x |= (Bc[k + 1] & (msk8 >>> r0)) << (r + r0)
        end
        k += cgap + (l + cinc >= 64 ? 1 : 0)
        l = Base._mod64(l + cinc)
        r += 8
    end
    return x
end

# note: assumes B is filled with 0's
function put_8x8_chunk(Bc::Vector{UInt64}, i1::Int, i2::Int, x::UInt64, m::Int, cgap::Int, cinc::Int, nc::Int, msk8::UInt64)
    k, l = Base.get_chunks_id(i1 + (i2 - 1) * m)
    r = 0
    for j = 1:8
        k > nc && break
        Bc[k] |= ((x >>> r) & msk8) << l
        if l + 8 >= 64 && nc > k
            r0 = 8 - Base._mod64(l + 8)
            Bc[k + 1] |= ((x >>> (r + r0)) & (msk8 >>> r0))
        end
        k += cgap + (l + cinc >= 64 ? 1 : 0)
        l = Base._mod64(l + cinc)
        r += 8
    end
    return
end

adjoint(B::Union{BitVector,BitMatrix}) = Adjoint(B)
transpose(B::Union{BitVector,BitMatrix}) = Transpose(B)
Base.copy(B::Adjoint{Bool,BitMatrix}) = transpose!(falses(size(B)), B.parent)
Base.copy(B::Transpose{Bool,BitMatrix}) = transpose!(falses(size(B)), B.parent)
function transpose!(C::BitMatrix, B::BitMatrix)
    @boundscheck size(C) == reverse(size(B)) || throw(DimensionMismatch())
    l1, l2 = size(B)

    cgap1, cinc1 = Base._div64(l1), Base._mod64(l1)
    cgap2, cinc2 = Base._div64(l2), Base._mod64(l2)

    Bc = B.chunks
    Cc = C.chunks

    nc = length(Bc)

    for i = 1:8:l1
        msk8_1 = UInt64(0xff)
        if (l1 < i + 7)
            msk8_1 >>>= i + 7 - l1
        end

        for j = 1:8:l2
            x = form_8x8_chunk(Bc, i, j, l1, cgap1, cinc1, nc, msk8_1)
            x = transpose8x8(x)

            msk8_2 = UInt64(0xff)
            if (l2 < j + 7)
                msk8_2 >>>= j + 7 - l2
            end

            put_8x8_chunk(Cc, j, i, x, l2, cgap2, cinc2, nc, msk8_2)
        end
    end
    return C
end
u   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LinearAlgebra/src/ldlt.jl/      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
    LDLt <: Factorization

Matrix factorization type of the `LDLt` factorization of a real [`SymTridiagonal`](@ref)
matrix `S` such that `S = L*Diagonal(d)*L'`, where `L` is a [`UnitLowerTriangular`](@ref)
matrix and `d` is a vector. The main use of an `LDLt` factorization `F = ldlt(S)`
is to solve the linear system of equations `Sx = b` with `F\\b`. This is the
return type of [`ldlt`](@ref), the corresponding matrix factorization function.

The individual components of the factorization `F::LDLt` can be accessed via `getproperty`:

| Component | Description                                 |
|:---------:|:--------------------------------------------|
| `F.L`     | `L` (unit lower triangular) part of `LDLt`  |
| `F.D`     | `D` (diagonal) part of `LDLt`               |
| `F.Lt`    | `Lt` (unit upper triangular) part of `LDLt` |
| `F.d`     | diagonal values of `D` as a `Vector`        |

# Examples
```jldoctest
julia> S = SymTridiagonal([3., 4., 5.], [1., 2.])
3×3 SymTridiagonal{Float64, Vector{Float64}}:
 3.0  1.0   ⋅
 1.0  4.0  2.0
  ⋅   2.0  5.0

julia> F = ldlt(S)
LDLt{Float64, SymTridiagonal{Float64, Vector{Float64}}}
L factor:
3×3 UnitLowerTriangular{Float64, SymTridiagonal{Float64, Vector{Float64}}}:
 1.0        ⋅         ⋅
 0.333333  1.0        ⋅
 0.0       0.545455  1.0
D factor:
3×3 Diagonal{Float64, Vector{Float64}}:
 3.0   ⋅        ⋅
  ⋅   3.66667   ⋅
  ⋅    ⋅       3.90909
```
"""
struct LDLt{T,S<:AbstractMatrix{T}} <: Factorization{T}
    data::S

    function LDLt{T,S}(data) where {T,S<:AbstractMatrix{T}}
        require_one_based_indexing(data)
        new{T,S}(data)
    end
end
LDLt(data::AbstractMatrix{T}) where {T} = LDLt{T,typeof(data)}(data)
LDLt{T}(data::AbstractMatrix) where {T} = LDLt(convert(AbstractMatrix{T}, data)::AbstractMatrix{T})

size(S::LDLt) = size(S.data)
size(S::LDLt, i::Integer) = size(S.data, i)

LDLt{T,S}(F::LDLt{T,S}) where {T,S<:AbstractMatrix{T}} = F
LDLt{T,S}(F::LDLt) where {T,S<:AbstractMatrix{T}} = LDLt{T,S}(convert(S, F.data)::S)
LDLt{T}(F::LDLt{T}) where {T} = F
LDLt{T}(F::LDLt) where {T} = LDLt(convert(AbstractMatrix{T}, F.data)::AbstractMatrix{T})

Factorization{T}(F::LDLt{T}) where {T} = F
Factorization{T}(F::LDLt) where {T} = LDLt{T}(F)

function getproperty(F::LDLt{<:Any, <:SymTridiagonal}, d::Symbol)
    Fdata = getfield(F, :data)
    if d === :d
        return Fdata.dv
    elseif d === :D
        return Diagonal(Fdata.dv)
    elseif d === :L
        return UnitLowerTriangular(Fdata)
    elseif d === :Lt
        return UnitUpperTriangular(Fdata)
    else
        return getfield(F, d)
    end
end

adjoint(F::LDLt{<:Real,<:SymTridiagonal}) = F
adjoint(F::LDLt) = LDLt(copy(adjoint(F.data)))

function show(io::IO, mime::MIME{Symbol("text/plain")}, F::LDLt)
    summary(io, F); println(io)
    println(io, "L factor:")
    show(io, mime, F.L)
    println(io, "\nD factor:")
    show(io, mime, F.D)
end

# SymTridiagonal
"""
    ldlt!(S::SymTridiagonal) -> LDLt

Same as [`ldlt`](@ref), but saves space by overwriting the input `S`, instead of creating a copy.

# Examples
```jldoctest
julia> S = SymTridiagonal([3., 4., 5.], [1., 2.])
3×3 SymTridiagonal{Float64, Vector{Float64}}:
 3.0  1.0   ⋅
 1.0  4.0  2.0
  ⋅   2.0  5.0

julia> ldltS = ldlt!(S);

julia> ldltS === S
false

julia> S
3×3 SymTridiagonal{Float64, Vector{Float64}}:
 3.0       0.333333   ⋅
 0.333333  3.66667   0.545455
  ⋅        0.545455  3.90909
```
"""
function ldlt!(S::SymTridiagonal{T,V}) where {T,V}
    n = size(S,1)
    d = S.dv
    e = S.ev
    @inbounds for i in 1:n-1
        iszero(d[i]) && throw(ZeroPivotException(i))
        e[i] /= d[i]
        d[i+1] -= e[i]^2*d[i]
    end
    return LDLt{T,SymTridiagonal{T,V}}(S)
end

"""
    ldlt(S::SymTridiagonal) -> LDLt

Compute an `LDLt` (i.e., ``LDL^T``) factorization of the real symmetric tridiagonal matrix `S` such that `S = L*Diagonal(d)*L'`
where `L` is a unit lower triangular matrix and `d` is a vector. The main use of an `LDLt`
factorization `F = ldlt(S)` is to solve the linear system of equations `Sx = b` with `F\\b`.

See also [`bunchkaufman`](@ref) for a similar, but pivoted, factorization of arbitrary symmetric or Hermitian matrices.

# Examples
```jldoctest
julia> S = SymTridiagonal([3., 4., 5.], [1., 2.])
3×3 SymTridiagonal{Float64, Vector{Float64}}:
 3.0  1.0   ⋅
 1.0  4.0  2.0
  ⋅   2.0  5.0

julia> ldltS = ldlt(S);

julia> b = [6., 7., 8.];

julia> ldltS \\ b
3-element Vector{Float64}:
 1.7906976744186047
 0.627906976744186
 1.3488372093023255

julia> S \\ b
3-element Vector{Float64}:
 1.7906976744186047
 0.627906976744186
 1.3488372093023255
```
"""
function ldlt(M::SymTridiagonal{T}; shift::Number=false) where T
    S = typeof((zero(T)+shift)/one(T))
    Mₛ = SymTridiagonal{S}(copymutable_oftype(M.dv, S), copymutable_oftype(M.ev, S))
    if !iszero(shift)
        Mₛ.dv .+= shift
    end
    return ldlt!(Mₛ)
end

factorize(S::SymTridiagonal) = ldlt(S)

function ldiv!(S::LDLt{<:Any,<:SymTridiagonal}, B::AbstractVecOrMat)
    require_one_based_indexing(B)
    n, nrhs = size(B, 1), size(B, 2)
    if size(S,1) != n
        throw(DimensionMismatch("Matrix has dimensions $(size(S)) but right hand side has first dimension $n"))
    end
    d = S.data.dv
    l = S.data.ev
    @inbounds begin
        for i = 2:n
            li1 = l[i-1]
            @simd for j = 1:nrhs
                B[i,j] -= li1*B[i-1,j]
            end
        end
        dn = d[n]
        @simd for j = 1:nrhs
            B[n,j] /= dn
        end
        for i = n-1:-1:1
            di = d[i]
            li = l[i]
            @simd for j = 1:nrhs
                B[i,j] /= di
                B[i,j] -= li*B[i+1,j]
            end
        end
    end
    return B
end

rdiv!(B::AbstractVecOrMat, S::LDLt{<:Any,<:SymTridiagonal}) =
    transpose(ldiv!(S, transpose(B)))

function logabsdet(F::LDLt{<:Any,<:SymTridiagonal})
    it = (F.data[i,i] for i in 1:size(F, 1))
    return sum(log∘abs, it), prod(sign, it)
end

# Conversion methods
function SymTridiagonal(F::LDLt{<:Any, <:SymTridiagonal})
    e = copy(F.data.ev)
    d = copy(F.data.dv)
    e .*= d[1:end-1]
    d[2:end] += e .* F.data.ev
    SymTridiagonal(d, e)
end
AbstractMatrix(F::LDLt) = SymTridiagonal(F)
AbstractArray(F::LDLt) = AbstractMatrix(F)
Matrix(F::LDLt) = Array(AbstractArray(F))
Array(F::LDLt) = Matrix(F)
v   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LinearAlgebra/src/schur.jl,=      # This file is a part of Julia. License is MIT: https://julialang.org/license

# Schur decomposition
"""
    Schur <: Factorization

Matrix factorization type of the Schur factorization of a matrix `A`. This is the
return type of [`schur(_)`](@ref), the corresponding matrix factorization function.

If `F::Schur` is the factorization object, the (quasi) triangular Schur factor can
be obtained via either `F.Schur` or `F.T` and the orthogonal/unitary Schur vectors
via `F.vectors` or `F.Z` such that `A = F.vectors * F.Schur * F.vectors'`. The
eigenvalues of `A` can be obtained with `F.values`.

Iterating the decomposition produces the components `F.T`, `F.Z`, and `F.values`.

# Examples
```jldoctest
julia> A = [5. 7.; -2. -4.]
2×2 Matrix{Float64}:
  5.0   7.0
 -2.0  -4.0

julia> F = schur(A)
Schur{Float64, Matrix{Float64}, Vector{Float64}}
T factor:
2×2 Matrix{Float64}:
 3.0   9.0
 0.0  -2.0
Z factor:
2×2 Matrix{Float64}:
  0.961524  0.274721
 -0.274721  0.961524
eigenvalues:
2-element Vector{Float64}:
  3.0
 -2.0

julia> F.vectors * F.Schur * F.vectors'
2×2 Matrix{Float64}:
  5.0   7.0
 -2.0  -4.0

julia> t, z, vals = F; # destructuring via iteration

julia> t == F.T && z == F.Z && vals == F.values
true
```
"""
struct Schur{Ty,S<:AbstractMatrix,C<:AbstractVector} <: Factorization{Ty}
    T::S
    Z::S
    values::C
    Schur{Ty,S,C}(T::AbstractMatrix{Ty}, Z::AbstractMatrix{Ty},
                  values::AbstractVector) where {Ty,S,C} = new(T, Z, values)
end
Schur(T::AbstractMatrix{Ty}, Z::AbstractMatrix{Ty}, values::AbstractVector) where {Ty} =
    Schur{Ty, typeof(T), typeof(values)}(T, Z, values)
# backwards-compatible constructors (remove with Julia 2.0)
@deprecate(Schur{Ty,S}(T::AbstractMatrix{Ty}, Z::AbstractMatrix{Ty},
                       values::AbstractVector) where {Ty,S},
           Schur{Ty,S,typeof(values)}(T, Z, values))

# iteration for destructuring into components
Base.iterate(S::Schur) = (S.T, Val(:Z))
Base.iterate(S::Schur, ::Val{:Z}) = (S.Z, Val(:values))
Base.iterate(S::Schur, ::Val{:values}) = (S.values, Val(:done))
Base.iterate(S::Schur, ::Val{:done}) = nothing

"""
    schur!(A) -> F::Schur

Same as [`schur`](@ref) but uses the input argument `A` as workspace.

# Examples
```jldoctest
julia> A = [5. 7.; -2. -4.]
2×2 Matrix{Float64}:
  5.0   7.0
 -2.0  -4.0

julia> F = schur!(A)
Schur{Float64, Matrix{Float64}, Vector{Float64}}
T factor:
2×2 Matrix{Float64}:
 3.0   9.0
 0.0  -2.0
Z factor:
2×2 Matrix{Float64}:
  0.961524  0.274721
 -0.274721  0.961524
eigenvalues:
2-element Vector{Float64}:
  3.0
 -2.0

julia> A
2×2 Matrix{Float64}:
 3.0   9.0
 0.0  -2.0
```
"""
schur!(A::StridedMatrix{<:BlasFloat}) = Schur(LinearAlgebra.LAPACK.gees!('V', A)...)

schur!(A::UpperHessenberg{T}) where {T<:BlasFloat} = Schur(LinearAlgebra.LAPACK.hseqr!(parent(A))...)

"""
    schur(A) -> F::Schur

Computes the Schur factorization of the matrix `A`. The (quasi) triangular Schur factor can
be obtained from the `Schur` object `F` with either `F.Schur` or `F.T` and the
orthogonal/unitary Schur vectors can be obtained with `F.vectors` or `F.Z` such that
`A = F.vectors * F.Schur * F.vectors'`. The eigenvalues of `A` can be obtained with `F.values`.

For real `A`, the Schur factorization is "quasitriangular", which means that it
is upper-triangular except with 2×2 diagonal blocks for any conjugate pair
of complex eigenvalues; this allows the factorization to be purely real even
when there are complex eigenvalues.  To obtain the (complex) purely upper-triangular
Schur factorization from a real quasitriangular factorization, you can use
`Schur{Complex}(schur(A))`.

Iterating the decomposition produces the components `F.T`, `F.Z`, and `F.values`.

# Examples
```jldoctest
julia> A = [5. 7.; -2. -4.]
2×2 Matrix{Float64}:
  5.0   7.0
 -2.0  -4.0

julia> F = schur(A)
Schur{Float64, Matrix{Float64}, Vector{Float64}}
T factor:
2×2 Matrix{Float64}:
 3.0   9.0
 0.0  -2.0
Z factor:
2×2 Matrix{Float64}:
  0.961524  0.274721
 -0.274721  0.961524
eigenvalues:
2-element Vector{Float64}:
  3.0
 -2.0

julia> F.vectors * F.Schur * F.vectors'
2×2 Matrix{Float64}:
  5.0   7.0
 -2.0  -4.0

julia> t, z, vals = F; # destructuring via iteration

julia> t == F.T && z == F.Z && vals == F.values
true
```
"""
schur(A::AbstractMatrix{T}) where {T} = schur!(copy_similar(A, eigtype(T)))
schur(A::UpperHessenberg{T}) where {T} = schur!(copy_similar(A, eigtype(T)))
function schur(A::RealHermSymComplexHerm)
    F = eigen(A; sortby=nothing)
    return Schur(typeof(F.vectors)(Diagonal(F.values)), F.vectors, F.values)
end
function schur(A::Union{UnitUpperTriangular{T},UpperTriangular{T}}) where {T}
    t = eigtype(T)
    Z = copy_similar(A, t)
    return Schur(Z, Matrix{t}(I, size(A)), convert(Vector{t}, diag(A)))
end
function schur(A::Union{UnitLowerTriangular{T},LowerTriangular{T}}) where {T}
    t = eigtype(T)
    # double flip the matrix A
    Z = copy_similar(A, t)
    reverse!(reshape(Z, :))
    # construct "reverse" identity
    n = size(A, 1)
    J = zeros(t, n, n)
    for i in axes(J, 2)
       J[n+1-i, i] = oneunit(t)
    end
    return Schur(Z, J, convert(Vector{t}, diag(A)))
end
function schur(A::Bidiagonal{T}) where {T}
    t = eigtype(T)
    if A.uplo == 'U'
        return Schur(Matrix{t}(A), Matrix{t}(I, size(A)), Vector{t}(A.dv))
    else # A.uplo == 'L'
        # construct "reverse" identity
        n = size(A, 1)
        J = zeros(t, n, n)
        for i in axes(J, 2)
            J[n+1-i, i] = oneunit(t)
        end
        dv = reverse!(Vector{t}(A.dv))
        ev = reverse!(Vector{t}(A.ev))
        return Schur(Matrix{t}(Bidiagonal(dv, ev, 'U')), J, dv)
    end
end

function getproperty(F::Schur, d::Symbol)
    if d === :Schur
        return getfield(F, :T)
    elseif d === :vectors
        return getfield(F, :Z)
    else
        getfield(F, d)
    end
end

Base.propertynames(F::Schur) =
    (:Schur, :vectors, fieldnames(typeof(F))...)

function show(io::IO, mime::MIME{Symbol("text/plain")}, F::Schur)
    summary(io, F); println(io)
    println(io, "T factor:")
    show(io, mime, F.T)
    println(io, "\nZ factor:")
    show(io, mime, F.Z)
    println(io, "\neigenvalues:")
    show(io, mime, F.values)
end

# convert a (standard-form) quasi-triangular real Schur factorization into a
# triangular complex Schur factorization.
#
# Based on the "triangularize" function from GenericSchur.jl,
# released under the MIT "Expat" license by @RalphAS
function Schur{CT}(S::Schur{<:Real}) where {CT<:Complex}
    Tr = S.T
    T = CT.(Tr)
    Z = CT.(S.Z)
    n = size(T,1)
    for j=n:-1:2
        if !iszero(Tr[j,j-1])
            # We want a unitary similarity transform from
            # ┌   ┐      ┌     ┐
            # │a b│      │w₁  x│
            # │c a│ into │0  w₂│ where bc < 0 (a,b,c real)
            # └   ┘      └     ┘
            # If we write it as
            # ┌     ┐
            # │u  v'│
            # │-v u'│
            # └     ┘
            # and make the Ansatz that u is real (so v is imaginary),
            # we arrive at a Givens rotation:
            # θ = atan(sqrt(-Tr[j,j-1]/Tr[j-1,j]))
            # s,c = sin(θ), cos(θ)
            s = sqrt(abs(Tr[j,j-1]))
            c = sqrt(abs(Tr[j-1,j]))
            r = hypot(s,c)
            G = Givens(j-1,j,complex(c/r),im*(-s/r))
            lmul!(G,T)
            rmul!(T,G')
            rmul!(Z,G')
        end
    end
    return Schur(triu!(T),Z,diag(T))
end

Schur{Complex}(S::Schur{<:Complex}) = S
Schur{T}(S::Schur{T}) where {T} = S
Schur{T}(S::Schur) where {T} = Schur(T.(S.T), T.(S.Z), T <: Real && !(eltype(S.values) <: Real) ? complex(T).(S.values) : T.(S.values))

"""
    ordschur!(F::Schur, select::Union{Vector{Bool},BitVector}) -> F::Schur

Same as [`ordschur`](@ref) but overwrites the factorization `F`.
"""
function ordschur!(schur::Schur, select::Union{Vector{Bool},BitVector})
    _, _, vals = _ordschur!(schur.T, schur.Z, select)
    schur.values[:] = vals
    return schur
end

_ordschur(T::StridedMatrix{Ty}, Z::StridedMatrix{Ty}, select::Union{Vector{Bool},BitVector}) where {Ty<:BlasFloat} =
    _ordschur!(copy(T), copy(Z), select)

_ordschur!(T::StridedMatrix{Ty}, Z::StridedMatrix{Ty}, select::Union{Vector{Bool},BitVector}) where {Ty<:BlasFloat} =
    LinearAlgebra.LAPACK.trsen!(convert(Vector{BlasInt}, select), T, Z)[1:3]

"""
    ordschur(F::Schur, select::Union{Vector{Bool},BitVector}) -> F::Schur

Reorders the Schur factorization `F` of a matrix `A = Z*T*Z'` according to the logical array
`select` returning the reordered factorization `F` object. The selected eigenvalues appear
in the leading diagonal of `F.Schur` and the corresponding leading columns of
`F.vectors` form an orthogonal/unitary basis of the corresponding right invariant
subspace. In the real case, a complex conjugate pair of eigenvalues must be either both
included or both excluded via `select`.
"""
ordschur(schur::Schur, select::Union{Vector{Bool},BitVector}) =
    Schur(_ordschur(schur.T, schur.Z, select)...)

"""
    GeneralizedSchur <: Factorization

Matrix factorization type of the generalized Schur factorization of two matrices
`A` and `B`. This is the return type of [`schur(_, _)`](@ref), the corresponding
matrix factorization function.

If `F::GeneralizedSchur` is the factorization object, the (quasi) triangular Schur
factors can be obtained via `F.S` and `F.T`, the left unitary/orthogonal Schur
vectors via `F.left` or `F.Q`, and the right unitary/orthogonal Schur vectors can
be obtained with `F.right` or `F.Z` such that `A=F.left*F.S*F.right'` and
`B=F.left*F.T*F.right'`. The generalized eigenvalues of `A` and `B` can be obtained
with `F.α./F.β`.

Iterating the decomposition produces the components `F.S`, `F.T`, `F.Q`, `F.Z`,
`F.α`, and `F.β`.
"""
struct GeneralizedSchur{Ty,M<:AbstractMatrix,A<:AbstractVector,B<:AbstractVector{Ty}} <: Factorization{Ty}
    S::M
    T::M
    α::A
    β::B
    Q::M
    Z::M
    function GeneralizedSchur{Ty,M,A,B}(S::AbstractMatrix{Ty}, T::AbstractMatrix{Ty},
                                        alpha::AbstractVector, beta::AbstractVector{Ty},
                                        Q::AbstractMatrix{Ty}, Z::AbstractMatrix{Ty}) where {Ty,M,A,B}
        new{Ty,M,A,B}(S, T, alpha, beta, Q, Z)
    end
end
function GeneralizedSchur(S::AbstractMatrix{Ty}, T::AbstractMatrix{Ty},
                          alpha::AbstractVector, beta::AbstractVector{Ty},
                          Q::AbstractMatrix{Ty}, Z::AbstractMatrix{Ty}) where Ty
    GeneralizedSchur{Ty, typeof(S), typeof(alpha), typeof(beta)}(S, T, alpha, beta, Q, Z)
end
# backwards-compatible constructors (remove with Julia 2.0)
@deprecate(GeneralizedSchur{Ty,M}(S::AbstractMatrix{Ty}, T::AbstractMatrix{Ty},
                                 alpha::AbstractVector, beta::AbstractVector{Ty},
                                 Q::AbstractMatrix{Ty}, Z::AbstractMatrix{Ty}) where {Ty,M},
           GeneralizedSchur{Ty,M,typeof(alpha),typeof(beta)}(S, T, alpha, beta, Q, Z))

# iteration for destructuring into components
Base.iterate(S::GeneralizedSchur) = (S.S, Val(:T))
Base.iterate(S::GeneralizedSchur, ::Val{:T}) = (S.T, Val(:Q))
Base.iterate(S::GeneralizedSchur, ::Val{:Q}) = (S.Q, Val(:Z))
Base.iterate(S::GeneralizedSchur, ::Val{:Z}) = (S.Z, Val(:α))
Base.iterate(S::GeneralizedSchur, ::Val{:α}) = (S.α, Val(:β))
Base.iterate(S::GeneralizedSchur, ::Val{:β}) = (S.β, Val(:done))
Base.iterate(S::GeneralizedSchur, ::Val{:done}) = nothing

"""
    schur!(A::StridedMatrix, B::StridedMatrix) -> F::GeneralizedSchur

Same as [`schur`](@ref) but uses the input matrices `A` and `B` as workspace.
"""
function schur!(A::StridedMatrix{T}, B::StridedMatrix{T}) where {T<:BlasFloat}
    if LAPACK.version() < v"3.6.0"
        GeneralizedSchur(LinearAlgebra.LAPACK.gges!('V', 'V', A, B)...)
    else
        GeneralizedSchur(LinearAlgebra.LAPACK.gges3!('V', 'V', A, B)...)
    end
end

"""
    schur(A, B) -> F::GeneralizedSchur

Computes the Generalized Schur (or QZ) factorization of the matrices `A` and `B`. The
(quasi) triangular Schur factors can be obtained from the `Schur` object `F` with `F.S`
and `F.T`, the left unitary/orthogonal Schur vectors can be obtained with `F.left` or
`F.Q` and the right unitary/orthogonal Schur vectors can be obtained with `F.right` or
`F.Z` such that `A=F.left*F.S*F.right'` and `B=F.left*F.T*F.right'`. The
generalized eigenvalues of `A` and `B` can be obtained with `F.α./F.β`.

Iterating the decomposition produces the components `F.S`, `F.T`, `F.Q`, `F.Z`,
`F.α`, and `F.β`.
"""
function schur(A::AbstractMatrix{TA}, B::AbstractMatrix{TB}) where {TA,TB}
    S = promote_type(eigtype(TA), TB)
    return schur!(copy_similar(A, S), copy_similar(B, S))
end

"""
    ordschur!(F::GeneralizedSchur, select::Union{Vector{Bool},BitVector}) -> F::GeneralizedSchur

Same as `ordschur` but overwrites the factorization `F`.
"""
function ordschur!(gschur::GeneralizedSchur, select::Union{Vector{Bool},BitVector})
    _, _, α, β, _, _ = _ordschur!(gschur.S, gschur.T, gschur.Q, gschur.Z, select)
    gschur.α[:] = α
    gschur.β[:] = β
    return gschur
end

_ordschur(S::StridedMatrix{Ty}, T::StridedMatrix{Ty}, Q::StridedMatrix{Ty},
    Z::StridedMatrix{Ty}, select::Union{Vector{Bool},BitVector}) where {Ty<:BlasFloat} =
        _ordschur!(copy(S), copy(T), copy(Q), copy(Z), select)

_ordschur!(S::StridedMatrix{Ty}, T::StridedMatrix{Ty}, Q::StridedMatrix{Ty},
    Z::StridedMatrix{Ty}, select::Union{Vector{Bool},BitVector}) where {Ty<:BlasFloat} =
        LinearAlgebra.LAPACK.tgsen!(convert(Vector{BlasInt}, select), S, T, Q, Z)

"""
    ordschur(F::GeneralizedSchur, select::Union{Vector{Bool},BitVector}) -> F::GeneralizedSchur

Reorders the Generalized Schur factorization `F` of a matrix pair `(A, B) = (Q*S*Z', Q*T*Z')`
according to the logical array `select` and returns a GeneralizedSchur object `F`. The
selected eigenvalues appear in the leading diagonal of both `F.S` and `F.T`, and the
left and right orthogonal/unitary Schur vectors are also reordered such that
`(A, B) = F.Q*(F.S, F.T)*F.Z'` still holds and the generalized eigenvalues of `A`
and `B` can still be obtained with `F.α./F.β`.
"""
ordschur(gschur::GeneralizedSchur, select::Union{Vector{Bool},BitVector}) =
    GeneralizedSchur(_ordschur(gschur.S, gschur.T, gschur.Q, gschur.Z, select)...)

function getproperty(F::GeneralizedSchur, d::Symbol)
    if d === :values
        return getfield(F, :α) ./ getfield(F, :β)
    elseif d === :alpha
        return getfield(F, :α)
    elseif d === :beta
        return getfield(F, :β)
    elseif d === :left
        return getfield(F, :Q)
    elseif d === :right
        return getfield(F, :Z)
    else
        getfield(F, d)
    end
end

Base.propertynames(F::GeneralizedSchur) =
    (:values, :left, :right, fieldnames(typeof(F))...)

function show(io::IO, mime::MIME{Symbol("text/plain")}, F::GeneralizedSchur)
    summary(io, F); println(io)
    println(io, "S factor:")
    show(io, mime, F.S)
    println(io, "\nT factor:")
    show(io, mime, F.T)
    println(io, "\nQ factor:")
    show(io, mime, F.Q)
    println(io, "\nZ factor:")
    show(io, mime, F.Z)
    println(io, "\nα:")
    show(io, mime, F.α)
    println(io, "\nβ:")
    show(io, mime, F.β)
end

# Conversion
AbstractMatrix(F::Schur) = (F.Z * F.T) * F.Z'
AbstractArray(F::Schur) = AbstractMatrix(F)
Matrix(F::Schur) = Array(AbstractArray(F))
Array(F::Schur) = Matrix(F)

copy(F::Schur) = Schur(copy(F.T), copy(F.Z), copy(F.values))
copy(F::GeneralizedSchur) = GeneralizedSchur(copy(F.S), copy(F.T), copy(F.α), copy(F.β), copy(F.Q), copy(F.Z))
�   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LinearAlgebra/src/structuredbroadcast.jl�4      # This file is a part of Julia. License is MIT: https://julialang.org/license

## Broadcast styles
import Base.Broadcast
using Base.Broadcast: DefaultArrayStyle, Broadcasted, tail

struct StructuredMatrixStyle{T} <: Broadcast.AbstractArrayStyle{2} end
StructuredMatrixStyle{T}(::Val{2}) where {T} = StructuredMatrixStyle{T}()
StructuredMatrixStyle{T}(::Val{N}) where {T,N} = Broadcast.DefaultArrayStyle{N}()

const StructuredMatrix = Union{Diagonal,Bidiagonal,SymTridiagonal,Tridiagonal,LowerTriangular,UnitLowerTriangular,UpperTriangular,UnitUpperTriangular}
for ST in Base.uniontypes(StructuredMatrix)
    @eval Broadcast.BroadcastStyle(::Type{<:$ST}) = $(StructuredMatrixStyle{ST}())
end

# Promotion of broadcasts between structured matrices. This is slightly unusual
# as we define them symmetrically. This allows us to have a fallback to DefaultArrayStyle{2}().
# Diagonal can cavort with all the other structured matrix types.
# Bidiagonal doesn't know if it's upper or lower, so it becomes Tridiagonal
Broadcast.BroadcastStyle(::StructuredMatrixStyle{Diagonal}, ::StructuredMatrixStyle{Diagonal}) =
    StructuredMatrixStyle{Diagonal}()
Broadcast.BroadcastStyle(::StructuredMatrixStyle{Diagonal}, ::StructuredMatrixStyle{Bidiagonal}) =
    StructuredMatrixStyle{Bidiagonal}()
Broadcast.BroadcastStyle(::StructuredMatrixStyle{Diagonal}, ::StructuredMatrixStyle{<:Union{SymTridiagonal,Tridiagonal}}) =
    StructuredMatrixStyle{Tridiagonal}()
Broadcast.BroadcastStyle(::StructuredMatrixStyle{Diagonal}, ::StructuredMatrixStyle{<:Union{LowerTriangular,UnitLowerTriangular}}) =
    StructuredMatrixStyle{LowerTriangular}()
Broadcast.BroadcastStyle(::StructuredMatrixStyle{Diagonal}, ::StructuredMatrixStyle{<:Union{UpperTriangular,UnitUpperTriangular}}) =
    StructuredMatrixStyle{UpperTriangular}()

Broadcast.BroadcastStyle(::StructuredMatrixStyle{Bidiagonal}, ::StructuredMatrixStyle{Diagonal}) =
    StructuredMatrixStyle{Bidiagonal}()
Broadcast.BroadcastStyle(::StructuredMatrixStyle{Bidiagonal}, ::StructuredMatrixStyle{<:Union{Bidiagonal,SymTridiagonal,Tridiagonal}}) =
    StructuredMatrixStyle{Tridiagonal}()
Broadcast.BroadcastStyle(::StructuredMatrixStyle{SymTridiagonal}, ::StructuredMatrixStyle{<:Union{Diagonal,Bidiagonal,SymTridiagonal,Tridiagonal}}) =
    StructuredMatrixStyle{Tridiagonal}()
Broadcast.BroadcastStyle(::StructuredMatrixStyle{Tridiagonal}, ::StructuredMatrixStyle{<:Union{Diagonal,Bidiagonal,SymTridiagonal,Tridiagonal}}) =
    StructuredMatrixStyle{Tridiagonal}()

Broadcast.BroadcastStyle(::StructuredMatrixStyle{LowerTriangular}, ::StructuredMatrixStyle{<:Union{Diagonal,LowerTriangular,UnitLowerTriangular}}) =
    StructuredMatrixStyle{LowerTriangular}()
Broadcast.BroadcastStyle(::StructuredMatrixStyle{UpperTriangular}, ::StructuredMatrixStyle{<:Union{Diagonal,UpperTriangular,UnitUpperTriangular}}) =
    StructuredMatrixStyle{UpperTriangular}()
Broadcast.BroadcastStyle(::StructuredMatrixStyle{UnitLowerTriangular}, ::StructuredMatrixStyle{<:Union{Diagonal,LowerTriangular,UnitLowerTriangular}}) =
    StructuredMatrixStyle{LowerTriangular}()
Broadcast.BroadcastStyle(::StructuredMatrixStyle{UnitUpperTriangular}, ::StructuredMatrixStyle{<:Union{Diagonal,UpperTriangular,UnitUpperTriangular}}) =
    StructuredMatrixStyle{UpperTriangular}()

Broadcast.BroadcastStyle(::StructuredMatrixStyle{<:Union{LowerTriangular,UnitLowerTriangular}}, ::StructuredMatrixStyle{<:Union{UpperTriangular,UnitUpperTriangular}}) =
    StructuredMatrixStyle{Matrix}()
Broadcast.BroadcastStyle(::StructuredMatrixStyle{<:Union{UpperTriangular,UnitUpperTriangular}}, ::StructuredMatrixStyle{<:Union{LowerTriangular,UnitLowerTriangular}}) =
    StructuredMatrixStyle{Matrix}()

# Make sure that `StructuredMatrixStyle{Matrix}` doesn't ever end up falling
# through and give back `DefaultArrayStyle{2}`
Broadcast.BroadcastStyle(T::StructuredMatrixStyle{Matrix}, ::StructuredMatrixStyle) = T
Broadcast.BroadcastStyle(::StructuredMatrixStyle, T::StructuredMatrixStyle{Matrix}) = T
Broadcast.BroadcastStyle(T::StructuredMatrixStyle{Matrix}, ::StructuredMatrixStyle{Matrix}) = T

# All other combinations fall back to the default style
Broadcast.BroadcastStyle(::StructuredMatrixStyle, ::StructuredMatrixStyle) = DefaultArrayStyle{2}()

# And a definition akin to similar using the structured type:
structured_broadcast_alloc(bc, ::Type{Diagonal}, ::Type{ElType}, n) where {ElType} =
    Diagonal(Array{ElType}(undef, n))
# Bidiagonal is tricky as we need to know if it's upper or lower. The promotion
# system will return Tridiagonal when there's more than one Bidiagonal, but when
# there's only one, we need to make figure out upper or lower
merge_uplos(::Nothing, ::Nothing) = nothing
merge_uplos(a, ::Nothing) = a
merge_uplos(::Nothing, b) = b
merge_uplos(a, b) = a == b ? a : 'T'

find_uplo(a::Bidiagonal) = a.uplo
find_uplo(a) = nothing
find_uplo(bc::Broadcasted) = mapfoldl(find_uplo, merge_uplos, Broadcast.cat_nested(bc), init=nothing)

function structured_broadcast_alloc(bc, ::Type{Bidiagonal}, ::Type{ElType}, n) where {ElType}
    uplo = n > 0 ? find_uplo(bc) : 'U'
    n1 = max(n - 1, 0)
    if uplo == 'T'
        return Tridiagonal(Array{ElType}(undef, n1), Array{ElType}(undef, n), Array{ElType}(undef, n1))
    end
    return Bidiagonal(Array{ElType}(undef, n),Array{ElType}(undef, n1), uplo)
end
structured_broadcast_alloc(bc, ::Type{SymTridiagonal}, ::Type{ElType}, n) where {ElType} =
    SymTridiagonal(Array{ElType}(undef, n),Array{ElType}(undef, n-1))
structured_broadcast_alloc(bc, ::Type{Tridiagonal}, ::Type{ElType}, n) where {ElType} =
    Tridiagonal(Array{ElType}(undef, n-1),Array{ElType}(undef, n),Array{ElType}(undef, n-1))
structured_broadcast_alloc(bc, ::Type{LowerTriangular}, ::Type{ElType}, n) where {ElType} =
    LowerTriangular(Array{ElType}(undef, n, n))
structured_broadcast_alloc(bc, ::Type{UpperTriangular}, ::Type{ElType}, n) where {ElType} =
    UpperTriangular(Array{ElType}(undef, n, n))
structured_broadcast_alloc(bc, ::Type{UnitLowerTriangular}, ::Type{ElType}, n) where {ElType} =
    UnitLowerTriangular(Array{ElType}(undef, n, n))
structured_broadcast_alloc(bc, ::Type{UnitUpperTriangular}, ::Type{ElType}, n) where {ElType} =
    UnitUpperTriangular(Array{ElType}(undef, n, n))
structured_broadcast_alloc(bc, ::Type{Matrix}, ::Type{ElType}, n) where {ElType} =
    Matrix(Array{ElType}(undef, n, n))

# A _very_ limited list of structure-preserving functions known at compile-time. This list is
# derived from the formerly-implemented `broadcast` methods in 0.6. Note that this must
# preserve both zeros and ones (for Unit***erTriangular) and symmetry (for SymTridiagonal)
const TypeFuncs = Union{typeof(round),typeof(trunc),typeof(floor),typeof(ceil)}
isstructurepreserving(bc::Broadcasted) = isstructurepreserving(bc.f, bc.args...)
isstructurepreserving(::Union{typeof(abs),typeof(big)}, ::StructuredMatrix) = true
isstructurepreserving(::TypeFuncs, ::StructuredMatrix) = true
isstructurepreserving(::TypeFuncs, ::Ref{<:Type}, ::StructuredMatrix) = true
function isstructurepreserving(::typeof(Base.literal_pow), ::Ref{typeof(^)}, ::StructuredMatrix, ::Ref{Val{N}}) where N
    return N isa Integer && N > 0
end
isstructurepreserving(f, args...) = false

"""
    iszerodefined(T::Type)

Return a `Bool` indicating whether `iszero` is well-defined for objects of type
`T`. By default, this function returns `false` unless `T <: Number`. Note that
this function may return `true` even if `zero(::T)` is not defined as long as
`iszero(::T)` has a method that does not requires `zero(::T)`.

This function is used to determine if mapping the elements of an array with
a specific structure of nonzero elements preserve this structure.
For instance, it is used to determine whether the output of
`tuple.(Diagonal([1, 2]))` is `Diagonal([(1,), (2,)])` or
`[(1,) (0,); (0,) (2,)]`. For this, we need to determine whether `(0,)` is
considered to be zero. `iszero((0,))` falls back to `(0,) == zero((0,))` which
fails as `zero(::Tuple{Int})` is not defined. However,
`iszerodefined(::Tuple{Int})` is `false` hence we falls back to the comparison
`(0,) == 0` which returns `false` and decides that the correct output is
`[(1,) (0,); (0,) (2,)]`.
"""
iszerodefined(::Type) = false
iszerodefined(::Type{<:Number}) = true
iszerodefined(::Type{<:AbstractArray{T}}) where T = iszerodefined(T)

fzeropreserving(bc) = (v = fzero(bc); !ismissing(v) && (iszerodefined(typeof(v)) ? iszero(v) : v == 0))
# Like sparse matrices, we assume that the zero-preservation property of a broadcasted
# expression is stable.  We can test the zero-preservability by applying the function
# in cases where all other arguments are known scalars against a zero from the structured
# matrix. If any non-structured matrix argument is not a known scalar, we give up.
fzero(x::Number) = x
fzero(::Type{T}) where T = T
fzero(r::Ref) = r[]
fzero(t::Tuple{Any}) = t[1]
fzero(S::StructuredMatrix) = zero(eltype(S))
fzero(x) = missing
function fzero(bc::Broadcast.Broadcasted)
    args = map(fzero, bc.args)
    return any(ismissing, args) ? missing : bc.f(args...)
end

function Base.similar(bc::Broadcasted{StructuredMatrixStyle{T}}, ::Type{ElType}) where {T,ElType}
    inds = axes(bc)
    if isstructurepreserving(bc) || (fzeropreserving(bc) && !(T <: Union{SymTridiagonal,UnitLowerTriangular,UnitUpperTriangular}))
        return structured_broadcast_alloc(bc, T, ElType, length(inds[1]))
    end
    return similar(convert(Broadcasted{DefaultArrayStyle{ndims(bc)}}, bc), ElType)
end

isvalidstructbc(dest, bc::Broadcasted{T}) where {T<:StructuredMatrixStyle} =
    Broadcast.combine_styles(dest, bc) === Broadcast.combine_styles(dest) &&
    (isstructurepreserving(bc) || fzeropreserving(bc))

isvalidstructbc(dest::Bidiagonal, bc::Broadcasted{StructuredMatrixStyle{Bidiagonal}}) =
    (size(dest, 1) < 2 || find_uplo(bc) == dest.uplo) &&
    (isstructurepreserving(bc) || fzeropreserving(bc))

function copyto!(dest::Diagonal, bc::Broadcasted{<:StructuredMatrixStyle})
    isvalidstructbc(dest, bc) || return copyto!(dest, convert(Broadcasted{Nothing}, bc))
    axs = axes(dest)
    axes(bc) == axs || Broadcast.throwdm(axes(bc), axs)
    for i in axs[1]
        dest.diag[i] = @inbounds Broadcast._broadcast_getindex(bc, CartesianIndex(i, i))
    end
    return dest
end

function copyto!(dest::Bidiagonal, bc::Broadcasted{<:StructuredMatrixStyle})
    isvalidstructbc(dest, bc) || return copyto!(dest, convert(Broadcasted{Nothing}, bc))
    axs = axes(dest)
    axes(bc) == axs || Broadcast.throwdm(axes(bc), axs)
    for i in axs[1]
        dest.dv[i] = @inbounds Broadcast._broadcast_getindex(bc, CartesianIndex(i, i))
    end
    if dest.uplo == 'U'
        for i = 1:size(dest, 1)-1
            dest.ev[i] = @inbounds Broadcast._broadcast_getindex(bc, CartesianIndex(i, i+1))
        end
    else
        for i = 1:size(dest, 1)-1
            dest.ev[i] = @inbounds Broadcast._broadcast_getindex(bc, CartesianIndex(i+1, i))
        end
    end
    return dest
end

function copyto!(dest::SymTridiagonal, bc::Broadcasted{<:StructuredMatrixStyle})
    isvalidstructbc(dest, bc) || return copyto!(dest, convert(Broadcasted{Nothing}, bc))
    axs = axes(dest)
    axes(bc) == axs || Broadcast.throwdm(axes(bc), axs)
    for i in axs[1]
        dest.dv[i] = @inbounds Broadcast._broadcast_getindex(bc, CartesianIndex(i, i))
    end
    for i = 1:size(dest, 1)-1
        v = @inbounds Broadcast._broadcast_getindex(bc, CartesianIndex(i, i+1))
        v == (@inbounds Broadcast._broadcast_getindex(bc, CartesianIndex(i+1, i))) || throw(ArgumentError("broadcasted assignment breaks symmetry between locations ($i, $(i+1)) and ($(i+1), $i)"))
        dest.ev[i] = v
    end
    return dest
end

function copyto!(dest::Tridiagonal, bc::Broadcasted{<:StructuredMatrixStyle})
    isvalidstructbc(dest, bc) || return copyto!(dest, convert(Broadcasted{Nothing}, bc))
    axs = axes(dest)
    axes(bc) == axs || Broadcast.throwdm(axes(bc), axs)
    for i in axs[1]
        dest.d[i] = @inbounds Broadcast._broadcast_getindex(bc, CartesianIndex(i, i))
    end
    for i = 1:size(dest, 1)-1
        dest.du[i] = @inbounds Broadcast._broadcast_getindex(bc, CartesianIndex(i, i+1))
        dest.dl[i] = @inbounds Broadcast._broadcast_getindex(bc, CartesianIndex(i+1, i))
    end
    return dest
end

function copyto!(dest::LowerTriangular, bc::Broadcasted{<:StructuredMatrixStyle})
    isvalidstructbc(dest, bc) || return copyto!(dest, convert(Broadcasted{Nothing}, bc))
    axs = axes(dest)
    axes(bc) == axs || Broadcast.throwdm(axes(bc), axs)
    for j in axs[2]
        for i in j:axs[1][end]
            @inbounds dest.data[i,j] = Broadcast._broadcast_getindex(bc, CartesianIndex(i, j))
        end
    end
    return dest
end

function copyto!(dest::UpperTriangular, bc::Broadcasted{<:StructuredMatrixStyle})
    isvalidstructbc(dest, bc) || return copyto!(dest, convert(Broadcasted{Nothing}, bc))
    axs = axes(dest)
    axes(bc) == axs || Broadcast.throwdm(axes(bc), axs)
    for j in axs[2]
        for i in 1:j
            @inbounds dest.data[i,j] = Broadcast._broadcast_getindex(bc, CartesianIndex(i, j))
        end
    end
    return dest
end

# We can also implement `map` and its promotion in terms of broadcast with a stricter dimension check
function map(f, A::StructuredMatrix, Bs::StructuredMatrix...)
    sz = size(A)
    all(map(B->size(B)==sz, Bs)) || throw(DimensionMismatch("dimensions must match"))
    return f.(A, Bs...)
end
{   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LinearAlgebra/src/deprecated.jl{      # This file is a part of Julia. License is MIT: https://julialang.org/license

# To be deprecated in 2.0
rank(A::AbstractMatrix, tol::Real) = rank(A,rtol=tol)
nullspace(A::AbstractVector, tol::Real) = nullspace(reshape(A, length(A), 1), rtol= tol)
nullspace(A::AbstractMatrix, tol::Real) = nullspace(A, rtol=tol)
pinv(A::AbstractMatrix{T}, tol::Real) where T = pinv(A, rtol=tol)
t   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Markdown/src/Markdown.jl#      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
Tools for working with the Markdown file format. Mainly for documentation.
"""
module Markdown

import Base: show, ==, with_output_color, mapany
using Base64: stringmime

# Margin for printing in terminal.
const margin = 2

include("parse/config.jl")
include("parse/util.jl")
include("parse/parse.jl")

include("Common/Common.jl")
include("GitHub/GitHub.jl")
include("IPython/IPython.jl")
include("Julia/Julia.jl")

include("render/plain.jl")
include("render/html.jl")
include("render/latex.jl")
include("render/rst.jl")
include("render/terminal/render.jl")

export @md_str, @doc_str

parse(markdown::AbstractString; flavor = julia) = parse(IOBuffer(markdown), flavor = flavor)
parse_file(file::AbstractString; flavor = julia) = parse(read(file, String), flavor = flavor)

function mdexpr(s, flavor = :julia)
    md = parse(s, flavor = Symbol(flavor))
    esc(toexpr(md))
end

function docexpr(source::LineNumberNode, mod::Module, s, flavor = :julia)
    :($doc_str($(mdexpr(s, flavor)), $(QuoteNode(source)), $mod))
end

macro md_str(s, t...)
    mdexpr(s, t...)
end

function doc_str(md, source::LineNumberNode, mod::Module)
    md.meta[:path] = isa(source.file, Symbol) ? String(source.file) : ""
    md.meta[:module] = mod
    md
end
doc_str(md::AbstractString, source::LineNumberNode, mod::Module) = doc_str(parse(md), source, mod)

macro doc_str(s::AbstractString, t...)
    docexpr(__source__, __module__, s, t...)
end

import Base.Docs: catdoc

catdoc(md::MD...) = MD(md...)

end
x   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Markdown/src/parse/config.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

const InnerConfig = Dict{Char, Vector{Function}}

mutable struct Config
    breaking::Vector{Function}
    regular::Vector{Function}
    inner::InnerConfig
end

Config() = Config(Function[], Function[], InnerConfig())

const META = IdDict{Function, Dict{Symbol, Any}}()

meta(f) = get!(Dict{Symbol,Any}, META, f)

breaking!(f) = meta(f)[:breaking] = true
breaking(f) = get(meta(f), :breaking, false)::Bool

triggers!(f, ts) = meta(f)[:triggers] = Set{Char}(ts)
triggers(f) = get!(Set{Char}, meta(f), :triggers)::Set{Char}

# Macros

isexpr(x::Expr, ts...) = x.head in ts
isexpr(x::T, ts...) where {T} = T in ts

macro breaking(ex)
    isexpr(ex, :->) || error("invalid @breaking form, use ->")
    b, def = ex.args
    if b
        quote
            f = $(esc(def))
            breaking!(f)
            f
        end
    else
        esc(def)
    end
end

macro trigger(ex)
    isexpr(ex, :->) || error("invalid @triggers form, use ->")
    ts, def = ex.args
    quote
        f = $(esc(def))
        triggers!(f, $ts)
        f
    end
end

# Construction

function config(parsers::Function...)
    c = Config()
    for parser in parsers
        ts = triggers(parser)
        if breaking(parser)
            push!(c.breaking, parser)
        elseif !isempty(ts)
            for t in ts
                push!(get!(Vector{Function}, c.inner, t), parser)
            end
        else
            push!(c.regular, parser)
        end
    end
    return c
end

# Flavour definitions

const flavors = Dict{Symbol, Config}()

macro flavor(name, features)
    quote
        const $(esc(name)) = config($(mapany(esc,features.args)...))
        flavors[$(Expr(:quote, name))] = $(esc(name))
    end
end
v   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Markdown/src/parse/util.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

macro dotimes(n, body)
    quote
        for i = 1:$(esc(n))
            $(esc(body))
        end
    end
end

const whitespace = " \t\r"

"""
Skip any leading whitespace. Returns io.
"""
function skipwhitespace(io::IO; newlines = true)
    while !eof(io) && (peek(io, Char) in whitespace || (newlines && peek(io) == UInt8('\n')))
        read(io, Char)
    end
    return io
end

"""
Skip any leading blank lines. Returns the number skipped.
"""
function skipblank(io::IO)
    start = position(io)
    i = 0
    for c in readeach(io, Char)
        c == '\n' && (start = position(io); i+=1; continue)
        c == '\r' && (start = position(io); i+=1; continue)
        c in whitespace || break
    end
    seek(io, start)
    return i
end

"""
Return true if the line contains only (and, unless allowempty,
at least one of) the characters given.
"""
function linecontains(io::IO, chars; allow_whitespace = true,
                                     eat = true,
                                     allowempty = false)
    start = position(io)
    l = readline(io)
    length(l) == 0 && return allowempty

    result = allowempty
    for c in l
        c in whitespace && (allow_whitespace ? continue : (result = false; break))
        c in chars && (result = true; continue)
        result = false; break
    end
    !(result && eat) && seek(io, start)
    return result
end

blankline(io::IO; eat = true) =
    linecontains(io, "",
                 allow_whitespace = true,
                 allowempty = true,
                 eat = eat)

"""
Test if the stream starts with the given string.
`eat` specifies whether to advance on success (true by default).
`padding` specifies whether leading whitespace should be ignored.
"""
function startswith(stream::IO, s::AbstractString; eat = true, padding = false, newlines = true)
    start = position(stream)
    padding && skipwhitespace(stream, newlines = newlines)
    result = true
    for char in s
        !eof(stream) && read(stream, Char) == char ||
            (result = false; break)
    end
    !(result && eat) && seek(stream, start)
    return result
end

function startswith(stream::IO, c::AbstractChar; eat = true)
    if !eof(stream) && peek(stream) == UInt8(c)
        eat && read(stream, Char)
        return true
    else
        return false
    end
end

function startswith(stream::IO, ss::Vector{<:AbstractString}; kws...)
    any(s->startswith(stream, s; kws...), ss)
end

function startswith(stream::IO, r::Regex; eat = true, padding = false)
    @assert Base.startswith(r.pattern, "^")
    start = position(stream)
    padding && skipwhitespace(stream)
    line = readline(stream)
    seek(stream, start)
    m = match(r, line)
    m === nothing && return ""
    eat && @dotimes length(m.match) read(stream, Char)
    return m.match
end

"""
Executes the block of code, and if the return value is `nothing`,
returns the stream to its initial position.
"""
function withstream(f, stream)
    pos = position(stream)
    result = f()
    (result ≡ nothing || result ≡ false) && seek(stream, pos)
    return result
end

"""
Consume the standard allowed markdown indent of
three spaces. Returns false if there are more than
three present.
"""
function eatindent(io::IO, n = 3)
    withstream(io) do
        m = 0
        while startswith(io, ' ') m += 1 end
        return m <= n
    end
end

"""
Read the stream until startswith(stream, delim)
The delimiter is consumed but not included.
Returns nothing and resets the stream if delim is
not found.
"""
function readuntil(stream::IO, delimiter; newlines = false, match = nothing)
    withstream(stream) do
        buffer = IOBuffer()
        count = 0
        while !eof(stream)
            if startswith(stream, delimiter)
                if count == 0
                    return String(take!(buffer))
                else
                    count -= 1
                    write(buffer, delimiter)
                    continue
                end
            end
            char = read(stream, Char)
            char == match && (count += 1)
            !newlines && char == '\n' && break
            write(buffer, char)
        end
    end
end

# TODO: refactor this. If we're going to assume
# the delimiter is a single character + a minimum
# repeat we may as well just pass that into the
# function.

"""
Parse a symmetrical delimiter which wraps words.
i.e. `*word word*` but not `*word * word`.
`repeat` specifies whether the delimiter can be repeated.
Escaped delimiters are not yet supported.
"""
function parse_inline_wrapper(stream::IO, delimiter::AbstractString; rep = false)
    delimiter, nmin = string(delimiter[1]), length(delimiter)
    withstream(stream) do
        if position(stream) >= 1
            # check the previous byte isn't a delimiter
            skip(stream, -1)
            (read(stream, Char) in delimiter) && return nothing
        end
        n = nmin
        startswith(stream, delimiter^n) || return nothing
        while startswith(stream, delimiter); n += 1; end
        !rep && n > nmin && return nothing
        !eof(stream) && peek(stream, Char) in whitespace && return nothing

        buffer = IOBuffer()
        for char in readeach(stream, Char)
            write(buffer, char)
            if !(char in whitespace || char == '\n' || char in delimiter) && startswith(stream, delimiter^n)
                trailing = 0
                while startswith(stream, delimiter); trailing += 1; end
                trailing == 0 && return String(take!(buffer))
                write(buffer, delimiter ^ (n + trailing))
            end
        end
    end
end

function showrest(io::IO)
    start = position(io)
    show(read(io, String))
    println()
    seek(io, start)
end
w   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Markdown/src/parse/parse.jl�
      # This file is a part of Julia. License is MIT: https://julialang.org/license

mutable struct MD
    content::Vector{Any}
    meta::Dict{Symbol, Any}

    MD(content::AbstractVector, meta::Dict = Dict()) =
        new(content, meta)
end

MD(xs...) = MD(vcat(xs...))

function MD(cfg::Config, xs...)
    md = MD(xs...)
    md.meta[:config] = cfg
    return md
end

config(md::MD) = md.meta[:config]::Config

# Forward some array methods

Base.push!(md::MD, x) = push!(md.content, x)
Base.getindex(md::MD, args...) = md.content[args...]
Base.setindex!(md::MD, args...) = setindex!(md.content, args...)
Base.lastindex(md::MD) = lastindex(md.content)
Base.firstindex(md::MD) = firstindex(md.content)
Base.length(md::MD) = length(md.content)
Base.isempty(md::MD) = isempty(md.content)
Base.copy(md::MD) = MD(copy(md.content), copy(md.meta))

==(a::MD, b::MD) = (html(a) == html(b))

# Parser functions:
#   md – should be modified appropriately
#   return – basically, true if parse was successful
#     false uses the next parser in the queue, true
#     goes back to the beginning
#
# Inner parsers:
#   return – element to use or nothing

# Inner parsing

function parseinline(stream::IO, md::MD, parsers::Vector{Function})
    for parser in parsers
        inner = parser(stream, md)
        inner ≡ nothing || return inner
    end
end

function parseinline(stream::IO, md::MD, config::Config)
    content = []
    buffer = IOBuffer()
    while !eof(stream)
        char = peek(stream, Char)
        if haskey(config.inner, char) &&
                (inner = parseinline(stream, md, config.inner[char])) !== nothing
            c = String(take!(buffer))
            !isempty(c) && push!(content, c)
            buffer = IOBuffer()
            push!(content, inner)
        else
            write(buffer, read(stream, Char))
        end
    end
    c = String(take!(buffer))
    !isempty(c) && push!(content, c)
    return content
end

parseinline(s::AbstractString, md::MD, c::Config) =
    parseinline(IOBuffer(s), md, c)

parseinline(s, md::MD) = parseinline(s, md, config(md))

# Block parsing

function parse(stream::IO, block::MD, config::Config; breaking = false)
    skipblank(stream)
    eof(stream) && return false
    for parser in (breaking ? config.breaking : [config.breaking; config.regular])
        parser(stream, block) && return true
    end
    return false
end

parse(stream::IO, block::MD; breaking = false) =
  parse(stream, block, config(block), breaking = breaking)

function parse(stream::IO; flavor = julia)
    isa(flavor, Symbol) && (flavor = flavors[flavor])
    markdown = MD(flavor)
    while parse(stream, markdown, flavor) end
    return markdown
end
y   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Markdown/src/Common/Common.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

include("block.jl")
include("inline.jl")

@flavor common [list, indentcode, blockquote, admonition, footnote, hashheader, horizontalrule,
                paragraph,

                linebreak, escapes, inline_code,
                asterisk_bold, underscore_bold, asterisk_italic, underscore_italic, image, footnote_link, link, autolink]
x   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Markdown/src/Common/block.jl�*      # This file is a part of Julia. License is MIT: https://julialang.org/license

# ––––––––––
# Paragraphs
# ––––––––––

mutable struct Paragraph
    content
end

Paragraph() = Paragraph([])

function paragraph(stream::IO, md::MD)
    buffer = IOBuffer()
    p = Paragraph()
    push!(md, p)
    skipwhitespace(stream)
    prev_char = '\n'
    for char in readeach(stream, Char)
        if char == '\n' || char == '\r'
            char == '\r' && !eof(stream) && peek(stream, Char) == '\n' && read(stream, Char)
            if prev_char == '\\'
                write(buffer, '\n')
            elseif blankline(stream) || parse(stream, md, breaking = true)
                break
            else
                write(buffer, ' ')
            end
        else
            write(buffer, char)
        end
        prev_char = char
    end
    p.content = parseinline(seek(buffer, 0), md)
    return true
end

# –––––––
# Headers
# –––––––

mutable struct Header{level}
    text
end

Header(s, level::Int) = Header{level}(s)
Header(s) = Header(s, 1)

@breaking true ->
function hashheader(stream::IO, md::MD)
    withstream(stream) do
        eatindent(stream) || return false
        level = 0
        while startswith(stream, '#') level += 1 end
        (level < 1 || level > 6) && return false

        c = ' '
        # Allow empty headers, but require a space
        !eof(stream) && (c = read(stream, Char); !(c in " \n")) &&
            return false

        if c != '\n' # Empty header
            h = strip(readline(stream))
            h = (match(r"(.*?)( +#+)?$", h)::AbstractMatch).captures[1]
            buffer = IOBuffer()
            print(buffer, h)
            push!(md.content, Header(parseinline(seek(buffer, 0), md), level))
        else
            push!(md.content, Header("", level))
        end
        return true
    end
end

function setextheader(stream::IO, md::MD)
    withstream(stream) do
        eatindent(stream) || return false
        header = strip(readline(stream))
        isempty(header) && return false

        eatindent(stream) || return false
        underline = strip(readline(stream))
        length(underline) < 3 && return false
        u = underline[1]
        u in "-=" || return false
        all(c -> c == u, underline) || return false
        level = (u == '=') ? 1 : 2

        push!(md.content, Header(parseinline(header, md), level))
        return true
    end
end

# ––––
# Code
# ––––

mutable struct Code
    language::String
    code::String
end

Code(code) = Code("", code)

function indentcode(stream::IO, block::MD)
    withstream(stream) do
        buffer = IOBuffer()
        while !eof(stream)
            if startswith(stream, "    ") || startswith(stream, "\t")
                write(buffer, readline(stream, keep=true))
            elseif blankline(stream)
                write(buffer, '\n')
            else
                break
            end
        end
        code = String(take!(buffer))
        !isempty(code) && (push!(block, Code(rstrip(code))); return true)
        return false
    end
end

# --------
# Footnote
# --------

mutable struct Footnote
    id::String
    text
end

function footnote(stream::IO, block::MD)
    withstream(stream) do
        regex = r"^\[\^(\w+)\]:"
        str = startswith(stream, regex)
        if isempty(str)
            return false
        else
            ref = (match(regex, str)::AbstractMatch).captures[1]
            buffer = IOBuffer()
            write(buffer, readline(stream, keep=true))
            while !eof(stream)
                if startswith(stream, "    ") || startswith(stream, "\t")
                    write(buffer, readline(stream, keep=true))
                elseif blankline(stream)
                    write(buffer, '\n')
                else
                    break
                end
            end
            content = parse(seekstart(buffer)).content
            push!(block, Footnote(ref, content))
            return true
        end
    end
end

# ––––––
# Quotes
# ––––––

mutable struct BlockQuote
    content
end

BlockQuote() = BlockQuote([])

# TODO: Laziness
@breaking true ->
function blockquote(stream::IO, block::MD)
    withstream(stream) do
        buffer = IOBuffer()
        empty = true
        while eatindent(stream) && startswith(stream, '>')
            startswith(stream, " ")
            write(buffer, readline(stream, keep=true))
            empty = false
        end
        empty && return false

        md = String(take!(buffer))
        push!(block, BlockQuote(parse(md, flavor = config(block)).content))
        return true
    end
end

# -----------
# Admonitions
# -----------

mutable struct Admonition
    category::String
    title::String
    content::Vector
end

@breaking true ->
function admonition(stream::IO, block::MD)
    withstream(stream) do
        # Admonition syntax:
        #
        # !!! category "optional explicit title within double quotes"
        #     Any number of other indented markdown elements.
        #
        #     This is the second paragraph.
        #
        startswith(stream, "!!! ") || return false
        # Extract the category of admonition and its title:
        category, title =
            let untitled = r"^([a-z]+)$",          # !!! <CATEGORY_NAME>
                titled   = r"^([a-z]+) \"(.*)\"$", # !!! <CATEGORY_NAME> "<TITLE>"
                line     = strip(readline(stream))
                if occursin(untitled, line)
                    m = match(untitled, line)::AbstractMatch
                    # When no title is provided we use CATEGORY_NAME, capitalising it.
                    m.captures[1], uppercasefirst(m.captures[1])
                elseif occursin(titled, line)
                    m = match(titled, line)::AbstractMatch
                    # To have a blank TITLE provide an explicit empty string as TITLE.
                    m.captures[1], m.captures[2]
                else
                    # Admonition header is invalid so we give up parsing here and move
                    # on to the next parser.
                    return false
                end
            end
        # Consume the following indented (4 spaces or tab) block.
        buffer = IOBuffer()
        while !eof(stream)
            if startswith(stream, "    ") || startswith(stream, "\t")
                write(buffer, readline(stream, keep=true))
            elseif blankline(stream)
                write(buffer, '\n')
            else
                break
            end
        end
        # Parse the nested block as markdown and create a new Admonition block.
        nested = parse(String(take!(buffer)), flavor = config(block))
        push!(block, Admonition(category, title, nested.content))
        return true
    end
end

# –––––
# Lists
# –––––

mutable struct List
    items::Vector{Any}
    ordered::Int # `-1` is unordered, `>= 0` is ordered.
    loose::Bool # TODO: Renderers should use this field
end
List(x::AbstractVector, b::Integer) = List(x, b, false)
List(x::AbstractVector) = List(x, -1)
List(b::Integer) = List(Any[], b)
List(xs...) = List(vcat(xs...))

isordered(list::List) = list.ordered >= 0

const BULLETS = r"^ {0,3}(\*|\+|-)( |$)"
const NUM_OR_BULLETS = r"^ {0,3}(\*|\+|-|\d+(\.|\)))( |$)"

@breaking true ->
function list(stream::IO, block::MD)
    withstream(stream) do
        bullet = startswith(stream, NUM_OR_BULLETS; eat = false)
        indent = isempty(bullet) ? (return false) : length(bullet)
        # Calculate the starting number and regex to use for bullet matching.
        initial, regex =
            if occursin(BULLETS, bullet)
                # An unordered list. Use `-1` to flag the list as unordered.
                -1, BULLETS
            elseif occursin(r"^ {0,3}\d+(\.|\))( |$)", bullet)
                # An ordered list. Either with `1. ` or `1) ` style numbering.
                r = occursin(".", bullet) ? r"^ {0,3}(\d+)\.( |$)" : r"^ {0,3}(\d+)\)( |$)"
                Base.parse(Int, (match(r, bullet)::AbstractMatch).captures[1]), r
            else
                # Failed to match any bullets. This branch shouldn't actually be needed
                # since the `NUM_OR_BULLETS` regex should cover this, but we include it
                # simply for thoroughness.
                return false
            end

        # Initialise the empty list object: either ordered or unordered.
        list = List(initial)

        buffer = IOBuffer() # For capturing nested text for recursive parsing.
        newline = false     # For checking if we have two consecutive newlines: end of list.
        count = 0           # Count of list items. Used to check if we need to push remaining
                            # content in `buffer` after leaving the `while` loop.
        while !eof(stream)
            if startswith(stream, "\n")
                if newline
                    # Double newline ends the current list.
                    pushitem!(list, buffer)
                    break
                else
                    newline = true
                    println(buffer)
                end
            else
                if startswith(stream, " "^indent)
                    newline && (list.loose = true)
                    # Indented text that is part of the current list item.
                    print(buffer, readline(stream, keep=true))
                else
                    matched = startswith(stream, regex)
                    if isempty(matched)
                        # Unindented text meaning we have left the current list.
                        pushitem!(list, buffer)
                        break
                    else
                        # Start of a new list item.
                        newline && (list.loose = true)
                        count += 1
                        count > 1 && pushitem!(list, buffer)
                        print(buffer, readline(stream, keep=true))
                    end
                end
                newline = false
            end
        end
        count == length(list.items) || pushitem!(list, buffer)
        push!(block, list)
        return true
    end
end
pushitem!(list, buffer) = push!(list.items, parse(String(take!(buffer))).content)

# ––––––––––––––
# HorizontalRule
# ––––––––––––––

mutable struct HorizontalRule
end

function horizontalrule(stream::IO, block::MD)
   withstream(stream) do
       n, rule = 0, ' '
       for char in readeach(stream, Char)
           char == '\n' && break
           isspace(char) && continue
           if n==0 || char==rule
               rule = char
               n += 1
           else
               return false
           end
       end
       is_hr = (n ≥ 3 && rule in "*-")
       is_hr && push!(block, HorizontalRule())
       return is_hr
   end
end
y   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Markdown/src/Common/inline.jl      # This file is a part of Julia. License is MIT: https://julialang.org/license

# ––––––––
# Emphasis
# ––––––––

mutable struct Italic
    text
end

@trigger '*' ->
function asterisk_italic(stream::IO, md::MD)
    result = parse_inline_wrapper(stream, "*")
    return result === nothing ? nothing : Italic(parseinline(result, md))
end

@trigger '_' ->
function underscore_italic(stream::IO, md::MD)
    result = parse_inline_wrapper(stream, "_")
    return result === nothing ? nothing : Italic(parseinline(result, md))
end

mutable struct Bold
    text
end

@trigger '*' ->
function asterisk_bold(stream::IO, md::MD)
    result = parse_inline_wrapper(stream, "**")
    return result === nothing ? nothing : Bold(parseinline(result, md))
end

@trigger '_' ->
function underscore_bold(stream::IO, md::MD)
    result = parse_inline_wrapper(stream, "__")
    return result === nothing ? nothing : Bold(parseinline(result, md))
end

# ––––
# Code
# ––––

@trigger '`' ->
function inline_code(stream::IO, md::MD)
    withstream(stream) do
        ticks = startswith(stream, r"^(`+)")
        result = readuntil(stream, ticks)
        if result === nothing
            nothing
        else
            result = strip(result)
            # An odd number of backticks wrapping the text will produce a `Code` node, while
            # an even number will result in a `LaTeX` node. This allows for arbitrary
            # backtick combinations to be embedded inside the resulting node, i.e.
            #
            # `a`, ``a``, `` `a` ``, ``` ``a`` ```, ``` `a` ```, etc.
            #  ^     ^        ^            ^             ^
            #  C     L        L            C             C       with C=Code and L=LaTeX.
            #
            isodd(length(ticks)) ? Code(result) : LaTeX(result)
        end
    end
end

# ––––––––––––––
# Images & Links
# ––––––––––––––

mutable struct Image
    url::String
    alt::String
end

@trigger '!' ->
function image(stream::IO, md::MD)
    withstream(stream) do
        startswith(stream, "![") || return
        alt = readuntil(stream, ']', match = '[')
        alt ≡ nothing && return
        skipwhitespace(stream)
        startswith(stream, '(') || return
        url = readuntil(stream, ')', match = '(')
        url ≡ nothing && return
        return Image(url, alt)
    end
end

mutable struct Link
    text
    url::String
end

@trigger '[' ->
function link(stream::IO, md::MD)
    withstream(stream) do
        startswith(stream, '[') || return
        text = readuntil(stream, ']', match = '[')
        text ≡ nothing && return
        skipwhitespace(stream)
        startswith(stream, '(') || return
        url = readuntil(stream, ')', match = '(')
        url ≡ nothing && return
        return Link(parseinline(text, md), url)
    end
end

@trigger '[' ->
function footnote_link(stream::IO, md::MD)
    withstream(stream) do
        regex = r"^\[\^(\w+)\]"
        str = startswith(stream, regex)
        if isempty(str)
            return
        else
            ref = (match(regex, str)::AbstractMatch).captures[1]
            return Footnote(ref, nothing)
        end
    end
end

@trigger '<' ->
function autolink(stream::IO, md::MD)
    withstream(stream) do
        startswith(stream, '<') || return
        url = readuntil(stream, '>')
        url ≡ nothing && return
        _is_link(url) && return Link(url, url)
        _is_mailto(url) && return Link(url, url)
        return
    end
end

# This list is taken from the commonmark spec
# http://spec.commonmark.org/0.19/#absolute-uri
const _allowable_schemes = Set(split("coap doi javascript aaa aaas about acap cap cid crid data dav dict dns file ftp geo go gopher h323 http https iax icap im imap info ipp iris iris.beep iris.xpc iris.xpcs iris.lwz ldap mailto mid msrp msrps mtqp mupdate news nfs ni nih nntp opaquelocktoken pop pres rtsp service session shttp sieve sip sips sms snmp,soap.beep soap.beeps tag tel telnet tftp thismessage tn3270 tip tv urn vemmi ws wss xcon xcon-userid xmlrpc.beep xmlrpc.beeps xmpp z39.50r z39.50s
adiumxtra afp afs aim apt,attachment aw beshare bitcoin bolo callto chrome,chrome-extension com-eventbrite-attendee content cvs,dlna-playsingle dlna-playcontainer dtn dvb ed2k facetime feed finger fish gg git gizmoproject gtalk hcp icon ipn irc irc6 ircs itms jar jms keyparc lastfm ldaps magnet maps market,message mms ms-help msnim mumble mvn notes oid palm paparazzi platform proxy psyc query res resource rmi rsync rtmp secondlife sftp sgn skype smb soldat spotify ssh steam svn teamspeak
things udp unreal ut2004 ventrilo view-source webcal wtai wyciwyg xfire xri ymsgr"))

function _is_link(s::AbstractString)
    '<' in s && return false

    m = match(r"^(.*)://(\S+?)(:\S*)?$", s)
    m ≡ nothing && return false
    scheme = lowercase(m.captures[1])
    return scheme in _allowable_schemes
end

# non-normative regex from the HTML5 spec
const _email_regex = r"^mailto\:[a-zA-Z0-9.!#$%&'*+/=?^_`{|}~-]+@[a-zA-Z0-9](?:[a-zA-Z0-9-]{0,61}[a-zA-Z0-9])?(?:\.[a-zA-Z0-9](?:[a-zA-Z0-9-]{0,61}[a-zA-Z0-9])?)*$"

function _is_mailto(s::AbstractString)
    return occursin(_email_regex, s)
end

# –––––––––––
# Punctuation
# –––––––––––

mutable struct LineBreak end

@trigger '\\' ->
function linebreak(stream::IO, md::MD)
    if startswith(stream, "\\\n")
        return LineBreak()
    end
end

@trigger '-' ->
function en_dash(stream::IO, md::MD)
    if startswith(stream, "--")
        return "–"
    end
end

const escape_chars = "\\`*_#+-.!{}[]()\$"

@trigger '\\' ->
function escapes(stream::IO, md::MD)
    withstream(stream) do
        if startswith(stream, "\\") && !eof(stream) && (c = read(stream, Char)) in escape_chars
            return string(c)
        end
    end
end
y   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Markdown/src/GitHub/GitHub.jl"      # This file is a part of Julia. License is MIT: https://julialang.org/license

include("table.jl")

@breaking true ->
function fencedcode(stream::IO, block::MD)
    withstream(stream) do
        startswith(stream, "~~~", padding = true) || startswith(stream, "```", padding = true) || return false
        skip(stream, -1)
        ch = read(stream, Char)
        trailing = strip(readline(stream))
        flavor = lstrip(trailing, ch)
        n = 3 + length(trailing) - length(flavor)

        # inline code block
        ch in flavor && return false

        buffer = IOBuffer()
        while !eof(stream)
            line_start = position(stream)
            if startswith(stream, string(ch) ^ n)
                if !startswith(stream, string(ch))
                    if flavor == "math"
                        push!(block, LaTeX(String(take!(buffer)) |> chomp))
                    else
                        push!(block, Code(flavor, String(take!(buffer)) |> chomp))
                    end
                    return true
                else
                    seek(stream, line_start)
                end
            end
            write(buffer, readline(stream, keep=true))
        end
        return false
    end
end

function github_paragraph(stream::IO, md::MD)
    skipwhitespace(stream)
    buffer = IOBuffer()
    p = Paragraph()
    push!(md, p)
    for char in readeach(stream, Char)
        if char == '\n'
            eof(stream) && break
            if blankline(stream) || parse(stream, md, breaking = true)
                break
            else
                write(buffer, '\n')
            end
        else
            write(buffer, char)
        end
    end
    p.content = parseinline(seek(buffer, 0), md)
    return true
end

@flavor github [list, indentcode, blockquote, admonition, footnote, fencedcode, hashheader,
                github_table, github_paragraph,

                linebreak, escapes, en_dash, inline_code, asterisk_bold,
                underscore_bold, asterisk_italic, underscore_italic, image, footnote_link, link, autolink]
x   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Markdown/src/GitHub/table.jl(      # This file is a part of Julia. License is MIT: https://julialang.org/license

mutable struct Table
    rows::Vector{Vector{Any}}
    align::Vector{Symbol}
end

function parserow(stream::IO)
    withstream(stream) do
        line = readline(stream)
        row = split(line, r"(?<!\\)\|")
        length(row) == 1 && return
        isempty(row[1]) && popfirst!(row)
        map!(x -> strip(replace(x, "\\|" => "|")), row, row)
        isempty(row[end]) && pop!(row)
        return row
    end
end

function rowlength!(row, len)
    while length(row) < len push!(row, "") end
    while length(row) > len pop!(row) end
    return row
end

const default_align = :r

function parsealign(row)
    align = Symbol[]
    for s in row
        (length(s) ≥ 3 && s ⊆ Set("-:")) || return
        push!(align,
              s[1] == ':' ? (s[end] == ':' ? :c : :l) :
              s[end] == ':' ? :r :
              default_align)
    end
    return align
end

function github_table(stream::IO, md::MD)
    withstream(stream) do
        skipblank(stream)
        rows = []
        cols = 0
        align = nothing
        while (row = parserow(stream)) !== nothing
            if length(rows) == 0
                cols = length(row)
            end
            if align === nothing && length(rows) == 1 # Must have a --- row
                align = parsealign(row)
                (align === nothing || length(align) != cols) && return false
            else
                push!(rows, map(x -> parseinline(x, md), rowlength!(row, cols)))
            end
        end
        length(rows) <= 1 && return false
        push!(md, Table(rows, align))
        return true
    end
end

function html(io::IO, md::Table)
    withtag(io, :table) do
        for (i, row) in enumerate(md.rows)
            withtag(io, :tr) do
                for (j, c) in enumerate(md.rows[i])
                    alignment = md.align[j]
                    alignment = alignment === :l ? "left" : alignment === :r ? "right" : "center"
                     withtag(io, i == 1 ? :th : :td, ("align", alignment)) do
                        htmlinline(io, c)
                    end
                end
            end
        end
    end
end

mapmap(f, xss) = map(xs->map(f, xs), xss)

colwidths(rows; len = length, min = 0) =
    reduce((x,y) -> max.(x,y), [min; convert(Vector{Vector{Int}}, mapmap(len, rows))])

padding(width, twidth, a) =
    a === :l ? (0, twidth - width) :
    a === :r ? (twidth - width, 0) :
    a === :c ? (floor(Int, (twidth-width)/2), ceil(Int, (twidth-width)/2)) :
    error("Invalid alignment $a")

function padcells!(rows, align; len = length, min = 0)
    widths = colwidths(rows, len = len, min = min)
    for i = 1:length(rows), j = axes(rows[1],1)
        cell = rows[i][j]
        lpad, rpad = padding(len(cell), widths[j], align[j])
        rows[i][j] = " "^lpad * cell * " "^rpad
    end
    return rows
end

_dash(width, align) =
    align === :l ? ":" * "-"^width * " " :
    align === :r ? " " * "-"^width * ":" :
    align === :c ? ":" * "-"^width * ":" :
    throw(ArgumentError("Invalid alignment $align"))

function plain(io::IO, md::Table)
    cells = mapmap(md.rows) do each
        replace(plaininline(each), "|" => "\\|")
    end
    padcells!(cells, md.align, len = length, min = 3)
    for i = axes(cells,1)
        print(io, "| ")
        join(io, cells[i], " | ")
        println(io, " |")
        if i == 1
            print(io, "|")
            join(io, [_dash(length(cells[i][j]), md.align[j]) for j = axes(cells[1],1)], "|")
            println(io, "|")
        end
    end
end

function rst(io::IO, md::Table)
    cells = mapmap(rstinline, md.rows)
    padcells!(cells, md.align, len = length, min = 3)
    single = ["-"^length(c) for c in cells[1]]
    double = ["="^length(c) for c in cells[1]]
    function print_row(row, row_sep, col_sep)
        print(io, col_sep, row_sep)
        join(io, row, string(row_sep, col_sep, row_sep))
        println(io, row_sep, col_sep)
    end
    print_row(single, '-', '+')
    for i = 1:length(cells)
        print_row(cells[i], ' ', '|')
        i ≡ 1 ? print_row(double, '=', '+') :
                print_row(single, '-', '+')
    end
end

function term(io::IO, md::Table, columns)
    margin_str = " "^margin
    cells = mapmap(x -> terminline_string(io, x), md.rows)
    padcells!(cells, md.align, len = ansi_length)
    for i = 1:length(cells)
        print(io, margin_str)
        join(io, cells[i], " ")
        if i == 1
            println(io)
            print(io, margin_str)
            join(io, ["–"^ansi_length(cells[i][j]) for j = 1:length(cells[1])], " ")
        end
        i < length(cells) && println(io)
    end
end

function latex(io::IO, md::Table)
    wrapblock(io, "tabular") do
        align = md.align
        println(io, "{$(join(align, " | "))}")
        for (i, row) in enumerate(md.rows)
            for (j, cell) in enumerate(row)
                j != 1 && print(io, " & ")
                latexinline(io, cell)
            end
            println(io, " \\\\")
            if i == 1
                println(io, "\\hline")
            end
        end
    end
end
{   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Markdown/src/IPython/IPython.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

mutable struct LaTeX
    formula::String
end

@trigger '$' ->
function tex(stream::IO, md::MD)
    result = parse_inline_wrapper(stream, "\$", rep = true)
    return result === nothing ? nothing : LaTeX(result)
end

function blocktex(stream::IO, md::MD)
    withstream(stream) do
        ex = tex(stream, md)
        if ex ≡ nothing
            return false
        else
            push!(md, ex)
            return true
        end
    end
end

show(io::IO, tex::LaTeX) =
    print(io, '$', tex.formula, '$')

latex(io::IO, tex::LaTeX) =
    println(io, "\$\$", tex.formula, "\$\$")

latexinline(io::IO, tex::LaTeX) =
    print(io, '$', tex.formula, '$')
w   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Markdown/src/Julia/Julia.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

# This file contains markdown extensions designed to make documenting
# Julia easy peasy.
#
# We start by borrowing GitHub's `fencedcode` extension – more to follow.

include("interp.jl")

@flavor julia [blocktex, blockinterp, hashheader, list, indentcode, fencedcode,
               blockquote, admonition, footnote, github_table, horizontalrule, setextheader, paragraph,

               linebreak, escapes, tex, interp, en_dash, inline_code,
               asterisk_bold, underscore_bold, asterisk_italic, underscore_italic, image, footnote_link, link, autolink]
x   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Markdown/src/Julia/interp.jl	      # This file is a part of Julia. License is MIT: https://julialang.org/license

function _parse(stream::IO; greedy::Bool = true, raise::Bool = true)
    pos = position(stream)
    ex, Δ = Meta.parse(read(stream, String), 1, greedy = greedy, raise = raise)
    seek(stream, pos + Δ - 1)
    return ex
end

function interpinner(stream::IO, greedy = false)
    startswith(stream, '$') || return
    (eof(stream) || peek(stream, Char) in whitespace) && return
    try
        return _parse(stream, greedy = greedy)
    catch e
        if isa(e, Meta.ParseError)
            return nothing
        else
            rethrow()
        end
    end
end

@trigger '$' ->
function interp(stream::IO, md::MD)
    withstream(stream) do
        ex = interpinner(stream)
        return ex
    end
end

function blockinterp(stream::IO, md::MD)
    withstream(stream) do
        ex = interpinner(stream)
        if ex ≡ nothing
            return false
        else
            push!(md, ex)
            return true
        end
    end
end

toexpr(x) = x

toexpr(xs::Union{Vector{Any},Vector{Vector{Any}}}) =
    Expr(:call, GlobalRef(Base,:getindex), Any, mapany(toexpr, xs)...)

for T in Any[MD, Paragraph, Header, Link, Bold, Italic]
    @eval function toexpr(md::$T)
        Expr(:call, typeof(md), $(map(x->:(toexpr(md.$x)), fieldnames(Base.unwrap_unionall(T)))...))
    end
end

function toexpr(md::Table)
    Expr(:call, Table, toexpr(md.rows), md.align)
end

function toexpr(md::List)
    Expr(:call, List, toexpr(md.items), md.ordered, md.loose)
end
x   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Markdown/src/render/plain.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

plain(x) = sprint(plain, x)

function plain(io::IO, content::Vector)
    isempty(content) && return
    for md in content[1:end-1]
        plain(io, md)
        println(io)
    end
    plain(io, content[end])
end

plain(io::IO, md::MD) = plain(io, md.content)

function plain(io::IO, header::Header{l}) where l
    print(io, "#"^l*" ")
    plaininline(io, header.text)
    println(io)
end

function plain(io::IO, code::Code)
    # If the code includes a fenced block this will break parsing,
    # so it must be enclosed by a longer ````-sequence.
    n = mapreduce(m -> length(m.match), max, eachmatch(r"^`+"m, code.code); init=2) + 1
    println(io, "`" ^ n, code.language)
    println(io, code.code)
    println(io, "`" ^ n)
end

function plain(io::IO, p::Paragraph)
    plaininline(io, p.content)
    println(io)
end

function plain(io::IO, list::List)
    for (i, item) in enumerate(list.items)
        print(io, isordered(list) ? "$(i + list.ordered - 1). " : "  * ")
        lines = split(rstrip(sprint(plain, item)), "\n")
        for (n, line) in enumerate(lines)
            print(io, (n == 1 || isempty(line)) ? "" : "    ", line)
            n < length(lines) && println(io)
        end
        println(io)
    end
end

function plain(io::IO, q::BlockQuote)
    s = sprint(plain, q.content)
    for line in split(rstrip(s), "\n")
        println(io, isempty(line) ? ">" : "> ", line)
    end
    println(io)
end

function plain(io::IO, f::Footnote)
    print(io, "[^", f.id, "]:")
    s = sprint(plain, f.text)
    lines = split(rstrip(s), "\n")
    # Single line footnotes are printed on the same line as their label
    # rather than taking up an additional line.
    if length(lines) == 1
        println(io, " ", lines[1])
    else
        println(io)
        for line in lines
            println(io, isempty(line) ? "" : "    ", line)
        end
        println(io)
    end
end

function plain(io::IO, md::Admonition)
    s = sprint(plain, md.content)
    title = md.title == uppercasefirst(md.category) ? "" : " \"$(md.title)\""
    println(io, "!!! ", md.category, title)
    for line in split(rstrip(s), "\n")
        println(io, isempty(line) ? "" : "    ", line)
    end
    println(io)
end

function plain(io::IO, md::HorizontalRule)
    println(io, "-" ^ 3)
end

function plain(io::IO, l::LaTeX)
    println(io, '$', '$')
    println(io, l.formula)
    println(io, '$', '$')
end

function plain(io::IO, md)
    show(io,  MIME"text/plain"(), md)
    println(io)
end

# Inline elements

plaininline(x) = sprint(plaininline, x)

function plaininline(io::IO, md...)
    for el in md
        plaininline(io, el)
    end
end

plaininline(io::IO, md::Vector) = !isempty(md) && plaininline(io, md...)

plaininline(io::IO, f::Footnote) = print(io, "[^", f.id, "]")

plaininline(io::IO, link::Link) = plaininline(io, "[", link.text, "](", link.url, ")")

plaininline(io::IO, md::Image) = plaininline(io, "![", md.alt, "](", md.url, ")")

plaininline(io::IO, s::AbstractString) = print(io, s)

plaininline(io::IO, md::Bold) = plaininline(io, "**", md.text, "**")

plaininline(io::IO, md::Italic) = plaininline(io, "*", md.text, "*")

function plaininline(io::IO, md::Code)
    if occursin("`", md.code)
        n = maximum(length(m.match) for m in eachmatch(r"(`+)", md.code))
        s = "`"^((iseven(n) ? 1 : 2) + n)
        print(io, s, Base.startswith(md.code, "`") ? " " : "")
        print(io, md.code, endswith(md.code, "`") ? " " : "", s)
    else
        print(io, "`", md.code, "`")
    end
end

plaininline(io::IO, br::LineBreak) = println(io)

plaininline(io::IO, x) = show(io, MIME"text/plain"(), x)

# show

Base.show(io::IO, md::MD) = plain(io, md)
Base.show(io::IO, ::MIME"text/markdown", md::MD) = plain(io, md)
w   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Markdown/src/render/html.jl|      # This file is a part of Julia. License is MIT: https://julialang.org/license

include("rich.jl")

# Utils

function withtag(f, io::IO, tag, attrs...)
    print(io, "<$tag")
    for (attr, value) in attrs
        print(io, " ")
        htmlesc(io, attr)
        print(io, "=\"")
        htmlesc(io, value)
        print(io, "\"")
    end
    f === nothing && return print(io, " />")

    print(io, ">")
    f()
    print(io, "</$tag>")
end

tag(io::IO, tag, attrs...) = withtag(nothing, io, tag, attrs...)

const _htmlescape_chars = Dict('<'=>"&lt;",   '>'=>"&gt;",
                               '"'=>"&quot;", '&'=>"&amp;",
                               # ' '=>"&nbsp;",
                               )
for ch in "'`!\$%()=+{}[]"
    _htmlescape_chars[ch] = "&#$(Int(ch));"
end

function htmlesc(io::IO, s::AbstractString)
    # s1 = replace(s, r"&(?!(\w+|\#\d+);)" => "&amp;")
    for ch in s
        print(io, get(_htmlescape_chars, ch, ch))
    end
end
function htmlesc(io::IO, s::Symbol)
    htmlesc(io, string(s))
end
function htmlesc(io::IO, xs::Union{AbstractString,Symbol}...)
    for s in xs
        htmlesc(io, s)
    end
end
function htmlesc(s::Union{AbstractString,Symbol})
    sprint(htmlesc, s)
end

# Block elements

function html(io::IO, content::Vector)
    for md in content
        html(io, md)
        println(io)
    end
end

html(io::IO, md::MD) = html(io, md.content)

function html(io::IO, header::Header{l}) where l
    withtag(io, "h$l") do
        htmlinline(io, header.text)
    end
end

function html(io::IO, code::Code)
    withtag(io, :pre) do
        maybe_lang = !isempty(code.language) ? Any[:class=>"language-$(code.language)"] : []
        withtag(io, :code, maybe_lang...) do
            htmlesc(io, code.code)
            # TODO should print newline if this is longer than one line ?
        end
    end
end

function html(io::IO, md::Paragraph)
    withtag(io, :p) do
        htmlinline(io, md.content)
    end
end

function html(io::IO, md::BlockQuote)
    withtag(io, :blockquote) do
        println(io)
        html(io, md.content)
    end
end

function html(io::IO, f::Footnote)
    withtag(io, :div, :class => "footnote", :id => "footnote-$(f.id)") do
        withtag(io, :p, :class => "footnote-title") do
            print(io, f.id)
        end
        html(io, f.text)
    end
end

function html(io::IO, md::Admonition)
    withtag(io, :div, :class => "admonition $(md.category)") do
        withtag(io, :p, :class => "admonition-title") do
            print(io, md.title)
        end
        html(io, md.content)
    end
end

function html(io::IO, md::List)
    maybe_attr = md.ordered > 1 ? Any[:start => string(md.ordered)] : []
    withtag(io, isordered(md) ? :ol : :ul, maybe_attr...) do
        for item in md.items
            println(io)
            withtag(io, :li) do
                html(io, item)
            end
        end
        println(io)
    end
end

function html(io::IO, md::HorizontalRule)
    tag(io, :hr)
end

html(io::IO, x) = tohtml(io, x)

# Inline elements

function htmlinline(io::IO, content::Vector)
    for x in content
        htmlinline(io, x)
    end
end

function htmlinline(io::IO, code::Code)
    withtag(io, :code) do
        htmlesc(io, code.code)
    end
end

function htmlinline(io::IO, md::Union{Symbol,AbstractString})
    htmlesc(io, md)
end

function htmlinline(io::IO, md::Bold)
    withtag(io, :strong) do
        htmlinline(io, md.text)
    end
end

function htmlinline(io::IO, md::Italic)
    withtag(io, :em) do
        htmlinline(io, md.text)
    end
end

function htmlinline(io::IO, md::Image)
    tag(io, :img, :src=>md.url, :alt=>md.alt)
end


function htmlinline(io::IO, f::Footnote)
    withtag(io, :a, :href => "#footnote-$(f.id)", :class => "footnote") do
        print(io, "[", f.id, "]")
    end
end

function htmlinline(io::IO, link::Link)
    withtag(io, :a, :href=>link.url) do
        htmlinline(io, link.text)
    end
end

function htmlinline(io::IO, br::LineBreak)
    tag(io, :br)
end

htmlinline(io::IO, x) = tohtml(io, x)

# API

export html

html(md) = sprint(html, md)

function show(io::IO, ::MIME"text/html", md::MD)
    withtag(io, :div, :class=>"markdown") do
        html(io, md)
    end
end
w   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Markdown/src/render/rich.jl      # This file is a part of Julia. License is MIT: https://julialang.org/license

function tohtml(io::IO, m::MIME"text/html", x)
    show(io, m, x)
end

function tohtml(io::IO, m::MIME"text/plain", x)
    htmlesc(io, sprint(show, m, x))
end

function tohtml(io::IO, m::MIME"image/png", img)
    print(io, """<img src="data:image/png;base64,""")
    print(io, stringmime(m, img))
    print(io, "\" />")
end

function tohtml(io::IO, m::MIME"image/svg+xml", img)
    show(io, m, img)
end

# AbstractDisplay infrastructure

function bestmime(val)
    for mime in ("text/html", "image/svg+xml", "image/png", "text/plain")
        showable(mime, val) && return MIME(Symbol(mime))
    end
    error("Cannot render $val to Markdown.")
end

tohtml(io::IO, x) = tohtml(io, bestmime(x), x)
x   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Markdown/src/render/latex.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

export latex

function wrapblock(f, io, env)
    println(io, "\\begin{", env, "}")
    f()
    println(io, "\\end{", env, "}")
end

function wrapinline(f, io, cmd)
    print(io, "\\", cmd, "{")
    f()
    print(io, "}")
end

# Block elements

latex(io::IO, md::MD) = latex(io, md.content)

function latex(io::IO, content::Vector)
    for c in content
        latex(io, c)
    end
end

function latex(io::IO, header::Header{l}) where l
    tag = l < 4 ? "sub"^(l-1) * "section" : "sub"^(l-4) * "paragraph"
    wrapinline(io, tag) do
        latexinline(io, header.text)
    end
    println(io)
end

function latex(io::IO, code::Code)
    occursin("\\end{verbatim}", code.code) && error("Cannot include \"\\end{verbatim}\" in a latex code block")
    wrapblock(io, "verbatim") do
        println(io, code.code)
    end
end

function latexinline(io::IO, code::Code)
    wrapinline(io, "texttt") do
        print(io, latexesc(code.code))
    end
end

function latex(io::IO, md::Paragraph)
    for mdc in md.content
        latexinline(io, mdc)
    end
    println(io)
    println(io)
end

function latex(io::IO, md::BlockQuote)
    wrapblock(io, "quote") do
        latex(io, md.content)
    end
end


function latex(io::IO, f::Footnote)
    print(io, "\\footnotetext[", f.id, "]{")
    latex(io, f.text)
    println(io, "}")
end

function latex(io::IO, md::Admonition)
    wrapblock(io, "quote") do
        wrapinline(io, "textbf") do
            print(io, md.category)
        end
        println(io, "\n\n", md.title, "\n")
        latex(io, md.content)
    end
end

function latex(io::IO, md::List)
    # `\begin{itemize}` is used here for both ordered and unordered lists since providing
    # custom starting numbers for enumerated lists is simpler to do by manually assigning
    # each number to `\item` ourselves rather than using `\setcounter{enumi}{<start>}`.
    #
    # For an ordered list starting at 5 the following will be generated:
    #
    # \begin{itemize}
    #   \item[5. ] ...
    #   \item[6. ] ...
    #   ...
    # \end{itemize}
    #
    pad = ndigits(md.ordered + length(md.items)) + 2
    fmt = n -> (isordered(md) ? "[$(rpad("$(n + md.ordered - 1).", pad))]" : "")
    wrapblock(io, "itemize") do
        for (n, item) in enumerate(md.items)
            print(io, "\\item$(fmt(n)) ")
            latex(io, item)
            n < length(md.items) && println(io)
        end
    end
end

function latex(io::IO, md::HorizontalRule)
    println(io, "\\rule{\\textwidth}{1pt}")
end

# Inline elements

function latexinline(io::IO, md::Vector)
    for c in md
        latexinline(io, c)
    end
end

function latexinline(io::IO, md::AbstractString)
    latexesc(io, md)
end

function latexinline(io::IO, md::Bold)
    wrapinline(io, "textbf") do
        latexinline(io, md.text)
    end
end

function latexinline(io::IO, md::Italic)
    wrapinline(io, "emph") do
        latexinline(io, md.text)
    end
end

function latexinline(io::IO, md::Image)
    wrapblock(io, "figure") do
        println(io, "\\centering")
        wrapinline(io, "includegraphics") do
            print(io, md.url)
        end
        println(io)
        wrapinline(io, "caption") do
            latexinline(io, md.alt)
        end
        println(io)
    end
end

latexinline(io::IO, f::Footnote) = print(io, "\\footnotemark[", f.id, "]")

function latexinline(io::IO, md::Link)
    wrapinline(io, "href") do
        print(io, md.url)
    end
    print(io, "{")
    latexinline(io, md.text)
    print(io, "}")
end

const _latexescape_chars = Dict{Char, AbstractString}(
    '~'=>"{\\textasciitilde}",
    '^'=>"\\^{}",
    '\\'=>"{\\textbackslash}")
for ch in "&%\$#_{}"
    _latexescape_chars[ch] = "\\$ch"
end

function latexesc(io, s::AbstractString)
    for ch in s
        print(io, get(_latexescape_chars, ch, ch))
    end
end

latex(md) = sprint(latex, md)
latexinline(md) = sprint(latexinline, md)
latexesc(s) = sprint(latexesc, s)

show(io::IO, ::MIME"text/latex", md::MD) = latex(io, md)
v   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Markdown/src/render/rst.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

rst(x) = sprint(rst, x)

function rst(io::IO, content::Vector)
    isempty(content) && return
    for md in content[1:end-1]
        rst(io, md)
        println(io)
    end
    rst(io, content[end])
end

rst(io::IO, md::MD) = rst(io, md.content)

function rst(io::IO, header::Header{l}) where l
    s = rstinline(header.text)
    println(io, s)
    println(io, string("*=-~:.^"[l])^length(s))
    println(io)
end

function rst(io::IO, code::Code)
    if code.language == "jldoctest"
        println(io, ".. doctest::\n")
    elseif code.language != "rst"
        println(io, ".. code-block:: julia\n")
    end
    for l in lines(code.code)
        println(io, "    ", l)
    end
end

function rst(io::IO, p::Paragraph)
    rstinline(io, p.content)
    println(io)
end

function rst(io::IO, list::List)
    for (i, item) in enumerate(list.items)
        bullet = isordered(list) ? "$(i + list.ordered - 1). " : "* "
        print(io, bullet)
        lines = split(rstrip(sprint(rst, item)), '\n')
        for (n, line) in enumerate(lines)
            print(io, (n == 1 || isempty(line)) ? "" : " "^length(bullet), line)
            n < length(lines) && println(io)
        end
        println(io)
    end
end

function rst(io::IO, q::BlockQuote)
    s = sprint(rst, q.content)
    for line in split(rstrip(s), "\n")
        println(io, "    ", line)
    end
    println(io)
end

function rst(io::IO, f::Footnote)
    print(io, ".. [", f.id, "]")
    s = sprint(rst, f.text)
    lines = split(rstrip(s), "\n")
    # Single line footnotes are printed on the same line as their label
    # rather than taking up an additional line.
    if length(lines) == 1
        println(io, " ", lines[1])
    else
        println(io)
        for line in lines
            println(io, isempty(line) ? "" : "   ", rstrip(line))
        end
        println(io)
    end
end

function rst(io::IO, md::Admonition)
    s = sprint(rst, md.content)
    title = md.title == uppercasefirst(md.category) ? "" : md.title
    println(io, ".. ", md.category, "::", isempty(title) ? "" : " $title")
    for line in split(rstrip(s), "\n")
        println(io, isempty(line) ? "" : "   ", line)
    end
    println(io)
end

function rst(io::IO, md::HorizontalRule)
    println(io, "–" ^ 5)
end

function rst(io::IO, l::LaTeX)
    println(io, ".. math::\n")
    for line in lines(l.formula)
        println(io, "    ", line)
    end
end

rst(io::IO, md) = show(io, "text/rst", md)

# Inline elements

rstinline(x) = sprint(rstinline, x)

function rstinline(io::IO, md...)
    wasCode = false
    for el in md
        wasCode && isa(el, AbstractString) && !Base.startswith(el, " ") && print(io, "\\ ")
        wasCode = (isa(el, Code) || isa(el, LaTeX) || isa(el, Link)) && (wasCode = true)
        rstinline(io, el)
    end
end

rstinline(io::IO, md::Vector) = !isempty(md) && rstinline(io, md...)

# rstinline(io::IO, md::Image) = rstinline(io, ".. image:: ", md.url)

function rstinline(io::IO, md::Link)
    if occursin(r":(func|obj|ref|exc|class|const|data):`\.*", md.url)
        rstinline(io, md.url)
    else
        rstinline(io, "`", md.text, " <", md.url, ">`_")
    end
end

rstinline(io::IO, f::Footnote) = print(io, "[", f.id, "]_")

rstescape(s) = replace(s, "\\" => "\\\\")

rstinline(io::IO, s::AbstractString) = print(io, rstescape(s))

rstinline(io::IO, md::Bold) = rstinline(io, "**", md.text, "**")

rstinline(io::IO, md::Italic) = rstinline(io, "*", md.text, "*")

rstinline(io::IO, md::Code) = print(io, "``", md.code, "``")

rstinline(io::IO, br::LineBreak) = println(io)

rstinline(io::IO, l::LaTeX) = print(io, ":math:`", l.formula, "`")

rstinline(io::IO, x) = show(io, MIME"text/rst"(), x)

# show

Base.show(io::IO, ::MIME"text/rst", md::MD) = rst(io, md)
�   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Markdown/src/render/terminal/render.jlK      # This file is a part of Julia. License is MIT: https://julialang.org/license

include("formatting.jl")

cols(io) = displaysize(io)[2]

function term(io::IO, content::Vector, cols)
    isempty(content) && return
    for md in content[1:end-1]
        term(io, md, cols)
        print(io, '\n', '\n')
    end
    term(io, content[end], cols)
end

term(io::IO, md::MD, columns = cols(io)) = term(io, md.content, columns)

function term(io::IO, md::Paragraph, columns)
    print(io, ' '^margin)
    print_wrapped(io, width = columns-2margin, pre = ' '^margin) do io
        terminline(io, md.content)
    end
end

function term(io::IO, md::BlockQuote, columns)
    s = sprint(term, md.content, columns - 10; context=io)
    lines = split(rstrip(s), '\n')
    print(io, ' '^margin, '│', lines[1])
    for i = 2:length(lines)
        print(io, '\n', ' '^margin, '│', lines[i])
    end
end

function term(io::IO, md::Admonition, columns)
    col = :default
    # If the types below are modified, the page manual/documentation.md must be updated accordingly.
    if md.category == "danger"
        col = Base.error_color()
    elseif md.category == "warning"
        col = Base.warn_color()
    elseif md.category in ("info", "note")
        col = Base.info_color()
    elseif md.category == "tip"
        col = :green
    end
    printstyled(io, ' '^margin, "│ "; color=col, bold=true)
    printstyled(io, isempty(md.title) ? md.category : md.title; color=col, bold=true)
    printstyled(io, '\n', ' '^margin, '│', '\n'; color=col, bold=true)
    s = sprint(term, md.content, columns - 10; context=io)
    lines = split(rstrip(s), '\n')
    for i in eachindex(lines)
        printstyled(io, ' '^margin, '│'; color=col, bold=true)
        print(io, lines[i])
        i < lastindex(lines) && println(io)
    end
end

function term(io::IO, f::Footnote, columns)
    print(io, ' '^margin, "│ ")
    printstyled(io, "[^$(f.id)]", bold=true)
    println(io, '\n', ' '^margin, '│')
    s = sprint(term, f.text, columns - 10; context=io)
    lines = split(rstrip(s), '\n')
    for i in eachindex(lines)
        print(io, ' '^margin, '│', lines[i])
        i < lastindex(lines) && println(io)
    end
end

function term(io::IO, md::List, columns)
    for (i, point) in enumerate(md.items)
        print(io, ' '^2margin, isordered(md) ? "$(i + md.ordered - 1). " : "•  ")
        print_wrapped(io, width = columns-(4margin+2), pre = ' '^(2margin+3),
                          i = 2margin+2) do io
            term(io, point, columns - 10)
        end
        i < lastindex(md.items) && print(io, '\n', '\n')
    end
end

function _term_header(io::IO, md, char, columns)
    text = terminline_string(io, md.text)
    with_output_color(:bold, io) do io
        pre = ' '^margin
        print(io, pre)
        line_no, lastline_width = print_wrapped(io, text,
                                                width=columns - 4margin; pre)
        line_width = min(lastline_width, columns)
        if line_no > 1
            line_width = max(line_width, div(columns, 3)+length(pre))
        end
        header_width = max(0, line_width-length(pre))
        char != ' ' && header_width > 0 && print(io, '\n', ' '^(margin), char^header_width)
    end
end

const _header_underlines = collect("≡=–-⋅ ")
# TODO settle on another option with unicode e.g. "≡=≃–∼⋅" ?

function term(io::IO, md::Header{l}, columns) where l
    underline = _header_underlines[l]
    _term_header(io, md, underline, columns)
end

function term(io::IO, md::Code, columns)
    with_output_color(:cyan, io) do io
        L = lines(md.code)
        for i in eachindex(L)
            print(io, ' '^margin, L[i])
            i < lastindex(L) && println(io)
        end
    end
end

function term(io::IO, tex::LaTeX, columns)
    printstyled(io, ' '^margin, tex.formula, color=:magenta)
end

term(io::IO, br::LineBreak, columns) = nothing # line breaks already printed between subsequent elements

function term(io::IO, br::HorizontalRule, columns)
   print(io, ' '^margin, '─'^(columns - 2margin))
end

term(io::IO, x, _) = show(io, MIME"text/plain"(), x)

# Inline Content

terminline_string(io::IO, md) = sprint(terminline, md; context=io)

terminline(io::IO, content...) = terminline(io, collect(content))

function terminline(io::IO, content::Vector)
    for md in content
        terminline(io, md)
    end
end

function terminline(io::IO, md::AbstractString)
    print(io, replace(md, r"[\s\t\n]+" => ' '))
end

function terminline(io::IO, md::Bold)
    with_output_color(terminline, :bold, io, md.text)
end

function terminline(io::IO, md::Italic)
    with_output_color(terminline, :underline, io, md.text)
end

function terminline(io::IO, md::LineBreak)
    println(io)
end

function terminline(io::IO, md::Image)
    terminline(io, "(Image: $(md.alt))")
end

terminline(io::IO, f::Footnote) = with_output_color(terminline, :bold, io, "[^$(f.id)]")

function terminline(io::IO, md::Link)
    url = !Base.startswith(md.url, "@ref") ? " ($(md.url))" : ""
    text = terminline_string(io, md.text)
    terminline(io, text, url)
end

function terminline(io::IO, code::Code)
    printstyled(io, code.code, color=:cyan)
end

function terminline(io::IO, tex::LaTeX)
    printstyled(io, tex.formula, color=:magenta)
end

terminline(io::IO, x) = show(io, MIME"text/plain"(), x)

# Show in terminal
Base.show(io::IO, ::MIME"text/plain", md::MD) = (term(io, md); nothing)
�   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Markdown/src/render/terminal/formatting.jl	      # This file is a part of Julia. License is MIT: https://julialang.org/license

# Wrapping

function ansi_length(s)
    replace(s, r"\e\[[0-9]+m" => "") |> textwidth
end

words(s) = split(s, " ")
lines(s) = split(s, "\n")

function wrapped_line(io::IO, s::AbstractString, width, i)
    ws = words(s)
    lines = String[]
    for word in ws
        word_length = ansi_length(word)
        word_length == 0 && continue
        if isempty(lines) || i + word_length + 1 > width
            i = word_length
            if length(lines) > 0
                last_line = lines[end]
                maybe_underline = findlast(Base.text_colors[:underline], last_line)
                if !isnothing(maybe_underline)
                    # disable underline style at end of line if not already disabled.
                    maybe_disable_underline = max(
                        last(something(findlast(Base.disable_text_style[:underline], last_line), -1)),
                        last(something(findlast(Base.text_colors[:normal], last_line), -1)),
                    )

                    if maybe_disable_underline < 0 || maybe_disable_underline < last(maybe_underline)

                        lines[end] = last_line * Base.disable_text_style[:underline]
                        word = Base.text_colors[:underline] * word
                    end
                end
            end
            push!(lines, word)
        else
            i += word_length + 1
            lines[end] *= " " * word   # this could be more efficient
        end
    end
    return i, lines
end

function wrapped_lines(io::IO, s::AbstractString; width = 80, i = 0)
    ls = String[]
    for ss in lines(s)
        i, line = wrapped_line(io, ss, width, i)
        append!(ls, line)
    end
    return ls
end

wrapped_lines(io::IO, f::Function, args...; width = 80, i = 0) =
    wrapped_lines(io, sprint(f, args...; context=io), width = width, i = 0)

function print_wrapped(io::IO, s...; width = 80, pre = "", i = 0)
    lines = wrapped_lines(io, s..., width = width, i = i)
    isempty(lines) && return 0, 0
    print(io, lines[1])
    for line in lines[2:end]
        print(io, '\n', pre, line)
    end
    length(lines), length(pre) + ansi_length(lines[end])
end

print_wrapped(f::Function, io::IO, args...; kws...) = print_wrapped(io, f, args...; kws...)
p   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Printf/src/Printf.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

module Printf

using Base.Ryu

export @printf, @sprintf

# format specifier categories
const Ints = Union{Val{'d'}, Val{'i'}, Val{'u'}, Val{'x'}, Val{'X'}, Val{'o'}}
const Floats = Union{Val{'e'}, Val{'E'}, Val{'f'}, Val{'F'}, Val{'g'}, Val{'G'}, Val{'a'}, Val{'A'}}
const Chars = Union{Val{'c'}, Val{'C'}}
const Strings = Union{Val{'s'}, Val{'S'}}
const Pointer = Val{'p'}
const HexBases = Union{Val{'x'}, Val{'X'}, Val{'a'}, Val{'A'}}
const PositionCounter = Val{'n'}

const MAX_FRACTIONAL_PART_WIDTH = 17  # max significant decimals + 1: `ceil(Int, log10(1 / eps(Float64))) + 1`
const MAX_INTEGER_PART_WIDTH = 309  # max exponent: `ceil(Int, log10(prevfloat(typemax(Float64))))`
const MAX_FMT_CHARS_WIDTH = 5  # hash | sign +/- | decimal dot | exponent e/E | exponent sign

"""
Typed representation of a format specifier.

`T` is a `Val{'_'}`, where `_` is a valid format specifier character.

Fields are the various modifiers allowed for various format specifiers.
"""
struct Spec{T} # T => %type => Val{'type'}
    leftalign::Bool
    plus::Bool
    space::Bool
    zero::Bool
    hash::Bool
    width::Int
    precision::Int
    dynamic_width::Bool
    dynamic_precision::Bool
end

# recreate the format specifier string from a typed Spec
Base.string(f::Spec{T}; modifier::String="") where {T} =
    string("%",
           f.leftalign ? "-" : "",
           f.plus ? "+" : "",
           f.space ? " " : "",
           f.zero ? "0" : "",
           f.hash ? "#" : "",
           f.dynamic_width ? "*" : (f.width > 0 ? f.width : ""),
           f.dynamic_precision ? ".*" : (f.precision == 0 ? ".0" : (f.precision > 0 ? ".$(f.precision)" : "")),
           modifier,
           char(T))

Base.show(io::IO, f::Spec) = print(io, string(f))

floatfmt(s::Spec{T}) where {T} =
    Spec{Val{'f'}}(s.leftalign, s.plus, s.space, s.zero, s.hash, s.width, 0, s.dynamic_width, s.dynamic_precision)
ptrfmt(s::Spec{T}, x) where {T} =
    Spec{Val{'x'}}(s.leftalign, s.plus, s.space, s.zero, true, s.width, sizeof(x) == 8 ? 16 : 8, s.dynamic_width, s.dynamic_precision)

"""
    Printf.Format(format_str)

Create a C printf-compatible format object that can be used for formatting values.

The input `format_str` can include any valid format specifier character and modifiers.

A `Format` object can be passed to `Printf.format(f::Format, args...)` to produce a
formatted string, or `Printf.format(io::IO, f::Format, args...)` to print the
formatted string directly to `io`.

For convenience, the `Printf.format"..."` string macro form can be used for building
a `Printf.Format` object at macro-expansion-time.

!!! compat "Julia 1.6"
    `Printf.Format` requires Julia 1.6 or later.
"""
struct Format{S, T}
    str::S # original full format string as CodeUnits
    # keep track of non-format specifier strings to print
    # length(substringranges) == length(formats) + 1
    # so when printing, we start with printing
      # str[substringranges[1]], then formats[1] + args[1]
      # then str[substringranges[2]], then formats[2] + args[2]
      # and so on, then at the end, str[substringranges[end]]
    substringranges::Vector{UnitRange{Int}}
    formats::T # Tuple of Specs
    numarguments::Int  # required for dynamic format specifiers
end

# what number base should be used for a given format specifier?
base(T) = T <: HexBases ? 16 : T <: Val{'o'} ? 8 : 10
char(::Type{Val{c}}) where {c} = c

struct InvalidFormatStringError <: Exception
    message::String
    format::String
    start_color::Int
    end_color::Int
end

function Base.showerror(io::IO, err::InvalidFormatStringError)
    io_has_color = get(io, :color, false)::Bool

    println(io, "InvalidFormatStringError: ", err.message)
    print(io, "    \"", @view(err.format[begin:prevind(err.format, err.start_color)]))
    invalid_text = @view err.format[err.start_color:err.end_color]

    printstyled(io, invalid_text, color=:red)

    # +1 is okay, since all format characters are single bytes
    println(io, @view(err.format[err.end_color+1:end]), "\"")

    arrow_error = '-'^(length(invalid_text)-1)
    arrow = "    " * ' '^err.start_color * arrow_error * "^\n"
    if io_has_color
        printstyled(io, arrow, color=:red)
    else
        print(io, arrow)
    end
end

# parse format string
function Format(f::AbstractString)
    bytes = codeunits(f)
    len = length(bytes)
    pos = 1
    numarguments = 0

    b = 0x00
    local last_percent_pos

    # skip ahead to first format specifier
    while pos <= len
        b = bytes[pos]
        pos += 1
        if b == UInt8('%')
            last_percent_pos = pos-1
            pos > len && throw(InvalidFormatStringError("Format specifier is incomplete", f, last_percent_pos, last_percent_pos))
            if bytes[pos] == UInt8('%')
                # escaped '%'
                b = bytes[pos]
                pos += 1
            else
                break
            end
        end
    end
    strs = [1:pos - 1 - (b == UInt8('%'))]
    fmts = []
    while pos <= len
        b = bytes[pos]
        pos += 1
        # positioned at start of first format str %
        # parse flags
        leftalign = plus = space = zero = hash = false
        while true
            if b == UInt8('-')
                leftalign = true
            elseif b == UInt8('+')
                plus = true
            elseif b == UInt8(' ')
                space = true
            elseif b == UInt8('0')
                zero = true
            elseif b == UInt8('#')
                hash = true
            else
                break
            end
            pos > len && throw(InvalidFormatStringError("Format specifier is incomplete", f, last_percent_pos, pos-1))
            b = bytes[pos]
            pos += 1
        end
        if leftalign
            zero = false
        end
        # parse width
        width = 0
        dynamic_width = false
        if b == UInt8('*')
            dynamic_width = true
            numarguments += 1
            b = bytes[pos]
            pos += 1
        else
            while b - UInt8('0') < 0x0a
            width = 10 * width + (b - UInt8('0'))
                b = bytes[pos]
                pos += 1
                pos > len && break
            end
        end
        # parse precision
        precision = 0
        parsedprecdigits = false
        dynamic_precision = false
        if b == UInt8('.')
            pos > len && throw(InvalidFormatStringError("Precision specifier is missing precision", f, last_percent_pos, pos-1))
            parsedprecdigits = true
            b = bytes[pos]
            pos += 1
            if pos <= len
                if b == UInt8('*')
                    dynamic_precision = true
                    numarguments += 1
                    b = bytes[pos]
                    pos += 1
                else
                    precision = 0
                    while b - UInt8('0') < 0x0a
                        precision = 10precision + (b - UInt8('0'))
                        b = bytes[pos]
                        pos += 1
                        pos > len && break
                    end
                end
            end
        end
        # parse length modifier (ignored)
        if b == UInt8('h') || b == UInt8('l')
            prev = b
            pos > len && throw(InvalidFormatStringError("Length modifier is missing type specifier", f, last_percent_pos, pos-1))
            b = bytes[pos]
            pos += 1
            if b == prev
                pos > len && throw(InvalidFormatStringError("Length modifier is missing type specifier", f, last_percent_pos, pos-1))
                b = bytes[pos]
                pos += 1
            end
        elseif b in b"Ljqtz" # q was a synonym for ll above, see `man 3 printf`. Not to be used.
            pos > len && throw(InvalidFormatStringError("Length modifier is missing type specifier", f, last_percent_pos, pos-1))
            b = bytes[pos]
            pos += 1
        end
        # parse type
        !(b in b"diouxXDOUeEfFgGaAcCsSpn") && throw(InvalidFormatStringError("'$(Char(b))' is not a valid type specifier", f, last_percent_pos, pos-1))
        type = Val{Char(b)}
        if type <: Ints && precision > 0
            # note - we should also set zero to false if dynamic precison > 0
            # this is taken care of in fmt() for Ints
            zero = false
        elseif (type <: Strings || type <: Chars) && !parsedprecdigits
            precision = -1
        elseif type <: Union{Val{'a'}, Val{'A'}} && !parsedprecdigits
            precision = -1
        elseif type <: Floats && !parsedprecdigits
            precision = 6
        end
        numarguments += 1
        push!(fmts, Spec{type}(leftalign, plus, space, zero, hash, width, precision, dynamic_width, dynamic_precision))
        start = pos
        while pos <= len
            b = bytes[pos]
            pos += 1
            if b == UInt8('%')
                last_percent_pos = pos-1
                pos > len && throw(InvalidFormatStringError("Format specifier is incomplete", f, last_percent_pos, last_percent_pos))
                if bytes[pos] == UInt8('%')
                    # escaped '%'
                    b = bytes[pos]
                    pos += 1
                else
                    break
                end
            end
        end
        push!(strs, start:pos - 1 - (b == UInt8('%')))
    end
    return Format(bytes, strs, Tuple(fmts), numarguments)
end

macro format_str(str)
    Format(str)
end

const hex = b"0123456789abcdef"
const HEX = b"0123456789ABCDEF"

# write out a single arg according to format options
# char
@inline function writechar(buf, pos, c)
    u = bswap(reinterpret(UInt32, c))
    while true
        buf[pos] = u % UInt8
        pos += 1
        (u >>= 8) == 0 && break
    end
    return pos
end


@inline function rmdynamic(spec::Spec{T}, args, argp) where {T}
    zero, width, precision = spec.zero, spec.width, spec.precision
    if spec.dynamic_width
        width = args[argp]
        argp += 1
    end
    if spec.dynamic_precision
        precision = args[argp]
        if zero && T <: Ints && precision > 0
            zero = false
        end
        argp += 1
    end
    (Spec{T}(spec.leftalign, spec.plus, spec.space, zero, spec.hash, width, precision, false, false), argp)
end

@inline function fmt(buf, pos, args, argp, spec::Spec{T}) where {T}
    spec, argp = rmdynamic(spec, args, argp)
    (fmt(buf, pos, args[argp], spec), argp+1)
end

@inline function fmt(buf, pos, arg, spec::Spec{T}) where {T <: Chars}
    leftalign, width = spec.leftalign, spec.width
    c = Char(first(arg))
    w = textwidth(c)
    if !leftalign && width > w
        for _ = 1:(width - w)
            buf[pos] = UInt8(' ')
            pos += 1
        end
    end
    pos = writechar(buf, pos, c)
    if leftalign && width > w
        for _ = 1:(width - w)
            buf[pos] = UInt8(' ')
            pos += 1
        end
    end
    return pos
end

# strings
@inline function fmt(buf, pos, arg, spec::Spec{T}) where {T <: Strings}
    leftalign, hash, width, prec = spec.leftalign, spec.hash, spec.width, spec.precision
    str = string(arg)
    slen = textwidth(str)::Int + (hash ? arg isa AbstractString ? 2 : 1 : 0)
    op = p = prec == -1 ? slen : min(slen, prec)
    if !leftalign && width > p
        for _ = 1:(width - p)
            buf[pos] = UInt8(' ')
            pos += 1
        end
    end
    if hash
        if arg isa Symbol
            buf[pos] = UInt8(':')
            pos += 1
            p -= 1
        elseif arg isa AbstractString
            buf[pos] = UInt8('"')
            pos += 1
            p -= 1
        end
    end
    for c in str
        p -= textwidth(c)
        p < 0 && break
        pos = writechar(buf, pos, c)
    end
    if hash && arg isa AbstractString && p > 0
        buf[pos] = UInt8('"')
        pos += 1
    end
    if leftalign && width > op
        for _ = 1:(width - op)
            buf[pos] = UInt8(' ')
            pos += 1
        end
    end
    return pos
end

# integers
toint(x) = x
toint(x::Rational) = Integer(x)

fmt(buf, pos, arg::AbstractFloat, spec::Spec{T}) where {T <: Ints} =
    fmt(buf, pos, arg, floatfmt(spec))

@inline function fmt(buf, pos, arg, spec::Spec{T}) where {T <: Ints}
    leftalign, plus, space, zero, hash, width, prec =
        spec.leftalign, spec.plus, spec.space, spec.zero, spec.hash, spec.width, spec.precision
    bs = base(T)
    arg2 = toint(arg)
    n = i = ndigits(arg2, base=bs, pad=1)
    neg = arg2 < 0
    x = arg2 isa Base.BitSigned ? unsigned(abs(arg2)) : abs(arg2)
    arglen = n + (neg || (plus | space)) +
        (T == Val{'o'} && hash ? 1 : 0) +
        (T == Val{'x'} && hash ? 2 : 0) + (T == Val{'X'} && hash ? 2 : 0)
    arglen2 = arglen < width && prec > 0 ? arglen + min(max(0, prec - n), width - arglen) : arglen
    if !leftalign && !zero && arglen2 < width
        # pad left w/ spaces
        for _ = 1:(width - arglen2)
            buf[pos] = UInt8(' ')
            pos += 1
        end
    end
    if neg
        buf[pos] = UInt8('-'); pos += 1
    elseif plus # plus overrides space
        buf[pos] = UInt8('+'); pos += 1
    elseif space
        buf[pos] = UInt8(' '); pos += 1
    end
    if T == Val{'o'} && hash
        buf[pos] = UInt8('0')
        pos += 1
    elseif T == Val{'x'} && hash
        buf[pos] = UInt8('0')
        buf[pos + 1] = UInt8('x')
        pos += 2
    elseif T == Val{'X'} && hash
        buf[pos] = UInt8('0')
        buf[pos + 1] = UInt8('X')
        pos += 2
    end
    if zero && arglen2 < width
        for _ = 1:(width - arglen2)
            buf[pos] = UInt8('0')
            pos += 1
        end
    elseif n < prec
        for _ = 1:(prec - n)
            buf[pos] = UInt8('0')
            pos += 1
        end
    elseif arglen < arglen2
        for _ = 1:(arglen2 - arglen)
            buf[pos] = UInt8('0')
            pos += 1
        end
    end
    while i > 0
        @inbounds buf[pos + i - 1] = bs == 16 ?
            (T == Val{'x'} ? hex[(x & 0x0f) + 1] : HEX[(x & 0x0f) + 1]) :
            (48 + (bs == 8 ? (x & 0x07) : rem(x, 10)))
        if bs == 8
            x >>= 3
        elseif bs == 16
            x >>= 4
        else
            x = oftype(x, div(x, 10))
        end
        i -= 1
    end
    pos += n
    if leftalign && arglen2 < width
        # pad right
        for _ = 1:(width - arglen2)
            buf[pos] = UInt8(' ')
            pos += 1
        end
    end
    return pos
end

# floats
"""
    Printf.tofloat(x)

Convert an argument to a Base float type for printf formatting.
By default, arguments are converted to `Float64` via `Float64(x)`.
Custom numeric types that have a conversion to a Base float type
that wish to hook into printf formatting can extend this method like:

```julia
Printf.tofloat(x::MyCustomType) = convert_my_custom_type_to_float(x)
```

For arbitrary precision numerics, you might extend the method like:

```julia
Printf.tofloat(x::MyArbitraryPrecisionType) = BigFloat(x)
```

!!! compat "Julia 1.6"
    This function requires Julia 1.6 or later.
"""
tofloat(x) = Float64(x)
tofloat(x::Base.IEEEFloat) = x
tofloat(x::BigFloat) = x

_snprintf(ptr, siz, str, arg) =
    @ccall "libmpfr".mpfr_snprintf(ptr::Ptr{UInt8}, siz::Csize_t, str::Ptr{UInt8};
                                   arg::Ref{BigFloat})::Cint

# Arbitrary constant for a maximum number of bytes we want to output for a BigFloat.
# 8KiB seems like a reasonable default. Larger BigFloat representations should probably
# use a custom printing routine. Printing values with results larger than this ourselves
# seems like a dangerous thing to do.
const __BIG_FLOAT_MAX__ = 8192

@inline function fmt(buf, pos, arg, spec::Spec{T}) where {T <: Floats}
    leftalign, plus, space, zero, hash, width, prec =
        spec.leftalign, spec.plus, spec.space, spec.zero, spec.hash, spec.width, spec.precision
    x = tofloat(arg)
    if x isa BigFloat
        if isfinite(x)
            GC.@preserve buf begin
                siz = length(buf) - pos + 1
                str = string(spec; modifier="R")
                required_length = _snprintf(pointer(buf, pos), siz, str, x)
                if required_length > siz
                    required_length > __BIG_FLOAT_MAX__ &&
                        throw(ArgumentError("The given BigFloat requires $required_length bytes to be printed, which is more than the maximum of $__BIG_FLOAT_MAX__ bytes supported."))
                    resize!(buf, required_length + 1)
                    required_length = _snprintf(pointer(buf, pos), required_length + 1, str, x)
                end
                required_length > 0 || throw(ArgumentError("The given BigFloat would produce less than the maximum allowed number of bytes $__BIG_FLOAT_MAX__, but still couldn't be printed fully for an unknown reason."))
                return pos + required_length
            end
        end
        x = Float64(x)
    end
    if T == Val{'e'} || T == Val{'E'}
        newpos = Ryu.writeexp(buf, pos, x, prec, plus, space, hash, char(T), UInt8('.'))
    elseif T == Val{'f'} || T == Val{'F'}
        newpos = Ryu.writefixed(buf, pos, x, prec, plus, space, hash, UInt8('.'))
    elseif T == Val{'g'} || T == Val{'G'}
        if isinf(x) || isnan(x)
            newpos = Ryu.writeshortest(buf, pos, x, plus, space)
        else
            # C11-compliant general format
            prec = prec == 0 ? 1 : prec
            # format the value in scientific notation and parse the exponent part
            exp = let p = Ryu.writeexp(buf, pos, x, prec)
                b1, b2, b3, b4 = buf[p-4], buf[p-3], buf[p-2], buf[p-1]
                Z = UInt8('0')
                if b1 == UInt8('e')
                    # two-digit exponent
                    sign = b2 == UInt8('+') ? 1 : -1
                    exp = 10 * (b3 - Z) + (b4 - Z)
                else
                    # three-digit exponent
                    sign = b1 == UInt8('+') ? 1 : -1
                    exp = 100 * (b2 - Z) + 10 * (b3 - Z) + (b4 - Z)
                end
                flipsign(exp, sign)
            end
            if -4 ≤ exp < prec
                newpos = Ryu.writefixed(buf, pos, x, prec - (exp + 1), plus, space, hash, UInt8('.'), !hash)
            else
                newpos = Ryu.writeexp(buf, pos, x, prec - 1, plus, space, hash, T == Val{'g'} ? UInt8('e') : UInt8('E'), UInt8('.'), !hash)
            end
        end
    elseif T == Val{'a'} || T == Val{'A'}
        x, neg = x < 0 || x === -Base.zero(x) ? (-x, true) : (x, false)
        newpos = pos
        if neg
            buf[newpos] = UInt8('-')
            newpos += 1
        elseif plus
            buf[newpos] = UInt8('+')
            newpos += 1
        elseif space
            buf[newpos] = UInt8(' ')
            newpos += 1
        end
        if isnan(x)
            buf[newpos] = UInt8('N')
            buf[newpos + 1] = UInt8('a')
            buf[newpos + 2] = UInt8('N')
            newpos += 3
        elseif !isfinite(x)
            buf[newpos] = UInt8('I')
            buf[newpos + 1] = UInt8('n')
            buf[newpos + 2] = UInt8('f')
            newpos += 3
        else
            buf[newpos] = UInt8('0')
            newpos += 1
            buf[newpos] = T <: Val{'a'} ? UInt8('x') : UInt8('X')
            newpos += 1
            if arg == 0
                buf[newpos] = UInt8('0')
                newpos += 1
                if prec > 0
                    buf[newpos] = UInt8('.')
                    newpos += 1
                    while prec > 0
                        buf[newpos] = UInt8('0')
                        newpos += 1
                        prec -= 1
                    end
                end
                buf[newpos] = T <: Val{'a'} ? UInt8('p') : UInt8('P')
                buf[newpos + 1] = UInt8('+')
                buf[newpos + 2] = UInt8('0')
                newpos += 3
            else
                if prec > -1
                    s, p = frexp(x)
                    sigbits = 4 * min(prec, 13)
                    s = 0.25 * round(ldexp(s, 1 + sigbits))
                    # ensure last 2 exponent bits either 01 or 10
                    u = (reinterpret(UInt64, s) & 0x003f_ffff_ffff_ffff) >> (52 - sigbits)
                    i = n = (sizeof(u) << 1) - (leading_zeros(u) >> 2)
                else
                    s, p = frexp(x)
                    s *= 2.0
                    u = (reinterpret(UInt64, s) & 0x001f_ffff_ffff_ffff)
                    t = (trailing_zeros(u) >> 2)
                    u >>= (t << 2)
                    i = n = 14 - t
                end
                frac = u > 9 || hash || prec > 0
                while i > 1
                    buf[newpos + i] = T == Val{'a'} ? hex[(u & 0x0f) + 1] : HEX[(u & 0x0f) + 1]
                    u >>= 4
                    i -= 1
                    prec -= 1
                end
                if frac
                    buf[newpos + 1] = UInt8('.')
                end
                buf[newpos] = T == Val{'a'} ? hex[(u & 0x0f) + 1] : HEX[(u & 0x0f) + 1]
                newpos += n + frac
                while prec > 0
                    buf[newpos] = UInt8('0')
                    newpos += 1
                    prec -= 1
                end
                buf[newpos] = T <: Val{'a'} ? UInt8('p') : UInt8('P')
                newpos += 1
                p -= 1
                buf[newpos] = p < 0 ? UInt8('-') : UInt8('+')
                p = p < 0 ? -p : p
                newpos += 1
                n = i = ndigits(p, base=10, pad=1)
                while i > 0
                    buf[newpos + i - 1] = 48 + rem(p, 10)
                    p = oftype(p, div(p, 10))
                    i -= 1
                end
                newpos += n
            end
        end
    end
    if newpos - pos < width
        # need to pad
        if leftalign
            # easy case, just pad spaces after number
            for _ = 1:(width - (newpos - pos))
                buf[newpos] = UInt8(' ')
                newpos += 1
            end
        else
            # right aligned
            n = width - (newpos - pos)
            if zero
                ex = (arg < 0 || (plus | space)) + (T <: Union{Val{'a'}, Val{'A'}} ? 2 : 0)
                so = pos + ex
                len = (newpos - pos) - ex
                copyto!(buf, so + n, buf, so, len)
                for i = so:(so + n - 1)
                    buf[i] = UInt8('0')
                end
                newpos += n
            else
                copyto!(buf, pos + n, buf, pos, newpos - pos)
                for i = pos:(pos + n - 1)
                    buf[i] = UInt8(' ')
                end
                newpos += n
            end
        end
    end
    return newpos
end

# pointers
fmt(buf, pos, arg, spec::Spec{Pointer}) = fmt(buf, pos, UInt64(arg), ptrfmt(spec, arg))

# position counters
function fmt(buf, pos, arg::Ref{<:Integer}, ::Spec{PositionCounter})
    arg[] = pos - 1
    pos
end

# old Printf compat
function fix_dec end
function ini_dec end

# generic fallback
function fmtfallback(buf, pos, arg, spec::Spec{T}) where {T}
    leftalign, plus, space, zero, hash, width, prec =
        spec.leftalign, spec.plus, spec.space, spec.zero, spec.hash, spec.width, spec.precision
    buf2 = Base.StringVector(
        MAX_INTEGER_PART_WIDTH + MAX_FRACTIONAL_PART_WIDTH + MAX_FMT_CHARS_WIDTH
    )
    ise = T <: Union{Val{'e'}, Val{'E'}}
    isg = T <: Union{Val{'g'}, Val{'G'}}
    isf = T <: Val{'f'}
    if isg
        prec = prec == 0 ? 1 : prec
        arg = round(arg, sigdigits=prec)
    end
    n, pt, neg = isf ? fix_dec(arg, prec, buf2) : ini_dec(arg, min(prec + ise, length(buf2) - 1), buf2)
    if isg && !hash
        while buf2[n] == UInt8('0')
            n -= 1
        end
    end
    expform = ise || (isg && !(-4 < pt <= prec))
    n2 = n + (expform ? 4 : 0) + (prec > 0 || hash) + (neg || (plus | space)) +
        (isf && pt >= n ? prec + 1 : 0)
    if !leftalign && !zero && n2 < width
        # pad left w/ spaces
        for _ = 1:(width - n2)
            buf[pos] = UInt8(' ')
            pos += 1
        end
    end
    if neg
        buf[pos] = UInt8('-'); pos += 1
    elseif plus # plus overrides space
        buf[pos] = UInt8('+'); pos += 1
    elseif space
        buf[pos] = UInt8(' '); pos += 1
    end
    if zero && n2 < width
        for _ = 1:(width - n2)
            buf[pos] = UInt8('0')
            pos += 1
        end
    end
    if expform
        buf[pos] = buf2[1]
        pos += 1
        if n > 1 || hash
            buf[pos] = UInt8('.')
            pos += 1
            for i = 2:n
                buf[pos] = buf2[i]
                pos += 1
            end
        end
        buf[pos] = T <: Val{'e'} || T <: Val{'g'} ? UInt8('e') : UInt8('E')
        pos += 1
        exp = pt - 1
        buf[pos] = exp < 0 ? UInt8('-') : UInt8('+')
        pos += 1
        exp = abs(exp)
        if exp < 10
            buf[pos] = UInt8('0')
            buf[pos + 1] = 48 + exp
            pos += 2
        else
            buf[pos] = 48 + div(exp, 10)
            buf[pos + 1] = 48 + rem(exp, 10)
            pos += 2
        end
    elseif pt <= 0
        buf[pos] = UInt8('0')
        buf[pos + 1] = UInt8('.')
        pos += 2
        while pt < 0
            buf[pos] = UInt8('0')
            pos += 1
            pt += 1
        end
        for i = 1:n
            buf[pos] = buf2[i]
            pos += 1
        end
    elseif pt >= n
        for i = 1:n
            buf[pos] = buf2[i]
            pos += 1
        end
        while pt > n
            buf[pos] = UInt8('0')
            pos += 1
            n += 1
        end
        if hash || (isf && prec > 0)
            buf[pos] = UInt8('.')
            pos += 1
            while prec > 0
                buf[pos] = UInt8('0')
                pos += 1
                prec -= 1
            end
        end
    else
        for i = 1:pt
            buf[pos] = buf2[i]
            pos += 1
        end
        buf[pos] = UInt8('.')
        pos += 1
        for i = pt+1:n
            buf[pos] = buf2[i]
            pos += 1
        end
    end

    if leftalign && n2 < width
        # pad right
        for _ = 1:(width - n2)
            buf[pos] = UInt8(' ')
            pos += 1
        end
    end
    return pos
end

const UNROLL_UPTO = 16
# if you have your own buffer + pos, write formatted args directly to it
@inline function format(buf::Vector{UInt8}, pos::Integer, f::Format, args...)
    # write out first substring
    escapechar = false
    for i in f.substringranges[1]
        b = f.str[i]
        if !escapechar
            buf[pos] = b
            pos += 1
            escapechar = b === UInt8('%')
        else
            escapechar = false
        end
    end
    # for each format, write out arg and next substring
    # unroll up to 16 formats
    N = length(f.formats)
    argp = 1
    Base.@nexprs 16 i -> begin
        if N >= i
            pos, argp = fmt(buf, pos, args, argp, f.formats[i])
            for j in f.substringranges[i + 1]
                b = f.str[j]
                if !escapechar
                    buf[pos] = b
                    pos += 1
                    escapechar = b === UInt8('%')
                else
                    escapechar = false
                end
            end
        end
    end
    if N > 16
        for i = 17:length(f.formats)
            pos, argp = fmt(buf, pos, args, argp, f.formats[i])
            for j in f.substringranges[i + 1]
                b = f.str[j]
                if !escapechar
                    buf[pos] = b
                    pos += 1
                    escapechar = b === UInt8('%')
                else
                    escapechar = false
                end
            end
        end
    end
    return pos
end

@inline function plength(f::Spec{T}, args, argp) where {T}
    f, argp = rmdynamic(f, args, argp)
    (plength(f, args[argp]), argp+1)
end

function plength(f::Spec{T}, x) where {T <: Chars}
    c = Char(first(x))
    w = textwidth(c)
    return max(f.width, w) + (ncodeunits(c) - w)
end

plength(f::Spec{Pointer}, x) = max(f.width, 2 * sizeof(x) + 2)

function plength(f::Spec{T}, x) where {T <: Strings}
    str = string(x)
    sw = textwidth(str)
    p = f.precision == -1 ? (sw + (f.hash ? (x isa Symbol ? 1 : 2) : 0)) : f.precision
    return max(f.width, p) + (sizeof(str) - sw)
end

function plength(f::Spec{T}, x) where {T <: Ints}
    x2 = toint(x)
    return max(
        f.width,
        f.precision + ndigits(x2, base=base(T), pad=1) + MAX_FMT_CHARS_WIDTH
    )
end

plength(f::Spec{T}, x::AbstractFloat) where {T <: Ints} =
    max(f.width, f.hash + MAX_INTEGER_PART_WIDTH + 0 + MAX_FMT_CHARS_WIDTH)
plength(f::Spec{T}, x) where {T <: Floats} =
    max(f.width, f.hash + MAX_INTEGER_PART_WIDTH + f.precision + MAX_FMT_CHARS_WIDTH)
plength(::Spec{PositionCounter}, x) = 0

@inline function computelen(substringranges, formats, args)
    len = sum(length, substringranges)
    N = length(formats)
    # unroll up to 16 formats
    argp = 1
    Base.@nexprs 16 i -> begin
        if N >= i
            l, argp = plength(formats[i], args, argp)
            len += l
        end
    end
    if N > 16
        for i = 17:length(formats)
            l, argp = plength(formats[i], args, argp)
            len += l
        end
    end
    return len
end

@noinline argmismatch(a, b) =
    throw(ArgumentError("Number of format specifiers and number of provided args differ: $a != $b"))

"""
    Printf.format(f::Printf.Format, args...) => String
    Printf.format(io::IO, f::Printf.Format, args...)

Apply a printf format object `f` to provided `args` and return the formatted string
(1st method), or print directly to an `io` object (2nd method). See [`@printf`](@ref)
for more details on C `printf` support.
"""
function format end

function format(io::IO, f::Format, args...) # => Nothing
    f.numarguments == length(args) || argmismatch(f.numarguments, length(args))
    buf = Base.StringVector(computelen(f.substringranges, f.formats, args))
    pos = format(buf, 1, f, args...)
    write(io, resize!(buf, pos - 1))
    return
end

function format(f::Format, args...) # => String
    f.numarguments == length(args) || argmismatch(f.numarguments, length(args))
    buf = Base.StringVector(computelen(f.substringranges, f.formats, args))
    pos = format(buf, 1, f, args...)
    return String(resize!(buf, pos - 1))
end

"""
    @printf([io::IO], "%Fmt", args...)

Print `args` using C `printf` style format specification string.
Optionally, an `IO` may be passed as the first argument to redirect output.

# Examples
```jldoctest
julia> @printf "Hello %s" "world"
Hello world

julia> @printf "Scientific notation %e" 1.234
Scientific notation 1.234000e+00

julia> @printf "Scientific notation three digits %.3e" 1.23456
Scientific notation three digits 1.235e+00

julia> @printf "Decimal two digits %.2f" 1.23456
Decimal two digits 1.23

julia> @printf "Padded to length 5 %5i" 123
Padded to length 5   123

julia> @printf "Padded with zeros to length 6 %06i" 123
Padded with zeros to length 6 000123

julia> @printf "Use shorter of decimal or scientific %g %g" 1.23 12300000.0
Use shorter of decimal or scientific 1.23 1.23e+07

julia> @printf "Use dynamic width and precision  %*.*f" 10 2 0.12345
Use dynamic width and precision        0.12
```
For a systematic specification of the format, see [here](https://en.cppreference.com/w/c/io/fprintf).
See also [`@sprintf`](@ref) to get the result as a `String` instead of it being printed.

# Caveats
`Inf` and `NaN` are printed consistently as `Inf` and `NaN` for flags `%a`, `%A`,
`%e`, `%E`, `%f`, `%F`, `%g`, and `%G`. Furthermore, if a floating point number is
equally close to the numeric values of two possible output strings, the output
string further away from zero is chosen.

# Examples
```jldoctest
julia> @printf("%f %F %f %F", Inf, Inf, NaN, NaN)
Inf Inf NaN NaN

julia> @printf "%.0f %.1f %f" 0.5 0.025 -0.0078125
0 0.0 -0.007812
```

!!! compat "Julia 1.8"
    Starting in Julia 1.8, `%s` (string) and `%c` (character) widths are computed
    using [`textwidth`](@ref), which e.g. ignores zero-width characters
    (such as combining characters for diacritical marks) and treats certain
    "wide" characters (e.g. emoji) as width `2`.

!!! compat "Julia 1.10"
    Dynamic width specifiers like `%*s` and `%0*.*f` require Julia 1.10.
"""
macro printf(io_or_fmt, args...)
    if io_or_fmt isa String
        fmt = Format(io_or_fmt)
        return esc(:($Printf.format(stdout, $fmt, $(args...))))
    else
        io = io_or_fmt
        isempty(args) && throw(ArgumentError("No format string provided to `@printf` - use like `@printf [io] <format string> [<args...>]."))
        fmt_str = first(args)
        fmt_str isa String || throw(ArgumentError("First argument to `@printf` after `io` must be a format string"))
        fmt = Format(fmt_str)
        return esc(:($Printf.format($io, $fmt, $(Base.tail(args)...))))
    end
end

"""
    @sprintf("%Fmt", args...)

Return [`@printf`](@ref) formatted output as string.

# Examples
```jldoctest
julia> @sprintf "this is a %s %15.1f" "test" 34.567
"this is a test            34.6"
```
"""
macro sprintf(fmt, args...)
    fmt isa String || throw(ArgumentError("First argument to `@sprintf` must be a format string."))
    f = Format(fmt)
    return esc(:($Printf.format($f, $(args...))))
end

end # module
p   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Random/src/Random.jl84      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
    Random

Support for generating random numbers. Provides [`rand`](@ref), [`randn`](@ref),
[`AbstractRNG`](@ref), [`MersenneTwister`](@ref), and [`RandomDevice`](@ref).
"""
module Random

include("DSFMT.jl")

using .DSFMT
using Base.GMP.MPZ
using Base.GMP: Limb
import SHA

using Base: BitInteger, BitInteger_types, BitUnsigned, require_one_based_indexing
import Base: copymutable, copy, copy!, ==, hash, convert,
             rand, randn, show

export rand!, randn!,
       randexp, randexp!,
       bitrand,
       randstring,
       randsubseq, randsubseq!,
       shuffle, shuffle!,
       randperm, randperm!,
       randcycle, randcycle!,
       AbstractRNG, MersenneTwister, RandomDevice, TaskLocalRNG, Xoshiro

## general definitions

"""
    AbstractRNG

Supertype for random number generators such as [`MersenneTwister`](@ref) and [`RandomDevice`](@ref).
"""
abstract type AbstractRNG end

Base.broadcastable(x::AbstractRNG) = Ref(x)

gentype(::Type{X}) where {X} = eltype(X)
gentype(x) = gentype(typeof(x))


### integers

# we define types which encode the generation of a specific number of bits
# the "raw" version means that the unused bits are not zeroed

abstract type UniformBits{T<:BitInteger} end

struct UInt10{T}    <: UniformBits{T} end
struct UInt10Raw{T} <: UniformBits{T} end

struct UInt23{T}    <: UniformBits{T} end
struct UInt23Raw{T} <: UniformBits{T} end

struct UInt52{T}    <: UniformBits{T} end
struct UInt52Raw{T} <: UniformBits{T} end

struct UInt104{T}    <: UniformBits{T} end
struct UInt104Raw{T} <: UniformBits{T} end

struct UInt2x52{T}    <: UniformBits{T} end
struct UInt2x52Raw{T} <: UniformBits{T} end

uint_sup(::Type{<:Union{UInt10,UInt10Raw}}) = UInt16
uint_sup(::Type{<:Union{UInt23,UInt23Raw}}) = UInt32
uint_sup(::Type{<:Union{UInt52,UInt52Raw}}) = UInt64
uint_sup(::Type{<:Union{UInt104,UInt104Raw}}) = UInt128
uint_sup(::Type{<:Union{UInt2x52,UInt2x52Raw}}) = UInt128

for UI = (:UInt10, :UInt10Raw, :UInt23, :UInt23Raw, :UInt52, :UInt52Raw,
          :UInt104, :UInt104Raw, :UInt2x52, :UInt2x52Raw)
    @eval begin
        $UI(::Type{T}=uint_sup($UI)) where {T} = $UI{T}()
        # useful for defining rand generically:
        uint_default(::$UI) = $UI{uint_sup($UI)}()
    end
end

gentype(::Type{<:UniformBits{T}}) where {T} = T

### floats

abstract type FloatInterval{T<:AbstractFloat} end

struct CloseOpen01{T<:AbstractFloat} <: FloatInterval{T} end # interval [0,1)
struct CloseOpen12{T<:AbstractFloat} <: FloatInterval{T} end # interval [1,2)

const FloatInterval_64 = FloatInterval{Float64}
const CloseOpen01_64   = CloseOpen01{Float64}
const CloseOpen12_64   = CloseOpen12{Float64}

CloseOpen01(::Type{T}=Float64) where {T<:AbstractFloat} = CloseOpen01{T}()
CloseOpen12(::Type{T}=Float64) where {T<:AbstractFloat} = CloseOpen12{T}()

gentype(::Type{<:FloatInterval{T}}) where {T<:AbstractFloat} = T

const BitFloatType = Union{Type{Float16},Type{Float32},Type{Float64}}

### Sampler

abstract type Sampler{E} end

gentype(::Type{<:Sampler{E}}) where {E} = E

# temporarily for BaseBenchmarks
RangeGenerator(x) = Sampler(default_rng(), x)

# In some cases, when only 1 random value is to be generated,
# the optimal sampler can be different than if multiple values
# have to be generated. Hence a `Repetition` parameter is used
# to choose the best one depending on the need.
const Repetition = Union{Val{1},Val{Inf}}

# these default fall-back for all RNGs would be nice,
# but generate difficult-to-solve ambiguities
# Sampler(::AbstractRNG, X, ::Val{Inf}) = Sampler(X)
# Sampler(::AbstractRNG, ::Type{X}, ::Val{Inf}) where {X} = Sampler(X)

"""
    Sampler(rng, x, repetition = Val(Inf))

Return a sampler object that can be used to generate random values from `rng` for `x`.

When `sp = Sampler(rng, x, repetition)`, `rand(rng, sp)` will be used to draw random values,
and should be defined accordingly.

`repetition` can be `Val(1)` or `Val(Inf)`, and should be used as a suggestion for deciding
the amount of precomputation, if applicable.

[`Random.SamplerType`](@ref) and [`Random.SamplerTrivial`](@ref) are default fallbacks for
*types* and *values*, respectively. [`Random.SamplerSimple`](@ref) can be used to store
pre-computed values without defining extra types for only this purpose.
"""
Sampler(rng::AbstractRNG, x, r::Repetition=Val(Inf)) = Sampler(typeof_rng(rng), x, r)
Sampler(rng::AbstractRNG, ::Type{X}, r::Repetition=Val(Inf)) where {X} =
    Sampler(typeof_rng(rng), X, r)

typeof_rng(rng::AbstractRNG) = typeof(rng)

# this method is necessary to prevent rand(rng::AbstractRNG, X) from
# recursively constructing nested Sampler types.
Sampler(T::Type{<:AbstractRNG}, sp::Sampler, r::Repetition) =
    throw(MethodError(Sampler, (T, sp, r)))

# default shortcut for the general case
Sampler(::Type{RNG}, X) where {RNG<:AbstractRNG} = Sampler(RNG, X, Val(Inf))
Sampler(::Type{RNG}, ::Type{X}) where {RNG<:AbstractRNG,X} = Sampler(RNG, X, Val(Inf))

#### pre-defined useful Sampler types

"""
    SamplerType{T}()

A sampler for types, containing no other information. The default fallback for `Sampler`
when called with types.
"""
struct SamplerType{T} <: Sampler{T} end

Sampler(::Type{<:AbstractRNG}, ::Type{T}, ::Repetition) where {T} = SamplerType{T}()

Base.getindex(::SamplerType{T}) where {T} = T

struct SamplerTrivial{T,E} <: Sampler{E}
    self::T
end

"""
    SamplerTrivial(x)

Create a sampler that just wraps the given value `x`. This is the default fall-back for
values.
The `eltype` of this sampler is equal to `eltype(x)`.

The recommended use case is sampling from values without precomputed data.
"""
SamplerTrivial(x::T) where {T} = SamplerTrivial{T,gentype(T)}(x)

Sampler(::Type{<:AbstractRNG}, x, ::Repetition) = SamplerTrivial(x)

Base.getindex(sp::SamplerTrivial) = sp.self

# simple sampler carrying data (which can be anything)
struct SamplerSimple{T,S,E} <: Sampler{E}
    self::T
    data::S
end

"""
    SamplerSimple(x, data)

Create a sampler that wraps the given value `x` and the `data`.
The `eltype` of this sampler is equal to `eltype(x)`.

The recommended use case is sampling from values with precomputed data.
"""
SamplerSimple(x::T, data::S) where {T,S} = SamplerSimple{T,S,gentype(T)}(x, data)

Base.getindex(sp::SamplerSimple) = sp.self

# simple sampler carrying a (type) tag T and data
struct SamplerTag{T,S,E} <: Sampler{E}
    data::S
    SamplerTag{T}(s::S) where {T,S} = new{T,S,gentype(T)}(s)
end


#### helper samplers

# TODO: make constraining constructors to enforce that those
# types are <: Sampler{T}

##### Adapter to generate a random value in [0, n]

struct LessThan{T<:Integer,S} <: Sampler{T}
    sup::T
    s::S    # the scalar specification/sampler to feed to rand
end

function rand(rng::AbstractRNG, sp::LessThan)
    while true
        x = rand(rng, sp.s)
        x <= sp.sup && return x
    end
end

struct Masked{T<:Integer,S} <: Sampler{T}
    mask::T
    s::S
end

rand(rng::AbstractRNG, sp::Masked) = rand(rng, sp.s) & sp.mask

##### Uniform

struct UniformT{T} <: Sampler{T} end

uniform(::Type{T}) where {T} = UniformT{T}()

rand(rng::AbstractRNG, ::UniformT{T}) where {T} = rand(rng, T)


### machinery for generation with Sampler

# This describes how to generate random scalars or arrays, by generating a Sampler
# and calling rand on it (which should be defined in "generation.jl").
# NOTE: this section could be moved into a separate file when more containers are supported.

#### scalars

rand(rng::AbstractRNG, X)                                           = rand(rng, Sampler(rng, X, Val(1)))
# this is needed to disambiguate
rand(rng::AbstractRNG, X::Dims)                                     = rand(rng, Sampler(rng, X, Val(1)))
rand(rng::AbstractRNG=default_rng(), ::Type{X}=Float64) where {X}   = rand(rng, Sampler(rng, X, Val(1)))::X

rand(X)                   = rand(default_rng(), X)
rand(::Type{X}) where {X} = rand(default_rng(), X)

#### arrays

rand!(A::AbstractArray{T}, X) where {T}             = rand!(default_rng(), A, X)
rand!(A::AbstractArray{T}, ::Type{X}=T) where {T,X} = rand!(default_rng(), A, X)

rand!(rng::AbstractRNG, A::AbstractArray{T}, X) where {T}             = rand!(rng, A, Sampler(rng, X))
rand!(rng::AbstractRNG, A::AbstractArray{T}, ::Type{X}=T) where {T,X} = rand!(rng, A, Sampler(rng, X))

function rand!(rng::AbstractRNG, A::AbstractArray{T}, sp::Sampler) where T
    for i in eachindex(A)
        @inbounds A[i] = rand(rng, sp)
    end
    A
end

rand(r::AbstractRNG, dims::Integer...) = rand(r, Float64, Dims(dims))
rand(                dims::Integer...) = rand(Float64, Dims(dims))

rand(r::AbstractRNG, X, dims::Dims)  = rand!(r, Array{gentype(X)}(undef, dims), X)
rand(                X, dims::Dims)  = rand(default_rng(), X, dims)

rand(r::AbstractRNG, X, d::Integer, dims::Integer...) = rand(r, X, Dims((d, dims...)))
rand(                X, d::Integer, dims::Integer...) = rand(X, Dims((d, dims...)))
# note: the above methods would trigger an ambiguity warning if d was not separated out:
# rand(r, ()) would match both this method and rand(r, dims::Dims)
# moreover, a call like rand(r, NotImplementedType()) would be an infinite loop

rand(r::AbstractRNG, ::Type{X}, dims::Dims) where {X} = rand!(r, Array{X}(undef, dims), X)
rand(                ::Type{X}, dims::Dims) where {X} = rand(default_rng(), X, dims)

rand(r::AbstractRNG, ::Type{X}, d::Integer, dims::Integer...) where {X} = rand(r, X, Dims((d, dims...)))
rand(                ::Type{X}, d::Integer, dims::Integer...) where {X} = rand(X, Dims((d, dims...)))

# SamplerUnion(X, Y, ...}) == Union{SamplerType{X}, SamplerType{Y}, ...}
SamplerUnion(U...) = Union{Any[SamplerType{T} for T in U]...}
const SamplerBoolBitInteger = SamplerUnion(Bool, BitInteger_types...)


include("Xoshiro.jl")
include("RNGs.jl")
include("generation.jl")
include("normal.jl")
include("misc.jl")
include("XoshiroSimd.jl")

## rand & rand! & seed! docstrings

"""
    rand([rng=default_rng()], [S], [dims...])

Pick a random element or array of random elements from the set of values specified by `S`;
`S` can be

* an indexable collection (for example `1:9` or `('x', "y", :z)`),
* an `AbstractDict` or `AbstractSet` object,
* a string (considered as a collection of characters), or
* a type: the set of values to pick from is then equivalent to `typemin(S):typemax(S)` for
  integers (this is not applicable to [`BigInt`](@ref)), to ``[0, 1)`` for floating
  point numbers and to ``[0, 1)+i[0, 1)`` for complex floating point numbers;

`S` defaults to [`Float64`](@ref).
When only one argument is passed besides the optional `rng` and is a `Tuple`, it is interpreted
as a collection of values (`S`) and not as `dims`.


See also [`randn`](@ref) for normally distributed numbers, and [`rand!`](@ref) and [`randn!`](@ref) for the in-place equivalents.

!!! compat "Julia 1.1"
    Support for `S` as a tuple requires at least Julia 1.1.

# Examples
```julia-repl
julia> rand(Int, 2)
2-element Array{Int64,1}:
 1339893410598768192
 1575814717733606317

julia> using Random

julia> rand(MersenneTwister(0), Dict(1=>2, 3=>4))
1=>2

julia> rand((2, 3))
3

julia> rand(Float64, (2, 3))
2×3 Array{Float64,2}:
 0.999717  0.0143835  0.540787
 0.696556  0.783855   0.938235
```

!!! note
    The complexity of `rand(rng, s::Union{AbstractDict,AbstractSet})`
    is linear in the length of `s`, unless an optimized method with
    constant complexity is available, which is the case for `Dict`,
    `Set` and dense `BitSet`s. For more than a few calls, use `rand(rng,
    collect(s))` instead, or either `rand(rng, Dict(s))` or `rand(rng,
    Set(s))` as appropriate.
"""
rand

"""
    rand!([rng=default_rng()], A, [S=eltype(A)])

Populate the array `A` with random values. If `S` is specified
(`S` can be a type or a collection, cf. [`rand`](@ref) for details),
the values are picked randomly from `S`.
This is equivalent to `copyto!(A, rand(rng, S, size(A)))`
but without allocating a new array.

# Examples
```jldoctest
julia> rng = MersenneTwister(1234);

julia> rand!(rng, zeros(5))
5-element Vector{Float64}:
 0.5908446386657102
 0.7667970365022592
 0.5662374165061859
 0.4600853424625171
 0.7940257103317943
```
"""
rand!

"""
    seed!([rng=default_rng()], seed) -> rng
    seed!([rng=default_rng()]) -> rng

Reseed the random number generator: `rng` will give a reproducible
sequence of numbers if and only if a `seed` is provided. Some RNGs
don't accept a seed, like `RandomDevice`.
After the call to `seed!`, `rng` is equivalent to a newly created
object initialized with the same seed.

If `rng` is not specified, it defaults to seeding the state of the
shared task-local generator.

# Examples
```julia-repl
julia> Random.seed!(1234);

julia> x1 = rand(2)
2-element Vector{Float64}:
 0.32597672886359486
 0.5490511363155669

julia> Random.seed!(1234);

julia> x2 = rand(2)
2-element Vector{Float64}:
 0.32597672886359486
 0.5490511363155669

julia> x1 == x2
true

julia> rng = Xoshiro(1234); rand(rng, 2) == x1
true

julia> Xoshiro(1) == Random.seed!(rng, 1)
true

julia> rand(Random.seed!(rng), Bool) # not reproducible
true

julia> rand(Random.seed!(rng), Bool) # not reproducible either
false

julia> rand(Xoshiro(), Bool) # not reproducible either
true
```
"""
seed!(rng::AbstractRNG, ::Nothing) = seed!(rng)

end # module
o   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Random/src/DSFMT.jl�D      # This file is a part of Julia. License is MIT: https://julialang.org/license

module DSFMT

import Base: copy, copy!, ==, hash
using Base.GMP.MPZ

export DSFMT_state, dsfmt_get_min_array_size, dsfmt_get_idstring,
       dsfmt_init_gen_rand, dsfmt_init_by_array, dsfmt_gv_init_by_array,
       dsfmt_fill_array_close_open!, dsfmt_fill_array_close1_open2!

"Mersenne Exponent"
const MEXP = 19937

"DSFMT internal state array size of N 128-bit integers."
const N = floor(Int, ((MEXP - 128) / 104 + 1))

"""
Julia DSFMT state representation size counted in 32-bit integers.

Size: (DSFMT state array of Int128 + 1)*4 + Int32 index + Int32 padding
"""
const JN32 = (N+1)*4+1+1


struct DSFMT_state
    val::Vector{Int32}

    function DSFMT_state(val::Vector{Int32} = zeros(Int32, JN32))
        length(val) == JN32 ||
            throw(DomainError(length(val), "Expected length: $JN32."))
        new(val)
    end
end

copy!(dst::DSFMT_state, src::DSFMT_state) = (copyto!(dst.val, src.val); dst)
copy(src::DSFMT_state) = DSFMT_state(copy(src.val))

==(s1::DSFMT_state, s2::DSFMT_state) = s1.val == s2.val

hash(s::DSFMT_state, h::UInt) = hash(s.val, h)


## wrapper functions

function dsfmt_get_idstring()
    idstring = ccall((:dsfmt_get_idstring,:libdSFMT),
                     Ptr{UInt8},
                     ())
    return unsafe_string(idstring)
end

function dsfmt_get_min_array_size()
    min_array_size = ccall((:dsfmt_get_min_array_size,:libdSFMT),
                           Int32,
                           ())
end

const dsfmt_min_array_size = dsfmt_get_min_array_size()

function dsfmt_init_gen_rand(s::DSFMT_state, seed::UInt32)
    ccall((:dsfmt_init_gen_rand,:libdSFMT),
          Cvoid,
          (Ptr{Cvoid}, UInt32,),
          s.val, seed)
end

function dsfmt_init_by_array(s::DSFMT_state, seed::Vector{UInt32})
    ccall((:dsfmt_init_by_array,:libdSFMT),
          Cvoid,
          (Ptr{Cvoid}, Ptr{UInt32}, Int32),
          s.val, seed, length(seed))
end

function dsfmt_gv_init_by_array(seed::Vector{UInt32})
    ccall((:dsfmt_gv_init_by_array,:libdSFMT),
          Cvoid,
          (Ptr{UInt32}, Int32),
          seed, length(seed))
end

function dsfmt_fill_array_close1_open2!(s::DSFMT_state, A::Ptr{Float64}, n::Int)
    @assert Csize_t(A) % 16 == 0 # the underlying C array must be 16-byte aligned
    @assert dsfmt_min_array_size <= n && iseven(n)
    ccall((:dsfmt_fill_array_close1_open2,:libdSFMT),
          Cvoid,
          (Ptr{Cvoid}, Ptr{Float64}, Int),
          s.val, A, n)
end

function dsfmt_fill_array_close_open!(s::DSFMT_state, A::Ptr{Float64}, n::Int)
    @assert Csize_t(A) % 16 == 0 # the underlying C array must be 16-byte aligned
    @assert dsfmt_min_array_size <= n && iseven(n)
    ccall((:dsfmt_fill_array_close_open,:libdSFMT),
          Cvoid,
          (Ptr{Cvoid}, Ptr{Float64}, Int),
          s.val, A, n)
end

# dSFMT jump poly calculation

"Represents a polynomial in GF(2)[X]"
struct GF2X
    z::BigInt
end

GF2X(s::AbstractString) = GF2X(parse(BigInt, reverse(s), base = 16))
Base.string(f::GF2X) = reverse(string(f.z, base = 16))
Base.:(==)(f::GF2X, g::GF2X) = f.z == g.z
Base.copy(f::GF2X) = GF2X(MPZ.set(f.z))

degree(f::GF2X) = Base.ndigits0z(f.z, 2) - 1
coeff(f::GF2X, i) = MPZ.tstbit(f.z, i)
setcoeff!(f::GF2X, i) = (MPZ.setbit!(f.z, i); f)

mulx!(f::GF2X, c::Int=1) = (MPZ.mul_2exp!(f.z, c), f)
xor!(f::GF2X, g::GF2X) = (MPZ.xor!(f.z, g.z); f)

# compute f*X mod m
function mulxmod!(f::GF2X, m::GF2X, deg=degree(m))::GF2X
    # precondition: degree(f) < degree(m)
    mulx!(f)
    degree(f) == deg && xor!(f, m)
    f
end

# cache for X^(2i) mod m
const _squares = Dict{GF2X, Vector{GF2X}}()

# compute f^2 mod m
function sqrmod!(f::GF2X, m::GF2X)::GF2X
    d = degree(m)-1
    0 <= degree(f) <= d || throw(DomainError("f must satisfy 0 <= degree(f) <= degree(m)-1"))
    sqrs = get!(_squares, m) do
        x2i = GF2X(1)
        GF2X[copy(mulxmod!(mulxmod!(x2i, m, d+1), m, d+1)) for i=1:d]
    end
    foldl(filter(i->coeff(f, i), 0:degree(f)); init=GF2X(0)) do g, i
        i <= d÷2 ? # optimization for "simple" squares
            setcoeff!(g, 2i) :
            xor!(g, sqrs[i])
    end
end

# compute X^e mod m
function powxmod(e::BigInt, m::GF2X)::GF2X
    e < 0 && throw(DomainError("e must be >= 0"))
    foldl(Base.ndigits0z(e, 2)-1:-1:0; init=GF2X(1)) do f, i
        MPZ.tstbit(e, i) ?
            mulxmod!(sqrmod!(f, m), m) :
            sqrmod!(f, m)
    end
end

"Cached jump polynomials for `MersenneTwister`."
const JumpPolys = Dict{BigInt,GF2X}()

const CharPoly_ref = Ref{GF2X}()
# Ref because it can not be initialized at load time
function CharPoly()
    if !isassigned(CharPoly_ref)
        CharPoly_ref[] = GF2X(Poly19937)
    end
    return CharPoly_ref[]
end

"""
    calc_jump(steps::Integer)

Compute the dSFMT jump polynomial for `steps` steps (by default for
the Mersenne-Twister with exponent 19937). Note that `steps` should be
less than the period (e.g. ``steps ≪ 2^19937-1``).
"""
function calc_jump(steps::Integer,
                   charpoly::GF2X=CharPoly())::GF2X
    steps < 0 && throw(DomainError("jump steps must be >= 0 (got $steps)"))
    if isempty(JumpPolys)
        JumpPolys[big(10)^20] = GF2X(JPOLY1e20)
    end
    get!(JumpPolys, steps) do
        powxmod(big(steps), charpoly)
    end
end


## dSFMT jump

function dsfmt_jump(s::DSFMT_state, jp::GF2X)
    degree(jp) < degree(CharPoly()) || throw(DomainError("degree of jump polynomial must be < $(degree(CharPoly())), got $(degree(jp))"))

    val = s.val
    nval = length(val)
    index = val[nval - 1]
    work = zeros(Int32, JN32)
    rwork = reinterpret(UInt64, work)
    dsfmt = Vector{UInt64}(undef, nval >> 1)
    GC.@preserve dsfmt val begin
        pdsfmt = Base.unsafe_convert(Ptr{Cvoid}, dsfmt)
        pval = Base.unsafe_convert(Ptr{Cvoid}, val)
        Base.Libc.memcpy(pdsfmt, pval, (nval - 1) * sizeof(Int32))
    end
    dsfmt[end] = UInt64(N*2)

    for i in 0:degree(jp)
        coeff(jp, i) && dsfmt_jump_add!(rwork, dsfmt)
        dsfmt_jump_next_state!(dsfmt)
    end

    rwork[end] = index
    return DSFMT_state(work)
end

function dsfmt_jump_add!(dest::AbstractVector{UInt64}, src::Vector{UInt64})
    dp = dest[end] >> 1
    sp = src[end] >> 1
    diff = ((sp - dp + N) % N)
    i = 1
    while i <= N-diff
        j = i*2-1
        p = j + diff*2
        dest[j]   ⊻= src[p]
        dest[j+1] ⊻= src[p+1]
        i += 1
    end
    while i <= N
        j = i*2-1
        p = j + (diff - N)*2
        dest[j]   ⊻= src[p]
        dest[j+1] ⊻= src[p+1]
        i += 1
    end
    dest[N*2+1] ⊻= src[N*2+1]
    dest[N*2+2] ⊻= src[N*2+2]
    return dest
end

function dsfmt_jump_next_state!(mts::Vector{UInt64})
    POS1 = 117
    SL1  = 19
    SR   = 12
    MSK1 = 0x000ffafffffffb3f
    MSK2 = 0x000ffdfffc90fffd

    idx = (mts[end] >> 1) % N

    a = idx*2+1
    b = ((idx + POS1) % N)*2+1
    u = N*2+1

    t0 = mts[a]
    t1 = mts[a+1]
    L0 = mts[u]
    L1 = mts[u+1]
    mts[u]   = xor(t0 << SL1, L1 >> 32, L1 << 32, mts[b])
    mts[u+1] = xor(t1 << SL1, L0 >> 32, L0 << 32, mts[b+1])
    mts[a]   = xor(mts[u]   >> SR, mts[u]   & MSK1, t0)
    mts[a+1] = xor(mts[u+1] >> SR, mts[u+1] & MSK2, t1)

    mts[end] = (mts[end] + 2) % (N*2)
    return mts
end

"Jump polynomial for 10^20 steps for dSFMT with exponent 19937"
const JPOLY1e20 = "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"

"Characteristic polynomial used by dSFMT with exponent 19937"
const Poly19937 = "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"

end # module
q   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Random/src/Xoshiro.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

## Xoshiro RNG
# Lots of implementation is shared with TaskLocalRNG

"""
    Xoshiro(seed)
    Xoshiro()

Xoshiro256++ is a fast pseudorandom number generator described by David Blackman and
Sebastiano Vigna in "Scrambled Linear Pseudorandom Number Generators",
ACM Trans. Math. Softw., 2021. Reference implementation is available
at http://prng.di.unimi.it

Apart from the high speed, Xoshiro has a small memory footprint, making it suitable for
applications where many different random states need to be held for long time.

Julia's Xoshiro implementation has a bulk-generation mode; this seeds new virtual PRNGs
from the parent, and uses SIMD to generate in parallel (i.e. the bulk stream consists of
multiple interleaved xoshiro instances).
The virtual PRNGs are discarded once the bulk request has been serviced (and should cause
no heap allocations).

# Examples
```jldoctest
julia> using Random

julia> rng = Xoshiro(1234);

julia> x1 = rand(rng, 2)
2-element Vector{Float64}:
 0.32597672886359486
 0.5490511363155669

julia> rng = Xoshiro(1234);

julia> x2 = rand(rng, 2)
2-element Vector{Float64}:
 0.32597672886359486
 0.5490511363155669

julia> x1 == x2
true
```
"""
mutable struct Xoshiro <: AbstractRNG
    s0::UInt64
    s1::UInt64
    s2::UInt64
    s3::UInt64
    s4::UInt64 # internal splitmix state

    Xoshiro(s0::Integer, s1::Integer, s2::Integer, s3::Integer, s4::Integer) = new(s0, s1, s2, s3, s4)
    Xoshiro(s0::UInt64, s1::UInt64, s2::UInt64, s3::UInt64) = new(s0, s1, s2, s3, 1s0 + 3s1 + 5s2 + 7s3)
    Xoshiro(seed=nothing) = seed!(new(), seed)
end

Xoshiro(s0::Integer, s1::Integer, s2::Integer, s3::Integer) = Xoshiro(UInt64(s0), UInt64(s1), UInt64(s2), UInt64(s3))

function setstate!(
    x::Xoshiro,
    s0::UInt64, s1::UInt64, s2::UInt64, s3::UInt64, # xoshiro256 state
    s4::UInt64, # internal splitmix state
)
    x.s0 = s0
    x.s1 = s1
    x.s2 = s2
    x.s3 = s3
    x.s4 = s4
    x
end

copy(rng::Xoshiro) = Xoshiro(rng.s0, rng.s1, rng.s2, rng.s3, rng.s4)

function copy!(dst::Xoshiro, src::Xoshiro)
    dst.s0, dst.s1, dst.s2, dst.s3, dst.s4 = src.s0, src.s1, src.s2, src.s3, src.s4
    dst
end

function ==(a::Xoshiro, b::Xoshiro)
    a.s0 == b.s0 && a.s1 == b.s1 && a.s2 == b.s2 && a.s3 == b.s3 && a.s4 == b.s4
end

hash(x::Xoshiro, h::UInt) =  hash((x.s0, x.s1, x.s2, x.s3, x.s4), h + 0x49a62c2dda6fa9be % UInt)

rng_native_52(::Xoshiro) = UInt64

@inline function rand(rng::Xoshiro, ::SamplerType{UInt64})
    s0, s1, s2, s3 = rng.s0, rng.s1, rng.s2, rng.s3
    tmp = s0 + s3
    res = ((tmp << 23) | (tmp >> 41)) + s0
    t = s1 << 17
    s2 = xor(s2, s0)
    s3 = xor(s3, s1)
    s1 = xor(s1, s2)
    s0 = xor(s0, s3)
    s2 = xor(s2, t)
    s3 = s3 << 45 | s3 >> 19
    rng.s0, rng.s1, rng.s2, rng.s3 = s0, s1, s2, s3
    res
end


## Task local RNG

"""
    TaskLocalRNG

The `TaskLocalRNG` has state that is local to its task, not its thread.
It is seeded upon task creation, from the state of its parent task.
Therefore, task creation is an event that changes the parent's RNG state.

As an upside, the `TaskLocalRNG` is pretty fast, and permits reproducible
multithreaded simulations (barring race conditions), independent of scheduler
decisions. As long as the number of threads is not used to make decisions on
task creation, simulation results are also independent of the number of available
threads / CPUs. The random stream should not depend on hardware specifics, up to
endianness and possibly word size.

Using or seeding the RNG of any other task than the one returned by `current_task()`
is undefined behavior: it will work most of the time, and may sometimes fail silently.
"""
struct TaskLocalRNG <: AbstractRNG end
TaskLocalRNG(::Nothing) = TaskLocalRNG()
rng_native_52(::TaskLocalRNG) = UInt64

function setstate!(
    x::TaskLocalRNG,
    s0::UInt64, s1::UInt64, s2::UInt64, s3::UInt64, # xoshiro256 state
    s4::UInt64, # internal splitmix state
)
    t = current_task()
    t.rngState0 = s0
    t.rngState1 = s1
    t.rngState2 = s2
    t.rngState3 = s3
    t.rngState4 = s4
    x
end

@inline function rand(::TaskLocalRNG, ::SamplerType{UInt64})
    task = current_task()
    s0, s1, s2, s3 = task.rngState0, task.rngState1, task.rngState2, task.rngState3
    tmp = s0 + s3
    res = ((tmp << 23) | (tmp >> 41)) + s0
    t = s1 << 17
    s2 ⊻= s0
    s3 ⊻= s1
    s1 ⊻= s2
    s0 ⊻= s3
    s2 ⊻= t
    s3 = s3 << 45 | s3 >> 19
    task.rngState0, task.rngState1, task.rngState2, task.rngState3 = s0, s1, s2, s3
    res
end

# Shared implementation between Xoshiro and TaskLocalRNG -- seeding

function seed!(rng::Union{TaskLocalRNG,Xoshiro})
    # as we get good randomness from RandomDevice, we can skip hashing
    rd = RandomDevice()
    s0 = rand(rd, UInt64)
    s1 = rand(rd, UInt64)
    s2 = rand(rd, UInt64)
    s3 = rand(rd, UInt64)
    s4 = 1s0 + 3s1 + 5s2 + 7s3
    setstate!(rng, s0, s1, s2, s3, s4)
end

function seed!(rng::Union{TaskLocalRNG,Xoshiro}, seed::Union{Vector{UInt32}, Vector{UInt64}})
    c = SHA.SHA2_256_CTX()
    SHA.update!(c, reinterpret(UInt8, seed))
    s0, s1, s2, s3 = reinterpret(UInt64, SHA.digest!(c))
    s4 = 1s0 + 3s1 + 5s2 + 7s3
    setstate!(rng, s0, s1, s2, s3, s4)
end

seed!(rng::Union{TaskLocalRNG, Xoshiro}, seed::Integer) = seed!(rng, make_seed(seed))


@inline function rand(rng::Union{TaskLocalRNG, Xoshiro}, ::SamplerType{UInt128})
    first = rand(rng, UInt64)
    second = rand(rng,UInt64)
    second + UInt128(first) << 64
end

@inline rand(rng::Union{TaskLocalRNG, Xoshiro}, ::SamplerType{Int128}) = rand(rng, UInt128) % Int128

@inline function rand(rng::Union{TaskLocalRNG, Xoshiro},
                      T::SamplerUnion(Bool, Int8, UInt8, Int16, UInt16, Int32, UInt32, Int64))
    S = T[]
    # use upper bits
    (rand(rng, UInt64) >>> (64 - 8*sizeof(S))) % S
end

function copy(rng::TaskLocalRNG)
    t = current_task()
    Xoshiro(t.rngState0, t.rngState1, t.rngState2, t.rngState3, t.rngState4)
end

function copy!(dst::TaskLocalRNG, src::Xoshiro)
    t = current_task()
    setstate!(dst, src.s0, src.s1, src.s2, src.s3, src.s4)
    return dst
end

function copy!(dst::Xoshiro, src::TaskLocalRNG)
    t = current_task()
    setstate!(dst, t.rngState0, t.rngState1, t.rngState2, t.rngState3, t.rngState4)
    return dst
end

function ==(a::Xoshiro, b::TaskLocalRNG)
    t = current_task()
    (
        a.s0 == t.rngState0 &&
        a.s1 == t.rngState1 &&
        a.s2 == t.rngState2 &&
        a.s3 == t.rngState3 &&
        a.s4 == t.rngState4
    )
end

==(a::TaskLocalRNG, b::Xoshiro) = b == a

function hash(x::TaskLocalRNG, h::UInt)
    t = current_task()
    hash((t.rngState0, t.rngState1, t.rngState2, t.rngState3, t.rngState4), h + 0x49a62c2dda6fa9be % UInt)
end


# for partial words, use upper bits from Xoshiro

rand(r::Union{TaskLocalRNG, Xoshiro}, ::SamplerTrivial{UInt52Raw{UInt64}}) = rand(r, UInt64) >>> 12
rand(r::Union{TaskLocalRNG, Xoshiro}, ::SamplerTrivial{UInt52{UInt64}})    = rand(r, UInt64) >>> 12
rand(r::Union{TaskLocalRNG, Xoshiro}, ::SamplerTrivial{UInt104{UInt128}})  = rand(r, UInt104Raw())

rand(r::Union{TaskLocalRNG, Xoshiro}, ::SamplerTrivial{CloseOpen01{Float16}}) =
    Float16(Float32(rand(r, UInt16) >>> 5) * Float32(0x1.0p-11))

rand(r::Union{TaskLocalRNG, Xoshiro}, ::SamplerTrivial{CloseOpen01{Float32}}) =
    Float32(rand(r, UInt32) >>> 8) * Float32(0x1.0p-24)

rand(r::Union{TaskLocalRNG, Xoshiro}, ::SamplerTrivial{CloseOpen01_64}) =
    Float64(rand(r, UInt64) >>> 11) * 0x1.0p-53
n   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Random/src/RNGs.jlIe      # This file is a part of Julia. License is MIT: https://julialang.org/license

## RandomDevice


"""
    RandomDevice()

Create a `RandomDevice` RNG object.
Two such objects will always generate different streams of random numbers.
The entropy is obtained from the operating system.
"""
struct RandomDevice <: AbstractRNG; end
RandomDevice(seed::Nothing) = RandomDevice()
seed!(rng::RandomDevice) = rng

rand(rd::RandomDevice, sp::SamplerBoolBitInteger) = Libc.getrandom!(Ref{sp[]}())[]
rand(rd::RandomDevice, ::SamplerType{Bool}) = rand(rd, UInt8) % Bool
function rand!(rd::RandomDevice, A::Array{Bool}, ::SamplerType{Bool})
    Libc.getrandom!(A)
    # we need to mask the result so that only the LSB in each byte can be non-zero
    GC.@preserve A begin
        p = Ptr{UInt8}(pointer(A))
        for i = 1:length(A)
            unsafe_store!(p, unsafe_load(p) & 0x1)
            p += 1
        end
    end
    return A
end
for T in BitInteger_types
    @eval rand!(rd::RandomDevice, A::Array{$T}, ::SamplerType{$T}) = Libc.getrandom!(A)
end

# RandomDevice produces natively UInt64
rng_native_52(::RandomDevice) = UInt64


## MersenneTwister

const MT_CACHE_F = 501 << 1 # number of Float64 in the cache
const MT_CACHE_I = 501 << 4 # number of bytes in the UInt128 cache

@assert dsfmt_get_min_array_size() <= MT_CACHE_F

mutable struct MersenneTwister <: AbstractRNG
    seed::Vector{UInt32}
    state::DSFMT_state
    vals::Vector{Float64}
    ints::Vector{UInt128}
    idxF::Int
    idxI::Int

    # counters for show
    adv::Int64          # state of advance at the DSFMT_state level
    adv_jump::BigInt    # number of skipped Float64 values via randjump
    adv_vals::Int64     # state of advance when vals is filled-up
    adv_ints::Int64     # state of advance when ints is filled-up

    function MersenneTwister(seed, state, vals, ints, idxF, idxI,
                             adv, adv_jump, adv_vals, adv_ints)
        length(vals) == MT_CACHE_F && 0 <= idxF <= MT_CACHE_F ||
            throw(DomainError((length(vals), idxF),
                      "`length(vals)` and `idxF` must be consistent with $MT_CACHE_F"))
        length(ints) == MT_CACHE_I >> 4 && 0 <= idxI <= MT_CACHE_I ||
            throw(DomainError((length(ints), idxI),
                      "`length(ints)` and `idxI` must be consistent with $MT_CACHE_I"))
        new(seed, state, vals, ints, idxF, idxI,
            adv, adv_jump, adv_vals, adv_ints)
    end
end

MersenneTwister(seed::Vector{UInt32}, state::DSFMT_state) =
    MersenneTwister(seed, state,
                    Vector{Float64}(undef, MT_CACHE_F),
                    Vector{UInt128}(undef, MT_CACHE_I >> 4),
                    MT_CACHE_F, 0, 0, 0, -1, -1)

"""
    MersenneTwister(seed)
    MersenneTwister()

Create a `MersenneTwister` RNG object. Different RNG objects can have
their own seeds, which may be useful for generating different streams
of random numbers.
The `seed` may be a non-negative integer or a vector of
`UInt32` integers. If no seed is provided, a randomly generated one
is created (using entropy from the system).
See the [`seed!`](@ref) function for reseeding an already existing
`MersenneTwister` object.


# Examples
```jldoctest
julia> rng = MersenneTwister(1234);

julia> x1 = rand(rng, 2)
2-element Vector{Float64}:
 0.5908446386657102
 0.7667970365022592

julia> rng = MersenneTwister(1234);

julia> x2 = rand(rng, 2)
2-element Vector{Float64}:
 0.5908446386657102
 0.7667970365022592

julia> x1 == x2
true
```
"""
MersenneTwister(seed=nothing) =
    seed!(MersenneTwister(Vector{UInt32}(), DSFMT_state()), seed)


function copy!(dst::MersenneTwister, src::MersenneTwister)
    copyto!(resize!(dst.seed, length(src.seed)), src.seed)
    copy!(dst.state, src.state)
    copyto!(dst.vals, src.vals)
    copyto!(dst.ints, src.ints)
    dst.idxF = src.idxF
    dst.idxI = src.idxI
    dst.adv = src.adv
    dst.adv_jump = src.adv_jump
    dst.adv_vals = src.adv_vals
    dst.adv_ints = src.adv_ints
    dst
end

copy(src::MersenneTwister) =
    MersenneTwister(copy(src.seed), copy(src.state), copy(src.vals), copy(src.ints),
                    src.idxF, src.idxI, src.adv, src.adv_jump, src.adv_vals, src.adv_ints)


==(r1::MersenneTwister, r2::MersenneTwister) =
    r1.seed == r2.seed && r1.state == r2.state &&
    isequal(r1.vals, r2.vals) &&
    isequal(r1.ints, r2.ints) &&
    r1.idxF == r2.idxF && r1.idxI == r2.idxI

hash(r::MersenneTwister, h::UInt) =
    foldr(hash, (r.seed, r.state, r.vals, r.ints, r.idxF, r.idxI); init=h)

function show(io::IO, rng::MersenneTwister)
    # seed
    seed = from_seed(rng.seed)
    seed_str = seed <= typemax(Int) ? string(seed) : "0x" * string(seed, base=16) # DWIM
    if rng.adv_jump == 0 && rng.adv == 0
        return print(io, MersenneTwister, "(", seed_str, ")")
    end
    print(io, MersenneTwister, "(", seed_str, ", (")
    # state
    adv = Integer[rng.adv_jump, rng.adv]
    if rng.adv_vals != -1 || rng.adv_ints != -1
        if rng.adv_vals == -1
            @assert rng.idxF == MT_CACHE_F
            push!(adv, 0, 0) # "(0, 0)" is nicer on the eyes than (-1, 1002)
        else
            push!(adv, rng.adv_vals, rng.idxF)
        end
    end
    if rng.adv_ints != -1
        idxI = (length(rng.ints)*16 - rng.idxI) / 8 # 8 represents one Int64
        idxI = Int(idxI) # idxI should always be an integer when using public APIs
        push!(adv, rng.adv_ints, idxI)
    end
    join(io, adv, ", ")
    print(io, "))")
end

### low level API

function reset_caches!(r::MersenneTwister)
    # zeroing the caches makes comparing two MersenneTwister RNGs easier
    fill!(r.vals, 0.0)
    fill!(r.ints, zero(UInt128))
    mt_setempty!(r)
    mt_setempty!(r, UInt128)
    r.adv_vals = -1
    r.adv_ints = -1
    r
end

#### floats

mt_avail(r::MersenneTwister) = MT_CACHE_F - r.idxF
mt_empty(r::MersenneTwister) = r.idxF == MT_CACHE_F
mt_setfull!(r::MersenneTwister) = r.idxF = 0
mt_setempty!(r::MersenneTwister) = r.idxF = MT_CACHE_F
mt_pop!(r::MersenneTwister) = @inbounds return r.vals[r.idxF+=1]

@noinline function gen_rand(r::MersenneTwister)
    r.adv_vals = r.adv
    GC.@preserve r fill_array!(r, pointer(r.vals), length(r.vals), CloseOpen12())
    mt_setfull!(r)
end

reserve_1(r::MersenneTwister) = (mt_empty(r) && gen_rand(r); nothing)
# `reserve` allows one to call `rand_inbounds` n times
# precondition: n <= MT_CACHE_F
reserve(r::MersenneTwister, n::Int) = (mt_avail(r) < n && gen_rand(r); nothing)

#### ints

logsizeof(::Type{<:Union{Bool,Int8,UInt8}}) = 0
logsizeof(::Type{<:Union{Int16,UInt16}}) = 1
logsizeof(::Type{<:Union{Int32,UInt32}}) = 2
logsizeof(::Type{<:Union{Int64,UInt64}}) = 3
logsizeof(::Type{<:Union{Int128,UInt128}}) = 4

idxmask(::Type{<:Union{Bool,Int8,UInt8}}) = 15
idxmask(::Type{<:Union{Int16,UInt16}}) = 7
idxmask(::Type{<:Union{Int32,UInt32}}) = 3
idxmask(::Type{<:Union{Int64,UInt64}}) = 1
idxmask(::Type{<:Union{Int128,UInt128}}) = 0


mt_avail(r::MersenneTwister, ::Type{T}) where {T<:BitInteger} =
    r.idxI >> logsizeof(T)

function mt_setfull!(r::MersenneTwister, ::Type{<:BitInteger})
    r.adv_ints = r.adv
    ints = r.ints

    @assert length(ints) == 501
    # dSFMT natively randomizes 52 out of 64 bits of each UInt64 words,
    # i.e. 12 bits are missing;
    # by generating 5 words == 5*52 == 260 bits, we can fully
    # randomize 4 UInt64 = 256 bits; IOW, at the array level, we must
    # randomize ceil(501*1.25) = 627 UInt128 words (with 2*52 bits each),
    # which we then condense into fully randomized 501 UInt128 words

    len = 501 + 126 # 126 == ceil(501 / 4)
    resize!(ints, len)
    p = pointer(ints) # must be *after* resize!
    GC.@preserve r fill_array!(r, Ptr{Float64}(p), len*2, CloseOpen12_64())

    k = 501
    n = 0
    @inbounds while n != 500
        u = ints[k+=1]
        ints[n+=1] ⊻= u << 48
        ints[n+=1] ⊻= u << 36
        ints[n+=1] ⊻= u << 24
        ints[n+=1] ⊻= u << 12
    end
    @assert k == len - 1
    @inbounds ints[501] ⊻= ints[len] << 48
    resize!(ints, 501)
    r.idxI = MT_CACHE_I
end

mt_setempty!(r::MersenneTwister, ::Type{<:BitInteger}) = r.idxI = 0

function reserve1(r::MersenneTwister, ::Type{T}) where T<:BitInteger
    r.idxI < sizeof(T) && mt_setfull!(r, T)
    nothing
end

function mt_pop!(r::MersenneTwister, ::Type{T}) where T<:BitInteger
    reserve1(r, T)
    r.idxI -= sizeof(T)
    i = r.idxI
    @inbounds x128 = r.ints[1 + i >> 4]
    i128 = (i >> logsizeof(T)) & idxmask(T) # 0-based "indice" in x128
    (x128 >> (i128 * (sizeof(T) << 3))) % T
end

function mt_pop!(r::MersenneTwister, ::Type{T}) where {T<:Union{Int128,UInt128}}
    reserve1(r, T)
    idx = r.idxI >> 4
    r.idxI = idx << 4 - 16
    @inbounds r.ints[idx] % T
end


### seeding

#### make_seed()

# make_seed produces values of type Vector{UInt32}, suitable for MersenneTwister seeding
function make_seed()
    try
        return rand(RandomDevice(), UInt32, 4)
    catch ex
        ex isa IOError || rethrow()
        @warn "Entropy pool not available to seed RNG; using ad-hoc entropy sources."
        return make_seed(Libc.rand())
    end
end

function make_seed(n::Integer)
    n < 0 && throw(DomainError(n, "`n` must be non-negative."))
    seed = UInt32[]
    while true
        push!(seed, n & 0xffffffff)
        n >>= 32
        if n == 0
            return seed
        end
    end
end

# inverse of make_seed(::Integer)
from_seed(a::Vector{UInt32})::BigInt = sum(a[i] * big(2)^(32*(i-1)) for i in 1:length(a))


#### seed!()

function seed!(r::MersenneTwister, seed::Vector{UInt32})
    copyto!(resize!(r.seed, length(seed)), seed)
    dsfmt_init_by_array(r.state, r.seed)
    reset_caches!(r)
    r.adv = 0
    r.adv_jump = 0
    return r
end

seed!(r::MersenneTwister) = seed!(r, make_seed())
seed!(r::MersenneTwister, n::Integer) = seed!(r, make_seed(n))


### Global RNG

struct _GLOBAL_RNG <: AbstractRNG
    global const GLOBAL_RNG = _GLOBAL_RNG.instance
end

# GLOBAL_RNG currently uses TaskLocalRNG
typeof_rng(::_GLOBAL_RNG) = TaskLocalRNG

"""
    default_rng() -> rng

Return the default global random number generator (RNG).

!!! note
    What the default RNG is is an implementation detail.  Across different versions of
    Julia, you should not expect the default RNG to be always the same, nor that it will
    return the same stream of random numbers for a given seed.

!!! compat "Julia 1.3"
    This function was introduced in Julia 1.3.
"""
@inline default_rng() = TaskLocalRNG()
@inline default_rng(tid::Int) = TaskLocalRNG()

copy!(dst::Xoshiro, ::_GLOBAL_RNG) = copy!(dst, default_rng())
copy!(::_GLOBAL_RNG, src::Xoshiro) = copy!(default_rng(), src)
copy(::_GLOBAL_RNG) = copy(default_rng())

GLOBAL_SEED = 0
set_global_seed!(seed) = global GLOBAL_SEED = seed

function seed!(::_GLOBAL_RNG, seed=rand(RandomDevice(), UInt64, 4))
    global GLOBAL_SEED = seed
    seed!(default_rng(), seed)
end

seed!(rng::_GLOBAL_RNG, ::Nothing) = seed!(rng)  # to resolve ambiguity

seed!(seed::Union{Nothing,Integer,Vector{UInt32},Vector{UInt64}}=nothing) =
    seed!(GLOBAL_RNG, seed)

rng_native_52(::_GLOBAL_RNG) = rng_native_52(default_rng())
rand(::_GLOBAL_RNG, sp::SamplerBoolBitInteger) = rand(default_rng(), sp)
for T in (:(SamplerTrivial{UInt52Raw{UInt64}}),
          :(SamplerTrivial{UInt2x52Raw{UInt128}}),
          :(SamplerTrivial{UInt104Raw{UInt128}}),
          :(SamplerTrivial{CloseOpen01_64}),
          :(SamplerTrivial{CloseOpen12_64}),
          :(SamplerUnion(Int64, UInt64, Int128, UInt128)),
          :(SamplerUnion(Bool, Int8, UInt8, Int16, UInt16, Int32, UInt32)),
         )
    @eval rand(::_GLOBAL_RNG, x::$T) = rand(default_rng(), x)
end

rand!(::_GLOBAL_RNG, A::AbstractArray{Float64}, I::SamplerTrivial{<:FloatInterval_64}) = rand!(default_rng(), A, I)
rand!(::_GLOBAL_RNG, A::Array{Float64}, I::SamplerTrivial{<:FloatInterval_64}) = rand!(default_rng(), A, I)
for T in (Float16, Float32)
    @eval rand!(::_GLOBAL_RNG, A::Array{$T}, I::SamplerTrivial{CloseOpen12{$T}}) = rand!(default_rng(), A, I)
    @eval rand!(::_GLOBAL_RNG, A::Array{$T}, I::SamplerTrivial{CloseOpen01{$T}}) = rand!(default_rng(), A, I)
end
for T in BitInteger_types
    @eval rand!(::_GLOBAL_RNG, A::Array{$T}, I::SamplerType{$T}) = rand!(default_rng(), A, I)
end

function __init__()
    seed!(GLOBAL_RNG)
    ccall(:jl_gc_init_finalizer_rng_state, Cvoid, ())
end


### generation

# MersenneTwister produces natively Float64
rng_native_52(::MersenneTwister) = Float64

#### helper functions

# precondition: !mt_empty(r)
rand_inbounds(r::MersenneTwister, ::CloseOpen12_64) = mt_pop!(r)
rand_inbounds(r::MersenneTwister, ::CloseOpen01_64=CloseOpen01()) =
    rand_inbounds(r, CloseOpen12()) - 1.0

rand_inbounds(r::MersenneTwister, ::UInt52Raw{T}) where {T<:BitInteger} =
    reinterpret(UInt64, rand_inbounds(r, CloseOpen12())) % T

function rand(r::MersenneTwister, x::SamplerTrivial{UInt52Raw{UInt64}})
    reserve_1(r)
    rand_inbounds(r, x[])
end

function rand(r::MersenneTwister, ::SamplerTrivial{UInt2x52Raw{UInt128}})
    reserve(r, 2)
    rand_inbounds(r, UInt52Raw(UInt128)) << 64 | rand_inbounds(r, UInt52Raw(UInt128))
end

function rand(r::MersenneTwister, ::SamplerTrivial{UInt104Raw{UInt128}})
    reserve(r, 2)
    rand_inbounds(r, UInt52Raw(UInt128)) << 52 ⊻ rand_inbounds(r, UInt52Raw(UInt128))
end

#### floats

rand(r::MersenneTwister, sp::SamplerTrivial{CloseOpen12_64}) =
    (reserve_1(r); rand_inbounds(r, sp[]))

#### integers

rand(r::MersenneTwister, T::SamplerUnion(Int64, UInt64, Int128, UInt128)) =
    mt_pop!(r, T[])

rand(r::MersenneTwister, T::SamplerUnion(Bool, Int8, UInt8, Int16, UInt16, Int32, UInt32)) =
    rand(r, UInt52Raw()) % T[]

#### arrays of floats

##### AbstractArray

function rand!(r::MersenneTwister, A::AbstractArray{Float64},
               I::SamplerTrivial{<:FloatInterval_64})
    region = LinearIndices(A)
    # what follows is equivalent to this simple loop but more efficient:
    # for i=region
    #     @inbounds A[i] = rand(r, I[])
    # end
    m = Base.checked_sub(first(region), 1)
    n = last(region)
    while m < n
        s = mt_avail(r)
        if s == 0
            gen_rand(r)
            s = mt_avail(r)
        end
        m2 = min(n, m+s)
        for i=m+1:m2
            @inbounds A[i] = rand_inbounds(r, I[])
        end
        m = m2
    end
    A
end


##### Array : internal functions

# internal array-like type to circumvent the lack of flexibility with reinterpret
struct UnsafeView{T} <: DenseArray{T,1}
    ptr::Ptr{T}
    len::Int
end

Base.length(a::UnsafeView) = a.len
Base.getindex(a::UnsafeView, i::Int) = unsafe_load(a.ptr, i)
Base.setindex!(a::UnsafeView, x, i::Int) = unsafe_store!(a.ptr, x, i)
Base.pointer(a::UnsafeView) = a.ptr
Base.size(a::UnsafeView) = (a.len,)
Base.elsize(::Type{UnsafeView{T}}) where {T} = sizeof(T)

# this is essentially equivalent to rand!(r, ::AbstractArray{Float64}, I) above, but due to
# optimizations which can't be done currently when working with pointers, we have to re-order
# manually the computation flow to get the performance
# (see https://discourse.julialang.org/t/unsafe-store-sometimes-slower-than-arrays-setindex)
function _rand_max383!(r::MersenneTwister, A::UnsafeView{Float64}, I::FloatInterval_64)
    n = length(A)
    @assert n <= dsfmt_get_min_array_size()+1 # == 383
    mt_avail(r) == 0 && gen_rand(r)
    # from now on, at most one call to gen_rand(r) will be necessary
    m = min(n, mt_avail(r))
    GC.@preserve r unsafe_copyto!(A.ptr, pointer(r.vals, r.idxF+1), m)
    if m == n
        r.idxF += m
    else # m < n
        gen_rand(r)
        GC.@preserve r unsafe_copyto!(A.ptr+m*sizeof(Float64), pointer(r.vals), n-m)
        r.idxF = n-m
    end
    if I isa CloseOpen01
        for i=1:n
            A[i] -= 1.0
        end
    end
    A
end

function fill_array!(rng::MersenneTwister, A::Ptr{Float64}, n::Int, I)
    rng.adv += n
    fill_array!(rng.state, A, n, I)
end

fill_array!(s::DSFMT_state, A::Ptr{Float64}, n::Int, ::CloseOpen01_64) =
    dsfmt_fill_array_close_open!(s, A, n)

fill_array!(s::DSFMT_state, A::Ptr{Float64}, n::Int, ::CloseOpen12_64) =
    dsfmt_fill_array_close1_open2!(s, A, n)


function rand!(r::MersenneTwister, A::UnsafeView{Float64},
               I::SamplerTrivial{<:FloatInterval_64})
    # depending on the alignment of A, the data written by fill_array! may have
    # to be left-shifted by up to 15 bytes (cf. unsafe_copyto! below) for
    # reproducibility purposes;
    # so, even for well aligned arrays, fill_array! is used to generate only
    # the n-2 first values (or n-3 if n is odd), and the remaining values are
    # generated by the scalar version of rand
    n = length(A)
    n2 = (n-2) ÷ 2 * 2
    n2 < dsfmt_get_min_array_size() && return _rand_max383!(r, A, I[])

    pA = A.ptr
    align = Csize_t(pA) % 16
    if align > 0
        pA2 = pA + 16 - align
        fill_array!(r, pA2, n2, I[]) # generate the data in-place, but shifted
        unsafe_copyto!(pA, pA2, n2) # move the data to the beginning of the array
    else
        fill_array!(r, pA, n2, I[])
    end
    for i=n2+1:n
        A[i] = rand(r, I[])
    end
    A
end

# fills up A reinterpreted as an array of Float64 with n64 values
function _rand!(r::MersenneTwister, A::Array{T}, n64::Int, I::FloatInterval_64) where T
    # n64 is the length in terms of `Float64` of the target
    @assert sizeof(Float64)*n64 <= sizeof(T)*length(A) && isbitstype(T)
    GC.@preserve A rand!(r, UnsafeView{Float64}(pointer(A), n64), SamplerTrivial(I))
    A
end

##### Array: Float64, Float16, Float32

rand!(r::MersenneTwister, A::Array{Float64}, I::SamplerTrivial{<:FloatInterval_64}) =
    _rand!(r, A, length(A), I[])

mask128(u::UInt128, ::Type{Float16}) =
    (u & 0x03ff03ff03ff03ff03ff03ff03ff03ff) | 0x3c003c003c003c003c003c003c003c00

mask128(u::UInt128, ::Type{Float32}) =
    (u & 0x007fffff007fffff007fffff007fffff) | 0x3f8000003f8000003f8000003f800000

for T in (Float16, Float32)
    @eval function rand!(r::MersenneTwister, A::Array{$T}, ::SamplerTrivial{CloseOpen12{$T}})
        n = length(A)
        n128 = n * sizeof($T) ÷ 16
        _rand!(r, A, 2*n128, CloseOpen12())
        GC.@preserve A begin
            A128 = UnsafeView{UInt128}(pointer(A), n128)
            for i in 1:n128
                u = A128[i]
                u ⊻= u << 26
                # at this point, the 64 low bits of u, "k" being the k-th bit of A128[i] and "+"
                # the bit xor, are:
                # [..., 58+32,..., 53+27, 52+26, ..., 33+7, 32+6, ..., 27+1, 26, ..., 1]
                # the bits needing to be random are
                # [1:10, 17:26, 33:42, 49:58] (for Float16)
                # [1:23, 33:55] (for Float32)
                # this is obviously satisfied on the 32 low bits side, and on the high side,
                # the entropy comes from bits 33:52 of A128[i] and then from bits 27:32
                # (which are discarded on the low side)
                # this is similar for the 64 high bits of u
                A128[i] = mask128(u, $T)
            end
        end
        for i in 16*n128÷sizeof($T)+1:n
            @inbounds A[i] = rand(r, $T) + one($T)
        end
        A
    end

    @eval function rand!(r::MersenneTwister, A::Array{$T}, ::SamplerTrivial{CloseOpen01{$T}})
        rand!(r, A, CloseOpen12($T))
        I32 = one(Float32)
        for i in eachindex(A)
            @inbounds A[i] = Float32(A[i])-I32 # faster than "A[i] -= one(T)" for T==Float16
        end
        A
    end
end

#### arrays of integers

function rand!(r::MersenneTwister, A::UnsafeView{UInt128}, ::SamplerType{UInt128})
    n::Int=length(A)
    i = n
    while true
        rand!(r, UnsafeView{Float64}(A.ptr, 2i), CloseOpen12())
        n < 5 && break
        i = 0
        while n-i >= 5
            u = A[i+=1]
            A[n]    ⊻= u << 48
            A[n-=1] ⊻= u << 36
            A[n-=1] ⊻= u << 24
            A[n-=1] ⊻= u << 12
            n-=1
        end
    end
    if n > 0
        u = rand(r, UInt2x52Raw())
        for i = 1:n
            A[i] ⊻= u << (12*i)
        end
    end
    A
end

for T in BitInteger_types
    @eval function rand!(r::MersenneTwister, A::Array{$T}, sp::SamplerType{$T})
        GC.@preserve A rand!(r, UnsafeView(pointer(A), length(A)), sp)
        A
    end

    T == UInt128 && continue

    @eval function rand!(r::MersenneTwister, A::UnsafeView{$T}, ::SamplerType{$T})
        n = length(A)
        n128 = n * sizeof($T) ÷ 16
        rand!(r, UnsafeView{UInt128}(pointer(A), n128))
        for i = 16*n128÷sizeof($T)+1:n
            @inbounds A[i] = rand(r, $T)
        end
        A
    end
end


#### arrays of Bool

# similar to Array{UInt8}, but we need to mask the result so that only the LSB
# in each byte can be non-zero

function rand!(r::MersenneTwister, A1::Array{Bool}, sp::SamplerType{Bool})
    n1 = length(A1)
    n128 = n1 ÷ 16

    if n128 == 0
        bits = rand(r, UInt52Raw())
    else
        GC.@preserve A1 begin
            A = UnsafeView{UInt128}(pointer(A1), n128)
            rand!(r, UnsafeView{Float64}(A.ptr, 2*n128), CloseOpen12())
            # without masking, non-zero bits could be observed in other
            # positions than the LSB of each byte
            mask = 0x01010101010101010101010101010101
            # we need up to 15 bits of entropy in `bits` for the final loop,
            # which we will extract from x = A[1] % UInt64;
            # let y = x % UInt32; y contains 32 bits of entropy, but 4
            # of them will be used for A[1] itself (the first of
            # each byte). To compensate, we xor with (y >> 17),
            # which gets the entropy from the second bit of each byte
            # of the upper-half of y, and sets it in the first bit
            # of each byte of the lower half; the first two bytes
            # now contain 16 usable random bits
            x = A[1] % UInt64
            bits = x ⊻ x >> 17
            for i = 1:n128
                # << 5 to randomize the first bit of the 8th & 16th byte
                # (i.e. we move bit 52 (resp. 52 + 64), which is unused,
                # to position 57 (resp. 57 + 64))
                A[i] = (A[i] ⊻ A[i] << 5) & mask
            end
        end
    end
    for i = 16*n128+1:n1
        @inbounds A1[i] = bits % Bool
        bits >>= 1
    end
    A1
end


### randjump

# Old randjump methods are deprecated, the scalar version is in the Future module.

function _randjump(r::MersenneTwister, jumppoly::DSFMT.GF2X)
    adv = r.adv
    adv_jump = r.adv_jump
    s = MersenneTwister(copy(r.seed), DSFMT.dsfmt_jump(r.state, jumppoly))
    reset_caches!(s)
    s.adv = adv
    s.adv_jump = adv_jump
    s
end

# NON-PUBLIC
function jump(r::MersenneTwister, steps::Integer)
    iseven(steps) || throw(DomainError(steps, "steps must be even"))
    # steps >= 0 checked in calc_jump (`steps >> 1 < 0` if `steps < 0`)
    j = _randjump(r, Random.DSFMT.calc_jump(steps >> 1))
    j.adv_jump += steps
    j
end

# NON-PUBLIC
jump!(r::MersenneTwister, steps::Integer) = copy!(r, jump(r, steps))


### constructors matching show (EXPERIMENTAL)

# parameters in the tuples are:
# 1: .adv_jump (jump steps)
# 2: .adv (number of generated floats at the DSFMT_state level since seeding, besides jumps)
# 3, 4: .adv_vals, .idxF (counters to reconstruct the float cache, optional if 5-6 not shown))
# 5, 6: .adv_ints, .idxI (counters to reconstruct the integer cache, optional)

Random.MersenneTwister(seed::Union{Integer,Vector{UInt32}}, advance::NTuple{6,Integer}) =
    advance!(MersenneTwister(seed), advance...)

Random.MersenneTwister(seed::Union{Integer,Vector{UInt32}}, advance::NTuple{4,Integer}) =
    MersenneTwister(seed, (advance..., 0, 0))

Random.MersenneTwister(seed::Union{Integer,Vector{UInt32}}, advance::NTuple{2,Integer}) =
    MersenneTwister(seed, (advance..., 0, 0, 0, 0))

# advances raw state (per fill_array!) of r by n steps (Float64 values)
function _advance_n!(r::MersenneTwister, n::Int64, work::Vector{Float64})
    n == 0 && return
    n < 0 && throw(DomainError(n, "can't advance $r to the specified state"))
    ms = dsfmt_get_min_array_size() % Int64
    @assert n >= ms
    lw = ms + n % ms
    resize!(work, lw)
    GC.@preserve work fill_array!(r, pointer(work), lw, CloseOpen12())
    c::Int64 = lw
    GC.@preserve work while n > c
        fill_array!(r, pointer(work), ms, CloseOpen12())
        c += ms
    end
    @assert n == c
end

function _advance_to!(r::MersenneTwister, adv::Int64, work)
    _advance_n!(r, adv - r.adv, work)
    @assert r.adv == adv
end

function _advance_F!(r::MersenneTwister, adv_vals, idxF, work)
    _advance_to!(r, adv_vals, work)
    gen_rand(r)
    @assert r.adv_vals == adv_vals
    r.idxF = idxF
end

function _advance_I!(r::MersenneTwister, adv_ints, idxI, work)
    _advance_to!(r, adv_ints, work)
    mt_setfull!(r, Int) # sets r.adv_ints
    @assert r.adv_ints == adv_ints
    r.idxI = 16*length(r.ints) - 8*idxI
end

function advance!(r::MersenneTwister, adv_jump, adv, adv_vals, idxF, adv_ints, idxI)
    adv_jump = BigInt(adv_jump)
    adv, adv_vals, adv_ints = Int64.((adv, adv_vals, adv_ints))
    idxF, idxI = Int.((idxF, idxI))

    ms = dsfmt_get_min_array_size() % Int
    work = sizehint!(Vector{Float64}(), 2ms)

    adv_jump != 0 && jump!(r, adv_jump)
    advF = (adv_vals, idxF) != (0, 0)
    advI = (adv_ints, idxI) != (0, 0)

    if advI && advF
        @assert adv_vals != adv_ints
        if adv_vals < adv_ints
            _advance_F!(r, adv_vals, idxF, work)
            _advance_I!(r, adv_ints, idxI, work)
        else
            _advance_I!(r, adv_ints, idxI, work)
            _advance_F!(r, adv_vals, idxF, work)
        end
    elseif advF
        _advance_F!(r, adv_vals, idxF, work)
    elseif advI
        _advance_I!(r, adv_ints, idxI, work)
    else
        @assert adv == 0
    end
    _advance_to!(r, adv, work)
    r
end
t   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Random/src/generation.jl�O      # This file is a part of Julia. License is MIT: https://julialang.org/license

# Uniform random generation

# This file contains the creation of Sampler objects and the associated generation of
# random values from them. More specifically, given the specification S of a set
# of values to pick from (e.g. 1:10, or "a string"), we define
#
# 1) Sampler(rng, S, ::Repetition) -> sampler
# 2) rand(rng, sampler) -> random value
#
# Note that the 1) is automated when the sampler is not intended to carry information,
# i.e. the default fall-backs SamplerType and SamplerTrivial are used.

## from types: rand(::Type, [dims...])

### random floats

Sampler(::Type{RNG}, ::Type{T}, n::Repetition) where {RNG<:AbstractRNG,T<:AbstractFloat} =
    Sampler(RNG, CloseOpen01(T), n)

# generic random generation function which can be used by RNG implementors
# it is not defined as a fallback rand method as this could create ambiguities

rand(r::AbstractRNG, ::SamplerTrivial{CloseOpen01{Float16}}) =
    Float16(reinterpret(Float32,
                        (rand(r, UInt10(UInt32)) << 13)  | 0x3f800000) - 1)

rand(r::AbstractRNG, ::SamplerTrivial{CloseOpen01{Float32}}) =
    reinterpret(Float32, rand(r, UInt23()) | 0x3f800000) - 1

rand(r::AbstractRNG, ::SamplerTrivial{CloseOpen12_64}) =
    reinterpret(Float64, 0x3ff0000000000000 | rand(r, UInt52()))

rand(r::AbstractRNG, ::SamplerTrivial{CloseOpen01_64}) = rand(r, CloseOpen12()) - 1.0

#### BigFloat

const bits_in_Limb = sizeof(Limb) << 3
const Limb_high_bit = one(Limb) << (bits_in_Limb-1)

struct SamplerBigFloat{I<:FloatInterval{BigFloat}} <: Sampler{BigFloat}
    prec::Int
    nlimbs::Int
    limbs::Vector{Limb}
    shift::UInt

    function SamplerBigFloat{I}(prec::Int) where I<:FloatInterval{BigFloat}
        nlimbs = (prec-1) ÷ bits_in_Limb + 1
        limbs = Vector{Limb}(undef, nlimbs)
        shift = nlimbs * bits_in_Limb - prec
        new(prec, nlimbs, limbs, shift)
    end
end

Sampler(::Type{<:AbstractRNG}, I::FloatInterval{BigFloat}, ::Repetition) =
    SamplerBigFloat{typeof(I)}(precision(BigFloat))

function _rand!(rng::AbstractRNG, z::BigFloat, sp::SamplerBigFloat)
    precision(z) == sp.prec || throw(ArgumentError("incompatible BigFloat precision"))
    limbs = sp.limbs
    rand!(rng, limbs)
    @inbounds begin
        limbs[1] <<= sp.shift
        randbool = iszero(limbs[end] & Limb_high_bit)
        limbs[end] |= Limb_high_bit
    end
    z.sign = 1
    GC.@preserve limbs unsafe_copyto!(z.d, pointer(limbs), sp.nlimbs)
    randbool
end

function _rand!(rng::AbstractRNG, z::BigFloat, sp::SamplerBigFloat, ::CloseOpen12{BigFloat})
    _rand!(rng, z, sp)
    z.exp = 1
    z
end

function _rand!(rng::AbstractRNG, z::BigFloat, sp::SamplerBigFloat, ::CloseOpen01{BigFloat})
    randbool = _rand!(rng, z, sp)
    z.exp = 0
    randbool &&
        ccall((:mpfr_sub_d, :libmpfr), Int32,
              (Ref{BigFloat}, Ref{BigFloat}, Cdouble, Base.MPFR.MPFRRoundingMode),
              z, z, 0.5, Base.MPFR.ROUNDING_MODE[])
    z
end

# alternative, with 1 bit less of precision
# TODO: make an API for requesting full or not-full precision
function _rand!(rng::AbstractRNG, z::BigFloat, sp::SamplerBigFloat, ::CloseOpen01{BigFloat},
                ::Nothing)
    _rand!(rng, z, sp, CloseOpen12(BigFloat))
    ccall((:mpfr_sub_ui, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Culong, Base.MPFR.MPFRRoundingMode),
          z, z, 1, Base.MPFR.ROUNDING_MODE[])
    z
end

rand!(rng::AbstractRNG, z::BigFloat, sp::SamplerBigFloat{T}
      ) where {T<:FloatInterval{BigFloat}} =
          _rand!(rng, z, sp, T())

rand(rng::AbstractRNG, sp::SamplerBigFloat{T}) where {T<:FloatInterval{BigFloat}} =
    rand!(rng, BigFloat(; precision=sp.prec), sp)


### random integers

#### UniformBits

rand(r::AbstractRNG, ::SamplerTrivial{UInt10Raw{UInt16}}) = rand(r, UInt16)
rand(r::AbstractRNG, ::SamplerTrivial{UInt23Raw{UInt32}}) = rand(r, UInt32)

rand(r::AbstractRNG, ::SamplerTrivial{UInt52Raw{UInt64}}) =
    _rand52(r, rng_native_52(r))

_rand52(r::AbstractRNG, ::Type{Float64}) = reinterpret(UInt64, rand(r, CloseOpen12()))
_rand52(r::AbstractRNG, ::Type{UInt64})  = rand(r, UInt64)

rand(r::AbstractRNG, ::SamplerTrivial{UInt104Raw{UInt128}}) =
    rand(r, UInt52Raw(UInt128)) << 52 ⊻ rand(r, UInt52Raw(UInt128))

rand(r::AbstractRNG, ::SamplerTrivial{UInt10{UInt16}})   = rand(r, UInt10Raw())  & 0x03ff
rand(r::AbstractRNG, ::SamplerTrivial{UInt23{UInt32}})   = rand(r, UInt23Raw())  & 0x007fffff
rand(r::AbstractRNG, ::SamplerTrivial{UInt52{UInt64}})   = rand(r, UInt52Raw())  & 0x000fffffffffffff
rand(r::AbstractRNG, ::SamplerTrivial{UInt104{UInt128}}) = rand(r, UInt104Raw()) & 0x000000ffffffffffffffffffffffffff

rand(r::AbstractRNG, sp::SamplerTrivial{<:UniformBits{T}}) where {T} =
        rand(r, uint_default(sp[])) % T

#### BitInteger

# rand_generic methods are intended to help RNG implementors with common operations
# we don't call them simply `rand` as this can easily contribute to create
# ambiguities with user-side methods (forcing the user to resort to @eval)

rand_generic(r::AbstractRNG, T::Union{Bool,Int8,UInt8,Int16,UInt16,Int32,UInt32}) =
    rand(r, UInt52Raw()) % T[]

rand_generic(r::AbstractRNG, ::Type{UInt64}) =
    rand(r, UInt52Raw()) << 32 ⊻ rand(r, UInt52Raw())

rand_generic(r::AbstractRNG, ::Type{UInt128}) = _rand128(r, rng_native_52(r))

_rand128(r::AbstractRNG, ::Type{UInt64}) =
    ((rand(r, UInt64) % UInt128) << 64) ⊻ rand(r, UInt64)

function _rand128(r::AbstractRNG, ::Type{Float64})
    xor(rand(r, UInt52Raw(UInt128))  << 96,
        rand(r, UInt52Raw(UInt128))  << 48,
        rand(r, UInt52Raw(UInt128)))
end

rand_generic(r::AbstractRNG, ::Type{Int128}) = rand(r, UInt128) % Int128
rand_generic(r::AbstractRNG, ::Type{Int64})  = rand(r, UInt64) % Int64

### random complex numbers

rand(r::AbstractRNG, ::SamplerType{Complex{T}}) where {T<:Real} =
    complex(rand(r, T), rand(r, T))

### random characters

# returns a random valid Unicode scalar value (i.e. 0 - 0xd7ff, 0xe000 - # 0x10ffff)
function rand(r::AbstractRNG, ::SamplerType{T}) where {T<:AbstractChar}
    c = rand(r, 0x00000000:0x0010f7ff)
    (c < 0xd800) ? T(c) : T(c+0x800)
end


## Generate random integer within a range

### BitInteger

# there are three implemented samplers for unit ranges, the second one
# assumes that Float64 (i.e. 52 random bits) is the native type for the RNG:
# 1) "Fast" (SamplerRangeFast), which is most efficient when the range length is close
#    (or equal) to a power of 2 from below.
#    The tradeoff is faster creation of the sampler, but more consumption of entropy bits.
# 2) "Slow" (SamplerRangeInt) which tries to use as few entropy bits as possible, at the
#    cost of a bigger upfront price associated with the creation of the sampler.
#    This sampler is most appropriate for slower random generators.
# 3) "Nearly Division Less" (NDL) which is generally the fastest algorithm for types of size
#    up to 64 bits. This is the default for these types since Julia 1.5.
#    The "Fast" algorithm can be faster than NDL when the length of the range is
#    less than and close to a power of 2.

Sampler(::Type{<:AbstractRNG}, r::AbstractUnitRange{T},
        ::Repetition) where {T<:Base.BitInteger64} = SamplerRangeNDL(r)

Sampler(::Type{<:AbstractRNG}, r::AbstractUnitRange{T},
        ::Repetition) where {T<:Union{Int128,UInt128}} = SamplerRangeFast(r)

#### helper functions

uint_sup(::Type{<:Base.BitInteger32}) = UInt32
uint_sup(::Type{<:Union{Int64,UInt64}}) = UInt64
uint_sup(::Type{<:Union{Int128,UInt128}}) = UInt128

#### Fast

struct SamplerRangeFast{U<:BitUnsigned,T<:BitInteger} <: Sampler{T}
    a::T      # first element of the range
    bw::UInt  # bit width
    m::U      # range length - 1
    mask::U   # mask generated values before threshold rejection
end

SamplerRangeFast(r::AbstractUnitRange{T}) where T<:BitInteger =
    SamplerRangeFast(r, uint_sup(T))

function SamplerRangeFast(r::AbstractUnitRange{T}, ::Type{U}) where {T,U}
    isempty(r) && throw(ArgumentError("collection must be non-empty"))
    m = (last(r) - first(r)) % unsigned(T) % U # % unsigned(T) to not propagate sign bit
    bw = (Base.top_set_bit(m)) % UInt # bit-width
    mask = ((1 % U) << bw) - (1 % U)
    SamplerRangeFast{U,T}(first(r), bw, m, mask)
end

function rand(rng::AbstractRNG, sp::SamplerRangeFast{UInt32,T}) where T
    a, bw, m, mask = sp.a, sp.bw, sp.m, sp.mask
    # below, we don't use UInt32, to get reproducible values, whether Int is Int64 or Int32
    x = rand(rng, LessThan(m, Masked(mask, UInt52Raw(UInt32))))
    (x + a % UInt32) % T
end

has_fast_64(rng::AbstractRNG) = rng_native_52(rng) != Float64
# for MersenneTwister, both options have very similar performance

function rand(rng::AbstractRNG, sp::SamplerRangeFast{UInt64,T}) where T
    a, bw, m, mask = sp.a, sp.bw, sp.m, sp.mask
    if !has_fast_64(rng) && bw <= 52
        x = rand(rng, LessThan(m, Masked(mask, UInt52Raw())))
    else
        x = rand(rng, LessThan(m, Masked(mask, uniform(UInt64))))
    end
    (x + a % UInt64) % T
end

function rand(rng::AbstractRNG, sp::SamplerRangeFast{UInt128,T}) where T
    a, bw, m, mask = sp.a, sp.bw, sp.m, sp.mask
    if has_fast_64(rng)
        x = bw <= 64 ?
            rand(rng, LessThan(m % UInt64, Masked(mask % UInt64, uniform(UInt64)))) % UInt128 :
            rand(rng, LessThan(m, Masked(mask, uniform(UInt128))))
    else
        x = bw <= 52  ?
            rand(rng, LessThan(m % UInt64, Masked(mask % UInt64, UInt52Raw()))) % UInt128 :
        bw <= 104 ?
            rand(rng, LessThan(m, Masked(mask, UInt104Raw()))) :
            rand(rng, LessThan(m, Masked(mask, uniform(UInt128))))
    end
    x % T + a
end

#### "Slow" / SamplerRangeInt

# remainder function according to Knuth, where rem_knuth(a, 0) = a
rem_knuth(a::UInt, b::UInt) = a % (b + (b == 0)) + a * (b == 0)
rem_knuth(a::T, b::T) where {T<:Unsigned} = b != 0 ? a % b : a

# maximum multiple of k <= sup decremented by one,
# that is 0xFFFF...FFFF if k = (typemax(T) - typemin(T)) + 1 and sup == typemax(T) - 1
# with intentional underflow
# see http://stackoverflow.com/questions/29182036/integer-arithmetic-add-1-to-uint-max-and-divide-by-n-without-overflow

# sup == 0 means typemax(T) + 1
maxmultiple(k::T, sup::T=zero(T)) where {T<:Unsigned} =
    (div(sup - k, k + (k == 0))*k + k - one(k))::T

# similar but sup must not be equal to typemax(T)
unsafe_maxmultiple(k::T, sup::T) where {T<:Unsigned} =
    div(sup, k + (k == 0))*k - one(k)

struct SamplerRangeInt{T<:Integer,U<:Unsigned} <: Sampler{T}
    a::T      # first element of the range
    bw::Int   # bit width
    k::U      # range length or zero for full range
    u::U      # rejection threshold
end


SamplerRangeInt(r::AbstractUnitRange{T}) where T<:BitInteger =
    SamplerRangeInt(r, uint_sup(T))

function SamplerRangeInt(r::AbstractUnitRange{T}, ::Type{U}) where {T,U}
    isempty(r) && throw(ArgumentError("collection must be non-empty"))
    a = first(r)
    m = (last(r) - first(r)) % unsigned(T) % U
    k = m + one(U)
    bw = (Base.top_set_bit(m)) % Int
    mult = if U === UInt32
        maxmultiple(k)
    elseif U === UInt64
        bw <= 52 ? unsafe_maxmultiple(k, one(UInt64) << 52) :
                   maxmultiple(k)
    else # U === UInt128
        bw <= 52  ? unsafe_maxmultiple(k, one(UInt128) << 52) :
        bw <= 104 ? unsafe_maxmultiple(k, one(UInt128) << 104) :
                    maxmultiple(k)
    end

    SamplerRangeInt{T,U}(a, bw, k, mult) # overflow ok
end

rand(rng::AbstractRNG, sp::SamplerRangeInt{T,UInt32}) where {T<:BitInteger} =
    (unsigned(sp.a) + rem_knuth(rand(rng, LessThan(sp.u, UInt52Raw(UInt32))), sp.k)) % T

# this function uses 52 bit entropy for small ranges of length <= 2^52
function rand(rng::AbstractRNG, sp::SamplerRangeInt{T,UInt64}) where T<:BitInteger
    x = sp.bw <= 52 ? rand(rng, LessThan(sp.u, UInt52())) :
                      rand(rng, LessThan(sp.u, uniform(UInt64)))
    return ((sp.a % UInt64) + rem_knuth(x, sp.k)) % T
end

function rand(rng::AbstractRNG, sp::SamplerRangeInt{T,UInt128}) where T<:BitInteger
    x = sp.bw <= 52  ? rand(rng, LessThan(sp.u, UInt52(UInt128))) :
        sp.bw <= 104 ? rand(rng, LessThan(sp.u, UInt104(UInt128))) :
                       rand(rng, LessThan(sp.u, uniform(UInt128)))
    return ((sp.a % UInt128) + rem_knuth(x, sp.k)) % T
end

#### Nearly Division Less

# cf. https://arxiv.org/abs/1805.10941 (algorithm 5)

struct SamplerRangeNDL{U<:Unsigned,T} <: Sampler{T}
    a::T  # first element of the range
    s::U  # range length or zero for full range
end

function SamplerRangeNDL(r::AbstractUnitRange{T}) where {T}
    isempty(r) && throw(ArgumentError("collection must be non-empty"))
    a = first(r)
    U = uint_sup(T)
    s = (last(r) - first(r)) % unsigned(T) % U + one(U) # overflow ok
    # mod(-s, s) could be put in the Sampler object for repeated calls, but
    # this would be an advantage only for very big s and number of calls
    SamplerRangeNDL(a, s)
end

function rand(rng::AbstractRNG, sp::SamplerRangeNDL{U,T}) where {U,T}
    s = sp.s
    x = widen(rand(rng, U))
    m = x * s
    l = m % U
    if l < s
        t = mod(-s, s) # as s is unsigned, -s is equal to 2^L - s in the paper
        while l < t
            x = widen(rand(rng, U))
            m = x * s
            l = m % U
        end
    end
    (s == 0 ? x : m >> (8*sizeof(U))) % T + sp.a
end


### BigInt

struct SamplerBigInt{SP<:Sampler{Limb}} <: Sampler{BigInt}
    a::BigInt         # first
    m::BigInt         # range length - 1
    nlimbs::Int       # number of limbs in generated BigInt's (z ∈ [0, m])
    nlimbsmax::Int    # max number of limbs for z+a
    highsp::SP        # sampler for the highest limb of z
end

function SamplerBigInt(::Type{RNG}, r::AbstractUnitRange{BigInt}, N::Repetition=Val(Inf)
                       ) where {RNG<:AbstractRNG}
    m = last(r) - first(r)
    m.size < 0 && throw(ArgumentError("collection must be non-empty"))
    nlimbs = Int(m.size)
    hm = nlimbs == 0 ? Limb(0) : GC.@preserve m unsafe_load(m.d, nlimbs)
    highsp = Sampler(RNG, Limb(0):hm, N)
    nlimbsmax = max(nlimbs, abs(last(r).size), abs(first(r).size))
    return SamplerBigInt(first(r), m, nlimbs, nlimbsmax, highsp)
end

Sampler(::Type{RNG}, r::AbstractUnitRange{BigInt}, N::Repetition) where {RNG<:AbstractRNG} =
    SamplerBigInt(RNG, r, N)

rand(rng::AbstractRNG, sp::SamplerBigInt) =
    rand!(rng, BigInt(nbits = sp.nlimbsmax*8*sizeof(Limb)), sp)

function rand!(rng::AbstractRNG, x::BigInt, sp::SamplerBigInt)
    nlimbs = sp.nlimbs
    nlimbs == 0 && return MPZ.set!(x, sp.a)
    MPZ.realloc2!(x, sp.nlimbsmax*8*sizeof(Limb))
    @assert x.alloc >= nlimbs
    # we randomize x ∈ [0, m] with rejection sampling:
    # 1. the first nlimbs-1 limbs of x are uniformly randomized
    # 2. the high limb hx of x is sampled from 0:hm where hm is the
    #    high limb of m
    # We repeat 1. and 2. until x <= m
    hm = GC.@preserve sp unsafe_load(sp.m.d, nlimbs)
    GC.@preserve x begin
        limbs = UnsafeView(x.d, nlimbs-1)
        while true
            rand!(rng, limbs)
            hx = limbs[nlimbs] = rand(rng, sp.highsp)
            hx < hm && break # avoid calling mpn_cmp most of the time
            MPZ.mpn_cmp(x, sp.m, nlimbs) <= 0 && break
        end
        # adjust x.size (normally done by mpz_limbs_finish, in GMP version >= 6)
        while nlimbs > 0
            limbs[nlimbs] != 0 && break
            nlimbs -= 1
        end
        x.size = nlimbs
    end
    MPZ.add!(x, sp.a)
end


## random values from AbstractArray

Sampler(::Type{RNG}, r::AbstractArray, n::Repetition) where {RNG<:AbstractRNG} =
    SamplerSimple(r, Sampler(RNG, firstindex(r):lastindex(r), n))

rand(rng::AbstractRNG, sp::SamplerSimple{<:AbstractArray,<:Sampler}) =
    @inbounds return sp[][rand(rng, sp.data)]


## random values from Dict

function Sampler(::Type{RNG}, t::Dict, ::Repetition) where RNG<:AbstractRNG
    isempty(t) && throw(ArgumentError("collection must be non-empty"))
    # we use Val(Inf) below as rand is called repeatedly internally
    # even for generating only one random value from t
    SamplerSimple(t, Sampler(RNG, LinearIndices(t.slots), Val(Inf)))
end

function rand(rng::AbstractRNG, sp::SamplerSimple{<:Dict,<:Sampler})
    while true
        i = rand(rng, sp.data)
        Base.isslotfilled(sp[], i) && @inbounds return (sp[].keys[i] => sp[].vals[i])
    end
end

## random values from Set

Sampler(::Type{RNG}, t::Set{T}, n::Repetition) where {RNG<:AbstractRNG,T} =
    SamplerTag{Set{T}}(Sampler(RNG, t.dict, n))

rand(rng::AbstractRNG, sp::SamplerTag{<:Set,<:Sampler}) = rand(rng, sp.data).first

## random values from BitSet

function Sampler(RNG::Type{<:AbstractRNG}, t::BitSet, n::Repetition)
    isempty(t) && throw(ArgumentError("collection must be non-empty"))
    SamplerSimple(t, Sampler(RNG, minimum(t):maximum(t), Val(Inf)))
end

function rand(rng::AbstractRNG, sp::SamplerSimple{BitSet,<:Sampler})
    while true
        n = rand(rng, sp.data)
        n in sp[] && return n
    end
end

## random values from AbstractDict/AbstractSet

# we defer to _Sampler to avoid ambiguities with a call like Sampler(rng, Set(1), Val(1))
Sampler(RNG::Type{<:AbstractRNG}, t::Union{AbstractDict,AbstractSet}, n::Repetition) =
    _Sampler(RNG, t, n)

# avoid linear complexity for repeated calls
_Sampler(RNG::Type{<:AbstractRNG}, t::Union{AbstractDict,AbstractSet}, n::Val{Inf}) =
    Sampler(RNG, collect(t), n)

# when generating only one element, avoid the call to collect
_Sampler(::Type{<:AbstractRNG}, t::Union{AbstractDict,AbstractSet}, ::Val{1}) =
    SamplerTrivial(t)

function nth(iter, n::Integer)::eltype(iter)
    for (i, x) in enumerate(iter)
        i == n && return x
    end
end

rand(rng::AbstractRNG, sp::SamplerTrivial{<:Union{AbstractDict,AbstractSet}}) =
    nth(sp[], rand(rng, 1:length(sp[])))


## random characters from a string

# we use collect(str), which is most of the time more efficient than specialized methods
# (except maybe for very small arrays)
Sampler(RNG::Type{<:AbstractRNG}, str::AbstractString, n::Val{Inf}) = Sampler(RNG, collect(str), n)

# when generating only one char from a string, the specialized method below
# is usually more efficient
Sampler(RNG::Type{<:AbstractRNG}, str::AbstractString, ::Val{1}) =
    SamplerSimple(str, Sampler(RNG, 1:_lastindex(str), Val(Inf)))

isvalid_unsafe(s::String, i) = !Base.is_valid_continuation(GC.@preserve s unsafe_load(pointer(s), i))
isvalid_unsafe(s::AbstractString, i) = isvalid(s, i)
_lastindex(s::String) = sizeof(s)
_lastindex(s::AbstractString) = lastindex(s)

function rand(rng::AbstractRNG, sp::SamplerSimple{<:AbstractString,<:Sampler})::Char
    str = sp[]
    while true
        pos = rand(rng, sp.data)
        isvalid_unsafe(str, pos) && return str[pos]
    end
end


## random elements from tuples

### 1

Sampler(::Type{<:AbstractRNG}, t::Tuple{A}, ::Repetition) where {A} =
    SamplerTrivial(t)

rand(rng::AbstractRNG, sp::SamplerTrivial{Tuple{A}}) where {A} =
    @inbounds return sp[][1]

### 2

Sampler(RNG::Type{<:AbstractRNG}, t::Tuple{A,B}, n::Repetition) where {A,B} =
    SamplerSimple(t, Sampler(RNG, Bool, n))

rand(rng::AbstractRNG, sp::SamplerSimple{Tuple{A,B}}) where {A,B} =
    @inbounds return sp[][1 + rand(rng, sp.data)]

### 3

Sampler(RNG::Type{<:AbstractRNG}, t::Tuple{A,B,C}, n::Repetition) where {A,B,C} =
    SamplerSimple(t, Sampler(RNG, UInt52(), n))

function rand(rng::AbstractRNG, sp::SamplerSimple{Tuple{A,B,C}}) where {A,B,C}
    local r
    while true
        r = rand(rng, sp.data)
        r != 0x000fffffffffffff && break # _very_ likely
    end
    @inbounds return sp[][1 + r ÷ 0x0005555555555555]
end

### n

@generated function Sampler(RNG::Type{<:AbstractRNG}, t::Tuple, n::Repetition)
    l = fieldcount(t)
    if l < typemax(UInt32) && ispow2(l)
        :(SamplerSimple(t, Sampler(RNG, UInt32, n)))
    else
        :(SamplerSimple(t, Sampler(RNG, Base.OneTo(length(t)), n)))
    end
end

@generated function rand(rng::AbstractRNG, sp::SamplerSimple{T}) where T<:Tuple
    l = fieldcount(T)
    if l < typemax(UInt32) && ispow2(l)
        quote
            r = rand(rng, sp.data) & ($l-1)
            @inbounds return sp[][1 + r]
        end
    else
        :(@inbounds return sp[][rand(rng, sp.data)])
    end
end
p   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Random/src/normal.jl��      # This file is a part of Julia. License is MIT: https://julialang.org/license

# Normally distributed random numbers using Ziggurat algorithm

# The Ziggurat Method for generating random variables - Marsaglia and Tsang
# Paper and reference code: http://www.jstatsoft.org/v05/i08/

# randmtzig (covers also exponential variates)

## randn

"""
    randn([rng=default_rng()], [T=Float64], [dims...])

Generate a normally-distributed random number of type `T`
with mean 0 and standard deviation 1.
Optionally generate an array of normally-distributed random numbers.
The `Base` module currently provides an implementation for the types
[`Float16`](@ref), [`Float32`](@ref), and [`Float64`](@ref) (the default), and their
[`Complex`](@ref) counterparts. When the type argument is complex, the values are drawn
from the circularly symmetric complex normal distribution of variance 1 (corresponding to real and imaginary part having independent normal distribution with mean zero and variance `1/2`).

See also [`randn!`](@ref) to act in-place.

# Examples
```jldoctest
julia> using Random

julia> rng = MersenneTwister(1234);

julia> randn(rng, ComplexF64)
0.6133070881429037 - 0.6376291670853887im

julia> randn(rng, ComplexF32, (2, 3))
2×3 Matrix{ComplexF32}:
 -0.349649-0.638457im  0.376756-0.192146im  -0.396334-0.0136413im
  0.611224+1.56403im   0.355204-0.365563im  0.0905552+1.31012im
```
"""
@inline function randn(rng::AbstractRNG=default_rng())
    #=
    When defining
    `@inline randn(rng::AbstractRNG=default_rng()) = _randn(rng, rand(rng, UInt52Raw()))`
    the function call to `_randn` is currently not inlined, resulting in slightly worse
    performance for scalar random normal numbers than repeating the code of `_randn`
    inside the following function.
    =#
    @inbounds begin
        r = rand(rng, UInt52())

        # the following code is identical to the one in `_randn(rng::AbstractRNG, r::UInt64)`
        rabs = Int64(r>>1) # One bit for the sign
        idx = rabs & 0xFF
        x = ifelse(r % Bool, -rabs, rabs)*wi[idx+1]
        rabs < ki[idx+1] && return x # 99.3% of the time we return here 1st try
        return randn_unlikely(rng, idx, rabs, x)
    end
end

@inline function _randn(rng::AbstractRNG, r::UInt64)
    @inbounds begin
        r &= 0x000fffffffffffff
        rabs = Int64(r>>1) # One bit for the sign
        idx = rabs & 0xFF
        x = ifelse(r % Bool, -rabs, rabs)*wi[idx+1]
        rabs < ki[idx+1] && return x # 99.3% of the time we return here 1st try
        return randn_unlikely(rng, idx, rabs, x)
    end
end

# this unlikely branch is put in a separate function for better efficiency
@noinline function randn_unlikely(rng, idx, rabs, x)
    @inbounds if idx == 0
        while true
            xx = -ziggurat_nor_inv_r*log(rand(rng))
            yy = -log(rand(rng))
            yy+yy > xx*xx &&
                return (rabs >> 8) % Bool ? -ziggurat_nor_r-xx : ziggurat_nor_r+xx
        end
    elseif (fi[idx] - fi[idx+1])*rand(rng) + fi[idx+1] < exp(-0.5*x*x)
        return x # return from the triangular area
    else
        return randn(rng)
    end
end

### complex randn

Base.@irrational SQRT_HALF 0.7071067811865475244008  sqrt(big(0.5))

randn(rng::AbstractRNG, ::Type{Complex{T}}) where {T<:AbstractFloat} =
    Complex{T}(SQRT_HALF * randn(rng, T), SQRT_HALF * randn(rng, T))


### fallback randn for float types defining rand:
function randn(rng::AbstractRNG, ::Type{T}) where {T<:AbstractFloat}
    # Marsaglia polar variant of Box–Muller transform:
    while true
        x, y = 2rand(rng, T)-1, 2rand(rng, T)-1
        0 < (s = x^2 + y^2) < 1 && return x * sqrt(-2log(s)/s)
    end
end

## randexp

"""
    randexp([rng=default_rng()], [T=Float64], [dims...])

Generate a random number of type `T` according to the
exponential distribution with scale 1.
Optionally generate an array of such random numbers.
The `Base` module currently provides an implementation for the types
[`Float16`](@ref), [`Float32`](@ref), and [`Float64`](@ref) (the default).

# Examples
```jldoctest
julia> rng = MersenneTwister(1234);

julia> randexp(rng, Float32)
2.4835055f0

julia> randexp(rng, 3, 3)
3×3 Matrix{Float64}:
 1.5167    1.30652   0.344435
 0.604436  2.78029   0.418516
 0.695867  0.693292  0.643644
```
"""
randexp(rng::AbstractRNG=default_rng()) = _randexp(rng, rand(rng, UInt52Raw()))

function _randexp(rng::AbstractRNG, ri::UInt64)
    @inbounds begin
        ri &= 0x000fffffffffffff
        idx = ri & 0xFF
        x = ri*we[idx+1]
        ri < ke[idx+1] && return x # 98.9% of the time we return here 1st try
        return randexp_unlikely(rng, idx, x)
    end
end

@noinline function randexp_unlikely(rng, idx, x)
    @inbounds if idx == 0
        return ziggurat_exp_r - log(rand(rng))
    elseif (fe[idx] - fe[idx+1])*rand(rng) + fe[idx+1] < exp(-x)
        return x # return from the triangular area
    else
        return randexp(rng)
    end
end

### fallback randexp for float types defining rand:
randexp(rng::AbstractRNG, ::Type{T}) where {T<:AbstractFloat} =
    -log1p(-rand(rng, T))

## arrays & other scalar methods

"""
    randn!([rng=default_rng()], A::AbstractArray) -> A

Fill the array `A` with normally-distributed (mean 0, standard deviation 1) random numbers.
Also see the [`rand`](@ref) function.

# Examples
```jldoctest
julia> rng = MersenneTwister(1234);

julia> randn!(rng, zeros(5))
5-element Vector{Float64}:
  0.8673472019512456
 -0.9017438158568171
 -0.4944787535042339
 -0.9029142938652416
  0.8644013132535154
```
"""
function randn! end

"""
    randexp!([rng=default_rng()], A::AbstractArray) -> A

Fill the array `A` with random numbers following the exponential distribution
(with scale 1).

# Examples
```jldoctest
julia> rng = MersenneTwister(1234);

julia> randexp!(rng, zeros(5))
5-element Vector{Float64}:
 2.4835053723904896
 1.516703605376473
 0.6044364871025417
 0.6958665886385867
 1.3065196315496677
```
"""
function randexp! end

for randfun in [:randn, :randexp]
    randfun! = Symbol(randfun, :!)
    _randfun = Symbol(:_, randfun)
    @eval begin
        # scalars
        $randfun(rng::AbstractRNG, T::BitFloatType) = convert(T, $randfun(rng))
        $randfun(::Type{T}) where {T} = $randfun(default_rng(), T)

        # filling arrays
        function $randfun!(rng::AbstractRNG, A::AbstractArray{T}) where T
            for i in eachindex(A)
                @inbounds A[i] = $randfun(rng, T)
            end
            A
        end

        # optimization for MersenneTwister, which randomizes natively Array{Float64}
        function $randfun!(rng::MersenneTwister, A::Array{Float64})
            if length(A) < 13
                for i in eachindex(A)
                    @inbounds A[i] = $randfun(rng, Float64)
                end
            else
                rand!(rng, A, CloseOpen12())
                for i in eachindex(A)
                    @inbounds A[i] = $_randfun(rng, reinterpret(UInt64, A[i]))
                end
            end
            A
        end

        # optimization for Xoshiro, which randomizes natively Array{UInt64}
        function $randfun!(rng::Union{Xoshiro, TaskLocalRNG}, A::Array{Float64})
            if length(A) < 7
                for i in eachindex(A)
                    @inbounds A[i] = $randfun(rng, Float64)
                end
            else
                GC.@preserve A rand!(rng, UnsafeView{UInt64}(pointer(A), length(A)))

                for i in eachindex(A)
                    @inbounds A[i] = $_randfun(rng, reinterpret(UInt64, A[i]) >>> 12)
                end
            end
            A
        end

        $randfun!(A::AbstractArray) = $randfun!(default_rng(), A)

        # generating arrays
        $randfun(rng::AbstractRNG, ::Type{T}, dims::Dims                     ) where {T} = $randfun!(rng, Array{T}(undef, dims))
        # Note that this method explicitly does not define $randfun(rng, T),
        # in order to prevent an infinite recursion.
        $randfun(rng::AbstractRNG, ::Type{T}, dim1::Integer, dims::Integer...) where {T} = $randfun!(rng, Array{T}(undef, dim1, dims...))
        $randfun(                  ::Type{T}, dims::Dims                     ) where {T} = $randfun(default_rng(), T, dims)
        $randfun(                  ::Type{T}, dims::Integer...               ) where {T} = $randfun(default_rng(), T, dims...)
        $randfun(rng::AbstractRNG,            dims::Dims                     )           = $randfun(rng, Float64, dims)
        $randfun(rng::AbstractRNG,            dims::Integer...               )           = $randfun(rng, Float64, dims...)
        $randfun(                             dims::Dims                     )           = $randfun(default_rng(), Float64, dims)
        $randfun(                             dims::Integer...               )           = $randfun(default_rng(), Float64, dims...)
    end
end

## Tables for normal variates

const ki =
    UInt64[0x0007799ec012f7b2,0x0000000000000000,0x0006045f4c7de363,0x0006d1aa7d5ec0a5,
           0x000728fb3f60f777,0x0007592af4e9fbc0,0x000777a5c0bf655d,0x00078ca3857d2256,
           0x00079bf6b0ffe58b,0x0007a7a34ab092ad,0x0007b0d2f20dd1cb,0x0007b83d3aa9cb52,
           0x0007be597614224d,0x0007c3788631abe9,0x0007c7d32bc192ee,0x0007cb9263a6e86d,
           0x0007ced483edfa84,0x0007d1b07ac0fd39,0x0007d437ef2da5fc,0x0007d678b069aa6e,
           0x0007d87db38c5c87,0x0007da4fc6a9ba62,0x0007dbf611b37f3b,0x0007dd7674d0f286,
           0x0007ded5ce8205f6,0x0007e018307fb62b,0x0007e141081bd124,0x0007e2533d712de8,
           0x0007e3514bbd7718,0x0007e43d54944b52,0x0007e5192f25ef42,0x0007e5e67481118d,
           0x0007e6a6897c1ce2,0x0007e75aa6c7f64c,0x0007e803df8ee498,0x0007e8a326eb6272,
           0x0007e93954717a28,0x0007e9c727f8648f,0x0007ea4d4cc85a3c,0x0007eacc5c4907a9,
           0x0007eb44e0474cf6,0x0007ebb754e47419,0x0007ec242a3d8474,0x0007ec8bc5d69645,
           0x0007ecee83d3d6e9,0x0007ed4cb8082f45,0x0007eda6aee0170f,0x0007edfcae2dfe68,
           0x0007ee4ef5dccd3e,0x0007ee9dc08c394e,0x0007eee9441a17c7,0x0007ef31b21b4fb1,
           0x0007ef773846a8a7,0x0007efba00d35a17,0x0007effa32ccf69f,0x0007f037f25e1278,
           0x0007f0736112d12c,0x0007f0ac9e145c25,0x0007f0e3c65e1fcc,0x0007f118f4ed8e54,
           0x0007f14c42ed0dc8,0x0007f17dc7daa0c3,0x0007f1ad99aac6a5,0x0007f1dbcce80015,
           0x0007f20874cf56bf,0x0007f233a36a3b9a,0x0007f25d69a604ad,0x0007f285d7694a92,
           0x0007f2acfba75e3b,0x0007f2d2e4720909,0x0007f2f79f09c344,0x0007f31b37ec883b,
           0x0007f33dbae36abc,0x0007f35f330f08d5,0x0007f37faaf2fa79,0x0007f39f2c805380,
           0x0007f3bdc11f4f1c,0x0007f3db71b83850,0x0007f3f846bba121,0x0007f4144829f846,
           0x0007f42f7d9a8b9d,0x0007f449ee420432,0x0007f463a0f8675e,0x0007f47c9c3ea77b,
           0x0007f494e643cd8e,0x0007f4ac84e9c475,0x0007f4c37dc9cd50,0x0007f4d9d638a432,
           0x0007f4ef934a5b6a,0x0007f504b9d5f33d,0x0007f5194e78b352,0x0007f52d55994a96,
           0x0007f540d36aba0c,0x0007f553cbef0e77,0x0007f56642f9ec8f,0x0007f5783c32f31e,
           0x0007f589bb17f609,0x0007f59ac2ff1525,0x0007f5ab5718b15a,0x0007f5bb7a71427c,
           0x0007f5cb2ff31009,0x0007f5da7a67cebe,0x0007f5e95c7a24e7,0x0007f5f7d8b7171e,
           0x0007f605f18f5ef4,0x0007f613a958ad0a,0x0007f621024ed7e9,0x0007f62dfe94f8cb,
           0x0007f63aa036777a,0x0007f646e928065a,0x0007f652db488f88,0x0007f65e786213ff,
           0x0007f669c22a7d8a,0x0007f674ba446459,0x0007f67f623fc8db,0x0007f689bb9ac294,
           0x0007f693c7c22481,0x0007f69d881217a6,0x0007f6a6fdd6ac36,0x0007f6b02a4c61ee,
           0x0007f6b90ea0a7f4,0x0007f6c1abf254c0,0x0007f6ca03521664,0x0007f6d215c2db82,
           0x0007f6d9e43a3559,0x0007f6e16fa0b329,0x0007f6e8b8d23729,0x0007f6efc09e4569,
           0x0007f6f687c84cbf,0x0007f6fd0f07ea09,0x0007f703570925e2,0x0007f709606cad03,
           0x0007f70f2bc8036f,0x0007f714b9a5b292,0x0007f71a0a85725d,0x0007f71f1edc4d9e,
           0x0007f723f714c179,0x0007f728938ed843,0x0007f72cf4a03fa0,0x0007f7311a945a16,
           0x0007f73505ac4bf8,0x0007f738b61f03bd,0x0007f73c2c193dc0,0x0007f73f67bd835c,
           0x0007f74269242559,0x0007f745305b31a1,0x0007f747bd666428,0x0007f74a103f12ed,
           0x0007f74c28d414f5,0x0007f74e0709a42d,0x0007f74faab939f9,0x0007f75113b16657,
           0x0007f75241b5a155,0x0007f753347e16b8,0x0007f753ebb76b7c,0x0007f75467027d05,
           0x0007f754a5f4199d,0x0007f754a814b207,0x0007f7546ce003ae,0x0007f753f3c4bb29,
           0x0007f7533c240e92,0x0007f75245514f41,0x0007f7510e91726c,0x0007f74f971a9012,
           0x0007f74dde135797,0x0007f74be2927971,0x0007f749a39e051c,0x0007f747202aba8a,
           0x0007f744571b4e3c,0x0007f741473f9efe,0x0007f73def53dc43,0x0007f73a4dff9bff,
           0x0007f73661d4deaf,0x0007f732294f003f,0x0007f72da2d19444,0x0007f728cca72bda,
           0x0007f723a5000367,0x0007f71e29f09627,0x0007f7185970156b,0x0007f7123156c102,
           0x0007f70baf5c1e2c,0x0007f704d1150a23,0x0007f6fd93f1a4e5,0x0007f6f5f53b10b6,
           0x0007f6edf211023e,0x0007f6e587671ce9,0x0007f6dcb2021679,0x0007f6d36e749c64,
           0x0007f6c9b91bf4c6,0x0007f6bf8e1c541b,0x0007f6b4e95ce015,0x0007f6a9c68356ff,
           0x0007f69e20ef5211,0x0007f691f3b517eb,0x0007f6853997f321,0x0007f677ed03ff19,
           0x0007f66a08075bdc,0x0007f65b844ab75a,0x0007f64c5b091860,0x0007f63c8506d4bc,
           0x0007f62bfa8798fe,0x0007f61ab34364b0,0x0007f608a65a599a,0x0007f5f5ca4737e8,
           0x0007f5e214d05b48,0x0007f5cd7af7066e,0x0007f5b7f0e4c2a1,0x0007f5a169d68fcf,
           0x0007f589d80596a5,0x0007f5712c8d0174,0x0007f557574c912b,0x0007f53c46c77193,
           0x0007f51fe7feb9f2,0x0007f5022646ecfb,0x0007f4e2eb17ab1d,0x0007f4c21dd4a3d1,
           0x0007f49fa38ea394,0x0007f47b5ebb62eb,0x0007f4552ee27473,0x0007f42cf03d58f5,
           0x0007f4027b48549f,0x0007f3d5a44119df,0x0007f3a63a8fb552,0x0007f37408155100,
           0x0007f33ed05b55ec,0x0007f3064f9c183e,0x0007f2ca399c7ba1,0x0007f28a384bb940,
           0x0007f245ea1b7a2b,0x0007f1fcdffe8f1b,0x0007f1ae9af758cd,0x0007f15a8917f27e,
           0x0007f10001ccaaab,0x0007f09e413c418a,0x0007f034627733d7,0x0007efc15815b8d5,
           0x0007ef43e2bf7f55,0x0007eeba84e31dfe,0x0007ee237294df89,0x0007ed7c7c170141,
           0x0007ecc2f0d95d3a,0x0007ebf377a46782,0x0007eb09d6deb285,0x0007ea00a4f17808,
           0x0007e8d0d3da63d6,0x0007e771023b0fcf,0x0007e5d46c2f08d8,0x0007e3e937669691,
           0x0007e195978f1176,0x0007deb2c0e05c1c,0x0007db0362002a19,0x0007d6202c151439,
           0x0007cf4b8f00a2cb,0x0007c4fd24520efd,0x0007b362fbf81816,0x00078d2d25998e24]
const wi =
    [1.7367254121602630e-15,9.5586603514556339e-17,1.2708704834810623e-16,
     1.4909740962495474e-16,1.6658733631586268e-16,1.8136120810119029e-16,
     1.9429720153135588e-16,2.0589500628482093e-16,2.1646860576895422e-16,
     2.2622940392218116e-16,2.3532718914045892e-16,2.4387234557428771e-16,
     2.5194879829274225e-16,2.5962199772528103e-16,2.6694407473648285e-16,
     2.7395729685142446e-16,2.8069646002484804e-16,2.8719058904113930e-16,
     2.9346417484728883e-16,2.9953809336782113e-16,3.0543030007192440e-16,
     3.1115636338921572e-16,3.1672988018581815e-16,3.2216280350549905e-16,
     3.2746570407939751e-16,3.3264798116841710e-16,3.3771803417353232e-16,
     3.4268340353119356e-16,3.4755088731729758e-16,3.5232663846002031e-16,
     3.5701624633953494e-16,3.6162480571598339e-16,3.6615697529653540e-16,
     3.7061702777236077e-16,3.7500889278747798e-16,3.7933619401549554e-16,
     3.8360228129677279e-16,3.8781025861250247e-16,3.9196300853257678e-16,
     3.9606321366256378e-16,4.0011337552546690e-16,4.0411583124143332e-16,
     4.0807276830960448e-16,4.1198623774807442e-16,4.1585816580828064e-16,
     4.1969036444740733e-16,4.2348454071520708e-16,4.2724230518899761e-16,
     4.3096517957162941e-16,4.3465460355128760e-16,4.3831194100854571e-16,
     4.4193848564470665e-16,4.4553546609579137e-16,4.4910405058828750e-16,
     4.5264535118571397e-16,4.5616042766900381e-16,4.5965029108849407e-16,
     4.6311590702081647e-16,4.6655819856008752e-16,4.6997804906941950e-16,
     4.7337630471583237e-16,4.7675377680908526e-16,4.8011124396270155e-16,
     4.8344945409350080e-16,4.8676912627422087e-16,4.9007095245229938e-16,
     4.9335559904654139e-16,4.9662370843221783e-16,4.9987590032409088e-16,
     5.0311277306593187e-16,5.0633490483427195e-16,5.0954285476338923e-16,
     5.1273716399787966e-16,5.1591835667857364e-16,5.1908694086703434e-16,
     5.2224340941340417e-16,5.2538824077194543e-16,5.2852189976823820e-16,
     5.3164483832166176e-16,5.3475749612647295e-16,5.3786030129452348e-16,
     5.4095367096239933e-16,5.4403801186554671e-16,5.4711372088173611e-16,
     5.5018118554603362e-16,5.5324078453927836e-16,5.5629288815190902e-16,
     5.5933785872484621e-16,5.6237605106900435e-16,5.6540781286489604e-16,
     5.6843348504368141e-16,5.7145340215092040e-16,5.7446789269419609e-16,
     5.7747727947569648e-16,5.8048187991076857e-16,5.8348200633338921e-16,
     5.8647796628943653e-16,5.8947006281858718e-16,5.9245859472561339e-16,
     5.9544385684180598e-16,5.9842614027720281e-16,6.0140573266426640e-16,
     6.0438291839361250e-16,6.0735797884236057e-16,6.1033119259564394e-16,
     6.1330283566179110e-16,6.1627318168165963e-16,6.1924250213258470e-16,
     6.2221106652737879e-16,6.2517914260879998e-16,6.2814699653988953e-16,
     6.3111489309056042e-16,6.3408309582080600e-16,6.3705186726088149e-16,
     6.4002146908880247e-16,6.4299216230548961e-16,6.4596420740788321e-16,
     6.4893786456033965e-16,6.5191339376461587e-16,6.5489105502874154e-16,
     6.5787110853507413e-16,6.6085381480782587e-16,6.6383943488035057e-16,
     6.6682823046247459e-16,6.6982046410815579e-16,6.7281639938375311e-16,
     6.7581630103719006e-16,6.7882043516829803e-16,6.8182906940062540e-16,
     6.8484247305500383e-16,6.8786091732516637e-16,6.9088467545571690e-16,
     6.9391402292275690e-16,6.9694923761748294e-16,6.9999060003307640e-16,
     7.0303839345521508e-16,7.0609290415654822e-16,7.0915442159548734e-16,
     7.1222323861967788e-16,7.1529965167453030e-16,7.1838396101720629e-16,
     7.2147647093647067e-16,7.2457748997883870e-16,7.2768733118146927e-16,
     7.3080631231227429e-16,7.3393475611774048e-16,7.3707299057898310e-16,
     7.4022134917657997e-16,7.4338017116476479e-16,7.4654980185558890e-16,
     7.4973059291369793e-16,7.5292290266240584e-16,7.5612709640179217e-16,
     7.5934354673958895e-16,7.6257263393567558e-16,7.6581474626104873e-16,
     7.6907028037219191e-16,7.7233964170182985e-16,7.7562324486711744e-16,
     7.7892151409638524e-16,7.8223488367564108e-16,7.8556379841610841e-16,
     7.8890871414417552e-16,7.9227009821522709e-16,7.9564843005293662e-16,
     7.9904420171571300e-16,8.0245791849212591e-16,8.0589009952726568e-16,
     8.0934127848215009e-16,8.1281200422845008e-16,8.1630284158098775e-16,
     8.1981437207065329e-16,8.2334719476060504e-16,8.2690192710884700e-16,
     8.3047920588053737e-16,8.3407968811366288e-16,8.3770405214202216e-16,
     8.4135299867980282e-16,8.4502725197240968e-16,8.4872756101861549e-16,
     8.5245470086955962e-16,8.5620947401062333e-16,8.5999271183276646e-16,
     8.6380527620052589e-16,8.6764806112455816e-16,8.7152199454736980e-16,
     8.7542804025171749e-16,8.7936719990210427e-16,8.8334051523084080e-16,
     8.8734907038131345e-16,8.9139399442240861e-16,8.9547646404950677e-16,
     8.9959770648910994e-16,9.0375900262601175e-16,9.0796169037400680e-16,
     9.1220716831348461e-16,9.1649689962191353e-16,9.2083241632623076e-16,
     9.2521532390956933e-16,9.2964730630864167e-16,9.3413013134252651e-16,
     9.3866565661866598e-16,9.4325583596767065e-16,9.4790272646517382e-16,
     9.5260849610662787e-16,9.5737543220974496e-16,9.6220595062948384e-16,
     9.6710260588230542e-16,9.7206810229016259e-16,9.7710530627072088e-16,
     9.8221725991905411e-16,9.8740719604806711e-16,9.9267855488079765e-16,
     9.9803500261836449e-16,1.0034804521436181e-15,1.0090190861637457e-15,
     1.0146553831467086e-15,1.0203941464683124e-15,1.0262405372613567e-15,
     1.0322001115486456e-15,1.0382788623515399e-15,1.0444832676000471e-15,
     1.0508203448355195e-15,1.0572977139009890e-15,1.0639236690676801e-15,
     1.0707072623632994e-15,1.0776584002668106e-15,1.0847879564403425e-15,
     1.0921079038149563e-15,1.0996314701785628e-15,1.1073733224935752e-15,
     1.1153497865853155e-15,1.1235791107110833e-15,1.1320817840164846e-15,
     1.1408809242582780e-15,1.1500027537839792e-15,1.1594771891449189e-15,
     1.1693385786910960e-15,1.1796266352955801e-15,1.1903876299282890e-15,
     1.2016759392543819e-15,1.2135560818666897e-15,1.2261054417450561e-15,
     1.2394179789163251e-15,1.2536093926602567e-15,1.2688244814255010e-15,
     1.2852479319096109e-15,1.3031206634689985e-15,1.3227655770195326e-15,
     1.3446300925011171e-15,1.3693606835128518e-15,1.3979436672775240e-15,
     1.4319989869661328e-15,1.4744848603597596e-15,1.5317872741611144e-15,
     1.6227698675312968e-15]
const fi =
    [1.0000000000000000e+00,9.7710170126767082e-01,9.5987909180010600e-01,
     9.4519895344229909e-01,9.3206007595922991e-01,9.1999150503934646e-01,
     9.0872644005213032e-01,8.9809592189834297e-01,8.8798466075583282e-01,
     8.7830965580891684e-01,8.6900868803685649e-01,8.6003362119633109e-01,
     8.5134625845867751e-01,8.4291565311220373e-01,8.3471629298688299e-01,
     8.2672683394622093e-01,8.1892919160370192e-01,8.1130787431265572e-01,
     8.0384948317096383e-01,7.9654233042295841e-01,7.8937614356602404e-01,
     7.8234183265480195e-01,7.7543130498118662e-01,7.6863731579848571e-01,
     7.6195334683679483e-01,7.5537350650709567e-01,7.4889244721915638e-01,
     7.4250529634015061e-01,7.3620759812686210e-01,7.2999526456147568e-01,
     7.2386453346862967e-01,7.1781193263072152e-01,7.1183424887824798e-01,
     7.0592850133275376e-01,7.0009191813651117e-01,6.9432191612611627e-01,
     6.8861608300467136e-01,6.8297216164499430e-01,6.7738803621877308e-01,
     6.7186171989708166e-01,6.6639134390874977e-01,6.6097514777666277e-01,
     6.5561147057969693e-01,6.5029874311081637e-01,6.4503548082082196e-01,
     6.3982027745305614e-01,6.3465179928762327e-01,6.2952877992483625e-01,
     6.2445001554702606e-01,6.1941436060583399e-01,6.1442072388891344e-01,
     6.0946806492577310e-01,6.0455539069746733e-01,5.9968175261912482e-01,
     5.9484624376798689e-01,5.9004799633282545e-01,5.8528617926337090e-01,
     5.8055999610079034e-01,5.7586868297235316e-01,5.7121150673525267e-01,
     5.6658776325616389e-01,5.6199677581452390e-01,5.5743789361876550e-01,
     5.5291049042583185e-01,5.4841396325526537e-01,5.4394773119002582e-01,
     5.3951123425695158e-01,5.3510393238045717e-01,5.3072530440366150e-01,
     5.2637484717168403e-01,5.2205207467232140e-01,5.1775651722975591e-01,
     5.1348772074732651e-01,5.0924524599574761e-01,5.0502866794346790e-01,
     5.0083757512614835e-01,4.9667156905248933e-01,4.9253026364386815e-01,
     4.8841328470545758e-01,4.8432026942668288e-01,4.8025086590904642e-01,
     4.7620473271950547e-01,4.7218153846772976e-01,4.6818096140569321e-01,
     4.6420268904817391e-01,4.6024641781284248e-01,4.5631185267871610e-01,
     4.5239870686184824e-01,4.4850670150720273e-01,4.4463556539573912e-01,
     4.4078503466580377e-01,4.3695485254798533e-01,4.3314476911265209e-01,
     4.2935454102944126e-01,4.2558393133802180e-01,4.2183270922949573e-01,
     4.1810064983784795e-01,4.1438753404089090e-01,4.1069314827018799e-01,
     4.0701728432947315e-01,4.0335973922111429e-01,3.9972031498019700e-01,
     3.9609881851583223e-01,3.9249506145931540e-01,3.8890886001878855e-01,
     3.8534003484007706e-01,3.8178841087339344e-01,3.7825381724561896e-01,
     3.7473608713789086e-01,3.7123505766823922e-01,3.6775056977903225e-01,
     3.6428246812900372e-01,3.6083060098964775e-01,3.5739482014578022e-01,
     3.5397498080007656e-01,3.5057094148140588e-01,3.4718256395679348e-01,
     3.4380971314685055e-01,3.4045225704452164e-01,3.3711006663700588e-01,
     3.3378301583071823e-01,3.3047098137916342e-01,3.2717384281360129e-01,
     3.2389148237639104e-01,3.2062378495690530e-01,3.1737063802991350e-01,
     3.1413193159633707e-01,3.1090755812628634e-01,3.0769741250429189e-01,
     3.0450139197664983e-01,3.0131939610080288e-01,2.9815132669668531e-01,
     2.9499708779996164e-01,2.9185658561709499e-01,2.8872972848218270e-01,
     2.8561642681550159e-01,2.8251659308370741e-01,2.7943014176163772e-01,
     2.7635698929566810e-01,2.7329705406857691e-01,2.7025025636587519e-01,
     2.6721651834356114e-01,2.6419576399726080e-01,2.6118791913272082e-01,
     2.5819291133761890e-01,2.5521066995466168e-01,2.5224112605594190e-01,
     2.4928421241852824e-01,2.4633986350126363e-01,2.4340801542275012e-01,
     2.4048860594050039e-01,2.3758157443123795e-01,2.3468686187232990e-01,
     2.3180441082433859e-01,2.2893416541468023e-01,2.2607607132238020e-01,
     2.2323007576391746e-01,2.2039612748015194e-01,2.1757417672433113e-01,
     2.1476417525117358e-01,2.1196607630703015e-01,2.0917983462112499e-01,
     2.0640540639788071e-01,2.0364274931033485e-01,2.0089182249465656e-01,
     1.9815258654577511e-01,1.9542500351413428e-01,1.9270903690358912e-01,
     1.9000465167046496e-01,1.8731181422380025e-01,1.8463049242679927e-01,
     1.8196065559952254e-01,1.7930227452284767e-01,1.7665532144373500e-01,
     1.7401977008183875e-01,1.7139559563750595e-01,1.6878277480121151e-01,
     1.6618128576448205e-01,1.6359110823236570e-01,1.6101222343751107e-01,
     1.5844461415592431e-01,1.5588826472447920e-01,1.5334316106026283e-01,
     1.5080929068184568e-01,1.4828664273257453e-01,1.4577520800599403e-01,
     1.4327497897351341e-01,1.4078594981444470e-01,1.3830811644855071e-01,
     1.3584147657125373e-01,1.3338602969166913e-01,1.3094177717364430e-01,
     1.2850872227999952e-01,1.2608687022018586e-01,1.2367622820159654e-01,
     1.2127680548479021e-01,1.1888861344290998e-01,1.1651166562561080e-01,
     1.1414597782783835e-01,1.1179156816383801e-01,1.0944845714681163e-01,
     1.0711666777468364e-01,1.0479622562248690e-01,1.0248715894193508e-01,
     1.0018949876880981e-01,9.7903279038862284e-02,9.5628536713008819e-02,
     9.3365311912690860e-02,9.1113648066373634e-02,8.8873592068275789e-02,
     8.6645194450557961e-02,8.4428509570353374e-02,8.2223595813202863e-02,
     8.0030515814663056e-02,7.7849336702096039e-02,7.5680130358927067e-02,
     7.3522973713981268e-02,7.1377949058890375e-02,6.9245144397006769e-02,
     6.7124653827788497e-02,6.5016577971242842e-02,6.2921024437758113e-02,
     6.0838108349539864e-02,5.8767952920933758e-02,5.6710690106202902e-02,
     5.4666461324888914e-02,5.2635418276792176e-02,5.0617723860947761e-02,
     4.8613553215868521e-02,4.6623094901930368e-02,4.4646552251294443e-02,
     4.2684144916474431e-02,4.0736110655940933e-02,3.8802707404526113e-02,
     3.6884215688567284e-02,3.4980941461716084e-02,3.3093219458578522e-02,
     3.1221417191920245e-02,2.9365939758133314e-02,2.7527235669603082e-02,
     2.5705804008548896e-02,2.3902203305795882e-02,2.2117062707308864e-02,
     2.0351096230044517e-02,1.8605121275724643e-02,1.6880083152543166e-02,
     1.5177088307935325e-02,1.3497450601739880e-02,1.1842757857907888e-02,
     1.0214971439701471e-02,8.6165827693987316e-03,7.0508754713732268e-03,
     5.5224032992509968e-03,4.0379725933630305e-03,2.6090727461021627e-03,
     1.2602859304985975e-03]

## Tables for exponential variates

const ke =
    UInt64[0x000e290a13924be3,0x0000000000000000,0x0009beadebce18bf,0x000c377ac71f9e08,
           0x000d4ddb99075857,0x000de893fb8ca23e,0x000e4a8e87c4328d,0x000e8dff16ae1cb9,
           0x000ebf2deab58c59,0x000ee49a6e8b9638,0x000f0204efd64ee4,0x000f19bdb8ea3c1b,
           0x000f2d458bbe5bd1,0x000f3da104b78236,0x000f4b86d784571f,0x000f577ad8a7784f,
           0x000f61de83da32ab,0x000f6afb7843cce7,0x000f730a57372b44,0x000f7a37651b0e68,
           0x000f80a5bb6eea52,0x000f867189d3cb5b,0x000f8bb1b4f8fbbd,0x000f9079062292b8,
           0x000f94d70ca8d43a,0x000f98d8c7dcaa99,0x000f9c8928abe083,0x000f9ff175b734a6,
           0x000fa319996bc47d,0x000fa6085f8e9d07,0x000fa8c3a62e1991,0x000fab5084e1f660,
           0x000fadb36c84cccb,0x000faff041086846,0x000fb20a6ea22bb9,0x000fb404fb42cb3c,
           0x000fb5e295158173,0x000fb7a59e99727a,0x000fb95038c8789d,0x000fbae44ba684eb,
           0x000fbc638d822e60,0x000fbdcf89209ffa,0x000fbf29a303cfc5,0x000fc0731df1089c,
           0x000fc1ad1ed6c8b1,0x000fc2d8b02b5c89,0x000fc3f6c4d92131,0x000fc5083ac9ba7d,
           0x000fc60ddd1e9cd6,0x000fc7086622e825,0x000fc7f881009f0b,0x000fc8decb41ac70,
           0x000fc9bbd623d7ec,0x000fca9027c5b26d,0x000fcb5c3c319c49,0x000fcc20864b4449,
           0x000fccdd70a35d40,0x000fcd935e34bf80,0x000fce42ab0db8bd,0x000fceebace7ec01,
           0x000fcf8eb3b0d0e7,0x000fd02c0a049b60,0x000fd0c3f59d199c,0x000fd156b7b5e27e,
           0x000fd1e48d670341,0x000fd26daff73551,0x000fd2f2552684be,0x000fd372af7233c1,
           0x000fd3eeee528f62,0x000fd4673e73543a,0x000fd4dbc9e72ff7,0x000fd54cb856dc2c,
           0x000fd5ba2f2c4119,0x000fd62451ba02c2,0x000fd68b415fcff4,0x000fd6ef1dabc160,
           0x000fd75004790eb6,0x000fd7ae120c583f,0x000fd809612dbd09,0x000fd8620b40effa,
           0x000fd8b8285b78fd,0x000fd90bcf594b1d,0x000fd95d15efd425,0x000fd9ac10bfa70c,
           0x000fd9f8d364df06,0x000fda437086566b,0x000fda8bf9e3c9fe,0x000fdad28062fed5,
           0x000fdb17141bff2c,0x000fdb59c4648085,0x000fdb9a9fda83cc,0x000fdbd9b46e3ed4,
           0x000fdc170f6b5d04,0x000fdc52bd81a3fb,0x000fdc8ccacd07ba,0x000fdcc542dd3902,
           0x000fdcfc30bcb793,0x000fdd319ef77143,0x000fdd6597a0f60b,0x000fdd98245a48a2,
           0x000fddc94e575271,0x000fddf91e64014f,0x000fde279ce914ca,0x000fde54d1f0a06a,
           0x000fde80c52a47cf,0x000fdeab7def394e,0x000fded50345eb35,0x000fdefd5be59fa0,
           0x000fdf248e39b26f,0x000fdf4aa064b4af,0x000fdf6f98435894,0x000fdf937b6f30ba,
           0x000fdfb64f414571,0x000fdfd818d48262,0x000fdff8dd07fed8,0x000fe018a08122c4,
           0x000fe03767adaa59,0x000fe05536c58a13,0x000fe07211ccb4c5,0x000fe08dfc94c532,
           0x000fe0a8fabe8ca1,0x000fe0c30fbb87a5,0x000fe0dc3ecf3a5a,0x000fe0f48b107521,
           0x000fe10bf76a82ef,0x000fe122869e41ff,0x000fe1383b4327e1,0x000fe14d17c83187,
           0x000fe1611e74c023,0x000fe1745169635a,0x000fe186b2a09176,0x000fe19843ef4e07,
           0x000fe1a90705bf63,0x000fe1b8fd6fb37c,0x000fe1c828951443,0x000fe1d689ba4bfd,
           0x000fe1e4220099a4,0x000fe1f0f26655a0,0x000fe1fcfbc726d4,0x000fe2083edc2830,
           0x000fe212bc3bfeb4,0x000fe21c745adfe3,0x000fe225678a8895,0x000fe22d95fa23f4,
           0x000fe234ffb62282,0x000fe23ba4a800d9,0x000fe2418495fddc,0x000fe2469f22bffb,
           0x000fe24af3cce90d,0x000fe24e81ee9858,0x000fe25148bcda19,0x000fe253474703fe,
           0x000fe2547c75fdc6,0x000fe254e70b754f,0x000fe25485a0fd1a,0x000fe25356a71450,
           0x000fe2515864173a,0x000fe24e88f316f1,0x000fe24ae64296fa,0x000fe2466e132f60,
           0x000fe2411df611bd,0x000fe23af34b6f73,0x000fe233eb40bf41,0x000fe22c02cee01b,
           0x000fe22336b81710,0x000fe2198385e5cc,0x000fe20ee586b707,0x000fe20358cb5dfb,
           0x000fe1f6d92465b1,0x000fe1e9621f2c9e,0x000fe1daef02c8da,0x000fe1cb7accb0a6,
           0x000fe1bb002d22c9,0x000fe1a9798349b8,0x000fe196e0d9140c,0x000fe1832fdebc44,
           0x000fe16e5fe5f931,0x000fe15869dccfcf,0x000fe1414647fe78,0x000fe128ed3cf8b2,
           0x000fe10f565b69cf,0x000fe0f478c633ab,0x000fe0d84b1bdd9e,0x000fe0bac36e6688,
           0x000fe09bd73a6b5b,0x000fe07b7b5d920a,0x000fe059a40c26d2,0x000fe03644c5d7f8,
           0x000fe011504979b2,0x000fdfeab887b95c,0x000fdfc26e94a447,0x000fdf986297e305,
           0x000fdf6c83bb8663,0x000fdf3ec0193eed,0x000fdf0f04a5d30a,0x000fdedd3d1aa204,
           0x000fdea953dcfc13,0x000fde7331e3100d,0x000fde3abe9626f2,0x000fddffdfb1dbd5,
           0x000fddc2791ff351,0x000fdd826cd068c6,0x000fdd3f9a8d3856,0x000fdcf9dfc95b0c,
           0x000fdcb1176a55fe,0x000fdc65198ba50b,0x000fdc15bb3b2daa,0x000fdbc2ce2dc4ae,
           0x000fdb6c206aaaca,0x000fdb117becb4a1,0x000fdab2a6379bf0,0x000fda4f5fdfb4e9,
           0x000fd9e76401f3a3,0x000fd97a67a9ce1f,0x000fd90819221429,0x000fd8901f2d4b02,
           0x000fd812182170e1,0x000fd78d98e23cd3,0x000fd7022bb3f082,0x000fd66f4edf96b9,
           0x000fd5d473200305,0x000fd530f9ccff94,0x000fd48432b7b351,0x000fd3cd59a8469e,
           0x000fd30b9368f90a,0x000fd23dea45f500,0x000fd16349e2e04a,0x000fd07a7a3ef98a,
           0x000fcf8219b5df05,0x000fce7895bcfcde,0x000fcd5c220ad5e2,0x000fcc2aadbc17dc,
           0x000fcae1d5e81fbc,0x000fc97ed4e778f9,0x000fc7fe6d4d720e,0x000fc65ccf39c2fc,
           0x000fc4957623cb03,0x000fc2a2fc826dc7,0x000fc07ee19b01cd,0x000fbe213c1cf493,
           0x000fbb8051ac1566,0x000fb890078d120e,0x000fb5411a5b9a95,0x000fb18000547133,
           0x000fad334827f1e2,0x000fa839276708b9,0x000fa263b32e37ed,0x000f9b72d1c52cd1,
           0x000f930a1a281a05,0x000f889f023d820a,0x000f7b577d2be5f3,0x000f69c650c40a8f,
           0x000f51530f0916d8,0x000f2cb0e3c5933e,0x000eeefb15d605d8,0x000e6da6ecf27460]

const we =
    [1.9311480126418366e-15,1.4178028487910829e-17,2.3278824993382448e-17,
     3.0487830247064320e-17,3.6665697714474878e-17,4.2179302189289733e-17,
     4.7222561556862764e-17,5.1911915446217879e-17,5.6323471083955047e-17,
     6.0510082606427647e-17,6.4510165096727506e-17,6.8352646803700541e-17,
     7.2059939574689050e-17,7.5649815537392981e-17,7.9136643961951065e-17,
     8.2532235563518929e-17,8.5846436168850513e-17,8.9087554865647428e-17,
     9.2262679629663719e-17,9.5377914505292719e-17,9.8438560874559257e-17,
     1.0144925809006294e-16,1.0441409405585343e-16,1.0733669323436384e-16,
     1.1022028745670189e-16,1.1306777346479334e-16,1.1588176009705533e-16,
     1.1866460730417886e-16,1.2141845865694359e-16,1.2414526862326387e-16,
     1.2684682560606153e-16,1.2952477151912284e-16,1.3218061851538810e-16,
     1.3481576335745444e-16,1.3743149982367625e-16,1.4002902946807859e-16,
     1.4260947099321287e-16,1.4517386844829297e-16,1.4772319842763584e-16,
     1.5025837641447456e-16,1.5278026239101652e-16,1.5528966581595696e-16,
     1.5778735005459581e-16,1.6027403633350909e-16,1.6275040728083524e-16,
     1.6521711010420076e-16,1.6767475945078279e-16,1.7012393998770646e-16,
     1.7256520873568226e-16,1.7499909718432365e-16,1.7742611321380505e-16,
     1.7984674284430714e-16,1.8226145183195818e-16,1.8467068712763576e-16,
     1.8707487821298258e-16,1.8947443832625899e-16,1.9186976558915995e-16,
     1.9426124404443042e-16,1.9664924461299023e-16,1.9903412597830144e-16,
     2.0141623540485899e-16,2.0379590949693882e-16,2.0617347490308439e-16,
     2.0854924897123771e-16,2.1092354035891528e-16,2.1329664960238294e-16,
     2.1566886964838970e-16,2.1804048635167009e-16,2.2041177894111562e-16,
     2.2278302045723950e-16,2.2515447816331350e-16,2.2752641393233694e-16,
     2.2989908461180186e-16,2.3227274236804366e-16,2.3464763501180916e-16,
     2.3702400630653389e-16,2.3940209626069303e-16,2.4178214140547710e-16,
     2.4416437505894123e-16,2.4654902757768304e-16,2.4893632659702250e-16,
     2.5132649726057970e-16,2.5371976244007951e-16,2.5611634294614988e-16,
     2.5851645773082391e-16,2.6092032408240577e-16,2.6332815781331452e-16,
     2.6574017344147618e-16,2.6815658436579989e-16,2.7057760303623509e-16,
     2.7300344111887955e-16,2.7543430965657619e-16,2.7787041922541278e-16,
     2.8031198008751431e-16,2.8275920234049704e-16,2.8521229606393309e-16,
     2.8767147146315804e-16,2.9013693901073754e-16,2.9260890958589514e-16,
     2.9508759461219033e-16,2.9757320619372521e-16,3.0006595725014739e-16,
     3.0256606165070789e-16,3.0507373434762511e-16,3.0758919150899939e-16,
     3.1011265065151543e-16,3.1264433077316750e-16,3.1518445248623523e-16,
     3.1773323815073683e-16,3.2029091200858335e-16,3.2285770031865573e-16,
     3.2543383149302610e-16,3.2801953623454359e-16,3.3061504767600738e-16,
     3.3322060152114841e-16,3.3583643618764577e-16,3.3846279295240445e-16,
     3.4109991609932597e-16,3.4374805306980633e-16,3.4640745461620167e-16,
     3.4907837495850680e-16,3.5176107194449828e-16,3.5445580721360130e-16,
     3.5716284636474652e-16,3.5988245912849274e-16,3.6261491954370031e-16,
     3.6536050613905045e-16,3.6811950211971757e-16,3.7089219555951389e-16,
     3.7367887959883854e-16,3.7647985264877841e-16,3.7929541860172334e-16,
     3.8212588704887531e-16,3.8497157350504876e-16,3.8783279964117988e-16,
     3.9070989352498183e-16,3.9360318987020748e-16,3.9651303029500381e-16,
     3.9943976358986842e-16,4.0238374599574693e-16,4.0534534149283966e-16,
     4.0832492210071775e-16,4.1132286819038357e-16,4.1433956880894741e-16,
     4.1737542201763194e-16,4.2043083524385856e-16,4.2350622564821518e-16,
     4.2660202050715582e-16,4.2971865761233266e-16,4.3285658568752094e-16,
     4.3601626482415681e-16,4.3919816693657415e-16,4.4240277623809919e-16,
     4.4563058973923611e-16,4.4888211776926172e-16,4.5215788452263475e-16,
     4.5545842863172421e-16,4.5878430376746227e-16,4.6213607926964266e-16,
     4.6551434080870692e-16,4.6891969108099157e-16,4.7235275053955480e-16,
     4.7581415816285534e-16,4.7930457226372470e-16,4.8282467134125866e-16,
     4.8637515497845119e-16,4.8995674478861404e-16,4.9357018541385775e-16,
     4.9721624557917034e-16,5.0089571920591141e-16,5.0460942658884340e-16,
     5.0835821564116245e-16,5.1214296321235415e-16,5.1596457648410618e-16,
     5.1982399444994938e-16,5.2372218948478484e-16,5.2766016901098856e-16,
     5.3163897726836902e-16,5.3565969719590503e-16,5.3972345243389779e-16,
     5.4383140945596370e-16,5.4798477984116296e-16,5.5218482269752343e-16,
     5.5643284724928722e-16,5.6073021560139669e-16,5.6507834569605064e-16,
     5.6947871447763482e-16,5.7393286128396354e-16,5.7844239148359912e-16,
     5.8300898038105864e-16,5.8763437741400573e-16,5.9232041066909314e-16,
     5.9706899174600906e-16,6.0188212100252363e-16,6.0676189321700068e-16,
     6.1171050370897217e-16,6.1673025496306200e-16,6.2182356380685327e-16,
     6.2699296919933262e-16,6.3224114069342115e-16,6.3757088764394262e-16,
     6.4298516924135947e-16,6.4848710546189033e-16,6.5407998903644809e-16,
     6.5976729855445663e-16,6.6555271283433428e-16,6.7144012671064882e-16,
     6.7743366840910103e-16,6.8353771870512740e-16,6.8975693209068478e-16,
     6.9609626020748846e-16,7.0256097784459588e-16,7.0915671184495837e-16,
     7.1588947332085531e-16,7.2276569364381212e-16,7.2979226475290851e-16,
     7.3697658441912426e-16,7.4432660721604146e-16,7.5185090208325131e-16,
     7.5955871753377488e-16,7.6746005575784274e-16,7.7556575712157906e-16,
     7.8388759686228577e-16,7.9243839615735500e-16,8.0123215021130834e-16,
     8.1028417659131464e-16,8.1961128778061250e-16,8.2923199285818092e-16,
     8.3916673441467979e-16,8.4943816836487701e-16,8.6007149633349414e-16,
     8.7109486293879040e-16,8.8253983380721398e-16,8.9444197485198646e-16,
     9.0684155971316690e-16,9.1978444098118649e-16,9.3332313294229516e-16,
     9.4751817065249841e-16,9.6243983456584759e-16,9.7817036547844198e-16,
     9.9480684723838795e-16,1.0124650144288319e-15,1.0312843657756166e-15,
     1.0514351604044550e-15,1.0731281954224043e-15,1.0966288068517408e-15,
     1.1222774909350319e-15,1.1505212963006663e-15,1.1819635283304206e-15,
     1.2174462832361815e-15,1.2581958069755114e-15,1.3060984107128082e-15,
     1.3642786158057857e-15,1.4384889932178723e-15,1.5412190700064194e-15,
     1.7091034077168055e-15]
const fe =
    [1.0000000000000000e+00,9.3814368086217470e-01,9.0046992992574648e-01,
     8.7170433238120359e-01,8.4778550062398961e-01,8.2699329664305032e-01,
     8.0842165152300838e-01,7.9152763697249562e-01,7.7595685204011555e-01,
     7.6146338884989628e-01,7.4786862198519510e-01,7.3503809243142348e-01,
     7.2286765959357202e-01,7.1127476080507601e-01,7.0019265508278816e-01,
     6.8956649611707799e-01,6.7935057226476536e-01,6.6950631673192473e-01,
     6.6000084107899970e-01,6.5080583341457110e-01,6.4189671642726609e-01,
     6.3325199421436607e-01,6.2485273870366598e-01,6.1668218091520766e-01,
     6.0872538207962201e-01,6.0096896636523223e-01,5.9340090169173343e-01,
     5.8601031847726803e-01,5.7878735860284503e-01,5.7172304866482582e-01,
     5.6480919291240017e-01,5.5803828226258745e-01,5.5140341654064129e-01,
     5.4489823767243961e-01,5.3851687200286191e-01,5.3225388026304332e-01,
     5.2610421398361973e-01,5.2006317736823360e-01,5.1412639381474856e-01,
     5.0828977641064288e-01,5.0254950184134772e-01,4.9690198724154955e-01,
     4.9134386959403253e-01,4.8587198734188491e-01,4.8048336393045421e-01,
     4.7517519303737737e-01,4.6994482528395998e-01,4.6478975625042618e-01,
     4.5970761564213769e-01,4.5469615747461550e-01,4.4975325116275500e-01,
     4.4487687341454851e-01,4.4006510084235390e-01,4.3531610321563657e-01,
     4.3062813728845883e-01,4.2599954114303434e-01,4.2142872899761658e-01,
     4.1691418643300288e-01,4.1245446599716118e-01,4.0804818315203240e-01,
     4.0369401253053028e-01,3.9939068447523107e-01,3.9513698183329016e-01,
     3.9093173698479711e-01,3.8677382908413765e-01,3.8266218149600983e-01,
     3.7859575940958079e-01,3.7457356761590216e-01,3.7059464843514600e-01,
     3.6665807978151416e-01,3.6276297335481777e-01,3.5890847294874978e-01,
     3.5509375286678746e-01,3.5131801643748334e-01,3.4758049462163698e-01,
     3.4388044470450241e-01,3.4021714906678002e-01,3.3658991402867761e-01,
     3.3299806876180899e-01,3.2944096426413633e-01,3.2591797239355619e-01,
     3.2242848495608917e-01,3.1897191284495724e-01,3.1554768522712895e-01,
     3.1215524877417955e-01,3.0879406693456019e-01,3.0546361924459026e-01,
     3.0216340067569353e-01,2.9889292101558179e-01,2.9565170428126120e-01,
     2.9243928816189257e-01,2.8925522348967775e-01,2.8609907373707683e-01,
     2.8297041453878075e-01,2.7986883323697292e-01,2.7679392844851736e-01,
     2.7374530965280297e-01,2.7072259679906002e-01,2.6772541993204479e-01,
     2.6475341883506220e-01,2.6180624268936298e-01,2.5888354974901623e-01,
     2.5598500703041538e-01,2.5311029001562946e-01,2.5025908236886230e-01,
     2.4743107566532763e-01,2.4462596913189211e-01,2.4184346939887721e-01,
     2.3908329026244918e-01,2.3634515245705964e-01,2.3362878343743335e-01,
     2.3093391716962741e-01,2.2826029393071670e-01,2.2560766011668407e-01,
     2.2297576805812019e-01,2.2036437584335949e-01,2.1777324714870053e-01,
     2.1520215107537868e-01,2.1265086199297828e-01,2.1011915938898826e-01,
     2.0760682772422204e-01,2.0511365629383771e-01,2.0263943909370902e-01,
     2.0018397469191127e-01,1.9774706610509887e-01,1.9532852067956322e-01,
     1.9292814997677135e-01,1.9054576966319539e-01,1.8818119940425432e-01,
     1.8583426276219711e-01,1.8350478709776746e-01,1.8119260347549629e-01,
     1.7889754657247831e-01,1.7661945459049488e-01,1.7435816917135349e-01,
     1.7211353531532006e-01,1.6988540130252766e-01,1.6767361861725019e-01,
     1.6547804187493600e-01,1.6329852875190182e-01,1.6113493991759203e-01,
     1.5898713896931421e-01,1.5685499236936523e-01,1.5473836938446808e-01,
     1.5263714202744286e-01,1.5055118500103989e-01,1.4848037564386679e-01,
     1.4642459387834494e-01,1.4438372216063478e-01,1.4235764543247220e-01,
     1.4034625107486245e-01,1.3834942886358020e-01,1.3636707092642886e-01,
     1.3439907170221363e-01,1.3244532790138752e-01,1.3050573846833077e-01,
     1.2858020454522817e-01,1.2666862943751067e-01,1.2477091858083096e-01,
     1.2288697950954514e-01,1.2101672182667483e-01,1.1916005717532768e-01,
     1.1731689921155557e-01,1.1548716357863353e-01,1.1367076788274431e-01,
     1.1186763167005630e-01,1.1007767640518538e-01,1.0830082545103380e-01,
     1.0653700405000166e-01,1.0478613930657017e-01,1.0304816017125772e-01,
     1.0132299742595363e-01,9.9610583670637132e-02,9.7910853311492199e-02,
     9.6223742550432798e-02,9.4549189376055859e-02,9.2887133556043541e-02,
     9.1237516631040155e-02,8.9600281910032858e-02,8.7975374467270218e-02,
     8.6362741140756913e-02,8.4762330532368119e-02,8.3174093009632383e-02,
     8.1597980709237419e-02,8.0033947542319905e-02,7.8481949201606421e-02,
     7.6941943170480503e-02,7.5413888734058410e-02,7.3897746992364746e-02,
     7.2393480875708738e-02,7.0901055162371829e-02,6.9420436498728755e-02,
     6.7951593421936601e-02,6.6494496385339774e-02,6.5049117786753749e-02,
     6.3615431999807334e-02,6.2193415408540995e-02,6.0783046445479633e-02,
     5.9384305633420266e-02,5.7997175631200659e-02,5.6621641283742877e-02,
     5.5257689676697037e-02,5.3905310196046087e-02,5.2564494593071692e-02,
     5.1235237055126281e-02,4.9917534282706372e-02,4.8611385573379497e-02,
     4.7316792913181548e-02,4.6033761076175170e-02,4.4762297732943282e-02,
     4.3502413568888183e-02,4.2254122413316234e-02,4.1017441380414819e-02,
     3.9792391023374125e-02,3.8578995503074857e-02,3.7377282772959361e-02,
     3.6187284781931423e-02,3.5009037697397410e-02,3.3842582150874330e-02,
     3.2687963508959535e-02,3.1545232172893609e-02,3.0414443910466604e-02,
     2.9295660224637393e-02,2.8188948763978636e-02,2.7094383780955800e-02,
     2.6012046645134217e-02,2.4942026419731783e-02,2.3884420511558171e-02,
     2.2839335406385240e-02,2.1806887504283581e-02,2.0787204072578117e-02,
     1.9780424338009743e-02,1.8786700744696030e-02,1.7806200410911362e-02,
     1.6839106826039948e-02,1.5885621839973163e-02,1.4945968011691148e-02,
     1.4020391403181938e-02,1.3109164931254991e-02,1.2212592426255381e-02,
     1.1331013597834597e-02,1.0464810181029979e-02,9.6144136425022099e-03,
     8.7803149858089753e-03,7.9630774380170400e-03,7.1633531836349839e-03,
     6.3819059373191791e-03,5.6196422072054830e-03,4.8776559835423923e-03,
     4.1572951208337953e-03,3.4602647778369040e-03,2.7887987935740761e-03,
     2.1459677437189063e-03,1.5362997803015724e-03,9.6726928232717454e-04,
     4.5413435384149677e-04]

## Constants

const ziggurat_nor_r      = 3.6541528853610087963519472518
const ziggurat_nor_inv_r  = inv(ziggurat_nor_r)
const ziggurat_exp_r      = 7.6971174701310497140446280481
n   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Random/src/misc.jl['      # This file is a part of Julia. License is MIT: https://julialang.org/license

## rand!(::BitArray) && bitrand

function rand!(rng::AbstractRNG, B::BitArray, ::SamplerType{Bool})
    isempty(B) && return B
    Bc = B.chunks
    rand!(rng, Bc)
    Bc[end] &= Base._msk_end(B)
    return B
end

"""
    bitrand([rng=default_rng()], [dims...])

Generate a `BitArray` of random boolean values.

# Examples
```jldoctest
julia> rng = MersenneTwister(1234);

julia> bitrand(rng, 10)
10-element BitVector:
 0
 0
 0
 0
 1
 0
 0
 0
 1
 1
```
"""
bitrand(r::AbstractRNG, dims::Dims)   = rand!(r, BitArray(undef, dims))
bitrand(r::AbstractRNG, dims::Integer...) = rand!(r, BitArray(undef, convert(Dims, dims)))

bitrand(dims::Dims)   = rand!(BitArray(undef, dims))
bitrand(dims::Integer...) = rand!(BitArray(undef, convert(Dims, dims)))


## randstring (often useful for temporary filenames/dirnames)

"""
    randstring([rng=default_rng()], [chars], [len=8])

Create a random string of length `len`, consisting of characters from
`chars`, which defaults to the set of upper- and lower-case letters
and the digits 0-9. The optional `rng` argument specifies a random
number generator, see [Random Numbers](@ref).

# Examples
```jldoctest
julia> Random.seed!(3); randstring()
"Lxz5hUwn"

julia> randstring(MersenneTwister(3), 'a':'z', 6)
"ocucay"

julia> randstring("ACGT")
"TGCTCCTC"
```

!!! note
    `chars` can be any collection of characters, of type `Char` or
    `UInt8` (more efficient), provided [`rand`](@ref) can randomly
    pick characters from it.
"""
function randstring end

let b = UInt8['0':'9';'A':'Z';'a':'z']
    global randstring

    function randstring(r::AbstractRNG, chars=b, n::Integer=8)
        T = eltype(chars)
        if T === UInt8
            str = Base._string_n(n)
            GC.@preserve str rand!(r, UnsafeView(pointer(str), n), chars)
            return str
        else
            v = Vector{T}(undef, n)
            rand!(r, v, chars)
            return String(v)
        end
    end

    randstring(r::AbstractRNG, n::Integer) = randstring(r, b, n)
    randstring(chars=b, n::Integer=8) = randstring(default_rng(), chars, n)
    randstring(n::Integer) = randstring(default_rng(), b, n)
end


## randsubseq & randsubseq!

# Fill S (resized as needed) with a random subsequence of A, where
# each element of A is included in S with independent probability p.
# (Note that this is different from the problem of finding a random
#  size-m subset of A where m is fixed!)
function randsubseq!(r::AbstractRNG, S::AbstractArray, A::AbstractArray, p::Real)
    require_one_based_indexing(S, A)
    0 <= p <= 1 || throw(ArgumentError("probability $p not in [0,1]"))
    n = length(A)
    p == 1 && return copyto!(resize!(S, n), A)
    empty!(S)
    p == 0 && return S
    nexpected = p * length(A)
    sizehint!(S, round(Int,nexpected + 5*sqrt(nexpected)))
    if p > 0.15 # empirical threshold for trivial O(n) algorithm to be better
        for i = 1:n
            rand(r) <= p && push!(S, A[i])
        end
    else
        # Skip through A, in order, from each element i to the next element i+s
        # included in S. The probability that the next included element is
        # s==k (k > 0) is (1-p)^(k-1) * p, and hence the probability (CDF) that
        # s is in {1,...,k} is 1-(1-p)^k = F(k).   Thus, we can draw the skip s
        # from this probability distribution via the discrete inverse-transform
        # method: s = ceil(F^{-1}(u)) where u = rand(), which is simply
        # s = ceil(log(rand()) / log1p(-p)).
        # -log(rand()) is an exponential variate, so can use randexp().
        L = -1 / log1p(-p) # L > 0
        i = 0
        while true
            s = randexp(r) * L
            s >= n - i && return S # compare before ceil to avoid overflow
            push!(S, A[i += ceil(Int,s)])
        end
        # [This algorithm is similar in spirit to, but much simpler than,
        #  the one by Vitter for a related problem in "Faster methods for
        #  random sampling," Comm. ACM Magazine 7, 703-718 (1984).]
    end
    return S
end

"""
    randsubseq!([rng=default_rng(),] S, A, p)

Like [`randsubseq`](@ref), but the results are stored in `S`
(which is resized as needed).

# Examples
```jldoctest
julia> rng = MersenneTwister(1234);

julia> S = Int64[];

julia> randsubseq!(rng, S, 1:8, 0.3)
2-element Vector{Int64}:
 7
 8

julia> S
2-element Vector{Int64}:
 7
 8
```
"""
randsubseq!(S::AbstractArray, A::AbstractArray, p::Real) = randsubseq!(default_rng(), S, A, p)

randsubseq(r::AbstractRNG, A::AbstractArray{T}, p::Real) where {T} =
    randsubseq!(r, T[], A, p)

"""
    randsubseq([rng=default_rng(),] A, p) -> Vector

Return a vector consisting of a random subsequence of the given array `A`, where each
element of `A` is included (in order) with independent probability `p`. (Complexity is
linear in `p*length(A)`, so this function is efficient even if `p` is small and `A` is
large.) Technically, this process is known as "Bernoulli sampling" of `A`.

# Examples
```jldoctest
julia> rng = MersenneTwister(1234);

julia> randsubseq(rng, 1:8, 0.3)
2-element Vector{Int64}:
 7
 8
```
"""
randsubseq(A::AbstractArray, p::Real) = randsubseq(default_rng(), A, p)


## rand Less Than Masked 52 bits (helper function)

"Return a sampler generating a random `Int` (masked with `mask`) in ``[0, n)``, when `n <= 2^52`."
ltm52(n::Int, mask::Int=nextpow(2, n)-1) = LessThan(n-1, Masked(mask, UInt52Raw(Int)))

## shuffle & shuffle!

"""
    shuffle!([rng=default_rng(),] v::AbstractArray)

In-place version of [`shuffle`](@ref): randomly permute `v` in-place,
optionally supplying the random-number generator `rng`.

# Examples
```jldoctest
julia> rng = MersenneTwister(1234);

julia> shuffle!(rng, Vector(1:16))
16-element Vector{Int64}:
  2
 15
  5
 14
  1
  9
 10
  6
 11
  3
 16
  7
  4
 12
  8
 13
```
"""
function shuffle!(r::AbstractRNG, a::AbstractArray)
    require_one_based_indexing(a)
    n = length(a)
    n <= 1 && return a # nextpow below won't work with n == 0
    @assert n <= Int64(2)^52
    mask = nextpow(2, n) - 1
    for i = n:-1:2
        (mask >> 1) == i && (mask >>= 1)
        j = 1 + rand(r, ltm52(i, mask))
        a[i], a[j] = a[j], a[i]
    end
    return a
end

shuffle!(a::AbstractArray) = shuffle!(default_rng(), a)

"""
    shuffle([rng=default_rng(),] v::AbstractArray)

Return a randomly permuted copy of `v`. The optional `rng` argument specifies a random
number generator (see [Random Numbers](@ref)).
To permute `v` in-place, see [`shuffle!`](@ref). To obtain randomly permuted
indices, see [`randperm`](@ref).

# Examples
```jldoctest
julia> rng = MersenneTwister(1234);

julia> shuffle(rng, Vector(1:10))
10-element Vector{Int64}:
  6
  1
 10
  2
  3
  9
  5
  7
  4
  8
```
"""
shuffle(r::AbstractRNG, a::AbstractArray) = shuffle!(r, copymutable(a))
shuffle(a::AbstractArray) = shuffle(default_rng(), a)

shuffle(r::AbstractRNG, a::Base.OneTo) = randperm(r, last(a))

## randperm & randperm!

"""
    randperm([rng=default_rng(),] n::Integer)

Construct a random permutation of length `n`. The optional `rng`
argument specifies a random number generator (see [Random
Numbers](@ref)). The element type of the result is the same as the type
of `n`.

To randomly permute an arbitrary vector, see [`shuffle`](@ref) or
[`shuffle!`](@ref).

!!! compat "Julia 1.1"
    In Julia 1.1 `randperm` returns a vector `v` with `eltype(v) == typeof(n)`
    while in Julia 1.0 `eltype(v) == Int`.

# Examples
```jldoctest
julia> randperm(MersenneTwister(1234), 4)
4-element Vector{Int64}:
 2
 1
 4
 3
```
"""
randperm(r::AbstractRNG, n::T) where {T <: Integer} = randperm!(r, Vector{T}(undef, n))
randperm(n::Integer) = randperm(default_rng(), n)

"""
    randperm!([rng=default_rng(),] A::Array{<:Integer})

Construct in `A` a random permutation of length `length(A)`. The
optional `rng` argument specifies a random number generator (see
[Random Numbers](@ref)). To randomly permute an arbitrary vector, see
[`shuffle`](@ref) or [`shuffle!`](@ref).

# Examples
```jldoctest
julia> randperm!(MersenneTwister(1234), Vector{Int}(undef, 4))
4-element Vector{Int64}:
 2
 1
 4
 3
```
"""
function randperm!(r::AbstractRNG, a::Array{<:Integer})
    n = length(a)
    @assert n <= Int64(2)^52
    n == 0 && return a
    a[1] = 1
    mask = 3
    @inbounds for i = 2:n
        j = 1 + rand(r, ltm52(i, mask))
        if i != j # a[i] is undef (and could be #undef)
            a[i] = a[j]
        end
        a[j] = i
        i == 1+mask && (mask = 2mask + 1)
    end
    return a
end

randperm!(a::Array{<:Integer}) = randperm!(default_rng(), a)


## randcycle & randcycle!

"""
    randcycle([rng=default_rng(),] n::Integer)

Construct a random cyclic permutation of length `n`. The optional `rng`
argument specifies a random number generator, see [Random Numbers](@ref).
The element type of the result is the same as the type of `n`.

!!! compat "Julia 1.1"
    In Julia 1.1 `randcycle` returns a vector `v` with `eltype(v) == typeof(n)`
    while in Julia 1.0 `eltype(v) == Int`.

# Examples
```jldoctest
julia> randcycle(MersenneTwister(1234), 6)
6-element Vector{Int64}:
 3
 5
 4
 6
 1
 2
```
"""
randcycle(r::AbstractRNG, n::T) where {T <: Integer} = randcycle!(r, Vector{T}(undef, n))
randcycle(n::Integer) = randcycle(default_rng(), n)

"""
    randcycle!([rng=default_rng(),] A::Array{<:Integer})

Construct in `A` a random cyclic permutation of length `length(A)`.
The optional `rng` argument specifies a random number generator, see
[Random Numbers](@ref).

# Examples
```jldoctest
julia> randcycle!(MersenneTwister(1234), Vector{Int}(undef, 6))
6-element Vector{Int64}:
 3
 5
 4
 6
 1
 2
```
"""
function randcycle!(r::AbstractRNG, a::Array{<:Integer})
    n = length(a)
    n == 0 && return a
    @assert n <= Int64(2)^52
    a[1] = 1
    mask = 3
    @inbounds for i = 2:n
        j = 1 + rand(r, ltm52(i-1, mask))
        a[i] = a[j]
        a[j] = i
        i == 1+mask && (mask = 2mask + 1)
    end
    return a
end

randcycle!(a::Array{<:Integer}) = randcycle!(default_rng(), a)
u   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Random/src/XoshiroSimd.jlz+      # This file is a part of Julia. License is MIT: https://julialang.org/license

module XoshiroSimd
# Getting the xoroshiro RNG to reliably vectorize is somewhat of a hassle without Simd.jl.
import ..Random: TaskLocalRNG, rand, rand!, Xoshiro, CloseOpen01, UnsafeView,
                 SamplerType, SamplerTrivial
using Base: BitInteger_types
using Base.Libc: memcpy
using Core.Intrinsics: llvmcall

# Vector-width. Influences random stream.
xoshiroWidth() = Val(8)
# Simd threshold. Influences random stream.
simdThreshold(::Type{T}) where T = 64
simdThreshold(::Type{Bool}) = 640

@inline _rotl45(x::UInt64) = (x<<45)|(x>>19)
@inline _shl17(x::UInt64) = x<<17
@inline _rotl23(x::UInt64) = (x<<23)|(x>>41)
@inline _plus(x::UInt64,y::UInt64) = x+y
@inline _xor(x::UInt64,y::UInt64) = xor(x,y)
@inline _and(x::UInt64, y::UInt64) = x & y
@inline _or(x::UInt64, y::UInt64) = x | y
@inline _lshr(x, y::Int32) = _lshr(x, y % Int64)
@inline _lshr(x::UInt64, y::Int64) = llvmcall("""
    %res = lshr i64 %0, %1
    ret i64 %res
    """,
    UInt64,
    Tuple{UInt64, Int64},
    x, y)

@inline _bits2float(x::UInt64, ::Type{Float64}) = reinterpret(UInt64, Float64(x >>> 11) * 0x1.0p-53)
@inline function _bits2float(x::UInt64, ::Type{Float32})
    #=
    # this implementation uses more high bits, but is harder to vectorize
    x = x >>> 16  # discard low 16 bits
    u = Float32(x >>> 24) * Float32(0x1.0p-24)
    l = Float32(x & 0x00ffffff) * Float32(0x1.0p-24)
    =#
    ui = (x>>>32) % UInt32
    li = x % UInt32
    u = Float32(ui >>> 8) * Float32(0x1.0p-24)
    l = Float32(li >>> 8) * Float32(0x1.0p-24)
    (UInt64(reinterpret(UInt32, u)) << 32) | UInt64(reinterpret(UInt32, l))
end

# required operations. These could be written more concisely with `ntuple`, but the compiler
# sometimes refuses to properly vectorize.
for N in [4,8,16]
    let code, s, fshl = "llvm.fshl.v$(N)i64",
        VT = :(NTuple{$N, VecElement{UInt64}})

        s = ntuple(_->VecElement(UInt64(45)), N)
        @eval @inline _rotl45(x::$VT) = ccall($fshl, llvmcall, $VT, ($VT, $VT, $VT), x, x, $s)

        s = ntuple(_->VecElement(UInt64(23)), N)
        @eval @inline _rotl23(x::$VT) = ccall($fshl, llvmcall, $VT, ($VT, $VT, $VT), x, x, $s)

        code = """
        %lshiftOp = shufflevector <1 x i64> <i64 17>, <1 x i64> undef, <$N x i32> zeroinitializer
        %res = shl <$N x i64> %0, %lshiftOp
        ret <$N x i64> %res
        """
        @eval @inline _shl17(x::$VT) = llvmcall($code, $VT, Tuple{$VT}, x)

        code = """
        %res = add <$N x i64> %1, %0
        ret <$N x i64> %res
        """
        @eval @inline _plus(x::$VT, y::$VT) = llvmcall($code, $VT, Tuple{$VT, $VT}, x, y)

        code = """
        %res = xor <$N x i64> %1, %0
        ret <$N x i64> %res
        """
        @eval @inline _xor(x::$VT, y::$VT) = llvmcall($code, $VT, Tuple{$VT, $VT}, x, y)

        code = """
        %res = and <$N x i64> %1, %0
        ret <$N x i64> %res
        """
        @eval @inline _and(x::$VT, y::$VT) = llvmcall($code, $VT, Tuple{$VT, $VT}, x, y)

        code = """
        %res = or <$N x i64> %1, %0
        ret <$N x i64> %res
        """
        @eval @inline _or(x::$VT, y::$VT) = llvmcall($code, $VT, Tuple{$VT, $VT}, x, y)

        code = """
        %tmp = insertelement <1 x i64> undef, i64 %1, i32 0
        %shift = shufflevector <1 x i64> %tmp, <1 x i64> %tmp, <$N x i32> zeroinitializer
        %res = lshr <$N x i64> %0, %shift
        ret <$N x i64> %res
        """
        @eval @inline _lshr(x::$VT, y::Int64) = llvmcall($code, $VT, Tuple{$VT, Int64}, x, y)

        code = """
        %shiftamt = shufflevector <1 x i64> <i64 11>, <1 x i64> undef, <$N x i32> zeroinitializer
        %sh = lshr <$N x i64> %0, %shiftamt
        %f = uitofp <$N x i64> %sh to <$N x double>
        %scale = shufflevector <1 x double> <double 0x3ca0000000000000>, <1 x double> undef, <$N x i32> zeroinitializer
        %m = fmul <$N x double> %f, %scale
        %i = bitcast <$N x double> %m to <$N x i64>
        ret <$N x i64> %i
        """
        @eval @inline _bits2float(x::$VT, ::Type{Float64}) = llvmcall($code, $VT, Tuple{$VT}, x)

        code = """
        %as32 = bitcast <$N x i64> %0 to <$(2N) x i32>
        %shiftamt = shufflevector <1 x i32> <i32 8>, <1 x i32> undef, <$(2N) x i32> zeroinitializer
        %sh = lshr <$(2N) x i32> %as32, %shiftamt
        %f = uitofp <$(2N) x i32> %sh to <$(2N) x float>
        %scale = shufflevector <1 x float> <float 0x3e70000000000000>, <1 x float> undef, <$(2N) x i32> zeroinitializer
        %m = fmul <$(2N) x float> %f, %scale
        %i = bitcast <$(2N) x float> %m to <$N x i64>
        ret <$N x i64> %i
        """
        @eval @inline _bits2float(x::$VT, ::Type{Float32}) = llvmcall($code, $VT, Tuple{$VT}, x)
    end
end


function forkRand(rng::Union{TaskLocalRNG, Xoshiro}, ::Val{N}) where N
    # constants have nothing up their sleeve. For more discussion, cf rng_split in task.c
    # 0x02011ce34bce797f == hash(UInt(1))|0x01
    # 0x5a94851fb48a6e05 == hash(UInt(2))|0x01
    # 0x3688cf5d48899fa7 == hash(UInt(3))|0x01
    # 0x867b4bb4c42e5661 == hash(UInt(4))|0x01
    s0 = ntuple(i->VecElement(0x02011ce34bce797f * rand(rng, UInt64)), Val(N))
    s1 = ntuple(i->VecElement(0x5a94851fb48a6e05 * rand(rng, UInt64)), Val(N))
    s2 = ntuple(i->VecElement(0x3688cf5d48899fa7 * rand(rng, UInt64)), Val(N))
    s3 = ntuple(i->VecElement(0x867b4bb4c42e5661 * rand(rng, UInt64)), Val(N))
    (s0, s1, s2, s3)
end

_id(x, T) = x

@inline function xoshiro_bulk(rng::Union{TaskLocalRNG, Xoshiro}, dst::Ptr{UInt8}, len::Int, T::Union{Type{UInt8}, Type{Bool}, Type{Float32}, Type{Float64}}, ::Val{N}, f::F = _id) where {N, F}
    if len >= simdThreshold(T)
        written = xoshiro_bulk_simd(rng, dst, len, T, Val(N), f)
        len -= written
        dst += written
    end
    if len != 0
        xoshiro_bulk_nosimd(rng, dst, len, T, f)
    end
    nothing
end

@noinline function xoshiro_bulk_nosimd(rng::Union{TaskLocalRNG, Xoshiro}, dst::Ptr{UInt8}, len::Int, ::Type{T}, f::F) where {T, F}
    if rng isa TaskLocalRNG
        task = current_task()
        s0, s1, s2, s3 = task.rngState0, task.rngState1, task.rngState2, task.rngState3
    else
        (; s0, s1, s2, s3) = rng::Xoshiro
    end

    i = 0
    while i+8 <= len
        res = _plus(_rotl23(_plus(s0,s3)),s0)
        unsafe_store!(reinterpret(Ptr{UInt64}, dst + i), f(res, T))
        t = _shl17(s1)
        s2 = _xor(s2, s0)
        s3 = _xor(s3, s1)
        s1 = _xor(s1, s2)
        s0 = _xor(s0, s3)
        s2 = _xor(s2, t)
        s3 = _rotl45(s3)
        i += 8
    end
    if i < len
        res = _plus(_rotl23(_plus(s0,s3)),s0)
        t = _shl17(s1)
        s2 = _xor(s2, s0)
        s3 = _xor(s3, s1)
        s1 = _xor(s1, s2)
        s0 = _xor(s0, s3)
        s2 = _xor(s2, t)
        s3 = _rotl45(s3)
        ref = Ref(f(res, T))
        # TODO: This may make the random-stream dependent on system endianness
        GC.@preserve ref memcpy(dst+i, Base.unsafe_convert(Ptr{Cvoid}, ref), len-i)
    end
    if rng isa TaskLocalRNG
        task.rngState0, task.rngState1, task.rngState2, task.rngState3 = s0, s1, s2, s3
    else
       rng.s0, rng.s1, rng.s2, rng.s3 =  s0, s1, s2, s3
    end
    nothing
end

@noinline function xoshiro_bulk_nosimd(rng::Union{TaskLocalRNG, Xoshiro}, dst::Ptr{UInt8}, len::Int, ::Type{Bool}, f)
    if rng isa TaskLocalRNG
        task = current_task()
        s0, s1, s2, s3 = task.rngState0, task.rngState1, task.rngState2, task.rngState3
    else
        (; s0, s1, s2, s3) = rng::Xoshiro
    end

    i = 0
    while i+8 <= len
        res = _plus(_rotl23(_plus(s0,s3)),s0)
        shift = 0
        while i+8 <= len && shift < 8
            resLoc = _and(_lshr(res, shift), 0x0101010101010101)
            unsafe_store!(reinterpret(Ptr{UInt64}, dst + i), resLoc)
            i += 8
            shift += 1
        end

        t = _shl17(s1)
        s2 = _xor(s2, s0)
        s3 = _xor(s3, s1)
        s1 = _xor(s1, s2)
        s0 = _xor(s0, s3)
        s2 = _xor(s2, t)
        s3 = _rotl45(s3)
    end
    if i < len
        # we may overgenerate some bytes here, if len mod 64 <= 56 and len mod 8 != 0
        res = _plus(_rotl23(_plus(s0,s3)),s0)
        resLoc = _and(res, 0x0101010101010101)
        ref = Ref(resLoc)
        GC.@preserve ref memcpy(dst+i, Base.unsafe_convert(Ptr{Cvoid}, ref), len-i)
        t = _shl17(s1)
        s2 = _xor(s2, s0)
        s3 = _xor(s3, s1)
        s1 = _xor(s1, s2)
        s0 = _xor(s0, s3)
        s2 = _xor(s2, t)
        s3 = _rotl45(s3)
    end
    if rng isa TaskLocalRNG
        task.rngState0, task.rngState1, task.rngState2, task.rngState3 = s0, s1, s2, s3
    else
        rng.s0, rng.s1, rng.s2, rng.s3 = s0, s1, s2, s3
    end
    nothing
end


@noinline function xoshiro_bulk_simd(rng::Union{TaskLocalRNG, Xoshiro}, dst::Ptr{UInt8}, len::Int, ::Type{T}, ::Val{N}, f::F) where {T,N,F}
    s0, s1, s2, s3 = forkRand(rng, Val(N))

    i = 0
    while i + 8*N <= len
        res = _plus(_rotl23(_plus(s0,s3)),s0)
        t = _shl17(s1)
        s2 = _xor(s2, s0)
        s3 = _xor(s3, s1)
        s1 = _xor(s1, s2)
        s0 = _xor(s0, s3)
        s2 = _xor(s2, t)
        s3 = _rotl45(s3)
        unsafe_store!(reinterpret(Ptr{NTuple{N,VecElement{UInt64}}}, dst + i), f(res, T))
        i += 8*N
    end
    return i
end

@noinline function xoshiro_bulk_simd(rng::Union{TaskLocalRNG, Xoshiro}, dst::Ptr{UInt8}, len::Int, ::Type{Bool}, ::Val{N}, f) where {N}
    s0, s1, s2, s3 = forkRand(rng, Val(N))
    msk = ntuple(i->VecElement(0x0101010101010101), Val(N))
    i = 0
    while i + 64*N <= len
        res = _plus(_rotl23(_plus(s0,s3)),s0)
        t = _shl17(s1)
        s2 = _xor(s2, s0)
        s3 = _xor(s3, s1)
        s1 = _xor(s1, s2)
        s0 = _xor(s0, s3)
        s2 = _xor(s2, t)
        s3 = _rotl45(s3)
        for k=0:7
            tmp = _lshr(res, k)
            toWrite = _and(tmp, msk)
            unsafe_store!(reinterpret(Ptr{NTuple{N,VecElement{UInt64}}}, dst + i + k*N*8), toWrite)
        end
        i += 64*N
    end
    return i
end


function rand!(rng::Union{TaskLocalRNG, Xoshiro}, dst::Array{Float32}, ::SamplerTrivial{CloseOpen01{Float32}})
    GC.@preserve dst xoshiro_bulk(rng, convert(Ptr{UInt8}, pointer(dst)), length(dst)*4, Float32, xoshiroWidth(), _bits2float)
    dst
end

function rand!(rng::Union{TaskLocalRNG, Xoshiro}, dst::Array{Float64}, ::SamplerTrivial{CloseOpen01{Float64}})
    GC.@preserve dst xoshiro_bulk(rng, convert(Ptr{UInt8}, pointer(dst)), length(dst)*8, Float64, xoshiroWidth(), _bits2float)
    dst
end

for T in BitInteger_types
    @eval function rand!(rng::Union{TaskLocalRNG, Xoshiro}, dst::Union{Array{$T}, UnsafeView{$T}}, ::SamplerType{$T})
        GC.@preserve dst xoshiro_bulk(rng, convert(Ptr{UInt8}, pointer(dst)), length(dst)*sizeof($T), UInt8, xoshiroWidth())
        dst
    end
end

function rand!(rng::Union{TaskLocalRNG, Xoshiro}, dst::Array{Bool}, ::SamplerType{Bool})
    GC.@preserve dst xoshiro_bulk(rng, convert(Ptr{UInt8}, pointer(dst)), length(dst), Bool, xoshiroWidth())
    dst
end

end # module
j   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Tar/src/Tar.jl�M      module Tar

using ArgTools

const true_predicate = _ -> true

# 2 MiB to take advantage of THP if enabled
const DEFAULT_BUFFER_SIZE = 2 * 1024 * 1024

# TODO: add some version of this method to Base
!hasmethod(skip, Tuple{Union{Base.Process, Base.ProcessChain}, Integer}) &&
function Base.skip(io::Union{Base.Process, Base.ProcessChain}, n::Integer)
    n < 0 && throw(ArgumentError("cannot skip backwards when reading from a process"))
    isempty(skip_buffer) && resize!(skip_buffer, DEFAULT_BUFFER_SIZE)
    while n > 0
        n -= readbytes!(io, skip_buffer, min(n, length(skip_buffer)))
    end
    # TODO: our skip data should throw if there's not enough data
    return io
end
const skip_buffer = UInt8[]

# method for this exists in Base since Julia 1.4 but not before
!hasmethod(read!, Tuple{IO, AbstractArray}) &&
function Base.read!(s::IO, a::AbstractArray{T}) where T
    if isbitstype(T) && (a isa Array || a isa Base.FastContiguousSubArray{T,<:Any,<:Array{T}})
        GC.@preserve a unsafe_read(s, pointer(a), sizeof(a))
    else
        for i in eachindex(a)
            a[i] = read(s, T)
        end
    end
    return a
end

function can_symlink(dir::AbstractString)
    # guaranteed to be an empty directory
    link_path = joinpath(dir, "link")
    return try
        symlink("target", link_path)
        true
    catch err
        err isa Base.IOError || rethrow()
        false
    finally
        rm(link_path, force=true)
    end
end

include("header.jl")
include("create.jl")
include("extract.jl")

## official API: create, list, extract, rewrite, tree_hash

"""
    create(
        [ predicate, ] dir, [ tarball ];
        [ skeleton, ] [ portable = false ]
    ) -> tarball

        predicate :: String --> Bool
        dir       :: AbstractString
        tarball   :: Union{AbstractString, AbstractCmd, IO}
        skeleton  :: Union{AbstractString, AbstractCmd, IO}
        portable  :: Bool

Create a tar archive ("tarball") of the directory `dir`. The resulting archive
is written to the path `tarball` or if no path is specified, a temporary path is
created and returned by the function call. If `tarball` is an IO object then the
tarball content is written to that handle instead (the handle is left open).

If a `predicate` function is passed, it is called on each system path that is
encountered while recursively searching `dir` and `path` is only included in the
tarball if `predicate(path)` is true. If `predicate(path)` returns false for a
directory, then the directory is excluded entirely: nothing under that directory
will be included in the archive.

If the `skeleton` keyword is passed then the file or IO handle given is used as
a "skeleton" to generate the tarball. You create a skeleton file by passing the
`skeleton` keyword to the `extract` command. If `create` is called with that
skeleton file and the extracted files haven't changed, an identical tarball is
recreated. The `skeleton` and `predicate` arguments cannot be used together.

If the `portable` flag is true then path names are checked for validity on
Windows, which ensures that they don't contain illegal characters or have names
that are reserved. See https://stackoverflow.com/a/31976060/659248 for details.
"""
function create(
    predicate::Function,
    dir::AbstractString,
    tarball::Union{ArgWrite, Nothing} = nothing;
    skeleton::Union{ArgRead, Nothing} = nothing,
    portable::Bool = false,
)
    check_create_dir(dir)
    if skeleton === nothing
        arg_write(tarball) do tar
            create_tarball(predicate, tar, dir, portable=portable)
        end
    else
        predicate === true_predicate ||
            error("create: predicate and skeleton cannot be used together")
        check_create_skeleton(skeleton)
        arg_read(skeleton) do skeleton
            arg_write(tarball) do tar
                recreate_tarball(tar, dir, skeleton, portable=portable)
            end
        end
    end
end

function create(
    dir::AbstractString,
    tarball::Union{ArgWrite, Nothing} = nothing;
    skeleton::Union{ArgRead, Nothing} = nothing,
    portable::Bool = false,
)
    create(true_predicate, dir, tarball, skeleton=skeleton, portable=portable)
end

"""
    list(tarball; [ strict = true ]) -> Vector{Header}
    list(callback, tarball; [ strict = true ])

        callback  :: Header, [ <data> ] --> Any
        tarball   :: Union{AbstractString, AbstractCmd, IO}
        strict    :: Bool

List the contents of a tar archive ("tarball") located at the path `tarball`. If
`tarball` is an IO handle, read the tar contents from that stream. Returns a
vector of `Header` structs. See [`Header`](@ref) for details.

If a `callback` is provided then instead of returning a vector of headers, the
callback is called on each `Header`. This can be useful if the number of items
in the tarball is large or if you want examine items prior to an error in the
tarball. If the `callback` function can accept a second argument of either type
`Vector{UInt8}` or `Vector{Pair{Symbol, String}}` then it will be called with a
representation of the raw header data either as a single byte vector or as a
vector of pairs mapping field names to the raw data for that field (if these
fields are concatenated together, the result is the raw data of the header).

By default `list` will error if it encounters any tarball contents which the
`extract` function would refuse to extract. With `strict=false` it will skip
these checks and list all the the contents of the tar file whether `extract`
would extract them or not. Beware that malicious tarballs can do all sorts of
crafty and unexpected things to try to trick you into doing something bad.

If the `tarball` argument is a skeleton file (see `extract` and `create`) then
`list` will detect that from the file header and appropriately list or iterate
the headers of the skeleton file.
"""
function list(
    callback::Function,
    tarball::ArgRead;
    raw::Bool = false,
    strict::Bool = !raw,
)
    raw && strict &&
        error("`raw=true` and `strict=true` options are incompatible")
    arg_read(tarball) do tar
        iterate_headers(callback, tar, raw=raw, strict=strict)
    end
end

function list(
    tarball::ArgRead;
    raw::Bool = false,
    strict::Bool = !raw,
)
    headers = Header[]
    list(tarball, raw=raw, strict=strict) do hdr
        push!(headers, hdr)
    end
    return headers
end

"""
    extract(
        [ predicate, ] tarball, [ dir ];
        [ skeleton = <none>, ]
        [ copy_symlinks = <auto>, ]
        [ set_permissions = true, ]
    ) -> dir

        predicate       :: Header --> Bool
        tarball         :: Union{AbstractString, AbstractCmd, IO}
        dir             :: AbstractString
        skeleton        :: Union{AbstractString, AbstractCmd, IO}
        copy_symlinks   :: Bool
        set_permissions :: Bool

Extract a tar archive ("tarball") located at the path `tarball` into the
directory `dir`. If `tarball` is an IO object instead of a path, then the
archive contents will be read from that IO stream. The archive is extracted to
`dir` which must either be an existing empty directory or a non-existent path
which can be created as a new directory. If `dir` is not specified, the archive
is extracted into a temporary directory which is returned by `extract`.

If a `predicate` function is passed, it is called on each `Header` object that
is encountered while extracting `tarball` and the entry is only extracted if the
`predicate(hdr)` is true. This can be used to selectively extract only parts of
an archive, to skip entries that cause `extract` to throw an error, or to record
what is extracted during the extraction process.

Before it is passed to the predicate function, the `Header` object is somewhat
modified from the raw header in the tarball: the `path` field is normalized to
remove `.` entries and replace multiple consecutive slashes with a single slash.
If the entry has type `:hardlink`, the link target path is normalized the same
way so that it will match the path of the target entry; the size field is set to
the size of the target path (which must be an already-seen file).

If the `skeleton` keyword is passed then a "skeleton" of the extracted tarball
is written to the file or IO handle given. This skeleton file can be used to
recreate an identical tarball by passing the `skeleton` keyword to the `create`
function. The `skeleton` and `predicate` arguments cannot be used together.

If `copy_symlinks` is `true` then instead of extracting symbolic links as such,
they will be extracted as copies of what they link to if they are internal to
the tarball and if it is possible to do so. Non-internal symlinks, such as a
link to `/etc/passwd` will not be copied. Symlinks which are in any way cyclic
will also not be copied and will instead be skipped. By default, `extract` will
detect whether symlinks can be created in `dir` or not and will automatically
copy symlinks if they cannot be created.

If `set_permissions` is `false`, no permissions are set on the extracted files.
"""
function extract(
    predicate::Function,
    tarball::ArgRead,
    dir::Union{AbstractString, Nothing} = nothing;
    skeleton::Union{ArgWrite, Nothing} = nothing,
    copy_symlinks::Union{Bool, Nothing} = nothing,
    set_permissions::Bool = true,
)
    predicate === true_predicate || skeleton === nothing ||
        error("extract: predicate and skeleton cannot be used together")
    skeleton = something(skeleton, devnull)
    check_extract_tarball(tarball)
    check_extract_dir(dir)
    arg_read(tarball) do tar
        arg_mkdir(dir) do dir
            if copy_symlinks === nothing
                copy_symlinks = !can_symlink(dir)
            end
            arg_write(skeleton) do skeleton
                extract_tarball(
                    predicate, tar, dir,
                    skeleton = skeleton,
                    copy_symlinks = copy_symlinks,
                    set_permissions = set_permissions,
                )
            end
        end
    end
end

function extract(
    tarball::ArgRead,
    dir::Union{AbstractString, Nothing} = nothing;
    skeleton::Union{ArgWrite, Nothing} = nothing,
    copy_symlinks::Union{Bool, Nothing} = nothing,
    set_permissions::Bool = true,
)
    extract(
        true_predicate, tarball, dir,
        skeleton = skeleton,
        copy_symlinks = copy_symlinks,
        set_permissions = set_permissions,
    )
end

"""
    rewrite(
        [ predicate, ] old_tarball, [ new_tarball ];
        [ portable = false, ]
    ) -> new_tarball

        predicate   :: Header --> Bool
        old_tarball :: Union{AbstractString, AbtractCmd, IO}
        new_tarball :: Union{AbstractString, AbtractCmd, IO}
        portable    :: Bool

Rewrite `old_tarball` to the standard format that `create` generates, while also
checking that it doesn't contain anything that would cause `extract` to raise an
error. This is functionally equivalent to doing

    Tar.create(Tar.extract(predicate, old_tarball), new_tarball)

However, it never extracts anything to disk and instead uses the `seek` function
to navigate the old tarball's data. If no `new_tarball` argument is passed, the
new tarball is written to a temporary file whose path is returned.

If a `predicate` function is passed, it is called on each `Header` object that
is encountered while extracting `old_tarball` and the entry is skipped unless
`predicate(hdr)` is true. This can be used to selectively rewrite only parts of
an archive, to skip entries that would cause `extract` to throw an error, or to
record what content is encountered during the rewrite process.

Before it is passed to the predicate function, the `Header` object is somewhat
modified from the raw header in the tarball: the `path` field is normalized to
remove `.` entries and replace multiple consecutive slashes with a single slash.
If the entry has type `:hardlink`, the link target path is normalized the same
way so that it will match the path of the target entry; the size field is set to
the size of the target path (which must be an already-seen file).

If the `portable` flag is true then path names are checked for validity on
Windows, which ensures that they don't contain illegal characters or have names
that are reserved. See https://stackoverflow.com/a/31976060/659248 for details.
"""
function rewrite(
    predicate::Function,
    old_tarball::ArgRead,
    new_tarball::Union{ArgWrite, Nothing} = nothing;
    portable::Bool = false,
)
    old_tarball = check_rewrite_old_tarball(old_tarball)
    arg_read(old_tarball) do old_tar
        arg_write(new_tarball) do new_tar
            rewrite_tarball(predicate, old_tar, new_tar, portable=portable)
        end
    end
end

function rewrite(
    old_tarball::ArgRead,
    new_tarball::Union{ArgWrite, Nothing} = nothing;
    portable::Bool = false,
)
    rewrite(true_predicate, old_tarball, new_tarball, portable=portable)
end

"""
    tree_hash([ predicate, ] tarball;
              [ algorithm = "git-sha1", ]
              [ skip_empty = false ]) -> hash::String

        predicate  :: Header --> Bool
        tarball    :: Union{AbstractString, AbstractCmd, IO}
        algorithm  :: AbstractString
        skip_empty :: Bool

Compute a tree hash value for the file tree that the tarball contains. By
default, this uses git's tree hashing algorithm with the SHA1 secure hash
function (like current versions of git). This means that for any tarball whose
file tree git can represent—i.e. one with only files, symlinks and non-empty
directories—the hash value computed by this function will be the same as the
hash value git would compute for that file tree. Note that tarballs can
represent file trees with empty directories, which git cannot store, and this
function can generate hashes for those, which will, by default (see `skip_empty`
below for how to change this behavior), differ from the hash of a tarball which
omits those empty directories. In short, the hash function agrees with git on
all trees which git can represent, but extends (in a consistent way) the domain
of hashable trees to other trees which git cannot represent.

If a `predicate` function is passed, it is called on each `Header` object that
is encountered while processing `tarball` and an entry is only hashed if
`predicate(hdr)` is true. This can be used to selectively hash only parts of an
archive, to skip entries that cause `extract` to throw an error, or to record
what is extracted during the hashing process.

Before it is passed to the predicate function, the `Header` object is somewhat
modified from the raw header in the tarball: the `path` field is normalized to
remove `.` entries and replace multiple consecutive slashes with a single slash.
If the entry has type `:hardlink`, the link target path is normalized the same
way so that it will match the path of the target entry; the size field is set to
the size of the target path (which must be an already-seen file).

Currently supported values for `algorithm` are `git-sha1` (the default) and
`git-sha256`, which uses the same basic algorithm as `git-sha1` but replaces the
SHA1 hash function with SHA2-256, the hash function that git will transition to
using in the future (due to known attacks on SHA1). Support for other file tree
hashing algorithms may be added in the future.

The `skip_empty` option controls whether directories in the tarball which
recursively contain no files or symlinks are included in the hash or ignored.
In general, if you are hashing the content of a tarball or a file tree, you care
about all directories, not just non-empty ones, so including these in the
computed hash is the default. So why does this function even provide the option
to skip empty directories? Because git refuses to store empty directories and
will ignore them if you try to add them to a repo. So if you compute a reference
tree hash by by adding files to a git repo and then asking git for the tree
hash, the hash value that you get will match the hash value computed by
`tree_hash` with `skip_empty=true`. In other words, this option allows
`tree_hash` to emulate how git would hash a tree with empty directories. If you
are hashing trees that may contain empty directories (i.e. do not come from a
git repo), however, it is recommended that you hash them using a tool (such as
this one) that does not ignore empty directories.
"""
function tree_hash(
    predicate::Function,
    tarball::ArgRead;
    algorithm::AbstractString = "git-sha1",
    skip_empty::Bool = false,
)
    HashType =
        algorithm == "git-sha1"   ? SHA.SHA1_CTX :
        algorithm == "git-sha256" ? SHA.SHA256_CTX :
            error("invalid tree hashing algorithm: $algorithm")

    check_tree_hash_tarball(tarball)
    arg_read(tarball) do tar
        git_tree_hash(predicate, tar, HashType, skip_empty)
    end
end

function tree_hash(
    tarball::ArgRead;
    algorithm::AbstractString = "git-sha1",
    skip_empty::Bool = false,
)
    tree_hash(
        true_predicate,
        tarball,
        algorithm = algorithm,
        skip_empty = skip_empty,
    )
end

## error checking utility functions

check_create_dir(dir::AbstractString) =
    isdir(dir) || error("""
    `dir` not a directory: $dir
    USAGE: create([predicate,] dir, [tarball])
    """)

check_create_skeleton(skeleton::AbstractString) =
    isfile(skeleton) || error("""
    `skeleton` not a file: $skeleton
    USAGE: create([predicate,] dir, [tarball]; [skeleton = <file>])
    """)

check_create_skeleton(skeleton::ArgRead) = nothing

check_list_tarball(tarball::AbstractString) =
    isfile(tarball) || error("""
    `tarball` not a file: $tarball
    USAGE: list([predicate,] tarball)
    """)

check_extract_tarball(tarball::AbstractString) =
    isfile(tarball) || error("""
    `tarball` not a file: $tarball
    USAGE: extract([predicate,] tarball, [dir])
    """)

check_extract_tarball(tarball::ArgWrite) = nothing

function check_extract_dir(dir::AbstractString)
    st = stat(dir)
    ispath(st) && !isdir(st) &&
        error("""
        `dir` not a directory: $dir
        USAGE: extract([predicate,] tarball, [dir])
        """)
    isdir(st) && !isempty(readdir(dir)) &&
        error("""
        `dir` not empty: $dir
        USAGE: extract([predicate,] tarball, [dir])
        """)
end

check_extract_dir(dir::Nothing) = nothing

check_rewrite_old_tarball(old_tarball::AbstractString) =
    isfile(old_tarball) ? old_tarball : error("""
    `old_tarball` not a file: $old_tarball
    USAGE: rewrite([predicate,] old_tarball, [new_tarball])
    """)

check_rewrite_old_tarball(old_tarball::ArgRead) =
    applicable(seek, old_tarball, 0) ?
        old_tarball : IOBuffer(read(old_tarball))

check_tree_hash_tarball(tarball::AbstractString) =
    isfile(tarball) || error("""
    `tarball` not a file: $tarball
    USAGE: tree_hash([predicate,] tarball)
    """)

check_tree_hash_tarball(tarball::ArgRead) = nothing

const Str = Union{String, SubString{String}}

# Special names on Windows: CON PRN AUX NUL COM1-9 LPT1-9
# we spell out uppercase/lowercase because of locales
const WIN_SPECIAL_NAMES = r"^(
    [Cc][Oo][Nn] |
    [Pp][Rr][Nn] |
    [Aa][Uu][Xx] |
    [Nn][Uu][Ll] |
  ( [Cc][Oo][Mm] |
    [Ll][Pp][Tt] )[1-9]
)(\.|$)"x

function check_windows_path(
    path  :: AbstractString,
    parts :: AbstractVector{<:Str} = split(path, r"/+"),
)
    for part in parts
        isempty(part) && continue
        if !isvalid(part)
            error("invalid Unicode: $(repr(part)) in $(repr(path))")
        end
        for ch in part
            ch < ' ' || ch ∈ "\"*:<>?\\|" || continue
            error("illegal Windows char: $(repr(ch)) in $(repr(path))")
        end
        if occursin(WIN_SPECIAL_NAMES, part)
            error("reserved Windows name: $(repr(part)) in $(repr(path))")
        end
    end
end

end # module
m   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Tar/src/header.jlD      """
The `Header` type is a struct representing the essential metadata for a single
record in a tar file with this definition:

    struct Header
        path :: String # path relative to the root
        type :: Symbol # type indicator (see below)
        mode :: UInt16 # mode/permissions (best viewed in octal)
        size :: Int64  # size of record data in bytes
        link :: String # target path of a symlink
    end

Types are represented with the following symbols: `file`, `hardlink`, `symlink`,
`chardev`, `blockdev`, `directory`, `fifo`, or for unknown types, the typeflag
character as a symbol. Note that [`extract`](@ref) refuses to extract records
types other than `file`, `symlink` and `directory`; [`list`](@ref) will only
list other kinds of records if called with `strict=false`.

The tar format includes various other metadata about records, including user and
group IDs, user and group names, and timestamps. The `Tar` package, by design,
completely ignores these. When creating tar files, these fields are always set
to zero/empty. When reading tar files, these fields are ignored aside from
verifying header checksums for each header record for all fields.
"""
struct Header
    path::String
    type::Symbol
    mode::UInt16
    size::Int64
    link::String
end

function Header(
    hdr::Header;
    path::AbstractString = hdr.path,
    type::Symbol         = hdr.type,
    mode::Integer        = hdr.mode,
    size::Integer        = hdr.size,
    link::AbstractString = hdr.link,
)
    Header(path, type, mode, size, link)
end

function Base.show(io::IO, hdr::Header)
    show(io, Header)
    print(io, "(")
    show(io, hdr.path)
    print(io, ", ")
    show(io, hdr.type)
    print(io, ", 0o", string(hdr.mode, base=8, pad=3), ", ")
    show(io, hdr.size)
    print(io, ", ")
    show(io, hdr.link)
    print(io, ")")
end

const TYPE_SYMBOLS = (
    '0'  => :file,
    '\0' => :file, # legacy encoding
    '1'  => :hardlink,
    '2'  => :symlink,
    '3'  => :chardev,
    '4'  => :blockdev,
    '5'  => :directory,
    '6'  => :fifo,
)

function to_symbolic_type(type::Char)
    for (t, s) in TYPE_SYMBOLS
        type == t && return s
    end
    isascii(type) ||
        error("invalid type flag: $(repr(type))")
    return Symbol(type)
end

function from_symbolic_type(sym::Symbol)
    for (t, s) in TYPE_SYMBOLS
        sym == s && return t
    end
    str = String(sym)
    ncodeunits(str) == 1 && isascii(str[1]) ||
        throw(ArgumentError("invalid type symbol: $(repr(sym))"))
    return str[1]
end

function check_header(hdr::Header)
    errors = String[]
    err(e::String) = push!(errors, e)

    # error checks
    isempty(hdr.path) &&
        err("path is empty")
    0x0 in codeunits(hdr.path) &&
        err("path contains NUL bytes")
    0x0 in codeunits(hdr.link) &&
        err("link contains NUL bytes")
    !isempty(hdr.path) && hdr.path[1] == '/' &&
        err("path is absolute")
    occursin(r"(^|/)\.\.(/|$)", hdr.path) &&
        err("path contains '..' component")
    hdr.type in (:file, :hardlink, :symlink, :directory) ||
        err("unsupported entry type")
    hdr.type ∉ (:hardlink, :symlink) && !isempty(hdr.link) &&
        err("non-link with link path")
    hdr.type ∈ (:hardlink, :symlink) && isempty(hdr.link) &&
        err("$(hdr.type) with empty link path")
    hdr.type ∈ (:hardlink, :symlink) && hdr.size != 0 &&
        err("$(hdr.type) with non-zero size")
    hdr.type == :hardlink && hdr.link[1] == '/' &&
        err("hardlink with absolute link path")
    hdr.type == :hardlink && occursin(r"(^|/)\.\.(/|$)", hdr.link) &&
        err("hardlink contains '..' component")
    hdr.type == :directory && hdr.size != 0 &&
        err("directory with non-zero size")
    hdr.type != :directory && endswith(hdr.path, "/") &&
        err("non-directory path ending with '/'")
    hdr.type != :directory && (hdr.path == "." || endswith(hdr.path, "/.")) &&
        err("non-directory path ending with '.' component")
    hdr.size < 0 &&
        err("negative file size")
    isempty(errors) && return

    # contruct error message
    if length(errors) == 1
        msg = errors[1] * "\n"
    else
        msg = "tar header with multiple errors:\n"
        for e in sort!(errors)
            msg *= " * $e\n"
        end
    end
    msg *= repr(hdr)
    error(msg)
end

function path_header(sys_path::AbstractString, tar_path::AbstractString)
    st = lstat(sys_path)
    if islink(st)
        size = 0
        type = :symlink
        mode = 0o755
        link = readlink(sys_path)
    elseif isdir(st)
        size = 0
        type = :directory
        mode = 0o755
        link = ""
    elseif isfile(st)
        size = filesize(st)
        type = :file
        # Windows can't re-use the `lstat` result, we need to ask
        # the system whether it's executable or not via `access()`
        if Sys.iswindows()
            mode = Sys.isexecutable(sys_path) ? 0o755 : 0o644
        else
            mode = iszero(filemode(st) & 0o100) ? 0o644 : 0o755
        end
        link = ""
    else
        error("unsupported file type: $(repr(sys_path))")
    end
    Header(tar_path, type, mode, size, link)
end
m   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Tar/src/create.jl�*      function create_tarball(
    predicate::Function,
    tar::IO,
    root::String;
    buf::Vector{UInt8} = Vector{UInt8}(undef, DEFAULT_BUFFER_SIZE),
    portable::Bool = false,
)
    write_tarball(tar, root, buf=buf) do sys_path, tar_path
        portable && check_windows_path(tar_path)
        hdr = path_header(sys_path, tar_path)
        hdr.type != :directory && return hdr, sys_path
        paths = Dict{String,String}()
        for name in readdir(sys_path)
            sys_path′ = joinpath(sys_path, name)
            predicate(sys_path′) || continue
            paths[name] = sys_path′
        end
        return hdr, paths
    end
end

function recreate_tarball(
    tar::IO,
    root::String,
    skeleton::IO;
    buf::Vector{UInt8} = Vector{UInt8}(undef, DEFAULT_BUFFER_SIZE),
    portable::Bool = false,
)
    check_skeleton_header(skeleton, buf=buf)
    globals = Dict{String,String}()
    while !eof(skeleton)
        hdr = read_header(skeleton, globals=globals, buf=buf, tee=tar)
        hdr === nothing && break
        check_header(hdr)
        portable && check_windows_path(hdr.path)
        sys_path = joinpath(root, hdr.path)
        if hdr.type == :file
            write_data(tar, sys_path, size=hdr.size, buf=buf)
        end
    end
end

function rewrite_tarball(
    predicate::Function,
    old_tar::IO,
    new_tar::IO;
    buf::Vector{UInt8} = Vector{UInt8}(undef, DEFAULT_BUFFER_SIZE),
    portable::Bool = false,
)
    tree = Dict{String,Any}()
    read_tarball(predicate, old_tar; buf=buf) do hdr, parts
        portable && check_windows_path(hdr.path, parts)
        isempty(parts) && return
        node = tree
        name = pop!(parts)
        for part in parts
            node′ = get(node, part, nothing)
            if !(node′ isa Dict)
                node′ = node[part] = Dict{String,Any}()
            end
            node = node′
        end
        if hdr.type == :hardlink
            node′ = tree
            for part in split(hdr.link, '/')
                node′ = node′[part]
            end
            hdr′ = Header(node′[1], path=hdr.path, mode=hdr.mode)
            node[name] = (hdr′, node′[2])
        else
            if !(hdr.type == :directory && get(node, name, nothing) isa Dict)
                node[name] = (hdr, position(old_tar))
            end
            skip_data(old_tar, hdr.size)
        end
    end
    write_tarball(new_tar, tree, buf=buf) do node, tar_path
        if node isa Dict
            hdr = Header(tar_path, :directory, 0o755, 0, "")
            return hdr, node
        else
            hdr, pos = node
            mode = hdr.type == :file && iszero(hdr.mode & 0o100) ? 0o644 : 0o755
            hdr′ = Header(hdr; path=tar_path, mode=mode)
            data = hdr.type == :directory ? nothing : (old_tar, pos)
            return hdr′, data
        end
    end
end

function write_tarball(
    callback::Function,
    tar::IO,
    sys_path::Any,
    tar_path::String = ".";
    buf::Vector{UInt8} = Vector{UInt8}(undef, DEFAULT_BUFFER_SIZE),
)
    hdr, data = callback(sys_path, tar_path)::Tuple{Header,Any}
    if hdr.type == :directory
        data isa Union{Nothing, AbstractDict{<:AbstractString}} ||
            error("callback must return a dict of strings, got: $(repr(data))")
    else
        data isa Union{Nothing, AbstractString, IO, Tuple{IO,Integer}} ||
            error("callback must return nothing, string or IO, got: $(repr(data))")
    end
    w = 0
    if tar_path != "."
        w += write_tarball(tar, hdr, data, buf=buf)
    end
    data isa AbstractDict && for name in sort!(collect(keys(data)))
        sys_path′ = data[name]
        tar_path′ = tar_path == "." ? name : "$tar_path/$name"
        w += write_tarball(callback, tar, sys_path′, tar_path′, buf=buf)
    end
    if tar_path == "." && w == 0
        w += write_tarball(tar, hdr, data, buf=buf)
    end
    return w
end

function write_tarball(
    tar::IO,
    hdr::Header,
    data::Any = nothing;
    buf::Vector{UInt8} = Vector{UInt8}(undef, DEFAULT_BUFFER_SIZE),
)
    check_header(hdr)
    w = write_header(tar, hdr, buf=buf)
    if hdr.type == :file
        data isa Union{AbstractString, IO, Tuple{IO,Integer}} ||
            throw(ArgumentError("file record requires path or IO: $(repr(hdr))"))
        w += write_data(tar, data, size=hdr.size, buf=buf)
    end
    return w
end

function write_header(
    tar::IO,
    hdr::Header;
    buf::Vector{UInt8} = Vector{UInt8}(undef, DEFAULT_BUFFER_SIZE),
)
    # extract values
    path = hdr.path
    size = hdr.size
    link = hdr.link

    # check for NULs
    0x0 in codeunits(path) &&
        throw(ArgumentError("path contains NUL bytes: $(repr(path))"))
    0x0 in codeunits(link) &&
        throw(ArgumentError("link contains NUL bytes: $(repr(path))"))

    # determine if an extended header is needed
    extended = Pair{String,String}[]
    # WARNING: don't change the order of these insertions
    # they are inserted and emitted in sorted order by key
    if ncodeunits(link) > 100
        push!(extended, "linkpath" => link)
        link = "" # empty in standard header
    end
    prefix = ""
    name = path
    if ncodeunits(path) > 100
        if ncodeunits(path) < 256
            i = findprev('/', path, 100)
            if i !== nothing
                # try splitting into prefix and name
                prefix = path[1:prevind(path, i)]
                name   = path[nextind(path, i):end]
            end
        end
        if ncodeunits(name) > 100 || ncodeunits(prefix) > 155
            push!(extended, "path" => path)
            prefix = name = "" # empty in standard header
        end
    end
    if size ≥ 68719476736 # 8^12
        push!(extended, "size" => string(size))
        # still written in binary in standard header
    end

    # emit extended header if necessary
    w = 0
    if !isempty(extended)
        @assert issorted(extended)
        w += write_extended_header(tar, extended, buf=buf)
    end
    # emit standard header
    std_hdr = Header(hdr; link=link)
    w += write_standard_header(tar, std_hdr, name=name, prefix=prefix, buf=buf)
end

function write_extended_header(
    tar::IO,
    metadata::Vector{Pair{String,String}};
    type::Symbol = :x, # default: non-global extended header
    name::AbstractString = "",
    prefix::AbstractString = "",
    link::AbstractString = "",
    mode::Integer = 0o000,
    buf::Vector{UInt8} = Vector{UInt8}(undef, DEFAULT_BUFFER_SIZE),
)
    type in (:x, :g) ||
        throw(ArgumentError("invalid type flag for extended header: $(repr(type))"))
    d = IOBuffer()
    for (key, val) in metadata
        entry = " $key=$val\n"
        n = l = ncodeunits(entry)
        while n < l + ndigits(n)
            n = l + ndigits(n)
        end
        @assert n == l + ndigits(n)
        write(d, "$n$entry")
    end
    path = isempty(name) || isempty(prefix) ? "$prefix$name" : "$prefix/$name"
    hdr = Header(path, type, mode, position(d), link)
    w = write_standard_header(tar, hdr, name=name, prefix=prefix, buf=buf)
    w += write_data(tar, seekstart(d), size=hdr.size, buf=buf)
end

function write_standard_header(
    tar::IO,
    hdr::Header;
    name::AbstractString = hdr.path,
    prefix::AbstractString = "",
    buf::Vector{UInt8} = Vector{UInt8}(undef, DEFAULT_BUFFER_SIZE),
)
    name = String(name)
    prefix = String(prefix)
    type = from_symbolic_type(hdr.type)
    link = hdr.link

    # octal strings for size and mode
    m = string(hdr.mode, base=8, pad=6)
    s = string(hdr.size, base=8, pad=11)

    # error checking (presumes checks done by write_header)
    hdr.size < 0 &&
        throw(ArgumentError("negative file size is invalid: $(hdr.size)"))
    ncodeunits(prefix) ≤ 155 ||
        throw(ArgumentError("path prefix too long for standard header: $(repr(prefix))"))
    ncodeunits(name) ≤ 100 ||
        throw(ArgumentError("path name too long for standard header: $(repr(name))"))
    ncodeunits(link) ≤ 100 ||
        throw(ArgumentError("symlink target too long for standard header: $(repr(link))"))
    ncodeunits(m) ≤ 6 ||
        throw(ArgumentError("mode too large for standard header: 0o$m"))
    isascii(type) ||
        throw(ArgumentError("non-ASCII type flag value: $(repr(type))"))

    # construct header block
    data = view(buf, 1:512)
    h = IOBuffer(fill!(data, 0x00), write=true, truncate=false)
    write(h, name)              # name
    seek(h, 100)
    write(h, "$m \0")           # mode
    write(h, "000000 \0")       # uid
    write(h, "000000 \0")       # gid
    if ncodeunits(s) ≤ 12       # size
        write(h, s)
        if ncodeunits(s) < 12
            write(h, ' ')
        end
    else
        # emulate GNU tar: write binary size with leading bit set
        # can encode up to 2^95; Int64 size field only up to 2^63-1
        write(h, 0x80 | ((hdr.size >> (8*11)) % UInt8))
        for i = 10:-1:0
            write(h, (hdr.size >> 8i) % UInt8)
        end
    end
    write(h, "00000000000 ")    # mtime
    write(h, "        ")        # chksum (blank)
    write(h, type)              # typeflag
    @assert position(h) == 157
    write(h, link)              # linkname
    seek(h, 257)
    write(h, "ustar\0")         # magic
    write(h, "00")              # version
    skip(h, 64)                 # uname & gname
    write(h, "000000 \0")       # devmajor
    write(h, "000000 \0")       # devminor
    @assert position(h) == 345
    write(h, prefix)            # prefix

    # fix the checksum
    c = string(sum(data), base=8, pad=6)
    @assert ncodeunits(c) ≤ 6
    seek(h, 148)
    write(h, "$c\0 ")
    @assert position(h) == 156

    # write header
    w = write(tar, data)
    @assert w == 512
    return w
end

function write_data(
    tar::IO,
    data::IO;
    size::Integer,
    buf::Vector{UInt8} = Vector{UInt8}(undef, DEFAULT_BUFFER_SIZE),
)
    size < 0 &&
        throw(ArgumentError("cannot write negative data: $size"))
    w, t = 0, round_up(size)
    while size > 0
        b = Int(min(size, length(buf)))::Int
        n = Int(readbytes!(data, buf, b))::Int
        n < b && eof(data) && throw(EOFError())
        w += write(tar, view(buf, 1:n))
        size -= n
        t -= n
    end
    @assert size == 0
    @assert 0 ≤ t < 512
    t > 0 && (w += write(tar, fill!(view(buf, 1:t), 0)))
    return w
end

function write_data(
    tar::IO,
    (data, pos)::Tuple{IO,Integer};
    size::Integer,
    buf::Vector{UInt8} = Vector{UInt8}(undef, DEFAULT_BUFFER_SIZE),
)
    seek(data, pos)
    write_data(tar, data, size=size, buf=buf)
end

function write_data(
    tar::IO,
    file::String;
    size::Integer,
    buf::Vector{UInt8} = Vector{UInt8}(undef, DEFAULT_BUFFER_SIZE),
)
    open(file) do data
        write_data(tar, data, size=size, buf=buf)
        eof(data) || error("data file too large: $data")
    end
end
n   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Tar/src/extract.jl�c      import SHA

function iterate_headers(
    callback::Function,
    tar::IO;
    raw::Bool = false,
    strict::Bool = !raw,
    buf::Vector{UInt8} = Vector{UInt8}(undef, DEFAULT_BUFFER_SIZE),
)
    eof(tar) && return
    hdr = read_standard_header(tar, buf=buf)
    hdr === nothing && return
    if !raw
        globals = Dict{String,String}()
    end
    if hdr.type == :g && hdr.path == SKELETON_MAGIC
        skip_data(tar, hdr.size)
        skeleton = true
    else
        if !raw
            hdr = read_header(tar, hdr, globals=globals, buf=buf)
        end
        skeleton = false
        @goto loop
    end
    while !eof(tar)
        hdr = if raw
            read_standard_header(tar, buf=buf)
        else
            read_header(tar, globals=globals, buf=buf)
        end
    @label loop
        hdr === nothing && break
        strict && check_header(hdr)
        if hasmethod(callback, Tuple{Header, Vector{Pair{Symbol, String}}})
            callback(hdr, dump_header(buf))
        elseif hasmethod(callback, Tuple{Header, Vector{UInt8}})
            callback(hdr, buf[1:512])
        else
            callback(hdr)
        end
        if !skeleton || hdr.type in (:g, :x) ||
            hdr.path == "././@LongLink" && hdr.type in (:L, :K)
            skip_data(tar, hdr.size)
        end
    end
end

# follow chains of symlinks
follow_symlink_chain(seen::Vector, what::Any, paths) = what == :symlink ? what : seen[end]
follow_symlink_chain(seen::Vector, what::String, paths) = what in seen ? :symlink : follow_symlink_chain(push!(seen, what), paths[what], paths)

 # our `cp` doesn't copy ACL properties, so manually set them via `chmod`
 function copy_mode(src::String, dst::String)
    chmod(dst, filemode(src))
    isdir(dst) || return
    for name in readdir(dst)
        sub_src = joinpath(src, name)
        sub_dst = joinpath(dst, name)
        copy_mode(sub_src, sub_dst)
    end
end

function extract_tarball(
    predicate::Function,
    tar::IO,
    root::String;
    buf::Vector{UInt8} = Vector{UInt8}(undef, DEFAULT_BUFFER_SIZE),
    skeleton::IO = devnull,
    copy_symlinks::Bool = false,
    set_permissions::Bool = true,
)
    root = normpath(root)
    paths = read_tarball(predicate, tar; buf=buf, skeleton=skeleton) do hdr, parts
        Sys.iswindows() && check_windows_path(hdr.path, parts)
        # get the file system version of the path
        sys_path = isempty(parts) ? "." : reduce(joinpath, parts)
        isabspath(sys_path) &&
            error("attempt to extract absolute path at $(repr(sys_path)) from $(repr(hdr.path))")
        sys_path = sys_path == "." ? root : normpath(root, sys_path)
        startswith(sys_path, root) ||
            error("attempt to extract relative path outside of root at $(repr(sys_path)) from $(repr(hdr.path))")
        src_path = joinpath(root, hdr.link)
        dir = dirname(sys_path)
        st = stat(dir)
        # ensure dirname(sys_path) is a directory
        if !isdir(st)
            ispath(st) && rm(dir, force=true, recursive=true)
            mkpath(dir)
        elseif hdr.type != :hardlink || src_path != sys_path
            st = lstat(sys_path)
            hdr.type == :directory && isdir(st) && return # from callback
            ispath(st) && rm(sys_path, force=true, recursive=true)
        end
        # create the path
        if hdr.type == :directory
            mkdir(sys_path)
        elseif hdr.type == :symlink
            copy_symlinks || symlink(hdr.link, sys_path)
        elseif hdr.type == :hardlink
            src_path != sys_path && cp(src_path, sys_path)
        elseif hdr.type == :file
            read_data(tar, sys_path, size=hdr.size, buf=buf)
        else # should already be caught by check_header
            error("unsupported tarball entry type: $(hdr.type)")
        end
        # apply tarball permissions
        if set_permissions && hdr.type in (:file, :hardlink)
            exec = 0o100 & hdr.mode != 0
            tar_mode = exec ? 0o755 : 0o644
            sys_mode = filemode(sys_path)
            if exec
                # copy read bits to execute bits with
                # at least the user execute bit on
                sys_mode |= 0o100 | (sys_mode & 0o444) >> 2
                # TODO: would be better to have the system
                # create an executable with default mode but
                # we don't have a way to do that afaik
            end
            chmod(sys_path, tar_mode & sys_mode)
        end
    end
    copy_symlinks || return

    # resolve the internal targets of symlinks
    for (path, what) in paths
        what isa String || continue
        target = link_target(paths, path, what)
        paths[path] = something(target, :symlink)
    end

    for (path, what) in paths
        what isa AbstractString || continue
        paths[path] = follow_symlink_chain([path], what, paths)
    end

    # copies that need to be made
    copies = Pair{String,String}[]
    for (path, what) in paths
        what isa AbstractString || continue
        push!(copies, path => String(what)::String)
    end
    sort!(copies, by=last)

    while !isempty(copies)
        i = 1
        while i ≤ length(copies)
            path, what = copies[i]
            # check if source is complete yet
            if any(startswith(p, "$what/") for (p, w) in copies)
                # `what` is an incomplete directory
                # need to wait for source to be complete
                i += 1
            else
                # source complete, can copy now
                deleteat!(copies, i)
                src = reduce(joinpath, init=root, split(what, '/'))
                dst = reduce(joinpath, init=root, split(path, '/'))
                cp(src, dst)
                if set_permissions && Sys.iswindows()
                    copy_mode(src, dst)
                end
            end
        end
    end
end

# resolve symlink target or nothing if not valid
function link_target(
    paths::Dict{String},
    path::AbstractString,
    link::AbstractString,
)
    first(link) == '/' && return
    path_parts = split(path, r"/+")
    link_parts = split(link, r"/+")
    pop!(path_parts)
    part = nothing # remember the last part
    while !isempty(link_parts)
        part = popfirst!(link_parts)
        part in ("", ".") && continue
        if part == ".."
            isempty(path_parts) && return
            pop!(path_parts)
        else
            push!(path_parts, part)
            prefix = join(path_parts, '/')
            prefix in keys(paths) || return
            isempty(link_parts) && break
            what = paths[prefix]
            if what isa AbstractString
                what = convert(String, what)::String
                prefix = link_target(paths, prefix, what)
                prefix === nothing && return
                path_parts = split(prefix, '/')
            end
        end
    end
    isempty(path_parts) && return
    target = join(path_parts, '/')
    # if link ends in `/` or `.` target must be a directory
    part in ("", ".") && paths[target] !== :directory && return
    # can't copy a circular link to a prefix of itself
    (path == target || startswith(path, "$target/")) && return
    return target
end

function git_tree_hash(
    predicate::Function,
    tar::IO,
    HashType::DataType,
    skip_empty::Bool;
    buf::Vector{UInt8} = Vector{UInt8}(undef, DEFAULT_BUFFER_SIZE),
)
    # build tree with leaves for files and symlinks
    tree = Dict{String,Any}()
    read_tarball(predicate, tar; buf=buf) do hdr, parts
        isempty(parts) && return
        name = pop!(parts)
        node = tree
        for part in parts
            node′ = get(node, part, nothing)
            if !(node′ isa Dict)
                node′ = node[part] = Dict{String,Any}()
            end
            node = node′
        end
        if hdr.type == :directory
            if !(get(node, name, nothing) isa Dict)
                node[name] = Dict{String,Any}()
            end
            return
        elseif hdr.type == :symlink
            mode = "120000"
            hash = git_object_hash("blob", HashType) do io
                write(io, hdr.link)
            end
        elseif hdr.type == :hardlink
            mode = iszero(hdr.mode & 0o100) ? "100644" : "100755"
            node′ = tree
            for part in split(hdr.link, '/')
                node′ = node′[part]
            end
            hash = node′[2] # hash of linked file
        elseif hdr.type == :file
            mode = iszero(hdr.mode & 0o100) ? "100644" : "100755"
            hash = git_file_hash(tar, hdr.size, HashType, buf=buf)
        else
            error("unsupported type for git tree hashing: $(hdr.type)")
        end
        node[name] = (mode, hash)
    end

    # prune directories that don't contain any files
    if skip_empty
        prune_empty!(node::Tuple) = true
        function prune_empty!(node::Dict)
            filter!(node) do (name, child)
                prune_empty!(child)
            end
            return !isempty(node)
        end
        prune_empty!(tree)
    end

    # reduce the tree to a single hash value
    hash_tree(node::Tuple) = node
    function hash_tree(node::Dict)
        by((name, child)) = child isa Dict ? "$name/" : name
        hash = git_object_hash("tree", HashType) do io
            for (name, child) in sort!(collect(node), by=by)
                mode, hash = hash_tree(child)
                print(io, mode, ' ', name, '\0')
                write(io, hex2bytes(hash))
            end
        end
        return "40000", hash
    end

    return hash_tree(tree)[end]
end

function git_object_hash(
    emit::Function,
    kind::AbstractString,
    HashType::DataType,
)
    ctx = HashType()
    body = codeunits(sprint(emit))
    SHA.update!(ctx, codeunits("$kind $(length(body))\0"))
    SHA.update!(ctx, body)
    return bytes2hex(SHA.digest!(ctx))
end

function git_file_hash(
    tar::IO,
    size::Integer,
    HashType::DataType;
    buf::Vector{UInt8} = Vector{UInt8}(undef, DEFAULT_BUFFER_SIZE),
)
    ctx = HashType()
    SHA.update!(ctx, codeunits("blob $size\0"))
    # TODO: this largely duplicates the logic of read_data
    # read_data could be used directly if SHA offered an interface
    # where you write data to an IO object and it maintains a hash
    padded_size = round_up(size)
    while padded_size > 0
        max_read_len = Int(min(padded_size, length(buf)))::Int
        read_len = Int(readbytes!(tar, buf, max_read_len))::Int
        read_len < max_read_len && eof(tar) && throw(EOFError())
        nonpadded_view = view(buf, 1:Int(min(read_len, size)))
        SHA.update!(ctx, nonpadded_view)
        size -= length(nonpadded_view)
        padded_size -= read_len
    end
    @assert size == padded_size == 0
    return bytes2hex(SHA.digest!(ctx))
end

const SKELETON_MAGIC = "%!skeleton:\x83\xe6\xa8\xfe"

function write_skeleton_header(
    skeleton::IO;
    buf::Vector{UInt8} = Vector{UInt8}(undef, DEFAULT_BUFFER_SIZE),
)
    skeleton === devnull || write_extended_header(
        skeleton, type = :g, name = SKELETON_MAGIC, buf = buf,
        ["comment" => "Tar.jl skeleton file", "size" => "0"],
    )
end

function check_skeleton_header(
    skeleton::IO;
    buf::Vector{UInt8} = Vector{UInt8}(undef, DEFAULT_BUFFER_SIZE),
)
    hdr = read_standard_header(skeleton, buf=buf)
    hdr.type == :g && hdr.path == SKELETON_MAGIC ||
        error("not a skeleton file: $skeleton")
    skip_data(skeleton, hdr.size)
end

function read_tarball(
    callback::Function,
    predicate::Function,
    tar::IO;
    buf::Vector{UInt8} = Vector{UInt8}(undef, DEFAULT_BUFFER_SIZE),
    skeleton::IO = devnull,
)
    write_skeleton_header(skeleton, buf=buf)
    # symbols for path types except symlinks store the link
    paths = Dict{String,Any}()
    globals = Dict{String,String}()
    while !eof(tar)
        hdr = read_header(tar, globals=globals, buf=buf, tee=skeleton)
        hdr === nothing && break
        err = nothing
        # normalize path and check for symlink attacks
        path = ""
        for part in split(hdr.path, '/')
            # check_header checks for ".." later
            (isempty(part) || part == ".") && continue
            if err === nothing && get(paths, path, nothing) isa String
                err = """
                Tarball contains path with symlink prefix:
                - path = $(repr(hdr.path))
                - prefix = $(repr(path))
                Refusing to extract — possible attack!
                """
            end
            path = isempty(path) ? String(part) : "$path/$part"
        end
        hdr′ = Header(hdr, path=path)
        # check that hardlinks refer to already-seen files
        if err === nothing && hdr.type == :hardlink
            parts = filter!(split(hdr.link, '/')) do part
                # check_header checks for ".." later
                !isempty(part) && part != "."
            end
            link = join(parts, '/')
            hdr = Header(hdr, link=link)
            hdr′ = Header(hdr′, link=link)
            what = get(paths, link, Symbol("non-existent"))
            if what isa Int64 # plain file
                hdr′ = Header(hdr′, size=what)
            else
                err = """
                Tarball contains hardlink with $what target:
                - path = $(repr(hdr.path))
                - target = $(repr(hdr.link))
                Refusing to extract — possible attack!
                """
            end
        end
        # check if we should extract or skip
        if !(predicate(hdr′)::Bool) # pass normalized header
            skip_data(tar, hdr.size)
            continue
        end
        check_header(hdr)
        err === nothing || error(err)
        # record info about path
        paths[path] =
            hdr.type == :symlink ? hdr.link :
            hdr.type == :file    ? hdr.size :
            hdr.type
        # apply callback, checking that it consumes IO correctly
        before = applicable(position, tar) ? position(tar) : 0
        callback(hdr, split(path, '/', keepempty=false))
        applicable(position, tar) || continue
        advanced = position(tar) - before
        expected = round_up(hdr.size)
        advanced == expected ||
            error("callback read $advanced bytes instead of $expected")
    end
    return paths
end

function read_header(
    io::IO;
    globals::Dict{String,String} = Dict{String,String}(),
    buf::Vector{UInt8} = Vector{UInt8}(undef, DEFAULT_BUFFER_SIZE),
    tee::IO = devnull,
)
    hdr = read_standard_header(io, buf=buf, tee=tee)
    hdr === nothing && return nothing
    read_header(io, hdr, globals=globals, buf=buf, tee=tee)
end

function read_header(
    io::IO,
    hdr::Header; # initial header
    globals::Dict{String,String} = Dict{String,String}(),
    buf::Vector{UInt8} = Vector{UInt8}(undef, DEFAULT_BUFFER_SIZE),
    tee::IO = devnull,
)
    # process zero or more extended headers
    metadata = copy(globals)
    while true
        if hdr.type in (:g, :x) # POSIX extended headers
            let hdr=hdr         # https://github.com/JuliaLang/julia/issues/15276
                read_extended_metadata(io, hdr.size, buf=buf, tee=tee) do key, val
                    if key in ("size", "path", "linkpath")
                        if hdr.type == :g
                            globals[key] = val
                        end
                        metadata[key] = val
                    end
                end
            end
        elseif hdr.path == "././@LongLink" && hdr.type in (:L, :K)
            # GNU long name or link header
            data = read_data(io, size=hdr.size, buf=buf, tee=tee)
            data[end] == 0 ||
                error("malformed GNU long header (trailing `\\0` expected): " *
                      repr(String(data)))
            key = hdr.type == :L ? "path" : "linkpath"
            metadata[key] = String(@view data[1:end-1])
        else
            break # non-extension header block
        end
        hdr = read_standard_header(io, buf=buf, tee=tee)
        hdr === nothing && throw(EOFError())
    end
    # determine final values for size, path & link
    size = hdr.size
    if "size" in keys(metadata)
        val = metadata["size"]
        size = tryparse(UInt64, val)
        size === nothing &&
            error("invalid extended header size value: $(repr(val))")
    end
    path = get(metadata, "path", hdr.path)
    link = get(metadata, "linkpath", hdr.link)
    # construct and return Header object
    return Header(hdr; path=path, size=size, link=link)
end

using Base.Checked: mul_with_overflow, add_with_overflow

function read_extended_metadata(
    callback::Function,
    io::IO,
    size::Integer;
    buf::Vector{UInt8} = Vector{UInt8}(undef, DEFAULT_BUFFER_SIZE),
    tee::IO = devnull,
)
    size > typemax(Int32) &&
        error("read_extended_metadata called with too large size: $size")
    size = Int(size)
    data = read_data(io, size=size, buf=buf, tee=tee)
    malformed() = error("malformed extended header metadata: $(repr(String(data)))")
    i = 0
    while i < size
        j, m = i, 0
        while j ≤ size
            byte = data[j += 1]
            byte == UInt8(' ') && break
            UInt8('0') ≤ byte ≤ UInt8('9') || malformed()
            m, fm = mul_with_overflow(m, 10)
            m, fa = add_with_overflow(m, Int(byte - UInt8('0')))
            fm | fa &&
                error("extended header record size too large: $(repr(String(data)))")
        end
        k, l = j, i + m
        while k ≤ l
            byte = data[k += 1]
            byte == UInt8('=') && break
        end
        # data[i]       is end of previous
        # data[i+1:j-1] is length in decimal
        # data[j]       is ` ` (space)
        # data[j+1:k-1] is key string
        # data[k]       is `=` (equals)
        # data[k+1:l-1] is value string
        # data[l]       is `\n` (newline)
        i+1 < j < k < l || malformed()
        @assert data[j] == UInt8(' ')
        @assert data[k] == UInt8('=')
        data[l] == UInt('\n') || malformed()
        i = l # next starting point
        # pass key, value back to caller
        key = String(@view data[j+1:k-1])
        val = String(@view data[k+1:l-1])
        callback(key, val)
    end
end

# For reference see
# https://www.gnu.org/software/tar/manual/html_node/Standard.html

const HEADER_FIELDS = (
    # field, offset, size
    (:name,       0, 100),
    (:mode,     100,   8),
    (:uid,      108,   8),
    (:gid,      116,   8),
    (:size,     124,  12),
    (:mtime,    136,  12),
    (:chksum,   148,   8),
    (:typeflag, 156,   1),
    (:linkname, 157, 100),
    (:magic,    257,   6),
    (:version,  263,   2),
    (:uname,    265,  32),
    (:gname,    297,  32),
    (:devmajor, 329,   8),
    (:devminor, 337,   8),
    (:prefix,   345, 155),
    (:rest,     500,  12),
)

function index_range(field::Symbol)
    for (fld, off, len) in HEADER_FIELDS
        fld == field && return off .+ (1:len)
    end
    error("[internal error] invalid field name: $field")
end

dump_header(buf::AbstractVector{UInt8}) =
    [ fld => String(buf[off .+ (1:len)])
        for (fld, off, len) in HEADER_FIELDS ]

function header_error(buf::AbstractVector{UInt8}, msg::AbstractString)
    sprint() do io
        println(io, msg, "\n[header block data]:")
        for (field, value) in dump_header(buf)
            print(io, "  ", rpad(field, 8), " = ")
            show(io, value)
            println(io)
        end
    end |> error
end

function header_error(buf::AbstractVector{UInt8}, fld::Symbol)
    value = read_header_str(buf, fld)
    header_error(buf, "malformed $fld field: $(repr(value))")
end

function read_standard_header(
    io::IO;
    buf::Vector{UInt8} = Vector{UInt8}(undef, DEFAULT_BUFFER_SIZE),
    tee::IO = devnull,
)
    data = read_data(io, size=512, buf=buf, tee=tee)
    # zero block indicates end of tarball
    if all(iszero, data)
        while !eof(io)
            r = Int(readbytes!(io, buf))::Int
            write(tee, view(buf, 1:r))
        end
        return nothing
    end
    # verify valid header
    try
        check_version_field(buf)
        check_checksum_field(buf)
    catch err
        if err isa ErrorException
            msg = match(r"^(.*?)\s*\[header block data\]"s, convert(Union{String, SubString{String}}, err.msg)::Union{String, SubString{String}}).captures[1]
            msg = "This does not appear to be a TAR file/stream — $msg. Note: Tar.jl does not handle decompression; if the tarball is compressed you must use an external command like `gzcat` or package like CodecZlib.jl to decompress it. See the README file for examples."
            err = ErrorException(msg)
        end
        rethrow(err)
    end
    # extract fields we care about
    size = read_header_size(buf)
    name = read_header_str(buf, :name)
    mode = read_header_int(buf, :mode)
    type = read_header_chr(buf, :typeflag)
    link = read_header_str(buf, :linkname)
    prefix = read_header_str(buf, :prefix)
    # check that mode isn't too big
    mode ≤ typemax(typemax(UInt16)) ||
        header_error(buf, "mode value too large: $(string(mode, base=8))")
    # combine prefix & name fields
    path = isempty(prefix) ? name : "$prefix/$name"
    return Header(path, to_symbolic_type(type), mode, size, link)
end

function check_version_field(buf::AbstractVector{UInt8})
    version = read_header_str(buf, :version)
    occursin(r"^0* *$", version) && return
    header_error(buf, "invalid version string for tar file: $(repr(version))")
end

function check_checksum_field(buf::AbstractVector{UInt8})
    chksum = read_header_int(buf, :chksum)
    actual = let r = index_range(:chksum)
        sum(i in r ? UInt8(' ') : buf[i] for i = 1:512)
    end
    chksum == actual && return
    header_error(buf, "incorrect header checksum = $chksum; should be $actual")
end

function read_header_size(buf::AbstractVector{UInt8})
    r = index_range(:size)
    b1 = buf[r[1]] # high bit set for binary
    b1 & 0x80 == 0 && return read_header_int(buf, :size)
    b1 == 0x80 && return read_header_bin(buf, :size, r[1]+1:r[end])
    val = String(buf[r])
    header_error(buf, "binary integer size value too large: $(repr(val))")
end

function read_header_chr(buf::AbstractVector{UInt8}, fld::Symbol)
    r = index_range(fld)
    length(r) == 1 || error("[internal error] not a character field: $fld")
    return Char(buf[first(r)])
end

function read_header_str(buf::AbstractVector{UInt8}, fld::Symbol)
    r = index_range(fld)
    for i in r
        byte = buf[i]
        byte == 0 && return String(buf[first(r):i-1])
    end
    return String(buf[r])
end

function read_header_int(buf::AbstractVector{UInt8}, fld::Symbol)
    r = index_range(fld)
    n = Int64(0)
    before = true
    for i in r
        byte = buf[i]
        before && byte == UInt8(' ') && continue
        byte in (0x00, UInt8(' ')) && break
        UInt8('0') <= byte <= UInt8('7') || header_error(buf, fld)
        if leading_zeros(n) <= 3
            val = String(buf[r])
            header_error(buf, "octal integer $fld value too large: $(repr(val))")
        end
        n <<= 3
        n |= byte - 0x30
        before = false
    end
    before && header_error(buf, fld)
    return n
end

function read_header_bin(
    buf::AbstractVector{UInt8}, fld::Symbol,
    r::UnitRange{<:Integer} = index_range(fld),
)
    n = Int64(0)
    for i in r
        if leading_zeros(n) <= 8
            val = String(buf[r])
            header_error(buf, "binary integer $fld value too large: $(repr(val))")
        end
        n <<= 8
        n |= buf[i]
    end
    return n
end

round_up(size) = 512 * ((size + 511) ÷ 512)

function skip_data(tar::IO, size::Integer)
    size < 0 && throw(ArgumentError("[internal error] negative skip: $size"))
    size > 0 && skip(tar, round_up(size))
end

function read_data(
    tar::IO,
    file::IO;
    size::Integer,
    buf::Vector{UInt8} = Vector{UInt8}(undef, DEFAULT_BUFFER_SIZE),
    tee::IO = devnull,
)::Nothing
    padded_size = round_up(size)
    while padded_size > 0
        max_read_len = Int(min(padded_size, length(buf)))::Int
        read_len = Int(readbytes!(tar, buf, max_read_len))::Int
        write(tee, view(buf, 1:read_len))
        read_len < max_read_len && eof(tar) && throw(EOFError())
        size -= write(file, view(buf, 1:Int(min(read_len, size))))
        padded_size -= read_len
    end
    @assert size == padded_size == 0
    return
end

function read_data(
    tar::IO,
    file::AbstractString;
    size::Integer,
    buf::Vector{UInt8} = Vector{UInt8}(undef, DEFAULT_BUFFER_SIZE),
    tee::IO = devnull,
)::Nothing
    open(file, write=true) do file′
        read_data(tar, file′, size=size, buf=buf, tee=tee)
    end
end

# WARNING: this returns a view into `buf` so you must either use
# the result before making another call using `buf` or make a copy
function read_data(
    tar::IO;
    size::Integer,
    buf::Vector{UInt8} = Vector{UInt8}(undef, DEFAULT_BUFFER_SIZE),
    tee::IO = devnull,
)::AbstractVector{UInt8}
    padded_size = round_up(size)
    padded_size > typemax(Int32) &&
        throw(ArgumentError("read_data(tar; size) called with too large size: $size"))
    padded_size = Int(padded_size)
    length(buf) < padded_size && resize!(buf, nextpow(2, padded_size))
    write(tee, read!(tar, view(buf, 1:padded_size)))
    return view(buf, 1:size)
end
n   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Dates/src/Dates.jlO
      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
    Dates

The `Dates` module provides `Date`, `DateTime`, `Time` types, and related functions.

The types are not aware of time zones, based on UT seconds
(86400 seconds a day, avoiding leap seconds), and
use the proleptic Gregorian calendar, as specified in [ISO 8601](https://en.wikipedia.org/wiki/ISO_8601).
For time zone functionality, see the TimeZones.jl package.

```jldoctest
julia> dt = DateTime(2017,12,31,23,59,59,999)
2017-12-31T23:59:59.999

julia> d1 = Date(Month(12), Year(2017))
2017-12-01

julia> d2 = Date("2017-12-31", DateFormat("y-m-d"))
2017-12-31

julia> yearmonthday(d2)
(2017, 12, 31)

julia> d2-d1
30 days
```

Please see the manual section on [`Date`](@ref) and [`DateTime`](@ref)
for more information.
"""
module Dates

import Base: ==, isless, div, fld, mod, rem, gcd, lcm, +, -, *, /, %, broadcast
using Printf: @sprintf

using Base.Iterators

include("types.jl")
include("periods.jl")
include("accessors.jl")
include("query.jl")
include("arithmetic.jl")
include("conversions.jl")
include("ranges.jl")
include("adjusters.jl")
include("rounding.jl")
include("io.jl")
include("parse.jl")
include("deprecated.jl")

export Period, DatePeriod, TimePeriod,
       Year, Quarter, Month, Week, Day, Hour, Minute, Second, Millisecond,
       Microsecond, Nanosecond,
       TimeZone, UTC, TimeType, DateTime, Date, Time,
       # periods.jl
       canonicalize,
       # accessors.jl
       yearmonthday, yearmonth, monthday, year, month, week, day,
       hour, minute, second, millisecond, dayofmonth,
       microsecond, nanosecond,
       # query.jl
       dayofweek, isleapyear, daysinmonth, daysinyear, dayofyear, dayname, dayabbr,
       dayofweekofmonth, daysofweekinmonth, monthname, monthabbr,
       quarterofyear, dayofquarter,
       Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday,
       Mon, Tue, Wed, Thu, Fri, Sat, Sun,
       January, February, March, April, May, June,
       July, August, September, October, November, December,
       Jan, Feb, Mar, Apr, May, Jun, Jul, Aug, Sep, Oct, Nov, Dec,
       # conversions.jl
       unix2datetime, datetime2unix, now, today,
       rata2datetime, datetime2rata, julian2datetime, datetime2julian,
       # adjusters.jl
       firstdayofweek, lastdayofweek,
       firstdayofmonth, lastdayofmonth,
       firstdayofyear, lastdayofyear,
       firstdayofquarter, lastdayofquarter,
       adjust, tonext, toprev, tofirst, tolast,
       # io.jl
       ISODateTimeFormat, ISODateFormat, ISOTimeFormat, DateFormat, RFC1123Format, @dateformat_str

end # module
n   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Dates/src/types.jl:<      # This file is a part of Julia. License is MIT: https://julialang.org/license

abstract type AbstractTime end

"""
    Period
    Year
    Quarter
    Month
    Week
    Day
    Hour
    Minute
    Second
    Millisecond
    Microsecond
    Nanosecond

`Period` types represent discrete, human representations of time.
"""
abstract type Period     <: AbstractTime end

"""
    DatePeriod
    Year
    Quarter
    Month
    Week
    Day

Intervals of time greater than or equal to a day.
Conventional comparisons between `DatePeriod`s are not all valid.
(eg `Week(1) == Day(7)`, but `Year(1) != Day(365)`)
"""
abstract type DatePeriod <: Period end

"""
    TimePeriod
    Hour
    Minute
    Second
    Millisecond
    Microsecond
    Nanosecond

Intervals of time less than a day.
Conversions between all `TimePeriod`s are permissible.
(eg `Hour(1) == Minute(60) == Second(3600)`)
"""
abstract type TimePeriod <: Period end

for T in (:Year, :Quarter, :Month, :Week, :Day)
    @eval struct $T <: DatePeriod
        value::Int64
        $T(v::Number) = new(v)
    end
end
for T in (:Hour, :Minute, :Second, :Millisecond, :Microsecond, :Nanosecond)
    @eval struct $T <: TimePeriod
        value::Int64
        $T(v::Number) = new(v)
    end
end

"""
    Year(v)
    Quarter(v)
    Month(v)
    Week(v)
    Day(v)
    Hour(v)
    Minute(v)
    Second(v)
    Millisecond(v)
    Microsecond(v)
    Nanosecond(v)

Construct a `Period` type with the given `v` value. Input must be losslessly convertible
to an [`Int64`](@ref).
"""
Period(v)

"""
    Instant

`Instant` types represent integer-based, machine representations of time as continuous
timelines starting from an epoch.
"""
abstract type Instant <: AbstractTime end

"""
    UTInstant{T}

The `UTInstant` represents a machine timeline based on UT time (1 day = one revolution of
the earth). The `T` is a `Period` parameter that indicates the resolution or precision of
the instant.
"""
struct UTInstant{P<:Period} <: Instant
    periods::P
end

# Convenience default constructors
UTM(x) = UTInstant(Millisecond(x))
UTD(x) = UTInstant(Day(x))

# Calendar types provide rules for interpreting instant
# timelines in human-readable form.
abstract type Calendar <: AbstractTime end

# ISOCalendar implements the ISO 8601 standard (en.wikipedia.org/wiki/ISO_8601)
# Notably based on the proleptic Gregorian calendar
# ISOCalendar provides interpretation rules for UTInstants to civil date and time parts
struct ISOCalendar <: Calendar end

"""
    TimeZone

Geographic zone generally based on longitude determining what the time is at a certain location.
Some time zones observe daylight savings (eg EST -> EDT).
For implementations and more support, see the [`TimeZones.jl`](https://github.com/JuliaTime/TimeZones.jl) package
"""
abstract type TimeZone end

"""
    UTC

`UTC`, or Coordinated Universal Time, is the [`TimeZone`](@ref) from which all others are measured.
It is associated with the time at 0° longitude. It is not adjusted for daylight savings.
"""
struct UTC <: TimeZone end

"""
    TimeType

`TimeType` types wrap `Instant` machine instances to provide human representations of the
machine instant. `Time`, `DateTime` and `Date` are subtypes of `TimeType`.
"""
abstract type TimeType <: AbstractTime end

abstract type AbstractDateTime <: TimeType end

"""
    DateTime

`DateTime` wraps a `UTInstant{Millisecond}` and interprets it according to the proleptic
Gregorian calendar.
"""
struct DateTime <: AbstractDateTime
    instant::UTInstant{Millisecond}
    DateTime(instant::UTInstant{Millisecond}) = new(instant)
end

"""
    Date

`Date` wraps a `UTInstant{Day}` and interprets it according to the proleptic Gregorian calendar.
"""
struct Date <: TimeType
    instant::UTInstant{Day}
    Date(instant::UTInstant{Day}) = new(instant)
end

"""
    Time

`Time` wraps a `Nanosecond` and represents a specific moment in a 24-hour day.
"""
struct Time <: TimeType
    instant::Nanosecond
    Time(instant::Nanosecond) = new(mod(instant, 86400000000000))
end

# Convert y,m,d to # of Rata Die days
# Works by shifting the beginning of the year to March 1,
# so a leap day is the very last day of the year
const SHIFTEDMONTHDAYS = (306, 337, 0, 31, 61, 92, 122, 153, 184, 214, 245, 275)
function totaldays(y, m, d)
    # If we're in Jan/Feb, shift the given year back one
    z = m < 3 ? y - 1 : y
    mdays = SHIFTEDMONTHDAYS[m]
    # days + month_days + year_days
    return d + mdays + 365z + fld(z, 4) - fld(z, 100) + fld(z, 400) - 306
end

# If the year is divisible by 4, except for every 100 years, except for every 400 years
isleapyear(y) = (y % 4 == 0) && ((y % 100 != 0) || (y % 400 == 0))

# Number of days in month
const DAYSINMONTH = (31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31)
daysinmonth(y,m) = DAYSINMONTH[m] + (m == 2 && isleapyear(y))

### UTILITIES ###

# These are necessary because the type constructors for TimeType subtypes can
# throw, and we want to be able to use tryparse without requiring a try/catch.
# This is made easier by providing a helper function that checks arguments, so
# we can validate arguments in tryparse.

"""
    validargs(::Type{<:TimeType}, args...) -> Union{ArgumentError, Nothing}

Determine whether the given arguments constitute valid inputs for the given type.
Returns either an `ArgumentError`, or [`nothing`](@ref) in case of success.
"""
function validargs end

# Julia uses 24-hour clocks internally, but user input can be AM/PM with 12pm == noon and 12am == midnight.
@enum AMPM AM PM TWENTYFOURHOUR
function adjusthour(h::Int64, ampm::AMPM)
    ampm == TWENTYFOURHOUR && return h
    ampm == PM && h < 12 && return h + 12
    ampm == AM && h == 12 && return Int64(0)
    return h
end

### CONSTRUCTORS ###
# Core constructors
"""
    DateTime(y, [m, d, h, mi, s, ms]) -> DateTime

Construct a `DateTime` type by parts. Arguments must be convertible to [`Int64`](@ref).
"""
function DateTime(y::Int64, m::Int64=1, d::Int64=1,
                  h::Int64=0, mi::Int64=0, s::Int64=0, ms::Int64=0, ampm::AMPM=TWENTYFOURHOUR)
    err = validargs(DateTime, y, m, d, h, mi, s, ms, ampm)
    err === nothing || throw(err)
    h = adjusthour(h, ampm)
    rata = ms + 1000 * (s + 60mi + 3600h + 86400 * totaldays(y, m, d))
    return DateTime(UTM(rata))
end

function validargs(::Type{DateTime}, y::Int64, m::Int64, d::Int64,
                   h::Int64, mi::Int64, s::Int64, ms::Int64, ampm::AMPM=TWENTYFOURHOUR)
    0 < m < 13 || return ArgumentError("Month: $m out of range (1:12)")
    0 < d < daysinmonth(y, m) + 1 || return ArgumentError("Day: $d out of range (1:$(daysinmonth(y, m)))")
    if ampm == TWENTYFOURHOUR # 24-hour clock
        -1 < h < 24 || (h == 24 && mi==s==ms==0) ||
            return ArgumentError("Hour: $h out of range (0:23)")
    else
        0 < h < 13 || return ArgumentError("Hour: $h out of range (1:12)")
    end
    -1 < mi < 60 || return ArgumentError("Minute: $mi out of range (0:59)")
    -1 < s < 60 || return ArgumentError("Second: $s out of range (0:59)")
    -1 < ms < 1000 || return ArgumentError("Millisecond: $ms out of range (0:999)")
    return nothing
end

DateTime(dt::Base.Libc.TmStruct) = DateTime(1900 + dt.year, 1 + dt.month, dt.mday, dt.hour, dt.min, dt.sec)

"""
    Date(y, [m, d]) -> Date

Construct a `Date` type by parts. Arguments must be convertible to [`Int64`](@ref).
"""
function Date(y::Int64, m::Int64=1, d::Int64=1)
    err = validargs(Date, y, m, d)
    err === nothing || throw(err)
    return Date(UTD(totaldays(y, m, d)))
end

function validargs(::Type{Date}, y::Int64, m::Int64, d::Int64)
    0 < m < 13 || return ArgumentError("Month: $m out of range (1:12)")
    0 < d < daysinmonth(y, m) + 1 || return ArgumentError("Day: $d out of range (1:$(daysinmonth(y, m)))")
    return nothing
end

Date(dt::Base.Libc.TmStruct) = Date(1900 + dt.year, 1 + dt.month, dt.mday)

"""
    Time(h, [mi, s, ms, us, ns]) -> Time

Construct a `Time` type by parts. Arguments must be convertible to [`Int64`](@ref).
"""
function Time(h::Int64, mi::Int64=0, s::Int64=0, ms::Int64=0, us::Int64=0, ns::Int64=0, ampm::AMPM=TWENTYFOURHOUR)
    err = validargs(Time, h, mi, s, ms, us, ns, ampm)
    err === nothing || throw(err)
    h = adjusthour(h, ampm)
    return Time(Nanosecond(ns + 1000us + 1000000ms + 1000000000s + 60000000000mi + 3600000000000h))
end

function validargs(::Type{Time}, h::Int64, mi::Int64, s::Int64, ms::Int64, us::Int64, ns::Int64, ampm::AMPM=TWENTYFOURHOUR)
    if ampm == TWENTYFOURHOUR # 24-hour clock
        -1 < h < 24 || return ArgumentError("Hour: $h out of range (0:23)")
    else
        0 < h < 13 || return ArgumentError("Hour: $h out of range (1:12)")
    end
    -1 < mi < 60 || return ArgumentError("Minute: $mi out of range (0:59)")
    -1 < s < 60 || return ArgumentError("Second: $s out of range (0:59)")
    -1 < ms < 1000 || return ArgumentError("Millisecond: $ms out of range (0:999)")
    -1 < us < 1000 || return ArgumentError("Microsecond: $us out of range (0:999)")
    -1 < ns < 1000 || return ArgumentError("Nanosecond: $ns out of range (0:999)")
    return nothing
end

Time(dt::Base.Libc.TmStruct) = Time(dt.hour, dt.min, dt.sec)

# Convenience constructors from Periods
function DateTime(y::Year, m::Month=Month(1), d::Day=Day(1),
                  h::Hour=Hour(0), mi::Minute=Minute(0),
                  s::Second=Second(0), ms::Millisecond=Millisecond(0))
    return DateTime(value(y), value(m), value(d),
                    value(h), value(mi), value(s), value(ms))
end

Date(y::Year, m::Month=Month(1), d::Day=Day(1)) = Date(value(y), value(m), value(d))

function Time(h::Hour, mi::Minute=Minute(0), s::Second=Second(0),
              ms::Millisecond=Millisecond(0),
              us::Microsecond=Microsecond(0), ns::Nanosecond=Nanosecond(0))
    return Time(value(h), value(mi), value(s), value(ms), value(us), value(ns))
end

# To allow any order/combination of Periods

"""
    DateTime(periods::Period...) -> DateTime

Construct a `DateTime` type by `Period` type parts. Arguments may be in any order. DateTime
parts not provided will default to the value of `Dates.default(period)`.
"""
function DateTime(period::Period, periods::Period...)
    y = Year(1); m = Month(1); d = Day(1)
    h = Hour(0); mi = Minute(0); s = Second(0); ms = Millisecond(0)
    for p in (period, periods...)
        isa(p, Year) && (y = p::Year)
        isa(p, Month) && (m = p::Month)
        isa(p, Day) && (d = p::Day)
        isa(p, Hour) && (h = p::Hour)
        isa(p, Minute) && (mi = p::Minute)
        isa(p, Second) && (s = p::Second)
        isa(p, Millisecond) && (ms = p::Millisecond)
    end
    return DateTime(y, m, d, h, mi, s, ms)
end

"""
    Date(period::Period...) -> Date

Construct a `Date` type by `Period` type parts. Arguments may be in any order. `Date` parts
not provided will default to the value of `Dates.default(period)`.
"""
function Date(period::Period, periods::Period...)
    y = Year(1); m = Month(1); d = Day(1)
    for p in (period, periods...)
        isa(p, Year) && (y = p::Year)
        isa(p, Month) && (m = p::Month)
        isa(p, Day) && (d = p::Day)
    end
    return Date(y, m, d)
end

"""
    Time(period::TimePeriod...) -> Time

Construct a `Time` type by `Period` type parts. Arguments may be in any order. `Time` parts
not provided will default to the value of `Dates.default(period)`.
"""
function Time(period::TimePeriod, periods::TimePeriod...)
    h = Hour(0); mi = Minute(0); s = Second(0)
    ms = Millisecond(0); us = Microsecond(0); ns = Nanosecond(0)
    for p in (period, periods...)
        isa(p, Hour) && (h = p::Hour)
        isa(p, Minute) && (mi = p::Minute)
        isa(p, Second) && (s = p::Second)
        isa(p, Millisecond) && (ms = p::Millisecond)
        isa(p, Microsecond) && (us = p::Microsecond)
        isa(p, Nanosecond) && (ns = p::Nanosecond)
    end
    return Time(h, mi, s, ms, us, ns)
end

# Convenience constructor for DateTime from Date and Time
"""
    DateTime(d::Date, t::Time)

Construct a `DateTime` type by `Date` and `Time`.
Non-zero microseconds or nanoseconds in the `Time` type will result in an
`InexactError`.

!!! compat "Julia 1.1"
    This function requires at least Julia 1.1.

```jldoctest
julia> d = Date(2018, 1, 1)
2018-01-01

julia> t = Time(8, 15, 42)
08:15:42

julia> DateTime(d, t)
2018-01-01T08:15:42
```
"""
function DateTime(dt::Date, t::Time)
    (microsecond(t) > 0 || nanosecond(t) > 0) && throw(InexactError(:DateTime, DateTime, t))
    y, m, d = yearmonthday(dt)
    return DateTime(y, m, d, hour(t), minute(t), second(t), millisecond(t))
end

# Fallback constructors
DateTime(y, m=1, d=1, h=0, mi=0, s=0, ms=0, ampm::AMPM=TWENTYFOURHOUR) = DateTime(Int64(y), Int64(m), Int64(d), Int64(h), Int64(mi), Int64(s), Int64(ms), ampm)
Date(y, m=1, d=1) = Date(Int64(y), Int64(m), Int64(d))
Time(h, mi=0, s=0, ms=0, us=0, ns=0, ampm::AMPM=TWENTYFOURHOUR) = Time(Int64(h), Int64(mi), Int64(s), Int64(ms), Int64(us), Int64(ns), ampm)

# Traits, Equality
Base.isfinite(::Union{Type{T}, T}) where {T<:TimeType} = true
calendar(dt::DateTime) = ISOCalendar
calendar(dt::Date) = ISOCalendar

"""
    eps(::Type{DateTime}) -> Millisecond
    eps(::Type{Date}) -> Day
    eps(::Type{Time}) -> Nanosecond
    eps(::TimeType) -> Period

Return the smallest unit value supported by the `TimeType`.

# Examples
```jldoctest
julia> eps(DateTime)
1 millisecond

julia> eps(Date)
1 day

julia> eps(Time)
1 nanosecond
```
"""
Base.eps(::Union{Type{DateTime}, Type{Date}, Type{Time}, TimeType})

Base.eps(::Type{DateTime}) = Millisecond(1)
Base.eps(::Type{Date}) = Day(1)
Base.eps(::Type{Time}) = Nanosecond(1)
Base.eps(::T) where T <: TimeType = eps(T)::Period

# zero returns dt::T - dt::T
Base.zero(::Type{DateTime}) = Millisecond(0)
Base.zero(::Type{Date}) = Day(0)
Base.zero(::Type{Time}) = Nanosecond(0)
Base.zero(::T) where T <: TimeType = zero(T)::Period


Base.typemax(::Union{DateTime, Type{DateTime}}) = DateTime(146138512, 12, 31, 23, 59, 59)
Base.typemin(::Union{DateTime, Type{DateTime}}) = DateTime(-146138511, 1, 1, 0, 0, 0)
Base.typemax(::Union{Date, Type{Date}}) = Date(252522163911149, 12, 31)
Base.typemin(::Union{Date, Type{Date}}) = Date(-252522163911150, 1, 1)
Base.typemax(::Union{Time, Type{Time}}) = Time(23, 59, 59, 999, 999, 999)
Base.typemin(::Union{Time, Type{Time}}) = Time(0)
# Date-DateTime promotion, isless, ==
Base.promote_rule(::Type{Date}, x::Type{DateTime}) = DateTime
Base.isless(x::T, y::T) where {T<:TimeType} = isless(value(x), value(y))
Base.isless(x::TimeType, y::TimeType) = isless(promote(x, y)...)
(==)(x::T, y::T) where {T<:TimeType} = (==)(value(x), value(y))
(==)(x::TimeType, y::TimeType) = (===)(promote(x, y)...)
Base.min(x::AbstractTime) = x
Base.max(x::AbstractTime) = x
Base.minmax(x::AbstractTime) = (x, x)
Base.hash(x::Time, h::UInt) =
    hash(hour(x), hash(minute(x), hash(second(x),
        hash(millisecond(x), hash(microsecond(x), hash(nanosecond(x), h))))))

Base.sleep(duration::Period) = sleep(toms(duration) / 1000)

function Base.Timer(delay::Period; interval::Period=Second(0))
    Timer(toms(delay) / 1000, interval=toms(interval) / 1000)
end

function Base.timedwait(testcb, timeout::Period; pollint::Period=Millisecond(100))
    timedwait(testcb, toms(timeout) / 1000, pollint=toms(pollint) / 1000)
end

Base.OrderStyle(::Type{<:AbstractTime}) = Base.Ordered()
Base.ArithmeticStyle(::Type{<:AbstractTime}) = Base.ArithmeticWraps()
p   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Dates/src/periods.jl�C      # This file is a part of Julia. License is MIT: https://julialang.org/license

#Period types
"""
    Dates.value(x::Period) -> Int64

For a given period, return the value associated with that period.  For example,
`value(Millisecond(10))` returns 10 as an integer.
"""
value(x::Period) = x.value

# The default constructors for Periods work well in almost all cases
# P(x) = new((convert(Int64,x))
# The following definitions are for Period-specific safety
for period in (:Year, :Quarter, :Month, :Week, :Day, :Hour, :Minute, :Second, :Millisecond, :Microsecond, :Nanosecond)
    period_str = string(period)
    accessor_str = lowercase(period_str)
    # Convenience method for show()
    @eval _units(x::$period) = " " * $accessor_str * (abs(value(x)) == 1 ? "" : "s")
    # AbstractString parsing (mainly for IO code)
    @eval $period(x::AbstractString) = $period(Base.parse(Int64, x))
    # The period type is printed when output, thus it already implies its own typeinfo
    @eval Base.typeinfo_implicit(::Type{$period}) = true
    # Period accessors
    typs = period in (:Microsecond, :Nanosecond) ? ["Time"] :
           period in (:Hour, :Minute, :Second, :Millisecond) ? ["Time", "DateTime"] : ["Date", "DateTime"]
    reference = period === :Week ? " For details see [`$accessor_str(::Union{Date, DateTime})`](@ref)." : ""
    for typ_str in typs
        @eval begin
            @doc """
                $($period_str)(dt::$($typ_str)) -> $($period_str)

            The $($accessor_str) part of a $($typ_str) as a `$($period_str)`.$($reference)
            """ $period(dt::$(Symbol(typ_str))) = $period($(Symbol(accessor_str))(dt))
        end
    end
    @eval begin
        @doc """
            $($period_str)(v)

        Construct a `$($period_str)` object with the given `v` value. Input must be
        losslessly convertible to an [`Int64`](@ref).
        """ $period(v)
    end
end

#Print/show/traits
Base.print(io::IO, x::Period) = print(io, value(x), _units(x))
Base.show(io::IO, ::MIME"text/plain", x::Period) = print(io, x)
Base.show(io::IO, p::P) where {P<:Period} = print(io, P, '(', value(p), ')')
Base.zero(::Union{Type{P},P}) where {P<:Period} = P(0)
Base.one(::Union{Type{P},P}) where {P<:Period} = 1  # see #16116
Base.typemin(::Type{P}) where {P<:Period} = P(typemin(Int64))
Base.typemax(::Type{P}) where {P<:Period} = P(typemax(Int64))
Base.isfinite(::Union{Type{P}, P}) where {P<:Period} = true

# Default values (as used by TimeTypes)
"""
    default(p::Period) -> Period

Return a sensible "default" value for the input Period by returning `T(1)` for Year,
Month, and Day, and `T(0)` for Hour, Minute, Second, and Millisecond.
"""
function default end

default(p::Union{T,Type{T}}) where {T<:DatePeriod} = T(1)
default(p::Union{T,Type{T}}) where {T<:TimePeriod} = T(0)

(-)(x::P) where {P<:Period} = P(-value(x))
==(x::P, y::P) where {P<:Period} = value(x) == value(y)
Base.isless(x::P, y::P) where {P<:Period} = isless(value(x), value(y))

# Period Arithmetic, grouped by dimensionality:
for op in (:+, :-, :lcm, :gcd)
    @eval ($op)(x::P, y::P) where {P<:Period} = P(($op)(value(x), value(y)))
end

/(x::P, y::P) where {P<:Period} = /(value(x), value(y))
/(x::P, y::Real) where {P<:Period} = P(/(value(x), y))
div(x::P, y::P, r::RoundingMode) where {P<:Period} = div(value(x), value(y), r)
div(x::P, y::Real, r::RoundingMode) where {P<:Period} = P(div(value(x), Int64(y), r))

for op in (:rem, :mod)
    @eval begin
        ($op)(x::P, y::P) where {P<:Period} = P(($op)(value(x), value(y)))
        ($op)(x::P, y::Real) where {P<:Period} = P(($op)(value(x), Int64(y)))
    end
end

(*)(x::P, y::Real) where {P<:Period} = P(value(x) * y)
(*)(y::Real, x::Period) = x * y

(*)(A::Period, B::AbstractArray) = Broadcast.broadcast_preserving_zero_d(*, A, B)
(*)(A::AbstractArray, B::Period) = Broadcast.broadcast_preserving_zero_d(*, A, B)

for op in (:(==), :isless, :/, :rem, :mod, :lcm, :gcd)
    @eval ($op)(x::Period, y::Period) = ($op)(promote(x, y)...)
end
div(x::Period, y::Period, r::RoundingMode) = div(promote(x, y)..., r)

# intfuncs
Base.gcdx(a::T, b::T) where {T<:Period} = ((g, x, y) = gcdx(value(a), value(b)); return T(g), x, y)
Base.abs(a::T) where {T<:Period} = T(abs(value(a)))
Base.sign(x::Period) = sign(value(x))

# return (next coarser period, conversion factor):
coarserperiod(::Type{P}) where {P<:Period} = (P, 1)
coarserperiod(::Type{Nanosecond})  = (Microsecond, 1000)
coarserperiod(::Type{Microsecond}) = (Millisecond, 1000)
coarserperiod(::Type{Millisecond}) = (Second, 1000)
coarserperiod(::Type{Second}) = (Minute, 60)
coarserperiod(::Type{Minute}) = (Hour, 60)
coarserperiod(::Type{Hour}) = (Day, 24)
coarserperiod(::Type{Day}) = (Week, 7)
coarserperiod(::Type{Month}) = (Year, 12)

# Stores multiple periods in greatest to least order by type, not values,
# canonicalized to eliminate zero periods, merge equal period types,
# and convert more-precise periods to less-precise periods when possible
"""
    CompoundPeriod

A `CompoundPeriod` is useful for expressing time periods that are not a fixed multiple of
smaller periods. For example, "a year and a  day" is not a fixed number of days, but can
be expressed using a `CompoundPeriod`. In fact, a `CompoundPeriod` is automatically
generated by addition of different period types, e.g. `Year(1) + Day(1)` produces a
`CompoundPeriod` result.
"""
struct CompoundPeriod <: AbstractTime
    periods::Vector{Period}
    function CompoundPeriod(p::Vector{Period})
        n = length(p)
        if n > 1
            # We sort periods in decreasing order (rev = true) according to the length of
            # the period's type (by = tons ∘ oneunit). We sort by type, not value, so that
            # we can merge equal types.
            #
            # This works by computing how many nanoseconds are in a single period, and sorting
            # by that. For example, (tons ∘ oneunit)(Week(10)) = tons(oneunit(Week(10))) =
            # tons(Week(1)) ≈ 6.0e14, which is less than (tons ∘ oneunit)(Month(-2)) ≈ 2.6e15
            sort!(p, rev = true, by = tons ∘ oneunit)
            # canonicalize p by merging equal period types and removing zeros
            i = j = 1
            while j <= n
                k = j + 1
                while k <= n && typeof(p[j]) == typeof(p[k])
                    p[j] += p[k]
                    k += 1
                end
                if !iszero(p[j])
                    p[i] = p[j]
                    i += 1
                end
                j = k
            end
            n = i - 1 # new length
            p = resize!(p, n)
        elseif n == 1 && value(p[1]) == 0
            p = Period[]
        end

        return new(p)
    end
end

"""
    Dates.periods(::CompoundPeriod) -> Vector{Period}

Return the `Vector` of `Period`s that comprise the given `CompoundPeriod`.

!!! compat "Julia 1.7"
    This function requires Julia 1.7 or later.
"""
periods(x::CompoundPeriod) = x.periods

"""
    CompoundPeriod(periods) -> CompoundPeriod

Construct a `CompoundPeriod` from a `Vector` of `Period`s. All `Period`s of the same type
will be added together.

# Examples
```jldoctest
julia> Dates.CompoundPeriod(Dates.Hour(12), Dates.Hour(13))
25 hours

julia> Dates.CompoundPeriod(Dates.Hour(-1), Dates.Minute(1))
-1 hour, 1 minute

julia> Dates.CompoundPeriod(Dates.Month(1), Dates.Week(-2))
1 month, -2 weeks

julia> Dates.CompoundPeriod(Dates.Minute(50000))
50000 minutes
```
"""
CompoundPeriod(p::Vector{<:Period}) = CompoundPeriod(Vector{Period}(p))

CompoundPeriod(t::Time) = CompoundPeriod(Period[Hour(t), Minute(t), Second(t), Millisecond(t),
                                                Microsecond(t), Nanosecond(t)])

CompoundPeriod(p::Period...) = CompoundPeriod(Period[p...])


"""
    canonicalize(::CompoundPeriod) -> CompoundPeriod

Reduces the `CompoundPeriod` into its canonical form by applying the following rules:

* Any `Period` large enough be partially representable by a coarser `Period` will be broken
  into multiple `Period`s (eg. `Hour(30)` becomes `Day(1) + Hour(6)`)
* `Period`s with opposite signs will be combined when possible
  (eg. `Hour(1) - Day(1)` becomes `-Hour(23)`)

# Examples
```jldoctest
julia> canonicalize(Dates.CompoundPeriod(Dates.Hour(12), Dates.Hour(13)))
1 day, 1 hour

julia> canonicalize(Dates.CompoundPeriod(Dates.Hour(-1), Dates.Minute(1)))
-59 minutes

julia> canonicalize(Dates.CompoundPeriod(Dates.Month(1), Dates.Week(-2)))
1 month, -2 weeks

julia> canonicalize(Dates.CompoundPeriod(Dates.Minute(50000)))
4 weeks, 6 days, 17 hours, 20 minutes
```
"""
canonicalize(x::Period) = canonicalize(CompoundPeriod(x))
function canonicalize(x::CompoundPeriod)
    # canonicalize Periods by pushing "overflow" into a coarser period.
    p = x.periods
    n = length(p)
    if n > 0
        pc = sizehint!(Period[], n)
        P = typeof(p[n])
        v = value(p[n])
        i = n - 1
        while true
            Pc, f = coarserperiod(P)
            if i > 0 && typeof(p[i]) == P
                v += value(p[i])
                i -= 1
            end
            v0 = f == 1 ? v : rem(v, f)
            v0 != 0 && push!(pc, P(v0))
            if v != v0
                P = Pc
                v = div(v - v0, f)
            elseif i > 0
                P = typeof(p[i])
                v = value(p[i])
                i -= 1
            else
                break
            end
        end
        p = reverse!(pc)
        n = length(p)
    else
        return x
    end

    # reduce the amount of mixed positive/negative Periods.
    if n > 0
        pc = sizehint!(Period[], n)
        i = n
        while i > 0
            j = i

            # Determine sign of the largest period in this group which
            # can be converted into via coarserperiod.
            last = Union{}
            current = typeof(p[i])
            while i > 0 && current != last
                if typeof(p[i]) == current
                    i -= 1
                end
                last, current = current, coarserperiod(current)[1]
            end
            s = sign(value(p[i + 1]))

            # Adjust all the periods in the group based upon the
            # largest period sign.
            P = typeof(p[j])
            v = 0
            while j > i
                Pc, f = coarserperiod(P)
                if j > 0 && typeof(p[j]) == P
                    v += value(p[j])
                    j -= 1
                end
                v0 = f == 1 ? v : mod(v, f * s)
                v0 != 0 && push!(pc, P(v0))
                if v != v0
                    P = Pc
                    v = div(v - v0, f)
                elseif j > 0
                    P = typeof(p[j])
                    v = 0
                else
                    break
                end
            end
        end
        p = reverse!(pc)
    end

    return CompoundPeriod(p)
end

Base.convert(::Type{CompoundPeriod}, x::Period) = CompoundPeriod(Period[x])
function Base.string(x::CompoundPeriod)
    if isempty(x.periods)
        return "empty period"
    else
        s = ""
        for p in x.periods
            s *= ", " * string(p)
        end
        return s[3:end]
    end
end
Base.show(io::IO,x::CompoundPeriod) = print(io, string(x))

Base.convert(::Type{T}, x::CompoundPeriod) where T<:Period =
    isconcretetype(T) ? sum(T, x.periods) : throw(MethodError(convert,(T,x)))

# E.g. Year(1) + Day(1)
(+)(x::Period,y::Period) = CompoundPeriod(Period[x, y])
(+)(x::CompoundPeriod, y::Period) = CompoundPeriod(vcat(x.periods, y))
(+)(y::Period, x::CompoundPeriod) = x + y
(+)(x::CompoundPeriod, y::CompoundPeriod) = CompoundPeriod(vcat(x.periods, y.periods))
# E.g. Year(1) - Month(1)
(-)(x::Period, y::Period) = CompoundPeriod(Period[x, -y])
(-)(x::CompoundPeriod, y::Period) = CompoundPeriod(vcat(x.periods, -y))
(-)(x::CompoundPeriod) = CompoundPeriod(-x.periods)
(-)(y::Union{Period, CompoundPeriod}, x::CompoundPeriod) = (-x) + y

GeneralPeriod = Union{Period, CompoundPeriod}
(+)(x::GeneralPeriod) = x

(==)(x::CompoundPeriod, y::Period) = x == CompoundPeriod(y)
(==)(x::Period, y::CompoundPeriod) = y == x
(==)(x::CompoundPeriod, y::CompoundPeriod) = canonicalize(x).periods == canonicalize(y).periods

Base.isequal(x::CompoundPeriod, y::Period) = isequal(x, CompoundPeriod(y))
Base.isequal(x::Period, y::CompoundPeriod) = isequal(y, x)
Base.isequal(x::CompoundPeriod, y::CompoundPeriod) = isequal(x.periods, y.periods)

# Capture TimeType+-Period methods
(+)(a::TimeType, b::Period, c::Period) = (+)(a, b + c)
(+)(a::TimeType, b::Period, c::Period, d::Period...) = (+)((+)(a, b + c), d...)

function (+)(x::TimeType, y::CompoundPeriod)
    for p in y.periods
        x += p
    end
    return x
end
(+)(x::CompoundPeriod, y::TimeType) = y + x

function (-)(x::TimeType, y::CompoundPeriod)
    for p in y.periods
        x -= p
    end
    return x
end

# Fixed-value Periods (periods corresponding to a well-defined time interval,
# as opposed to variable calendar intervals like Year).
const FixedPeriod = Union{Week, Day, Hour, Minute, Second, Millisecond, Microsecond, Nanosecond}

# like div but throw an error if remainder is nonzero
function divexact(x, y)
    q, r = divrem(x, y)
    r == 0 || throw(InexactError(:divexact, Int, x/y))
    return q
end

# TODO: this is needed to prevent undefined Period constructors from
# hitting the deprecated construct-to-convert fallback.
(::Type{T})(p::Period) where {T<:Period} = convert(T, p)::T

# Conversions and promotion rules
function define_conversions(periods)
    for i = eachindex(periods)
        T, n = periods[i]
        N = Int64(1)
        for j = (i - 1):-1:firstindex(periods) # less-precise periods
            Tc, nc = periods[j]
            N *= nc
            vmax = typemax(Int64) ÷ N
            vmin = typemin(Int64) ÷ N
            @eval function Base.convert(::Type{$T}, x::$Tc)
                $vmin ≤ value(x) ≤ $vmax || throw(InexactError(:convert, $T, x))
                return $T(value(x) * $N)
            end
        end
        N = n
        for j = (i + 1):lastindex(periods) # more-precise periods
            Tc, nc = periods[j]
            @eval Base.convert(::Type{$T}, x::$Tc) = $T(divexact(value(x), $N))
            @eval Base.promote_rule(::Type{$T}, ::Type{$Tc}) = $Tc
            N *= nc
        end
    end
end
define_conversions([(:Week, 7), (:Day, 24), (:Hour, 60), (:Minute, 60), (:Second, 1000),
                    (:Millisecond, 1000), (:Microsecond, 1000), (:Nanosecond, 1)])
define_conversions([(:Year, 4), (:Quarter, 3), (:Month, 1)])

# fixed is not comparable to other periods, except when both are zero (#37459)
const OtherPeriod = Union{Month, Quarter, Year}
(==)(x::FixedPeriod, y::OtherPeriod) = iszero(x) & iszero(y)
(==)(x::OtherPeriod, y::FixedPeriod) = y == x

const zero_or_fixedperiod_seed = UInt === UInt64 ? 0x5b7fc751bba97516 : 0xeae0fdcb
const nonzero_otherperiod_seed = UInt === UInt64 ? 0xe1837356ff2d2ac9 : 0x170d1b00
otherperiod_seed(x) = iszero(value(x)) ? zero_or_fixedperiod_seed : nonzero_otherperiod_seed
# tons() will overflow for periods longer than ~300,000 years, implying a hash collision
# which is relatively harmless given how infrequently such periods should appear
Base.hash(x::FixedPeriod, h::UInt) = hash(tons(x), h + zero_or_fixedperiod_seed)
# Overflow can also happen here for really long periods (~8e17 years)
Base.hash(x::Year, h::UInt) = hash(12 * value(x), h + otherperiod_seed(x))
Base.hash(x::Quarter, h::UInt) = hash(3 * value(x), h + otherperiod_seed(x))
Base.hash(x::Month, h::UInt) = hash(value(x), h + otherperiod_seed(x))

function Base.hash(x::CompoundPeriod, h::UInt)
    isempty(x.periods) && return hash(0, h + zero_or_fixedperiod_seed)
    for p in x.periods
        h = hash(p, h)
    end
    return h
end

Base.isless(x::FixedPeriod, y::OtherPeriod) = throw(MethodError(isless, (x, y)))
Base.isless(x::OtherPeriod, y::FixedPeriod) = throw(MethodError(isless, (x, y)))

Base.isless(x::Period, y::CompoundPeriod) = CompoundPeriod(x) < y
Base.isless(x::CompoundPeriod, y::Period) = x < CompoundPeriod(y)
Base.isless(x::CompoundPeriod, y::CompoundPeriod) = tons(x) < tons(y)
# truncating conversions to milliseconds, nanoseconds and days:
# overflow can happen for periods longer than ~300,000 years
toms(c::Nanosecond)  = div(value(c), 1000000)
toms(c::Microsecond) = div(value(c), 1000)
toms(c::Millisecond) = value(c)
toms(c::Second)      = 1000 * value(c)
toms(c::Minute)      = 60000 * value(c)
toms(c::Hour)        = 3600000 * value(c)
toms(c::Period)      = 86400000 * days(c)
toms(c::CompoundPeriod) = isempty(c.periods) ? 0.0 : Float64(sum(toms, c.periods))
tons(x)              = toms(x) * 1000000
tons(x::Microsecond) = value(x) * 1000
tons(x::Nanosecond)  = value(x)
tons(c::CompoundPeriod) = isempty(c.periods) ? 0.0 : Float64(sum(tons, c.periods))
days(c::Millisecond) = div(value(c), 86400000)
days(c::Second)      = div(value(c), 86400)
days(c::Minute)      = div(value(c), 1440)
days(c::Hour)        = div(value(c), 24)
days(c::Day)         = value(c)
days(c::Week)        = 7 * value(c)
days(c::Year)        = 365.2425 * value(c)
days(c::Quarter)     = 91.310625 * value(c)
days(c::Month)       = 30.436875 * value(c)
days(c::CompoundPeriod) = isempty(c.periods) ? 0.0 : Float64(sum(days, c.periods))
r   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Dates/src/accessors.jlx      # This file is a part of Julia. License is MIT: https://julialang.org/license

# Convert # of Rata Die days to proleptic Gregorian calendar y,m,d,w
# Reference: http://mysite.verizon.net/aesir_research/date/date0.htm
function yearmonthday(days)
    z = days + 306; h = 100z - 25; a = fld(h, 3652425); b = a - fld(a, 4)
    y = fld(100b + h, 36525); c = b + z - 365y - fld(y, 4); m = div(5c + 456, 153)
    d = c - div(153m - 457, 5); return m > 12 ? (y + 1, m - 12, d) : (y, m, d)
end
function year(days)
   z = days + 306; h = 100z - 25; a = fld(h, 3652425); b = a - fld(a, 4)
   y = fld(100b + h, 36525); c = b + z - 365y - fld(y, 4); m = div(5c + 456, 153)
   return m > 12 ? y + 1 : y
end
function yearmonth(days)
    z = days + 306; h = 100z - 25; a = fld(h,3652425); b = a - fld(a,4)
    y = fld(100b + h, 36525); c = b + z - 365y - fld(y, 4); m = div(5c + 456, 153)
    return m > 12 ? (y + 1, m - 12) : (y, m)
end
function month(days)
    z = days + 306; h = 100z - 25; a = fld(h,3652425); b = a - fld(a,4)
    y = fld(100b + h, 36525); c = b + z - 365y - fld(y, 4); m = div(5c + 456, 153)
    return m > 12 ? m - 12 : m
end
function monthday(days)
    z = days + 306; h = 100z - 25; a = fld(h,3652425); b = a - fld(a,4)
    y = fld(100b + h, 36525); c = b + z - 365y - fld(y, 4); m = div(5c + 456, 153)
    d = c - div(153m - 457, 5); return m > 12 ? (m - 12, d) : (m, d)
end
function day(days)
    z = days + 306; h = 100z - 25; a = fld(h,3652425); b = a - fld(a,4)
    y = fld(100b + h, 36525); c = b + z - 365y - fld(y, 4); m = div(5c + 456, 153)
    return c - div(153m - 457, 5)
end
# https://en.wikipedia.org/wiki/Talk:ISO_week_date#Algorithms
const WEEK_INDEX = (15, 23, 3, 11)
function week(days)
    w = div(abs(days - 1), 7) % 20871
    c, w = divrem((w + (w >= 10435)), 5218)
    w = (w * 28 + WEEK_INDEX[c + 1]) % 1461
    return div(w, 28) + 1
end

function quarter(days)
    m = month(days)
    return m < 4 ? 1 : m < 7 ? 2 : m < 10 ? 3 : 4
end


# Accessor functions
value(dt::TimeType) = dt.instant.periods.value
value(t::Time) = t.instant.value
days(dt::Date) = value(dt)
days(dt::DateTime) = fld(value(dt), 86400000)
year(dt::TimeType) = year(days(dt))
quarter(dt::TimeType) = quarter(days(dt))
month(dt::TimeType) = month(days(dt))
week(dt::TimeType) = week(days(dt))
day(dt::TimeType) = day(days(dt))
hour(dt::DateTime)   = mod(fld(value(dt), 3600000), 24)
minute(dt::DateTime) = mod(fld(value(dt), 60000), 60)
second(dt::DateTime) = mod(fld(value(dt), 1000), 60)
millisecond(dt::DateTime) = mod(value(dt), 1000)
hour(t::Time)   = mod(fld(value(t), 3600000000000), Int64(24))
minute(t::Time) = mod(fld(value(t), 60000000000), Int64(60))
second(t::Time) = mod(fld(value(t), 1000000000), Int64(60))
millisecond(t::Time) = mod(fld(value(t), Int64(1000000)), Int64(1000))
microsecond(t::Time) = mod(fld(value(t), Int64(1000)), Int64(1000))
nanosecond(t::Time) = mod(value(t), Int64(1000))

dayofmonth(dt::TimeType) = day(dt)

yearmonth(dt::TimeType) = yearmonth(days(dt))
monthday(dt::TimeType) = monthday(days(dt))
yearmonthday(dt::TimeType) = yearmonthday(days(dt))

# Documentation for exported accessors
for func in (:year, :month, :quarter)
    name = string(func)
    @eval begin
        @doc """
            $($name)(dt::TimeType) -> Int64

        The $($name) of a `Date` or `DateTime` as an [`Int64`](@ref).
        """ $func(dt::TimeType)
    end
end

"""
    week(dt::TimeType) -> Int64

Return the [ISO week date](https://en.wikipedia.org/wiki/ISO_week_date) of a `Date` or
`DateTime` as an [`Int64`](@ref). Note that the first week of a year is the week that
contains the first Thursday of the year, which can result in dates prior to January 4th
being in the last week of the previous year. For example, `week(Date(2005, 1, 1))` is the 53rd
week of 2004.

# Examples
```jldoctest
julia> week(Date(1989, 6, 22))
25

julia> week(Date(2005, 1, 1))
53

julia> week(Date(2004, 12, 31))
53
```
"""
week(dt::TimeType)

for func in (:day, :dayofmonth)
    name = string(func)
    @eval begin
        @doc """
            $($name)(dt::TimeType) -> Int64

        The day of month of a `Date` or `DateTime` as an [`Int64`](@ref).
        """ $func(dt::TimeType)
    end
end

"""
    hour(dt::DateTime) -> Int64

The hour of day of a `DateTime` as an [`Int64`](@ref).
"""
hour(dt::DateTime)

for func in (:minute, :second, :millisecond)
    name = string(func)
    @eval begin
        @doc """
            $($name)(dt::DateTime) -> Int64

        The $($name) of a `DateTime` as an [`Int64`](@ref).
        """ $func(dt::DateTime)
    end
end

for parts in (["year", "month"], ["month", "day"], ["year", "month", "day"])
    name = join(parts)
    func = Symbol(name)
    @eval begin
        @doc """
            $($name)(dt::TimeType) -> ($(join(repeated(Int64, length($parts)), ", ")))

        Simultaneously return the $(join($parts, ", ", " and ")) parts of a `Date` or
        `DateTime`.
        """ $func(dt::TimeType)
    end
end

for func in (:hour, :minute, :second, :millisecond, :microsecond, :nanosecond)
    name = string(func)
    @eval begin
        @doc """
            $($name)(t::Time) -> Int64

        The $($name) of a `Time` as an [`Int64`](@ref).
        """ $func(t::Time)
    end
end
n   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Dates/src/query.jl�1      # This file is a part of Julia. License is MIT: https://julialang.org/license

# Date Locales

struct DateLocale
    months::Vector{String}
    months_abbr::Vector{String}
    days_of_week::Vector{String}
    days_of_week_abbr::Vector{String}
    month_value::Dict{String, Int64}
    month_abbr_value::Dict{String, Int64}
    day_of_week_value::Dict{String, Int64}
    day_of_week_abbr_value::Dict{String, Int64}
end

function locale_dict(names::Vector{<:AbstractString})
    result = Dict{String, Int}()

    # Keep both the common case-sensitive version of the name and an all lowercase
    # version for case-insensitive matches. Storing both allows us to avoid using the
    # lowercase function during parsing.
    for i in 1:length(names)
        name = names[i]
        result[name] = i
        result[lowercase(name)] = i
    end
    return result
end

"""
    DateLocale(["January", "February",...], ["Jan", "Feb",...],
               ["Monday", "Tuesday",...], ["Mon", "Tue",...])

Create a locale for parsing or printing textual month names.

Arguments:

- `months::Vector`: 12 month names
- `months_abbr::Vector`: 12 abbreviated month names
- `days_of_week::Vector`: 7 days of week
- `days_of_week_abbr::Vector`: 7 days of week abbreviated

This object is passed as the last argument to `tryparsenext` and `format`
methods defined for each `AbstractDateToken` type.
"""
function DateLocale(months::Vector, months_abbr::Vector,
                    days_of_week::Vector, days_of_week_abbr::Vector)
    DateLocale(
        months, months_abbr, days_of_week, days_of_week_abbr,
        locale_dict(months), locale_dict(months_abbr),
        locale_dict(days_of_week), locale_dict(days_of_week_abbr),
    )
end

const ENGLISH = DateLocale(
    ["January", "February", "March", "April", "May", "June",
     "July", "August", "September", "October", "November", "December"],
    ["Jan", "Feb", "Mar", "Apr", "May", "Jun",
     "Jul", "Aug", "Sep", "Oct", "Nov", "Dec"],
    ["Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday", "Sunday"],
    ["Mon", "Tue", "Wed", "Thu", "Fri", "Sat", "Sun"],
)

const LOCALES = Dict{String, DateLocale}("english" => ENGLISH)

for (fn, field) in zip(
    [:dayname_to_value, :dayabbr_to_value, :monthname_to_value, :monthabbr_to_value],
    [:day_of_week_value, :day_of_week_abbr_value, :month_value, :month_abbr_value],
)
    @eval @inline function $fn(word::AbstractString, locale::DateLocale)
        # Maximize performance by attempting to avoid the use of `lowercase` and trying
        # a case-sensitive lookup first
        value = get(locale.$field, word, 0)
        if value == 0
            value = get(locale.$field, lowercase(word), 0)
        end
        value
    end
end

# Date functions

### Core query functions

# Monday = 1....Sunday = 7
dayofweek(days) = mod1(days, 7)

# Number of days in year
"""
    daysinyear(dt::TimeType) -> Int

Return 366 if the year of `dt` is a leap year, otherwise return 365.

# Examples
```jldoctest
julia> daysinyear(1999)
365

julia> daysinyear(2000)
366
```
"""
daysinyear(y) = 365 + isleapyear(y)

# Day of the year
const MONTHDAYS = (0, 31, 59, 90, 120, 151, 181, 212, 243, 273, 304, 334)
dayofyear(y, m, d) = MONTHDAYS[m] + d + (m > 2 && isleapyear(y))

### Days of the Week
"""
    dayofweek(dt::TimeType) -> Int64

Return the day of the week as an [`Int64`](@ref) with `1 = Monday, 2 = Tuesday, etc.`.

# Examples
```jldoctest
julia> dayofweek(Date("2000-01-01"))
6
```
"""
dayofweek(dt::TimeType) = dayofweek(days(dt))

const Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday = 1, 2, 3, 4, 5, 6, 7
const Mon, Tue, Wed, Thu, Fri, Sat, Sun = 1, 2, 3, 4, 5, 6, 7
for (ii, day_ind, short_day, long_day) in ((1, "first", :Mon, :Monday), (2, "second", :Tue, :Tuesday), (3, "third", :Wed, :Wednesday), (4, "fourth", :Thu, :Thursday), (5, "fifth", :Fri, :Friday), (6, "sixth", :Sat, :Saturday), (7, "seventh", :Sun, :Sunday))
    short_name = string(short_day)
    long_name = string(long_day)
    name_ind = day_ind
    ind_str = string(ii)
    @eval begin
        @doc """
        $($long_name)
        $($short_name)

        The $($name_ind) day of the week.

        # Examples
        ```jldoctest
        julia> $($long_name)
        $($ind_str)

        julia> $($short_name)
        $($ind_str)
        ```
        """ ($long_day, $short_day)
   end
end
dayname(day::Integer, locale::DateLocale) = locale.days_of_week[day]
dayabbr(day::Integer, locale::DateLocale) = locale.days_of_week_abbr[day]
dayname(day::Integer; locale::AbstractString="english") = dayname(day, LOCALES[locale])
dayabbr(day::Integer; locale::AbstractString="english") = dayabbr(day, LOCALES[locale])

"""
    dayname(dt::TimeType; locale="english") -> String
    dayname(day::Integer; locale="english") -> String

Return the full day name corresponding to the day of the week of the `Date` or `DateTime` in
the given `locale`. Also accepts `Integer`.

# Examples
```jldoctest
julia> dayname(Date("2000-01-01"))
"Saturday"

julia> dayname(4)
"Thursday"
```
"""
function dayname(dt::TimeType;locale::AbstractString="english")
    dayname(dayofweek(dt); locale=locale)
end

"""
    dayabbr(dt::TimeType; locale="english") -> String
    dayabbr(day::Integer; locale="english") -> String

Return the abbreviated name corresponding to the day of the week of the `Date` or `DateTime`
in the given `locale`. Also accepts `Integer`.

# Examples
```jldoctest
julia> dayabbr(Date("2000-01-01"))
"Sat"

julia> dayabbr(3)
"Wed"
```
"""
function dayabbr(dt::TimeType;locale::AbstractString="english")
    dayabbr(dayofweek(dt); locale=locale)
end

# Convenience methods for each day
ismonday(dt::TimeType) = dayofweek(dt) == Mon
istuesday(dt::TimeType) = dayofweek(dt) == Tue
iswednesday(dt::TimeType) = dayofweek(dt) == Wed
isthursday(dt::TimeType) = dayofweek(dt) == Thu
isfriday(dt::TimeType) = dayofweek(dt) == Fri
issaturday(dt::TimeType) = dayofweek(dt) == Sat
issunday(dt::TimeType) = dayofweek(dt) == Sun

# i.e. 1st Monday? 2nd Monday? 3rd Wednesday? 5th Sunday?
"""
    dayofweekofmonth(dt::TimeType) -> Int

For the day of week of `dt`, return which number it is in `dt`'s month. So if the day of
the week of `dt` is Monday, then `1 = First Monday of the month, 2 = Second Monday of the
month, etc.` In the range 1:5.

# Examples
```jldoctest
julia> dayofweekofmonth(Date("2000-02-01"))
1

julia> dayofweekofmonth(Date("2000-02-08"))
2

julia> dayofweekofmonth(Date("2000-02-15"))
3
```
"""
function dayofweekofmonth(dt::TimeType)
    d = day(dt)
    return d < 8 ? 1 : d < 15 ? 2 : d < 22 ? 3 : d < 29 ? 4 : 5
end

# Total number of a day of week in the month
# e.g. are there 4 or 5 Mondays in this month?
const TWENTYNINE = BitSet([1, 8, 15, 22, 29])
const THIRTY = BitSet([1, 2, 8, 9, 15, 16, 22, 23, 29, 30])
const THIRTYONE = BitSet([1, 2, 3, 8, 9, 10, 15, 16, 17, 22, 23, 24, 29, 30, 31])

"""
    daysofweekinmonth(dt::TimeType) -> Int

For the day of week of `dt`, return the total number of that day of the week in `dt`'s
month. Returns 4 or 5. Useful in temporal expressions for specifying the last day of a week
in a month by including `dayofweekofmonth(dt) == daysofweekinmonth(dt)` in the adjuster
function.

# Examples
```jldoctest
julia> daysofweekinmonth(Date("2005-01-01"))
5

julia> daysofweekinmonth(Date("2005-01-04"))
4
```
"""
function daysofweekinmonth(dt::TimeType)
    y, m, d = yearmonthday(dt)
    ld = daysinmonth(y, m)
    return ld == 28 ? 4 : ld == 29 ? ((d in TWENTYNINE) ? 5 : 4) :
           ld == 30 ? ((d in THIRTY) ? 5 : 4) :
           (d in THIRTYONE) ? 5 : 4
end

### Months
"""
    January

The first month of the year.

# Examples
```jldoctest
julia> January
1
```
"""
const January = 1

"""
    Jan

Abbreviation for [`January`](@ref).

# Examples
```jldoctest
julia> Jan
1
```
"""
const Jan = 1

"""
    February

The second month of the year.

# Examples
```jldoctest
julia> February
2
```
"""
const February = 2

"""
    Feb

Abbreviation for [`February`](@ref).

# Examples
```jldoctest
julia> Feb
2
```
"""
const Feb = 2

"""
    March

The third month of the year.

# Examples
```jldoctest
julia> March
3
```
"""
const March = 3

"""
    Mar

Abbreviation for [`March`](@ref).

# Examples
```jldoctest
julia> Mar
3
```
"""
const Mar = 3

"""
    April

The fourth month of the year.

# Examples
```jldoctest
julia> April
4
```
"""
const April = 4

"""
    Apr

Abbreviation for [`April`](@ref).

# Examples
```jldoctest
julia> Apr
4
```
"""
const Apr = 4

"""
    May

The fifth month of the year.

# Examples
```jldoctest
julia> May
5
```
"""
const May = 5

"""
    June

The sixth month of the year.

# Examples
```jldoctest
julia> June
6
```
"""
const June = 6

"""
    Jun

Abbreviation for [`June`](@ref).

# Examples
```jldoctest
julia> Jun
6
```
"""
const Jun = 6

"""
    July

The seventh month of the year.

# Examples
```jldoctest
julia> July
7
```
"""
const July = 7

"""
    Jul

Abbreviation for [`July`](@ref).

# Examples
```jldoctest
julia> Jul
7
```
"""
const Jul = 7

"""
    August

The eighth month of the year.

# Examples
```jldoctest
julia> August
8
```
"""
const August = 8

"""
    Aug

Abbreviation for [`August`](@ref).

# Examples
```jldoctest
julia> Aug
8
```
"""
const Aug = 8

"""
    September

The ninth month of the year.

# Examples
```jldoctest
julia> September
9
```
"""
const September = 9

"""
    Sep

Abbreviation for [`September`](@ref).

# Examples
```jldoctest
julia> Sep
9
```
"""
const Sep = 9

"""
    October

The tenth month of the year.

# Examples
```jldoctest
julia> October
10
```
"""
const October = 10

"""
    Oct

Abbreviation for [`October`](@ref).

# Examples
```jldoctest
julia> Oct
10
```
"""
const Oct = 10

"""
    November

The eleventh month of the year.

# Examples
```jldoctest
julia> November
11
```
"""
const November = 11

"""
    Nov

Abbreviation for [`November`](@ref).

# Examples
```jldoctest
julia> Nov
11
```
"""
const Nov = 11

"""
    December

The last month of the year.

# Examples
```jldoctest
julia> December
12
```
"""
const December = 12

"""
    Dec

Abbreviation for [`December`](@ref).

# Examples
```jldoctest
julia> Dec
12
```
"""
const Dec = 12

monthname(month::Integer, locale::DateLocale) = locale.months[month]
monthabbr(month::Integer, locale::DateLocale) = locale.months_abbr[month]
monthname(month::Integer; locale::AbstractString="english") = monthname(month, LOCALES[locale])
monthabbr(month::Integer; locale::AbstractString="english") = monthabbr(month, LOCALES[locale])

"""
    monthname(dt::TimeType; locale="english") -> String
    monthname(month::Integer, locale="english") -> String


Return the full name of the month of the `Date` or `DateTime` or `Integer` in the given `locale`.

# Examples
```jldoctest
julia> monthname(Date("2005-01-04"))
"January"

julia> monthname(2)
"February"
```
"""
function monthname(dt::TimeType; locale::AbstractString="english")
    monthname(month(dt); locale=locale)
end

"""
    monthabbr(dt::TimeType; locale="english") -> String
    monthabbr(month::Integer, locale="english") -> String

Return the abbreviated month name of the `Date` or `DateTime` or `Integer` in the given `locale`.

# Examples
```jldoctest
julia> monthabbr(Date("2005-01-04"))
"Jan"

julia> monthabbr(2)
"Feb"
```
"""
function monthabbr(dt::TimeType; locale::AbstractString="english")
    monthabbr(month(dt); locale=locale)
end

"""
    daysinmonth(dt::TimeType) -> Int

Return the number of days in the month of `dt`. Value will be 28, 29, 30, or 31.

# Examples
```jldoctest
julia> daysinmonth(Date("2000-01"))
31

julia> daysinmonth(Date("2001-02"))
28

julia> daysinmonth(Date("2000-02"))
29
```
"""
daysinmonth(dt::TimeType) = ((y, m) = yearmonth(dt); return daysinmonth(y, m))

### Years
"""
    isleapyear(dt::TimeType) -> Bool

Return `true` if the year of `dt` is a leap year.

# Examples
```jldoctest
julia> isleapyear(Date("2004"))
true

julia> isleapyear(Date("2005"))
false
```
"""
isleapyear(dt::TimeType) = isleapyear(year(dt))

"""
    dayofyear(dt::TimeType) -> Int

Return the day of the year for `dt` with January 1st being day 1.
"""
dayofyear(dt::TimeType) = ((y, m, d) = yearmonthday(dt); return dayofyear(y, m, d))

daysinyear(dt::TimeType) = 365 + isleapyear(dt)

### Quarters
"""
    quarterofyear(dt::TimeType) -> Int

Return the quarter that `dt` resides in. Range of value is 1:4.
"""
quarterofyear(dt::TimeType) = quarter(dt)

const QUARTERDAYS = (0, 31, 59, 0, 30, 61, 0, 31, 62, 0, 31, 61)

"""
    dayofquarter(dt::TimeType) -> Int

Return the day of the current quarter of `dt`. Range of value is 1:92.
"""
function dayofquarter(dt::TimeType)
    (y, m, d) = yearmonthday(dt)
    return QUARTERDAYS[m] + d + (m == 3 && isleapyear(y))
end
s   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Dates/src/arithmetic.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

# Instant arithmetic
(+)(x::Instant) = x
(-)(x::T, y::T) where {T<:Instant} = x.periods - y.periods

# TimeType arithmetic
(+)(x::TimeType) = x
(-)(x::T, y::T) where {T<:TimeType} = x.instant - y.instant
(-)(x::T, y::T) where {T<:AbstractDateTime} = x.instant - y.instant
(-)(x::AbstractDateTime, y::AbstractDateTime) = -(promote(x, y)...)

# Date-Time arithmetic
"""
    dt::Date + t::Time -> DateTime

The addition of a `Date` with a `Time` produces a `DateTime`. The hour, minute, second, and millisecond parts of
the `Time` are used along with the year, month, and day of the `Date` to create the new `DateTime`.
Non-zero microseconds or nanoseconds in the `Time` type will result in an `InexactError` being thrown.
"""
(+)(dt::Date, t::Time) = DateTime(dt ,t)
(+)(t::Time, dt::Date) = DateTime(dt, t)

# TimeType-Year arithmetic
function (+)(dt::DateTime, y::Year)
    oy, m, d = yearmonthday(dt); ny = oy + value(y); ld = daysinmonth(ny, m)
    return DateTime(ny, m, d <= ld ? d : ld, hour(dt), minute(dt), second(dt), millisecond(dt))
end
function (+)(dt::Date,y::Year)
    oy, m, d = yearmonthday(dt); ny = oy + value(y); ld = daysinmonth(ny, m)
    return Date(ny, m, d <= ld ? d : ld)
end
function (-)(dt::DateTime,y::Year)
    oy, m, d = yearmonthday(dt); ny = oy - value(y); ld = daysinmonth(ny, m)
    return DateTime(ny, m, d <= ld ? d : ld, hour(dt), minute(dt), second(dt), millisecond(dt))
end
function (-)(dt::Date,y::Year)
    oy, m, d = yearmonthday(dt); ny = oy - value(y); ld = daysinmonth(ny, m)
    return Date(ny, m, d <= ld ? d : ld)
end

# TimeType-Month arithmetic
# monthwrap adds two months with wraparound behavior (i.e. 12 + 1 == 1)
monthwrap(m1, m2) = (v = mod1(m1 + m2, 12); return v < 0 ? 12 + v : v)
# yearwrap takes a starting year/month and a month to add and returns
# the resulting year with wraparound behavior (i.e. 2000-12 + 1 == 2001)
yearwrap(y, m1, m2) = y + fld(m1 + m2 - 1, 12)

function (+)(dt::DateTime, z::Month)
    y,m,d = yearmonthday(dt)
    ny = yearwrap(y, m, value(z))
    mm = monthwrap(m, value(z)); ld = daysinmonth(ny, mm)
    return DateTime(ny, mm, d <= ld ? d : ld, hour(dt), minute(dt), second(dt), millisecond(dt))
end

function (+)(dt::Date, z::Month)
    y,m,d = yearmonthday(dt)
    ny = yearwrap(y, m, value(z))
    mm = monthwrap(m, value(z)); ld = daysinmonth(ny, mm)
    return Date(ny, mm, d <= ld ? d : ld)
end
function (-)(dt::DateTime, z::Month)
    y,m,d = yearmonthday(dt)
    ny = yearwrap(y, m, -value(z))
    mm = monthwrap(m, -value(z)); ld = daysinmonth(ny, mm)
    return DateTime(ny, mm, d <= ld ? d : ld, hour(dt), minute(dt), second(dt), millisecond(dt))
end
function (-)(dt::Date, z::Month)
    y,m,d = yearmonthday(dt)
    ny = yearwrap(y, m, -value(z))
    mm = monthwrap(m, -value(z)); ld = daysinmonth(ny, mm)
    return Date(ny, mm, d <= ld ? d : ld)
end

(+)(x::Date, y::Quarter) = x + Month(y)
(-)(x::Date, y::Quarter) = x - Month(y)
(+)(x::DateTime, y::Quarter) = x + Month(y)
(-)(x::DateTime, y::Quarter) = x - Month(y)
(+)(x::Date, y::Week) = return Date(UTD(value(x) + 7 * value(y)))
(-)(x::Date, y::Week) = return Date(UTD(value(x) - 7 * value(y)))
(+)(x::Date, y::Day)  = return Date(UTD(value(x) + value(y)))
(-)(x::Date, y::Day)  = return Date(UTD(value(x) - value(y)))
(+)(x::DateTime, y::Period) = return DateTime(UTM(value(x) + toms(y)))
(-)(x::DateTime, y::Period) = return DateTime(UTM(value(x) - toms(y)))
(+)(x::Time, y::TimePeriod) = return Time(Nanosecond(value(x) + tons(y)))
(-)(x::Time, y::TimePeriod) = return Time(Nanosecond(value(x) - tons(y)))
(+)(y::Period, x::TimeType) = x + y

# Missing support
(+)(x::AbstractTime, y::Missing) = missing
(+)(x::Missing, y::AbstractTime) = missing
(-)(x::AbstractTime, y::Missing) = missing
(-)(x::Missing, y::AbstractTime) = missing

# AbstractArray{TimeType}, AbstractArray{TimeType}
(-)(x::OrdinalRange{T}, y::OrdinalRange{T}) where {T<:TimeType} = Vector(x) - Vector(y)
(-)(x::AbstractRange{T}, y::AbstractRange{T}) where {T<:TimeType} = Vector(x) - Vector(y)

# Allow dates, times, and time zones to broadcast as unwrapped scalars
Base.Broadcast.broadcastable(x::AbstractTime) = Ref(x)
Base.Broadcast.broadcastable(x::TimeZone) = Ref(x)
t   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Dates/src/conversions.jl&      # This file is a part of Julia. License is MIT: https://julialang.org/license

# Conversion/Promotion

"""
    Date(dt::DateTime) -> Date

Convert a `DateTime` to a `Date`. The hour, minute, second, and millisecond parts of
the `DateTime` are truncated, so only the year, month and day parts are used in
construction.
"""
Date(dt::TimeType) = convert(Date, dt)

"""
    DateTime(dt::Date) -> DateTime

Convert a `Date` to a `DateTime`. The hour, minute, second, and millisecond parts of
the new `DateTime` are assumed to be zero.
"""
DateTime(dt::TimeType) = convert(DateTime, dt)

"""
    Time(dt::DateTime) -> Time

Convert a `DateTime` to a `Time`. The hour, minute, second, and millisecond parts of
the `DateTime` are used to create the new `Time`. Microsecond and nanoseconds are zero by default.
"""
Time(dt::DateTime) = convert(Time, dt)

Base.convert(::Type{DateTime}, dt::Date) = DateTime(UTM(value(dt) * 86400000))
Base.convert(::Type{Date}, dt::DateTime) = Date(UTD(days(dt)))
Base.convert(::Type{Time}, dt::DateTime) = Time(Nanosecond((value(dt) % 86400000) * 1000000))

Base.convert(::Type{DateTime},x::Millisecond)  = DateTime(Dates.UTInstant(x))  # Converts Rata Die milliseconds to a DateTime
Base.convert(::Type{Millisecond},dt::DateTime) = Millisecond(value(dt))        # Converts DateTime to Rata Die milliseconds
Base.convert(::Type{Date},x::Day)  = Date(Dates.UTInstant(x))  # Converts Rata Die days to a Date
Base.convert(::Type{Day},dt::Date) = Day(value(dt))            # Converts Date to Rata Die days

### External Conversions
const UNIXEPOCH = value(DateTime(1970)) #Rata Die milliseconds for 1970-01-01T00:00:00

"""
    unix2datetime(x) -> DateTime

Take the number of seconds since unix epoch `1970-01-01T00:00:00` and convert to the
corresponding `DateTime`.
"""
function unix2datetime(x)
    # Rounding should match `now` below
    rata = UNIXEPOCH + trunc(Int64, Int64(1000) * x)
    return DateTime(UTM(rata))
end

"""
    datetime2unix(dt::DateTime) -> Float64

Take the given `DateTime` and return the number of seconds
since the unix epoch `1970-01-01T00:00:00` as a [`Float64`](@ref).
"""
datetime2unix(dt::DateTime) = (value(dt) - UNIXEPOCH) / 1000.0

"""
    now() -> DateTime

Return a `DateTime` corresponding to the user's system time including the system timezone
locale.
"""
function now()
    tv = Libc.TimeVal()
    tm = Libc.TmStruct(tv.sec)
    return DateTime(tm.year + 1900, tm.month + 1, tm.mday, tm.hour, tm.min, tm.sec, div(tv.usec, 1000))
end

"""
    today() -> Date

Return the date portion of `now()`.
"""
today() = Date(now())

"""
    now(::Type{UTC}) -> DateTime

Return a `DateTime` corresponding to the user's system time as UTC/GMT.
For other time zones, see the TimeZones.jl package.

# Example
```julia
julia> now(UTC)
2023-01-04T10:52:24.864
```
"""
now(::Type{UTC}) = unix2datetime(time())

"""
    rata2datetime(days) -> DateTime

Take the number of Rata Die days since epoch `0000-12-31T00:00:00` and return the
corresponding `DateTime`.
"""
rata2datetime(days) = DateTime(yearmonthday(days)...)

"""
    datetime2rata(dt::TimeType) -> Int64

Return the number of Rata Die days since epoch from the given `Date` or `DateTime`.
"""
datetime2rata(dt::TimeType) = days(dt)

# Julian conversions
const JULIANEPOCH = value(DateTime(-4713, 11, 24, 12))

"""
    julian2datetime(julian_days) -> DateTime

Take the number of Julian calendar days since epoch `-4713-11-24T12:00:00` and return the
corresponding `DateTime`.
"""
function julian2datetime(f)
    rata = JULIANEPOCH + round(Int64, Int64(86400000) * f)
    return DateTime(UTM(rata))
end

"""
    datetime2julian(dt::DateTime) -> Float64

Take the given `DateTime` and return the number of Julian calendar days since the julian
epoch `-4713-11-24T12:00:00` as a [`Float64`](@ref).
"""
datetime2julian(dt::DateTime) = (value(dt) - JULIANEPOCH) / 86400000.0
o   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Dates/src/ranges.jl       # This file is a part of Julia. License is MIT: https://julialang.org/license

# Date/DateTime Ranges

StepRange{<:Dates.DatePeriod,<:Real}(start, step, stop) =
    throw(ArgumentError("must specify step as a Period when constructing Dates ranges"))
Base.:(:)(a::T, b::T) where {T<:Date} = (:)(a, Day(1), b)

# Given a start and end date, how many steps/periods are in between
guess(a::DateTime, b::DateTime, c) = floor(Int64, (Int128(value(b)) - Int128(value(a))) / toms(c))
guess(a::Date, b::Date, c) = Int64(div(value(b - a), days(c)))
len(a::Time, b::Time, c) = Int64(div(value(b - a), tons(c)))
function len(a, b, c)
    lo, hi, st = min(a, b), max(a, b), abs(c)
    i = guess(a, b, c)
    v = lo + st * i
    prev = v  # Ensure `v` does not overflow
    while v <= hi && prev <= v
        prev = v
        v += st
        i += 1
    end
    return i - 1
end
Base.length(r::StepRange{<:TimeType}) = isempty(r) ? Int64(0) : len(r.start, r.stop, r.step) + 1
# Period ranges hook into Int64 overflow detection
Base.length(r::StepRange{<:Period}) = length(StepRange(value(r.start), value(r.step), value(r.stop)))
Base.checked_length(r::StepRange{<:Period}) = Base.checked_length(StepRange(value(r.start), value(r.step), value(r.stop)))

# Overload Base.steprange_last because `step::Period` may be a variable amount of time (e.g. for Month and Year)
function Base.steprange_last(start::T, step, stop) where T<:TimeType
    if isa(step, AbstractFloat)
        throw(ArgumentError("StepRange should not be used with floating point"))
    end
    z = zero(step)
    step == z && throw(ArgumentError("step cannot be zero"))

    if stop == start
        last = stop
    else
        if (step > z) != (stop > start)
            last = Base.steprange_last_empty(start, step, stop)
        else
            diff = stop - start
            if (diff > zero(diff)) != (stop > start)
                throw(OverflowError("Difference between stop and start overflowed"))
            end
            remain = stop - (start + step * len(start, stop, step))
            last = stop - remain
        end
    end
    return last
end

import Base.in
function in(x::T, r::StepRange{T}) where T<:TimeType
    n = len(first(r), x, step(r)) + 1
    n >= 1 && n <= length(r) && r[n] == x
end

Base.iterate(r::StepRange{<:TimeType}) = length(r) <= 0 ? nothing : (r.start, (length(r), 1))
Base.iterate(r::StepRange{<:TimeType}, (l, i)) = l <= i ? nothing : (r.start + r.step * i, (l, i + 1))

+(x::Period, r::AbstractRange{<:TimeType}) = (x + first(r)):step(r):(x + last(r))
+(r::AbstractRange{<:TimeType}, x::Period) = x + r
-(r::AbstractRange{<:TimeType}, x::Period) = (first(r)-x):step(r):(last(r)-x)
*(x::Period, r::AbstractRange{<:Real}) = (x * first(r)):(x * step(r)):(x * last(r))
*(r::AbstractRange{<:Real}, x::Period) = x * r
/(r::AbstractRange{<:P}, x::P) where {P<:Period} = (first(r)/x):(step(r)/x):(last(r)/x)

# Combinations of types and periods for which the range step is regular
Base.RangeStepStyle(::Type{<:OrdinalRange{<:TimeType, <:FixedPeriod}}) =
    Base.RangeStepRegular()
r   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Dates/src/adjusters.jl�5      # This file is a part of Julia. License is MIT: https://julialang.org/license

### truncation
Base.trunc(dt::Date, p::Type{Year}) = Date(UTD(totaldays(year(dt), 1, 1)))
Base.trunc(dt::Date, p::Type{Quarter}) = firstdayofquarter(dt)
Base.trunc(dt::Date, p::Type{Month}) = firstdayofmonth(dt)
Base.trunc(dt::Date, p::Type{Day}) = dt

Base.trunc(dt::DateTime, p::Type{Year}) = DateTime(trunc(Date(dt), Year))
Base.trunc(dt::DateTime, p::Type{Quarter}) = DateTime(trunc(Date(dt), Quarter))
Base.trunc(dt::DateTime, p::Type{Month}) = DateTime(trunc(Date(dt), Month))
Base.trunc(dt::DateTime, p::Type{Day}) = DateTime(Date(dt))
Base.trunc(dt::DateTime, p::Type{Hour}) = dt - Minute(dt) - Second(dt) - Millisecond(dt)
Base.trunc(dt::DateTime, p::Type{Minute}) = dt - Second(dt) - Millisecond(dt)
Base.trunc(dt::DateTime, p::Type{Second}) = dt - Millisecond(dt)
Base.trunc(dt::DateTime, p::Type{Millisecond}) = dt

Base.trunc(t::Time, p::Type{Hour}) = Time(Hour(t))
Base.trunc(t::Time, p::Type{Minute}) = Time(Hour(t), Minute(t))
Base.trunc(t::Time, p::Type{Second}) = Time(Hour(t), Minute(t), Second(t))
Base.trunc(t::Time, p::Type{Millisecond}) = t - Microsecond(t) - Nanosecond(t)
Base.trunc(t::Time, p::Type{Microsecond}) = t - Nanosecond(t)
Base.trunc(t::Time, p::Type{Nanosecond})  = t

"""
    trunc(dt::TimeType, ::Type{Period}) -> TimeType

Truncates the value of `dt` according to the provided `Period` type.

# Examples
```jldoctest
julia> trunc(DateTime("1996-01-01T12:30:00"), Day)
1996-01-01T00:00:00
```
"""
Dates.trunc(::Dates.TimeType, ::Type{Dates.Period})

# Adjusters
"""
    firstdayofweek(dt::TimeType) -> TimeType

Adjusts `dt` to the Monday of its week.

# Examples
```jldoctest
julia> firstdayofweek(DateTime("1996-01-05T12:30:00"))
1996-01-01T00:00:00
```
"""
function firstdayofweek end

firstdayofweek(dt::Date) = Date(UTD(value(dt) - dayofweek(dt) + 1))
firstdayofweek(dt::DateTime) = DateTime(firstdayofweek(Date(dt)))

"""
    lastdayofweek(dt::TimeType) -> TimeType

Adjusts `dt` to the Sunday of its week.

# Examples
```jldoctest
julia> lastdayofweek(DateTime("1996-01-05T12:30:00"))
1996-01-07T00:00:00
```
"""
function lastdayofweek end

lastdayofweek(dt::Date) = Date(UTD(value(dt) + (7 - dayofweek(dt))))
lastdayofweek(dt::DateTime) = DateTime(lastdayofweek(Date(dt)))

"""
    firstdayofmonth(dt::TimeType) -> TimeType

Adjusts `dt` to the first day of its month.

# Examples
```jldoctest
julia> firstdayofmonth(DateTime("1996-05-20"))
1996-05-01T00:00:00
```
"""
function firstdayofmonth end

firstdayofmonth(dt::Date) = Date(UTD(value(dt) - day(dt) + 1))
firstdayofmonth(dt::DateTime) = DateTime(firstdayofmonth(Date(dt)))

"""
    lastdayofmonth(dt::TimeType) -> TimeType

Adjusts `dt` to the last day of its month.

# Examples
```jldoctest
julia> lastdayofmonth(DateTime("1996-05-20"))
1996-05-31T00:00:00
```
"""
function lastdayofmonth end

function lastdayofmonth(dt::Date)
    y, m, d = yearmonthday(dt)
    return Date(UTD(value(dt) + daysinmonth(y, m) - d))
end
lastdayofmonth(dt::DateTime) = DateTime(lastdayofmonth(Date(dt)))

"""
    firstdayofyear(dt::TimeType) -> TimeType

Adjusts `dt` to the first day of its year.

# Examples
```jldoctest
julia> firstdayofyear(DateTime("1996-05-20"))
1996-01-01T00:00:00
```
"""
function firstdayofyear end

firstdayofyear(dt::Date) = Date(UTD(value(dt) - dayofyear(dt) + 1))
firstdayofyear(dt::DateTime) = DateTime(firstdayofyear(Date(dt)))

"""
    lastdayofyear(dt::TimeType) -> TimeType

Adjusts `dt` to the last day of its year.

# Examples
```jldoctest
julia> lastdayofyear(DateTime("1996-05-20"))
1996-12-31T00:00:00
```
"""
function lastdayofyear end

function lastdayofyear(dt::Date)
    y, m, d = yearmonthday(dt)
    return Date(UTD(value(dt) + daysinyear(y) - dayofyear(y, m, d)))
end
lastdayofyear(dt::DateTime) = DateTime(lastdayofyear(Date(dt)))

"""
    firstdayofquarter(dt::TimeType) -> TimeType

Adjusts `dt` to the first day of its quarter.

# Examples
```jldoctest
julia> firstdayofquarter(DateTime("1996-05-20"))
1996-04-01T00:00:00

julia> firstdayofquarter(DateTime("1996-08-20"))
1996-07-01T00:00:00
```
"""
function firstdayofquarter end

function firstdayofquarter(dt::Date)
    y,m = yearmonth(dt)
    mm = m < 4 ? 1 : m < 7 ? 4 : m < 10 ? 7 : 10
    return Date(y, mm, 1)
end
firstdayofquarter(dt::DateTime) = DateTime(firstdayofquarter(Date(dt)))

"""
    lastdayofquarter(dt::TimeType) -> TimeType

Adjusts `dt` to the last day of its quarter.

# Examples
```jldoctest
julia> lastdayofquarter(DateTime("1996-05-20"))
1996-06-30T00:00:00

julia> lastdayofquarter(DateTime("1996-08-20"))
1996-09-30T00:00:00
```
"""
function lastdayofquarter end

function lastdayofquarter(dt::Date)
    y,m = yearmonth(dt)
    mm, d = m < 4 ? (3, 31) : m < 7 ? (6, 30) : m < 10 ? (9, 30) : (12, 31)
    return Date(y, mm, d)
end
lastdayofquarter(dt::DateTime) = DateTime(lastdayofquarter(Date(dt)))

# Temporal Adjusters
struct DateFunction
    f::Function
    # validate boolean, single-arg inner constructor
    function DateFunction(@nospecialize(f), dt::TimeType)
        isa(f(dt), Bool) || throw(ArgumentError("Provided function must take a single TimeType argument and return true or false"))
        return new(f)
    end
end
Base.show(io::IO, df::DateFunction) = println(io, df.f)

# Core adjuster
function adjust(df::DateFunction, start, step, limit)
    for i = 1:limit
        df.f(start) && return start
        start += step
    end
    throw(ArgumentError("Adjustment limit reached: $limit iterations"))
end

function adjust(func::Function, start; step::Period=Day(1), limit::Int=10000)
    return adjust(DateFunction(func, start), start, step, limit)
end

# Constructors using DateFunctions

"""
    Date(f::Function, y[, m, d]; step=Day(1), limit=10000) -> Date

Create a `Date` through the adjuster API. The starting point will be constructed from the
provided `y, m, d` arguments, and will be adjusted until `f::Function` returns `true`.
The step size in adjusting can be provided manually through the `step` keyword.
`limit` provides a limit to the max number of iterations the adjustment API will
pursue before throwing an error (given that `f::Function` is never satisfied).

# Examples
```jldoctest
julia> Date(date -> week(date) == 20, 2010, 01, 01)
2010-05-17

julia> Date(date -> year(date) == 2010, 2000, 01, 01)
2010-01-01

julia> Date(date -> month(date) == 10, 2000, 01, 01; limit = 5)
ERROR: ArgumentError: Adjustment limit reached: 5 iterations
Stacktrace:
[...]
```
"""
function Date(func::Function, y, m=1, d=1; step::Period=Day(1), limit::Int=10000)
    return adjust(DateFunction(func, Date(y, m, d)), Date(y, m, d), step, limit)
end

"""
    DateTime(f::Function, y[, m, d, h, mi, s]; step=Day(1), limit=10000) -> DateTime

Create a `DateTime` through the adjuster API. The starting point will be constructed from
the provided `y, m, d...` arguments, and will be adjusted until `f::Function` returns
`true`. The step size in adjusting can be provided manually through the `step` keyword.
`limit` provides a limit to the max number of iterations the adjustment API will
pursue before throwing an error (in the case that `f::Function` is never satisfied).

# Examples
```jldoctest
julia> DateTime(dt -> second(dt) == 40, 2010, 10, 20, 10; step = Second(1))
2010-10-20T10:00:40

julia> DateTime(dt -> hour(dt) == 20, 2010, 10, 20, 10; step = Hour(1), limit = 5)
ERROR: ArgumentError: Adjustment limit reached: 5 iterations
Stacktrace:
[...]
```
"""
DateTime(::Function, args...)

function DateTime(func::Function, y, m=1; step::Period=Day(1), limit::Int=10000)
    return adjust(DateFunction(func, DateTime(y, m)), DateTime(y, m), step, limit)
end
function DateTime(func::Function, y, m, d; step::Period=Hour(1), limit::Int=10000)
    return adjust(DateFunction(func, DateTime(y)), DateTime(y, m, d), step, limit)
end
function DateTime(func::Function, y, m, d, h; step::Period=Minute(1), limit::Int=10000)
    return adjust(DateFunction(func, DateTime(y)), DateTime(y, m, d, h), step, limit)
end
function DateTime(func::Function, y, m, d, h, mi; step::Period=Second(1), limit::Int=10000)
    return adjust(DateFunction(func, DateTime(y)), DateTime(y, m, d, h, mi), step, limit)
end
function DateTime(func::Function, y, m, d, h, mi, s; step::Period=Millisecond(1), limit::Int=10000)
    return adjust(DateFunction(func, DateTime(y)), DateTime(y, m, d, h, mi, s), step, limit)
end

"""
    Time(f::Function, h, mi=0; step::Period=Second(1), limit::Int=10000)
    Time(f::Function, h, mi, s; step::Period=Millisecond(1), limit::Int=10000)
    Time(f::Function, h, mi, s, ms; step::Period=Microsecond(1), limit::Int=10000)
    Time(f::Function, h, mi, s, ms, us; step::Period=Nanosecond(1), limit::Int=10000)

Create a `Time` through the adjuster API. The starting point will be constructed from the
provided `h, mi, s, ms, us` arguments, and will be adjusted until `f::Function` returns `true`.
The step size in adjusting can be provided manually through the `step` keyword. `limit`
provides a limit to the max number of iterations the adjustment API will pursue before
throwing an error (in the case that `f::Function` is never satisfied). Note that the default step
will adjust to allow for greater precision for the given arguments; i.e. if hour, minute, and second
arguments are provided, the default step will be `Millisecond(1)` instead of `Second(1)`.

# Examples
```jldoctest
julia> Time(t -> minute(t) == 30, 20)
20:30:00

julia> Time(t -> minute(t) == 0, 20)
20:00:00

julia> Time(t -> hour(t) == 10, 3; limit = 5)
ERROR: ArgumentError: Adjustment limit reached: 5 iterations
Stacktrace:
[...]
```
"""
Time(::Function, args...)

function Time(func::Function, h, mi=0; step::Period=Second(1), limit::Int=10000)
    return adjust(DateFunction(func, Time(h, mi)), Time(h, mi), step, limit)
end
function Time(func::Function, h, mi, s; step::Period=Millisecond(1), limit::Int=10000)
    return adjust(DateFunction(func, Time(h, mi, s)), Time(h, mi, s), step, limit)
end
function Time(func::Function, h, mi, s, ms; step::Period=Microsecond(1), limit::Int=10000)
    return adjust(DateFunction(func, Time(h, mi, s, ms)), Time(h, mi, s, ms), step, limit)
end
function Time(func::Function, h, mi, s, ms, us; step::Period=Nanosecond(1), limit::Int=10000)
    return adjust(DateFunction(func, Time(h, mi, s, ms, us)), Time(h, mi, s, ms, us), step, limit)
end

# Return the next TimeType that falls on dow
ISDAYOFWEEK = Dict(Mon => DateFunction(ismonday, Date(0)),
                   Tue => DateFunction(istuesday, Date(0)),
                   Wed => DateFunction(iswednesday, Date(0)),
                   Thu => DateFunction(isthursday, Date(0)),
                   Fri => DateFunction(isfriday, Date(0)),
                   Sat => DateFunction(issaturday, Date(0)),
                   Sun => DateFunction(issunday, Date(0)))

# "same" indicates whether the current date can be considered or not
"""
    tonext(dt::TimeType, dow::Int; same::Bool=false) -> TimeType

Adjusts `dt` to the next day of week corresponding to `dow` with `1 = Monday, 2 = Tuesday,
etc`. Setting `same=true` allows the current `dt` to be considered as the next `dow`,
allowing for no adjustment to occur.
"""
tonext(dt::TimeType, dow::Int; same::Bool=false) = adjust(ISDAYOFWEEK[dow], same ? dt : dt + Day(1), Day(1), 7)

# Return the next TimeType where func evals true using step in incrementing
"""
    tonext(func::Function, dt::TimeType; step=Day(1), limit=10000, same=false) -> TimeType

Adjusts `dt` by iterating at most `limit` iterations by `step` increments until `func`
returns `true`. `func` must take a single `TimeType` argument and return a [`Bool`](@ref).
`same` allows `dt` to be considered in satisfying `func`.
"""
function tonext(func::Function, dt::TimeType; step::Period=Day(1), limit::Int=10000, same::Bool=false)
    return adjust(DateFunction(func, dt), same ? dt : dt + step, step, limit)
end

"""
    toprev(dt::TimeType, dow::Int; same::Bool=false) -> TimeType

Adjusts `dt` to the previous day of week corresponding to `dow` with `1 = Monday, 2 =
Tuesday, etc`. Setting `same=true` allows the current `dt` to be considered as the previous
`dow`, allowing for no adjustment to occur.
"""
toprev(dt::TimeType, dow::Int; same::Bool=false) = adjust(ISDAYOFWEEK[dow], same ? dt : dt + Day(-1), Day(-1), 7)

"""
    toprev(func::Function, dt::TimeType; step=Day(-1), limit=10000, same=false) -> TimeType

Adjusts `dt` by iterating at most `limit` iterations by `step` increments until `func`
returns `true`. `func` must take a single `TimeType` argument and return a [`Bool`](@ref).
`same` allows `dt` to be considered in satisfying `func`.
"""
function toprev(func::Function, dt::TimeType; step::Period=Day(-1), limit::Int=10000, same::Bool=false)
    return adjust(DateFunction(func, dt), same ? dt : dt + step, step, limit)
end

# Return the first TimeType that falls on dow in the Month or Year
"""
    tofirst(dt::TimeType, dow::Int; of=Month) -> TimeType

Adjusts `dt` to the first `dow` of its month. Alternatively, `of=Year` will adjust to the
first `dow` of the year.
"""
function tofirst(dt::TimeType, dow::Int; of::Union{Type{Year}, Type{Month}}=Month)
    dt = of <: Month ? firstdayofmonth(dt) : firstdayofyear(dt)
    return adjust(ISDAYOFWEEK[dow], dt, Day(1), 366)
end

# Return the last TimeType that falls on dow in the Month or Year
"""
    tolast(dt::TimeType, dow::Int; of=Month) -> TimeType

Adjusts `dt` to the last `dow` of its month. Alternatively, `of=Year` will adjust to the
last `dow` of the year.
"""
function tolast(dt::TimeType, dow::Int; of::Union{Type{Year}, Type{Month}}=Month)
    dt = of <: Month ? lastdayofmonth(dt) : lastdayofyear(dt)
    return adjust(ISDAYOFWEEK[dow], dt, Day(-1), 366)
end
q   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Dates/src/rounding.jl�%      # This file is a part of Julia. License is MIT: https://julialang.org/license

# The epochs used for date rounding are based ISO 8601's "year zero" notation
const DATEEPOCH = value(Date(0))
const DATETIMEEPOCH = value(DateTime(0))

# According to ISO 8601, the first day of the first week of year 0000 is 0000-01-03
const WEEKEPOCH = value(Date(0, 1, 3))

const ConvertiblePeriod = Union{TimePeriod, Week, Day}
const TimeTypeOrPeriod = Union{TimeType, ConvertiblePeriod}

"""
    epochdays2date(days) -> Date

Take the number of days since the rounding epoch (`0000-01-01T00:00:00`) and return the
corresponding `Date`.
"""
epochdays2date(i) = Date(UTD(DATEEPOCH + Int64(i)))

"""
    epochms2datetime(milliseconds) -> DateTime

Take the number of milliseconds since the rounding epoch (`0000-01-01T00:00:00`) and
return the corresponding `DateTime`.
"""
epochms2datetime(i) = DateTime(UTM(DATETIMEEPOCH + Int64(i)))

"""
    date2epochdays(dt::Date) -> Int64

Take the given `Date` and return the number of days since the rounding epoch
(`0000-01-01T00:00:00`) as an [`Int64`](@ref).
"""
date2epochdays(dt::Date) = value(dt) - DATEEPOCH

"""
    datetime2epochms(dt::DateTime) -> Int64

Take the given `DateTime` and return the number of milliseconds since the rounding epoch
(`0000-01-01T00:00:00`) as an [`Int64`](@ref).
"""
datetime2epochms(dt::DateTime) = value(dt) - DATETIMEEPOCH

function Base.floor(dt::Date, p::Year)
    value(p) < 1 && throw(DomainError(p))
    years = year(dt)
    return Date(years - mod(years, value(p)))
end

function Base.floor(dt::Date, p::Month)
    value(p) < 1 && throw(DomainError(p))
    y, m = yearmonth(dt)
    months_since_epoch = y * 12 + m - 1
    month_offset = months_since_epoch - mod(months_since_epoch, value(p))
    target_month = mod(month_offset, 12) + 1
    target_year = div(month_offset, 12) - (month_offset < 0 && target_month != 1)
    return Date(target_year, target_month)
end

function Base.floor(dt::Date, p::Quarter)
    return floor(dt, Month(p))
end


function Base.floor(dt::Date, p::Week)
    value(p) < 1 && throw(DomainError(p))
    days = value(dt) - WEEKEPOCH
    days = days - mod(days, value(Day(p)))
    return Date(UTD(WEEKEPOCH + Int64(days)))
end

function Base.floor(dt::Date, p::Day)
    value(p) < 1 && throw(DomainError(p))
    days = date2epochdays(dt)
    return epochdays2date(days - mod(days, value(p)))
end

Base.floor(dt::DateTime, p::DatePeriod) = DateTime(Base.floor(Date(dt), p))

function Base.floor(dt::DateTime, p::TimePeriod)
    value(p) < 1 && throw(DomainError(p))
    milliseconds = datetime2epochms(dt)
    return epochms2datetime(milliseconds - mod(milliseconds, value(Millisecond(p))))
end

"""
    floor(x::Period, precision::T) where T <: Union{TimePeriod, Week, Day} -> T

Round `x` down to the nearest multiple of `precision`. If `x` and `precision` are different
subtypes of `Period`, the return value will have the same type as `precision`.

For convenience, `precision` may be a type instead of a value: `floor(x, Dates.Hour)` is a
shortcut for `floor(x, Dates.Hour(1))`.

```jldoctest
julia> floor(Day(16), Week)
2 weeks

julia> floor(Minute(44), Minute(15))
30 minutes

julia> floor(Hour(36), Day)
1 day
```

Rounding to a `precision` of `Month`s or `Year`s is not supported, as these `Period`s are of
inconsistent length.
"""
function Base.floor(x::ConvertiblePeriod, precision::T) where T <: ConvertiblePeriod
    value(precision) < 1 && throw(DomainError(precision))
    _x, _precision = promote(x, precision)
    return T(_x - mod(_x, _precision))
end

"""
    floor(dt::TimeType, p::Period) -> TimeType

Return the nearest `Date` or `DateTime` less than or equal to `dt` at resolution `p`.

For convenience, `p` may be a type instead of a value: `floor(dt, Dates.Hour)` is a shortcut
for `floor(dt, Dates.Hour(1))`.

```jldoctest
julia> floor(Date(1985, 8, 16), Month)
1985-08-01

julia> floor(DateTime(2013, 2, 13, 0, 31, 20), Minute(15))
2013-02-13T00:30:00

julia> floor(DateTime(2016, 8, 6, 12, 0, 0), Day)
2016-08-06T00:00:00
```
"""
Base.floor(::Dates.TimeType, ::Dates.Period)

"""
    ceil(dt::TimeType, p::Period) -> TimeType

Return the nearest `Date` or `DateTime` greater than or equal to `dt` at resolution `p`.

For convenience, `p` may be a type instead of a value: `ceil(dt, Dates.Hour)` is a shortcut
for `ceil(dt, Dates.Hour(1))`.

```jldoctest
julia> ceil(Date(1985, 8, 16), Month)
1985-09-01

julia> ceil(DateTime(2013, 2, 13, 0, 31, 20), Minute(15))
2013-02-13T00:45:00

julia> ceil(DateTime(2016, 8, 6, 12, 0, 0), Day)
2016-08-07T00:00:00
```
"""
function Base.ceil(dt::TimeType, p::Period)
    f = floor(dt, p)
    return (dt == f) ? f : f + p
end

"""
    ceil(x::Period, precision::T) where T <: Union{TimePeriod, Week, Day} -> T

Round `x` up to the nearest multiple of `precision`. If `x` and `precision` are different
subtypes of `Period`, the return value will have the same type as `precision`.

For convenience, `precision` may be a type instead of a value: `ceil(x, Dates.Hour)` is a
shortcut for `ceil(x, Dates.Hour(1))`.

```jldoctest
julia> ceil(Day(16), Week)
3 weeks

julia> ceil(Minute(44), Minute(15))
45 minutes

julia> ceil(Hour(36), Day)
2 days
```

Rounding to a `precision` of `Month`s or `Year`s is not supported, as these `Period`s are of
inconsistent length.
"""
function Base.ceil(x::ConvertiblePeriod, precision::ConvertiblePeriod)
    f = floor(x, precision)
    return (x == f) ? f : f + precision
end

"""
    floorceil(dt::TimeType, p::Period) -> (TimeType, TimeType)

Simultaneously return the `floor` and `ceil` of a `Date` or `DateTime` at resolution `p`.
More efficient than calling both `floor` and `ceil` individually.
"""
function floorceil(dt::TimeType, p::Period)
    f = floor(dt, p)
    return f, (dt == f) ? f : f + p
end

"""
    floorceil(x::Period, precision::T) where T <: Union{TimePeriod, Week, Day} -> (T, T)

Simultaneously return the `floor` and `ceil` of `Period` at resolution `p`.  More efficient
than calling both `floor` and `ceil` individually.
"""
function floorceil(x::ConvertiblePeriod, precision::ConvertiblePeriod)
    f = floor(x, precision)
    return f, (x == f) ? f : f + precision
end

"""
    round(dt::TimeType, p::Period, [r::RoundingMode]) -> TimeType

Return the `Date` or `DateTime` nearest to `dt` at resolution `p`. By default
(`RoundNearestTiesUp`), ties (e.g., rounding 9:30 to the nearest hour) will be rounded up.

For convenience, `p` may be a type instead of a value: `round(dt, Dates.Hour)` is a shortcut
for `round(dt, Dates.Hour(1))`.

```jldoctest
julia> round(Date(1985, 8, 16), Month)
1985-08-01

julia> round(DateTime(2013, 2, 13, 0, 31, 20), Minute(15))
2013-02-13T00:30:00

julia> round(DateTime(2016, 8, 6, 12, 0, 0), Day)
2016-08-07T00:00:00
```

Valid rounding modes for `round(::TimeType, ::Period, ::RoundingMode)` are
`RoundNearestTiesUp` (default), `RoundDown` (`floor`), and `RoundUp` (`ceil`).
"""
function Base.round(dt::TimeType, p::Period, r::RoundingMode{:NearestTiesUp})
    f, c = floorceil(dt, p)
    return (dt - f) < (c - dt) ? f : c
end

"""
    round(x::Period, precision::T, [r::RoundingMode]) where T <: Union{TimePeriod, Week, Day} -> T

Round `x` to the nearest multiple of `precision`. If `x` and `precision` are different
subtypes of `Period`, the return value will have the same type as `precision`. By default
(`RoundNearestTiesUp`), ties (e.g., rounding 90 minutes to the nearest hour) will be rounded
up.

For convenience, `precision` may be a type instead of a value: `round(x, Dates.Hour)` is a
shortcut for `round(x, Dates.Hour(1))`.

```jldoctest
julia> round(Day(16), Week)
2 weeks

julia> round(Minute(44), Minute(15))
45 minutes

julia> round(Hour(36), Day)
2 days
```

Valid rounding modes for `round(::Period, ::T, ::RoundingMode)` are `RoundNearestTiesUp`
(default), `RoundDown` (`floor`), and `RoundUp` (`ceil`).

Rounding to a `precision` of `Month`s or `Year`s is not supported, as these `Period`s are of
inconsistent length.
"""
function Base.round(x::ConvertiblePeriod, precision::ConvertiblePeriod, r::RoundingMode{:NearestTiesUp})
    f, c = floorceil(x, precision)
    _x, _f, _c = promote(x, f, c)
    return (_x - _f) < (_c - _x) ? f : c
end

Base.round(x::TimeTypeOrPeriod, p::Period, r::RoundingMode{:Down}) = Base.floor(x, p)
Base.round(x::TimeTypeOrPeriod, p::Period, r::RoundingMode{:Up}) = Base.ceil(x, p)

# No implementation of other `RoundingMode`s: rounding to nearest "even" is skipped because
# "even" is not defined for Period; rounding toward/away from zero is skipped because ISO
# 8601's year 0000 is not really "zero".
Base.round(::TimeTypeOrPeriod, p::Period, ::RoundingMode) = throw(DomainError(p))

# Default to RoundNearestTiesUp.
Base.round(x::TimeTypeOrPeriod, p::Period) = Base.round(x, p, RoundNearestTiesUp)

# Make rounding functions callable using Period types in addition to values.
Base.floor(x::TimeTypeOrPeriod, ::Type{P}) where P <: Period = Base.floor(x, oneunit(P))
Base.ceil(x::TimeTypeOrPeriod, ::Type{P}) where P <: Period = Base.ceil(x, oneunit(P))
Base.floor(::Type{Date}, x::TimeTypeOrPeriod, ::Type{P}) where P <: Period = Base.floor(Date(x), oneunit(P))
Base.ceil(::Type{Date}, x::TimeTypeOrPeriod, ::Type{P}) where P <: Period = Base.ceil(Date(x), oneunit(P))

function Base.round(x::TimeTypeOrPeriod, ::Type{P}, r::RoundingMode=RoundNearestTiesUp) where P <: Period
    return Base.round(x, oneunit(P), r)
end

function Base.round(::Type{Date}, x::TimeTypeOrPeriod, ::Type{P}, r::RoundingMode=RoundNearestTiesUp) where P <: Period
    return Base.round(Date(x), oneunit(P), r)
end
k   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Dates/src/io.jl�_      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
    AbstractDateToken

A token used in parsing or formatting a date time string. Each subtype must
define the tryparsenext and format methods.

"""
abstract type AbstractDateToken end

"""
    tryparsenext(tok::AbstractDateToken, str::String, i::Int, len::Int, locale::DateLocale)

`tryparsenext` parses for the `tok` token in `str` starting at index `i`.
`len` is the length of the string.  parsing can be optionally based on the
`locale`. If a `tryparsenext` method does not need a locale, it can leave
the argument out in the method definition.

If parsing succeeds, returns a tuple of 2 elements `(res, idx)`, where:

* `res` is the result of the parsing.
* `idx::Int`, is the index _after_ the index at which parsing ended.
"""
function tryparsenext end

"""
    format(io::IO, tok::AbstractDateToken, dt::TimeType, locale)

Format the `tok` token from `dt` and write it to `io`. The formatting can
be based on `locale`.

All subtypes of `AbstractDateToken` must define this method in order
to be able to print a Date / DateTime object according to a `DateFormat`
containing that token.
"""
format(io::IO, tok::AbstractDateToken, dt::TimeType, locale)

# fallback to tryparsenext/format methods that don't care about locale
@inline function tryparsenext(d::AbstractDateToken, str, i, len, locale)
    return tryparsenext(d, str, i, len)
end

function Base.string(t::Time)
    h, mi, s = hour(t), minute(t), second(t)
    hh = lpad(h, 2, "0")
    mii = lpad(mi, 2, "0")
    ss = lpad(s, 2, "0")
    nss = tons(Millisecond(t)) + tons(Microsecond(t)) + tons(Nanosecond(t))
    ns = nss == 0 ? "" : rstrip(@sprintf("%.9f", nss / 1e+9)[2:end], '0')
    return "$hh:$mii:$ss$ns"
end

Base.show(io::IO, ::MIME"text/plain", t::Time) = print(io, t)
Base.print(io::IO, t::Time) = print(io, string(t))

function Base.show(io::IO, t::Time)
    if get(io, :compact, false)::Bool
        print(io, t)
    else
        values = [
            hour(t)
            minute(t)
            second(t)
            millisecond(t)
            microsecond(t)
            nanosecond(t)
        ]
        index = something(findlast(!iszero, values), 1)

        print(io, Time, "(")
        for i in 1:index
            show(io, values[i])
            i != index && print(io, ", ")
        end
        print(io, ")")
    end
end

@inline function format(io, d::AbstractDateToken, dt, locale)
    format(io, d, dt)
end

# Information for parsing and formatting date time values.
struct DateFormat{S, T<:Tuple}
    tokens::T
    locale::DateLocale
end

### Token types ###

struct DatePart{letter} <: AbstractDateToken
    width::Int
    fixed::Bool
end

@inline min_width(d::DatePart) = d.fixed ? d.width : 1
@inline max_width(d::DatePart) = d.fixed ? d.width : 0

function _show_content(io::IO, d::DatePart{c}) where c
    for i = 1:d.width
        print(io, c)
    end
end

function Base.show(io::IO, d::DatePart{c}) where c
    print(io, "DatePart(")
    _show_content(io, d)
    print(io, ")")
end

### Parse tokens

for c in "yYmdHIMS"
    @eval begin
        @inline function tryparsenext(d::DatePart{$c}, str, i, len)
            return tryparsenext_base10(str, i, len, min_width(d), max_width(d))
        end
    end
end

function tryparsenext(d::DatePart{'p'}, str, i, len)
    i+1 > len && return nothing
    c, ii = iterate(str, i)::Tuple{Char, Int}
    ap = lowercase(c)
    (ap == 'a' || ap == 'p') || return nothing
    c, ii = iterate(str, ii)::Tuple{Char, Int}
    lowercase(c) == 'm' || return nothing
    return ap == 'a' ? AM : PM, ii
end

for (tok, fn) in zip("uUeE", Any[monthabbr_to_value, monthname_to_value, dayabbr_to_value, dayname_to_value])
    @eval @inline function tryparsenext(d::DatePart{$tok}, str, i, len, locale)
        next = tryparsenext_word(str, i, len, locale, max_width(d))
        next === nothing && return nothing
        word, i = next
        val = $fn(word, locale)
        val == 0 && return nothing
        return val, i
    end
end

# 3-digit (base 10) number following a decimal point. For InexactError below.
struct Decimal3 end

@inline function tryparsenext(d::DatePart{'s'}, str, i, len)
    val = tryparsenext_base10(str, i, len, min_width(d), max_width(d))
    val === nothing && return nothing
    ms0, ii = val
    len = ii - i
    if len > 3
        ms, r = divrem(ms0, Int64(10) ^ (len - 3))
        r == 0 || return nothing
    else
        ms = ms0 * Int64(10) ^ (3 - len)
    end
    return ms, ii
end

### Format tokens

hour12(dt) = let h = hour(dt); h > 12 ? h - 12 : h == 0 ? 12 : h; end

for (c, fn) in zip("YmdHIMS", Any[year, month, day, hour, hour12, minute, second])
    @eval function format(io, d::DatePart{$c}, dt)
        print(io, string($fn(dt), base = 10, pad = d.width))
    end
end

for (tok, fn) in zip("uU", Any[monthabbr, monthname])
    @eval function format(io, d::DatePart{$tok}, dt, locale)
        print(io, $fn(month(dt), locale))
    end
end

function format(io, d::DatePart{'p'}, dt, locale)
    ampm = hour(dt) < 12 ? "AM" : "PM" # fixme: locale-specific?
    print(io, ampm)
end

for (tok, fn) in zip("eE", Any[dayabbr, dayname])
    @eval function format(io, ::DatePart{$tok}, dt, locale)
        print(io, $fn(dayofweek(dt), locale))
    end
end

@inline function format(io, d::DatePart{'y'}, dt)
    y = year(dt)
    n = d.width

    # the last n digits of y
    # will be 0 padded if y has less than n digits
    str = string(y, base = 10, pad = n)
    l = lastindex(str)
    if l == n
        # fast path
        print(io, str)
    else
        print(io, SubString(str, l - (n - 1), l))
    end
end

function format(io, d::DatePart{'s'}, dt)
    ms = millisecond(dt)
    if ms % 100 == 0
        str = string(div(ms, 100))
    elseif ms % 10 == 0
        str = string(div(ms, 10), pad = 2)
    else
        str = string(ms, pad = 3)
    end

    print(io, rpad(str, d.width, '0'))
end

### Delimiters

struct Delim{T, length} <: AbstractDateToken
    d::T
end

Delim(d::T) where {T<:AbstractChar} = Delim{T, 1}(d)
Delim(d::String) = Delim{String, length(d)}(d)

@inline function tryparsenext(d::Delim{<:AbstractChar, N}, str, i::Int, len) where N
    for j = 1:N
        i > len && return nothing
        next = iterate(str, i)
        @assert next !== nothing
        c, i = next
        c != d.d && return nothing
    end
    return true, i
end

@inline function tryparsenext(d::Delim{String, N}, str, i::Int, len) where N
    i1 = i
    i2 = firstindex(d.d)
    for j = 1:N
        if i1 > len
            return nothing
        end
        next1 = iterate(str, i1)
        @assert next1 !== nothing
        c1, i1 = next1
        next2 = iterate(d.d, i2)
        @assert next2 !== nothing
        c2, i2 = next2
        if c1 != c2
            return nothing
        end
    end
    return true, i1
end

@inline function format(io, d::Delim, dt, locale)
    print(io, d.d)
end

function _show_content(io::IO, d::Delim{<:AbstractChar, N}) where N
    if d.d in keys(CONVERSION_SPECIFIERS)
        for i = 1:N
            print(io, '\\', d.d)
        end
    else
        for i = 1:N
            print(io, d.d)
        end
    end
end

function _show_content(io::IO, d::Delim)
    for c in d.d
        if c in keys(CONVERSION_SPECIFIERS)
            print(io, '\\')
        end
        print(io, c)
    end
end

function Base.show(io::IO, d::Delim)
    print(io, "Delim(")
    _show_content(io, d)
    print(io, ")")
end

### DateFormat construction

abstract type DayOfWeekToken end # special addition to Period types

# Map conversion specifiers or character codes to tokens.
# Note: Allow addition of new character codes added by packages
const CONVERSION_SPECIFIERS = Dict{Char, Type}(
    'y' => Year,
    'Y' => Year,
    'm' => Month,
    'u' => Month,
    'U' => Month,
    'e' => DayOfWeekToken,
    'E' => DayOfWeekToken,
    'd' => Day,
    'H' => Hour,
    'I' => Hour,
    'M' => Minute,
    'S' => Second,
    's' => Millisecond,
    'p' => AMPM,
)

# Default values are needed when a conversion specifier is used in a DateFormat for parsing
# and we have reached the end of the input string.
# Note: Allow `Any` value as a default to support extensibility
const CONVERSION_DEFAULTS = IdDict{Type, Any}(
    Year => Int64(1),
    Month => Int64(1),
    DayOfWeekToken => Int64(0),
    Day => Int64(1),
    Hour => Int64(0),
    Minute => Int64(0),
    Second => Int64(0),
    Millisecond => Int64(0),
    Microsecond => Int64(0),
    Nanosecond => Int64(0),
    AMPM => TWENTYFOURHOUR,
)

# Specifies the required fields in order to parse a TimeType
# Note: Allows for addition of new TimeTypes
const CONVERSION_TRANSLATIONS = IdDict{Type, Any}(
    Date => (Year, Month, Day),
    DateTime => (Year, Month, Day, Hour, Minute, Second, Millisecond, AMPM),
    Time => (Hour, Minute, Second, Millisecond, Microsecond, Nanosecond, AMPM),
)

# The `DateFormat(format, locale)` method just below consumes the following Regex.
# Constructing this Regex is fairly expensive; doing so in the method itself can
# consume half or better of `DateFormat(format, locale)`'s runtime. So instead we
# construct and cache it outside the method body. Note, however, that when
# `keys(CONVERSION_SPECIFIERS)` changes, the cached Regex must be updated accordingly;
# hence the mutability (Ref-ness) of the cache, the helper method with which to populate
# the cache, the cache of the hash of `keys(CONVERSION_SPECIFIERS)` (to facilitate checking
# for changes), and the lock (to maintain consistency of these objects across threads when
# threads simultaneously modify `CONVERSION_SPECIFIERS` and construct `DateFormat`s).
function compute_dateformat_regex(conversion_specifiers)
    letters = String(collect(keys(conversion_specifiers)))
    return Regex("(?<!\\\\)([\\Q$letters\\E])\\1*")
end
const DATEFORMAT_REGEX_LOCK = ReentrantLock()
const DATEFORMAT_REGEX_HASH = Ref(hash(keys(CONVERSION_SPECIFIERS)))
const DATEFORMAT_REGEX_CACHE = Ref(compute_dateformat_regex(CONVERSION_SPECIFIERS))

"""
    DateFormat(format::AbstractString, locale="english") -> DateFormat

Construct a date formatting object that can be used for parsing date strings or
formatting a date object as a string. The following character codes can be used to construct the `format`
string:

| Code       | Matches   | Comment                                                       |
|:-----------|:----------|:--------------------------------------------------------------|
| `Y`        | 1996, 96  | Returns year of 1996, 0096                                    |
| `y`        | 1996, 96  | Same as `Y` on `parse` but discards excess digits on `format` |
| `m`        | 1, 01     | Matches 1 or 2-digit months                                   |
| `u`        | Jan       | Matches abbreviated months according to the `locale` keyword  |
| `U`        | January   | Matches full month names according to the `locale` keyword    |
| `d`        | 1, 01     | Matches 1 or 2-digit days                                     |
| `H`        | 00        | Matches hours (24-hour clock)                                 |
| `I`        | 00        | For outputting hours with 12-hour clock                       |
| `M`        | 00        | Matches minutes                                               |
| `S`        | 00        | Matches seconds                                               |
| `s`        | .500      | Matches milliseconds                                          |
| `e`        | Mon, Tues | Matches abbreviated days of the week                          |
| `E`        | Monday    | Matches full name days of the week                            |
| `p`        | AM        | Matches AM/PM (case-insensitive)                              |
| `yyyymmdd` | 19960101  | Matches fixed-width year, month, and day                      |

Characters not listed above are normally treated as delimiters between date and time slots.
For example a `dt` string of "1996-01-15T00:00:00.0" would have a `format` string like
"y-m-dTH:M:S.s". If you need to use a code character as a delimiter you can escape it using
backslash. The date "1995y01m" would have the format "y\\ym\\m".

Note that 12:00AM corresponds 00:00 (midnight), and 12:00PM corresponds to 12:00 (noon).
When parsing a time with a `p` specifier, any hour (either `H` or `I`) is interpreted as
as a 12-hour clock, so the `I` code is mainly useful for output.

Creating a DateFormat object is expensive. Whenever possible, create it once and use it many times
or try the [`dateformat""`](@ref @dateformat_str) string macro. Using this macro creates the DateFormat
object once at macro expansion time and reuses it later. There are also several [pre-defined formatters](@ref
Common-Date-Formatters), listed later.

See [`DateTime`](@ref) and [`format`](@ref) for how to use a DateFormat object to parse and write Date strings
respectively.
"""
function DateFormat(f::AbstractString, locale::DateLocale=ENGLISH)
    tokens = AbstractDateToken[]
    prev = ()
    prev_offset = 1

    # To understand this block, please see the comments attached to the definitions of
    # DATEFORMAT_REGEX_LOCK, DATEFORMAT_REGEX_HASH, and DATEFORMAT_REGEX_CACHE.
    lock(DATEFORMAT_REGEX_LOCK)
    try
        dateformat_regex_hash = hash(keys(CONVERSION_SPECIFIERS))
        if dateformat_regex_hash != DATEFORMAT_REGEX_HASH[]
            DATEFORMAT_REGEX_HASH[] = dateformat_regex_hash
            DATEFORMAT_REGEX_CACHE[] = compute_dateformat_regex(CONVERSION_SPECIFIERS)
        end
    finally
        unlock(DATEFORMAT_REGEX_LOCK)
    end

    for m in eachmatch(DATEFORMAT_REGEX_CACHE[], f)
        tran = replace(f[prev_offset:prevind(f, m.offset)], r"\\(.)" => s"\1")

        if !isempty(prev)
            letter, width = prev
            push!(tokens, DatePart{letter}(width, isempty(tran)))
        end

        if !isempty(tran)
            push!(tokens, Delim(length(tran) == 1 ? first(tran) : tran))
        end

        letter = f[m.offset]
        width = length(m.match)

        prev = (letter, width)
        prev_offset = m.offset + width
    end

    tran = replace(f[prev_offset:lastindex(f)], r"\\(.)" => s"\1")

    if !isempty(prev)
        letter, width = prev
        push!(tokens, DatePart{letter}(width, false))
    end

    if !isempty(tran)
        push!(tokens, Delim(length(tran) == 1 ? first(tran) : tran))
    end

    tokens_tuple = (tokens...,)
    return DateFormat{Symbol(f),typeof(tokens_tuple)}(tokens_tuple, locale)
end

function DateFormat(f::AbstractString, locale::AbstractString)
    DateFormat(f, LOCALES[locale])
end

function Base.show(io::IO, df::DateFormat{S,T}) where {S,T}
    print(io, "dateformat\"", S, '"')
end
Base.Broadcast.broadcastable(x::DateFormat) = Ref(x)

"""
    dateformat"Y-m-d H:M:S"

Create a [`DateFormat`](@ref) object. Similar to `DateFormat("Y-m-d H:M:S")`
but creates the DateFormat object once during macro expansion.

See [`DateFormat`](@ref) for details about format specifiers.
"""
macro dateformat_str(str)
    DateFormat(str)
end

# Standard formats

"""
    Dates.ISODateTimeFormat

Describes the ISO8601 formatting for a date and time. This is the default value for `Dates.format`
of a `DateTime`.

# Example
```jldoctest
julia> Dates.format(DateTime(2018, 8, 8, 12, 0, 43, 1), ISODateTimeFormat)
"2018-08-08T12:00:43.001"
```
"""
const ISODateTimeFormat = DateFormat("yyyy-mm-dd\\THH:MM:SS.s")
default_format(::Type{DateTime}) = ISODateTimeFormat

"""
    Dates.ISODateFormat

Describes the ISO8601 formatting for a date. This is the default value for `Dates.format` of a `Date`.

# Example
```jldoctest
julia> Dates.format(Date(2018, 8, 8), ISODateFormat)
"2018-08-08"
```
"""
const ISODateFormat = DateFormat("yyyy-mm-dd")
default_format(::Type{Date}) = ISODateFormat

"""
    Dates.ISOTimeFormat

Describes the ISO8601 formatting for a time. This is the default value for `Dates.format` of a `Time`.

# Example
```jldoctest
julia> Dates.format(Time(12, 0, 43, 1), ISOTimeFormat)
"12:00:43.001"
```
"""
const ISOTimeFormat = DateFormat("HH:MM:SS.s")
default_format(::Type{Time}) = ISOTimeFormat

"""
    Dates.RFC1123Format

Describes the RFC1123 formatting for a date and time.

# Example
```jldoctest
julia> Dates.format(DateTime(2018, 8, 8, 12, 0, 43, 1), RFC1123Format)
"Wed, 08 Aug 2018 12:00:43"
```
"""
const RFC1123Format = DateFormat("e, dd u yyyy HH:MM:SS")


### API

const Locale = Union{DateLocale, String}

"""
    DateTime(dt::AbstractString, format::AbstractString; locale="english") -> DateTime

Construct a `DateTime` by parsing the `dt` date time string following the
pattern given in the `format` string (see [`DateFormat`](@ref)  for syntax).

!!! note
    This method creates a `DateFormat` object each time it is called. It is recommended
    that you create a [`DateFormat`](@ref) object instead and use that as the second
    argument to avoid performance loss when using the same format repeatedly.

# Example
```jldoctest
julia> DateTime("2020-01-01", "yyyy-mm-dd")
2020-01-01T00:00:00

julia> a = ("2020-01-01", "2020-01-02");

julia> [DateTime(d, dateformat"yyyy-mm-dd") for d ∈ a] # preferred
2-element Vector{DateTime}:
 2020-01-01T00:00:00
 2020-01-02T00:00:00
```
"""
function DateTime(dt::AbstractString, format::AbstractString; locale::Locale=ENGLISH)
    return parse(DateTime, dt, DateFormat(format, locale))
end

"""
    DateTime(dt::AbstractString, df::DateFormat=ISODateTimeFormat) -> DateTime

Construct a `DateTime` by parsing the `dt` date time string following the
pattern given in the [`DateFormat`](@ref) object, or $ISODateTimeFormat if omitted.

Similar to `DateTime(::AbstractString, ::AbstractString)` but more efficient when
repeatedly parsing similarly formatted date time strings with a pre-created
`DateFormat` object.
"""
DateTime(dt::AbstractString, df::DateFormat=ISODateTimeFormat) = parse(DateTime, dt, df)

"""
    Date(d::AbstractString, format::AbstractString; locale="english") -> Date

Construct a `Date` by parsing the `d` date string following the pattern given
in the `format` string (see [`DateFormat`](@ref) for syntax).

!!! note
    This method creates a `DateFormat` object each time it is called. It is recommended
    that you create a [`DateFormat`](@ref) object instead and use that as the second
    argument to avoid performance loss when using the same format repeatedly.

# Example
```jldoctest
julia> Date("2020-01-01", "yyyy-mm-dd")
2020-01-01

julia> a = ("2020-01-01", "2020-01-02");

julia> [Date(d, dateformat"yyyy-mm-dd") for d ∈ a] # preferred
2-element Vector{Date}:
 2020-01-01
 2020-01-02
```
"""
function Date(d::AbstractString, format::AbstractString; locale::Locale=ENGLISH)
    parse(Date, d, DateFormat(format, locale))
end

"""
    Date(d::AbstractString, df::DateFormat=ISODateFormat) -> Date

Construct a `Date` by parsing the `d` date string following the
pattern given in the [`DateFormat`](@ref) object, or $ISODateFormat if omitted.

Similar to `Date(::AbstractString, ::AbstractString)` but more efficient when
repeatedly parsing similarly formatted date strings with a pre-created
`DateFormat` object.
"""
Date(d::AbstractString, df::DateFormat=ISODateFormat) = parse(Date, d, df)

"""
    Time(t::AbstractString, format::AbstractString; locale="english") -> Time

Construct a `Time` by parsing the `t` time string following the pattern given
in the `format` string (see [`DateFormat`](@ref) for syntax).

!!! note
    This method creates a `DateFormat` object each time it is called. It is recommended
    that you create a [`DateFormat`](@ref) object instead and use that as the second
    argument to avoid performance loss when using the same format repeatedly.

# Example
```jldoctest
julia> Time("12:34pm", "HH:MMp")
12:34:00

julia> a = ("12:34pm", "2:34am");

julia> [Time(d, dateformat"HH:MMp") for d ∈ a] # preferred
2-element Vector{Time}:
 12:34:00
 02:34:00
```
"""
function Time(t::AbstractString, format::AbstractString; locale::Locale=ENGLISH)
    parse(Time, t, DateFormat(format, locale))
end

"""
    Time(t::AbstractString, df::DateFormat=ISOTimeFormat) -> Time

Construct a `Time` by parsing the `t` date time string following the
pattern given in the [`DateFormat`](@ref) object, or $ISOTimeFormat if omitted.

Similar to `Time(::AbstractString, ::AbstractString)` but more efficient when
repeatedly parsing similarly formatted time strings with a pre-created
`DateFormat` object.
"""
Time(t::AbstractString, df::DateFormat=ISOTimeFormat) = parse(Time, t, df)

@generated function format(io::IO, dt::TimeType, fmt::DateFormat{<:Any,T}) where T
    N = fieldcount(T)
    quote
        ts = fmt.tokens
        loc = fmt.locale
        Base.@nexprs $N i -> format(io, ts[i], dt, loc)
    end
end

function format(dt::TimeType, fmt::DateFormat, bufsize=12)
    # preallocate to reduce resizing
    io = IOBuffer(Vector{UInt8}(undef, bufsize), read=true, write=true)
    format(io, dt, fmt)
    String(io.data[1:io.ptr - 1])
end


"""
    format(dt::TimeType, format::AbstractString; locale="english") -> AbstractString

Construct a string by using a `TimeType` object and applying the provided `format`. The
following character codes can be used to construct the `format` string:

| Code       | Examples  | Comment                                                      |
|:-----------|:----------|:-------------------------------------------------------------|
| `y`        | 6         | Numeric year with a fixed width                              |
| `Y`        | 1996      | Numeric year with a minimum width                            |
| `m`        | 1, 12     | Numeric month with a minimum width                           |
| `u`        | Jan       | Month name shortened to 3-chars according to the `locale`    |
| `U`        | January   | Full month name according to the `locale` keyword            |
| `d`        | 1, 31     | Day of the month with a minimum width                        |
| `H`        | 0, 23     | Hour (24-hour clock) with a minimum width                    |
| `M`        | 0, 59     | Minute with a minimum width                                  |
| `S`        | 0, 59     | Second with a minimum width                                  |
| `s`        | 000, 500  | Millisecond with a minimum width of 3                        |
| `e`        | Mon, Tue  | Abbreviated days of the week                                 |
| `E`        | Monday    | Full day of week name                                        |

The number of sequential code characters indicate the width of the code. A format of
`yyyy-mm` specifies that the code `y` should have a width of four while `m` a width of two.
Codes that yield numeric digits have an associated mode: fixed-width or minimum-width.
The fixed-width mode left-pads the value with zeros when it is shorter than the specified
width and truncates the value when longer. Minimum-width mode works the same as fixed-width
except that it does not truncate values longer than the width.

When creating a `format` you can use any non-code characters as a separator. For example to
generate the string "1996-01-15T00:00:00" you could use `format`: "yyyy-mm-ddTHH:MM:SS".
Note that if you need to use a code character as a literal you can use the escape character
backslash. The string "1996y01m" can be produced with the format "yyyy\\ymm\\m".
"""
function format(dt::TimeType, f::AbstractString; locale::Locale=ENGLISH)
    format(dt, DateFormat(f, locale))
end

# show
function Base.print(io::IO, dt::DateTime)
    str = if millisecond(dt) == 0
        format(dt, dateformat"YYYY-mm-dd\THH:MM:SS", 19)
    else
        format(dt, dateformat"YYYY-mm-dd\THH:MM:SS.sss", 23)
    end
    print(io, str)
end

function Base.print(io::IO, dt::Date)
    # don't use format - bypassing IOBuffer creation
    # saves a bit of time here.
    y,m,d = yearmonthday(value(dt))
    yy = y < 0 ? @sprintf("%05i", y) : lpad(y, 4, "0")
    mm = lpad(m, 2, "0")
    dd = lpad(d, 2, "0")
    print(io, "$yy-$mm-$dd")
end

for date_type in (:Date, :DateTime)
    # Human readable output (i.e. "2012-01-01")
    @eval Base.show(io::IO, ::MIME"text/plain", dt::$date_type) = print(io, dt)
    # Parsable output (i.e. Date("2012-01-01"))
    @eval Base.show(io::IO, dt::$date_type) = print(io, typeof(dt), "(\"", dt, "\")")
    # Parsable output will have type info displayed, thus it is implied
    @eval Base.typeinfo_implicit(::Type{$date_type}) = true
end
n   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Dates/src/parse.jl�+      # This file is a part of Julia. License is MIT: https://julialang.org/license

### Parsing utilities

_directives(::Type{DateFormat{S,T}}) where {S,T} = T.parameters

character_codes(df::Type{DateFormat{S,T}}) where {S,T} = character_codes(_directives(df))
function character_codes(directives::Core.SimpleVector)
    letters = sizehint!(Char[], length(directives))
    for (i, directive) in enumerate(directives)
        if directive <: DatePart
            letter = first(directive.parameters)
            push!(letters, letter)
        end
    end
    return letters
end

genvar(t::DataType) = Symbol(lowercase(string(nameof(t))))

"""
    tryparsenext_core(str::AbstractString, pos::Int, len::Int, df::DateFormat, raise=false)

Parse the string according to the directives within the `DateFormat`. Parsing will start at
character index `pos` and will stop when all directives are used or we have parsed up to
the end of the string, `len`. When a directive cannot be parsed the returned value
will be `nothing` if `raise` is false otherwise an exception will be thrown.

If successful, return a 3-element tuple `(values, pos, num_parsed)`:
* `values::Tuple`: A tuple which contains a value
  for each `DatePart` within the `DateFormat` in the order
  in which they occur. If the string ends before we finish parsing all the directives
  the missing values will be filled in with default values.
* `pos::Int`: The character index at which parsing stopped.
* `num_parsed::Int`: The number of values which were parsed and stored within `values`.
  Useful for distinguishing parsed values from default values.
"""
@generated function tryparsenext_core(str::AbstractString, pos::Int, len::Int,
                                      df::DateFormat, raise::Bool=false)
    directives = _directives(df)
    letters = character_codes(directives)

    tokens = Type[CONVERSION_SPECIFIERS[letter] for letter in letters]
    value_names = Symbol[genvar(t) for t in tokens]
    value_defaults = Tuple(CONVERSION_DEFAULTS[t] for t in tokens)

    # Pre-assign variables to defaults. Allows us to use `@goto done` without worrying about
    # unassigned variables.
    assign_defaults = Expr[]
    for (name, default) in zip(value_names, value_defaults)
        push!(assign_defaults, quote
            $name = $default
        end)
    end

    vi = 1
    parsers = Expr[]
    for i = 1:length(directives)
        if directives[i] <: DatePart
            name = value_names[vi]
            vi += 1
            push!(parsers, quote
                pos > len && @goto done
                let val = tryparsenext(directives[$i], str, pos, len, locale)
                    val === nothing && @goto error
                    $name, pos = val
                end
                num_parsed += 1
                directive_index += 1
            end)
        else
            push!(parsers, quote
                pos > len && @goto done
                let val = tryparsenext(directives[$i], str, pos, len, locale)
                    val === nothing && @goto error
                    delim, pos = val
                end
                directive_index += 1
            end)
        end
    end

    return quote
        directives = df.tokens
        locale::DateLocale = df.locale

        num_parsed = 0
        directive_index = 1

        $(assign_defaults...)
        $(parsers...)

        pos > len || @goto error

        @label done
        return $(Expr(:tuple, value_names...)), pos, num_parsed

        @label error
        if raise
            if directive_index > length(directives)
                throw(ArgumentError("Found extra characters at the end of date time string"))
            else
                d = directives[directive_index]
                throw(ArgumentError("Unable to parse date time. Expected directive $d at char $pos"))
            end
        end
        return nothing
    end
end

"""
    tryparsenext_internal(::Type{<:TimeType}, str, pos, len, df::DateFormat, raise=false)

Parse the string according to the directives within the `DateFormat`. The specified `TimeType`
type determines the type of and order of tokens returned. If the given `DateFormat` or string
does not provide a required token a default value will be used. When the string cannot be
parsed the returned value will be `nothing` if `raise` is false otherwise an exception will
be thrown.

If successful, returns a 2-element tuple `(values, pos)`:
* `values::Tuple`: A tuple which contains a value
  for each token as specified by the passed in type.
* `pos::Int`: The character index at which parsing stopped.
"""
@generated function tryparsenext_internal(::Type{T}, str::AbstractString, pos::Int, len::Int,
                                          df::DateFormat, raise::Bool=false) where T<:TimeType
    letters = character_codes(df)

    tokens = Type[CONVERSION_SPECIFIERS[letter] for letter in letters]
    value_names = Symbol[genvar(t) for t in tokens]

    output_tokens = CONVERSION_TRANSLATIONS[T]
    output_names = Symbol[genvar(t) for t in output_tokens]
    output_defaults = Tuple(CONVERSION_DEFAULTS[t] for t in output_tokens)

    # Pre-assign output variables to defaults. Ensures that all output variables are
    # assigned as the value tuple returned from `tryparsenext_core` may not include all
    # of the required variables.
    assign_defaults = Expr[
        quote
            $name = $default
        end
        for (name, default) in zip(output_names, output_defaults)
    ]

    # Unpacks the value tuple returned by `tryparsenext_core` into separate variables.
    value_tuple = Expr(:tuple, value_names...)

    return quote
        val = tryparsenext_core(str, pos, len, df, raise)
        val === nothing && return nothing
        values, pos, num_parsed = val
        $(assign_defaults...)
        $value_tuple = values
        return $(Expr(:tuple, output_names...)), pos
    end
end

@inline function tryparsenext_base10(str::AbstractString, i::Int, len::Int, min_width::Int=1, max_width::Int=0)
    i > len && return nothing
    min_pos = min_width <= 0 ? i : i + min_width - 1
    max_pos = max_width <= 0 ? len : min(i + max_width - 1, len)
    d::Int64 = 0
    @inbounds while i <= max_pos
        c, ii = iterate(str, i)::Tuple{Char, Int}
        if '0' <= c <= '9'
            d = d * 10 + (c - '0')
        else
            break
        end
        i = ii
    end
    if i <= min_pos
        return nothing
    else
        return d, i
    end
end

@inline function tryparsenext_word(str::AbstractString, i, len, locale, maxchars=0)
    word_start, word_end = i, 0
    max_pos = maxchars <= 0 ? len : min(len, nextind(str, i, maxchars-1))
    @inbounds while i <= max_pos
        c, ii = iterate(str, i)::Tuple{Char, Int}
        if isletter(c)
            word_end = i
        else
            break
        end
        i = ii
    end
    if word_end == 0
        return nothing
    else
        return SubString(str, word_start, word_end), i
    end
end

function Base.parse(::Type{DateTime}, s::AbstractString, df::typeof(ISODateTimeFormat))
    i, end_pos = firstindex(s), lastindex(s)
    i > end_pos && throw(ArgumentError("Cannot parse an empty string as a DateTime"))

    local dy
    dm = dd = Int64(1)
    th = tm = ts = tms = Int64(0)

    let val = tryparsenext_base10(s, i, end_pos, 1)
        val === nothing && @goto error
        dy, i = val
        i > end_pos && @goto error
    end

    c, i = iterate(s, i)::Tuple{Char, Int}
    c != '-' && @goto error
    i > end_pos && @goto done

    let val = tryparsenext_base10(s, i, end_pos, 1, 2)
        val === nothing && @goto error
        dm, i = val
        i > end_pos && @goto done
    end

    c, i = iterate(s, i)::Tuple{Char, Int}
    c != '-' && @goto error
    i > end_pos && @goto done

    let val = tryparsenext_base10(s, i, end_pos, 1, 2)
        val === nothing && @goto error
        dd, i = val
        i > end_pos && @goto done
    end

    c, i = iterate(s, i)::Tuple{Char, Int}
    c != 'T' && @goto error
    i > end_pos && @goto done

    let val = tryparsenext_base10(s, i, end_pos, 1, 2)
        val === nothing && @goto error
        th, i = val
        i > end_pos && @goto done
    end

    c, i = iterate(s, i)::Tuple{Char, Int}
    c != ':' && @goto error
    i > end_pos && @goto done

    let val = tryparsenext_base10(s, i, end_pos, 1, 2)
        val === nothing && @goto error
        tm, i = val
        i > end_pos && @goto done
    end

    c, i = iterate(s, i)::Tuple{Char, Int}
    c != ':' && @goto error
    i > end_pos && @goto done

    let val = tryparsenext_base10(s, i, end_pos, 1, 2)
        val === nothing && @goto error
        ts, i = val
        i > end_pos && @goto done
    end

    c, i = iterate(s, i)::Tuple{Char, Int}
    c != '.' && @goto error
    i > end_pos && @goto done

    let val = tryparsenext_base10(s, i, end_pos, 1, 3)
        val === nothing && @goto error
        tms, j = val
        tms *= 10 ^ (3 - (j - i))
        j > end_pos || @goto error
    end

    @label done
    return DateTime(dy, dm, dd, th, tm, ts, tms)

    @label error
    throw(ArgumentError("Invalid DateTime string"))
end

function Base.parse(::Type{T}, str::AbstractString, df::DateFormat=default_format(T)) where T<:TimeType
    pos, len = firstindex(str), lastindex(str)
    pos > len && throw(ArgumentError("Cannot parse an empty string as a Date or Time"))
    val = tryparsenext_internal(T, str, pos, len, df, true)
    @assert val !== nothing
    values, endpos = val
    return T(values...)::T
end

function Base.tryparse(::Type{T}, str::AbstractString, df::DateFormat=default_format(T)) where T<:TimeType
    pos, len = firstindex(str), lastindex(str)
    pos > len && return nothing
    res = tryparsenext_internal(T, str, pos, len, df, false)
    res === nothing && return nothing
    values, endpos = res
    if validargs(T, values...) === nothing
        # TODO: validargs gets called twice, since it's called again in the T constructor
        return T(values...)::T
    end
    return nothing
end

"""
    parse_components(str::AbstractString, df::DateFormat) -> Array{Any}

Parse the string into its components according to the directives in the `DateFormat`.
Each component will be a distinct type, typically a subtype of Period. The order of the
components will match the order of the `DatePart` directives within the `DateFormat`. The
number of components may be less than the total number of `DatePart`.
"""
@generated function parse_components(str::AbstractString, df::DateFormat)
    letters = character_codes(df)
    tokens = Type[CONVERSION_SPECIFIERS[letter] for letter in letters]

    return quote
        pos, len = firstindex(str), lastindex(str)
        val = tryparsenext_core(str, pos, len, df, #=raise=#true)
        @assert val !== nothing
        values, pos, num_parsed = val
        types = $(Expr(:tuple, tokens...))
        result = Vector{Any}(undef, num_parsed)
        for (i, typ) in enumerate(types)
            i > num_parsed && break
            result[i] = typ(values[i])  # Constructing types takes most of the time
        end
        return result
    end
end
s   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Dates/src/deprecated.jl       # This file is a part of Julia. License is MIT: https://julialang.org/license

using Base: @deprecate, depwarn

# 1.0 deprecations
function (+)(x::AbstractArray{<:TimeType}, y::GeneralPeriod)
    # depwarn("non-broadcasted arithmetic is deprecated for Dates.TimeType; use broadcasting instead", nothing)
    x .+ y
end
function (+)(x::StridedArray{<:GeneralPeriod}, y::TimeType)
    # depwarn("non-broadcasted arithmetic is deprecated for Dates.TimeType; use broadcasting instead", nothing)
    x .+ y
end
function (+)(y::GeneralPeriod, x::AbstractArray{<:TimeType})
    # depwarn("non-broadcasted arithmetic is deprecated for Dates.TimeType; use broadcasting instead", nothing)
    x .+ y
end
function (+)(y::TimeType, x::StridedArray{<:GeneralPeriod})
    # depwarn("non-broadcasted arithmetic is deprecated for Dates.TimeType; use broadcasting instead", nothing)
    x .+ y
end
function (-)(x::AbstractArray{<:TimeType}, y::GeneralPeriod)
    # depwarn("non-broadcasted arithmetic is deprecated for Dates.TimeType; use broadcasting instead", nothing)
    x .- y
end
function (-)(x::StridedArray{<:GeneralPeriod}, y::TimeType)
    # depwarn("non-broadcasted arithmetic is deprecated for Dates.TimeType; use broadcasting instead", nothing)
    x .- y
end

# TimeType, AbstractArray{TimeType}
function (-)(x::AbstractArray{T}, y::T) where {T<:TimeType}
    # depwarn("non-broadcasted arithmetic is deprecated for Dates.TimeType; use broadcasting instead", nothing)
    x .- y
end
function (-)(y::T, x::AbstractArray{T}) where {T<:TimeType}
    # depwarn("non-broadcasted arithmetic is deprecated for Dates.TimeType; use broadcasting instead", nothing)
    y .- x
end

for (op, Ty, Tz) in ((:*, Real, :P),
                   (:/, :P, Float64), (:/, Real, :P))
    @eval begin
        function ($op)(X::StridedArray{P}, y::$Ty) where P<:Period
            # depwarn("non-broadcasted arithmetic is deprecated for Dates.TimeType; use broadcasting instead", nothing)
            Z = similar(X, $Tz)
            for (Idst, Isrc) in zip(eachindex(Z), eachindex(X))
                @inbounds Z[Idst] = ($op)(X[Isrc], y)
            end
            return Z
        end
    end
end

function (+)(x::StridedArray{<:GeneralPeriod})
    # depwarn("non-broadcasted operations are deprecated for Dates.TimeType; use broadcasting instead", nothing)
    x
end

for op in (:+, :-)
    @eval begin
        function ($op)(X::StridedArray{<:GeneralPeriod}, Y::StridedArray{<:GeneralPeriod})
            # depwarn("non-broadcasted arithmetic is deprecated for Dates.TimeType; use broadcasting instead", nothing)
            reshape(CompoundPeriod[($op)(x, y) for (x, y) in zip(X, Y)], promote_shape(size(X), size(Y)))
        end
    end
end

@deprecate argerror(msg::String) ArgumentError(msg) false
@deprecate argerror() nothing false
p   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Future/src/Future.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

"The `Future` module implements future behavior of already existing functions,
which will replace the current version in a future release of Julia."
module Future

using Random

## copy!

# This has now been moved to Base (#29178), and should be deprecated in the
# next "deprecation phase".

"""
    Future.copy!(dst, src) -> dst

Copy `src` into `dst`.

!!! compat "Julia 1.1"
    This function has moved to `Base` with Julia 1.1, consider using `copy!(dst, src)` instead.
    `Future.copy!` will be deprecated in the future.
"""
copy!(dst::AbstractSet, src::AbstractSet) = Base.copy!(dst, src)
copy!(dst::AbstractDict, src::AbstractDict) = Base.copy!(dst, src)
copy!(dst::AbstractArray, src::AbstractArray) = Base.copy!(dst, src)


## randjump

"""
    randjump(r::MersenneTwister, steps::Integer) -> MersenneTwister

Create an initialized `MersenneTwister` object, whose state is moved forward
(without generating numbers) from `r` by `steps` steps.
One such step corresponds to the generation of two `Float64` numbers.
For each different value of `steps`, a large polynomial has to be generated internally.
One is already pre-computed for `steps=big(10)^20`.
"""
function randjump(r::MersenneTwister, steps::Integer)
    j = Random._randjump(r, Random.DSFMT.calc_jump(steps))
    j.adv_jump += 2*big(steps) # convert to BigInt to prevent overflow
    j
end

end # module Future
�   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/InteractiveUtils/src/InteractiveUtils.jl�6      # This file is a part of Julia. License is MIT: https://julialang.org/license

module InteractiveUtils

Base.Experimental.@optlevel 1

export apropos, edit, less, code_warntype, code_llvm, code_native, methodswith, varinfo,
    versioninfo, subtypes, supertypes, @which, @edit, @less, @functionloc, @code_warntype,
    @code_typed, @code_lowered, @code_llvm, @code_native, @time_imports, clipboard

import Base.Docs.apropos

using Base: unwrap_unionall, rewrap_unionall, isdeprecated, Bottom, show_unquoted, summarysize,
    signature_type, format_bytes
using Base.Libc
using Markdown

include("editless.jl")
include("codeview.jl")
include("macros.jl")
include("clipboard.jl")

"""
    varinfo(m::Module=Main, pattern::Regex=r""; all=false, imported=false, recursive=false, sortby::Symbol=:name, minsize::Int=0)

Return a markdown table giving information about exported global variables in a module, optionally restricted
to those matching `pattern`.

The memory consumption estimate is an approximate lower bound on the size of the internal structure of the object.

- `all` : also list non-exported objects defined in the module, deprecated objects, and compiler-generated objects.
- `imported` : also list objects explicitly imported from other modules.
- `recursive` : recursively include objects in sub-modules, observing the same settings in each.
- `sortby` : the column to sort results by. Options are `:name` (default), `:size`, and `:summary`.
- `minsize` : only includes objects with size at least `minsize` bytes. Defaults to `0`.

The output of `varinfo` is intended for display purposes only.  See also [`names`](@ref) to get an array of symbols defined in
a module, which is suitable for more general manipulations.
"""
function varinfo(m::Module=Base.active_module(), pattern::Regex=r""; all::Bool = false, imported::Bool = false, recursive::Bool = false, sortby::Symbol = :name, minsize::Int=0)
    sortby in (:name, :size, :summary) || throw(ArgumentError("Unrecognized `sortby` value `:$sortby`. Possible options are `:name`, `:size`, and `:summary`"))
    rows = Vector{Any}[]
    workqueue = [(m, ""),]
    while !isempty(workqueue)
        m2, prep = popfirst!(workqueue)
        for v in names(m2; all, imported)
            if !isdefined(m2, v) || !occursin(pattern, string(v))
                continue
            end
            value = getfield(m2, v)
            isbuiltin = value === Base || value === Base.active_module() || value === Core
            if recursive && !isbuiltin && isa(value, Module) && value !== m2 && nameof(value) === v && parentmodule(value) === m2
                push!(workqueue, (value, "$prep$v."))
            end
            ssize_str, ssize = if isbuiltin
                    ("", typemax(Int))
                else
                    ss = summarysize(value)
                    (format_bytes(ss), ss)
                end
            if ssize >= minsize
                push!(rows, Any[string(prep, v), ssize_str, summary(value), ssize])
            end
        end
    end
    let (col, rev) = if sortby === :name
            1, false
        elseif sortby === :size
            4, true
        elseif sortby === :summary
            3, false
        else
            @assert "unreachable"
        end
        sort!(rows; by=r->r[col], rev)
    end
    pushfirst!(rows, Any["name", "size", "summary"])

    return Markdown.MD(Any[Markdown.Table(map(r->r[1:3], rows), Symbol[:l, :r, :l])])
end
varinfo(pat::Regex; kwargs...) = varinfo(Base.active_module(), pat; kwargs...)

"""
    versioninfo(io::IO=stdout; verbose::Bool=false)

Print information about the version of Julia in use. The output is
controlled with boolean keyword arguments:

- `verbose`: print all additional information

!!! warning "Warning"
    The output of this function may contain sensitive information. Before sharing the output,
    please review the output and remove any data that should not be shared publicly.

See also: [`VERSION`](@ref).
"""
function versioninfo(io::IO=stdout; verbose::Bool=false)
    println(io, "Julia Version $VERSION")
    if !isempty(Base.GIT_VERSION_INFO.commit_short)
        println(io, "Commit $(Base.GIT_VERSION_INFO.commit_short) ($(Base.GIT_VERSION_INFO.date_string))")
    end
    official_release = Base.TAGGED_RELEASE_BANNER == "Official https://julialang.org/ release"
    if Base.isdebugbuild() || !isempty(Base.TAGGED_RELEASE_BANNER) || (Base.GIT_VERSION_INFO.tagged_commit && !official_release)
        println(io, "Build Info:")
        if Base.isdebugbuild()
            println(io, "  DEBUG build")
        end
        if !isempty(Base.TAGGED_RELEASE_BANNER)
            println(io, "  ", Base.TAGGED_RELEASE_BANNER)
        end
        if Base.GIT_VERSION_INFO.tagged_commit && !official_release
            println(io,
                """

                    Note: This is an unofficial build, please report bugs to the project
                    responsible for this build and not to the Julia project unless you can
                    reproduce the issue using official builds available at https://julialang.org/downloads
                """
            )
        end
    end
    println(io, "Platform Info:")
    println(io, "  OS: ", Sys.iswindows() ? "Windows" : Sys.isapple() ?
        "macOS" : Sys.KERNEL, " (", Sys.MACHINE, ")")

    if verbose
        lsb = ""
        if Sys.islinux()
            try lsb = readchomp(pipeline(`lsb_release -ds`, stderr=devnull)); catch; end
        end
        if Sys.iswindows()
            try lsb = strip(read(`$(ENV["COMSPEC"]) /c ver`, String)); catch; end
        end
        if !isempty(lsb)
            println(io, "      ", lsb)
        end
        if Sys.isunix()
            println(io, "  uname: ", readchomp(`uname -mprsv`))
        end
    end

    if verbose
        cpuio = IOBuffer() # print cpu_summary with correct alignment
        Sys.cpu_summary(cpuio)
        for (i, line) in enumerate(split(chomp(String(take!(cpuio))), "\n"))
            prefix = i == 1 ? "  CPU: " : "       "
            println(io, prefix, line)
        end
    else
        cpu = Sys.cpu_info()
        println(io, "  CPU: ", length(cpu), " × ", cpu[1].model)
    end

    if verbose
        println(io, "  Memory: $(Sys.total_memory()/2^30) GB ($(Sys.free_memory()/2^20) MB free)")
        try println(io, "  Uptime: $(Sys.uptime()) sec"); catch; end
        print(io, "  Load Avg: ")
        Base.print_matrix(io, Sys.loadavg()')
        println(io)
    end
    println(io, "  WORD_SIZE: ", Sys.WORD_SIZE)
    println(io, "  LIBM: ",Base.libm_name)
    println(io, "  LLVM: libLLVM-",Base.libllvm_version," (", Sys.JIT, ", ", Sys.CPU_NAME, ")")
    println(io, """Threads: $(Threads.nthreads(:default)) default, $(Threads.nthreads(:interactive)) interactive, \
      $(Threads.ngcthreads()) GC (on $(Sys.CPU_THREADS) virtual cores)""")

    function is_nonverbose_env(k::String)
        return occursin(r"^JULIA_|^DYLD_|^LD_", k)
    end
    function is_verbose_env(k::String)
        return occursin(r"PATH|FLAG|^TERM$|HOME", k) && !is_nonverbose_env(k)
    end
    env_strs = String[
        String["  $(k) = $(v)" for (k,v) in ENV if is_nonverbose_env(uppercase(k))];
        (verbose ?
         String["  $(k) = $(v)" for (k,v) in ENV if is_verbose_env(uppercase(k))] :
         String[]);
    ]
    if !isempty(env_strs)
        println(io, "Environment:")
        for str in env_strs
            println(io, str)
        end
    end
end


function type_close_enough(@nospecialize(x), @nospecialize(t))
    x == t && return true
    # TODO: handle UnionAll properly
    return (isa(x, DataType) && isa(t, DataType) && x.name === t.name && x <: t) ||
           (isa(x, Union) && isa(t, DataType) && (type_close_enough(x.a, t) || type_close_enough(x.b, t)))
end

# `methodswith` -- shows a list of methods using the type given
"""
    methodswith(typ[, module or function]; supertypes::Bool=false])

Return an array of methods with an argument of type `typ`.

The optional second argument restricts the search to a particular module or function
(the default is all top-level modules).

If keyword `supertypes` is `true`, also return arguments with a parent type of `typ`,
excluding type `Any`.
"""
function methodswith(@nospecialize(t::Type), @nospecialize(f::Base.Callable), meths = Method[]; supertypes::Bool=false)
    for d in methods(f)
        if any(function (x)
                   let x = rewrap_unionall(x, d.sig)
                       (type_close_enough(x, t) ||
                        (supertypes ? (isa(x, Type) && t <: x && (!isa(x,TypeVar) || x.ub != Any)) :
                         (isa(x,TypeVar) && x.ub != Any && t == x.ub)) &&
                        x != Any)
                   end
               end,
               unwrap_unionall(d.sig).parameters)
            push!(meths, d)
        end
    end
    return meths
end

function _methodswith(@nospecialize(t::Type), m::Module, supertypes::Bool)
    meths = Method[]
    for nm in names(m)
        if isdefined(m, nm)
            f = getfield(m, nm)
            if isa(f, Base.Callable)
                methodswith(t, f, meths; supertypes = supertypes)
            end
        end
    end
    return unique(meths)
end

methodswith(@nospecialize(t::Type), m::Module; supertypes::Bool=false) = _methodswith(t, m, supertypes)

function methodswith(@nospecialize(t::Type); supertypes::Bool=false)
    meths = Method[]
    for mod in Base.loaded_modules_array()
        append!(meths, _methodswith(t, mod, supertypes))
    end
    return unique(meths)
end

# subtypes
function _subtypes_in!(mods::Array, x::Type)
    xt = unwrap_unionall(x)
    if !isabstracttype(x) || !isa(xt, DataType)
        # Fast path
        return Type[]
    end
    sts = Vector{Any}()
    while !isempty(mods)
        m = pop!(mods)
        xt = xt::DataType
        for s in names(m, all = true)
            if isdefined(m, s) && !isdeprecated(m, s)
                t = getfield(m, s)
                dt = isa(t, UnionAll) ? unwrap_unionall(t) : t
                if isa(dt, DataType)
                    if dt.name.name === s && dt.name.module == m && supertype(dt).name == xt.name
                        ti = typeintersect(t, x)
                        ti != Bottom && push!(sts, ti)
                    end
                elseif isa(t, Module) && nameof(t) === s && parentmodule(t) === m && t !== m
                    t === Base || push!(mods, t) # exclude Base, since it also parented by Main
                end
            end
        end
    end
    return permute!(sts, sortperm(map(string, sts)))
end

subtypes(m::Module, x::Type) = _subtypes_in!([m], x)

"""
    subtypes(T::DataType)

Return a list of immediate subtypes of DataType `T`. Note that all currently loaded subtypes
are included, including those not visible in the current module.

See also [`supertype`](@ref), [`supertypes`](@ref), [`methodswith`](@ref).

# Examples
```jldoctest
julia> subtypes(Integer)
3-element Vector{Any}:
 Bool
 Signed
 Unsigned
```
"""
subtypes(x::Type) = _subtypes_in!(Base.loaded_modules_array(), x)

"""
    supertypes(T::Type)

Return a tuple `(T, ..., Any)` of `T` and all its supertypes, as determined by
successive calls to the [`supertype`](@ref) function, listed in order of `<:`
and terminated by `Any`.

See also [`subtypes`](@ref).

# Examples
```jldoctest
julia> supertypes(Int)
(Int64, Signed, Integer, Real, Number, Any)
```
"""
function supertypes(T::Type)
    S = supertype(T)
    # note: we return a tuple here, not an Array as for subtypes, because in
    #       the future we could evaluate this function statically if desired.
    return S === T ? (T,) : (T, supertypes(S)...)
end

# TODO: @deprecate peakflops to LinearAlgebra
export peakflops
"""
    peakflops(n::Integer=4096; eltype::DataType=Float64, ntrials::Integer=3, parallel::Bool=false)

`peakflops` computes the peak flop rate of the computer by using double precision
[`gemm!`](@ref LinearAlgebra.BLAS.gemm!). For more information see
[`LinearAlgebra.peakflops`](@ref).

!!! compat "Julia 1.1"
    This function will be moved from `InteractiveUtils` to `LinearAlgebra` in the
    future. In Julia 1.1 and later it is available as `LinearAlgebra.peakflops`.
"""
function peakflops(n::Integer=4096; eltype::DataType=Float64, ntrials::Integer=3, parallel::Bool=false)
    # Base.depwarn("`peakflops` has moved to the LinearAlgebra module, " *
    #              "add `using LinearAlgebra` to your imports.", :peakflops)
    let LinearAlgebra = Base.require(Base.PkgId(
            Base.UUID((0x37e2e46d_f89d_539d,0xb4ee_838fcccc9c8e)), "LinearAlgebra"))
        return LinearAlgebra.peakflops(n, eltype=eltype, ntrials=ntrials, parallel=parallel)
    end
end

function report_bug(kind)
    @info "Loading BugReporting package..."
    BugReportingId = Base.PkgId(
        Base.UUID((0xbcf9a6e7_4020_453c,0xb88e_690564246bb8)), "BugReporting")
    # Check if the BugReporting package exists in the current environment
    local BugReporting
    if Base.locate_package(BugReportingId) === nothing
        @info "Package `BugReporting` not found - attempting temporary installation"
        # Create a temporary environment and add BugReporting
        let Pkg = Base.require(Base.PkgId(
            Base.UUID((0x44cfe95a_1eb2_52ea,0xb672_e2afdf69b78f)), "Pkg"))
            mktempdir() do tmp
                old_load_path = copy(LOAD_PATH)
                push!(empty!(LOAD_PATH), joinpath(tmp, "Project.toml"))
                old_active_project = Base.ACTIVE_PROJECT[]
                Base.ACTIVE_PROJECT[] = nothing
                Pkg.add(Pkg.PackageSpec(BugReportingId.name, BugReportingId.uuid))
                BugReporting = Base.require(BugReportingId)
                append!(empty!(LOAD_PATH), old_load_path)
                Base.ACTIVE_PROJECT[] = old_active_project
            end
        end
    else
        BugReporting = Base.require(BugReportingId)
    end
    return Base.invokelatest(BugReporting.make_interactive_report, kind, ARGS)
end

end
|   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/InteractiveUtils/src/editless.jlQ*      # This file is a part of Julia. License is MIT: https://julialang.org/license

# editing and paging files

using Base: shell_split, shell_escape, find_source_file

"""
    EDITOR_CALLBACKS :: Vector{Function}

A vector of editor callback functions, which take as arguments `cmd`, `path`, `line`
and `column` and which is then expected to either open an editor and return `true` to
indicate that it has handled the request, or return `false` to decline the
editing request.
"""
const EDITOR_CALLBACKS = Function[]

"""
    define_editor(fn, pattern; wait=false)

Define a new editor matching `pattern` that can be used to open a file (possibly
at a given line number) using `fn`.

The `fn` argument is a function that determines how to open a file with the
given editor. It should take four arguments, as follows:

* `cmd` - a base command object for the editor
* `path` - the path to the source file to open
* `line` - the line number to open the editor at
* `column` - the column number to open the editor at

Editors which cannot open to a specific line with a command or a specific column
may ignore the `line` and/or `column` argument. The `fn` callback must return
either an appropriate `Cmd` object to open a file or `nothing` to indicate that
they cannot edit this file. Use `nothing` to indicate that this editor is not
appropriate for the current environment and another editor should be attempted.
It is possible to add more general editing hooks that need not spawn
external commands by pushing a callback directly to the vector `EDITOR_CALLBACKS`.

The `pattern` argument is a string, regular expression, or an array of strings
and regular expressions. For the `fn` to be called, one of the patterns must
match the value of `EDITOR`, `VISUAL` or `JULIA_EDITOR`. For strings, the string
must equal the [`basename`](@ref) of the first word of the editor command, with
its extension, if any, removed. E.g. "vi" doesn't match "vim -g" but matches
"/usr/bin/vi -m"; it also matches `vi.exe`. If `pattern` is a regex it is
matched against all of the editor command as a shell-escaped string. An array
pattern matches if any of its items match. If multiple editors match, the one
added most recently is used.

By default julia does not wait for the editor to close, running it in the
background. However, if the editor is terminal based, you will probably want to
set `wait=true` and julia will wait for the editor to close before resuming.

If one of the editor environment variables is set, but no editor entry matches it,
the default editor entry is invoked:

    (cmd, path, line, column) -> `\$cmd \$path`

Note that many editors are already defined. All of the following commands should
already work:

- emacs
- emacsclient
- vim
- nvim
- nano
- micro
- kak
- helix
- textmate
- mate
- kate
- subl
- atom
- notepad++
- Visual Studio Code
- open
- pycharm
- bbedit

# Example:

The following defines the usage of terminal-based `emacs`:

    define_editor(
        r"\\bemacs\\b.*\\s(-nw|--no-window-system)\\b", wait=true) do cmd, path, line
        `\$cmd +\$line \$path`
    end

!!! compat "Julia 1.4"
    `define_editor` was introduced in Julia 1.4.
"""
function define_editor(fn::Function, pattern; wait::Bool=false)
    callback = function (cmd::Cmd, path::AbstractString, line::Integer, column::Integer)
        editor_matches(pattern, cmd) || return false
        editor = if !applicable(fn, cmd, path, line, column)
            # Be backwards compatible with editors that did not define the newly added column argument
            fn(cmd, path, line)
        else
            fn(cmd, path, line, column)
        end
        if editor isa Cmd
            if wait
                run(editor) # blocks while editor runs
            else
                run(pipeline(editor, stderr=stderr), wait=false)
            end
            return true
        elseif editor isa Nothing
            return false
        end
        @warn "invalid editor value returned" pattern=pattern editor=editor
        return false
    end
    pushfirst!(EDITOR_CALLBACKS, callback)
end

editor_matches(p::Regex, cmd::Cmd) = occursin(p, shell_escape(cmd))
editor_matches(p::String, cmd::Cmd) = p == splitext(basename(first(cmd)))[1]
editor_matches(ps::AbstractArray, cmd::Cmd) = any(editor_matches(p, cmd) for p in ps)

function define_default_editors()
    # fallback: just call the editor with the path as argument
    define_editor(r".*") do cmd, path, line, column
        `$cmd $path`
    end
    # vim family
    for (editors, wait) in [
        [["vim", "vi", "nvim", "mvim"], true],
        [[r"\bgvim"], false],
    ]
        define_editor(editors; wait) do cmd, path, line, column
            cmd = line == 0 ? `$cmd $path` :
                column == 0 ? `$cmd +$line $path` :
                `$cmd "+normal $(line)G$(column)|" $path`
        end
    end
    define_editor("nano"; wait=true) do cmd, path, line, column
        cmd = `$cmd +$line,$column $path`
    end
    # emacs (must check that emacs not running in -t/-nw
    # before regex match for general emacs)
    for (editors, wait) in [
        [[r"\bemacs"], false],
        [[r"\bemacs\b.*\s(-nw|--no-window-system)\b",
          r"\bemacsclient\b.\s*-(-?nw|t|-?tty)\b"], true],
    ]
        define_editor(editors; wait) do cmd, path, line, column
            `$cmd +$line:$column $path`
        end
    end
    # other editors
    define_editor("gedit") do cmd, path, line, column
        `$cmd +$line:$column $path`
    end
    define_editor(["micro", "kak"]; wait=true) do cmd, path, line, column
        `$cmd +$line $path`
    end
    define_editor(["hx", "helix"]; wait=true) do cmd, path, line, column
        `$cmd $path:$line:$column`
    end
    define_editor(["textmate", "mate", "kate"]) do cmd, path, line, column
        `$cmd $path -l $line`
    end
    define_editor([r"\bsubl", r"\batom", "pycharm", "bbedit"]) do cmd, path, line, column
        `$cmd $path:$line`
    end
    define_editor(["code", "code-insiders"]) do cmd, path, line, column
        `$cmd -g $path:$line:$column`
    end
    define_editor(r"\bnotepad++") do cmd, path, line, column
        `$cmd $path -n$line`
    end
    if Sys.iswindows()
        define_editor(r"\bCODE\.EXE\b"i) do cmd, path, line, column
            `$cmd -g $path:$line:$column`
        end
        callback = function (cmd::Cmd, path::AbstractString, line::Integer)
            cmd == `open` || return false
            # don't emit this ccall on other platforms
            @static if Sys.iswindows()
                result = ccall((:ShellExecuteW, "shell32"), stdcall,
                               Int, (Ptr{Cvoid}, Cwstring, Cwstring,
                                     Ptr{Cvoid}, Ptr{Cvoid}, Cint),
                               C_NULL, "open", path, C_NULL, C_NULL, 10)
                systemerror(:edit, result ≤ 32)
            end
            return true
        end
        pushfirst!(EDITOR_CALLBACKS, callback)
    elseif Sys.isapple()
        define_editor("open") do cmd, path, line, column
            `open -t $path`
        end
    end
end
define_default_editors()

"""
    editor()

Determine the editor to use when running functions like `edit`. Returns a `Cmd`
object. Change editor by setting `JULIA_EDITOR`, `VISUAL` or `EDITOR`
environment variables.
"""
function editor()
    # Note: the editor path can include spaces (if escaped) and flags.
    for var in ["JULIA_EDITOR", "VISUAL", "EDITOR"]
        str = get(ENV, var, nothing)
        str === nothing && continue
        isempty(str) && error("invalid editor \$$var: $(repr(str))")
        return Cmd(shell_split(str))
    end
    editor_file = "/etc/alternatives/editor"
    editor = (Sys.iswindows() || Sys.isapple()) ? "open" :
        isfile(editor_file) ? realpath(editor_file) : "emacs"
    return Cmd([editor])
end

"""
    edit(path::AbstractString, line::Integer=0, column::Integer=0)

Edit a file or directory optionally providing a line number to edit the file at.
Return to the `julia` prompt when you quit the editor. The editor can be changed
by setting `JULIA_EDITOR`, `VISUAL` or `EDITOR` as an environment variable.

See also [`define_editor`](@ref).
"""
function edit(path::AbstractString, line::Integer=0, column::Integer=0)
    path isa String || (path = convert(String, path))
    if endswith(path, ".jl")
        p = find_source_file(path)
        p !== nothing && (path = p)
    end
    cmd = editor()
    for callback in EDITOR_CALLBACKS
        if !applicable(callback, cmd, path, line, column)
            callback(cmd, path, line) && return
        else
            callback(cmd, path, line, column) && return
        end
    end
    # shouldn't happen unless someone has removed fallback entry
    error("no editor found")
end

"""
    edit(function, [types])
    edit(module)

Edit the definition of a function, optionally specifying a tuple of types to indicate which
method to edit. For modules, open the main source file. The module needs to be loaded with
`using` or `import` first.

!!! compat "Julia 1.1"
    `edit` on modules requires at least Julia 1.1.

To ensure that the file can be opened at the given line, you may need to call
`define_editor` first.
"""
function edit(@nospecialize f)
    ms = methods(f).ms
    length(ms) == 1 && edit(functionloc(ms[1])...)
    length(ms) > 1 && return ms
    length(ms) == 0 && functionloc(f) # throws
    nothing
end
edit(m::Method) = edit(functionloc(m)...)
edit(@nospecialize(f), idx::Integer) = edit(methods(f).ms[idx])
edit(f, t)  = (@nospecialize; edit(functionloc(f, t)...))
edit(file::Nothing, line::Integer) = error("could not find source file for function")
edit(m::Module) = edit(pathof(m))

# terminal pager

if Sys.iswindows()
    function less(file::AbstractString, line::Integer)
        pager = shell_split(get(ENV, "PAGER", "more"))
        if pager[1] == "more"
            g = ""
            line -= 1
        else
            g = "g"
        end
        run(Cmd(`$pager +$(line)$(g) \"$file\"`, windows_verbatim = true))
        nothing
    end
else
    function less(file::AbstractString, line::Integer)
        pager = shell_split(get(ENV, "PAGER", "less"))
        run(`$pager +$(line)g $file`)
        nothing
    end
end

"""
    less(file::AbstractString, [line::Integer])

Show a file using the default pager, optionally providing a starting line number. Returns to
the `julia` prompt when you quit the pager.
"""
less(file::AbstractString) = less(file, 1)

"""
    less(function, [types])

Show the definition of a function using the default pager, optionally specifying a tuple of
types to indicate which method to see.
"""
less(f)                   = less(functionloc(f)...)
less(f, @nospecialize t)  = less(functionloc(f,t)...)
less(file, line::Integer) = error("could not find source file for function")
|   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/InteractiveUtils/src/codeview.jl�W      # This file is a part of Julia. License is MIT: https://julialang.org/license

# highlighting settings
const highlighting = Dict{Symbol, Bool}(
    :warntype => true,
    :llvm => true,
    :native => true,
)

const llstyle = Dict{Symbol, Tuple{Bool, Union{Symbol, Int}}}(
    :default     => (false, :normal), # e.g. comma, equal sign, unknown token
    :comment     => (false, :light_black),
    :label       => (false, :light_red),
    :instruction => ( true, :light_cyan),
    :type        => (false, :cyan),
    :number      => (false, :yellow),
    :bracket     => (false, :yellow),
    :variable    => (false, :normal), # e.g. variable, register
    :keyword     => (false, :light_magenta),
    :funcname    => (false, :light_yellow),
)

function printstyled_ll(io::IO, x, s::Symbol, trailing_spaces="")
    printstyled(io, x, bold=llstyle[s][1], color=llstyle[s][2])
    print(io, trailing_spaces)
end

# displaying type warnings

function warntype_type_printer(io::IO; @nospecialize(type), used::Bool, show_type::Bool=true, _...)
    (show_type && used) || return nothing
    str = "::$type"
    if !highlighting[:warntype]
        print(io, str)
    elseif type isa Union && is_expected_union(type)
        Base.emphasize(io, str, Base.warn_color()) # more mild user notification
    elseif type isa Type && (!Base.isdispatchelem(type) || type == Core.Box)
        Base.emphasize(io, str)
    else
        Base.printstyled(io, str, color=:cyan) # show the "good" type
    end
    return nothing
end

# True if one can be pretty certain that the compiler handles this union well,
# i.e. must be small with concrete types.
function is_expected_union(u::Union)
    Base.unionlen(u) < 4 || return false
    for x in Base.uniontypes(u)
        if !Base.isdispatchelem(x) || x == Core.Box
            return false
        end
    end
    return true
end

"""
    code_warntype([io::IO], f, types; debuginfo=:default)

Prints lowered and type-inferred ASTs for the methods matching the given generic function
and type signature to `io` which defaults to `stdout`. The ASTs are annotated in such a way
as to cause "non-leaf" types which may be problematic for performance to be emphasized
(if color is available, displayed in red). This serves as a warning of potential type instability.

Not all non-leaf types are particularly problematic for performance, and the performance
characteristics of a particular type is an implementation detail of the compiler.
`code_warntype` will err on the side of coloring types red if they might be a performance
concern, so some types may be colored red even if they do not impact performance.
Small unions of concrete types are usually not a concern, so these are highlighted in yellow.

Keyword argument `debuginfo` may be one of `:source` or `:none` (default), to specify the verbosity of code comments.

See the [`@code_warntype`](@ref man-code-warntype) section in the Performance Tips page of the manual for more information.
"""
function code_warntype(io::IO, @nospecialize(f), @nospecialize(t=Base.default_tt(f));
                       debuginfo::Symbol=:default, optimize::Bool=false, kwargs...)
    debuginfo = Base.IRShow.debuginfo(debuginfo)
    lineprinter = Base.IRShow.__debuginfo[debuginfo]
    for (src, rettype) in code_typed(f, t; optimize, kwargs...)
        if !(src isa Core.CodeInfo)
            println(io, src)
            println(io, "  failed to infer")
            continue
        end
        lambda_io::IOContext = io
        p = src.parent
        nargs::Int = 0
        if p isa Core.MethodInstance
            println(io, p)
            print(io, "  from ")
            println(io, p.def)
            p.def isa Method && (nargs = p.def.nargs)
            if !isempty(p.sparam_vals)
                println(io, "Static Parameters")
                sig = p.def.sig
                warn_color = Base.warn_color() # more mild user notification
                for i = 1:length(p.sparam_vals)
                    sig = sig::UnionAll
                    name = sig.var.name
                    val = p.sparam_vals[i]
                    print_highlighted(io::IO, v::String, color::Symbol) =
                        if highlighting[:warntype]
                            Base.printstyled(io, v; color)
                        else
                            Base.print(io, v)
                        end
                    if val isa TypeVar
                        if val.lb === Union{}
                            print(io, "  ", name, " <: ")
                            print_highlighted(io, "$(val.ub)", warn_color)
                        elseif val.ub === Any
                            print(io, "  ", sig.var.name, " >: ")
                            print_highlighted(io, "$(val.lb)", warn_color)
                        else
                            print(io, "  ")
                            print_highlighted(io, "$(val.lb)", warn_color)
                            print(io, " <: ", sig.var.name, " <: ")
                            print_highlighted(io, "$(val.ub)", warn_color)
                        end
                    elseif val isa typeof(Vararg)
                        print(io, "  ", name, "::")
                        print_highlighted(io, "Int", warn_color)
                    else
                        print(io, "  ", sig.var.name, " = ")
                        print_highlighted(io, "$(val)", :cyan) # show the "good" type
                    end
                    println(io)
                    sig = sig.body
                end
            end
        end
        if src.slotnames !== nothing
            slotnames = Base.sourceinfo_slotnames(src)
            lambda_io = IOContext(lambda_io, :SOURCE_SLOTNAMES => slotnames)
            slottypes = src.slottypes
            nargs > 0 && println(io, "Arguments")
            for i = 1:length(slotnames)
                if i == nargs + 1
                    println(io, "Locals")
                end
                print(io, "  ", slotnames[i])
                if isa(slottypes, Vector{Any})
                    warntype_type_printer(io; type=slottypes[i], used=true)
                end
                println(io)
            end
        end
        print(io, "Body")
        warntype_type_printer(io; type=rettype, used=true)
        println(io)
        irshow_config = Base.IRShow.IRShowConfig(lineprinter(src), warntype_type_printer)
        Base.IRShow.show_ir(lambda_io, src, irshow_config)
        println(io)
    end
    nothing
end
code_warntype(@nospecialize(f), @nospecialize(t=Base.default_tt(f)); kwargs...) =
    code_warntype(stdout, f, t; kwargs...)

import Base.CodegenParams

const GENERIC_SIG_WARNING = "; WARNING: This code may not match what actually runs.\n"
const OC_MISMATCH_WARNING =
"""
; WARNING: The pre-inferred opaque closure is not callable with the given arguments
;          and will error on dispatch with this signature.
"""

# Printing code representations in IR and assembly

function _dump_function(@nospecialize(f), @nospecialize(t), native::Bool, wrapper::Bool,
                        raw::Bool, dump_module::Bool, syntax::Symbol,
                        optimize::Bool, debuginfo::Symbol, binary::Bool)
        params = CodegenParams(debug_info_kind=Cint(0),
                               safepoint_on_entry=raw, gcstack_arg=raw)
        _dump_function(f, t, native, wrapper, raw, dump_module, syntax,
                       optimize, debuginfo, binary, params)
end
function _dump_function(@nospecialize(f), @nospecialize(t), native::Bool, wrapper::Bool,
                        raw::Bool, dump_module::Bool, syntax::Symbol,
                        optimize::Bool, debuginfo::Symbol, binary::Bool, params::CodegenParams)
    ccall(:jl_is_in_pure_context, Bool, ()) && error("code reflection cannot be used from generated functions")
    if isa(f, Core.Builtin)
        throw(ArgumentError("argument is not a generic function"))
    end
    warning = ""
    # get the MethodInstance for the method match
    if !isa(f, Core.OpaqueClosure)
        world = Base.get_world_counter()
        match = Base._which(signature_type(f, t); world)
        mi = Core.Compiler.specialize_method(match)
        # TODO: use jl_is_cacheable_sig instead of isdispatchtuple
        isdispatchtuple(mi.specTypes) || (warning = GENERIC_SIG_WARNING)
    else
        world = UInt64(f.world)
        if Core.Compiler.is_source_inferred(f.source.source)
            # OC was constructed from inferred source. There's only one
            # specialization and we can't infer anything more precise either.
            world = f.source.primary_world
            mi = f.source.specializations::Core.MethodInstance
            Core.Compiler.hasintersect(typeof(f).parameters[1], t) || (warning = OC_MISMATCH_WARNING)
        else
            mi = Core.Compiler.specialize_method(f.source, Tuple{typeof(f.captures), t.parameters...}, Core.svec())
            actual = isdispatchtuple(mi.specTypes)
            isdispatchtuple(mi.specTypes) || (warning = GENERIC_SIG_WARNING)
        end
    end
    # get the code for it
    if debuginfo === :default
        debuginfo = :source
    elseif debuginfo !== :source && debuginfo !== :none
        throw(ArgumentError("'debuginfo' must be either :source or :none"))
    end
    if native
        if syntax !== :att && syntax !== :intel
            throw(ArgumentError("'syntax' must be either :intel or :att"))
        end
        if dump_module
            # we want module metadata, so use LLVM to generate assembly output
            str = _dump_function_native_assembly(mi, world, wrapper, syntax, debuginfo, binary, raw, params)
        else
            # if we don't want the module metadata, just disassemble what our JIT has
            str = _dump_function_native_disassembly(mi, world, wrapper, syntax, debuginfo, binary)
        end
    else
        str = _dump_function_llvm(mi, world, wrapper, !raw, dump_module, optimize, debuginfo, params)
    end
    str = warning * str
    return str
end

function _dump_function_native_disassembly(mi::Core.MethodInstance, world::UInt,
                                           wrapper::Bool, syntax::Symbol,
                                           debuginfo::Symbol, binary::Bool)
    str = @ccall jl_dump_method_asm(mi::Any, world::UInt, false::Bool, wrapper::Bool,
                                    syntax::Ptr{UInt8}, debuginfo::Ptr{UInt8},
                                    binary::Bool)::Ref{String}
    return str
end

struct LLVMFDump
    tsm::Ptr{Cvoid} # opaque
    f::Ptr{Cvoid} # opaque
end

function _dump_function_native_assembly(mi::Core.MethodInstance, world::UInt,
                                        wrapper::Bool, syntax::Symbol, debuginfo::Symbol,
                                        binary::Bool, raw::Bool, params::CodegenParams)
    llvmf_dump = Ref{LLVMFDump}()
    @ccall jl_get_llvmf_defn(llvmf_dump::Ptr{LLVMFDump},mi::Any, world::UInt, wrapper::Bool,
                             true::Bool, params::CodegenParams)::Cvoid
    llvmf_dump[].f == C_NULL && error("could not compile the specified method")
    str = @ccall jl_dump_function_asm(llvmf_dump::Ptr{LLVMFDump}, false::Bool,
                                      syntax::Ptr{UInt8}, debuginfo::Ptr{UInt8},
                                      binary::Bool, raw::Bool)::Ref{String}
    return str
end

function _dump_function_llvm(
        mi::Core.MethodInstance, world::UInt, wrapper::Bool,
        strip_ir_metadata::Bool, dump_module::Bool,
        optimize::Bool, debuginfo::Symbol,
        params::CodegenParams)
    llvmf_dump = Ref{LLVMFDump}()
    @ccall jl_get_llvmf_defn(llvmf_dump::Ptr{LLVMFDump}, mi::Any, world::UInt,
                             wrapper::Bool, optimize::Bool, params::CodegenParams)::Cvoid
    llvmf_dump[].f == C_NULL && error("could not compile the specified method")
    str = @ccall jl_dump_function_ir(llvmf_dump::Ptr{LLVMFDump}, strip_ir_metadata::Bool,
                                     dump_module::Bool, debuginfo::Ptr{UInt8})::Ref{String}
    return str
end

"""
    code_llvm([io=stdout,], f, types; raw=false, dump_module=false, optimize=true, debuginfo=:default)

Prints the LLVM bitcodes generated for running the method matching the given generic
function and type signature to `io`.

If the `optimize` keyword is unset, the code will be shown before LLVM optimizations.
All metadata and dbg.* calls are removed from the printed bitcode. For the full IR, set the `raw` keyword to true.
To dump the entire module that encapsulates the function (with declarations), set the `dump_module` keyword to true.
Keyword argument `debuginfo` may be one of source (default) or none, to specify the verbosity of code comments.
"""
function code_llvm(io::IO, @nospecialize(f), @nospecialize(types), raw::Bool,
                   dump_module::Bool=false, optimize::Bool=true, debuginfo::Symbol=:default)
    d = _dump_function(f, types, false, false, raw, dump_module, :intel, optimize, debuginfo, false)
    if highlighting[:llvm] && get(io, :color, false)::Bool
        print_llvm(io, d)
    else
        print(io, d)
    end
end
code_llvm(io::IO, @nospecialize(f), @nospecialize(types=Base.default_tt(f)); raw::Bool=false, dump_module::Bool=false, optimize::Bool=true, debuginfo::Symbol=:default) =
    code_llvm(io, f, types, raw, dump_module, optimize, debuginfo)
code_llvm(@nospecialize(f), @nospecialize(types=Base.default_tt(f)); raw=false, dump_module=false, optimize=true, debuginfo::Symbol=:default) =
    code_llvm(stdout, f, types; raw, dump_module, optimize, debuginfo)

"""
    code_native([io=stdout,], f, types; syntax=:intel, debuginfo=:default, binary=false, dump_module=true)

Prints the native assembly instructions generated for running the method matching the given
generic function and type signature to `io`.

* Set assembly syntax by setting `syntax` to `:intel` (default) for intel syntax or `:att` for AT&T syntax.
* Specify verbosity of code comments by setting `debuginfo` to `:source` (default) or `:none`.
* If `binary` is `true`, also print the binary machine code for each instruction precedented by an abbreviated address.
* If `dump_module` is `false`, do not print metadata such as rodata or directives.
* If `raw` is `false`, uninteresting instructions (like the safepoint function prologue) are elided.

See also: [`@code_native`](@ref), [`code_llvm`](@ref), [`code_typed`](@ref) and [`code_lowered`](@ref)
"""
function code_native(io::IO, @nospecialize(f), @nospecialize(types=Base.default_tt(f));
                     dump_module::Bool=true, syntax::Symbol=:intel, raw::Bool=false,
                     debuginfo::Symbol=:default, binary::Bool=false)
    d = _dump_function(f, types, true, false, raw, dump_module, syntax, true, debuginfo, binary)
    if highlighting[:native] && get(io, :color, false)::Bool
        print_native(io, d)
    else
        print(io, d)
    end
end
code_native(@nospecialize(f), @nospecialize(types=Base.default_tt(f)); dump_module::Bool=true, syntax::Symbol=:intel, raw::Bool=false, debuginfo::Symbol=:default, binary::Bool=false) =
    code_native(stdout, f, types; dump_module, syntax, raw, debuginfo, binary)
code_native(::IO, ::Any, ::Symbol) = error("invalid code_native call") # resolve ambiguous call

## colorized IR and assembly printing

const num_regex = r"^(?:\$?-?\d+|0x[0-9A-Fa-f]+|-?(?:\d+\.?\d*|\.\d+)(?:[eE][+-]?\d+)?)$"

function print_llvm(io::IO, code::String)
    buf = IOBuffer(code)
    for line in eachline(buf)
        m = match(r"^(\s*)((?:[^;]|;\")*)(.*)$", line)
        m === nothing && continue
        indent, tokens, comment = m.captures
        print(io, indent)
        print_llvm_tokens(io, tokens)
        printstyled_ll(io, comment, :comment)
        println(io)
    end
end

const llvm_types =
    r"^(?:void|half|float|double|x86_\w+|ppc_\w+|label|metadata|type|opaque|token|i\d+)$"
const llvm_cond = r"^(?:[ou]?eq|[ou]?ne|[uso][gl][te]|ord|uno)$" # true|false

function print_llvm_tokens(io, tokens)
    m = match(r"^((?:[^\s:]+:)?)(\s*)(.*)", tokens)
    if m !== nothing
        label, spaces, tokens = m.captures
        printstyled_ll(io, label, :label, spaces)
    end
    m = match(r"^(%[^\s=]+)(\s*)=(\s*)(.*)", tokens)
    if m !== nothing
        result, spaces, spaces2, tokens = m.captures
        printstyled_ll(io, result, :variable, spaces)
        printstyled_ll(io, '=', :default, spaces2)
    end
    m = match(r"^([a-z]\w*)(\s*)(.*)", tokens)
    if m !== nothing
        inst, spaces, tokens = m.captures
        iskeyword = occursin(r"^(?:define|declare|type)$", inst) || occursin("=", tokens)
        printstyled_ll(io, inst, iskeyword ? :keyword : :instruction, spaces)
    end

    print_llvm_operands(io, tokens)
end

function print_llvm_operands(io, tokens)
    while !isempty(tokens)
        tokens = print_llvm_operand(io, tokens)
    end
    return tokens
end

function print_llvm_operand(io, tokens)
    islabel = false
    while !isempty(tokens)
        m = match(r"^,(\s*)(.*)", tokens)
        if m !== nothing
            spaces, tokens = m.captures
            printstyled_ll(io, ',', :default, spaces)
            break
        end
        m = match(r"^(\*+|=)(\s*)(.*)", tokens)
        if m !== nothing
            sym, spaces, tokens = m.captures
            printstyled_ll(io, sym, :default, spaces)
            continue
        end
        m = match(r"^(\"[^\"]*\")(\s*)(.*)", tokens)
        if m !== nothing
            str, spaces, tokens = m.captures
            printstyled_ll(io, str, :variable, spaces)
            continue
        end
        m = match(r"^([({\[<])(\s*)(.*)", tokens)
        if m !== nothing
            bracket, spaces, tokens = m.captures
            printstyled_ll(io, bracket, :bracket, spaces)
            tokens = print_llvm_operands(io, tokens) # enter
            continue
        end
        m = match(r"^([)}\]>])(\s*)(.*)", tokens)
        if m !== nothing
            bracket, spaces, tokens = m.captures
            printstyled_ll(io, bracket, :bracket, spaces)
            break # leave
        end

        m = match(r"^([^\s,*=(){}\[\]<>]+)(\s*)(.*)", tokens)
        m === nothing && break
        token, spaces, tokens = m.captures
        if occursin(llvm_types, token)
            printstyled_ll(io, token, :type)
            islabel = token == "label"
        elseif occursin(llvm_cond, token) # condition code is instruction-level
            printstyled_ll(io, token, :instruction)
        elseif occursin(num_regex, token)
            printstyled_ll(io, token, :number)
        elseif occursin(r"^@.+$", token)
            printstyled_ll(io, token, :funcname)
        elseif occursin(r"^%.+$", token)
            islabel |= occursin(r"^%[^\d].*$", token) & occursin(r"^\]", tokens)
            printstyled_ll(io, token, islabel ? :label : :variable)
            islabel = false
        elseif occursin(r"^[a-z]\w+$", token)
            printstyled_ll(io, token, :keyword)
        else
            printstyled_ll(io, token, :default)
        end
        print(io, spaces)
    end
    return tokens
end

function print_native(io::IO, code::String, arch::Symbol=sys_arch_category())
    archv = Val(arch)
    buf = IOBuffer(code)
    for line in eachline(buf)
        m = match(r"^(\s*)((?:[^;#/]|#\S|;\"|/[^/])*)(.*)$", line)
        m === nothing && continue
        indent, tokens, comment = m.captures
        print(io, indent)
        print_native_tokens(io, tokens, archv)
        printstyled_ll(io, comment, :comment)
        println(io)
    end
end

function sys_arch_category()
    if Sys.ARCH === :x86_64 || Sys.ARCH === :i686
        :x86
    elseif Sys.ARCH === :aarch64 || startswith(string(Sys.ARCH), "arm")
        :arm
    else
        :unsupported
    end
end

print_native_tokens(io, line, ::Val) = print(io, line)

const x86_ptr = r"^(?:(?:[xyz]mm|[dq])?word|byte|ptr|offset)$"
const avx512flags = r"^(?:z|r[nduz]-sae|sae|1to1?\d)$"
const arm_cond = r"^(?:eq|ne|cs|ho|cc|lo|mi|pl|vs|vc|hi|ls|[lg][te]|al|nv)$"
const arm_keywords = r"^(?:lsl|lsr|asr|ror|rrx|!|/[zm])$"

function print_native_tokens(io, tokens, arch::Union{Val{:x86}, Val{:arm}})
    x86 = arch isa Val{:x86}
    m = match(r"^((?:[^\s:]+:|\"[^\"]+\":)?)(\s*)(.*)", tokens)
    if m !== nothing
        label, spaces, tokens = m.captures
        printstyled_ll(io, label, :label, spaces)
    end
    haslabel = false
    m = match(r"^([a-z][\w.]*)(\s*)(.*)", tokens)
    if m !== nothing
        instruction, spaces, tokens = m.captures
        printstyled_ll(io, instruction, :instruction, spaces)
        haslabel = occursin(r"^(?:bl?|bl?\.\w{2,5}|[ct]bn?z)?$", instruction)
    end

    isfuncname = false
    while !isempty(tokens)
        m = match(r"^([,:*])(\s*)(.*)", tokens)
        if m !== nothing
            sym, spaces, tokens = m.captures
            printstyled_ll(io, sym, :default, spaces)
            isfuncname = false
            continue
        end
        m = match(r"^([(){}\[\]])(\s*)(.*)", tokens)
        if m !== nothing
            bracket, spaces, tokens = m.captures
            printstyled_ll(io, bracket, :bracket, spaces)
            continue
        end
        m = match(r"^#([0-9a-fx.-]+)(\s*)(.*)", tokens)
        if !x86 && m !== nothing && occursin(num_regex, m.captures[1])
            num, spaces, tokens = m.captures
            printstyled_ll(io, "#" * num, :number, spaces)
            continue
        end

        m = match(r"^([^\s,:*(){}\[\]][^\s,:*/(){}\[\]]*)(\s*)(.*)", tokens)
        m === nothing && break
        token, spaces, tokens = m.captures
        if occursin(num_regex, token)
            printstyled_ll(io, token, :number)
        elseif x86 && occursin(x86_ptr, token) || occursin(avx512flags, token)
            printstyled_ll(io, token, :keyword)
            isfuncname = token == "offset"
        elseif !x86 && (occursin(arm_keywords, token) || occursin(arm_cond, token))
            printstyled_ll(io, token, :keyword)
        elseif occursin(r"^L.+$", token)
            printstyled_ll(io, token, :label)
        elseif occursin(r"^\$.+$", token)
            printstyled_ll(io, token, :funcname)
        elseif occursin(r"^%?(?:[a-z][\w.]+|\"[^\"]+\")$", token)
            islabel = haslabel & !occursin(',', tokens)
            printstyled_ll(io, token, islabel ? :label : isfuncname ? :funcname : :variable)
            isfuncname = false
        else
            printstyled_ll(io, token, :default)
        end
        print(io, spaces)
    end
end
z   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/InteractiveUtils/src/macros.jl^;      # This file is a part of Julia. License is MIT: https://julialang.org/license

# macro wrappers for various reflection functions

import Base: typesof, insert!, replace_ref_begin_end!, infer_effects

separate_kwargs(args...; kwargs...) = (args, values(kwargs))

"""
Transform a dot expression into one where each argument has been replaced by a
variable "xj" (with j an integer from 1 to the returned i).
The list `args` contains the original arguments that have been replaced.
"""
function recursive_dotcalls!(ex, args, i=1)
    if !(ex isa Expr) || ((ex.head !== :. || !(ex.args[2] isa Expr)) &&
                          (ex.head !== :call || string(ex.args[1])[1] != '.'))
        newarg = Symbol('x', i)
        if Meta.isexpr(ex, :...)
            push!(args, only(ex.args))
            return Expr(:..., newarg), i+1
        else
            push!(args, ex)
            return newarg, i+1
        end
    end
    (start, branches) = ex.head === :. ? (1, ex.args[2].args) : (2, ex.args)
    length_branches = length(branches)::Int
    for j in start:length_branches
        branch, i = recursive_dotcalls!(branches[j], args, i)
        branches[j] = branch
    end
    return ex, i
end

function gen_call_with_extracted_types(__module__, fcn, ex0, kws=Expr[])
    if Meta.isexpr(ex0, :ref)
        ex0 = replace_ref_begin_end!(ex0)
    end
    if isa(ex0, Expr)
        if ex0.head === :do && Meta.isexpr(get(ex0.args, 1, nothing), :call)
            if length(ex0.args) != 2
                return Expr(:call, :error, "ill-formed do call")
            end
            i = findlast(a->(Meta.isexpr(a, :kw) || Meta.isexpr(a, :parameters)), ex0.args[1].args)
            args = copy(ex0.args[1].args)
            insert!(args, (isnothing(i) ? 2 : 1+i::Int), ex0.args[2])
            ex0 = Expr(:call, args...)
        end
        if ex0.head === :. || (ex0.head === :call && ex0.args[1] !== :.. && string(ex0.args[1])[1] == '.')
            codemacro = startswith(string(fcn), "code_")
            if codemacro && (ex0.head === :call || ex0.args[2] isa Expr)
                # Manually wrap a dot call in a function
                args = Any[]
                ex, i = recursive_dotcalls!(copy(ex0), args)
                xargs = [Symbol('x', j) for j in 1:i-1]
                dotfuncname = gensym("dotfunction")
                dotfuncdef = Expr(:local, Expr(:(=), Expr(:call, dotfuncname, xargs...), ex))
                return quote
                    $(esc(dotfuncdef))
                    local args = $typesof($(map(esc, args)...))
                    $(fcn)($(esc(dotfuncname)), args; $(kws...))
                end
            elseif !codemacro
                fully_qualified_symbol = true # of the form A.B.C.D
                ex1 = ex0
                while ex1 isa Expr && ex1.head === :.
                    fully_qualified_symbol = (length(ex1.args) == 2 &&
                                              ex1.args[2] isa QuoteNode &&
                                              ex1.args[2].value isa Symbol)
                    fully_qualified_symbol || break
                    ex1 = ex1.args[1]
                end
                fully_qualified_symbol &= ex1 isa Symbol
                if fully_qualified_symbol
                    return quote
                        local arg1 = $(esc(ex0.args[1]))
                        if isa(arg1, Module)
                            $(if string(fcn) == "which"
                                  :(which(arg1, $(ex0.args[2])))
                              else
                                  :(error("expression is not a function call"))
                              end)
                        else
                            local args = $typesof($(map(esc, ex0.args)...))
                            $(fcn)(Base.getproperty, args)
                        end
                    end
                else
                    return Expr(:call, :error, "dot expressions are not lowered to "
                                * "a single function call, so @$fcn cannot analyze "
                                * "them. You may want to use Meta.@lower to identify "
                                * "which function call to target.")
                end
            end
        end
        if any(a->(Meta.isexpr(a, :kw) || Meta.isexpr(a, :parameters)), ex0.args)
            return quote
                local arg1 = $(esc(ex0.args[1]))
                local args, kwargs = $separate_kwargs($(map(esc, ex0.args[2:end])...))
                $(fcn)(Core.kwcall,
                       Tuple{typeof(kwargs), Core.Typeof(arg1), map(Core.Typeof, args)...};
                       $(kws...))
            end
        elseif ex0.head === :call
            return Expr(:call, fcn, esc(ex0.args[1]),
                        Expr(:call, typesof, map(esc, ex0.args[2:end])...),
                        kws...)
        elseif ex0.head === :(=) && length(ex0.args) == 2
            lhs, rhs = ex0.args
            if isa(lhs, Expr)
                if lhs.head === :(.)
                    return Expr(:call, fcn, Base.setproperty!,
                                Expr(:call, typesof, map(esc, lhs.args)..., esc(rhs)), kws...)
                elseif lhs.head === :ref
                    return Expr(:call, fcn, Base.setindex!,
                                Expr(:call, typesof, esc(lhs.args[1]), esc(rhs), map(esc, lhs.args[2:end])...), kws...)
                end
            end
        elseif ex0.head === :vcat || ex0.head === :typed_vcat
            if ex0.head === :vcat
                f, hf = Base.vcat, Base.hvcat
                args = ex0.args
            else
                f, hf = Base.typed_vcat, Base.typed_hvcat
                args = ex0.args[2:end]
            end
            if any(a->isa(a,Expr) && a.head === :row, args)
                rows = Any[ (isa(x,Expr) && x.head === :row ? x.args : Any[x]) for x in args ]
                lens = map(length, rows)
                return Expr(:call, fcn, hf,
                            Expr(:call, typesof,
                                 (ex0.head === :vcat ? [] : Any[esc(ex0.args[1])])...,
                                 Expr(:tuple, lens...),
                                 map(esc, vcat(rows...))...), kws...)
            else
                return Expr(:call, fcn, f,
                            Expr(:call, typesof, map(esc, ex0.args)...), kws...)
            end
        else
            for (head, f) in (:ref => Base.getindex, :hcat => Base.hcat, :(.) => Base.getproperty, :vect => Base.vect, Symbol("'") => Base.adjoint, :typed_hcat => Base.typed_hcat, :string => string)
                if ex0.head === head
                    return Expr(:call, fcn, f,
                                Expr(:call, typesof, map(esc, ex0.args)...), kws...)
                end
            end
        end
    end
    if isa(ex0, Expr) && ex0.head === :macrocall # Make @edit @time 1+2 edit the macro by using the types of the *expressions*
        return Expr(:call, fcn, esc(ex0.args[1]), Tuple{#=__source__=#LineNumberNode, #=__module__=#Module, Any[ Core.Typeof(a) for a in ex0.args[3:end] ]...}, kws...)
    end

    ex = Meta.lower(__module__, ex0)
    if !isa(ex, Expr)
        return Expr(:call, :error, "expression is not a function call or symbol")
    end

    exret = Expr(:none)
    if ex.head === :call
        if any(e->(isa(e, Expr) && e.head === :(...)), ex0.args) &&
            (ex.args[1] === GlobalRef(Core,:_apply_iterate) ||
             ex.args[1] === GlobalRef(Base,:_apply_iterate))
            # check for splatting
            exret = Expr(:call, ex.args[2], fcn,
                        Expr(:tuple, esc(ex.args[3]),
                            Expr(:call, typesof, map(esc, ex.args[4:end])...)))
        else
            exret = Expr(:call, fcn, esc(ex.args[1]),
                         Expr(:call, typesof, map(esc, ex.args[2:end])...), kws...)
        end
    end
    if ex.head === :thunk || exret.head === :none
        exret = Expr(:call, :error, "expression is not a function call, "
                                  * "or is too complex for @$fcn to analyze; "
                                  * "break it down to simpler parts if possible. "
                                  * "In some cases, you may want to use Meta.@lower.")
    end
    return exret
end

"""
Same behaviour as `gen_call_with_extracted_types` except that keyword arguments
of the form "foo=bar" are passed on to the called function as well.
The keyword arguments must be given before the mandatory argument.
"""
function gen_call_with_extracted_types_and_kwargs(__module__, fcn, ex0)
    kws = Expr[]
    arg = ex0[end] # Mandatory argument
    for i in 1:length(ex0)-1
        x = ex0[i]
        if x isa Expr && x.head === :(=) # Keyword given of the form "foo=bar"
            if length(x.args) != 2
                return Expr(:call, :error, "Invalid keyword argument: $x")
            end
            push!(kws, Expr(:kw, esc(x.args[1]), esc(x.args[2])))
        else
            return Expr(:call, :error, "@$fcn expects only one non-keyword argument")
        end
    end
    return gen_call_with_extracted_types(__module__, fcn, arg, kws)
end

for fname in [:which, :less, :edit, :functionloc]
    @eval begin
        macro ($fname)(ex0)
            gen_call_with_extracted_types(__module__, $(Expr(:quote, fname)), ex0)
        end
    end
end

macro which(ex0::Symbol)
    ex0 = QuoteNode(ex0)
    return :(which($__module__, $ex0))
end

for fname in [:code_warntype, :code_llvm, :code_native, :infer_effects]
    @eval begin
        macro ($fname)(ex0...)
            gen_call_with_extracted_types_and_kwargs(__module__, $(Expr(:quote, fname)), ex0)
        end
    end
end

macro code_typed(ex0...)
    thecall = gen_call_with_extracted_types_and_kwargs(__module__, :code_typed, ex0)
    quote
        local results = $thecall
        length(results) == 1 ? results[1] : results
    end
end

macro code_lowered(ex0...)
    thecall = gen_call_with_extracted_types_and_kwargs(__module__, :code_lowered, ex0)
    quote
        local results = $thecall
        length(results) == 1 ? results[1] : results
    end
end

macro time_imports(ex)
    quote
        try
            Base.Threads.atomic_add!(Base.TIMING_IMPORTS, 1)
            $(esc(ex))
        finally
            Base.Threads.atomic_sub!(Base.TIMING_IMPORTS, 1)
        end
    end
end

"""
    @functionloc

Applied to a function or macro call, it evaluates the arguments to the specified call, and
returns a tuple `(filename,line)` giving the location for the method that would be called for those arguments.
It calls out to the [`functionloc`](@ref) function.
"""
:@functionloc

"""
    @which

Applied to a function or macro call, it evaluates the arguments to the specified call, and
returns the `Method` object for the method that would be called for those arguments. Applied
to a variable, it returns the module in which the variable was bound. It calls out to the
[`which`](@ref) function.

See also: [`@less`](@ref), [`@edit`](@ref).
"""
:@which

"""
    @less

Evaluates the arguments to the function or macro call, determines their types, and calls the [`less`](@ref)
function on the resulting expression.

See also: [`@edit`](@ref), [`@which`](@ref), [`@code_lowered`](@ref).
"""
:@less

"""
    @edit

Evaluates the arguments to the function or macro call, determines their types, and calls the [`edit`](@ref)
function on the resulting expression.

See also: [`@less`](@ref), [`@which`](@ref).
"""
:@edit

"""
    @code_typed

Evaluates the arguments to the function or macro call, determines their types, and calls
[`code_typed`](@ref) on the resulting expression. Use the optional argument `optimize` with

    @code_typed optimize=true foo(x)

to control whether additional optimizations, such as inlining, are also applied.
"""
:@code_typed

"""
    @code_lowered

Evaluates the arguments to the function or macro call, determines their types, and calls
[`code_lowered`](@ref) on the resulting expression.
"""
:@code_lowered

"""
    @code_warntype

Evaluates the arguments to the function or macro call, determines their types, and calls
[`code_warntype`](@ref) on the resulting expression.
"""
:@code_warntype

"""
    @code_llvm

Evaluates the arguments to the function or macro call, determines their types, and calls
[`code_llvm`](@ref) on the resulting expression.
Set the optional keyword arguments `raw`, `dump_module`, `debuginfo`, `optimize`
by putting them and their value before the function call, like this:

    @code_llvm raw=true dump_module=true debuginfo=:default f(x)
    @code_llvm optimize=false f(x)

`optimize` controls whether additional optimizations, such as inlining, are also applied.
`raw` makes all metadata and dbg.* calls visible.
`debuginfo` may be one of `:source` (default) or `:none`,  to specify the verbosity of code comments.
`dump_module` prints the entire module that encapsulates the function.
"""
:@code_llvm

"""
    @code_native

Evaluates the arguments to the function or macro call, determines their types, and calls
[`code_native`](@ref) on the resulting expression.

Set any of the optional keyword arguments `syntax`, `debuginfo`, `binary` or `dump_module`
by putting it before the function call, like this:

    @code_native syntax=:intel debuginfo=:default binary=true dump_module=false f(x)

* Set assembly syntax by setting `syntax` to `:intel` (default) for Intel syntax or `:att` for AT&T syntax.
* Specify verbosity of code comments by setting `debuginfo` to `:source` (default) or `:none`.
* If `binary` is `true`, also print the binary machine code for each instruction precedented by an abbreviated address.
* If `dump_module` is `false`, do not print metadata such as rodata or directives.

See also: [`code_native`](@ref), [`@code_llvm`](@ref), [`@code_typed`](@ref) and [`@code_lowered`](@ref)
"""
:@code_native

"""
    @time_imports

A macro to execute an expression and produce a report of any time spent importing packages and their
dependencies. Any compilation time will be reported as a percentage, and how much of which was recompilation, if any.

One line is printed per package or package extension. The duration shown is the time to import that package itself, not including the time to load any of its dependencies.

On Julia 1.9+ [package extensions](@ref man-extensions) will show as Parent → Extension.

!!! note
    During the load process a package sequentially imports all of its dependencies, not just its direct dependencies.

```julia-repl
julia> @time_imports using CSV
     50.7 ms  Parsers 17.52% compilation time
      0.2 ms  DataValueInterfaces
      1.6 ms  DataAPI
      0.1 ms  IteratorInterfaceExtensions
      0.1 ms  TableTraits
     17.5 ms  Tables
     26.8 ms  PooledArrays
    193.7 ms  SentinelArrays 75.12% compilation time
      8.6 ms  InlineStrings
     20.3 ms  WeakRefStrings
      2.0 ms  TranscodingStreams
      1.4 ms  Zlib_jll
      1.8 ms  CodecZlib
      0.8 ms  Compat
     13.1 ms  FilePathsBase 28.39% compilation time
   1681.2 ms  CSV 92.40% compilation time
```

!!! compat "Julia 1.8"
    This macro requires at least Julia 1.8

"""
:@time_imports
}   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/InteractiveUtils/src/clipboard.jlj      # This file is a part of Julia. License is MIT: https://julialang.org/license

# clipboard copy and paste

if Sys.isapple()
    function clipboard(x)
        pbcopy_cmd = `pbcopy`

        # OSX shells, especially when run within `tmux` or `screen`, can be
        # disconnected from the global shell namespace, which causes problems
        # with clipboards.  Luckily, the `reattach-to-user-namespace` utility
        # dodges these issues quite nicely, so we automatically utilize it if
        # it is installed.
        if Sys.which("reattach-to-user-namespace") !== nothing
            pbcopy_cmd = `reattach-to-user-namespace pbcopy`
        end

        open(pipeline(pbcopy_cmd, stderr=stderr), "w") do io
            print(io, x)
        end
        nothing
    end
    function clipboard()
        pbpaste_cmd = `pbpaste`

        # See above comment in `clipboard(x)`
        if Sys.which("reattach-to-user-namespace") !== nothing
            pbpaste_cmd = `reattach-to-user-namespace pbpaste`
        end
        return read(pbpaste_cmd, String)
    end

elseif Sys.islinux() || Sys.KERNEL === :FreeBSD
    _clipboardcmd = nothing
    const _clipboard_copy = Dict(
            :xsel  => Sys.islinux() ?
                `xsel --input --clipboard` :
                `xsel -c`,
            :xclip => `xclip -silent -in -selection clipboard`,
            :wlclipboard => `wl-copy`
        )
    const _clipboard_paste = Dict(
            :xsel  => Sys.islinux() ?
                `xsel --nodetach --output --clipboard` :
                `xsel -p`,
            :xclip => `xclip -quiet -out -selection clipboard`,
            :wlclipboard => `wl-paste`
        )
    function clipboardcmd()
        global _clipboardcmd
        _clipboardcmd !== nothing && return _clipboardcmd
        for cmd in (:xclip, :xsel, :wlclipboard)
            # wl-clipboard ships wl-copy/paste individually
            c = cmd === :wlclipboard ? Symbol("wl-copy") : cmd
            success(pipeline(`which $c`, devnull)) && return _clipboardcmd = cmd
        end
        pkgs = @static if Sys.KERNEL === :FreeBSD
            "x11/xsel or x11/xclip"
        else
            "xsel or xclip or wl-clipboard"
        end
        error("no clipboard command found, please install $pkgs")
    end
    function clipboard(x)
        c = clipboardcmd()
        cmd = _clipboard_copy[c]
        open(pipeline(cmd, stderr=stderr), "w") do io
            print(io, x)
        end
        nothing
    end
    function clipboard()
        c = clipboardcmd()
        cmd = _clipboard_paste[c]
        return read(pipeline(cmd, stderr=stderr), String)
    end

elseif Sys.iswindows()
    function clipboard(x::AbstractString)
        if Base.containsnul(x)
            throw(ArgumentError("Windows clipboard strings cannot contain NUL character"))
        end
        x_u16 = Base.cwstring(x)
        pdata = Ptr{UInt16}(C_NULL)
        function cleanup(cause)
            errno = cause === :success ? UInt32(0) : Libc.GetLastError()
            if cause !== :OpenClipboard
                if cause !== :success && pdata != C_NULL
                    ccall((:GlobalFree, "kernel32"), stdcall, Cint, (Ptr{UInt16},), pdata)
                end
                ccall((:CloseClipboard, "user32"), stdcall, Cint, ()) == 0 && Base.windowserror(:CloseClipboard) # this should never fail
            end
            cause === :success || Base.windowserror(cause, errno)
            nothing
        end
        ccall((:OpenClipboard, "user32"), stdcall, Cint, (Ptr{Cvoid},), C_NULL) == 0 && return Base.windowserror(:OpenClipboard)
        ccall((:EmptyClipboard, "user32"), stdcall, Cint, ()) == 0 && return cleanup(:EmptyClipboard)
        # copy data to locked, allocated space
        pdata = ccall((:GlobalAlloc, "kernel32"), stdcall, Ptr{UInt16}, (Cuint, Csize_t), 2 #=GMEM_MOVEABLE=#, sizeof(x_u16))
        pdata == C_NULL && return cleanup(:GlobalAlloc)
        plock = ccall((:GlobalLock, "kernel32"), stdcall, Ptr{UInt16}, (Ptr{UInt16},), pdata)
        plock == C_NULL && return cleanup(:GlobalLock)
        GC.@preserve x_u16 memcpy(plock, Base.unsafe_convert(Ptr{UInt16}, x_u16), sizeof(x_u16))
        unlock = ccall((:GlobalUnlock, "kernel32"), stdcall, Cint, (Ptr{UInt16},), pdata)
        (unlock == 0 && Libc.GetLastError() == 0) || return cleanup(:GlobalUnlock) # this should never fail
        pset = ccall((:SetClipboardData, "user32"), stdcall, Ptr{UInt16}, (Cuint, Ptr{UInt16}), 13, pdata) # CF_UNICODETEXT
        pdata != pset && return cleanup(:SetClipboardData)
        cleanup(:success)
    end
    clipboard(x) = clipboard(sprint(print, x)::String)
    function clipboard()
        function cleanup(cause)
            errno = cause === :success ? UInt32(0) : Libc.GetLastError()
            if cause !== :OpenClipboard
                ccall((:CloseClipboard, "user32"), stdcall, Cint, ()) == 0 && Base.windowserror(:CloseClipboard) # this should never fail
            end
            if cause !== :success && !(cause === :GetClipboardData && (errno == 0x8004006A || errno == 0x800401D3)) # ignore DV_E_CLIPFORMAT and CLIPBRD_E_BAD_DATA from GetClipboardData
                Base.windowserror(cause, errno)
            end
            ""
        end
        ccall((:OpenClipboard, "user32"), stdcall, Cint, (Ptr{Cvoid},), C_NULL) == 0 && return Base.windowserror(:OpenClipboard)
        ccall(:SetLastError, stdcall, Cvoid, (UInt32,), 0) # allow distinguishing if the clipboard simply didn't have text
        pdata = ccall((:GetClipboardData, "user32"), stdcall, Ptr{UInt16}, (Cuint,), 13) # CF_UNICODETEXT
        pdata == C_NULL && return cleanup(:GetClipboardData)
        plock = ccall((:GlobalLock, "kernel32"), stdcall, Ptr{UInt16}, (Ptr{UInt16},), pdata)
        plock == C_NULL && return cleanup(:GlobalLock)
        s = try
            # find NUL terminator (0x0000 16-bit code unit)
            len = 0
            while unsafe_load(plock, len + 1) != 0
                len += 1
            end
            # get Vector{UInt16}, transcode data to UTF-8, make a String of it
            transcode(String, unsafe_wrap(Array, plock, len))
        finally
           unlock = ccall((:GlobalUnlock, "kernel32"), stdcall, Cint, (Ptr{UInt16},), pdata)
           (unlock != 0 || Libc.GetLastError() == 0) || return cleanup(:GlobalUnlock) # this should never fail
           cleanup(:success)
        end
        return s
    end

else
    clipboard(x="") = error("`clipboard` function not implemented for $(Sys.KERNEL)")
end


"""
    clipboard(x)

Send a printed form of `x` to the operating system clipboard ("copy").
"""
clipboard(x)

"""
    clipboard() -> String

Return a string with the contents of the operating system clipboard ("paste").
"""
clipboard()
r   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LibGit2/src/LibGit2.jlǇ      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
Interface to [libgit2](https://libgit2.org/).
"""
module LibGit2

import Base: ==
using Base: something, notnothing
using Base64: base64decode
using NetworkOptions
using Printf: @printf
using SHA: sha1, sha256

export with, GitRepo, GitConfig

using LibGit2_jll

const GITHUB_REGEX =
    r"^(?:(?:ssh://)?git@|git://|https://(?:[\w\.\+\-]+@)?)github.com[:/](([^/].+)/(.+?))(?:\.git)?$"i

const REFCOUNT = Threads.Atomic{Int}(0)

function ensure_initialized end

include("error.jl")
include("utils.jl")
include("consts.jl")
include("types.jl")
include("signature.jl")
include("oid.jl")
include("reference.jl")
include("commit.jl")
include("repository.jl")
include("config.jl")
include("walker.jl")
include("remote.jl")
include("strarray.jl")
include("index.jl")
include("merge.jl")
include("tag.jl")
include("blob.jl")
include("diff.jl")
include("rebase.jl")
include("blame.jl")
include("status.jl")
include("tree.jl")
include("gitcredential.jl")
include("callbacks.jl")

using .Error

struct State
    head::GitHash
    index::GitHash
    work::GitHash
end

"""
    head(pkg::AbstractString) -> String

Return current HEAD [`GitHash`](@ref) of
the `pkg` repo as a string.
"""
function head(pkg::AbstractString)
    with(GitRepo, pkg) do repo
        string(head_oid(repo))
    end
end

"""
    need_update(repo::GitRepo)

Equivalent to `git update-index`. Return `true`
if `repo` needs updating.
"""
function need_update(repo::GitRepo)
    if !isbare(repo)
        # read updates index from filesystem
        read!(repo, true)
    end
end

"""
    iscommit(id::AbstractString, repo::GitRepo) -> Bool

Check if commit `id` (which is a [`GitHash`](@ref) in string form)
is in the repository.

# Examples
```julia-repl
julia> repo = GitRepo(repo_path);

julia> LibGit2.add!(repo, test_file);

julia> commit_oid = LibGit2.commit(repo, "add test_file");

julia> LibGit2.iscommit(string(commit_oid), repo)
true
```
"""
function iscommit(id::AbstractString, repo::GitRepo)
    res = true
    try
        c = GitCommit(repo, id)
        if c === nothing
            res = false
        else
            close(c)
        end
    catch
        res = false
    end
    return res
end

"""
    LibGit2.isdirty(repo::GitRepo, pathspecs::AbstractString=""; cached::Bool=false) -> Bool

Check if there have been any changes to tracked files in the working tree (if
`cached=false`) or the index (if `cached=true`).
`pathspecs` are the specifications for options for the diff.

# Examples
```julia
repo = LibGit2.GitRepo(repo_path)
LibGit2.isdirty(repo) # should be false
open(joinpath(repo_path, new_file), "a") do f
    println(f, "here's my cool new file")
end
LibGit2.isdirty(repo) # now true
LibGit2.isdirty(repo, new_file) # now true
```

Equivalent to `git diff-index HEAD [-- <pathspecs>]`.
"""
isdirty(repo::GitRepo, paths::AbstractString=""; cached::Bool=false) =
    isdiff(repo, Consts.HEAD_FILE, paths, cached=cached)

"""
    LibGit2.isdiff(repo::GitRepo, treeish::AbstractString, pathspecs::AbstractString=""; cached::Bool=false)

Checks if there are any differences between the tree specified by `treeish` and the
tracked files in the working tree (if `cached=false`) or the index (if `cached=true`).
`pathspecs` are the specifications for options for the diff.

# Examples
```julia
repo = LibGit2.GitRepo(repo_path)
LibGit2.isdiff(repo, "HEAD") # should be false
open(joinpath(repo_path, new_file), "a") do f
    println(f, "here's my cool new file")
end
LibGit2.isdiff(repo, "HEAD") # now true
```

Equivalent to `git diff-index <treeish> [-- <pathspecs>]`.
"""
function isdiff(repo::GitRepo, treeish::AbstractString, paths::AbstractString=""; cached::Bool=false)
    tree = GitTree(repo, "$treeish^{tree}")
    try
        diff = diff_tree(repo, tree, paths, cached=cached)
        result = count(diff) > 0
        close(diff)
        return result
    finally
        close(tree)
    end
end

"""
    diff_files(repo::GitRepo, branch1::AbstractString, branch2::AbstractString; kwarg...) -> Vector{AbstractString}

Show which files have changed in the git repository `repo` between branches `branch1`
and `branch2`.

The keyword argument is:
  * `filter::Set{Consts.DELTA_STATUS}=Set([Consts.DELTA_ADDED, Consts.DELTA_MODIFIED, Consts.DELTA_DELETED]))`,
    and it sets options for the diff. The default is to show files added, modified, or deleted.

Return only the *names* of the files which have changed, *not* their contents.

# Examples
```julia
LibGit2.branch!(repo, "branch/a")
LibGit2.branch!(repo, "branch/b")
# add a file to repo
open(joinpath(LibGit2.path(repo),"file"),"w") do f
    write(f, "hello repo\n")
end
LibGit2.add!(repo, "file")
LibGit2.commit(repo, "add file")
# returns ["file"]
filt = Set([LibGit2.Consts.DELTA_ADDED])
files = LibGit2.diff_files(repo, "branch/a", "branch/b", filter=filt)
# returns [] because existing files weren't modified
filt = Set([LibGit2.Consts.DELTA_MODIFIED])
files = LibGit2.diff_files(repo, "branch/a", "branch/b", filter=filt)
```

Equivalent to `git diff --name-only --diff-filter=<filter> <branch1> <branch2>`.
"""
function diff_files(repo::GitRepo, branch1::AbstractString, branch2::AbstractString;
                    filter::Set{Consts.DELTA_STATUS}=Set([Consts.DELTA_ADDED, Consts.DELTA_MODIFIED, Consts.DELTA_DELETED]))
    b1_id = revparseid(repo, branch1*"^{tree}")
    b2_id = revparseid(repo, branch2*"^{tree}")
    tree1 = GitTree(repo, b1_id)
    tree2 = GitTree(repo, b2_id)
    files = AbstractString[]
    try
        diff = diff_tree(repo, tree1, tree2)
        for i in 1:count(diff)
            delta = diff[i]
            delta === nothing && break
            if Consts.DELTA_STATUS(delta.status) in filter
                Base.push!(files, unsafe_string(delta.new_file.path))
            end
        end
        close(diff)
    finally
        close(tree1)
        close(tree2)
    end
    return files
end

"""
    is_ancestor_of(a::AbstractString, b::AbstractString, repo::GitRepo) -> Bool

Return `true` if `a`, a [`GitHash`](@ref) in string form, is an ancestor of
`b`, a [`GitHash`](@ref) in string form.

# Examples
```julia-repl
julia> repo = GitRepo(repo_path);

julia> LibGit2.add!(repo, test_file1);

julia> commit_oid1 = LibGit2.commit(repo, "commit1");

julia> LibGit2.add!(repo, test_file2);

julia> commit_oid2 = LibGit2.commit(repo, "commit2");

julia> LibGit2.is_ancestor_of(string(commit_oid1), string(commit_oid2), repo)
true
```
"""
function is_ancestor_of(a::AbstractString, b::AbstractString, repo::GitRepo)
    A = revparseid(repo, a)
    merge_base(repo, a, b) == A
end

"""
    fetch(repo::GitRepo; kwargs...)

Fetches updates from an upstream of the repository `repo`.

The keyword arguments are:
  * `remote::AbstractString="origin"`: which remote, specified by name,
    of `repo` to fetch from. If this is empty, the URL will be used to
    construct an anonymous remote.
  * `remoteurl::AbstractString=""`: the URL of `remote`. If not specified,
    will be assumed based on the given name of `remote`.
  * `refspecs=AbstractString[]`: determines properties of the fetch.
  * `credentials=nothing`: provides credentials and/or settings when authenticating against
    a private `remote`.
  * `callbacks=Callbacks()`: user provided callbacks and payloads.

Equivalent to `git fetch [<remoteurl>|<repo>] [<refspecs>]`.
"""
function fetch(repo::GitRepo; remote::AbstractString="origin",
               remoteurl::AbstractString="",
               refspecs::Vector{<:AbstractString}=AbstractString[],
               credentials::Creds=nothing,
               callbacks::Callbacks=Callbacks())
    rmt = if isempty(remoteurl)
        get(GitRemote, repo, remote)
    else
        GitRemoteAnon(repo, remoteurl)
    end

    cred_payload = reset!(CredentialPayload(credentials), GitConfig(repo))
    if !haskey(callbacks, :credentials)
        callbacks[:credentials] = (credentials_cb(), cred_payload)
    elseif haskey(callbacks, :credentials) && credentials !== nothing
        throw(ArgumentError(string(
            "Unable to both use the provided `credentials` as a payload when the ",
            "`callbacks` also contain a credentials payload.")))
    end

    result = try
        remote_callbacks = RemoteCallbacks(callbacks)
        fo = FetchOptions(callbacks=remote_callbacks)
        fetch(rmt, refspecs, msg="from $(url(rmt))", options=fo)
    catch err
        if isa(err, GitError) && err.code === Error.EAUTH
            reject(cred_payload)
        else
            Base.shred!(cred_payload)
        end
        rethrow()
    finally
        close(rmt)
    end
    approve(cred_payload)
    return result
end

"""
    push(repo::GitRepo; kwargs...)

Pushes updates to an upstream of `repo`.

The keyword arguments are:
  * `remote::AbstractString="origin"`: the name of the upstream remote to push to.
  * `remoteurl::AbstractString=""`: the URL of `remote`.
  * `refspecs=AbstractString[]`: determines properties of the push.
  * `force::Bool=false`: determines if the push will be a force push,
     overwriting the remote branch.
  * `credentials=nothing`: provides credentials and/or settings when authenticating against
     a private `remote`.
  * `callbacks=Callbacks()`: user provided callbacks and payloads.

Equivalent to `git push [<remoteurl>|<repo>] [<refspecs>]`.
"""
function push(repo::GitRepo; remote::AbstractString="origin",
              remoteurl::AbstractString="",
              refspecs::Vector{<:AbstractString}=AbstractString[],
              force::Bool=false,
              credentials::Creds=nothing,
              callbacks::Callbacks=Callbacks())
    rmt = if isempty(remoteurl)
        get(GitRemote, repo, remote)
    else
        GitRemoteAnon(repo, remoteurl)
    end

    cred_payload = reset!(CredentialPayload(credentials), GitConfig(repo))
    if !haskey(callbacks, :credentials)
        callbacks[:credentials] = (credentials_cb(), cred_payload)
    elseif haskey(callbacks, :credentials) && credentials !== nothing
        throw(ArgumentError(string(
            "Unable to both use the provided `credentials` as a payload when the ",
            "`callbacks` also contain a credentials payload.")))
    end

    result = try
        remote_callbacks = RemoteCallbacks(callbacks)
        push_opts = PushOptions(callbacks=remote_callbacks)
        push(rmt, refspecs, force=force, options=push_opts)
    catch err
        if isa(err, GitError) && err.code === Error.EAUTH
            reject(cred_payload)
        else
            Base.shred!(cred_payload)
        end
        rethrow()
    finally
        close(rmt)
    end
    approve(cred_payload)
    return result
end

"""
    branch(repo::GitRepo)

Equivalent to `git branch`.
Create a new branch from the current HEAD.
"""
function branch(repo::GitRepo)
    head_ref = head(repo)
    try
        branch(head_ref)
    finally
        close(head_ref)
    end
end

"""
    branch!(repo::GitRepo, branch_name::AbstractString, commit::AbstractString=""; kwargs...)

Checkout a new git branch in the `repo` repository. `commit` is the [`GitHash`](@ref),
in string form, which will be the start of the new branch.
If `commit` is an empty string, the current HEAD will be used.

The keyword arguments are:
  * `track::AbstractString=""`: the name of the
    remote branch this new branch should track, if any.
    If empty (the default), no remote branch
    will be tracked.
  * `force::Bool=false`: if `true`, branch creation will
    be forced.
  * `set_head::Bool=true`: if `true`, after the branch creation
    finishes the branch head will be set as the HEAD of `repo`.

Equivalent to `git checkout [-b|-B] <branch_name> [<commit>] [--track <track>]`.

# Examples
```julia
repo = LibGit2.GitRepo(repo_path)
LibGit2.branch!(repo, "new_branch", set_head=false)
```
"""
function branch!(repo::GitRepo, branch_name::AbstractString,
                 commit::AbstractString = ""; # start point
                 track::AbstractString  = "", # track remote branch
                 force::Bool=false,           # force branch creation
                 set_head::Bool=true)         # set as head reference on exit
    # try to lookup branch first
    branch_ref = force ? nothing : lookup_branch(repo, branch_name)
    if branch_ref === nothing
        branch_rmt_ref = isempty(track) ? nothing : lookup_branch(repo, "$track/$branch_name", true)
        # if commit is empty get head commit oid
        commit_id = if isempty(commit)
            if branch_rmt_ref === nothing
                with(head(repo)) do head_ref
                    with(peel(GitCommit, head_ref)) do hrc
                        GitHash(hrc)
                    end
                end
            else
                tmpcmt = with(peel(GitCommit, branch_rmt_ref)) do hrc
                    GitHash(hrc)
                end
                close(branch_rmt_ref)
                tmpcmt
            end
        else
            GitHash(commit)
        end
        iszero(commit_id) && return
        cmt =  GitCommit(repo, commit_id)
        new_branch_ref = nothing
        try
            new_branch_ref = create_branch(repo, branch_name, cmt, force=force)
        finally
            close(cmt)
            new_branch_ref === nothing && throw(GitError(Error.Object, Error.ERROR, "cannot create branch `$branch_name` with `$commit_id`"))
            branch_ref = new_branch_ref
        end
    end
    try
        #TODO: what if branch tracks other then "origin" remote
        if !isempty(track) # setup tracking
            try
                with(GitConfig, repo) do cfg
                    set!(cfg, "branch.$branch_name.remote", Consts.REMOTE_ORIGIN)
                    set!(cfg, "branch.$branch_name.merge", name(branch_ref))
                end
            catch
                @warn "Please provide remote tracking for branch '$branch_name' in '$(path(repo))'"
            end
        end

        if set_head
            # checkout selected branch
            with(peel(GitTree, branch_ref)) do btree
                checkout_tree(repo, btree)
            end

            # switch head to the branch
            head!(repo, branch_ref)
        end
    finally
        close(branch_ref)
    end
    return
end

"""
    checkout!(repo::GitRepo, commit::AbstractString=""; force::Bool=true)

Equivalent to `git checkout [-f] --detach <commit>`.
Checkout the git commit `commit` (a [`GitHash`](@ref) in string form)
in `repo`. If `force` is `true`, force the checkout and discard any
current changes. Note that this detaches the current HEAD.

# Examples
```julia
repo = LibGit2.GitRepo(repo_path)
open(joinpath(LibGit2.path(repo), "file1"), "w") do f
    write(f, "111\n")
end
LibGit2.add!(repo, "file1")
commit_oid = LibGit2.commit(repo, "add file1")
open(joinpath(LibGit2.path(repo), "file1"), "w") do f
    write(f, "112\n")
end
# would fail without the force=true
# since there are modifications to the file
LibGit2.checkout!(repo, string(commit_oid), force=true)
```
"""
function checkout!(repo::GitRepo, commit::AbstractString = "";
                  force::Bool = true)
    # nothing to do
    isempty(commit) && return

    # grab head name
    head_name = Consts.HEAD_FILE
    try
        with(head(repo)) do head_ref
            head_name = shortname(head_ref)
            # if it is HEAD use short OID instead
            if head_name == Consts.HEAD_FILE
                head_name = string(GitHash(head_ref))
            end
        end
    catch
    end

    # search for commit to get a commit object
    obj = GitObject(repo, GitHash(commit))
    peeled = peel(GitCommit, obj)
    obj_oid = GitHash(peeled)

    # checkout commit
    checkout_tree(repo, peeled, options = force ? CheckoutOptions(checkout_strategy = Consts.CHECKOUT_FORCE) : CheckoutOptions())

    GitReference(repo, obj_oid, force=force,
                 msg="libgit2.checkout: moving from $head_name to $(obj_oid))")

    return nothing
end

"""
    clone(repo_url::AbstractString, repo_path::AbstractString; kwargs...)

Clone a remote repository located at `repo_url` to the local filesystem location `repo_path`.

The keyword arguments are:
  * `branch::AbstractString=""`: which branch of the remote to clone,
    if not the default repository branch (usually `master`).
  * `isbare::Bool=false`: if `true`, clone the remote as a bare repository,
    which will make `repo_path` itself the git directory instead of `repo_path/.git`.
    This means that a working tree cannot be checked out. Plays the role of the
    git CLI argument `--bare`.
  * `remote_cb::Ptr{Cvoid}=C_NULL`: a callback which will be used to create the remote
    before it is cloned. If `C_NULL` (the default), no attempt will be made to create
    the remote - it will be assumed to already exist.
  * `credentials::Creds=nothing`: provides credentials and/or settings when authenticating
    against a private repository.
  * `callbacks::Callbacks=Callbacks()`: user provided callbacks and payloads.

Equivalent to `git clone [-b <branch>] [--bare] <repo_url> <repo_path>`.

# Examples
```julia
repo_url = "https://github.com/JuliaLang/Example.jl"
repo1 = LibGit2.clone(repo_url, "test_path")
repo2 = LibGit2.clone(repo_url, "test_path", isbare=true)
julia_url = "https://github.com/JuliaLang/julia"
julia_repo = LibGit2.clone(julia_url, "julia_path", branch="release-0.6")
```
"""
function clone(repo_url::AbstractString, repo_path::AbstractString;
               branch::AbstractString="",
               isbare::Bool = false,
               remote_cb::Ptr{Cvoid} = C_NULL,
               credentials::Creds=nothing,
               callbacks::Callbacks=Callbacks())
    cred_payload = reset!(CredentialPayload(credentials))
    if !haskey(callbacks, :credentials)
        callbacks[:credentials] = (credentials_cb(), cred_payload)
    elseif haskey(callbacks, :credentials) && credentials !== nothing
        throw(ArgumentError(string(
            "Unable to both use the provided `credentials` as a payload when the ",
            "`callbacks` also contain a credentials payload.")))
    end

    # setup clone options
    lbranch = Base.cconvert(Cstring, branch)
    GC.@preserve lbranch begin
        remote_callbacks = RemoteCallbacks(callbacks)
        fetch_opts = FetchOptions(callbacks=remote_callbacks)
        clone_opts = CloneOptions(
                    bare = Cint(isbare),
                    checkout_branch = isempty(lbranch) ? Cstring(C_NULL) : Base.unsafe_convert(Cstring, lbranch),
                    fetch_opts = fetch_opts,
                    remote_cb = remote_cb
                )
        repo = try
            clone(repo_url, repo_path, clone_opts)
        catch err
            if isa(err, GitError) && err.code === Error.EAUTH
                reject(cred_payload)
            else
                Base.shred!(cred_payload)
            end
            rethrow()
        end
    end
    approve(cred_payload)
    return repo
end

""" git reset [<committish>] [--] <pathspecs>... """
function reset!(repo::GitRepo, committish::AbstractString, pathspecs::AbstractString...)
    obj = GitObject(repo, isempty(committish) ? Consts.HEAD_FILE : committish)
    # do not remove entries in the index matching the provided pathspecs with empty target commit tree
    reset!(repo, obj, pathspecs...)
end

"""
    reset!(repo::GitRepo, id::GitHash, mode::Cint=Consts.RESET_MIXED)

Reset the repository `repo` to its state at `id`, using one of three modes
set by `mode`:
  1. `Consts.RESET_SOFT` - move HEAD to `id`.
  2. `Consts.RESET_MIXED` - default, move HEAD to `id` and reset the index to `id`.
  3. `Consts.RESET_HARD` - move HEAD to `id`, reset the index to `id`, and discard all working changes.

# Examples
```julia
# fetch changes
LibGit2.fetch(repo)
isfile(joinpath(repo_path, our_file)) # will be false

# fastforward merge the changes
LibGit2.merge!(repo, fastforward=true)

# because there was not any file locally, but there is
# a file remotely, we need to reset the branch
head_oid = LibGit2.head_oid(repo)
new_head = LibGit2.reset!(repo, head_oid, LibGit2.Consts.RESET_HARD)
```
In this example, the remote which is being fetched from *does* have
a file called `our_file` in its index, which is why we must reset.

Equivalent to `git reset [--soft | --mixed | --hard] <id>`.

# Examples
```julia
repo = LibGit2.GitRepo(repo_path)
head_oid = LibGit2.head_oid(repo)
open(joinpath(repo_path, "file1"), "w") do f
    write(f, "111\n")
end
LibGit2.add!(repo, "file1")
mode = LibGit2.Consts.RESET_HARD
# will discard the changes to file1
# and unstage it
new_head = LibGit2.reset!(repo, head_oid, mode)
```
"""
reset!(repo::GitRepo, id::GitHash, mode::Cint = Consts.RESET_MIXED) =
    reset!(repo, GitObject(repo, id), mode)

"""
    LibGit2.revcount(repo::GitRepo, commit1::AbstractString, commit2::AbstractString)

List the number of revisions between `commit1` and `commit2` (committish OIDs in string form).
Since `commit1` and `commit2` may be on different branches, `revcount` performs a "left-right"
revision list (and count), returning a tuple of `Int`s - the number of left and right
commits, respectively. A left (or right) commit refers to which side of a symmetric
difference in a tree the commit is reachable from.

Equivalent to `git rev-list --left-right --count <commit1> <commit2>`.

# Examples
```julia
repo = LibGit2.GitRepo(repo_path)
repo_file = open(joinpath(repo_path, test_file), "a")
println(repo_file, "hello world")
flush(repo_file)
LibGit2.add!(repo, test_file)
commit_oid1 = LibGit2.commit(repo, "commit 1")
println(repo_file, "hello world again")
flush(repo_file)
LibGit2.add!(repo, test_file)
commit_oid2 = LibGit2.commit(repo, "commit 2")
LibGit2.revcount(repo, string(commit_oid1), string(commit_oid2))
```

This will return `(-1, 0)`.
"""
function revcount(repo::GitRepo, commit1::AbstractString, commit2::AbstractString)
    commit1_id = revparseid(repo, commit1)
    commit2_id = revparseid(repo, commit2)
    base_id = merge_base(repo, string(commit1_id), string(commit2_id))
    fc = with(GitRevWalker(repo)) do walker
        count((i,r)->i!=base_id, walker, oid=commit1_id, by=Consts.SORT_TOPOLOGICAL)
    end
    sc = with(GitRevWalker(repo)) do walker
        count((i,r)->i!=base_id, walker, oid=commit2_id, by=Consts.SORT_TOPOLOGICAL)
    end
    return (fc-1, sc-1)
end

"""
    merge!(repo::GitRepo; kwargs...) -> Bool

Perform a git merge on the repository `repo`, merging commits
with diverging history into the current branch. Return `true`
if the merge succeeded, `false` if not.

The keyword arguments are:
  * `committish::AbstractString=""`: Merge the named commit(s) in `committish`.
  * `branch::AbstractString=""`: Merge the branch `branch` and all its commits
    since it diverged from the current branch.
  * `fastforward::Bool=false`: If `fastforward` is `true`, only merge if the
    merge is a fast-forward (the current branch head is an ancestor of the
    commits to be merged), otherwise refuse to merge and return `false`.
    This is equivalent to the git CLI option `--ff-only`.
  * `merge_opts::MergeOptions=MergeOptions()`: `merge_opts` specifies options
    for the merge, such as merge strategy in case of conflicts.
  * `checkout_opts::CheckoutOptions=CheckoutOptions()`: `checkout_opts` specifies
    options for the checkout step.

Equivalent to `git merge [--ff-only] [<committish> | <branch>]`.

!!! note
    If you specify a `branch`, this must be done in reference format, since
    the string will be turned into a `GitReference`. For example, if you
    wanted to merge branch `branch_a`, you would call
    `merge!(repo, branch="refs/heads/branch_a")`.
"""
function merge!(repo::GitRepo;
                committish::AbstractString = "",
                branch::AbstractString = "",
                fastforward::Bool = false,
                merge_opts::MergeOptions = MergeOptions(),
                checkout_opts::CheckoutOptions = CheckoutOptions())
    # merge into head branch
    upst_anns = if !isempty(committish) # merge committish into HEAD
        if committish == Consts.FETCH_HEAD # merge FETCH_HEAD
            fheads = fetchheads(repo)
            filter!(fh->fh.ismerge, fheads)
            if isempty(fheads)
                throw(GitError(Error.Merge, Error.ERROR,
                               "There is no fetch reference for this branch."))
            end
            Base.map(fh->GitAnnotated(repo,fh), fheads)
        else # merge committish
            [GitAnnotated(repo, committish)]
        end
    else
        if !isempty(branch) # merge provided branch into HEAD
            with(GitReference(repo, branch)) do brn_ref
                [GitAnnotated(repo, brn_ref)]
            end
        else # try to get tracking remote branch for the head
            if !isattached(repo)
                throw(GitError(Error.Merge, Error.ERROR,
                               "Repository HEAD is detached. Remote tracking branch cannot be used."))
            end
            if isorphan(repo)
                # this isn't really a merge, but really moving HEAD
                # https://github.com/libgit2/libgit2/issues/2135#issuecomment-35997764
                # try to figure out remote tracking of orphan head

                m = with(GitReference(repo, Consts.HEAD_FILE)) do head_sym_ref
                    match(r"refs/heads/(.*)", fullname(head_sym_ref))
                end
                if m === nothing
                    throw(GitError(Error.Merge, Error.ERROR,
                                   "Unable to determine name of orphan branch."))
                end
                branchname = m.captures[1]
                remotename = with(GitConfig, repo) do cfg
                    LibGit2.get(String, cfg, "branch.$branchname.remote")
                end
                oid = with(GitReference(repo, "refs/remotes/$remotename/$branchname")) do ref
                    LibGit2.GitHash(ref)
                end
                with(GitCommit(repo, oid)) do cmt
                    LibGit2.create_branch(repo, branchname, cmt)
                end
                return true
            else
                with(head(repo)) do head_ref
                    tr_brn_ref = upstream(head_ref)
                    if tr_brn_ref === nothing
                        throw(GitError(Error.Merge, Error.ERROR,
                                       "There is no tracking information for the current branch."))
                    end
                    try
                        [GitAnnotated(repo, tr_brn_ref)]
                    finally
                        close(tr_brn_ref)
                    end
                end
            end
        end
    end
    try
        merge!(repo, upst_anns, fastforward,
               merge_opts=merge_opts,
               checkout_opts=checkout_opts)
    finally
        Base.foreach(close, upst_anns)
    end
end

"""
    LibGit2.rebase!(repo::GitRepo, upstream::AbstractString="", newbase::AbstractString="")

Attempt an automatic merge rebase of the current branch, from `upstream` if provided, or
otherwise from the upstream tracking branch.
`newbase` is the branch to rebase onto. By default this is `upstream`.

If any conflicts arise which cannot be automatically resolved, the rebase will abort,
leaving the repository and working tree in its original state, and the function will throw
a `GitError`. This is roughly equivalent to the following command line statement:

    git rebase --merge [<upstream>]
    if [ -d ".git/rebase-merge" ]; then
        git rebase --abort
    fi

"""
function rebase!(repo::GitRepo, upstream::AbstractString="", newbase::AbstractString="")
    with(head(repo)) do head_ref
        head_ann = GitAnnotated(repo, head_ref)
        upst_ann = if isempty(upstream)
            brn_ref = LibGit2.upstream(head_ref)
            if brn_ref === nothing
                throw(GitError(Error.Rebase, Error.ERROR,
                               "There is no tracking information for the current branch."))
            end
            try
                GitAnnotated(repo, brn_ref)
            finally
                close(brn_ref)
            end
        else
            GitAnnotated(repo, upstream)
        end
        onto_ann = isempty(newbase) ? nothing : GitAnnotated(repo, newbase)
        try
            sig = default_signature(repo)
            try
                rbs = GitRebase(repo, head_ann, upst_ann, onto=onto_ann)
                try
                    for rbs_op in rbs
                        commit(rbs, sig)
                    end
                    finish(rbs, sig)
                catch
                    abort(rbs)
                    rethrow()
                finally
                    close(rbs)
                end
            finally
                #onto_ann !== nothing && close(onto_ann)
                close(sig)
            end
        finally
            if !isempty(newbase)
                close(onto_ann::GitAnnotated)
            end
            close(upst_ann)
            close(head_ann)
        end
    end
    return head_oid(repo)
end


"""
    authors(repo::GitRepo) -> Vector{Signature}

Return all authors of commits to the `repo` repository.

# Examples
```julia
repo = LibGit2.GitRepo(repo_path)
repo_file = open(joinpath(repo_path, test_file), "a")

println(repo_file, commit_msg)
flush(repo_file)
LibGit2.add!(repo, test_file)
sig = LibGit2.Signature("TEST", "TEST@TEST.COM", round(time(), 0), 0)
commit_oid1 = LibGit2.commit(repo, "commit1"; author=sig, committer=sig)
println(repo_file, randstring(10))
flush(repo_file)
LibGit2.add!(repo, test_file)
commit_oid2 = LibGit2.commit(repo, "commit2"; author=sig, committer=sig)

# will be a Vector of [sig, sig]
auths = LibGit2.authors(repo)
```
"""
function authors(repo::GitRepo)
    return with(GitRevWalker(repo)) do walker
        map((oid,repo)->with(GitCommit(repo, oid)) do cmt
                            author(cmt)::Signature
                        end,
            walker) #, by = Consts.SORT_TIME)
    end
end

"""
    snapshot(repo::GitRepo) -> State

Take a snapshot of the current state of the repository `repo`,
storing the current HEAD, index, and any uncommitted work.
The output `State` can be used later during a call to [`restore`](@ref)
to return the repository to the snapshotted state.
"""
function snapshot(repo::GitRepo)
    head = GitHash(repo, Consts.HEAD_FILE)
    index = with(GitIndex, repo) do idx; write_tree!(idx) end
    work = try
        with(GitIndex, repo) do idx
            if length(readdir(path(repo))) > 1
                add!(idx, ".")
                write!(idx)
            end
            write_tree!(idx)
        end
    finally
        # restore index
        with(GitIndex, repo) do idx
            read_tree!(idx, index)
            write!(idx)
        end
    end
    State(head, index, work)
end

"""
    restore(s::State, repo::GitRepo)

Return a repository `repo` to a previous `State` `s`, for
example the HEAD of a branch before a merge attempt. `s`
can be generated using the [`snapshot`](@ref) function.
"""
function restore(s::State, repo::GitRepo)
    head = reset!(repo, Consts.HEAD_FILE, "*")  # unstage everything
    with(GitIndex, repo) do idx
        read_tree!(idx, s.work)            # move work tree to index
        opts = CheckoutOptions(
                checkout_strategy = Consts.CHECKOUT_FORCE |     # check the index out to work
                                    Consts.CHECKOUT_REMOVE_UNTRACKED) # remove everything else
        checkout_index(repo, idx, options = opts)

        read_tree!(idx, s.index)  # restore index
    end
    reset!(repo, s.head, Consts.RESET_SOFT) # restore head
end

"""
    transact(f::Function, repo::GitRepo)

Apply function `f` to the git repository `repo`, taking a [`snapshot`](@ref) before
applying `f`. If an error occurs within `f`, `repo` will be returned to its snapshot
state using [`restore`](@ref). The error which occurred will be rethrown, but the
state of `repo` will not be corrupted.
"""
function transact(f::Function, repo::GitRepo)
    state = snapshot(repo)
    try f(repo) catch
        restore(state, repo)
        rethrow()
    finally
        close(repo)
    end
end

## lazy libgit2 initialization

const ENSURE_INITIALIZED_LOCK = ReentrantLock()

@noinline function throw_negative_refcount_error(x::Int)
    error("Negative LibGit2 REFCOUNT $x\nThis shouldn't happen, please file a bug report!")
end

function ensure_initialized()
    lock(ENSURE_INITIALIZED_LOCK) do
        x = Threads.atomic_cas!(REFCOUNT, 0, 1)
        x > 0 && return
        x < 0 && throw_negative_refcount_error(x)
        try initialize()
        catch
            Threads.atomic_sub!(REFCOUNT, 1)
            @assert REFCOUNT[] == 0
            rethrow()
        end
    end
    return nothing
end

@noinline function initialize()
    @check ccall((:git_libgit2_init, libgit2), Cint, ())

    cert_loc = NetworkOptions.ca_roots()
    cert_loc !== nothing && set_ssl_cert_locations(cert_loc)

    atexit() do
        # refcount zero, no objects to be finalized
        if Threads.atomic_sub!(REFCOUNT, 1) == 1
            ccall((:git_libgit2_shutdown, libgit2), Cint, ())
        end
    end
end

function set_ssl_cert_locations(cert_loc)
    cert_file = cert_dir = Cstring(C_NULL)
    if isdir(cert_loc) # directories
        cert_dir = cert_loc
    else # files, /dev/null, non-existent paths, etc.
        cert_file = cert_loc
    end
        ret = @ccall libgit2.git_libgit2_opts(
        Consts.SET_SSL_CERT_LOCATIONS::Cint;
        cert_file::Cstring,
        cert_dir::Cstring)::Cint
    ret >= 0 && return ret
    err = Error.GitError(ret)
    err.class == Error.SSL &&
        err.msg == "TLS backend doesn't support certificate locations" ||
        throw(err)
    var = nothing
    for v in NetworkOptions.CA_ROOTS_VARS
        haskey(ENV, v) && (var = v)
    end
    @assert var !== nothing # otherwise we shouldn't be here
    msg = """
    Your Julia is built with a SSL/TLS engine that libgit2 doesn't know how to configure to use a file or directory of certificate authority roots, but your environment specifies one via the $var variable. If you believe your system's root certificates are safe to use, you can `export JULIA_SSL_CA_ROOTS_PATH=""` in your environment to use those instead.
    """
    throw(Error.GitError(err.class, err.code, chomp(msg)))
end

"""
    trace_set(level::Union{Integer,GIT_TRACE_LEVEL})

Sets the system tracing configuration to the specified level.
"""
function trace_set(level::Union{Integer,Consts.GIT_TRACE_LEVEL}, cb=trace_cb())
    @check @ccall libgit2.git_trace_set(level::Cint, cb::Ptr{Cvoid})::Cint
end

end # module
z   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LibGit2_jll/src/LibGit2_jll.jl`      # This file is a part of Julia. License is MIT: https://julialang.org/license

## dummy stub for https://github.com/JuliaBinaryWrappers/LibGit2_jll.jl

baremodule LibGit2_jll
using Base, Libdl, MbedTLS_jll, LibSSH2_jll
Base.Experimental.@compiler_options compile=min optimize=0 infer=false

const PATH_list = String[]
const LIBPATH_list = String[]

export libgit2

# These get calculated in __init__()
const PATH = Ref("")
const LIBPATH = Ref("")
artifact_dir::String = ""
libgit2_handle::Ptr{Cvoid} = C_NULL
libgit2_path::String = ""

if Sys.iswindows()
    const libgit2 = "libgit2.dll"
elseif Sys.isapple()
    const libgit2 = "@rpath/libgit2.1.6.dylib"
else
    const libgit2 = "libgit2.so.1.6"
end

function __init__()
    global libgit2_handle = dlopen(libgit2)
    global libgit2_path = dlpath(libgit2_handle)
    global artifact_dir = dirname(Sys.BINDIR)
    LIBPATH[] = dirname(libgit2_path)
    push!(LIBPATH_list, LIBPATH[])
end

# JLLWrappers API compatibility shims.  Note that not all of these will really make sense.
# For instance, `find_artifact_dir()` won't actually be the artifact directory, because
# there isn't one.  It instead returns the overall Julia prefix.
is_available() = true
find_artifact_dir() = artifact_dir
dev_jll() = error("stdlib JLLs cannot be dev'ed")
best_wrapper = nothing
get_libgit2_path() = libgit2_path

end  # module LibGit2_jll
z   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/MbedTLS_jll/src/MbedTLS_jll.jly      # This file is a part of Julia. License is MIT: https://julialang.org/license

## dummy stub for https://github.com/JuliaBinaryWrappers/MbedTLS_jll.jl

baremodule MbedTLS_jll
using Base, Libdl
Base.Experimental.@compiler_options compile=min optimize=0 infer=false

const PATH_list = String[]
const LIBPATH_list = String[]

export libmbedcrypto, libmbedtls, libmbedx509

# These get calculated in __init__()
const PATH = Ref("")
const LIBPATH = Ref("")
artifact_dir::String = ""
libmbedcrypto_handle::Ptr{Cvoid} = C_NULL
libmbedcrypto_path::String = ""
libmbedtls_handle::Ptr{Cvoid} = C_NULL
libmbedtls_path::String = ""
libmbedx509_handle::Ptr{Cvoid} = C_NULL
libmbedx509_path::String = ""

if Sys.iswindows()
    const libmbedcrypto = "libmbedcrypto.dll"
    const libmbedtls = "libmbedtls.dll"
    const libmbedx509 = "libmbedx509.dll"
elseif Sys.isapple()
    const libmbedcrypto = "@rpath/libmbedcrypto.7.dylib"
    const libmbedtls = "@rpath/libmbedtls.14.dylib"
    const libmbedx509 = "@rpath/libmbedx509.1.dylib"
else
    const libmbedcrypto = "libmbedcrypto.so.7"
    const libmbedtls = "libmbedtls.so.14"
    const libmbedx509 = "libmbedx509.so.1"
end

function __init__()
    global libmbedcrypto_handle = dlopen(libmbedcrypto)
    global libmbedcrypto_path = dlpath(libmbedcrypto_handle)
    global libmbedtls_handle = dlopen(libmbedtls)
    global libmbedtls_path = dlpath(libmbedtls_handle)
    global libmbedx509_handle = dlopen(libmbedx509)
    global libmbedx509_path = dlpath(libmbedx509_handle)
    global artifact_dir = dirname(Sys.BINDIR)
    LIBPATH[] = dirname(libmbedtls_path)
    push!(LIBPATH_list, LIBPATH[])
end

# JLLWrappers API compatibility shims.  Note that not all of these will really make sense.
# For instance, `find_artifact_dir()` won't actually be the artifact directory, because
# there isn't one.  It instead returns the overall Julia prefix.
is_available() = true
find_artifact_dir() = artifact_dir
dev_jll() = error("stdlib JLLs cannot be dev'ed")
best_wrapper = nothing
get_libmbedcrypto_path() =libmbedcrypto_path
get_libmbedtls_path() = libmbedtls_path
get_libmbedx509_path() = libmbedx509_path

end  # module MbedTLS_jll
z   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LibSSH2_jll/src/LibSSH2_jll.jlP      # This file is a part of Julia. License is MIT: https://julialang.org/license

## dummy stub for https://github.com/JuliaBinaryWrappers/LibSSH2_jll.jl

baremodule LibSSH2_jll
using Base, Libdl, MbedTLS_jll
Base.Experimental.@compiler_options compile=min optimize=0 infer=false

const PATH_list = String[]
const LIBPATH_list = String[]

export libssh2

# These get calculated in __init__()
const PATH = Ref("")
const LIBPATH = Ref("")
artifact_dir::String = ""
libssh2_handle::Ptr{Cvoid} = C_NULL
libssh2_path::String = ""

if Sys.iswindows()
    const libssh2 = "libssh2.dll"
elseif Sys.isapple()
    const libssh2 = "@rpath/libssh2.1.dylib"
else
    const libssh2 = "libssh2.so.1"
end

function __init__()
    global libssh2_handle = dlopen(libssh2)
    global libssh2_path = dlpath(libssh2_handle)
    global artifact_dir = dirname(Sys.BINDIR)
    LIBPATH[] = dirname(libssh2_path)
    push!(LIBPATH_list, LIBPATH[])
end


# JLLWrappers API compatibility shims.  Note that not all of these will really make sense.
# For instance, `find_artifact_dir()` won't actually be the artifact directory, because
# there isn't one.  It instead returns the overall Julia prefix.
is_available() = true
find_artifact_dir() = artifact_dir
dev_jll() = error("stdlib JLLs cannot be dev'ed")
best_wrapper = nothing
get_libssh2_path() = libssh2_path

end  # module LibSSH2_jll
p   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LibGit2/src/error.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

module Error

import ..LibGit2: ensure_initialized
using LibGit2_jll

export GitError

@enum(Code, GIT_OK          = Cint(0),   # no error
            ERROR           = Cint(-01), # generic error
            ENOTFOUND       = Cint(-03), # requested object could not be found
            EEXISTS         = Cint(-04), # object exits preventing op
            EAMBIGUOUS      = Cint(-05), # more than one object matches
            EBUFS           = Cint(-06), # output buffer too small to hold data
            EUSER           = Cint(-07), # user callback generated error
            EBAREREPO       = Cint(-08), # operation not allowed on bare repo
            EUNBORNBRANCH   = Cint(-09), # HEAD refers to branch with 0 commits
            EUNMERGED       = Cint(-10), # merge in progress prevented op
            ENONFASTFORWARD = Cint(-11), # ref not fast-forwardable
            EINVALIDSPEC    = Cint(-12), # name / ref not in valid format
            EMERGECONFLICT  = Cint(-13), # merge conflict prevented op
            ELOCKED         = Cint(-14), # lock file prevented op
            EMODIFIED       = Cint(-15), # ref value does not match expected
            EAUTH           = Cint(-16), # authentication error
            ECERTIFICATE    = Cint(-17), # server certificate is invalid
            EAPPLIED        = Cint(-18), # patch/merge has already been applied
            EPEEL           = Cint(-19), # the requested peel operation is not possible
            EEOF            = Cint(-20), # unexpected EOF
            PASSTHROUGH     = Cint(-30), # internal only
            ITEROVER        = Cint(-31), # signals end of iteration
            RETRY           = Cint(-32), # internal only
            EMISMATCH       = Cint(-33), # hashsum mismatch in object
            EINDEXDIRTY     = Cint(-34), # unsaved changes in the index would be overwritten
            EAPPLYFAIL      = Cint(-35), # patch application failed
            EOWNER          = Cint(-36)) # the object is not owned by the current user

@enum(Class, None,
             NoMemory,
             OS,
             Invalid,
             Reference,
             Zlib,
             Repository,
             Config,
             Regex,
             Odb,
             Index,
             Object,
             Net,
             Tag,
             Tree,
             Indexer,
             SSL,
             Submodule,
             Thread,
             Stash,
             Checkout,
             FetchHead,
             Merge,
             SSH,
             Filter,
             Revert,
             Callback,
             CherryPick,
             Describe,
             Rebase,
             Filesystem,
             Patch,
             WorkTree,
             SHA1,
             HTTP)

struct ErrorStruct
    message::Ptr{UInt8}
    class::Cint
end

struct GitError <: Exception
    class::Class
    code::Code
    msg::String
end
Base.show(io::IO, err::GitError) = print(io, "GitError(Code:$(err.code), Class:$(err.class), $(err.msg))")

function last_error()
    ensure_initialized()
    err = ccall((:giterr_last, libgit2), Ptr{ErrorStruct}, ())
    if err != C_NULL
        err_obj   = unsafe_load(err)
        err_class = Class(err_obj.class)
        err_msg   = unsafe_string(err_obj.message)
    else
        err_class = Class(0)
        err_msg = "No errors"
    end
    return (err_class, err_msg)
end

GitError(err_code::Integer) = GitError(Code(err_code))
function GitError(err_code::Code)
    err_class, err_msg = last_error()
    return GitError(err_class, err_code, err_msg)
end

end # Error module

macro check(git_func)
    quote
        err = Cint($(esc(git_func::Expr)))
        if err < 0
            throw(Error.GitError(err))
        end
        err
    end
end
p   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LibGit2/src/utils.jly      # This file is a part of Julia. License is MIT: https://julialang.org/license

# Parse "GIT URLs" syntax (URLs and a scp-like syntax). For details see:
# https://git-scm.com/docs/git-clone#_git_urls_a_id_urls_a
# Note that using a Regex like this is inherently insecure with regards to its
# handling of passwords; we are unable to deterministically and securely erase
# the passwords from memory after use.
# TODO: reimplement with a Julian parser instead of leaning on this regex
const URL_REGEX = r"""
^(?:(?<scheme>ssh|git|https?)://)?+
(?:
    (?<user>.*?)
    (?:\:(?<password>.*?))?@
)?
(?<host>[A-Za-z0-9\-\.]+)
(?(<scheme>)
    # Only parse port when not using scp-like syntax
    (?:\:(?<port>\d+))?
    /?
    |
    :?
)
(?<path>
    # Require path to be preceded by '/'. Alternatively, ':' when using scp-like syntax.
    (?<=(?(<scheme>)/|:))
    .*
)?
$
"""x

"""
    version() -> VersionNumber

Return the version of libgit2 in use, as a [`VersionNumber`](@ref man-version-number-literals).
"""
function version()
    major = Ref{Cint}(0)
    minor = Ref{Cint}(0)
    patch = Ref{Cint}(0)
    @check ccall((:git_libgit2_version, libgit2), Cint,
                 (Ref{Cint}, Ref{Cint}, Ref{Cint}), major, minor, patch)
    return VersionNumber(major[], minor[], patch[])
end
const VERSION = version()

"""
    isset(val::Integer, flag::Integer)

Test whether the bits of `val` indexed by `flag` are set (`1`) or unset (`0`).
"""
isset(val::Integer, flag::Integer) = (val & flag == flag)

"""
    reset(val::Integer, flag::Integer)

Unset the bits of `val` indexed by `flag`, returning them to `0`.
"""
reset(val::Integer, flag::Integer) = (val &= ~flag)

"""
    toggle(val::Integer, flag::Integer)

Flip the bits of `val` indexed by `flag`, so that if a bit is `0` it
will be `1` after the toggle, and vice-versa.
"""
toggle(val::Integer, flag::Integer) = (val |= flag)

"""
    features()

Return a list of git features the current version of libgit2 supports, such as
threading or using HTTPS or SSH.
"""
function features()
    feat = ccall((:git_libgit2_features, libgit2), Cint, ())
    res = Consts.GIT_FEATURE[]
    for f in instances(Consts.GIT_FEATURE)
        isset(feat, Cuint(f)) && Base.push!(res, f)
    end
    return res
end

"""
    LibGit2.posixpath(path)

Standardise the path string `path` to use POSIX separators.
"""
function posixpath end
if Sys.iswindows()
    posixpath(path) = replace(path,'\\' => '/')
elseif Sys.isunix()
    posixpath(path) = path
end

"""
    LibGit2.git_url(; kwargs...) -> String

Create a string based upon the URL components provided. When the `scheme` keyword is not
provided the URL produced will use the alternative [scp-like syntax](https://git-scm.com/docs/git-clone#_git_urls_a_id_urls_a).

# Keywords

  * `scheme::AbstractString=""`: the URL scheme which identifies the protocol to be used.
    For HTTP use "http", SSH use "ssh", etc. When `scheme` is not provided the output format
    will be "ssh" but using the scp-like syntax.
  * `username::AbstractString=""`: the username to use in the output if provided.
  * `password::AbstractString=""`: the password to use in the output if provided.
  * `host::AbstractString=""`: the hostname to use in the output. A hostname is required to
    be specified.
  * `port::Union{AbstractString,Integer}=""`: the port number to use in the output if
    provided. Cannot be specified when using the scp-like syntax.
  * `path::AbstractString=""`: the path to use in the output if provided.

!!! warning
    Avoid using passwords in URLs. Unlike the credential objects, Julia is not able
    to securely zero or destroy the sensitive data after use and the password may
    remain in memory; possibly to be exposed by an uninitialized memory.

# Examples
```jldoctest
julia> LibGit2.git_url(username="git", host="github.com", path="JuliaLang/julia.git")
"git@github.com:JuliaLang/julia.git"

julia> LibGit2.git_url(scheme="https", host="github.com", path="/JuliaLang/julia.git")
"https://github.com/JuliaLang/julia.git"

julia> LibGit2.git_url(scheme="ssh", username="git", host="github.com", port=2222, path="JuliaLang/julia.git")
"ssh://git@github.com:2222/JuliaLang/julia.git"
```
"""
function git_url(;
        scheme::AbstractString="",
        username::AbstractString="",
        host::AbstractString="",
        port::Union{AbstractString, Integer}="",
        path::AbstractString="")

    port_str = port isa Integer ? string(port) : port
    scp_syntax = isempty(scheme)

    isempty(host) && throw(ArgumentError("A host needs to be specified"))
    scp_syntax && !isempty(port_str) && throw(ArgumentError("Port cannot be specified when using scp-like syntax"))

    io = IOBuffer()
    !isempty(scheme) && write(io, scheme, "://")

    if !isempty(username)
        write(io, username)
        write(io, '@')
    end

    write(io, host)
    !isempty(port_str) && write(io, ':', port_str)

    if !isempty(path)
        if scp_syntax
            write(io, ':')
        elseif !startswith(path, '/')
            write(io, '/')
        end
        write(io, path)
    end
    seekstart(io)

    return String(take!(io))
end

function credential_identifier(scheme::AbstractString, host::AbstractString)
    string(isempty(scheme) ? "ssh" : scheme, "://", host)
end

function credential_identifier(url::AbstractString)
    m = match(URL_REGEX, url)
    scheme = something(m[:scheme], SubString(""))
    host = something(m[:host])
    credential_identifier(scheme, host)
end
q   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LibGit2/src/consts.jljT      # This file is a part of Julia. License is MIT: https://julialang.org/license

module Consts

import ..LibGit2: version, ensure_initialized

const HEAD_FILE  = "HEAD"
const FETCH_HEAD  = "FETCH_HEAD"
const REMOTE_ORIGIN = "origin"

# objs
@enum(OBJECT,
      OBJ_ANY    = -2,
      OBJ_BAD    = -1,
      OBJ_COMMIT = 1,
      OBJ_TREE   = 2,
      OBJ_BLOB   = 3,
      OBJ_TAG    = 4)

#revwalk
const SORT_NONE        = Cint(0)
const SORT_TOPOLOGICAL = Cint(1 << 0)
const SORT_TIME        = Cint(1 << 1)
const SORT_REVERSE     = Cint(1 << 2)

# refs
const REF_INVALID  = Cint(0)
const REF_OID      = Cint(1)
const REF_SYMBOLIC = Cint(2)
const REF_LISTALL  = REF_OID | REF_SYMBOLIC

# blame
const BLAME_NORMAL                          = Cuint(0)
const BLAME_TRACK_COPIES_SAME_FILE          = Cuint(1 << 0)
const BLAME_TRACK_COPIES_SAME_COMMIT_MOVES  = Cuint(1 << 1)
const BLAME_TRACK_COPIES_SAME_COMMIT_COPIES = Cuint(1 << 2)
const BLAME_TRACK_COPIES_ANY_COMMIT_COPIES  = Cuint(1 << 3)
const BLAME_FIRST_PARENT                    = Cuint(1 << 4)

# checkout
const CHECKOUT_NONE                    = Cuint(0)
const CHECKOUT_SAFE                    = Cuint(1 << 0)
const CHECKOUT_FORCE                   = Cuint(1 << 1)
const CHECKOUT_RECREATE_MISSING        = Cuint(1 << 2)
const CHECKOUT_ALLOW_CONFLICTS         = Cuint(1 << 4)
const CHECKOUT_REMOVE_UNTRACKED        = Cuint(1 << 5)
const CHECKOUT_REMOVE_IGNORED          = Cuint(1 << 6)
const CHECKOUT_UPDATE_ONLY             = Cuint(1 << 7)
const CHECKOUT_DONT_UPDATE_INDEX       = Cuint(1 << 8)
const CHECKOUT_NO_REFRESH              = Cuint(1 << 9)
const CHECKOUT_SKIP_UNMERGED           = Cuint(1 << 10)
const CHECKOUT_USE_OURS                = Cuint(1 << 11)
const CHECKOUT_USE_THEIRS              = Cuint(1 << 12)
const CHECKOUT_DISABLE_PATHSPEC_MATCH  = Cuint(1 << 13)
const CHECKOUT_SKIP_LOCKED_DIRECTORIES = Cuint(1 << 18)
const CHECKOUT_DONT_OVERWRITE_IGNORED  = Cuint(1 << 19)
const CHECKOUT_CONFLICT_STYLE_MERGE    = Cuint(1 << 20)
const CHECKOUT_CONFLICT_STYLE_DIFF3    = Cuint(1 << 21)
const CHECKOUT_DONT_REMOVE_EXISTING    = Cuint(1 << 22)

const CHECKOUT_UPDATE_SUBMODULES       = Cuint(1 << 16)
const CHECKOUT_UPDATE_SUBMODULES_IF_CHANGED = Cuint(1 << 17)

const CHECKOUT_NOTIFY_NONE      = Cuint(0)
const CHECKOUT_NOTIFY_CONFLICT  = Cuint(1 << 0)
const CHECKOUT_NOTIFY_DIRTY     = Cuint(1 << 1)
const CHECKOUT_NOTIFY_UPDATED   = Cuint(1 << 2)
const CHECKOUT_NOTIFY_UNTRACKED = Cuint(1 << 3)
const CHECKOUT_NOTIFY_IGNORED   = Cuint(1 << 4)
const CHECKOUT_NOTIFY_ALL       = 0x0FFFF

# diff
const DIFF_OPTIONS_VERSION = Cuint(1)

const DIFF_NORMAL                     = Cuint(0)
const DIFF_REVERSE                    = Cuint(1 << 0)
const DIFF_INCLUDE_IGNORED            = Cuint(1 << 1)
const DIFF_RECURSE_IGNORED_DIRS       = Cuint(1 << 2)
const DIFF_INCLUDE_UNTRACKED          = Cuint(1 << 3)
const DIFF_RECURSE_UNTRACKED_DIRS     = Cuint(1 << 4)
const DIFF_INCLUDE_UNMODIFIED         = Cuint(1 << 5)
const DIFF_INCLUDE_TYPECHANGE         = Cuint(1 << 6)
const DIFF_INCLUDE_TYPECHANGE_TREES   = Cuint(1 << 7)
const DIFF_IGNORE_FILEMODE            = Cuint(1 << 8)
const DIFF_IGNORE_SUBMODULES          = Cuint(1 << 9)
const DIFF_IGNORE_CASE                = Cuint(1 << 10)
const DIFF_DISABLE_PATHSPEC_MATCH     = Cuint(1 << 12)
const DIFF_SKIP_BINARY_CHECK          = Cuint(1 << 13)
const DIFF_ENABLE_FAST_UNTRACKED_DIRS = Cuint(1 << 14)

const DIFF_FORCE_TEXT               = Cuint(1 << 20)
const DIFF_FORCE_BINARY             = Cuint(1 << 21)
const DIFF_IGNORE_WHITESPACE        = Cuint(1 << 22)
const DIFF_IGNORE_WHITESPACE_CHANGE = Cuint(1 << 23)
const DIFF_IGNORE_WHITESPACE_EOL    = Cuint(1 << 24)
const DIFF_SHOW_UNTRACKED_CONTENT   = Cuint(1 << 25)
const DIFF_SHOW_UNMODIFIED          = Cuint(1 << 26)
const DIFF_PATIENCE                 = Cuint(1 << 28)
const DIFF_MINIMAL                  = Cuint(1 << 29)

const DIFF_FLAG_BINARY     = Cuint(1 << 0)
const DIFF_FLAG_NOT_BINARY = Cuint(1 << 1)
const DIFF_FLAG_VALID_OID  = Cuint(1 << 2)

const DIFF_FORMAT_PATCH        = Cuint(1)
const DIFF_FORMAT_PATCH_HEADER = Cuint(2)
const DIFF_FORMAT_RAW          = Cuint(3)
const DIFF_FORMAT_NAME_ONLY    = Cuint(4)
const DIFF_FORMAT_NAME_STATUS  = Cuint(5)

@enum(DELTA_STATUS, DELTA_UNMODIFIED = Cint(0),
                    DELTA_ADDED      = Cint(1),
                    DELTA_DELETED    = Cint(2),
                    DELTA_MODIFIED   = Cint(3),
                    DELTA_RENAMED    = Cint(4),
                    DELTA_COPIED     = Cint(5),
                    DELTA_IGNORED    = Cint(6),
                    DELTA_UNTRACKED  = Cint(7),
                    DELTA_TYPECHANGE = Cint(8))

# index
const IDXENTRY_NAMEMASK   = (0x0fff)
const IDXENTRY_STAGEMASK  = (0x3000)
const IDXENTRY_EXTENDED   = (0x4000)
const IDXENTRY_VALID      = (0x8000)
const IDXENTRY_STAGESHIFT = Cint(12)

const IDXENTRY_UPDATE            = Cint(1 << 0)
const IDXENTRY_REMOVE            = Cint(1 << 1)
const IDXENTRY_UPTODATE          = Cint(1 << 2)
const IDXENTRY_ADDED             = Cint(1 << 3)

const IDXENTRY_HASHED            = Cint(1 << 4)
const IDXENTRY_UNHASHED          = Cint(1 << 5)
const IDXENTRY_WT_REMOVE         = Cint(1 << 6)
const IDXENTRY_CONFLICTED        = Cint(1 << 7)

const IDXENTRY_UNPACKED          = Cint(1 << 8)
const IDXENTRY_NEW_SKIP_WORKTREE = Cint(1 << 9)

const INDEXCAP_IGNORE_CASE = Cuint(1)
const INDEXCAP_NO_FILEMODE = Cuint(2)
const INDEXCAP_NO_SYMLINKS = Cuint(4)
const INDEXCAP_FROM_OWNER  = ~Cuint(0)

const INDEX_ADD_DEFAULT                = Cuint(0)
const INDEX_ADD_FORCE                  = Cuint(1 << 0)
const INDEX_ADD_DISABLE_PATHSPEC_MATCH = Cuint(1 << 1)
const INDEX_ADD_CHECK_PATHSPEC         = Cuint(1 << 2)

const INDEX_STAGE_ANY = Cint(-1)

# merge
""" Option flags for git merge.
* `MERGE_FIND_RENAMES`: detect if a file has been renamed between the common
  ancestor and the "ours" or "theirs" side of the merge. Allows merges where
  a file has been renamed.
* `MERGE_FAIL_ON_CONFLICT`: exit immediately if a conflict is found rather
  than trying to resolve it.
* `MERGE_SKIP_REUC`: do not write the REUC extension on the index resulting
  from the merge.
* `MERGE_NO_RECURSIVE`: if the commits being merged have multiple merge bases,
  use the first one, rather than trying to recursively merge the bases.
"""
@enum(GIT_MERGE, MERGE_FIND_RENAMES     = 1 << 0,
                 MERGE_FAIL_ON_CONFLICT = 1 << 1,
                 MERGE_SKIP_REUC        = 1 << 2,
                 MERGE_NO_RECURSIVE     = 1 << 3)

@enum(GIT_MERGE_FILE, MERGE_FILE_DEFAULT                  = 0,       # Defaults
                      MERGE_FILE_STYLE_MERGE              = 1 << 0,  # Create standard conflicted merge files
                      MERGE_FILE_STYLE_DIFF3              = 1 << 1,  # Create diff3-style files
                      MERGE_FILE_SIMPLIFY_ALNUM           = 1 << 2,  # Condense non-alphanumeric regions for simplified diff file
                      MERGE_FILE_IGNORE_WHITESPACE        = 1 << 3,  # Ignore all whitespace
                      MERGE_FILE_IGNORE_WHITESPACE_CHANGE = 1 << 4,  # Ignore changes in amount of whitespace
                      MERGE_FILE_IGNORE_WHITESPACE_EOL    = 1 << 5,  # Ignore whitespace at end of line
                      MERGE_FILE_DIFF_PATIENCE            = 1 << 6,  # Use the "patience diff" algorithm
                      MERGE_FILE_DIFF_MINIMAL             = 1 << 7)  # Take extra time to find minimal diff
""" Option flags for git merge file favoritism.
  * `MERGE_FILE_FAVOR_NORMAL`: if both sides of the merge have changes to a section,
    make a note of the conflict in the index which `git checkout` will use to create
    a merge file, which the user can then reference to resolve the conflicts. This is
    the default.
  * `MERGE_FILE_FAVOR_OURS`: if both sides of the merge have changes to a section,
    use the version in the "ours" side of the merge in the index.
  * `MERGE_FILE_FAVOR_THEIRS`: if both sides of the merge have changes to a section,
    use the version in the "theirs" side of the merge in the index.
  * `MERGE_FILE_FAVOR_UNION`: if both sides of the merge have changes to a section,
    include each unique line from both sides in the file which is put into the index.
"""
@enum(GIT_MERGE_FILE_FAVOR, MERGE_FILE_FAVOR_NORMAL = 0,
                            MERGE_FILE_FAVOR_OURS   = 1,
                            MERGE_FILE_FAVOR_THEIRS = 2,
                            MERGE_FILE_FAVOR_UNION  = 3)
""" The user's instructions for how to perform a possible merge.
* `MERGE_PREFERENCE_NONE`: the user has no preference.
* `MERGE_PREFERENCE_NO_FASTFORWARD`: do not allow any fast-forward merges.
* `MERGE_PREFERENCE_FASTFORWARD_ONLY`: allow only fast-forward merges and no
  other type (which may introduce conflicts).
"""
@enum(GIT_MERGE_PREFERENCE, MERGE_PREFERENCE_NONE             = 0,
                            MERGE_PREFERENCE_NO_FASTFORWARD   = 1,
                            MERGE_PREFERENCE_FASTFORWARD_ONLY = 2)
""" Result of analysis on merge possibilities.
* `MERGE_ANALYSIS_NONE`: it is not possible to merge the elements of the input commits.
* `MERGE_ANALYSIS_NORMAL`: a regular merge, when HEAD and the commits that the
  user wishes to merge have all diverged from a common ancestor. In this case the
  changes have to be resolved and conflicts may occur.
* `MERGE_ANALYSIS_UP_TO_DATE`: all the input commits the user wishes to merge can
  be reached from HEAD, so no merge needs to be performed.
* `MERGE_ANALYSIS_FASTFORWARD`: the input commit is a descendant of HEAD and so no
  merge needs to be performed - instead, the user can simply checkout the
  input commit(s).
* `MERGE_ANALYSIS_UNBORN`: the HEAD of the repository refers to a commit which does not
  exist. It is not possible to merge, but it may be possible to checkout the input
  commits.
"""
@enum(GIT_MERGE_ANALYSIS, MERGE_ANALYSIS_NONE        = 0,
                          MERGE_ANALYSIS_NORMAL      = 1 << 0,
                          MERGE_ANALYSIS_UP_TO_DATE  = 1 << 1,
                          MERGE_ANALYSIS_FASTFORWARD = 1 << 2,
                          MERGE_ANALYSIS_UNBORN      = 1 << 3)

# reset
const RESET_SOFT  = Cint(1) # Move the head to the given commit
const RESET_MIXED = Cint(2) # SOFT plus reset index to the commit
const RESET_HARD  = Cint(3) # MIXED plus changes in working tree discarded

# rebase
""" Options for what rebase operation is currently being performed on a commit.
* `REBASE_OPERATION_PICK`: cherry-pick the commit in question.
* `REBASE_OPERATION_REWORD`: cherry-pick the commit in question, but rewrite its
  message using the prompt.
* `REBASE_OPERATION_EDIT`: cherry-pick the commit in question, but allow the user
  to edit the commit's contents and its message.
* `REBASE_OPERATION_SQUASH`: squash the commit in question into the previous commit.
  The commit messages of the two commits will be merged.
* `REBASE_OPERATION_FIXUP`: squash the commit in question into the previous commit.
  Only the commit message of the previous commit will be used.
* `REBASE_OPERATION_EXEC`: do not cherry-pick a commit. Run a command and continue if
  the command exits successfully.
"""
@enum(GIT_REBASE_OPERATION, REBASE_OPERATION_PICK   = Cint(0),
                            REBASE_OPERATION_REWORD = Cint(1),
                            REBASE_OPERATION_EDIT   = Cint(2),
                            REBASE_OPERATION_SQUASH = Cint(3),
                            REBASE_OPERATION_FIXUP  = Cint(4),
                            REBASE_OPERATION_EXEC   = Cint(5))

# fetch_prune
const FETCH_PRUNE_UNSPECIFIED = Cint(0)
const FETCH_PRUNE             = Cint(1)
const FETCH_NO_PRUNE          = Cint(2)

# remote_autotag
const REMOTE_DOWNLOAD_TAGS_UNSPECIFIED = Cint(0)
const REMOTE_DOWNLOAD_TAGS_AUTO        = Cint(1)
const REMOTE_DOWNLOAD_TAGS_NONE        = Cint(2)
const REMOTE_DOWNLOAD_TAGS_ALL         = Cint(3)

# remote_redirect
const REMOTE_REDIRECT_NONE    = Cuint(1 << 0)
const REMOTE_REDIRECT_INITIAL = Cuint(1 << 1)
const REMOTE_REDIRECT_ALL     = Cuint(1 << 2)

# clone
const CLONE_LOCAL_AUTO     = Cint(0)
const CLONE_LOCAL          = Cint(1)
const CLONE_NO_LOCAL       = Cint(2)
const CLONE_LOCAL_NO_LINKS = Cint(3)

# describe
const DESCRIBE_DEFAULT = Cuint(0)
const DESCRIBE_TAGS    = Cuint(1 << 0)
const DESCRIBE_ALL     = Cuint(1 << 1)

# status
const STATUS_CURRENT          = Cuint(0)
const STATUS_INDEX_NEW        = Cuint(1 << 0)
const STATUS_INDEX_MODIFIED   = Cuint(1 << 1)
const STATUS_INDEX_DELETED    = Cuint(1 << 2)
const STATUS_INDEX_RENAMED    = Cuint(1 << 3)
const STATUS_INDEX_TYPECHANGE = Cuint(1 << 4)
const STATUS_WT_NEW           = Cuint(1 << 7)
const STATUS_WT_MODIFIED      = Cuint(1 << 8)
const STATUS_WT_DELETED       = Cuint(1 << 9)
const STATUS_WT_TYPECHANGE    = Cuint(1 << 10)
const STATUS_WT_RENAMED       = Cuint(1 << 11)
const STATUS_WT_UNREADABLE    = Cuint(1 << 12)
const STATUS_IGNORED          = Cuint(1 << 14)
const STATUS_CONFLICTED       = Cuint(1 << 15)

# status show
const STATUS_SHOW_INDEX_AND_WORKDIR = Cint(0)
const STATUS_SHOW_INDEX_ONLY        = Cint(1)
const STATUS_SHOW_WORKDIR_ONLY      = Cint(2)

# status options
const STATUS_OPT_INCLUDE_UNTRACKED                = Cuint(1 << 0)
const STATUS_OPT_INCLUDE_IGNORED                  = Cuint(1 << 1)
const STATUS_OPT_INCLUDE_UNMODIFIED               = Cuint(1 << 2)
const STATUS_OPT_EXCLUDE_SUBMODULES               = Cuint(1 << 3)
const STATUS_OPT_RECURSE_UNTRACKED_DIRS           = Cuint(1 << 4)
const STATUS_OPT_DISABLE_PATHSPEC_MATCH           = Cuint(1 << 5)
const STATUS_OPT_RECURSE_IGNORED_DIRS             = Cuint(1 << 6)
const STATUS_OPT_RENAMES_HEAD_TO_INDEX            = Cuint(1 << 7)
const STATUS_OPT_RENAMES_INDEX_TO_WORKDIR         = Cuint(1 << 8)
const STATUS_OPT_SORT_CASE_SENSITIVELY            = Cuint(1 << 9)
const STATUS_OPT_SORT_CASE_INSENSITIVELY          = Cuint(1 << 10)
const STATUS_OPT_RENAMES_FROM_REWRITES            = Cuint(1 << 11)
const STATUS_OPT_NO_REFRESH                       = Cuint(1 << 12)
const STATUS_OPT_UPDATE_INDEX                     = Cuint(1 << 13)
const STATUS_OPT_INCLUDE_UNREADABLE               = Cuint(1 << 14)
const STATUS_OPT_INCLUDE_UNREADABLE_AS_UNTRACKED  = Cuint(1 << 15)

# certificate types from `enum git_cert_t` in `cert.h`.
const CERT_TYPE_TLS = 1 # GIT_CERT_X509
const CERT_TYPE_SSH = 2 # GIT_CERT_HOSTKEY_LIBSSH2

# certificate callback return values
const PASSTHROUGH = -30
const CERT_REJECT = -1
const CERT_ACCEPT =  0

# certificate hash flags
const CERT_SSH_MD5    = 1 << 0
const CERT_SSH_SHA1   = 1 << 1
const CERT_SSH_SHA256 = 1 << 2

# libssh2 known host constants
const LIBSSH2_KNOWNHOST_TYPE_PLAIN  = 1
const LIBSSH2_KNOWNHOST_TYPE_SHA1   = 2
const LIBSSH2_KNOWNHOST_TYPE_CUSTOM = 3

const LIBSSH2_KNOWNHOST_KEYENC_RAW    = 1 << 16
const LIBSSH2_KNOWNHOST_KEYENC_BASE64 = 2 << 16

# libssh2 host check return values
const LIBSSH2_KNOWNHOST_CHECK_MATCH    = 0
const LIBSSH2_KNOWNHOST_CHECK_MISMATCH = 1
const LIBSSH2_KNOWNHOST_CHECK_NOTFOUND = 2
const LIBSSH2_KNOWNHOST_CHECK_FAILURE  = 3

@enum(GIT_SUBMODULE_IGNORE, SUBMODULE_IGNORE_UNSPECIFIED  = -1, # use the submodule's configuration
                            SUBMODULE_IGNORE_NONE         = 1,  # any change or untracked == dirty
                            SUBMODULE_IGNORE_UNTRACKED    = 2,  # dirty if tracked files change
                            SUBMODULE_IGNORE_DIRTY        = 3,  # only dirty if HEAD moved
                            SUBMODULE_IGNORE_ALL          = 4)  # never dirty

"""
Option flags for `GitRepo`.

* `REPOSITORY_OPEN_NO_SEARCH` - Only open the repository if it can be immediately found in the `path`.  Do not walk up from the `path` looking at parent directories.
* `REPOSITORY_OPEN_CROSS_FS` - Unless this flag is set, open will not continue searching across filesystem boundaries. (E.g. Searching in a user's home directory `/home/user/source/` will not return `/.git/` as the found repo if `/` is a different filesystem than `/home`.)
* `REPOSITORY_OPEN_BARE` - Open repository as a bare repo regardless of core.bare config, and defer loading config file for faster setup.
"""
@enum(GIT_REPOSITORY_OPEN, REPOSITORY_OPEN_DEFAULT   = 0,
                           REPOSITORY_OPEN_NO_SEARCH = 1<<0,
                           REPOSITORY_OPEN_CROSS_FS  = 1<<1,
                           REPOSITORY_OPEN_BARE      = 1<<2)

@enum(GIT_BRANCH, BRANCH_LOCAL = 1, BRANCH_REMOTE = 2)

@enum(GIT_FILEMODE, FILEMODE_UNREADABLE          = 0o000000,
                    FILEMODE_TREE                = 0o040000,
                    FILEMODE_BLOB                = 0o100644,
                    FILEMODE_BLOB_EXECUTABLE     = 0o100755,
                    FILEMODE_LINK                = 0o120000,
                    FILEMODE_COMMIT              = 0o160000)

@enum(GIT_CREDTYPE, CREDTYPE_USERPASS_PLAINTEXT = Cuint(1 << 0),
                    CREDTYPE_SSH_KEY            = Cuint(1 << 1),
                    CREDTYPE_SSH_CUSTOM         = Cuint(1 << 2),
                    CREDTYPE_DEFAULT            = Cuint(1 << 3),
                    CREDTYPE_SSH_INTERACTIVE    = Cuint(1 << 4),
                    CREDTYPE_USERNAME           = Cuint(1 << 5),
                    CREDTYPE_SSH_MEMORY         = Cuint(1 << 6))

@enum(GIT_FEATURE, FEATURE_THREADS = Cuint(1 << 0),
                   FEATURE_HTTPS   = Cuint(1 << 1),
                   FEATURE_SSH     = Cuint(1 << 2),
                   FEATURE_NSEC    = Cuint(1 << 3))

if version() >= v"0.24.0"
    @doc """
    Priority level of a config file.

    These priority levels correspond to the natural escalation logic (from higher to lower) when searching for config entries in git.

    * `CONFIG_LEVEL_DEFAULT` - Open the global, XDG and system configuration files if any available.
    * `CONFIG_LEVEL_PROGRAMDATA` - System-wide on Windows, for compatibility with portable git
    * `CONFIG_LEVEL_SYSTEM` - System-wide configuration file; `/etc/gitconfig` on Linux systems
    * `CONFIG_LEVEL_XDG` - XDG compatible configuration file; typically `~/.config/git/config`
    * `CONFIG_LEVEL_GLOBAL` - User-specific configuration file (also called Global configuration file); typically `~/.gitconfig`
    * `CONFIG_LEVEL_LOCAL` - Repository specific configuration file; `\$WORK_DIR/.git/config` on non-bare repos
    * `CONFIG_LEVEL_APP` - Application specific configuration file; freely defined by applications
    * `CONFIG_HIGHEST_LEVEL` - Represents the highest level available config file (i.e. the most specific config file available that actually is loaded)
    """
    @enum(GIT_CONFIG, CONFIG_LEVEL_DEFAULT     = 0,
                      CONFIG_LEVEL_PROGRAMDATA = 1,
                      CONFIG_LEVEL_SYSTEM      = 2,
                      CONFIG_LEVEL_XDG         = 3,
                      CONFIG_LEVEL_GLOBAL      = 4,
                      CONFIG_LEVEL_LOCAL       = 5,
                      CONFIG_LEVEL_APP         = 6,
                      CONFIG_HIGHEST_LEVEL     =-1)
else
    @doc """
    Priority level of a config file.

    These priority levels correspond to the natural escalation logic (from higher to lower) when searching for config entries in git.

    * `CONFIG_LEVEL_DEFAULT` - Open the global, XDG and system configuration files if any available.
    * `CONFIG_LEVEL_SYSTEM` - System-wide configuration file; `/etc/gitconfig` on Linux systems
    * `CONFIG_LEVEL_XDG` - XDG compatible configuration file; typically `~/.config/git/config`
    * `CONFIG_LEVEL_GLOBAL` - User-specific configuration file (also called Global configuration file); typically `~/.gitconfig`
    * `CONFIG_LEVEL_LOCAL` - Repository specific configuration file; `\$WORK_DIR/.git/config` on non-bare repos
    * `CONFIG_LEVEL_APP` - Application specific configuration file; freely defined by applications
    * `CONFIG_HIGHEST_LEVEL` - Represents the highest level available config file (i.e. the most specific config file available that actually is loaded)
    """
    @enum(GIT_CONFIG, CONFIG_LEVEL_DEFAULT     = 0,
                      CONFIG_LEVEL_SYSTEM      = 1,
                      CONFIG_LEVEL_XDG         = 2,
                      CONFIG_LEVEL_GLOBAL      = 3,
                      CONFIG_LEVEL_LOCAL       = 4,
                      CONFIG_LEVEL_APP         = 5,
                      CONFIG_HIGHEST_LEVEL     =-1)
end

"""
Global library options.

These are used to select which global option to set or get and are used in `git_libgit2_opts()`.
"""
@enum(GIT_OPT, GET_MWINDOW_SIZE         = 0,
               SET_MWINDOW_SIZE         = 1,
               GET_MWINDOW_MAPPED_LIMIT = 2,
               SET_MWINDOW_MAPPED_LIMIT = 3,
               GET_SEARCH_PATH          = 4,
               SET_SEARCH_PATH          = 5,
               SET_CACHE_OBJECT_LIMIT   = 6,
               SET_CACHE_MAX_SIZE       = 7,
               ENABLE_CACHING           = 8,
               GET_CACHED_MEMORY        = 9,
               GET_TEMPLATE_PATH        = 10,
               SET_TEMPLATE_PATH        = 11,
               SET_SSL_CERT_LOCATIONS   = 12)

"""
Option flags for `GitProxy`.

* `PROXY_NONE`: do not attempt the connection through a proxy.
* `PROXY_AUTO`: attempt to figure out the proxy configuration from the git configuration.
* `PROXY_SPECIFIED`: connect using the URL given in the `url` field of this struct.
"""
@enum(GIT_PROXY, PROXY_NONE,
                 PROXY_AUTO,
                 PROXY_SPECIFIED)

# Available tracing levels.
@enum GIT_TRACE_LEVEL begin
    TRACE_NONE
    TRACE_FATAL
    TRACE_ERROR
    TRACE_WARN
    TRACE_INFO
    TRACE_DEBUG
    TRACE_TRACE
end

end
p   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LibGit2/src/types.jl_�      # This file is a part of Julia. License is MIT: https://julialang.org/license

using Base: something
import Base.@kwdef
import .Consts: GIT_SUBMODULE_IGNORE, GIT_MERGE_FILE_FAVOR, GIT_MERGE_FILE, GIT_CONFIG

const OID_RAWSZ = 20
const OID_HEXSZ = OID_RAWSZ * 2
const OID_MINPREFIXLEN = 4

abstract type AbstractGitHash end

"""
    GitHash

A git object identifier, based on the sha-1 hash. It is a $OID_RAWSZ byte string
($OID_HEXSZ hex digits) used to identify a `GitObject` in a repository.
"""
struct GitHash <: AbstractGitHash
    val::NTuple{OID_RAWSZ, UInt8}
    GitHash(val::NTuple{OID_RAWSZ, UInt8}) = new(val)
end
GitHash() = GitHash(ntuple(i->zero(UInt8), OID_RAWSZ))
GitHash(h::GitHash) = h

"""
    GitShortHash(hash::GitHash, len::Integer)

A shortened git object identifier, which can be used to identify a git object when it is
unique, consisting of the initial `len` hexadecimal digits of `hash` (the remaining digits
are ignored).
"""
struct GitShortHash <: AbstractGitHash
    hash::GitHash   # underlying hash: unused digits are ignored
    len::Csize_t    # length in hex digits
end


"""
    LibGit2.TimeStruct

Time in a signature.
Matches the [`git_time`](https://libgit2.org/libgit2/#HEAD/type/git_time) struct.
"""
struct TimeStruct
    time::Int64     # time in seconds from epoch
    offset::Cint    # timezone offset in minutes
    @static if LibGit2.VERSION >= v"0.27.0"
        sign::Cchar
    end
end

"""
    LibGit2.SignatureStruct

An action signature (e.g. for committers, taggers, etc).
Matches the [`git_signature`](https://libgit2.org/libgit2/#HEAD/type/git_signature) struct.

The fields represent:
  * `name`: The full name of the committer or author of the commit.
  * `email`: The email at which the committer/author can be contacted.
  * `when`: a [`TimeStruct`](@ref) indicating when the commit was
     authored/committed into the repository.
"""
struct SignatureStruct
    name::Ptr{UInt8}  # full name of the author
    email::Ptr{UInt8} # email of the author
    when::TimeStruct  # time when the action happened
end

"""
    LibGit2.StrArrayStruct

A LibGit2 representation of an array of strings.
Matches the [`git_strarray`](https://libgit2.org/libgit2/#HEAD/type/git_strarray) struct.

When fetching data from LibGit2, a typical usage would look like:
```julia
sa_ref = Ref(StrArrayStruct())
@check ccall(..., (Ptr{StrArrayStruct},), sa_ref)
res = convert(Vector{String}, sa_ref[])
free(sa_ref)
```
In particular, note that `LibGit2.free` should be called afterward on the `Ref` object.

Conversely, when passing a vector of strings to LibGit2, it is generally simplest to rely
on implicit conversion:
```julia
strs = String[...]
@check ccall(..., (Ptr{StrArrayStruct},), strs)
```
Note that no call to `free` is required as the data is allocated by Julia.
"""
struct StrArrayStruct
   strings::Ptr{Cstring}
   count::Csize_t
end
StrArrayStruct() = StrArrayStruct(C_NULL, 0)

function free(sa_ref::Base.Ref{StrArrayStruct})
    ensure_initialized()
    ccall((:git_strarray_free, libgit2), Cvoid, (Ptr{StrArrayStruct},), sa_ref)
end

"""
    LibGit2.Buffer

A data buffer for exporting data from libgit2.
Matches the [`git_buf`](https://libgit2.org/libgit2/#HEAD/type/git_buf) struct.

When fetching data from LibGit2, a typical usage would look like:
```julia
buf_ref = Ref(Buffer())
@check ccall(..., (Ptr{Buffer},), buf_ref)
# operation on buf_ref
free(buf_ref)
```
In particular, note that `LibGit2.free` should be called afterward on the `Ref` object.
"""
struct Buffer
    ptr::Ptr{Cchar}
    asize::Csize_t
    size::Csize_t
end
Buffer() = Buffer(C_NULL, 0, 0)

function free(buf_ref::Base.Ref{Buffer})
    ensure_initialized()
    ccall((:git_buf_free, libgit2), Cvoid, (Ptr{Buffer},), buf_ref)
end

"""
    LibGit2.CheckoutOptions

Matches the [`git_checkout_options`](https://libgit2.org/libgit2/#HEAD/type/git_checkout_options) struct.

The fields represent:
  * `version`: version of the struct in use, in case this changes later. For now, always `1`.
  * `checkout_strategy`: determine how to handle conflicts and whether to force the
     checkout/recreate missing files.
  * `disable_filters`: if nonzero, do not apply filters like CLRF (to convert file newlines between UNIX and DOS).
  * `dir_mode`: read/write/access mode for any directories involved in the checkout. Default is `0755`.
  * `file_mode`: read/write/access mode for any files involved in the checkout.
     Default is `0755` or `0644`, depending on the blob.
  * `file_open_flags`: bitflags used to open any files during the checkout.
  * `notify_flags`: Flags for what sort of conflicts the user should be notified about.
  * `notify_cb`: An optional callback function to notify the user if a checkout conflict occurs.
     If this function returns a non-zero value, the checkout will be cancelled.
  * `notify_payload`: Payload for the notify callback function.
  * `progress_cb`: An optional callback function to display checkout progress.
  * `progress_payload`: Payload for the progress callback.
  * `paths`: If not empty, describes which paths to search during the checkout.
     If empty, the checkout will occur over all files in the repository.
  * `baseline`: Expected content of the [`workdir`](@ref), captured in a (pointer to a)
     [`GitTree`](@ref). Defaults to the state of the tree at HEAD.
  * `baseline_index`: Expected content of the [`workdir`](@ref), captured in a (pointer to a)
     `GitIndex`. Defaults to the state of the index at HEAD.
  * `target_directory`: If not empty, checkout to this directory instead of the `workdir`.
  * `ancestor_label`: In case of conflicts, the name of the common ancestor side.
  * `our_label`: In case of conflicts, the name of "our" side.
  * `their_label`: In case of conflicts, the name of "their" side.
  * `perfdata_cb`: An optional callback function to display performance data.
  * `perfdata_payload`: Payload for the performance callback.
"""
@kwdef struct CheckoutOptions
    version::Cuint               = Cuint(1)

    checkout_strategy::Cuint     = Consts.CHECKOUT_SAFE

    disable_filters::Cint        = Cint(0)
    dir_mode::Cuint              = Cuint(0)
    file_mode::Cuint             = Cuint(0)
    file_open_flags::Cint        = Cint(0)

    notify_flags::Cuint          = Consts.CHECKOUT_NOTIFY_NONE
    notify_cb::Ptr{Cvoid}        = C_NULL
    notify_payload::Any          = nothing

    progress_cb::Ptr{Cvoid}      = C_NULL
    progress_payload::Any        = nothing

    paths::StrArrayStruct        = StrArrayStruct()

    baseline::Ptr{Cvoid}         = C_NULL
    baseline_index::Ptr{Cvoid}   = C_NULL

    target_directory::Cstring    = Cstring(C_NULL)
    ancestor_label::Cstring      = Cstring(C_NULL)
    our_label::Cstring           = Cstring(C_NULL)
    their_label::Cstring         = Cstring(C_NULL)

    perfdata_cb::Ptr{Cvoid}      = C_NULL
    perfdata_payload::Any        = Nothing
end
@assert Base.allocatedinline(CheckoutOptions)

"""
    LibGit2.TransferProgress

Transfer progress information used by the `transfer_progress` remote callback.
Matches the [`git_indexer_progress`](https://libgit2.org/libgit2/#HEAD/type/git_indexer_progress) struct.
"""
@kwdef struct TransferProgress
    total_objects::Cuint    = Cuint(0)
    indexed_objects::Cuint  = Cuint(0)
    received_objects::Cuint = Cuint(0)
    local_objects::Cuint    = Cuint(0)
    total_deltas::Cuint     = Cuint(0)
    indexed_deltas::Cuint   = Cuint(0)
    received_bytes::Csize_t = Csize_t(0)
end
@assert Base.allocatedinline(TransferProgress)

"""
    LibGit2.RemoteCallbacks

Callback settings.
Matches the [`git_remote_callbacks`](https://libgit2.org/libgit2/#HEAD/type/git_remote_callbacks) struct.
"""
@kwdef struct RemoteCallbacks
    version::Cuint                     = Cuint(1)
    sideband_progress::Ptr{Cvoid}      = C_NULL
    completion::Ptr{Cvoid}             = C_NULL
    credentials::Ptr{Cvoid}            = C_NULL
    certificate_check::Ptr{Cvoid}      = certificate_cb()
    transfer_progress::Ptr{Cvoid}      = C_NULL
    update_tips::Ptr{Cvoid}            = C_NULL
    pack_progress::Ptr{Cvoid}          = C_NULL
    push_transfer_progress::Ptr{Cvoid} = C_NULL
    push_update_reference::Ptr{Cvoid}  = C_NULL
    push_negotiation::Ptr{Cvoid}       = C_NULL
    transport::Ptr{Cvoid}              = C_NULL
    @static if LibGit2.VERSION >= v"1.2.0"
        remote_ready::Ptr{Cvoid}       = C_NULL
    end
    payload::Any                       = nothing
    @static if LibGit2.VERSION >= v"0.99.0"
        resolve_url::Ptr{Cvoid}        = C_NULL
    end
end
@assert Base.allocatedinline(RemoteCallbacks)

"""
    LibGit2.Callbacks

A dictionary which containing the callback name as the key and the value as a tuple of the
callback function and payload.

The `Callback` dictionary to construct `RemoteCallbacks` allows each callback to use a
distinct payload. Each callback, when called, will receive `Dict` which will hold the
callback's custom payload which can be accessed using the callback name.

# Examples
```julia-repl
julia> c = LibGit2.Callbacks(:credentials => (LibGit2.credentials_cb(), LibGit2.CredentialPayload()));

julia> LibGit2.clone(url, callbacks=c);
```

See [`git_remote_callbacks`](https://libgit2.org/libgit2/#HEAD/type/git_remote_callbacks)
for details on supported callbacks.
"""
const Callbacks = Dict{Symbol, Tuple{Ptr{Cvoid}, Any}}

function RemoteCallbacks(c::Callbacks)
    callbacks = Dict{Symbol, Ptr{Cvoid}}()
    payloads = Dict{Symbol, Any}()

    for (name, (callback, payload)) in c
        callbacks[name] = callback
        payloads[name] = payload
    end

    RemoteCallbacks(; payload=payloads, callbacks...)
end


"""
    LibGit2.ProxyOptions

Options for connecting through a proxy.

Matches the [`git_proxy_options`](https://libgit2.org/libgit2/#HEAD/type/git_proxy_options) struct.

The fields represent:
  * `version`: version of the struct in use, in case this changes later. For now, always `1`.
  * `proxytype`: an `enum` for the type of proxy to use.
     Defined in [`git_proxy_t`](https://libgit2.org/libgit2/#HEAD/type/git_proxy_t).
     The corresponding Julia enum is `GIT_PROXY` and has values:
     - `PROXY_NONE`: do not attempt the connection through a proxy.
     - `PROXY_AUTO`: attempt to figure out the proxy configuration from the git configuration.
     - `PROXY_SPECIFIED`: connect using the URL given in the `url` field of this struct.
     Default is to auto-detect the proxy type.
  * `url`: the URL of the proxy.
  * `credential_cb`: a pointer to a callback function which will be called if the remote
    requires authentication to connect.
  * `certificate_cb`: a pointer to a callback function which will be called if certificate
    verification fails. This lets the user decide whether or not to keep connecting. If
    the function returns `1`, connecting will be allowed. If it returns `0`, the connection
    will not be allowed. A negative value can be used to return errors.
  * `payload`: the payload to be provided to the two callback functions.

# Examples
```julia-repl
julia> fo = LibGit2.FetchOptions(
           proxy_opts = LibGit2.ProxyOptions(url = Cstring("https://my_proxy_url.com")))

julia> fetch(remote, "master", options=fo)
```
"""
@kwdef struct ProxyOptions
    version::Cuint               = Cuint(1)
    proxytype::Consts.GIT_PROXY  = Consts.PROXY_AUTO
    url::Cstring                 = Cstring(C_NULL)
    credential_cb::Ptr{Cvoid}    = C_NULL
    certificate_cb::Ptr{Cvoid}   = certificate_cb()
    payload::Any                 = nothing
end
@assert Base.allocatedinline(ProxyOptions)

"""
    LibGit2.FetchOptions

Matches the [`git_fetch_options`](https://libgit2.org/libgit2/#HEAD/type/git_fetch_options) struct.

The fields represent:
  * `version`: version of the struct in use, in case this changes later. For now, always `1`.
  * `callbacks`: remote callbacks to use during the fetch.
  * `prune`: whether to perform a prune after the fetch or not. The default is to
     use the setting from the `GitConfig`.
  * `update_fetchhead`: whether to update the [`FetchHead`](@ref) after the fetch.
     The default is to perform the update, which is the normal git behavior.
  * `download_tags`: whether to download tags present at the remote or not. The default
     is to request the tags for objects which are being downloaded anyway from the server.
  * `proxy_opts`: options for connecting to the remote through a proxy. See [`ProxyOptions`](@ref).
     Only present on libgit2 versions newer than or equal to 0.25.0.
  * `custom_headers`: any extra headers needed for the fetch. Only present on libgit2 versions
     newer than or equal to 0.24.0.
"""
@kwdef struct FetchOptions
    version::Cuint                     = Cuint(1)
    callbacks::RemoteCallbacks         = RemoteCallbacks()
    prune::Cint                        = Consts.FETCH_PRUNE_UNSPECIFIED
    update_fetchhead::Cint             = Cint(1)
    download_tags::Cint                = Consts.REMOTE_DOWNLOAD_TAGS_AUTO
    @static if LibGit2.VERSION >= v"0.25.0"
        proxy_opts::ProxyOptions       = ProxyOptions()
    end
    @static if LibGit2.VERSION >= v"1.4.0"
        follow_redirects::Cuint        = Cuint(0)
    end
    @static if LibGit2.VERSION >= v"0.24.0"
        custom_headers::StrArrayStruct = StrArrayStruct()
    end
end
@assert Base.allocatedinline(FetchOptions)


"""
    LibGit2.CloneOptions

Matches the [`git_clone_options`](https://libgit2.org/libgit2/#HEAD/type/git_clone_options) struct.

The fields represent:
  * `version`: version of the struct in use, in case this changes later. For now, always `1`.
  * `checkout_opts`: The options for performing the checkout of the remote as part of the clone.
  * `fetch_opts`: The options for performing the pre-checkout fetch of the remote as part of the clone.
  * `bare`: If `0`, clone the full remote repository. If non-zero, perform a bare clone, in which
     there is no local copy of the source files in the repository and the [`gitdir`](@ref) and [`workdir`](@ref)
     are the same.
  * `localclone`: Flag whether to clone a local object database or do a fetch. The default is to let git decide.
     It will not use the git-aware transport for a local clone, but will use it for URLs which begin with `file://`.
  * `checkout_branch`: The name of the branch to checkout. If an empty string, the default branch of the
     remote will be checked out.
  * `repository_cb`: An optional callback which will be used to create the *new* repository into which
     the clone is made.
  * `repository_cb_payload`: The payload for the repository callback.
  * `remote_cb`: An optional callback used to create the [`GitRemote`](@ref) before making the clone from it.
  * `remote_cb_payload`: The payload for the remote callback.
"""
@kwdef struct CloneOptions
    version::Cuint                      = Cuint(1)
    checkout_opts::CheckoutOptions      = CheckoutOptions()
    fetch_opts::FetchOptions            = FetchOptions()
    bare::Cint                          = Cint(0)
    localclone::Cint                    = Consts.CLONE_LOCAL_AUTO
    checkout_branch::Cstring            = Cstring(C_NULL)
    repository_cb::Ptr{Cvoid}           = C_NULL
    repository_cb_payload::Any          = nothing
    remote_cb::Ptr{Cvoid}               = C_NULL
    remote_cb_payload::Any              = nothing
end
@assert Base.allocatedinline(CloneOptions)

"""
    LibGit2.DiffOptionsStruct

Matches the [`git_diff_options`](https://libgit2.org/libgit2/#HEAD/type/git_diff_options) struct.

The fields represent:
  * `version`: version of the struct in use, in case this changes later. For now, always `1`.
  * `flags`: flags controlling which files will appear in the diff. Defaults to `DIFF_NORMAL`.
  * `ignore_submodules`: whether to look at files in submodules or not. Defaults to
    `SUBMODULE_IGNORE_UNSPECIFIED`, which means the submodule's configuration will control
     whether it appears in the diff or not.
  * `pathspec`: path to files to include in the diff. Default is to use all files in the repository.
  * `notify_cb`: optional callback which will notify the user of changes to the diff as file deltas are
     added to it.
  * `progress_cb`: optional callback which will display diff progress. Only relevant on libgit2 versions
     at least as new as 0.24.0.
  * `payload`: the payload to pass to `notify_cb` and `progress_cb`.
  * `context_lines`: the number of *unchanged* lines used to define the edges of a hunk.
     This is also the number of lines which will be shown before/after a hunk to provide
     context. Default is 3.
  * `interhunk_lines`: the maximum number of *unchanged* lines *between* two separate
     hunks allowed before the hunks will be combined. Default is 0.
  * `id_abbrev`: sets the length of the abbreviated [`GitHash`](@ref) to print.
     Default is `7`.
  * `max_size`: the maximum file size of a blob. Above this size, it will be treated
     as a binary blob. The default is 512 MB.
  * `old_prefix`: the virtual file directory in which to place old files on one side
     of the diff. Default is `"a"`.
  * `new_prefix`: the virtual file directory in which to place new files on one side
     of the diff. Default is `"b"`.
"""
@kwdef struct DiffOptionsStruct
    version::Cuint                           = Consts.DIFF_OPTIONS_VERSION
    flags::UInt32                            = Consts.DIFF_NORMAL

    # options controlling which files are in the diff
    ignore_submodules::GIT_SUBMODULE_IGNORE  = Consts.SUBMODULE_IGNORE_UNSPECIFIED
    pathspec::StrArrayStruct                 = StrArrayStruct()
    notify_cb::Ptr{Cvoid}                    = C_NULL
    @static if LibGit2.VERSION >= v"0.24.0"
        progress_cb::Ptr{Cvoid}              = C_NULL
    end
    payload::Any                             = nothing

    # options controlling how the diff text is generated
    context_lines::UInt32                    = UInt32(3)
    interhunk_lines::UInt32                  = UInt32(0)
    id_abbrev::UInt16                        = UInt16(7)
    max_size::Int64                          = Int64(512*1024*1024) #512Mb
    old_prefix::Cstring                      = Cstring(C_NULL)
    new_prefix::Cstring                      = Cstring(C_NULL)
end
@assert Base.allocatedinline(DiffOptionsStruct)

"""
    LibGit2.DescribeOptions

Matches the [`git_describe_options`](https://libgit2.org/libgit2/#HEAD/type/git_describe_options) struct.

The fields represent:
  * `version`: version of the struct in use, in case this changes later. For now, always `1`.
  * `max_candidates_tags`: consider this many most recent tags in `refs/tags` to describe a commit.
     Defaults to 10 (so that the 10 most recent tags would be examined to see if they describe a commit).
  * `describe_strategy`: whether to consider all entries in `refs/tags` (equivalent to `git-describe --tags`)
     or all entries in `refs/` (equivalent to `git-describe --all`). The default is to only show annotated tags.
     If `Consts.DESCRIBE_TAGS` is passed, all tags, annotated or not, will be considered.
     If `Consts.DESCRIBE_ALL` is passed, any ref in `refs/` will be considered.
  * `pattern`: only consider tags which match `pattern`. Supports glob expansion.
  * `only_follow_first_parent`: when finding the distance from a matching reference to the described
     object, only consider the distance from the first parent.
  * `show_commit_oid_as_fallback`: if no matching reference can be found which describes a commit, show the
     commit's [`GitHash`](@ref) instead of throwing an error (the default behavior).
"""
@kwdef struct DescribeOptions
    version::Cuint                    = Cuint(1)
    max_candidates_tags::Cuint        = Cuint(10)
    describe_strategy::Cuint          = Consts.DESCRIBE_DEFAULT

    pattern::Cstring                  = Cstring(C_NULL)
    only_follow_first_parent::Cint    = Cint(0)
    show_commit_oid_as_fallback::Cint = Cint(0)
end
@assert Base.allocatedinline(DescribeOptions)

"""
    LibGit2.DescribeFormatOptions

Matches the [`git_describe_format_options`](https://libgit2.org/libgit2/#HEAD/type/git_describe_format_options) struct.

The fields represent:
  * `version`: version of the struct in use, in case this changes later. For now, always `1`.
  * `abbreviated_size`: lower bound on the size of the abbreviated `GitHash` to use, defaulting to `7`.
  * `always_use_long_format`: set to `1` to use the long format for strings even if a short format can be used.
  * `dirty_suffix`: if set, this will be appended to the end of the description string if the [`workdir`](@ref) is dirty.
"""
@kwdef struct DescribeFormatOptions
    version::Cuint               = Cuint(1)
    abbreviated_size::Cuint      = Cuint(7)
    always_use_long_format::Cint = Cint(0)
    dirty_suffix::Cstring        = Cstring(C_NULL)
end
@assert Base.allocatedinline(DescribeFormatOptions)

"""
    LibGit2.DiffFile

Description of one side of a delta.
Matches the [`git_diff_file`](https://libgit2.org/libgit2/#HEAD/type/git_diff_file) struct.

The fields represent:
  * `id`: the [`GitHash`](@ref) of the item in the diff. If the item is empty on this
     side of the diff (for instance, if the diff is of the removal of a file), this will
     be `GitHash(0)`.
  * `path`: a `NULL` terminated path to the item relative to the working directory of the repository.
  * `size`: the size of the item in bytes.
  * `flags`: a combination of the [`git_diff_flag_t`](https://libgit2.org/libgit2/#HEAD/type/git_diff_flag_t)
     flags. The `i`th bit of this integer sets the `i`th flag.
  * `mode`: the [`stat`](@ref) mode for the item.
  * `id_abbrev`: only present in LibGit2 versions newer than or equal to `0.25.0`.
     The length of the `id` field when converted using [`string`](@ref). Usually equal to `OID_HEXSZ` ($OID_HEXSZ).
"""
struct DiffFile
    id::GitHash
    path::Cstring
    size::Int64
    flags::UInt32
    mode::UInt16
    @static if LibGit2.VERSION >= v"0.25.0"
        id_abbrev::UInt16
    end
end

function Base.show(io::IO, df::DiffFile)
    println(io, "DiffFile:")
    println(io, "Oid: $(df.id)")
    println(io, "Path: $(df.path)")
    println(io, "Size: $(df.size)")
end

"""
    LibGit2.DiffDelta

Description of changes to one entry.
Matches the [`git_diff_delta`](https://libgit2.org/libgit2/#HEAD/type/git_diff_delta) struct.

The fields represent:
  * `status`: One of `Consts.DELTA_STATUS`, indicating whether the file has been added/modified/deleted.
  * `flags`: Flags for the delta and the objects on each side. Determines whether to treat the file(s)
     as binary/text, whether they exist on each side of the diff, and whether the object ids are known
     to be correct.
  * `similarity`: Used to indicate if a file has been renamed or copied.
  * `nfiles`: The number of files in the delta (for instance, if the delta
     was run on a submodule commit id, it may contain more than one file).
  * `old_file`: A [`DiffFile`](@ref) containing information about the file(s) before the changes.
  * `new_file`: A [`DiffFile`](@ref) containing information about the file(s) after the changes.
"""
struct DiffDelta
    status::Cint
    flags::UInt32
    similarity::UInt16
    nfiles::UInt16
    old_file::DiffFile
    new_file::DiffFile
end

function Base.show(io::IO, dd::DiffDelta)
    println(io, "DiffDelta:")
    println(io, "Status: $(Consts.DELTA_STATUS(dd.status))")
    println(io, "Number of files: $(dd.nfiles)")
    println(io, "Old file:\n$(dd.old_file)")
    println(io, "New file:\n$(dd.new_file)")
end

"""
    LibGit2.MergeOptions

Matches the [`git_merge_options`](https://libgit2.org/libgit2/#HEAD/type/git_merge_options) struct.

The fields represent:
  * `version`: version of the struct in use, in case this changes later. For now, always `1`.
  * `flags`: an `enum` for flags describing merge behavior.
     Defined in [`git_merge_flag_t`](https://github.com/libgit2/libgit2/blob/HEAD/include/git2/merge.h#L95).
     The corresponding Julia enum is `GIT_MERGE` and has values:
     - `MERGE_FIND_RENAMES`: detect if a file has been renamed between the common
       ancestor and the "ours" or "theirs" side of the merge. Allows merges where
       a file has been renamed.
     - `MERGE_FAIL_ON_CONFLICT`: exit immediately if a conflict is found rather
       than trying to resolve it.
     - `MERGE_SKIP_REUC`: do not write the REUC extension on the index resulting
       from the merge.
     - `MERGE_NO_RECURSIVE`: if the commits being merged have multiple merge bases,
       use the first one, rather than trying to recursively merge the bases.
  * `rename_threshold`: how similar two files must to consider one a rename of the other.
    This is an integer that sets the percentage similarity. The default is 50.
  * `target_limit`: the maximum number of files to compare with to look for renames.
    The default is 200.
  * `metric`: optional custom function to use to determine the similarity between two
    files for rename detection.
  * `recursion_limit`: the upper limit on the number of merges of common ancestors to
    perform to try to build a new virtual merge base for the merge. The default is no
    limit. This field is only present on libgit2 versions newer than 0.24.0.
  * `default_driver`: the merge driver to use if both sides have changed. This field
    is only present on libgit2 versions newer than 0.25.0.
  * `file_favor`: how to handle conflicting file contents for the `text` driver.
    - `MERGE_FILE_FAVOR_NORMAL`: if both sides of the merge have changes to a section,
       make a note of the conflict in the index which `git checkout` will use to create
       a merge file, which the user can then reference to resolve the conflicts. This is
       the default.
    - `MERGE_FILE_FAVOR_OURS`: if both sides of the merge have changes to a section,
       use the version in the "ours" side of the merge in the index.
    - `MERGE_FILE_FAVOR_THEIRS`: if both sides of the merge have changes to a section,
       use the version in the "theirs" side of the merge in the index.
    - `MERGE_FILE_FAVOR_UNION`: if both sides of the merge have changes to a section,
       include each unique line from both sides in the file which is put into the index.
  * `file_flags`: guidelines for merging files.
"""
@kwdef struct MergeOptions
    version::Cuint                    = Cuint(1)
    flags::Cint                       = Cint(0)
    rename_threshold::Cuint           = Cuint(50)
    target_limit::Cuint               = Cuint(200)
    metric::Ptr{Cvoid}                = C_NULL
    @static if LibGit2.VERSION >= v"0.24.0"
        recursion_limit::Cuint        = Cuint(0)
    end
    @static if LibGit2.VERSION >= v"0.25.0"
        default_driver::Cstring       = Cstring(C_NULL)
    end
    file_favor::GIT_MERGE_FILE_FAVOR  = Consts.MERGE_FILE_FAVOR_NORMAL
    file_flags::GIT_MERGE_FILE        = Consts.MERGE_FILE_DEFAULT
end
@assert Base.allocatedinline(MergeOptions)

"""
    LibGit2.BlameOptions

Matches the [`git_blame_options`](https://libgit2.org/libgit2/#HEAD/type/git_blame_options) struct.

The fields represent:
  * `version`: version of the struct in use, in case this changes later. For now, always `1`.
  * `flags`: one of `Consts.BLAME_NORMAL` or `Consts.BLAME_FIRST_PARENT` (the other blame flags
     are not yet implemented by libgit2).
  * `min_match_characters`: the minimum number of *alphanumeric* characters which much change
    in a commit in order for the change to be associated with that commit. The default is 20.
    Only takes effect if one of the `Consts.BLAME_*_COPIES` flags are used, which libgit2 does
    not implement yet.
  * `newest_commit`: the [`GitHash`](@ref) of the newest commit from which to look at changes.
  * `oldest_commit`: the [`GitHash`](@ref) of the oldest commit from which to look at changes.
  * `min_line`: the first line of the file from which to starting blaming. The default is `1`.
  * `max_line`: the last line of the file to which to blame. The default is `0`, meaning the
    last line of the file.
"""
@kwdef struct BlameOptions
    version::Cuint                    = Cuint(1)
    flags::UInt32                     = UInt32(0)
    min_match_characters::UInt16      = UInt16(20)
    newest_commit::GitHash            = GitHash()
    oldest_commit::GitHash            = GitHash()
    min_line::Csize_t                 = Csize_t(1)
    max_line::Csize_t                 = Csize_t(0)
end
@assert Base.allocatedinline(BlameOptions)


"""
    LibGit2.PushOptions

Matches the [`git_push_options`](https://libgit2.org/libgit2/#HEAD/type/git_push_options) struct.

The fields represent:
  * `version`: version of the struct in use, in case this changes later. For now, always `1`.
  * `parallelism`: if a pack file must be created, this variable sets the number of worker
     threads which will be spawned by the packbuilder. If `0`, the packbuilder will auto-set
     the number of threads to use. The default is `1`.
  * `callbacks`: the callbacks (e.g. for authentication with the remote) to use for the push.
  * `proxy_opts`: only relevant if the LibGit2 version is greater than or equal to `0.25.0`.
     Sets options for using a proxy to communicate with a remote. See [`ProxyOptions`](@ref)
     for more information.
  * `custom_headers`: only relevant if the LibGit2 version is greater than or equal to `0.24.0`.
     Extra headers needed for the push operation.
"""
@kwdef struct PushOptions
    version::Cuint                     = Cuint(1)
    parallelism::Cint                  = Cint(1)
    callbacks::RemoteCallbacks         = RemoteCallbacks()
    @static if LibGit2.VERSION >= v"0.25.0"
        proxy_opts::ProxyOptions       = ProxyOptions()
    end
    @static if LibGit2.VERSION >= v"1.4.0"
        follow_redirects::Cuint        = Cuint(0)
    end
    @static if LibGit2.VERSION >= v"0.24.0"
        custom_headers::StrArrayStruct = StrArrayStruct()
    end
end
@assert Base.allocatedinline(PushOptions)


"""
    LibGit2.CherrypickOptions

Matches the [`git_cherrypick_options`](https://libgit2.org/libgit2/#HEAD/type/git_cherrypick_options) struct.

The fields represent:
  * `version`: version of the struct in use, in case this changes later. For now, always `1`.
  * `mainline`: if cherrypicking a merge commit, specifies the parent number (starting at `1`)
    which will allow cherrypick to apply the changes relative to that parent. Only relevant if
    cherrypicking a merge commit. Default is `0`.
  * `merge_opts`: options for merging the changes in. See [`MergeOptions`](@ref) for more information.
  * `checkout_opts`: options for the checkout of the commit being cherrypicked. See [`CheckoutOptions`](@ref)
     for more information.
"""
@kwdef struct CherrypickOptions
    version::Cuint = Cuint(1)
    mainline::Cuint = Cuint(0)
    merge_opts::MergeOptions = MergeOptions()
    checkout_opts::CheckoutOptions = CheckoutOptions()
end
@assert Base.allocatedinline(CherrypickOptions)


"""
    LibGit2.IndexTime

Matches the [`git_index_time`](https://libgit2.org/libgit2/#HEAD/type/git_index_time) struct.
"""
struct IndexTime
    seconds::Int64
    nanoseconds::Cuint
end

"""
    LibGit2.IndexEntry

In-memory representation of a file entry in the index.
Matches the [`git_index_entry`](https://libgit2.org/libgit2/#HEAD/type/git_index_entry) struct.
"""
struct IndexEntry
    ctime::IndexTime
    mtime::IndexTime

    dev::UInt32
    ino::UInt32
    mode::UInt32
    uid::UInt32
    gid::UInt32
    file_size::Int64

    id::GitHash

    flags::UInt16
    flags_extended::UInt16

    path::Ptr{UInt8}
end
Base.show(io::IO, ie::IndexEntry) = print(io, "IndexEntry($(string(ie.id)))")

"""
    LibGit2.RebaseOptions

Matches the `git_rebase_options` struct.

The fields represent:
  * `version`: version of the struct in use, in case this changes later. For now, always `1`.
  * `quiet`: inform other git clients helping with/working on the rebase that the rebase
    should be done "quietly". Used for interoperability. The default is `1`.
  * `inmemory`: start an in-memory rebase. Callers working on the rebase can go through its
    steps and commit any changes, but cannot rewind HEAD or update the repository. The
    [`workdir`](@ref) will not be modified. Only present on libgit2 versions newer than or equal to 0.24.0.
  * `rewrite_notes_ref`: name of the reference to notes to use to rewrite the commit notes as
    the rebase is finished.
  * `merge_opts`: merge options controlling how the trees will be merged at each rebase step.
     Only present on libgit2 versions newer than or equal to 0.24.0.
  * `checkout_opts`: checkout options for writing files when initializing the rebase, stepping
    through it, and aborting it. See [`CheckoutOptions`](@ref) for more information.
"""
@kwdef struct RebaseOptions
    version::Cuint                 = Cuint(1)
    quiet::Cint                    = Cint(1)
    @static if LibGit2.VERSION >= v"0.24.0"
        inmemory::Cint             = Cint(0)
    end
    rewrite_notes_ref::Cstring     = Cstring(C_NULL)
    @static if LibGit2.VERSION >= v"0.24.0"
        merge_opts::MergeOptions   = MergeOptions()
    end
    checkout_opts::CheckoutOptions = CheckoutOptions()
end
@assert Base.allocatedinline(RebaseOptions)

"""
    LibGit2.RebaseOperation

Describes a single instruction/operation to be performed during the rebase.
Matches the [`git_rebase_operation`](https://libgit2.org/libgit2/#HEAD/type/git_rebase_operation_t) struct.

The fields represent:
  * `optype`: the type of rebase operation currently being performed. The options are:
      - `REBASE_OPERATION_PICK`: cherry-pick the commit in question.
      - `REBASE_OPERATION_REWORD`: cherry-pick the commit in question, but rewrite its
        message using the prompt.
      - `REBASE_OPERATION_EDIT`: cherry-pick the commit in question, but allow the user
        to edit the commit's contents and its message.
      - `REBASE_OPERATION_SQUASH`: squash the commit in question into the previous commit.
        The commit messages of the two commits will be merged.
      - `REBASE_OPERATION_FIXUP`: squash the commit in question into the previous commit.
        Only the commit message of the previous commit will be used.
      - `REBASE_OPERATION_EXEC`: do not cherry-pick a commit. Run a command and continue if
        the command exits successfully.
  * `id`: the [`GitHash`](@ref) of the commit being worked on during this rebase step.
  * `exec`: in case `REBASE_OPERATION_EXEC` is used, the command to run during this step
    (for instance, running the test suite after each commit).
"""
struct RebaseOperation
    optype::Cint
    id::GitHash
    exec::Cstring
end
function Base.show(io::IO, rbo::RebaseOperation)
    println(io, "RebaseOperation($(string(rbo.id)))")
    println(io, "Operation type: $(Consts.GIT_REBASE_OPERATION(rbo.optype))")
end

"""
    LibGit2.StatusOptions

Options to control how `git_status_foreach_ext()` will issue callbacks.
Matches the [`git_status_opt_t`](https://libgit2.org/libgit2/#HEAD/type/git_status_opt_t) struct.

The fields represent:
  * `version`: version of the struct in use, in case this changes later. For now, always `1`.
  * `show`: a flag for which files to examine and in which order.
    The default is `Consts.STATUS_SHOW_INDEX_AND_WORKDIR`.
  * `flags`: flags for controlling any callbacks used in a status call.
  * `pathspec`: an array of paths to use for path-matching. The behavior of the path-matching
    will vary depending on the values of `show` and `flags`.
  * The `baseline` is the tree to be used for comparison to the working directory and
    index; defaults to HEAD.
"""
@kwdef struct StatusOptions
    version::Cuint           = Cuint(1)
    show::Cint               = Consts.STATUS_SHOW_INDEX_AND_WORKDIR
    flags::Cuint             = Consts.STATUS_OPT_INCLUDE_UNTRACKED |
                               Consts.STATUS_OPT_RECURSE_UNTRACKED_DIRS |
                               Consts.STATUS_OPT_RENAMES_HEAD_TO_INDEX |
                               Consts.STATUS_OPT_SORT_CASE_SENSITIVELY
    pathspec::StrArrayStruct = StrArrayStruct()
    @static if LibGit2.VERSION >= v"0.27.0"
        baseline::Ptr{Cvoid} = C_NULL
    end
end
@assert Base.allocatedinline(StatusOptions)

"""
    LibGit2.StatusEntry

Providing the differences between the file as it exists in HEAD and the index, and
providing the differences between the index and the working directory.
Matches the `git_status_entry` struct.

The fields represent:
  * `status`: contains the status flags for the file, indicating if it is current,
    or has been changed in some way in the index or work tree.
  * `head_to_index`: a pointer to a [`DiffDelta`](@ref) which encapsulates the difference(s)
    between the file as it exists in HEAD and in the index.
  * `index_to_workdir`: a pointer to a `DiffDelta` which encapsulates the difference(s)
    between the file as it exists in the index and in the [`workdir`](@ref).
"""
struct StatusEntry
    status::Cuint
    head_to_index::Ptr{DiffDelta}
    index_to_workdir::Ptr{DiffDelta}
end

"""
    LibGit2.FetchHead

Contains the information about HEAD during a fetch, including the name and URL
of the branch fetched from, the oid of the HEAD, and whether the fetched HEAD
has been merged locally.

The fields represent:
  * `name`: The name in the local reference database of the fetch head, for example,
     `"refs/heads/master"`.
  * `url`: The URL of the fetch head.
  * `oid`: The [`GitHash`](@ref) of the tip of the fetch head.
  * `ismerge`: Boolean flag indicating whether the changes at the
     remote have been merged into the local copy yet or not. If `true`, the local
     copy is up to date with the remote fetch head.
"""
struct FetchHead
    name::String
    url::String
    oid::GitHash
    ismerge::Bool
end

function Base.show(io::IO, fh::FetchHead)
    println(io, "FetchHead:")
    println(io, "Name: $(fh.name)")
    println(io, "URL: $(fh.url)")
    print(io, "OID: ")
    show(io, fh.oid)
    println(io)
    println(io, "Merged: $(fh.ismerge)")
end

"""
    LibGit2.ConfigEntry

Matches the [`git_config_entry`](https://libgit2.org/libgit2/#HEAD/type/git_config_entry) struct.
"""
struct ConfigEntry
    name::Cstring
    value::Cstring
    include_depth::Cuint
    level::GIT_CONFIG
    free::Ptr{Cvoid}
    payload::Ptr{Cvoid} # User is not permitted to read or write this field
end
@assert Base.allocatedinline(ConfigEntry)

function Base.show(io::IO, ce::ConfigEntry)
    print(io, "ConfigEntry(\"", unsafe_string(ce.name), "\", \"", unsafe_string(ce.value), "\")")
end

"""
    LibGit2.split_cfg_entry(ce::LibGit2.ConfigEntry) -> Tuple{String,String,String,String}

Break the `ConfigEntry` up to the following pieces: section, subsection, name, and value.

# Examples
Given the git configuration file containing:
```
[credential "https://example.com"]
    username = me
```

The `ConfigEntry` would look like the following:

```julia-repl
julia> entry
ConfigEntry("credential.https://example.com.username", "me")

julia> LibGit2.split_cfg_entry(entry)
("credential", "https://example.com", "username", "me")
```

Refer to the [git config syntax documentation](https://git-scm.com/docs/git-config#_syntax)
for more details.
"""
function split_cfg_entry(ce::ConfigEntry)
    key = unsafe_string(ce.name)

    # Determine the positions of the delimiters
    subsection_delim = something(findfirst(isequal('.'), key), 0)
    name_delim = something(findlast(isequal('.'), key), 0)

    section = SubString(key, 1, subsection_delim - 1)
    subsection = SubString(key, subsection_delim + 1, name_delim - 1)
    name = SubString(key, name_delim + 1)
    value = unsafe_string(ce.value)

    return (section, subsection, name, value)
end

# Abstract object types

"""
    AbstractGitObject

`AbstractGitObject`s must obey the following interface:
- `obj.owner`, if present, must be a `Union{Nothing,GitRepo,GitTree}`
- `obj.ptr`, if present, must be a `Union{Ptr{Cvoid},Ptr{SignatureStruct}}`
"""
abstract type AbstractGitObject end

function Base.getproperty(obj::AbstractGitObject, name::Symbol)
    # These type-assertions enforce the interface requirements above.
    # They assist type-inference in cases where the compiler only knows that it
    # has an `AbstractGitObject` without being certain about the concrete type.
    # See detailed explanation in https://github.com/JuliaLang/julia/pull/36452.
    if name === :owner
        return getfield(obj, :owner)::Union{Nothing,GitRepo,GitTree}
    elseif name === :ptr
        return getfield(obj, :ptr)::Union{Ptr{Cvoid},Ptr{SignatureStruct}}
    else
        return getfield(obj, name)
    end
end

Base.isempty(obj::AbstractGitObject) = (obj.ptr == C_NULL)

# `GitObject`s must obey the following interface:
# - `obj.owner` must be a `GitRepo`
# - `obj.ptr` must be a Ptr{Cvoid}
abstract type GitObject <: AbstractGitObject end

function Base.getproperty(obj::GitObject, name::Symbol)
    if name === :owner
        return getfield(obj, :owner)::GitRepo
    elseif name === :ptr
        return getfield(obj, :ptr)::Ptr{Cvoid}
    else
        return getfield(obj, name)
    end
end

for (typ, owntyp, sup, cname) in Tuple{Symbol,Any,Symbol,Symbol}[
    (:GitRepo,           nothing,                 :AbstractGitObject, :git_repository),
    (:GitConfig,         :(Union{GitRepo, Nothing}), :AbstractGitObject, :git_config),
    (:GitIndex,          :(Union{GitRepo, Nothing}), :AbstractGitObject, :git_index),
    (:GitRemote,         :GitRepo,                :AbstractGitObject, :git_remote),
    (:GitRevWalker,      :GitRepo,                :AbstractGitObject, :git_revwalk),
    (:GitReference,      :GitRepo,                :AbstractGitObject, :git_reference),
    (:GitDescribeResult, :GitRepo,                :AbstractGitObject, :git_describe_result),
    (:GitDiff,           :GitRepo,                :AbstractGitObject, :git_diff),
    (:GitDiffStats,      :GitRepo,                :AbstractGitObject, :git_diff_stats),
    (:GitAnnotated,      :GitRepo,                :AbstractGitObject, :git_annotated_commit),
    (:GitRebase,         :GitRepo,                :AbstractGitObject, :git_rebase),
    (:GitBlame,          :GitRepo,                :AbstractGitObject, :git_blame),
    (:GitStatus,         :GitRepo,                :AbstractGitObject, :git_status_list),
    (:GitBranchIter,     :GitRepo,                :AbstractGitObject, :git_branch_iterator),
    (:GitConfigIter,     nothing,                 :AbstractGitObject, :git_config_iterator),
    (:GitUnknownObject,  :GitRepo,                :GitObject,         :git_object),
    (:GitCommit,         :GitRepo,                :GitObject,         :git_commit),
    (:GitBlob,           :GitRepo,                :GitObject,         :git_blob),
    (:GitTree,           :GitRepo,                :GitObject,         :git_tree),
    (:GitTag,            :GitRepo,                :GitObject,         :git_tag),
    (:GitTreeEntry,      :GitTree,                :AbstractGitObject, :git_tree_entry),
    ]

    if owntyp === nothing
        @eval mutable struct $typ <: $sup
            ptr::Ptr{Cvoid}
            function $typ(ptr::Ptr{Cvoid}, fin::Bool=true)
                # fin=false should only be used when the pointer should not be free'd
                # e.g. from within callback functions which are passed a pointer
                @assert ptr != C_NULL
                obj = new(ptr)
                if fin
                    Threads.atomic_add!(REFCOUNT, 1)
                    finalizer(Base.close, obj)
                end
                return obj
            end
        end
        @eval Base.unsafe_convert(::Type{Ptr{Cvoid}}, x::$typ) = x.ptr
    else
        @eval mutable struct $typ <: $sup
            owner::$owntyp
            ptr::Ptr{Cvoid}
            function $typ(owner::$owntyp, ptr::Ptr{Cvoid}, fin::Bool=true)
                @assert ptr != C_NULL
                obj = new(owner, ptr)
                if fin
                    Threads.atomic_add!(REFCOUNT, 1)
                    finalizer(Base.close, obj)
                end
                return obj
            end
        end
        @eval Base.unsafe_convert(::Type{Ptr{Cvoid}}, x::$typ) = x.ptr
        if isa(owntyp, Expr) && owntyp.args[1] === :Union && owntyp.args[3] === :Nothing
            @eval begin
                $typ(ptr::Ptr{Cvoid}, fin::Bool=true) = $typ(nothing, ptr, fin)
            end
        end
    end
    @eval function Base.close(obj::$typ)
        if obj.ptr != C_NULL
            ensure_initialized()
            ccall(($(string(cname, :_free)), libgit2), Cvoid, (Ptr{Cvoid},), obj.ptr)
            obj.ptr = C_NULL
            if Threads.atomic_sub!(REFCOUNT, 1) == 1
                # will the last finalizer please turn out the lights?
                ccall((:git_libgit2_shutdown, libgit2), Cint, ())
            end
        end
    end
end

## Calling `GitObject(repo, ...)` will automatically resolve to the appropriate type.
function GitObject(repo::GitRepo, ptr::Ptr{Cvoid})
    T = objtype(Consts.OBJECT(ptr))
    T(repo, ptr)
end

"""
    LibGit2.GitSignature

This is a Julia wrapper around a pointer to a
[`git_signature`](https://libgit2.org/libgit2/#HEAD/type/git_signature) object.
"""
mutable struct GitSignature <: AbstractGitObject
    ptr::Ptr{SignatureStruct}
    function GitSignature(ptr::Ptr{SignatureStruct})
        @assert ptr != C_NULL
        obj = new(ptr)
        finalizer(Base.close, obj)
        return obj
    end
end
function Base.close(obj::GitSignature)
    if obj.ptr != C_NULL
        ensure_initialized()
        ccall((:git_signature_free, libgit2), Cvoid, (Ptr{SignatureStruct},), obj.ptr)
        obj.ptr = C_NULL
    end
end

# Structure has the same layout as SignatureStruct
mutable struct Signature
    name::String
    email::String
    time::Int64
    time_offset::Cint
end

"""
    LibGit2.BlameHunk

Matches the [`git_blame_hunk`](https://libgit2.org/libgit2/#HEAD/type/git_blame_hunk) struct.
The fields represent:
    * `lines_in_hunk`: the number of lines in this hunk of the blame.
    * `final_commit_id`: the [`GitHash`](@ref) of the commit where this section was last changed.
    * `final_start_line_number`: the *one based* line number in the file where the
       hunk starts, in the *final* version of the file.
    * `final_signature`: the signature of the person who last modified this hunk. You will
       need to pass this to `Signature` to access its fields.
    * `orig_commit_id`: the [`GitHash`](@ref) of the commit where this hunk was first found.
    * `orig_path`: the path to the file where the hunk originated. This may be different
       than the current/final path, for instance if the file has been moved.
    * `orig_start_line_number`: the *one based* line number in the file where the
       hunk starts, in the *original* version of the file at `orig_path`.
    * `orig_signature`: the signature of the person who introduced this hunk. You will
       need to pass this to `Signature` to access its fields.
    * `boundary`: `'1'` if the original commit is a "boundary" commit (for instance, if it's
       equal to an oldest commit set in `options`).
"""
@kwdef struct BlameHunk
    lines_in_hunk::Csize_t                = Csize_t(0)

    final_commit_id::GitHash              = GitHash()
    final_start_line_number::Csize_t      = Csize_t(0)
    final_signature::Ptr{SignatureStruct} = Ptr{SignatureStruct}(C_NULL)

    orig_commit_id::GitHash               = GitHash()
    orig_path::Cstring                    = Cstring(C_NULL)
    orig_start_line_number::Csize_t       = Csize_t(0)
    orig_signature::Ptr{SignatureStruct}  = Ptr{SignatureStruct}(C_NULL)

    boundary::Char                        = '\0'
end
@assert Base.allocatedinline(BlameHunk)

"""
    with(f::Function, obj)

Resource management helper function. Applies `f` to `obj`, making sure to call
`close` on `obj` after `f` successfully returns or throws an error. Ensures that
allocated git resources are finalized as soon as they are no longer needed.
"""
function with(f::Function, obj)
    try
        f(obj)
    finally
        close(obj)
    end
end

with(f::Function, ::Type{T}, args...) where {T} = with(f, T(args...))

"""
    with_warn(f::Function, ::Type{T}, args...)

Resource management helper function. Apply `f` to `args`, first constructing
an instance of type `T` from `args`. Makes sure to call `close` on the resulting
object after `f` successfully returns or throws an error. Ensures that
allocated git resources are finalized as soon as they are no longer needed. If an
error is thrown by `f`, a warning is shown containing the error.
"""
function with_warn(f::Function, ::Type{T}, args...) where T
    obj = T(args...)
    try
        with(f, obj)
    catch err
        @warn "$(string(T)) thrown exception:" exception=err
    end
end

"""
    LibGit2.Consts.OBJECT(::Type{T}) where T<:GitObject

The `OBJECT` enum value corresponding to type `T`.
"""
Consts.OBJECT(::Type{GitCommit})        = Consts.OBJ_COMMIT
Consts.OBJECT(::Type{GitTree})          = Consts.OBJ_TREE
Consts.OBJECT(::Type{GitBlob})          = Consts.OBJ_BLOB
Consts.OBJECT(::Type{GitTag})           = Consts.OBJ_TAG
Consts.OBJECT(::Type{GitUnknownObject}) = Consts.OBJ_ANY
Consts.OBJECT(::Type{GitObject})        = Consts.OBJ_ANY

function Consts.OBJECT(ptr::Ptr{Cvoid})
    ensure_initialized()
    ccall((:git_object_type, libgit2), Consts.OBJECT, (Ptr{Cvoid},), ptr)
end

"""
    objtype(obj_type::Consts.OBJECT)

Return the type corresponding to the enum value.
"""
function objtype(obj_type::Consts.OBJECT)
    if obj_type == Consts.OBJ_COMMIT
        GitCommit
    elseif obj_type == Consts.OBJ_TREE
        GitTree
    elseif obj_type == Consts.OBJ_BLOB
        GitBlob
    elseif obj_type == Consts.OBJ_TAG
        GitTag
    elseif obj_type == Consts.OBJ_ANY #this name comes from the header
        GitUnknownObject
    else
        throw(GitError(Error.Object, Error.ENOTFOUND, "Object type $obj_type is not supported"))
    end
end

abstract type AbstractCredential end

"""
    isfilled(cred::AbstractCredential) -> Bool

Verifies that a credential is ready for use in authentication.
"""
isfilled(::AbstractCredential)

"Credential that support only `user` and `password` parameters"
mutable struct UserPasswordCredential <: AbstractCredential
    user::String
    pass::Base.SecretBuffer
    function UserPasswordCredential(user::AbstractString="", pass::Union{AbstractString, Base.SecretBuffer}="")
        new(user, pass)
    end
end

function Base.setproperty!(cred::UserPasswordCredential, name::Symbol, value)
    if name === :pass
        field = getfield(cred, name)
        Base.shred!(field)
    end
    setfield!(cred, name, convert(fieldtype(typeof(cred), name), value))
end

function Base.shred!(cred::UserPasswordCredential)
    cred.user = ""
    Base.shred!(cred.pass)
    return cred
end

function Base.:(==)(a::UserPasswordCredential, b::UserPasswordCredential)
    a.user == b.user && a.pass == b.pass
end

function isfilled(cred::UserPasswordCredential)
    !isempty(cred.user) && !isempty(cred.pass)
end

"SSH credential type"
mutable struct SSHCredential <: AbstractCredential
    user::String
    pass::Base.SecretBuffer
    # Paths to private keys
    prvkey::String
    pubkey::String
    function SSHCredential(user="", pass="",
                           prvkey="", pubkey="")
        new(user, pass, prvkey, pubkey)
    end
end

function Base.setproperty!(cred::SSHCredential, name::Symbol, value)
    if name === :pass
        field = getfield(cred, name)
        Base.shred!(field)
    end
    setfield!(cred, name, convert(fieldtype(typeof(cred), name), value))
end


function Base.shred!(cred::SSHCredential)
    cred.user = ""
    Base.shred!(cred.pass)
    cred.prvkey = ""
    cred.pubkey = ""
    return cred
end

function Base.:(==)(a::SSHCredential, b::SSHCredential)
    a.user == b.user && a.pass == b.pass && a.prvkey == b.prvkey && a.pubkey == b.pubkey
end

function isfilled(cred::SSHCredential)
    !isempty(cred.user) && isfile(cred.prvkey) && isfile(cred.pubkey) &&
    (!isempty(cred.pass) || !is_passphrase_required(cred.prvkey))
end

"Caches credential information for re-use"
struct CachedCredentials
    cred::Dict{String,AbstractCredential}
    CachedCredentials() = new(Dict{String,AbstractCredential}())
end

Base.haskey(cache::CachedCredentials, cred_id) = Base.haskey(cache.cred, cred_id)
Base.getindex(cache::CachedCredentials, cred_id) = Base.getindex(cache.cred, cred_id)
Base.get!(cache::CachedCredentials, cred_id, default) = Base.get!(cache.cred, cred_id, default)

function Base.shred!(p::CachedCredentials)
    foreach(Base.shred!, values(p.cred))
    return p
end

function approve(cache::CachedCredentials, cred::AbstractCredential, url::AbstractString)
    cred_id = credential_identifier(url)
    if haskey(cache.cred, cred_id)
        # Shred the cached credential we'll be overwriting if it isn't identical
        cred !== cache.cred[cred_id] && Base.shred!(cache.cred[cred_id])
    end
    cache.cred[cred_id] = cred
    nothing
end

function reject(cache::CachedCredentials, cred::AbstractCredential, url::AbstractString)
    cred_id = credential_identifier(url)
    if haskey(cache.cred, cred_id)
        # Shred the cached credential if it isn't the `cred` passed in
        cred !== cache.cred[cred_id] && Base.shred!(cache.cred[cred_id])
        delete!(cache.cred, cred_id)
    end
    nothing
end

"""
    LibGit2.CredentialPayload

Retains the state between multiple calls to the credential callback for the same URL.
A `CredentialPayload` instance is expected to be `reset!` whenever it will be used with a
different URL.
"""
mutable struct CredentialPayload
    explicit::Union{AbstractCredential, Nothing}
    cache::Union{CachedCredentials, Nothing}
    allow_ssh_agent::Bool    # Allow the use of the SSH agent to get credentials
    allow_git_helpers::Bool  # Allow the use of git credential helpers
    allow_prompt::Bool       # Allow prompting the user for credentials

    config::GitConfig

    # Ephemeral state fields
    credential::Union{AbstractCredential, Nothing}
    first_pass::Bool
    use_ssh_agent::Bool
    use_env::Bool
    use_git_helpers::Bool
    remaining_prompts::Int

    url::String
    scheme::String
    username::String
    host::String

    function CredentialPayload(
            credential::Union{AbstractCredential, Nothing}=nothing,
            cache::Union{CachedCredentials, Nothing}=nothing,
            config::GitConfig=GitConfig();
            allow_ssh_agent::Bool=true,
            allow_git_helpers::Bool=true,
            allow_prompt::Bool=true)

        payload = new(credential, cache, allow_ssh_agent, allow_git_helpers, allow_prompt, config)
        return reset!(payload)
    end
end

function CredentialPayload(credential::AbstractCredential; kwargs...)
    CredentialPayload(credential, nothing; kwargs...)
end

function CredentialPayload(cache::CachedCredentials; kwargs...)
    CredentialPayload(nothing, cache; kwargs...)
end

CredentialPayload(p::CredentialPayload) = p

function Base.shred!(p::CredentialPayload)
    # Note: Avoid shredding the `explicit` or `cache` fields as these are just references
    # and it is not our responsibility to shred them.
    credential = p.credential
    credential !== nothing && Base.shred!(credential)
    p.credential = nothing
end

"""
    reset!(payload, [config]) -> CredentialPayload

Reset the `payload` state back to the initial values so that it can be used again within
the credential callback. If a `config` is provided the configuration will also be updated.
"""
function reset!(p::CredentialPayload, config::GitConfig=p.config)
    p.config = config
    p.credential = nothing
    p.first_pass = true
    p.use_ssh_agent = p.allow_ssh_agent
    p.use_env = true
    p.use_git_helpers = p.allow_git_helpers
    p.remaining_prompts = p.allow_prompt ? 3 : 0
    p.url = ""
    p.scheme = ""
    p.username = ""
    p.host = ""

    return p
end

"""
    approve(payload::CredentialPayload; shred::Bool=true) -> Nothing

Store the `payload` credential for re-use in a future authentication. Should only be called
when authentication was successful.

The `shred` keyword controls whether sensitive information in the payload credential field
should be destroyed. Should only be set to `false` during testing.
"""
function approve(p::CredentialPayload; shred::Bool=true)
    cred = p.credential
    cred === nothing && return  # No credential was used

    # Each `approve` call needs to avoid shredding the passed in credential as we need
    # the credential information intact for subsequent approve calls.
    cache = p.cache
    if cache !== nothing
        approve(cache, cred, p.url)
        shred = false  # Avoid wiping `cred` as this would also wipe the cached copy
    end
    if p.allow_git_helpers
        approve(p.config, cred, p.url)
    end

    if shred
        Base.shred!(cred)
        p.credential = nothing
    end
    nothing
end

"""
    reject(payload::CredentialPayload; shred::Bool=true) -> Nothing

Discard the `payload` credential from begin re-used in future authentication. Should only be
called when authentication was unsuccessful.

The `shred` keyword controls whether sensitive information in the payload credential field
should be destroyed. Should only be set to `false` during testing.
"""
function reject(p::CredentialPayload; shred::Bool=true)
    cred = p.credential
    cred === nothing && return  # No credential was used

    # Note: each `reject` call needs to avoid shredding the passed in credential as we need
    # the credential information intact for subsequent reject calls.
    cache = p.cache
    if cache !== nothing
        reject(cache, cred, p.url)
    end
    if p.allow_git_helpers
        reject(p.config, cred, p.url)
    end

    if shred
        Base.shred!(cred)
        p.credential = nothing
    end
    nothing
end

# Useful for functions which can handle various kinds of credentials
const Creds = Union{CredentialPayload, AbstractCredential, CachedCredentials, Nothing}
t   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LibGit2/src/signature.jl	
      # This file is a part of Julia. License is MIT: https://julialang.org/license

function Signature(ptr::Ptr{SignatureStruct})
    sig   = unsafe_load(ptr)::SignatureStruct
    name  = unsafe_string(sig.name)
    email = unsafe_string(sig.email)
    time   = sig.when.time
    offset = sig.when.offset
    return Signature(name, email, time, offset)
end
Signature(sig::GitSignature) = Signature(sig.ptr)

function Signature(name::AbstractString, email::AbstractString)
    ensure_initialized()
    sig_ptr_ptr = Ref{Ptr{SignatureStruct}}(C_NULL)
    @check ccall((:git_signature_now, libgit2), Cint,
                 (Ptr{Ptr{SignatureStruct}}, Cstring, Cstring), sig_ptr_ptr, name, email)
    sig = GitSignature(sig_ptr_ptr[])
    s = Signature(sig.ptr)
    close(sig)
    return s
end

function Signature(repo::GitRepo)
    sig = default_signature(repo)
    s = Signature(sig.ptr)
    close(sig)
    return s
end

function Base.convert(::Type{GitSignature}, sig::Signature)
    ensure_initialized()
    sig_ptr_ptr = Ref{Ptr{SignatureStruct}}(C_NULL)
    @check ccall((:git_signature_new, libgit2), Cint,
                 (Ptr{Ptr{SignatureStruct}}, Cstring, Cstring, Int64, Cint),
                 sig_ptr_ptr, sig.name, sig.email, sig.time, sig.time_offset)
    return GitSignature(sig_ptr_ptr[])
end

function yearmonthday(days)
    z = days + 306; h = 100z - 25; a = fld(h, 3652425); b = a - fld(a, 4)
    y = fld(100b + h, 36525); c = b + z - 365y - fld(y, 4); m = div(5c + 456, 153)
    d = c - div(153m - 457, 5); return m > 12 ? (y + 1, m - 12, d) : (y, m, d)
end
lpad0(x) = lpad(x, 2, '0')

function unix2date(t)
   UNIXEPOCH = 62135683200000
   rata = UNIXEPOCH + round(Int64, Int64(1000) * t)
   year, month, day = yearmonthday(fld(rata, 86400000))
   secs = t % (24 * 60 * 60)
   mins = div(secs, 60)
   m, d = lpad0(month), lpad0(day)
   h, mi, s = lpad0.(round.(Int, (div(mins, 60), mins % 60, secs % 60)))
   return "$year-$m-$d $h:$mi:$s"
end

function Base.show(io::IO, sig::Signature)
    print(io, "Name: ", sig.name, ", ")
    print(io, "Email: ", sig.email, ", ")
    print(io, "Time: ", unix2date(sig.time + 60*sig.time_offset))
    @printf(io, "%+03i:%02i", divrem(sig.time_offset, 60)...)
end

"""Return signature object. Free it after use."""
function default_signature(repo::GitRepo)
    ensure_initialized()
    sig_ptr_ptr = Ref{Ptr{SignatureStruct}}(C_NULL)
    @check ccall((:git_signature_default, libgit2), Cint,
                 (Ptr{Ptr{SignatureStruct}}, Ptr{Cvoid}), sig_ptr_ptr, repo.ptr)
    return GitSignature(sig_ptr_ptr[])
end
n   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LibGit2/src/oid.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
    GitHash(ptr::Ptr{UInt8})

Construct a `GitHash` from a pointer to `UInt8` data containing the bytes of the
SHA-1 hash. The constructor throws an error if the pointer is null, i.e. equal to
`C_NULL`.
"""
function GitHash(ptr::Ptr{UInt8})
    if ptr == C_NULL
        throw(ArgumentError("NULL pointer passed to GitHash() constructor"))
    end
    ensure_initialized()
    oid_ptr = Ref(GitHash())
    @check ccall((:git_oid_fromraw, libgit2), Cint,
                 (Ptr{GitHash}, Ptr{UInt8}), oid_ptr, ptr)
    return oid_ptr[]
end

"""
    GitHash(id::Vector{UInt8})

Construct a `GitHash` from a vector of $OID_RAWSZ bytes.
"""
function GitHash(id::Array{UInt8,1})
    if length(id) != OID_RAWSZ
        throw(ArgumentError("invalid raw buffer size"))
    end
    return GitHash(pointer(id))
end

"""
    GitHash(id::AbstractString)

Construct a `GitHash` from a string of $OID_HEXSZ hexadecimal digits.
"""
function GitHash(id::AbstractString)
    bstr = String(id)
    len = sizeof(bstr)
    if len < OID_HEXSZ
        throw(ArgumentError("Input string is too short, use `GitShortHash` for partial hashes"))
    end
    ensure_initialized()
    oid_ptr = Ref{GitHash}()
    @check ccall((:git_oid_fromstrn, libgit2), Cint,
              (Ptr{GitHash}, Ptr{UInt8}, Csize_t), oid_ptr, bstr, len)
    return oid_ptr[]
end

"""
    GitShortHash(buf::Buffer)

Construct a `GitShortHash` from the data stored in the given [`Buffer`](@ref).
"""
function GitShortHash(buf::Buffer)
    ensure_initialized()
    oid_ptr = Ref{GitHash}()
    @check ccall((:git_oid_fromstrn, libgit2), Cint,
              (Ptr{GitHash}, Ptr{UInt8}, Csize_t), oid_ptr, buf.ptr, buf.size)
    GitShortHash(oid_ptr[], buf.size)
end

"""
    GitShortHash(id::AbstractString)

Construct a `GitShortHash` from a string of at most $OID_HEXSZ hexadecimal digits.
"""
function GitShortHash(id::AbstractString)
    ensure_initialized()
    bstr = String(id)
    len = sizeof(bstr)
    oid_ptr = Ref{GitHash}()
    @check ccall((:git_oid_fromstrn, libgit2), Cint,
              (Ptr{GitHash}, Ptr{UInt8}, Csize_t), oid_ptr, bstr, len)
    GitShortHash(oid_ptr[], len)
end

"""
    @githash_str -> AbstractGitHash

Construct a git hash object from the given string, returning a `GitShortHash` if
the string is shorter than $OID_HEXSZ hexadecimal digits, otherwise a `GitHash`.

# Examples
```jldoctest
julia> LibGit2.githash"d114feb74ce633"
GitShortHash("d114feb74ce633")

julia> LibGit2.githash"d114feb74ce63307afe878a5228ad014e0289a85"
GitHash("d114feb74ce63307afe878a5228ad014e0289a85")
```
"""
macro githash_str(id)
    bstr = String(id)
    if sizeof(bstr) < OID_HEXSZ
        GitShortHash(id)
    else
        GitHash(id)
    end
end


"""
    GitHash(ref::GitReference)

Get the identifier (`GitHash`) of the object referred to by the direct reference
`ref`. Note: this does not work for symbolic references; in such cases use
`GitHash(repo::GitRepo, ref_name::AbstractString)` instead.
"""
function GitHash(ref::GitReference)
    isempty(ref) && return GitHash()
    reftype(ref) != Consts.REF_OID && return GitHash()
    ensure_initialized()
    GC.@preserve ref begin
        oid_ptr = ccall((:git_reference_target, libgit2), Ptr{UInt8}, (Ptr{Cvoid},), ref.ptr)
        oid_ptr == C_NULL && return GitHash()
        oid = GitHash(oid_ptr)
    end
    return oid
end


"""
    GitHash(repo::GitRepo, ref_name::AbstractString)

Get the identifier (`GitHash`) of the object referred to by reference specified by
`ref_name`.
"""
function GitHash(repo::GitRepo, ref_name::AbstractString)
    isempty(repo) && return GitHash()
    ensure_initialized()
    oid_ptr  = Ref(GitHash())
    @check ccall((:git_reference_name_to_id, libgit2), Cint,
                    (Ptr{GitHash}, Ptr{Cvoid}, Cstring),
                     oid_ptr, repo.ptr, ref_name)
    return oid_ptr[]
end

"""
    GitHash(obj::GitObject)

Get the identifier (`GitHash`) of `obj`.
"""
function GitHash(obj::GitObject)
    ensure_initialized()
    GitHash(ccall((:git_object_id, libgit2), Ptr{UInt8}, (Ptr{Cvoid},), obj.ptr))
end

==(obj1::GitObject, obj2::GitObject) = GitHash(obj1) == GitHash(obj2)

"""
    GitShortHash(obj::GitObject)

Get a shortened identifier (`GitShortHash`) of `obj`. The minimum length (in characters)
is determined by the `core.abbrev` config option, and will be of sufficient length to
unambiguously identify the object in the repository.
"""
function GitShortHash(obj::GitObject)
    ensure_initialized()
    buf_ref = Ref(Buffer())
    @check ccall((:git_object_short_id, libgit2), Cint,
                 (Ptr{Buffer},Ptr{Cvoid}), buf_ref, obj.ptr)
    sid = GitShortHash(buf_ref[])
    free(buf_ref)
    return sid
end

"""
    raw(id::GitHash) -> Vector{UInt8}

Obtain the raw bytes of the [`GitHash`](@ref) as a vector of length $OID_RAWSZ.
"""
raw(id::GitHash) = collect(id.val)

function Base.print(io::IO, id::GitHash)
    for i in id.val
        print(io, string(i, base = 16, pad = 2))
    end
end
Base.string(id::GitShortHash) = string(id.hash)[1:id.len]

Base.show(io::IO, id::GitHash) = print(io, "GitHash(\"$(string(id))\")")
Base.show(io::IO, id::GitShortHash) = print(io, "GitShortHash(\"$(string(id))\")")

Base.hash(id::GitHash, h::UInt) = hash(id.val, h)

function Base.cmp(id1::GitHash, id2::GitHash)
    ensure_initialized()
    Int(ccall((:git_oid_cmp, libgit2), Cint,
              (Ptr{GitHash}, Ptr{GitHash}),
              Ref(id1), Ref(id2)))
end
function Base.cmp(id1::GitShortHash, id2::GitShortHash)
    ensure_initialized()
    # shortened hashes appear at the beginning of the order, i.e.
    # 000 < 01 < 010 < 011 < 0112
    c = Int(ccall((:git_oid_ncmp, libgit2), Cint,
                  (Ptr{GitHash}, Ptr{GitHash}, Csize_t),
                  Ref(id1.hash), Ref(id2.hash), min(id1.len, id2.len)))
    return c == 0 ? cmp(id1.len, id2.len) : c
end
Base.cmp(id1::GitHash, id2::GitShortHash) = cmp(GitShortHash(id1, OID_HEXSZ), id2)
Base.cmp(id1::GitShortHash, id2::GitHash) = cmp(id1, GitShortHash(id2, OID_HEXSZ))

==(id1::GitHash, id2::GitHash) = cmp(id1, id2) == 0
Base.isless(id1::AbstractGitHash, id2::AbstractGitHash)  = cmp(id1, id2) < 0

"""
    iszero(id::GitHash) -> Bool

Determine whether all hexadecimal digits of the given [`GitHash`](@ref) are zero.
"""
function iszero(id::GitHash)
    for i in 1:OID_RAWSZ
        id.val[i] != zero(UInt8) && return false
    end
    return true
end

Base.zero(::Type{GitHash}) = GitHash()
t   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LibGit2/src/reference.jlu-      # This file is a part of Julia. License is MIT: https://julialang.org/license

function GitReference(repo::GitRepo, refname::AbstractString)
    ensure_initialized()
    ref_ptr_ptr = Ref{Ptr{Cvoid}}(C_NULL)
    @check ccall((:git_reference_lookup, libgit2), Cint,
                  (Ptr{Ptr{Cvoid}}, Ptr{Cvoid}, Cstring),
                   ref_ptr_ptr, repo.ptr, refname)
    return GitReference(repo, ref_ptr_ptr[])
end

function GitReference(repo::GitRepo, obj_oid::GitHash, refname::AbstractString = Consts.HEAD_FILE;
                      force::Bool=false, msg::AbstractString="")
    ensure_initialized()
    ref_ptr_ptr = Ref{Ptr{Cvoid}}(C_NULL)
    @check ccall((:git_reference_create, libgit2), Cint,
                  (Ptr{Ptr{Cvoid}}, Ptr{Cvoid}, Ptr{UInt8}, Ptr{GitHash}, Cint, Cstring),
                   ref_ptr_ptr, repo.ptr, refname, Ref(obj_oid), Cint(force),
                   isempty(msg) ? C_NULL : msg)
    return GitReference(repo, ref_ptr_ptr[])
end

"""
    LibGit2.isorphan(repo::GitRepo)

Check if the current branch is an "orphan" branch, i.e. has no commits. The first commit
to this branch will have no parents.
"""
function isorphan(repo::GitRepo)
    ensure_initialized()
    r = @check ccall((:git_repository_head_unborn, libgit2), Cint,
                     (Ptr{Cvoid},), repo.ptr)
    r != 0
end

"""
    LibGit2.head(repo::GitRepo) -> GitReference

Return a `GitReference` to the current HEAD of `repo`.
"""
function head(repo::GitRepo)
    ensure_initialized()
    head_ptr_ptr = Ref{Ptr{Cvoid}}(C_NULL)
    @check ccall((:git_repository_head, libgit2), Cint,
                  (Ptr{Ptr{Cvoid}}, Ptr{Cvoid}), head_ptr_ptr, repo.ptr)
    return GitReference(repo, head_ptr_ptr[])
end

"""
    LibGit2.shortname(ref::GitReference)

Return a shortened version of the name of `ref` that's
"human-readable".

```julia-repl
julia> repo = GitRepo(path_to_repo);

julia> branch_ref = LibGit2.head(repo);

julia> LibGit2.name(branch_ref)
"refs/heads/master"

julia> LibGit2.shortname(branch_ref)
"master"
```
"""
function shortname(ref::GitReference)
    isempty(ref) && return ""
    ensure_initialized()
    GC.@preserve ref begin
        name_ptr = ccall((:git_reference_shorthand, libgit2), Cstring, (Ptr{Cvoid},), ref.ptr)
        name_ptr == C_NULL && return ""
        name = unsafe_string(name_ptr)
    end
    return name
end

"""
    LibGit2.reftype(ref::GitReference) -> Cint

Return a `Cint` corresponding to the type of `ref`:
  * `0` if the reference is invalid
  * `1` if the reference is an object id
  * `2` if the reference is symbolic
"""
function reftype(ref::GitReference)
    ensure_initialized()
    return ccall((:git_reference_type, libgit2), Cint, (Ptr{Cvoid},), ref.ptr)
end

"""
    LibGit2.fullname(ref::GitReference)

Return the name of the reference pointed to by the
symbolic reference `ref`. If `ref` is not a symbolic
reference, return an empty string.
"""
function fullname(ref::GitReference)
    isempty(ref) && return ""
    reftype(ref) == Consts.REF_OID && return ""
    ensure_initialized()
    GC.@preserve ref begin
        rname = ccall((:git_reference_symbolic_target, libgit2), Cstring, (Ptr{Cvoid},), ref.ptr)
        rname == C_NULL && return ""
        name = unsafe_string(rname)
    end
    return name
end

"""
    LibGit2.name(ref::GitReference)

Return the full name of `ref`.
"""
function name(ref::GitReference)
    isempty(ref) && return ""
    ensure_initialized()
    GC.@preserve ref begin
        name_ptr = ccall((:git_reference_name, libgit2), Cstring, (Ptr{Cvoid},), ref.ptr)
        name_ptr == C_NULL && return ""
        name = unsafe_string(name_ptr)
    end
    return name
end

function branch(ref::GitReference)
    isempty(ref) && return ""
    ensure_initialized()
    str_ptr_ptr = Ref{Cstring}()
    GC.@preserve ref begin
        @check ccall((:git_branch_name, libgit2), Cint,
                      (Ptr{Cstring}, Ptr{Cvoid},), str_ptr_ptr, ref.ptr)
        str = unsafe_string(str_ptr_ptr[])
    end
    return str
end

function ishead(ref::GitReference)
    isempty(ref) && return false
    ensure_initialized()
    err = ccall((:git_branch_is_head, libgit2), Cint,
                  (Ptr{Cvoid},), ref.ptr)
    return err == 1
end

function isbranch(ref::GitReference)
    isempty(ref) && return false
    ensure_initialized()
    err = ccall((:git_reference_is_branch, libgit2), Cint,
                  (Ptr{Cvoid},), ref.ptr)
    return err == 1
end

function istag(ref::GitReference)
    isempty(ref) && return false
    ensure_initialized()
    err = ccall((:git_reference_is_tag, libgit2), Cint,
                  (Ptr{Cvoid},), ref.ptr)
    return err == 1
end

function isremote(ref::GitReference)
    isempty(ref) && return false
    ensure_initialized()
    err = ccall((:git_reference_is_remote, libgit2), Cint,
                  (Ptr{Cvoid},), ref.ptr)
    return err == 1
end

function Base.show(io::IO, ref::GitReference)
    println(io, "GitReference:")
    if isremote(ref)
        println(io, "Remote with name ", name(ref))
    elseif isbranch(ref)
        println(io, "Branch with name ", name(ref))
        if ishead(ref)
            println(io, "Branch is HEAD.")
        else
            println(io, "Branch is not HEAD.")
        end
    elseif istag(ref)
        println(io, "Tag with name ", name(ref))
    end
end

"""
    peel([T,] ref::GitReference)

Recursively peel `ref` until an object of type `T` is obtained. If no `T` is provided,
then `ref` will be peeled until an object other than a [`GitTag`](@ref) is obtained.

- A `GitTag` will be peeled to the object it references.
- A [`GitCommit`](@ref) will be peeled to a [`GitTree`](@ref).

!!! note
    Only annotated tags can be peeled to `GitTag` objects. Lightweight tags (the default)
    are references under `refs/tags/` which point directly to `GitCommit` objects.
"""
function peel(::Type{T}, ref::GitReference) where T<:GitObject
    ensure_initialized()
    obj_ptr_ptr = Ref{Ptr{Cvoid}}(C_NULL)
    @check ccall((:git_reference_peel, libgit2), Cint,
                 (Ptr{Ptr{Cvoid}}, Ptr{Cvoid}, Cint), obj_ptr_ptr, ref.ptr, Consts.OBJECT(T))
    return T(ref.owner, obj_ptr_ptr[])
end
peel(ref::GitReference) = peel(GitObject, ref)

"""
    LibGit2.ref_list(repo::GitRepo) -> Vector{String}

Get a list of all reference names in the `repo` repository.
"""
function ref_list(repo::GitRepo)
    ensure_initialized()
    sa_ref = Ref(StrArrayStruct())
    @check ccall((:git_reference_list, libgit2), Cint,
                      (Ptr{StrArrayStruct}, Ptr{Cvoid}), sa_ref, repo.ptr)
    res = convert(Vector{String}, sa_ref[])
    free(sa_ref)
    res
end

"""
    LibGit2.create_branch(repo::GitRepo, bname::AbstractString, commit_obj::GitCommit; force::Bool=false)

Create a new branch in the repository `repo` with name `bname`, which
points to commit `commit_obj` (which has to be part of `repo`). If
`force` is `true`, overwrite an existing branch named `bname` if it
exists. If `force` is `false` and a branch already exists named `bname`,
this function will throw an error.
"""
function create_branch(repo::GitRepo,
                       bname::AbstractString,
                       commit_obj::GitCommit;
                       force::Bool=false)
    ensure_initialized()
    ref_ptr_ptr = Ref{Ptr{Cvoid}}(C_NULL)
    @check ccall((:git_branch_create, libgit2), Cint,
                  (Ptr{Ptr{Cvoid}}, Ptr{Cvoid}, Cstring, Ptr{Cvoid}, Cint),
                   ref_ptr_ptr, repo.ptr, bname, commit_obj.ptr, Cint(force))
    return GitReference(repo, ref_ptr_ptr[])
end

"""
    LibGit2.delete_branch(branch::GitReference)

Delete the branch pointed to by `branch`.
"""
function delete_branch(branch::GitReference)
    ensure_initialized()
    @check ccall((:git_branch_delete, libgit2), Cint, (Ptr{Cvoid},), branch.ptr)
end

"""
    LibGit2.head!(repo::GitRepo, ref::GitReference) -> GitReference

Set the HEAD of `repo` to the object pointed to by `ref`.
"""
function head!(repo::GitRepo, ref::GitReference)
    ensure_initialized()
    ref_name = name(ref)
    @check ccall((:git_repository_set_head, libgit2), Cint,
                  (Ptr{Cvoid}, Cstring), repo.ptr, ref_name)
    return ref
end

"""
    lookup_branch(repo::GitRepo, branch_name::AbstractString, remote::Bool=false) -> Union{GitReference, Nothing}

Determine if the branch specified by `branch_name` exists in the repository `repo`.
If `remote` is `true`, `repo` is assumed to be a remote git repository. Otherwise, it
is part of the local filesystem.

Return either a `GitReference` to the requested branch
if it exists, or [`nothing`](@ref) if not.
"""
function lookup_branch(repo::GitRepo,
                       branch_name::AbstractString,
                       remote::Bool=false)
    ensure_initialized()
    ref_ptr_ptr = Ref{Ptr{Cvoid}}(C_NULL)
    branch_type = remote ? Consts.BRANCH_REMOTE : Consts.BRANCH_LOCAL
    err = ccall((:git_branch_lookup, libgit2), Cint,
                 (Ptr{Ptr{Cvoid}}, Ptr{Cvoid}, Ptr{UInt8}, Cint),
                  ref_ptr_ptr, repo.ptr, branch_name, branch_type)
    if err != Int(Error.GIT_OK)
        if err == Int(Error.ENOTFOUND)
            return nothing
        end
        if ref_ptr_ptr[] != C_NULL
            close(GitReference(repo, ref_ptr_ptr[]))
        end
        throw(Error.GitError(err))
    end
    return GitReference(repo, ref_ptr_ptr[])
end

"""
    upstream(ref::GitReference) -> Union{GitReference, Nothing}

Determine if the branch containing `ref` has a specified upstream branch.

Return either a `GitReference` to the upstream branch if it exists,
or [`nothing`](@ref) if the requested branch does not have an upstream counterpart.
"""
function upstream(ref::GitReference)
    isempty(ref) && return nothing
    ensure_initialized()
    ref_ptr_ptr = Ref{Ptr{Cvoid}}(C_NULL)
    err = ccall((:git_branch_upstream, libgit2), Cint,
                  (Ref{Ptr{Cvoid}}, Ptr{Cvoid},), ref_ptr_ptr, ref.ptr)
    if err != Int(Error.GIT_OK)
        if err == Int(Error.ENOTFOUND)
            return nothing
        end
        if ref_ptr_ptr[] != C_NULL
            close(GitReference(ref.owner, ref_ptr_ptr[]))
        end
        throw(Error.GitError(err))
    end
    return GitReference(ref.owner, ref_ptr_ptr[])
end

repository(ref::GitReference) = ref.owner

function target!(ref::GitReference, new_oid::GitHash; msg::AbstractString="")
    ensure_initialized()
    ref_ptr_ptr = Ref{Ptr{Cvoid}}(C_NULL)
    @check ccall((:git_reference_set_target, libgit2), Cint,
             (Ptr{Ptr{Cvoid}}, Ptr{Cvoid}, Ptr{GitHash}, Cstring),
             ref_ptr_ptr, ref.ptr, Ref(new_oid), isempty(msg) ? C_NULL : msg)
    return GitReference(ref.owner, ref_ptr_ptr[])
end

function GitBranchIter(repo::GitRepo, flags::Cint=Cint(Consts.BRANCH_LOCAL))
    ensure_initialized()
    bi_ptr = Ref{Ptr{Cvoid}}(C_NULL)
    @check ccall((:git_branch_iterator_new, libgit2), Cint,
                  (Ptr{Ptr{Cvoid}}, Ptr{Cvoid}, Cint), bi_ptr, repo.ptr, flags)
    return GitBranchIter(repo, bi_ptr[])
end

function Base.iterate(bi::GitBranchIter, state=nothing)
    ensure_initialized()
    ref_ptr_ptr = Ref{Ptr{Cvoid}}(C_NULL)
    btype = Ref{Cint}()
    err = ccall((:git_branch_next, libgit2), Cint,
                 (Ptr{Ptr{Cvoid}}, Ptr{Cint}, Ptr{Cvoid}),
                  ref_ptr_ptr, btype, bi.ptr)
    if err == Cint(Error.GIT_OK)
        return ((GitReference(bi.owner, ref_ptr_ptr[]), btype[]), nothing)
    elseif err == Cint(Error.ITEROVER)
        return nothing
    else
        throw(GitError(err))
    end
end

Base.IteratorSize(::Type{GitBranchIter}) = Base.SizeUnknown()
q   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LibGit2/src/commit.jl(      # This file is a part of Julia. License is MIT: https://julialang.org/license

repository(c::GitCommit) = c.owner

"""
    message(c::GitCommit, raw::Bool=false)

Return the commit message describing the changes made in commit `c`. If
`raw` is `false`, return a slightly "cleaned up" message (which has any
leading newlines removed). If `raw` is `true`, the message is not stripped
of any such newlines.
"""
function message(c::GitCommit, raw::Bool=false)
    ensure_initialized()
    GC.@preserve c begin
        local msg_ptr::Cstring
        msg_ptr = raw ? ccall((:git_commit_message_raw, libgit2), Cstring, (Ptr{Cvoid},), c.ptr) :
                        ccall((:git_commit_message, libgit2), Cstring, (Ptr{Cvoid},), c.ptr)
        if msg_ptr == C_NULL
            return nothing
        end
        msg_str = unsafe_string(msg_ptr)
    end
    return msg_str
end

"""
    author(c::GitCommit)

Return the `Signature` of the author of the commit `c`. The author is
the person who made changes to the relevant file(s). See also [`committer`](@ref).
"""
function author(c::GitCommit)
    ensure_initialized()
    GC.@preserve c begin
        ptr = ccall((:git_commit_author, libgit2), Ptr{SignatureStruct}, (Ptr{Cvoid},), c.ptr)
        @assert ptr != C_NULL
        sig = Signature(ptr)
    end
    return sig
end

"""
    committer(c::GitCommit)

Return the `Signature` of the committer of the commit `c`. The committer is
the person who committed the changes originally authored by the [`author`](@ref), but
need not be the same as the `author`, for example, if the `author` emailed a patch to
a `committer` who committed it.
"""
function committer(c::GitCommit)
    ensure_initialized()
    GC.@preserve c begin
        ptr = ccall((:git_commit_committer, libgit2), Ptr{SignatureStruct}, (Ptr{Cvoid},), c.ptr)
        sig = Signature(ptr)
    end
    return sig
end

function Base.show(io::IO, c::GitCommit)
    authstr = sprint(show, author(c))
    cmtrstr = sprint(show, committer(c))
    print(io, "Git Commit:\nCommit Author: $authstr\nCommitter: $cmtrstr\nSHA: $(GitHash(c))\nMessage:\n$(message(c))")
end

function commit(repo::GitRepo,
                refname::AbstractString,
                msg::AbstractString,
                author::GitSignature,
                committer::GitSignature,
                tree::GitTree,
                parents::GitCommit...)
    ensure_initialized()
    commit_id_ptr = Ref(GitHash())
    nparents = length(parents)
    parentptrs = Ptr{Cvoid}[c.ptr for c in parents]
    @check ccall((:git_commit_create, libgit2), Cint,
                 (Ptr{GitHash}, Ptr{Cvoid}, Ptr{UInt8},
                  Ptr{SignatureStruct}, Ptr{SignatureStruct},
                  Ptr{UInt8}, Ptr{UInt8}, Ptr{Cvoid},
                  Csize_t, Ptr{Ptr{Cvoid}}),
                 commit_id_ptr, repo.ptr, isempty(refname) ? C_NULL : refname,
                 author.ptr, committer.ptr,
                 C_NULL, msg, tree.ptr,
                 nparents, nparents > 0 ? parentptrs : C_NULL)
    return commit_id_ptr[]
end

"""
    commit(repo::GitRepo, msg::AbstractString; kwargs...) -> GitHash

Wrapper around [`git_commit_create`](https://libgit2.org/libgit2/#HEAD/group/commit/git_commit_create).
Create a commit in the repository `repo`. `msg` is the commit message. Return the OID of the new commit.

The keyword arguments are:
  * `refname::AbstractString=Consts.HEAD_FILE`: if not NULL, the name of the reference to update to point to
    the new commit. For example, `"HEAD"` will update the HEAD of the current branch. If the reference does
    not yet exist, it will be created.
  * `author::Signature = Signature(repo)` is a `Signature` containing information about the person who authored the commit.
  * `committer::Signature = Signature(repo)` is a `Signature` containing information about the person who committed the commit to
    the repository. Not necessarily the same as `author`, for instance if `author` emailed a patch to
    `committer` who committed it.
  * `tree_id::GitHash = GitHash()` is a git tree to use to create the commit, showing its ancestry and relationship with
    any other history. `tree` must belong to `repo`.
  * `parent_ids::Vector{GitHash}=GitHash[]` is a list of commits by [`GitHash`](@ref) to use as parent
    commits for the new one, and may be empty. A commit might have multiple parents if it is a merge commit, for example.
"""
function commit(repo::GitRepo, msg::AbstractString;
                refname::AbstractString=Consts.HEAD_FILE,
                author::Signature = Signature(repo),
                committer::Signature = Signature(repo),
                tree_id::GitHash = GitHash(),
                parent_ids::Vector{GitHash}=GitHash[])
    # Retrieve tree identifier
    if iszero(tree_id)
        tree_id = with(GitIndex, repo) do idx; write_tree!(idx) end
    end

    # Retrieve parents from HEAD
    if isempty(parent_ids)
        try # if throws then HEAD not found -> empty repo
            Base.push!(parent_ids, GitHash(repo, refname))
        catch
        end
    end

    # return commit id
    commit_id  = GitHash()

    # get necessary objects
    tree = GitTree(repo, tree_id)
    auth_sig = convert(GitSignature, author)
    comm_sig = convert(GitSignature, committer)
    parents = GitCommit[]
    try
        for id in parent_ids
            Base.push!(parents, GitCommit(repo, id))
        end
        commit_id = commit(repo, refname, msg, auth_sig, comm_sig, tree, parents...)
    finally
        for parent in parents
            close(parent)
        end
        close(tree)
        close(auth_sig)
        close(comm_sig)
    end
    return commit_id
end
u   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LibGit2/src/repository.jl�G      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
    LibGit2.GitRepo(path::AbstractString)

Open a git repository at `path`.
"""
function GitRepo(path::AbstractString)
    ensure_initialized()
    repo_ptr_ptr = Ref{Ptr{Cvoid}}(C_NULL)
    @check ccall((:git_repository_open, libgit2), Cint,
                 (Ptr{Ptr{Cvoid}}, Cstring), repo_ptr_ptr, path)
    return GitRepo(repo_ptr_ptr[])
end

"""
    LibGit2.GitRepoExt(path::AbstractString, flags::Cuint = Cuint(Consts.REPOSITORY_OPEN_DEFAULT))

Open a git repository at `path` with extended controls (for instance, if the current
user must be a member of a special access group to read `path`).
"""
function GitRepoExt(path::AbstractString, flags::Cuint = Cuint(Consts.REPOSITORY_OPEN_DEFAULT))
    ensure_initialized()
    separator = @static Sys.iswindows() ? ";" : ":"
    repo_ptr_ptr = Ref{Ptr{Cvoid}}(C_NULL)
    @check ccall((:git_repository_open_ext, libgit2), Cint,
                 (Ptr{Ptr{Cvoid}}, Cstring, Cuint, Cstring),
                 repo_ptr_ptr, path, flags, separator)
    return GitRepo(repo_ptr_ptr[])
end

function cleanup(r::GitRepo)
    if r.ptr != C_NULL
        ensure_initialized()
        @check ccall((:git_repository__cleanup, libgit2), Cint, (Ptr{Cvoid},), r.ptr)
    end
end

"""
    LibGit2.init(path::AbstractString, bare::Bool=false) -> GitRepo

Open a new git repository at `path`. If `bare` is `false`,
the working tree will be created in `path/.git`. If `bare`
is `true`, no working directory will be created.
"""
function init(path::AbstractString, bare::Bool=false)
    ensure_initialized()
    repo_ptr_ptr = Ref{Ptr{Cvoid}}(C_NULL)
    @check ccall((:git_repository_init, libgit2), Cint,
                (Ptr{Ptr{Cvoid}}, Cstring, Cuint), repo_ptr_ptr, path, bare)
    return GitRepo(repo_ptr_ptr[])
end

"""
    LibGit2.head_oid(repo::GitRepo) -> GitHash

Lookup the object id of the current HEAD of git
repository `repo`.
"""
function head_oid(repo::GitRepo)
    head_ref = head(repo)
    try
        return GitHash(head_ref)
    finally
        close(head_ref)
    end
end

"""
    LibGit2.headname(repo::GitRepo)

Lookup the name of the current HEAD of git
repository `repo`. If `repo` is currently
detached, return the name of the HEAD it's
detached from.
"""
function headname(repo::GitRepo)
    with(head(repo)) do href
        if isattached(repo)
            shortname(href)
        else
            "(detached from $(string(GitHash(href))[1:7]))"
        end
    end
end

"""
    isbare(repo::GitRepo) -> Bool

Determine if `repo` is bare. Suppose the top level directory of `repo` is `DIR`.
A non-bare repository is one in which the git directory (see [`gitdir`](@ref)) is
`DIR/.git`, and the working tree can be checked out. A bare repository is one in
which all of git's administrative files are simply in `DIR`, rather than "hidden"
in the `.git` subdirectory. This means that there is nowhere to check out the working
tree, and no tracking information for remote branches or configurations is present.
"""
function isbare(repo::GitRepo)
    ensure_initialized()
    @assert repo.ptr != C_NULL
    return ccall((:git_repository_is_bare, libgit2), Cint, (Ptr{Cvoid},), repo.ptr) == 1
end

"""
    isattached(repo::GitRepo) -> Bool

Determine if `repo` is detached - that is, whether its HEAD points to a commit
(detached) or whether HEAD points to a branch tip (attached).
"""
function isattached(repo::GitRepo)
    ensure_initialized()
    @assert repo.ptr != C_NULL
    ccall((:git_repository_head_detached, libgit2), Cint, (Ptr{Cvoid},), repo.ptr) != 1
end

@doc """
    GitObject(repo::GitRepo, hash::AbstractGitHash)
    GitObject(repo::GitRepo, spec::AbstractString)

Return the specified object ([`GitCommit`](@ref), [`GitBlob`](@ref), [`GitTree`](@ref) or [`GitTag`](@ref)) from `repo`
specified by `hash`/`spec`.

- `hash` is a full (`GitHash`) or partial (`GitShortHash`) hash.
- `spec` is a textual specification: see [the git docs](https://git-scm.com/docs/git-rev-parse.html#_specifying_revisions) for a full list.
""" GitObject

for T in (:GitCommit, :GitBlob, :GitTree, :GitTag)
    @eval @doc $"""
    $T(repo::GitRepo, hash::AbstractGitHash)
    $T(repo::GitRepo, spec::AbstractString)

Return a `$T` object from `repo` specified by `hash`/`spec`.

- `hash` is a full (`GitHash`) or partial (`GitShortHash`) hash.
- `spec` is a textual specification: see [the git docs](https://git-scm.com/docs/git-rev-parse.html#_specifying_revisions) for a full list.
""" $T
end

function (::Type{T})(repo::GitRepo, spec::AbstractString) where T<:GitObject
    ensure_initialized()
    obj_ptr_ptr = Ref{Ptr{Cvoid}}(C_NULL)
    @assert repo.ptr != C_NULL
    @check ccall((:git_revparse_single, libgit2), Cint,
                 (Ptr{Ptr{Cvoid}}, Ptr{Cvoid}, Cstring), obj_ptr_ptr, repo.ptr, spec)
    # check object is of correct type
    if T != GitObject && T != GitUnknownObject
        t = Consts.OBJECT(obj_ptr_ptr[])
        t == Consts.OBJECT(T) || throw(GitError(Error.Object, Error.ERROR, "Expected object of type $T, received object of type $(objtype(t))"))
    end
    return T(repo, obj_ptr_ptr[])
end

function (::Type{T})(repo::GitRepo, oid::GitHash) where T<:GitObject
    ensure_initialized()
    oid_ptr  = Ref(oid)
    obj_ptr_ptr = Ref{Ptr{Cvoid}}(C_NULL)

    @assert repo.ptr != C_NULL
    @check ccall((:git_object_lookup, libgit2), Cint,
                 (Ptr{Ptr{Cvoid}}, Ptr{Cvoid}, Ptr{GitHash}, Consts.OBJECT),
                 obj_ptr_ptr, repo.ptr, oid_ptr, Consts.OBJECT(T))

    return T(repo, obj_ptr_ptr[])
end
function (::Type{T})(repo::GitRepo, oid::GitShortHash) where T<:GitObject
    ensure_initialized()
    oid_ptr  = Ref(oid.hash)
    obj_ptr_ptr = Ref{Ptr{Cvoid}}(C_NULL)

    @assert repo.ptr != C_NULL
    @check ccall((:git_object_lookup_prefix, libgit2), Cint,
                 (Ptr{Ptr{Cvoid}}, Ptr{Cvoid}, Ptr{GitHash}, Csize_t, Consts.OBJECT),
                 obj_ptr_ptr, repo.ptr, oid_ptr, oid.len, Consts.OBJECT(T))

    return T(repo, obj_ptr_ptr[])
end

# TODO: deprecate this function
revparseid(repo::GitRepo, spec) = GitHash(GitUnknownObject(repo, spec))

"""
    LibGit2.gitdir(repo::GitRepo)

Return the location of the "git" files of `repo`:

 - for normal repositories, this is the location of the `.git` folder.
 - for bare repositories, this is the location of the repository itself.

See also [`workdir`](@ref), [`path`](@ref).
"""
function gitdir(repo::GitRepo)
    ensure_initialized()
    @assert repo.ptr != C_NULL
    return unsafe_string(ccall((:git_repository_path, libgit2), Cstring,
                        (Ptr{Cvoid},), repo.ptr))
end

"""
    LibGit2.workdir(repo::GitRepo)

Return the location of the working directory of `repo`.
This will throw an error for bare repositories.

!!! note

    This will typically be the parent directory of `gitdir(repo)`, but can be different in
    some cases: e.g. if either the `core.worktree` configuration variable or the
    `GIT_WORK_TREE` environment variable is set.

See also [`gitdir`](@ref), [`path`](@ref).
"""
function workdir(repo::GitRepo)
    ensure_initialized()
    @assert repo.ptr != C_NULL
    sptr = ccall((:git_repository_workdir, libgit2), Cstring,
                (Ptr{Cvoid},), repo.ptr)
    sptr == C_NULL && throw(GitError(Error.Object, Error.ERROR, "No working directory found."))
    return unsafe_string(sptr)
end

"""
    LibGit2.path(repo::GitRepo)

Return the base file path of the repository `repo`.

 - for normal repositories, this will typically be the parent directory of the ".git"
   directory (note: this may be different than the working directory, see `workdir` for
   more details).
 - for bare repositories, this is the location of the "git" files.

See also [`gitdir`](@ref), [`workdir`](@ref).
"""
function path(repo::GitRepo)
    d = gitdir(repo)
    if isdirpath(d)
        d = dirname(d) # strip trailing separator
    end
    if isbare(repo)
        return d
    else
        parent, base = splitdir(d)
        return base == ".git" ? parent : d
    end
end

"""
    peel([T,] obj::GitObject)

Recursively peel `obj` until an object of type `T` is obtained. If no `T` is provided,
then `obj` will be peeled until the type changes.

- A `GitTag` will be peeled to the object it references.
- A `GitCommit` will be peeled to a `GitTree`.
"""
function peel(::Type{T}, obj::GitObject) where T<:GitObject
    ensure_initialized()
    new_ptr_ptr = Ref{Ptr{Cvoid}}(C_NULL)

    @check ccall((:git_object_peel, libgit2), Cint,
                (Ptr{Ptr{Cvoid}}, Ptr{Cvoid}, Cint), new_ptr_ptr, obj.ptr, Consts.OBJECT(T))

    return T(obj.owner, new_ptr_ptr[])
end
peel(obj::GitObject) = peel(GitObject, obj)

"""
    LibGit2.GitDescribeResult(committish::GitObject; kwarg...)

Produce a `GitDescribeResult` of the `committish` `GitObject`, which
contains detailed information about it based on the keyword argument:

  * `options::DescribeOptions=DescribeOptions()`

A git description of a `committish` object looks for the tag (by default, annotated,
although a search of all tags can be performed) which can be reached from `committish`
which is most recent. If the tag is pointing to `committish`, then only the tag is
included in the description. Otherwise, a suffix is included which contains the
number of commits between `committish` and the most recent tag. If there is no such
tag, the default behavior is for the description to fail, although this can be
changed through `options`.

Equivalent to `git describe <committish>`. See [`DescribeOptions`](@ref) for more
information.
"""
function GitDescribeResult(committish::GitObject;
                           options::DescribeOptions=DescribeOptions())
    ensure_initialized()
    result_ptr_ptr = Ref{Ptr{Cvoid}}(C_NULL)
    @check ccall((:git_describe_commit, libgit2), Cint,
                 (Ptr{Ptr{Cvoid}}, Ptr{Cvoid}, Ptr{DescribeOptions}),
                 result_ptr_ptr, committish.ptr, Ref(options))
    return GitDescribeResult(committish.owner, result_ptr_ptr[])
end

"""
    LibGit2.GitDescribeResult(repo::GitRepo; kwarg...)

Produce a `GitDescribeResult` of the repository `repo`'s working directory.
The `GitDescribeResult` contains detailed information about the workdir based
on the keyword argument:

  * `options::DescribeOptions=DescribeOptions()`

In this case, the description is run on HEAD, producing the most recent tag
which is an ancestor of HEAD. Afterwards, a status check on
the [`workdir`](@ref) is performed and if the `workdir` is dirty
(see [`isdirty`](@ref)) the description is also considered dirty.

Equivalent to `git describe`. See [`DescribeOptions`](@ref) for more
information.
"""
function GitDescribeResult(repo::GitRepo; options::DescribeOptions=DescribeOptions())
    ensure_initialized()
    result_ptr_ptr = Ref{Ptr{Cvoid}}(C_NULL)
    @assert repo.ptr != C_NULL
    @check ccall((:git_describe_workdir, libgit2), Cint,
                 (Ptr{Ptr{Cvoid}}, Ptr{Cvoid}, Ptr{DescribeOptions}),
                 result_ptr_ptr, repo.ptr, Ref(options))
    return GitDescribeResult(repo, result_ptr_ptr[])
end

"""
    LibGit2.format(result::GitDescribeResult; kwarg...) -> String

Produce a formatted string based on a `GitDescribeResult`.
Formatting options are controlled by the keyword argument:

  * `options::DescribeFormatOptions=DescribeFormatOptions()`
"""
function format(result::GitDescribeResult; options::DescribeFormatOptions=DescribeFormatOptions())
    ensure_initialized()
    buf_ref = Ref(Buffer())
    @check ccall((:git_describe_format, libgit2), Cint,
                 (Ptr{Buffer}, Ptr{Cvoid}, Ptr{DescribeFormatOptions}),
                 buf_ref, result.ptr, Ref(options))
    buf = buf_ref[]
    str = unsafe_string(buf.ptr, buf.size)
    free(buf_ref)
    return str
end

function Base.show(io::IO, result::GitDescribeResult)
    fmt_desc = format(result)
    println(io, "GitDescribeResult:")
    println(io, fmt_desc)
end

"""
    checkout_tree(repo::GitRepo, obj::GitObject; options::CheckoutOptions = CheckoutOptions())

Update the working tree and index of `repo` to match the tree pointed to by `obj`.
`obj` can be a commit, a tag, or a tree. `options` controls how the checkout will
be performed. See [`CheckoutOptions`](@ref) for more information.
"""
function checkout_tree(repo::GitRepo, obj::GitObject;
                       options::CheckoutOptions = CheckoutOptions())
    ensure_initialized()
    @assert repo.ptr != C_NULL
    @check ccall((:git_checkout_tree, libgit2), Cint,
                 (Ptr{Cvoid}, Ptr{Cvoid}, Ptr{CheckoutOptions}),
                 repo.ptr, obj.ptr, Ref(options))
end

"""
    checkout_index(repo::GitRepo, idx::Union{GitIndex, Nothing} = nothing; options::CheckoutOptions = CheckoutOptions())

Update the working tree of `repo` to match the index `idx`. If `idx` is `nothing`, the
index of `repo` will be used. `options` controls how the checkout will be performed.
See [`CheckoutOptions`](@ref) for more information.
"""
function checkout_index(repo::GitRepo, idx::Union{GitIndex, Nothing} = nothing;
                        options::CheckoutOptions = CheckoutOptions())
    ensure_initialized()
    @assert repo.ptr != C_NULL
    @check ccall((:git_checkout_index, libgit2), Cint,
                 (Ptr{Cvoid}, Ptr{Cvoid}, Ptr{CheckoutOptions}),
                 repo.ptr,
                 idx === nothing ? C_NULL : idx.ptr,
                 Ref(options))
end

"""
    checkout_head(repo::GitRepo; options::CheckoutOptions = CheckoutOptions())

Update the index and working tree of `repo` to match the commit pointed to by HEAD.
`options` controls how the checkout will be performed. See [`CheckoutOptions`](@ref) for more information.

!!! warning
    *Do not* use this function to switch branches! Doing so will cause checkout
    conflicts.
"""
function checkout_head(repo::GitRepo; options::CheckoutOptions = CheckoutOptions())
    ensure_initialized()
    @assert repo.ptr != C_NULL
    @check ccall((:git_checkout_head, libgit2), Cint,
                 (Ptr{Cvoid}, Ptr{CheckoutOptions}),
                 repo.ptr, Ref(options))
end

"""
    LibGit2.cherrypick(repo::GitRepo, commit::GitCommit; options::CherrypickOptions = CherrypickOptions())

Cherrypick the commit `commit` and apply the changes in it to the current state of `repo`.
The keyword argument `options` sets checkout and merge options for the cherrypick.

!!! note
    `cherrypick` will *apply* the changes in `commit` but not *commit* them, so `repo` will
    be left in a dirty state. If you want to also commit the changes in `commit` you must
    call [`commit`](@ref) yourself.
"""
function cherrypick(repo::GitRepo, commit::GitCommit; options::CherrypickOptions = CherrypickOptions())
    ensure_initialized()
    @assert repo.ptr != C_NULL
    @check ccall((:git_cherrypick, libgit2), Cint,
                 (Ptr{Cvoid}, Ptr{Cvoid}, Ptr{CherrypickOptions}),
                 repo.ptr, commit.ptr, Ref(options))
end

"""Updates some entries, determined by the `pathspecs`, in the index from the target commit tree."""
function reset!(repo::GitRepo, obj::Union{GitObject, Nothing}, pathspecs::AbstractString...)
    ensure_initialized()
    @assert repo.ptr != C_NULL
    @check ccall((:git_reset_default, libgit2), Cint,
                 (Ptr{Cvoid}, Ptr{Cvoid}, Ptr{StrArrayStruct}),
                 repo.ptr,
                 obj === nothing ? C_NULL : obj.ptr,
                 collect(pathspecs))
    return head_oid(repo)
end

"""Sets the current head to the specified commit oid and optionally resets the index and working tree to match."""
function reset!(repo::GitRepo, obj::GitObject, mode::Cint;
               checkout_opts::CheckoutOptions = CheckoutOptions())
    ensure_initialized()
    @assert repo.ptr != C_NULL
    @check ccall((:git_reset, libgit2), Cint,
                 (Ptr{Cvoid}, Ptr{Cvoid}, Cint, Ptr{CheckoutOptions}),
                  repo.ptr, obj.ptr, mode, Ref(checkout_opts))
    return head_oid(repo)
end

"""
    clone(repo_url::AbstractString, repo_path::AbstractString, clone_opts::CloneOptions)

Clone the remote repository at `repo_url` (which can be a remote URL or a path on the local
filesystem) to `repo_path` (which must be a path on the local filesystem). Options for the
clone, such as whether to perform a bare clone or not, are set by [`CloneOptions`](@ref).

# Examples
```julia
repo_url = "https://github.com/JuliaLang/Example.jl"
repo = LibGit2.clone(repo_url, "/home/me/projects/Example")
```
"""
function clone(repo_url::AbstractString, repo_path::AbstractString,
               clone_opts::CloneOptions)
    ensure_initialized()
    clone_opts_ref = Ref(clone_opts)
    repo_ptr_ptr = Ref{Ptr{Cvoid}}(C_NULL)
    @check ccall((:git_clone, libgit2), Cint,
            (Ptr{Ptr{Cvoid}}, Cstring, Cstring, Ref{CloneOptions}),
            repo_ptr_ptr, repo_url, repo_path, clone_opts_ref)
    return GitRepo(repo_ptr_ptr[])
end

"""
    fetchheads(repo::GitRepo) -> Vector{FetchHead}

Return the list of all the fetch heads for `repo`, each represented as a [`FetchHead`](@ref),
including their names, URLs, and merge statuses.

# Examples
```julia-repl
julia> fetch_heads = LibGit2.fetchheads(repo);

julia> fetch_heads[1].name
"refs/heads/master"

julia> fetch_heads[1].ismerge
true

julia> fetch_heads[2].name
"refs/heads/test_branch"

julia> fetch_heads[2].ismerge
false
```
"""
function fetchheads(repo::GitRepo)
    ensure_initialized()
    fh = FetchHead[]
    ffcb = fetchhead_foreach_cb()
    @assert repo.ptr != C_NULL
    @check ccall((:git_repository_fetchhead_foreach, libgit2), Cint,
                 (Ptr{Cvoid}, Ptr{Cvoid}, Any),
                 repo.ptr, ffcb, fh)
    return fh
end

"""
    LibGit2.remotes(repo::GitRepo)

Return a vector of the names of the remotes of `repo`.
"""
function remotes(repo::GitRepo)
    ensure_initialized()
    sa_ref = Ref(StrArrayStruct())
    @assert repo.ptr != C_NULL
    @check ccall((:git_remote_list, libgit2), Cint,
                  (Ptr{StrArrayStruct}, Ptr{Cvoid}), sa_ref, repo.ptr)
    res = convert(Vector{String}, sa_ref[])
    free(sa_ref)
    return res
end

function Base.show(io::IO, repo::GitRepo)
    print(io, "LibGit2.GitRepo(")
    if repo.ptr == C_NULL
        print(io, "<closed>")
    else
        show(io, path(repo))
    end
    print(io, ")")
end
q   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LibGit2/src/config.jlI!      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
    GitConfig(path::AbstractString, level::Consts.GIT_CONFIG=Consts.CONFIG_LEVEL_APP, force::Bool=false)

Create a new `GitConfig` by loading configuration information from the file at `path`. See
[`addfile`](@ref) for more information about the `level`, `repo` and `force` options.
"""
function GitConfig(path::AbstractString,
                   level::Consts.GIT_CONFIG = Consts.CONFIG_LEVEL_APP,
                   repo::Union{GitRepo, Nothing}=nothing,
                   force::Bool=false)
    ensure_initialized()
    # create new config object
    cfg_ptr_ptr = Ref{Ptr{Cvoid}}(C_NULL)
    @check ccall((:git_config_new, libgit2), Cint, (Ptr{Ptr{Cvoid}},), cfg_ptr_ptr)
    cfg = GitConfig(cfg_ptr_ptr[])
    try
        addfile(cfg, path, level, repo, force)
    catch
        close(cfg)
        rethrow()
    end
    return cfg
end

"""
    GitConfig(repo::GitRepo)

Get the stored configuration for the git repository `repo`. If `repo` does not
have a specific configuration file set, the default git configuration will be
used.
"""
function GitConfig(repo::GitRepo)
    ensure_initialized()
    cfg_ptr_ptr = Ref{Ptr{Cvoid}}(C_NULL)
    @check ccall((:git_repository_config, libgit2), Cint,
                  (Ptr{Ptr{Cvoid}}, Ptr{Cvoid}), cfg_ptr_ptr, repo.ptr)
    return GitConfig(repo, cfg_ptr_ptr[])
end

"""
    GitConfig(level::Consts.GIT_CONFIG=Consts.CONFIG_LEVEL_DEFAULT)

Get the default git configuration by loading the global and system configuration
files into a prioritized configuration. This can be used to access default configuration
options outside a specific git repository.
"""
function GitConfig(level::Consts.GIT_CONFIG = Consts.CONFIG_LEVEL_DEFAULT)
    ensure_initialized()
    cfg_ptr_ptr = Ref{Ptr{Cvoid}}(C_NULL)
    @check ccall((:git_config_open_default, libgit2), Cint,
                  (Ptr{Ptr{Cvoid}},), cfg_ptr_ptr)
    cfg = GitConfig(cfg_ptr_ptr[])
    if level != Consts.CONFIG_LEVEL_DEFAULT
        glb_cfg_ptr_ptr = Ref{Ptr{Cvoid}}(C_NULL)
        tmpcfg = cfg
        try
            @check ccall((:git_config_open_level, libgit2), Cint,
                         (Ptr{Ptr{Cvoid}}, Ptr{Cvoid}, Cint),
                          glb_cfg_ptr_ptr, cfg.ptr, Cint(level))
            cfg = GitConfig(glb_cfg_ptr_ptr[])
        finally
            close(tmpcfg)
        end
    end
    return cfg
end

"""
    addfile(cfg::GitConfig, path::AbstractString,
            level::Consts.GIT_CONFIG=Consts.CONFIG_LEVEL_APP,
            repo::Union{GitRepo, Nothing} = nothing,
            force::Bool=false)

Add an existing git configuration file located at `path` to the current
`GitConfig` `cfg`. If the file does not exist, it will be created.

 - `level` sets the git configuration priority level and is determined by
[`Consts.GIT_CONFIG`](@ref).
 - `repo` is an optional repository to allow parsing of conditional includes.
 - If `force` is `false` and a configuration for the given priority level already exists,
`addfile` will error. If `force` is `true`, the existing configuration will be replaced by
the one in the file at `path`.

"""
function addfile(cfg::GitConfig, path::AbstractString,
                 level::Consts.GIT_CONFIG = Consts.CONFIG_LEVEL_APP,
                 repo::Union{GitRepo, Nothing} = nothing,
                 force::Bool=false)
    ensure_initialized()
    @static if LibGit2.VERSION >= v"0.27.0"
        @check ccall((:git_config_add_file_ondisk, libgit2), Cint,
                     (Ptr{Ptr{Cvoid}}, Cstring, Cint, Ptr{Cvoid}, Cint),
                     cfg.ptr, path, Cint(level), isa(repo, GitRepo) ? repo.ptr : C_NULL, Cint(force))
    else
        repo === nothing || error("repo argument is not supported in this version of LibGit2")
        @check ccall((:git_config_add_file_ondisk, libgit2), Cint,
                     (Ptr{Ptr{Cvoid}}, Cstring, Cint, Cint),
                     cfg.ptr, path, Cint(level), Cint(force))
    end
end

function get(::Type{<:AbstractString}, c::GitConfig, name::AbstractString)
    ensure_initialized()
    buf_ref = Ref(Buffer())
    @check ccall((:git_config_get_string_buf, libgit2), Cint,
                 (Ptr{Buffer}, Ptr{Cvoid}, Cstring), buf_ref, c.ptr, name)
    buf = buf_ref[]
    str = unsafe_string(buf.ptr, buf.size)
    free(buf_ref)
    str
end

function get(::Type{Bool}, c::GitConfig, name::AbstractString)
    ensure_initialized()
    val_ptr = Ref(Cint(0))
    @check ccall((:git_config_get_bool, libgit2), Cint,
          (Ptr{Cint}, Ptr{Cvoid}, Cstring), val_ptr, c.ptr, name)
    return Bool(val_ptr[])
end

function get(::Type{Int32}, c::GitConfig, name::AbstractString)
    ensure_initialized()
    val_ptr = Ref(Cint(0))
    @check ccall((:git_config_get_int32, libgit2), Cint,
          (Ptr{Cint}, Ptr{Cvoid}, Cstring), val_ptr, c.ptr, name)
    return val_ptr[]
end

function get(::Type{Int64}, c::GitConfig, name::AbstractString)
    ensure_initialized()
    val_ptr = Ref(Cintmax_t(0))
    @check ccall((:git_config_get_int64, libgit2), Cint,
          (Ptr{Cintmax_t}, Ptr{Cvoid}, Cstring), val_ptr, c.ptr, name)
    return val_ptr[]
end

function get(c::GitConfig, name::AbstractString, default::T) where T
    res = default
    try res = get(T,c,name); catch; end
    return res
end

function getconfig(r::GitRepo, name::AbstractString, default)
    with(GitConfig, r) do cfg
        get(cfg, name, default)
    end
end

function getconfig(rname::AbstractString, name::AbstractString, default)
    with(GitRepo, rname) do r
        with(GitConfig, r) do cfg
            get(cfg, name, default)
        end
    end
end

function getconfig(name::AbstractString, default)
    with(GitConfig) do cfg
        get(cfg, name, default)
    end
end

function set!(c::GitConfig, name::AbstractString, value::AbstractString)
    ensure_initialized()
    @check ccall((:git_config_set_string, libgit2), Cint,
                  (Ptr{Cvoid}, Cstring, Cstring), c.ptr, name, value)
end

function set!(c::GitConfig, name::AbstractString, value::Bool)
    ensure_initialized()
    bval = Int32(value)
    @check ccall((:git_config_set_bool, libgit2), Cint,
                  (Ptr{Cvoid}, Cstring, Cint), c.ptr, name, bval)
end

function set!(c::GitConfig, name::AbstractString, value::Int32)
    ensure_initialized()
    @check ccall((:git_config_set_int32, libgit2), Cint,
                  (Ptr{Cvoid}, Cstring, Cint), c.ptr, name, value)
end

function set!(c::GitConfig, name::AbstractString, value::Int64)
    ensure_initialized()
    @check ccall((:git_config_set_int64, libgit2), Cint,
                  (Ptr{Cvoid}, Cstring, Cintmax_t), c.ptr, name, value)
end

function GitConfigIter(cfg::GitConfig)
    ensure_initialized()
    ci_ptr = Ref{Ptr{Cvoid}}(C_NULL)
    @check ccall((:git_config_iterator_new, libgit2), Cint,
                  (Ptr{Ptr{Cvoid}}, Ptr{Cvoid}), ci_ptr, cfg.ptr)
    return GitConfigIter(ci_ptr[])
end

function GitConfigIter(cfg::GitConfig, name::AbstractString)
    ensure_initialized()
    ci_ptr = Ref{Ptr{Cvoid}}(C_NULL)
    @check ccall((:git_config_multivar_iterator_new, libgit2), Cint,
                  (Ptr{Ptr{Cvoid}}, Ptr{Cvoid}, Cstring, Cstring),
                  ci_ptr, cfg.ptr, name, C_NULL)
    return GitConfigIter(ci_ptr[])
end

function GitConfigIter(cfg::GitConfig, name::AbstractString, value::Regex)
    ensure_initialized()
    ci_ptr = Ref{Ptr{Cvoid}}(C_NULL)
    @check ccall((:git_config_multivar_iterator_new, libgit2), Cint,
                  (Ptr{Ptr{Cvoid}}, Ptr{Cvoid}, Cstring, Cstring),
                  ci_ptr, cfg.ptr, name, value.pattern)
    return GitConfigIter(ci_ptr[])
end

function GitConfigIter(cfg::GitConfig, name::Regex)
    ensure_initialized()
    ci_ptr = Ref{Ptr{Cvoid}}(C_NULL)
    @check ccall((:git_config_iterator_glob_new, libgit2), Cint,
                  (Ptr{Ptr{Cvoid}}, Ptr{Cvoid}, Cstring),
                  ci_ptr, cfg.ptr, name.pattern)
    return GitConfigIter(ci_ptr[])
end

function Base.iterate(ci::GitConfigIter, state=nothing)
    ensure_initialized()
    entry_ptr_ptr = Ref{Ptr{ConfigEntry}}(C_NULL)
    err = ccall((:git_config_next, libgit2), Cint,
                 (Ptr{Ptr{ConfigEntry}}, Ptr{Cvoid}), entry_ptr_ptr, ci.ptr)
    if err == Cint(Error.GIT_OK)
        return (unsafe_load(entry_ptr_ptr[]), nothing)
    elseif err == Cint(Error.ITEROVER)
        return nothing
    else
        throw(GitError(err))
    end
end

Base.IteratorSize(::Type{GitConfigIter}) = Base.SizeUnknown()
q   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LibGit2/src/walker.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
    GitRevWalker(repo::GitRepo)

A `GitRevWalker` *walks* through the *revisions* (i.e. commits) of
a git repository `repo`. It is a collection of the commits
in the repository, and supports iteration and calls to [`LibGit2.map`](@ref)
and [`LibGit2.count`](@ref) (for instance, `LibGit2.count` could be used to determine
what percentage of commits in a repository were made by a certain
author).

```julia
cnt = LibGit2.with(LibGit2.GitRevWalker(repo)) do walker
    LibGit2.count((oid,repo)->(oid == commit_oid1), walker, oid=commit_oid1, by=LibGit2.Consts.SORT_TIME)
end
```
Here, `LibGit2.count` finds the number of commits along the walk with a certain `GitHash`.
Since the `GitHash` is unique to a commit, `cnt` will be `1`.
"""
function GitRevWalker(repo::GitRepo)
    ensure_initialized()
    w_ptr = Ref{Ptr{Cvoid}}(C_NULL)
    @check ccall((:git_revwalk_new, libgit2), Cint,
                  (Ptr{Ptr{Cvoid}}, Ptr{Cvoid}), w_ptr, repo.ptr)
    return GitRevWalker(repo, w_ptr[])
end

function Base.iterate(w::GitRevWalker, state=nothing)
    ensure_initialized()
    id_ptr = Ref(GitHash())
    err = ccall((:git_revwalk_next, libgit2), Cint,
                (Ptr{GitHash}, Ptr{Cvoid}), id_ptr, w.ptr)
    if err == Cint(Error.GIT_OK)
        return (id_ptr[], nothing)
    elseif err == Cint(Error.ITEROVER)
        return nothing
    else
        throw(GitError(err))
    end
end

Base.IteratorSize(::Type{GitRevWalker}) = Base.SizeUnknown()

"""
    LibGit2.push_head!(w::GitRevWalker)

Push the HEAD commit and its ancestors onto the [`GitRevWalker`](@ref)
`w`. This ensures that HEAD and all its ancestor commits will be encountered
during the walk.
"""
function push_head!(w::GitRevWalker)
    ensure_initialized()
    @check ccall((:git_revwalk_push_head, libgit2), Cint, (Ptr{Cvoid},), w.ptr)
    return w
end

"""
    LibGit2.push!(w::GitRevWalker, cid::GitHash)

Start the [`GitRevWalker`](@ref) `walker` at commit `cid`. This function can be used
to apply a function to all commits since a certain year, by passing the first commit
of that year as `cid` and then passing the resulting `w` to [`LibGit2.map`](@ref).
"""
function push!(w::GitRevWalker, cid::GitHash)
    ensure_initialized()
    @check ccall((:git_revwalk_push, libgit2), Cint, (Ptr{Cvoid}, Ptr{GitHash}), w.ptr, Ref(cid))
    return w
end

function push!(w::GitRevWalker, range::AbstractString)
    ensure_initialized()
    @check ccall((:git_revwalk_push_range, libgit2), Cint, (Ptr{Cvoid}, Ptr{UInt8}), w.ptr, range)
    return w
end

function Base.sort!(w::GitRevWalker; by::Cint = Consts.SORT_NONE, rev::Bool=false)
    ensure_initialized()
    rev && (by |= Consts.SORT_REVERSE)
    @check ccall((:git_revwalk_sorting, libgit2), Cint, (Ptr{Cvoid}, Cint), w.ptr, by)
    return w
end

repository(w::GitRevWalker) = w.owner

"""
    LibGit2.map(f::Function, walker::GitRevWalker; oid::GitHash=GitHash(), range::AbstractString="", by::Cint=Consts.SORT_NONE, rev::Bool=false)

Using the [`GitRevWalker`](@ref) `walker` to "walk" over every commit in the repository's history,
apply `f` to each commit in the walk. The keyword arguments are:
    * `oid`: The [`GitHash`](@ref) of the commit to begin the walk from. The default is to use
      [`push_head!`](@ref) and therefore the HEAD commit and all its ancestors.
    * `range`: A range of `GitHash`s in the format `oid1..oid2`. `f` will be
      applied to all commits between the two.
    * `by`: The sorting method. The default is not to sort. Other options are to sort by
      topology (`LibGit2.Consts.SORT_TOPOLOGICAL`), to sort forwards in time
      (`LibGit2.Consts.SORT_TIME`, most ancient first) or to sort backwards in time
      (`LibGit2.Consts.SORT_REVERSE`, most recent first).
    * `rev`: Whether to reverse the sorted order (for instance, if topological sorting is used).

# Examples
```julia
oids = LibGit2.with(LibGit2.GitRevWalker(repo)) do walker
    LibGit2.map((oid, repo)->string(oid), walker, by=LibGit2.Consts.SORT_TIME)
end
```
Here, `LibGit2.map` visits each commit using the `GitRevWalker` and finds its `GitHash`.
"""
function map(f::Function, walker::GitRevWalker;
                  oid::GitHash=GitHash(),
                  range::AbstractString="",
                  by::Cint = Consts.SORT_NONE,
                  rev::Bool=false,
                  count::Int=0)
    res = []
    sort!(walker, by=by, rev=rev)
    if !iszero(oid)
        push!(walker, oid)
    elseif !isempty(range)
        push!(walker, range)
    else
        push_head!(walker)
    end

    repo = repository(walker)
    for val in (count == 0 ? walker : Iterators.take(walker, count))
        Base.push!(res, f(val, repo))
    end
    return res
end

"""
    LibGit2.count(f::Function, walker::GitRevWalker; oid::GitHash=GitHash(), by::Cint=Consts.SORT_NONE, rev::Bool=false)

Using the [`GitRevWalker`](@ref) `walker` to "walk" over every commit in the repository's history,
find the number of commits which return `true` when `f` is applied to them. The keyword arguments
are:
    * `oid`: The [`GitHash`](@ref) of the commit to begin the walk from. The default is to use
      [`push_head!`](@ref) and therefore the HEAD commit and all its ancestors.
    * `by`: The sorting method. The default is not to sort. Other options are to sort by
      topology (`LibGit2.Consts.SORT_TOPOLOGICAL`), to sort forwards in time
      (`LibGit2.Consts.SORT_TIME`, most ancient first) or to sort backwards in time
      (`LibGit2.Consts.SORT_REVERSE`, most recent first).
    * `rev`: Whether to reverse the sorted order (for instance, if topological sorting is used).

# Examples
```julia
cnt = LibGit2.with(LibGit2.GitRevWalker(repo)) do walker
    LibGit2.count((oid, repo)->(oid == commit_oid1), walker, oid=commit_oid1, by=LibGit2.Consts.SORT_TIME)
end
```
`LibGit2.count` finds the number of commits along the walk with a certain `GitHash` `commit_oid1`, starting
the walk from that commit and moving forwards in time from it. Since the `GitHash` is unique to
a commit, `cnt` will be `1`.
"""
function count(f::Function, walker::GitRevWalker;
                  oid::GitHash=GitHash(),
                  by::Cint = Consts.SORT_NONE,
                  rev::Bool=false)
    c = 0
    sort!(walker, by=by, rev=rev)
    if !iszero(oid)
        push!(walker, oid)
    else
        push_head!(walker)
    end

    repo = repository(walker)
    for val in walker
        c += f(val, repo) == true
    end
    return c
end
q   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LibGit2/src/remote.jl�4      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
    GitRemote(repo::GitRepo, rmt_name::AbstractString, rmt_url::AbstractString) -> GitRemote

Look up a remote git repository using its name and URL. Uses the default fetch refspec.

# Examples
```julia
repo = LibGit2.init(repo_path)
remote = LibGit2.GitRemote(repo, "upstream", repo_url)
```
"""
function GitRemote(repo::GitRepo, rmt_name::AbstractString, rmt_url::AbstractString)
    ensure_initialized()
    rmt_ptr_ptr = Ref{Ptr{Cvoid}}(C_NULL)
    @check ccall((:git_remote_create, libgit2), Cint,
                (Ptr{Ptr{Cvoid}}, Ptr{Cvoid}, Cstring, Cstring),
                rmt_ptr_ptr, repo.ptr, rmt_name, rmt_url)
    return GitRemote(repo, rmt_ptr_ptr[])
end

"""
    GitRemote(repo::GitRepo, rmt_name::AbstractString, rmt_url::AbstractString, fetch_spec::AbstractString) -> GitRemote

Look up a remote git repository using the repository's name and URL,
as well as specifications for how to fetch from the remote
(e.g. which remote branch to fetch from).

# Examples
```julia
repo = LibGit2.init(repo_path)
refspec = "+refs/heads/mybranch:refs/remotes/origin/mybranch"
remote = LibGit2.GitRemote(repo, "upstream", repo_url, refspec)
```
"""
function GitRemote(repo::GitRepo, rmt_name::AbstractString, rmt_url::AbstractString, fetch_spec::AbstractString)
    ensure_initialized()
    rmt_ptr_ptr = Ref{Ptr{Cvoid}}(C_NULL)
    @check ccall((:git_remote_create_with_fetchspec, libgit2), Cint,
                (Ptr{Ptr{Cvoid}}, Ptr{Cvoid}, Cstring, Cstring, Cstring),
                rmt_ptr_ptr, repo.ptr, rmt_name, rmt_url, fetch_spec)
    return GitRemote(repo, rmt_ptr_ptr[])
end

"""
    GitRemoteAnon(repo::GitRepo, url::AbstractString) -> GitRemote

Look up a remote git repository using only its URL, not its name.

# Examples
```julia
repo = LibGit2.init(repo_path)
remote = LibGit2.GitRemoteAnon(repo, repo_url)
```
"""
function GitRemoteAnon(repo::GitRepo, url::AbstractString)
    ensure_initialized()
    rmt_ptr_ptr = Ref{Ptr{Cvoid}}(C_NULL)
    @check ccall((:git_remote_create_anonymous, libgit2), Cint,
                (Ptr{Ptr{Cvoid}}, Ptr{Cvoid}, Cstring),
                rmt_ptr_ptr, repo.ptr, url)
    return GitRemote(repo, rmt_ptr_ptr[])
end

"""
    lookup_remote(repo::GitRepo, remote_name::AbstractString) -> Union{GitRemote, Nothing}

Determine if the `remote_name` specified exists within the `repo`. Return
either a [`GitRemote`](@ref) to the remote name if it exists, or [`nothing`](@ref)
if not.

# Examples
```julia
repo = LibGit2.GitRepo(path)
remote_name = "test"
LibGit2.lookup_remote(repo, remote_name) # will return nothing
```
"""
function lookup_remote(repo::GitRepo, remote_name::AbstractString)
    ensure_initialized()
    rmt_ptr_ptr = Ref{Ptr{Cvoid}}(C_NULL)
    err = ccall((:git_remote_lookup, libgit2), Cint,
                (Ptr{Ptr{Cvoid}}, Ptr{Cvoid}, Cstring),
                rmt_ptr_ptr, repo.ptr, remote_name)
    if err == Int(Error.GIT_OK)
        return GitRemote(repo, rmt_ptr_ptr[])
    elseif err == Int(Error.ENOTFOUND)
        return nothing
    else
        throw(Error.GitError(err))
    end
end

function get(::Type{GitRemote}, repo::GitRepo, rmt_name::AbstractString)
    ensure_initialized()
    rmt_ptr_ptr = Ref{Ptr{Cvoid}}(C_NULL)
    @check ccall((:git_remote_lookup, libgit2), Cint,
                (Ptr{Ptr{Cvoid}}, Ptr{Cvoid}, Cstring),
                rmt_ptr_ptr, repo.ptr, rmt_name)
    return GitRemote(repo, rmt_ptr_ptr[])
end

"""
    url(rmt::GitRemote)

Get the fetch URL of a remote git repository.

# Examples
```julia-repl
julia> repo_url = "https://github.com/JuliaLang/Example.jl";

julia> repo = LibGit2.init(mktempdir());

julia> remote = LibGit2.GitRemote(repo, "origin", repo_url);

julia> LibGit2.url(remote)
"https://github.com/JuliaLang/Example.jl"
```
"""
function url(rmt::GitRemote)
    ensure_initialized()
    url_ptr = ccall((:git_remote_url, libgit2), Cstring, (Ptr{Cvoid},), rmt.ptr)
    url_ptr == C_NULL && return ""
    return unsafe_string(url_ptr)
end

"""
    push_url(rmt::GitRemote)

Get the push URL of a remote git repository.

# Examples
```julia-repl
julia> repo_url = "https://github.com/JuliaLang/Example.jl";

julia> repo = LibGit2.init(mktempdir());

julia> LibGit2.set_remote_push_url(repo, "origin", repo_url);

julia> LibGit2.push_url(LibGit2.get(LibGit2.GitRemote, repo, "origin"))
"https://github.com/JuliaLang/Example.jl"
```
"""
function push_url(rmt::GitRemote)
    ensure_initialized()
    url_ptr = ccall((:git_remote_pushurl, libgit2), Cstring, (Ptr{Cvoid},), rmt.ptr)
    url_ptr == C_NULL && return ""
    return unsafe_string(url_ptr)
end

"""
    name(rmt::GitRemote)

Get the name of a remote repository, for instance `"origin"`.
If the remote is anonymous (see [`GitRemoteAnon`](@ref))
the name will be an empty string `""`.

# Examples
```julia-repl
julia> repo_url = "https://github.com/JuliaLang/Example.jl";

julia> repo = LibGit2.clone(cache_repo, "test_directory");

julia> remote = LibGit2.GitRemote(repo, "origin", repo_url);

julia> name(remote)
"origin"
```
"""
function name(rmt::GitRemote)
    ensure_initialized()
    name_ptr = ccall((:git_remote_name, libgit2), Cstring, (Ptr{Cvoid},), rmt.ptr)
    name_ptr == C_NULL && return ""
    return unsafe_string(name_ptr)
end

"""
    fetch_refspecs(rmt::GitRemote) -> Vector{String}

Get the *fetch* refspecs for the specified `rmt`. These refspecs contain
information about which branch(es) to fetch from.

# Examples
```julia-repl
julia> remote = LibGit2.get(LibGit2.GitRemote, repo, "upstream");

julia> LibGit2.add_fetch!(repo, remote, "upstream");

julia> LibGit2.fetch_refspecs(remote)
String["+refs/heads/*:refs/remotes/upstream/*"]
```
"""
function fetch_refspecs(rmt::GitRemote)
    ensure_initialized()
    sa_ref = Ref(StrArrayStruct())
    @check ccall((:git_remote_get_fetch_refspecs, libgit2), Cint,
                 (Ptr{StrArrayStruct}, Ptr{Cvoid}), sa_ref, rmt.ptr)
    res = convert(Vector{String}, sa_ref[])
    free(sa_ref)
    res
end

"""
    push_refspecs(rmt::GitRemote) -> Vector{String}

Get the *push* refspecs for the specified `rmt`. These refspecs contain
information about which branch(es) to push to.

# Examples
```julia-repl
julia> remote = LibGit2.get(LibGit2.GitRemote, repo, "upstream");

julia> LibGit2.add_push!(repo, remote, "refs/heads/master");

julia> close(remote);

julia> remote = LibGit2.get(LibGit2.GitRemote, repo, "upstream");

julia> LibGit2.push_refspecs(remote)
String["refs/heads/master"]
```
"""
function push_refspecs(rmt::GitRemote)
    ensure_initialized()
    sa_ref = Ref(StrArrayStruct())
    @check ccall((:git_remote_get_push_refspecs, libgit2), Cint,
                 (Ptr{StrArrayStruct}, Ptr{Cvoid}), sa_ref, rmt.ptr)
    res = convert(Vector{String}, sa_ref[])
    free(sa_ref)
    res
end

"""
    add_fetch!(repo::GitRepo, rmt::GitRemote, fetch_spec::String)

Add a *fetch* refspec for the specified `rmt`. This refspec will contain
information about which branch(es) to fetch from.

# Examples
```julia-repl
julia> LibGit2.add_fetch!(repo, remote, "upstream");

julia> LibGit2.fetch_refspecs(remote)
String["+refs/heads/*:refs/remotes/upstream/*"]
```
"""
function add_fetch!(repo::GitRepo, rmt::GitRemote, fetch_spec::String)
    ensure_initialized()
    @check ccall((:git_remote_add_fetch, libgit2), Cint,
                 (Ptr{Cvoid}, Cstring, Cstring), repo.ptr,
                 name(rmt), fetch_spec)
end

"""
    add_push!(repo::GitRepo, rmt::GitRemote, push_spec::String)

Add a *push* refspec for the specified `rmt`. This refspec will contain
information about which branch(es) to push to.

# Examples
```julia-repl
julia> LibGit2.add_push!(repo, remote, "refs/heads/master");

julia> remote = LibGit2.get(LibGit2.GitRemote, repo, branch);

julia> LibGit2.push_refspecs(remote)
String["refs/heads/master"]
```

!!! note
    You may need to [`close`](@ref) and reopen the `GitRemote`
    in question after updating its push refspecs in order for
    the change to take effect and for calls to [`push`](@ref)
    to work.
"""
function add_push!(repo::GitRepo, rmt::GitRemote, push_spec::String)
    ensure_initialized()
    @check ccall((:git_remote_add_push, libgit2), Cint,
                 (Ptr{Cvoid}, Cstring, Cstring), repo.ptr,
                 name(rmt), push_spec)
end

"""
    fetch(rmt::GitRemote, refspecs; options::FetchOptions=FetchOptions(), msg="")

Fetch from the specified `rmt` remote git repository, using `refspecs` to
determine which remote branch(es) to fetch.
The keyword arguments are:
  * `options`: determines the options for the fetch, e.g. whether to prune afterwards.
    See [`FetchOptions`](@ref) for more information.
  * `msg`: a message to insert into the reflogs.
"""
function fetch(rmt::GitRemote, refspecs::Vector{<:AbstractString};
               options::FetchOptions = FetchOptions(),
               msg::AbstractString="")
    ensure_initialized()
    msg = "libgit2.fetch: $msg"
    @check ccall((:git_remote_fetch, libgit2), Cint,
                 (Ptr{Cvoid}, Ptr{StrArrayStruct}, Ptr{FetchOptions}, Cstring),
                 rmt.ptr, isempty(refspecs) ? C_NULL : refspecs, Ref(options), msg)
end

"""
    push(rmt::GitRemote, refspecs; force::Bool=false, options::PushOptions=PushOptions())

Push to the specified `rmt` remote git repository, using `refspecs` to
determine which remote branch(es) to push to.
The keyword arguments are:
  * `force`: if `true`, a force-push will occur, disregarding conflicts.
  * `options`: determines the options for the push, e.g. which proxy headers to use.
    See [`PushOptions`](@ref) for more information.

!!! note
    You can add information about the push refspecs in two other ways: by setting
    an option in the repository's `GitConfig` (with `push.default` as the key) or
    by calling [`add_push!`](@ref). Otherwise you will need to explicitly specify
    a push refspec in the call to `push` for it to have any effect, like so:
    `LibGit2.push(repo, refspecs=["refs/heads/master"])`.
"""
function push(rmt::GitRemote, refspecs::Vector{<:AbstractString};
              force::Bool = false, options::PushOptions = PushOptions())
    ensure_initialized()
    @check ccall((:git_remote_push, libgit2), Cint,
                 (Ptr{Cvoid}, Ptr{StrArrayStruct}, Ptr{PushOptions}),
                 rmt.ptr, isempty(refspecs) ? C_NULL : refspecs, Ref(options))
end

"""
    remote_delete(repo::GitRepo, remote_name::AbstractString) -> Nothing

Delete the `remote_name` from the git `repo`.
"""
function remote_delete(repo::GitRepo, remote_name::AbstractString)
    ensure_initialized()
    @check ccall((:git_remote_delete, libgit2), Cint,
                 (Ptr{Cvoid}, Cstring),
                 repo.ptr, remote_name)
end

Base.show(io::IO, rmt::GitRemote) = print(io, "GitRemote:\nRemote name: ", name(rmt), " url: ", url(rmt))


"""
    set_remote_fetch_url(repo::GitRepo, remote_name, url)
    set_remote_fetch_url(path::String, remote_name, url)

Set the fetch `url` for the specified `remote_name` for the [`GitRepo`](@ref) or the git repository
located at `path`. Typically git repos use `"origin"` as the remote name.
"""
function set_remote_fetch_url end

function set_remote_fetch_url(repo::GitRepo, remote_name::AbstractString, url::AbstractString)
    ensure_initialized()
    @check ccall((:git_remote_set_url, libgit2), Cint,
                 (Ptr{Cvoid}, Cstring, Cstring),
                 repo.ptr, remote_name, url)
end

function set_remote_fetch_url(path::AbstractString, remote_name::AbstractString, url::AbstractString)
    with(GitRepo, path) do repo
        set_remote_fetch_url(repo, remote_name, url)
    end
end


"""
    set_remote_push_url(repo::GitRepo, remote_name, url)
    set_remote_push_url(path::String, remote_name, url)

Set the push `url` for the specified `remote_name` for the [`GitRepo`](@ref) or the git repository
located at `path`. Typically git repos use `"origin"` as the remote name.
"""
function set_remote_push_url end

function set_remote_push_url(repo::GitRepo, remote_name::AbstractString, url::AbstractString)
    ensure_initialized()
    @check ccall((:git_remote_set_pushurl, libgit2), Cint,
                 (Ptr{Cvoid}, Cstring, Cstring),
                 repo.ptr, remote_name, url)
end

function set_remote_push_url(path::AbstractString, remote_name::AbstractString, url::AbstractString)
    with(GitRepo, path) do repo
        set_remote_push_url(repo, remote_name, url)
    end
end


"""
    set_remote_url(repo::GitRepo, remote_name, url)
    set_remote_url(repo::String, remote_name, url)

Set both the fetch and push `url` for `remote_name` for the [`GitRepo`](@ref) or the git repository
located at `path`. Typically git repos use `"origin"` as the remote name.

# Examples
```julia
repo_path = joinpath(tempdir(), "Example")
repo = LibGit2.init(repo_path)
LibGit2.set_remote_url(repo, "upstream", "https://github.com/JuliaLang/Example.jl")
LibGit2.set_remote_url(repo_path, "upstream2", "https://github.com/JuliaLang/Example2.jl")
```
"""
function set_remote_url end

function set_remote_url(repo::GitRepo, remote_name::AbstractString, url::AbstractString)
    set_remote_fetch_url(repo, remote_name, url)
    set_remote_push_url(repo, remote_name, url)
end

function set_remote_url(path::AbstractString, remote_name::AbstractString, url::AbstractString)
    with(GitRepo, path) do repo
        set_remote_url(repo, remote_name, url)
    end
end
s   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LibGit2/src/strarray.jlZ      # This file is a part of Julia. License is MIT: https://julialang.org/license


function Base.cconvert(::Type{Ptr{StrArrayStruct}}, x::Vector)
    str_ref = Base.cconvert(Ref{Cstring}, x)
    sa_ref = Ref(StrArrayStruct(Base.unsafe_convert(Ref{Cstring}, str_ref), length(x)))
    sa_ref, str_ref
end
function Base.unsafe_convert(::Type{Ptr{StrArrayStruct}}, rr::Tuple{Ref{StrArrayStruct}, Ref{Cstring}})
    Base.unsafe_convert(Ptr{StrArrayStruct}, first(rr))
end

function Base.convert(::Type{Vector{String}}, sa::StrArrayStruct)
    [unsafe_string(unsafe_load(sa.strings, i)) for i = 1:sa.count]
end
p   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LibGit2/src/index.jl#       # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
    GitIndex(repo::GitRepo)

Load the index file for the repository `repo`.
"""
function GitIndex(repo::GitRepo)
    ensure_initialized()
    idx_ptr_ptr = Ref{Ptr{Cvoid}}(C_NULL)
    @check ccall((:git_repository_index, libgit2), Cint,
                 (Ptr{Ptr{Cvoid}}, Ptr{Cvoid}), idx_ptr_ptr, repo.ptr)
    return GitIndex(repo, idx_ptr_ptr[])
end

"""
    read!(idx::GitIndex, force::Bool = false) -> GitIndex

Update the contents of `idx` by reading changes made on disk. For example, `idx`
might be updated if a file has been added to the repository since it was created.
If `force` is `true`, any changes in memory (any changes in `idx` since its last
[`write!`](@ref), or since its creation if no writes have occurred) are discarded.
If `force` is `false`, the index data is only updated from disk if the data on disk
has changed since the last time it was loaded into `idx`.
"""
function read!(idx::GitIndex, force::Bool = false)
    ensure_initialized()
    @check ccall((:git_index_read, libgit2), Cint, (Ptr{Cvoid}, Cint), idx.ptr, Cint(force))
    return idx
end

"""
    write!(idx::GitIndex) -> GitIndex

Write the state of index `idx` to disk using a file lock.
"""
function write!(idx::GitIndex)
    ensure_initialized()
    @check ccall((:git_index_write, libgit2), Cint, (Ptr{Cvoid},), idx.ptr)
    return idx
end

"""
    write_tree!(idx::GitIndex) -> GitHash

Write the index `idx` as a [`GitTree`](@ref) on disk. Trees will be recursively
created for each subtree in `idx`. The returned [`GitHash`](@ref) can be used to
create a [`GitCommit`](@ref). `idx` must have a parent repository and this
repository cannot be bare. `idx` must not contain any files with conflicts.
"""
function write_tree!(idx::GitIndex)
    ensure_initialized()
    oid_ptr = Ref(GitHash())
    @check ccall((:git_index_write_tree, libgit2), Cint,
                 (Ptr{GitHash}, Ptr{Cvoid}), oid_ptr, idx.ptr)
    return oid_ptr[]
end

function repository(idx::GitIndex)
    if idx.owner === nothing
        throw(GitError(Error.Index, Error.ENOTFOUND, "Index does not have an owning repository."))
    else
        return idx.owner
    end
end

"""
    LibGit2.read_tree!(idx::GitIndex, tree::GitTree)
    LibGit2.read_tree!(idx::GitIndex, treehash::AbstractGitHash)

Read the tree `tree` (or the tree pointed to by `treehash` in the repository owned by
`idx`) into the index `idx`. The current index contents will be replaced.
"""
function read_tree!(idx::GitIndex, tree::GitTree)
    ensure_initialized()
    @check ccall((:git_index_read_tree, libgit2), Cint,
                 (Ptr{Cvoid}, Ptr{Cvoid}), idx.ptr, tree.ptr)
end
read_tree!(idx::GitIndex, hash::AbstractGitHash) =
    read_tree!(idx, GitTree(repository(idx), hash))

"""
    add!(repo::GitRepo, files::AbstractString...; flags::Cuint = Consts.INDEX_ADD_DEFAULT)
    add!(idx::GitIndex, files::AbstractString...; flags::Cuint = Consts.INDEX_ADD_DEFAULT)

Add all the files with paths specified by `files` to the index `idx` (or the index
of the `repo`). If the file already exists, the index entry will be updated.
If the file does not exist already, it will be newly added into the index.
`files` may contain glob patterns which will be expanded and any matching files will
be added (unless `INDEX_ADD_DISABLE_PATHSPEC_MATCH` is set, see below).
If a file has been ignored (in `.gitignore` or in the config), it *will not* be
added, *unless* it is already being tracked in the index, in which case it *will* be
updated. The keyword argument `flags` is a set of bit-flags which control the behavior
with respect to ignored files:
  * `Consts.INDEX_ADD_DEFAULT` - default, described above.
  * `Consts.INDEX_ADD_FORCE` - disregard the existing ignore rules and force addition of
    the file to the index even if it is already ignored.
  * `Consts.INDEX_ADD_CHECK_PATHSPEC` - cannot be used at the same time as `INDEX_ADD_FORCE`.
    Check that each file in `files` which exists on disk is not in the ignore list. If one
    of the files *is* ignored, the function will return `EINVALIDSPEC`.
  * `Consts.INDEX_ADD_DISABLE_PATHSPEC_MATCH` - turn off glob matching, and only add files
    to the index which exactly match the paths specified in `files`.
"""
function add!(idx::GitIndex, files::AbstractString...;
              flags::Cuint = Consts.INDEX_ADD_DEFAULT)
    ensure_initialized()
    @check ccall((:git_index_add_all, libgit2), Cint,
                 (Ptr{Cvoid}, Ptr{StrArrayStruct}, Cuint, Ptr{Cvoid}, Ptr{Cvoid}),
                 idx.ptr, collect(files), flags, C_NULL, C_NULL)
end

"""
    update!(repo::GitRepo, files::AbstractString...)
    update!(idx::GitIndex, files::AbstractString...)

Update all the files with paths specified by `files` in the index `idx` (or the index
of the `repo`). Match the state of each file in the index with the current state on
disk, removing it if it has been removed on disk, or updating its entry in the object
database.
"""
function update!(idx::GitIndex, files::AbstractString...)
    ensure_initialized()
    @check ccall((:git_index_update_all, libgit2), Cint,
                 (Ptr{Cvoid}, Ptr{StrArrayStruct}, Ptr{Cvoid}, Ptr{Cvoid}),
                 idx.ptr, collect(files), C_NULL, C_NULL)
end

"""
    remove!(repo::GitRepo, files::AbstractString...)
    remove!(idx::GitIndex, files::AbstractString...)

Remove all the files with paths specified by `files` in the index `idx` (or the index
of the `repo`).
"""
function remove!(idx::GitIndex, files::AbstractString...)
    ensure_initialized()
    @check ccall((:git_index_remove_all, libgit2), Cint,
                 (Ptr{Cvoid}, Ptr{StrArrayStruct}, Ptr{Cvoid}, Ptr{Cvoid}),
                 idx.ptr, collect(files), C_NULL, C_NULL)
end

function add!(repo::GitRepo, files::AbstractString...;
              flags::Cuint = Consts.INDEX_ADD_DEFAULT)
    with(GitIndex, repo) do idx
        add!(idx, files..., flags = flags)
        write!(idx)
    end
    return
end

function update!(repo::GitRepo, files::AbstractString...)
    with(GitIndex, repo) do idx
        update!(idx, files...)
        write!(idx)
    end
    return
end

function remove!(repo::GitRepo, files::AbstractString...)
    with(GitIndex, repo) do idx
        remove!(idx, files...)
        write!(idx)
    end
    return
end

function read!(repo::GitRepo, force::Bool = false)
    with(GitIndex, repo) do idx
        read!(idx, force)
    end
    return
end

function count(idx::GitIndex)
    ensure_initialized()
    return ccall((:git_index_entrycount, libgit2), Csize_t, (Ptr{Cvoid},), idx.ptr)
end

function Base.getindex(idx::GitIndex, i::Integer)
    ensure_initialized()
    GC.@preserve idx begin
        ie_ptr = ccall((:git_index_get_byindex, libgit2),
                       Ptr{IndexEntry},
                       (Ptr{Cvoid}, Csize_t), idx.ptr, i-1)
        ie_ptr == C_NULL && return nothing
        elem = unsafe_load(ie_ptr)
    end
    return elem
end

function Base.findall(path::String, idx::GitIndex)
    ensure_initialized()
    pos_ref = Ref{Csize_t}(0)
    ret = ccall((:git_index_find, libgit2), Cint,
                  (Ref{Csize_t}, Ptr{Cvoid}, Cstring), pos_ref, idx.ptr, path)
    ret == Cint(Error.ENOTFOUND) && return nothing
    return pos_ref[]+1
end

"""
    stage(ie::IndexEntry) -> Cint

Get the stage number of `ie`. The stage number `0` represents the current state
of the working tree, but other numbers can be used in the case of a merge conflict.
In such a case, the various stage numbers on an `IndexEntry` describe which side(s)
of the conflict the current state of the file belongs to. Stage `0` is the state
before the attempted merge, stage `1` is the changes which have been made locally,
stages `2` and larger are for changes from other branches (for instance, in the case
of a multi-branch "octopus" merge, stages `2`, `3`, and `4` might be used).
"""
function stage(ie::IndexEntry)
    ensure_initialized()
    return ccall((:git_index_entry_stage, libgit2), Cint, (Ptr{IndexEntry},), Ref(ie))
end

function Base.show(io::IO, idx::GitIndex)
    println(io, "GitIndex:\nRepository: ", repository(idx), "\nNumber of elements: ", count(idx))
end
p   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LibGit2/src/merge.jl,      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
    GitAnnotated(repo::GitRepo, commit_id::GitHash)
    GitAnnotated(repo::GitRepo, ref::GitReference)
    GitAnnotated(repo::GitRepo, fh::FetchHead)
    GitAnnotated(repo::GitRepo, committish::AbstractString)

An annotated git commit carries with it information about how it was looked up and
why, so that rebase or merge operations have more information about the context of
the commit. Conflict files contain information about the source/target branches in
the merge which are conflicting, for instance. An annotated commit can refer to the
tip of a remote branch, for instance when a [`FetchHead`](@ref) is passed, or to a
branch head described using `GitReference`.
"""
function GitAnnotated(repo::GitRepo, commit_id::GitHash)
    ensure_initialized()
    ann_ptr_ptr = Ref{Ptr{Cvoid}}(C_NULL)
    @check ccall((:git_annotated_commit_lookup, libgit2), Cint,
                  (Ptr{Ptr{Cvoid}}, Ptr{Cvoid}, Ptr{GitHash}),
                   ann_ptr_ptr, repo.ptr, Ref(commit_id))
    return GitAnnotated(repo, ann_ptr_ptr[])
end

function GitAnnotated(repo::GitRepo, ref::GitReference)
    ensure_initialized()
    ann_ref_ref = Ref{Ptr{Cvoid}}(C_NULL)
    @check ccall((:git_annotated_commit_from_ref, libgit2), Cint,
                  (Ptr{Ptr{Cvoid}}, Ptr{Cvoid}, Ptr{Cvoid}),
                   ann_ref_ref, repo.ptr, ref.ptr)
    return GitAnnotated(repo, ann_ref_ref[])
end

function GitAnnotated(repo::GitRepo, fh::FetchHead)
    ensure_initialized()
    ann_ref_ref = Ref{Ptr{Cvoid}}(C_NULL)
    @check ccall((:git_annotated_commit_from_fetchhead, libgit2), Cint,
                  (Ptr{Ptr{Cvoid}}, Ptr{Cvoid}, Cstring, Cstring, Ptr{GitHash}),
                   ann_ref_ref, repo.ptr, fh.name, fh.url, Ref(fh.oid))
    return GitAnnotated(repo, ann_ref_ref[])
end

function GitAnnotated(repo::GitRepo, committish::AbstractString)
    obj = GitObject(repo, committish)
    cmt = peel(GitCommit, obj)
    return GitAnnotated(repo, GitHash(cmt))
end

function GitHash(ann::GitAnnotated)
    ensure_initialized()
    GC.@preserve ann begin
        oid = unsafe_load(ccall((:git_annotated_commit_id, libgit2), Ptr{GitHash}, (Ptr{Cvoid},), ann.ptr))
    end
    return oid
end

"""
    merge_analysis(repo::GitRepo, anns::Vector{GitAnnotated}) -> analysis, preference

Run analysis on the branches pointed to by the annotated branch tips `anns` and
determine under what circumstances they can be merged. For instance, if `anns[1]`
is simply an ancestor of `ann[2]`, then `merge_analysis` will report that a
fast-forward merge is possible.

Return two outputs, `analysis` and `preference`. `analysis` has several possible values:
    * `MERGE_ANALYSIS_NONE`: it is not possible to merge the elements of `anns`.
    * `MERGE_ANALYSIS_NORMAL`: a regular merge, when HEAD and the commits that the
      user wishes to merge have all diverged from a common ancestor. In this case the
      changes have to be resolved and conflicts may occur.
    * `MERGE_ANALYSIS_UP_TO_DATE`: all the input commits the user wishes to merge can
      be reached from HEAD, so no merge needs to be performed.
    * `MERGE_ANALYSIS_FASTFORWARD`: the input commit is a descendant of HEAD and so no
      merge needs to be performed - instead, the user can simply checkout the
      input commit(s).
    * `MERGE_ANALYSIS_UNBORN`: the HEAD of the repository refers to a commit which does not
      exist. It is not possible to merge, but it may be possible to checkout the input
      commits.
`preference` also has several possible values:
    * `MERGE_PREFERENCE_NONE`: the user has no preference.
    * `MERGE_PREFERENCE_NO_FASTFORWARD`: do not allow any fast-forward merges.
    * `MERGE_PREFERENCE_FASTFORWARD_ONLY`: allow only fast-forward merges and no
      other type (which may introduce conflicts).
`preference` can be controlled through the repository or global git configuration.
"""
function merge_analysis(repo::GitRepo, anns::Vector{GitAnnotated})
    ensure_initialized()
    analysis = Ref{Cint}(0)
    preference = Ref{Cint}(0)
    anns_ref = Ref(Base.map(a->a.ptr, anns), 1)
    anns_size = Csize_t(length(anns))
    @check ccall((:git_merge_analysis, libgit2), Cint,
                  (Ptr{Cint}, Ptr{Cint}, Ptr{Cvoid}, Ptr{Ptr{Cvoid}}, Csize_t),
                   analysis, preference, repo.ptr, anns_ref, anns_size)
    return analysis[], preference[]
end

"""
    ffmerge!(repo::GitRepo, ann::GitAnnotated)

Fastforward merge changes into current HEAD. This is only possible if the commit
referred to by `ann` is descended from the current HEAD (e.g. if pulling changes
from a remote branch which is simply ahead of the local branch tip).
"""
function ffmerge!(repo::GitRepo, ann::GitAnnotated)
    cmt = GitCommit(repo, GitHash(ann))

    checkout_tree(repo, cmt)
    with(head(repo)) do head_ref
        cmt_oid = GitHash(cmt)
        msg = "libgit2.merge: fastforward $(string(cmt_oid)) into $(name(head_ref))"
        new_head_ref = if reftype(head_ref) == Consts.REF_OID
            target!(head_ref, cmt_oid, msg=msg)
        else
            GitReference(repo, cmt_oid, fullname(head_ref), msg=msg)
        end
        close(new_head_ref)
    end
    return true
end

# Merge changes into current head
"""
    merge!(repo::GitRepo, anns::Vector{GitAnnotated}; kwargs...) -> Bool

Merge changes from the annotated commits (captured as [`GitAnnotated`](@ref) objects)
`anns` into the HEAD of the repository `repo`. The keyword arguments are:
  * `merge_opts::MergeOptions = MergeOptions()`: options for how to perform the merge,
    including whether fastforwarding is allowed. See [`MergeOptions`](@ref) for more
    information.
  * `checkout_opts::CheckoutOptions = CheckoutOptions()`: options for how to perform
    the checkout. See [`CheckoutOptions`](@ref) for more information.

`anns` may refer to remote or local branch heads. Return `true` if the merge is
successful, otherwise return `false` (for instance, if no merge is possible
because the branches have no common ancestor).

# Examples
```julia
upst_ann = LibGit2.GitAnnotated(repo, "branch/a")

# merge the branch in
LibGit2.merge!(repo, [upst_ann])
```
"""
function merge!(repo::GitRepo, anns::Vector{GitAnnotated};
                merge_opts::MergeOptions = MergeOptions(),
                checkout_opts::CheckoutOptions = CheckoutOptions())
    ensure_initialized()
    anns_size = Csize_t(length(anns))
    @check ccall((:git_merge, libgit2), Cint,
                  (Ptr{Cvoid}, Ptr{Ptr{Cvoid}}, Csize_t,
                   Ptr{MergeOptions}, Ptr{CheckoutOptions}),
                   repo.ptr, Base.map(x->x.ptr, anns), anns_size,
                   Ref(merge_opts), Ref(checkout_opts))
    @info "Review and commit merged changes"
    return true
end

# Internal implementation of merge.
# Returns `true` if merge was successful, otherwise `false`
"""
    merge!(repo::GitRepo, anns::Vector{GitAnnotated}, fastforward::Bool; kwargs...) -> Bool

Merge changes from the annotated commits (captured as [`GitAnnotated`](@ref) objects)
`anns` into the HEAD of the repository `repo`. If `fastforward` is `true`, *only* a
fastforward merge is allowed. In this case, if conflicts occur, the merge will fail.
Otherwise, if `fastforward` is `false`, the merge may produce a conflict file which
the user will need to resolve.

The keyword arguments are:
  * `merge_opts::MergeOptions = MergeOptions()`: options for how to perform the merge,
    including whether fastforwarding is allowed. See [`MergeOptions`](@ref) for more
    information.
  * `checkout_opts::CheckoutOptions = CheckoutOptions()`: options for how to perform
    the checkout. See [`CheckoutOptions`](@ref) for more information.

`anns` may refer to remote or local branch heads. Return `true` if the merge is
successful, otherwise return `false` (for instance, if no merge is possible
because the branches have no common ancestor).

# Examples
```julia
upst_ann_1 = LibGit2.GitAnnotated(repo, "branch/a")

# merge the branch in, fastforward
LibGit2.merge!(repo, [upst_ann_1], true)

# merge conflicts!
upst_ann_2 = LibGit2.GitAnnotated(repo, "branch/b")
# merge the branch in, try to fastforward
LibGit2.merge!(repo, [upst_ann_2], true) # will return false
LibGit2.merge!(repo, [upst_ann_2], false) # will return true
```
"""
function merge!(repo::GitRepo, anns::Vector{GitAnnotated}, fastforward::Bool;
                merge_opts::MergeOptions = MergeOptions(),
                checkout_opts::CheckoutOptions = CheckoutOptions())
    ma, mp = merge_analysis(repo, anns)
    if isset(ma, Cint(Consts.MERGE_ANALYSIS_UP_TO_DATE))
        return true # no merge - everything is up to date
    end

    ffpref = if fastforward
        Consts.MERGE_PREFERENCE_FASTFORWARD_ONLY
    elseif isset(mp, Cint(Consts.MERGE_PREFERENCE_NONE))
        Consts.MERGE_PREFERENCE_NONE
    elseif isset(mp, Cint(Consts.MERGE_PREFERENCE_NO_FASTFORWARD))
        Consts.MERGE_PREFERENCE_NO_FASTFORWARD
    elseif isset(mp, Cint(Consts.MERGE_PREFERENCE_FASTFORWARD_ONLY))
        Consts.MERGE_PREFERENCE_FASTFORWARD_ONLY
    else
        throw(ArgumentError("unknown merge preference: $(mp)."))
    end

    merge_result = if ffpref == Consts.MERGE_PREFERENCE_NONE
        if isset(ma, Cint(Consts.MERGE_ANALYSIS_FASTFORWARD))
            if length(anns) > 1
                @warn "Unable to perform Fast-Forward merge with mith multiple merge heads"
                false
            else
                ffmerge!(repo, anns[1])
            end
        elseif isset(ma, Cint(Consts.MERGE_ANALYSIS_NORMAL))
            merge!(repo, anns,
                   merge_opts=merge_opts,
                   checkout_opts=checkout_opts)
        end
    elseif ffpref == Consts.MERGE_PREFERENCE_FASTFORWARD_ONLY
        if isset(ma, Cint(Consts.MERGE_ANALYSIS_FASTFORWARD))
            if length(anns) > 1
                @warn "Unable to perform Fast-Forward merge with mith multiple merge heads"
                false
            else
                ffmerge!(repo, anns[1])
            end
        else
            @warn "Cannot perform fast-forward merge"
            false
        end
    elseif ffpref == Consts.MERGE_PREFERENCE_NO_FASTFORWARD
        if isset(ma, Cint(Consts.MERGE_ANALYSIS_NORMAL))
            merge!(repo, anns,
                   merge_opts=merge_opts,
                   checkout_opts=checkout_opts)
        end
    else
        throw(ArgumentError("unknown merge analysis result: $(ma)"))
    end
    return merge_result
end

"""
    merge_base(repo::GitRepo, one::AbstractString, two::AbstractString) -> GitHash

Find a merge base (a common ancestor) between the commits `one` and `two`.
`one` and `two` may both be in string form. Return the `GitHash` of the merge base.
"""
function merge_base(repo::GitRepo, one::AbstractString, two::AbstractString)
    ensure_initialized()
    oid1_ptr = Ref(GitHash(one))
    oid2_ptr = Ref(GitHash(two))
    moid_ptr = Ref(GitHash())
    moid = try
        @check ccall((:git_merge_base, libgit2), Cint,
                (Ptr{GitHash}, Ptr{Cvoid}, Ptr{GitHash}, Ptr{GitHash}),
                moid_ptr, repo.ptr, oid1_ptr, oid2_ptr)
        moid_ptr[]
    catch e
        GitHash()
    end
    return moid
end
n   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LibGit2/src/tag.jlB      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
    LibGit2.tag_list(repo::GitRepo) -> Vector{String}

Get a list of all tags in the git repository `repo`.
"""
function tag_list(repo::GitRepo)
    ensure_initialized()
    sa_ref = Ref(StrArrayStruct())
    @check ccall((:git_tag_list, libgit2), Cint,
                 (Ptr{StrArrayStruct}, Ptr{Cvoid}), sa_ref, repo.ptr)
    res = convert(Vector{String}, sa_ref[])
    free(sa_ref)
    res
end

"""
    LibGit2.tag_delete(repo::GitRepo, tag::AbstractString)

Remove the git tag `tag` from the repository `repo`.
"""
function tag_delete(repo::GitRepo, tag::AbstractString)
    ensure_initialized()
    @check ccall((:git_tag_delete, libgit2), Cint,
                  (Ptr{Cvoid}, Cstring), repo.ptr, tag)
end

"""
    LibGit2.tag_create(repo::GitRepo, tag::AbstractString, commit; kwargs...)

Create a new git tag `tag` (e.g. `"v0.5"`) in the repository `repo`, at
the commit `commit`.

The keyword arguments are:
  * `msg::AbstractString=""`: the message for the tag.
  * `force::Bool=false`: if `true`, existing references will be overwritten.
  * `sig::Signature=Signature(repo)`: the tagger's signature.
"""
function tag_create(repo::GitRepo, tag::AbstractString, commit::Union{AbstractString,AbstractGitHash};
                    msg::AbstractString = "",
                    force::Bool = false,
                    sig::Signature = Signature(repo))
    oid_ptr = Ref(GitHash())
    with(GitCommit(repo, commit)) do commit_obj
        commit_obj === nothing && return oid_ptr[] # return empty oid
        with(convert(GitSignature, sig)) do git_sig
            ensure_initialized()
            @check ccall((:git_tag_create, libgit2), Cint,
                 (Ptr{GitHash}, Ptr{Cvoid}, Cstring, Ptr{Cvoid}, Ptr{SignatureStruct}, Cstring, Cint),
                  oid_ptr, repo.ptr, tag, commit_obj.ptr, git_sig.ptr, msg, Cint(force))
        end
    end
    return oid_ptr[]
end

"""
    LibGit2.name(tag::GitTag)

The name of `tag` (e.g. `"v0.5"`).
"""
function name(tag::GitTag)
    ensure_initialized()
    GC.@preserve tag begin
        str_ptr = ccall((:git_tag_name, libgit2), Cstring, (Ptr{Cvoid},), tag.ptr)
        str_ptr == C_NULL && throw(Error.GitError(Error.ERROR))
        str = unsafe_string(str_ptr)
    end
    return str
end

# should we return the actual object? i.e. git_tag_target?
"""
    LibGit2.target(tag::GitTag)

The `GitHash` of the target object of `tag`.
"""
function target(tag::GitTag)
    ensure_initialized()
    GC.@preserve tag begin
        oid_ptr = ccall((:git_tag_target_id, libgit2), Ptr{GitHash}, (Ptr{Cvoid},), tag.ptr)
        oid_ptr == C_NULL && throw(Error.GitError(Error.ERROR))
        str = unsafe_load(oid_ptr)
    end
    return str
end

Base.show(io::IO, tag::GitTag) = print(io, "GitTag:\nTag name: $(name(tag)) target: $(target(tag))")
o   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LibGit2/src/blob.jl~      # This file is a part of Julia. License is MIT: https://julialang.org/license

function Base.length(blob::GitBlob)
    ensure_initialized()
    return ccall((:git_blob_rawsize, libgit2), Int64, (Ptr{Cvoid},), blob.ptr)
end

"""
    rawcontent(blob::GitBlob) -> Vector{UInt8}

Fetch the *raw* contents of the [`GitBlob`](@ref) `blob`. This is an
`Array` containing the contents of the blob, which may be binary or may be Unicode.
If you write to this `Array` the blob on disk will not be updated.
`rawcontent` will allow the user to load the raw binary data into
the output `Array` and will not check to ensure it is valid Unicode, so errors
may occur if the result is passed to functions which expect valid Unicode data.

See also [`content`](@ref), which *will* throw an error if the content of the `blob`
is binary and not valid Unicode.
"""
function rawcontent(blob::GitBlob)
    ensure_initialized()
    ptr = ccall((:git_blob_rawcontent, libgit2), Ptr{UInt8}, (Ptr{Cvoid},), blob.ptr)
    copy(unsafe_wrap(Array, ptr, (length(blob),), own = false))
end

"""
    content(blob::GitBlob) -> String

Fetch the contents of the [`GitBlob`](@ref) `blob`. If the `blob` contains
binary data (which can be determined using [`isbinary`](@ref)),
throw an error. Otherwise, return a `String` containing the contents
of the `blob`.
"""
function content(blob::GitBlob)
    s = String(rawcontent(blob))
    isvalid(s) || error("Blob does not contain valid UTF-8 data")
    return s
end

"""
    isbinary(blob::GitBlob) -> Bool

Use a heuristic to guess if a file is binary: searching for NULL bytes and
looking for a reasonable ratio of printable to non-printable characters among
the first 8000 bytes.
"""
function isbinary(blob::GitBlob)
    ensure_initialized()
    bin_flag = ccall((:git_blob_is_binary, libgit2), Cint, (Ptr{Cvoid},), blob.ptr)
    return bin_flag == 1
end

"""
    LibGit2.addblob!(repo::GitRepo, path::AbstractString)

Read the file at `path` and adds it to the object database of `repo` as a loose blob.
Return the [`GitHash`](@ref) of the resulting blob.

# Examples
```julia
hash_str = string(commit_oid)
blob_file = joinpath(repo_path, ".git", "objects", hash_str[1:2], hash_str[3:end])
id = LibGit2.addblob!(repo, blob_file)
```
"""
function addblob!(repo::GitRepo, path::AbstractString)
    ensure_initialized()
    id_ref = Ref{GitHash}()
    @check ccall((:git_blob_create_from_disk, libgit2), Cint,
                 (Ptr{GitHash}, Ptr{Cvoid}, Cstring),
                 id_ref, repo.ptr, path)
    return id_ref[]
end

function Base.show(io::IO, blob::GitBlob)
    if !isbinary(blob)
        conts   = split(content(blob), "\n")
        showlen = max(length(conts), 3)
        println(io, "GitBlob:\nBlob id: ", GitHash(blob), "\nContents:")
        for i in 1:showlen
            println(io, conts[i])
        end
    else
        println(io, "GitBlob:\nBlob id: ", GitHash(blob), "\nContents are binary.")
    end
end
o   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LibGit2/src/diff.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

# TODO: make this a general purpose solution
function Base.cconvert(::Type{Ptr{DiffOptionsStruct}}, pathspecs::AbstractString)
    str_ref = Base.cconvert(Ref{Cstring}, [pathspecs])
    sa = StrArrayStruct(Base.unsafe_convert(Ref{Cstring}, str_ref), 1)
    do_ref = Ref(DiffOptionsStruct(pathspec = sa))
    do_ref, str_ref
end
function Base.unsafe_convert(::Type{Ptr{DiffOptionsStruct}}, rr::Tuple{Ref{DiffOptionsStruct}, Ref{Cstring}})
    Base.unsafe_convert(Ptr{DiffOptionsStruct}, first(rr))
end

"""
    diff_tree(repo::GitRepo, tree::GitTree, pathspecs::AbstractString=""; cached::Bool=false)

Generate a [`GitDiff`](@ref) between `tree` (which will be used for the "old"
side of the [`DiffDelta`](@ref)) and `repo` (which will be used for the "new" side).
If `repo` is `cached`, calls [`git_diff_tree_to_index`](https://libgit2.org/libgit2/#HEAD/group/diff/git_diff_tree_to_index).
The `cached` version is generally used to examine the diff for staged changes from one
commit to the next. If `cached` is `false`, calls
[`git_diff_tree_to_workdir_with_index`](https://libgit2.org/libgit2/#HEAD/group/diff/git_diff_tree_to_workdir_with_index).
This compares the current working directory against the [`GitIndex`](@ref) and can,
for example, be used to examine the changes in staged files before a commit.
"""
function diff_tree(repo::GitRepo, tree::GitTree, pathspecs::AbstractString=""; cached::Bool=false)
    ensure_initialized()
    diff_ptr_ptr = Ref{Ptr{Cvoid}}(C_NULL)
    if cached
        @check ccall((:git_diff_tree_to_index, libgit2), Cint,
                     (Ptr{Ptr{Cvoid}}, Ptr{Cvoid}, Ptr{Cvoid}, Ptr{Cvoid}, Ptr{DiffOptionsStruct}),
                     diff_ptr_ptr, repo.ptr, tree.ptr, C_NULL, isempty(pathspecs) ? C_NULL : pathspecs)
    else
        @check ccall((:git_diff_tree_to_workdir_with_index, libgit2), Cint,
                     (Ptr{Ptr{Cvoid}}, Ptr{Cvoid}, Ptr{Cvoid}, Ptr{DiffOptionsStruct}),
                     diff_ptr_ptr, repo.ptr, tree.ptr, isempty(pathspecs) ? C_NULL : pathspecs)
    end
    return GitDiff(repo, diff_ptr_ptr[])
end

"""
    diff_tree(repo::GitRepo, oldtree::GitTree, newtree::GitTree)

Generate a [`GitDiff`](@ref) between `oldtree` (which will be used for the "old"
side of the [`DiffDelta`](@ref)) and `newtree` (which will be used for the "new"
side of the `DiffDelta`). Equivalent to [`git_diff_tree_to_tree`](https://libgit2.org/libgit2/#HEAD/group/diff/git_diff_tree_to_tree).
This can be used to generate a diff between two commits. For instance, it could
be used to compare a commit made 2 months ago with the current latest commit, or
to compare a commit on another branch with the current latest commit on `master`.
"""
function diff_tree(repo::GitRepo, oldtree::GitTree, newtree::GitTree)
    ensure_initialized()
    diff_ptr_ptr = Ref{Ptr{Cvoid}}(C_NULL)
    @check ccall((:git_diff_tree_to_tree, libgit2), Cint,
                  (Ptr{Ptr{Cvoid}}, Ptr{Cvoid}, Ptr{Cvoid}, Ptr{Cvoid}, Ptr{DiffOptionsStruct}),
                   diff_ptr_ptr, repo.ptr, oldtree.ptr, newtree.ptr, C_NULL)
    return GitDiff(repo, diff_ptr_ptr[])
end

"""
    GitDiffStats(diff::GitDiff)

Get the diff statistics from the [`GitDiff`](@ref) `diff`. This object records a
summary of changes made across the `diff`. In particular, it records how many
files were changed, how many insertions were made, and how many deletions were made.
"""
function GitDiffStats(diff::GitDiff)
    ensure_initialized()
    diff_stat_ptr_ptr = Ref{Ptr{Cvoid}}(C_NULL)
    @check ccall((:git_diff_get_stats, libgit2), Cint,
                  (Ptr{Ptr{Cvoid}}, Ptr{Cvoid}),
                  diff_stat_ptr_ptr, diff.ptr)
    return GitDiffStats(diff.owner, diff_stat_ptr_ptr[])
end

"""
    files_changed(diff_stat::GitDiffStats) -> Csize_t

Return how many files were changed (added/modified/deleted) in the [`GitDiff`](@ref)
summarized by `diff_stat`. The result may vary depending on the [`DiffOptionsStruct`](@ref)
used to generate the parent `GitDiff` of `diff_stat` (for instance, whether ignored files
are to be included or not).
"""
function files_changed(diff_stat::GitDiffStats)
    ensure_initialized()
    return ccall((:git_diff_stats_files_changed, libgit2), Csize_t, (Ptr{Cvoid},), diff_stat.ptr)
end

"""
    insertions(diff_stat::GitDiffStats) -> Csize_t

Return the total number of insertions (lines added) in the [`GitDiff`](@ref)
summarized by `diff_stat`. The result may vary depending on the [`DiffOptionsStruct`](@ref)
used to generate the parent `GitDiff` of `diff_stat` (for instance, whether ignored files
are to be included or not).
"""
function insertions(diff_stat::GitDiffStats)
    ensure_initialized()
    return ccall((:git_diff_stats_insertions, libgit2), Csize_t, (Ptr{Cvoid},), diff_stat.ptr)
end

"""
    deletions(diff_stat::GitDiffStats) -> Csize_t

Return the total number of deletions (lines removed) in the [`GitDiff`](@ref)
summarized by `diff_stat`. The result may vary depending on the [`DiffOptionsStruct`](@ref)
used to generate the parent `GitDiff` of `diff_stat` (for instance, whether ignored files
are to be included or not).
"""
function deletions(diff_stat::GitDiffStats)
    ensure_initialized()
    return ccall((:git_diff_stats_deletions, libgit2), Csize_t, (Ptr{Cvoid},), diff_stat.ptr)
end

function count(diff::GitDiff)
    ensure_initialized()
    return ccall((:git_diff_num_deltas, libgit2), Cint, (Ptr{Cvoid},), diff.ptr)
end

function Base.getindex(diff::GitDiff, i::Integer)
    if i < 1 || i > count(diff)
        throw(BoundsError(diff, (i,)))
    end
    ensure_initialized()
    delta_ptr = ccall((:git_diff_get_delta, libgit2),
                      Ptr{DiffDelta},
                      (Ptr{Cvoid}, Csize_t), diff.ptr, i-1)
    return unsafe_load(delta_ptr)
end

function Base.show(io::IO, diff_stat::GitDiffStats)
    println(io, "GitDiffStats:")
    println(io, "Files changed: $(files_changed(diff_stat))")
    println(io, "Insertions: $(insertions(diff_stat))")
    println(io, "Deletions: $(deletions(diff_stat))")
end

function Base.show(io::IO, diff::GitDiff)
    println(io, "GitDiff:")
    println(io, "Number of deltas: $(count(diff))")
    show(io, GitDiffStats(diff))
end
q   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LibGit2/src/rebase.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

function GitRebase(repo::GitRepo, branch::GitAnnotated, upstream::GitAnnotated;
                   onto::Union{GitAnnotated, Nothing}=nothing,
                   opts::RebaseOptions = RebaseOptions())
    ensure_initialized()
    rebase_ptr_ptr = Ref{Ptr{Cvoid}}(C_NULL)
    @check ccall((:git_rebase_init, libgit2), Cint,
                  (Ptr{Ptr{Cvoid}}, Ptr{Cvoid}, Ptr{Cvoid}, Ptr{Cvoid},
                   Ptr{Cvoid}, Ptr{RebaseOptions}),
                   rebase_ptr_ptr, repo.ptr, branch.ptr, upstream.ptr,
                   onto === nothing ? C_NULL : onto.ptr, Ref(opts))
    return GitRebase(repo, rebase_ptr_ptr[])
end

function count(rb::GitRebase)
    ensure_initialized()
    return ccall((:git_rebase_operation_entrycount, libgit2), Csize_t, (Ptr{Cvoid},), rb.ptr)
end

"""
    current(rb::GitRebase) -> Csize_t

Return the index of the current [`RebaseOperation`](@ref). If no operation has
yet been applied (because the [`GitRebase`](@ref) has been constructed but `next`
has not yet been called or iteration over `rb` has not yet begun), return
`GIT_REBASE_NO_OPERATION`, which is equal to `typemax(Csize_t)`.
"""
function current(rb::GitRebase)
    ensure_initialized()
    return ccall((:git_rebase_operation_current, libgit2), Csize_t, (Ptr{Cvoid},), rb.ptr)
end

function Base.getindex(rb::GitRebase, i::Integer)
    if !(1 <= i <= count(rb))
        throw(BoundsError(rb, (i,)))
    end
    ensure_initialized()
    GC.@preserve rb begin
        rb_op_ptr = ccall((:git_rebase_operation_byindex, libgit2),
                          Ptr{RebaseOperation},
                          (Ptr{Cvoid}, Csize_t), rb.ptr, i-1)
        rb_op = unsafe_load(rb_op_ptr)
    end
    return rb_op
end

function Base.iterate(rb::GitRebase, state=nothing)
    ensure_initialized()
    rb_op_ptr_ptr = Ref{Ptr{RebaseOperation}}(C_NULL)
    GC.@preserve rb begin
        err = ccall((:git_rebase_next, libgit2), Cint,
                    (Ptr{Ptr{RebaseOperation}}, Ptr{Cvoid}),
                    rb_op_ptr_ptr, rb.ptr)
        if err == Cint(Error.GIT_OK)
            return unsafe_load(rb_op_ptr_ptr[]), nothing
        elseif err == Cint(Error.ITEROVER)
            return nothing
        else
            throw(GitError(err))
        end
    end
end

function Base.show(io::IO, rb::GitRebase)
    println(io, "GitRebase:")
    println(io, "Number: ", count(rb))
    println(io, "Currently performing operation: ", current(rb)+1)
end

"""
    LibGit2.commit(rb::GitRebase, sig::GitSignature)

Commit the current patch to the rebase `rb`, using `sig` as the committer. Is silent if
the commit has already been applied.
"""
function commit(rb::GitRebase, sig::GitSignature)
    ensure_initialized()
    oid_ptr = Ref(GitHash())
    try
        @check ccall((:git_rebase_commit, libgit2), Error.Code,
                     (Ptr{GitHash}, Ptr{Cvoid}, Ptr{SignatureStruct}, Ptr{SignatureStruct}, Ptr{UInt8}, Ptr{UInt8}),
                      oid_ptr, rb.ptr, C_NULL, sig.ptr, C_NULL, C_NULL)
    catch err
        # TODO: return current HEAD instead
        err isa GitError && err.code === Error.EAPPLIED && return nothing
        rethrow()
    end
    return oid_ptr[]
end

"""
    abort(rb::GitRebase) -> Csize_t

Cancel the in-progress rebase, undoing all changes made so far and returning
the parent repository of `rb` and its working directory to their state before
the rebase was initiated. Return `0` if the abort is successful,
`LibGit2.Error.ENOTFOUND` if no rebase is in progress (for example, if the
rebase had completed), and `-1` for other errors.
"""
function abort(rb::GitRebase)
    ensure_initialized()
    return ccall((:git_rebase_abort, libgit2), Csize_t,
                      (Ptr{Cvoid},), rb.ptr)
end

"""
    finish(rb::GitRebase, sig::GitSignature) -> Csize_t

Complete the rebase described by `rb`. `sig` is a [`GitSignature`](@ref)
to specify the identity of the user finishing the rebase. Return `0` if the
rebase finishes successfully, `-1` if there is an error.
"""
function finish(rb::GitRebase, sig::GitSignature)
    ensure_initialized()
    return ccall((:git_rebase_finish, libgit2), Csize_t,
                  (Ptr{Cvoid}, Ptr{SignatureStruct}),
                   rb.ptr, sig.ptr)
end
p   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LibGit2/src/blame.jl7	      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
    GitBlame(repo::GitRepo, path::AbstractString; options::BlameOptions=BlameOptions())

Construct a `GitBlame` object for the file at `path`, using change information gleaned
from the history of `repo`. The `GitBlame` object records who changed which chunks of
the file when, and how. `options` controls how to separate the contents of the file and
which commits to probe - see [`BlameOptions`](@ref) for more information.
"""
function GitBlame(repo::GitRepo, path::AbstractString; options::BlameOptions=BlameOptions())
    ensure_initialized()
    blame_ptr_ptr = Ref{Ptr{Cvoid}}(C_NULL)
    @check ccall((:git_blame_file, libgit2), Cint,
                  (Ptr{Ptr{Cvoid}}, Ptr{Cvoid}, Cstring, Ptr{BlameOptions}),
                   blame_ptr_ptr, repo.ptr, path, Ref(options))
    return GitBlame(repo, blame_ptr_ptr[])
end

"""
    counthunks(blame::GitBlame)

Return the number of distinct "hunks" with a file. A hunk may contain multiple lines.
A hunk is usually a piece of a file that was added/changed/removed together, for example,
a function added to a source file or an inner loop that was optimized out of
that function later.
"""
function counthunks(blame::GitBlame)
    ensure_initialized()
    return ccall((:git_blame_get_hunk_count, libgit2), Int32, (Ptr{Cvoid},), blame.ptr)
end

function Base.getindex(blame::GitBlame, i::Integer)
    if !(1 <= i <= counthunks(blame))
        throw(BoundsError(blame, (i,)))
    end
    ensure_initialized()
    GC.@preserve blame begin
        hunk_ptr = ccall((:git_blame_get_hunk_byindex, libgit2),
                          Ptr{BlameHunk},
                          (Ptr{Cvoid}, Csize_t), blame.ptr, i-1)
        elem = unsafe_load(hunk_ptr)
    end
    return elem
end

function Base.show(io::IO, blame_hunk::BlameHunk)
    println(io, "GitBlameHunk:")
    println(io, "Original path: ", unsafe_string(blame_hunk.orig_path))
    println(io, "Lines in hunk: ", blame_hunk.lines_in_hunk)
    println(io, "Final commit oid: ", blame_hunk.final_commit_id)
    print(io, "Final signature: ")
    show(io, Signature(blame_hunk.final_signature))
    println(io)
    println(io, "Original commit oid: ", blame_hunk.orig_commit_id)
    print(io, "Original signature: ")
    show(io, Signature(blame_hunk.orig_signature))
end
q   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LibGit2/src/status.jll      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
    LibGit2.GitStatus(repo::GitRepo; status_opts=StatusOptions())

Collect information about the status of each file in the git
repository `repo` (e.g. is the file modified, staged, etc.).
`status_opts` can be used to set various options, for instance
whether or not to look at untracked files or whether to include
submodules or not. See [`StatusOptions`](@ref) for more information.
"""
function GitStatus(repo::GitRepo; status_opts=StatusOptions())
    ensure_initialized()
    stat_ptr_ptr = Ref{Ptr{Cvoid}}(C_NULL)
    @check ccall((:git_status_list_new, libgit2), Cint,
                  (Ptr{Ptr{Cvoid}}, Ptr{Cvoid}, Ptr{StatusOptions}),
                  stat_ptr_ptr, repo.ptr, Ref(status_opts))
    return GitStatus(repo, stat_ptr_ptr[])
end

function Base.length(status::GitStatus)
    ensure_initialized()
    return Int(ccall((:git_status_list_entrycount, libgit2), Csize_t,
                      (Ptr{Ptr{Cvoid}},), status.ptr))
end

function Base.getindex(status::GitStatus, i::Integer)
    1 <= i <= length(status) || throw(BoundsError())
    ensure_initialized()
    GC.@preserve status begin
        entry_ptr = ccall((:git_status_byindex, libgit2),
                          Ptr{StatusEntry},
                          (Ptr{Cvoid}, Csize_t),
                          status.ptr, i-1)
        entry_ptr == C_NULL && throw(Error.GitError(Error.ERROR))
        entry = unsafe_load(entry_ptr)
    end
    return entry
end

"""
    LibGit2.status(repo::GitRepo, path::String) -> Union{Cuint, Cvoid}

Lookup the status of the file at `path` in the git
repository `repo`. For instance, this can be used
to check if the file at `path` has been modified
and needs to be staged and committed.
"""
function status(repo::GitRepo, path::String)
    ensure_initialized()
    status_ptr = Ref{Cuint}(0)
    ret =  ccall((:git_status_file, libgit2), Cint,
                  (Ref{Cuint}, Ptr{Cvoid}, Cstring),
                  status_ptr, repo.ptr, path)
    (ret == Cint(Error.ENOTFOUND) || ret == Cint(Error.EAMBIGUOUS)) && return nothing
    return status_ptr[]
end
o   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LibGit2/src/tree.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

function GitTree(c::GitCommit)
    tree_out = Ref{Ptr{Cvoid}}(C_NULL)
    @check ccall((:git_commit_tree, libgit2), Cint, (Ptr{Ptr{Cvoid}}, Ptr{Cvoid}), tree_out, c)
    GitTree(repository(c), tree_out[])
end

"""
    treewalk(f, tree::GitTree, post::Bool=false)

Traverse the entries in `tree` and its subtrees in post or pre order. Preorder
means beginning at the root and then traversing the leftmost subtree (and
recursively on down through that subtree's leftmost subtrees) and moving right
through the subtrees. Postorder means beginning at the bottom of the leftmost
subtree, traversing upwards through it, then traversing the next right subtree
(again beginning at the bottom) and finally visiting the tree root last of all.

The function parameter `f` should have following signature:

    (String, GitTreeEntry) -> Cint

A negative value returned from `f` stops the tree walk. A positive value means
that the entry will be skipped if `post` is `false`.
"""
function treewalk(f, tree::GitTree, post::Bool = false)
    ensure_initialized()
    # NOTE: don't use @check/GitError directly, because the code can be arbitrary
    payload = Any[ tree, f ]
    cbf = @cfunction(function treewalk_callback(root_cstr::Cstring, entry_ptr::Ptr{Cvoid}, payload::Vector{Any})::Cint
            # decode arguments
            root = unsafe_string(root_cstr)
            tree = payload[1]::GitTree
            f = payload[2]
            entry = GitTreeEntry(tree, entry_ptr, false)
            return f(root, entry)
        end, Cint, (Cstring, Ptr{Cvoid}, Ref{Vector{Any}}))
    err = ccall((:git_tree_walk, libgit2), Cint,
                (Ptr{Cvoid}, Cint, Ptr{Cvoid}, Any),
                tree.ptr, post, cbf, payload)
    if err < 0
        err_class, _ = Error.last_error()
        if err_class != Error.Callback
            # now we now the code is valid
            throw(GitError(err))
        end
    end
    nothing
end

repository(tree::GitTree) = tree.owner
repository(te::GitTreeEntry) = repository(te.owner)

"""
    filename(te::GitTreeEntry)

Return the filename of the object on disk to which `te` refers.
"""
function filename(te::GitTreeEntry)
    ensure_initialized()
    str = ccall((:git_tree_entry_name, libgit2), Cstring, (Ptr{Cvoid},), te.ptr)
    str != C_NULL && return unsafe_string(str)
    return nothing
end

"""
    filemode(te::GitTreeEntry) -> Cint

Return the UNIX filemode of the object on disk to which `te` refers as an integer.
"""
function filemode(te::GitTreeEntry)
    ensure_initialized()
    return ccall((:git_tree_entry_filemode, libgit2), Cint, (Ptr{Cvoid},), te.ptr)
end

"""
    entrytype(te::GitTreeEntry)

Return the type of the object to which `te` refers. The result will be
one of the types which [`objtype`](@ref) returns, e.g. a `GitTree` or `GitBlob`.
"""
function entrytype(te::GitTreeEntry)
    ensure_initialized()
    otype = ccall((:git_tree_entry_type, libgit2), Cint, (Ptr{Cvoid},), te.ptr)
    return objtype(Consts.OBJECT(otype))
end

"""
    entryid(te::GitTreeEntry)

Return the [`GitHash`](@ref) of the object to which `te` refers.
"""
function entryid(te::GitTreeEntry)
    ensure_initialized()
    GC.@preserve te begin
        oid_ptr = ccall((:git_tree_entry_id, libgit2), Ptr{UInt8}, (Ptr{Cvoid},), te.ptr)
        oid = GitHash(oid_ptr)
    end
    return oid
end

function count(tree::GitTree)
    ensure_initialized()
    return ccall((:git_tree_entrycount, libgit2), Csize_t, (Ptr{Cvoid},), tree.ptr)
end

function Base.getindex(tree::GitTree, i::Integer)
    if i < 1 || i > count(tree)
        throw(BoundsError(tree, i))
    end
    ensure_initialized()
    te_ptr = ccall((:git_tree_entry_byindex, libgit2),
                   Ptr{Cvoid},
                   (Ptr{Cvoid}, Csize_t), tree.ptr, i-1)
    return GitTreeEntry(tree, te_ptr, false)
end

"""
    (::Type{T})(te::GitTreeEntry) where T<:GitObject

Get the git object to which `te` refers and return it as its actual type (the type
[`entrytype`](@ref) would show), for instance a `GitBlob` or `GitTag`.

# Examples
```julia
tree = LibGit2.GitTree(repo, "HEAD^{tree}")
tree_entry = tree[1]
blob = LibGit2.GitBlob(tree_entry)
```
"""
GitObject(e::GitTreeEntry)
function (::Type{T})(te::GitTreeEntry) where T<:GitObject
    ensure_initialized()
    repo = repository(te)
    obj_ptr_ptr = Ref{Ptr{Cvoid}}(C_NULL)
    @check ccall((:git_tree_entry_to_object, libgit2), Cint,
                  (Ptr{Ptr{Cvoid}}, Ptr{Cvoid}, Ptr{Cvoid}),
                   obj_ptr_ptr, repo, te)
    return T(repo, obj_ptr_ptr[])
end

function Base.show(io::IO, te::GitTreeEntry)
    println(io, "GitTreeEntry:")
    println(io, "Entry name: ", filename(te))
    println(io, "Entry type: ", entrytype(te))
    println(io, "Entry OID: ", entryid(te))
end

function Base.show(io::IO, tree::GitTree)
    println(io, "GitTree:")
    println(io, "Owner: ", repository(tree))
    println(io, "Number of entries: ", count(tree))
end

function _getindex(tree::GitTree, target::AbstractString)
    if basename(target) == ""
        # get rid of any trailing separator
        target = dirname(target)
    end
    if isempty(target) || target == "/"
        return tree
    end

    entry = Ref{Ptr{Cvoid}}(C_NULL)
    err = ccall((:git_tree_entry_bypath, libgit2), Cint, (Ptr{Ptr{Cvoid}}, Ptr{Cvoid}, Cstring), entry, tree, target)
    err == Int(Error.ENOTFOUND) && return nothing
    err < 0 && throw(Error.GitError(err))
    entry = GitTreeEntry(tree, entry[], true #= N.B.: Most other lookups need false here =#)
    return GitObject(entry)
end

"""
    getindex(tree::GitTree, target::AbstractString) -> GitObject

Look up `target` path in the `tree`, returning a [`GitObject`](@ref) (a [`GitBlob`](@ref) in
the case of a file, or another [`GitTree`](@ref) if looking up a directory).

# Examples
```julia
tree = LibGit2.GitTree(repo, "HEAD^{tree}")
readme = tree["README.md"]
subtree = tree["test"]
runtests = subtree["runtests.jl"]
```
"""
function Base.getindex(tree::GitTree, target::AbstractString)
    e = _getindex(tree, target)
    e === nothing && throw(KeyError(target))
    return e
end

function Base.haskey(tree::GitTree, target::AbstractString)
    return _getindex(tree, target) !== nothing
end
x   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LibGit2/src/gitcredential.jl)      # This file is a part of Julia. License is MIT: https://julialang.org/license

const GIT_CRED_ATTRIBUTES = ("protocol", "host", "path", "username", "password", "url")

"""
    GitCredential

Git credential information used in communication with git credential helpers. The field are
named using the [input/output key specification](https://git-scm.com/docs/git-credential#IOFMT).
"""
mutable struct GitCredential
    protocol::Union{String, Nothing}
    host::Union{String, Nothing}
    path::Union{String, Nothing}
    username::Union{String, Nothing}
    password::Union{Base.SecretBuffer, Nothing}
    use_http_path::Bool

    function GitCredential(
            protocol::Union{AbstractString, Nothing}=nothing,
            host::Union{AbstractString, Nothing}=nothing,
            path::Union{AbstractString, Nothing}=nothing,
            username::Union{AbstractString, Nothing}=nothing,
            password::Union{AbstractString, Nothing}=nothing)
        new(protocol, host, path, username, password, true)
    end
end

function GitCredential(cfg::GitConfig, url::AbstractString)
    fill!(cfg, parse(GitCredential, url))
end

function GitCredential(user_pass_cred::UserPasswordCredential, url::AbstractString)
    cred = parse(GitCredential, url)
    cred.username = user_pass_cred.user
    cred.password = deepcopy(user_pass_cred.pass)
    return cred
end

Base.:(==)(c1::GitCredential, c2::GitCredential) = (c1.protocol, c1.host, c1.path, c1.username, c1.password, c1.use_http_path) ==
                                                   (c2.protocol, c2.host, c2.path, c2.username, c2.password, c2.use_http_path)
Base.hash(cred::GitCredential, h::UInt) = hash(GitCredential, hash((cred.protocol, cred.host, cred.path, cred.username, cred.password, cred.use_http_path), h))

function Base.shred!(cred::GitCredential)
    cred.protocol = nothing
    cred.host = nothing
    cred.path = nothing
    cred.username = nothing
    pwd = cred.password
    pwd !== nothing && Base.shred!(pwd)
    cred.password = nothing
    return cred
end


"""
    ismatch(url, git_cred) -> Bool

Checks if the `git_cred` is valid for the given `url`.
"""
function ismatch(url::AbstractString, git_cred::GitCredential)
    isempty(url) && return true

    m = match(URL_REGEX, url)
    m === nothing && error("Unable to parse URL")

    # Note: missing URL groups match anything
    (m[:scheme] === nothing ? true : m[:scheme] == git_cred.protocol) &&
    (m[:host] === nothing ? true : m[:host] == git_cred.host) &&
    (m[:path] === nothing ? true : m[:path] == git_cred.path) &&
    (m[:user] === nothing ? true : m[:user] == git_cred.username)
end

function isfilled(cred::GitCredential)
    cred.username !== nothing && cred.password !== nothing
end

function Base.parse(::Type{GitCredential}, url::AbstractString)
    m = match(URL_REGEX, url)
    m === nothing && error("Unable to parse URL")
    return GitCredential(
        m[:scheme],
        m[:host],
        m[:path],
        m[:user],
        m[:password],
    )
end

function Base.copy!(a::GitCredential, b::GitCredential)
    Base.shred!(a)
    a.protocol = b.protocol
    a.host = b.host
    a.path = b.path
    a.username = b.username
    a.password = b.password === nothing ? nothing : copy(b.password)
    return a
end

function Base.write(io::IO, cred::GitCredential)
    cred.protocol !== nothing && write(io, "protocol=", cred.protocol, '\n')
    cred.host !== nothing && write(io, "host=", cred.host, '\n')
    cred.path !== nothing && cred.use_http_path && write(io, "path=", cred.path, '\n')
    cred.username !== nothing && write(io, "username=", cred.username, '\n')
    cred.password !== nothing && write(io, "password=", cred.password, '\n')
    nothing
end

function Base.read!(io::IO, cred::GitCredential)
    # https://git-scm.com/docs/git-credential#IOFMT
    while !(eof(io)::Bool)
        key::AbstractString = readuntil(io, '=')
        if key == "password"
            value = Base.SecretBuffer()
            while !(eof(io)::Bool) && (c = read(io, UInt8)) != UInt8('\n')
                write(value, c)
            end
            seekstart(value)
        else
            value = readuntil(io, '\n')
        end

        if key == "url"
            # Any components which are missing from the URL will be set to empty
            # https://git-scm.com/docs/git-credential#git-credential-codeurlcode
            Base.shred!(parse(GitCredential, value::AbstractString)) do urlcred
                copy!(cred, urlcred)
            end
        elseif key in GIT_CRED_ATTRIBUTES
            field = getproperty(cred, Symbol(key))
            field !== nothing && Symbol(key) === :password && Base.shred!(field)
            setproperty!(cred, Symbol(key), value)
        elseif !all(isspace, key)
            @warn "Unknown git credential attribute found: $(repr(key))"
        end
    end

    return cred
end

function fill!(cfg::GitConfig, cred::GitCredential)
    cred.use_http_path = use_http_path(cfg, cred)

    # When the username is missing default to using the username set in the configuration
    if cred.username === nothing
        cred.username = default_username(cfg, cred)
    end

    for helper in credential_helpers(cfg, cred)
        fill!(helper, cred)

        # "Once Git has acquired both a username and a password, no more helpers will be
        # tried." – https://git-scm.com/docs/gitcredentials#gitcredentials-helper
        !isfilled(cred) && break
    end

    return cred
end

struct GitCredentialHelper
    cmd::Cmd
end

function Base.parse(::Type{GitCredentialHelper}, helper::AbstractString)
    # The helper string can take on different behaviors depending on the value:
    # - "Code after `!` evaluated in shell" – https://git-scm.com/book/en/v2/Git-Tools-Credential-Storage
    # - "If the helper name is not an absolute path, then the string `git credential-` is
    #   prepended." – https://git-scm.com/docs/gitcredentials#gitcredentials-helper
    if startswith(helper, '!')
        cmd_str = helper[2:end]
    elseif isabspath(first(Base.shell_split(helper)))
        cmd_str = helper
    else
        cmd_str = "git credential-$helper"
    end

    GitCredentialHelper(`$(Base.shell_split(cmd_str))`)
end

function Base.:(==)(a::GitCredentialHelper, b::GitCredentialHelper)
    a.cmd == b.cmd
end

function run!(helper::GitCredentialHelper, operation::AbstractString, cred::GitCredential)
    cmd = `$(helper.cmd) $operation`
    p = open(cmd, "r+")

    # Provide the helper with the credential information we know
    write(p, cred)
    write(p, "\n")
    t = @async close(p.in)

    # Process the response from the helper
    Base.read!(p, cred)
    wait(p)

    return cred
end

function run(helper::GitCredentialHelper, operation::AbstractString, cred::GitCredential)
    run!(helper, operation, deepcopy(cred))
end

# The available actions between using `git credential` and helpers are slightly different.
# We will directly interact with the helpers as that way we can request credential
# information without a prompt (helper `get` vs. git credential `fill`).
# https://git-scm.com/book/en/v2/Git-Tools-Credential-Storage

fill!(helper::GitCredentialHelper, cred::GitCredential) = run!(helper, "get", cred)
approve(helper::GitCredentialHelper, cred::GitCredential) = run(helper, "store", cred)
reject(helper::GitCredentialHelper, cred::GitCredential) = run(helper, "erase", cred)

"""
    credential_helpers(config, git_cred) -> Vector{GitCredentialHelper}

Return all of the `GitCredentialHelper`s found within the provided `config` which are valid
for the specified `git_cred`.
"""
function credential_helpers(cfg::GitConfig, cred::GitCredential)
    helpers = GitCredentialHelper[]

    # https://git-scm.com/docs/gitcredentials#gitcredentials-helper
    for entry in GitConfigIter(cfg, r"credential.*\.helper$")
        section, url, name, value = split_cfg_entry(entry)
        @assert name == "helper"

        # Only use configuration settings where the URL applies to the git credential
        ismatch(url, cred) || continue

        # An empty credential.helper resets the list to empty
        if isempty(value)
            empty!(helpers)
        else
            Base.push!(helpers, parse(GitCredentialHelper, value))
        end
    end

    return helpers
end

"""
    default_username(config, git_cred) -> Union{String, Nothing}

Return the default username, if any, provided by the `config` which is valid for the
specified `git_cred`.
"""
function default_username(cfg::GitConfig, cred::GitCredential)
    # https://git-scm.com/docs/gitcredentials#gitcredentials-username
    for entry in GitConfigIter(cfg, r"credential.*\.username")
        section, url, name, value = split_cfg_entry(entry)
        @assert name == "username"

        # Only use configuration settings where the URL applies to the git credential
        ismatch(url, cred) || continue
        return value
    end

    return nothing
end

function use_http_path(cfg::GitConfig, cred::GitCredential)
    seen_specific = false
    use_path = false  # Default is to ignore the path

    # https://git-scm.com/docs/gitcredentials#gitcredentials-useHttpPath
    #
    # Note: Ideally the regular expression should use "useHttpPath"
    # https://github.com/libgit2/libgit2/issues/4390
    for entry in GitConfigIter(cfg, r"credential.*\.usehttppath")
        section, url, name, value = split_cfg_entry(entry)

        # Ignore global configuration if we have already encountered more specific entry
        if ismatch(url, cred) && (!isempty(url) || !seen_specific)
            seen_specific = !isempty(url)
            use_path = value == "true"
        end
    end

    return use_path
end

approve(cfg::GitConfig, cred::AbstractCredential, url::AbstractString) = nothing
reject(cfg::GitConfig, cred::AbstractCredential, url::AbstractString) = nothing

function approve(cfg::GitConfig, cred::UserPasswordCredential, url::AbstractString)
    git_cred = GitCredential(cred, url)
    git_cred.use_http_path = use_http_path(cfg, git_cred)

    for helper in credential_helpers(cfg, git_cred)
        approve(helper, git_cred)
    end

    Base.shred!(git_cred)
    nothing
end

function reject(cfg::GitConfig, cred::UserPasswordCredential, url::AbstractString)
    git_cred = GitCredential(cred, url)
    git_cred.use_http_path = use_http_path(cfg, git_cred)

    for helper in credential_helpers(cfg, git_cred)
        reject(helper, git_cred)
    end

    Base.shred!(git_cred)
    nothing
end
t   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LibGit2/src/callbacks.jl�P      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""Mirror callback function

Function sets `+refs/*:refs/*` refspecs and `mirror` flag for remote reference.
"""
function mirror_callback(remote::Ptr{Ptr{Cvoid}}, repo_ptr::Ptr{Cvoid},
                         name::Cstring, url::Cstring, payload::Ptr{Cvoid})
    ensure_initialized()
    # Create the remote with a mirroring url
    fetch_spec = "+refs/*:refs/*"
    err = ccall((:git_remote_create_with_fetchspec, libgit2), Cint,
                (Ptr{Ptr{Cvoid}}, Ptr{Cvoid}, Cstring, Cstring, Cstring),
                remote, repo_ptr, name, url, fetch_spec)
    err != 0 && return Cint(err)

    # And set the configuration option to true for the push command
    config = GitConfig(GitRepo(repo_ptr,false))
    name_str = unsafe_string(name)
    err= try set!(config, "remote.$name_str.mirror", true)
         catch; -1
         finally close(config)
         end
    err != 0 && return Cint(err)
    return Cint(0)
end

"""
    LibGit2.is_passphrase_required(private_key) -> Bool

Return `true` if the `private_key` file requires a passphrase, `false` otherwise.
"""
function is_passphrase_required(private_key::AbstractString)
    !isfile(private_key) && return false

    # In encrypted private keys, the second line is "Proc-Type: 4,ENCRYPTED"
    return open(private_key) do f
        readline(f)
        readline(f) == "Proc-Type: 4,ENCRYPTED"
    end
end

function user_abort()
    ensure_initialized()
    # Note: Potentially it could be better to just throw a Julia error.
    ccall((:giterr_set_str, libgit2), Cvoid,
          (Cint, Cstring), Cint(Error.Callback),
          "Aborting, user cancelled credential request.")
    return Cint(Error.EUSER)
end

function prompt_limit()
    ensure_initialized()
    ccall((:giterr_set_str, libgit2), Cvoid,
          (Cint, Cstring), Cint(Error.Callback),
          "Aborting, maximum number of prompts reached.")
    return Cint(Error.EAUTH)
end

function exhausted_abort()
    ensure_initialized()
    ccall((:giterr_set_str, libgit2), Cvoid,
          (Cint, Cstring), Cint(Error.Callback),
          "All authentication methods have failed.")
    return Cint(Error.EAUTH)
end

function authenticate_ssh(libgit2credptr::Ptr{Ptr{Cvoid}}, p::CredentialPayload, username_ptr)
    ensure_initialized()
    cred = p.credential::SSHCredential
    revised = false

    # Use a filled credential as-is on the first pass. Reset password on successive calls.
    if p.first_pass && isfilled(cred)
        revised = true
    elseif !p.first_pass
        cred.pass = ""
    end

    # first try ssh-agent if credentials support its usage
    if p.use_ssh_agent && username_ptr != Cstring(C_NULL) && (!revised || !isfilled(cred))
        err = ccall((:git_cred_ssh_key_from_agent, libgit2), Cint,
                    (Ptr{Ptr{Cvoid}}, Cstring), libgit2credptr, username_ptr)

        p.use_ssh_agent = false  # use ssh-agent only one time
        err == 0 && return Cint(0)
    end

    if p.use_env && (!revised || !isfilled(cred))
        if isempty(cred.user) && username_ptr != Cstring(C_NULL)
            cred.user = unsafe_string(username_ptr)
        end

        if haskey(ENV, "SSH_KEY_PATH")
            cred.prvkey = ENV["SSH_KEY_PATH"]
        elseif isempty(cred.prvkey)
            for keytype in ("rsa", "ecdsa")
                private_key_file = joinpath(homedir(), ".ssh", "id_$keytype")
                if isfile(private_key_file)
                    cred.prvkey = private_key_file
                    break
                end
            end
        end

        cred.pubkey = Base.get(ENV, "SSH_PUB_KEY_PATH") do
            default = cred.prvkey * ".pub"
            if isempty(cred.pubkey) && isfile(default)
                default
            else
                cred.pubkey
            end
        end

        cred.pass = Base.get(ENV, "SSH_KEY_PASS", cred.pass)

        revised = true
        p.use_env = false
    end

    if p.remaining_prompts > 0 && (!revised || !isfilled(cred))
        if isempty(cred.user) || username_ptr == Cstring(C_NULL)
            url = git_url(scheme=p.scheme, host=p.host)
            response = Base.prompt("Username for '$url'", default=cred.user)
            response === nothing && return user_abort()
            cred.user = response
        end

        url = git_url(scheme=p.scheme, host=p.host, username=cred.user)

        # For SSH we need a private key location
        last_private_key = cred.prvkey
        if !isfile(cred.prvkey) || !revised || !haskey(ENV, "SSH_KEY_PATH")
            response = Base.prompt("Private key location for '$url'", default=cred.prvkey)
            response === nothing && return user_abort()
            cred.prvkey = expanduser(response)

            # Only update the public key if the private key changed
            if cred.prvkey != last_private_key
                cred.pubkey = cred.prvkey * ".pub"
            end
        end

        # For SSH we need a public key location. Avoid asking about the public key as
        # typically this will just annoy users.
        stale = !p.first_pass && cred.prvkey == last_private_key && cred.pubkey != cred.prvkey * ".pub"
        if isfile(cred.prvkey) && (stale || !isfile(cred.pubkey))
            response = Base.prompt("Public key location for '$url'", default=cred.pubkey)
            response === nothing && return user_abort()
            cred.pubkey = expanduser(response)
        end

        # Ask for a passphrase when the private key exists and requires a passphrase
        if isempty(cred.pass) && is_passphrase_required(cred.prvkey)
            if Sys.iswindows()
                response = Base.winprompt(
                    "Your SSH Key requires a password, please enter it now:",
                    "Passphrase required", cred.prvkey; prompt_username=false)
                response === nothing && return user_abort()
                cred.pass = response[2]
            else
                response = Base.getpass("Passphrase for $(cred.prvkey)")
                response === nothing && return user_abort()
                cred.pass = response
                isempty(cred.pass) && return user_abort()  # Ambiguous if EOF or newline
            end
        end

        revised = true

        p.remaining_prompts -= 1
        p.remaining_prompts <= 0 && return prompt_limit()
    end

    if !revised
        return exhausted_abort()
    end
    return ccall((:git_cred_ssh_key_new, libgit2), Cint,
                 (Ptr{Ptr{Cvoid}}, Cstring, Cstring, Cstring, Cstring),
                 libgit2credptr, cred.user, cred.pubkey, cred.prvkey, cred.pass)
end

function authenticate_userpass(libgit2credptr::Ptr{Ptr{Cvoid}}, p::CredentialPayload)
    ensure_initialized()
    cred = p.credential::UserPasswordCredential
    revised = false

    # Use a filled credential as-is on the first pass. Reset password on successive calls.
    if p.first_pass && isfilled(cred)
        revised = true
    elseif !p.first_pass
        cred.pass = ""
    end

    if p.use_git_helpers && (!revised || !isfilled(cred))
        git_cred = GitCredential(p.config, p.url)

         # Use `deepcopy` to ensure shredding the `git_cred` does not shred the `cred`s copy
        cred.user = something(git_cred.username, "")
        cred.pass = deepcopy(something(git_cred.password, ""))
        Base.shred!(git_cred)
        revised = true

        p.use_git_helpers = false
    end

    if p.remaining_prompts > 0 && (!revised || !isfilled(cred))
        url = git_url(scheme=p.scheme, host=p.host)
        username = isempty(cred.user) ? p.username : cred.user
        if Sys.iswindows()
            response = Base.winprompt(
                "Please enter your credentials for '$url'", "Credentials required",
                username; prompt_username=true)
            response === nothing && return user_abort()
            cred.user, cred.pass = response
        else
            response = Base.prompt("Username for '$url'", default=username)
            response === nothing && return user_abort()
            cred.user = response

            url = git_url(scheme=p.scheme, host=p.host, username=cred.user)
            response = Base.getpass("Password for '$url'")
            response === nothing && return user_abort()
            cred.pass = response
            isempty(cred.pass) && return user_abort()  # Ambiguous if EOF or newline
        end

        revised = true

        p.remaining_prompts -= 1
        p.remaining_prompts <= 0 && return prompt_limit()
    end

    if !revised
        return exhausted_abort()
    end

    return ccall((:git_cred_userpass_plaintext_new, libgit2), Cint,
                 (Ptr{Ptr{Cvoid}}, Cstring, Cstring),
                 libgit2credptr, cred.user, cred.pass)
end


"""
    credential_callback(...) -> Cint

A LibGit2 credential callback function which provides different credential acquisition
functionality w.r.t. a connection protocol. The `payload_ptr` is required to contain a
`LibGit2.CredentialPayload` object which will keep track of state and settings.

The `allowed_types` contains a bitmask of `LibGit2.Consts.GIT_CREDTYPE` values specifying
which authentication methods should be attempted.

Credential authentication is done in the following order (if supported):
- SSH agent
- SSH private/public key pair
- Username/password plain text

If a user is presented with a credential prompt they can abort the prompt by typing `^D`
(pressing the control key together with the `d` key).

**Note**: Due to the specifics of the `libgit2` authentication procedure, when
authentication fails, this function is called again without any indication whether
authentication was successful or not. To avoid an infinite loop from repeatedly
using the same faulty credentials, we will keep track of state using the payload.

For addition details see the LibGit2 guide on
[authenticating against a server](https://libgit2.org/docs/guides/authentication/).
"""
function credentials_callback(libgit2credptr::Ptr{Ptr{Cvoid}}, url_ptr::Cstring,
                              username_ptr::Cstring, allowed_types::Cuint,
                              p::CredentialPayload)
    err = Cint(0)

    # Parse URL only during the first call to this function. Future calls will use the
    # information cached inside the payload.
    if isempty(p.url)
        p.url = unsafe_string(url_ptr)
        m = match(URL_REGEX, p.url)::RegexMatch

        p.scheme = something(m[:scheme], SubString(""))
        p.username = something(m[:user], SubString(""))
        p.host = something(m[:host])

        # When an explicit credential is supplied we will make sure to use the given
        # credential during the first callback by modifying the allowed types. The
        # modification only is in effect for the first callback since `allowed_types` cannot
        # be mutated.
        cache = p.cache
        explicit = p.explicit
        if explicit !== nothing
            cred = explicit

            # Copy explicit credentials to avoid mutating approved credentials.
            # invalidation fix from cred being non-inferrable
            p.credential = Base.invokelatest(deepcopy, cred)

            if isa(cred, SSHCredential)
                allowed_types &= Cuint(Consts.CREDTYPE_SSH_KEY)
            elseif isa(cred, UserPasswordCredential)
                allowed_types &= Cuint(Consts.CREDTYPE_USERPASS_PLAINTEXT)
            else
                allowed_types &= Cuint(0)  # Unhandled credential type
            end
        elseif cache !== nothing
            cred_id = credential_identifier(p.scheme, p.host)

            # Perform a deepcopy as we do not want to mutate approved cached credentials
            if haskey(cache, cred_id)
                # invalidation fix from cache[cred_id] being non-inferrable
                p.credential = Base.invokelatest(deepcopy, cache[cred_id])
            end
        end
        p.first_pass = true
    else
        p.first_pass = false
    end

    # use ssh key or ssh-agent
    if isset(allowed_types, Cuint(Consts.CREDTYPE_SSH_KEY))
        if p.credential === nothing || !isa(p.credential, SSHCredential)
            p.credential = SSHCredential(p.username)
        end
        err = authenticate_ssh(libgit2credptr, p, username_ptr)
        err == 0 && return err
    end

    if isset(allowed_types, Cuint(Consts.CREDTYPE_USERPASS_PLAINTEXT))
        if p.credential === nothing || !isa(p.credential, UserPasswordCredential)
            p.credential = UserPasswordCredential(p.username)
        end
        err = authenticate_userpass(libgit2credptr, p)
        err == 0 && return err
    end

    # No authentication method we support succeeded. The most likely cause is
    # that explicit credentials were passed in, but said credentials are incompatible
    # with the requested authentication method.
    if err == 0
        if p.explicit !== nothing
            ensure_initialized()
            ccall((:giterr_set_str, libgit2), Cvoid, (Cint, Cstring), Cint(Error.Callback),
                  "The explicitly provided credential is incompatible with the requested " *
                  "authentication methods.")
        end
        err = Cint(Error.EAUTH)
    end
    return err
end

function credentials_callback(libgit2credptr::Ptr{Ptr{Cvoid}}, url_ptr::Cstring,
                              username_ptr::Cstring, allowed_types::Cuint,
                              payloads::Dict{Symbol, Any})
    p = payloads[:credentials]
    return credentials_callback(libgit2credptr, url_ptr, username_ptr, allowed_types, p)
end

function fetchhead_foreach_callback(ref_name::Cstring, remote_url::Cstring,
                                    oid_ptr::Ptr{GitHash}, is_merge::Cuint, payload::Any)
    fhead_vec = payload::Vector{FetchHead}
    Base.push!(fhead_vec, FetchHead(unsafe_string(ref_name), unsafe_string(remote_url),
        unsafe_load(oid_ptr), is_merge == 1))
    return Cint(0)
end

struct CertHostKey
    parent  :: Cint
    mask    :: Cint
    md5     :: NTuple{16,UInt8}
    sha1    :: NTuple{20,UInt8}
    sha256  :: NTuple{32,UInt8}
    type    :: Cint
    hostkey :: Ptr{Cchar}
    len     :: Csize_t
end

function verify_host_error(message::AbstractString)
    printstyled(stderr, "$message\n", color = :cyan, bold = true)
end

function certificate_callback(
    cert_p :: Ptr{CertHostKey},
    valid  :: Cint,
    host_p :: Ptr{Cchar},
    data_p :: Ptr{Cvoid},
)::Cint
    valid != 0 && return Consts.CERT_ACCEPT
    host = unsafe_string(host_p)
    cert_type = unsafe_load(convert(Ptr{Cint}, cert_p))
    transport = cert_type == Consts.CERT_TYPE_TLS ? "TLS" :
                cert_type == Consts.CERT_TYPE_SSH ? "SSH" : nothing
    if !NetworkOptions.verify_host(host, transport)
        # user has opted out of host verification
        return Consts.CERT_ACCEPT
    end
    if transport == "TLS"
        # TLS verification is done before the callback and indicated with the
        # incoming `valid` flag, so if we get here then host verification failed
        verify_host_error("TLS host verification: the identity of the server `$host` could not be verified. Someone could be trying to man-in-the-middle your connection. It is also possible that the correct server is using an invalid certificate or that your system's certificate authority root store is misconfigured.")
        return Consts.CERT_REJECT
    elseif transport == "SSH"
        # SSH verification has to be done here
        files = NetworkOptions.ssh_known_hosts_files()
        cert = unsafe_load(cert_p)
        check = ssh_knownhost_check(files, host, cert)
        valid = false
        if check == Consts.LIBSSH2_KNOWNHOST_CHECK_MATCH
            valid = true
        elseif check == Consts.LIBSSH2_KNOWNHOST_CHECK_NOTFOUND
            if Sys.which("ssh-keyscan") !== nothing
                msg = "Please run `ssh-keyscan $host >> $(files[1])` in order to add the server to your known hosts file and then try again."
            else
                msg = "Please connect once using `ssh $host` in order to add the server to your known hosts file and then try again. You may not be allowed to log in (wrong user and/or no login allowed), but ssh will prompt you to add a host key for the server which will allow libgit2 to verify the server."
            end
            verify_host_error("SSH host verification: the server `$host` is not a known host. $msg")
        elseif check == Consts.LIBSSH2_KNOWNHOST_CHECK_MISMATCH
            verify_host_error("SSH host verification: the identity of the server `$host` does not match its known hosts record. Someone could be trying to man-in-the-middle your connection. It is also possible that the server has changed its key, in which case you should check with the server administrator and if they confirm that the key has been changed, update your known hosts file.")
        else
            @error("unexpected SSH known host check result", check)
        end
        return valid ? Consts.CERT_ACCEPT : Consts.CERT_REJECT
    end
    @error("unexpected transport encountered, refusing to validate", cert_type)
    return Consts.CERT_REJECT
end

struct KnownHost
    magic :: Cuint
    node  :: Ptr{Cvoid}
    name  :: Ptr{Cchar}
    key   :: Ptr{Cchar}
    type  :: Cint
end

function ssh_knownhost_check(
    files :: AbstractVector{<:AbstractString},
    host  :: AbstractString,
    cert  :: CertHostKey,
)
    key = unsafe_wrap(Array, cert.hostkey, cert.len)
    return ssh_knownhost_check(files, host, key)
end

function ssh_knownhost_check(
    files :: AbstractVector{<:AbstractString},
    host  :: AbstractString,
    key   :: Vector{Cchar},
)
    if (m = match(r"^(.+):(\d+)$", host)) !== nothing
        host = m.captures[1]
        port = parse(Int, something(m.captures[2]))
    else
        port = 22 # default SSH port
    end
    len = length(key)
    mask = Consts.LIBSSH2_KNOWNHOST_TYPE_PLAIN |
           Consts.LIBSSH2_KNOWNHOST_KEYENC_RAW
    session = @ccall "libssh2".libssh2_session_init_ex(
        C_NULL :: Ptr{Cvoid},
        C_NULL :: Ptr{Cvoid},
        C_NULL :: Ptr{Cvoid},
        C_NULL :: Ptr{Cvoid},
    ) :: Ptr{Cvoid}
    for file in files
        ispath(file) || continue
        hosts = @ccall "libssh2".libssh2_knownhost_init(
            session :: Ptr{Cvoid},
        ) :: Ptr{Cvoid}
        count = @ccall "libssh2".libssh2_knownhost_readfile(
            hosts :: Ptr{Cvoid},
            file  :: Cstring,
            1     :: Cint, # standard OpenSSH format
        ) :: Cint
        if count < 0
            @warn("Error parsing SSH known hosts file `$file`")
            @ccall "libssh2".libssh2_knownhost_free(hosts::Ptr{Cvoid})::Cvoid
            continue
        end
        check = @ccall "libssh2".libssh2_knownhost_checkp(
            hosts  :: Ptr{Cvoid},
            host   :: Cstring,
            port   :: Cint,
            key    :: Ptr{Cchar},
            len    :: Csize_t,
            mask   :: Cint,
            C_NULL :: Ptr{Ptr{KnownHost}},
        ) :: Cint
        if check == Consts.LIBSSH2_KNOWNHOST_CHECK_MATCH ||
            check == Consts.LIBSSH2_KNOWNHOST_CHECK_MISMATCH
            @ccall "libssh2".libssh2_knownhost_free(hosts::Ptr{Cvoid})::Cvoid
            @assert 0 == @ccall "libssh2".libssh2_session_free(session::Ptr{Cvoid})::Cint
            return check
        else
            @ccall "libssh2".libssh2_knownhost_free(hosts::Ptr{Cvoid})::Cvoid
            if check == Consts.LIBSSH2_KNOWNHOST_CHECK_FAILURE
                @warn("Error searching SSH known hosts file `$file`")
            end
            continue
        end
    end
    # name not found in any known hosts files
    @assert 0 == @ccall "libssh2".libssh2_session_free(session::Ptr{Cvoid})::Cint
    return Consts.LIBSSH2_KNOWNHOST_CHECK_NOTFOUND
end

function trace_callback(level::Cint, msg::Cstring)::Cint
    println(stderr, "[$level]: $(unsafe_string(msg))")
    return 0
end

"C function pointer for `mirror_callback`"
mirror_cb() = @cfunction(mirror_callback, Cint, (Ptr{Ptr{Cvoid}}, Ptr{Cvoid}, Cstring, Cstring, Ptr{Cvoid}))
"C function pointer for `credentials_callback`"
credentials_cb() = @cfunction(credentials_callback, Cint, (Ptr{Ptr{Cvoid}}, Cstring, Cstring, Cuint, Any))
"C function pointer for `fetchhead_foreach_callback`"
fetchhead_foreach_cb() = @cfunction(fetchhead_foreach_callback, Cint, (Cstring, Cstring, Ptr{GitHash}, Cuint, Any))
"C function pointer for `certificate_callback`"
certificate_cb() = @cfunction(certificate_callback, Cint, (Ptr{CertHostKey}, Cint, Ptr{Cchar}, Ptr{Cvoid}))
"C function pointer for `trace_callback`"
trace_cb() = @cfunction(trace_callback, Cint, (Cint, Cstring))
n   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/UUIDs/src/UUIDs.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
This module provides universally unique identifiers (UUIDs),
along with functions creating the different variants.
"""
module UUIDs

using Random

import SHA

export UUID, uuid1, uuid4, uuid5, uuid_version

import Base: UUID

"""
    uuid_version(u::UUID) -> Int

Inspects the given UUID and returns its version
(see [RFC 4122](https://www.ietf.org/rfc/rfc4122)).

# Examples
```jldoctest
julia> uuid_version(uuid4())
4
```
"""
uuid_version(u::UUID) = Int((u.value >> 76) & 0xf)

# Some UUID namespaces provided in the appendix of RFC 4122
# https://tools.ietf.org/html/rfc4122.html#appendix-C
const namespace_dns  = UUID(0x6ba7b8109dad11d180b400c04fd430c8) # 6ba7b810-9dad-11d1-80b4-00c04fd430c8
const namespace_url  = UUID(0x6ba7b8119dad11d180b400c04fd430c8) # 6ba7b811-9dad-11d1-80b4-00c04fd430c8
const namespace_oid  = UUID(0x6ba7b8129dad11d180b400c04fd430c8) # 6ba7b812-9dad-11d1-80b4-00c04fd430c8
const namespace_x500 = UUID(0x6ba7b8149dad11d180b400c04fd430c8) # 6ba7b814-9dad-11d1-80b4-00c04fd430c8

"""
    uuid1([rng::AbstractRNG]) -> UUID

Generates a version 1 (time-based) universally unique identifier (UUID), as specified
by RFC 4122. Note that the Node ID is randomly generated (does not identify the host)
according to section 4.5 of the RFC.

The default rng used by `uuid1` is not `GLOBAL_RNG` and every invocation of `uuid1()` without
an argument should be expected to return a unique identifier. Importantly, the outputs of
`uuid1` do not repeat even when `Random.seed!(seed)` is called. Currently (as of Julia 1.6),
`uuid1` uses `Random.RandomDevice` as the default rng. However, this is an implementation
detail that may change in the future.

!!! compat "Julia 1.6"
    The output of `uuid1` does not depend on `GLOBAL_RNG` as of Julia 1.6.

# Examples
```jldoctest; filter = r"[a-z0-9]{8}-([a-z0-9]{4}-){3}[a-z0-9]{12}"
julia> rng = MersenneTwister(1234);

julia> uuid1(rng)
UUID("cfc395e8-590f-11e8-1f13-43a2532b2fa8")
```
"""
function uuid1(rng::AbstractRNG=Random.RandomDevice())
    u = rand(rng, UInt128)

    # mask off clock sequence and node
    u &= 0x00000000000000003fffffffffffffff

    # set the unicast/multicast bit and version
    u |= 0x00000000000010000000010000000000

    # 0x01b21dd213814000 is the number of 100 nanosecond intervals
    # between the UUID epoch and Unix epoch
    timestamp = round(UInt64, time() * 1e7) + 0x01b21dd213814000
    ts_low = timestamp & typemax(UInt32)
    ts_mid = (timestamp >> 32) & typemax(UInt16)
    ts_hi = (timestamp >> 48) & 0x0fff

    u |= UInt128(ts_low) << 96
    u |= UInt128(ts_mid) << 80
    u |= UInt128(ts_hi) << 64

    UUID(u)
end

"""
    uuid4([rng::AbstractRNG]) -> UUID

Generates a version 4 (random or pseudo-random) universally unique identifier (UUID),
as specified by RFC 4122.

The default rng used by `uuid4` is not `GLOBAL_RNG` and every invocation of `uuid4()` without
an argument should be expected to return a unique identifier. Importantly, the outputs of
`uuid4` do not repeat even when `Random.seed!(seed)` is called. Currently (as of Julia 1.6),
`uuid4` uses `Random.RandomDevice` as the default rng. However, this is an implementation
detail that may change in the future.

!!! compat "Julia 1.6"
    The output of `uuid4` does not depend on `GLOBAL_RNG` as of Julia 1.6.

# Examples
```jldoctest
julia> rng = MersenneTwister(1234);

julia> uuid4(rng)
UUID("7a052949-c101-4ca3-9a7e-43a2532b2fa8")
```
"""
function uuid4(rng::AbstractRNG=Random.RandomDevice())
    u = rand(rng, UInt128)
    u &= 0xffffffffffff0fff3fffffffffffffff
    u |= 0x00000000000040008000000000000000
    UUID(u)
end

"""
    uuid5(ns::UUID, name::String) -> UUID

Generates a version 5 (namespace and domain-based) universally unique identifier (UUID),
as specified by RFC 4122.

!!! compat "Julia 1.1"
    This function requires at least Julia 1.1.

# Examples
```jldoctest
julia> rng = MersenneTwister(1234);

julia> u4 = uuid4(rng)
UUID("7a052949-c101-4ca3-9a7e-43a2532b2fa8")

julia> u5 = uuid5(u4, "julia")
UUID("086cc5bb-2461-57d8-8068-0aed7f5b5cd1")
```
"""
function uuid5(ns::UUID, name::String)
    nsbytes = zeros(UInt8, 16)
    nsv = ns.value
    for idx in Base.OneTo(16)
        nsbytes[idx] = nsv >> 120
        nsv = nsv << 8
    end
    hash_result = SHA.sha1(append!(nsbytes, convert(Vector{UInt8}, codeunits(unescape_string(name)))))
    # set version number to 5
    hash_result[7] = (hash_result[7] & 0x0F) | (0x50)
    hash_result[9] = (hash_result[9] & 0x3F) | (0x80)
    v = zero(UInt128)
    #use only the first 16 bytes of the SHA1 hash
    for idx in Base.OneTo(16)
        v = (v << 0x08) | hash_result[idx]
    end
    return UUID(v)
end

end
l   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/REPL/src/REPL.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""
Run Evaluate Print Loop (REPL)

Example minimal code

```julia
import REPL
term = REPL.Terminals.TTYTerminal("dumb", stdin, stdout, stderr)
repl = REPL.LineEditREPL(term, true)
REPL.run_repl(repl)
```
"""
module REPL

Base.Experimental.@optlevel 1
Base.Experimental.@max_methods 1

using Base.Meta, Sockets
import InteractiveUtils

export
    AbstractREPL,
    BasicREPL,
    LineEditREPL,
    StreamREPL

import Base:
    AbstractDisplay,
    display,
    show,
    AnyDict,
    ==

_displaysize(io::IO) = displaysize(io)::Tuple{Int,Int}

include("Terminals.jl")
using .Terminals

abstract type AbstractREPL end

include("options.jl")

include("LineEdit.jl")
using .LineEdit
import ..LineEdit:
    CompletionProvider,
    HistoryProvider,
    add_history,
    complete_line,
    history_next,
    history_next_prefix,
    history_prev,
    history_prev_prefix,
    history_first,
    history_last,
    history_search,
    accept_result,
    setmodifiers!,
    terminal,
    MIState,
    PromptState,
    TextInterface,
    mode_idx

include("REPLCompletions.jl")
using .REPLCompletions

include("TerminalMenus/TerminalMenus.jl")
include("docview.jl")

@nospecialize # use only declared type signatures

answer_color(::AbstractREPL) = ""

const JULIA_PROMPT = "julia> "
const PKG_PROMPT = "pkg> "
const SHELL_PROMPT = "shell> "
const HELP_PROMPT = "help?> "

mutable struct REPLBackend
    "channel for AST"
    repl_channel::Channel{Any}
    "channel for results: (value, iserror)"
    response_channel::Channel{Any}
    "flag indicating the state of this backend"
    in_eval::Bool
    "transformation functions to apply before evaluating expressions"
    ast_transforms::Vector{Any}
    "current backend task"
    backend_task::Task

    REPLBackend(repl_channel, response_channel, in_eval, ast_transforms=copy(repl_ast_transforms)) =
        new(repl_channel, response_channel, in_eval, ast_transforms)
end
REPLBackend() = REPLBackend(Channel(1), Channel(1), false)

"""
    softscope(ex)

Return a modified version of the parsed expression `ex` that uses
the REPL's "soft" scoping rules for global syntax blocks.
"""
function softscope(@nospecialize ex)
    if ex isa Expr
        h = ex.head
        if h === :toplevel
            ex′ = Expr(h)
            map!(softscope, resize!(ex′.args, length(ex.args)), ex.args)
            return ex′
        elseif h in (:meta, :import, :using, :export, :module, :error, :incomplete, :thunk)
            return ex
        elseif h === :global && all(x->isa(x, Symbol), ex.args)
            return ex
        else
            return Expr(:block, Expr(:softscope, true), ex)
        end
    end
    return ex
end

# Temporary alias until Documenter updates
const softscope! = softscope

const repl_ast_transforms = Any[softscope] # defaults for new REPL backends

# Allows an external package to add hooks into the code loading.
# The hook should take a Vector{Symbol} of package names and
# return true if all packages could be installed, false if not
# to e.g. install packages on demand
const install_packages_hooks = Any[]

function eval_user_input(@nospecialize(ast), backend::REPLBackend, mod::Module)
    lasterr = nothing
    Base.sigatomic_begin()
    while true
        try
            Base.sigatomic_end()
            if lasterr !== nothing
                put!(backend.response_channel, Pair{Any, Bool}(lasterr, true))
            else
                backend.in_eval = true
                if !isempty(install_packages_hooks)
                    check_for_missing_packages_and_run_hooks(ast)
                end
                for xf in backend.ast_transforms
                    ast = Base.invokelatest(xf, ast)
                end
                value = Core.eval(mod, ast)
                backend.in_eval = false
                setglobal!(Base.MainInclude, :ans, value)
                put!(backend.response_channel, Pair{Any, Bool}(value, false))
            end
            break
        catch err
            if lasterr !== nothing
                println("SYSTEM ERROR: Failed to report error to REPL frontend")
                println(err)
            end
            lasterr = current_exceptions()
        end
    end
    Base.sigatomic_end()
    nothing
end

function check_for_missing_packages_and_run_hooks(ast)
    isa(ast, Expr) || return
    mods = modules_to_be_loaded(ast)
    filter!(mod -> isnothing(Base.identify_package(String(mod))), mods) # keep missing modules
    if !isempty(mods)
        for f in install_packages_hooks
            Base.invokelatest(f, mods) && return
        end
    end
end

function modules_to_be_loaded(ast::Expr, mods::Vector{Symbol} = Symbol[])
    ast.head === :quote && return mods # don't search if it's not going to be run during this eval
    if ast.head === :using || ast.head === :import
        for arg in ast.args
            arg = arg::Expr
            arg1 = first(arg.args)
            if arg1 isa Symbol # i.e. `Foo`
                if arg1 != :. # don't include local imports
                    push!(mods, arg1)
                end
            else # i.e. `Foo: bar`
                push!(mods, first((arg1::Expr).args))
            end
        end
    end
    for arg in ast.args
        if isexpr(arg, (:block, :if, :using, :import))
            modules_to_be_loaded(arg, mods)
        end
    end
    filter!(mod -> !in(String(mod), ["Base", "Main", "Core"]), mods) # Exclude special non-package modules
    return unique(mods)
end

"""
    start_repl_backend(repl_channel::Channel, response_channel::Channel)

    Starts loop for REPL backend
    Returns a REPLBackend with backend_task assigned

    Deprecated since sync / async behavior cannot be selected
"""
function start_repl_backend(repl_channel::Channel{Any}, response_channel::Channel{Any}
                            ; get_module::Function = ()->Main)
    # Maintain legacy behavior of asynchronous backend
    backend = REPLBackend(repl_channel, response_channel, false)
    # Assignment will be made twice, but will be immediately available
    backend.backend_task = @async start_repl_backend(backend; get_module)
    return backend
end

"""
    start_repl_backend(backend::REPLBackend)

    Call directly to run backend loop on current Task.
    Use @async for run backend on new Task.

    Does not return backend until loop is finished.
"""
function start_repl_backend(backend::REPLBackend,  @nospecialize(consumer = x -> nothing); get_module::Function = ()->Main)
    backend.backend_task = Base.current_task()
    consumer(backend)
    repl_backend_loop(backend, get_module)
    return backend
end

function repl_backend_loop(backend::REPLBackend, get_module::Function)
    # include looks at this to determine the relative include path
    # nothing means cwd
    while true
        tls = task_local_storage()
        tls[:SOURCE_PATH] = nothing
        ast, show_value = take!(backend.repl_channel)
        if show_value == -1
            # exit flag
            break
        end
        eval_user_input(ast, backend, get_module())
    end
    return nothing
end

struct REPLDisplay{R<:AbstractREPL} <: AbstractDisplay
    repl::R
end

==(a::REPLDisplay, b::REPLDisplay) = a.repl === b.repl

function display(d::REPLDisplay, mime::MIME"text/plain", x)
    x = Ref{Any}(x)
    with_repl_linfo(d.repl) do io
        io = IOContext(io, :limit => true, :module => active_module(d)::Module)
        if d.repl isa LineEditREPL
            mistate = d.repl.mistate
            mode = LineEdit.mode(mistate)
            if mode isa LineEdit.Prompt
                LineEdit.write_output_prefix(io, mode, get(io, :color, false)::Bool)
            end
        end
        get(io, :color, false)::Bool && write(io, answer_color(d.repl))
        if isdefined(d.repl, :options) && isdefined(d.repl.options, :iocontext)
            # this can override the :limit property set initially
            io = foldl(IOContext, d.repl.options.iocontext, init=io)
        end
        show(io, mime, x[])
        println(io)
    end
    return nothing
end
display(d::REPLDisplay, x) = display(d, MIME("text/plain"), x)

function print_response(repl::AbstractREPL, response, show_value::Bool, have_color::Bool)
    repl.waserror = response[2]
    with_repl_linfo(repl) do io
        io = IOContext(io, :module => active_module(repl)::Module)
        print_response(io, response, show_value, have_color, specialdisplay(repl))
    end
    return nothing
end

function repl_display_error(errio::IO, @nospecialize errval)
    # this will be set to true if types in the stacktrace are truncated
    limitflag = Ref(false)
    errio = IOContext(errio, :stacktrace_types_limited => limitflag)
    Base.invokelatest(Base.display_error, errio, errval)
    if limitflag[]
        print(errio, "Some type information was truncated. Use `show(err)` to see complete types.")
        println(errio)
    end
    return nothing
end

function print_response(errio::IO, response, show_value::Bool, have_color::Bool, specialdisplay::Union{AbstractDisplay,Nothing}=nothing)
    Base.sigatomic_begin()
    val, iserr = response
    while true
        try
            Base.sigatomic_end()
            if iserr
                val = Base.scrub_repl_backtrace(val)
                Base.istrivialerror(val) || setglobal!(Base.MainInclude, :err, val)
                repl_display_error(errio, val)
            else
                if val !== nothing && show_value
                    try
                        if specialdisplay === nothing
                            Base.invokelatest(display, val)
                        else
                            Base.invokelatest(display, specialdisplay, val)
                        end
                    catch
                        println(errio, "Error showing value of type ", typeof(val), ":")
                        rethrow()
                    end
                end
            end
            break
        catch ex
            if iserr
                println(errio) # an error during printing is likely to leave us mid-line
                println(errio, "SYSTEM (REPL): showing an error caused an error")
                try
                    excs = Base.scrub_repl_backtrace(current_exceptions())
                    setglobal!(Base.MainInclude, :err, excs)
                    repl_display_error(errio, excs)
                catch e
                    # at this point, only print the name of the type as a Symbol to
                    # minimize the possibility of further errors.
                    println(errio)
                    println(errio, "SYSTEM (REPL): caught exception of type ", typeof(e).name.name,
                            " while trying to handle a nested exception; giving up")
                end
                break
            end
            val = current_exceptions()
            iserr = true
        end
    end
    Base.sigatomic_end()
    nothing
end

# A reference to a backend that is not mutable
struct REPLBackendRef
    repl_channel::Channel{Any}
    response_channel::Channel{Any}
end
REPLBackendRef(backend::REPLBackend) = REPLBackendRef(backend.repl_channel, backend.response_channel)

function destroy(ref::REPLBackendRef, state::Task)
    if istaskfailed(state)
        close(ref.repl_channel, TaskFailedException(state))
        close(ref.response_channel, TaskFailedException(state))
    end
    close(ref.repl_channel)
    close(ref.response_channel)
end

"""
    run_repl(repl::AbstractREPL)
    run_repl(repl, consumer = backend->nothing; backend_on_current_task = true)

    Main function to start the REPL

    consumer is an optional function that takes a REPLBackend as an argument
"""
function run_repl(repl::AbstractREPL, @nospecialize(consumer = x -> nothing); backend_on_current_task::Bool = true, backend = REPLBackend())
    backend_ref = REPLBackendRef(backend)
    cleanup = @task try
            destroy(backend_ref, t)
        catch e
            Core.print(Core.stderr, "\nINTERNAL ERROR: ")
            Core.println(Core.stderr, e)
            Core.println(Core.stderr, catch_backtrace())
        end
    get_module = () -> active_module(repl)
    if backend_on_current_task
        t = @async run_frontend(repl, backend_ref)
        errormonitor(t)
        Base._wait2(t, cleanup)
        start_repl_backend(backend, consumer; get_module)
    else
        t = @async start_repl_backend(backend, consumer; get_module)
        errormonitor(t)
        Base._wait2(t, cleanup)
        run_frontend(repl, backend_ref)
    end
    return backend
end

## BasicREPL ##

mutable struct BasicREPL <: AbstractREPL
    terminal::TextTerminal
    waserror::Bool
    frontend_task::Task
    BasicREPL(t) = new(t, false)
end

outstream(r::BasicREPL) = r.terminal
hascolor(r::BasicREPL) = hascolor(r.terminal)

function run_frontend(repl::BasicREPL, backend::REPLBackendRef)
    repl.frontend_task = current_task()
    d = REPLDisplay(repl)
    dopushdisplay = !in(d,Base.Multimedia.displays)
    dopushdisplay && pushdisplay(d)
    hit_eof = false
    while true
        Base.reseteof(repl.terminal)
        write(repl.terminal, JULIA_PROMPT)
        line = ""
        ast = nothing
        interrupted = false
        while true
            try
                line *= readline(repl.terminal, keep=true)
            catch e
                if isa(e,InterruptException)
                    try # raise the debugger if present
                        ccall(:jl_raise_debugger, Int, ())
                    catch
                    end
                    line = ""
                    interrupted = true
                    break
                elseif isa(e,EOFError)
                    hit_eof = true
                    break
                else
                    rethrow()
                end
            end
            ast = Base.parse_input_line(line)
            (isa(ast,Expr) && ast.head === :incomplete) || break
        end
        if !isempty(line)
            response = eval_with_backend(ast, backend)
            print_response(repl, response, !ends_with_semicolon(line), false)
        end
        write(repl.terminal, '\n')
        ((!interrupted && isempty(line)) || hit_eof) && break
    end
    # terminate backend
    put!(backend.repl_channel, (nothing, -1))
    dopushdisplay && popdisplay(d)
    nothing
end

## LineEditREPL ##

mutable struct LineEditREPL <: AbstractREPL
    t::TextTerminal
    hascolor::Bool
    prompt_color::String
    input_color::String
    answer_color::String
    shell_color::String
    help_color::String
    history_file::Bool
    in_shell::Bool
    in_help::Bool
    envcolors::Bool
    waserror::Bool
    specialdisplay::Union{Nothing,AbstractDisplay}
    options::Options
    mistate::Union{MIState,Nothing}
    last_shown_line_infos::Vector{Tuple{String,Int}}
    interface::ModalInterface
    backendref::REPLBackendRef
    frontend_task::Task
    function LineEditREPL(t,hascolor,prompt_color,input_color,answer_color,shell_color,help_color,history_file,in_shell,in_help,envcolors)
        opts = Options()
        opts.hascolor = hascolor
        if !hascolor
            opts.beep_colors = [""]
        end
        new(t,hascolor,prompt_color,input_color,answer_color,shell_color,help_color,history_file,in_shell,
            in_help,envcolors,false,nothing, opts, nothing, Tuple{String,Int}[])
    end
end
outstream(r::LineEditREPL) = (t = r.t; t isa TTYTerminal ? t.out_stream : t)
specialdisplay(r::LineEditREPL) = r.specialdisplay
specialdisplay(r::AbstractREPL) = nothing
terminal(r::LineEditREPL) = r.t
hascolor(r::LineEditREPL) = r.hascolor

LineEditREPL(t::TextTerminal, hascolor::Bool, envcolors::Bool=false) =
    LineEditREPL(t, hascolor,
        hascolor ? Base.text_colors[:green] : "",
        hascolor ? Base.input_color() : "",
        hascolor ? Base.answer_color() : "",
        hascolor ? Base.text_colors[:red] : "",
        hascolor ? Base.text_colors[:yellow] : "",
        false, false, false, envcolors
    )

mutable struct REPLCompletionProvider <: CompletionProvider
    modifiers::LineEdit.Modifiers
end
REPLCompletionProvider() = REPLCompletionProvider(LineEdit.Modifiers())

mutable struct ShellCompletionProvider <: CompletionProvider end
struct LatexCompletions <: CompletionProvider end

function active_module() # this method is also called from Base
    isdefined(Base, :active_repl) || return Main
    return active_module(Base.active_repl::AbstractREPL)
end
active_module((; mistate)::LineEditREPL) = mistate === nothing ? Main : mistate.active_module
active_module(::AbstractREPL) = Main
active_module(d::REPLDisplay) = active_module(d.repl)

setmodifiers!(c::CompletionProvider, m::LineEdit.Modifiers) = nothing

setmodifiers!(c::REPLCompletionProvider, m::LineEdit.Modifiers) = c.modifiers = m

"""
    activate(mod::Module=Main)

Set `mod` as the default contextual module in the REPL,
both for evaluating expressions and printing them.
"""
function activate(mod::Module=Main)
    mistate = (Base.active_repl::LineEditREPL).mistate
    mistate === nothing && return nothing
    mistate.active_module = mod
    Base.load_InteractiveUtils(mod)
    return nothing
end

beforecursor(buf::IOBuffer) = String(buf.data[1:buf.ptr-1])

function complete_line(c::REPLCompletionProvider, s::PromptState, mod::Module)
    partial = beforecursor(s.input_buffer)
    full = LineEdit.input_string(s)
    ret, range, should_complete = completions(full, lastindex(partial), mod, c.modifiers.shift)
    c.modifiers = LineEdit.Modifiers()
    return unique!(map(completion_text, ret)), partial[range], should_complete
end

function complete_line(c::ShellCompletionProvider, s::PromptState)
    # First parse everything up to the current position
    partial = beforecursor(s.input_buffer)
    full = LineEdit.input_string(s)
    ret, range, should_complete = shell_completions(full, lastindex(partial))
    return unique!(map(completion_text, ret)), partial[range], should_complete
end

function complete_line(c::LatexCompletions, s)
    partial = beforecursor(LineEdit.buffer(s))
    full = LineEdit.input_string(s)::String
    ret, range, should_complete = bslash_completions(full, lastindex(partial))[2]
    return unique!(map(completion_text, ret)), partial[range], should_complete
end

with_repl_linfo(f, repl) = f(outstream(repl))
function with_repl_linfo(f, repl::LineEditREPL)
    linfos = Tuple{String,Int}[]
    io = IOContext(outstream(repl), :last_shown_line_infos => linfos)
    f(io)
    if !isempty(linfos)
        repl.last_shown_line_infos = linfos
    end
    nothing
end

mutable struct REPLHistoryProvider <: HistoryProvider
    history::Vector{String}
    file_path::String
    history_file::Union{Nothing,IO}
    start_idx::Int
    cur_idx::Int
    last_idx::Int
    last_buffer::IOBuffer
    last_mode::Union{Nothing,Prompt}
    mode_mapping::Dict{Symbol,Prompt}
    modes::Vector{Symbol}
end
REPLHistoryProvider(mode_mapping::Dict{Symbol}) =
    REPLHistoryProvider(String[], "", nothing, 0, 0, -1, IOBuffer(),
                        nothing, mode_mapping, UInt8[])

invalid_history_message(path::String) = """
Invalid history file ($path) format:
If you have a history file left over from an older version of Julia,
try renaming or deleting it.
Invalid character: """

munged_history_message(path::String) = """
Invalid history file ($path) format:
An editor may have converted tabs to spaces at line """

function hist_open_file(hp::REPLHistoryProvider)
    f = open(hp.file_path, read=true, write=true, create=true)
    hp.history_file = f
    seekend(f)
end

function hist_from_file(hp::REPLHistoryProvider, path::String)
    getline(lines, i) = i > length(lines) ? "" : lines[i]
    file_lines = readlines(path)
    countlines = 0
    while true
        # First parse the metadata that starts with '#' in particular the REPL mode
        countlines += 1
        line = getline(file_lines, countlines)
        mode = :julia
        isempty(line) && break
        line[1] != '#' &&
            error(invalid_history_message(path), repr(line[1]), " at line ", countlines)
        while !isempty(line)
            startswith(line, '#') || break
            if startswith(line, "# mode: ")
                mode = Symbol(SubString(line, 9))
            end
            countlines += 1
            line = getline(file_lines, countlines)
        end
        isempty(line) && break

        # Now parse the code for the current REPL mode
        line[1] == ' '  &&
            error(munged_history_message(path), countlines)
        line[1] != '\t' &&
            error(invalid_history_message(path), repr(line[1]), " at line ", countlines)
        lines = String[]
        while !isempty(line)
            push!(lines, chomp(SubString(line, 2)))
            next_line = getline(file_lines, countlines+1)
            isempty(next_line) && break
            first(next_line) == ' '  && error(munged_history_message(path), countlines)
            # A line not starting with a tab means we are done with code for this entry
            first(next_line) != '\t' && break
            countlines += 1
            line = getline(file_lines, countlines)
        end
        push!(hp.modes, mode)
        push!(hp.history, join(lines, '\n'))
    end
    hp.start_idx = length(hp.history)
    return hp
end

function add_history(hist::REPLHistoryProvider, s::PromptState)
    str = rstrip(String(take!(copy(s.input_buffer))))
    isempty(strip(str)) && return
    mode = mode_idx(hist, LineEdit.mode(s))
    !isempty(hist.history) &&
        isequal(mode, hist.modes[end]) && str == hist.history[end] && return
    push!(hist.modes, mode)
    push!(hist.history, str)
    hist.history_file === nothing && return
    entry = """
    # time: $(Libc.strftime("%Y-%m-%d %H:%M:%S %Z", time()))
    # mode: $mode
    $(replace(str, r"^"ms => "\t"))
    """
    # TODO: write-lock history file
    try
        seekend(hist.history_file)
    catch err
        (err isa SystemError) || rethrow()
        # File handle might get stale after a while, especially under network file systems
        # If this doesn't fix it (e.g. when file is deleted), we'll end up rethrowing anyway
        hist_open_file(hist)
    end
    print(hist.history_file, entry)
    flush(hist.history_file)
    nothing
end

function history_move(s::Union{LineEdit.MIState,LineEdit.PrefixSearchState}, hist::REPLHistoryProvider, idx::Int, save_idx::Int = hist.cur_idx)
    max_idx = length(hist.history) + 1
    @assert 1 <= hist.cur_idx <= max_idx
    (1 <= idx <= max_idx) || return :none
    idx != hist.cur_idx || return :none

    # save the current line
    if save_idx == max_idx
        hist.last_mode = LineEdit.mode(s)
        hist.last_buffer = copy(LineEdit.buffer(s))
    else
        hist.history[save_idx] = LineEdit.input_string(s)
        hist.modes[save_idx] = mode_idx(hist, LineEdit.mode(s))
    end

    # load the saved line
    if idx == max_idx
        last_buffer = hist.last_buffer
        LineEdit.transition(s, hist.last_mode) do
            LineEdit.replace_line(s, last_buffer)
        end
        hist.last_mode = nothing
        hist.last_buffer = IOBuffer()
    else
        if haskey(hist.mode_mapping, hist.modes[idx])
            LineEdit.transition(s, hist.mode_mapping[hist.modes[idx]]) do
                LineEdit.replace_line(s, hist.history[idx])
            end
        else
            return :skip
        end
    end
    hist.cur_idx = idx

    return :ok
end

# REPL History can also transitions modes
function LineEdit.accept_result_newmode(hist::REPLHistoryProvider)
    if 1 <= hist.cur_idx <= length(hist.modes)
        return hist.mode_mapping[hist.modes[hist.cur_idx]]
    end
    return nothing
end

function history_prev(s::LineEdit.MIState, hist::REPLHistoryProvider,
                      num::Int=1, save_idx::Int = hist.cur_idx)
    num <= 0 && return history_next(s, hist, -num, save_idx)
    hist.last_idx = -1
    m = history_move(s, hist, hist.cur_idx-num, save_idx)
    if m === :ok
        LineEdit.move_input_start(s)
        LineEdit.reset_key_repeats(s) do
            LineEdit.move_line_end(s)
        end
        return LineEdit.refresh_line(s)
    elseif m === :skip
        return history_prev(s, hist, num+1, save_idx)
    else
        return Terminals.beep(s)
    end
end

function history_next(s::LineEdit.MIState, hist::REPLHistoryProvider,
                      num::Int=1, save_idx::Int = hist.cur_idx)
    if num == 0
        Terminals.beep(s)
        return
    end
    num < 0 && return history_prev(s, hist, -num, save_idx)
    cur_idx = hist.cur_idx
    max_idx = length(hist.history) + 1
    if cur_idx == max_idx && 0 < hist.last_idx
        # issue #6312
        cur_idx = hist.last_idx
        hist.last_idx = -1
    end
    m = history_move(s, hist, cur_idx+num, save_idx)
    if m === :ok
        LineEdit.move_input_end(s)
        return LineEdit.refresh_line(s)
    elseif m === :skip
        return history_next(s, hist, num+1, save_idx)
    else
        return Terminals.beep(s)
    end
end

history_first(s::LineEdit.MIState, hist::REPLHistoryProvider) =
    history_prev(s, hist, hist.cur_idx - 1 -
                 (hist.cur_idx > hist.start_idx+1 ? hist.start_idx : 0))

history_last(s::LineEdit.MIState, hist::REPLHistoryProvider) =
    history_next(s, hist, length(hist.history) - hist.cur_idx + 1)

function history_move_prefix(s::LineEdit.PrefixSearchState,
                             hist::REPLHistoryProvider,
                             prefix::AbstractString,
                             backwards::Bool,
                             cur_idx::Int = hist.cur_idx)
    cur_response = String(take!(copy(LineEdit.buffer(s))))
    # when searching forward, start at last_idx
    if !backwards && hist.last_idx > 0
        cur_idx = hist.last_idx
    end
    hist.last_idx = -1
    max_idx = length(hist.history)+1
    idxs = backwards ? ((cur_idx-1):-1:1) : ((cur_idx+1):1:max_idx)
    for idx in idxs
        if (idx == max_idx) || (startswith(hist.history[idx], prefix) && (hist.history[idx] != cur_response || get(hist.mode_mapping, hist.modes[idx], nothing) !== LineEdit.mode(s)))
            m = history_move(s, hist, idx)
            if m === :ok
                if idx == max_idx
                    # on resuming the in-progress edit, leave the cursor where the user last had it
                elseif isempty(prefix)
                    # on empty prefix search, move cursor to the end
                    LineEdit.move_input_end(s)
                else
                    # otherwise, keep cursor at the prefix position as a visual cue
                    seek(LineEdit.buffer(s), sizeof(prefix))
                end
                LineEdit.refresh_line(s)
                return :ok
            elseif m === :skip
                return history_move_prefix(s,hist,prefix,backwards,idx)
            end
        end
    end
    Terminals.beep(s)
    nothing
end
history_next_prefix(s::LineEdit.PrefixSearchState, hist::REPLHistoryProvider, prefix::AbstractString) =
    history_move_prefix(s, hist, prefix, false)
history_prev_prefix(s::LineEdit.PrefixSearchState, hist::REPLHistoryProvider, prefix::AbstractString) =
    history_move_prefix(s, hist, prefix, true)

function history_search(hist::REPLHistoryProvider, query_buffer::IOBuffer, response_buffer::IOBuffer,
                        backwards::Bool=false, skip_current::Bool=false)

    qpos = position(query_buffer)
    qpos > 0 || return true
    searchdata = beforecursor(query_buffer)
    response_str = String(take!(copy(response_buffer)))

    # Alright, first try to see if the current match still works
    a = position(response_buffer) + 1 # position is zero-indexed
    # FIXME: I'm pretty sure this is broken since it uses an index
    # into the search data to index into the response string
    b = a + sizeof(searchdata)
    b = b ≤ ncodeunits(response_str) ? prevind(response_str, b) : b-1
    b = min(lastindex(response_str), b) # ensure that b is valid

    searchstart = backwards ? b : a
    if searchdata == response_str[a:b]
        if skip_current
            searchstart = backwards ? prevind(response_str, b) : nextind(response_str, a)
        else
            return true
        end
    end

    # Start searching
    # First the current response buffer
    if 1 <= searchstart <= lastindex(response_str)
        match = backwards ? findprev(searchdata, response_str, searchstart) :
                            findnext(searchdata, response_str, searchstart)
        if match !== nothing
            seek(response_buffer, first(match) - 1)
            return true
        end
    end

    # Now search all the other buffers
    idxs = backwards ? ((hist.cur_idx-1):-1:1) : ((hist.cur_idx+1):1:length(hist.history))
    for idx in idxs
        h = hist.history[idx]
        match = backwards ? findlast(searchdata, h) : findfirst(searchdata, h)
        if match !== nothing && h != response_str && haskey(hist.mode_mapping, hist.modes[idx])
            truncate(response_buffer, 0)
            write(response_buffer, h)
            seek(response_buffer, first(match) - 1)
            hist.cur_idx = idx
            return true
        end
    end

    return false
end

function history_reset_state(hist::REPLHistoryProvider)
    if hist.cur_idx != length(hist.history) + 1
        hist.last_idx = hist.cur_idx
        hist.cur_idx = length(hist.history) + 1
    end
    nothing
end
LineEdit.reset_state(hist::REPLHistoryProvider) = history_reset_state(hist)

function return_callback(s)
    ast = Base.parse_input_line(String(take!(copy(LineEdit.buffer(s)))), depwarn=false)
    return !(isa(ast, Expr) && ast.head === :incomplete)
end

find_hist_file() = get(ENV, "JULIA_HISTORY",
                       !isempty(DEPOT_PATH) ? joinpath(DEPOT_PATH[1], "logs", "repl_history.jl") :
                       error("DEPOT_PATH is empty and and ENV[\"JULIA_HISTORY\"] not set."))

backend(r::AbstractREPL) = r.backendref

function eval_with_backend(ast, backend::REPLBackendRef)
    put!(backend.repl_channel, (ast, 1))
    return take!(backend.response_channel) # (val, iserr)
end

function respond(f, repl, main; pass_empty::Bool = false, suppress_on_semicolon::Bool = true)
    return function do_respond(s::MIState, buf, ok::Bool)
        if !ok
            return transition(s, :abort)
        end
        line = String(take!(buf)::Vector{UInt8})
        if !isempty(line) || pass_empty
            reset(repl)
            local response
            try
                ast = Base.invokelatest(f, line)
                response = eval_with_backend(ast, backend(repl))
            catch
                response = Pair{Any, Bool}(current_exceptions(), true)
            end
            hide_output = suppress_on_semicolon && ends_with_semicolon(line)
            print_response(repl, response, !hide_output, hascolor(repl))
        end
        prepare_next(repl)
        reset_state(s)
        return s.current_mode.sticky ? true : transition(s, main)
    end
end

function reset(repl::LineEditREPL)
    raw!(repl.t, false)
    hascolor(repl) && print(repl.t, Base.text_colors[:normal])
    nothing
end

function prepare_next(repl::LineEditREPL)
    println(terminal(repl))
end

function mode_keymap(julia_prompt::Prompt)
    AnyDict(
    '\b' => function (s::MIState,o...)
        if isempty(s) || position(LineEdit.buffer(s)) == 0
            buf = copy(LineEdit.buffer(s))
            transition(s, julia_prompt) do
                LineEdit.state(s, julia_prompt).input_buffer = buf
            end
        else
            LineEdit.edit_backspace(s)
        end
    end,
    "^C" => function (s::MIState,o...)
        LineEdit.move_input_end(s)
        LineEdit.refresh_line(s)
        print(LineEdit.terminal(s), "^C\n\n")
        transition(s, julia_prompt)
        transition(s, :reset)
        LineEdit.refresh_line(s)
    end)
end

repl_filename(repl, hp::REPLHistoryProvider) = "REPL[$(max(length(hp.history)-hp.start_idx, 1))]"
repl_filename(repl, hp) = "REPL"

const JL_PROMPT_PASTE = Ref(true)
enable_promptpaste(v::Bool) = JL_PROMPT_PASTE[] = v

function contextual_prompt(repl::LineEditREPL, prompt::Union{String,Function})
    function ()
        mod = active_module(repl)
        prefix = mod == Main ? "" : string('(', mod, ") ")
        pr = prompt isa String ? prompt : prompt()
        prefix * pr
    end
end

setup_interface(
    repl::LineEditREPL;
    # those keyword arguments may be deprecated eventually in favor of the Options mechanism
    hascolor::Bool = repl.options.hascolor,
    extra_repl_keymap::Any = repl.options.extra_keymap
) = setup_interface(repl, hascolor, extra_repl_keymap)

# This non keyword method can be precompiled which is important
function setup_interface(
    repl::LineEditREPL,
    hascolor::Bool,
    extra_repl_keymap::Any, # Union{Dict,Vector{<:Dict}},
)
    # The precompile statement emitter has problem outputting valid syntax for the
    # type of `Union{Dict,Vector{<:Dict}}` (see #28808).
    # This function is however important to precompile for REPL startup time, therefore,
    # make the type Any and just assert that we have the correct type below.
    @assert extra_repl_keymap isa Union{Dict,Vector{<:Dict}}

    ###
    #
    # This function returns the main interface that describes the REPL
    # functionality, it is called internally by functions that setup a
    # Terminal-based REPL frontend.
    #
    # See run_frontend(repl::LineEditREPL, backend::REPLBackendRef)
    # for usage
    #
    ###

    ###
    # We setup the interface in two stages.
    # First, we set up all components (prompt,rsearch,shell,help)
    # Second, we create keymaps with appropriate transitions between them
    #   and assign them to the components
    #
    ###

    ############################### Stage I ################################

    # This will provide completions for REPL and help mode
    replc = REPLCompletionProvider()

    # Set up the main Julia prompt
    julia_prompt = Prompt(contextual_prompt(repl, JULIA_PROMPT);
        # Copy colors from the prompt object
        prompt_prefix = hascolor ? repl.prompt_color : "",
        prompt_suffix = hascolor ?
            (repl.envcolors ? Base.input_color : repl.input_color) : "",
        repl = repl,
        complete = replc,
        on_enter = return_callback)

    # Setup help mode
    help_mode = Prompt(contextual_prompt(repl, "help?> "),
        prompt_prefix = hascolor ? repl.help_color : "",
        prompt_suffix = hascolor ?
            (repl.envcolors ? Base.input_color : repl.input_color) : "",
        repl = repl,
        complete = replc,
        # When we're done transform the entered line into a call to helpmode function
        on_done = respond(line::String->helpmode(outstream(repl), line, repl.mistate.active_module),
                          repl, julia_prompt, pass_empty=true, suppress_on_semicolon=false))


    # Set up shell mode
    shell_mode = Prompt(SHELL_PROMPT;
        prompt_prefix = hascolor ? repl.shell_color : "",
        prompt_suffix = hascolor ?
            (repl.envcolors ? Base.input_color : repl.input_color) : "",
        repl = repl,
        complete = ShellCompletionProvider(),
        # Transform "foo bar baz" into `foo bar baz` (shell quoting)
        # and pass into Base.repl_cmd for processing (handles `ls` and `cd`
        # special)
        on_done = respond(repl, julia_prompt) do line
            Expr(:call, :(Base.repl_cmd),
                :(Base.cmd_gen($(Base.shell_parse(line::String)[1]))),
                outstream(repl))
        end,
        sticky = true)


    ################################# Stage II #############################

    # Setup history
    # We will have a unified history for all REPL modes
    hp = REPLHistoryProvider(Dict{Symbol,Prompt}(:julia => julia_prompt,
                                                 :shell => shell_mode,
                                                 :help  => help_mode))
    if repl.history_file
        try
            hist_path = find_hist_file()
            mkpath(dirname(hist_path))
            hp.file_path = hist_path
            hist_open_file(hp)
            finalizer(replc) do replc
                close(hp.history_file)
            end
            hist_from_file(hp, hist_path)
        catch
            # use REPL.hascolor to avoid using the local variable with the same name
            print_response(repl, Pair{Any, Bool}(current_exceptions(), true), true, REPL.hascolor(repl))
            println(outstream(repl))
            @info "Disabling history file for this session"
            repl.history_file = false
        end
    end
    history_reset_state(hp)
    julia_prompt.hist = hp
    shell_mode.hist = hp
    help_mode.hist = hp

    julia_prompt.on_done = respond(x->Base.parse_input_line(x,filename=repl_filename(repl,hp)), repl, julia_prompt)


    search_prompt, skeymap = LineEdit.setup_search_keymap(hp)
    search_prompt.complete = LatexCompletions()

    shell_prompt_len = length(SHELL_PROMPT)
    help_prompt_len = length(HELP_PROMPT)
    jl_prompt_regex = r"^In \[[0-9]+\]: |^(?:\(.+\) )?julia> "
    pkg_prompt_regex = r"^(?:\(.+\) )?pkg> "

    # Canonicalize user keymap input
    if isa(extra_repl_keymap, Dict)
        extra_repl_keymap = AnyDict[extra_repl_keymap]
    end

    repl_keymap = AnyDict(
        ';' => function (s::MIState,o...)
            if isempty(s) || position(LineEdit.buffer(s)) == 0
                buf = copy(LineEdit.buffer(s))
                transition(s, shell_mode) do
                    LineEdit.state(s, shell_mode).input_buffer = buf
                end
            else
                edit_insert(s, ';')
            end
        end,
        '?' => function (s::MIState,o...)
            if isempty(s) || position(LineEdit.buffer(s)) == 0
                buf = copy(LineEdit.buffer(s))
                transition(s, help_mode) do
                    LineEdit.state(s, help_mode).input_buffer = buf
                end
            else
                edit_insert(s, '?')
            end
        end,

        # Bracketed Paste Mode
        "\e[200~" => (s::MIState,o...)->begin
            input = LineEdit.bracketed_paste(s) # read directly from s until reaching the end-bracketed-paste marker
            sbuffer = LineEdit.buffer(s)
            curspos = position(sbuffer)
            seek(sbuffer, 0)
            shouldeval = (bytesavailable(sbuffer) == curspos && !occursin(UInt8('\n'), sbuffer))
            seek(sbuffer, curspos)
            if curspos == 0
                # if pasting at the beginning, strip leading whitespace
                input = lstrip(input)
            end
            if !shouldeval
                # when pasting in the middle of input, just paste in place
                # don't try to execute all the WIP, since that's rather confusing
                # and is often ill-defined how it should behave
                edit_insert(s, input)
                return
            end
            LineEdit.push_undo(s)
            edit_insert(sbuffer, input)
            input = String(take!(sbuffer))
            oldpos = firstindex(input)
            firstline = true
            isprompt_paste = false
            curr_prompt_len = 0
            pasting_help = false

            while oldpos <= lastindex(input) # loop until all lines have been executed
                if JL_PROMPT_PASTE[]
                    # Check if the next statement starts with a prompt i.e. "julia> ", in that case
                    # skip it. But first skip whitespace unless pasting in a docstring which may have
                    # indented prompt examples that we don't want to execute
                    while input[oldpos] in (pasting_help ? ('\n') : ('\n', ' ', '\t'))
                        oldpos = nextind(input, oldpos)
                        oldpos >= sizeof(input) && return
                    end
                    substr = SubString(input, oldpos)
                    # Check if input line starts with "julia> ", remove it if we are in prompt paste mode
                    if (firstline || isprompt_paste) && startswith(substr, jl_prompt_regex)
                        detected_jl_prompt = match(jl_prompt_regex, substr).match
                        isprompt_paste = true
                        curr_prompt_len = sizeof(detected_jl_prompt)
                        oldpos += curr_prompt_len
                        transition(s, julia_prompt)
                        pasting_help = false
                    # Check if input line starts with "pkg> " or "(...) pkg> ", remove it if we are in prompt paste mode and switch mode
                    elseif (firstline || isprompt_paste) && startswith(substr, pkg_prompt_regex)
                        detected_pkg_prompt = match(pkg_prompt_regex, substr).match
                        isprompt_paste = true
                        curr_prompt_len = sizeof(detected_pkg_prompt)
                        oldpos += curr_prompt_len
                        Base.active_repl.interface.modes[1].keymap_dict[']'](s, o...)
                        pasting_help = false
                    # Check if input line starts with "shell> ", remove it if we are in prompt paste mode and switch mode
                    elseif (firstline || isprompt_paste) && startswith(substr, SHELL_PROMPT)
                        isprompt_paste = true
                        oldpos += shell_prompt_len
                        curr_prompt_len = shell_prompt_len
                        transition(s, shell_mode)
                        pasting_help = false
                    # Check if input line starts with "help?> ", remove it if we are in prompt paste mode and switch mode
                    elseif (firstline || isprompt_paste) && startswith(substr, HELP_PROMPT)
                        isprompt_paste = true
                        oldpos += help_prompt_len
                        curr_prompt_len = help_prompt_len
                        transition(s, help_mode)
                        pasting_help = true
                    # If we are prompt pasting and current statement does not begin with a mode prefix, skip to next line
                    elseif isprompt_paste
                        while input[oldpos] != '\n'
                            oldpos = nextind(input, oldpos)
                            oldpos >= sizeof(input) && return
                        end
                        continue
                    end
                end
                dump_tail = false
                nl_pos = findfirst('\n', input[oldpos:end])
                if s.current_mode == julia_prompt
                    ast, pos = Meta.parse(input, oldpos, raise=false, depwarn=false)
                    if (isa(ast, Expr) && (ast.head === :error || ast.head === :incomplete)) ||
                            (pos > ncodeunits(input) && !endswith(input, '\n'))
                        # remaining text is incomplete (an error, or parser ran to the end but didn't stop with a newline):
                        # Insert all the remaining text as one line (might be empty)
                        dump_tail = true
                    end
                elseif isnothing(nl_pos) # no newline at end, so just dump the tail into the prompt and don't execute
                    dump_tail = true
                elseif s.current_mode == shell_mode # handle multiline shell commands
                    lines = split(input[oldpos:end], '\n')
                    pos = oldpos + sizeof(lines[1]) + 1
                    if length(lines) > 1
                        for line in lines[2:end]
                            # to be recognized as a multiline shell command, the lines must be indented to the
                            # same prompt position
                            if !startswith(line, ' '^curr_prompt_len)
                                break
                            end
                            pos += sizeof(line) + 1
                        end
                    end
                else
                    pos = oldpos + nl_pos
                end
                if dump_tail
                    tail = input[oldpos:end]
                    if !firstline
                        # strip leading whitespace, but only if it was the result of executing something
                        # (avoids modifying the user's current leading wip line)
                        tail = lstrip(tail)
                    end
                    if isprompt_paste # remove indentation spaces corresponding to the prompt
                        tail = replace(tail, r"^"m * ' '^curr_prompt_len => "")
                    end
                    LineEdit.replace_line(s, tail, true)
                    LineEdit.refresh_line(s)
                    break
                end
                # get the line and strip leading and trailing whitespace
                line = strip(input[oldpos:prevind(input, pos)])
                if !isempty(line)
                    if isprompt_paste # remove indentation spaces corresponding to the prompt
                        line = replace(line, r"^"m * ' '^curr_prompt_len => "")
                    end
                    # put the line on the screen and history
                    LineEdit.replace_line(s, line)
                    LineEdit.commit_line(s)
                    # execute the statement
                    terminal = LineEdit.terminal(s) # This is slightly ugly but ok for now
                    raw!(terminal, false) && disable_bracketed_paste(terminal)
                    LineEdit.mode(s).on_done(s, LineEdit.buffer(s), true)
                    raw!(terminal, true) && enable_bracketed_paste(terminal)
                    LineEdit.push_undo(s) # when the last line is incomplete
                end
                oldpos = pos
                firstline = false
            end
        end,

        # Open the editor at the location of a stackframe or method
        # This is accessing a contextual variable that gets set in
        # the show_backtrace and show_method_table functions.
        "^Q" => (s::MIState, o...) -> begin
            linfos = repl.last_shown_line_infos
            str = String(take!(LineEdit.buffer(s)))
            n = tryparse(Int, str)
            n === nothing && @goto writeback
            if n <= 0 || n > length(linfos) || startswith(linfos[n][1], "REPL[")
                @goto writeback
            end
            try
                InteractiveUtils.edit(Base.fixup_stdlib_path(linfos[n][1]), linfos[n][2])
            catch ex
                ex isa ProcessFailedException || ex isa Base.IOError || ex isa SystemError || rethrow()
                @info "edit failed" _exception=ex
            end
            LineEdit.refresh_line(s)
            return
            @label writeback
            write(LineEdit.buffer(s), str)
            return
        end,
    )

    prefix_prompt, prefix_keymap = LineEdit.setup_prefix_keymap(hp, julia_prompt)

    a = Dict{Any,Any}[skeymap, repl_keymap, prefix_keymap, LineEdit.history_keymap, LineEdit.default_keymap, LineEdit.escape_defaults]
    prepend!(a, extra_repl_keymap)

    julia_prompt.keymap_dict = LineEdit.keymap(a)

    mk = mode_keymap(julia_prompt)

    b = Dict{Any,Any}[skeymap, mk, prefix_keymap, LineEdit.history_keymap, LineEdit.default_keymap, LineEdit.escape_defaults]
    prepend!(b, extra_repl_keymap)

    shell_mode.keymap_dict = help_mode.keymap_dict = LineEdit.keymap(b)

    allprompts = LineEdit.TextInterface[julia_prompt, shell_mode, help_mode, search_prompt, prefix_prompt]
    return ModalInterface(allprompts)
end

function run_frontend(repl::LineEditREPL, backend::REPLBackendRef)
    repl.frontend_task = current_task()
    d = REPLDisplay(repl)
    dopushdisplay = repl.specialdisplay === nothing && !in(d,Base.Multimedia.displays)
    dopushdisplay && pushdisplay(d)
    if !isdefined(repl,:interface)
        interface = repl.interface = setup_interface(repl)
    else
        interface = repl.interface
    end
    repl.backendref = backend
    repl.mistate = LineEdit.init_state(terminal(repl), interface)
    run_interface(terminal(repl), interface, repl.mistate)
    # Terminate Backend
    put!(backend.repl_channel, (nothing, -1))
    dopushdisplay && popdisplay(d)
    nothing
end

## StreamREPL ##

mutable struct StreamREPL <: AbstractREPL
    stream::IO
    prompt_color::String
    input_color::String
    answer_color::String
    waserror::Bool
    frontend_task::Task
    StreamREPL(stream,pc,ic,ac) = new(stream,pc,ic,ac,false)
end
StreamREPL(stream::IO) = StreamREPL(stream, Base.text_colors[:green], Base.input_color(), Base.answer_color())
run_repl(stream::IO) = run_repl(StreamREPL(stream))

outstream(s::StreamREPL) = s.stream
hascolor(s::StreamREPL) = get(s.stream, :color, false)::Bool

answer_color(r::LineEditREPL) = r.envcolors ? Base.answer_color() : r.answer_color
answer_color(r::StreamREPL) = r.answer_color
input_color(r::LineEditREPL) = r.envcolors ? Base.input_color() : r.input_color
input_color(r::StreamREPL) = r.input_color

let matchend = Dict("\"" => r"\"", "\"\"\"" => r"\"\"\"", "'" => r"'",
    "`" => r"`", "```" => r"```", "#" => r"$"m, "#=" => r"=#|#=")
    global _rm_strings_and_comments
    function _rm_strings_and_comments(code::Union{String,SubString{String}})
        buf = IOBuffer(sizehint = sizeof(code))
        pos = 1
        while true
            i = findnext(r"\"(?!\"\")|\"\"\"|'|`(?!``)|```|#(?!=)|#=", code, pos)
            isnothing(i) && break
            match = SubString(code, i)
            j = findnext(matchend[match]::Regex, code, nextind(code, last(i)))
            if match == "#=" # possibly nested
                nested = 1
                while j !== nothing
                    nested += SubString(code, j) == "#=" ? +1 : -1
                    iszero(nested) && break
                    j = findnext(r"=#|#=", code, nextind(code, last(j)))
                end
            elseif match[1] != '#' # quote match: check non-escaped
                while j !== nothing
                    notbackslash = findprev(!=('\\'), code, prevind(code, first(j)))::Int
                    isodd(first(j) - notbackslash) && break # not escaped
                    j = findnext(matchend[match]::Regex, code, nextind(code, first(j)))
                end
            end
            isnothing(j) && break
            if match[1] == '#'
                print(buf, SubString(code, pos, prevind(code, first(i))))
            else
                print(buf, SubString(code, pos, last(i)), ' ', SubString(code, j))
            end
            pos = nextind(code, last(j))
        end
        print(buf, SubString(code, pos, lastindex(code)))
        return String(take!(buf))
    end
end

# heuristic function to decide if the presence of a semicolon
# at the end of the expression was intended for suppressing output
ends_with_semicolon(code::AbstractString) = ends_with_semicolon(String(code))
ends_with_semicolon(code::Union{String,SubString{String}}) =
    contains(_rm_strings_and_comments(code), r";\s*$")

function run_frontend(repl::StreamREPL, backend::REPLBackendRef)
    repl.frontend_task = current_task()
    have_color = hascolor(repl)
    Base.banner(repl.stream)
    d = REPLDisplay(repl)
    dopushdisplay = !in(d,Base.Multimedia.displays)
    dopushdisplay && pushdisplay(d)
    while !eof(repl.stream)::Bool
        if have_color
            print(repl.stream,repl.prompt_color)
        end
        print(repl.stream, "julia> ")
        if have_color
            print(repl.stream, input_color(repl))
        end
        line = readline(repl.stream, keep=true)
        if !isempty(line)
            ast = Base.parse_input_line(line)
            if have_color
                print(repl.stream, Base.color_normal)
            end
            response = eval_with_backend(ast, backend)
            print_response(repl, response, !ends_with_semicolon(line), have_color)
        end
    end
    # Terminate Backend
    put!(backend.repl_channel, (nothing, -1))
    dopushdisplay && popdisplay(d)
    nothing
end

module Numbered

using ..REPL

__current_ast_transforms() = isdefined(Base, :active_repl_backend) ? Base.active_repl_backend.ast_transforms : REPL.repl_ast_transforms

function repl_eval_counter(hp)
    return length(hp.history) - hp.start_idx
end

function out_transform(@nospecialize(x), n::Ref{Int})
    return Expr(:toplevel, get_usings!([], x)..., quote
        let __temp_val_a72df459 = $x
            $capture_result($n, __temp_val_a72df459)
            __temp_val_a72df459
        end
    end)
end

function get_usings!(usings, ex)
    ex isa Expr || return usings
    # get all `using` and `import` statements which are at the top level
    for (i, arg) in enumerate(ex.args)
        if Base.isexpr(arg, :toplevel)
            get_usings!(usings, arg)
        elseif Base.isexpr(arg, [:using, :import])
            push!(usings, popat!(ex.args, i))
        end
    end
    return usings
end

function capture_result(n::Ref{Int}, @nospecialize(x))
    n = n[]
    mod = Base.MainInclude
    if !isdefined(mod, :Out)
        @eval mod global Out
        @eval mod export Out
        setglobal!(mod, :Out, Dict{Int, Any}())
    end
    if x !== getglobal(mod, :Out) && x !== nothing # remove this?
        getglobal(mod, :Out)[n] = x
    end
    nothing
end

function set_prompt(repl::LineEditREPL, n::Ref{Int})
    julia_prompt = repl.interface.modes[1]
    julia_prompt.prompt = function()
        n[] = repl_eval_counter(julia_prompt.hist)+1
        string("In [", n[], "]: ")
    end
    nothing
end

function set_output_prefix(repl::LineEditREPL, n::Ref{Int})
    julia_prompt = repl.interface.modes[1]
    if REPL.hascolor(repl)
        julia_prompt.output_prefix_prefix = Base.text_colors[:red]
    end
    julia_prompt.output_prefix = () -> string("Out[", n[], "]: ")
    nothing
end

function __current_ast_transforms(backend)
    if backend === nothing
        isdefined(Base, :active_repl_backend) ? Base.active_repl_backend.ast_transforms : REPL.repl_ast_transforms
    else
        backend.ast_transforms
    end
end


function numbered_prompt!(repl::LineEditREPL=Base.active_repl, backend=nothing)
    n = Ref{Int}(0)
    set_prompt(repl, n)
    set_output_prefix(repl, n)
    push!(__current_ast_transforms(backend), @nospecialize(ast) -> out_transform(ast, n))
    return
end

"""
    Out[n]

A variable referring to all previously computed values, automatically imported to the interactive prompt.
Only defined and exists while using [Numbered prompt](@ref Numbered-prompt).

See also [`ans`](@ref).
"""
Base.MainInclude.Out

end

import .Numbered.numbered_prompt!

end # module
q   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/REPL/src/Terminals.jl      # This file is a part of Julia. License is MIT: https://julialang.org/license

module Terminals

export
    AbstractTerminal,
    TextTerminal,
    UnixTerminal,
    TerminalBuffer,
    TTYTerminal,
    cmove,
    cmove_col,
    cmove_down,
    cmove_left,
    cmove_line_down,
    cmove_line_up,
    cmove_right,
    cmove_up,
    disable_bracketed_paste,
    enable_bracketed_paste,
    end_keypad_transmit_mode,
    getX,
    getY,
    hascolor,
    pos,
    raw!

import Base:
    check_open, # stream.jl
    displaysize,
    flush,
    pipe_reader,
    pipe_writer,
    read,
    readuntil

## AbstractTerminal: abstract supertype of all terminals ##

abstract type AbstractTerminal <: Base.AbstractPipe end

## TextTerminal ##

abstract type TextTerminal <: AbstractTerminal end

# Terminal interface:
pipe_reader(::TextTerminal) = error("Unimplemented")
pipe_writer(::TextTerminal) = error("Unimplemented")
displaysize(::TextTerminal) = error("Unimplemented")
cmove(t::TextTerminal, x, y) = error("Unimplemented")
getX(t::TextTerminal) = error("Unimplemented")
getY(t::TextTerminal) = error("Unimplemented")
pos(t::TextTerminal) = (getX(t), getY(t))

# Relative moves (Absolute position fallbacks)
cmove_up(t::TextTerminal, n) = cmove(getX(t), max(1, getY(t)-n))
cmove_up(t) = cmove_up(t, 1)

cmove_down(t::TextTerminal, n) = cmove(getX(t), max(height(t), getY(t)+n))
cmove_down(t) = cmove_down(t, 1)

cmove_left(t::TextTerminal, n) = cmove(max(1, getX(t)-n), getY(t))
cmove_left(t) = cmove_left(t, 1)

cmove_right(t::TextTerminal, n) = cmove(max(width(t), getX(t)+n), getY(t))
cmove_right(t) = cmove_right(t, 1)

cmove_line_up(t::TextTerminal, n) = cmove(1, max(1, getY(t)-n))
cmove_line_up(t) = cmove_line_up(t, 1)

cmove_line_down(t::TextTerminal, n) = cmove(1, max(height(t), getY(t)+n))
cmove_line_down(t) = cmove_line_down(t, 1)

cmove_col(t::TextTerminal, c) = cmove(c, getY(t))

# Defaults
hascolor(::TextTerminal) = false

# Utility Functions
width(t::TextTerminal) = (displaysize(t)::Tuple{Int,Int})[2]
height(t::TextTerminal) = (displaysize(t)::Tuple{Int,Int})[1]

# For terminals with buffers
flush(t::TextTerminal) = nothing

clear(t::TextTerminal) = error("Unimplemented")
clear_line(t::TextTerminal, row) = error("Unimplemented")
clear_line(t::TextTerminal) = error("Unimplemented")

raw!(t::TextTerminal, raw::Bool) = error("Unimplemented")

beep(t::TextTerminal) = nothing
enable_bracketed_paste(t::TextTerminal) = nothing
disable_bracketed_paste(t::TextTerminal) = nothing

## UnixTerminal ##

abstract type UnixTerminal <: TextTerminal end

pipe_reader(t::UnixTerminal) = t.in_stream::IO
pipe_writer(t::UnixTerminal) = t.out_stream::IO

mutable struct TerminalBuffer <: UnixTerminal
    out_stream::IO
end

mutable struct TTYTerminal <: UnixTerminal
    term_type::String
    in_stream::IO
    out_stream::IO
    err_stream::IO
end

const CSI = "\x1b["

cmove_up(t::UnixTerminal, n) = write(t.out_stream, "$(CSI)$(n)A")
cmove_down(t::UnixTerminal, n) = write(t.out_stream, "$(CSI)$(n)B")
cmove_right(t::UnixTerminal, n) = write(t.out_stream, "$(CSI)$(n)C")
cmove_left(t::UnixTerminal, n) = write(t.out_stream, "$(CSI)$(n)D")
cmove_line_up(t::UnixTerminal, n) = (cmove_up(t, n); cmove_col(t, 1))
cmove_line_down(t::UnixTerminal, n) = (cmove_down(t, n); cmove_col(t, 1))
cmove_col(t::UnixTerminal, n) = (write(t.out_stream, '\r'); n > 1 && cmove_right(t, n-1))

const is_precompiling = Ref(false)
if Sys.iswindows()
    function raw!(t::TTYTerminal,raw::Bool)
        is_precompiling[] && return true
        check_open(t.in_stream)
        if Base.ispty(t.in_stream)
            run((raw ? `stty raw -echo onlcr -ocrnl opost` : `stty sane`),
                t.in_stream, t.out_stream, t.err_stream)
            true
        else
            ccall(:jl_tty_set_mode, Int32, (Ptr{Cvoid},Int32), t.in_stream.handle::Ptr{Cvoid}, raw) != -1
        end
    end
else
    function raw!(t::TTYTerminal, raw::Bool)
        check_open(t.in_stream)
        ccall(:jl_tty_set_mode, Int32, (Ptr{Cvoid},Int32), t.in_stream.handle::Ptr{Cvoid}, raw) != -1
    end
end

# eval some of these definitions to insert CSI as a constant string
@eval enable_bracketed_paste(t::UnixTerminal) = write(t.out_stream, $"$(CSI)?2004h")
@eval disable_bracketed_paste(t::UnixTerminal) = write(t.out_stream, $"$(CSI)?2004l")
@eval end_keypad_transmit_mode(t::UnixTerminal) = # tput rmkx
    write(t.out_stream, $"$(CSI)?1l\x1b>")

@eval clear(t::UnixTerminal) = write(t.out_stream, $"$(CSI)H$(CSI)2J")
@eval clear_line(t::UnixTerminal) = write(t.out_stream, $"\r$(CSI)0K")
beep(t::UnixTerminal) = write(t.err_stream,"\x7")

Base.displaysize(t::UnixTerminal) = displaysize(t.out_stream)

hascolor(t::TTYTerminal) = get(t.out_stream, :color, false)::Bool

# use cached value of have_color
Base.in(key_value::Pair, t::TTYTerminal) = in(key_value, pipe_writer(t))
Base.haskey(t::TTYTerminal, key) = haskey(pipe_writer(t), key)
Base.getindex(t::TTYTerminal, key) = getindex(pipe_writer(t), key)
Base.get(t::TTYTerminal, key, default) = get(pipe_writer(t), key, default)

Base.peek(t::TTYTerminal, ::Type{T}) where {T} = peek(t.in_stream, T)::T

end # module
o   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/REPL/src/options.jl�	      # This file is a part of Julia. License is MIT: https://julialang.org/license

## User Options

mutable struct Options
    hascolor::Bool
    extra_keymap::Union{Dict,Vector{<:Dict}}
    # controls the presumed tab width of code pasted into the REPL.
    # Must satisfy `0 < tabwidth <= 16`.
    tabwidth::Int
    # Maximum number of entries in the kill ring queue.
    # Beyond this number, oldest entries are discarded first.
    kill_ring_max::Int
    region_animation_duration::Float64
    beep_duration::Float64
    beep_blink::Float64
    beep_maxduration::Float64
    beep_colors::Vector{String}
    beep_use_current::Bool
    backspace_align::Bool
    backspace_adjust::Bool
    confirm_exit::Bool # ^D must be repeated to confirm exit
    auto_indent::Bool # indent a newline like line above
    auto_indent_tmp_off::Bool # switch auto_indent temporarily off if copy&paste
    auto_indent_bracketed_paste::Bool # set to true if terminal knows paste mode
    # cancel auto-indent when next character is entered within this time frame :
    auto_indent_time_threshold::Float64
    # refresh after time delay
    auto_refresh_time_delay::Float64
    # default IOContext settings at the REPL
    iocontext::Dict{Symbol,Any}
end

Options(;
        hascolor = true,
        extra_keymap = AnyDict[],
        tabwidth = 8,
        kill_ring_max = 100,
        region_animation_duration = 0.2,
        beep_duration = 0.2, beep_blink = 0.2, beep_maxduration = 1.0,
        beep_colors = ["\e[90m"], # gray (text_colors not yet available)
        beep_use_current = true,
        backspace_align = true, backspace_adjust = backspace_align,
        confirm_exit = false,
        auto_indent = true,
        auto_indent_tmp_off = false,
        auto_indent_bracketed_paste = false,
        auto_indent_time_threshold = 0.005,
        auto_refresh_time_delay = Sys.iswindows() ? 0.05 : 0.0,
        iocontext = Dict{Symbol,Any}()) =
            Options(hascolor, extra_keymap, tabwidth,
                    kill_ring_max, region_animation_duration,
                    beep_duration, beep_blink, beep_maxduration,
                    beep_colors, beep_use_current,
                    backspace_align, backspace_adjust, confirm_exit,
                    auto_indent, auto_indent_tmp_off, auto_indent_bracketed_paste,
                    auto_indent_time_threshold, auto_refresh_time_delay,
                    iocontext)

# for use by REPLs not having an options field
const GlobalOptions = Options()
p   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/REPL/src/LineEdit.jl�l     # This file is a part of Julia. License is MIT: https://julialang.org/license

module LineEdit

import ..REPL
using REPL: AbstractREPL, Options

using ..Terminals
import ..Terminals: raw!, width, height, cmove, getX,
                       getY, clear_line, beep

import Base: ensureroom, show, AnyDict, position
using Base: something

using InteractiveUtils: InteractiveUtils

abstract type TextInterface end                # see interface immediately below
abstract type ModeState end                    # see interface below
abstract type HistoryProvider end
abstract type CompletionProvider end

export run_interface, Prompt, ModalInterface, transition, reset_state, edit_insert, keymap

@nospecialize # use only declared type signatures

const StringLike = Union{Char,String,SubString{String}}

# interface for TextInterface
function Base.getproperty(ti::TextInterface, name::Symbol)
    if name === :hp
        return getfield(ti, :hp)::HistoryProvider
    elseif name === :complete
        return getfield(ti, :complete)::CompletionProvider
    elseif name === :keymap_dict
        return getfield(ti, :keymap_dict)::Dict{Char,Any}
    end
    return getfield(ti, name)
end

struct ModalInterface <: TextInterface
    modes::Vector{TextInterface}
end

mutable struct Prompt <: TextInterface
    # A string or function to be printed as the prompt.
    prompt::Union{String,Function}
    # A string or function to be printed before the prompt. May not change the length of the prompt.
    # This may be used for changing the color, issuing other terminal escape codes, etc.
    prompt_prefix::Union{String,Function}
    # Same as prefix except after the prompt
    prompt_suffix::Union{String,Function}
    output_prefix::Union{String,Function}
    output_prefix_prefix::Union{String,Function}
    output_prefix_suffix::Union{String,Function}
    keymap_dict::Dict{Char,Any}
    repl::Union{AbstractREPL,Nothing}
    complete::CompletionProvider
    on_enter::Function
    on_done::Function
    hist::HistoryProvider  # TODO?: rename this `hp` (consistency with other TextInterfaces), or is the type-assert useful for mode(s)?
    sticky::Bool
end

show(io::IO, x::Prompt) = show(io, string("Prompt(\"", prompt_string(x.prompt), "\",...)"))


mutable struct MIState
    interface::ModalInterface
    active_module::Module
    current_mode::TextInterface
    aborted::Bool
    mode_state::IdDict{TextInterface,ModeState}
    kill_ring::Vector{String}
    kill_idx::Int
    previous_key::Vector{Char}
    key_repeats::Int
    last_action::Symbol
    current_action::Symbol
end

MIState(i, mod, c, a, m) = MIState(i, mod, c, a, m, String[], 0, Char[], 0, :none, :none)

const BufferLike = Union{MIState,ModeState,IOBuffer}
const State = Union{MIState,ModeState}

function show(io::IO, s::MIState)
    print(io, "MI State (", mode(s), " active)")
end

struct InputAreaState
    num_rows::Int64
    curs_row::Int64
end

mutable struct PromptState <: ModeState
    terminal::AbstractTerminal
    p::Prompt
    input_buffer::IOBuffer
    region_active::Symbol # :shift or :mark or :off
    undo_buffers::Vector{IOBuffer}
    undo_idx::Int
    ias::InputAreaState
    # indentation of lines which do not include the prompt
    # if negative, the width of the prompt is used
    indent::Int
    refresh_lock::Threads.SpinLock
    # this would better be Threads.Atomic{Float64}, but not supported on some platforms
    beeping::Float64
    # this option is to detect when code is pasted in non-"bracketed paste mode" :
    last_newline::Float64 # register when last newline was entered
    # this option is to speed up output
    refresh_wait::Union{Timer,Nothing}
end

struct Modifiers
    shift::Bool
end
Modifiers() = Modifiers(false)

options(s::PromptState) =
    if isdefined(s.p, :repl) && isdefined(s.p.repl, :options)
        # we can't test isa(s.p.repl, LineEditREPL) as LineEditREPL is defined
        # in the REPL module
        s.p.repl.options::Options
    else
        REPL.GlobalOptions::Options
    end

function setmark(s::MIState, guess_region_active::Bool=true)
    refresh = set_action!(s, :setmark)
    s.current_action === :setmark && s.key_repeats > 0 && activate_region(s, :mark)
    mark(buffer(s))
    refresh && refresh_line(s)
    nothing
end

# the default mark is 0
getmark(s::BufferLike) = max(0, buffer(s).mark)

const Region = Pair{Int,Int}

_region(s::BufferLike) = getmark(s) => position(s)
region(s::BufferLike) = Pair(extrema(_region(s))...)

bufend(s::BufferLike) = buffer(s).size

axes(reg::Region) = first(reg)+1:last(reg)

content(s::BufferLike, reg::Region = 0=>bufend(s)) = String(buffer(s).data[axes(reg)])

function activate_region(s::PromptState, state::Symbol)
    @assert state in (:mark, :shift, :off)
    s.region_active = state
    nothing
end

activate_region(s::ModeState, state::Symbol) = false
deactivate_region(s::ModeState) = activate_region(s, :off)

is_region_active(s::PromptState) = s.region_active in (:shift, :mark)
is_region_active(s::ModeState) = false

region_active(s::PromptState) = s.region_active
region_active(s::ModeState) = :off


input_string(s::PromptState) = String(take!(copy(s.input_buffer)))

input_string_newlines(s::PromptState) = count(c->(c == '\n'), input_string(s))
function input_string_newlines_aftercursor(s::PromptState)
    str = input_string(s)
    isempty(str) && return 0
    rest = str[nextind(str, position(s)):end]
    return count(c->(c == '\n'), rest)
end

struct EmptyCompletionProvider <: CompletionProvider end
struct EmptyHistoryProvider <: HistoryProvider end

reset_state(::EmptyHistoryProvider) = nothing

complete_line(c::EmptyCompletionProvider, s) = String[], "", true

# complete_line can be specialized for only two arguments, when the active module
# doesn't matter (e.g. Pkg does this)
complete_line(c::CompletionProvider, s, ::Module) = complete_line(c, s)

terminal(s::IO) = s
terminal(s::PromptState) = s.terminal


function beep(s::PromptState, duration::Real=options(s).beep_duration,
              blink::Real=options(s).beep_blink,
              maxduration::Real=options(s).beep_maxduration;
              colors=options(s).beep_colors,
              use_current::Bool=options(s).beep_use_current)
    isinteractive() || return # some tests fail on some platforms
    s.beeping = min(s.beeping + duration, maxduration)
    let colors = Base.copymutable(colors)
        errormonitor(@async begin
            trylock(s.refresh_lock) || return
            try
                orig_prefix = s.p.prompt_prefix
                use_current && push!(colors, prompt_string(orig_prefix))
                i = 0
                while s.beeping > 0.0
                    prefix = colors[mod1(i+=1, end)]
                    s.p.prompt_prefix = prefix
                    refresh_multi_line(s, beeping=true)
                    sleep(blink)
                    s.beeping -= blink
                end
                s.p.prompt_prefix = orig_prefix
                refresh_multi_line(s, beeping=true)
                s.beeping = 0.0
            finally
                unlock(s.refresh_lock)
            end
        end)
    end
    nothing
end

function cancel_beep(s::PromptState)
    # wait till beeping finishes
    while !trylock(s.refresh_lock)
        s.beeping = 0.0
        sleep(.05)
    end
    unlock(s.refresh_lock)
    nothing
end

beep(::ModeState) = nothing
cancel_beep(::ModeState) = nothing

for f in Union{Symbol,Expr}[
          :terminal, :on_enter, :add_history, :_buffer, :(Base.isempty),
          :replace_line, :refresh_multi_line, :input_string, :update_display_buffer,
          :empty_undo, :push_undo, :pop_undo, :options, :cancel_beep, :beep,
          :deactivate_region, :activate_region, :is_region_active, :region_active]
    @eval ($f)(s::MIState, args...) = $(f)(state(s), args...)
end

for f in [:edit_insert, :edit_insert_newline, :edit_backspace, :edit_move_left,
          :edit_move_right, :edit_move_word_left, :edit_move_word_right]
    @eval function ($f)(s::MIState, args...)
        set_action!(s, $(Expr(:quote, f)))
        $(f)(state(s), args...)
    end
end

const COMMAND_GROUPS =
    Dict(:movement    => [:edit_move_left, :edit_move_right, :edit_move_word_left, :edit_move_word_right,
                          :edit_move_up, :edit_move_down, :edit_exchange_point_and_mark],
         :deletion    => [:edit_clear, :edit_backspace, :edit_delete, :edit_werase,
                          :edit_delete_prev_word,
                          :edit_delete_next_word,
                          :edit_kill_line_forwards, :edit_kill_line_backwards, :edit_kill_region],
         :insertion   => [:edit_insert, :edit_insert_newline, :edit_yank],
         :replacement => [:edit_yank_pop, :edit_transpose_chars, :edit_transpose_words,
                          :edit_upper_case, :edit_lower_case, :edit_title_case, :edit_indent,
                          :edit_transpose_lines_up!, :edit_transpose_lines_down!],
         :copy        => [:edit_copy_region],
         :misc        => [:complete_line, :setmark, :edit_undo!, :edit_redo!])

const COMMAND_GROUP = Dict{Symbol,Symbol}(command=>group for (group, commands) in COMMAND_GROUPS for command in commands)
command_group(command::Symbol) = get(COMMAND_GROUP, command, :nogroup)
command_group(command::Function) = command_group(nameof(command))

# return true if command should keep active a region
function preserve_active(command::Symbol)
    command ∈ [:edit_indent, :edit_transpose_lines_down!, :edit_transpose_lines_up!]
end

# returns whether the "active region" status changed visibly,
# i.e. whether there should be a visual refresh
function set_action!(s::MIState, command::Symbol)
    # if a command is already running, don't update the current_action field,
    # as the caller is used as a helper function
    s.current_action === :unknown || return false

    active = region_active(s)

    ## record current action
    s.current_action = command

    ## handle activeness of the region
    if startswith(String(command), "shift_") # shift-move command
        if active !== :shift
            setmark(s) # s.current_action must already have been set
            activate_region(s, :shift)
            # NOTE: if the region was already active from a non-shift
            # move (e.g. ^Space^Space), the region is visibly changed
            return active !== :off # active status is reset
        end
    elseif !(preserve_active(command) ||
             command_group(command) === :movement && region_active(s) === :mark)
        # if we move after a shift-move, the region is de-activated
        # (e.g. like emacs behavior)
        deactivate_region(s)
        return active !== :off
    end
    false
end

set_action!(s, command::Symbol) = nothing

function common_prefix(completions::Vector{String})
    ret = ""
    c1 = completions[1]
    isempty(c1) && return ret
    i = 1
    cc, nexti = iterate(c1, i)
    while true
        for c in completions
            (i > lastindex(c) || c[i] != cc) && return ret
        end
        ret = string(ret, cc)
        i >= lastindex(c1) && return ret
        i = nexti
        cc, nexti = iterate(c1, i)
    end
end

# This is the maximum number of completions that will be displayed in a single
# column, anything above that and multiple columns will be used. Note that this
# does not restrict column length when multiple columns are used.
const MULTICOLUMN_THRESHOLD = 5

# Show available completions
function show_completions(s::PromptState, completions::Vector{String})
    # skip any lines of input after the cursor
    cmove_down(terminal(s), input_string_newlines_aftercursor(s))
    println(terminal(s))
    if any(Base.Fix1(occursin, '\n'), completions)
        foreach(Base.Fix1(println, terminal(s)), completions)
    else
        n = length(completions)
        colmax = 2 + maximum(length, completions; init=1) # n.b. length >= textwidth

        num_cols = min(cld(n, MULTICOLUMN_THRESHOLD),
                       max(div(width(terminal(s)), colmax), 1))

        entries_per_col = cld(n, num_cols)
        idx = 0
        for _ in 1:entries_per_col
            for col = 0:(num_cols-1)
                idx += 1
                idx > n && break
                cmove_col(terminal(s), colmax*col+1)
                print(terminal(s), completions[idx])
            end
            println(terminal(s))
        end
    end

    # make space for the prompt
    for i = 1:input_string_newlines(s)
        println(terminal(s))
    end
end

# Prompt Completions
function complete_line(s::MIState)
    set_action!(s, :complete_line)
    if complete_line(state(s), s.key_repeats, s.active_module)
        return refresh_line(s)
    else
        beep(s)
        return :ignore
    end
end

function complete_line(s::PromptState, repeats::Int, mod::Module)
    completions, partial, should_complete = complete_line(s.p.complete, s, mod)::Tuple{Vector{String},String,Bool}
    isempty(completions) && return false
    if !should_complete
        # should_complete is false for cases where we only want to show
        # a list of possible completions but not complete, e.g. foo(\t
        show_completions(s, completions)
    elseif length(completions) == 1
        # Replace word by completion
        prev_pos = position(s)
        push_undo(s)
        edit_splice!(s, (prev_pos - sizeof(partial)) => prev_pos, completions[1])
    else
        p = common_prefix(completions)
        if !isempty(p) && p != partial
            # All possible completions share the same prefix, so we might as
            # well complete that
            prev_pos = position(s)
            push_undo(s)
            edit_splice!(s, (prev_pos - sizeof(partial)) => prev_pos, p)
        elseif repeats > 0
            show_completions(s, completions)
        end
    end
    return true
end

function clear_input_area(terminal::AbstractTerminal, s::PromptState)
    if s.refresh_wait !== nothing
        close(s.refresh_wait)
        s.refresh_wait = nothing
    end
    _clear_input_area(terminal, s.ias)
    s.ias = InputAreaState(0, 0)
end
clear_input_area(terminal::AbstractTerminal, s::ModeState) = (_clear_input_area(terminal, s.ias); s.ias = InputAreaState(0, 0))
clear_input_area(s::ModeState) = clear_input_area(s.terminal, s)

function _clear_input_area(terminal::AbstractTerminal, state::InputAreaState)
    # Go to the last line
    if state.curs_row < state.num_rows
        cmove_down(terminal, state.num_rows - state.curs_row)
    end

    # Clear lines one by one going up
    for j = 2:state.num_rows
        clear_line(terminal)
        cmove_up(terminal)
    end

    # Clear top line
    clear_line(terminal)
    nothing
end

prompt_string(s::PromptState) = prompt_string(s.p)
prompt_string(p::Prompt) = prompt_string(p.prompt)
prompt_string(s::AbstractString) = s
prompt_string(f::Function) = Base.invokelatest(f)

function refresh_multi_line(s::PromptState; kw...)
    if s.refresh_wait !== nothing
        close(s.refresh_wait)
        s.refresh_wait = nothing
    end
    refresh_multi_line(terminal(s), s; kw...)
end
refresh_multi_line(s::ModeState; kw...) = refresh_multi_line(terminal(s), s; kw...)
refresh_multi_line(termbuf::TerminalBuffer, s::ModeState; kw...) = refresh_multi_line(termbuf, terminal(s), s; kw...)
refresh_multi_line(termbuf::TerminalBuffer, term, s::ModeState; kw...) = (@assert term === terminal(s); refresh_multi_line(termbuf,s; kw...))

function refresh_multi_line(termbuf::TerminalBuffer, terminal::UnixTerminal, buf::IOBuffer,
                            state::InputAreaState, prompt = "";
                            indent::Int = 0, region_active::Bool = false)
    _clear_input_area(termbuf, state)

    cols = width(terminal)
    rows = height(terminal)
    curs_row = -1 # relative to prompt (1-based)
    curs_pos = -1 # 1-based column position of the cursor
    cur_row = 0   # count of the number of rows
    buf_pos = position(buf)
    line_pos = buf_pos
    regstart, regstop = region(buf)
    written = 0
    # Write out the prompt string
    lindent = write_prompt(termbuf, prompt, hascolor(terminal))::Int
    # Count the '\n' at the end of the line if the terminal emulator does (specific to DOS cmd prompt)
    miscountnl = @static Sys.iswindows() ? (isa(Terminals.pipe_reader(terminal), Base.TTY) && !(Base.ispty(Terminals.pipe_reader(terminal)))::Bool) : false

    # Now go through the buffer line by line
    seek(buf, 0)
    moreinput = true # add a blank line if there is a trailing newline on the last line
    lastline = false # indicates when to stop printing lines, even when there are potentially
                     # more (for the case where rows is too small to print everything)
                     # Note: when there are too many lines for rows, we still print the first lines
                     # even if they are going to not be visible in the end: for simplicity, but
                     # also because it does the 'right thing' when the window is resized
    while moreinput
        line = readline(buf, keep=true)
        moreinput = endswith(line, "\n")
        if rows == 1 && line_pos <= sizeof(line) - moreinput
            # we special case rows == 1, as otherwise by the time the cursor is seen to
            # be in the current line, it's too late to chop the '\n' away
            lastline = true
            curs_row = 1
            curs_pos = lindent + line_pos
        end
        if moreinput && lastline # we want to print only one "visual" line, so
            line = chomp(line)   # don't include the trailing "\n"
        end
        # We need to deal with on-screen characters, so use textwidth to compute occupied columns
        llength = textwidth(line)
        slength = sizeof(line)
        cur_row += 1
        # lwrite: what will be written to termbuf
        lwrite = region_active ? highlight_region(line, regstart, regstop, written, slength) :
                                 line
        written += slength
        cmove_col(termbuf, lindent + 1)
        write(termbuf, lwrite)
        # We expect to be line after the last valid output line (due to
        # the '\n' at the end of the previous line)
        if curs_row == -1
            line_pos -= slength # '\n' gets an extra pos
            # in this case, we haven't yet written the cursor position
            if line_pos < 0 || !moreinput
                num_chars = line_pos >= 0 ?
                                llength :
                                textwidth(line[1:prevind(line, line_pos + slength + 1)])
                curs_row, curs_pos = divrem(lindent + num_chars - 1, cols)
                curs_row += cur_row
                curs_pos += 1
                # There's an issue if the cursor is after the very right end of the screen. In that case we need to
                # move the cursor to the next line, and emit a newline if needed
                if curs_pos == cols
                    # only emit the newline if the cursor is at the end of the line we're writing
                    if line_pos == 0
                        write(termbuf, "\n")
                        cur_row += 1
                    end
                    curs_row += 1
                    curs_pos = 0
                    cmove_col(termbuf, 1)
                end
            end
        end
        cur_row += div(max(lindent + llength + miscountnl - 1, 0), cols)
        lindent = indent < 0 ? lindent : indent

        lastline && break
        if curs_row >= 0 && cur_row + 1 >= rows &&             # when too many lines,
                            cur_row - curs_row + 1 >= rows ÷ 2 # center the cursor
            lastline = true
        end
    end
    seek(buf, buf_pos)

    # Let's move the cursor to the right position
    # The line first
    n = cur_row - curs_row
    if n > 0
        cmove_up(termbuf, n)
    end

    #columns are 1 based
    cmove_col(termbuf, curs_pos + 1)
    # Updated cur_row,curs_row
    return InputAreaState(cur_row, curs_row)
end

function highlight_region(lwrite::Union{String,SubString{String}}, regstart::Int, regstop::Int, written::Int, slength::Int)
    if written <= regstop <= written+slength
        i = thisind(lwrite, regstop-written)
        lwrite = lwrite[1:i] * Base.disable_text_style[:reverse] * lwrite[nextind(lwrite, i):end]
    end
    if written <= regstart <= written+slength
        i = thisind(lwrite, regstart-written)
        lwrite = lwrite[1:i] * Base.text_colors[:reverse] * lwrite[nextind(lwrite, i):end]
    end
    return lwrite
end

function refresh_multi_line(terminal::UnixTerminal, args...; kwargs...)
    outbuf = IOBuffer()
    termbuf = TerminalBuffer(outbuf)
    ret = refresh_multi_line(termbuf, terminal, args...;kwargs...)
    # Output the entire refresh at once
    write(terminal, take!(outbuf))
    flush(terminal)
    return ret
end


# Edit functionality
is_non_word_char(c::Char) = c in """ \t\n\"\\'`@\$><=:;|&{}()[].,+-*/?%^~"""

function reset_key_repeats(f::Function, s::MIState)
    key_repeats_sav = s.key_repeats
    try
        s.key_repeats = 0
        return f()
    finally
        s.key_repeats = key_repeats_sav
    end
end

function edit_exchange_point_and_mark(s::MIState)
    set_action!(s, :edit_exchange_point_and_mark)
    return edit_exchange_point_and_mark(buffer(s)) ? refresh_line(s) : false
end

function edit_exchange_point_and_mark(buf::IOBuffer)
    m = getmark(buf)
    m == position(buf) && return false
    mark(buf)
    seek(buf, m)
    return true
end

char_move_left(s::PromptState) = char_move_left(s.input_buffer)
function char_move_left(buf::IOBuffer)
    while position(buf) > 0
        seek(buf, position(buf)-1)
        c = peek(buf)
        (((c & 0x80) == 0) || ((c & 0xc0) == 0xc0)) && break
    end
    pos = position(buf)
    c = read(buf, Char)
    seek(buf, pos)
    return c
end

function edit_move_left(buf::IOBuffer)
    if position(buf) > 0
        #move to the next base UTF8 character to the left
        while true
            c = char_move_left(buf)
            if textwidth(c) != 0 || c == '\n' || position(buf) == 0
                break
            end
        end
        return true
    end
    return false
end

edit_move_left(s::PromptState) = edit_move_left(s.input_buffer) ? refresh_line(s) : false

function edit_move_word_left(s::PromptState)
    if position(s) > 0
        char_move_word_left(s.input_buffer)
        return refresh_line(s)
    end
    return nothing
end

char_move_right(s::MIState) = char_move_right(buffer(s))
function char_move_right(buf::IOBuffer)
    return !eof(buf) && read(buf, Char)
end

function char_move_word_right(buf::IOBuffer, is_delimiter::Function=is_non_word_char)
    while !eof(buf) && is_delimiter(char_move_right(buf))
    end
    while !eof(buf)
        pos = position(buf)
        if is_delimiter(char_move_right(buf))
            seek(buf, pos)
            break
        end
    end
end

function char_move_word_left(buf::IOBuffer, is_delimiter::Function=is_non_word_char)
    while position(buf) > 0 && is_delimiter(char_move_left(buf))
    end
    while position(buf) > 0
        pos = position(buf)
        if is_delimiter(char_move_left(buf))
            seek(buf, pos)
            break
        end
    end
end

char_move_word_right(s::Union{MIState,ModeState}) = char_move_word_right(buffer(s))
char_move_word_left(s::Union{MIState,ModeState}) = char_move_word_left(buffer(s))

function edit_move_right(buf::IOBuffer)
    if !eof(buf)
        # move to the next base UTF8 character to the right
        while true
            c = char_move_right(buf)
            eof(buf) && break
            pos = position(buf)
            nextc = read(buf,Char)
            seek(buf,pos)
            (textwidth(nextc) != 0 || nextc == '\n') && break
        end
        return true
    end
    return false
end
edit_move_right(s::PromptState) = edit_move_right(s.input_buffer) ? refresh_line(s) : false

function edit_move_word_right(s::PromptState)
    if !eof(s.input_buffer)
        char_move_word_right(s)
        return refresh_line(s)
    end
    return nothing
end

## Move line up/down
# Querying the terminal is expensive, memory access is cheap
# so to find the current column, we find the offset for the start
# of the line.

function edit_move_up(buf::IOBuffer)
    npos = findprev(isequal(UInt8('\n')), buf.data, position(buf))
    npos === nothing && return false # we're in the first line
    # We're interested in character count, not byte count
    offset = length(content(buf, npos => position(buf)))
    npos2 = something(findprev(isequal(UInt8('\n')), buf.data, npos-1), 0)
    seek(buf, npos2)
    for _ = 1:offset
        pos = position(buf)
        if read(buf, Char) == '\n'
            seek(buf, pos)
            break
        end
    end
    return true
end
function edit_move_up(s::MIState)
    set_action!(s, :edit_move_up)
    changed = edit_move_up(buffer(s))
    changed && refresh_line(s)
    return changed
end

function edit_move_down(buf::IOBuffer)
    npos = something(findprev(isequal(UInt8('\n')), buf.data[1:buf.size], position(buf)), 0)
    # We're interested in character count, not byte count
    offset = length(String(buf.data[(npos+1):(position(buf))]))
    npos2 = findnext(isequal(UInt8('\n')), buf.data[1:buf.size], position(buf)+1)
    if npos2 === nothing #we're in the last line
        return false
    end
    seek(buf, npos2)
    for _ = 1:offset
        pos = position(buf)
        if eof(buf) || read(buf, Char) == '\n'
            seek(buf, pos)
            break
        end
    end
    return true
end
function edit_move_down(s::MIState)
    set_action!(s, :edit_move_down)
    changed = edit_move_down(buffer(s))
    changed && refresh_line(s)
    return changed
end

function edit_shift_move(s::MIState, move_function::Function)
    @assert command_group(move_function) === :movement
    set_action!(s, Symbol(:shift_, move_function))
    return move_function(s)
end


# splice! for IOBuffer: convert from close-open region to index, update the size,
# and keep the cursor position and mark stable with the text
# returns the removed portion as a String
function edit_splice!(s::BufferLike, r::Region=region(s), ins::String = ""; rigid_mark::Bool=true)
    A, B = first(r), last(r)
    A >= B && isempty(ins) && return String(ins)
    buf = buffer(s)
    pos = position(buf)
    adjust_pos = true
    if A <= pos < B
        seek(buf, A)
    elseif B <= pos
        seek(buf, pos - B + A)
    else
        adjust_pos = false
    end
    if A < buf.mark  < B || A == buf.mark == B
        # rigid_mark is used only if the mark is strictly "inside"
        # the region, or the region is empty and the mark is at the boundary
        buf.mark = rigid_mark ? A : A + sizeof(ins)
    elseif buf.mark >= B
        buf.mark += sizeof(ins) - B + A
    end
    ensureroom(buf, B) # handle !buf.reinit from take!
    ret = splice!(buf.data, A+1:B, codeunits(String(ins))) # position(), etc, are 0-indexed
    buf.size = buf.size + sizeof(ins) - B + A
    adjust_pos && seek(buf, position(buf) + sizeof(ins))
    return String(copy(ret))
end

edit_splice!(s::MIState, ins::AbstractString) = edit_splice!(s, region(s), ins)

function edit_insert(s::PromptState, c::StringLike)
    push_undo(s)
    buf = s.input_buffer

    if ! options(s).auto_indent_bracketed_paste
        pos = position(buf)
        if pos > 0
            if buf.data[pos] != _space && string(c) != " "
                options(s).auto_indent_tmp_off = false
            end
            if buf.data[pos] == _space
                #tabulators are already expanded to space
                #this expansion may take longer than auto_indent_time_threshold which breaks the timing
                s.last_newline = time()
            else
                #if characters after new line are coming in very fast
                #its probably copy&paste => switch auto-indent off for the next coming new line
                if ! options(s).auto_indent_tmp_off && time() - s.last_newline < options(s).auto_indent_time_threshold
                    options(s).auto_indent_tmp_off = true
                end
            end
        end
    end

    old_wait = s.refresh_wait !== nothing
    if old_wait
        close(s.refresh_wait)
        s.refresh_wait = nothing
    end
    str = string(c)
    edit_insert(buf, str)
    if '\n' in str
        refresh_line(s)
    else
        after = options(s).auto_refresh_time_delay
        termbuf = terminal(s)
        w = width(termbuf)
        offset = s.ias.curs_row == 1 || s.indent < 0 ?
            sizeof(prompt_string(s.p.prompt)::String) : s.indent
        offset += position(buf) - beginofline(buf) # size of current line
        spinner = '\0'
        delayup = !eof(buf) || old_wait
        if offset + textwidth(str) <= w && !(after == 0 && delayup)
            # Avoid full update when appending characters to the end
            # and an update of curs_row isn't necessary (conservatively estimated)
            write(termbuf, str)
            spinner = ' ' # temporarily clear under the cursor
        elseif after == 0
            refresh_line(s)
            delayup = false
        else # render a spinner for each key press
            if old_wait || length(str) != 1
                spinner = spin_seq[mod1(position(buf) - w, length(spin_seq))]
            else
                spinner = str[end]
            end
            delayup = true
        end
        if delayup
            if spinner != '\0'
                write(termbuf, spinner)
                cmove_left(termbuf)
            end
            s.refresh_wait = Timer(after) do t
                s.refresh_wait === t || return
                s.refresh_wait = nothing
                refresh_line(s)
            end
        end
    end
    nothing
end
const spin_seq = ("⋯", "⋱", "⋮", "⋰")

function edit_insert(buf::IOBuffer, c::StringLike)
    if eof(buf)
        return write(buf, c)
    else
        s = string(c)
        edit_splice!(buf, position(buf) => position(buf), s)
        return sizeof(s)
    end
end

# align: number of ' ' to insert after '\n'
# if align < 0: align like line above
function edit_insert_newline(s::PromptState, align::Int = 0 - options(s).auto_indent)
    push_undo(s)
    buf = buffer(s)
    autoindent = align < 0
    if autoindent && ! options(s).auto_indent_tmp_off
        beg = beginofline(buf)
        align = min(something(findnext(_notspace, buf.data[beg+1:buf.size], 1), 0) - 1,
                    position(buf) - beg) # indentation must not increase
        align < 0 && (align = buf.size-beg)
    #else
    #    align = 0
    end
    align < 0 && (align = 0)
    edit_insert(buf, '\n' * ' '^align)
    refresh_line(s)
    # updating s.last_newline should happen after refresh_line(s) which can take
    # an unpredictable amount of time and makes "paste detection" unreliable
    if ! options(s).auto_indent_bracketed_paste
        s.last_newline = time()
    end
    nothing
end

# align: delete up to 4 spaces to align to a multiple of 4 chars
# adjust: also delete spaces on the right of the cursor to try to keep aligned what is
# on the right
function edit_backspace(s::PromptState, align::Bool=options(s).backspace_align,
                        adjust::Bool=options(s).backspace_adjust)
    push_undo(s)
    if edit_backspace(buffer(s), align, adjust)
        return refresh_line(s)
    else
        pop_undo(s)
        return beep(s)
    end
end

const _newline =  UInt8('\n')
const _space = UInt8(' ')

_notspace(c) = c != _space

beginofline(buf::IOBuffer, pos::Int=position(buf)) = something(findprev(isequal(_newline), buf.data, pos), 0)

function endofline(buf::IOBuffer, pos::Int=position(buf))
    eol = findnext(isequal(_newline), buf.data[pos+1:buf.size], 1)
    eol === nothing ? buf.size : pos + eol - 1
end

function edit_backspace(buf::IOBuffer, align::Bool=false, adjust::Bool=false)
    !align && adjust &&
        throw(DomainError((align, adjust),
                          "if `adjust` is `true`, `align` must be `true`"))
    oldpos = position(buf)
    oldpos == 0 && return false
    c = char_move_left(buf)
    newpos = position(buf)
    if align && c == ' ' # maybe delete multiple spaces
        beg = beginofline(buf, newpos)
        align = textwidth(String(buf.data[1+beg:newpos])) % 4
        nonspace = something(findprev(_notspace, buf.data, newpos), 0)
        if newpos - align >= nonspace
            newpos -= align
            seek(buf, newpos)
            if adjust
                spaces = something(findnext(_notspace, buf.data[newpos+2:buf.size], 1), 0)
                oldpos = spaces == 0 ? buf.size :
                    buf.data[newpos+1+spaces] == _newline ? newpos+spaces :
                    newpos + min(spaces, 4)
            end
        end
    end
    edit_splice!(buf, newpos => oldpos)
    return true
end

function edit_delete(s::MIState)
    set_action!(s, :edit_delete)
    push_undo(s)
    if edit_delete(buffer(s))
        return refresh_line(s)
    else
        pop_undo(s)
        return beep(s)
    end
end

function edit_delete(buf::IOBuffer)
    eof(buf) && return false
    oldpos = position(buf)
    char_move_right(buf)
    edit_splice!(buf, oldpos => position(buf))
    return true
end

function edit_werase(buf::IOBuffer)
    pos1 = position(buf)
    char_move_word_left(buf, isspace)
    pos0 = position(buf)
    return edit_splice!(buf, pos0 => pos1)
end

function edit_werase(s::MIState)
    set_action!(s, :edit_werase)
    push_undo(s)
    if push_kill!(s, edit_werase(buffer(s)), rev=true)
        return refresh_line(s)
    else
        pop_undo(s)
        return :ignore
    end
end

function edit_delete_prev_word(buf::IOBuffer)
    pos1 = position(buf)
    char_move_word_left(buf)
    pos0 = position(buf)
    return edit_splice!(buf, pos0 => pos1)
end

function edit_delete_prev_word(s::MIState)
    set_action!(s, :edit_delete_prev_word)
    push_undo(s)
    if push_kill!(s, edit_delete_prev_word(buffer(s)), rev=true)
        return refresh_line(s)
    else
        pop_undo(s)
        return :ignore
    end
end

function edit_delete_next_word(buf::IOBuffer)
    pos0 = position(buf)
    char_move_word_right(buf)
    pos1 = position(buf)
    return edit_splice!(buf, pos0 => pos1)
end

function edit_delete_next_word(s::MIState)
    set_action!(s, :edit_delete_next_word)
    push_undo(s)
    if push_kill!(s, edit_delete_next_word(buffer(s)))
        return refresh_line(s)
    else
        pop_undo(s)
        return :ignore
    end
end

function edit_yank(s::MIState)
    set_action!(s, :edit_yank)
    if isempty(s.kill_ring)
        beep(s)
        return :ignore
    end
    setmark(s) # necessary for edit_yank_pop
    push_undo(s)
    edit_insert(buffer(s), s.kill_ring[mod1(s.kill_idx, end)])
    return refresh_line(s)
end

function edit_yank_pop(s::MIState, require_previous_yank::Bool=true)
    set_action!(s, :edit_yank_pop)
    repeat = s.last_action ∈ (:edit_yank, :edit_yank_pop)
    if require_previous_yank && !repeat || isempty(s.kill_ring)
        beep(s)
        return :ignore
    else
        require_previous_yank || repeat || setmark(s)
        push_undo(s)
        edit_splice!(s, s.kill_ring[mod1(s.kill_idx -= 1, end)])
        return refresh_line(s)
    end
end

function push_kill!(s::MIState, killed::String, concat::Bool = s.key_repeats > 0; rev::Bool=false)
    isempty(killed) && return false
    if concat && !isempty(s.kill_ring)
        s.kill_ring[end] = rev ?
            killed * s.kill_ring[end] : # keep expected order for backward deletion
            s.kill_ring[end] * killed
    else
        push!(s.kill_ring, killed)
        length(s.kill_ring) > options(s).kill_ring_max && popfirst!(s.kill_ring)
    end
    s.kill_idx = lastindex(s.kill_ring)
    return true
end

function edit_kill_line(s::MIState, backwards::Bool=false)
    buf = buffer(s)
    if backwards
        set_action!(s, :edit_kill_line_backwards)
        pos = beginofline(buf)
        endpos = position(buf)
        pos == endpos && pos > 0 && (pos -= 1)
    else
        set_action!(s, :edit_kill_line_forwards)
        pos = position(buf)
        endpos = endofline(buf)
        endpos == pos && buf.size > pos && (endpos += 1)
    end
    push_undo(s)
    if push_kill!(s, edit_splice!(s, pos => endpos); rev=backwards)
        return refresh_line(s)
    else
        pop_undo(s)
        beep(s)
        return :ignore
    end
end

edit_kill_line_forwards(s::MIState) = edit_kill_line(s, false)
edit_kill_line_backwards(s::MIState) = edit_kill_line(s, true)

function edit_copy_region(s::MIState)
    set_action!(s, :edit_copy_region)
    buf = buffer(s)
    push_kill!(s, content(buf, region(buf)), false) || return :ignore
    if options(s).region_animation_duration > 0.0
        edit_exchange_point_and_mark(s)
        sleep(options(s).region_animation_duration)
        edit_exchange_point_and_mark(s)
    end
    nothing
end

function edit_kill_region(s::MIState)
    set_action!(s, :edit_kill_region)
    push_undo(s)
    if push_kill!(s, edit_splice!(s), false)
        return refresh_line(s)
    else
        pop_undo(s)
        return :ignore
    end
end

function edit_transpose_chars(s::MIState)
    set_action!(s, :edit_transpose_chars)
    push_undo(s)
    return edit_transpose_chars(buffer(s)) ? refresh_line(s) : pop_undo(s)
end

function edit_transpose_chars(buf::IOBuffer)
    # Moving left but not transpoing anything is intentional, and matches Emacs's behavior
    eof(buf) && position(buf) !== 0 && char_move_left(buf)
    position(buf) == 0 && return false
    char_move_left(buf)
    pos = position(buf)
    a, b = read(buf, Char), read(buf, Char)
    seek(buf, pos)
    write(buf, b, a)
    return true
end

function edit_transpose_words(s::MIState)
    set_action!(s, :edit_transpose_words)
    push_undo(s)
    return edit_transpose_words(buffer(s)) ? refresh_line(s) : pop_undo(s)
end

function edit_transpose_words(buf::IOBuffer, mode::Symbol=:emacs)
    mode in [:readline, :emacs] ||
        throw(ArgumentError("`mode` must be `:readline` or `:emacs`"))
    pos = position(buf)
    if mode === :emacs
        char_move_word_left(buf)
        char_move_word_right(buf)
    end
    char_move_word_right(buf)
    e2 = position(buf)
    char_move_word_left(buf)
    b2 = position(buf)
    char_move_word_left(buf)
    b1 = position(buf)
    char_move_word_right(buf)
    e1 = position(buf)
    e1 >= b2 && (seek(buf, pos); return false)
    word2 = edit_splice!(buf, b2 => e2, content(buf, b1 => e1))
    edit_splice!(buf, b1 => e1, word2)
    seek(buf, e2)
    return true
end


# swap all lines intersecting the region with line above
function edit_transpose_lines_up!(buf::IOBuffer, reg::Region)
    b2 = beginofline(buf, first(reg))
    b2 == 0 && return false
    b1 = beginofline(buf, b2-1)
    # we do in this order so that the buffer's position is maintained in current line
    line1 = edit_splice!(buf, b1 => b2) # delete whole previous line
    line1 = '\n'*line1[1:end-1] # don't include the final '\n'
    pos = position(buf) # save pos in case it's at the end of line
    b = endofline(buf, last(reg) - b2 + b1) # b2-b1 is the size of the removed line1
    edit_splice!(buf, b => b, line1)
    seek(buf, pos)
    return true
end

# swap all lines intersecting the region with line below
function edit_transpose_lines_down!(buf::IOBuffer, reg::Region)
    e1 = endofline(buf, last(reg))
    e1 == buf.size && return false
    e2 = endofline(buf, e1+1)
    line2 = edit_splice!(buf, e1 => e2) # delete whole next line
    line2 = line2[2:end]*'\n' # don't include leading '\n'
    b = beginofline(buf, first(reg))
    edit_splice!(buf, b => b, line2, rigid_mark=false)
    return true
end

# return the region if active, or the current position as a Region otherwise
region_if_active(s::MIState)::Region = is_region_active(s) ? region(s) : position(s)=>position(s)

function edit_transpose_lines_up!(s::MIState)
    set_action!(s, :edit_transpose_lines_up!)
    if edit_transpose_lines_up!(buffer(s), region_if_active(s))
        return refresh_line(s)
    else
        # beeping would be too noisy here
        return :ignore
    end
end

function edit_transpose_lines_down!(s::MIState)
    set_action!(s, :edit_transpose_lines_down!)
    if edit_transpose_lines_down!(buffer(s), region_if_active(s))
        return refresh_line(s)
    else
        return :ignore
    end
end

function edit_upper_case(s::BufferLike)
    set_action!(s, :edit_upper_case)
    return edit_replace_word_right(s, uppercase)
end
function edit_lower_case(s::BufferLike)
    set_action!(s, :edit_lower_case)
    return edit_replace_word_right(s, lowercase)
end
function edit_title_case(s::BufferLike)
    set_action!(s, :edit_title_case)
    return edit_replace_word_right(s, titlecase)
end

function edit_replace_word_right(s::Union{MIState,ModeState}, replace::Function)
    push_undo(s)
    return edit_replace_word_right(buffer(s), replace) ? refresh_line(s) : pop_undo(s)
end

function edit_replace_word_right(buf::IOBuffer, replace::Function)
    # put the cursor at the beginning of the next word
    skipchars(is_non_word_char, buf)
    b = position(buf)
    char_move_word_right(buf)
    e = position(buf)
    e == b && return false
    edit_splice!(buf, b => e, replace(content(buf, b => e)))
    return true
end

edit_clear(buf::IOBuffer) = truncate(buf, 0)

function edit_clear(s::MIState)
    set_action!(s, :edit_clear)
    push_undo(s)
    if push_kill!(s, edit_splice!(s, 0 => bufend(s)), false)
        return refresh_line(s)
    else
        pop_undo(s)
        return :ignore
    end
end

function replace_line(s::PromptState, l::IOBuffer)
    empty_undo(s)
    s.input_buffer = copy(l)
    deactivate_region(s)
    nothing
end

function replace_line(s::PromptState, l::Union{String,SubString{String}}, keep_undo::Bool=false)
    keep_undo || empty_undo(s)
    s.input_buffer.ptr = 1
    s.input_buffer.size = 0
    write(s.input_buffer, l)
    deactivate_region(s)
    nothing
end


edit_indent_left(s::MIState, n=1) = edit_indent(s, -n)
edit_indent_right(s::MIState, n=1) = edit_indent(s, n)

function edit_indent(s::MIState, num::Int)
    set_action!(s, :edit_indent)
    push_undo(s)
    if edit_indent(buffer(s), num, is_region_active(s))
        return refresh_line(s)
    else
        pop_undo(s)
        return :ignore
    end
end

# return the indices in buffer(s) of the beginning of each lines
# having a non-empty intersection with region(s)
function get_lines_in_region(s::BufferLike)
    buf = buffer(s)
    b, e = region(buf)
    bol = Int[beginofline(buf, b)] # begin of lines
    while true
        b = endofline(buf, b)
        b >= e && break
        # b < e ==> b+1 <= e <= buf.size
        push!(bol, b += 1)
    end
    return bol
end

# compute the number of spaces from b till the next non-space on the right
# (which can also be "end of line" or "end of buffer")
function leadingspaces(buf::IOBuffer, b::Int)
    @views ls = something(findnext(_notspace, buf.data[1:buf.size], b+1), 0)-1
    ls == -1 && (ls = buf.size)
    ls -= b
    return ls
end

# indent by abs(num) characters, on the right if num >= 0, on the left otherwise
# if multiline is true, indent all the lines in the region as a block.
function edit_indent(buf::IOBuffer, num::Int, multiline::Bool)
    bol = multiline ? get_lines_in_region(buf) : Int[beginofline(buf)]
    if num < 0
        # count leading spaces on the lines, which are an upper bound
        # on the number of spaces characters that can be removed
        ls_min = minimum(leadingspaces(buf, b) for b in bol)
        ls_min == 0 && return false # can't left-indent, no space can be removed
        num = -min(-num, ls_min)
    end
    for b in reverse!(bol) # reverse! to not mess-up the bol's offsets
        _edit_indent(buf, b, num)
    end
    return true
end

# indents line starting a position b by num positions
# if num < 0, it is assumed that there are at least num white spaces
# at the beginning of line
_edit_indent(buf::IOBuffer, b::Int, num::Int) =
    num >= 0 ? edit_splice!(buf, b => b, ' '^num, rigid_mark=false) :
               edit_splice!(buf, b => (b - num))

function mode_idx(hist::HistoryProvider, mode::TextInterface)
    c = :julia
    for (k,v) in hist.mode_mapping
        isequal(v, mode) && (c = k)
    end
    return c
end

function guess_current_mode_name(s)
    try
        mode_idx(s.current_mode.hist, s.current_mode)
    catch
        nothing
    end
end

# edit current input in editor
function edit_input(s, f = (filename, line, column) -> InteractiveUtils.edit(filename, line, column))
    mode_name = guess_current_mode_name(s)
    filename = tempname()
    if mode_name === :julia
        filename *= ".jl"
    elseif mode_name === :shell
        filename *= ".sh"
    end
    buf = buffer(s)
    pos = position(buf)
    str = String(take!(buf))
    lines = readlines(IOBuffer(str); keep=true)

    # Compute line
    line_start_offset = 0
    line = 1
    while line < length(lines) && line_start_offset + sizeof(lines[line]) <= pos
        line_start_offset += sizeof(lines[line])
        line += 1
    end

    # Compute column
    col = 0
    off = line_start_offset
    while off <= pos
        off = nextind(str, off)
        col += 1
    end

    # Write current input to temp file, edit, read back
    write(filename, str)
    f(filename, line, col)
    str_mod = readchomp(filename)
    rm(filename)

    # Write updated content
    write(buf, str_mod)
    if str == str_mod
        # If input was not modified: reset cursor
        seek(buf, pos)
    else
        # If input was modified: move cursor to end
        move_input_end(s)
    end
    refresh_line(s)
end

# return the identifier under the cursor, possibly with other words concatenated
# to it with dots (e.g. "A.B.C" in "X; A.B.C*3", if the cursor is between "A" and "C")
function current_word_with_dots(buf::IOBuffer)
    pos = position(buf)
    while true
        char_move_word_right(buf)
        if eof(buf) || peek(buf, Char) != '.'
            break
        end
    end
    pend = position(buf)
    while true
        char_move_word_left(buf)
        p = position(buf)
        p == 0 && break
        seek(buf, p-1)
        if peek(buf, Char) != '.'
            seek(buf, p)
            break
        end
    end
    pbegin = position(buf)
    word = pend > pbegin ?
        String(buf.data[pbegin+1:pend]) :
        ""
    seek(buf, pos)
    word
end

current_word_with_dots(s::MIState) = current_word_with_dots(buffer(s))

function activate_module(s::MIState)
    word = current_word_with_dots(s);
    isempty(word) && return beep(s)
    try
        mod = Base.Core.eval(Base.active_module(), Base.Meta.parse(word))
        REPL.activate(mod)
        edit_clear(s)
    catch
        beep(s)
    end
end

history_prev(::EmptyHistoryProvider) = ("", false)
history_next(::EmptyHistoryProvider) = ("", false)
history_first(::EmptyHistoryProvider) = ("", false)
history_last(::EmptyHistoryProvider) = ("", false)
history_search(::EmptyHistoryProvider, args...) = false
add_history(::EmptyHistoryProvider, s) = nothing
add_history(s::PromptState) = add_history(mode(s).hist, s)
history_next_prefix(s, hist, prefix) = false
history_prev_prefix(s, hist, prefix) = false

function history_prev(s::ModeState, hist)
    l, ok = history_prev(mode(s).hist)
    if ok
        replace_line(s, l)
        move_input_start(s)
        refresh_line(s)
    else
        beep(s)
    end
    nothing
end
function history_next(s::ModeState, hist)
    l, ok = history_next(mode(s).hist)
    if ok
        replace_line(s, l)
        move_input_end(s)
        refresh_line(s)
    else
        beep(s)
    end
    nothing
end

refresh_line(s::BufferLike) = refresh_multi_line(s)
refresh_line(s::BufferLike, termbuf::AbstractTerminal) = refresh_multi_line(termbuf, s)

default_completion_cb(::IOBuffer) = []
default_enter_cb(_) = true

write_prompt(terminal::AbstractTerminal, s::PromptState, color::Bool) = write_prompt(terminal, s.p, color)
function write_prompt(terminal::AbstractTerminal, p::Prompt, color::Bool)
    prefix = prompt_string(p.prompt_prefix)
    suffix = prompt_string(p.prompt_suffix)
    write(terminal, prefix)
    color && write(terminal, Base.text_colors[:bold])
    width = write_prompt(terminal, p.prompt, color)
    color && write(terminal, Base.text_colors[:normal])
    write(terminal, suffix)
    return width
end

function write_output_prefix(io::IO, p::Prompt, color::Bool)
    prefix = prompt_string(p.output_prefix_prefix)
    suffix = prompt_string(p.output_prefix_suffix)
    print(io, prefix)
    color && write(io, Base.text_colors[:bold])
    width = write_prompt(io, p.output_prefix, color)
    color && write(io, Base.text_colors[:normal])
    print(io, suffix)
    return width
end

# On Windows, when launching external processes, we cannot control what assumption they make on the
# console mode. We thus forcibly reset the console mode at the start of the prompt to ensure they do
# not leave the console mode in a corrupt state.
# FIXME: remove when pseudo-tty are implemented for child processes
if Sys.iswindows()
function _console_mode()
    hOutput = ccall(:GetStdHandle, stdcall, Ptr{Cvoid}, (UInt32,), -11 % UInt32) # STD_OUTPUT_HANDLE
    dwMode = Ref{UInt32}()
    ccall(:GetConsoleMode, stdcall, Int32, (Ref{Cvoid}, Ref{UInt32}), hOutput, dwMode)
    return dwMode[]
end
const default_console_mode_ref = Ref{UInt32}()
const default_console_mode_assigned = Ref(false)
function get_default_console_mode()
    if default_console_mode_assigned[] == false
        default_console_mode_assigned[] = true
        default_console_mode_ref[] = _console_mode()
    end
    return default_console_mode_ref[]
end
function _reset_console_mode()
    mode = _console_mode()
    if mode !== get_default_console_mode()
        hOutput = ccall(:GetStdHandle, stdcall, Ptr{Cvoid}, (UInt32,), -11 % UInt32) # STD_OUTPUT_HANDLE
        ccall(:SetConsoleMode, stdcall, Int32, (Ptr{Cvoid}, UInt32), hOutput, default_console_mode_ref[])
    end
    nothing
end
end

# returns the width of the written prompt
function write_prompt(terminal::Union{IO, AbstractTerminal}, s::Union{AbstractString,Function}, color::Bool)
    @static Sys.iswindows() && _reset_console_mode()
    promptstr = prompt_string(s)::String
    write(terminal, promptstr)
    return textwidth(promptstr)
end

### Keymap Support

const wildcard = '\U10f7ff' # "Private Use" Char

normalize_key(key::Char) = string(key)
normalize_key(key::Union{Int,UInt8}) = normalize_key(Char(key))
function normalize_key(key::Union{String,SubString{String}})
    wildcard in key && error("Matching '\U10f7ff' not supported.")
    buf = IOBuffer()
    i = firstindex(key)
    while i <= ncodeunits(key)
        c, i = iterate(key, i)
        if c == '*'
            write(buf, wildcard)
        elseif c == '^'
            c, i = iterate(key, i)
            write(buf, uppercase(c)-64)
        elseif c == '\\'
            c, i = iterate(key, i)
            if c == 'C'
                c, i = iterate(key, i)
                c == '-' || error("the Control key specifier must start with \"\\\\C-\"")
                c, i = iterate(key, i)
                write(buf, uppercase(c)-64)
            elseif c == 'M'
                c, i = iterate(key, i)
                c == '-' || error("the Meta key specifier must start with \"\\\\M-\"")
                c, i = iterate(key, i)
                write(buf, '\e')
                write(buf, c)
            end
        else
            write(buf, c)
        end
    end
    return String(take!(buf))
end

function normalize_keys(keymap::Union{Dict{Char,Any},AnyDict})
    ret = Dict{Any,Any}()
    for (k,v) in keymap
        normalized = normalize_key(k)
        if haskey(ret,normalized)
            error("""Multiple spellings of a key in a single keymap
                     (\"$k\" conflicts with existing mapping)""")
        end
        ret[normalized] = v
    end
    return ret
end

function add_nested_key!(keymap::Dict{Char, Any}, key::Union{String, Char}, value; override::Bool = false)
    y = iterate(key)
    while y !== nothing
        c, i = y
        y = iterate(key, i)
        if !override && c in keys(keymap) && (y === nothing || !isa(keymap[c], Dict))
            error("Conflicting definitions for keyseq " * escape_string(key) *
                  " within one keymap")
        end
        if y === nothing
            keymap[c] = value
            break
        elseif !(c in keys(keymap) && isa(keymap[c], Dict))
            keymap[c] = Dict{Char,Any}()
        end
        keymap = keymap[c]::Dict{Char, Any}
    end
end

# Redirect a key as if `seq` had been the keysequence instead in a lazy fashion.
# This is different from the default eager redirect, which only looks at the current and lower
# layers of the stack.
struct KeyAlias
    seq::String
    KeyAlias(seq) = new(normalize_key(seq))
end

function match_input(f::Function, s::Union{Nothing,MIState}, term, cs::Vector{Char}, keymap)
    update_key_repeats(s, cs)
    c = String(cs)
    return function (s, p)  # s::Union{Nothing,MIState}; p can be (at least) a LineEditREPL, PrefixSearchState, Nothing
        r = Base.invokelatest(f, s, p, c)
        if isa(r, Symbol)
            return r
        else
            return :ok
        end
    end
end

match_input(k::Nothing, s, term, cs, keymap) = (s,p) -> return :ok
match_input(k::KeyAlias, s::Union{Nothing,MIState}, term, cs, keymap::Dict{Char}) =
    match_input(keymap, s, IOBuffer(k.seq), Char[], keymap)

function match_input(k::Dict{Char}, s::Union{Nothing,MIState}, term::Union{AbstractTerminal,IOBuffer}=terminal(s), cs::Vector{Char}=Char[], keymap::Dict{Char} = k)
    # if we run out of characters to match before resolving an action,
    # return an empty keymap function
    eof(term) && return (s, p) -> :abort
    c = read(term, Char)
    # Ignore any `wildcard` as this is used as a
    # placeholder for the wildcard (see normalize_key("*"))
    c == wildcard && return (s, p) -> :ok
    push!(cs, c)
    key = haskey(k, c) ? c : wildcard
    # if we don't match on the key, look for a default action then fallback on 'nothing' to ignore
    return match_input(get(k, key, nothing), s, term, cs, keymap)
end

update_key_repeats(s, keystroke) = nothing
function update_key_repeats(s::MIState, keystroke::Vector{Char})
    s.key_repeats  = s.previous_key == keystroke ? s.key_repeats + 1 : 0
    s.previous_key = keystroke
    return
end


## Conflict fixing
# Consider a keymap of the form
#
# {
#   "**" => f
#   "ab" => g
# }
#
# Naively this is transformed into a tree as
#
# {
#   '*' => {
#       '*' => f
#   }
#   'a' => {
#       'b' => g
#   }
# }
#
# However, that's not what we want, because now "ac" is
# is not defined. We need to fix this up and turn it into
#
# {
#   '*' => {
#       '*' => f
#   }
#   'a' => {
#       '*' => f
#       'b' => g
#   }
# }
#
# i.e. copy over the appropriate default subdict
#

# deep merge where target has higher precedence
function keymap_merge!(target::Dict{Char,Any}, source::Union{Dict{Char,Any},AnyDict})
    for k in keys(source)
        if !haskey(target, k)
            target[k] = source[k]
        elseif isa(target[k], Dict)
            keymap_merge!(target[k], source[k])
        else
            # Ignore, target has higher precedence
        end
    end
end

fixup_keymaps!(d, l, s, sk) = nothing
function fixup_keymaps!(dict::Dict{Char,Any}, level, s, subkeymap)
    if level > 0
        for d in values(dict)
            fixup_keymaps!(d, level-1, s, subkeymap)
        end
    else
        if haskey(dict, s)
            if isa(dict[s], Dict) && isa(subkeymap, Dict)
                keymap_merge!(dict[s], subkeymap)
            end
        else
            dict[s] = deepcopy(subkeymap)
        end
    end
    nothing
end

function add_specialisations(dict::Dict{Char,Any}, subdict::Dict{Char,Any}, level::Int)
    default_branch = subdict[wildcard]
    if isa(default_branch, Dict)
        default_branch = default_branch::Dict{Char,Any}
        # Go through all the keymaps in the default branch
        # and copy them over to dict
        for s in keys(default_branch)
            s == wildcard && add_specialisations(dict, default_branch, level+1)
            fixup_keymaps!(dict, level, s, default_branch[s])
        end
    end
end

postprocess!(others) = nothing
function postprocess!(dict::Dict{Char,Any})
    # needs to be done first for every branch
    if haskey(dict, wildcard)
        add_specialisations(dict, dict, 1)
    end
    for (k,v) in dict
        k == wildcard && continue
        postprocess!(v)
    end
end

function getEntry(keymap::Dict{Char,Any},key::Union{String,Char})
    v = keymap
    for c in key
        if !(haskey(v,c)::Bool)
            return nothing
        end
        v = v[c]
    end
    return v
end

# `target` is the total keymap being built up, already being a nested tree of Dicts.
# source is the keymap specified by the user (with normalized keys)
function keymap_merge(target::Dict{Char,Any}, source::Union{Dict{Char,Any},AnyDict})
    ret = copy(target)
    direct_keys = filter(p -> isa(p.second, Union{Function, KeyAlias, Nothing}), source)
    # first direct entries
    for key in keys(direct_keys)
        add_nested_key!(ret, key, source[key]; override = true)
    end
    # then redirected entries
    for key in setdiff(keys(source), keys(direct_keys))
        key::Union{String, Char}
        # We first resolve redirects in the source
        value = source[key]
        visited = Vector{Any}()
        while isa(value, Union{Char,String})
            value = normalize_key(value)
            if value in visited
                throw_eager_redirection_cycle(key)
            end
            push!(visited,value)
            if !haskey(source,value)
                break
            end
            value = source[value]
        end

        if isa(value, Union{Char,String})
            value = getEntry(ret, value)
            if value === nothing
                throw_could_not_find_redirected_value(key)
            end
        end
        add_nested_key!(ret, key, value; override = true)
    end
    return ret
end

throw_eager_redirection_cycle(key::Union{Char, String}) =
    error("Eager redirection cycle detected for key ", repr(key))
throw_could_not_find_redirected_value(key::Union{Char, String}) =
    error("Could not find redirected value ", repr(key))

function keymap_unify(keymaps)
    ret = Dict{Char,Any}()
    for keymap in keymaps
        ret = keymap_merge(ret, keymap)
    end
    postprocess!(ret)
    return ret
end

function validate_keymap(keymap)
    for key in keys(keymap)
        visited_keys = Any[key]
        v = getEntry(keymap,key)
        while isa(v,KeyAlias)
            if v.seq in visited_keys
                error("Alias cycle detected in keymap")
            end
            push!(visited_keys,v.seq)
            v = getEntry(keymap,v.seq)
        end
    end
end

function keymap(keymaps::Union{Vector{AnyDict},Vector{Dict{Char,Any}}})
    # keymaps is a vector of prioritized keymaps, with highest priority first
    ret = keymap_unify(map(normalize_keys, reverse(keymaps)))
    validate_keymap(ret)
    return ret
end

const escape_defaults = merge!(
    AnyDict(Char(i) => nothing for i=vcat(0:26, 28:31)), # Ignore control characters by default
    AnyDict( # And ignore other escape sequences by default
        "\e*" => nothing,
        "\e[*" => nothing,
        "\eO*" => nothing,
        # Also ignore extended escape sequences
        # TODO: Support ranges of characters
        "\e[1**" => nothing,
        "\e[2**" => nothing,
        "\e[3**" => nothing,
        "\e[4**" => nothing,
        "\e[5**" => nothing,
        "\e[6**" => nothing,
        # less commonly used VT220 editing keys
        "\e[2~" => nothing, # insert
        "\e[3~" => nothing, # delete
        "\e[5~" => nothing, # page up
        "\e[6~" => nothing, # page down
        # These are different spellings of arrow keys, home keys, etc.
        # and should always do the same as the canonical key sequence
        "\e[1~" => KeyAlias("\e[H"), # home
        "\e[4~" => KeyAlias("\e[F"), # end
        "\e[7~" => KeyAlias("\e[H"), # home
        "\e[8~" => KeyAlias("\e[F"), # end
        "\eOA"  => KeyAlias("\e[A"),
        "\eOB"  => KeyAlias("\e[B"),
        "\eOC"  => KeyAlias("\e[C"),
        "\eOD"  => KeyAlias("\e[D"),
        "\eOH"  => KeyAlias("\e[H"),
        "\eOF"  => KeyAlias("\e[F"),
    ),
    # set mode commands
    AnyDict("\e[$(c)h" => nothing for c in 1:20),
    # reset mode commands
    AnyDict("\e[$(c)l" => nothing for c in 1:20)
    )

mutable struct HistoryPrompt <: TextInterface
    hp::HistoryProvider
    complete::CompletionProvider
    keymap_dict::Dict{Char,Any}
    HistoryPrompt(hp) = new(hp, EmptyCompletionProvider())
end

mutable struct SearchState <: ModeState
    terminal::AbstractTerminal
    histprompt::HistoryPrompt
    #rsearch (true) or ssearch (false)
    backward::Bool
    query_buffer::IOBuffer
    response_buffer::IOBuffer
    failed::Bool
    ias::InputAreaState
    #The prompt whose input will be replaced by the matched history
    parent::Prompt
    SearchState(terminal, histprompt, backward, query_buffer, response_buffer) =
        new(terminal, histprompt, backward, query_buffer, response_buffer, false, InputAreaState(0,0))
end

init_state(terminal, p::HistoryPrompt) = SearchState(terminal, p, true, IOBuffer(), IOBuffer())

terminal(s::SearchState) = s.terminal

function update_display_buffer(s::SearchState, data::ModeState)
    s.failed = !history_search(data.histprompt.hp, data.query_buffer, data.response_buffer, data.backward, false)
    s.failed && beep(s)
    refresh_line(s)
    nothing
end

function history_next_result(s::MIState, data::ModeState)
    data.failed = !history_search(data.histprompt.hp, data.query_buffer, data.response_buffer, data.backward, true)
    data.failed && beep(s)
    refresh_line(data)
    nothing
end

function history_set_backward(s::SearchState, backward::Bool)
    s.backward = backward
    nothing
end

input_string(s::SearchState) = String(take!(copy(s.query_buffer)))

function reset_state(s::SearchState)
    if s.query_buffer.size != 0
        s.query_buffer.size = 0
        s.query_buffer.ptr = 1
    end
    if s.response_buffer.size != 0
        s.response_buffer.size = 0
        s.response_buffer.ptr = 1
    end
    reset_state(s.histprompt.hp)
    s.failed = false
    nothing
end

# a meta-prompt that presents itself as parent_prompt, but which has an independent keymap
# for prefix searching
mutable struct PrefixHistoryPrompt <: TextInterface
    hp::HistoryProvider
    parent_prompt::Prompt
    complete::CompletionProvider
    keymap_dict::Dict{Char,Any}
    PrefixHistoryPrompt(hp, parent_prompt) =
        new(hp, parent_prompt, EmptyCompletionProvider())
end

mutable struct PrefixSearchState <: ModeState
    terminal::AbstractTerminal
    histprompt::PrefixHistoryPrompt
    prefix::String
    response_buffer::IOBuffer
    ias::InputAreaState
    indent::Int
    # The modal interface state, if present
    mi::MIState
    #The prompt whose input will be replaced by the matched history
    parent::Prompt
    PrefixSearchState(terminal, histprompt, prefix, response_buffer) =
        new(terminal, histprompt, prefix, response_buffer, InputAreaState(0,0), 0)
end

# interface for ModeState
function Base.getproperty(s::ModeState, name::Symbol)
    if name === :terminal
        return getfield(s, :terminal)::AbstractTerminal
    elseif name === :prompt
        return getfield(s, :prompt)::Prompt
    elseif name === :histprompt
        return getfield(s, :histprompt)::Union{HistoryPrompt,PrefixHistoryPrompt}
    elseif name === :parent
        return getfield(s, :parent)::Prompt
    elseif name === :response_buffer
        return getfield(s, :response_buffer)::IOBuffer
    elseif name === :ias
        return getfield(s, :ias)::InputAreaState
    elseif name === :indent
        return getfield(s, :indent)::Int
    # # unique fields, but no harm in declaring them
    # elseif name === :input_buffer
    #     return getfield(s, :input_buffer)::IOBuffer
    # elseif name === :region_active
    #     return getfield(s, :region_active)::Symbol
    # elseif name === :undo_buffers
    #     return getfield(s, :undo_buffers)::Vector{IOBuffer}
    # elseif name === :undo_idx
    end
    return getfield(s, name)
end

init_state(terminal, p::PrefixHistoryPrompt) = PrefixSearchState(terminal, p, "", IOBuffer())

function show(io::IO, s::PrefixSearchState)
    print(io, "PrefixSearchState ", isdefined(s,:parent) ?
     string("(", s.parent, " active)") : "(no parent)", " for ",
     isdefined(s,:mi) ? s.mi : "no MI")
end

function refresh_multi_line(termbuf::TerminalBuffer, terminal::UnixTerminal,
                            s::Union{PromptState,PrefixSearchState}; beeping::Bool=false)
    beeping || cancel_beep(s)
    ias = refresh_multi_line(termbuf, terminal, buffer(s), s.ias, s;
                             indent = s.indent,
                             region_active = is_region_active(s))
    s.ias = ias
    return ias
end

input_string(s::PrefixSearchState) = String(take!(copy(s.response_buffer)))

write_prompt(terminal, s::PrefixSearchState, color::Bool) = write_prompt(terminal, s.histprompt.parent_prompt, color)
prompt_string(s::PrefixSearchState) = prompt_string(s.histprompt.parent_prompt.prompt)

terminal(s::PrefixSearchState) = s.terminal

function reset_state(s::PrefixSearchState)
    if s.response_buffer.size != 0
        s.response_buffer.size = 0
        s.response_buffer.ptr = 1
    end
    reset_state(s.histprompt.hp)
    nothing
end

function transition(f::Function, s::PrefixSearchState, mode::Prompt)
    if isdefined(s, :mi)
        transition(s.mi, mode)
    end
    s.parent = mode
    s.histprompt.parent_prompt = mode
    if isdefined(s, :mi)
        transition(f, s.mi, s.histprompt)
    else
        f()
    end
    nothing
end

replace_line(s::PrefixSearchState, l::IOBuffer) = (s.response_buffer = l; nothing)
function replace_line(s::PrefixSearchState, l::Union{String,SubString{String}})
    s.response_buffer.ptr = 1
    s.response_buffer.size = 0
    write(s.response_buffer, l)
    nothing
end

function refresh_multi_line(termbuf::TerminalBuffer, s::SearchState)
    buf = IOBuffer()
    unsafe_write(buf, pointer(s.query_buffer.data), s.query_buffer.ptr-1)
    write(buf, "': ")
    offset = buf.ptr
    ptr = s.response_buffer.ptr
    seek(s.response_buffer, 0)
    write(buf, read(s.response_buffer, String))
    buf.ptr = offset + ptr - 1
    s.response_buffer.ptr = ptr
    failed = s.failed ? "failed " : ""
    ias = refresh_multi_line(termbuf, s.terminal, buf, s.ias,
                             s.backward ? "($(failed)reverse-i-search)`" : "($(failed)forward-i-search)`")
    s.ias = ias
    return ias
end

state(s::MIState, p::TextInterface=mode(s)) = s.mode_state[p]
state(s::PromptState, p::Prompt=mode(s)) = (@assert s.p == p; s)

mode(s::MIState) = s.current_mode   # ::TextInterface, and might be a Prompt
mode(s::PromptState) = s.p          # ::Prompt
mode(s::SearchState) = @assert false
mode(s::PrefixSearchState) = s.histprompt.parent_prompt   # ::Prompt

setmodifiers!(s::MIState, m::Modifiers) = setmodifiers!(mode(s), m)
setmodifiers!(p::Prompt, m::Modifiers) = setmodifiers!(p.complete, m)
setmodifiers!(c) = nothing

# Search Mode completions
function complete_line(s::SearchState, repeats, mod::Module)
    completions, partial, should_complete = complete_line(s.histprompt.complete, s, mod)
    # For now only allow exact completions in search mode
    if length(completions) == 1
        prev_pos = position(s)
        push_undo(s)
        edit_splice!(s, (prev_pos - sizeof(partial)) => prev_pos, completions[1])
        return true
    end
    return false
end

accept_result_newmode(hp::HistoryProvider) = nothing
function accept_result(s::MIState, p::TextInterface)
    parent = something(accept_result_newmode(p.hp), state(s, p).parent)
    transition(s, parent) do
        replace_line(state(s, parent), state(s, p).response_buffer)
        nothing
    end
    nothing
end

function copybuf!(dst::IOBuffer, src::IOBuffer)
    n = src.size
    ensureroom(dst, n)
    copyto!(dst.data, 1, src.data, 1, n)
    dst.size = src.size
    dst.ptr = src.ptr
    nothing
end

function enter_search(s::MIState, p::HistoryPrompt, backward::Bool)
    # a bit of hack to help fix #6325
    buf = copy(buffer(s))
    parent = mode(s)
    p.hp.last_mode = mode(s)
    p.hp.last_buffer = buf

    transition(s, p) do
        ss = state(s, p)
        ss.parent = parent
        ss.backward = backward
        truncate(ss.query_buffer, 0)
        ss.failed = false
        copybuf!(ss.response_buffer, buf)
    end
    nothing
end

function enter_prefix_search(s::MIState, p::PrefixHistoryPrompt, backward::Bool)
    buf = copy(buffer(s))
    parent = mode(s)

    transition(s, p) do
        local pss = state(s, p)
        pss.parent = parent
        pss.histprompt.parent_prompt = parent
        pss.prefix = String(buf.data[1:position(buf)])
        copybuf!(pss.response_buffer, buf)
        pss.indent = state(s, parent).indent
        pss.mi = s
    end
    pss = state(s, p)
    if backward
        history_prev_prefix(pss, pss.histprompt.hp, pss.prefix)
    else
        history_next_prefix(pss, pss.histprompt.hp, pss.prefix)
    end
    nothing
end

function setup_search_keymap(hp)
    p = HistoryPrompt(hp)
    pkeymap = AnyDict(
        "^R"      => (s::MIState,data::ModeState,c)->(history_set_backward(data, true); history_next_result(s, data)),
        "^S"      => (s::MIState,data::ModeState,c)->(history_set_backward(data, false); history_next_result(s, data)),
        '\r'      => (s::MIState,o...)->accept_result(s, p),
        '\n'      => '\r',
        # Limited form of tab completions
        '\t'      => (s::MIState,data::ModeState,c)->(complete_line(s); update_display_buffer(s, data)),
        "^L"      => (s::MIState,data::ModeState,c)->(Terminals.clear(terminal(s)); update_display_buffer(s, data)),

        # Backspace/^H
        '\b'      => (s::MIState,data::ModeState,c)->(edit_backspace(data.query_buffer) ?
                        update_display_buffer(s, data) : beep(s)),
        127       => KeyAlias('\b'),
        # Meta Backspace
        "\e\b"    => (s::MIState,data::ModeState,c)->(isempty(edit_delete_prev_word(data.query_buffer)) ?
                                  beep(s) : update_display_buffer(s, data)),
        "\e\x7f"  => "\e\b",
        # Word erase to whitespace
        "^W"      => (s::MIState,data::ModeState,c)->(isempty(edit_werase(data.query_buffer)) ?
                                  beep(s) : update_display_buffer(s, data)),
        # ^C and ^D
        "^C"      => (s::MIState,data::ModeState,c)->(edit_clear(data.query_buffer);
                       edit_clear(data.response_buffer);
                       update_display_buffer(s, data);
                       reset_state(data.histprompt.hp);
                       transition(s, data.parent)),
        "^D"      => "^C",
        # Other ways to cancel search mode (it's difficult to bind \e itself)
        "^G"      => "^C",
        "\e\e"    => "^C",
        "^K"      => (s::MIState,o...)->transition(s, state(s, p).parent),
        "^Y"      => (s::MIState,data::ModeState,c)->(edit_yank(s); update_display_buffer(s, data)),
        "^U"      => (s::MIState,data::ModeState,c)->(edit_clear(data.query_buffer);
                     edit_clear(data.response_buffer);
                     update_display_buffer(s, data)),
        # Right Arrow
        "\e[C"    => (s::MIState,o...)->(accept_result(s, p); edit_move_right(s)),
        # Left Arrow
        "\e[D"    => (s::MIState,o...)->(accept_result(s, p); edit_move_left(s)),
        # Up Arrow
        "\e[A"    => (s::MIState,o...)->(accept_result(s, p); edit_move_up(s)),
        # Down Arrow
        "\e[B"    => (s::MIState,o...)->(accept_result(s, p); edit_move_down(s)),
        "^B"      => (s::MIState,o...)->(accept_result(s, p); edit_move_left(s)),
        "^F"      => (s::MIState,o...)->(accept_result(s, p); edit_move_right(s)),
        # Meta B
        "\eb"     => (s::MIState,o...)->(accept_result(s, p); edit_move_word_left(s)),
        # Meta F
        "\ef"     => (s::MIState,o...)->(accept_result(s, p); edit_move_word_right(s)),
        # Ctrl-Left Arrow
        "\e[1;5D" => "\eb",
        # Ctrl-Left Arrow on rxvt
        "\eOd" => "\eb",
        # Ctrl-Right Arrow
        "\e[1;5C" => "\ef",
        # Ctrl-Right Arrow on rxvt
        "\eOc" => "\ef",
        "^A"         => (s::MIState,o...)->(accept_result(s, p); move_line_start(s); refresh_line(s)),
        "^E"         => (s::MIState,o...)->(accept_result(s, p); move_line_end(s); refresh_line(s)),
        "^Z"      => (s::MIState,o...)->(return :suspend),
        # Try to catch all Home/End keys
        "\e[H"    => (s::MIState,o...)->(accept_result(s, p); move_input_start(s); refresh_line(s)),
        "\e[F"    => (s::MIState,o...)->(accept_result(s, p); move_input_end(s); refresh_line(s)),
        # Use ^N and ^P to change search directions and iterate through results
        "^N"      => (s::MIState,data::ModeState,c)->(history_set_backward(data, false); history_next_result(s, data)),
        "^P"      => (s::MIState,data::ModeState,c)->(history_set_backward(data, true); history_next_result(s, data)),
        # Bracketed paste mode
        "\e[200~" => (s::MIState,data::ModeState,c)-> begin
            ps = state(s, mode(s))
            input = readuntil(ps.terminal, "\e[201~", keep=false)
            edit_insert(data.query_buffer, input); update_display_buffer(s, data)
        end,
        "*"       => (s::MIState,data::ModeState,c::StringLike)->(edit_insert(data.query_buffer, c); update_display_buffer(s, data))
    )
    p.keymap_dict = keymap([pkeymap, escape_defaults])
    skeymap = AnyDict(
        "^R"    => (s::MIState,o...)->(enter_search(s, p, true)),
        "^S"    => (s::MIState,o...)->(enter_search(s, p, false)),
    )
    return (p, skeymap)
end

keymap(state, p::Union{HistoryPrompt,PrefixHistoryPrompt}) = p.keymap_dict
keymap_data(state, ::Union{HistoryPrompt, PrefixHistoryPrompt}) = state

Base.isempty(s::PromptState) = s.input_buffer.size == 0

on_enter(s::PromptState) = s.p.on_enter(s)

move_input_start(s::BufferLike) = (seek(buffer(s), 0); nothing)
move_input_end(buf::IOBuffer) = (seekend(buf); nothing)
move_input_end(s::Union{MIState,ModeState}) = (move_input_end(buffer(s)); nothing)

function move_line_start(s::MIState)
    set_action!(s, :move_line_start)
    buf = buffer(s)
    curpos = position(buf)
    curpos == 0 && return
    if s.key_repeats > 0
        move_input_start(s)
    else
        seek(buf, something(findprev(isequal(UInt8('\n')), buf.data, curpos), 0))
    end
    nothing
end

function move_line_end(s::MIState)
    set_action!(s, :move_line_end)
    s.key_repeats > 0 ?
        move_input_end(s) :
        move_line_end(buffer(s))
    nothing
end

function move_line_end(buf::IOBuffer)
    eof(buf) && return
    @views pos = findnext(isequal(UInt8('\n')), buf.data[1:buf.size], position(buf)+1)
    if pos === nothing
        move_input_end(buf)
        return
    end
    seek(buf, pos - 1)
    nothing
end

edit_insert_last_word(s::MIState) =
    edit_insert(s, get_last_word(IOBuffer(mode(s).hist.history[end])))

function get_last_word(buf::IOBuffer)
    move_line_end(buf)
    char_move_word_left(buf)
    posbeg = position(buf)
    char_move_word_right(buf)
    posend = position(buf)
    buf = take!(buf)
    word = String(buf[posbeg+1:posend])
    rest = String(buf[posend+1:end])
    lp, rp, lb, rb = count.(.==(('(', ')', '[', ']')), rest)
    special = any(in.(('\'', '"', '`'), rest))
    !special && lp == rp && lb == rb ?
        word *= rest :
        word
end

function commit_line(s::MIState)
    cancel_beep(s)
    move_input_end(s)
    refresh_line(s)
    println(terminal(s))
    add_history(s)
    ias = InputAreaState(0, 0)
    state(s, mode(s)).ias = ias
    nothing
end

function bracketed_paste(s::MIState; tabwidth::Int=options(s).tabwidth)
    options(s).auto_indent_bracketed_paste = true
    ps = state(s, mode(s))::PromptState
    input = readuntil(ps.terminal, "\e[201~")
    input = replace(input, '\r' => '\n')
    if position(buffer(s)) == 0
        indent = Base.indentation(input; tabwidth=tabwidth)[1]
        input = Base.unindent(input, indent; tabwidth=tabwidth)
    end
    return replace(input, '\t' => " "^tabwidth)
end

function tab_should_complete(s::MIState)
    # Yes, we are ignoring the possibility
    # the we could be in the middle of a multi-byte
    # sequence, here but that's ok, since any
    # whitespace we're interested in is only one byte
    buf = buffer(s)
    pos = position(buf)
    pos == 0 && return true
    c = buf.data[pos]
    return c != _newline && c != UInt8('\t') &&
        # hack to allow path completion in cmds
        # after a space, e.g., `cd <tab>`, while still
        # allowing multiple indent levels
        (c != _space || pos <= 3 || buf.data[pos-1] != _space)
end

# jump_spaces: if cursor is on a ' ', move it to the first non-' ' char on the right
# if `delete_trailing`, ignore trailing ' ' by deleting them
function edit_tab(s::MIState, jump_spaces::Bool=false, delete_trailing::Bool=jump_spaces)
    tab_should_complete(s) && return complete_line(s)
    set_action!(s, :edit_insert_tab)
    push_undo(s)
    edit_insert_tab(buffer(s), jump_spaces, delete_trailing) || pop_undo(s)
    return refresh_line(s)
end

function shift_tab_completion(s::MIState)
    setmodifiers!(s, Modifiers(true))
    return complete_line(s)
end

# return true iff the content of the buffer is modified
# return false when only the position changed
function edit_insert_tab(buf::IOBuffer, jump_spaces::Bool=false, delete_trailing::Bool=jump_spaces)
    i = position(buf)
    if jump_spaces && i < buf.size && buf.data[i+1] == _space
        spaces = something(findnext(_notspace, buf.data[i+1:buf.size], 1), 0)
        if delete_trailing && (spaces == 0 || buf.data[i+spaces] == _newline)
            edit_splice!(buf, i => (spaces == 0 ? buf.size : i+spaces-1))
        else
            jump = spaces == 0 ? buf.size : i+spaces-1
            seek(buf, jump)
            return false
        end
    end
    # align to multiples of 4:
    align = 4 - textwidth(String(buf.data[1+beginofline(buf, i):i])) % 4
    edit_insert(buf, ' '^align)
    return true
end

function edit_abort(s::MIState, confirm::Bool=options(s).confirm_exit; key="^D")
    set_action!(s, :edit_abort)
    if !confirm || s.last_action === :edit_abort
        println(terminal(s))
        return :abort
    else
        println("Type $key again to exit.\n")
        return refresh_line(s)
    end
end

const default_keymap =
AnyDict(
    # Tab
    '\t' => (s::MIState,o...)->edit_tab(s, true),
    # Shift-tab
    "\e[Z" => (s::MIState,o...)->shift_tab_completion(s),
    # Enter
    '\r' => (s::MIState,o...)->begin
        if on_enter(s) || (eof(buffer(s)) && s.key_repeats > 1)
            commit_line(s)
            return :done
        else
            edit_insert_newline(s)
        end
    end,
    '\n' => KeyAlias('\r'),
    # Backspace/^H
    '\b' => (s::MIState,o...) -> is_region_active(s) ? edit_kill_region(s) : edit_backspace(s),
    127 => KeyAlias('\b'),
    # Meta Backspace
    "\e\b" => (s::MIState,o...)->edit_delete_prev_word(s),
    "\e\x7f" => "\e\b",
    # ^D
    "^D" => (s::MIState,o...)->begin
        if buffer(s).size > 0
            edit_delete(s)
        else
            edit_abort(s)
        end
    end,
    # Ctrl-Space
    "\0" => (s::MIState,o...)->setmark(s),
    "^G" => (s::MIState,o...)->(deactivate_region(s); refresh_line(s)),
    "^X^X" => (s::MIState,o...)->edit_exchange_point_and_mark(s),
    "^B" => (s::MIState,o...)->edit_move_left(s),
    "^F" => (s::MIState,o...)->edit_move_right(s),
    "^P" => (s::MIState,o...)->edit_move_up(s),
    "^N" => (s::MIState,o...)->edit_move_down(s),
    # Meta-Up
    "\e[1;3A" => (s::MIState,o...) -> edit_transpose_lines_up!(s),
    # Meta-Down
    "\e[1;3B" => (s::MIState,o...) -> edit_transpose_lines_down!(s),
    "\e[1;2D" => (s::MIState,o...)->edit_shift_move(s, edit_move_left),
    "\e[1;2C" => (s::MIState,o...)->edit_shift_move(s, edit_move_right),
    "\e[1;2A" => (s::MIState,o...)->edit_shift_move(s, edit_move_up),
    "\e[1;2B" => (s::MIState,o...)->edit_shift_move(s, edit_move_down),
    # Meta B
    "\eb" => (s::MIState,o...)->edit_move_word_left(s),
    # Meta F
    "\ef" => (s::MIState,o...)->edit_move_word_right(s),
    # Ctrl-Left Arrow
    "\e[1;5D" => "\eb",
    # Ctrl-Left Arrow on rxvt
    "\eOd" => "\eb",
    # Ctrl-Right Arrow
    "\e[1;5C" => "\ef",
    # Ctrl-Right Arrow on rxvt
    "\eOc" => "\ef",
    # Meta Enter
    "\e\r" => (s::MIState,o...)->edit_insert_newline(s),
    "\e." =>  (s::MIState,o...)->edit_insert_last_word(s),
    "\e\n" => "\e\r",
    "^_" => (s::MIState,o...)->edit_undo!(s),
    "\e_" => (s::MIState,o...)->edit_redo!(s),
    # Simply insert it into the buffer by default
    "*" => (s::MIState,data,c::StringLike)->(edit_insert(s, c)),
    "^U" => (s::MIState,o...)->edit_kill_line_backwards(s),
    "^K" => (s::MIState,o...)->edit_kill_line_forwards(s),
    "^Y" => (s::MIState,o...)->edit_yank(s),
    "\ey" => (s::MIState,o...)->edit_yank_pop(s),
    "\ew" => (s::MIState,o...)->edit_copy_region(s),
    "\eW" => (s::MIState,o...)->edit_kill_region(s),
    "^A" => (s::MIState,o...)->(move_line_start(s); refresh_line(s)),
    "^E" => (s::MIState,o...)->(move_line_end(s); refresh_line(s)),
    # Try to catch all Home/End keys
    "\e[H"  => (s::MIState,o...)->(move_input_start(s); refresh_line(s)),
    "\e[F"  => (s::MIState,o...)->(move_input_end(s); refresh_line(s)),
    "^L" => (s::MIState,o...)->(Terminals.clear(terminal(s)); refresh_line(s)),
    "^W" => (s::MIState,o...)->edit_werase(s),
    # Meta D
    "\ed" => (s::MIState,o...)->edit_delete_next_word(s),
    "^C" => (s::MIState,o...)->begin
        try # raise the debugger if present
            ccall(:jl_raise_debugger, Int, ())
        catch
        end
        cancel_beep(s)
        move_input_end(s)
        refresh_line(s)
        print(terminal(s), "^C\n\n")
        transition(s, :reset)
        refresh_line(s)
    end,
    "^Z" => (s::MIState,o...)->(return :suspend),
    # Right Arrow
    "\e[C" => (s::MIState,o...)->edit_move_right(s),
    # Left Arrow
    "\e[D" => (s::MIState,o...)->edit_move_left(s),
    # Up Arrow
    "\e[A" => (s::MIState,o...)->edit_move_up(s),
    # Down Arrow
    "\e[B" => (s::MIState,o...)->edit_move_down(s),
    # Meta-Right Arrow
    "\e[1;3C" => (s::MIState,o...) -> edit_indent_right(s, 1),
    # Meta-Left Arrow
    "\e[1;3D" => (s::MIState,o...) -> edit_indent_left(s, 1),
    # Delete
    "\e[3~" => (s::MIState,o...)->edit_delete(s),
    # Bracketed Paste Mode
    "\e[200~" => (s::MIState,o...)->begin
        input = bracketed_paste(s)
        edit_insert(s, input)
    end,
    "^T" => (s::MIState,o...)->edit_transpose_chars(s),
    "\et" => (s::MIState,o...)->edit_transpose_words(s),
    "\eu" => (s::MIState,o...)->edit_upper_case(s),
    "\el" => (s::MIState,o...)->edit_lower_case(s),
    "\ec" => (s::MIState,o...)->edit_title_case(s),
    "\ee" => (s::MIState,o...) -> edit_input(s),
    "\em" => (s::MIState, o...) -> activate_module(s)
)

const history_keymap = AnyDict(
    "^P" => (s::MIState,o...)->(edit_move_up(s) || history_prev(s, mode(s).hist)),
    "^N" => (s::MIState,o...)->(edit_move_down(s) || history_next(s, mode(s).hist)),
    "\ep" => (s::MIState,o...)->(history_prev(s, mode(s).hist)),
    "\en" => (s::MIState,o...)->(history_next(s, mode(s).hist)),
    # Up Arrow
    "\e[A" => (s::MIState,o...)->(edit_move_up(s) || history_prev(s, mode(s).hist)),
    # Down Arrow
    "\e[B" => (s::MIState,o...)->(edit_move_down(s) || history_next(s, mode(s).hist)),
    # Page Up
    "\e[5~" => (s::MIState,o...)->(history_prev(s, mode(s).hist)),
    # Page Down
    "\e[6~" => (s::MIState,o...)->(history_next(s, mode(s).hist)),
    "\e<" => (s::MIState,o...)->(history_first(s, mode(s).hist)),
    "\e>" => (s::MIState,o...)->(history_last(s, mode(s).hist)),
)

const prefix_history_keymap = merge!(
    AnyDict(
        "^P" => (s::MIState,data::ModeState,c)->history_prev_prefix(data, data.histprompt.hp, data.prefix),
        "^N" => (s::MIState,data::ModeState,c)->history_next_prefix(data, data.histprompt.hp, data.prefix),
        # Up Arrow
        "\e[A" => (s::MIState,data::ModeState,c)->history_prev_prefix(data, data.histprompt.hp, data.prefix),
        # Down Arrow
        "\e[B" => (s::MIState,data::ModeState,c)->history_next_prefix(data, data.histprompt.hp, data.prefix),
        # by default, pass through to the parent mode
        "*"    => (s::MIState,data::ModeState,c::StringLike)->begin
            accept_result(s, data.histprompt);
            ps = state(s, mode(s))
            map = keymap(ps, mode(s))
            match_input(map, s, IOBuffer(c))(s, keymap_data(ps, mode(s)))
        end,
        # match escape sequences for pass through
        "^x*" => "*",
        "\em*" => "*",
        "\e*" => "*",
        "\e[*" => "*",
        "\eO*"  => "*",
        "\e[1;5*" => "*", # Ctrl-Arrow
        "\e[1;2*" => "*", # Shift-Arrow
        "\e[1;3*" => "*", # Meta-Arrow
        "\e[200~" => "*"
    ),
    # VT220 editing commands
    AnyDict("\e[$(n)~" => "*" for n in 1:8),
    # set mode commands
    AnyDict("\e[$(c)h" => "*" for c in 1:20),
    # reset mode commands
    AnyDict("\e[$(c)l" => "*" for c in 1:20)
)

function setup_prefix_keymap(hp::HistoryProvider, parent_prompt::Prompt)
    p = PrefixHistoryPrompt(hp, parent_prompt)
    p.keymap_dict = keymap([prefix_history_keymap])
    pkeymap = AnyDict(
        "^P" => (s::MIState,o...)->(edit_move_up(s) || enter_prefix_search(s, p, true)),
        "^N" => (s::MIState,o...)->(edit_move_down(s) || enter_prefix_search(s, p, false)),
        # Up Arrow
        "\e[A" => (s::MIState,o...)->(edit_move_up(s) || enter_prefix_search(s, p, true)),
        # Down Arrow
        "\e[B" => (s::MIState,o...)->(edit_move_down(s) || enter_prefix_search(s, p, false)),
    )
    return (p, pkeymap)
end

function deactivate(p::TextInterface, s::ModeState, termbuf::AbstractTerminal, term::TextTerminal)
    clear_input_area(termbuf, s)
    return s
end

function activate(p::TextInterface, s::ModeState, termbuf::AbstractTerminal, term::TextTerminal)
    s.ias = InputAreaState(0, 0)
    refresh_line(s, termbuf)
    nothing
end

function activate(p::TextInterface, s::MIState, termbuf::AbstractTerminal, term::TextTerminal)
    @assert p == mode(s)
    activate(p, state(s), termbuf, term)
    nothing
end
activate(m::ModalInterface, s::MIState, termbuf::AbstractTerminal, term::TextTerminal) =
    activate(mode(s), s, termbuf, term)

commit_changes(t::UnixTerminal, termbuf::TerminalBuffer) = (write(t, take!(termbuf.out_stream)); nothing)

function transition(f::Function, s::MIState, newmode::Union{TextInterface,Symbol})
    cancel_beep(s)
    if newmode === :abort
        s.aborted = true
        return
    end
    if newmode === :reset
        reset_state(s)
        return
    end
    if !haskey(s.mode_state, newmode)
        s.mode_state[newmode] = init_state(terminal(s), newmode)
    end
    termbuf = TerminalBuffer(IOBuffer())
    t = terminal(s)
    s.mode_state[mode(s)] = deactivate(mode(s), state(s), termbuf, t)
    s.current_mode = newmode
    f()
    activate(newmode, state(s, newmode), termbuf, t)
    commit_changes(t, termbuf)
    nothing
end
transition(s::MIState, mode::Union{TextInterface,Symbol}) = transition((args...)->nothing, s, mode)

function reset_state(s::PromptState)
    if s.input_buffer.size != 0
        s.input_buffer.size = 0
        s.input_buffer.ptr = 1
    end
    empty_undo(s)
    deactivate_region(s)
    ias = InputAreaState(0, 0)
    s.ias = ias
    return ias
end

function reset_state(s::MIState)
    for (mode, state) in s.mode_state
        reset_state(state)
    end
end

const default_keymap_dict = keymap([default_keymap, escape_defaults])

function Prompt(prompt
    ;
    prompt_prefix = "",
    prompt_suffix = "",
    output_prefix = "",
    output_prefix_prefix = "",
    output_prefix_suffix = "",
    keymap_dict = default_keymap_dict,
    repl = nothing,
    complete = EmptyCompletionProvider(),
    on_enter = default_enter_cb,
    on_done = ()->nothing,
    hist = EmptyHistoryProvider(),
    sticky = false)

    return Prompt(prompt, prompt_prefix, prompt_suffix, output_prefix, output_prefix_prefix, output_prefix_suffix,
                   keymap_dict, repl, complete, on_enter, on_done, hist, sticky)
end

run_interface(::Prompt) = nothing

init_state(terminal, prompt::Prompt) =
    PromptState(terminal, prompt, IOBuffer(), :off, IOBuffer[], 1, InputAreaState(1, 1),
                #=indent(spaces)=# -1, Threads.SpinLock(), 0.0, -Inf, nothing)

function init_state(terminal, m::ModalInterface)
    s = MIState(m, Main, m.modes[1], false, IdDict{Any,Any}())
    for mode in m.modes
        s.mode_state[mode] = init_state(terminal, mode)
    end
    return s
end


function run_interface(terminal::TextTerminal, m::ModalInterface, s::MIState=init_state(terminal, m))
    while !s.aborted
        buf, ok, suspend = prompt!(terminal, m, s)
        while suspend
            @static if Sys.isunix(); ccall(:jl_repl_raise_sigtstp, Cint, ()); end
            buf, ok, suspend = prompt!(terminal, m, s)
        end
        Base.invokelatest(mode(state(s)).on_done, s, buf, ok)
    end
end

buffer(s) = _buffer(s)::IOBuffer
_buffer(s::PromptState) = s.input_buffer
_buffer(s::SearchState) = s.query_buffer
_buffer(s::PrefixSearchState) = s.response_buffer
_buffer(s::IOBuffer) = s

position(s::Union{MIState,ModeState}) = position(buffer(s))

function empty_undo(s::PromptState)
    empty!(s.undo_buffers)
    s.undo_idx = 1
    nothing
end

empty_undo(s) = nothing

function push_undo(s::PromptState, advance::Bool=true)
    resize!(s.undo_buffers, s.undo_idx)
    s.undo_buffers[end] = copy(s.input_buffer)
    advance && (s.undo_idx += 1)
    nothing
end

push_undo(s) = nothing

# must be called after a push_undo
function pop_undo(s::PromptState)
    pop!(s.undo_buffers)
    s.undo_idx -= 1
    nothing
end

function edit_undo!(s::MIState)
    set_action!(s, :edit_undo!)
    s.last_action ∉ (:edit_redo!, :edit_undo!) && push_undo(s, false)
    if !edit_undo!(state(s))
        beep(s)
        return :ignore
    end
    return nothing
end

function edit_undo!(s::PromptState)
    s.undo_idx > 1 || return false
    s.input_buffer = s.undo_buffers[s.undo_idx -=1]
    refresh_line(s)
    return true
end
edit_undo!(s) = nothing

function edit_redo!(s::MIState)
    set_action!(s, :edit_redo!)
    if s.last_action ∉ (:edit_redo!, :edit_undo!) || !edit_redo!(state(s))
        beep(s)
        return :ignore
    end
    return nothing
end

function edit_redo!(s::PromptState)
    s.undo_idx < length(s.undo_buffers) || return false
    s.input_buffer = s.undo_buffers[s.undo_idx += 1]
    refresh_line(s)
    return true
end
edit_redo!(s) = nothing

keymap(s::PromptState, prompt::Prompt) = prompt.keymap_dict
keymap_data(s::PromptState, prompt::Prompt) = prompt.repl
keymap(ms::MIState, m::ModalInterface) = keymap(state(ms), mode(ms))
keymap_data(ms::MIState, m::ModalInterface) = keymap_data(state(ms), mode(ms))

function prompt!(term::TextTerminal, prompt::ModalInterface, s::MIState = init_state(term, prompt))
    Base.reseteof(term)
    raw!(term, true)
    enable_bracketed_paste(term)
    try
        activate(prompt, s, term, term)
        old_state = mode(s)
        while true
            kmap = keymap(s, prompt)
            fcn = match_input(kmap, s)
            kdata = keymap_data(s, prompt)
            s.current_action = :unknown # if the to-be-run action doesn't update this field,
                                        # :unknown will be recorded in the last_action field
            local status
            # errors in keymaps shouldn't cause the REPL to fail, so wrap in a
            # try/catch block
            try
                status = fcn(s, kdata)
            catch e
                @error "Error in the keymap" exception=e,catch_backtrace()
                # try to cleanup and get `s` back to its original state before returning
                transition(s, :reset)
                transition(s, old_state)
                status = :done
            end
            status !== :ignore && (s.last_action = s.current_action)
            if status === :abort
                s.aborted = true
                return buffer(s), false, false
            elseif status === :done
                return buffer(s), true, false
            elseif status === :suspend
                if Sys.isunix()
                    return buffer(s), true, true
                end
            else
                @assert status ∈ (:ok, :ignore)
            end
        end
    finally
        raw!(term, false) && disable_bracketed_paste(term)
    end
    # unreachable
end


end # module
w   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/REPL/src/REPLCompletions.jl"�      # This file is a part of Julia. License is MIT: https://julialang.org/license

module REPLCompletions

export completions, shell_completions, bslash_completions, completion_text

using Core: CodeInfo, MethodInstance, CodeInstance, Const
const CC = Core.Compiler
using Base.Meta
using Base: propertynames, something, IdSet

abstract type Completion end

struct TextCompletion <: Completion
    text::String
end

struct KeywordCompletion <: Completion
    keyword::String
end

struct KeyvalCompletion <: Completion
    keyval::String
end

struct PathCompletion <: Completion
    path::String
end

struct ModuleCompletion <: Completion
    parent::Module
    mod::String
end

struct PackageCompletion <: Completion
    package::String
end

struct PropertyCompletion <: Completion
    value
    property::Symbol
end

struct FieldCompletion <: Completion
    typ::DataType
    field::Symbol
end

struct MethodCompletion <: Completion
    tt # may be used by an external consumer to infer return type, etc.
    method::Method
    MethodCompletion(@nospecialize(tt), method::Method) = new(tt, method)
end

struct BslashCompletion <: Completion
    bslash::String
end

struct ShellCompletion <: Completion
    text::String
end

struct DictCompletion <: Completion
    dict::AbstractDict
    key::String
end

struct KeywordArgumentCompletion <: Completion
    kwarg::String
end

# interface definition
function Base.getproperty(c::Completion, name::Symbol)
    if name === :text
        return getfield(c, :text)::String
    elseif name === :keyword
        return getfield(c, :keyword)::String
    elseif name === :path
        return getfield(c, :path)::String
    elseif name === :parent
        return getfield(c, :parent)::Module
    elseif name === :mod
        return getfield(c, :mod)::String
    elseif name === :package
        return getfield(c, :package)::String
    elseif name === :property
        return getfield(c, :property)::Symbol
    elseif name === :field
        return getfield(c, :field)::Symbol
    elseif name === :method
        return getfield(c, :method)::Method
    elseif name === :bslash
        return getfield(c, :bslash)::String
    elseif name === :text
        return getfield(c, :text)::String
    elseif name === :key
        return getfield(c, :key)::String
    elseif name === :kwarg
        return getfield(c, :kwarg)::String
    end
    return getfield(c, name)
end

_completion_text(c::TextCompletion) = c.text
_completion_text(c::KeywordCompletion) = c.keyword
_completion_text(c::KeyvalCompletion) = c.keyval
_completion_text(c::PathCompletion) = c.path
_completion_text(c::ModuleCompletion) = c.mod
_completion_text(c::PackageCompletion) = c.package
_completion_text(c::PropertyCompletion) = sprint(Base.show_sym, c.property)
_completion_text(c::FieldCompletion) = sprint(Base.show_sym, c.field)
_completion_text(c::MethodCompletion) = repr(c.method)
_completion_text(c::BslashCompletion) = c.bslash
_completion_text(c::ShellCompletion) = c.text
_completion_text(c::DictCompletion) = c.key
_completion_text(c::KeywordArgumentCompletion) = c.kwarg*'='

completion_text(c) = _completion_text(c)::String

const Completions = Tuple{Vector{Completion}, UnitRange{Int}, Bool}

function completes_global(x, name)
    return startswith(x, name) && !('#' in x)
end

function appendmacro!(syms, macros, needle, endchar)
    for macsym in macros
        s = String(macsym)
        if endswith(s, needle)
            from = nextind(s, firstindex(s))
            to = prevind(s, sizeof(s)-sizeof(needle)+1)
            push!(syms, s[from:to]*endchar)
        end
    end
end

function filtered_mod_names(ffunc::Function, mod::Module, name::AbstractString, all::Bool = false, imported::Bool = false)
    ssyms = names(mod, all = all, imported = imported)
    filter!(ffunc, ssyms)
    macros = filter(x -> startswith(String(x), "@" * name), ssyms)
    syms = String[sprint((io,s)->Base.show_sym(io, s; allow_macroname=true), s) for s in ssyms if completes_global(String(s), name)]
    appendmacro!(syms, macros, "_str", "\"")
    appendmacro!(syms, macros, "_cmd", "`")
    return [ModuleCompletion(mod, sym) for sym in syms]
end

# REPL Symbol Completions
function complete_symbol(@nospecialize(ex), name::String, @nospecialize(ffunc), context_module::Module=Main)
    mod = context_module

    lookup_module = true
    t = Union{}
    val = nothing
    if ex !== nothing
        res = repl_eval_ex(ex, context_module)
        res === nothing && return Completion[]
        if res isa Const
            val = res.val
            if isa(val, Module)
                mod = val
                lookup_module = true
            else
                lookup_module = false
                t = typeof(val)
            end
        else
            lookup_module = false
            t = CC.widenconst(res)
        end
    end

    suggestions = Completion[]
    if lookup_module
        # We will exclude the results that the user does not want, as well
        # as excluding Main.Main.Main, etc., because that's most likely not what
        # the user wants
        p = let mod=mod, modname=nameof(mod)
            s->(!Base.isdeprecated(mod, s) && s != modname && ffunc(mod, s)::Bool)
        end
        # Looking for a binding in a module
        if mod == context_module
            # Also look in modules we got through `using`
            mods = ccall(:jl_module_usings, Any, (Any,), context_module)::Vector
            for m in mods
                append!(suggestions, filtered_mod_names(p, m::Module, name))
            end
            append!(suggestions, filtered_mod_names(p, mod, name, true, true))
        else
            append!(suggestions, filtered_mod_names(p, mod, name, true, false))
        end
    elseif val !== nothing # looking for a property of an instance
        for property in propertynames(val, false)
            # TODO: support integer arguments (#36872)
            if property isa Symbol && startswith(string(property), name)
                push!(suggestions, PropertyCompletion(val, property))
            end
        end
    else
        # Looking for a member of a type
        if t isa DataType && t != Any
            # Check for cases like Type{typeof(+)}
            if Base.isType(t)
                t = typeof(t.parameters[1])
            end
            # Only look for fields if this is a concrete type
            if isconcretetype(t)
                fields = fieldnames(t)
                for field in fields
                    isa(field, Symbol) || continue # Tuple type has ::Int field name
                    s = string(field)
                    if startswith(s, name)
                        push!(suggestions, FieldCompletion(t, field))
                    end
                end
            end
        end
    end
    suggestions
end

function complete_from_list(T::Type, list::Vector{String}, s::Union{String,SubString{String}})
    r = searchsorted(list, s)
    i = first(r)
    n = length(list)
    while i <= n && startswith(list[i],s)
        r = first(r):i
        i += 1
    end
    Completion[T(kw) for kw in list[r]]
end

const sorted_keywords = [
    "abstract type", "baremodule", "begin", "break", "catch", "ccall",
    "const", "continue", "do", "else", "elseif", "end", "export",
    "finally", "for", "function", "global", "if", "import",
    "let", "local", "macro", "module", "mutable struct",
    "primitive type", "quote", "return", "struct",
    "try", "using", "while"]

complete_keyword(s::Union{String,SubString{String}}) = complete_from_list(KeywordCompletion, sorted_keywords, s)

const sorted_keyvals = ["false", "true"]

complete_keyval(s::Union{String,SubString{String}}) = complete_from_list(KeyvalCompletion, sorted_keyvals, s)

function do_raw_escape(s)
    # escape_raw_string with delim='`' and ignoring the rule for the ending \
    return replace(s, r"(\\+)`" => s"\1\\`")
end
function do_shell_escape(s)
    return Base.shell_escape_posixly(s)
end
function do_string_escape(s)
    return escape_string(s, ('\"','$'))
end

function complete_path(path::AbstractString;
                       use_envpath=false,
                       shell_escape=false,
                       raw_escape=false,
                       string_escape=false)
    @assert !(shell_escape && string_escape)
    if Base.Sys.isunix() && occursin(r"^~(?:/|$)", path)
        # if the path is just "~", don't consider the expanded username as a prefix
        if path == "~"
            dir, prefix = homedir(), ""
        else
            dir, prefix = splitdir(homedir() * path[2:end])
        end
    else
        dir, prefix = splitdir(path)
    end
    files = try
        if isempty(dir)
            readdir()
        elseif isdir(dir)
            readdir(dir)
        else
            return Completion[], dir, false
        end
    catch ex
        ex isa Base.IOError || rethrow()
        return Completion[], dir, false
    end

    matches = Set{String}()
    for file in files
        if startswith(file, prefix)
            p = joinpath(dir, file)
            is_dir = try isdir(p) catch ex; ex isa Base.IOError ? false : rethrow() end
            push!(matches, is_dir ? file * "/" : file)
        end
    end

    if use_envpath && isempty(dir)
        # Look for files in PATH as well
        pathdirs = split(ENV["PATH"], @static Sys.iswindows() ? ";" : ":")

        for pathdir in pathdirs
            actualpath = try
                realpath(pathdir)
            catch ex
                ex isa Base.IOError || rethrow()
                # Bash doesn't expect every folder in PATH to exist, so neither shall we
                continue
            end

            if actualpath != pathdir && in(actualpath, pathdirs)
                # Remove paths which (after resolving links) are in the env path twice.
                # Many distros eg. point /bin to /usr/bin but have both in the env path.
                continue
            end

            filesinpath = try
                readdir(pathdir)
            catch e
                # Bash allows dirs in PATH that can't be read, so we should as well.
                if isa(e, Base.IOError) || isa(e, Base.ArgumentError)
                    continue
                else
                    # We only handle IOError and ArgumentError here
                    rethrow()
                end
            end

            for file in filesinpath
                # In a perfect world, we would filter on whether the file is executable
                # here, or even on whether the current user can execute the file in question.
                if startswith(file, prefix) && isfile(joinpath(pathdir, file))
                    push!(matches, file)
                end
            end
        end
    end

    matches = ((shell_escape ? do_shell_escape(s) : string_escape ? do_string_escape(s) : s) for s in matches)
    matches = ((raw_escape ? do_raw_escape(s) : s) for s in matches)
    matches = Completion[PathCompletion(s) for s in matches]
    return matches, dir, !isempty(matches)
end

function complete_path(path::AbstractString,
                       pos::Int;
                       use_envpath=false,
                       shell_escape=false,
                       string_escape=false)
    ## TODO: enable this depwarn once Pkg is fixed
    #Base.depwarn("complete_path with pos argument is deprecated because the return value [2] is incorrect to use", :complete_path)
    paths, dir, success = complete_path(path; use_envpath, shell_escape, string_escape)
    if Base.Sys.isunix() && occursin(r"^~(?:/|$)", path)
        # if the path is just "~", don't consider the expanded username as a prefix
        if path == "~"
            dir, prefix = homedir(), ""
        else
            dir, prefix = splitdir(homedir() * path[2:end])
        end
    else
        dir, prefix = splitdir(path)
    end
    startpos = pos - lastindex(prefix) + 1
    Sys.iswindows() && map!(paths, paths) do c::PathCompletion
        # emulation for unnecessarily complicated return value, since / is a
        # perfectly acceptable path character which does not require quoting
        # but is required by Pkg's awkward parser handling
        return endswith(c.path, "/") ? PathCompletion(chop(c.path) * "\\\\") : c
    end
    return paths, startpos:pos, success
end

function complete_expanduser(path::AbstractString, r)
    expanded =
        try expanduser(path)
        catch e
            e isa ArgumentError || rethrow()
            path
        end
    return Completion[PathCompletion(expanded)], r, path != expanded
end

# Returns a range that includes the method name in front of the first non
# closed start brace from the end of the string.
function find_start_brace(s::AbstractString; c_start='(', c_end=')')
    braces = 0
    r = reverse(s)
    i = firstindex(r)
    in_single_quotes = false
    in_double_quotes = false
    in_back_ticks = false
    in_comment = 0
    while i <= ncodeunits(r)
        c, i = iterate(r, i)
        if c == '#' && i <= ncodeunits(r) && iterate(r, i)[1] == '='
            c, i = iterate(r, i) # consume '='
            new_comments = 1
            # handle #=#=#=#, by counting =# pairs
            while i <= ncodeunits(r) && iterate(r, i)[1] == '#'
                c, i = iterate(r, i) # consume '#'
                iterate(r, i)[1] == '=' || break
                c, i = iterate(r, i) # consume '='
                new_comments += 1
            end
            if c == '='
                in_comment += new_comments
            else
                in_comment -= new_comments
            end
        elseif !in_single_quotes && !in_double_quotes && !in_back_ticks && in_comment == 0
            if c == c_start
                braces += 1
            elseif c == c_end
                braces -= 1
            elseif c == '\''
                in_single_quotes = true
            elseif c == '"'
                in_double_quotes = true
            elseif c == '`'
                in_back_ticks = true
            end
        else
            if in_single_quotes &&
                c == '\'' && i <= ncodeunits(r) && iterate(r, i)[1] != '\\'
                in_single_quotes = false
            elseif in_double_quotes &&
                c == '"' && i <= ncodeunits(r) && iterate(r, i)[1] != '\\'
                in_double_quotes = false
            elseif in_back_ticks &&
                c == '`' && i <= ncodeunits(r) && iterate(r, i)[1] != '\\'
                in_back_ticks = false
            elseif in_comment > 0 &&
                c == '=' && i <= ncodeunits(r) && iterate(r, i)[1] == '#'
                # handle =#=#=#=, by counting #= pairs
                c, i = iterate(r, i) # consume '#'
                old_comments = 1
                while i <= ncodeunits(r) && iterate(r, i)[1] == '='
                    c, i = iterate(r, i) # consume '='
                    iterate(r, i)[1] == '#' || break
                    c, i = iterate(r, i) # consume '#'
                    old_comments += 1
                end
                if c == '#'
                    in_comment -= old_comments
                else
                    in_comment += old_comments
                end
            end
        end
        braces == 1 && break
    end
    braces != 1 && return 0:-1, -1
    method_name_end = reverseind(s, i)
    startind = nextind(s, something(findprev(in(non_identifier_chars), s, method_name_end), 0))::Int
    return (startind:lastindex(s), method_name_end)
end

struct REPLInterpreterCache
    dict::IdDict{MethodInstance,CodeInstance}
end
REPLInterpreterCache() = REPLInterpreterCache(IdDict{MethodInstance,CodeInstance}())
const REPL_INTERPRETER_CACHE = REPLInterpreterCache()

function get_code_cache()
    # XXX Avoid storing analysis results into the cache that persists across precompilation,
    #     as [sys|pkg]image currently doesn't support serializing externally created `CodeInstance`.
    #     Otherwise, `CodeInstance`s created by `REPLInterpreter`, that are much less optimized
    #     that those produced by `NativeInterpreter`, will leak into the native code cache,
    #     potentially causing runtime slowdown.
    #     (see https://github.com/JuliaLang/julia/issues/48453).
    if (@ccall jl_generating_output()::Cint) == 1
        return REPLInterpreterCache()
    else
        return REPL_INTERPRETER_CACHE
    end
end

struct REPLInterpreter <: CC.AbstractInterpreter
    repl_frame::CC.InferenceResult
    world::UInt
    inf_params::CC.InferenceParams
    opt_params::CC.OptimizationParams
    inf_cache::Vector{CC.InferenceResult}
    code_cache::REPLInterpreterCache
    function REPLInterpreter(repl_frame::CC.InferenceResult;
                             world::UInt = Base.get_world_counter(),
                             inf_params::CC.InferenceParams = CC.InferenceParams(),
                             opt_params::CC.OptimizationParams = CC.OptimizationParams(),
                             inf_cache::Vector{CC.InferenceResult} = CC.InferenceResult[],
                             code_cache::REPLInterpreterCache = get_code_cache())
        return new(repl_frame, world, inf_params, opt_params, inf_cache, code_cache)
    end
end
CC.InferenceParams(interp::REPLInterpreter) = interp.inf_params
CC.OptimizationParams(interp::REPLInterpreter) = interp.opt_params
CC.get_world_counter(interp::REPLInterpreter) = interp.world
CC.get_inference_cache(interp::REPLInterpreter) = interp.inf_cache
CC.code_cache(interp::REPLInterpreter) = CC.WorldView(interp.code_cache, CC.WorldRange(interp.world))
CC.get(wvc::CC.WorldView{REPLInterpreterCache}, mi::MethodInstance, default) = get(wvc.cache.dict, mi, default)
CC.getindex(wvc::CC.WorldView{REPLInterpreterCache}, mi::MethodInstance) = getindex(wvc.cache.dict, mi)
CC.haskey(wvc::CC.WorldView{REPLInterpreterCache}, mi::MethodInstance) = haskey(wvc.cache.dict, mi)
CC.setindex!(wvc::CC.WorldView{REPLInterpreterCache}, ci::CodeInstance, mi::MethodInstance) = setindex!(wvc.cache.dict, ci, mi)

# REPLInterpreter is only used for type analysis, so it should disable optimization entirely
CC.may_optimize(::REPLInterpreter) = false

# REPLInterpreter analyzes a top-level frame, so better to not bail out from it
CC.bail_out_toplevel_call(::REPLInterpreter, ::CC.InferenceLoopState, ::CC.InferenceState) = false

# `REPLInterpreter` aggressively resolves global bindings to enable reasonable completions
# for lines like `Mod.a.|` (where `|` is the cursor position).
# Aggressive binding resolution poses challenges for the inference cache validation
# (until https://github.com/JuliaLang/julia/issues/40399 is implemented).
# To avoid the cache validation issues, `REPLInterpreter` only allows aggressive binding
# resolution for top-level frame representing REPL input code (`repl_frame`) and for child
# `getproperty` frames that are constant propagated from the `repl_frame`. This works, since
# a.) these frames are never cached, and
# b.) their results are only observed by the non-cached `repl_frame`.
#
# `REPLInterpreter` also aggressively concrete evaluate `:inconsistent` calls within
# `repl_frame` to provide reasonable completions for lines like `Ref(Some(42))[].|`.
# Aggressive concrete evaluation allows us to get accurate type information about complex
# expressions that otherwise can not be constant folded, in a safe way, i.e. it still
# doesn't evaluate effectful expressions like `pop!(xs)`.
# Similarly to the aggressive binding resolution, aggressive concrete evaluation doesn't
# present any cache validation issues because `repl_frame` is never cached.

is_repl_frame(interp::REPLInterpreter, sv::CC.InferenceState) = interp.repl_frame === sv.result

# aggressive global binding resolution within `repl_frame`
function CC.abstract_eval_globalref(interp::REPLInterpreter, g::GlobalRef,
                                    sv::CC.InferenceState)
    if is_repl_frame(interp, sv)
        if CC.isdefined_globalref(g)
            return Const(ccall(:jl_get_globalref_value, Any, (Any,), g))
        end
        return Union{}
    end
    return @invoke CC.abstract_eval_globalref(interp::CC.AbstractInterpreter, g::GlobalRef,
                                              sv::CC.InferenceState)
end

function is_repl_frame_getproperty(interp::REPLInterpreter, sv::CC.InferenceState)
    def = sv.linfo.def
    def isa Method || return false
    def.name === :getproperty || return false
    sv.cached && return false
    return is_repl_frame(interp, sv.parent)
end

# aggressive global binding resolution for `getproperty(::Module, ::Symbol)` calls within `repl_frame`
function CC.builtin_tfunction(interp::REPLInterpreter, @nospecialize(f),
                              argtypes::Vector{Any}, sv::CC.InferenceState)
    if f === Core.getglobal && is_repl_frame_getproperty(interp, sv)
        if length(argtypes) == 2
            a1, a2 = argtypes
            if isa(a1, Const) && isa(a2, Const)
                a1val, a2val = a1.val, a2.val
                if isa(a1val, Module) && isa(a2val, Symbol)
                    g = GlobalRef(a1val, a2val)
                    if CC.isdefined_globalref(g)
                        return Const(ccall(:jl_get_globalref_value, Any, (Any,), g))
                    end
                    return Union{}
                end
            end
        end
    end
    return @invoke CC.builtin_tfunction(interp::CC.AbstractInterpreter, f::Any,
                                        argtypes::Vector{Any}, sv::CC.InferenceState)
end

# aggressive concrete evaluation for `:inconsistent` frames within `repl_frame`
function CC.concrete_eval_eligible(interp::REPLInterpreter, @nospecialize(f),
                                   result::CC.MethodCallResult, arginfo::CC.ArgInfo,
                                   sv::CC.InferenceState)
    if is_repl_frame(interp, sv)
        neweffects = CC.Effects(result.effects; consistent=CC.ALWAYS_TRUE)
        result = CC.MethodCallResult(result.rt, result.edgecycle, result.edgelimited,
                                     result.edge, neweffects)
    end
    return @invoke CC.concrete_eval_eligible(interp::CC.AbstractInterpreter, f::Any,
                                             result::CC.MethodCallResult, arginfo::CC.ArgInfo,
                                             sv::CC.InferenceState)
end

function resolve_toplevel_symbols!(mod::Module, src::Core.CodeInfo)
    newsrc = copy(src)
    @ccall jl_resolve_globals_in_ir(
        #=jl_array_t *stmts=# newsrc.code::Any,
        #=jl_module_t *m=# mod::Any,
        #=jl_svec_t *sparam_vals=# Core.svec()::Any,
        #=int binding_effects=# 0::Int)::Cvoid
    return newsrc
end

# lower `ex` and run type inference on the resulting top-level expression
function repl_eval_ex(@nospecialize(ex), context_module::Module)
    lwr = try
        Meta.lower(context_module, ex)
    catch # macro expansion failed, etc.
        return nothing
    end
    if lwr isa Symbol
        return isdefined(context_module, lwr) ? Const(getfield(context_module, lwr)) : nothing
    end
    lwr isa Expr || return Const(lwr) # `ex` is literal
    isexpr(lwr, :thunk) || return nothing # lowered to `Expr(:error, ...)` or similar
    src = lwr.args[1]::Core.CodeInfo

    # construct top-level `MethodInstance`
    mi = ccall(:jl_new_method_instance_uninit, Ref{Core.MethodInstance}, ());
    mi.specTypes = Tuple{}

    mi.def = context_module
    src = resolve_toplevel_symbols!(context_module, src)
    @atomic mi.uninferred = src

    result = CC.InferenceResult(mi)
    interp = REPLInterpreter(result)
    frame = CC.InferenceState(result, src, #=cache=#:no, interp)::CC.InferenceState

    # NOTE Use the fixed world here to make `REPLInterpreter` robust against
    #      potential invalidations of `Core.Compiler` methods.
    Base.invoke_in_world(COMPLETION_WORLD[], CC.typeinf, interp, frame)

    result = frame.result.result
    result === Union{} && return nothing # for whatever reason, callers expect this as the Bottom and/or Top type instead
    return result
end

# `COMPLETION_WORLD[]` will be initialized within `__init__`
# (to allow us to potentially remove REPL from the sysimage in the future).
# Note that inference from the `code_typed` call below will use the current world age
# rather than `typemax(UInt)`, since `Base.invoke_in_world` uses the current world age
# when the given world age is higher than the current one.
const COMPLETION_WORLD = Ref{UInt}(typemax(UInt))

# Generate code cache for `REPLInterpreter` now:
# This code cache will be available at the world of `COMPLETION_WORLD`,
# assuming no invalidation will happen before initializing REPL.
# Once REPL is loaded, `REPLInterpreter` will be resilient against future invalidations.
code_typed(CC.typeinf, (REPLInterpreter, CC.InferenceState))

# Method completion on function call expression that look like :(max(1))
MAX_METHOD_COMPLETIONS::Int = 40
function _complete_methods(ex_org::Expr, context_module::Module, shift::Bool)
    funct = repl_eval_ex(ex_org.args[1], context_module)
    funct === nothing && return 2, nothing, [], Set{Symbol}()
    funct = CC.widenconst(funct)
    args_ex, kwargs_ex, kwargs_flag = complete_methods_args(ex_org, context_module, true, true)
    return kwargs_flag, funct, args_ex, kwargs_ex
end

function complete_methods(ex_org::Expr, context_module::Module=Main, shift::Bool=false)
    kwargs_flag, funct, args_ex, kwargs_ex = _complete_methods(ex_org, context_module, shift)::Tuple{Int, Any, Vector{Any}, Set{Symbol}}
    out = Completion[]
    kwargs_flag == 2 && return out # one of the kwargs is invalid
    kwargs_flag == 0 && push!(args_ex, Vararg{Any}) # allow more arguments if there is no semicolon
    complete_methods!(out, funct, args_ex, kwargs_ex, shift ? -2 : MAX_METHOD_COMPLETIONS, kwargs_flag == 1)
    return out
end

MAX_ANY_METHOD_COMPLETIONS::Int = 10
function recursive_explore_names!(seen::IdSet, callee_module::Module, initial_module::Module, exploredmodules::IdSet{Module}=IdSet{Module}())
    push!(exploredmodules, callee_module)
    for name in names(callee_module; all=true, imported=true)
        if !Base.isdeprecated(callee_module, name) && !startswith(string(name), '#') && isdefined(initial_module, name)
            func = getfield(callee_module, name)
            if !isa(func, Module)
                funct = Core.Typeof(func)
                push!(seen, funct)
            elseif isa(func, Module) && func ∉ exploredmodules
                recursive_explore_names!(seen, func, initial_module, exploredmodules)
            end
        end
    end
end
function recursive_explore_names(callee_module::Module, initial_module::Module)
    seen = IdSet{Any}()
    recursive_explore_names!(seen, callee_module, initial_module)
    seen
end

function complete_any_methods(ex_org::Expr, callee_module::Module, context_module::Module, moreargs::Bool, shift::Bool)
    out = Completion[]
    args_ex, kwargs_ex, kwargs_flag = try
        # this may throw, since we set default_any to false
        complete_methods_args(ex_org, context_module, false, false)
    catch ex
        ex isa ArgumentError || rethrow()
        return out
    end
    kwargs_flag == 2 && return out # one of the kwargs is invalid

    # moreargs determines whether to accept more args, independently of the presence of a
    # semicolon for the ".?(" syntax
    moreargs && push!(args_ex, Vararg{Any})

    for seen_name in recursive_explore_names(callee_module, callee_module)
        complete_methods!(out, seen_name, args_ex, kwargs_ex, MAX_ANY_METHOD_COMPLETIONS, false)
    end

    if !shift
        # Filter out methods where all arguments are `Any`
        filter!(out) do c
            isa(c, TextCompletion) && return false
            isa(c, MethodCompletion) || return true
            sig = Base.unwrap_unionall(c.method.sig)::DataType
            return !all(T -> T === Any || T === Vararg{Any}, sig.parameters[2:end])
        end
    end

    return out
end

function detect_invalid_kwarg!(kwargs_ex::Vector{Symbol}, @nospecialize(x), kwargs_flag::Int, possible_splat::Bool)
    n = isexpr(x, :kw) ? x.args[1] : x
    if n isa Symbol
        push!(kwargs_ex, n)
        return kwargs_flag
    end
    possible_splat && isexpr(x, :...) && return kwargs_flag
    return 2 # The kwarg is invalid
end

function detect_args_kwargs(funargs::Vector{Any}, context_module::Module, default_any::Bool, broadcasting::Bool)
    args_ex = Any[]
    kwargs_ex = Symbol[]
    kwargs_flag = 0
    # kwargs_flag is:
    # * 0 if there is no semicolon and no invalid kwarg
    # * 1 if there is a semicolon and no invalid kwarg
    # * 2 if there are two semicolons or more, or if some kwarg is invalid, which
    #        means that it is not of the form "bar=foo", "bar" or "bar..."
    for i in (1+!broadcasting):length(funargs)
        ex = funargs[i]
        if isexpr(ex, :parameters)
            kwargs_flag = ifelse(kwargs_flag == 0, 1, 2) # there should be at most one :parameters
            for x in ex.args
                kwargs_flag = detect_invalid_kwarg!(kwargs_ex, x, kwargs_flag, true)
            end
        elseif isexpr(ex, :kw)
            kwargs_flag = detect_invalid_kwarg!(kwargs_ex, ex, kwargs_flag, false)
        else
            if broadcasting
                # handle broadcasting, but only handle number of arguments instead of
                # argument types
                push!(args_ex, Any)
            else
                argt = repl_eval_ex(ex, context_module)
                if argt !== nothing
                    push!(args_ex, CC.widenconst(argt))
                elseif default_any
                    push!(args_ex, Any)
                else
                    throw(ArgumentError("argument not found"))
                end
            end
        end
    end
    return args_ex, Set{Symbol}(kwargs_ex), kwargs_flag
end

is_broadcasting_expr(ex::Expr) = ex.head === :. && isexpr(ex.args[2], :tuple)

function complete_methods_args(ex::Expr, context_module::Module, default_any::Bool, allow_broadcasting::Bool)
    if allow_broadcasting && is_broadcasting_expr(ex)
        return detect_args_kwargs((ex.args[2]::Expr).args, context_module, default_any, true)
    end
    return detect_args_kwargs(ex.args, context_module, default_any, false)
end

function complete_methods!(out::Vector{Completion}, @nospecialize(funct), args_ex::Vector{Any}, kwargs_ex::Set{Symbol}, max_method_completions::Int, exact_nargs::Bool)
    # Input types and number of arguments
    t_in = Tuple{funct, args_ex...}
    m = Base._methods_by_ftype(t_in, nothing, max_method_completions, Base.get_world_counter(),
        #=ambig=# true, Ref(typemin(UInt)), Ref(typemax(UInt)), Ptr{Int32}(C_NULL))
    if !isa(m, Vector)
        push!(out, TextCompletion(sprint(Base.show_signature_function, funct) * "( too many methods, use SHIFT-TAB to show )"))
        return
    end
    for match in m
        # TODO: if kwargs_ex, filter out methods without kwargs?
        push!(out, MethodCompletion(match.spec_types, match.method))
    end
    # TODO: filter out methods with wrong number of arguments if `exact_nargs` is set
end

include("latex_symbols.jl")
include("emoji_symbols.jl")

const non_identifier_chars = [" \t\n\r\"\\'`\$><=:;|&{}()[],+-*/?%^~"...]
const whitespace_chars = [" \t\n\r"...]
# "\"'`"... is added to whitespace_chars as non of the bslash_completions
# characters contain any of these characters. It prohibits the
# bslash_completions function to try and complete on escaped characters in strings
const bslash_separators = [whitespace_chars..., "\"'`"...]

const subscripts = Dict(k[3]=>v[1] for (k,v) in latex_symbols if startswith(k, "\\_") && length(k)==3)
const subscript_regex = Regex("^\\\\_[" * join(isdigit(k) || isletter(k) ? "$k" : "\\$k" for k in keys(subscripts)) * "]+\\z")
const superscripts = Dict(k[3]=>v[1] for (k,v) in latex_symbols if startswith(k, "\\^") && length(k)==3)
const superscript_regex = Regex("^\\\\\\^[" * join(isdigit(k) || isletter(k) ? "$k" : "\\$k" for k in keys(superscripts)) * "]+\\z")

# Aux function to detect whether we're right after a
# using or import keyword
function afterusing(string::String, startpos::Int)
    (isempty(string) || startpos == 0) && return false
    str = string[1:prevind(string,startpos)]
    isempty(str) && return false
    rstr = reverse(str)
    r = findfirst(r"\s(gnisu|tropmi)\b", rstr)
    r === nothing && return false
    fr = reverseind(str, last(r))
    return occursin(r"^\b(using|import)\s*((\w+[.])*\w+\s*,\s*)*$", str[fr:end])
end

function close_path_completion(dir, paths, str, pos)
    length(paths) == 1 || return false  # Only close if there's a single choice...
    path = (paths[1]::PathCompletion).path
    path = unescape_string(replace(path, "\\\$"=>"\$"))
    path = joinpath(dir, path)
    # ...except if it's a directory...
    try
        isdir(path)
    catch e
        e isa Base.IOError || rethrow() # `path` cannot be determined to be a file
    end && return false
    # ...and except if there's already a " at the cursor.
    return lastindex(str) <= pos || str[nextind(str, pos)] != '"'
end

function bslash_completions(string::String, pos::Int)
    slashpos = something(findprev(isequal('\\'), string, pos), 0)
    if (something(findprev(in(bslash_separators), string, pos), 0) < slashpos &&
        !(1 < slashpos && (string[prevind(string, slashpos)]=='\\')))
        # latex / emoji symbol substitution
        s = string[slashpos:pos]
        latex = get(latex_symbols, s, "")
        if !isempty(latex) # complete an exact match
            return (true, (Completion[BslashCompletion(latex)], slashpos:pos, true))
        elseif occursin(subscript_regex, s)
            sub = map(c -> subscripts[c], s[3:end])
            return (true, (Completion[BslashCompletion(sub)], slashpos:pos, true))
        elseif occursin(superscript_regex, s)
            sup = map(c -> superscripts[c], s[3:end])
            return (true, (Completion[BslashCompletion(sup)], slashpos:pos, true))
        end
        emoji = get(emoji_symbols, s, "")
        if !isempty(emoji)
            return (true, (Completion[BslashCompletion(emoji)], slashpos:pos, true))
        end
        # return possible matches; these cannot be mixed with regular
        # Julian completions as only latex / emoji symbols contain the leading \
        if startswith(s, "\\:") # emoji
            namelist = Iterators.filter(k -> startswith(k, s), keys(emoji_symbols))
        else # latex
            namelist = Iterators.filter(k -> startswith(k, s), keys(latex_symbols))
        end
        return (true, (Completion[BslashCompletion(name) for name in sort!(collect(namelist))], slashpos:pos, true))
    end
    return (false, (Completion[], 0:-1, false))
end

function dict_identifier_key(str::String, tag::Symbol, context_module::Module=Main)
    if tag === :string
        str_close = str*"\""
    elseif tag === :cmd
        str_close = str*"`"
    else
        str_close = str
    end

    frange, end_of_identifier = find_start_brace(str_close, c_start='[', c_end=']')
    isempty(frange) && return (nothing, nothing, nothing)
    obj = context_module
    for name in split(str[frange[1]:end_of_identifier], '.')
        Base.isidentifier(name) || return (nothing, nothing, nothing)
        sym = Symbol(name)
        isdefined(obj, sym) || return (nothing, nothing, nothing)
        obj = getfield(obj, sym)
    end
    (isa(obj, AbstractDict) && length(obj)::Int < 1_000_000) || return (nothing, nothing, nothing)
    begin_of_key = something(findnext(!isspace, str, nextind(str, end_of_identifier) + 1), # +1 for [
                             lastindex(str)+1)
    return (obj::AbstractDict, str[begin_of_key:end], begin_of_key)
end

# This needs to be a separate non-inlined function, see #19441
@noinline function find_dict_matches(identifier::AbstractDict, partial_key)
    matches = String[]
    for key in keys(identifier)
        rkey = repr(key)
        startswith(rkey,partial_key) && push!(matches,rkey)
    end
    return matches
end

# Identify an argument being completed in a method call. If the argument is empty, method
# suggestions will be provided instead of argument completions.
function identify_possible_method_completion(partial, last_idx)
    fail = 0:-1, Expr(:nothing), 0:-1, 0

    # First, check that the last punctuation is either ',', ';' or '('
    idx_last_punct = something(findprev(x -> ispunct(x) && x != '_' && x != '!', partial, last_idx), 0)::Int
    idx_last_punct == 0 && return fail
    last_punct = partial[idx_last_punct]
    last_punct == ',' || last_punct == ';' || last_punct == '(' || return fail

    # Then, check that `last_punct` is only followed by an identifier or nothing
    before_last_word_start = something(findprev(in(non_identifier_chars), partial, last_idx), 0)
    before_last_word_start == 0 && return fail
    all(isspace, @view partial[nextind(partial, idx_last_punct):before_last_word_start]) || return fail

    # Check that `last_punct` is either the last '(' or placed after a previous '('
    frange, method_name_end = find_start_brace(@view partial[1:idx_last_punct])
    method_name_end ∈ frange || return fail

    # Strip the preceding ! operators, if any, and close the expression with a ')'
    s = replace(partial[frange], r"\G\!+([^=\(]+)" => s"\1"; count=1) * ')'
    ex = Meta.parse(s, raise=false, depwarn=false)
    isa(ex, Expr) || return fail

    # `wordrange` is the position of the last argument to complete
    wordrange = nextind(partial, before_last_word_start):last_idx
    return frange, ex, wordrange, method_name_end
end

# Provide completion for keyword arguments in function calls
function complete_keyword_argument(partial, last_idx, context_module)
    frange, ex, wordrange, = identify_possible_method_completion(partial, last_idx)
    fail = Completion[], 0:-1, frange
    ex.head === :call || is_broadcasting_expr(ex) || return fail

    kwargs_flag, funct, args_ex, kwargs_ex = _complete_methods(ex, context_module, true)::Tuple{Int, Any, Vector{Any}, Set{Symbol}}
    kwargs_flag == 2 && return fail # one of the previous kwargs is invalid

    methods = Completion[]
    complete_methods!(methods, funct, Any[Vararg{Any}], kwargs_ex, -1, kwargs_flag == 1)
    # TODO: use args_ex instead of Any[Vararg{Any}] and only provide kwarg completion for
    # method calls compatible with the current arguments.

    # For each method corresponding to the function call, provide completion suggestions
    # for each keyword that starts like the last word and that is not already used
    # previously in the expression. The corresponding suggestion is "kwname=".
    # If the keyword corresponds to an existing name, also include "kwname" as a suggestion
    # since the syntax "foo(; kwname)" is equivalent to "foo(; kwname=kwname)".
    last_word = partial[wordrange] # the word to complete
    kwargs = Set{String}()
    for m in methods
        m::MethodCompletion
        possible_kwargs = Base.kwarg_decl(m.method)
        current_kwarg_candidates = String[]
        for _kw in possible_kwargs
            kw = String(_kw)
            if !endswith(kw, "...") && startswith(kw, last_word) && _kw ∉ kwargs_ex
                push!(current_kwarg_candidates, kw)
            end
        end
        union!(kwargs, current_kwarg_candidates)
    end

    suggestions = Completion[KeywordArgumentCompletion(kwarg) for kwarg in kwargs]
    append!(suggestions, complete_symbol(nothing, last_word, Returns(true), context_module))
    append!(suggestions, complete_keyval(last_word))

    return sort!(suggestions, by=completion_text), wordrange
end

function project_deps_get_completion_candidates(pkgstarts::String, project_file::String)
    loading_candidates = String[]
    d = Base.parsed_toml(project_file)
    pkg = get(d, "name", nothing)::Union{String, Nothing}
    if pkg !== nothing && startswith(pkg, pkgstarts)
        push!(loading_candidates, pkg)
    end
    deps = get(d, "deps", nothing)::Union{Dict{String, Any}, Nothing}
    if deps !== nothing
        for (pkg, _) in deps
            startswith(pkg, pkgstarts) && push!(loading_candidates, pkg)
        end
    end
    return Completion[PackageCompletion(name) for name in loading_candidates]
end

function complete_identifiers!(suggestions::Vector{Completion}, @nospecialize(ffunc),
                               context_module::Module, string::String, name::String,
                               pos::Int, dotpos::Int, startpos::Int;
                               comp_keywords=false)
    ex = nothing
    if comp_keywords
        append!(suggestions, complete_keyword(name))
        append!(suggestions, complete_keyval(name))
    end
    if dotpos > 1 && string[dotpos] == '.'
        s = string[1:prevind(string, dotpos)]
        # First see if the whole string up to `pos` is a valid expression. If so, use it.
        ex = Meta.parse(s, raise=false, depwarn=false)
        if isexpr(ex, :incomplete)
            s = string[startpos:pos]
            # Heuristic to find the start of the expression. TODO: This would be better
            # done with a proper error-recovering parser.
            if 0 < startpos <= lastindex(string) && string[startpos] == '.'
                i = prevind(string, startpos)
                while 0 < i
                    c = string[i]
                    if c in (')', ']')
                        if c == ')'
                            c_start = '('
                            c_end = ')'
                        elseif c == ']'
                            c_start = '['
                            c_end = ']'
                        end
                        frange, end_of_identifier = find_start_brace(string[1:prevind(string, i)], c_start=c_start, c_end=c_end)
                        isempty(frange) && break # unbalanced parens
                        startpos = first(frange)
                        i = prevind(string, startpos)
                    elseif c in ('\'', '\"', '\`')
                        s = "$c$c"*string[startpos:pos]
                        break
                    else
                        break
                    end
                    s = string[startpos:pos]
                end
            end
            if something(findlast(in(non_identifier_chars), s), 0) < something(findlast(isequal('.'), s), 0)
                lookup_name, name = rsplit(s, ".", limit=2)
                name = String(name)
                ex = Meta.parse(lookup_name, raise=false, depwarn=false)
            end
            isexpr(ex, :incomplete) && (ex = nothing)
        elseif isexpr(ex, (:using, :import))
            arg1 = ex.args[1]
            if isexpr(arg1, :.)
                # We come here for cases like:
                # - `string`: "using Mod1.Mod2.M"
                # - `ex`: :(using Mod1.Mod2)
                # - `name`: "M"
                # Now we transform `ex` to `:(Mod1.Mod2)` to allow `complete_symbol` to
                # complete for inner modules whose name starts with `M`.
                # Note that `ffunc` is set to `module_filter` within `completions`
                ex = nothing
                firstdot = true
                for arg = arg1.args
                    if arg === :.
                        # override `context_module` if multiple `.` accessors are used
                        if firstdot
                            firstdot = false
                        else
                            context_module = parentmodule(context_module)
                        end
                    elseif arg isa Symbol
                        if ex === nothing
                            ex = arg
                        else
                            ex = Expr(:., ex, QuoteNode(arg))
                        end
                    else # invalid expression
                        ex = nothing
                        break
                    end
                end
            end
        elseif isexpr(ex, :call) && length(ex.args) > 1
            isinfix = s[end] != ')'
            # A complete call expression that does not finish with ')' is an infix call.
            if !isinfix
                # Handle infix call argument completion of the form bar + foo(qux).
                frange, end_of_identifier = find_start_brace(@view s[1:prevind(s, end)])
                isinfix = Meta.parse(@view(s[frange[1]:end]), raise=false, depwarn=false) == ex.args[end]
            end
            if isinfix
                ex = ex.args[end]
            end
        elseif isexpr(ex, :macrocall) && length(ex.args) > 1
            # allow symbol completions within potentially incomplete macrocalls
            if s[end] ≠ '`' && s[end] ≠ ')'
                ex = ex.args[end]
            end
        end
    end
    append!(suggestions, complete_symbol(ex, name, ffunc, context_module))
    return sort!(unique(suggestions), by=completion_text), (dotpos+1):pos, true
end

function completions(string::String, pos::Int, context_module::Module=Main, shift::Bool=true)
    # First parse everything up to the current position
    partial = string[1:pos]
    inc_tag = Base.incomplete_tag(Meta.parse(partial, raise=false, depwarn=false))

    # ?(x, y)TAB lists methods you can call with these objects
    # ?(x, y TAB lists methods that take these objects as the first two arguments
    # MyModule.?(x, y)TAB restricts the search to names in MyModule
    rexm = match(r"(\w+\.|)\?\((.*)$", partial)
    if rexm !== nothing
        # Get the module scope
        if isempty(rexm.captures[1])
            callee_module = context_module
        else
            modname = Symbol(rexm.captures[1][1:end-1])
            if isdefined(context_module, modname)
                callee_module = getfield(context_module, modname)
                if !isa(callee_module, Module)
                    callee_module = context_module
                end
            else
                callee_module = context_module
            end
        end
        moreargs = !endswith(rexm.captures[2], ')')
        callstr = "_(" * rexm.captures[2]
        if moreargs
            callstr *= ')'
        end
        ex_org = Meta.parse(callstr, raise=false, depwarn=false)
        if isa(ex_org, Expr)
            return complete_any_methods(ex_org, callee_module::Module, context_module, moreargs, shift), (0:length(rexm.captures[1])+1) .+ rexm.offset, false
        end
    end

    # if completing a key in a Dict
    identifier, partial_key, loc = dict_identifier_key(partial, inc_tag, context_module)
    if identifier !== nothing
        matches = find_dict_matches(identifier, partial_key)
        length(matches)==1 && (lastindex(string) <= pos || string[nextind(string,pos)] != ']') && (matches[1]*=']')
        length(matches)>0 && return Completion[DictCompletion(identifier, match) for match in sort!(matches)], loc::Int:pos, true
    end

    ffunc = Returns(true)
    suggestions = Completion[]

    # Check if this is a var"" string macro that should be completed like
    # an identifier rather than a string.
    # TODO: It would be nice for the parser to give us more information here
    # so that we can lookup the macro by identity rather than pattern matching
    # its invocation.
    varrange = findprev("var\"", string, pos)

    if varrange !== nothing
        ok, ret = bslash_completions(string, pos)
        ok && return ret
        startpos = first(varrange) + 4
        dotpos = something(findprev(isequal('.'), string, first(varrange)-1), 0)
        name = string[startpos:pos]
        return complete_identifiers!(Completion[], ffunc, context_module, string, name, pos,
                                     dotpos, startpos)
    elseif inc_tag === :cmd
        # TODO: should this call shell_completions instead of partially reimplementing it?
        let m = match(r"[\t\n\r\"`><=*?|]| (?!\\)", reverse(partial)) # fuzzy shell_parse in reverse
            startpos = nextind(partial, reverseind(partial, m.offset))
            r = startpos:pos
            scs::String = string[r]

            expanded = complete_expanduser(scs, r)
            expanded[3] && return expanded  # If user expansion available, return it

            path::String = replace(scs, r"(\\+)\g1(\\?)`" => "\1\2`") # fuzzy unescape_raw_string: match an even number of \ before ` and replace with half as many
            # This expansion with "\\ "=>' ' replacement and shell_escape=true
            # assumes the path isn't further quoted within the cmd backticks.
            path = replace(path, r"\\ " => " ", r"\$" => "\$") # fuzzy shell_parse (reversed by shell_escape_posixly)
            paths, dir, success = complete_path(path, shell_escape=true, raw_escape=true)

            if success && !isempty(dir)
                let dir = do_raw_escape(do_shell_escape(dir))
                    # if escaping of dir matches scs prefix, remove that from the completions
                    # otherwise make it the whole completion
                    if endswith(dir, "/") && startswith(scs, dir)
                        r = (startpos + sizeof(dir)):pos
                    elseif startswith(scs, dir * "/")
                        r = nextind(string, startpos + sizeof(dir)):pos
                    else
                        map!(paths, paths) do c::PathCompletion
                            return PathCompletion(dir * "/" * c.path)
                        end
                    end
                end
            end
            return sort!(paths, by=p->p.path), r, success
        end
    elseif inc_tag === :string
        # Find first non-escaped quote
        let m = match(r"\"(?!\\)", reverse(partial))
            startpos = nextind(partial, reverseind(partial, m.offset))
            r = startpos:pos
            scs::String = string[r]

            expanded = complete_expanduser(scs, r)
            expanded[3] && return expanded  # If user expansion available, return it

            path = try
                unescape_string(replace(scs, "\\\$"=>"\$"))
            catch ex
                ex isa ArgumentError || rethrow()
                nothing
            end
            if !isnothing(path)
                paths, dir, success = complete_path(path::String, string_escape=true)

                if close_path_completion(dir, paths, path, pos)
                    paths[1] = PathCompletion((paths[1]::PathCompletion).path * "\"")
                end

                if success && !isempty(dir)
                    let dir = do_string_escape(dir)
                        # if escaping of dir matches scs prefix, remove that from the completions
                        # otherwise make it the whole completion
                        if endswith(dir, "/") && startswith(scs, dir)
                            r = (startpos + sizeof(dir)):pos
                        elseif startswith(scs, dir * "/")
                            r = nextind(string, startpos + sizeof(dir)):pos
                        else
                            map!(paths, paths) do c::PathCompletion
                                return PathCompletion(dir * "/" * c.path)
                            end
                        end
                    end
                end

                # Fallthrough allowed so that Latex symbols can be completed in strings
                success && return sort!(paths, by=p->p.path), r, success
            end
        end
    end

    ok, ret = bslash_completions(string, pos)
    ok && return ret

    # Make sure that only bslash_completions is working on strings
    inc_tag === :string && return Completion[], 0:-1, false
    if inc_tag === :other
        frange, ex, wordrange, method_name_end = identify_possible_method_completion(partial, pos)
        if last(frange) != -1 && all(isspace, @view partial[wordrange]) # no last argument to complete
            if ex.head === :call
                return complete_methods(ex, context_module, shift), first(frange):method_name_end, false
            elseif is_broadcasting_expr(ex)
                return complete_methods(ex, context_module, shift), first(frange):(method_name_end - 1), false
            end
        end
    elseif inc_tag === :comment
        return Completion[], 0:-1, false
    end

    # Check whether we can complete a keyword argument in a function call
    kwarg_completion, wordrange = complete_keyword_argument(partial, pos, context_module)
    isempty(wordrange) || return kwarg_completion, wordrange, !isempty(kwarg_completion)

    dotpos = something(findprev(isequal('.'), string, pos), 0)
    startpos = nextind(string, something(findprev(in(non_identifier_chars), string, pos), 0))
    # strip preceding ! operator
    if (m = match(r"\G\!+", partial, startpos)) isa RegexMatch
        startpos += length(m.match)
    end

    name = string[max(startpos, dotpos+1):pos]
    comp_keywords = !isempty(name) && startpos > dotpos
    if afterusing(string, startpos)
        # We're right after using or import. Let's look only for packages
        # and modules we can reach from here

        # If there's no dot, we're in toplevel, so we should
        # also search for packages
        s = string[startpos:pos]
        if dotpos <= startpos
            for dir in Base.load_path()
                if basename(dir) in Base.project_names && isfile(dir)
                    append!(suggestions, project_deps_get_completion_candidates(s, dir))
                end
                isdir(dir) || continue
                for pname in readdir(dir)
                    if pname[1] != '.' && pname != "METADATA" &&
                        pname != "REQUIRE" && startswith(pname, s)
                        # Valid file paths are
                        #   <Mod>.jl
                        #   <Mod>/src/<Mod>.jl
                        #   <Mod>.jl/src/<Mod>.jl
                        if isfile(joinpath(dir, pname))
                            endswith(pname, ".jl") && push!(suggestions,
                                                            PackageCompletion(pname[1:prevind(pname, end-2)]))
                        else
                            mod_name = if endswith(pname, ".jl")
                                pname[1:prevind(pname, end-2)]
                            else
                                pname
                            end
                            if isfile(joinpath(dir, pname, "src",
                                               "$mod_name.jl"))
                                push!(suggestions, PackageCompletion(mod_name))
                            end
                        end
                    end
                end
            end
        end
        ffunc = module_filter
        comp_keywords = false
    end

    startpos == 0 && (pos = -1)
    dotpos < startpos && (dotpos = startpos - 1)
    return complete_identifiers!(suggestions, ffunc, context_module, string, name, pos,
                                 dotpos, startpos;
                                 comp_keywords)
end

module_filter(mod::Module, x::Symbol) =
    Base.isbindingresolved(mod, x) && isdefined(mod, x) && isa(getglobal(mod, x), Module)

function shell_completions(string, pos)
    # First parse everything up to the current position
    scs = string[1:pos]
    args, last_arg_start = try
        Base.shell_parse(scs, true)::Tuple{Expr,Int}
    catch ex
        ex isa ArgumentError || ex isa ErrorException || rethrow()
        return Completion[], 0:-1, false
    end
    ex = args.args[end]::Expr
    # Now look at the last thing we parsed
    isempty(ex.args) && return Completion[], 0:-1, false
    lastarg = ex.args[end]
    # As Base.shell_parse throws away trailing spaces (unless they are escaped),
    # we need to special case here.
    # If the last char was a space, but shell_parse ignored it search on "".
    if isexpr(lastarg, :incomplete) || isexpr(lastarg, :error)
        partial = string[last_arg_start:pos]
        ret, range = completions(partial, lastindex(partial))
        range = range .+ (last_arg_start - 1)
        return ret, range, true
    elseif endswith(scs, ' ') && !endswith(scs, "\\ ")
        r = pos+1:pos
        paths, dir, success = complete_path("", use_envpath=false, shell_escape=true)
        return paths, r, success
    elseif all(arg -> arg isa AbstractString, ex.args)
        # Join these and treat this as a path
        path::String = join(ex.args)
        r = last_arg_start:pos

        # Also try looking into the env path if the user wants to complete the first argument
        use_envpath = length(args.args) < 2

        # TODO: call complete_expanduser here?

        paths, dir, success = complete_path(path, use_envpath=use_envpath, shell_escape=true)

        if success && !isempty(dir)
            let dir = do_shell_escape(dir)
                # if escaping of dir matches scs prefix, remove that from the completions
                # otherwise make it the whole completion
                partial = string[last_arg_start:pos]
                if endswith(dir, "/") && startswith(partial, dir)
                    r = (last_arg_start + sizeof(dir)):pos
                elseif startswith(partial, dir * "/")
                    r = nextind(string, last_arg_start + sizeof(dir)):pos
                else
                    map!(paths, paths) do c::PathCompletion
                        return PathCompletion(dir * "/" * c.path)
                    end
                end
            end
        end

        return paths, r, success
    end
    return Completion[], 0:-1, false
end

function UndefVarError_hint(io::IO, ex::UndefVarError)
    var = ex.var
    if var === :or
        print(io, "\nsuggestion: Use `||` for short-circuiting boolean OR.")
    elseif var === :and
        print(io, "\nsuggestion: Use `&&` for short-circuiting boolean AND.")
    elseif var === :help
        println(io)
        # Show friendly help message when user types help or help() and help is undefined
        show(io, MIME("text/plain"), Base.Docs.parsedoc(Base.Docs.keywords[:help]))
    elseif var === :quit
        print(io, "\nsuggestion: To exit Julia, use Ctrl-D, or type exit() and press enter.")
    end
end

function __init__()
    Base.Experimental.register_error_hint(UndefVarError_hint, UndefVarError)
    COMPLETION_WORLD[] = Base.get_world_counter()
    nothing
end

end # module
u   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/REPL/src/latex_symbols.jl�     # This file is a part of Julia. License is MIT: https://julialang.org/license

# Mapping from LaTeX math symbol to the corresponding Unicode codepoint.
# This is used for tab substitution in the REPL.

# The initial symbol listing was generated from the W3C symbol mapping file:
#         http://www.w3.org/Math/characters/unicode.xml
# by the following Julia script:
#=
import REPL
using LightXML
xdoc = parse_file("unicode.xml")
latexsym = []
Ls = Set()
for c in child_nodes(root(xdoc))
    if name(c) == "character" && is_elementnode(c)
        ce = XMLElement(c)
        latex = nothing
        for el in ("AMS", "IEEE", "mathlatex", "latex")
            latex = find_element(ce, el)
            latex !== nothing && break
        end
        if latex !== nothing
            L = strip(content(latex))
            id = attribute(ce, "id")
            U = string(map(s -> Char(parse(Int, s, base = 16)),
                           split(id[2:end], "-"))...)
            if occursin(r"^\\[A-Za-z]+$", L) && !isa(U,String)
                if L in Ls
                    println("# duplicated symbol $L ($id)")
                else
                    if U[1] == '\u22a5' # unicode.xml incorrectly uses \perp for \bot
                        L = "\\bot"
                    elseif U[1] == '\u21be'
                        L = "\\upharpoonright"
                    elseif U[1] == '\u21bf'
                        L = "\\upharpoonleft"
                    end
                    push!(latexsym, (L, U))
                    push!(Ls, L)
                end
            end
        end
    end
end
println("# ", length(latexsym), " symbols generated from unicode.xml")
for (L, U) in latexsym
    println("    \"$(escape_string(L))\" => \"$(escape_string(U))\",")
end
=#

# Additional symbols were generated from the unicode-math LaTeX package
# symbol listing, using the following script:
#=
fname = "unicode-math-table.tex"
isfile(fname) || download("http://mirror.math.ku.edu/tex-archive/macros/latex/contrib/unicode-math/$fname", fname)
const latex_strings = Set(values(REPL.REPLCompletions.latex_symbols))
open(fname) do f
    for L in eachline(f)
        x = map(s -> rstrip(s, [' ','\t','\n']),
                split(replace(L, r"[{}\"]+" => "\t"), "\t"))
        c = Char(parse(Int, x[2], base = 16))
        if (Base.is_id_char(c) || Base.isoperator(Symbol(c))) &&
           string(c) ∉ latex_strings && !isascii(c)
            tabcomname = escape_string(x[3])
            if startswith(tabcomname, "\\\\math")
                tabcomname = string("\\\\", tabcomname[7:end])
            end
            println("    \"", tabcomname, "\" => \"",
                    escape_string("$c"), "\",  # ", x[5])
        end
    end
end
=#

# Finally, we also add some symbols manually (at the top) as needed,
# and edited others for consistency (e.g. #21646 and #14751).

# When a symbol has several completions, a canonical reverse mapping is
# specified at the bottom of this file. The complete reverse mapping is
# generated lazily in docview.jl.

# "font" prefixes
const bold = "\\bf"
const italic = "\\it"
const bolditalic = "\\bi"
const blackboard = "\\bb"
const italicblackboard = "\\bbi"
const script = "\\scr"
const boldscript = "\\bscr"
const sans = "\\sans"
const boldsans = "\\bsans"
const italicsans = "\\isans"
const bolditalicsans = "\\bisans"
const frak = "\\frak"
const boldfrak = "\\bfrak"
const mono = "\\tt"

const latex_symbols = Dict(

# manual additions:

    "\\sqrt" => "\u221A",
    "\\cbrt" => "\u221B",
    "\\female" => "♀",
    "\\mars" => "♂",
    "\\pprime" => "″",
    "\\ppprime" => "‴",
    "\\pppprime" => "⁗",
    "\\backpprime" => "‶",
    "\\backppprime" => "‷",
    "\\xor" => "⊻",
    "\\nand" => "⊼",
    "\\nor" => "⊽",
    "\\iff" => "⟺",
    "\\implies" => "⟹",
    "\\impliedby" => "⟸",
    "\\to" => "→",
    "\\euler" => "ℯ",
    "\\ohm" => "Ω",

    # Superscripts
    "\\^0" => "⁰",
    "\\^1" => "¹",
    "\\^2" => "²",
    "\\^3" => "³",
    "\\^4" => "⁴",
    "\\^5" => "⁵",
    "\\^6" => "⁶",
    "\\^7" => "⁷",
    "\\^8" => "⁸",
    "\\^9" => "⁹",
    "\\^+" => "⁺",
    "\\^-" => "⁻",
    "\\^=" => "⁼",
    "\\^(" => "⁽",
    "\\^)" => "⁾",
    "\\^a" => "ᵃ",
    "\\^b" => "ᵇ",
    "\\^c" => "ᶜ",
    "\\^d" => "ᵈ",
    "\\^e" => "ᵉ",
    "\\^f" => "ᶠ",
    "\\^g" => "ᵍ",
    "\\^h" => "ʰ",
    "\\^i" => "ⁱ",
    "\\^j" => "ʲ",
    "\\^k" => "ᵏ",
    "\\^l" => "ˡ",
    "\\^m" => "ᵐ",
    "\\^n" => "ⁿ",
    "\\^o" => "ᵒ",
    "\\^p" => "ᵖ",
    "\\^r" => "ʳ",
    "\\^s" => "ˢ",
    "\\^t" => "ᵗ",
    "\\^u" => "ᵘ",
    "\\^v" => "ᵛ",
    "\\^w" => "ʷ",
    "\\^x" => "ˣ",
    "\\^y" => "ʸ",
    "\\^z" => "ᶻ",
    "\\^A" => "ᴬ",
    "\\^B" => "ᴮ",
    "\\^D" => "ᴰ",
    "\\^E" => "ᴱ",
    "\\^G" => "ᴳ",
    "\\^H" => "ᴴ",
    "\\^I" => "ᴵ",
    "\\^J" => "ᴶ",
    "\\^K" => "ᴷ",
    "\\^L" => "ᴸ",
    "\\^M" => "ᴹ",
    "\\^N" => "ᴺ",
    "\\^O" => "ᴼ",
    "\\^P" => "ᴾ",
    "\\^R" => "ᴿ",
    "\\^T" => "ᵀ",
    "\\^U" => "ᵁ",
    "\\^V" => "ⱽ",
    "\\^W" => "ᵂ",
    "\\^alpha" => "ᵅ",
    "\\^beta" => "ᵝ",
    "\\^gamma" => "ᵞ",
    "\\^delta" => "ᵟ",
    "\\^epsilon" => "ᵋ",
    "\\^theta" => "ᶿ",
    "\\^iota" => "ᶥ",
    "\\^phi" => "ᵠ",
    "\\^chi" => "ᵡ",
    "\\^ltphi" => "ᶲ",
    "\\^uparrow" => "ꜛ",
    "\\^downarrow" => "ꜜ",
    "\\^!" => "ꜝ",

    # Subscripts
    "\\_0" => "₀",
    "\\_1" => "₁",
    "\\_2" => "₂",
    "\\_3" => "₃",
    "\\_4" => "₄",
    "\\_5" => "₅",
    "\\_6" => "₆",
    "\\_7" => "₇",
    "\\_8" => "₈",
    "\\_9" => "₉",
    "\\_+" => "₊",
    "\\_-" => "₋",
    "\\_=" => "₌",
    "\\_(" => "₍",
    "\\_)" => "₎",
    "\\_a" => "ₐ",
    "\\_e" => "ₑ",
    "\\_h" => "ₕ",
    "\\_i" => "ᵢ",
    "\\_j" => "ⱼ",
    "\\_k" => "ₖ",
    "\\_l" => "ₗ",
    "\\_m" => "ₘ",
    "\\_n" => "ₙ",
    "\\_o" => "ₒ",
    "\\_p" => "ₚ",
    "\\_r" => "ᵣ",
    "\\_s" => "ₛ",
    "\\_t" => "ₜ",
    "\\_u" => "ᵤ",
    "\\_v" => "ᵥ",
    "\\_x" => "ₓ",
    "\\_schwa" => "ₔ",
    "\\_beta" => "ᵦ",
    "\\_gamma" => "ᵧ",
    "\\_rho" => "ᵨ",
    "\\_phi" => "ᵩ",
    "\\_chi" => "ᵪ",

    # Misc. Math and Physics
    "\\ldots" => "…",
    "\\hbar" => "ħ",
    "\\del" => "∇",

    "\\sout" => "̶",# ulem package, same as Elzbar
    "\\euro" => "€",

# 732 symbols generated from unicode.xml
    "\\exclamdown" => "¡",
    "\\sterling" => "£",
    "\\yen" => "¥",
    "\\brokenbar" => "¦",
    "\\S" => "§",
    "\\copyright" => "©",
    "\\ordfeminine" => "ª",
    "\\neg" => "¬",
    "\\circledR" => "®",
    "\\highminus" => "¯", # APL "high minus", or non-combining macron above
    "\\degree" => "°",
    "\\pm" => "±",
    "\\P" => "¶",
    "\\cdotp" => "·",
    "\\ordmasculine" => "º",
    "\\questiondown" => "¿",
    "\\AA" => "Å",
    "\\AE" => "Æ",
    "\\DH" => "Ð",
    "\\times" => "×",
    "\\O" => "Ø",
    "\\TH" => "Þ",
    "\\ss" => "ß",
    "\\aa" => "å",
    "\\ae" => "æ",
    "\\eth" => "ð",
    "\\dh" => "ð",
    "\\div" => "÷",
    "\\o" => "ø",
    "\\th" => "þ",
    "\\DJ" => "Đ",
    "\\dj" => "đ",
    "\\imath" => "ı",
    "\\jmath" => "ȷ",
    "\\L" => "Ł",
    "\\l" => "ł",
    "\\NG" => "Ŋ",
    "\\ng" => "ŋ",
    "\\OE" => "Œ",
    "\\oe" => "œ",
    "\\hvlig" => "ƕ",
    "\\nrleg" => "ƞ",
    "\\doublepipe" => "ǂ",
    "\\trna" => "ɐ",
    "\\trnsa" => "ɒ",
    "\\openo" => "ɔ",
    "\\rtld" => "ɖ",
    "\\schwa" => "ə",
    "\\varepsilon" => "ε",
    "\\pgamma" => "ɣ",
    "\\pbgam" => "ɤ",
    "\\trnh" => "ɥ",
    "\\btdl" => "ɬ",
    "\\rtll" => "ɭ",
    "\\trnm" => "ɯ",
    "\\trnmlr" => "ɰ",
    "\\ltlmr" => "ɱ",
    "\\ltln" => "ɲ",
    "\\rtln" => "ɳ",
    "\\clomeg" => "ɷ",
    "\\ltphi" => "ɸ", # latin ϕ
    "\\trnr" => "ɹ",
    "\\trnrl" => "ɺ",
    "\\rttrnr" => "ɻ",
    "\\rl" => "ɼ",
    "\\rtlr" => "ɽ",
    "\\fhr" => "ɾ",
    "\\rtls" => "ʂ",
    "\\esh" => "ʃ",
    "\\trnt" => "ʇ",
    "\\rtlt" => "ʈ",
    "\\pupsil" => "ʊ",
    "\\pscrv" => "ʋ",
    "\\invv" => "ʌ",
    "\\invw" => "ʍ",
    "\\trny" => "ʎ",
    "\\rtlz" => "ʐ",
    "\\yogh" => "ʒ",
    "\\glst" => "ʔ",
    "\\reglst" => "ʕ",
    "\\inglst" => "ʖ",
    "\\turnk" => "ʞ",
    "\\dyogh" => "ʤ",
    "\\tesh" => "ʧ",
    "\\rasp" => "ʼ",
    "\\verts" => "ˈ",
    "\\verti" => "ˌ",
    "\\lmrk" => "ː",
    "\\hlmrk" => "ˑ",
    "\\sbrhr" => "˒",
    "\\sblhr" => "˓",
    "\\rais" => "˔",
    "\\low" => "˕",
    "\\u" => "˘",
    "\\tildelow" => "˜",
    "\\grave" => "̀",
    "\\acute" => "́",
    "\\hat" => "̂",
    "\\tilde" => "̃",
    "\\bar" => "̄",
    "\\breve" => "̆",
    "\\dot" => "̇",
    "\\ddot" => "̈",
    "\\ocirc" => "̊",
    "\\H" => "̋",
    "\\check" => "̌",
    "\\palh" => "̡",
    "\\rh" => "̢",
    "\\c" => "̧",
    "\\k" => "̨",
    "\\sbbrg" => "̪",
    "\\strike" => "̶",
    "\\Alpha" => "Α",
    "\\Beta" => "Β",
    "\\Gamma" => "Γ",
    "\\Delta" => "Δ",
    "\\Epsilon" => "Ε",
    "\\Zeta" => "Ζ",
    "\\Eta" => "Η",
    "\\Theta" => "Θ",
    "\\Iota" => "Ι",
    "\\Kappa" => "Κ",
    "\\Lambda" => "Λ",
    "\\Xi" => "Ξ",
    "\\Pi" => "Π",
    "\\Rho" => "Ρ",
    "\\Sigma" => "Σ",
    "\\Tau" => "Τ",
    "\\Upsilon" => "Υ",
    "\\Phi" => "Φ",
    "\\Chi" => "Χ",
    "\\Psi" => "Ψ",
    "\\Omega" => "Ω",
    "\\alpha" => "α",
    "\\beta" => "β",
    "\\gamma" => "γ",
    "\\delta" => "δ",
    "\\zeta" => "ζ",
    "\\eta" => "η",
    "\\theta" => "θ",
    "\\iota" => "ι",
    "\\kappa" => "κ",
    "\\lambda" => "λ",
    "\\mu" => "μ",
    "\\nu" => "ν",
    "\\xi" => "ξ",
    "\\pi" => "π",
    "\\rho" => "ρ",
    "\\varsigma" => "ς",
    "\\sigma" => "σ",
    "\\tau" => "τ",
    "\\upsilon" => "υ",
    "\\varphi" => "φ",
    "\\chi" => "χ",
    "\\psi" => "ψ",
    "\\omega" => "ω",
    "\\vartheta" => "ϑ",
    "\\phi" => "ϕ",
    "\\varpi" => "ϖ",
    "\\Stigma" => "Ϛ",
    "\\Digamma" => "Ϝ",
    "\\digamma" => "ϝ",
    "\\Koppa" => "Ϟ",
    "\\Sampi" => "Ϡ",
    "\\varkappa" => "ϰ",
    "\\varrho" => "ϱ",
    "\\varTheta" => "ϴ",
    "\\epsilon" => "ϵ",
    "\\backepsilon" => "϶",
    "\\enspace" => " ",
    "\\quad" => " ",
    "\\thickspace" => " ",
    "\\thinspace" => " ",
    "\\hspace" => " ",
    "\\endash" => "–",
    "\\emdash" => "—",
    "\\Vert" => "‖",
    "\\lq" => "‘",
    "\\rq" => "’",
    "\\reapos" => "‛",
    "\\ldq" => "“",
    "\\rdq" => "”",
    "\\dagger" => "†",
    "\\ddagger" => "‡",
    "\\bullet" => "•",
    "\\dots" => "…",
    "\\perthousand" => "‰",
    "\\pertenthousand" => "‱",
    "\\prime" => "′",
    "\\backprime" => "‵",
    "\\guilsinglleft" => "‹",
    "\\guilsinglright" => "›",
    "\\nolinebreak" => "\u2060",
    "\\pes" => "₧",
    "\\dddot" => "⃛",
    "\\ddddot" => "⃜",
    "\\hslash" => "ℏ",
    "\\Im" => "ℑ",
    "\\ell" => "ℓ",
    "\\numero" => "№",
    "\\wp" => "℘",
    "\\Re" => "ℜ",
    "\\xrat" => "℞",
    "\\trademark" => "™",
    "\\mho" => "℧",
    "\\aleph" => "ℵ",
    "\\beth" => "ℶ",
    "\\gimel" => "ℷ",
    "\\daleth" => "ℸ",
    blackboard*"Pi" => "ℿ",
    "\\bbsum" => "⅀",
    "\\Game" => "⅁",
    "\\leftarrow" => "←",
    "\\uparrow" => "↑",
    "\\rightarrow" => "→",
    "\\downarrow" => "↓",
    "\\leftrightarrow" => "↔",
    "\\updownarrow" => "↕",
    "\\nwarrow" => "↖",
    "\\nearrow" => "↗",
    "\\searrow" => "↘",
    "\\swarrow" => "↙",
    "\\nleftarrow" => "↚",
    "\\nrightarrow" => "↛",
    "\\twoheadleftarrow" => "↞",
    "\\twoheadrightarrow" => "↠",
    "\\leftarrowtail" => "↢",
    "\\rightarrowtail" => "↣",
    "\\mapsto" => "↦",
    "\\hookleftarrow" => "↩",
    "\\hookrightarrow" => "↪",
    "\\looparrowleft" => "↫",
    "\\looparrowright" => "↬",
    "\\leftrightsquigarrow" => "↭",
    "\\nleftrightarrow" => "↮",
    "\\Lsh" => "↰",
    "\\Rsh" => "↱",
    "\\curvearrowleft" => "↶",
    "\\curvearrowright" => "↷",
    "\\circlearrowleft" => "↺",
    "\\circlearrowright" => "↻",
    "\\leftharpoonup" => "↼",
    "\\leftharpoondown" => "↽",
    "\\upharpoonright" => "↾",
    "\\upharpoonleft" => "↿",
    "\\rightharpoonup" => "⇀",
    "\\rightharpoondown" => "⇁",
    "\\downharpoonright" => "⇂",
    "\\downharpoonleft" => "⇃",
    "\\rightleftarrows" => "⇄",
    "\\dblarrowupdown" => "⇅",
    "\\leftrightarrows" => "⇆",
    "\\leftleftarrows" => "⇇",
    "\\upuparrows" => "⇈",
    "\\rightrightarrows" => "⇉",
    "\\downdownarrows" => "⇊",
    "\\leftrightharpoons" => "⇋",
    "\\rightleftharpoons" => "⇌",
    "\\nLeftarrow" => "⇍",
    "\\nRightarrow" => "⇏",
    "\\Leftarrow" => "⇐",
    "\\Uparrow" => "⇑",
    "\\Rightarrow" => "⇒",
    "\\Downarrow" => "⇓",
    "\\Leftrightarrow" => "⇔",
    "\\Updownarrow" => "⇕",
    "\\Lleftarrow" => "⇚",
    "\\Rrightarrow" => "⇛",
    "\\DownArrowUpArrow" => "⇵",
    "\\leftarrowtriangle" => "⇽",
    "\\rightarrowtriangle" => "⇾",
    "\\forall" => "∀",
    "\\complement" => "∁",
    "\\partial" => "∂",
    "\\exists" => "∃",
    "\\nexists" => "∄",
    "\\varnothing" => "∅",
    "\\emptyset" => "∅",
    "\\nabla" => "∇",
    "\\in" => "∈",
    "\\notin" => "∉",
    "\\ni" => "∋",
    "\\prod" => "∏",
    "\\coprod" => "∐",
    "\\sum" => "∑",
    "\\minus" => "−",
    "\\mp" => "∓",
    "\\dotplus" => "∔",
    "\\setminus" => "∖",
    "\\ast" => "∗",
    "\\circ" => "∘",
    blackboard*"semi" => "⨟",
    "\\surd" => "√",
    "\\propto" => "∝",
    "\\infty" => "∞",
    "\\rightangle" => "∟",
    "\\angle" => "∠",
    "\\measuredangle" => "∡",
    "\\sphericalangle" => "∢",
    "\\mid" => "∣",
    "\\nmid" => "∤",
    "\\parallel" => "∥",
    "\\nparallel" => "∦",
    "\\wedge" => "∧",
    "\\vee" => "∨",
    "\\cap" => "∩",
    "\\cup" => "∪",
    "\\int" => "∫",
    "\\iint" => "∬",
    "\\iiint" => "∭",
    "\\oint" => "∮",
    "\\oiint" => "∯",
    "\\oiiint" => "∰",
    "\\clwintegral" => "∱",
    "\\therefore" => "∴",
    "\\because" => "∵",
    "\\Colon" => "∷",
    "\\dotminus" => "∸",
    "\\kernelcontraction" => "∻",
    "\\sim" => "∼",
    "\\backsim" => "∽",
    "\\lazysinv" => "∾",
    "\\wr" => "≀",
    "\\nsim" => "≁",
    "\\eqsim" => "≂",
    "\\neqsim" => "≂̸",
    "\\simeq" => "≃",
    "\\nsime" => "≄",
    "\\cong" => "≅",
    "\\approxnotequal" => "≆",
    "\\ncong" => "≇",
    "\\approx" => "≈",
    "\\napprox" => "≉",
    "\\approxeq" => "≊",
    "\\tildetrpl" => "≋",
    "\\allequal" => "≌",
    "\\asymp" => "≍",
    "\\Bumpeq" => "≎",
    "\\nBumpeq" => "≎̸",
    "\\bumpeq" => "≏",
    "\\nbumpeq" => "≏̸",
    "\\doteq" => "≐",
    "\\Doteq" => "≑",
    "\\fallingdotseq" => "≒",
    "\\risingdotseq" => "≓",
    "\\coloneq" => "≔",
    "\\eqcolon" => "≕",
    "\\eqcirc" => "≖",
    "\\circeq" => "≗",
    "\\wedgeq" => "≙",
    "\\starequal" => "≛",
    "\\triangleq" => "≜",
    "\\questeq" => "≟",
    "\\ne" => "≠",
    "\\neq" => "≠",
    "\\equiv" => "≡",
    "\\nequiv" => "≢",
    "\\le" => "≤",
    "\\leq" => "≤",
    "\\ge" => "≥",
    "\\geq" => "≥",
    "\\leqq" => "≦",
    "\\geqq" => "≧",
    "\\lneqq" => "≨",
    "\\lvertneqq" => "≨︀",
    "\\gneqq" => "≩",
    "\\gvertneqq" => "≩︀",
    "\\ll" => "≪",
    "\\NotLessLess" => "≪̸",
    "\\gg" => "≫",
    "\\NotGreaterGreater" => "≫̸",
    "\\between" => "≬",
    "\\nless" => "≮",
    "\\ngtr" => "≯",
    "\\nleq" => "≰",
    "\\ngeq" => "≱",
    "\\lesssim" => "≲",
    "\\gtrsim" => "≳",
    "\\lessgtr" => "≶",
    "\\gtrless" => "≷",
    "\\notlessgreater" => "≸",
    "\\notgreaterless" => "≹",
    "\\prec" => "≺",
    "\\succ" => "≻",
    "\\preccurlyeq" => "≼",
    "\\succcurlyeq" => "≽",
    "\\precsim" => "≾",
    "\\nprecsim" => "≾̸",
    "\\succsim" => "≿",
    "\\nsuccsim" => "≿̸",
    "\\nprec" => "⊀",
    "\\nsucc" => "⊁",
    "\\subset" => "⊂",
    "\\supset" => "⊃",
    "\\nsubset" => "⊄",
    "\\nsupset" => "⊅",
    "\\subseteq" => "⊆",
    "\\supseteq" => "⊇",
    "\\nsubseteq" => "⊈",
    "\\nsupseteq" => "⊉",
    "\\subsetneq" => "⊊",
    "\\varsubsetneqq" => "⊊︀",
    "\\supsetneq" => "⊋",
    "\\varsupsetneq" => "⊋︀",
    "\\cupdot" => "⊍",
    "\\uplus" => "⊎",
    "\\sqsubset" => "⊏",
    "\\NotSquareSubset" => "⊏̸",
    "\\sqsupset" => "⊐",
    "\\NotSquareSuperset" => "⊐̸",
    "\\sqsubseteq" => "⊑",
    "\\sqsupseteq" => "⊒",
    "\\sqcap" => "⊓",
    "\\sqcup" => "⊔",
    "\\oplus" => "⊕",
    "\\ominus" => "⊖",
    "\\otimes" => "⊗",
    "\\oslash" => "⊘",
    "\\odot" => "⊙",
    "\\circledcirc" => "⊚",
    "\\circledast" => "⊛",
    "\\circleddash" => "⊝",
    "\\boxplus" => "⊞",
    "\\boxminus" => "⊟",
    "\\boxtimes" => "⊠",
    "\\boxdot" => "⊡",
    "\\vdash" => "⊢",
    "\\dashv" => "⊣",
    "\\top" => "⊤",
    "\\bot" => "⊥",
    "\\Top" => "⫪",
    "\\Bot" => "⫫",
    "\\indep" => "⫫",
    "\\models" => "⊧",
    "\\vDash" => "⊨",
    "\\downvDash" => "⫪",
    "\\upvDash" => "⫫",
    "\\Vdash" => "⊩",
    "\\Vvdash" => "⊪",
    "\\VDash" => "⊫",
    "\\nvdash" => "⊬",
    "\\nvDash" => "⊭",
    "\\nVdash" => "⊮",
    "\\nVDash" => "⊯",
    "\\vartriangleleft" => "⊲",
    "\\vartriangleright" => "⊳",
    "\\trianglelefteq" => "⊴",
    "\\trianglerighteq" => "⊵",
    "\\original" => "⊶",
    "\\image" => "⊷",
    "\\multimap" => "⊸",
    "\\hermitconjmatrix" => "⊹",
    "\\intercal" => "⊺",
    "\\veebar" => "⊻",
    "\\rightanglearc" => "⊾",
    "\\bigwedge" => "⋀",
    "\\bigvee" => "⋁",
    "\\bigcap" => "⋂",
    "\\bigcup" => "⋃",
    "\\diamond" => "⋄",
    "\\cdot" => "⋅",
    "\\star" => "⋆",
    "\\divideontimes" => "⋇",
    "\\bowtie" => "⋈",
    "\\ltimes" => "⋉",
    "\\rtimes" => "⋊",
    "\\leftthreetimes" => "⋋",
    "\\rightthreetimes" => "⋌",
    "\\backsimeq" => "⋍",
    "\\curlyvee" => "⋎",
    "\\curlywedge" => "⋏",
    "\\Subset" => "⋐",
    "\\Supset" => "⋑",
    "\\Cap" => "⋒",
    "\\Cup" => "⋓",
    "\\pitchfork" => "⋔",
    "\\lessdot" => "⋖",
    "\\gtrdot" => "⋗",
    "\\verymuchless" => "⋘",
    "\\ggg" => "⋙",
    "\\lesseqgtr" => "⋚",
    "\\gtreqless" => "⋛",
    "\\curlyeqprec" => "⋞",
    "\\curlyeqsucc" => "⋟",
    "\\lnsim" => "⋦",
    "\\gnsim" => "⋧",
    "\\precnsim" => "⋨",
    "\\succnsim" => "⋩",
    "\\ntriangleleft" => "⋪",
    "\\ntriangleright" => "⋫",
    "\\ntrianglelefteq" => "⋬",
    "\\ntrianglerighteq" => "⋭",
    "\\vdots" => "⋮",
    "\\cdots" => "⋯",
    "\\adots" => "⋰",
    "\\ddots" => "⋱",
    "\\lceil" => "⌈",
    "\\rceil" => "⌉",
    "\\lfloor" => "⌊",
    "\\rfloor" => "⌋",
    "\\recorder" => "⌕",
    "\\ulcorner" => "⌜",
    "\\urcorner" => "⌝",
    "\\llcorner" => "⌞",
    "\\lrcorner" => "⌟",
    "\\frown" => "⌢",
    "\\smile" => "⌣",
    "\\langle" => "⟨",
    "\\rangle" => "⟩",
    "\\obar" => "⌽",
    "\\dlcorn" => "⎣",
    "\\lmoustache" => "⎰",
    "\\rmoustache" => "⎱",
    "\\visiblespace" => "␣",
    "\\circledS" => "Ⓢ",
    "\\dshfnc" => "┆",
    "\\sqfnw" => "┙",
    "\\diagup" => "╱",
    "\\diagdown" => "╲",
    "\\blacksquare" => "■",
    "\\square" => "□",
    "\\vrecto" => "▯",
    "\\bigtriangleup" => "△",
    "\\blacktriangle" => "▴",
    "\\vartriangle" => "▵",
    "\\bigtriangledown" => "▽",
    "\\blacktriangledown" => "▾",
    "\\triangledown" => "▿",
    "\\lozenge" => "◊",
    "\\bigcirc" => "○",
    "\\cirfl" => "◐",
    "\\cirfr" => "◑",
    "\\cirfb" => "◒",
    "\\rvbull" => "◘",
    "\\sqfl" => "◧",
    "\\sqfr" => "◨",
    "\\sqfse" => "◪",
    "\\bigstar" => "★",
    "\\mercury" => "☿",
    "\\venus" => "♀",
    "\\male" => "♂",
    "\\jupiter" => "♃",
    "\\saturn" => "♄",
    "\\uranus" => "♅",
    "\\neptune" => "♆",
    "\\pluto" => "♇",
    "\\aries" => "♈",
    "\\taurus" => "♉",
    "\\gemini" => "♊",
    "\\cancer" => "♋",
    "\\leo" => "♌",
    "\\virgo" => "♍",
    "\\libra" => "♎",
    "\\scorpio" => "♏",
    "\\sagittarius" => "♐",
    "\\capricornus" => "♑",
    "\\aquarius" => "♒",
    "\\pisces" => "♓",
    "\\spadesuit" => "♠",
    "\\heartsuit" => "♡",
    "\\diamondsuit" => "♢",
    "\\clubsuit" => "♣",
    "\\quarternote" => "♩",
    "\\eighthnote" => "♪",
    "\\flat" => "♭",
    "\\natural" => "♮",
    "\\sharp" => "♯",
    "\\checkmark" => "✓",
    "\\maltese" => "✠",
    "\\longleftarrow" => "⟵",
    "\\longrightarrow" => "⟶",
    "\\longleftrightarrow" => "⟷",
    "\\Longleftarrow" => "⟸",
    "\\Longrightarrow" => "⟹",
    "\\Longleftrightarrow" => "⟺",
    "\\longmapsto" => "⟼",
    "\\Mapsfrom" => "⤆",
    "\\Mapsto" => "⤇",
    "\\Uuparrow" => "⤊",
    "\\Ddownarrow" => "⤋",
    "\\bkarow" => "⤍",
    "\\dbkarow" => "⤏",
    "\\drbkarrow" => "⤐",
    "\\UpArrowBar" => "⤒",
    "\\DownArrowBar" => "⤓",
    "\\twoheadrightarrowtail" => "⤖",
    "\\hksearow" => "⤥",
    "\\hkswarow" => "⤦",
    "\\tona" => "⤧",
    "\\toea" => "⤨",
    "\\tosa" => "⤩",
    "\\towa" => "⤪",
    "\\rdiagovfdiag" => "⤫",
    "\\fdiagovrdiag" => "⤬",
    "\\seovnearrow" => "⤭",
    "\\neovsearrow" => "⤮",
    "\\fdiagovnearrow" => "⤯",
    "\\rdiagovsearrow" => "⤰",
    "\\neovnwarrow" => "⤱",
    "\\nwovnearrow" => "⤲",
    "\\Rlarr" => "⥂",
    "\\rLarr" => "⥄",
    "\\rarrx" => "⥇",
    "\\LeftRightVector" => "⥎",
    "\\RightUpDownVector" => "⥏",
    "\\DownLeftRightVector" => "⥐",
    "\\LeftUpDownVector" => "⥑",
    "\\LeftVectorBar" => "⥒",
    "\\RightVectorBar" => "⥓",
    "\\RightUpVectorBar" => "⥔",
    "\\RightDownVectorBar" => "⥕",
    "\\DownLeftVectorBar" => "⥖",
    "\\DownRightVectorBar" => "⥗",
    "\\LeftUpVectorBar" => "⥘",
    "\\LeftDownVectorBar" => "⥙",
    "\\LeftTeeVector" => "⥚",
    "\\RightTeeVector" => "⥛",
    "\\RightUpTeeVector" => "⥜",
    "\\RightDownTeeVector" => "⥝",
    "\\DownLeftTeeVector" => "⥞",
    "\\DownRightTeeVector" => "⥟",
    "\\LeftUpTeeVector" => "⥠",
    "\\LeftDownTeeVector" => "⥡",
    "\\UpEquilibrium" => "⥮",
    "\\ReverseUpEquilibrium" => "⥯",
    "\\RoundImplies" => "⥰",
    "\\Vvert" => "⦀",
    "\\Elroang" => "⦆",
    "\\ddfnc" => "⦙",
    "\\Angle" => "⦜",
    "\\lpargt" => "⦠",
    "\\obslash" => "⦸",
    "\\boxdiag" => "⧄",
    "\\boxbslash" => "⧅",
    "\\boxast" => "⧆",
    "\\boxcircle" => "⧇",
    "\\Lap" => "⧊",
    "\\defas" => "⧋",
    "\\LeftTriangleBar" => "⧏",
    "\\NotLeftTriangleBar" => "⧏̸",
    "\\RightTriangleBar" => "⧐",
    "\\NotRightTriangleBar" => "⧐̸",
    "\\dualmap" => "⧟",
    "\\shuffle" => "⧢",
    "\\blacklozenge" => "⧫",
    "\\RuleDelayed" => "⧴",
    "\\bigodot" => "⨀",
    "\\bigoplus" => "⨁",
    "\\bigotimes" => "⨂",
    "\\bigcupdot" => "⨃",
    "\\biguplus" => "⨄",
    "\\bigsqcap" => "⨅",
    "\\bigsqcup" => "⨆",
    "\\conjquant" => "⨇",
    "\\disjquant" => "⨈",
    "\\bigtimes" => "⨉",
    "\\iiiint" => "⨌",
    "\\intbar" => "⨍",
    "\\intBar" => "⨎",
    "\\clockoint" => "⨏",
    "\\sqrint" => "⨖",
    "\\intx" => "⨘",
    "\\intcap" => "⨙",
    "\\intcup" => "⨚",
    "\\upint" => "⨛",
    "\\lowint" => "⨜",
    "\\plusdot" => "⨥",
    "\\minusdot" => "⨪",
    "\\Times" => "⨯",
    "\\btimes" => "⨲",
    "\\intprod" => "⨼",
    "\\intprodr" => "⨽",
    "\\amalg" => "⨿",
    "\\And" => "⩓",
    "\\Or" => "⩔",
    "\\ElOr" => "⩖",
    "\\perspcorrespond" => "⩞",
    "\\minhat" => "⩟",
    "\\Equal" => "⩵",
    "\\ddotseq" => "⩷",
    "\\leqslant" => "⩽",
    "\\nleqslant" => "⩽̸",
    "\\geqslant" => "⩾",
    "\\ngeqslant" => "⩾̸",
    "\\lessapprox" => "⪅",
    "\\gtrapprox" => "⪆",
    "\\lneq" => "⪇",
    "\\gneq" => "⪈",
    "\\lnapprox" => "⪉",
    "\\gnapprox" => "⪊",
    "\\lesseqqgtr" => "⪋",
    "\\gtreqqless" => "⪌",
    "\\eqslantless" => "⪕",
    "\\eqslantgtr" => "⪖",
    "\\NestedLessLess" => "⪡",
    "\\NotNestedLessLess" => "⪡̸",
    "\\NestedGreaterGreater" => "⪢",
    "\\NotNestedGreaterGreater" => "⪢̸",
    "\\partialmeetcontraction" => "⪣",
    "\\bumpeqq" => "⪮",
    "\\preceq" => "⪯",
    "\\npreceq" => "⪯̸",
    "\\succeq" => "⪰",
    "\\nsucceq" => "⪰̸",
    "\\precneqq" => "⪵",
    "\\succneqq" => "⪶",
    "\\precapprox" => "⪷",
    "\\succapprox" => "⪸",
    "\\precnapprox" => "⪹",
    "\\succnapprox" => "⪺",
    "\\subseteqq" => "⫅",
    "\\nsubseteqq" => "⫅̸",
    "\\supseteqq" => "⫆",
    "\\nsupseteqq" => "⫆̸",
    "\\subsetneqq" => "⫋",
    "\\supsetneqq" => "⫌",
    "\\mlcp" => "⫛",
    "\\forks" => "⫝̸",
    "\\forksnot" => "⫝",
    "\\dashV" => "⫣",
    "\\Dashv" => "⫤",
    "\\interleave" => "⫴",
    "\\tdcol" => "⫶",
    "\\openbracketleft" => "⟦",
    "\\llbracket" => "⟦",
    "\\openbracketright" => "⟧",
    "\\rrbracket" => "⟧",
    "\\overbrace" => "⏞",
    "\\underbrace" => "⏟",

# 1607 symbols generated from unicode-math-table.tex:
    "\\Zbar" => "Ƶ",  # impedance (latin capital letter z with stroke)
    "\\overbar" => "̅",  # overbar embellishment
    "\\ovhook" => "̉",  # combining hook above
    "\\candra" => "̐",  # candrabindu (non-spacing)
    "\\oturnedcomma" => "̒",  # combining turned comma above
    "\\ocommatopright" => "̕",  # combining comma above right
    "\\droang" => "̚",  # left angle above (non-spacing)
    "\\wideutilde" => "̰",  # under tilde accent (multiple characters and non-spacing)
    "\\not" => "̸",  # combining long solidus overlay
    "\\upMu" => "Μ",  # capital mu, greek
    "\\upNu" => "Ν",  # capital nu, greek
    "\\upOmicron" => "Ο",  # capital omicron, greek
    "\\upepsilon" => "ε",  # rounded small epsilon, greek
    "\\upomicron" => "ο",  # small omicron, greek
    "\\upvarbeta" => "ϐ",  # rounded small beta, greek
    "\\upoldKoppa" => "Ϙ",  # greek letter archaic koppa
    "\\upoldkoppa" => "ϙ",  # greek small letter archaic koppa
    "\\upstigma" => "ϛ",  # greek small letter stigma
    "\\upkoppa" => "ϟ",  # greek small letter koppa
    "\\upsampi" => "ϡ",  # greek small letter sampi
    "\\tieconcat" => "⁀",  # character tie, z notation sequence concatenation
    "\\leftharpoonaccent" => "⃐",  # combining left harpoon above
    "\\rightharpoonaccent" => "⃑",  # combining right harpoon above
    "\\vertoverlay" => "⃒",  # combining long vertical line overlay
    "\\overleftarrow" => "⃖",  # combining left arrow above
    "\\vec" => "⃗",  # combining right arrow above
    "\\enclosecircle" => "⃝",  # combining enclosing circle
    "\\enclosesquare" => "⃞",  # combining enclosing square
    "\\enclosediamond" => "⃟",  # combining enclosing diamond
    "\\overleftrightarrow" => "⃡",  # combining left right arrow above
    "\\enclosetriangle" => "⃤",  # combining enclosing upward pointing triangle
    "\\annuity" => "⃧",  # combining annuity symbol
    "\\threeunderdot" => "⃨",  # combining triple underdot
    "\\widebridgeabove" => "⃩",  # combining wide bridge above
    "\\underrightharpoondown" => "\u20ec",  # combining rightwards harpoon with barb downwards
    "\\underleftharpoondown" => "\u20ed",  # combining leftwards harpoon with barb downwards
    "\\underleftarrow" => "\u20ee",  # combining left arrow below
    "\\underrightarrow" => "\u20ef",  # combining right arrow below
    "\\asteraccent" => "\u20f0",  # combining asterisk above
    blackboard*"C" => "ℂ",  # /bbb c, open face c
    "\\eulermascheroni" => "ℇ",  # euler-mascheroni constant U+2107
    script*"g" => "ℊ",  # /scr g, script letter g
    script*"H" => "ℋ",  # hamiltonian (script capital h)
    frak*"H" => "ℌ",  # /frak h, upper case h
    blackboard*"H" => "ℍ",  # /bbb h, open face h
    "\\planck" => "ℎ",  # planck constant
    script*"I" => "ℐ",  # /scr i, script letter i
    script*"L" => "ℒ",  # lagrangian (script capital l)
    blackboard*"N" => "ℕ",  # /bbb n, open face n
    blackboard*"P" => "ℙ",  # /bbb p, open face p
    blackboard*"Q" => "ℚ",  # /bbb q, open face q
    script*"R" => "ℛ",  # /scr r, script letter r
    blackboard*"R" => "ℝ",  # /bbb r, open face r
    blackboard*"Z" => "ℤ",  # /bbb z, open face z
    frak*"Z" => "ℨ",  # /frak z, upper case z
    "\\turnediota" => "℩",  # turned iota
    "\\Angstrom" => "Å",  # angstrom capital a, ring
    script*"B" => "ℬ",  # bernoulli function (script capital b)
    frak*"C" => "ℭ",  # black-letter capital c
    script*"e" => "ℯ",  # /scr e, script letter e
    script*"E" => "ℰ",  # /scr e, script letter e
    script*"F" => "ℱ",  # /scr f, script letter f
    "\\Finv" => "Ⅎ",  # turned capital f
    script*"M" => "ℳ",  # physics m-matrix (script capital m)
    script*"o" => "ℴ",  # order of (script small o)
    blackboard*"pi" => "\u213c",  # double-struck small pi
    blackboard*"gamma" => "ℽ",  # double-struck small gamma
    blackboard*"Gamma" => "ℾ",  # double-struck capital gamma
    "\\sansLturned" => "⅂",  # turned sans-serif capital l
    "\\sansLmirrored" => "⅃",  # reversed sans-serif capital l
    "\\Yup" => "⅄",  # turned sans-serif capital y
    italicblackboard*"D" => "ⅅ",  # double-struck italic capital d
    italicblackboard*"d" => "ⅆ",  # double-struck italic small d
    italicblackboard*"e" => "ⅇ",  # double-struck italic small e
    italicblackboard*"i" => "ⅈ",  # double-struck italic small i
    italicblackboard*"j" => "ⅉ",  # double-struck italic small j
    "\\PropertyLine" => "⅊",  # property line
    "\\upand" => "⅋",  # turned ampersand
    "\\twoheaduparrow" => "↟",  # up two-headed arrow
    "\\twoheaddownarrow" => "↡",  # down two-headed arrow
    "\\mapsfrom" => "↤",  # maps to, leftward
    "\\mapsup" => "↥",  # maps to, upward
    "\\mapsdown" => "↧",  # maps to, downward
    "\\updownarrowbar" => "↨",  # up down arrow with base (perpendicular)
    "\\downzigzagarrow" => "↯",  # downwards zigzag arrow
    "\\Ldsh" => "↲",  # left down angled arrow
    "\\Rdsh" => "↳",  # right down angled arrow
    "\\linefeed" => "↴",  # rightwards arrow with corner downwards
    "\\carriagereturn" => "↵",  # downwards arrow with corner leftward = carriage return
    "\\barovernorthwestarrow" => "↸",  # north west arrow to long bar
    "\\barleftarrowrightarrowbar" => "↹",  # leftwards arrow to bar over rightwards arrow to bar
    "\\nLeftrightarrow" => "⇎",  # not left and right double arrows
    "\\Nwarrow" => "⇖",  # nw pointing double arrow
    "\\Nearrow" => "⇗",  # ne pointing double arrow
    "\\Searrow" => "⇘",  # se pointing double arrow
    "\\Swarrow" => "⇙",  # sw pointing double arrow
    "\\leftsquigarrow" => "⇜",  # leftwards squiggle arrow
    "\\rightsquigarrow" => "⇝",  # rightwards squiggle arrow
    "\\nHuparrow" => "⇞",  # upwards arrow with double stroke
    "\\nHdownarrow" => "⇟",  # downwards arrow with double stroke
    "\\leftdasharrow" => "⇠",  # leftwards dashed arrow
    "\\updasharrow" => "⇡",  # upwards dashed arrow
    "\\rightdasharrow" => "⇢",  # rightwards dashed arrow
    "\\downdasharrow" => "⇣",  # downwards dashed arrow
    "\\barleftarrow" => "⇤",  # leftwards arrow to bar
    "\\rightarrowbar" => "⇥",  # rightwards arrow to bar
    "\\leftwhitearrow" => "⇦",  # leftwards white arrow
    "\\upwhitearrow" => "⇧",  # upwards white arrow
    "\\rightwhitearrow" => "⇨",  # rightwards white arrow
    "\\downwhitearrow" => "⇩",  # downwards white arrow
    "\\whitearrowupfrombar" => "⇪",  # upwards white arrow from bar
    "\\circleonrightarrow" => "⇴",  # right arrow with small circle
    "\\rightthreearrows" => "⇶",  # three rightwards arrows
    "\\nvleftarrow" => "⇷",  # leftwards arrow with vertical stroke
    "\\nvrightarrow" => "⇸",  # rightwards arrow with vertical stroke
    "\\nvleftrightarrow" => "⇹",  # left right arrow with vertical stroke
    "\\nVleftarrow" => "⇺",  # leftwards arrow with double vertical stroke
    "\\nVrightarrow" => "⇻",  # rightwards arrow with double vertical stroke
    "\\nVleftrightarrow" => "⇼",  # left right arrow with double vertical stroke
    "\\leftrightarrowtriangle" => "⇿",  # left right open-headed arrow
    "\\increment" => "∆",  # laplacian (delta; nabla\string^2)
    "\\smallin" => "∊",  # set membership (small set membership)
    "\\nni" => "∌",  # negated contains, variant
    "\\smallni" => "∍",  # /ni /owns r: contains (small contains as member)
    "\\QED" => "∎",  # end of proof
    "\\vysmblkcircle" => "∙",  # bullet operator
    "\\fourthroot" => "∜",  # fourth root
    "\\varointclockwise" => "∲",  # contour integral, clockwise
    "\\ointctrclockwise" => "∳",  # contour integral, anticlockwise
    "\\dotsminusdots" => "∺",  # minus with four dots, geometric properties
    "\\sinewave" => "∿",  # sine wave
    "\\arceq" => "≘",  # arc, equals; corresponds to
    "\\veeeq" => "≚",  # logical or, equals
    "\\eqdef" => "≝",  # equals by definition
    "\\measeq" => "≞",  # measured by (m over equals)
    "\\Equiv" => "≣",  # strict equivalence (4 lines)
    "\\nasymp" => "≭",  # not asymptotically equal to
    "\\nlesssim" => "≴",  # not less, similar
    "\\ngtrsim" => "≵",  # not greater, similar
    "\\circledequal" => "⊜",  # equal in circle
    "\\prurel" => "⊰",  # element precedes under relation
    "\\scurel" => "⊱",  # succeeds under relation
    "\\barwedge" => "⊼",  # bar, wedge (large wedge)
    "\\barvee" => "⊽",  # bar, vee (large vee)
    "\\varlrtriangle" => "⊿",  # right triangle
    "\\equalparallel" => "⋕",  # parallel, equal; equal or parallel
    "\\eqless" => "⋜",  # equal-or-less
    "\\eqgtr" => "⋝",  # equal-or-greater
    "\\npreccurlyeq" => "⋠",  # not precedes, curly equals
    "\\nsucccurlyeq" => "⋡",  # not succeeds, curly equals
    "\\nsqsubseteq" => "⋢",  # not, square subset, equals
    "\\nsqsupseteq" => "⋣",  # not, square superset, equals
    "\\sqsubsetneq" => "⋤",  # square subset, not equals
    "\\sqsupsetneq" => "⋥",  # square superset, not equals
    "\\disin" => "⋲",  # element of with long horizontal stroke
    "\\varisins" => "⋳",  # element of with vertical bar at end of horizontal stroke
    "\\isins" => "⋴",  # small element of with vertical bar at end of horizontal stroke
    "\\isindot" => "⋵",  # element of with dot above
    "\\varisinobar" => "⋶",  # element of with overbar
    "\\isinobar" => "⋷",  # small element of with overbar
    "\\isinvb" => "⋸",  # element of with underbar
    "\\isinE" => "⋹",  # element of with two horizontal strokes
    "\\nisd" => "⋺",  # contains with long horizontal stroke
    "\\varnis" => "⋻",  # contains with vertical bar at end of horizontal stroke
    "\\nis" => "⋼",  # small contains with vertical bar at end of horizontal stroke
    "\\varniobar" => "⋽",  # contains with overbar
    "\\niobar" => "⋾",  # small contains with overbar
    "\\bagmember" => "⋿",  # z notation bag membership
    "\\diameter" => "⌀",  # diameter sign
    "\\house" => "⌂",  # house
    "\\vardoublebarwedge" => "⌆",  # /doublebarwedge b: logical and, double bar above [perspective (double bar over small wedge)]
    "\\invnot" => "⌐",  # reverse not
    "\\sqlozenge" => "⌑",  # square lozenge
    "\\profline" => "⌒",  # profile of a line
    "\\profsurf" => "⌓",  # profile of a surface
    "\\viewdata" => "⌗",  # viewdata square
    "\\turnednot" => "⌙",  # turned not sign
    "\\varhexagonlrbonds" => "⌬",  # six carbon ring, corner down, double bonds lower right etc
    "\\conictaper" => "⌲",  # conical taper
    "\\topbot" => "⌶",  # top and bottom
    "\\notslash" => "⌿",  # solidus, bar through (apl functional symbol slash bar)
    "\\notbackslash" => "⍀",  # apl functional symbol backslash bar
    "\\boxupcaret" => "⍓",  # boxed up caret
    "\\boxquestion" => "⍰",  # boxed question mark
    "\\hexagon" => "⎔",  # horizontal benzene ring [hexagon flat open]
    "\\overbracket" => "⎴",  # top square bracket
    "\\underbracket" => "⎵",  # bottom square bracket
    "\\bbrktbrk" => "⎶",  # bottom square bracket over top square bracket
    "\\sqrtbottom" => "⎷",  # radical symbol bottom
    "\\lvboxline" => "⎸",  # left vertical box line
    "\\rvboxline" => "⎹",  # right vertical box line
    "\\varcarriagereturn" => "⏎",  # return symbol
    "\\trapezium" => "\u23e2",  # white trapezium
    "\\benzenr" => "\u23e3",  # benzene ring with circle
    "\\strns" => "\u23e4",  # straightness
    "\\fltns" => "\u23e5",  # flatness
    "\\accurrent" => "\u23e6",  # ac current
    "\\elinters" => "\u23e7",  # electrical intersection
    "\\blanksymbol" => "␢",  # blank symbol
    "\\blockuphalf" => "▀",  # upper half block
    "\\blocklowhalf" => "▄",  # lower half block
    "\\blockfull" => "█",  # full block
    "\\blocklefthalf" => "▌",  # left half block
    "\\blockrighthalf" => "▐",  # right half block
    "\\blockqtrshaded" => "░",  # 25\% shaded block
    "\\blockhalfshaded" => "▒",  # 50\% shaded block
    "\\blockthreeqtrshaded" => "▓",  # 75\% shaded block
    "\\squoval" => "▢",  # white square with rounded corners
    "\\blackinwhitesquare" => "▣",  # white square containing black small square
    "\\squarehfill" => "▤",  # square, horizontal rule filled
    "\\squarevfill" => "▥",  # square, vertical rule filled
    "\\squarehvfill" => "▦",  # square with orthogonal crosshatch fill
    "\\squarenwsefill" => "▧",  # square, nw-to-se rule filled
    "\\squareneswfill" => "▨",  # square, ne-to-sw rule filled
    "\\squarecrossfill" => "▩",  # square with diagonal crosshatch fill
    "\\smblksquare" => "▪",  # /blacksquare - sq bullet, filled
    "\\smwhtsquare" => "▫",  # white small square
    "\\hrectangleblack" => "▬",  # black rectangle
    "\\hrectangle" => "▭",  # horizontal rectangle, open
    "\\vrectangleblack" => "▮",  # black vertical rectangle
    "\\parallelogramblack" => "▰",  # black parallelogram
    "\\parallelogram" => "▱",  # parallelogram, open
    "\\bigblacktriangleup" => "▲",  #    0x25b2 6 6d      black up-pointing triangle
    "\\blacktriangleright" => "▶",  # (large) right triangle, filled
    "\\blackpointerright" => "►",  # black right-pointing pointer
    "\\whitepointerright" => "▻",  # white right-pointing pointer
    "\\bigblacktriangledown" => "▼",  # big down triangle, filled
    "\\blacktriangleleft" => "◀",  # (large) left triangle, filled
    "\\blackpointerleft" => "◄",  # black left-pointing pointer
    "\\whitepointerleft" => "◅",  # white left-pointing pointer
    "\\mdlgblkdiamond" => "◆",  # black diamond
    "\\mdlgwhtdiamond" => "◇",  # white diamond; diamond, open
    "\\blackinwhitediamond" => "◈",  # white diamond containing black small diamond
    "\\fisheye" => "◉",  # fisheye
    "\\dottedcircle" => "◌",  # dotted circle
    "\\circlevertfill" => "◍",  # circle with vertical fill
    "\\bullseye" => "◎",  # bullseye
    "\\mdlgblkcircle" => "●",  # circle, filled
    "\\circletophalfblack" => "◓",  # circle, filled top half
    "\\circleurquadblack" => "◔",  # circle with upper right quadrant black
    "\\blackcircleulquadwhite" => "◕",  # circle with all but upper left quadrant black
    "\\blacklefthalfcircle" => "◖",  # left half black circle
    "\\blackrighthalfcircle" => "◗",  # right half black circle
    "\\inversewhitecircle" => "◙",  # inverse white circle
    "\\invwhiteupperhalfcircle" => "◚",  # upper half inverse white circle
    "\\invwhitelowerhalfcircle" => "◛",  # lower half inverse white circle
    "\\ularc" => "◜",  # upper left quadrant circular arc
    "\\urarc" => "◝",  # upper right quadrant circular arc
    "\\lrarc" => "◞",  # lower right quadrant circular arc
    "\\llarc" => "◟",  # lower left quadrant circular arc
    "\\topsemicircle" => "◠",  # upper half circle
    "\\botsemicircle" => "◡",  # lower half circle
    "\\lrblacktriangle" => "◢",  # lower right triangle, filled
    "\\llblacktriangle" => "◣",  # lower left triangle, filled
    "\\ulblacktriangle" => "◤",  # upper left triangle, filled
    "\\urblacktriangle" => "◥",  # upper right triangle, filled
    "\\smwhtcircle" => "◦",  # white bullet
    "\\squareulblack" => "◩",  # square, filled top left corner
    "\\boxbar" => "◫",  # vertical bar in box
    "\\trianglecdot" => "◬",  # triangle with centered dot
    "\\triangleleftblack" => "◭",  # up-pointing triangle with left half black
    "\\trianglerightblack" => "◮",  # up-pointing triangle with right half black
    "\\lgwhtcircle" => "◯",  # large circle
    "\\squareulquad" => "◰",  # white square with upper left quadrant
    "\\squarellquad" => "◱",  # white square with lower left quadrant
    "\\squarelrquad" => "◲",  # white square with lower right quadrant
    "\\squareurquad" => "◳",  # white square with upper right quadrant
    "\\circleulquad" => "◴",  # white circle with upper left quadrant
    "\\circlellquad" => "◵",  # white circle with lower left quadrant
    "\\circlelrquad" => "◶",  # white circle with lower right quadrant
    "\\circleurquad" => "◷",  # white circle with upper right quadrant
    "\\ultriangle" => "◸",  # upper left triangle
    "\\urtriangle" => "◹",  # upper right triangle
    "\\lltriangle" => "◺",  # lower left triangle
    "\\mdwhtsquare" => "◻",  # white medium square
    "\\mdblksquare" => "◼",  # black medium square
    "\\mdsmwhtsquare" => "◽",  # white medium small square
    "\\mdsmblksquare" => "◾",  # black medium small square
    "\\lrtriangle" => "◿",  # lower right triangle
    "\\bigwhitestar" => "☆",  # star, open
    "\\astrosun" => "☉",  # sun
    "\\danger" => "☡",  # dangerous bend (caution sign)
    "\\blacksmiley" => "☻",  # black smiling face
    "\\sun" => "☼",  # white sun with rays
    "\\rightmoon" => "☽",  # first quarter moon
    "\\varspadesuit" => "♤",  # spade, white (card suit)
    "\\varheartsuit" => "♥",  # filled heart (card suit)
    "\\vardiamondsuit" => "♦",  # filled diamond (card suit)
    "\\varclubsuit" => "♧",  # club, white (card suit)
    "\\twonotes" => "♫",  # beamed eighth notes
    "\\acidfree" => "\u267e",  # permanent paper sign
    "\\dicei" => "⚀",  # die face-1
    "\\diceii" => "⚁",  # die face-2
    "\\diceiii" => "⚂",  # die face-3
    "\\diceiv" => "⚃",  # die face-4
    "\\dicev" => "⚄",  # die face-5
    "\\dicevi" => "⚅",  # die face-6
    "\\circledrightdot" => "⚆",  # white circle with dot right
    "\\circledtwodots" => "⚇",  # white circle with two dots
    "\\blackcircledrightdot" => "⚈",  # black circle with white dot right
    "\\blackcircledtwodots" => "⚉",  # black circle with two white dots
    "\\hermaphrodite" => "\u26a5",  # male and female sign
    "\\mdwhtcircle" => "\u26aa",  # medium white circle
    "\\mdblkcircle" => "\u26ab",  # medium black circle
    "\\mdsmwhtcircle" => "\u26ac",  # medium small white circle
    "\\neuter" => "\u26b2",  # neuter
    "\\circledstar" => "✪",  # circled white star
    "\\varstar" => "✶",  # six pointed black star
    "\\dingasterisk" => "✽",  # heavy teardrop-spoked asterisk
    "\\draftingarrow" => "➛",  # right arrow with bold head (drafting)
    "\\threedangle" => "\u27c0",  # three dimensional angle
    "\\whiteinwhitetriangle" => "\u27c1",  # white triangle containing small white triangle
    "\\perp" => "\u27c2",  # perpendicular
    "\\bsolhsub" => "\u27c8",  # reverse solidus preceding subset
    "\\suphsol" => "\u27c9",  # superset preceding solidus
    "\\wedgedot" => "⟑",  # and with dot
    "\\veedot" => "⟇",  # or with dot
    "\\upin" => "⟒",  # element of opening upwards
    "\\bigbot" => "⟘",  # large up tack
    "\\bigtop" => "⟙",  # large down tack
    "\\UUparrow" => "⟰",  # upwards quadruple arrow
    "\\DDownarrow" => "⟱",  # downwards quadruple arrow
    "\\longmapsfrom" => "⟻",  # long leftwards arrow from bar
    "\\Longmapsfrom" => "⟽",  # long leftwards double arrow from bar
    "\\Longmapsto" => "⟾",  # long rightwards double arrow from bar
    "\\longrightsquigarrow" => "⟿",  # long rightwards squiggle arrow
    "\\nvtwoheadrightarrow" => "⤀",  # rightwards two-headed arrow with vertical stroke
    "\\nVtwoheadrightarrow" => "⤁",  # rightwards two-headed arrow with double vertical stroke
    "\\nvLeftarrow" => "⤂",  # leftwards double arrow with vertical stroke
    "\\nvRightarrow" => "⤃",  # rightwards double arrow with vertical stroke
    "\\nvLeftrightarrow" => "⤄",  # left right double arrow with vertical stroke
    "\\twoheadmapsto" => "⤅",  # rightwards two-headed arrow from bar
    "\\downarrowbarred" => "⤈",  # downwards arrow with horizontal stroke
    "\\uparrowbarred" => "⤉",  # upwards arrow with horizontal stroke
    "\\leftbkarrow" => "⤌",  # leftwards double dash arrow
    "\\leftdbkarrow" => "⤎",  # leftwards triple dash arrow
    "\\rightdotarrow" => "⤑",  # rightwards arrow with dotted stem
    "\\nvrightarrowtail" => "⤔",  # rightwards arrow with tail with vertical stroke
    "\\nVrightarrowtail" => "⤕",  # rightwards arrow with tail with double vertical stroke
    "\\nvtwoheadrightarrowtail" => "⤗",  # rightwards two-headed arrow with tail with vertical stroke
    "\\nVtwoheadrightarrowtail" => "⤘",  # rightwards two-headed arrow with tail with double vertical stroke
    "\\diamondleftarrow" => "⤝",  # leftwards arrow to black diamond
    "\\rightarrowdiamond" => "⤞",  # rightwards arrow to black diamond
    "\\diamondleftarrowbar" => "⤟",  # leftwards arrow from bar to black diamond
    "\\barrightarrowdiamond" => "⤠",  # rightwards arrow from bar to black diamond
    "\\rightarrowplus" => "⥅",  # rightwards arrow with plus below
    "\\leftarrowplus" => "⥆",  # leftwards arrow with plus below
    "\\leftrightarrowcircle" => "⥈",  # left right arrow through small circle
    "\\twoheaduparrowcircle" => "⥉",  # upwards two-headed arrow from small circle
    "\\leftrightharpoonupdown" => "⥊",  # left barb up right barb down harpoon
    "\\leftrightharpoondownup" => "⥋",  # left barb down right barb up harpoon
    "\\updownharpoonrightleft" => "⥌",  # up barb right down barb left harpoon
    "\\updownharpoonleftright" => "⥍",  # up barb left down barb right harpoon
    "\\leftharpoonsupdown" => "⥢",  # leftwards harpoon with barb up above leftwards harpoon with barb down
    "\\upharpoonsleftright" => "⥣",  # upwards harpoon with barb left beside upwards harpoon with barb right
    "\\rightharpoonsupdown" => "⥤",  # rightwards harpoon with barb up above rightwards harpoon with barb down
    "\\downharpoonsleftright" => "⥥",  # downwards harpoon with barb left beside downwards harpoon with barb right
    "\\leftrightharpoonsup" => "⥦",  # leftwards harpoon with barb up above rightwards harpoon with barb up
    "\\leftrightharpoonsdown" => "⥧",  # leftwards harpoon with barb down above rightwards harpoon with barb down
    "\\rightleftharpoonsup" => "⥨",  # rightwards harpoon with barb up above leftwards harpoon with barb up
    "\\rightleftharpoonsdown" => "⥩",  # rightwards harpoon with barb down above leftwards harpoon with barb down
    "\\leftharpoonupdash" => "⥪",  # leftwards harpoon with barb up above long dash
    "\\dashleftharpoondown" => "⥫",  # leftwards harpoon with barb down below long dash
    "\\rightharpoonupdash" => "⥬",  # rightwards harpoon with barb up above long dash
    "\\dashrightharpoondown" => "⥭",  # rightwards harpoon with barb down below long dash
    "\\measuredangleleft" => "⦛",  # measured angle opening left
    "\\rightanglemdot" => "⦝",  # measured right angle with dot
    "\\angles" => "⦞",  # angle with s inside
    "\\angdnr" => "⦟",  # acute angle
    "\\sphericalangleup" => "⦡",  # spherical angle opening up
    "\\turnangle" => "⦢",  # turned angle
    "\\revangle" => "⦣",  # reversed angle
    "\\angleubar" => "⦤",  # angle with underbar
    "\\revangleubar" => "⦥",  # reversed angle with underbar
    "\\wideangledown" => "⦦",  # oblique angle opening up
    "\\wideangleup" => "⦧",  # oblique angle opening down
    "\\measanglerutone" => "⦨",  # measured angle with open arm ending in arrow pointing up and right
    "\\measanglelutonw" => "⦩",  # measured angle with open arm ending in arrow pointing up and left
    "\\measanglerdtose" => "⦪",  # measured angle with open arm ending in arrow pointing down and right
    "\\measangleldtosw" => "⦫",  # measured angle with open arm ending in arrow pointing down and left
    "\\measangleurtone" => "⦬",  # measured angle with open arm ending in arrow pointing right and up
    "\\measangleultonw" => "⦭",  # measured angle with open arm ending in arrow pointing left and up
    "\\measangledrtose" => "⦮",  # measured angle with open arm ending in arrow pointing right and down
    "\\measangledltosw" => "⦯",  # measured angle with open arm ending in arrow pointing left and down
    "\\revemptyset" => "⦰",  # reversed empty set
    "\\emptysetobar" => "⦱",  # empty set with overbar
    "\\emptysetocirc" => "⦲",  # empty set with small circle above
    "\\emptysetoarr" => "⦳",  # empty set with right arrow above
    "\\emptysetoarrl" => "⦴",  # empty set with left arrow above
    "\\circledparallel" => "⦷",  # circled parallel
    "\\odotslashdot" => "⦼",  # circled anticlockwise-rotated division sign
    "\\circledwhitebullet" => "⦾",  # circled white bullet
    "\\circledbullet" => "⦿",  # circled bullet
    "\\olessthan" => "⧀",  # circled less-than
    "\\ogreaterthan" => "⧁",  # circled greater-than
    "\\lrtriangleeq" => "⧡",  # increases as
    "\\eparsl" => "⧣",  # equals sign and slanted parallel
    "\\smeparsl" => "⧤",  # equals sign and slanted parallel with tilde above
    "\\eqvparsl" => "⧥",  # identical to and slanted parallel
    "\\dsol" => "⧶",  # solidus with overbar
    "\\rsolbar" => "⧷",  # reverse solidus with horizontal stroke
    "\\doubleplus" => "⧺",  # double plus
    "\\tripleplus" => "⧻",  # triple plus
    "\\modtwosum" => "⨊",  # modulo two sum
    "\\sumint" => "⨋",  # summation with integral
    "\\cirfnint" => "⨐",  # circulation function
    "\\awint" => "⨑",  # anticlockwise integration
    "\\rppolint" => "⨒",  # line integration with rectangular path around pole
    "\\scpolint" => "⨓",  # line integration with semicircular path around pole
    "\\npolint" => "⨔",  # line integration not including the pole
    "\\pointint" => "⨕",  # integral around a point operator
    "\\ringplus" => "⨢",  # plus sign with small circle above
    "\\plushat" => "⨣",  # plus sign with circumflex accent above
    "\\simplus" => "⨤",  # plus sign with tilde above
    "\\plussim" => "⨦",  # plus sign with tilde below
    "\\plussubtwo" => "⨧",  # plus sign with subscript two
    "\\plustrif" => "⨨",  # plus sign with black triangle
    "\\commaminus" => "⨩",  # minus sign with comma above
    "\\minusfdots" => "⨫",  # minus sign with falling dots
    "\\minusrdots" => "⨬",  # minus sign with rising dots
    "\\opluslhrim" => "⨭",  # plus sign in left half circle
    "\\oplusrhrim" => "⨮",  # plus sign in right half circle
    "\\dottimes" => "⨰",  # multiplication sign with dot above
    "\\timesbar" => "⨱",  # multiplication sign with underbar
    "\\smashtimes" => "⨳",  # smash product
    "\\otimeslhrim" => "⨴",  # multiplication sign in left half circle
    "\\otimesrhrim" => "⨵",  # multiplication sign in right half circle
    "\\otimeshat" => "⨶",  # circled multiplication sign with circumflex accent
    "\\Otimes" => "⨷",  # multiplication sign in double circle
    "\\odiv" => "⨸",  # circled division sign
    "\\triangleplus" => "⨹",  # plus sign in triangle
    "\\triangleminus" => "⨺",  # minus sign in triangle
    "\\triangletimes" => "⨻",  # multiplication sign in triangle
    "\\capdot" => "⩀",  # intersection with dot
    "\\uminus" => "⩁",  # union with minus sign
    "\\barcup" => "⩂",  # union with overbar
    "\\barcap" => "⩃",  # intersection with overbar
    "\\capwedge" => "⩄",  # intersection with logical and
    "\\cupvee" => "⩅",  # union with logical or
    "\\twocups" => "⩊",  # union beside and joined with union
    "\\twocaps" => "⩋",  # intersection beside and joined with intersection
    "\\closedvarcup" => "⩌",  # closed union with serifs
    "\\closedvarcap" => "⩍",  # closed intersection with serifs
    "\\Sqcap" => "⩎",  # double square intersection
    "\\Sqcup" => "⩏",  # double square union
    "\\closedvarcupsmashprod" => "⩐",  # closed union with serifs and smash product
    "\\wedgeodot" => "⩑",  # logical and with dot above
    "\\veeodot" => "⩒",  # logical or with dot above
    "\\wedgeonwedge" => "⩕",  # two intersecting logical and
    "\\bigslopedvee" => "⩗",  # sloping large or
    "\\bigslopedwedge" => "⩘",  # sloping large and
    "\\wedgemidvert" => "⩚",  # logical and with middle stem
    "\\veemidvert" => "⩛",  # logical or with middle stem
    "\\midbarwedge" => "⩜",  # ogical and with horizontal dash
    "\\midbarvee" => "⩝",  # logical or with horizontal dash
    "\\wedgedoublebar" => "⩠",  # logical and with double underbar
    "\\varveebar" => "⩡",  # small vee with underbar
    "\\doublebarvee" => "⩢",  # logical or with double overbar
    "\\veedoublebar" => "⩣",  # logical or with double underbar
    "\\eqdot" => "⩦",  # equals sign with dot below
    "\\dotequiv" => "⩧",  # identical with dot above
    "\\dotsim" => "⩪",  # tilde operator with dot above
    "\\simrdots" => "⩫",  # tilde operator with rising dots
    "\\simminussim" => "⩬",  # similar minus similar
    "\\congdot" => "⩭",  # congruent with dot above
    "\\asteq" => "⩮",  # equals with asterisk
    "\\hatapprox" => "⩯",  # almost equal to with circumflex accent
    "\\approxeqq" => "⩰",  # approximately equal or equal to
    "\\eqqplus" => "⩱",  # equals sign above plus sign
    "\\pluseqq" => "⩲",  # plus sign above equals sign
    "\\eqqsim" => "⩳",  # equals sign above tilde operator
    "\\Coloneq" => "⩴",  # double colon equal
    "\\eqeqeq" => "⩶",  # three consecutive equals signs
    "\\equivDD" => "⩸",  # equivalent with four dots above
    "\\ltcir" => "⩹",  # less-than with circle inside
    "\\gtcir" => "⩺",  # greater-than with circle inside
    "\\ltquest" => "⩻",  # less-than with question mark above
    "\\gtquest" => "⩼",  # greater-than with question mark above
    "\\lesdot" => "⩿",  # less-than or slanted equal to with dot inside
    "\\gesdot" => "⪀",  # greater-than or slanted equal to with dot inside
    "\\lesdoto" => "⪁",  # less-than or slanted equal to with dot above
    "\\gesdoto" => "⪂",  # greater-than or slanted equal to with dot above
    "\\lesdotor" => "⪃",  # less-than or slanted equal to with dot above right
    "\\gesdotol" => "⪄",  # greater-than or slanted equal to with dot above left
    "\\lsime" => "⪍",  # less-than above similar or equal
    "\\gsime" => "⪎",  # greater-than above similar or equal
    "\\lsimg" => "⪏",  # less-than above similar above greater-than
    "\\gsiml" => "⪐",  # greater-than above similar above less-than
    "\\lgE" => "⪑",  # less-than above greater-than above double-line equal
    "\\glE" => "⪒",  # greater-than above less-than above double-line equal
    "\\lesges" => "⪓",  # less-than above slanted equal above greater-than above slanted equal
    "\\gesles" => "⪔",  # greater-than above slanted equal above less-than above slanted equal
    "\\elsdot" => "⪗",  # slanted equal to or less-than with dot inside
    "\\egsdot" => "⪘",  # slanted equal to or greater-than with dot inside
    "\\eqqless" => "⪙",  # double-line equal to or less-than
    "\\eqqgtr" => "⪚",  # double-line equal to or greater-than
    "\\eqqslantless" => "⪛",  # double-line slanted equal to or less-than
    "\\eqqslantgtr" => "⪜",  # double-line slanted equal to or greater-than
    "\\simless" => "⪝",  # similar or less-than
    "\\simgtr" => "⪞",  # similar or greater-than
    "\\simlE" => "⪟",  # similar above less-than above equals sign
    "\\simgE" => "⪠",  # similar above greater-than above equals sign
    "\\glj" => "⪤",  # greater-than overlapping less-than
    "\\gla" => "⪥",  # greater-than beside less-than
    "\\ltcc" => "⪦",  # less-than closed by curve
    "\\gtcc" => "⪧",  # greater-than closed by curve
    "\\lescc" => "⪨",  # less-than closed by curve above slanted equal
    "\\gescc" => "⪩",  # greater-than closed by curve above slanted equal
    "\\smt" => "⪪",  # smaller than
    "\\lat" => "⪫",  # larger than
    "\\smte" => "⪬",  # smaller than or equal to
    "\\late" => "⪭",  # larger than or equal to
    "\\precneq" => "⪱",  # precedes above single-line not equal to
    "\\succneq" => "⪲",  # succeeds above single-line not equal to
    "\\preceqq" => "⪳",  # precedes above equals sign
    "\\succeqq" => "⪴",  # succeeds above equals sign
    "\\Prec" => "⪻",  # double precedes
    "\\Succ" => "⪼",  # double succeeds
    "\\subsetdot" => "⪽",  # subset with dot
    "\\supsetdot" => "⪾",  # superset with dot
    "\\subsetplus" => "⪿",  # subset with plus sign below
    "\\supsetplus" => "⫀",  # superset with plus sign below
    "\\submult" => "⫁",  # subset with multiplication sign below
    "\\supmult" => "⫂",  # superset with multiplication sign below
    "\\subedot" => "⫃",  # subset of or equal to with dot above
    "\\supedot" => "⫄",  # superset of or equal to with dot above
    "\\subsim" => "⫇",  # subset of above tilde operator
    "\\supsim" => "⫈",  # superset of above tilde operator
    "\\subsetapprox" => "⫉",  # subset of above almost equal to
    "\\supsetapprox" => "⫊",  # superset of above almost equal to
    "\\lsqhook" => "⫍",  # square left open box operator
    "\\rsqhook" => "⫎",  # square right open box operator
    "\\csub" => "⫏",  # closed subset
    "\\csup" => "⫐",  # closed superset
    "\\csube" => "⫑",  # closed subset or equal to
    "\\csupe" => "⫒",  # closed superset or equal to
    "\\subsup" => "⫓",  # subset above superset
    "\\supsub" => "⫔",  # superset above subset
    "\\subsub" => "⫕",  # subset above subset
    "\\supsup" => "⫖",  # superset above superset
    "\\suphsub" => "⫗",  # superset beside subset
    "\\supdsub" => "⫘",  # superset beside and joined by dash with subset
    "\\forkv" => "⫙",  # element of opening downwards
    "\\lllnest" => "⫷",  # stacked very much less-than
    "\\gggnest" => "⫸",  # stacked very much greater-than
    "\\leqqslant" => "⫹",  # double-line slanted less-than or equal to
    "\\geqqslant" => "⫺",  # double-line slanted greater-than or equal to
    "\\squaretopblack" => "\u2b12",  # square with top half black
    "\\squarebotblack" => "\u2b13",  # square with bottom half black
    "\\squareurblack" => "\u2b14",  # square with upper right diagonal half black
    "\\squarellblack" => "\u2b15",  # square with lower left diagonal half black
    "\\diamondleftblack" => "\u2b16",  # diamond with left half black
    "\\diamondrightblack" => "\u2b17",  # diamond with right half black
    "\\diamondtopblack" => "\u2b18",  # diamond with top half black
    "\\diamondbotblack" => "\u2b19",  # diamond with bottom half black
    "\\dottedsquare" => "\u2b1a",  # dotted square
    "\\lgblksquare" => "\u2b1b",  # black large square
    "\\lgwhtsquare" => "\u2b1c",  # white large square
    "\\vysmblksquare" => "\u2b1d",  # black very small square
    "\\vysmwhtsquare" => "\u2b1e",  # white very small square
    "\\pentagonblack" => "\u2b1f",  # black pentagon
    "\\pentagon" => "\u2b20",  # white pentagon
    "\\varhexagon" => "\u2b21",  # white hexagon
    "\\varhexagonblack" => "\u2b22",  # black hexagon
    "\\hexagonblack" => "\u2b23",  # horizontal black hexagon
    "\\lgblkcircle" => "\u2b24",  # black large circle
    "\\mdblkdiamond" => "\u2b25",  # black medium diamond
    "\\mdwhtdiamond" => "\u2b26",  # white medium diamond
    "\\mdblklozenge" => "\u2b27",  # black medium lozenge
    "\\mdwhtlozenge" => "\u2b28",  # white medium lozenge
    "\\smblkdiamond" => "\u2b29",  # black small diamond
    "\\smblklozenge" => "\u2b2a",  # black small lozenge
    "\\smwhtlozenge" => "\u2b2b",  # white small lozenge
    "\\blkhorzoval" => "\u2b2c",  # black horizontal ellipse
    "\\whthorzoval" => "\u2b2d",  # white horizontal ellipse
    "\\blkvertoval" => "\u2b2e",  # black vertical ellipse
    "\\whtvertoval" => "\u2b2f",  # white vertical ellipse
    "\\circleonleftarrow" => "\u2b30",  # left arrow with small circle
    "\\leftthreearrows" => "\u2b31",  # three leftwards arrows
    "\\leftarrowonoplus" => "\u2b32",  # left arrow with circled plus
    "\\longleftsquigarrow" => "\u2b33",  # long leftwards squiggle arrow
    "\\nvtwoheadleftarrow" => "\u2b34",  # leftwards two-headed arrow with vertical stroke
    "\\nVtwoheadleftarrow" => "\u2b35",  # leftwards two-headed arrow with double vertical stroke
    "\\twoheadmapsfrom" => "\u2b36",  # leftwards two-headed arrow from bar
    "\\twoheadleftdbkarrow" => "\u2b37",  # leftwards two-headed triple-dash arrow
    "\\leftdotarrow" => "\u2b38",  # leftwards arrow with dotted stem
    "\\nvleftarrowtail" => "\u2b39",  # leftwards arrow with tail with vertical stroke
    "\\nVleftarrowtail" => "\u2b3a",  # leftwards arrow with tail with double vertical stroke
    "\\twoheadleftarrowtail" => "\u2b3b",  # leftwards two-headed arrow with tail
    "\\nvtwoheadleftarrowtail" => "\u2b3c",  # leftwards two-headed arrow with tail with vertical stroke
    "\\nVtwoheadleftarrowtail" => "\u2b3d",  # leftwards two-headed arrow with tail with double vertical stroke
    "\\leftarrowx" => "\u2b3e",  # leftwards arrow through x
    "\\leftcurvedarrow" => "\u2b3f",  # wave arrow pointing directly left
    "\\equalleftarrow" => "\u2b40",  # equals sign above leftwards arrow
    "\\bsimilarleftarrow" => "\u2b41",  # reverse tilde operator above leftwards arrow
    "\\leftarrowbackapprox" => "\u2b42",  # leftwards arrow above reverse almost equal to
    "\\rightarrowgtr" => "\u2b43",  # rightwards arrow through greater-than
    "\\leftarrowless" => "\u2977",  # leftwards arrow through less-than
    "\\rightarrowsupset" => "\u2b44",  # rightwards arrow through superset
    "\\leftarrowsubset" => "\u297a",  # leftwards arrow through subset
    "\\LLeftarrow" => "\u2b45",  # leftwards quadruple arrow
    "\\RRightarrow" => "\u2b46",  # rightwards quadruple arrow
    "\\bsimilarrightarrow" => "\u2b47",  # reverse tilde operator above rightwards arrow
    "\\rightarrowbackapprox" => "\u2b48",  # rightwards arrow above reverse almost equal to
    "\\similarleftarrow" => "\u2b49",  # tilde operator above leftwards arrow
    "\\leftarrowapprox" => "\u2b4a",  # leftwards arrow above almost equal to
    "\\leftarrowbsimilar" => "\u2b4b",  # leftwards arrow above reverse tilde operator
    "\\rightarrowbsimilar" => "\u2b4c",  # righttwards arrow above reverse tilde operator
    "\\medwhitestar" => "\u2b50",  # white medium star
    "\\medblackstar" => "\u2b51",  # black medium star
    "\\smwhitestar" => "\u2b52",  # white small star
    "\\rightpentagonblack" => "\u2b53",  # black right-pointing pentagon
    "\\rightpentagon" => "\u2b54",  # white right-pointing pentagon
    "\\postalmark" => "〒",  # postal mark
    bold*"A" => "𝐀",  # mathematical bold capital a
    bold*"B" => "𝐁",  # mathematical bold capital b
    bold*"C" => "𝐂",  # mathematical bold capital c
    bold*"D" => "𝐃",  # mathematical bold capital d
    bold*"E" => "𝐄",  # mathematical bold capital e
    bold*"F" => "𝐅",  # mathematical bold capital f
    bold*"G" => "𝐆",  # mathematical bold capital g
    bold*"H" => "𝐇",  # mathematical bold capital h
    bold*"I" => "𝐈",  # mathematical bold capital i
    bold*"J" => "𝐉",  # mathematical bold capital j
    bold*"K" => "𝐊",  # mathematical bold capital k
    bold*"L" => "𝐋",  # mathematical bold capital l
    bold*"M" => "𝐌",  # mathematical bold capital m
    bold*"N" => "𝐍",  # mathematical bold capital n
    bold*"O" => "𝐎",  # mathematical bold capital o
    bold*"P" => "𝐏",  # mathematical bold capital p
    bold*"Q" => "𝐐",  # mathematical bold capital q
    bold*"R" => "𝐑",  # mathematical bold capital r
    bold*"S" => "𝐒",  # mathematical bold capital s
    bold*"T" => "𝐓",  # mathematical bold capital t
    bold*"U" => "𝐔",  # mathematical bold capital u
    bold*"V" => "𝐕",  # mathematical bold capital v
    bold*"W" => "𝐖",  # mathematical bold capital w
    bold*"X" => "𝐗",  # mathematical bold capital x
    bold*"Y" => "𝐘",  # mathematical bold capital y
    bold*"Z" => "𝐙",  # mathematical bold capital z
    bold*"a" => "𝐚",  # mathematical bold small a
    bold*"b" => "𝐛",  # mathematical bold small b
    bold*"c" => "𝐜",  # mathematical bold small c
    bold*"d" => "𝐝",  # mathematical bold small d
    bold*"e" => "𝐞",  # mathematical bold small e
    bold*"f" => "𝐟",  # mathematical bold small f
    bold*"g" => "𝐠",  # mathematical bold small g
    bold*"h" => "𝐡",  # mathematical bold small h
    bold*"i" => "𝐢",  # mathematical bold small i
    bold*"j" => "𝐣",  # mathematical bold small j
    bold*"k" => "𝐤",  # mathematical bold small k
    bold*"l" => "𝐥",  # mathematical bold small l
    bold*"m" => "𝐦",  # mathematical bold small m
    bold*"n" => "𝐧",  # mathematical bold small n
    bold*"o" => "𝐨",  # mathematical bold small o
    bold*"p" => "𝐩",  # mathematical bold small p
    bold*"q" => "𝐪",  # mathematical bold small q
    bold*"r" => "𝐫",  # mathematical bold small r
    bold*"s" => "𝐬",  # mathematical bold small s
    bold*"t" => "𝐭",  # mathematical bold small t
    bold*"u" => "𝐮",  # mathematical bold small u
    bold*"v" => "𝐯",  # mathematical bold small v
    bold*"w" => "𝐰",  # mathematical bold small w
    bold*"x" => "𝐱",  # mathematical bold small x
    bold*"y" => "𝐲",  # mathematical bold small y
    bold*"z" => "𝐳",  # mathematical bold small z
    italic*"A" => "𝐴",  # mathematical italic capital a
    italic*"B" => "𝐵",  # mathematical italic capital b
    italic*"C" => "𝐶",  # mathematical italic capital c
    italic*"D" => "𝐷",  # mathematical italic capital d
    italic*"E" => "𝐸",  # mathematical italic capital e
    italic*"F" => "𝐹",  # mathematical italic capital f
    italic*"G" => "𝐺",  # mathematical italic capital g
    italic*"H" => "𝐻",  # mathematical italic capital h
    italic*"I" => "𝐼",  # mathematical italic capital i
    italic*"J" => "𝐽",  # mathematical italic capital j
    italic*"K" => "𝐾",  # mathematical italic capital k
    italic*"L" => "𝐿",  # mathematical italic capital l
    italic*"M" => "𝑀",  # mathematical italic capital m
    italic*"N" => "𝑁",  # mathematical italic capital n
    italic*"O" => "𝑂",  # mathematical italic capital o
    italic*"P" => "𝑃",  # mathematical italic capital p
    italic*"Q" => "𝑄",  # mathematical italic capital q
    italic*"R" => "𝑅",  # mathematical italic capital r
    italic*"S" => "𝑆",  # mathematical italic capital s
    italic*"T" => "𝑇",  # mathematical italic capital t
    italic*"U" => "𝑈",  # mathematical italic capital u
    italic*"V" => "𝑉",  # mathematical italic capital v
    italic*"W" => "𝑊",  # mathematical italic capital w
    italic*"X" => "𝑋",  # mathematical italic capital x
    italic*"Y" => "𝑌",  # mathematical italic capital y
    italic*"Z" => "𝑍",  # mathematical italic capital z
    italic*"a" => "𝑎",  # mathematical italic small a
    italic*"b" => "𝑏",  # mathematical italic small b
    italic*"c" => "𝑐",  # mathematical italic small c
    italic*"d" => "𝑑",  # mathematical italic small d
    italic*"e" => "𝑒",  # mathematical italic small e
    italic*"f" => "𝑓",  # mathematical italic small f
    italic*"g" => "𝑔",  # mathematical italic small g
    italic*"h" => "ℎ",  # mathematical italic small h (planck constant)
    italic*"i" => "𝑖",  # mathematical italic small i
    italic*"j" => "𝑗",  # mathematical italic small j
    italic*"k" => "𝑘",  # mathematical italic small k
    italic*"l" => "𝑙",  # mathematical italic small l
    italic*"m" => "𝑚",  # mathematical italic small m
    italic*"n" => "𝑛",  # mathematical italic small n
    italic*"o" => "𝑜",  # mathematical italic small o
    italic*"p" => "𝑝",  # mathematical italic small p
    italic*"q" => "𝑞",  # mathematical italic small q
    italic*"r" => "𝑟",  # mathematical italic small r
    italic*"s" => "𝑠",  # mathematical italic small s
    italic*"t" => "𝑡",  # mathematical italic small t
    italic*"u" => "𝑢",  # mathematical italic small u
    italic*"v" => "𝑣",  # mathematical italic small v
    italic*"w" => "𝑤",  # mathematical italic small w
    italic*"x" => "𝑥",  # mathematical italic small x
    italic*"y" => "𝑦",  # mathematical italic small y
    italic*"z" => "𝑧",  # mathematical italic small z
    bolditalic*"A" => "𝑨",  # mathematical bold italic capital a
    bolditalic*"B" => "𝑩",  # mathematical bold italic capital b
    bolditalic*"C" => "𝑪",  # mathematical bold italic capital c
    bolditalic*"D" => "𝑫",  # mathematical bold italic capital d
    bolditalic*"E" => "𝑬",  # mathematical bold italic capital e
    bolditalic*"F" => "𝑭",  # mathematical bold italic capital f
    bolditalic*"G" => "𝑮",  # mathematical bold italic capital g
    bolditalic*"H" => "𝑯",  # mathematical bold italic capital h
    bolditalic*"I" => "𝑰",  # mathematical bold italic capital i
    bolditalic*"J" => "𝑱",  # mathematical bold italic capital j
    bolditalic*"K" => "𝑲",  # mathematical bold italic capital k
    bolditalic*"L" => "𝑳",  # mathematical bold italic capital l
    bolditalic*"M" => "𝑴",  # mathematical bold italic capital m
    bolditalic*"N" => "𝑵",  # mathematical bold italic capital n
    bolditalic*"O" => "𝑶",  # mathematical bold italic capital o
    bolditalic*"P" => "𝑷",  # mathematical bold italic capital p
    bolditalic*"Q" => "𝑸",  # mathematical bold italic capital q
    bolditalic*"R" => "𝑹",  # mathematical bold italic capital r
    bolditalic*"S" => "𝑺",  # mathematical bold italic capital s
    bolditalic*"T" => "𝑻",  # mathematical bold italic capital t
    bolditalic*"U" => "𝑼",  # mathematical bold italic capital u
    bolditalic*"V" => "𝑽",  # mathematical bold italic capital v
    bolditalic*"W" => "𝑾",  # mathematical bold italic capital w
    bolditalic*"X" => "𝑿",  # mathematical bold italic capital x
    bolditalic*"Y" => "𝒀",  # mathematical bold italic capital y
    bolditalic*"Z" => "𝒁",  # mathematical bold italic capital z
    bolditalic*"a" => "𝒂",  # mathematical bold italic small a
    bolditalic*"b" => "𝒃",  # mathematical bold italic small b
    bolditalic*"c" => "𝒄",  # mathematical bold italic small c
    bolditalic*"d" => "𝒅",  # mathematical bold italic small d
    bolditalic*"e" => "𝒆",  # mathematical bold italic small e
    bolditalic*"f" => "𝒇",  # mathematical bold italic small f
    bolditalic*"g" => "𝒈",  # mathematical bold italic small g
    bolditalic*"h" => "𝒉",  # mathematical bold italic small h
    bolditalic*"i" => "𝒊",  # mathematical bold italic small i
    bolditalic*"j" => "𝒋",  # mathematical bold italic small j
    bolditalic*"k" => "𝒌",  # mathematical bold italic small k
    bolditalic*"l" => "𝒍",  # mathematical bold italic small l
    bolditalic*"m" => "𝒎",  # mathematical bold italic small m
    bolditalic*"n" => "𝒏",  # mathematical bold italic small n
    bolditalic*"o" => "𝒐",  # mathematical bold italic small o
    bolditalic*"p" => "𝒑",  # mathematical bold italic small p
    bolditalic*"q" => "𝒒",  # mathematical bold italic small q
    bolditalic*"r" => "𝒓",  # mathematical bold italic small r
    bolditalic*"s" => "𝒔",  # mathematical bold italic small s
    bolditalic*"t" => "𝒕",  # mathematical bold italic small t
    bolditalic*"u" => "𝒖",  # mathematical bold italic small u
    bolditalic*"v" => "𝒗",  # mathematical bold italic small v
    bolditalic*"w" => "𝒘",  # mathematical bold italic small w
    bolditalic*"x" => "𝒙",  # mathematical bold italic small x
    bolditalic*"y" => "𝒚",  # mathematical bold italic small y
    bolditalic*"z" => "𝒛",  # mathematical bold italic small z
    script*"A" => "𝒜",  # mathematical script capital a
    script*"C" => "𝒞",  # mathematical script capital c
    script*"D" => "𝒟",  # mathematical script capital d
    script*"G" => "𝒢",  # mathematical script capital g
    script*"J" => "𝒥",  # mathematical script capital j
    script*"K" => "𝒦",  # mathematical script capital k
    script*"N" => "𝒩",  # mathematical script capital n
    script*"O" => "𝒪",  # mathematical script capital o
    script*"P" => "𝒫",  # mathematical script capital p
    script*"Q" => "𝒬",  # mathematical script capital q
    script*"S" => "𝒮",  # mathematical script capital s
    script*"T" => "𝒯",  # mathematical script capital t
    script*"U" => "𝒰",  # mathematical script capital u
    script*"V" => "𝒱",  # mathematical script capital v
    script*"W" => "𝒲",  # mathematical script capital w
    script*"X" => "𝒳",  # mathematical script capital x
    script*"Y" => "𝒴",  # mathematical script capital y
    script*"Z" => "𝒵",  # mathematical script capital z
    script*"a" => "𝒶",  # mathematical script small a
    script*"b" => "𝒷",  # mathematical script small b
    script*"c" => "𝒸",  # mathematical script small c
    script*"d" => "𝒹",  # mathematical script small d
    script*"f" => "𝒻",  # mathematical script small f
    script*"h" => "𝒽",  # mathematical script small h
    script*"i" => "𝒾",  # mathematical script small i
    script*"j" => "𝒿",  # mathematical script small j
    script*"k" => "𝓀",  # mathematical script small k
    script*"l" => "\U1d4c1",  # mathematical script small l
    script*"m" => "𝓂",  # mathematical script small m
    script*"n" => "𝓃",  # mathematical script small n
    script*"p" => "𝓅",  # mathematical script small p
    script*"q" => "𝓆",  # mathematical script small q
    script*"r" => "𝓇",  # mathematical script small r
    script*"s" => "𝓈",  # mathematical script small s
    script*"t" => "𝓉",  # mathematical script small t
    script*"u" => "𝓊",  # mathematical script small u
    script*"v" => "𝓋",  # mathematical script small v
    script*"w" => "𝓌",  # mathematical script small w
    script*"x" => "𝓍",  # mathematical script small x
    script*"y" => "𝓎",  # mathematical script small y
    script*"z" => "𝓏",  # mathematical script small z
    boldscript*"A" => "𝓐",  # mathematical bold script capital a
    boldscript*"B" => "𝓑",  # mathematical bold script capital b
    boldscript*"C" => "𝓒",  # mathematical bold script capital c
    boldscript*"D" => "𝓓",  # mathematical bold script capital d
    boldscript*"E" => "𝓔",  # mathematical bold script capital e
    boldscript*"F" => "𝓕",  # mathematical bold script capital f
    boldscript*"G" => "𝓖",  # mathematical bold script capital g
    boldscript*"H" => "𝓗",  # mathematical bold script capital h
    boldscript*"I" => "𝓘",  # mathematical bold script capital i
    boldscript*"J" => "𝓙",  # mathematical bold script capital j
    boldscript*"K" => "𝓚",  # mathematical bold script capital k
    boldscript*"L" => "𝓛",  # mathematical bold script capital l
    boldscript*"M" => "𝓜",  # mathematical bold script capital m
    boldscript*"N" => "𝓝",  # mathematical bold script capital n
    boldscript*"O" => "𝓞",  # mathematical bold script capital o
    boldscript*"P" => "𝓟",  # mathematical bold script capital p
    boldscript*"Q" => "𝓠",  # mathematical bold script capital q
    boldscript*"R" => "𝓡",  # mathematical bold script capital r
    boldscript*"S" => "𝓢",  # mathematical bold script capital s
    boldscript*"T" => "𝓣",  # mathematical bold script capital t
    boldscript*"U" => "𝓤",  # mathematical bold script capital u
    boldscript*"V" => "𝓥",  # mathematical bold script capital v
    boldscript*"W" => "𝓦",  # mathematical bold script capital w
    boldscript*"X" => "𝓧",  # mathematical bold script capital x
    boldscript*"Y" => "𝓨",  # mathematical bold script capital y
    boldscript*"Z" => "𝓩",  # mathematical bold script capital z
    boldscript*"a" => "𝓪",  # mathematical bold script small a
    boldscript*"b" => "𝓫",  # mathematical bold script small b
    boldscript*"c" => "𝓬",  # mathematical bold script small c
    boldscript*"d" => "𝓭",  # mathematical bold script small d
    boldscript*"e" => "𝓮",  # mathematical bold script small e
    boldscript*"f" => "𝓯",  # mathematical bold script small f
    boldscript*"g" => "𝓰",  # mathematical bold script small g
    boldscript*"h" => "𝓱",  # mathematical bold script small h
    boldscript*"i" => "𝓲",  # mathematical bold script small i
    boldscript*"j" => "𝓳",  # mathematical bold script small j
    boldscript*"k" => "𝓴",  # mathematical bold script small k
    boldscript*"l" => "𝓵",  # mathematical bold script small l
    boldscript*"m" => "𝓶",  # mathematical bold script small m
    boldscript*"n" => "𝓷",  # mathematical bold script small n
    boldscript*"o" => "𝓸",  # mathematical bold script small o
    boldscript*"p" => "𝓹",  # mathematical bold script small p
    boldscript*"q" => "𝓺",  # mathematical bold script small q
    boldscript*"r" => "𝓻",  # mathematical bold script small r
    boldscript*"s" => "𝓼",  # mathematical bold script small s
    boldscript*"t" => "𝓽",  # mathematical bold script small t
    boldscript*"u" => "𝓾",  # mathematical bold script small u
    boldscript*"v" => "𝓿",  # mathematical bold script small v
    boldscript*"w" => "𝔀",  # mathematical bold script small w
    boldscript*"x" => "𝔁",  # mathematical bold script small x
    boldscript*"y" => "𝔂",  # mathematical bold script small y
    boldscript*"z" => "𝔃",  # mathematical bold script small z
    frak*"A" => "𝔄",  # mathematical fraktur capital a
    frak*"B" => "𝔅",  # mathematical fraktur capital b
    frak*"D" => "𝔇",  # mathematical fraktur capital d
    frak*"E" => "𝔈",  # mathematical fraktur capital e
    frak*"F" => "𝔉",  # mathematical fraktur capital f
    frak*"G" => "𝔊",  # mathematical fraktur capital g
    frak*"I" => "ℑ",  # black-letter capital i (manual addition)
    frak*"J" => "𝔍",  # mathematical fraktur capital j
    frak*"K" => "𝔎",  # mathematical fraktur capital k
    frak*"L" => "𝔏",  # mathematical fraktur capital l
    frak*"M" => "𝔐",  # mathematical fraktur capital m
    frak*"N" => "𝔑",  # mathematical fraktur capital n
    frak*"O" => "𝔒",  # mathematical fraktur capital o
    frak*"P" => "𝔓",  # mathematical fraktur capital p
    frak*"Q" => "𝔔",  # mathematical fraktur capital q
    frak*"R" => "ℜ",  # black-letter capital r (manual addition)
    frak*"S" => "𝔖",  # mathematical fraktur capital s
    frak*"T" => "𝔗",  # mathematical fraktur capital t
    frak*"U" => "𝔘",  # mathematical fraktur capital u
    frak*"V" => "𝔙",  # mathematical fraktur capital v
    frak*"W" => "𝔚",  # mathematical fraktur capital w
    frak*"X" => "𝔛",  # mathematical fraktur capital x
    frak*"Y" => "𝔜",  # mathematical fraktur capital y
    frak*"a" => "𝔞",  # mathematical fraktur small a
    frak*"b" => "𝔟",  # mathematical fraktur small b
    frak*"c" => "𝔠",  # mathematical fraktur small c
    frak*"d" => "𝔡",  # mathematical fraktur small d
    frak*"e" => "𝔢",  # mathematical fraktur small e
    frak*"f" => "𝔣",  # mathematical fraktur small f
    frak*"g" => "𝔤",  # mathematical fraktur small g
    frak*"h" => "𝔥",  # mathematical fraktur small h
    frak*"i" => "𝔦",  # mathematical fraktur small i
    frak*"j" => "𝔧",  # mathematical fraktur small j
    frak*"k" => "𝔨",  # mathematical fraktur small k
    frak*"l" => "𝔩",  # mathematical fraktur small l
    frak*"m" => "𝔪",  # mathematical fraktur small m
    frak*"n" => "𝔫",  # mathematical fraktur small n
    frak*"o" => "𝔬",  # mathematical fraktur small o
    frak*"p" => "𝔭",  # mathematical fraktur small p
    frak*"q" => "𝔮",  # mathematical fraktur small q
    frak*"r" => "𝔯",  # mathematical fraktur small r
    frak*"s" => "𝔰",  # mathematical fraktur small s
    frak*"t" => "𝔱",  # mathematical fraktur small t
    frak*"u" => "𝔲",  # mathematical fraktur small u
    frak*"v" => "𝔳",  # mathematical fraktur small v
    frak*"w" => "𝔴",  # mathematical fraktur small w
    frak*"x" => "𝔵",  # mathematical fraktur small x
    frak*"y" => "𝔶",  # mathematical fraktur small y
    frak*"z" => "𝔷",  # mathematical fraktur small z
    blackboard*"A" => "𝔸",  # mathematical double-struck capital a
    blackboard*"B" => "𝔹",  # mathematical double-struck capital b
    blackboard*"D" => "𝔻",  # mathematical double-struck capital d
    blackboard*"E" => "𝔼",  # mathematical double-struck capital e
    blackboard*"F" => "𝔽",  # mathematical double-struck capital f
    blackboard*"G" => "𝔾",  # mathematical double-struck capital g
    blackboard*"I" => "𝕀",  # mathematical double-struck capital i
    blackboard*"J" => "𝕁",  # mathematical double-struck capital j
    blackboard*"K" => "𝕂",  # mathematical double-struck capital k
    blackboard*"L" => "𝕃",  # mathematical double-struck capital l
    blackboard*"M" => "𝕄",  # mathematical double-struck capital m
    blackboard*"O" => "𝕆",  # mathematical double-struck capital o
    blackboard*"S" => "𝕊",  # mathematical double-struck capital s
    blackboard*"T" => "𝕋",  # mathematical double-struck capital t
    blackboard*"U" => "𝕌",  # mathematical double-struck capital u
    blackboard*"V" => "𝕍",  # mathematical double-struck capital v
    blackboard*"W" => "𝕎",  # mathematical double-struck capital w
    blackboard*"X" => "𝕏",  # mathematical double-struck capital x
    blackboard*"Y" => "𝕐",  # mathematical double-struck capital y
    blackboard*"a" => "𝕒",  # mathematical double-struck small a
    blackboard*"b" => "𝕓",  # mathematical double-struck small b
    blackboard*"c" => "𝕔",  # mathematical double-struck small c
    blackboard*"d" => "𝕕",  # mathematical double-struck small d
    blackboard*"e" => "𝕖",  # mathematical double-struck small e
    blackboard*"f" => "𝕗",  # mathematical double-struck small f
    blackboard*"g" => "𝕘",  # mathematical double-struck small g
    blackboard*"h" => "𝕙",  # mathematical double-struck small h
    blackboard*"i" => "𝕚",  # mathematical double-struck small i
    blackboard*"j" => "𝕛",  # mathematical double-struck small j
    blackboard*"k" => "𝕜",  # mathematical double-struck small k
    blackboard*"l" => "𝕝",  # mathematical double-struck small l
    blackboard*"m" => "𝕞",  # mathematical double-struck small m
    blackboard*"n" => "𝕟",  # mathematical double-struck small n
    blackboard*"o" => "𝕠",  # mathematical double-struck small o
    blackboard*"p" => "𝕡",  # mathematical double-struck small p
    blackboard*"q" => "𝕢",  # mathematical double-struck small q
    blackboard*"r" => "𝕣",  # mathematical double-struck small r
    blackboard*"s" => "𝕤",  # mathematical double-struck small s
    blackboard*"t" => "𝕥",  # mathematical double-struck small t
    blackboard*"u" => "𝕦",  # mathematical double-struck small u
    blackboard*"v" => "𝕧",  # mathematical double-struck small v
    blackboard*"w" => "𝕨",  # mathematical double-struck small w
    blackboard*"x" => "𝕩",  # mathematical double-struck small x
    blackboard*"y" => "𝕪",  # mathematical double-struck small y
    blackboard*"z" => "𝕫",  # mathematical double-struck small z
    boldfrak*"A" => "𝕬",  # mathematical bold fraktur capital a
    boldfrak*"B" => "𝕭",  # mathematical bold fraktur capital b
    boldfrak*"C" => "𝕮",  # mathematical bold fraktur capital c
    boldfrak*"D" => "𝕯",  # mathematical bold fraktur capital d
    boldfrak*"E" => "𝕰",  # mathematical bold fraktur capital e
    boldfrak*"F" => "𝕱",  # mathematical bold fraktur capital f
    boldfrak*"G" => "𝕲",  # mathematical bold fraktur capital g
    boldfrak*"H" => "𝕳",  # mathematical bold fraktur capital h
    boldfrak*"I" => "𝕴",  # mathematical bold fraktur capital i
    boldfrak*"J" => "𝕵",  # mathematical bold fraktur capital j
    boldfrak*"K" => "𝕶",  # mathematical bold fraktur capital k
    boldfrak*"L" => "𝕷",  # mathematical bold fraktur capital l
    boldfrak*"M" => "𝕸",  # mathematical bold fraktur capital m
    boldfrak*"N" => "𝕹",  # mathematical bold fraktur capital n
    boldfrak*"O" => "𝕺",  # mathematical bold fraktur capital o
    boldfrak*"P" => "𝕻",  # mathematical bold fraktur capital p
    boldfrak*"Q" => "𝕼",  # mathematical bold fraktur capital q
    boldfrak*"R" => "𝕽",  # mathematical bold fraktur capital r
    boldfrak*"S" => "𝕾",  # mathematical bold fraktur capital s
    boldfrak*"T" => "𝕿",  # mathematical bold fraktur capital t
    boldfrak*"U" => "𝖀",  # mathematical bold fraktur capital u
    boldfrak*"V" => "𝖁",  # mathematical bold fraktur capital v
    boldfrak*"W" => "𝖂",  # mathematical bold fraktur capital w
    boldfrak*"X" => "𝖃",  # mathematical bold fraktur capital x
    boldfrak*"Y" => "𝖄",  # mathematical bold fraktur capital y
    boldfrak*"Z" => "𝖅",  # mathematical bold fraktur capital z
    boldfrak*"a" => "𝖆",  # mathematical bold fraktur small a
    boldfrak*"b" => "𝖇",  # mathematical bold fraktur small b
    boldfrak*"c" => "𝖈",  # mathematical bold fraktur small c
    boldfrak*"d" => "𝖉",  # mathematical bold fraktur small d
    boldfrak*"e" => "𝖊",  # mathematical bold fraktur small e
    boldfrak*"f" => "𝖋",  # mathematical bold fraktur small f
    boldfrak*"g" => "𝖌",  # mathematical bold fraktur small g
    boldfrak*"h" => "𝖍",  # mathematical bold fraktur small h
    boldfrak*"i" => "𝖎",  # mathematical bold fraktur small i
    boldfrak*"j" => "𝖏",  # mathematical bold fraktur small j
    boldfrak*"k" => "𝖐",  # mathematical bold fraktur small k
    boldfrak*"l" => "𝖑",  # mathematical bold fraktur small l
    boldfrak*"m" => "𝖒",  # mathematical bold fraktur small m
    boldfrak*"n" => "𝖓",  # mathematical bold fraktur small n
    boldfrak*"o" => "𝖔",  # mathematical bold fraktur small o
    boldfrak*"p" => "𝖕",  # mathematical bold fraktur small p
    boldfrak*"q" => "𝖖",  # mathematical bold fraktur small q
    boldfrak*"r" => "𝖗",  # mathematical bold fraktur small r
    boldfrak*"s" => "𝖘",  # mathematical bold fraktur small s
    boldfrak*"t" => "𝖙",  # mathematical bold fraktur small t
    boldfrak*"u" => "𝖚",  # mathematical bold fraktur small u
    boldfrak*"v" => "𝖛",  # mathematical bold fraktur small v
    boldfrak*"w" => "𝖜",  # mathematical bold fraktur small w
    boldfrak*"x" => "𝖝",  # mathematical bold fraktur small x
    boldfrak*"y" => "𝖞",  # mathematical bold fraktur small y
    boldfrak*"z" => "𝖟",  # mathematical bold fraktur small z
    sans*"A" => "𝖠",  # mathematical sans-serif capital a
    sans*"B" => "𝖡",  # mathematical sans-serif capital b
    sans*"C" => "𝖢",  # mathematical sans-serif capital c
    sans*"D" => "𝖣",  # mathematical sans-serif capital d
    sans*"E" => "𝖤",  # mathematical sans-serif capital e
    sans*"F" => "𝖥",  # mathematical sans-serif capital f
    sans*"G" => "𝖦",  # mathematical sans-serif capital g
    sans*"H" => "𝖧",  # mathematical sans-serif capital h
    sans*"I" => "𝖨",  # mathematical sans-serif capital i
    sans*"J" => "𝖩",  # mathematical sans-serif capital j
    sans*"K" => "𝖪",  # mathematical sans-serif capital k
    sans*"L" => "𝖫",  # mathematical sans-serif capital l
    sans*"M" => "𝖬",  # mathematical sans-serif capital m
    sans*"N" => "𝖭",  # mathematical sans-serif capital n
    sans*"O" => "𝖮",  # mathematical sans-serif capital o
    sans*"P" => "𝖯",  # mathematical sans-serif capital p
    sans*"Q" => "𝖰",  # mathematical sans-serif capital q
    sans*"R" => "𝖱",  # mathematical sans-serif capital r
    sans*"S" => "𝖲",  # mathematical sans-serif capital s
    sans*"T" => "𝖳",  # mathematical sans-serif capital t
    sans*"U" => "𝖴",  # mathematical sans-serif capital u
    sans*"V" => "𝖵",  # mathematical sans-serif capital v
    sans*"W" => "𝖶",  # mathematical sans-serif capital w
    sans*"X" => "𝖷",  # mathematical sans-serif capital x
    sans*"Y" => "𝖸",  # mathematical sans-serif capital y
    sans*"Z" => "𝖹",  # mathematical sans-serif capital z
    sans*"a" => "𝖺",  # mathematical sans-serif small a
    sans*"b" => "𝖻",  # mathematical sans-serif small b
    sans*"c" => "𝖼",  # mathematical sans-serif small c
    sans*"d" => "𝖽",  # mathematical sans-serif small d
    sans*"e" => "𝖾",  # mathematical sans-serif small e
    sans*"f" => "𝖿",  # mathematical sans-serif small f
    sans*"g" => "𝗀",  # mathematical sans-serif small g
    sans*"h" => "𝗁",  # mathematical sans-serif small h
    sans*"i" => "𝗂",  # mathematical sans-serif small i
    sans*"j" => "𝗃",  # mathematical sans-serif small j
    sans*"k" => "𝗄",  # mathematical sans-serif small k
    sans*"l" => "𝗅",  # mathematical sans-serif small l
    sans*"m" => "𝗆",  # mathematical sans-serif small m
    sans*"n" => "𝗇",  # mathematical sans-serif small n
    sans*"o" => "𝗈",  # mathematical sans-serif small o
    sans*"p" => "𝗉",  # mathematical sans-serif small p
    sans*"q" => "𝗊",  # mathematical sans-serif small q
    sans*"r" => "𝗋",  # mathematical sans-serif small r
    sans*"s" => "𝗌",  # mathematical sans-serif small s
    sans*"t" => "𝗍",  # mathematical sans-serif small t
    sans*"u" => "𝗎",  # mathematical sans-serif small u
    sans*"v" => "𝗏",  # mathematical sans-serif small v
    sans*"w" => "𝗐",  # mathematical sans-serif small w
    sans*"x" => "𝗑",  # mathematical sans-serif small x
    sans*"y" => "𝗒",  # mathematical sans-serif small y
    sans*"z" => "𝗓",  # mathematical sans-serif small z
    boldsans*"A" => "𝗔",  # mathematical sans-serif bold capital a
    boldsans*"B" => "𝗕",  # mathematical sans-serif bold capital b
    boldsans*"C" => "𝗖",  # mathematical sans-serif bold capital c
    boldsans*"D" => "𝗗",  # mathematical sans-serif bold capital d
    boldsans*"E" => "𝗘",  # mathematical sans-serif bold capital e
    boldsans*"F" => "𝗙",  # mathematical sans-serif bold capital f
    boldsans*"G" => "𝗚",  # mathematical sans-serif bold capital g
    boldsans*"H" => "𝗛",  # mathematical sans-serif bold capital h
    boldsans*"I" => "𝗜",  # mathematical sans-serif bold capital i
    boldsans*"J" => "𝗝",  # mathematical sans-serif bold capital j
    boldsans*"K" => "𝗞",  # mathematical sans-serif bold capital k
    boldsans*"L" => "𝗟",  # mathematical sans-serif bold capital l
    boldsans*"M" => "𝗠",  # mathematical sans-serif bold capital m
    boldsans*"N" => "𝗡",  # mathematical sans-serif bold capital n
    boldsans*"O" => "𝗢",  # mathematical sans-serif bold capital o
    boldsans*"P" => "𝗣",  # mathematical sans-serif bold capital p
    boldsans*"Q" => "𝗤",  # mathematical sans-serif bold capital q
    boldsans*"R" => "𝗥",  # mathematical sans-serif bold capital r
    boldsans*"S" => "𝗦",  # mathematical sans-serif bold capital s
    boldsans*"T" => "𝗧",  # mathematical sans-serif bold capital t
    boldsans*"U" => "𝗨",  # mathematical sans-serif bold capital u
    boldsans*"V" => "𝗩",  # mathematical sans-serif bold capital v
    boldsans*"W" => "𝗪",  # mathematical sans-serif bold capital w
    boldsans*"X" => "𝗫",  # mathematical sans-serif bold capital x
    boldsans*"Y" => "𝗬",  # mathematical sans-serif bold capital y
    boldsans*"Z" => "𝗭",  # mathematical sans-serif bold capital z
    boldsans*"a" => "𝗮",  # mathematical sans-serif bold small a
    boldsans*"b" => "𝗯",  # mathematical sans-serif bold small b
    boldsans*"c" => "𝗰",  # mathematical sans-serif bold small c
    boldsans*"d" => "𝗱",  # mathematical sans-serif bold small d
    boldsans*"e" => "𝗲",  # mathematical sans-serif bold small e
    boldsans*"f" => "𝗳",  # mathematical sans-serif bold small f
    boldsans*"g" => "𝗴",  # mathematical sans-serif bold small g
    boldsans*"h" => "𝗵",  # mathematical sans-serif bold small h
    boldsans*"i" => "𝗶",  # mathematical sans-serif bold small i
    boldsans*"j" => "𝗷",  # mathematical sans-serif bold small j
    boldsans*"k" => "𝗸",  # mathematical sans-serif bold small k
    boldsans*"l" => "𝗹",  # mathematical sans-serif bold small l
    boldsans*"m" => "𝗺",  # mathematical sans-serif bold small m
    boldsans*"n" => "𝗻",  # mathematical sans-serif bold small n
    boldsans*"o" => "𝗼",  # mathematical sans-serif bold small o
    boldsans*"p" => "𝗽",  # mathematical sans-serif bold small p
    boldsans*"q" => "𝗾",  # mathematical sans-serif bold small q
    boldsans*"r" => "𝗿",  # mathematical sans-serif bold small r
    boldsans*"s" => "𝘀",  # mathematical sans-serif bold small s
    boldsans*"t" => "𝘁",  # mathematical sans-serif bold small t
    boldsans*"u" => "𝘂",  # mathematical sans-serif bold small u
    boldsans*"v" => "𝘃",  # mathematical sans-serif bold small v
    boldsans*"w" => "𝘄",  # mathematical sans-serif bold small w
    boldsans*"x" => "𝘅",  # mathematical sans-serif bold small x
    boldsans*"y" => "𝘆",  # mathematical sans-serif bold small y
    boldsans*"z" => "𝘇",  # mathematical sans-serif bold small z
    italicsans*"A" => "𝘈",  # mathematical sans-serif italic capital a
    italicsans*"B" => "𝘉",  # mathematical sans-serif italic capital b
    italicsans*"C" => "𝘊",  # mathematical sans-serif italic capital c
    italicsans*"D" => "𝘋",  # mathematical sans-serif italic capital d
    italicsans*"E" => "𝘌",  # mathematical sans-serif italic capital e
    italicsans*"F" => "𝘍",  # mathematical sans-serif italic capital f
    italicsans*"G" => "𝘎",  # mathematical sans-serif italic capital g
    italicsans*"H" => "𝘏",  # mathematical sans-serif italic capital h
    italicsans*"I" => "𝘐",  # mathematical sans-serif italic capital i
    italicsans*"J" => "𝘑",  # mathematical sans-serif italic capital j
    italicsans*"K" => "𝘒",  # mathematical sans-serif italic capital k
    italicsans*"L" => "𝘓",  # mathematical sans-serif italic capital l
    italicsans*"M" => "𝘔",  # mathematical sans-serif italic capital m
    italicsans*"N" => "𝘕",  # mathematical sans-serif italic capital n
    italicsans*"O" => "𝘖",  # mathematical sans-serif italic capital o
    italicsans*"P" => "𝘗",  # mathematical sans-serif italic capital p
    italicsans*"Q" => "𝘘",  # mathematical sans-serif italic capital q
    italicsans*"R" => "𝘙",  # mathematical sans-serif italic capital r
    italicsans*"S" => "𝘚",  # mathematical sans-serif italic capital s
    italicsans*"T" => "𝘛",  # mathematical sans-serif italic capital t
    italicsans*"U" => "𝘜",  # mathematical sans-serif italic capital u
    italicsans*"V" => "𝘝",  # mathematical sans-serif italic capital v
    italicsans*"W" => "𝘞",  # mathematical sans-serif italic capital w
    italicsans*"X" => "𝘟",  # mathematical sans-serif italic capital x
    italicsans*"Y" => "𝘠",  # mathematical sans-serif italic capital y
    italicsans*"Z" => "𝘡",  # mathematical sans-serif italic capital z
    italicsans*"a" => "𝘢",  # mathematical sans-serif italic small a
    italicsans*"b" => "𝘣",  # mathematical sans-serif italic small b
    italicsans*"c" => "𝘤",  # mathematical sans-serif italic small c
    italicsans*"d" => "𝘥",  # mathematical sans-serif italic small d
    italicsans*"e" => "𝘦",  # mathematical sans-serif italic small e
    italicsans*"f" => "𝘧",  # mathematical sans-serif italic small f
    italicsans*"g" => "𝘨",  # mathematical sans-serif italic small g
    italicsans*"h" => "𝘩",  # mathematical sans-serif italic small h
    italicsans*"i" => "𝘪",  # mathematical sans-serif italic small i
    italicsans*"j" => "𝘫",  # mathematical sans-serif italic small j
    italicsans*"k" => "𝘬",  # mathematical sans-serif italic small k
    italicsans*"l" => "𝘭",  # mathematical sans-serif italic small l
    italicsans*"m" => "𝘮",  # mathematical sans-serif italic small m
    italicsans*"n" => "𝘯",  # mathematical sans-serif italic small n
    italicsans*"o" => "𝘰",  # mathematical sans-serif italic small o
    italicsans*"p" => "𝘱",  # mathematical sans-serif italic small p
    italicsans*"q" => "𝘲",  # mathematical sans-serif italic small q
    italicsans*"r" => "𝘳",  # mathematical sans-serif italic small r
    italicsans*"s" => "𝘴",  # mathematical sans-serif italic small s
    italicsans*"t" => "𝘵",  # mathematical sans-serif italic small t
    italicsans*"u" => "𝘶",  # mathematical sans-serif italic small u
    italicsans*"v" => "𝘷",  # mathematical sans-serif italic small v
    italicsans*"w" => "𝘸",  # mathematical sans-serif italic small w
    italicsans*"x" => "𝘹",  # mathematical sans-serif italic small x
    italicsans*"y" => "𝘺",  # mathematical sans-serif italic small y
    italicsans*"z" => "𝘻",  # mathematical sans-serif italic small z
    bolditalicsans*"A" => "𝘼",  # mathematical sans-serif bold italic capital a
    bolditalicsans*"B" => "𝘽",  # mathematical sans-serif bold italic capital b
    bolditalicsans*"C" => "𝘾",  # mathematical sans-serif bold italic capital c
    bolditalicsans*"D" => "𝘿",  # mathematical sans-serif bold italic capital d
    bolditalicsans*"E" => "𝙀",  # mathematical sans-serif bold italic capital e
    bolditalicsans*"F" => "𝙁",  # mathematical sans-serif bold italic capital f
    bolditalicsans*"G" => "𝙂",  # mathematical sans-serif bold italic capital g
    bolditalicsans*"H" => "𝙃",  # mathematical sans-serif bold italic capital h
    bolditalicsans*"I" => "𝙄",  # mathematical sans-serif bold italic capital i
    bolditalicsans*"J" => "𝙅",  # mathematical sans-serif bold italic capital j
    bolditalicsans*"K" => "𝙆",  # mathematical sans-serif bold italic capital k
    bolditalicsans*"L" => "𝙇",  # mathematical sans-serif bold italic capital l
    bolditalicsans*"M" => "𝙈",  # mathematical sans-serif bold italic capital m
    bolditalicsans*"N" => "𝙉",  # mathematical sans-serif bold italic capital n
    bolditalicsans*"O" => "𝙊",  # mathematical sans-serif bold italic capital o
    bolditalicsans*"P" => "𝙋",  # mathematical sans-serif bold italic capital p
    bolditalicsans*"Q" => "𝙌",  # mathematical sans-serif bold italic capital q
    bolditalicsans*"R" => "𝙍",  # mathematical sans-serif bold italic capital r
    bolditalicsans*"S" => "𝙎",  # mathematical sans-serif bold italic capital s
    bolditalicsans*"T" => "𝙏",  # mathematical sans-serif bold italic capital t
    bolditalicsans*"U" => "𝙐",  # mathematical sans-serif bold italic capital u
    bolditalicsans*"V" => "𝙑",  # mathematical sans-serif bold italic capital v
    bolditalicsans*"W" => "𝙒",  # mathematical sans-serif bold italic capital w
    bolditalicsans*"X" => "𝙓",  # mathematical sans-serif bold italic capital x
    bolditalicsans*"Y" => "𝙔",  # mathematical sans-serif bold italic capital y
    bolditalicsans*"Z" => "𝙕",  # mathematical sans-serif bold italic capital z
    bolditalicsans*"a" => "𝙖",  # mathematical sans-serif bold italic small a
    bolditalicsans*"b" => "𝙗",  # mathematical sans-serif bold italic small b
    bolditalicsans*"c" => "𝙘",  # mathematical sans-serif bold italic small c
    bolditalicsans*"d" => "𝙙",  # mathematical sans-serif bold italic small d
    bolditalicsans*"e" => "𝙚",  # mathematical sans-serif bold italic small e
    bolditalicsans*"f" => "𝙛",  # mathematical sans-serif bold italic small f
    bolditalicsans*"g" => "𝙜",  # mathematical sans-serif bold italic small g
    bolditalicsans*"h" => "𝙝",  # mathematical sans-serif bold italic small h
    bolditalicsans*"i" => "𝙞",  # mathematical sans-serif bold italic small i
    bolditalicsans*"j" => "𝙟",  # mathematical sans-serif bold italic small j
    bolditalicsans*"k" => "𝙠",  # mathematical sans-serif bold italic small k
    bolditalicsans*"l" => "𝙡",  # mathematical sans-serif bold italic small l
    bolditalicsans*"m" => "𝙢",  # mathematical sans-serif bold italic small m
    bolditalicsans*"n" => "𝙣",  # mathematical sans-serif bold italic small n
    bolditalicsans*"o" => "𝙤",  # mathematical sans-serif bold italic small o
    bolditalicsans*"p" => "𝙥",  # mathematical sans-serif bold italic small p
    bolditalicsans*"q" => "𝙦",  # mathematical sans-serif bold italic small q
    bolditalicsans*"r" => "𝙧",  # mathematical sans-serif bold italic small r
    bolditalicsans*"s" => "𝙨",  # mathematical sans-serif bold italic small s
    bolditalicsans*"t" => "𝙩",  # mathematical sans-serif bold italic small t
    bolditalicsans*"u" => "𝙪",  # mathematical sans-serif bold italic small u
    bolditalicsans*"v" => "𝙫",  # mathematical sans-serif bold italic small v
    bolditalicsans*"w" => "𝙬",  # mathematical sans-serif bold italic small w
    bolditalicsans*"x" => "𝙭",  # mathematical sans-serif bold italic small x
    bolditalicsans*"y" => "𝙮",  # mathematical sans-serif bold italic small y
    bolditalicsans*"z" => "𝙯",  # mathematical sans-serif bold italic small z
    mono*"A" => "𝙰",  # mathematical monospace capital a
    mono*"B" => "𝙱",  # mathematical monospace capital b
    mono*"C" => "𝙲",  # mathematical monospace capital c
    mono*"D" => "𝙳",  # mathematical monospace capital d
    mono*"E" => "𝙴",  # mathematical monospace capital e
    mono*"F" => "𝙵",  # mathematical monospace capital f
    mono*"G" => "𝙶",  # mathematical monospace capital g
    mono*"H" => "𝙷",  # mathematical monospace capital h
    mono*"I" => "𝙸",  # mathematical monospace capital i
    mono*"J" => "𝙹",  # mathematical monospace capital j
    mono*"K" => "𝙺",  # mathematical monospace capital k
    mono*"L" => "𝙻",  # mathematical monospace capital l
    mono*"M" => "𝙼",  # mathematical monospace capital m
    mono*"N" => "𝙽",  # mathematical monospace capital n
    mono*"O" => "𝙾",  # mathematical monospace capital o
    mono*"P" => "𝙿",  # mathematical monospace capital p
    mono*"Q" => "𝚀",  # mathematical monospace capital q
    mono*"R" => "𝚁",  # mathematical monospace capital r
    mono*"S" => "𝚂",  # mathematical monospace capital s
    mono*"T" => "𝚃",  # mathematical monospace capital t
    mono*"U" => "𝚄",  # mathematical monospace capital u
    mono*"V" => "𝚅",  # mathematical monospace capital v
    mono*"W" => "𝚆",  # mathematical monospace capital w
    mono*"X" => "𝚇",  # mathematical monospace capital x
    mono*"Y" => "𝚈",  # mathematical monospace capital y
    mono*"Z" => "𝚉",  # mathematical monospace capital z
    mono*"a" => "𝚊",  # mathematical monospace small a
    mono*"b" => "𝚋",  # mathematical monospace small b
    mono*"c" => "𝚌",  # mathematical monospace small c
    mono*"d" => "𝚍",  # mathematical monospace small d
    mono*"e" => "𝚎",  # mathematical monospace small e
    mono*"f" => "𝚏",  # mathematical monospace small f
    mono*"g" => "𝚐",  # mathematical monospace small g
    mono*"h" => "𝚑",  # mathematical monospace small h
    mono*"i" => "𝚒",  # mathematical monospace small i
    mono*"j" => "𝚓",  # mathematical monospace small j
    mono*"k" => "𝚔",  # mathematical monospace small k
    mono*"l" => "𝚕",  # mathematical monospace small l
    mono*"m" => "𝚖",  # mathematical monospace small m
    mono*"n" => "𝚗",  # mathematical monospace small n
    mono*"o" => "𝚘",  # mathematical monospace small o
    mono*"p" => "𝚙",  # mathematical monospace small p
    mono*"q" => "𝚚",  # mathematical monospace small q
    mono*"r" => "𝚛",  # mathematical monospace small r
    mono*"s" => "𝚜",  # mathematical monospace small s
    mono*"t" => "𝚝",  # mathematical monospace small t
    mono*"u" => "𝚞",  # mathematical monospace small u
    mono*"v" => "𝚟",  # mathematical monospace small v
    mono*"w" => "𝚠",  # mathematical monospace small w
    mono*"x" => "𝚡",  # mathematical monospace small x
    mono*"y" => "𝚢",  # mathematical monospace small y
    mono*"z" => "𝚣",  # mathematical monospace small z
    italic*"imath" => "\U1d6a4",  # mathematical italic small dotless i
    italic*"jmath" => "\U1d6a5",  # mathematical italic small dotless j
    bold*"Alpha" => "𝚨",  # mathematical bold capital alpha
    bold*"Beta" => "𝚩",  # mathematical bold capital beta
    bold*"Gamma" => "𝚪",  # mathematical bold capital gamma
    bold*"Delta" => "𝚫",  # mathematical bold capital delta
    bold*"Epsilon" => "𝚬",  # mathematical bold capital epsilon
    bold*"Zeta" => "𝚭",  # mathematical bold capital zeta
    bold*"Eta" => "𝚮",  # mathematical bold capital eta
    bold*"Theta" => "𝚯",  # mathematical bold capital theta
    bold*"Iota" => "𝚰",  # mathematical bold capital iota
    bold*"Kappa" => "𝚱",  # mathematical bold capital kappa
    bold*"Lambda" => "𝚲",  # mathematical bold capital lambda
    bold*"Mu" => "𝚳",  # mathematical bold capital mu
    bold*"Nu" => "𝚴",  # mathematical bold capital nu
    bold*"Xi" => "𝚵",  # mathematical bold capital xi
    bold*"Omicron" => "𝚶",  # mathematical bold capital omicron
    bold*"Pi" => "𝚷",  # mathematical bold capital pi
    bold*"Rho" => "𝚸",  # mathematical bold capital rho
    bold*"varTheta" => "𝚹",  # mathematical bold capital theta symbol
    bold*"Sigma" => "𝚺",  # mathematical bold capital sigma
    bold*"Tau" => "𝚻",  # mathematical bold capital tau
    bold*"Upsilon" => "𝚼",  # mathematical bold capital upsilon
    bold*"Phi" => "𝚽",  # mathematical bold capital phi
    bold*"Chi" => "𝚾",  # mathematical bold capital chi
    bold*"Psi" => "𝚿",  # mathematical bold capital psi
    bold*"Omega" => "𝛀",  # mathematical bold capital omega
    bold*"nabla" => "𝛁",  # mathematical bold nabla
    bold*"alpha" => "𝛂",  # mathematical bold small alpha
    bold*"beta" => "𝛃",  # mathematical bold small beta
    bold*"gamma" => "𝛄",  # mathematical bold small gamma
    bold*"delta" => "𝛅",  # mathematical bold small delta
    bold*"varepsilon" => "𝛆",  # mathematical bold small epsilon
    bold*"zeta" => "𝛇",  # mathematical bold small zeta
    bold*"eta" => "𝛈",  # mathematical bold small eta
    bold*"theta" => "𝛉",  # mathematical bold small theta
    bold*"iota" => "𝛊",  # mathematical bold small iota
    bold*"kappa" => "𝛋",  # mathematical bold small kappa
    bold*"lambda" => "𝛌",  # mathematical bold small lambda
    bold*"mu" => "𝛍",  # mathematical bold small mu
    bold*"nu" => "𝛎",  # mathematical bold small nu
    bold*"xi" => "𝛏",  # mathematical bold small xi
    bold*"omicron" => "𝛐",  # mathematical bold small omicron
    bold*"pi" => "𝛑",  # mathematical bold small pi
    bold*"rho" => "𝛒",  # mathematical bold small rho
    bold*"varsigma" => "𝛓",  # mathematical bold small final sigma
    bold*"sigma" => "𝛔",  # mathematical bold small sigma
    bold*"tau" => "𝛕",  # mathematical bold small tau
    bold*"upsilon" => "𝛖",  # mathematical bold small upsilon
    bold*"varphi" => "𝛗",  # mathematical bold small phi
    bold*"chi" => "𝛘",  # mathematical bold small chi
    bold*"psi" => "𝛙",  # mathematical bold small psi
    bold*"omega" => "𝛚",  # mathematical bold small omega
    bold*"partial" => "𝛛",  # mathematical bold partial differential
    bold*"epsilon" => "𝛜",  # mathematical bold epsilon symbol
    bold*"vartheta" => "𝛝",  # mathematical bold theta symbol
    bold*"varkappa" => "𝛞",  # mathematical bold kappa symbol
    bold*"phi" => "𝛟",  # mathematical bold phi symbol
    bold*"varrho" => "𝛠",  # mathematical bold rho symbol
    bold*"varpi" => "𝛡",  # mathematical bold pi symbol
    italic*"Alpha" => "𝛢",  # mathematical italic capital alpha
    italic*"Beta" => "𝛣",  # mathematical italic capital beta
    italic*"Gamma" => "𝛤",  # mathematical italic capital gamma
    italic*"Delta" => "𝛥",  # mathematical italic capital delta
    italic*"Epsilon" => "𝛦",  # mathematical italic capital epsilon
    italic*"Zeta" => "𝛧",  # mathematical italic capital zeta
    italic*"Eta" => "𝛨",  # mathematical italic capital eta
    italic*"Theta" => "𝛩",  # mathematical italic capital theta
    italic*"Iota" => "𝛪",  # mathematical italic capital iota
    italic*"Kappa" => "𝛫",  # mathematical italic capital kappa
    italic*"Lambda" => "𝛬",  # mathematical italic capital lambda
    italic*"Mu" => "𝛭",  # mathematical italic capital mu
    italic*"Nu" => "𝛮",  # mathematical italic capital nu
    italic*"Xi" => "𝛯",  # mathematical italic capital xi
    italic*"Omicron" => "𝛰",  # mathematical italic capital omicron
    italic*"Pi" => "𝛱",  # mathematical italic capital pi
    italic*"Rho" => "𝛲",  # mathematical italic capital rho
    italic*"varTheta" => "𝛳",  # mathematical italic capital theta symbol
    italic*"Sigma" => "𝛴",  # mathematical italic capital sigma
    italic*"Tau" => "𝛵",  # mathematical italic capital tau
    italic*"Upsilon" => "𝛶",  # mathematical italic capital upsilon
    italic*"Phi" => "𝛷",  # mathematical italic capital phi
    italic*"Chi" => "𝛸",  # mathematical italic capital chi
    italic*"Psi" => "𝛹",  # mathematical italic capital psi
    italic*"Omega" => "𝛺",  # mathematical italic capital omega
    italic*"nabla" => "𝛻",  # mathematical italic nabla
    italic*"alpha" => "𝛼",  # mathematical italic small alpha
    italic*"beta" => "𝛽",  # mathematical italic small beta
    italic*"gamma" => "𝛾",  # mathematical italic small gamma
    italic*"delta" => "𝛿",  # mathematical italic small delta
    italic*"varepsilon" => "𝜀",  # mathematical italic small epsilon
    italic*"zeta" => "𝜁",  # mathematical italic small zeta
    italic*"eta" => "𝜂",  # mathematical italic small eta
    italic*"theta" => "𝜃",  # mathematical italic small theta
    italic*"iota" => "𝜄",  # mathematical italic small iota
    italic*"kappa" => "𝜅",  # mathematical italic small kappa
    italic*"lambda" => "𝜆",  # mathematical italic small lambda
    italic*"mu" => "𝜇",  # mathematical italic small mu
    italic*"nu" => "𝜈",  # mathematical italic small nu
    italic*"xi" => "𝜉",  # mathematical italic small xi
    italic*"omicron" => "𝜊",  # mathematical italic small omicron
    italic*"pi" => "𝜋",  # mathematical italic small pi
    italic*"rho" => "𝜌",  # mathematical italic small rho
    italic*"varsigma" => "𝜍",  # mathematical italic small final sigma
    italic*"sigma" => "𝜎",  # mathematical italic small sigma
    italic*"tau" => "𝜏",  # mathematical italic small tau
    italic*"upsilon" => "𝜐",  # mathematical italic small upsilon
    italic*"varphi" => "𝜑",  # mathematical italic small phi
    italic*"chi" => "𝜒",  # mathematical italic small chi
    italic*"psi" => "𝜓",  # mathematical italic small psi
    italic*"omega" => "𝜔",  # mathematical italic small omega
    italic*"partial" => "𝜕",  # mathematical italic partial differential
    italic*"epsilon" => "𝜖",  # mathematical italic epsilon symbol
    italic*"vartheta" => "𝜗",  # mathematical italic theta symbol
    italic*"varkappa" => "𝜘",  # mathematical italic kappa symbol
    italic*"phi" => "𝜙",  # mathematical italic phi symbol
    italic*"varrho" => "𝜚",  # mathematical italic rho symbol
    italic*"varpi" => "𝜛",  # mathematical italic pi symbol
    bolditalic*"Alpha" => "𝜜",  # mathematical bold italic capital alpha
    bolditalic*"Beta" => "𝜝",  # mathematical bold italic capital beta
    bolditalic*"Gamma" => "𝜞",  # mathematical bold italic capital gamma
    bolditalic*"Delta" => "𝜟",  # mathematical bold italic capital delta
    bolditalic*"Epsilon" => "𝜠",  # mathematical bold italic capital epsilon
    bolditalic*"Zeta" => "𝜡",  # mathematical bold italic capital zeta
    bolditalic*"Eta" => "𝜢",  # mathematical bold italic capital eta
    bolditalic*"Theta" => "𝜣",  # mathematical bold italic capital theta
    bolditalic*"Iota" => "𝜤",  # mathematical bold italic capital iota
    bolditalic*"Kappa" => "𝜥",  # mathematical bold italic capital kappa
    bolditalic*"Lambda" => "𝜦",  # mathematical bold italic capital lambda
    bolditalic*"Mu" => "𝜧",  # mathematical bold italic capital mu
    bolditalic*"Nu" => "𝜨",  # mathematical bold italic capital nu
    bolditalic*"Xi" => "𝜩",  # mathematical bold italic capital xi
    bolditalic*"Omicron" => "𝜪",  # mathematical bold italic capital omicron
    bolditalic*"Pi" => "𝜫",  # mathematical bold italic capital pi
    bolditalic*"Rho" => "𝜬",  # mathematical bold italic capital rho
    bolditalic*"varTheta" => "𝜭",  # mathematical bold italic capital theta symbol
    bolditalic*"Sigma" => "𝜮",  # mathematical bold italic capital sigma
    bolditalic*"Tau" => "𝜯",  # mathematical bold italic capital tau
    bolditalic*"Upsilon" => "𝜰",  # mathematical bold italic capital upsilon
    bolditalic*"Phi" => "𝜱",  # mathematical bold italic capital phi
    bolditalic*"Chi" => "𝜲",  # mathematical bold italic capital chi
    bolditalic*"Psi" => "𝜳",  # mathematical bold italic capital psi
    bolditalic*"Omega" => "𝜴",  # mathematical bold italic capital omega
    bolditalic*"nabla" => "𝜵",  # mathematical bold italic nabla
    bolditalic*"alpha" => "𝜶",  # mathematical bold italic small alpha
    bolditalic*"beta" => "𝜷",  # mathematical bold italic small beta
    bolditalic*"gamma" => "𝜸",  # mathematical bold italic small gamma
    bolditalic*"delta" => "𝜹",  # mathematical bold italic small delta
    bolditalic*"varepsilon" => "𝜺",  # mathematical bold italic small epsilon
    bolditalic*"zeta" => "𝜻",  # mathematical bold italic small zeta
    bolditalic*"eta" => "𝜼",  # mathematical bold italic small eta
    bolditalic*"theta" => "𝜽",  # mathematical bold italic small theta
    bolditalic*"iota" => "𝜾",  # mathematical bold italic small iota
    bolditalic*"kappa" => "𝜿",  # mathematical bold italic small kappa
    bolditalic*"lambda" => "𝝀",  # mathematical bold italic small lambda
    bolditalic*"mu" => "𝝁",  # mathematical bold italic small mu
    bolditalic*"nu" => "𝝂",  # mathematical bold italic small nu
    bolditalic*"xi" => "𝝃",  # mathematical bold italic small xi
    bolditalic*"omicron" => "𝝄",  # mathematical bold italic small omicron
    bolditalic*"pi" => "𝝅",  # mathematical bold italic small pi
    bolditalic*"rho" => "𝝆",  # mathematical bold italic small rho
    bolditalic*"varsigma" => "𝝇",  # mathematical bold italic small final sigma
    bolditalic*"sigma" => "𝝈",  # mathematical bold italic small sigma
    bolditalic*"tau" => "𝝉",  # mathematical bold italic small tau
    bolditalic*"upsilon" => "𝝊",  # mathematical bold italic small upsilon
    bolditalic*"varphi" => "𝝋",  # mathematical bold italic small phi
    bolditalic*"chi" => "𝝌",  # mathematical bold italic small chi
    bolditalic*"psi" => "𝝍",  # mathematical bold italic small psi
    bolditalic*"omega" => "𝝎",  # mathematical bold italic small omega
    bolditalic*"partial" => "𝝏",  # mathematical bold italic partial differential
    bolditalic*"epsilon" => "𝝐",  # mathematical bold italic epsilon symbol
    bolditalic*"vartheta" => "𝝑",  # mathematical bold italic theta symbol
    bolditalic*"varkappa" => "𝝒",  # mathematical bold italic kappa symbol
    bolditalic*"phi" => "𝝓",  # mathematical bold italic phi symbol
    bolditalic*"varrho" => "𝝔",  # mathematical bold italic rho symbol
    bolditalic*"varpi" => "𝝕",  # mathematical bold italic pi symbol
    boldsans*"Alpha" => "𝝖",  # mathematical sans-serif bold capital alpha
    boldsans*"Beta" => "𝝗",  # mathematical sans-serif bold capital beta
    boldsans*"Gamma" => "𝝘",  # mathematical sans-serif bold capital gamma
    boldsans*"Delta" => "𝝙",  # mathematical sans-serif bold capital delta
    boldsans*"Epsilon" => "𝝚",  # mathematical sans-serif bold capital epsilon
    boldsans*"Zeta" => "𝝛",  # mathematical sans-serif bold capital zeta
    boldsans*"Eta" => "𝝜",  # mathematical sans-serif bold capital eta
    boldsans*"Theta" => "𝝝",  # mathematical sans-serif bold capital theta
    boldsans*"Iota" => "𝝞",  # mathematical sans-serif bold capital iota
    boldsans*"Kappa" => "𝝟",  # mathematical sans-serif bold capital kappa
    boldsans*"Lambda" => "𝝠",  # mathematical sans-serif bold capital lambda
    boldsans*"Mu" => "𝝡",  # mathematical sans-serif bold capital mu
    boldsans*"Nu" => "𝝢",  # mathematical sans-serif bold capital nu
    boldsans*"Xi" => "𝝣",  # mathematical sans-serif bold capital xi
    boldsans*"Omicron" => "𝝤",  # mathematical sans-serif bold capital omicron
    boldsans*"Pi" => "𝝥",  # mathematical sans-serif bold capital pi
    boldsans*"Rho" => "𝝦",  # mathematical sans-serif bold capital rho
    boldsans*"varTheta" => "𝝧",  # mathematical sans-serif bold capital theta symbol
    boldsans*"Sigma" => "𝝨",  # mathematical sans-serif bold capital sigma
    boldsans*"Tau" => "𝝩",  # mathematical sans-serif bold capital tau
    boldsans*"Upsilon" => "𝝪",  # mathematical sans-serif bold capital upsilon
    boldsans*"Phi" => "𝝫",  # mathematical sans-serif bold capital phi
    boldsans*"Chi" => "𝝬",  # mathematical sans-serif bold capital chi
    boldsans*"Psi" => "𝝭",  # mathematical sans-serif bold capital psi
    boldsans*"Omega" => "𝝮",  # mathematical sans-serif bold capital omega
    boldsans*"nabla" => "𝝯",  # mathematical sans-serif bold nabla
    boldsans*"alpha" => "𝝰",  # mathematical sans-serif bold small alpha
    boldsans*"beta" => "𝝱",  # mathematical sans-serif bold small beta
    boldsans*"gamma" => "𝝲",  # mathematical sans-serif bold small gamma
    boldsans*"delta" => "𝝳",  # mathematical sans-serif bold small delta
    boldsans*"varepsilon" => "𝝴",  # mathematical sans-serif bold small epsilon
    boldsans*"zeta" => "𝝵",  # mathematical sans-serif bold small zeta
    boldsans*"eta" => "𝝶",  # mathematical sans-serif bold small eta
    boldsans*"theta" => "𝝷",  # mathematical sans-serif bold small theta
    boldsans*"iota" => "𝝸",  # mathematical sans-serif bold small iota
    boldsans*"kappa" => "𝝹",  # mathematical sans-serif bold small kappa
    boldsans*"lambda" => "𝝺",  # mathematical sans-serif bold small lambda
    boldsans*"mu" => "𝝻",  # mathematical sans-serif bold small mu
    boldsans*"nu" => "𝝼",  # mathematical sans-serif bold small nu
    boldsans*"xi" => "𝝽",  # mathematical sans-serif bold small xi
    boldsans*"omicron" => "𝝾",  # mathematical sans-serif bold small omicron
    boldsans*"pi" => "𝝿",  # mathematical sans-serif bold small pi
    boldsans*"rho" => "𝞀",  # mathematical sans-serif bold small rho
    boldsans*"varsigma" => "𝞁",  # mathematical sans-serif bold small final sigma
    boldsans*"sigma" => "𝞂",  # mathematical sans-serif bold small sigma
    boldsans*"tau" => "𝞃",  # mathematical sans-serif bold small tau
    boldsans*"upsilon" => "𝞄",  # mathematical sans-serif bold small upsilon
    boldsans*"varphi" => "𝞅",  # mathematical sans-serif bold small phi
    boldsans*"chi" => "𝞆",  # mathematical sans-serif bold small chi
    boldsans*"psi" => "𝞇",  # mathematical sans-serif bold small psi
    boldsans*"omega" => "𝞈",  # mathematical sans-serif bold small omega
    boldsans*"partial" => "𝞉",  # mathematical sans-serif bold partial differential
    boldsans*"epsilon" => "𝞊",  # mathematical sans-serif bold epsilon symbol
    boldsans*"vartheta" => "𝞋",  # mathematical sans-serif bold theta symbol
    boldsans*"varkappa" => "𝞌",  # mathematical sans-serif bold kappa symbol
    boldsans*"phi" => "𝞍",  # mathematical sans-serif bold phi symbol
    boldsans*"varrho" => "𝞎",  # mathematical sans-serif bold rho symbol
    boldsans*"varpi" => "𝞏",  # mathematical sans-serif bold pi symbol
    bolditalicsans*"Alpha" => "𝞐",  # mathematical sans-serif bold italic capital alpha
    bolditalicsans*"Beta" => "𝞑",  # mathematical sans-serif bold italic capital beta
    bolditalicsans*"Gamma" => "𝞒",  # mathematical sans-serif bold italic capital gamma
    bolditalicsans*"Delta" => "𝞓",  # mathematical sans-serif bold italic capital delta
    bolditalicsans*"Epsilon" => "𝞔",  # mathematical sans-serif bold italic capital epsilon
    bolditalicsans*"Zeta" => "𝞕",  # mathematical sans-serif bold italic capital zeta
    bolditalicsans*"Eta" => "𝞖",  # mathematical sans-serif bold italic capital eta
    bolditalicsans*"Theta" => "𝞗",  # mathematical sans-serif bold italic capital theta
    bolditalicsans*"Iota" => "𝞘",  # mathematical sans-serif bold italic capital iota
    bolditalicsans*"Kappa" => "𝞙",  # mathematical sans-serif bold italic capital kappa
    bolditalicsans*"Lambda" => "𝞚",  # mathematical sans-serif bold italic capital lambda
    bolditalicsans*"Mu" => "𝞛",  # mathematical sans-serif bold italic capital mu
    bolditalicsans*"Nu" => "𝞜",  # mathematical sans-serif bold italic capital nu
    bolditalicsans*"Xi" => "𝞝",  # mathematical sans-serif bold italic capital xi
    bolditalicsans*"Omicron" => "𝞞",  # mathematical sans-serif bold italic capital omicron
    bolditalicsans*"Pi" => "𝞟",  # mathematical sans-serif bold italic capital pi
    bolditalicsans*"Rho" => "𝞠",  # mathematical sans-serif bold italic capital rho
    bolditalicsans*"varTheta" => "𝞡",  # mathematical sans-serif bold italic capital theta symbol
    bolditalicsans*"Sigma" => "𝞢",  # mathematical sans-serif bold italic capital sigma
    bolditalicsans*"Tau" => "𝞣",  # mathematical sans-serif bold italic capital tau
    bolditalicsans*"Upsilon" => "𝞤",  # mathematical sans-serif bold italic capital upsilon
    bolditalicsans*"Phi" => "𝞥",  # mathematical sans-serif bold italic capital phi
    bolditalicsans*"Chi" => "𝞦",  # mathematical sans-serif bold italic capital chi
    bolditalicsans*"Psi" => "𝞧",  # mathematical sans-serif bold italic capital psi
    bolditalicsans*"Omega" => "𝞨",  # mathematical sans-serif bold italic capital omega
    bolditalicsans*"nabla" => "𝞩",  # mathematical sans-serif bold italic nabla
    bolditalicsans*"alpha" => "𝞪",  # mathematical sans-serif bold italic small alpha
    bolditalicsans*"beta" => "𝞫",  # mathematical sans-serif bold italic small beta
    bolditalicsans*"gamma" => "𝞬",  # mathematical sans-serif bold italic small gamma
    bolditalicsans*"delta" => "𝞭",  # mathematical sans-serif bold italic small delta
    bolditalicsans*"varepsilon" => "𝞮",  # mathematical sans-serif bold italic small epsilon
    bolditalicsans*"zeta" => "𝞯",  # mathematical sans-serif bold italic small zeta
    bolditalicsans*"eta" => "𝞰",  # mathematical sans-serif bold italic small eta
    bolditalicsans*"theta" => "𝞱",  # mathematical sans-serif bold italic small theta
    bolditalicsans*"iota" => "𝞲",  # mathematical sans-serif bold italic small iota
    bolditalicsans*"kappa" => "𝞳",  # mathematical sans-serif bold italic small kappa
    bolditalicsans*"lambda" => "𝞴",  # mathematical sans-serif bold italic small lambda
    bolditalicsans*"mu" => "𝞵",  # mathematical sans-serif bold italic small mu
    bolditalicsans*"nu" => "𝞶",  # mathematical sans-serif bold italic small nu
    bolditalicsans*"xi" => "𝞷",  # mathematical sans-serif bold italic small xi
    bolditalicsans*"omicron" => "𝞸",  # mathematical sans-serif bold italic small omicron
    bolditalicsans*"pi" => "𝞹",  # mathematical sans-serif bold italic small pi
    bolditalicsans*"rho" => "𝞺",  # mathematical sans-serif bold italic small rho
    bolditalicsans*"varsigma" => "𝞻",  # mathematical sans-serif bold italic small final sigma
    bolditalicsans*"sigma" => "𝞼",  # mathematical sans-serif bold italic small sigma
    bolditalicsans*"tau" => "𝞽",  # mathematical sans-serif bold italic small tau
    bolditalicsans*"upsilon" => "𝞾",  # mathematical sans-serif bold italic small upsilon
    bolditalicsans*"varphi" => "𝞿",  # mathematical sans-serif bold italic small phi
    bolditalicsans*"chi" => "𝟀",  # mathematical sans-serif bold italic small chi
    bolditalicsans*"psi" => "𝟁",  # mathematical sans-serif bold italic small psi
    bolditalicsans*"omega" => "𝟂",  # mathematical sans-serif bold italic small omega
    bolditalicsans*"partial" => "𝟃",  # mathematical sans-serif bold italic partial differential
    bolditalicsans*"epsilon" => "𝟄",  # mathematical sans-serif bold italic epsilon symbol
    bolditalicsans*"vartheta" => "𝟅",  # mathematical sans-serif bold italic theta symbol
    bolditalicsans*"varkappa" => "𝟆",  # mathematical sans-serif bold italic kappa symbol
    bolditalicsans*"phi" => "𝟇",  # mathematical sans-serif bold italic phi symbol
    bolditalicsans*"varrho" => "𝟈",  # mathematical sans-serif bold italic rho symbol
    bolditalicsans*"varpi" => "𝟉",  # mathematical sans-serif bold italic pi symbol
    bold*"Digamma" => "\U1d7ca",  # mathematical bold capital digamma
    bold*"digamma" => "\U1d7cb",  # mathematical bold small digamma
    bold*"zero" => "𝟎",  # mathematical bold digit 0
    bold*"one" => "𝟏",  # mathematical bold digit 1
    bold*"two" => "𝟐",  # mathematical bold digit 2
    bold*"three" => "𝟑",  # mathematical bold digit 3
    bold*"four" => "𝟒",  # mathematical bold digit 4
    bold*"five" => "𝟓",  # mathematical bold digit 5
    bold*"six" => "𝟔",  # mathematical bold digit 6
    bold*"seven" => "𝟕",  # mathematical bold digit 7
    bold*"eight" => "𝟖",  # mathematical bold digit 8
    bold*"nine" => "𝟗",  # mathematical bold digit 9
    blackboard*"zero" => "𝟘",  # mathematical double-struck digit 0
    blackboard*"one" => "𝟙",  # mathematical double-struck digit 1
    blackboard*"two" => "𝟚",  # mathematical double-struck digit 2
    blackboard*"three" => "𝟛",  # mathematical double-struck digit 3
    blackboard*"four" => "𝟜",  # mathematical double-struck digit 4
    blackboard*"five" => "𝟝",  # mathematical double-struck digit 5
    blackboard*"six" => "𝟞",  # mathematical double-struck digit 6
    blackboard*"seven" => "𝟟",  # mathematical double-struck digit 7
    blackboard*"eight" => "𝟠",  # mathematical double-struck digit 8
    blackboard*"nine" => "𝟡",  # mathematical double-struck digit 9
    sans*"zero" => "𝟢",  # mathematical sans-serif digit 0
    sans*"one" => "𝟣",  # mathematical sans-serif digit 1
    sans*"two" => "𝟤",  # mathematical sans-serif digit 2
    sans*"three" => "𝟥",  # mathematical sans-serif digit 3
    sans*"four" => "𝟦",  # mathematical sans-serif digit 4
    sans*"five" => "𝟧",  # mathematical sans-serif digit 5
    sans*"six" => "𝟨",  # mathematical sans-serif digit 6
    sans*"seven" => "𝟩",  # mathematical sans-serif digit 7
    sans*"eight" => "𝟪",  # mathematical sans-serif digit 8
    sans*"nine" => "𝟫",  # mathematical sans-serif digit 9
    boldsans*"zero" => "𝟬",  # mathematical sans-serif bold digit 0
    boldsans*"one" => "𝟭",  # mathematical sans-serif bold digit 1
    boldsans*"two" => "𝟮",  # mathematical sans-serif bold digit 2
    boldsans*"three" => "𝟯",  # mathematical sans-serif bold digit 3
    boldsans*"four" => "𝟰",  # mathematical sans-serif bold digit 4
    boldsans*"five" => "𝟱",  # mathematical sans-serif bold digit 5
    boldsans*"six" => "𝟲",  # mathematical sans-serif bold digit 6
    boldsans*"seven" => "𝟳",  # mathematical sans-serif bold digit 7
    boldsans*"eight" => "𝟴",  # mathematical sans-serif bold digit 8
    boldsans*"nine" => "𝟵",  # mathematical sans-serif bold digit 9
    mono*"zero" => "𝟶",  # mathematical monospace digit 0
    mono*"one" => "𝟷",  # mathematical monospace digit 1
    mono*"two" => "𝟸",  # mathematical monospace digit 2
    mono*"three" => "𝟹",  # mathematical monospace digit 3
    mono*"four" => "𝟺",  # mathematical monospace digit 4
    mono*"five" => "𝟻",  # mathematical monospace digit 5
    mono*"six" => "𝟼",  # mathematical monospace digit 6
    mono*"seven" => "𝟽",  # mathematical monospace digit 7
    mono*"eight" => "𝟾",  # mathematical monospace digit 8
    mono*"nine" => "𝟿",  # mathematical monospace digit 9

    "\\triangleright" => "▷",  # (large) right triangle, open; z notation range restriction
    "\\triangleleft" => "◁",  # (large) left triangle, open; z notation domain restriction
    "\\leftouterjoin" => "⟕",  # left outer join
    "\\rightouterjoin" => "⟖",  # right outer join
    "\\fullouterjoin" => "⟗",  # full outer join
    "\\join" => "⨝",  # join
    "\\underbar" => "̲",  # combining low line
    "\\underleftrightarrow" => "͍",  # underleftrightarrow accent
    "\\leftwavearrow" => "↜",  # left arrow-wavy
    "\\rightwavearrow" => "↝",  # right arrow-wavy
    "\\varbarwedge" => "⌅",  # /barwedge b: logical and, bar above [projective (bar over small wedge)]
    "\\smallblacktriangleright" => "▸",  # right triangle, filled
    "\\smallblacktriangleleft" => "◂",  # left triangle, filled
    "\\leftmoon" => "☾",  # last quarter moon
    "\\smalltriangleright" => "▹",  # right triangle, open
    "\\smalltriangleleft" => "◃",  # left triangle, open

    "\\tricolon" => "⁝",  # tricolon

    # fractions
    "\\1/4" => "¼", # vulgar fraction one quarter
    "\\1/2" => "½", # vulgar fraction one half
    "\\3/4" => "¾", # vulgar fraction three quarters
    "\\1/7" => "⅐", # vulgar fraction one seventh
    "\\1/9" => "⅑", # vulgar fraction one ninth
    "\\1/10" => "⅒", # vulgar fraction one tenth
    "\\1/3" => "⅓", # vulgar fraction one third
    "\\2/3" => "⅔", # vulgar fraction two thirds
    "\\1/5" => "⅕", # vulgar fraction one fifth
    "\\2/5" => "⅖", # vulgar fraction two fifths
    "\\3/5" => "⅗", # vulgar fraction three fifths
    "\\4/5" => "⅘", # vulgar fraction four fifths
    "\\1/6" => "⅙", # vulgar fraction one sixth
    "\\5/6" => "⅚", # vulgar fraction five sixths
    "\\1/8" => "⅛", # vulgar fraction one eigth
    "\\3/8" => "⅜", # vulgar fraction three eigths
    "\\5/8" => "⅝", # vulgar fraction five eigths
    "\\7/8" => "⅞", # vulgar fraction seventh eigths
    "\\1/" => "⅟", # fraction numerator one
    "\\0/3" => "↉", # vulgar fraction zero thirds
    "\\1/4" => "¼", # vulgar fraction one quarter
)


# Canonical reverse mapping for symbols that have several completions (#39148).
#
# These duplicate mappings can be investigated with the following commands:
#=
ls = REPL.REPLCompletions.latex_symbols; symbols = values(ls)
duplicates = [v for v in unique(symbols) if count(==(v), symbols) > 1]
[(v, REPL.symbol_latex(v)) => findall(==(v), ls) for v in duplicates]
=#
const symbols_latex_canonical = Dict(
    "⫫" => "\\Bot",
    "ð" => "\\dh",
    "…" => "\\ldots",
    "∅" => "\\emptyset",
    "ℯ" => "\\euler",
    "♀" => "\\female",
    "≥" => "\\ge",
    "⟺" => "\\iff",
    "ℑ" => "\\Im",
    "⟸" => "\\impliedby",
    "⟹" => "\\implies",
    "≤" => "\\le",
    "⟦" => "\\llbracket",
    "♂" => "\\male",
    "∇" => "\\del",
    "ℎ" => "\\planck",
    "ℜ" => "\\Re",
    "⟧" => "\\rrbracket",
    "√" => "\\sqrt",
    "̶" => "\\sout",
    "→" => "\\to",
    "⫪" => "\\Top",
    "ε" => "\\varepsilon",
    "⊻" => "\\xor",
    "⊼" => "\\nand",
    "⊽" => "\\nor",
    "≠" => "\\ne",
)
u   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/REPL/src/emoji_symbols.jlǗ      # This file is a part of Julia. License is MIT: https://julialang.org/license

#==
using Pkg: @pkg_str
pkg"activate --temp"
pkg"add JSON@0.21"

import JSON

function emoji_data(url)
    emojis = JSON.parsefile(download(url))
    result = Dict()
    for emj in emojis
        name = "\\:" * emj["short_name"] * ":"
        unicode = emj["unified"]
        if '-' in unicode
            continue
        end
        result[name] = "$(Char(parse(UInt32, unicode, base = 16)))"
    end
    return result
end

# We combine multiple versions as the data changes, and not only by growing.
result = mapfoldr(emoji_data, merge, [
    # Newer versions must be added to the bottom list as we want the newer versions to
    # overwrite the old with names that changed but still keep old ones that were removed
    "https://raw.githubusercontent.com/iamcal/emoji-data/0f0cf4ea8845eb52d26df2a48c3c31c3b8cad14e/emoji_pretty.json",
    "https://raw.githubusercontent.com/iamcal/emoji-data/e512953312c012f6bd00e3f2ef6bf152ca3710f8/emoji_pretty.json",
    ];
    init=Dict()
)

skeys = sort(collect(keys(result)))
open("emoji_symbols.jl", "w") do fh
    println(fh, "const emoji_symbols = Dict(")
    for key in skeys
        println(fh, "    \"", escape_string(key), "\" => \"",
                 escape_string(result[key]), "\",")
    end
    println(fh, ")")
end
=#

const emoji_symbols = Dict(
    "\\:+1:" => "👍",
    "\\:-1:" => "👎",
    "\\:100:" => "💯",
    "\\:1234:" => "🔢",
    "\\:8ball:" => "🎱",
    "\\:a:" => "🅰",
    "\\:ab:" => "🆎",
    "\\:abacus:" => "🧮",
    "\\:abc:" => "🔤",
    "\\:abcd:" => "🔡",
    "\\:accept:" => "🉑",
    "\\:accordion:" => "🪗",
    "\\:adhesive_bandage:" => "🩹",
    "\\:adult:" => "🧑",
    "\\:aerial_tramway:" => "🚡",
    "\\:airplane:" => "✈",
    "\\:airplane_arriving:" => "🛬",
    "\\:airplane_departure:" => "🛫",
    "\\:alarm_clock:" => "⏰",
    "\\:alien:" => "👽",
    "\\:ambulance:" => "🚑",
    "\\:amphora:" => "🏺",
    "\\:anatomical_heart:" => "🫀",
    "\\:anchor:" => "⚓",
    "\\:angel:" => "👼",
    "\\:anger:" => "💢",
    "\\:angry:" => "😠",
    "\\:anguished:" => "😧",
    "\\:ant:" => "🐜",
    "\\:apple:" => "🍎",
    "\\:aquarius:" => "♒",
    "\\:aries:" => "♈",
    "\\:arrow_backward:" => "◀",
    "\\:arrow_double_down:" => "⏬",
    "\\:arrow_double_up:" => "⏫",
    "\\:arrow_down:" => "⬇",
    "\\:arrow_down_small:" => "🔽",
    "\\:arrow_forward:" => "▶",
    "\\:arrow_heading_down:" => "⤵",
    "\\:arrow_heading_up:" => "⤴",
    "\\:arrow_left:" => "⬅",
    "\\:arrow_lower_left:" => "↙",
    "\\:arrow_lower_right:" => "↘",
    "\\:arrow_right:" => "➡",
    "\\:arrow_right_hook:" => "↪",
    "\\:arrow_up:" => "⬆",
    "\\:arrow_up_down:" => "↕",
    "\\:arrow_up_small:" => "🔼",
    "\\:arrow_upper_left:" => "↖",
    "\\:arrow_upper_right:" => "↗",
    "\\:arrows_clockwise:" => "🔃",
    "\\:arrows_counterclockwise:" => "🔄",
    "\\:art:" => "🎨",
    "\\:articulated_lorry:" => "🚛",
    "\\:astonished:" => "😲",
    "\\:athletic_shoe:" => "👟",
    "\\:atm:" => "🏧",
    "\\:auto_rickshaw:" => "🛺",
    "\\:avocado:" => "🥑",
    "\\:axe:" => "🪓",
    "\\:b:" => "🅱",
    "\\:baby:" => "👶",
    "\\:baby_bottle:" => "🍼",
    "\\:baby_chick:" => "🐤",
    "\\:baby_symbol:" => "🚼",
    "\\:back:" => "🔙",
    "\\:bacon:" => "🥓",
    "\\:badger:" => "🦡",
    "\\:badminton_racquet_and_shuttlecock:" => "🏸",
    "\\:bagel:" => "🥯",
    "\\:baggage_claim:" => "🛄",
    "\\:baguette_bread:" => "🥖",
    "\\:ballet_shoes:" => "🩰",
    "\\:balloon:" => "🎈",
    "\\:ballot_box_with_check:" => "☑",
    "\\:bamboo:" => "🎍",
    "\\:banana:" => "🍌",
    "\\:bangbang:" => "‼",
    "\\:banjo:" => "🪕",
    "\\:bank:" => "🏦",
    "\\:bar_chart:" => "📊",
    "\\:barber:" => "💈",
    "\\:baseball:" => "⚾",
    "\\:basket:" => "🧺",
    "\\:basketball:" => "🏀",
    "\\:bat:" => "🦇",
    "\\:bath:" => "🛀",
    "\\:bathtub:" => "🛁",
    "\\:battery:" => "🔋",
    "\\:bear:" => "🐻",
    "\\:bearded_person:" => "🧔",
    "\\:beaver:" => "🦫",
    "\\:bee:" => "🐝",
    "\\:beer:" => "🍺",
    "\\:beers:" => "🍻",
    "\\:beetle:" => "🪲",
    "\\:beginner:" => "🔰",
    "\\:bell:" => "🔔",
    "\\:bell_pepper:" => "🫑",
    "\\:bento:" => "🍱",
    "\\:beverage_box:" => "🧃",
    "\\:bicyclist:" => "🚴",
    "\\:bike:" => "🚲",
    "\\:bikini:" => "👙",
    "\\:billed_cap:" => "🧢",
    "\\:bird:" => "🐦",
    "\\:birthday:" => "🎂",
    "\\:bison:" => "🦬",
    "\\:black_circle:" => "⚫",
    "\\:black_heart:" => "🖤",
    "\\:black_joker:" => "🃏",
    "\\:black_large_square:" => "⬛",
    "\\:black_medium_small_square:" => "◾",
    "\\:black_medium_square:" => "◼",
    "\\:black_nib:" => "✒",
    "\\:black_small_square:" => "▪",
    "\\:black_square_button:" => "🔲",
    "\\:blossom:" => "🌼",
    "\\:blowfish:" => "🐡",
    "\\:blue_book:" => "📘",
    "\\:blue_car:" => "🚙",
    "\\:blue_heart:" => "💙",
    "\\:blueberries:" => "🫐",
    "\\:blush:" => "😊",
    "\\:boar:" => "🐗",
    "\\:boat:" => "⛵",
    "\\:bomb:" => "💣",
    "\\:bone:" => "🦴",
    "\\:book:" => "📖",
    "\\:bookmark:" => "🔖",
    "\\:bookmark_tabs:" => "📑",
    "\\:books:" => "📚",
    "\\:boom:" => "💥",
    "\\:boomerang:" => "🪃",
    "\\:boot:" => "👢",
    "\\:bouquet:" => "💐",
    "\\:bow:" => "🙇",
    "\\:bow_and_arrow:" => "🏹",
    "\\:bowl_with_spoon:" => "🥣",
    "\\:bowling:" => "🎳",
    "\\:boxing_glove:" => "🥊",
    "\\:boy:" => "👦",
    "\\:brain:" => "🧠",
    "\\:bread:" => "🍞",
    "\\:breast-feeding:" => "🤱",
    "\\:bricks:" => "🧱",
    "\\:bride_with_veil:" => "👰",
    "\\:bridge_at_night:" => "🌉",
    "\\:briefcase:" => "💼",
    "\\:briefs:" => "🩲",
    "\\:broccoli:" => "🥦",
    "\\:broken_heart:" => "💔",
    "\\:broom:" => "🧹",
    "\\:brown_heart:" => "🤎",
    "\\:bubble_tea:" => "🧋",
    "\\:bucket:" => "🪣",
    "\\:bug:" => "🐛",
    "\\:bulb:" => "💡",
    "\\:bullettrain_front:" => "🚅",
    "\\:bullettrain_side:" => "🚄",
    "\\:burrito:" => "🌯",
    "\\:bus:" => "🚌",
    "\\:busstop:" => "🚏",
    "\\:bust_in_silhouette:" => "👤",
    "\\:busts_in_silhouette:" => "👥",
    "\\:butter:" => "🧈",
    "\\:butterfly:" => "🦋",
    "\\:cactus:" => "🌵",
    "\\:cake:" => "🍰",
    "\\:calendar:" => "📆",
    "\\:call_me_hand:" => "🤙",
    "\\:calling:" => "📲",
    "\\:camel:" => "🐫",
    "\\:camera:" => "📷",
    "\\:camera_with_flash:" => "📸",
    "\\:cancer:" => "♋",
    "\\:candy:" => "🍬",
    "\\:canned_food:" => "🥫",
    "\\:canoe:" => "🛶",
    "\\:capital_abcd:" => "🔠",
    "\\:capricorn:" => "♑",
    "\\:car:" => "🚗",
    "\\:card_index:" => "📇",
    "\\:carousel_horse:" => "🎠",
    "\\:carpentry_saw:" => "🪚",
    "\\:carrot:" => "🥕",
    "\\:cat2:" => "🐈",
    "\\:cat:" => "🐱",
    "\\:cd:" => "💿",
    "\\:chair:" => "🪑",
    "\\:champagne:" => "🍾",
    "\\:chart:" => "💹",
    "\\:chart_with_downwards_trend:" => "📉",
    "\\:chart_with_upwards_trend:" => "📈",
    "\\:checkered_flag:" => "🏁",
    "\\:cheese_wedge:" => "🧀",
    "\\:cherries:" => "🍒",
    "\\:cherry_blossom:" => "🌸",
    "\\:chestnut:" => "🌰",
    "\\:chicken:" => "🐔",
    "\\:child:" => "🧒",
    "\\:children_crossing:" => "🚸",
    "\\:chocolate_bar:" => "🍫",
    "\\:chopsticks:" => "🥢",
    "\\:christmas_tree:" => "🎄",
    "\\:church:" => "⛪",
    "\\:cinema:" => "🎦",
    "\\:circus_tent:" => "🎪",
    "\\:city_sunrise:" => "🌇",
    "\\:city_sunset:" => "🌆",
    "\\:cl:" => "🆑",
    "\\:clap:" => "👏",
    "\\:clapper:" => "🎬",
    "\\:clinking_glasses:" => "🥂",
    "\\:clipboard:" => "📋",
    "\\:clock1030:" => "🕥",
    "\\:clock10:" => "🕙",
    "\\:clock1130:" => "🕦",
    "\\:clock11:" => "🕚",
    "\\:clock1230:" => "🕧",
    "\\:clock12:" => "🕛",
    "\\:clock130:" => "🕜",
    "\\:clock1:" => "🕐",
    "\\:clock230:" => "🕝",
    "\\:clock2:" => "🕑",
    "\\:clock330:" => "🕞",
    "\\:clock3:" => "🕒",
    "\\:clock430:" => "🕟",
    "\\:clock4:" => "🕓",
    "\\:clock530:" => "🕠",
    "\\:clock5:" => "🕔",
    "\\:clock630:" => "🕡",
    "\\:clock6:" => "🕕",
    "\\:clock730:" => "🕢",
    "\\:clock7:" => "🕖",
    "\\:clock830:" => "🕣",
    "\\:clock8:" => "🕗",
    "\\:clock930:" => "🕤",
    "\\:clock9:" => "🕘",
    "\\:closed_book:" => "📕",
    "\\:closed_lock_with_key:" => "🔐",
    "\\:closed_umbrella:" => "🌂",
    "\\:cloud:" => "☁",
    "\\:clown_face:" => "🤡",
    "\\:clubs:" => "♣",
    "\\:coat:" => "🧥",
    "\\:cockroach:" => "🪳",
    "\\:cocktail:" => "🍸",
    "\\:coconut:" => "🥥",
    "\\:coffee:" => "☕",
    "\\:coin:" => "🪙",
    "\\:cold_face:" => "🥶",
    "\\:cold_sweat:" => "😰",
    "\\:compass:" => "🧭",
    "\\:computer:" => "💻",
    "\\:confetti_ball:" => "🎊",
    "\\:confounded:" => "😖",
    "\\:confused:" => "😕",
    "\\:congratulations:" => "㊗",
    "\\:construction:" => "🚧",
    "\\:construction_worker:" => "👷",
    "\\:convenience_store:" => "🏪",
    "\\:cookie:" => "🍪",
    "\\:cool:" => "🆒",
    "\\:cop:" => "👮",
    "\\:copyright:" => "©",
    "\\:corn:" => "🌽",
    "\\:couple:" => "👫",
    "\\:couple_with_heart:" => "💑",
    "\\:couplekiss:" => "💏",
    "\\:cow2:" => "🐄",
    "\\:cow:" => "🐮",
    "\\:crab:" => "🦀",
    "\\:credit_card:" => "💳",
    "\\:crescent_moon:" => "🌙",
    "\\:cricket:" => "🦗",
    "\\:cricket_bat_and_ball:" => "🏏",
    "\\:crocodile:" => "🐊",
    "\\:croissant:" => "🥐",
    "\\:crossed_fingers:" => "🤞",
    "\\:crossed_flags:" => "🎌",
    "\\:crown:" => "👑",
    "\\:cry:" => "😢",
    "\\:crying_cat_face:" => "😿",
    "\\:crystal_ball:" => "🔮",
    "\\:cucumber:" => "🥒",
    "\\:cup_with_straw:" => "🥤",
    "\\:cupcake:" => "🧁",
    "\\:cupid:" => "💘",
    "\\:curling_stone:" => "🥌",
    "\\:curly_loop:" => "➰",
    "\\:currency_exchange:" => "💱",
    "\\:curry:" => "🍛",
    "\\:custard:" => "🍮",
    "\\:customs:" => "🛃",
    "\\:cut_of_meat:" => "🥩",
    "\\:cyclone:" => "🌀",
    "\\:dancer:" => "💃",
    "\\:dancers:" => "👯",
    "\\:dango:" => "🍡",
    "\\:dart:" => "🎯",
    "\\:dash:" => "💨",
    "\\:date:" => "📅",
    "\\:deaf_person:" => "🧏",
    "\\:deciduous_tree:" => "🌳",
    "\\:deer:" => "🦌",
    "\\:department_store:" => "🏬",
    "\\:diamond_shape_with_a_dot_inside:" => "💠",
    "\\:diamonds:" => "♦",
    "\\:disappointed:" => "😞",
    "\\:disappointed_relieved:" => "😥",
    "\\:disguised_face:" => "🥸",
    "\\:diving_mask:" => "🤿",
    "\\:diya_lamp:" => "🪔",
    "\\:dizzy:" => "💫",
    "\\:dizzy_face:" => "😵",
    "\\:dna:" => "🧬",
    "\\:do_not_litter:" => "🚯",
    "\\:dodo:" => "🦤",
    "\\:dog2:" => "🐕",
    "\\:dog:" => "🐶",
    "\\:dollar:" => "💵",
    "\\:dolls:" => "🎎",
    "\\:dolphin:" => "🐬",
    "\\:door:" => "🚪",
    "\\:doughnut:" => "🍩",
    "\\:dragon:" => "🐉",
    "\\:dragon_face:" => "🐲",
    "\\:dress:" => "👗",
    "\\:dromedary_camel:" => "🐪",
    "\\:drooling_face:" => "🤤",
    "\\:drop_of_blood:" => "🩸",
    "\\:droplet:" => "💧",
    "\\:drum_with_drumsticks:" => "🥁",
    "\\:duck:" => "🦆",
    "\\:dumpling:" => "🥟",
    "\\:dvd:" => "📀",
    "\\:e-mail:" => "📧",
    "\\:eagle:" => "🦅",
    "\\:ear:" => "👂",
    "\\:ear_of_rice:" => "🌾",
    "\\:ear_with_hearing_aid:" => "🦻",
    "\\:earth_africa:" => "🌍",
    "\\:earth_americas:" => "🌎",
    "\\:earth_asia:" => "🌏",
    "\\:egg:" => "🥚",
    "\\:eggplant:" => "🍆",
    "\\:eight_pointed_black_star:" => "✴",
    "\\:eight_spoked_asterisk:" => "✳",
    "\\:electric_plug:" => "🔌",
    "\\:elephant:" => "🐘",
    "\\:elevator:" => "🛗",
    "\\:elf:" => "🧝",
    "\\:email:" => "✉",
    "\\:end:" => "🔚",
    "\\:envelope_with_arrow:" => "📩",
    "\\:euro:" => "💶",
    "\\:european_castle:" => "🏰",
    "\\:european_post_office:" => "🏤",
    "\\:evergreen_tree:" => "🌲",
    "\\:exclamation:" => "❗",
    "\\:exploding_head:" => "🤯",
    "\\:expressionless:" => "😑",
    "\\:eyeglasses:" => "👓",
    "\\:eyes:" => "👀",
    "\\:face_palm:" => "🤦",
    "\\:face_vomiting:" => "🤮",
    "\\:face_with_cowboy_hat:" => "🤠",
    "\\:face_with_hand_over_mouth:" => "🤭",
    "\\:face_with_head_bandage:" => "🤕",
    "\\:face_with_monocle:" => "🧐",
    "\\:face_with_raised_eyebrow:" => "🤨",
    "\\:face_with_rolling_eyes:" => "🙄",
    "\\:face_with_symbols_on_mouth:" => "🤬",
    "\\:face_with_thermometer:" => "🤒",
    "\\:facepunch:" => "👊",
    "\\:factory:" => "🏭",
    "\\:fairy:" => "🧚",
    "\\:falafel:" => "🧆",
    "\\:fallen_leaf:" => "🍂",
    "\\:family:" => "👪",
    "\\:fast_forward:" => "⏩",
    "\\:fax:" => "📠",
    "\\:fearful:" => "😨",
    "\\:feather:" => "🪶",
    "\\:feet:" => "🐾",
    "\\:fencer:" => "🤺",
    "\\:ferris_wheel:" => "🎡",
    "\\:field_hockey_stick_and_ball:" => "🏑",
    "\\:file_folder:" => "📁",
    "\\:fire:" => "🔥",
    "\\:fire_engine:" => "🚒",
    "\\:fire_extinguisher:" => "🧯",
    "\\:firecracker:" => "🧨",
    "\\:fireworks:" => "🎆",
    "\\:first_place_medal:" => "🥇",
    "\\:first_quarter_moon:" => "🌓",
    "\\:first_quarter_moon_with_face:" => "🌛",
    "\\:fish:" => "🐟",
    "\\:fish_cake:" => "🍥",
    "\\:fishing_pole_and_fish:" => "🎣",
    "\\:fist:" => "✊",
    "\\:flags:" => "🎏",
    "\\:flamingo:" => "🦩",
    "\\:flashlight:" => "🔦",
    "\\:flatbread:" => "🫓",
    "\\:floppy_disk:" => "💾",
    "\\:flower_playing_cards:" => "🎴",
    "\\:flushed:" => "😳",
    "\\:fly:" => "🪰",
    "\\:flying_disc:" => "🥏",
    "\\:flying_saucer:" => "🛸",
    "\\:foggy:" => "🌁",
    "\\:fondue:" => "🫕",
    "\\:foot:" => "🦶",
    "\\:football:" => "🏈",
    "\\:footprints:" => "👣",
    "\\:fork_and_knife:" => "🍴",
    "\\:fortune_cookie:" => "🥠",
    "\\:fountain:" => "⛲",
    "\\:four_leaf_clover:" => "🍀",
    "\\:fox_face:" => "🦊",
    "\\:free:" => "🆓",
    "\\:fried_egg:" => "🍳",
    "\\:fried_shrimp:" => "🍤",
    "\\:fries:" => "🍟",
    "\\:frog:" => "🐸",
    "\\:frowning:" => "😦",
    "\\:fuelpump:" => "⛽",
    "\\:full_moon:" => "🌕",
    "\\:full_moon_with_face:" => "🌝",
    "\\:game_die:" => "🎲",
    "\\:garlic:" => "🧄",
    "\\:gem:" => "💎",
    "\\:gemini:" => "♊",
    "\\:genie:" => "🧞",
    "\\:ghost:" => "👻",
    "\\:gift:" => "🎁",
    "\\:gift_heart:" => "💝",
    "\\:giraffe_face:" => "🦒",
    "\\:girl:" => "👧",
    "\\:glass_of_milk:" => "🥛",
    "\\:globe_with_meridians:" => "🌐",
    "\\:gloves:" => "🧤",
    "\\:goal_net:" => "🥅",
    "\\:goat:" => "🐐",
    "\\:goggles:" => "🥽",
    "\\:golf:" => "⛳",
    "\\:gorilla:" => "🦍",
    "\\:grapes:" => "🍇",
    "\\:green_apple:" => "🍏",
    "\\:green_book:" => "📗",
    "\\:green_heart:" => "💚",
    "\\:green_salad:" => "🥗",
    "\\:grey_exclamation:" => "❕",
    "\\:grey_question:" => "❔",
    "\\:grimacing:" => "😬",
    "\\:grin:" => "😁",
    "\\:grinning:" => "😀",
    "\\:guardsman:" => "💂",
    "\\:guide_dog:" => "🦮",
    "\\:guitar:" => "🎸",
    "\\:gun:" => "🔫",
    "\\:haircut:" => "💇",
    "\\:hamburger:" => "🍔",
    "\\:hammer:" => "🔨",
    "\\:hamster:" => "🐹",
    "\\:hand:" => "✋",
    "\\:handbag:" => "👜",
    "\\:handball:" => "🤾",
    "\\:handshake:" => "🤝",
    "\\:hankey:" => "💩",
    "\\:hatched_chick:" => "🐥",
    "\\:hatching_chick:" => "🐣",
    "\\:headphones:" => "🎧",
    "\\:headstone:" => "🪦",
    "\\:hear_no_evil:" => "🙉",
    "\\:heart:" => "❤",
    "\\:heart_decoration:" => "💟",
    "\\:heart_eyes:" => "😍",
    "\\:heart_eyes_cat:" => "😻",
    "\\:heartbeat:" => "💓",
    "\\:heartpulse:" => "💗",
    "\\:hearts:" => "♥",
    "\\:heavy_check_mark:" => "✔",
    "\\:heavy_division_sign:" => "➗",
    "\\:heavy_dollar_sign:" => "💲",
    "\\:heavy_minus_sign:" => "➖",
    "\\:heavy_multiplication_x:" => "✖",
    "\\:heavy_plus_sign:" => "➕",
    "\\:hedgehog:" => "🦔",
    "\\:helicopter:" => "🚁",
    "\\:herb:" => "🌿",
    "\\:hibiscus:" => "🌺",
    "\\:high_brightness:" => "🔆",
    "\\:high_heel:" => "👠",
    "\\:hiking_boot:" => "🥾",
    "\\:hindu_temple:" => "🛕",
    "\\:hippopotamus:" => "🦛",
    "\\:hocho:" => "🔪",
    "\\:honey_pot:" => "🍯",
    "\\:hook:" => "🪝",
    "\\:horse:" => "🐴",
    "\\:horse_racing:" => "🏇",
    "\\:hospital:" => "🏥",
    "\\:hot_face:" => "🥵",
    "\\:hotdog:" => "🌭",
    "\\:hotel:" => "🏨",
    "\\:hotsprings:" => "♨",
    "\\:hourglass:" => "⌛",
    "\\:hourglass_flowing_sand:" => "⏳",
    "\\:house:" => "🏠",
    "\\:house_with_garden:" => "🏡",
    "\\:hugging_face:" => "🤗",
    "\\:hushed:" => "😯",
    "\\:hut:" => "🛖",
    "\\:i_love_you_hand_sign:" => "🤟",
    "\\:ice_cream:" => "🍨",
    "\\:ice_cube:" => "🧊",
    "\\:ice_hockey_stick_and_puck:" => "🏒",
    "\\:icecream:" => "🍦",
    "\\:id:" => "🆔",
    "\\:ideograph_advantage:" => "🉐",
    "\\:imp:" => "👿",
    "\\:inbox_tray:" => "📥",
    "\\:incoming_envelope:" => "📨",
    "\\:information_desk_person:" => "💁",
    "\\:information_source:" => "ℹ",
    "\\:innocent:" => "😇",
    "\\:interrobang:" => "⁉",
    "\\:iphone:" => "📱",
    "\\:izakaya_lantern:" => "🏮",
    "\\:jack_o_lantern:" => "🎃",
    "\\:japan:" => "🗾",
    "\\:japanese_castle:" => "🏯",
    "\\:japanese_goblin:" => "👺",
    "\\:japanese_ogre:" => "👹",
    "\\:jeans:" => "👖",
    "\\:jigsaw:" => "🧩",
    "\\:joy:" => "😂",
    "\\:joy_cat:" => "😹",
    "\\:juggling:" => "🤹",
    "\\:kaaba:" => "🕋",
    "\\:kangaroo:" => "🦘",
    "\\:key:" => "🔑",
    "\\:keycap_ten:" => "🔟",
    "\\:kimono:" => "👘",
    "\\:kiss:" => "💋",
    "\\:kissing:" => "😗",
    "\\:kissing_cat:" => "😽",
    "\\:kissing_closed_eyes:" => "😚",
    "\\:kissing_heart:" => "😘",
    "\\:kissing_smiling_eyes:" => "😙",
    "\\:kite:" => "🪁",
    "\\:kiwifruit:" => "🥝",
    "\\:kneeling_person:" => "🧎",
    "\\:knot:" => "🪢",
    "\\:koala:" => "🐨",
    "\\:koko:" => "🈁",
    "\\:lab_coat:" => "🥼",
    "\\:lacrosse:" => "🥍",
    "\\:ladder:" => "🪜",
    "\\:ladybug:" => "🐞",
    "\\:large_blue_circle:" => "🔵",
    "\\:large_blue_diamond:" => "🔷",
    "\\:large_blue_square:" => "🟦",
    "\\:large_brown_circle:" => "🟤",
    "\\:large_brown_square:" => "🟫",
    "\\:large_green_circle:" => "🟢",
    "\\:large_green_square:" => "🟩",
    "\\:large_orange_circle:" => "🟠",
    "\\:large_orange_diamond:" => "🔶",
    "\\:large_orange_square:" => "🟧",
    "\\:large_purple_circle:" => "🟣",
    "\\:large_purple_square:" => "🟪",
    "\\:large_red_square:" => "🟥",
    "\\:large_yellow_circle:" => "🟡",
    "\\:large_yellow_square:" => "🟨",
    "\\:last_quarter_moon:" => "🌗",
    "\\:last_quarter_moon_with_face:" => "🌜",
    "\\:laughing:" => "😆",
    "\\:leafy_green:" => "🥬",
    "\\:leaves:" => "🍃",
    "\\:ledger:" => "📒",
    "\\:left-facing_fist:" => "🤛",
    "\\:left_luggage:" => "🛅",
    "\\:left_right_arrow:" => "↔",
    "\\:leftwards_arrow_with_hook:" => "↩",
    "\\:leg:" => "🦵",
    "\\:lemon:" => "🍋",
    "\\:leo:" => "♌",
    "\\:leopard:" => "🐆",
    "\\:libra:" => "♎",
    "\\:light_rail:" => "🚈",
    "\\:link:" => "🔗",
    "\\:lion_face:" => "🦁",
    "\\:lips:" => "👄",
    "\\:lipstick:" => "💄",
    "\\:lizard:" => "🦎",
    "\\:llama:" => "🦙",
    "\\:lobster:" => "🦞",
    "\\:lock:" => "🔒",
    "\\:lock_with_ink_pen:" => "🔏",
    "\\:lollipop:" => "🍭",
    "\\:long_drum:" => "🪘",
    "\\:loop:" => "➿",
    "\\:lotion_bottle:" => "🧴",
    "\\:loud_sound:" => "🔊",
    "\\:loudspeaker:" => "📢",
    "\\:love_hotel:" => "🏩",
    "\\:love_letter:" => "💌",
    "\\:low_brightness:" => "🔅",
    "\\:luggage:" => "🧳",
    "\\:lungs:" => "🫁",
    "\\:lying_face:" => "🤥",
    "\\:m:" => "Ⓜ",
    "\\:mag:" => "🔍",
    "\\:mag_right:" => "🔎",
    "\\:mage:" => "🧙",
    "\\:magic_wand:" => "🪄",
    "\\:magnet:" => "🧲",
    "\\:mahjong:" => "🀄",
    "\\:mailbox:" => "📫",
    "\\:mailbox_closed:" => "📪",
    "\\:mailbox_with_mail:" => "📬",
    "\\:mailbox_with_no_mail:" => "📭",
    "\\:mammoth:" => "🦣",
    "\\:man:" => "👨",
    "\\:man_and_woman_holding_hands:" => "👫",
    "\\:man_dancing:" => "🕺",
    "\\:man_with_gua_pi_mao:" => "👲",
    "\\:man_with_turban:" => "👳",
    "\\:mango:" => "🥭",
    "\\:mans_shoe:" => "👞",
    "\\:manual_wheelchair:" => "🦽",
    "\\:maple_leaf:" => "🍁",
    "\\:martial_arts_uniform:" => "🥋",
    "\\:mask:" => "😷",
    "\\:massage:" => "💆",
    "\\:mate_drink:" => "🧉",
    "\\:meat_on_bone:" => "🍖",
    "\\:mechanical_arm:" => "🦾",
    "\\:mechanical_leg:" => "🦿",
    "\\:mega:" => "📣",
    "\\:melon:" => "🍈",
    "\\:memo:" => "📝",
    "\\:menorah_with_nine_branches:" => "🕎",
    "\\:mens:" => "🚹",
    "\\:merperson:" => "🧜",
    "\\:metro:" => "🚇",
    "\\:microbe:" => "🦠",
    "\\:microphone:" => "🎤",
    "\\:microscope:" => "🔬",
    "\\:middle_finger:" => "🖕",
    "\\:military_helmet:" => "🪖",
    "\\:milky_way:" => "🌌",
    "\\:minibus:" => "🚐",
    "\\:minidisc:" => "💽",
    "\\:mirror:" => "🪞",
    "\\:mobile_phone_off:" => "📴",
    "\\:money_mouth_face:" => "🤑",
    "\\:money_with_wings:" => "💸",
    "\\:moneybag:" => "💰",
    "\\:monkey:" => "🐒",
    "\\:monkey_face:" => "🐵",
    "\\:monorail:" => "🚝",
    "\\:moon:" => "🌔",
    "\\:moon_cake:" => "🥮",
    "\\:mortar_board:" => "🎓",
    "\\:mosque:" => "🕌",
    "\\:mosquito:" => "🦟",
    "\\:motor_scooter:" => "🛵",
    "\\:motorized_wheelchair:" => "🦼",
    "\\:mount_fuji:" => "🗻",
    "\\:mountain_bicyclist:" => "🚵",
    "\\:mountain_cableway:" => "🚠",
    "\\:mountain_railway:" => "🚞",
    "\\:mouse2:" => "🐁",
    "\\:mouse:" => "🐭",
    "\\:mouse_trap:" => "🪤",
    "\\:movie_camera:" => "🎥",
    "\\:moyai:" => "🗿",
    "\\:mrs_claus:" => "🤶",
    "\\:muscle:" => "💪",
    "\\:mushroom:" => "🍄",
    "\\:musical_keyboard:" => "🎹",
    "\\:musical_note:" => "🎵",
    "\\:musical_score:" => "🎼",
    "\\:mute:" => "🔇",
    "\\:nail_care:" => "💅",
    "\\:name_badge:" => "📛",
    "\\:nauseated_face:" => "🤢",
    "\\:nazar_amulet:" => "🧿",
    "\\:necktie:" => "👔",
    "\\:negative_squared_cross_mark:" => "❎",
    "\\:nerd_face:" => "🤓",
    "\\:nesting_dolls:" => "🪆",
    "\\:neutral_face:" => "😐",
    "\\:new:" => "🆕",
    "\\:new_moon:" => "🌑",
    "\\:new_moon_with_face:" => "🌚",
    "\\:newspaper:" => "📰",
    "\\:ng:" => "🆖",
    "\\:night_with_stars:" => "🌃",
    "\\:ninja:" => "🥷",
    "\\:no_bell:" => "🔕",
    "\\:no_bicycles:" => "🚳",
    "\\:no_entry:" => "⛔",
    "\\:no_entry_sign:" => "🚫",
    "\\:no_good:" => "🙅",
    "\\:no_mobile_phones:" => "📵",
    "\\:no_mouth:" => "😶",
    "\\:no_pedestrians:" => "🚷",
    "\\:no_smoking:" => "🚭",
    "\\:non-potable_water:" => "🚱",
    "\\:nose:" => "👃",
    "\\:notebook:" => "📓",
    "\\:notebook_with_decorative_cover:" => "📔",
    "\\:notes:" => "🎶",
    "\\:nut_and_bolt:" => "🔩",
    "\\:o2:" => "🅾",
    "\\:o:" => "⭕",
    "\\:ocean:" => "🌊",
    "\\:octagonal_sign:" => "🛑",
    "\\:octopus:" => "🐙",
    "\\:oden:" => "🍢",
    "\\:office:" => "🏢",
    "\\:ok:" => "🆗",
    "\\:ok_hand:" => "👌",
    "\\:ok_woman:" => "🙆",
    "\\:older_adult:" => "🧓",
    "\\:older_man:" => "👴",
    "\\:older_woman:" => "👵",
    "\\:olive:" => "🫒",
    "\\:on:" => "🔛",
    "\\:oncoming_automobile:" => "🚘",
    "\\:oncoming_bus:" => "🚍",
    "\\:oncoming_police_car:" => "🚔",
    "\\:oncoming_taxi:" => "🚖",
    "\\:one-piece_swimsuit:" => "🩱",
    "\\:onion:" => "🧅",
    "\\:open_file_folder:" => "📂",
    "\\:open_hands:" => "👐",
    "\\:open_mouth:" => "😮",
    "\\:ophiuchus:" => "⛎",
    "\\:orange_book:" => "📙",
    "\\:orange_heart:" => "🧡",
    "\\:orangutan:" => "🦧",
    "\\:otter:" => "🦦",
    "\\:outbox_tray:" => "📤",
    "\\:owl:" => "🦉",
    "\\:ox:" => "🐂",
    "\\:oyster:" => "🦪",
    "\\:package:" => "📦",
    "\\:page_facing_up:" => "📄",
    "\\:page_with_curl:" => "📃",
    "\\:pager:" => "📟",
    "\\:palm_tree:" => "🌴",
    "\\:palms_up_together:" => "🤲",
    "\\:pancakes:" => "🥞",
    "\\:panda_face:" => "🐼",
    "\\:paperclip:" => "📎",
    "\\:parachute:" => "🪂",
    "\\:parking:" => "🅿",
    "\\:parrot:" => "🦜",
    "\\:part_alternation_mark:" => "〽",
    "\\:partly_sunny:" => "⛅",
    "\\:partying_face:" => "🥳",
    "\\:passport_control:" => "🛂",
    "\\:peach:" => "🍑",
    "\\:peacock:" => "🦚",
    "\\:peanuts:" => "🥜",
    "\\:pear:" => "🍐",
    "\\:pencil2:" => "✏",
    "\\:penguin:" => "🐧",
    "\\:pensive:" => "😔",
    "\\:people_hugging:" => "🫂",
    "\\:performing_arts:" => "🎭",
    "\\:persevere:" => "😣",
    "\\:person_climbing:" => "🧗",
    "\\:person_doing_cartwheel:" => "🤸",
    "\\:person_frowning:" => "🙍",
    "\\:person_in_lotus_position:" => "🧘",
    "\\:person_in_steamy_room:" => "🧖",
    "\\:person_in_tuxedo:" => "🤵",
    "\\:person_with_blond_hair:" => "👱",
    "\\:person_with_headscarf:" => "🧕",
    "\\:person_with_pouting_face:" => "🙎",
    "\\:petri_dish:" => "🧫",
    "\\:phone:" => "☎",
    "\\:pickup_truck:" => "🛻",
    "\\:pie:" => "🥧",
    "\\:pig2:" => "🐖",
    "\\:pig:" => "🐷",
    "\\:pig_nose:" => "🐽",
    "\\:pill:" => "💊",
    "\\:pinata:" => "🪅",
    "\\:pinched_fingers:" => "🤌",
    "\\:pinching_hand:" => "🤏",
    "\\:pineapple:" => "🍍",
    "\\:pisces:" => "♓",
    "\\:pizza:" => "🍕",
    "\\:placard:" => "🪧",
    "\\:place_of_worship:" => "🛐",
    "\\:pleading_face:" => "🥺",
    "\\:plunger:" => "🪠",
    "\\:point_down:" => "👇",
    "\\:point_left:" => "👈",
    "\\:point_right:" => "👉",
    "\\:point_up:" => "☝",
    "\\:point_up_2:" => "👆",
    "\\:police_car:" => "🚓",
    "\\:poodle:" => "🐩",
    "\\:popcorn:" => "🍿",
    "\\:post_office:" => "🏣",
    "\\:postal_horn:" => "📯",
    "\\:postbox:" => "📮",
    "\\:potable_water:" => "🚰",
    "\\:potato:" => "🥔",
    "\\:potted_plant:" => "🪴",
    "\\:pouch:" => "👝",
    "\\:poultry_leg:" => "🍗",
    "\\:pound:" => "💷",
    "\\:pouting_cat:" => "😾",
    "\\:pray:" => "🙏",
    "\\:prayer_beads:" => "📿",
    "\\:pregnant_woman:" => "🤰",
    "\\:pretzel:" => "🥨",
    "\\:prince:" => "🤴",
    "\\:princess:" => "👸",
    "\\:probing_cane:" => "🦯",
    "\\:purple_heart:" => "💜",
    "\\:purse:" => "👛",
    "\\:pushpin:" => "📌",
    "\\:put_litter_in_its_place:" => "🚮",
    "\\:question:" => "❓",
    "\\:rabbit2:" => "🐇",
    "\\:rabbit:" => "🐰",
    "\\:raccoon:" => "🦝",
    "\\:racehorse:" => "🐎",
    "\\:radio:" => "📻",
    "\\:radio_button:" => "🔘",
    "\\:rage:" => "😡",
    "\\:railway_car:" => "🚃",
    "\\:rainbow:" => "🌈",
    "\\:raised_back_of_hand:" => "🤚",
    "\\:raised_hands:" => "🙌",
    "\\:raising_hand:" => "🙋",
    "\\:ram:" => "🐏",
    "\\:ramen:" => "🍜",
    "\\:rat:" => "🐀",
    "\\:razor:" => "🪒",
    "\\:receipt:" => "🧾",
    "\\:recycle:" => "♻",
    "\\:red_circle:" => "🔴",
    "\\:red_envelope:" => "🧧",
    "\\:registered:" => "®",
    "\\:relaxed:" => "☺",
    "\\:relieved:" => "😌",
    "\\:repeat:" => "🔁",
    "\\:repeat_one:" => "🔂",
    "\\:restroom:" => "🚻",
    "\\:revolving_hearts:" => "💞",
    "\\:rewind:" => "⏪",
    "\\:rhinoceros:" => "🦏",
    "\\:ribbon:" => "🎀",
    "\\:rice:" => "🍚",
    "\\:rice_ball:" => "🍙",
    "\\:rice_cracker:" => "🍘",
    "\\:rice_scene:" => "🎑",
    "\\:right-facing_fist:" => "🤜",
    "\\:ring:" => "💍",
    "\\:ringed_planet:" => "🪐",
    "\\:robot_face:" => "🤖",
    "\\:rock:" => "🪨",
    "\\:rocket:" => "🚀",
    "\\:roll_of_paper:" => "🧻",
    "\\:roller_coaster:" => "🎢",
    "\\:roller_skate:" => "🛼",
    "\\:rolling_on_the_floor_laughing:" => "🤣",
    "\\:rooster:" => "🐓",
    "\\:rose:" => "🌹",
    "\\:rotating_light:" => "🚨",
    "\\:round_pushpin:" => "📍",
    "\\:rowboat:" => "🚣",
    "\\:rugby_football:" => "🏉",
    "\\:runner:" => "🏃",
    "\\:running_shirt_with_sash:" => "🎽",
    "\\:sa:" => "🈂",
    "\\:safety_pin:" => "🧷",
    "\\:safety_vest:" => "🦺",
    "\\:sagittarius:" => "♐",
    "\\:sake:" => "🍶",
    "\\:salt:" => "🧂",
    "\\:sandal:" => "👡",
    "\\:sandwich:" => "🥪",
    "\\:santa:" => "🎅",
    "\\:sari:" => "🥻",
    "\\:satellite:" => "📡",
    "\\:satellite_antenna:" => "📡",
    "\\:sauropod:" => "🦕",
    "\\:saxophone:" => "🎷",
    "\\:scarf:" => "🧣",
    "\\:school:" => "🏫",
    "\\:school_satchel:" => "🎒",
    "\\:scissors:" => "✂",
    "\\:scooter:" => "🛴",
    "\\:scorpion:" => "🦂",
    "\\:scorpius:" => "♏",
    "\\:scream:" => "😱",
    "\\:scream_cat:" => "🙀",
    "\\:screwdriver:" => "🪛",
    "\\:scroll:" => "📜",
    "\\:seal:" => "🦭",
    "\\:seat:" => "💺",
    "\\:second_place_medal:" => "🥈",
    "\\:secret:" => "㊙",
    "\\:see_no_evil:" => "🙈",
    "\\:seedling:" => "🌱",
    "\\:selfie:" => "🤳",
    "\\:sewing_needle:" => "🪡",
    "\\:shallow_pan_of_food:" => "🥘",
    "\\:shark:" => "🦈",
    "\\:shaved_ice:" => "🍧",
    "\\:sheep:" => "🐑",
    "\\:shell:" => "🐚",
    "\\:ship:" => "🚢",
    "\\:shirt:" => "👕",
    "\\:shopping_trolley:" => "🛒",
    "\\:shorts:" => "🩳",
    "\\:shower:" => "🚿",
    "\\:shrimp:" => "🦐",
    "\\:shrug:" => "🤷",
    "\\:shushing_face:" => "🤫",
    "\\:signal_strength:" => "📶",
    "\\:six_pointed_star:" => "🔯",
    "\\:skateboard:" => "🛹",
    "\\:ski:" => "🎿",
    "\\:skin-tone-2:" => "🏻",
    "\\:skin-tone-3:" => "🏼",
    "\\:skin-tone-4:" => "🏽",
    "\\:skin-tone-5:" => "🏾",
    "\\:skin-tone-6:" => "🏿",
    "\\:skull:" => "💀",
    "\\:skunk:" => "🦨",
    "\\:sled:" => "🛷",
    "\\:sleeping:" => "😴",
    "\\:sleeping_accommodation:" => "🛌",
    "\\:sleepy:" => "😪",
    "\\:slightly_frowning_face:" => "🙁",
    "\\:slightly_smiling_face:" => "🙂",
    "\\:slot_machine:" => "🎰",
    "\\:sloth:" => "🦥",
    "\\:small_blue_diamond:" => "🔹",
    "\\:small_orange_diamond:" => "🔸",
    "\\:small_red_triangle:" => "🔺",
    "\\:small_red_triangle_down:" => "🔻",
    "\\:smile:" => "😄",
    "\\:smile_cat:" => "😸",
    "\\:smiley:" => "😃",
    "\\:smiley_cat:" => "😺",
    "\\:smiling_face_with_3_hearts:" => "🥰",
    "\\:smiling_face_with_tear:" => "🥲",
    "\\:smiling_imp:" => "😈",
    "\\:smirk:" => "😏",
    "\\:smirk_cat:" => "😼",
    "\\:smoking:" => "🚬",
    "\\:snail:" => "🐌",
    "\\:snake:" => "🐍",
    "\\:sneezing_face:" => "🤧",
    "\\:snowboarder:" => "🏂",
    "\\:snowflake:" => "❄",
    "\\:snowman:" => "⛄",
    "\\:snowman_without_snow:" => "⛄",
    "\\:soap:" => "🧼",
    "\\:sob:" => "😭",
    "\\:soccer:" => "⚽",
    "\\:socks:" => "🧦",
    "\\:softball:" => "🥎",
    "\\:soon:" => "🔜",
    "\\:sos:" => "🆘",
    "\\:sound:" => "🔉",
    "\\:space_invader:" => "👾",
    "\\:spades:" => "♠",
    "\\:spaghetti:" => "🍝",
    "\\:sparkle:" => "❇",
    "\\:sparkler:" => "🎇",
    "\\:sparkles:" => "✨",
    "\\:sparkling_heart:" => "💖",
    "\\:speak_no_evil:" => "🙊",
    "\\:speaker:" => "🔈",
    "\\:speech_balloon:" => "💬",
    "\\:speedboat:" => "🚤",
    "\\:spock-hand:" => "🖖",
    "\\:sponge:" => "🧽",
    "\\:spoon:" => "🥄",
    "\\:sports_medal:" => "🏅",
    "\\:squid:" => "🦑",
    "\\:standing_person:" => "🧍",
    "\\:star-struck:" => "🤩",
    "\\:star2:" => "🌟",
    "\\:star:" => "⭐",
    "\\:stars:" => "🌠",
    "\\:station:" => "🚉",
    "\\:statue_of_liberty:" => "🗽",
    "\\:steam_locomotive:" => "🚂",
    "\\:stethoscope:" => "🩺",
    "\\:stew:" => "🍲",
    "\\:straight_ruler:" => "📏",
    "\\:strawberry:" => "🍓",
    "\\:stuck_out_tongue:" => "😛",
    "\\:stuck_out_tongue_closed_eyes:" => "😝",
    "\\:stuck_out_tongue_winking_eye:" => "😜",
    "\\:stuffed_flatbread:" => "🥙",
    "\\:sun_with_face:" => "🌞",
    "\\:sunflower:" => "🌻",
    "\\:sunglasses:" => "😎",
    "\\:sunny:" => "☀",
    "\\:sunrise:" => "🌅",
    "\\:sunrise_over_mountains:" => "🌄",
    "\\:superhero:" => "🦸",
    "\\:supervillain:" => "🦹",
    "\\:surfer:" => "🏄",
    "\\:sushi:" => "🍣",
    "\\:suspension_railway:" => "🚟",
    "\\:swan:" => "🦢",
    "\\:sweat:" => "😓",
    "\\:sweat_drops:" => "💦",
    "\\:sweat_smile:" => "😅",
    "\\:sweet_potato:" => "🍠",
    "\\:swimmer:" => "🏊",
    "\\:symbols:" => "🔣",
    "\\:synagogue:" => "🕍",
    "\\:syringe:" => "💉",
    "\\:t-rex:" => "🦖",
    "\\:table_tennis_paddle_and_ball:" => "🏓",
    "\\:taco:" => "🌮",
    "\\:tada:" => "🎉",
    "\\:takeout_box:" => "🥡",
    "\\:tamale:" => "🫔",
    "\\:tanabata_tree:" => "🎋",
    "\\:tangerine:" => "🍊",
    "\\:taurus:" => "♉",
    "\\:taxi:" => "🚕",
    "\\:tea:" => "🍵",
    "\\:teapot:" => "🫖",
    "\\:teddy_bear:" => "🧸",
    "\\:telephone_receiver:" => "📞",
    "\\:telescope:" => "🔭",
    "\\:tennis:" => "🎾",
    "\\:tent:" => "⛺",
    "\\:test_tube:" => "🧪",
    "\\:the_horns:" => "🤘",
    "\\:thinking_face:" => "🤔",
    "\\:third_place_medal:" => "🥉",
    "\\:thong_sandal:" => "🩴",
    "\\:thought_balloon:" => "💭",
    "\\:thread:" => "🧵",
    "\\:ticket:" => "🎫",
    "\\:tiger2:" => "🐅",
    "\\:tiger:" => "🐯",
    "\\:tired_face:" => "😫",
    "\\:tm:" => "™",
    "\\:toilet:" => "🚽",
    "\\:tokyo_tower:" => "🗼",
    "\\:tomato:" => "🍅",
    "\\:tongue:" => "👅",
    "\\:toolbox:" => "🧰",
    "\\:tooth:" => "🦷",
    "\\:toothbrush:" => "🪥",
    "\\:top:" => "🔝",
    "\\:tophat:" => "🎩",
    "\\:tractor:" => "🚜",
    "\\:traffic_light:" => "🚥",
    "\\:train2:" => "🚆",
    "\\:train:" => "🚋",
    "\\:tram:" => "🚊",
    "\\:triangular_flag_on_post:" => "🚩",
    "\\:triangular_ruler:" => "📐",
    "\\:trident:" => "🔱",
    "\\:triumph:" => "😤",
    "\\:trolleybus:" => "🚎",
    "\\:trophy:" => "🏆",
    "\\:tropical_drink:" => "🍹",
    "\\:tropical_fish:" => "🐠",
    "\\:truck:" => "🚚",
    "\\:trumpet:" => "🎺",
    "\\:tulip:" => "🌷",
    "\\:tumbler_glass:" => "🥃",
    "\\:turkey:" => "🦃",
    "\\:turtle:" => "🐢",
    "\\:tv:" => "📺",
    "\\:twisted_rightwards_arrows:" => "🔀",
    "\\:two_hearts:" => "💕",
    "\\:two_men_holding_hands:" => "👬",
    "\\:two_women_holding_hands:" => "👭",
    "\\:u5272:" => "🈹",
    "\\:u5408:" => "🈴",
    "\\:u55b6:" => "🈺",
    "\\:u6307:" => "🈯",
    "\\:u6708:" => "🈷",
    "\\:u6709:" => "🈶",
    "\\:u6e80:" => "🈵",
    "\\:u7121:" => "🈚",
    "\\:u7533:" => "🈸",
    "\\:u7981:" => "🈲",
    "\\:u7a7a:" => "🈳",
    "\\:umbrella:" => "☔",
    "\\:umbrella_with_rain_drops:" => "☔",
    "\\:unamused:" => "😒",
    "\\:underage:" => "🔞",
    "\\:unicorn_face:" => "🦄",
    "\\:unlock:" => "🔓",
    "\\:up:" => "🆙",
    "\\:upside_down_face:" => "🙃",
    "\\:v:" => "✌",
    "\\:vampire:" => "🧛",
    "\\:vertical_traffic_light:" => "🚦",
    "\\:vhs:" => "📼",
    "\\:vibration_mode:" => "📳",
    "\\:video_camera:" => "📹",
    "\\:video_game:" => "🎮",
    "\\:violin:" => "🎻",
    "\\:virgo:" => "♍",
    "\\:volcano:" => "🌋",
    "\\:volleyball:" => "🏐",
    "\\:vs:" => "🆚",
    "\\:waffle:" => "🧇",
    "\\:walking:" => "🚶",
    "\\:waning_crescent_moon:" => "🌘",
    "\\:waning_gibbous_moon:" => "🌖",
    "\\:warning:" => "⚠",
    "\\:watch:" => "⌚",
    "\\:water_buffalo:" => "🐃",
    "\\:water_polo:" => "🤽",
    "\\:watermelon:" => "🍉",
    "\\:wave:" => "👋",
    "\\:waving_black_flag:" => "🏴",
    "\\:wavy_dash:" => "〰",
    "\\:waxing_crescent_moon:" => "🌒",
    "\\:wc:" => "🚾",
    "\\:weary:" => "😩",
    "\\:wedding:" => "💒",
    "\\:whale2:" => "🐋",
    "\\:whale:" => "🐳",
    "\\:wheelchair:" => "♿",
    "\\:white_check_mark:" => "✅",
    "\\:white_circle:" => "⚪",
    "\\:white_flower:" => "💮",
    "\\:white_heart:" => "🤍",
    "\\:white_large_square:" => "⬜",
    "\\:white_medium_small_square:" => "◽",
    "\\:white_medium_square:" => "◻",
    "\\:white_small_square:" => "▫",
    "\\:white_square_button:" => "🔳",
    "\\:wilted_flower:" => "🥀",
    "\\:wind_chime:" => "🎐",
    "\\:window:" => "🪟",
    "\\:wine_glass:" => "🍷",
    "\\:wink:" => "😉",
    "\\:wolf:" => "🐺",
    "\\:woman:" => "👩",
    "\\:womans_clothes:" => "👚",
    "\\:womans_flat_shoe:" => "🥿",
    "\\:womans_hat:" => "👒",
    "\\:womens:" => "🚺",
    "\\:wood:" => "🪵",
    "\\:woozy_face:" => "🥴",
    "\\:worm:" => "🪱",
    "\\:worried:" => "😟",
    "\\:wrench:" => "🔧",
    "\\:wrestlers:" => "🤼",
    "\\:x:" => "❌",
    "\\:yarn:" => "🧶",
    "\\:yawning_face:" => "🥱",
    "\\:yellow_heart:" => "💛",
    "\\:yen:" => "💴",
    "\\:yo-yo:" => "🪀",
    "\\:yum:" => "😋",
    "\\:zany_face:" => "🤪",
    "\\:zap:" => "⚡",
    "\\:zebra_face:" => "🦓",
    "\\:zipper_mouth_face:" => "🤐",
    "\\:zombie:" => "🧟",
    "\\:zzz:" => "💤",
)
�   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/REPL/src/TerminalMenus/TerminalMenus.jla      # This file is a part of Julia. License is MIT: https://julialang.org/license

module TerminalMenus

terminal = nothing  # The user terminal

import REPL

function __init__()
    global terminal
    terminal = REPL.Terminals.TTYTerminal(get(ENV, "TERM", Sys.iswindows() ? "" : "dumb"), stdin, stdout, stderr)
end

include("util.jl")
include("config.jl")

include("AbstractMenu.jl")
include("RadioMenu.jl")
include("MultiSelectMenu.jl")
include("Pager.jl")

export
    RadioMenu,
    MultiSelectMenu,
    Pager,
    request

# TODO: remove in Julia 2.0
# While not exported, AbstractMenu documented these as an extension interface
@deprecate printMenu printmenu
function writeLine(buf::IOBuffer, m::AbstractMenu, idx::Int, cursor::Bool)
    Base.depwarn("`writeLine` is deprecated, use `writeline` instead.", :writeLine)
    error("unimplemented")
end

end # module
z   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/REPL/src/TerminalMenus/util.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

# Enum for escaped (multi-byte) keys such as the arrows or the home/end keys
@enum(Key,
    ARROW_LEFT = 1000,
    ARROW_RIGHT,
    ARROW_UP,
    ARROW_DOWN,
    DEL_KEY,
    HOME_KEY,
    END_KEY,
    PAGE_UP,
    PAGE_DOWN)

readbyte(stream::IO=stdin) = read(stream, Char)

# Read the next key from stdin. It is also able to read several bytes for
#   escaped keys such as the arrow keys, home/end keys, etc.
# Escaped keys are returned using the `Key` enum.
readkey(stream::IO=stdin) = UInt32(_readkey(stream))
function _readkey(stream::IO=stdin)
    c = readbyte(stream)

    # Escape characters
    if c == '\x1b'
        bytesavailable(stream) < 1 && return '\x1b'
        esc_a = readbyte(stream)
        esc_a == 'v' && return PAGE_UP  # M-v
        esc_a == '<' && return HOME_KEY # M-<
        esc_a == '>' && return END_KEY  # M->

        bytesavailable(stream) < 1 && return '\x1b'
        esc_b = readbyte(stream)

        if esc_a == '[' || esc_a == 'O'
            if esc_b >= '0' && esc_b <= '9'
                bytesavailable(stream) < 1 && return '\x1b'
                esc_c = readbyte(stream)
                if esc_c == '~'
                    esc_b == '1' && return HOME_KEY
                    esc_b == '4' && return END_KEY
                    esc_b == '3' && return DEL_KEY
                    esc_b == '5' && return PAGE_UP
                    esc_b == '6' && return PAGE_DOWN
                    esc_b == '7' && return HOME_KEY
                    esc_b == '8' && return END_KEY
                    return '\x1b'
                end
            else
                # Arrow keys
                esc_b == 'A' && return ARROW_UP
                esc_b == 'B' && return ARROW_DOWN
                esc_b == 'C' && return ARROW_RIGHT
                esc_b == 'D' && return ARROW_LEFT
                esc_b == 'H' && return HOME_KEY
                esc_b == 'F' && return END_KEY
                return '\x1b'
            end
        end
        esc_a == 'H' && return HOME_KEY
        esc_a == 'F' && return END_KEY
        return '\x1b'
    end
    c == '\x16' && return PAGE_DOWN  # C-v
    c == '\x10' && return ARROW_UP   # C-p
    c == '\x0e' && return ARROW_DOWN # C-n
    return c
end
|   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/REPL/src/TerminalMenus/config.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

abstract type AbstractConfig end

struct Config <: AbstractConfig
    cursor::Char
    up_arrow::Char
    down_arrow::Char
    updown_arrow::Char
    scroll_wrap::Bool
    ctrl_c_interrupt::Bool
end

struct MultiSelectConfig <: AbstractConfig
    config::Config
    checked::String
    unchecked::String
end

"""
    Config(; scroll_wrap=false, ctrl_c_interrupt=true, charset=:ascii, cursor::Char, up_arrow::Char, down_arrow::Char)

Configure behavior for selection menus via keyword arguments:

- `scroll_wrap`, if `true`, causes the menu to wrap around when scrolling above the first
  or below the last entry
- `ctrl_c_interrupt`, if `true`, throws an `InterruptException` if the user hits Ctrl-C
  during menu selection. If `false`, [`TerminalMenus.request`](@ref) will return the
  default result from [`TerminalMenus.selected`](@ref).
- `charset` affects the default values for `cursor`, `up_arrow`, and `down_arrow`,
  and can be `:ascii` or `:unicode`
- `cursor` is the character printed to indicate the option that will be chosen by
  hitting "Enter." Defaults are '>' or '→', depending on `charset`.
- `up_arrow` is the character printed when the display does not include the first entry.
  Defaults are '^' or '↑', depending on `charset`.
- `down_arrow` is the character printed when the display does not include the last entry.
  Defaults are 'v' or '↓', depending on `charset`.

Subtypes of `ConfiguredMenu` will print `cursor`, `up_arrow`, and `down_arrow` automatically
as needed, your `writeline` method should not print them.

!!! compat "Julia 1.6"
    `Config` is available as of Julia 1.6. On older releases use the global `CONFIG`.
"""
function Config(;
                charset::Symbol = :ascii,
                cursor::Char = '\0',
                up_arrow::Char = '\0',
                down_arrow::Char = '\0',
                updown_arrow::Char = '\0',
                scroll_wrap::Bool = false,
                ctrl_c_interrupt::Bool = true)
    charset === :ascii || charset === :unicode ||
        throw(ArgumentError("charset should be :ascii or :unicode, received $charset"))
    if cursor == '\0'
        cursor = charset === :ascii ? '>' : '→'
    end
    if up_arrow == '\0'
        up_arrow = charset === :ascii ? '^' : '↑'
    end
    if down_arrow == '\0'
        down_arrow = charset === :ascii ? 'v' : '↓'
    end
    if updown_arrow == '\0'
        updown_arrow = charset === :ascii ? 'I' : '↕'
    end
    return Config(cursor, up_arrow, down_arrow, updown_arrow, scroll_wrap, ctrl_c_interrupt)
end

"""
    MultiSelectConfig(; charset=:ascii, checked::String, unchecked::String, kwargs...)

Configure behavior for a multiple-selection menu via keyword arguments:

- `checked` is the string to print when an option has been selected.
  Defaults are "[X]" or "✓", depending on `charset`.
- `unchecked` is the string to print when an option has not been selected.
  Defaults are "[ ]" or "⬚", depending on `charset`.

All other keyword arguments are as described for [`TerminalMenus.Config`](@ref).
`checked` and `unchecked` are not printed automatically, and should be printed by
your `writeline` method.

!!! compat "Julia 1.6"
    `MultiSelectConfig` is available as of Julia 1.6. On older releases use the global `CONFIG`.
"""
function MultiSelectConfig(;
                           charset::Symbol = :ascii,
                           checked::String = "",
                           unchecked::String = "",
                           kwargs...)
    charset === :ascii || charset === :unicode || throw(ArgumentError("charset should be :ascii or :unicode, received $charset"))
    if isempty(checked)
        checked = charset === :ascii ? "[X]" : "✓"
    end
    if isempty(unchecked)
        unchecked = charset === :ascii ? "[ ]" : "⬚"
    end
    return MultiSelectConfig(Config(; charset=charset, kwargs...), checked, unchecked)
end


## Below is the old-style CONFIG interface, kept for backwards compatibility.
## Not recommended for any new menu types.

"""
    CONFIG

Global menu configuration parameters

!!! compat "Julia 1.6"
    `CONFIG` is deprecated, instead configure menus via their constructors.
"""
const CONFIG = Dict{Symbol,Union{Char,String,Bool}}()

"""
    config( <see arguments> )

Keyword-only function to configure global menu parameters

# Arguments
 - `charset::Symbol=:na`: ui characters to use (`:ascii` or `:unicode`); overridden by other arguments
 - `cursor::Char='>'|'→'`: character to use for cursor
 - `up_arrow::Char='^'|'↑'`: character to use for up arrow
 - `down_arrow::Char='v'|'↓'`: character to use for down arrow
 - `checked::String="[X]"|"✓"`: string to use for checked
 - `unchecked::String="[ ]"|"⬚")`: string to use for unchecked
 - `scroll::Symbol=:nowrap`: If `:wrap` wrap cursor around top and bottom, if :`nowrap` do not wrap cursor
 - `supress_output::Bool=false`: Ignored legacy argument, pass `suppress_output` as a keyword argument to `request` instead.
 - `ctrl_c_interrupt::Bool=true`: If `false`, return empty on ^C, if `true` throw InterruptException() on ^C

!!! compat "Julia 1.6"
    As of Julia 1.6, `config` is deprecated. Use `Config` or `MultiSelectConfig` instead.
"""
function config(;charset::Symbol = :na,
                scroll::Symbol = :na,
                cursor::Char = '\0',
                up_arrow::Char = '\0',
                down_arrow::Char = '\0',
                updown_arrow::Char = '\0',
                checked::String = "",
                unchecked::String = "",
                supress_output::Union{Nothing, Bool}=nothing,   # typo was documented, unfortunately
                ctrl_c_interrupt::Union{Nothing, Bool}=nothing)

    if charset === :ascii
        cursor     = '>'
        up_arrow   = '^'
        down_arrow = 'v'
        updown_arrow = 'I'
        checked    = "[X]"
        unchecked  = "[ ]"
    elseif charset === :unicode
        cursor     = '→'
        up_arrow   = '↑'
        down_arrow = '↓'
        updown_arrow = '↕'
        checked    = "✓"
        unchecked  = "⬚"
    elseif charset === :na
    else
        throw(ArgumentError("charset should be :ascii or :unicode, received $charset"))
    end

    scroll ∉ [:na, :wrap, :nowrap] && throw(ArgumentError("scroll must be :wrap or :nowrap, received $scroll"))
    scroll === :wrap   && (CONFIG[:scroll_wrap] = true)
    scroll === :nowrap && (CONFIG[:scroll_wrap] = false)

    cursor     != '\0' && (CONFIG[:cursor]     = cursor)
    up_arrow   != '\0' && (CONFIG[:up_arrow]   = up_arrow)
    down_arrow != '\0' && (CONFIG[:down_arrow] = down_arrow)
    updown_arrow != '\0' && (CONFIG[:updown_arrow] = updown_arrow)
    checked    != ""   && (CONFIG[:checked]    = checked)
    unchecked  != ""   && (CONFIG[:unchecked]  = unchecked)
    supress_output isa Bool   && (CONFIG[:supress_output] = supress_output)
    ctrl_c_interrupt isa Bool && (CONFIG[:ctrl_c_interrupt] = ctrl_c_interrupt)

    return nothing
end

# Set up defaults
config(charset=:ascii, scroll=:nowrap, supress_output=false, ctrl_c_interrupt=true)
�   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/REPL/src/TerminalMenus/AbstractMenu.jll5      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""

    AbstractMenu

The supertype for all Menu types.


# Functions

The following functions can be called on all <:AbstractMenu types.
Details can be found in

## Exported

  - `request(m::AbstractMenu)`
  - `request(msg::AbstractString, m::AbstractMenu)`

## Hidden

  - `printmenu(m::AbstractMenu, cursor::Int; init::Bool=false, oldstate=nothing)`


# Subtypes

All subtypes must be mutable, and must contain the fields `pagesize::Int` and
`pageoffset::Int`. They must also implement the following functions.

## Necessary Functions

These functions must be implemented for all subtypes of AbstractMenu.

  - `pick(m::AbstractMenu, cursor::Int)`
  - `cancel(m::AbstractMenu)`
  - `options(m::AbstractMenu)`   # `numoptions` is an alternative
  - `writeline(buf::IO, m::AbstractMenu, idx::Int, iscursor::Bool)`

If `m` does not have a field called `selected`, then you must also implement `selected(m)`.

## Optional Functions

These functions do not need to be implemented for all AbstractMenu
subtypes.

  - `header(m::AbstractMenu)`
  - `keypress(m::AbstractMenu, i::UInt32)`
  - `numoptions(m::AbstractMenu)`
  - `selected(m::AbstractMenu)`

"""
abstract type AbstractMenu end

function getproperty(m::AbstractMenu, name::Symbol)
    if name === :pagesize
        return getfield(m, :pagesize)::Int
    elseif name === :pageoffset
        return getfield(m, :pageoffset)::Int
    end
    return getfield(m, name)
end


# TODO Julia2.0: get rid of parametric intermediate, making it just
#   abstract type ConfiguredMenu <: AbstractMenu end
# Or perhaps just make all menus ConfiguredMenus
# Also consider making `cursor` a mandatory field in the Menu structs
# instead of going via the RefValue in `request`.
abstract type _ConfiguredMenu{C} <: AbstractMenu end
const ConfiguredMenu = _ConfiguredMenu{<:AbstractConfig}

# NECESSARY FUNCTIONS
# These functions must be implemented for all subtypes of AbstractMenu
######################################################################

"""
    pick(m::AbstractMenu, cursor::Int)

Defines what happens when a user presses the Enter key while the menu is open.
If `true` is returned, `request()` will exit.
`cursor` indexes the position of the selection.
"""
pick(m::AbstractMenu, cursor::Int) = error("unimplemented")

"""
    cancel(m::AbstractMenu)

Define what happens when a user cancels ('q' or ctrl-c) a menu.
`request()` will always exit after calling this function.
"""
cancel(m::AbstractMenu) = error("unimplemented")

"""
    options(m::AbstractMenu)

Return a list of strings to be displayed as options in the current page.

Alternatively, implement `numoptions`, in which case `options` is not needed.
"""
options(m::AbstractMenu) = error("unimplemented")

"""
    writeline(buf::IO, m::AbstractMenu, idx::Int, iscursor::Bool)

Write the option at index `idx` to `buf`. `iscursor`, if `true`, indicates that this
item is at the current cursor position (the one that will be selected by hitting "Enter").

If `m` is a `ConfiguredMenu`, `TerminalMenus` will print the cursor indicator.
Otherwise the callee is expected to handle such printing.

!!! compat "Julia 1.6"
    `writeline` requires Julia 1.6 or higher.

    On older versions of Julia, this was
        `writeLine(buf::IO, m::AbstractMenu, idx, iscursor::Bool)`
    and `m` is assumed to be unconfigured. The selection and cursor indicators can be
    obtained from `TerminalMenus.CONFIG`.

    This older function is supported on all Julia 1.x versions but will be dropped in Julia 2.0.
"""
function writeline(buf::IO, m::AbstractMenu, idx::Int, iscursor::Bool)
    # error("unimplemented")    # TODO: use this in Julia 2.0
    writeLine(buf, m, idx, iscursor)
end


# OPTIONAL FUNCTIONS
# These functions do not need to be implemented for all menu types
##################################################################

"""
    header(m::AbstractMenu) -> String

Return a header string to be printed above the menu.
Defaults to "".
"""
header(m::AbstractMenu) = ""

"""
    keypress(m::AbstractMenu, i::UInt32) -> Bool

Handle any non-standard keypress event.
If `true` is returned, [`TerminalMenus.request`](@ref) will exit.
Defaults to `false`.
"""
keypress(m::AbstractMenu, i::UInt32) = false

"""
    numoptions(m::AbstractMenu) -> Int

Return the number of options in menu `m`. Defaults to `length(options(m))`.

!!! compat "Julia 1.6"
    This function requires Julia 1.6 or later.
"""
numoptions(m::AbstractMenu) = length(options(m))

"""
    selected(m::AbstractMenu)

Return information about the user-selected option.
By default it returns `m.selected`.
"""
selected(m::AbstractMenu) = m.selected

"""
    request(m::AbstractMenu; cursor=1)

Display the menu and enter interactive mode. `cursor` indicates the item
number used for the initial cursor position. `cursor` can be either an
`Int` or a `RefValue{Int}`. The latter is useful for observation and
control of the cursor position from the outside.

Returns `selected(m)`.

!!! compat "Julia 1.6"
    The `cursor` argument requires Julia 1.6 or later.
"""
request(m::AbstractMenu; kwargs...) = request(terminal, m; kwargs...)

function request(term::REPL.Terminals.TTYTerminal, m::AbstractMenu; cursor::Union{Int, Base.RefValue{Int}}=1, suppress_output=false)
    if cursor isa Int
        cursor = Ref(cursor)
    end

    state = nothing
    if !suppress_output
        state = printmenu(term.out_stream, m, cursor[], init=true)
    end

    raw_mode_enabled = try
        REPL.Terminals.raw!(term, true)
        true
    catch err
        suppress_output || @warn "TerminalMenus: Unable to enter raw mode: " exception=(err, catch_backtrace())
        false
    end
    # hide the cursor
    raw_mode_enabled && !suppress_output && print(term.out_stream, "\x1b[?25l")

    try
        while true
            lastoption = numoptions(m)
            c = readkey(term.in_stream)

            if c == Int(ARROW_UP)
                cursor[] = move_up!(m, cursor[], lastoption)
            elseif c == Int(ARROW_DOWN)
                cursor[] = move_down!(m, cursor[], lastoption)
            elseif c == Int(PAGE_UP)
                cursor[] = page_up!(m, cursor[], lastoption)
            elseif c == Int(PAGE_DOWN)
                cursor[] = page_down!(m, cursor[], lastoption)
            elseif c == Int(HOME_KEY)
                cursor[] = 1
                m.pageoffset = 0
            elseif c == Int(END_KEY)
                cursor[] = lastoption
                m.pageoffset = max(0, lastoption - m.pagesize)
            elseif c == 13 # <enter>
                # will break if pick returns true
                pick(m, cursor[]) && break
            elseif c == UInt32('q')
                cancel(m)
                break
            elseif c == 3 # ctrl-c
                cancel(m)
                ctrl_c_interrupt(m) ? throw(InterruptException()) : break
            else
                # will break if keypress returns true
                keypress(m, c) && break
            end

            if !suppress_output
                state = printmenu(term.out_stream, m, cursor[], oldstate=state)
            end
        end
    finally # always disable raw mode
        if raw_mode_enabled
            !suppress_output && print(term.out_stream, "\x1b[?25h") # unhide cursor
            REPL.Terminals.raw!(term, false)
        end
    end
    !suppress_output && println(term.out_stream)

    return selected(m)
end


"""
    request([term,] msg::AbstractString, m::AbstractMenu)

Shorthand for `println(msg); request(m)`.
"""
request(msg::AbstractString, m::AbstractMenu; kwargs...) = request(terminal, msg, m; kwargs...)

function request(term::REPL.Terminals.TTYTerminal, msg::AbstractString, m::AbstractMenu; kwargs...)
    println(term.out_stream, msg)
    request(term, m; kwargs...)
end


function move_up!(m::AbstractMenu, cursor::Int, lastoption::Int=numoptions(m))
    if cursor > 1
        cursor -= 1 # move selection up
        if cursor < (2+m.pageoffset) && m.pageoffset > 0
            m.pageoffset -= 1 # scroll page up
        end
    elseif scroll_wrap(m)
        # wrap to bottom
        cursor = lastoption
        m.pageoffset = max(0, lastoption - m.pagesize)
    end
    return cursor
end

function move_down!(m::AbstractMenu, cursor::Int, lastoption::Int=numoptions(m))
    if cursor < lastoption
        cursor += 1 # move selection down
        pagepos = m.pagesize + m.pageoffset
        if pagepos <= cursor && pagepos < lastoption
            m.pageoffset += 1 # scroll page down
        end
    elseif scroll_wrap(m)
        # wrap to top
        cursor = 1
        m.pageoffset = 0
    end
    return cursor
end

function page_up!(m::AbstractMenu, cursor::Int, lastoption::Int=numoptions(m))
    # If we're at the bottom, move the page 1 less to move the cursor up from
    # the bottom entry, since we try to avoid putting the cursor at bounds.
    m.pageoffset -= m.pagesize - (cursor == lastoption ? 1 : 0)
    m.pageoffset = max(m.pageoffset, 0)
    return max(cursor - m.pagesize, 1)
end

function page_down!(m::AbstractMenu, cursor::Int, lastoption::Int=numoptions(m))
    m.pageoffset += m.pagesize - (cursor == 1 ? 1 : 0)
    m.pageoffset = max(0, min(m.pageoffset, lastoption - m.pagesize))
    return min(cursor + m.pagesize, lastoption)
end

"""
    printmenu(out, m::AbstractMenu, cursoridx::Int; init::Bool=false, oldstate=nothing) -> newstate

Display the state of a menu. `init=true` causes `m.pageoffset` to be initialized to start printing at
or just above the current cursor location; when `init` is false, the terminal will
preserve the current setting of `m.pageoffset` and overwrite the previous display.
Returns `newstate`, which can be passed in as `oldstate` on the next call to allow accurate
overwriting of the previous display.

!!! compat "Julia 1.6"
    `printmenu` requires Julia 1.6 or higher.

    On older versions of Julia, this was called `printMenu` and it lacked the `state` argument/return value.
    This older function is supported on all Julia 1.x versions but will be dropped in Julia 2.0.
"""
function printmenu(out::IO, m::AbstractMenu, cursoridx::Int; oldstate=nothing, init::Bool=false)
    # TODO Julia 2.0?: get rid of `init` and just use `oldstate`
    buf = IOBuffer()
    lastoption = numoptions(m)::Int
    ncleared = oldstate === nothing ? m.pagesize-1 : oldstate

    if init
        # like clamp, except this takes the min if max < min
        m.pageoffset = max(0, min(cursoridx - m.pagesize ÷ 2, lastoption - m.pagesize))
    else
        print(buf, "\r")
        if ncleared > 0
            # Move up `ncleared` lines. However, moving up zero lines
            # is interpreted as one line, so need to do this
            # conditionally. (More specifically, the `0` value means
            # to use the default, and for move up this is one.)
            print(buf, "\x1b[$(ncleared)A")
        end
    end

    nheaderlines = 0
    for headerline in split(header(m), "\n", keepempty=false)
        print(buf, "\x1b[2K", headerline, "\r\n")
        nheaderlines += 1
    end

    firstline = m.pageoffset+1
    lastline = min(m.pagesize+m.pageoffset, lastoption)

    for i in firstline:lastline
        # clearline
        print(buf, "\x1b[2K")

        upscrollable = i == firstline && m.pageoffset > 0
        downscrollable = i == lastline && i != lastoption

        if upscrollable && downscrollable
            print(buf, updown_arrow(m)::Union{Char,String})
        elseif upscrollable
            print(buf, up_arrow(m)::Union{Char,String})
        elseif downscrollable
            print(buf, down_arrow(m)::Union{Char,String})
        else
            print(buf, ' ')
        end

        printcursor(buf, m, i == cursoridx)
        writeline(buf, m, i, i == cursoridx)

        (i != lastline) && print(buf, "\r\n")
    end

    newstate = nheaderlines + lastline - firstline  # final line doesn't have `\n`

    if newstate < ncleared && oldstate !== nothing
        # we printed fewer lines than last time. Erase the leftovers.
        for i = newstate+1:ncleared
            print(buf, "\r\n\x1b[2K")
        end
        print(buf, "\x1b[$(ncleared-newstate)A")
    end

    print(out, String(take!(buf)))

    return newstate
end

scroll_wrap(m::ConfiguredMenu) = scroll_wrap(m.config)
scroll_wrap(c::AbstractConfig) = scroll_wrap(c.config)
scroll_wrap(c::Config) = c.scroll_wrap
scroll_wrap(::AbstractMenu) = CONFIG[:scroll_wrap]::Bool

ctrl_c_interrupt(m::ConfiguredMenu) = ctrl_c_interrupt(m.config)
ctrl_c_interrupt(c::AbstractConfig) = ctrl_c_interrupt(c.config)
ctrl_c_interrupt(c::Config) = c.ctrl_c_interrupt
ctrl_c_interrupt(::AbstractMenu) = CONFIG[:ctrl_c_interrupt]::Bool

up_arrow(m::ConfiguredMenu) = up_arrow(m.config)
up_arrow(c::AbstractConfig) = up_arrow(c.config)
up_arrow(c::Config) = c.up_arrow
up_arrow(::AbstractMenu) = CONFIG[:up_arrow]::Char

down_arrow(m::ConfiguredMenu) = down_arrow(m.config)
down_arrow(c::AbstractConfig) = down_arrow(c.config)
down_arrow(c::Config) = c.down_arrow
down_arrow(::AbstractMenu) = CONFIG[:down_arrow]::Char

updown_arrow(m::ConfiguredMenu) = updown_arrow(m.config)
updown_arrow(c::AbstractConfig) = updown_arrow(c.config)
updown_arrow(c::Config) = c.updown_arrow
updown_arrow(::AbstractMenu) = CONFIG[:updown_arrow]::Char

printcursor(buf, m::ConfiguredMenu, iscursor::Bool) = print(buf, iscursor ? cursor(m.config) : ' ', ' ')
cursor(c::AbstractConfig) = cursor(c.config)
cursor(c::Config) = c.cursor
printcursor(buf, ::AbstractMenu, ::Bool) = nothing   # `writeLine` is expected to do the printing (get from CONFIG[:cursor])
   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/REPL/src/TerminalMenus/RadioMenu.jl*      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""

    RadioMenu

A menu that allows a user to select a single option from a list.

# Sample Output

```julia-repl
julia> request(RadioMenu(options, pagesize=4))
Choose your favorite fruit:
^  grape
   strawberry
 > blueberry
v  peach
Your favorite fruit is blueberry!
```

"""
mutable struct RadioMenu{C} <: _ConfiguredMenu{C}
    options::Array{String,1}
    keybindings::Vector{Char}
    pagesize::Int
    pageoffset::Int
    selected::Int
    config::C
end


"""

    RadioMenu(options::Array{String,1}; pagesize::Int=10,
                                        keybindings::Vector{Char}=Char[],
                                        kwargs...)

Create a RadioMenu object. Use `request(menu::RadioMenu)` to get user input.
`request()` returns an `Int` which is the index of the option selected by the
user.

# Arguments

  - `options::Array{String, 1}`: Options to be displayed
  - `pagesize::Int=10`: The number of options to be displayed at one time, the menu will scroll if length(options) > pagesize
  - `keybindings::Vector{Char}=Char[]`: Shortcuts to pick corresponding entry from `options`

Any additional keyword arguments will be passed to [`TerminalMenus.Config`](@ref).

!!! compat "Julia 1.8"
    The `keybindings` argument requires Julia 1.8 or later.
"""
function RadioMenu(options::Array{String,1}; pagesize::Int=10, warn::Bool=true, keybindings::Vector{Char}=Char[], kwargs...)
    length(options) < 1 && error("RadioMenu must have at least one option")
    length(keybindings) in [0, length(options)] || error("RadioMenu must have either no keybindings, or one per option")

    # if pagesize is -1, use automatic paging
    pagesize = pagesize == -1 ? length(options) : pagesize
    # pagesize shouldn't be bigger than options
    pagesize = min(length(options), pagesize)
    # after other checks, pagesize must be greater than 1
    pagesize < 1 && error("pagesize must be >= 1")

    pageoffset = 0
    selected = -1 # none

    if !isempty(kwargs)
        RadioMenu(options, keybindings, pagesize, pageoffset, selected, Config(; kwargs...))
    else
        warn && Base.depwarn("Legacy `RadioMenu` interface is deprecated, set a configuration option such as `RadioMenu(options; charset=:ascii)` to trigger the new interface.", :RadioMenu)
        RadioMenu(options, keybindings, pagesize, pageoffset, selected, CONFIG)
    end
end


# AbstractMenu implementation functions
# See AbstractMenu.jl
#######################################

options(m::RadioMenu) = m.options

cancel(m::RadioMenu) = m.selected = -1

function pick(menu::RadioMenu, cursor::Int)
    menu.selected = cursor
    return true #break out of the menu
end

function writeline(buf::IOBuffer, menu::RadioMenu{Config}, idx::Int, iscursor::Bool)
    print(buf, replace(menu.options[idx], "\n" => "\\n"))
end

function keypress(m::RadioMenu, i::UInt32)
    isempty(m.keybindings) && return false
    i = findfirst(isequal(i), Int.(m.keybindings))
    isnothing(i) && return false
    m.selected = i
    return true
end

# Legacy interface
function writeLine(buf::IOBuffer, menu::RadioMenu{<:Dict}, idx::Int, cursor::Bool)
    # print a ">" on the selected entry
    cursor ? print(buf, menu.config[:cursor] ," ") : print(buf, "  ")

    print(buf, replace(menu.options[idx], "\n" => "\\n"))
end
�   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/REPL/src/TerminalMenus/MultiSelectMenu.jlY      # This file is a part of Julia. License is MIT: https://julialang.org/license

"""

    MultiSelectMenu

A menu that allows a user to select a multiple options from a list.

# Sample Output

```julia-repl
julia> request(MultiSelectMenu(options))
Select the fruits you like:
[press: Enter=toggle, a=all, n=none, d=done, q=abort]
   [ ] apple
 > [X] orange
   [X] grape
   [ ] strawberry
   [ ] blueberry
   [X] peach
   [ ] lemon
   [ ] lime
You like the following fruits:
  - orange
  - grape
  - peach
```

"""
mutable struct MultiSelectMenu{C} <: _ConfiguredMenu{C}
    options::Array{String,1}
    pagesize::Int
    pageoffset::Int
    selected::Set{Int}
    config::C
end


"""

    MultiSelectMenu(options::Array{String,1}; pagesize::Int=10, selected=[], kwargs...)

Create a MultiSelectMenu object. Use `request(menu::MultiSelectMenu)` to get
user input. It returns a `Set` containing the indices of options that
were selected by the user.

# Arguments

  - `options::Array{String, 1}`: Options to be displayed
  - `pagesize::Int=10`: The number of options to be displayed at one time, the menu will scroll if length(options) > pagesize
  - `selected=[]`: pre-selected items. `i ∈ selected` means that `options[i]` is preselected.

Any additional keyword arguments will be passed to [`TerminalMenus.MultiSelectConfig`](@ref).

!!! compat "Julia 1.6"
    The `selected` argument requires Julia 1.6 or later.
"""
function MultiSelectMenu(options::Array{String,1}; pagesize::Int=10, selected=Int[], warn::Bool=true, kwargs...)
    length(options) < 1 && error("MultiSelectMenu must have at least one option")

    # if pagesize is -1, use automatic paging
    pagesize = pagesize == -1 ? length(options) : pagesize
    # pagesize shouldn't be bigger than options
    pagesize = min(length(options), pagesize)
    # after other checks, pagesize must be at least 1
    pagesize < 1 && error("pagesize must be >= 1")

    pageoffset = 0
    _selected = Set{Int}()
    for item in selected
        push!(_selected, item)
    end

    if !isempty(kwargs)
        MultiSelectMenu(options, pagesize, pageoffset, _selected, MultiSelectConfig(; kwargs...))
    else
        warn && Base.depwarn("Legacy `MultiSelectMenu` interface is deprecated, set a configuration option such as `MultiSelectMenu(options; charset=:ascii)` to trigger the new interface.", :MultiSelectMenu)
        MultiSelectMenu(options, pagesize, pageoffset, _selected, CONFIG)
    end

end


# AbstractMenu implementation functions
# See AbstractMenu.jl
#######################################

header(m::MultiSelectMenu) = "[press: Enter=toggle, a=all, n=none, d=done, q=abort]"

options(m::MultiSelectMenu) = m.options

cancel(m::MultiSelectMenu) = m.selected = Set{Int}()

# Do not exit menu when a user selects one of the options
function pick(menu::MultiSelectMenu, cursor::Int)
    if cursor in menu.selected
        delete!(menu.selected, cursor)
    else
        push!(menu.selected, cursor)
    end

    return false #break out of the menu
end

function writeline(buf::IOBuffer, menu::MultiSelectMenu{MultiSelectConfig}, idx::Int, iscursor::Bool)
    if idx in menu.selected
        print(buf, menu.config.checked, " ")
    else
        print(buf, menu.config.unchecked, " ")
    end

    print(buf, replace(menu.options[idx], "\n" => "\\n"))
end

# d: Done, return from request
# a: Select all
# n: Deselect all
function keypress(menu::MultiSelectMenu, key::UInt32)
    if key == UInt32('d') || key == UInt32('D')
        return true # break
    elseif key == UInt32('a') || key == UInt32('A')
        menu.selected = Set(1:length(menu.options))
    elseif key == UInt32('n') || key == UInt32('N')
        menu.selected = Set{Int}()
    end
    false # don't break
end


## Legacy interface
function TerminalMenus.writeLine(buf::IOBuffer, menu::MultiSelectMenu{<:Dict}, idx::Int, cursor::Bool)
    # print a ">" on the selected entry
    cursor ? print(buf, menu.config[:cursor]," ") : print(buf, "  ")
    if idx in menu.selected
        print(buf, menu.config[:checked], " ")
    else
        print(buf, menu.config[:unchecked], " ")
    end

    print(buf, replace(menu.options[idx], "\n" => "\\n"))
end
{   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/REPL/src/TerminalMenus/Pager.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

mutable struct Pager{C} <: _ConfiguredMenu{C}
    lines::Vector{String}
    pagesize::Int
    pageoffset::Int
    selected::Nothing
    config::C
end

function Pager(text::AbstractString; pagesize::Int=10, kwargs...)
    lines = readlines(IOBuffer(text))
    return Pager(lines, pagesize, 0, nothing, Config(; kwargs...))
end

function header(p::Pager)
    total = length(p.lines)
    current = min(p.pageoffset + p.pagesize, total)
    percent = round(Int, (current / total) * 100)
    return "($(lpad(current, ndigits(total))) / $total) $(lpad(percent, 3))%"
end

options(p::Pager) = p.lines

cancel(::Pager) = nothing

pick(::Pager, ::Int) = true

function writeline(buf::IOBuffer, pager::Pager{Config}, idx::Int, iscursor::Bool)
    print(buf, pager.lines[idx])
end

function pager(terminal, object)
    lines, columns = displaysize(terminal)::Tuple{Int,Int}
    columns -= 3
    buffer = IOBuffer()
    ctx = IOContext(buffer, :color => REPL.Terminals.hascolor(terminal), :displaysize => (lines, columns))
    show(ctx, "text/plain", object)
    pager = Pager(String(take!(buffer)); pagesize = div(lines, 2))
    return request(terminal, pager)
end
pager(object) = pager(terminal, object)
o   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/REPL/src/docview.jlor      # This file is a part of Julia. License is MIT: https://julialang.org/license

## Code for searching and viewing documentation

using Markdown

using Base.Docs: catdoc, modules, DocStr, Binding, MultiDoc, keywords, isfield, namify, bindingexpr,
    defined, resolve, getdoc, meta, aliasof, signature

import Base.Docs: doc, formatdoc, parsedoc, apropos

using Base: with_output_color, mapany

import REPL

using InteractiveUtils: subtypes

using Unicode: normalize

## Help mode ##

# This is split into helpmode and _helpmode to easier unittest _helpmode
helpmode(io::IO, line::AbstractString, mod::Module=Main) = :($REPL.insert_hlines($io, $(REPL._helpmode(io, line, mod))))
helpmode(line::AbstractString, mod::Module=Main) = helpmode(stdout, line, mod)

const extended_help_on = Ref{Any}(nothing)

function _helpmode(io::IO, line::AbstractString, mod::Module=Main)
    line = strip(line)
    ternary_operator_help = (line == "?" || line == "?:")
    if startswith(line, '?') && !ternary_operator_help
        line = line[2:end]
        extended_help_on[] = line
        brief = false
    else
        extended_help_on[] = nothing
        brief = true
    end
    # interpret anything starting with # or #= as asking for help on comments
    if startswith(line, "#")
        if startswith(line, "#=")
            line = "#="
        else
            line = "#"
        end
    end
    x = Meta.parse(line, raise = false, depwarn = false)
    assym = Symbol(line)
    expr =
        if haskey(keywords, Symbol(line)) || Base.isoperator(assym) || isexpr(x, :error) ||
            isexpr(x, :invalid) || isexpr(x, :incomplete)
            # Docs for keywords must be treated separately since trying to parse a single
            # keyword such as `function` would throw a parse error due to the missing `end`.
            assym
        elseif isexpr(x, (:using, :import))
            (x::Expr).head
        else
            # Retrieving docs for macros requires us to make a distinction between the text
            # `@macroname` and `@macroname()`. These both parse the same, but are used by
            # the docsystem to return different results. The first returns all documentation
            # for `@macroname`, while the second returns *only* the docs for the 0-arg
            # definition if it exists.
            (isexpr(x, :macrocall, 1) && !endswith(line, "()")) ? quot(x) : x
        end
    # the following must call repl(io, expr) via the @repl macro
    # so that the resulting expressions are evaluated in the Base.Docs namespace
    :($REPL.@repl $io $expr $brief $mod)
end
_helpmode(line::AbstractString, mod::Module=Main) = _helpmode(stdout, line, mod)

# Print vertical lines along each docstring if there are multiple docs
function insert_hlines(io::IO, docs)
    if !isa(docs, Markdown.MD) || !haskey(docs.meta, :results) || isempty(docs.meta[:results])
        return docs
    end
    docs = docs::Markdown.MD
    v = Any[]
    for (n, doc) in enumerate(docs.content)
        push!(v, doc)
        n == length(docs.content) || push!(v, Markdown.HorizontalRule())
    end
    return Markdown.MD(v)
end

function formatdoc(d::DocStr)
    buffer = IOBuffer()
    for part in d.text
        formatdoc(buffer, d, part)
    end
    Markdown.MD(Any[Markdown.parse(seekstart(buffer))])
end
@noinline formatdoc(buffer, d, part) = print(buffer, part)

function parsedoc(d::DocStr)
    if d.object === nothing
        md = formatdoc(d)
        md.meta[:module] = d.data[:module]
        md.meta[:path]   = d.data[:path]
        d.object = md
    end
    d.object
end

## Trimming long help ("# Extended help")

struct Message  # For direct messages to the terminal
    msg    # AbstractString
    fmt    # keywords to `printstyled`
end
Message(msg) = Message(msg, ())

function Markdown.term(io::IO, msg::Message, columns)
    printstyled(io, msg.msg; msg.fmt...)
end

trimdocs(doc, brief::Bool) = doc

function trimdocs(md::Markdown.MD, brief::Bool)
    brief || return md
    md, trimmed = _trimdocs(md, brief)
    if trimmed
        line = extended_help_on[]
        line = isa(line, AbstractString) ? line : ""
        push!(md.content, Message("Extended help is available with `??$line`", (color=Base.info_color(), bold=true)))
    end
    return md
end

function _trimdocs(md::Markdown.MD, brief::Bool)
    content, trimmed = [], false
    for c in md.content
        if isa(c, Markdown.Header{1}) && isa(c.text, AbstractArray) && !isempty(c.text)
            item = c.text[1]
            if isa(item, AbstractString) &&
                lowercase(item) ∈ ("extended help",
                                   "extended documentation",
                                   "extended docs")
                trimmed = true
                break
            end
        end
        c, trm = _trimdocs(c, brief)
        trimmed |= trm
        push!(content, c)
    end
    return Markdown.MD(content, md.meta), trimmed
end

_trimdocs(md, brief::Bool) = md, false

"""
    Docs.doc(binding, sig)

Return all documentation that matches both `binding` and `sig`.

If `getdoc` returns a non-`nothing` result on the value of the binding, then a
dynamic docstring is returned instead of one based on the binding itself.
"""
function doc(binding::Binding, sig::Type = Union{})
    if defined(binding)
        result = getdoc(resolve(binding), sig)
        result === nothing || return result
    end
    results, groups = DocStr[], MultiDoc[]
    # Lookup `binding` and `sig` for matches in all modules of the docsystem.
    for mod in modules
        dict = meta(mod; autoinit=false)
        isnothing(dict) && continue
        if haskey(dict, binding)
            multidoc = dict[binding]
            push!(groups, multidoc)
            for msig in multidoc.order
                sig <: msig && push!(results, multidoc.docs[msig])
            end
        end
    end
    if isempty(groups)
        # When no `MultiDoc`s are found that match `binding` then we check whether `binding`
        # is an alias of some other `Binding`. When it is we then re-run `doc` with that
        # `Binding`, otherwise if it's not an alias then we generate a summary for the
        # `binding` and display that to the user instead.
        alias = aliasof(binding)
        alias == binding ? summarize(alias, sig) : doc(alias, sig)
    else
        # There was at least one match for `binding` while searching. If there weren't any
        # matches for `sig` then we concatenate *all* the docs from the matching `Binding`s.
        if isempty(results)
            for group in groups, each in group.order
                push!(results, group.docs[each])
            end
        end
        # Get parsed docs and concatenate them.
        md = catdoc(mapany(parsedoc, results)...)
        # Save metadata in the generated markdown.
        if isa(md, Markdown.MD)
            md.meta[:results] = results
            md.meta[:binding] = binding
            md.meta[:typesig] = sig
        end
        return md
    end
end

# Some additional convenience `doc` methods that take objects rather than `Binding`s.
doc(obj::UnionAll) = doc(Base.unwrap_unionall(obj))
doc(object, sig::Type = Union{}) = doc(aliasof(object, typeof(object)), sig)
doc(object, sig...)              = doc(object, Tuple{sig...})

function lookup_doc(ex)
    if isa(ex, Expr) && ex.head !== :(.) && Base.isoperator(ex.head)
        # handle syntactic operators, e.g. +=, ::, .=
        ex = ex.head
    end
    if haskey(keywords, ex)
        return parsedoc(keywords[ex])
    elseif Meta.isexpr(ex, :incomplete)
        return :($(Markdown.md"No documentation found."))
    elseif !isa(ex, Expr) && !isa(ex, Symbol)
        return :($(doc)($(typeof)($(esc(ex)))))
    end
    if isa(ex, Symbol) && Base.isoperator(ex)
        str = string(ex)
        isdotted = startswith(str, ".")
        if endswith(str, "=") && Base.operator_precedence(ex) == Base.prec_assignment && ex !== :(:=)
            op = chop(str)
            eq = isdotted ? ".=" : "="
            return Markdown.parse("`x $op= y` is a synonym for `x $eq x $op y`")
        elseif isdotted && ex !== :(..)
            op = str[2:end]
            if op in ("&&", "||")
                return Markdown.parse("`x $ex y` broadcasts the boolean operator `$op` to `x` and `y`. See [`broadcast`](@ref).")
            else
                return Markdown.parse("`x $ex y` is akin to `broadcast($op, x, y)`. See [`broadcast`](@ref).")
            end
        end
    end
    binding = esc(bindingexpr(namify(ex)))
    if isexpr(ex, :call) || isexpr(ex, :macrocall) || isexpr(ex, :where)
        sig = esc(signature(ex))
        :($(doc)($binding, $sig))
    else
        :($(doc)($binding))
    end
end

# Object Summaries.
# =================

function summarize(binding::Binding, sig)
    io = IOBuffer()
    if defined(binding)
        binding_res = resolve(binding)
        !isa(binding_res, Module) && println(io, "No documentation found.\n")
        summarize(io, binding_res, binding)
    else
        println(io, "No documentation found.\n")
        quot = any(isspace, sprint(print, binding)) ? "'" : ""
        if Base.isbindingresolved(binding.mod, binding.var)
            println(io, "Binding ", quot, "`", binding, "`", quot, " exists, but has not been assigned a value.")
        else
            println(io, "Binding ", quot, "`", binding, "`", quot, " does not exist.")
        end
    end
    md = Markdown.parse(seekstart(io))
    # Save metadata in the generated markdown.
    md.meta[:results] = DocStr[]
    md.meta[:binding] = binding
    md.meta[:typesig] = sig
    return md
end

function summarize(io::IO, λ::Function, binding::Binding)
    kind = startswith(string(binding.var), '@') ? "macro" : "`Function`"
    println(io, "`", binding, "` is a ", kind, ".")
    println(io, "```\n", methods(λ), "\n```")
end

function summarize(io::IO, TT::Type, binding::Binding)
    println(io, "# Summary")
    T = Base.unwrap_unionall(TT)
    if T isa DataType
        println(io, "```")
        print(io,
            Base.isabstracttype(T) ? "abstract type " :
            Base.ismutabletype(T)  ? "mutable struct " :
            Base.isstructtype(T) ? "struct " :
            "primitive type ")
        supert = supertype(T)
        println(io, T)
        println(io, "```")
        if !Base.isabstracttype(T) && T.name !== Tuple.name && !isempty(fieldnames(T))
            println(io, "# Fields")
            println(io, "```")
            pad = maximum(length(string(f)) for f in fieldnames(T))
            for (f, t) in zip(fieldnames(T), fieldtypes(T))
                println(io, rpad(f, pad), " :: ", t)
            end
            println(io, "```")
        end
        subt = subtypes(TT)
        if !isempty(subt)
            println(io, "# Subtypes")
            println(io, "```")
            for t in subt
                println(io, Base.unwrap_unionall(t))
            end
            println(io, "```")
        end
        if supert != Any
            println(io, "# Supertype Hierarchy")
            println(io, "```")
            Base.show_supertypes(io, T)
            println(io)
            println(io, "```")
        end
    elseif T isa Union
        println(io, "`", binding, "` is of type `", typeof(TT), "`.\n")
        println(io, "# Union Composed of Types")
        for T1 in Base.uniontypes(T)
            println(io, " - `", Base.rewrap_unionall(T1, TT), "`")
        end
    else # unreachable?
        println(io, "`", binding, "` is of type `", typeof(TT), "`.\n")
    end
end

function find_readme(m::Module)::Union{String, Nothing}
    mpath = pathof(m)
    isnothing(mpath) && return nothing
    !isfile(mpath) && return nothing # modules in sysimage, where src files are omitted
    path = dirname(mpath)
    top_path = pkgdir(m)
    while true
        for file in readdir(path; join=true, sort=true)
            isfile(file) && (basename(lowercase(file)) in ["readme.md", "readme"]) || continue
            return file
        end
        path == top_path && break # go no further than pkgdir
        path = dirname(path) # work up through nested modules
    end
    return nothing
end
function summarize(io::IO, m::Module, binding::Binding; nlines::Int = 200)
    readme_path = find_readme(m)
    if isnothing(readme_path)
        println(io, "No docstring or readme file found for module `$m`.\n")
    else
        println(io, "No docstring found for module `$m`.")
    end
    exports = filter!(!=(nameof(m)), names(m))
    if isempty(exports)
        println(io, "Module does not export any names.")
    else
        println(io, "# Exported names")
        print(io, "  `")
        join(io, exports, "`, `")
        println(io, "`\n")
    end
    if !isnothing(readme_path)
        readme_lines = readlines(readme_path)
        isempty(readme_lines) && return  # don't say we are going to print empty file
        println(io, "# Displaying contents of readme found at `$(readme_path)`")
        for line in first(readme_lines, nlines)
            println(io, line)
        end
        length(readme_lines) > nlines && println(io, "\n[output truncated to first $nlines lines]")
    end
end

function summarize(io::IO, @nospecialize(T), binding::Binding)
    T = typeof(T)
    println(io, "`", binding, "` is of type `", T, "`.\n")
    summarize(io, T, binding)
end

# repl search and completions for help


quote_spaces(x) = any(isspace, x) ? "'" * x * "'" : x

function repl_search(io::IO, s::Union{Symbol,String}, mod::Module)
    pre = "search:"
    print(io, pre)
    printmatches(io, s, map(quote_spaces, doc_completions(s, mod)), cols = _displaysize(io)[2] - length(pre))
    println(io, "\n")
end

# TODO: document where this is used
repl_search(s, mod::Module) = repl_search(stdout, s, mod)

function repl_corrections(io::IO, s, mod::Module)
    print(io, "Couldn't find ")
    quot = any(isspace, s) ? "'" : ""
    print(io, quot)
    printstyled(io, s, color=:cyan)
    print(io, quot, '\n')
    print_correction(io, s, mod)
end
repl_corrections(s) = repl_corrections(stdout, s)

# inverse of latex_symbols Dict, lazily created as needed
const symbols_latex = Dict{String,String}()
function symbol_latex(s::String)
    if isempty(symbols_latex) && isassigned(Base.REPL_MODULE_REF)
        for (k,v) in Iterators.flatten((REPLCompletions.latex_symbols,
                                        REPLCompletions.emoji_symbols))
            symbols_latex[v] = k
        end

        # Overwrite with canonical mapping when a symbol has several completions (#39148)
        merge!(symbols_latex, REPLCompletions.symbols_latex_canonical)
    end

    return get(symbols_latex, s, "")
end
function repl_latex(io::IO, s0::String)
    # This has rampant `Core.Box` problems (#15276). Use the tricks of
    # https://docs.julialang.org/en/v1/manual/performance-tips/#man-performance-captured
    # We're changing some of the values so the `let` trick isn't applicable.
    s::String = s0
    latex::String = symbol_latex(s)
    if isempty(latex)
        # Decompose NFC-normalized identifier to match tab-completion
        # input if the first search came up empty.
        s = normalize(s, :NFD)
        latex = symbol_latex(s)
    end
    if !isempty(latex)
        print(io, "\"")
        printstyled(io, s, color=:cyan)
        print(io, "\" can be typed by ")
        printstyled(io, latex, "<tab>", color=:cyan)
        println(io, '\n')
    elseif any(c -> haskey(symbols_latex, string(c)), s)
        print(io, "\"")
        printstyled(io, s, color=:cyan)
        print(io, "\" can be typed by ")
        state::Char = '\0'
        with_output_color(:cyan, io) do io
            for c in s
                cstr = string(c)
                if haskey(symbols_latex, cstr)
                    latex = symbols_latex[cstr]
                    if length(latex) == 3 && latex[2] in ('^','_')
                        # coalesce runs of sub/superscripts
                        if state != latex[2]
                            '\0' != state && print(io, "<tab>")
                            print(io, latex[1:2])
                            state = latex[2]
                        end
                        print(io, latex[3])
                    else
                        if '\0' != state
                            print(io, "<tab>")
                            state = '\0'
                        end
                        print(io, latex, "<tab>")
                    end
                else
                    if '\0' != state
                        print(io, "<tab>")
                        state = '\0'
                    end
                    print(io, c)
                end
            end
            '\0' != state && print(io, "<tab>")
        end
        println(io, '\n')
    end
end
repl_latex(s::String) = repl_latex(stdout, s)

macro repl(ex, brief::Bool=false, mod::Module=Main) repl(ex; brief, mod) end
macro repl(io, ex, brief, mod) repl(io, ex; brief, mod) end

function repl(io::IO, s::Symbol; brief::Bool=true, mod::Module=Main)
    str = string(s)
    quote
        repl_latex($io, $str)
        repl_search($io, $str, $mod)
        $(if !isdefined(mod, s) && !Base.isbindingresolved(mod, s) && !haskey(keywords, s) && !Base.isoperator(s)
               # n.b. we call isdefined for the side-effect of resolving the binding, if possible
               :(repl_corrections($io, $str, $mod))
          end)
        $(_repl(s, brief))
    end
end
isregex(x) = isexpr(x, :macrocall, 3) && x.args[1] === Symbol("@r_str") && !isempty(x.args[3])

repl(io::IO, ex::Expr; brief::Bool=true, mod::Module=Main) = isregex(ex) ? :(apropos($io, $ex)) : _repl(ex, brief)
repl(io::IO, str::AbstractString; brief::Bool=true, mod::Module=Main) = :(apropos($io, $str))
repl(io::IO, other; brief::Bool=true, mod::Module=Main) = esc(:(@doc $other))
#repl(io::IO, other) = lookup_doc(other) # TODO

repl(x; brief::Bool=true, mod::Module=Main) = repl(stdout, x; brief, mod)

function _repl(x, brief::Bool=true)
    if isexpr(x, :call)
        x = x::Expr
        # determine the types of the values
        kwargs = nothing
        pargs = Any[]
        for arg in x.args[2:end]
            if isexpr(arg, :parameters)
                kwargs = mapany(arg.args) do kwarg
                    if kwarg isa Symbol
                        kwarg = :($kwarg::Any)
                    elseif isexpr(kwarg, :kw)
                        lhs = kwarg.args[1]
                        rhs = kwarg.args[2]
                        if lhs isa Symbol
                            if rhs isa Symbol
                                kwarg.args[1] = :($lhs::(@isdefined($rhs) ? typeof($rhs) : Any))
                            else
                                kwarg.args[1] = :($lhs::typeof($rhs))
                            end
                        end
                    end
                    kwarg
                end
            elseif isexpr(arg, :kw)
                if kwargs === nothing
                    kwargs = Any[]
                end
                lhs = arg.args[1]
                rhs = arg.args[2]
                if lhs isa Symbol
                    if rhs isa Symbol
                        arg.args[1] = :($lhs::(@isdefined($rhs) ? typeof($rhs) : Any))
                    else
                        arg.args[1] = :($lhs::typeof($rhs))
                    end
                end
                push!(kwargs, arg)
            else
                if arg isa Symbol
                    arg = :($arg::(@isdefined($arg) ? typeof($arg) : Any))
                elseif !isexpr(arg, :(::))
                    arg = :(::typeof($arg))
                end
                push!(pargs, arg)
            end
        end
        if kwargs === nothing
            x.args = Any[x.args[1], pargs...]
        else
            x.args = Any[x.args[1], Expr(:parameters, kwargs...), pargs...]
        end
    end
    #docs = lookup_doc(x) # TODO
    docs = esc(:(@doc $x))
    docs = if isfield(x)
        quote
            if isa($(esc(x.args[1])), DataType)
                fielddoc($(esc(x.args[1])), $(esc(x.args[2])))
            else
                $docs
            end
        end
    else
        docs
    end
    :(REPL.trimdocs($docs, $brief))
end

"""
    fielddoc(binding, field)

Return documentation for a particular `field` of a type if it exists.
"""
function fielddoc(binding::Binding, field::Symbol)
    for mod in modules
        dict = meta(mod; autoinit=false)
        isnothing(dict) && continue
        if haskey(dict, binding)
            multidoc = dict[binding]
            if haskey(multidoc.docs, Union{})
                fields = multidoc.docs[Union{}].data[:fields]
                if haskey(fields, field)
                    doc = fields[field]
                    return isa(doc, Markdown.MD) ? doc : Markdown.parse(doc)
                end
            end
        end
    end
    fields = join(["`$f`" for f in fieldnames(resolve(binding))], ", ", ", and ")
    fields = isempty(fields) ? "no fields" : "fields $fields"
    Markdown.parse("`$(resolve(binding))` has $fields.")
end

# As with the additional `doc` methods, this converts an object to a `Binding` first.
fielddoc(object, field::Symbol) = fielddoc(aliasof(object, typeof(object)), field)


# Search & Rescue
# Utilities for correcting user mistakes and (eventually)
# doing full documentation searches from the repl.

# Fuzzy Search Algorithm

function matchinds(needle, haystack; acronym::Bool = false)
    chars = collect(needle)
    is = Int[]
    lastc = '\0'
    for (i, char) in enumerate(haystack)
        while !isempty(chars) && isspace(first(chars))
            popfirst!(chars) # skip spaces
        end
        isempty(chars) && break
        if lowercase(char) == lowercase(chars[1]) &&
           (!acronym || !isletter(lastc))
            push!(is, i)
            popfirst!(chars)
        end
        lastc = char
    end
    return is
end

longer(x, y) = length(x) ≥ length(y) ? (x, true) : (y, false)

bestmatch(needle, haystack) =
    longer(matchinds(needle, haystack, acronym = true),
           matchinds(needle, haystack))

avgdistance(xs) =
    isempty(xs) ? 0 :
    (xs[end] - xs[1] - length(xs)+1)/length(xs)

function fuzzyscore(needle, haystack)
    score = 0.
    is, acro = bestmatch(needle, haystack)
    score += (acro ? 2 : 1)*length(is) # Matched characters
    score -= 2(length(needle)-length(is)) # Missing characters
    !acro && (score -= avgdistance(is)/10) # Contiguous
    !isempty(is) && (score -= sum(is)/length(is)/100) # Closer to beginning
    return score
end

function fuzzysort(search::String, candidates::Vector{String})
    scores = map(cand -> (fuzzyscore(search, cand), -Float64(levenshtein(search, cand))), candidates)
    candidates[sortperm(scores)] |> reverse
end

# Levenshtein Distance

function levenshtein(s1, s2)
    a, b = collect(s1), collect(s2)
    m = length(a)
    n = length(b)
    d = Matrix{Int}(undef, m+1, n+1)

    d[1:m+1, 1] = 0:m
    d[1, 1:n+1] = 0:n

    for i = 1:m, j = 1:n
        d[i+1,j+1] = min(d[i  , j+1] + 1,
                         d[i+1, j  ] + 1,
                         d[i  , j  ] + (a[i] != b[j]))
    end

    return d[m+1, n+1]
end

function levsort(search::String, candidates::Vector{String})
    scores = map(cand -> (Float64(levenshtein(search, cand)), -fuzzyscore(search, cand)), candidates)
    candidates = candidates[sortperm(scores)]
    i = 0
    for outer i = 1:length(candidates)
        levenshtein(search, candidates[i]) > 3 && break
    end
    return candidates[1:i]
end

# Result printing

function printmatch(io::IO, word, match)
    is, _ = bestmatch(word, match)
    for (i, char) = enumerate(match)
        if i in is
            printstyled(io, char, bold=true)
        else
            print(io, char)
        end
    end
end

function printmatches(io::IO, word, matches; cols::Int = _displaysize(io)[2])
    total = 0
    for match in matches
        total + length(match) + 1 > cols && break
        fuzzyscore(word, match) < 0 && break
        print(io, " ")
        printmatch(io, word, match)
        total += length(match) + 1
    end
end

printmatches(args...; cols::Int = _displaysize(stdout)[2]) = printmatches(stdout, args..., cols = cols)

function print_joined_cols(io::IO, ss::Vector{String}, delim = "", last = delim; cols::Int = _displaysize(io)[2])
    i = 0
    total = 0
    for outer i = 1:length(ss)
        total += length(ss[i])
        total + max(i-2,0)*length(delim) + (i>1 ? 1 : 0)*length(last) > cols && (i-=1; break)
    end
    join(io, ss[1:i], delim, last)
end

print_joined_cols(args...; cols::Int = _displaysize(stdout)[2]) = print_joined_cols(stdout, args...; cols=cols)

function print_correction(io::IO, word::String, mod::Module)
    cors = map(quote_spaces, levsort(word, accessible(mod)))
    pre = "Perhaps you meant "
    print(io, pre)
    print_joined_cols(io, cors, ", ", " or "; cols = _displaysize(io)[2] - length(pre))
    println(io)
    return
end

# TODO: document where this is used
print_correction(word, mod::Module) = print_correction(stdout, word, mod)

# Completion data


moduleusings(mod) = ccall(:jl_module_usings, Any, (Any,), mod)

filtervalid(names) = filter(x->!occursin(r"#", x), map(string, names))

accessible(mod::Module) =
    Symbol[filter!(s -> !Base.isdeprecated(mod, s), names(mod, all=true, imported=true));
           map(names, moduleusings(mod))...;
           collect(keys(Base.Docs.keywords))] |> unique |> filtervalid

function doc_completions(name, mod::Module=Main)
    res = fuzzysort(name, accessible(mod))

    # to insert an entry like `raw""` for `"@raw_str"` in `res`
    ms = match.(r"^@(.*?)_str$", res)
    idxs = findall(!isnothing, ms)

    # avoid messing up the order while inserting
    for i in reverse!(idxs)
        c = only((ms[i]::AbstractMatch).captures)
        insert!(res, i, "$(c)\"\"")
    end
    res
end
doc_completions(name::Symbol) = doc_completions(string(name), mod)


# Searching and apropos

# Docsearch simply returns true or false if an object contains the given needle
docsearch(haystack::AbstractString, needle) = occursin(needle, haystack)
docsearch(haystack::Symbol, needle) = docsearch(string(haystack), needle)
docsearch(::Nothing, needle) = false
function docsearch(haystack::Array, needle)
    for elt in haystack
        docsearch(elt, needle) && return true
    end
    false
end
function docsearch(haystack, needle)
    @warn "Unable to search documentation of type $(typeof(haystack))" maxlog=1
    false
end

## Searching specific documentation objects
function docsearch(haystack::MultiDoc, needle)
    for v in values(haystack.docs)
        docsearch(v, needle) && return true
    end
    false
end

function docsearch(haystack::DocStr, needle)
    docsearch(parsedoc(haystack), needle) && return true
    if haskey(haystack.data, :fields)
        for doc in values(haystack.data[:fields])
            docsearch(doc, needle) && return true
        end
    end
    false
end

## doc search

## Markdown search simply strips all markup and searches plain text version
docsearch(haystack::Markdown.MD, needle) = docsearch(stripmd(haystack.content), needle)

"""
    stripmd(x)

Strip all Markdown markup from x, leaving the result in plain text. Used
internally by apropos to make docstrings containing more than one markdown
element searchable.
"""
stripmd(@nospecialize x) = string(x) # for random objects interpolated into the docstring
stripmd(x::AbstractString) = x  # base case
stripmd(x::Nothing) = " "
stripmd(x::Vector) = string(map(stripmd, x)...)

stripmd(x::Markdown.BlockQuote) = "$(stripmd(x.content))"
stripmd(x::Markdown.Admonition) = "$(stripmd(x.content))"
stripmd(x::Markdown.Bold) = "$(stripmd(x.text))"
stripmd(x::Markdown.Code) = "$(stripmd(x.code))"
stripmd(x::Markdown.Header) = stripmd(x.text)
stripmd(x::Markdown.HorizontalRule) = " "
stripmd(x::Markdown.Image) = "$(stripmd(x.alt)) $(x.url)"
stripmd(x::Markdown.Italic) = "$(stripmd(x.text))"
stripmd(x::Markdown.LaTeX) = "$(x.formula)"
stripmd(x::Markdown.LineBreak) = " "
stripmd(x::Markdown.Link) = "$(stripmd(x.text)) $(x.url)"
stripmd(x::Markdown.List) = join(map(stripmd, x.items), " ")
stripmd(x::Markdown.MD) = join(map(stripmd, x.content), " ")
stripmd(x::Markdown.Paragraph) = stripmd(x.content)
stripmd(x::Markdown.Footnote) = "$(stripmd(x.id)) $(stripmd(x.text))"
stripmd(x::Markdown.Table) =
    join([join(map(stripmd, r), " ") for r in x.rows], " ")

"""
    apropos([io::IO=stdout], pattern::Union{AbstractString,Regex})

Search available docstrings for entries containing `pattern`.

When `pattern` is a string, case is ignored. Results are printed to `io`.

`apropos` can be called from the help mode in the REPL by wrapping the query in double quotes:
```
help?> "pattern"
```
"""
apropos(string) = apropos(stdout, string)
apropos(io::IO, string) = apropos(io, Regex("\\Q$string", "i"))

function apropos(io::IO, needle::Regex)
    for mod in modules
        # Module doc might be in README.md instead of the META dict
        docsearch(doc(mod), needle) && println(io, mod)
        dict = meta(mod; autoinit=false)
        isnothing(dict) && continue
        for (k, v) in dict
            docsearch(v, needle) && println(io, k)
        end
    end
end
l   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/TOML/src/TOML.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

module TOML

module Internals
    # The parser is defined in Base
    using Base.TOML: Parser, parse, tryparse, ParserError, isvalid_barekey_char, reinit!
    # Put the error instances in this module
    for errtype in instances(Base.TOML.ErrorType)
        @eval using Base.TOML: $(Symbol(errtype))
    end
    # We put the printing functionality in a separate module since It
    # defines a function `print` and we don't want that to collide with normal
    # usage of `(Base.)print` in other files
    module Printer
        include("print.jl")
    end
end

# https://github.com/JuliaLang/julia/issues/36605
readstring(f::AbstractString) = isfile(f) ? read(f, String) : error(repr(f), ": No such file")

"""
    Parser()

Constructor for a TOML `Parser`.  Note that in most cases one does not need to
explicitly create a `Parser` but instead one directly use use
[`TOML.parsefile`](@ref) or [`TOML.parse`](@ref).  Using an explicit parser
will however reuse some internal data structures which can be beneficial for
performance if a larger number of small files are parsed.
"""
const Parser = Internals.Parser

"""
    parsefile(f::AbstractString)
    parsefile(p::Parser, f::AbstractString)

Parse file `f` and return the resulting table (dictionary). Throw a
[`ParserError`](@ref) upon failure.

See also [`TOML.tryparsefile`](@ref).
"""
parsefile(f::AbstractString) =
    Internals.parse(Parser(readstring(f); filepath=abspath(f)))
parsefile(p::Parser, f::AbstractString) =
    Internals.parse(Internals.reinit!(p, readstring(f); filepath=abspath(f)))

"""
    tryparsefile(f::AbstractString)
    tryparsefile(p::Parser, f::AbstractString)

Parse file `f` and return the resulting table (dictionary). Return a
[`ParserError`](@ref) upon failure.

See also [`TOML.parsefile`](@ref).
"""
tryparsefile(f::AbstractString) =
    Internals.tryparse(Parser(readstring(f); filepath=abspath(f)))
tryparsefile(p::Parser, f::AbstractString) =
    Internals.tryparse(Internals.reinit!(p, readstring(f); filepath=abspath(f)))

"""
    parse(x::Union{AbstractString, IO})
    parse(p::Parser, x::Union{AbstractString, IO})

Parse the string  or stream `x`, and return the resulting table (dictionary).
Throw a [`ParserError`](@ref) upon failure.

See also [`TOML.tryparse`](@ref).
"""
parse(str::AbstractString) =
    Internals.parse(Parser(String(str)))
parse(p::Parser, str::AbstractString) =
    Internals.parse(Internals.reinit!(p, String(str)))
parse(io::IO) = parse(read(io, String))
parse(p::Parser, io::IO) = parse(p, read(io, String))

"""
    tryparse(x::Union{AbstractString, IO})
    tryparse(p::Parser, x::Union{AbstractString, IO})

Parse the string or stream `x`, and return the resulting table (dictionary).
Return a [`ParserError`](@ref) upon failure.

See also [`TOML.parse`](@ref).
"""
tryparse(str::AbstractString) =
    Internals.tryparse(Parser(String(str)))
tryparse(p::Parser, str::AbstractString) =
    Internals.tryparse(Internals.reinit!(p, String(str)))
tryparse(io::IO) = tryparse(read(io, String))
tryparse(p::Parser, io::IO) = tryparse(p, read(io, String))

"""
    ParserError

Type that is returned from [`tryparse`](@ref) and [`tryparsefile`](@ref)
when parsing fails. It contains (among others) the following fields:

- `pos`, the position in the string when the error happened
- `table`, the result that so far was successfully parsed
- `type`, an error type, different for different types of errors
"""
const ParserError = Internals.ParserError


"""
    print([to_toml::Function], io::IO [=stdout], data::AbstractDict; sorted=false, by=identity)

Write `data` as TOML syntax to the stream `io`. If the keyword argument `sorted` is set to `true`,
sort tables according to the function given by the keyword argument `by`.

The following data types are supported: `AbstractDict`, `AbstractVector`, `AbstractString`, `Integer`, `AbstractFloat`, `Bool`,
`Dates.DateTime`, `Dates.Time`, `Dates.Date`. Note that the integers and floats
need to be convertible to `Float64` and `Int64` respectively. For other data types,
pass the function `to_toml` that takes the data types and returns a value of a
supported type.
"""
const print = Internals.Printer.print

end
m   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/TOML/src/print.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

import Dates

import Base: @invokelatest
import ..isvalid_barekey_char

function print_toml_escaped(io::IO, s::AbstractString)
    for c::AbstractChar in s
        if !isvalid(c)
            error("TOML print: invalid character $(repr(c)) encountered when printing string")
        end
        if c == '\b'
            Base.print(io, '\\', 'b')
        elseif c == '\t'
            Base.print(io, '\\', 't')
        elseif c == '\n'
            Base.print(io, '\\', 'n')
        elseif c == '\f'
            Base.print(io, '\\', 'f')
        elseif c == '\r'
            Base.print(io, '\\', 'r')
        elseif c == '"'
            Base.print(io, '\\', '"')
        elseif c == '\\'
            Base.print(io, "\\", '\\')
        elseif Base.iscntrl(c)
            Base.print(io, "\\u")
            Base.print(io, string(UInt32(c), base=16, pad=4))
        else
            Base.print(io, c)
        end
    end
end

const MbyFunc = Union{Function, Nothing}
const TOMLValue = Union{AbstractVector, AbstractDict, Dates.DateTime, Dates.Time, Dates.Date, Bool, Integer, AbstractFloat, AbstractString}


########
# Keys #
########

function printkey(io::IO, keys::Vector{String})
    for (i, k) in enumerate(keys)
        i != 1 && Base.print(io, ".")
        if length(k) == 0
            # empty key
            Base.print(io, "\"\"")
        elseif any(!isvalid_barekey_char, k)
            # quoted key
            Base.print(io, "\"")
            print_toml_escaped(io, k)
            Base.print(io, "\"")
        else
            Base.print(io, k)
        end
    end
end

function to_toml_value(f::MbyFunc, value)
    if f === nothing
        error("type `$(typeof(value))` is not a valid TOML type, pass a conversion function to `TOML.print`")
    end
    toml_value = f(value)
    if !(toml_value isa TOMLValue)
        error("TOML syntax function for type `$(typeof(value))` did not return a valid TOML type but a `$(typeof(toml_value))`")
    end
    return toml_value
end

##########
# Values #
##########

# Fallback
function printvalue(f::MbyFunc, io::IO, value)
    toml_value = to_toml_value(f, value)
    @invokelatest printvalue(f, io, toml_value)
end

function printvalue(f::MbyFunc, io::IO, value::AbstractVector)
    Base.print(io, "[")
    for (i, x) in enumerate(value)
        i != 1 && Base.print(io, ", ")
        printvalue(f, io, x)
    end
    Base.print(io, "]")
end

function printvalue(f::MbyFunc, io::IO, value::TOMLValue)
    value isa Dates.DateTime ? Base.print(io, Dates.format(value, Dates.dateformat"YYYY-mm-dd\THH:MM:SS.sss\Z")) :
    value isa Dates.Time     ? Base.print(io, Dates.format(value, Dates.dateformat"HH:MM:SS.sss")) :
    value isa Dates.Date     ? Base.print(io, Dates.format(value, Dates.dateformat"YYYY-mm-dd")) :
    value isa Bool           ? Base.print(io, value ? "true" : "false") :
    value isa Integer        ? print_integer(io, value) :  # Julia's own printing should be compatible with TOML on integers
    value isa AbstractFloat  ? Base.print(io, isnan(value) ? "nan" :
                                              isinf(value) ? string(value > 0 ? "+" : "-", "inf") :
                                              Float64(value)) :  # TOML specifies IEEE 754 binary64 for float
    value isa AbstractString ? (Base.print(io, "\"");
                                print_toml_escaped(io, value);
                                Base.print(io, "\"")) :
    value isa AbstractDict ? print_inline_table(f, io, value) :
    error("internal error in TOML printing, unhandled value")
end

function print_integer(io::IO, value::Integer)
    value isa Signed && return Base.show(io, value)
    # unsigned integers are printed as hex
    n = 2 * ndigits(value, base=256)
    Base.print(io, "0x", string(value, base=16, pad=n))
    return
end

function print_inline_table(f::MbyFunc, io::IO, value::AbstractDict)
    Base.print(io, "{")
    for (i, (k,v)) in enumerate(value)
        i != 1 && Base.print(io, ", ")
        printkey(io, [String(k)])
        Base.print(io, " = ")
        printvalue(f, io, v)
    end
    Base.print(io, "}")
end


##########
# Tables #
##########

is_table(value)           = isa(value, AbstractDict)
is_array_of_tables(value) = isa(value, AbstractArray) &&
                            length(value) > 0 && (
                                isa(value, AbstractArray{<:AbstractDict}) ||
                                all(v -> isa(v, AbstractDict), value)
                            )
is_tabular(value)         = is_table(value) || @invokelatest(is_array_of_tables(value))

function print_table(f::MbyFunc, io::IO, a::AbstractDict,
    ks::Vector{String} = String[];
    indent::Int = 0,
    first_block::Bool = true,
    sorted::Bool = false,
    by::Function = identity,
)
    akeys = keys(a)
    if sorted
        akeys = sort!(collect(akeys); by=by)
    end

    # First print non-tabular entries
    for key in akeys
        value = a[key]
        if !isa(value, TOMLValue)
            value = to_toml_value(f, value)
        end
        is_tabular(value) && continue

        Base.print(io, ' '^4max(0,indent-1))
        printkey(io, [String(key)])
        Base.print(io, " = ") # print separator
        printvalue(f, io, value)
        Base.print(io, "\n")  # new line?
        first_block = false
    end

    for key in akeys
        value = a[key]
        if !isa(value, TOMLValue)
            value = to_toml_value(f, value)
        end
        if is_table(value)
            push!(ks, String(key))
            _values = @invokelatest values(value)
            header = isempty(value) || !all(is_tabular(v) for v in _values)::Bool
            if header
                # print table
                first_block || println(io)
                first_block = false
                Base.print(io, ' '^4indent)
                Base.print(io,"[")
                printkey(io, ks)
                Base.print(io,"]\n")
            end
            # Use runtime dispatch here since the type of value seems not to be enforced other than as AbstractDict
            @invokelatest print_table(f, io, value, ks; indent = indent + header, first_block = header, sorted=sorted, by=by)
            pop!(ks)
        elseif @invokelatest(is_array_of_tables(value))
            # print array of tables
            first_block || println(io)
            first_block = false
            push!(ks, String(key))
            for v in value
                Base.print(io, ' '^4indent)
                Base.print(io,"[[")
                printkey(io, ks)
                Base.print(io,"]]\n")
                # TODO, nicer error here
                !isa(v, AbstractDict) && error("array should contain only tables")
                @invokelatest print_table(f, io, v, ks; indent = indent + 1, sorted=sorted, by=by)
            end
            pop!(ks)
        end
    end
end


#######
# API #
#######

print(f::MbyFunc, io::IO, a::AbstractDict; sorted::Bool=false, by=identity) = print_table(f, io, a; sorted=sorted, by=by)
print(f::MbyFunc, a::AbstractDict; sorted::Bool=false, by=identity) = print(f, stdout, a; sorted=sorted, by=by)
print(io::IO, a::AbstractDict; sorted::Bool=false, by=identity) = print_table(nothing, io, a; sorted=sorted, by=by)
print(a::AbstractDict; sorted::Bool=false, by=identity) = print(nothing, stdout, a; sorted=sorted, by=by)
r   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LibCURL/src/LibCURL.jl	      
module LibCURL

using LibCURL_jll
using MozillaCACerts_jll

const time_t = Int
const size_t = Csize_t
const curl_off_t = Int64
const fd_set = Union{}
const socklen_t = Int32

cacert = ""

export Mime_ext

function __init__()
    # Note: `MozillaCACerts_jll.cacert` is filled by `__init__` which requires LibCURL's
    # copy to also be filled in during initialization. Doing this ensures compatibility
    # with building system images.
    global cacert = MozillaCACerts_jll.cacert
end

include("lC_exports_h.jl")
include("lC_common_h.jl")
include("lC_curl_h.jl")

# curl_easy_getinfo, curl_easy_setopt, and curl_multi_setopt are vararg C functions

curl_easy_setopt(handle, opt, ptrval::Array{T}) where T = ccall((:curl_easy_setopt, libcurl), CURLcode, (Ptr{CURL}, CURLoption, Ptr{T}...), handle, opt, ptrval)
curl_easy_setopt(handle, opt, ptrval::Integer) = ccall((:curl_easy_setopt, libcurl), CURLcode, (Ptr{CURL}, CURLoption, Clong...), handle, opt, ptrval)
curl_easy_setopt(handle, opt, ptrval::Ptr{T}) where {T} = ccall((:curl_easy_setopt, libcurl), CURLcode, (Ptr{CURL}, CURLoption, Ptr{T}...), handle, opt, ptrval)
curl_easy_setopt(handle, opt, ptrval::AbstractString) = ccall((:curl_easy_setopt, libcurl), CURLcode, (Ptr{CURL}, CURLoption, Ptr{UInt8}...), handle, opt, ptrval)

curl_multi_setopt(handle, opt, ptrval::Array{T}) where T = ccall((:curl_multi_setopt, libcurl), CURLMcode, (Ptr{CURLM}, CURLMoption, Ptr{T}...), handle, opt, ptrval)
curl_multi_setopt(handle, opt, ptrval::Integer) = ccall((:curl_multi_setopt, libcurl), CURLMcode, (Ptr{CURLM}, CURLMoption, Clong...), handle, opt, ptrval)
curl_multi_setopt(handle, opt, ptrval::Ptr{T}) where {T} = ccall((:curl_multi_setopt, libcurl), CURLMcode, (Ptr{CURLM}, CURLMoption, Ptr{T}...), handle, opt, ptrval)
curl_multi_setopt(handle, opt, ptrval::AbstractString) = ccall((:curl_multi_setopt, libcurl), CURLMcode, (Ptr{CURLM}, CURLMoption, Ptr{UInt8}...), handle, opt, ptrval)

curl_easy_getinfo(handle, opt, ptrval::Array{T}) where T = ccall((:curl_easy_getinfo, libcurl), CURLcode, (Ptr{CURL}, CURLoption, Ptr{T}...), handle, opt, ptrval)
curl_easy_getinfo(handle, opt, ptrval::AbstractString) = ccall((:curl_easy_getinfo, libcurl), CURLcode, (Ptr{CURL}, CURLoption, Ptr{UInt8}...), handle, opt, ptrval)

include("lC_defines_h.jl")

include("Mime_ext.jl")

end
z   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LibCURL_jll/src/LibCURL_jll.jlQ      # This file is a part of Julia. License is MIT: https://julialang.org/license

## dummy stub for https://github.com/JuliaBinaryWrappers/LibCURL_jll.jl

baremodule LibCURL_jll
using Base, Libdl, nghttp2_jll
Base.Experimental.@compiler_options compile=min optimize=0 infer=false

const PATH_list = String[]
const LIBPATH_list = String[]

export libcurl

# These get calculated in __init__()
const PATH = Ref("")
const LIBPATH = Ref("")
artifact_dir::String = ""
libcurl_handle::Ptr{Cvoid} = C_NULL
libcurl_path::String = ""

if Sys.iswindows()
    const libcurl = "libcurl-4.dll"
elseif Sys.isapple()
    const libcurl = "@rpath/libcurl.4.dylib"
else
    const libcurl = "libcurl.so.4"
end

function __init__()
    global libcurl_handle = dlopen(libcurl)
    global libcurl_path = dlpath(libcurl_handle)
    global artifact_dir = dirname(Sys.BINDIR)
    LIBPATH[] = dirname(libcurl_path)
    push!(LIBPATH_list, LIBPATH[])
end

# JLLWrappers API compatibility shims.  Note that not all of these will really make sense.
# For instance, `find_artifact_dir()` won't actually be the artifact directory, because
# there isn't one.  It instead returns the overall Julia prefix.
is_available() = true
find_artifact_dir() = artifact_dir
dev_jll() = error("stdlib JLLs cannot be dev'ed")
best_wrapper = nothing
get_libcurl_path() = libcurl_path

end  # module LibCURL_jll
z   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/nghttp2_jll/src/nghttp2_jll.jlv      # This file is a part of Julia. License is MIT: https://julialang.org/license

## dummy stub for https://github.com/JuliaBinaryWrappers/nghttp2_jll.jl
baremodule nghttp2_jll
using Base, Libdl
Base.Experimental.@compiler_options compile=min optimize=0 infer=false

const PATH_list = String[]
const LIBPATH_list = String[]

export libnghttp2

# These get calculated in __init__()
const PATH = Ref("")
const LIBPATH = Ref("")
artifact_dir::String = ""
libnghttp2_handle::Ptr{Cvoid} = C_NULL
libnghttp2_path::String = ""

if Sys.iswindows()
    const libnghttp2 = "libnghttp2-14.dll"
elseif Sys.isapple()
    const libnghttp2 = "@rpath/libnghttp2.14.dylib"
else
    const libnghttp2 = "libnghttp2.so.14"
end

function __init__()
    global libnghttp2_handle = dlopen(libnghttp2)
    global libnghttp2_path = dlpath(libnghttp2_handle)
    global artifact_dir = dirname(Sys.BINDIR)
    LIBPATH[] = dirname(libnghttp2_path)
    push!(LIBPATH_list, LIBPATH[])
end

# JLLWrappers API compatibility shims.  Note that not all of these will really make sense.
# For instance, `find_artifact_dir()` won't actually be the artifact directory, because
# there isn't one.  It instead returns the overall Julia prefix.
is_available() = true
find_artifact_dir() = artifact_dir
dev_jll() = error("stdlib JLLs cannot be dev'ed")
best_wrapper = nothing
get_libnghttp2_path() = libnghttp2_path

end  # module nghttp2_jll
�   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/MozillaCACerts_jll/src/MozillaCACerts_jll.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

## dummy stub for https://github.com/JuliaBinaryWrappers/MozillaCACerts_jll.jl

baremodule MozillaCACerts_jll
using Base
Base.Experimental.@compiler_options compile=min optimize=0 infer=false

const PATH_list = String[]
const LIBPATH_list = String[]

# These get calculated in __init__()
const PATH = Ref("")
const LIBPATH = Ref("")
global artifact_dir::String = ""
global cacert::String = ""

function __init__()
    global artifact_dir = dirname(Sys.BINDIR)
    global cacert = normpath(Sys.BINDIR, Base.DATAROOTDIR, "julia", "cert.pem")
end

# JLLWrappers API compatibility shims.  Note that not all of these will really make sense.
# For instance, `find_artifact_dir()` won't actually be the artifact directory, because
# there isn't one.  It instead returns the overall Julia prefix.
is_available() = true
find_artifact_dir() = artifact_dir
dev_jll() = error("stdlib JLLs cannot be dev'ed")
best_wrapper = nothing

end # module
w   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LibCURL/src/lC_exports_h.jlH�      #   Generating exports
export curl_strequal
export curl_strnequal
export curl_mime_init
export curl_mime_free
export curl_mime_addpart
export curl_mime_name
export curl_mime_filename
export curl_mime_type
export curl_mime_encoder
export curl_mime_data
export curl_mime_filedata
export curl_mime_data_cb
export curl_mime_subparts
export curl_mime_headers
export curl_formget
export curl_formfree
export curl_getenv
export curl_version
export curl_easy_escape
export curl_escape
export curl_easy_unescape
export curl_unescape
export curl_free
export curl_global_init
export curl_global_init_mem
export curl_global_cleanup
export curl_global_sslset
export curl_slist_append
export curl_slist_free_all
export curl_getdate
export curl_share_init
export curl_share_setopt
export curl_share_cleanup
export curl_version_info
export curl_easy_strerror
export curl_share_strerror
export curl_easy_pause
export curl_easy_init
export curl_easy_setopt
export curl_easy_perform
export curl_easy_cleanup
export curl_easy_getinfo
export curl_easy_duphandle
export curl_easy_reset
export curl_easy_recv
export curl_easy_send
export curl_multi_init
export curl_multi_add_handle
export curl_multi_remove_handle
export curl_multi_fdset
export curl_multi_wait
export curl_multi_perform
export curl_multi_cleanup
export curl_multi_info_read
export curl_multi_strerror
export curl_multi_socket
export curl_multi_socket_action
export curl_multi_socket_all
export curl_multi_timeout
export curl_multi_setopt
export curl_multi_assign
export curl_pushheader_bynum
export curl_pushheader_byname
export CURL
export CURLSH
export curl_socket_t
export CURL_SOCKET_BAD
export curl_sslbackend
export CURLSSLBACKEND_NONE
export CURLSSLBACKEND_OPENSSL
export CURLSSLBACKEND_GNUTLS
export CURLSSLBACKEND_NSS
export CURLSSLBACKEND_OBSOLETE4
export CURLSSLBACKEND_GSKIT
export CURLSSLBACKEND_POLARSSL
export CURLSSLBACKEND_WOLFSSL
export CURLSSLBACKEND_SCHANNEL
export CURLSSLBACKEND_DARWINSSL
export CURLSSLBACKEND_AXTLS
export CURLSSLBACKEND_MBEDTLS
export CURLSSLBACKEND_LIBRESSL
export CURLSSLBACKEND_BORINGSSL
export CURLSSLBACKEND_CYASSL
export CURL_HTTPPOST_FILENAME
export CURL_HTTPPOST_READFILE
export CURL_HTTPPOST_PTRNAME
export CURL_HTTPPOST_PTRCONTENTS
export CURL_HTTPPOST_BUFFER
export CURL_HTTPPOST_PTRBUFFER
export CURL_HTTPPOST_CALLBACK
export CURL_HTTPPOST_LARGE
export curl_progress_callback
export curl_xferinfo_callback
export CURL_MAX_READ_SIZE
export CURL_MAX_WRITE_SIZE
export CURL_MAX_HTTP_HEADER
export CURL_WRITEFUNC_PAUSE
export curl_write_callback
export curl_resolver_start_callback
export CURLFINFOFLAG_KNOWN_FILENAME
export CURLFINFOFLAG_KNOWN_FILETYPE
export CURLFINFOFLAG_KNOWN_TIME
export CURLFINFOFLAG_KNOWN_PERM
export CURLFINFOFLAG_KNOWN_UID
export CURLFINFOFLAG_KNOWN_GID
export CURLFINFOFLAG_KNOWN_SIZE
export CURLFINFOFLAG_KNOWN_HLINKCOUNT
export CURL_CHUNK_BGN_FUNC_OK
export CURL_CHUNK_BGN_FUNC_FAIL
export CURL_CHUNK_BGN_FUNC_SKIP
export CURL_CHUNK_END_FUNC_OK
export CURL_CHUNK_END_FUNC_FAIL
export CURL_FNMATCHFUNC_MATCH
export CURL_FNMATCHFUNC_NOMATCH
export CURL_FNMATCHFUNC_FAIL
export CURL_SEEKFUNC_OK
export CURL_SEEKFUNC_FAIL
export CURL_SEEKFUNC_CANTSEEK
export CURL_READFUNC_ABORT
export CURL_READFUNC_PAUSE
export CURL_SOCKOPT_OK
export CURL_SOCKOPT_ERROR
export CURL_SOCKOPT_ALREADY_CONNECTED
export curlfiletype
export CURLFILETYPE_FILE
export CURLFILETYPE_DIRECTORY
export CURLFILETYPE_SYMLINK
export CURLFILETYPE_DEVICE_BLOCK
export CURLFILETYPE_DEVICE_CHAR
export CURLFILETYPE_NAMEDPIPE
export CURLFILETYPE_SOCKET
export CURLFILETYPE_DOOR
export CURLFILETYPE_UNKNOWN
export curl_chunk_bgn_callback
export curl_chunk_end_callback
export curl_fnmatch_callback
export curl_seek_callback
export curl_read_callback
export curlsocktype
export CURLSOCKTYPE_IPCXN
export CURLSOCKTYPE_ACCEPT
export CURLSOCKTYPE_LAST
export curl_sockopt_callback
export curl_opensocket_callback
export curl_closesocket_callback
export curlioerr
export CURLIOE_OK
export CURLIOE_UNKNOWNCMD
export CURLIOE_FAILRESTART
export CURLIOE_LAST
export curliocmd
export CURLIOCMD_NOP
export CURLIOCMD_RESTARTREAD
export CURLIOCMD_LAST
export curl_ioctl_callback
export curl_malloc_callback
export curl_free_callback
export curl_realloc_callback
export curl_strdup_callback
export curl_calloc_callback
export curl_infotype
export CURLINFO_TEXT
export CURLINFO_HEADER_IN
export CURLINFO_HEADER_OUT
export CURLINFO_DATA_IN
export CURLINFO_DATA_OUT
export CURLINFO_SSL_DATA_IN
export CURLINFO_SSL_DATA_OUT
export CURLINFO_END
export curl_debug_callback
export CURLcode
export CURLE_OK
export CURLE_UNSUPPORTED_PROTOCOL
export CURLE_FAILED_INIT
export CURLE_URL_MALFORMAT
export CURLE_NOT_BUILT_IN
export CURLE_COULDNT_RESOLVE_PROXY
export CURLE_COULDNT_RESOLVE_HOST
export CURLE_COULDNT_CONNECT
export CURLE_WEIRD_SERVER_REPLY
export CURLE_REMOTE_ACCESS_DENIED
export CURLE_FTP_ACCEPT_FAILED
export CURLE_FTP_WEIRD_PASS_REPLY
export CURLE_FTP_ACCEPT_TIMEOUT
export CURLE_FTP_WEIRD_PASV_REPLY
export CURLE_FTP_WEIRD_227_FORMAT
export CURLE_FTP_CANT_GET_HOST
export CURLE_HTTP2
export CURLE_FTP_COULDNT_SET_TYPE
export CURLE_PARTIAL_FILE
export CURLE_FTP_COULDNT_RETR_FILE
export CURLE_OBSOLETE20
export CURLE_QUOTE_ERROR
export CURLE_HTTP_RETURNED_ERROR
export CURLE_WRITE_ERROR
export CURLE_OBSOLETE24
export CURLE_UPLOAD_FAILED
export CURLE_READ_ERROR
export CURLE_OUT_OF_MEMORY
export CURLE_OPERATION_TIMEDOUT
export CURLE_OBSOLETE29
export CURLE_FTP_PORT_FAILED
export CURLE_FTP_COULDNT_USE_REST
export CURLE_OBSOLETE32
export CURLE_RANGE_ERROR
export CURLE_HTTP_POST_ERROR
export CURLE_SSL_CONNECT_ERROR
export CURLE_BAD_DOWNLOAD_RESUME
export CURLE_FILE_COULDNT_READ_FILE
export CURLE_LDAP_CANNOT_BIND
export CURLE_LDAP_SEARCH_FAILED
export CURLE_OBSOLETE40
export CURLE_FUNCTION_NOT_FOUND
export CURLE_ABORTED_BY_CALLBACK
export CURLE_BAD_FUNCTION_ARGUMENT
export CURLE_OBSOLETE44
export CURLE_INTERFACE_FAILED
export CURLE_OBSOLETE46
export CURLE_TOO_MANY_REDIRECTS
export CURLE_UNKNOWN_OPTION
export CURLE_TELNET_OPTION_SYNTAX
export CURLE_OBSOLETE50
export CURLE_PEER_FAILED_VERIFICATION
export CURLE_GOT_NOTHING
export CURLE_SSL_ENGINE_NOTFOUND
export CURLE_SSL_ENGINE_SETFAILED
export CURLE_SEND_ERROR
export CURLE_RECV_ERROR
export CURLE_OBSOLETE57
export CURLE_SSL_CERTPROBLEM
export CURLE_SSL_CIPHER
export CURLE_SSL_CACERT
export CURLE_BAD_CONTENT_ENCODING
export CURLE_LDAP_INVALID_URL
export CURLE_FILESIZE_EXCEEDED
export CURLE_USE_SSL_FAILED
export CURLE_SEND_FAIL_REWIND
export CURLE_SSL_ENGINE_INITFAILED
export CURLE_LOGIN_DENIED
export CURLE_TFTP_NOTFOUND
export CURLE_TFTP_PERM
export CURLE_REMOTE_DISK_FULL
export CURLE_TFTP_ILLEGAL
export CURLE_TFTP_UNKNOWNID
export CURLE_REMOTE_FILE_EXISTS
export CURLE_TFTP_NOSUCHUSER
export CURLE_CONV_FAILED
export CURLE_CONV_REQD
export CURLE_SSL_CACERT_BADFILE
export CURLE_REMOTE_FILE_NOT_FOUND
export CURLE_SSH
export CURLE_SSL_SHUTDOWN_FAILED
export CURLE_AGAIN
export CURLE_SSL_CRL_BADFILE
export CURLE_SSL_ISSUER_ERROR
export CURLE_FTP_PRET_FAILED
export CURLE_RTSP_CSEQ_ERROR
export CURLE_RTSP_SESSION_ERROR
export CURLE_FTP_BAD_FILE_LIST
export CURLE_CHUNK_FAILED
export CURLE_NO_CONNECTION_AVAILABLE
export CURLE_SSL_PINNEDPUBKEYNOTMATCH
export CURLE_SSL_INVALIDCERTSTATUS
export CURLE_HTTP2_STREAM
export CURLE_RECURSIVE_API_CALL
export CURL_LAST
export curl_conv_callback
export curl_ssl_ctx_callback
export curl_proxytype
export CURLPROXY_HTTP
export CURLPROXY_HTTP_1_0
export CURLPROXY_HTTPS
export CURLPROXY_SOCKS4
export CURLPROXY_SOCKS5
export CURLPROXY_SOCKS4A
export CURLPROXY_SOCKS5_HOSTNAME
export CURLSSH_AUTH_ANY
export CURLSSH_AUTH_NONE
export CURLSSH_AUTH_PUBLICKEY
export CURLSSH_AUTH_PASSWORD
export CURLSSH_AUTH_HOST
export CURLSSH_AUTH_KEYBOARD
export CURLSSH_AUTH_AGENT
export CURLSSH_AUTH_GSSAPI
export CURLSSH_AUTH_DEFAULT
export CURLGSSAPI_DELEGATION_NONE
export CURLGSSAPI_DELEGATION_POLICY_FLAG
export CURLGSSAPI_DELEGATION_FLAG
export CURL_ERROR_SIZE
export curl_khtype
export CURLKHTYPE_UNKNOWN
export CURLKHTYPE_RSA1
export CURLKHTYPE_RSA
export CURLKHTYPE_DSS
export CURLKHTYPE_ECDSA
export CURLKHTYPE_ED25519
export curl_khstat
export CURLKHSTAT_FINE_ADD_TO_FILE
export CURLKHSTAT_FINE
export CURLKHSTAT_REJECT
export CURLKHSTAT_DEFER
export CURLKHSTAT_LAST
export curl_khmatch
export CURLKHMATCH_OK
export CURLKHMATCH_MISMATCH
export CURLKHMATCH_MISSING
export CURLKHMATCH_LAST
export curl_sshkeycallback
export curl_usessl
export CURLUSESSL_NONE
export CURLUSESSL_TRY
export CURLUSESSL_CONTROL
export CURLUSESSL_ALL
export CURLUSESSL_LAST
export CURLSSLOPT_ALLOW_BEAST
export CURLSSLOPT_NO_REVOKE
export CURL_HET_DEFAULT
export curl_ftpssl
export CURLFTPSSL_NONE
export CURLFTPSSL_TRY
export CURLFTPSSL_CONTROL
export CURLFTPSSL_ALL
export CURLFTPSSL_LAST
export curl_ftpccc
export CURLFTPSSL_CCC_NONE
export CURLFTPSSL_CCC_PASSIVE
export CURLFTPSSL_CCC_ACTIVE
export CURLFTPSSL_CCC_LAST
export curl_ftpauth
export CURLFTPAUTH_DEFAULT
export CURLFTPAUTH_SSL
export CURLFTPAUTH_TLS
export CURLFTPAUTH_LAST
export curl_ftpcreatedir
export CURLFTP_CREATE_DIR_NONE
export CURLFTP_CREATE_DIR
export CURLFTP_CREATE_DIR_RETRY
export CURLFTP_CREATE_DIR_LAST
export curl_ftpmethod
export CURLFTPMETHOD_DEFAULT
export CURLFTPMETHOD_MULTICWD
export CURLFTPMETHOD_NOCWD
export CURLFTPMETHOD_SINGLECWD
export CURLFTPMETHOD_LAST
export CURLHEADER_UNIFIED
export CURLHEADER_SEPARATE
export CURLPROTO_HTTP
export CURLPROTO_HTTPS
export CURLPROTO_FTP
export CURLPROTO_FTPS
export CURLPROTO_SCP
export CURLPROTO_SFTP
export CURLPROTO_TELNET
export CURLPROTO_LDAP
export CURLPROTO_LDAPS
export CURLPROTO_DICT
export CURLPROTO_FILE
export CURLPROTO_TFTP
export CURLPROTO_IMAP
export CURLPROTO_IMAPS
export CURLPROTO_POP3
export CURLPROTO_POP3S
export CURLPROTO_SMTP
export CURLPROTO_SMTPS
export CURLPROTO_RTSP
export CURLPROTO_RTMP
export CURLPROTO_RTMPT
export CURLPROTO_RTMPE
export CURLPROTO_RTMPTE
export CURLPROTO_RTMPS
export CURLPROTO_RTMPTS
export CURLPROTO_GOPHER
export CURLPROTO_SMB
export CURLPROTO_SMBS
export CURLPROTO_ALL
export CURLOPTTYPE_LONG
export CURLOPTTYPE_OBJECTPOINT
export CURLOPTTYPE_STRINGPOINT
export CURLOPTTYPE_FUNCTIONPOINT
export CURLOPTTYPE_OFF_T
export CURLoption
export CURLOPT_WRITEDATA
export CURLOPT_URL
export CURLOPT_PORT
export CURLOPT_PROXY
export CURLOPT_USERPWD
export CURLOPT_PROXYUSERPWD
export CURLOPT_RANGE
export CURLOPT_READDATA
export CURLOPT_ERRORBUFFER
export CURLOPT_WRITEFUNCTION
export CURLOPT_READFUNCTION
export CURLOPT_TIMEOUT
export CURLOPT_INFILESIZE
export CURLOPT_POSTFIELDS
export CURLOPT_REFERER
export CURLOPT_FTPPORT
export CURLOPT_USERAGENT
export CURLOPT_LOW_SPEED_LIMIT
export CURLOPT_LOW_SPEED_TIME
export CURLOPT_RESUME_FROM
export CURLOPT_COOKIE
export CURLOPT_HTTPHEADER
export CURLOPT_HTTPPOST
export CURLOPT_SSLCERT
export CURLOPT_KEYPASSWD
export CURLOPT_CRLF
export CURLOPT_QUOTE
export CURLOPT_HEADERDATA
export CURLOPT_COOKIEFILE
export CURLOPT_SSLVERSION
export CURLOPT_TIMECONDITION
export CURLOPT_TIMEVALUE
export CURLOPT_CUSTOMREQUEST
export CURLOPT_STDERR
export CURLOPT_POSTQUOTE
export CURLOPT_OBSOLETE40
export CURLOPT_VERBOSE
export CURLOPT_HEADER
export CURLOPT_NOPROGRESS
export CURLOPT_NOBODY
export CURLOPT_FAILONERROR
export CURLOPT_UPLOAD
export CURLOPT_POST
export CURLOPT_DIRLISTONLY
export CURLOPT_APPEND
export CURLOPT_NETRC
export CURLOPT_FOLLOWLOCATION
export CURLOPT_TRANSFERTEXT
export CURLOPT_PUT
export CURLOPT_PROGRESSFUNCTION
export CURLOPT_PROGRESSDATA
export CURLOPT_AUTOREFERER
export CURLOPT_PROXYPORT
export CURLOPT_POSTFIELDSIZE
export CURLOPT_HTTPPROXYTUNNEL
export CURLOPT_INTERFACE
export CURLOPT_KRBLEVEL
export CURLOPT_SSL_VERIFYPEER
export CURLOPT_CAINFO
export CURLOPT_MAXREDIRS
export CURLOPT_FILETIME
export CURLOPT_TELNETOPTIONS
export CURLOPT_MAXCONNECTS
export CURLOPT_OBSOLETE72
export CURLOPT_FRESH_CONNECT
export CURLOPT_FORBID_REUSE
export CURLOPT_RANDOM_FILE
export CURLOPT_EGDSOCKET
export CURLOPT_CONNECTTIMEOUT
export CURLOPT_HEADERFUNCTION
export CURLOPT_HTTPGET
export CURLOPT_SSL_VERIFYHOST
export CURLOPT_COOKIEJAR
export CURLOPT_SSL_CIPHER_LIST
export CURLOPT_HTTP_VERSION
export CURLOPT_FTP_USE_EPSV
export CURLOPT_SSLCERTTYPE
export CURLOPT_SSLKEY
export CURLOPT_SSLKEYTYPE
export CURLOPT_SSLENGINE
export CURLOPT_SSLENGINE_DEFAULT
export CURLOPT_DNS_USE_GLOBAL_CACHE
export CURLOPT_DNS_CACHE_TIMEOUT
export CURLOPT_PREQUOTE
export CURLOPT_DEBUGFUNCTION
export CURLOPT_DEBUGDATA
export CURLOPT_COOKIESESSION
export CURLOPT_CAPATH
export CURLOPT_BUFFERSIZE
export CURLOPT_NOSIGNAL
export CURLOPT_SHARE
export CURLOPT_PROXYTYPE
export CURLOPT_ACCEPT_ENCODING
export CURLOPT_PRIVATE
export CURLOPT_HTTP200ALIASES
export CURLOPT_UNRESTRICTED_AUTH
export CURLOPT_FTP_USE_EPRT
export CURLOPT_HTTPAUTH
export CURLOPT_SSL_CTX_FUNCTION
export CURLOPT_SSL_CTX_DATA
export CURLOPT_FTP_CREATE_MISSING_DIRS
export CURLOPT_PROXYAUTH
export CURLOPT_FTP_RESPONSE_TIMEOUT
export CURLOPT_IPRESOLVE
export CURLOPT_MAXFILESIZE
export CURLOPT_INFILESIZE_LARGE
export CURLOPT_RESUME_FROM_LARGE
export CURLOPT_MAXFILESIZE_LARGE
export CURLOPT_NETRC_FILE
export CURLOPT_USE_SSL
export CURLOPT_POSTFIELDSIZE_LARGE
export CURLOPT_TCP_NODELAY
export CURLOPT_FTPSSLAUTH
export CURLOPT_IOCTLFUNCTION
export CURLOPT_IOCTLDATA
export CURLOPT_FTP_ACCOUNT
export CURLOPT_COOKIELIST
export CURLOPT_IGNORE_CONTENT_LENGTH
export CURLOPT_FTP_SKIP_PASV_IP
export CURLOPT_FTP_FILEMETHOD
export CURLOPT_LOCALPORT
export CURLOPT_LOCALPORTRANGE
export CURLOPT_CONNECT_ONLY
export CURLOPT_CONV_FROM_NETWORK_FUNCTION
export CURLOPT_CONV_TO_NETWORK_FUNCTION
export CURLOPT_CONV_FROM_UTF8_FUNCTION
export CURLOPT_MAX_SEND_SPEED_LARGE
export CURLOPT_MAX_RECV_SPEED_LARGE
export CURLOPT_FTP_ALTERNATIVE_TO_USER
export CURLOPT_SOCKOPTFUNCTION
export CURLOPT_SOCKOPTDATA
export CURLOPT_SSL_SESSIONID_CACHE
export CURLOPT_SSH_AUTH_TYPES
export CURLOPT_SSH_PUBLIC_KEYFILE
export CURLOPT_SSH_PRIVATE_KEYFILE
export CURLOPT_FTP_SSL_CCC
export CURLOPT_TIMEOUT_MS
export CURLOPT_CONNECTTIMEOUT_MS
export CURLOPT_HTTP_TRANSFER_DECODING
export CURLOPT_HTTP_CONTENT_DECODING
export CURLOPT_NEW_FILE_PERMS
export CURLOPT_NEW_DIRECTORY_PERMS
export CURLOPT_POSTREDIR
export CURLOPT_SSH_HOST_PUBLIC_KEY_MD5
export CURLOPT_OPENSOCKETFUNCTION
export CURLOPT_OPENSOCKETDATA
export CURLOPT_COPYPOSTFIELDS
export CURLOPT_PROXY_TRANSFER_MODE
export CURLOPT_SEEKFUNCTION
export CURLOPT_SEEKDATA
export CURLOPT_CRLFILE
export CURLOPT_ISSUERCERT
export CURLOPT_ADDRESS_SCOPE
export CURLOPT_CERTINFO
export CURLOPT_USERNAME
export CURLOPT_PASSWORD
export CURLOPT_PROXYUSERNAME
export CURLOPT_PROXYPASSWORD
export CURLOPT_NOPROXY
export CURLOPT_TFTP_BLKSIZE
export CURLOPT_SOCKS5_GSSAPI_SERVICE
export CURLOPT_SOCKS5_GSSAPI_NEC
export CURLOPT_PROTOCOLS
export CURLOPT_REDIR_PROTOCOLS
export CURLOPT_SSH_KNOWNHOSTS
export CURLOPT_SSH_KEYFUNCTION
export CURLOPT_SSH_KEYDATA
export CURLOPT_MAIL_FROM
export CURLOPT_MAIL_RCPT
export CURLOPT_FTP_USE_PRET
export CURLOPT_RTSP_REQUEST
export CURLOPT_RTSP_SESSION_ID
export CURLOPT_RTSP_STREAM_URI
export CURLOPT_RTSP_TRANSPORT
export CURLOPT_RTSP_CLIENT_CSEQ
export CURLOPT_RTSP_SERVER_CSEQ
export CURLOPT_INTERLEAVEDATA
export CURLOPT_INTERLEAVEFUNCTION
export CURLOPT_WILDCARDMATCH
export CURLOPT_CHUNK_BGN_FUNCTION
export CURLOPT_CHUNK_END_FUNCTION
export CURLOPT_FNMATCH_FUNCTION
export CURLOPT_CHUNK_DATA
export CURLOPT_FNMATCH_DATA
export CURLOPT_RESOLVE
export CURLOPT_TLSAUTH_USERNAME
export CURLOPT_TLSAUTH_PASSWORD
export CURLOPT_TLSAUTH_TYPE
export CURLOPT_TRANSFER_ENCODING
export CURLOPT_CLOSESOCKETFUNCTION
export CURLOPT_CLOSESOCKETDATA
export CURLOPT_GSSAPI_DELEGATION
export CURLOPT_DNS_SERVERS
export CURLOPT_ACCEPTTIMEOUT_MS
export CURLOPT_TCP_KEEPALIVE
export CURLOPT_TCP_KEEPIDLE
export CURLOPT_TCP_KEEPINTVL
export CURLOPT_SSL_OPTIONS
export CURLOPT_MAIL_AUTH
export CURLOPT_SASL_IR
export CURLOPT_XFERINFOFUNCTION
export CURLOPT_XOAUTH2_BEARER
export CURLOPT_DNS_INTERFACE
export CURLOPT_DNS_LOCAL_IP4
export CURLOPT_DNS_LOCAL_IP6
export CURLOPT_LOGIN_OPTIONS
export CURLOPT_SSL_ENABLE_NPN
export CURLOPT_SSL_ENABLE_ALPN
export CURLOPT_EXPECT_100_TIMEOUT_MS
export CURLOPT_PROXYHEADER
export CURLOPT_HEADEROPT
export CURLOPT_PINNEDPUBLICKEY
export CURLOPT_UNIX_SOCKET_PATH
export CURLOPT_SSL_VERIFYSTATUS
export CURLOPT_SSL_FALSESTART
export CURLOPT_PATH_AS_IS
export CURLOPT_PROXY_SERVICE_NAME
export CURLOPT_SERVICE_NAME
export CURLOPT_PIPEWAIT
export CURLOPT_DEFAULT_PROTOCOL
export CURLOPT_STREAM_WEIGHT
export CURLOPT_STREAM_DEPENDS
export CURLOPT_STREAM_DEPENDS_E
export CURLOPT_TFTP_NO_OPTIONS
export CURLOPT_CONNECT_TO
export CURLOPT_TCP_FASTOPEN
export CURLOPT_KEEP_SENDING_ON_ERROR
export CURLOPT_PROXY_CAINFO
export CURLOPT_PROXY_CAPATH
export CURLOPT_PROXY_SSL_VERIFYPEER
export CURLOPT_PROXY_SSL_VERIFYHOST
export CURLOPT_PROXY_SSLVERSION
export CURLOPT_PROXY_TLSAUTH_USERNAME
export CURLOPT_PROXY_TLSAUTH_PASSWORD
export CURLOPT_PROXY_TLSAUTH_TYPE
export CURLOPT_PROXY_SSLCERT
export CURLOPT_PROXY_SSLCERTTYPE
export CURLOPT_PROXY_SSLKEY
export CURLOPT_PROXY_SSLKEYTYPE
export CURLOPT_PROXY_KEYPASSWD
export CURLOPT_PROXY_SSL_CIPHER_LIST
export CURLOPT_PROXY_CRLFILE
export CURLOPT_PROXY_SSL_OPTIONS
export CURLOPT_PRE_PROXY
export CURLOPT_PROXY_PINNEDPUBLICKEY
export CURLOPT_ABSTRACT_UNIX_SOCKET
export CURLOPT_SUPPRESS_CONNECT_HEADERS
export CURLOPT_REQUEST_TARGET
export CURLOPT_SOCKS5_AUTH
export CURLOPT_SSH_COMPRESSION
export CURLOPT_MIMEPOST
export CURLOPT_TIMEVALUE_LARGE
export CURLOPT_HAPPY_EYEBALLS_TIMEOUT_MS
export CURLOPT_RESOLVER_START_FUNCTION
export CURLOPT_RESOLVER_START_DATA
export CURLOPT_HAPROXYPROTOCOL
export CURLOPT_DNS_SHUFFLE_ADDRESSES
export CURLOPT_TLS13_CIPHERS
export CURLOPT_PROXY_TLS13_CIPHERS
export CURLOPT_DISALLOW_USERNAME_IN_URL
export CURLOPT_LASTENTRY
export CURLOPT_XFERINFODATA
export CURLOPT_SERVER_RESPONSE_TIMEOUT
export CURLOPT_POST301
export CURLOPT_SSLKEYPASSWD
export CURLOPT_FTPAPPEND
export CURLOPT_FTPLISTONLY
export CURLOPT_FTP_SSL
export CURLOPT_SSLCERTPASSWD
export CURLOPT_KRB4LEVEL
export CURL_IPRESOLVE_WHATEVER
export CURL_IPRESOLVE_V4
export CURL_IPRESOLVE_V6
export CURLOPT_RTSPHEADER
export CURL_HTTP_VERSION_NONE
export CURL_HTTP_VERSION_1_0
export CURL_HTTP_VERSION_1_1
export CURL_HTTP_VERSION_2_0
export CURL_HTTP_VERSION_2TLS
export CURL_HTTP_VERSION_2_PRIOR_KNOWLEDGE
export CURL_HTTP_VERSION_LAST
export CURL_HTTP_VERSION_2
export CURL_RTSPREQ_NONE
export CURL_RTSPREQ_OPTIONS
export CURL_RTSPREQ_DESCRIBE
export CURL_RTSPREQ_ANNOUNCE
export CURL_RTSPREQ_SETUP
export CURL_RTSPREQ_PLAY
export CURL_RTSPREQ_PAUSE
export CURL_RTSPREQ_TEARDOWN
export CURL_RTSPREQ_GET_PARAMETER
export CURL_RTSPREQ_SET_PARAMETER
export CURL_RTSPREQ_RECORD
export CURL_RTSPREQ_RECEIVE
export CURL_RTSPREQ_LAST
export CURL_NETRC_OPTION
export CURL_NETRC_IGNORED
export CURL_NETRC_OPTIONAL
export CURL_NETRC_REQUIRED
export CURL_NETRC_LAST
export CURL_SSLVERSION_DEFAULT
export CURL_SSLVERSION_TLSv1
export CURL_SSLVERSION_SSLv2
export CURL_SSLVERSION_SSLv3
export CURL_SSLVERSION_TLSv1_0
export CURL_SSLVERSION_TLSv1_1
export CURL_SSLVERSION_TLSv1_2
export CURL_SSLVERSION_TLSv1_3
export CURL_SSLVERSION_LAST
export CURL_SSLVERSION_MAX_NONE
export CURL_SSLVERSION_MAX_DEFAULT
export CURL_SSLVERSION_MAX_TLSv1_0
export CURL_SSLVERSION_MAX_TLSv1_1
export CURL_SSLVERSION_MAX_TLSv1_2
export CURL_SSLVERSION_MAX_TLSv1_3
export CURL_SSLVERSION_MAX_LAST
export CURL_TLSAUTH
export CURL_TLSAUTH_NONE
export CURL_TLSAUTH_SRP
export CURL_TLSAUTH_LAST
export CURL_REDIR_GET_ALL
export CURL_REDIR_POST_301
export CURL_REDIR_POST_302
export CURL_REDIR_POST_303
export CURL_REDIR_POST_ALL
export curl_TimeCond
export CURL_TIMECOND_NONE
export CURL_TIMECOND_IFMODSINCE
export CURL_TIMECOND_IFUNMODSINCE
export CURL_TIMECOND_LASTMOD
export CURL_TIMECOND_LAST
export curl_mime
export curl_mimepart
export CURLformoption
export CURLFORM_NOTHING
export CURLFORM_COPYNAME
export CURLFORM_PTRNAME
export CURLFORM_NAMELENGTH
export CURLFORM_COPYCONTENTS
export CURLFORM_PTRCONTENTS
export CURLFORM_CONTENTSLENGTH
export CURLFORM_FILECONTENT
export CURLFORM_ARRAY
export CURLFORM_OBSOLETE
export CURLFORM_FILE
export CURLFORM_BUFFER
export CURLFORM_BUFFERPTR
export CURLFORM_BUFFERLENGTH
export CURLFORM_CONTENTTYPE
export CURLFORM_CONTENTHEADER
export CURLFORM_FILENAME
export CURLFORM_END
export CURLFORM_OBSOLETE2
export CURLFORM_STREAM
export CURLFORM_CONTENTLEN
export CURLFORM_LASTENTRY
export CURLFORMcode
export CURL_FORMADD_OK
export CURL_FORMADD_MEMORY
export CURL_FORMADD_OPTION_TWICE
export CURL_FORMADD_NULL
export CURL_FORMADD_UNKNOWN_OPTION
export CURL_FORMADD_INCOMPLETE
export CURL_FORMADD_ILLEGAL_ARRAY
export CURL_FORMADD_DISABLED
export CURL_FORMADD_LAST
export curl_formget_callback
export curl_ssl_backend
export CURLsslset
export CURLSSLSET_OK
export CURLSSLSET_UNKNOWN_BACKEND
export CURLSSLSET_TOO_LATE
export CURLSSLSET_NO_BACKENDS
export CURLINFO_STRING
export CURLINFO_LONG
export CURLINFO_DOUBLE
export CURLINFO_SLIST
export CURLINFO_PTR
export CURLINFO_SOCKET
export CURLINFO_OFF_T
export CURLINFO_MASK
export CURLINFO_TYPEMASK
export CURLINFO
export CURLINFO_NONE
export CURLINFO_EFFECTIVE_URL
export CURLINFO_RESPONSE_CODE
export CURLINFO_TOTAL_TIME
export CURLINFO_NAMELOOKUP_TIME
export CURLINFO_CONNECT_TIME
export CURLINFO_PRETRANSFER_TIME
export CURLINFO_SIZE_UPLOAD
export CURLINFO_SIZE_UPLOAD_T
export CURLINFO_SIZE_DOWNLOAD
export CURLINFO_SIZE_DOWNLOAD_T
export CURLINFO_SPEED_DOWNLOAD
export CURLINFO_SPEED_DOWNLOAD_T
export CURLINFO_SPEED_UPLOAD
export CURLINFO_SPEED_UPLOAD_T
export CURLINFO_HEADER_SIZE
export CURLINFO_REQUEST_SIZE
export CURLINFO_SSL_VERIFYRESULT
export CURLINFO_FILETIME
export CURLINFO_FILETIME_T
export CURLINFO_CONTENT_LENGTH_DOWNLOAD
export CURLINFO_CONTENT_LENGTH_DOWNLOAD_T
export CURLINFO_CONTENT_LENGTH_UPLOAD
export CURLINFO_CONTENT_LENGTH_UPLOAD_T
export CURLINFO_STARTTRANSFER_TIME
export CURLINFO_CONTENT_TYPE
export CURLINFO_REDIRECT_TIME
export CURLINFO_REDIRECT_COUNT
export CURLINFO_PRIVATE
export CURLINFO_HTTP_CONNECTCODE
export CURLINFO_HTTPAUTH_AVAIL
export CURLINFO_PROXYAUTH_AVAIL
export CURLINFO_OS_ERRNO
export CURLINFO_NUM_CONNECTS
export CURLINFO_SSL_ENGINES
export CURLINFO_COOKIELIST
export CURLINFO_LASTSOCKET
export CURLINFO_FTP_ENTRY_PATH
export CURLINFO_REDIRECT_URL
export CURLINFO_PRIMARY_IP
export CURLINFO_APPCONNECT_TIME
export CURLINFO_CERTINFO
export CURLINFO_CONDITION_UNMET
export CURLINFO_RTSP_SESSION_ID
export CURLINFO_RTSP_CLIENT_CSEQ
export CURLINFO_RTSP_SERVER_CSEQ
export CURLINFO_RTSP_CSEQ_RECV
export CURLINFO_PRIMARY_PORT
export CURLINFO_LOCAL_IP
export CURLINFO_LOCAL_PORT
export CURLINFO_TLS_SESSION
export CURLINFO_ACTIVESOCKET
export CURLINFO_TLS_SSL_PTR
export CURLINFO_HTTP_VERSION
export CURLINFO_PROXY_SSL_VERIFYRESULT
export CURLINFO_PROTOCOL
export CURLINFO_SCHEME
export CURLINFO_TOTAL_TIME_T
export CURLINFO_NAMELOOKUP_TIME_T
export CURLINFO_CONNECT_TIME_T
export CURLINFO_PRETRANSFER_TIME_T
export CURLINFO_STARTTRANSFER_TIME_T
export CURLINFO_REDIRECT_TIME_T
export CURLINFO_APPCONNECT_TIME_T
export CURLINFO_LASTONE
export CURLINFO_HTTP_CODE
export curl_closepolicy
export CURLCLOSEPOLICY_NONE
export CURLCLOSEPOLICY_OLDEST
export CURLCLOSEPOLICY_LEAST_RECENTLY_USED
export CURLCLOSEPOLICY_LEAST_TRAFFIC
export CURLCLOSEPOLICY_SLOWEST
export CURLCLOSEPOLICY_CALLBACK
export CURLCLOSEPOLICY_LAST
export CURL_GLOBAL_SSL
export CURL_GLOBAL_WIN32
export CURL_GLOBAL_ALL
export CURL_GLOBAL_NOTHING
export CURL_GLOBAL_DEFAULT
export CURL_GLOBAL_ACK_EINTR
export curl_lock_data
export CURL_LOCK_DATA_NONE
export CURL_LOCK_DATA_SHARE
export CURL_LOCK_DATA_COOKIE
export CURL_LOCK_DATA_DNS
export CURL_LOCK_DATA_SSL_SESSION
export CURL_LOCK_DATA_CONNECT
export CURL_LOCK_DATA_PSL
export CURL_LOCK_DATA_LAST
export curl_lock_access
export CURL_LOCK_ACCESS_NONE
export CURL_LOCK_ACCESS_SHARED
export CURL_LOCK_ACCESS_SINGLE
export CURL_LOCK_ACCESS_LAST
export curl_lock_function
export curl_unlock_function
export CURLSHcode
export CURLSHE_OK
export CURLSHE_BAD_OPTION
export CURLSHE_IN_USE
export CURLSHE_INVALID
export CURLSHE_NOMEM
export CURLSHE_NOT_BUILT_IN
export CURLSHE_LAST
export CURLSHoption
export CURLSHOPT_NONE
export CURLSHOPT_SHARE
export CURLSHOPT_UNSHARE
export CURLSHOPT_LOCKFUNC
export CURLSHOPT_UNLOCKFUNC
export CURLSHOPT_USERDATA
export CURLSHOPT_LAST
export CURLversion
export CURLVERSION_FIRST
export CURLVERSION_SECOND
export CURLVERSION_THIRD
export CURLVERSION_FOURTH
export CURLVERSION_FIFTH
export CURLVERSION_LAST
export CURLVERSION_NOW
export CURL_VERSION_IPV6
export CURL_VERSION_KERBEROS4
export CURL_VERSION_SSL
export CURL_VERSION_LIBZ
export CURL_VERSION_NTLM
export CURL_VERSION_GSSNEGOTIATE
export CURL_VERSION_DEBUG
export CURL_VERSION_ASYNCHDNS
export CURL_VERSION_SPNEGO
export CURL_VERSION_LARGEFILE
export CURL_VERSION_IDN
export CURL_VERSION_SSPI
export CURL_VERSION_CONV
export CURL_VERSION_CURLDEBUG
export CURL_VERSION_TLSAUTH_SRP
export CURL_VERSION_NTLM_WB
export CURL_VERSION_HTTP2
export CURL_VERSION_GSSAPI
export CURL_VERSION_KERBEROS5
export CURL_VERSION_UNIX_SOCKETS
export CURL_VERSION_PSL
export CURL_VERSION_HTTPS_PROXY
export CURL_VERSION_MULTI_SSL
export CURL_VERSION_BROTLI
export CURLPAUSE_RECV
export CURLPAUSE_RECV_CONT
export CURLPAUSE_SEND
export CURLPAUSE_SEND_CONT
export CURLPAUSE_ALL
export CURLPAUSE_CONT
export CURLE_OBSOLETE16
export CURLE_OBSOLETE10
export CURLE_OBSOLETE12
export CURLOPT_ENCODING
export CURLE_FTP_WEIRD_SERVER_REPLY
export CURLE_UNKNOWN_TELNET_OPTION
export CURLE_SSL_PEER_CERTIFICATE
export CURLE_OBSOLETE
export CURLE_BAD_PASSWORD_ENTERED
export CURLE_BAD_CALLING_ORDER
export CURLE_FTP_USER_PASSWORD_INCORRECT
export CURLE_FTP_CANT_RECONNECT
export CURLE_FTP_COULDNT_GET_SIZE
export CURLE_FTP_COULDNT_SET_ASCII
export CURLE_FTP_WEIRD_USER_REPLY
export CURLE_FTP_WRITE_ERROR
export CURLE_LIBRARY_NOT_FOUND
export CURLE_MALFORMAT_USER
export CURLE_SHARE_IN_USE
export CURLE_URL_MALFORMAT_USER
export CURLE_FTP_ACCESS_DENIED
export CURLE_FTP_COULDNT_SET_BINARY
export CURLE_FTP_QUOTE_ERROR
export CURLE_TFTP_DISKFULL
export CURLE_TFTP_EXISTS
export CURLE_HTTP_RANGE_ERROR
export CURLE_FTP_SSL_FAILED
export CURLE_OPERATION_TIMEOUTED
export CURLE_HTTP_NOT_FOUND
export CURLE_HTTP_PORT_FAILED
export CURLE_FTP_COULDNT_STOR_FILE
export CURLE_FTP_PARTIAL_FILE
export CURLE_FTP_BAD_DOWNLOAD_RESUME
export CURLE_ALREADY_COMPLETE
export CURLOPT_FILE
export CURLOPT_INFILE
export CURLOPT_WRITEHEADER
export CURLOPT_WRITEINFO
export CURLOPT_CLOSEPOLICY
export CURLM
export CURLMcode
export CURLM_CALL_MULTI_PERFORM
export CURLM_OK
export CURLM_BAD_HANDLE
export CURLM_BAD_EASY_HANDLE
export CURLM_OUT_OF_MEMORY
export CURLM_INTERNAL_ERROR
export CURLM_BAD_SOCKET
export CURLM_UNKNOWN_OPTION
export CURLM_ADDED_ALREADY
export CURLM_RECURSIVE_API_CALL
export CURLM_LAST
export CURLM_CALL_MULTI_SOCKET
export CURLPIPE_NOTHING
export CURLPIPE_HTTP1
export CURLPIPE_MULTIPLEX
export CURLMSG
export CURLMSG_NONE
export CURLMSG_DONE
export CURLMSG_LAST
export CURL_WAIT_POLLIN
export CURL_WAIT_POLLPRI
export CURL_WAIT_POLLOUT
export CURL_POLL_NONE
export CURL_POLL_IN
export CURL_POLL_OUT
export CURL_POLL_INOUT
export CURL_POLL_REMOVE
export CURL_SOCKET_TIMEOUT
export CURL_CSELECT_IN
export CURL_CSELECT_OUT
export CURL_CSELECT_ERR
export curl_socket_callback
export curl_multi_timer_callback
export CURLMoption
export CURLMOPT_SOCKETFUNCTION
export CURLMOPT_SOCKETDATA
export CURLMOPT_PIPELINING
export CURLMOPT_TIMERFUNCTION
export CURLMOPT_TIMERDATA
export CURLMOPT_MAXCONNECTS
export CURLMOPT_MAX_HOST_CONNECTIONS
export CURLMOPT_MAX_PIPELINE_LENGTH
export CURLMOPT_CONTENT_LENGTH_PENALTY_SIZE
export CURLMOPT_CHUNK_LENGTH_PENALTY_SIZE
export CURLMOPT_PIPELINING_SITE_BL
export CURLMOPT_PIPELINING_SERVER_BL
export CURLMOPT_MAX_TOTAL_CONNECTIONS
export CURLMOPT_PUSHFUNCTION
export CURLMOPT_PUSHDATA
export CURLMOPT_LASTENTRY
export CURL_PUSH_OK
export CURL_PUSH_DENY
export curl_push_callback
export CURL_TYPEOF_CURL_OFF_T
export CURL_FORMAT_CURL_OFF_T
export CURL_FORMAT_CURL_OFF_TU
export CURL_SUFFIX_CURL_OFF_T
export CURL_SUFFIX_CURL_OFF_TU
export CURL_TYPEOF_CURL_SOCKLEN_T
export CURL_PULL_SYS_TYPES_H
export CURL_PULL_SYS_SOCKET_H
export CURL_SOCKET_BAD
export CURLSSLBACKEND_LIBRESSL
export CURLSSLBACKEND_BORINGSSL
export CURLSSLBACKEND_CYASSL
export CURL_HTTPPOST_FILENAME
export CURL_HTTPPOST_READFILE
export CURL_HTTPPOST_PTRNAME
export CURL_HTTPPOST_PTRCONTENTS
export CURL_HTTPPOST_BUFFER
export CURL_HTTPPOST_PTRBUFFER
export CURL_HTTPPOST_CALLBACK
export CURL_HTTPPOST_LARGE
export CURL_MAX_READ_SIZE
export CURL_MAX_WRITE_SIZE
export CURL_MAX_HTTP_HEADER
export CURL_WRITEFUNC_PAUSE
export CURLFINFOFLAG_KNOWN_FILENAME
export CURLFINFOFLAG_KNOWN_FILETYPE
export CURLFINFOFLAG_KNOWN_TIME
export CURLFINFOFLAG_KNOWN_PERM
export CURLFINFOFLAG_KNOWN_UID
export CURLFINFOFLAG_KNOWN_GID
export CURLFINFOFLAG_KNOWN_SIZE
export CURLFINFOFLAG_KNOWN_HLINKCOUNT
export CURL_CHUNK_BGN_FUNC_OK
export CURL_CHUNK_BGN_FUNC_FAIL
export CURL_CHUNK_BGN_FUNC_SKIP
export CURL_CHUNK_END_FUNC_OK
export CURL_CHUNK_END_FUNC_FAIL
export CURL_FNMATCHFUNC_MATCH
export CURL_FNMATCHFUNC_NOMATCH
export CURL_FNMATCHFUNC_FAIL
export CURL_SEEKFUNC_OK
export CURL_SEEKFUNC_FAIL
export CURL_SEEKFUNC_CANTSEEK
export CURL_READFUNC_ABORT
export CURL_READFUNC_PAUSE
export CURL_SOCKOPT_OK
export CURL_SOCKOPT_ERROR
export CURL_SOCKOPT_ALREADY_CONNECTED
export CURLE_OBSOLETE16
export CURLE_OBSOLETE10
export CURLE_OBSOLETE12
export CURLOPT_ENCODING
export CURLE_FTP_WEIRD_SERVER_REPLY
export CURLE_UNKNOWN_TELNET_OPTION
export CURLE_SSL_PEER_CERTIFICATE
export CURLE_OBSOLETE
export CURLE_BAD_PASSWORD_ENTERED
export CURLE_BAD_CALLING_ORDER
export CURLE_FTP_USER_PASSWORD_INCORRECT
export CURLE_FTP_CANT_RECONNECT
export CURLE_FTP_COULDNT_GET_SIZE
export CURLE_FTP_COULDNT_SET_ASCII
export CURLE_FTP_WEIRD_USER_REPLY
export CURLE_FTP_WRITE_ERROR
export CURLE_LIBRARY_NOT_FOUND
export CURLE_MALFORMAT_USER
export CURLE_SHARE_IN_USE
export CURLE_URL_MALFORMAT_USER
export CURLE_FTP_ACCESS_DENIED
export CURLE_FTP_COULDNT_SET_BINARY
export CURLE_FTP_QUOTE_ERROR
export CURLE_TFTP_DISKFULL
export CURLE_TFTP_EXISTS
export CURLE_HTTP_RANGE_ERROR
export CURLE_FTP_SSL_FAILED
export CURLE_OPERATION_TIMEOUTED
export CURLE_HTTP_NOT_FOUND
export CURLE_HTTP_PORT_FAILED
export CURLE_FTP_COULDNT_STOR_FILE
export CURLE_FTP_PARTIAL_FILE
export CURLE_FTP_BAD_DOWNLOAD_RESUME
export CURLE_ALREADY_COMPLETE
export CURLOPT_FILE
export CURLOPT_INFILE
export CURLOPT_WRITEHEADER
export CURLOPT_WRITEINFO
export CURLOPT_CLOSEPOLICY
export CURLAUTH_NONE
export CURLAUTH_BASIC
export CURLAUTH_DIGEST
export CURLAUTH_NEGOTIATE
export CURLAUTH_GSSNEGOTIATE
export CURLAUTH_GSSAPI
export CURLAUTH_NTLM
export CURLAUTH_DIGEST_IE
export CURLAUTH_NTLM_WB
export CURLAUTH_BEARER
export CURLAUTH_ONLY
export CURLAUTH_ANY
export CURLAUTH_ANYSAFE
export CURLSSH_AUTH_ANY
export CURLSSH_AUTH_NONE
export CURLSSH_AUTH_PUBLICKEY
export CURLSSH_AUTH_PASSWORD
export CURLSSH_AUTH_HOST
export CURLSSH_AUTH_KEYBOARD
export CURLSSH_AUTH_AGENT
export CURLSSH_AUTH_GSSAPI
export CURLSSH_AUTH_DEFAULT
export CURLGSSAPI_DELEGATION_NONE
export CURLGSSAPI_DELEGATION_POLICY_FLAG
export CURLGSSAPI_DELEGATION_FLAG
export CURL_ERROR_SIZE
export CURLSSLOPT_ALLOW_BEAST
export CURLSSLOPT_NO_REVOKE
export CURL_HET_DEFAULT
export CURLFTPSSL_NONE
export CURLFTPSSL_TRY
export CURLFTPSSL_CONTROL
export CURLFTPSSL_ALL
export CURLFTPSSL_LAST
export CURLHEADER_UNIFIED
export CURLHEADER_SEPARATE
export CURLPROTO_HTTP
export CURLPROTO_HTTPS
export CURLPROTO_FTP
export CURLPROTO_FTPS
export CURLPROTO_SCP
export CURLPROTO_SFTP
export CURLPROTO_TELNET
export CURLPROTO_LDAP
export CURLPROTO_LDAPS
export CURLPROTO_DICT
export CURLPROTO_FILE
export CURLPROTO_TFTP
export CURLPROTO_IMAP
export CURLPROTO_IMAPS
export CURLPROTO_POP3
export CURLPROTO_POP3S
export CURLPROTO_SMTP
export CURLPROTO_SMTPS
export CURLPROTO_RTSP
export CURLPROTO_RTMP
export CURLPROTO_RTMPT
export CURLPROTO_RTMPE
export CURLPROTO_RTMPTE
export CURLPROTO_RTMPS
export CURLPROTO_RTMPTS
export CURLPROTO_GOPHER
export CURLPROTO_SMB
export CURLPROTO_SMBS
export CURLPROTO_ALL
export CURLOPTTYPE_LONG
export CURLOPTTYPE_OBJECTPOINT
export CURLOPTTYPE_STRINGPOINT
export CURLOPTTYPE_FUNCTIONPOINT
export CURLOPTTYPE_OFF_T
export CURLOPT_XFERINFODATA
export CURLOPT_SERVER_RESPONSE_TIMEOUT
export CURLOPT_POST301
export CURLOPT_SSLKEYPASSWD
export CURLOPT_FTPAPPEND
export CURLOPT_FTPLISTONLY
export CURLOPT_FTP_SSL
export CURLOPT_SSLCERTPASSWD
export CURLOPT_KRB4LEVEL
export CURL_IPRESOLVE_WHATEVER
export CURL_IPRESOLVE_V4
export CURL_IPRESOLVE_V6
export CURLOPT_RTSPHEADER
export CURL_HTTP_VERSION_2
export CURL_REDIR_GET_ALL
export CURL_REDIR_POST_301
export CURL_REDIR_POST_302
export CURL_REDIR_POST_303
export CURL_REDIR_POST_ALL
export CURL_ZERO_TERMINATED
export CURLINFO_STRING
export CURLINFO_LONG
export CURLINFO_DOUBLE
export CURLINFO_SLIST
export CURLINFO_PTR
export CURLINFO_SOCKET
export CURLINFO_OFF_T
export CURLINFO_MASK
export CURLINFO_TYPEMASK
export CURLINFO_HTTP_CODE
export CURL_GLOBAL_SSL
export CURL_GLOBAL_WIN32
export CURL_GLOBAL_ALL
export CURL_GLOBAL_NOTHING
export CURL_GLOBAL_DEFAULT
export CURL_GLOBAL_ACK_EINTR
export CURLVERSION_NOW
export CURL_VERSION_IPV6
export CURL_VERSION_KERBEROS4
export CURL_VERSION_SSL
export CURL_VERSION_LIBZ
export CURL_VERSION_NTLM
export CURL_VERSION_GSSNEGOTIATE
export CURL_VERSION_DEBUG
export CURL_VERSION_ASYNCHDNS
export CURL_VERSION_SPNEGO
export CURL_VERSION_LARGEFILE
export CURL_VERSION_IDN
export CURL_VERSION_SSPI
export CURL_VERSION_CONV
export CURL_VERSION_CURLDEBUG
export CURL_VERSION_TLSAUTH_SRP
export CURL_VERSION_NTLM_WB
export CURL_VERSION_HTTP2
export CURL_VERSION_GSSAPI
export CURL_VERSION_KERBEROS5
export CURL_VERSION_UNIX_SOCKETS
export CURL_VERSION_PSL
export CURL_VERSION_HTTPS_PROXY
export CURL_VERSION_MULTI_SSL
export CURL_VERSION_BROTLI
export CURLPAUSE_RECV
export CURLPAUSE_RECV_CONT
export CURLPAUSE_SEND
export CURLPAUSE_SEND_CONT
export CURLPAUSE_ALL
export CURLPAUSE_CONT
export CURLM_CALL_MULTI_SOCKET
export CURLPIPE_NOTHING
export CURLPIPE_HTTP1
export CURLPIPE_MULTIPLEX
export CURL_WAIT_POLLIN
export CURL_WAIT_POLLPRI
export CURL_WAIT_POLLOUT
export CURL_POLL_NONE
export CURL_POLL_IN
export CURL_POLL_OUT
export CURL_POLL_INOUT
export CURL_POLL_REMOVE
export CURL_SOCKET_TIMEOUT
export CURL_CSELECT_IN
export CURL_CSELECT_OUT
export CURL_CSELECT_ERR
export CURL_PUSH_OK
export CURL_PUSH_DENY
export CURLOPT_MAXAGE_CONN
v   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LibCURL/src/lC_common_h.jl-�      # Automatically generated using Clang.jl wrap_c, version 0.0.0

const CURL = Cvoid
const CURLSH = Cvoid

const curl_socket_t = Cint
const CURL_SOCKET_BAD = -1

# begin enum curl_sslbackend
const curl_sslbackend = UInt32
const CURLSSLBACKEND_NONE = (UInt32)(0)
const CURLSSLBACKEND_OPENSSL = (UInt32)(1)
const CURLSSLBACKEND_GNUTLS = (UInt32)(2)
const CURLSSLBACKEND_NSS = (UInt32)(3)
const CURLSSLBACKEND_OBSOLETE4 = (UInt32)(4)
const CURLSSLBACKEND_GSKIT = (UInt32)(5)
const CURLSSLBACKEND_POLARSSL = (UInt32)(6)
const CURLSSLBACKEND_WOLFSSL = (UInt32)(7)
const CURLSSLBACKEND_SCHANNEL = (UInt32)(8)
const CURLSSLBACKEND_DARWINSSL = (UInt32)(9)
const CURLSSLBACKEND_AXTLS = (UInt32)(10)
const CURLSSLBACKEND_MBEDTLS = (UInt32)(11)
# end enum curl_sslbackend

const CURLSSLBACKEND_LIBRESSL = CURLSSLBACKEND_OPENSSL
const CURLSSLBACKEND_BORINGSSL = CURLSSLBACKEND_OPENSSL
const CURLSSLBACKEND_CYASSL = CURLSSLBACKEND_WOLFSSL

mutable struct curl_httppost
    next::Ptr{Cvoid}
    name::Ptr{UInt8}
    namelength::Clong
    contents::Ptr{UInt8}
    contentslength::Clong
    buffer::Ptr{UInt8}
    bufferlength::Clong
    contenttype::Ptr{UInt8}
    contentheader::Ptr{Cvoid}
    more::Ptr{Cvoid}
    flags::Clong
    showfilename::Ptr{UInt8}
    userp::Ptr{Cvoid}
    contentlen::curl_off_t
end

const CURL_HTTPPOST_FILENAME = 1 << 0
const CURL_HTTPPOST_READFILE = 1 << 1
const CURL_HTTPPOST_PTRNAME = 1 << 2
const CURL_HTTPPOST_PTRCONTENTS = 1 << 3
const CURL_HTTPPOST_BUFFER = 1 << 4
const CURL_HTTPPOST_PTRBUFFER = 1 << 5
const CURL_HTTPPOST_CALLBACK = 1 << 6
const CURL_HTTPPOST_LARGE = 1 << 7

const curl_progress_callback = Ptr{Cvoid}
const curl_xferinfo_callback = Ptr{Cvoid}

const CURL_MAX_READ_SIZE = 524288
const CURL_MAX_WRITE_SIZE = 16384
const CURL_MAX_HTTP_HEADER = 100 * 1024
const CURL_WRITEFUNC_PAUSE = 0x10000001

const curl_write_callback = Ptr{Cvoid}
const curl_resolver_start_callback = Ptr{Cvoid}

const CURLFINFOFLAG_KNOWN_FILENAME = 1 << 0
const CURLFINFOFLAG_KNOWN_FILETYPE = 1 << 1
const CURLFINFOFLAG_KNOWN_TIME = 1 << 2
const CURLFINFOFLAG_KNOWN_PERM = 1 << 3
const CURLFINFOFLAG_KNOWN_UID = 1 << 4
const CURLFINFOFLAG_KNOWN_GID = 1 << 5
const CURLFINFOFLAG_KNOWN_SIZE = 1 << 6
const CURLFINFOFLAG_KNOWN_HLINKCOUNT = 1 << 7
const CURL_CHUNK_BGN_FUNC_OK = 0
const CURL_CHUNK_BGN_FUNC_FAIL = 1
const CURL_CHUNK_BGN_FUNC_SKIP = 2
const CURL_CHUNK_END_FUNC_OK = 0
const CURL_CHUNK_END_FUNC_FAIL = 1
const CURL_FNMATCHFUNC_MATCH = 0
const CURL_FNMATCHFUNC_NOMATCH = 1
const CURL_FNMATCHFUNC_FAIL = 2
const CURL_SEEKFUNC_OK = 0
const CURL_SEEKFUNC_FAIL = 1
const CURL_SEEKFUNC_CANTSEEK = 2
const CURL_READFUNC_ABORT = 0x10000000
const CURL_READFUNC_PAUSE = 0x10000001
const CURL_SOCKOPT_OK = 0
const CURL_SOCKOPT_ERROR = 1
const CURL_SOCKOPT_ALREADY_CONNECTED = 2

# begin enum curlfiletype
const curlfiletype = UInt32
const CURLFILETYPE_FILE = (UInt32)(0)
const CURLFILETYPE_DIRECTORY = (UInt32)(1)
const CURLFILETYPE_SYMLINK = (UInt32)(2)
const CURLFILETYPE_DEVICE_BLOCK = (UInt32)(3)
const CURLFILETYPE_DEVICE_CHAR = (UInt32)(4)
const CURLFILETYPE_NAMEDPIPE = (UInt32)(5)
const CURLFILETYPE_SOCKET = (UInt32)(6)
const CURLFILETYPE_DOOR = (UInt32)(7)
const CURLFILETYPE_UNKNOWN = (UInt32)(8)
# end enum curlfiletype

mutable struct curl_fileinfo
    filename::Ptr{UInt8}
    filetype::curlfiletype
    time::time_t
    perm::UInt32
    uid::Cint
    gid::Cint
    size::curl_off_t
    hardlinks::Clong
    strings::Cvoid
    flags::UInt32
    b_data::Ptr{UInt8}
    b_size::Csize_t
    b_used::Csize_t
end

const curl_chunk_bgn_callback = Ptr{Cvoid}
const curl_chunk_end_callback = Ptr{Cvoid}
const curl_fnmatch_callback = Ptr{Cvoid}
const curl_seek_callback = Ptr{Cvoid}
const curl_read_callback = Ptr{Cvoid}

# begin enum curlsocktype
const curlsocktype = UInt32
const CURLSOCKTYPE_IPCXN = (UInt32)(0)
const CURLSOCKTYPE_ACCEPT = (UInt32)(1)
const CURLSOCKTYPE_LAST = (UInt32)(2)
# end enum curlsocktype

const curl_sockopt_callback = Ptr{Cvoid}

mutable struct curl_sockaddr
    family::Cint
    socktype::Cint
    protocol::Cint
    addrlen::UInt32
    addr::Cvoid
end

const curl_opensocket_callback = Ptr{Cvoid}
const curl_closesocket_callback = Ptr{Cvoid}

# begin enum curlioerr
const curlioerr = UInt32
const CURLIOE_OK = (UInt32)(0)
const CURLIOE_UNKNOWNCMD = (UInt32)(1)
const CURLIOE_FAILRESTART = (UInt32)(2)
const CURLIOE_LAST = (UInt32)(3)
# end enum curlioerr

# begin enum curliocmd
const curliocmd = UInt32
const CURLIOCMD_NOP = (UInt32)(0)
const CURLIOCMD_RESTARTREAD = (UInt32)(1)
const CURLIOCMD_LAST = (UInt32)(2)
# end enum curliocmd

const curl_ioctl_callback = Ptr{Cvoid}
const curl_malloc_callback = Ptr{Cvoid}
const curl_free_callback = Ptr{Cvoid}
const curl_realloc_callback = Ptr{Cvoid}
const curl_strdup_callback = Ptr{Cvoid}
const curl_calloc_callback = Ptr{Cvoid}

# begin enum curl_infotype
const curl_infotype = UInt32
const CURLINFO_TEXT = (UInt32)(0)
const CURLINFO_HEADER_IN = (UInt32)(1)
const CURLINFO_HEADER_OUT = (UInt32)(2)
const CURLINFO_DATA_IN = (UInt32)(3)
const CURLINFO_DATA_OUT = (UInt32)(4)
const CURLINFO_SSL_DATA_IN = (UInt32)(5)
const CURLINFO_SSL_DATA_OUT = (UInt32)(6)
const CURLINFO_END = (UInt32)(7)
# end enum curl_infotype

const curl_debug_callback = Ptr{Cvoid}

# begin enum CURLcode
const CURLcode = UInt32
const CURLE_OK = (UInt32)(0)
const CURLE_UNSUPPORTED_PROTOCOL = (UInt32)(1)
const CURLE_FAILED_INIT = (UInt32)(2)
const CURLE_URL_MALFORMAT = (UInt32)(3)
const CURLE_NOT_BUILT_IN = (UInt32)(4)
const CURLE_COULDNT_RESOLVE_PROXY = (UInt32)(5)
const CURLE_COULDNT_RESOLVE_HOST = (UInt32)(6)
const CURLE_COULDNT_CONNECT = (UInt32)(7)
const CURLE_WEIRD_SERVER_REPLY = (UInt32)(8)
const CURLE_REMOTE_ACCESS_DENIED = (UInt32)(9)
const CURLE_FTP_ACCEPT_FAILED = (UInt32)(10)
const CURLE_FTP_WEIRD_PASS_REPLY = (UInt32)(11)
const CURLE_FTP_ACCEPT_TIMEOUT = (UInt32)(12)
const CURLE_FTP_WEIRD_PASV_REPLY = (UInt32)(13)
const CURLE_FTP_WEIRD_227_FORMAT = (UInt32)(14)
const CURLE_FTP_CANT_GET_HOST = (UInt32)(15)
const CURLE_HTTP2 = (UInt32)(16)
const CURLE_FTP_COULDNT_SET_TYPE = (UInt32)(17)
const CURLE_PARTIAL_FILE = (UInt32)(18)
const CURLE_FTP_COULDNT_RETR_FILE = (UInt32)(19)
const CURLE_OBSOLETE20 = (UInt32)(20)
const CURLE_QUOTE_ERROR = (UInt32)(21)
const CURLE_HTTP_RETURNED_ERROR = (UInt32)(22)
const CURLE_WRITE_ERROR = (UInt32)(23)
const CURLE_OBSOLETE24 = (UInt32)(24)
const CURLE_UPLOAD_FAILED = (UInt32)(25)
const CURLE_READ_ERROR = (UInt32)(26)
const CURLE_OUT_OF_MEMORY = (UInt32)(27)
const CURLE_OPERATION_TIMEDOUT = (UInt32)(28)
const CURLE_OBSOLETE29 = (UInt32)(29)
const CURLE_FTP_PORT_FAILED = (UInt32)(30)
const CURLE_FTP_COULDNT_USE_REST = (UInt32)(31)
const CURLE_OBSOLETE32 = (UInt32)(32)
const CURLE_RANGE_ERROR = (UInt32)(33)
const CURLE_HTTP_POST_ERROR = (UInt32)(34)
const CURLE_SSL_CONNECT_ERROR = (UInt32)(35)
const CURLE_BAD_DOWNLOAD_RESUME = (UInt32)(36)
const CURLE_FILE_COULDNT_READ_FILE = (UInt32)(37)
const CURLE_LDAP_CANNOT_BIND = (UInt32)(38)
const CURLE_LDAP_SEARCH_FAILED = (UInt32)(39)
const CURLE_OBSOLETE40 = (UInt32)(40)
const CURLE_FUNCTION_NOT_FOUND = (UInt32)(41)
const CURLE_ABORTED_BY_CALLBACK = (UInt32)(42)
const CURLE_BAD_FUNCTION_ARGUMENT = (UInt32)(43)
const CURLE_OBSOLETE44 = (UInt32)(44)
const CURLE_INTERFACE_FAILED = (UInt32)(45)
const CURLE_OBSOLETE46 = (UInt32)(46)
const CURLE_TOO_MANY_REDIRECTS = (UInt32)(47)
const CURLE_UNKNOWN_OPTION = (UInt32)(48)
const CURLE_TELNET_OPTION_SYNTAX = (UInt32)(49)
const CURLE_OBSOLETE50 = (UInt32)(50)
const CURLE_PEER_FAILED_VERIFICATION = (UInt32)(51)
const CURLE_GOT_NOTHING = (UInt32)(52)
const CURLE_SSL_ENGINE_NOTFOUND = (UInt32)(53)
const CURLE_SSL_ENGINE_SETFAILED = (UInt32)(54)
const CURLE_SEND_ERROR = (UInt32)(55)
const CURLE_RECV_ERROR = (UInt32)(56)
const CURLE_OBSOLETE57 = (UInt32)(57)
const CURLE_SSL_CERTPROBLEM = (UInt32)(58)
const CURLE_SSL_CIPHER = (UInt32)(59)
const CURLE_SSL_CACERT = (UInt32)(60)
const CURLE_BAD_CONTENT_ENCODING = (UInt32)(61)
const CURLE_LDAP_INVALID_URL = (UInt32)(62)
const CURLE_FILESIZE_EXCEEDED = (UInt32)(63)
const CURLE_USE_SSL_FAILED = (UInt32)(64)
const CURLE_SEND_FAIL_REWIND = (UInt32)(65)
const CURLE_SSL_ENGINE_INITFAILED = (UInt32)(66)
const CURLE_LOGIN_DENIED = (UInt32)(67)
const CURLE_TFTP_NOTFOUND = (UInt32)(68)
const CURLE_TFTP_PERM = (UInt32)(69)
const CURLE_REMOTE_DISK_FULL = (UInt32)(70)
const CURLE_TFTP_ILLEGAL = (UInt32)(71)
const CURLE_TFTP_UNKNOWNID = (UInt32)(72)
const CURLE_REMOTE_FILE_EXISTS = (UInt32)(73)
const CURLE_TFTP_NOSUCHUSER = (UInt32)(74)
const CURLE_CONV_FAILED = (UInt32)(75)
const CURLE_CONV_REQD = (UInt32)(76)
const CURLE_SSL_CACERT_BADFILE = (UInt32)(77)
const CURLE_REMOTE_FILE_NOT_FOUND = (UInt32)(78)
const CURLE_SSH = (UInt32)(79)
const CURLE_SSL_SHUTDOWN_FAILED = (UInt32)(80)
const CURLE_AGAIN = (UInt32)(81)
const CURLE_SSL_CRL_BADFILE = (UInt32)(82)
const CURLE_SSL_ISSUER_ERROR = (UInt32)(83)
const CURLE_FTP_PRET_FAILED = (UInt32)(84)
const CURLE_RTSP_CSEQ_ERROR = (UInt32)(85)
const CURLE_RTSP_SESSION_ERROR = (UInt32)(86)
const CURLE_FTP_BAD_FILE_LIST = (UInt32)(87)
const CURLE_CHUNK_FAILED = (UInt32)(88)
const CURLE_NO_CONNECTION_AVAILABLE = (UInt32)(89)
const CURLE_SSL_PINNEDPUBKEYNOTMATCH = (UInt32)(90)
const CURLE_SSL_INVALIDCERTSTATUS = (UInt32)(91)
const CURLE_HTTP2_STREAM = (UInt32)(92)
const CURLE_RECURSIVE_API_CALL = (UInt32)(93)
const CURL_LAST = (UInt32)(94)
# end enum CURLcode

const curl_conv_callback = Ptr{Cvoid}
const curl_ssl_ctx_callback = Ptr{Cvoid}

# begin enum curl_proxytype
const curl_proxytype = UInt32
const CURLPROXY_HTTP = (UInt32)(0)
const CURLPROXY_HTTP_1_0 = (UInt32)(1)
const CURLPROXY_HTTPS = (UInt32)(2)
const CURLPROXY_SOCKS4 = (UInt32)(4)
const CURLPROXY_SOCKS5 = (UInt32)(5)
const CURLPROXY_SOCKS4A = (UInt32)(6)
const CURLPROXY_SOCKS5_HOSTNAME = (UInt32)(7)
# end enum curl_proxytype

const CURLSSH_AUTH_ANY = ~0
const CURLSSH_AUTH_NONE = 0
const CURLSSH_AUTH_PUBLICKEY = 1 << 0
const CURLSSH_AUTH_PASSWORD = 1 << 1
const CURLSSH_AUTH_HOST = 1 << 2
const CURLSSH_AUTH_KEYBOARD = 1 << 3
const CURLSSH_AUTH_AGENT = 1 << 4
const CURLSSH_AUTH_GSSAPI = 1 << 5
const CURLSSH_AUTH_DEFAULT = CURLSSH_AUTH_ANY
const CURLGSSAPI_DELEGATION_NONE = 0
const CURLGSSAPI_DELEGATION_POLICY_FLAG = 1 << 0
const CURLGSSAPI_DELEGATION_FLAG = 1 << 1
const CURL_ERROR_SIZE = 256

# begin enum curl_khtype
const curl_khtype = UInt32
const CURLKHTYPE_UNKNOWN = (UInt32)(0)
const CURLKHTYPE_RSA1 = (UInt32)(1)
const CURLKHTYPE_RSA = (UInt32)(2)
const CURLKHTYPE_DSS = (UInt32)(3)
const CURLKHTYPE_ECDSA = (UInt32)(4)
const CURLKHTYPE_ED25519 = (UInt32)(5)
# end enum curl_khtype

mutable struct curl_khkey
    key::Ptr{UInt8}
    len::Csize_t
    keytype::Cvoid
end

# begin enum curl_khstat
const curl_khstat = UInt32
const CURLKHSTAT_FINE_ADD_TO_FILE = (UInt32)(0)
const CURLKHSTAT_FINE = (UInt32)(1)
const CURLKHSTAT_REJECT = (UInt32)(2)
const CURLKHSTAT_DEFER = (UInt32)(3)
const CURLKHSTAT_LAST = (UInt32)(4)
# end enum curl_khstat

# begin enum curl_khmatch
const curl_khmatch = UInt32
const CURLKHMATCH_OK = (UInt32)(0)
const CURLKHMATCH_MISMATCH = (UInt32)(1)
const CURLKHMATCH_MISSING = (UInt32)(2)
const CURLKHMATCH_LAST = (UInt32)(3)
# end enum curl_khmatch

const curl_sshkeycallback = Ptr{Cvoid}

# begin enum curl_usessl
const curl_usessl = UInt32
const CURLUSESSL_NONE = (UInt32)(0)
const CURLUSESSL_TRY = (UInt32)(1)
const CURLUSESSL_CONTROL = (UInt32)(2)
const CURLUSESSL_ALL = (UInt32)(3)
const CURLUSESSL_LAST = (UInt32)(4)
# end enum curl_usessl

const CURLSSLOPT_ALLOW_BEAST = 1 << 0
const CURLSSLOPT_NO_REVOKE = 1 << 1
const CURL_HET_DEFAULT = Clong(200)

const curl_ftpssl = curl_usessl
const CURLFTPSSL_NONE = CURLUSESSL_NONE
const CURLFTPSSL_TRY = CURLUSESSL_TRY
const CURLFTPSSL_CONTROL = CURLUSESSL_CONTROL
const CURLFTPSSL_ALL = CURLUSESSL_ALL
const CURLFTPSSL_LAST = CURLUSESSL_LAST

# begin enum curl_ftpccc
const curl_ftpccc = UInt32
const CURLFTPSSL_CCC_NONE = (UInt32)(0)
const CURLFTPSSL_CCC_PASSIVE = (UInt32)(1)
const CURLFTPSSL_CCC_ACTIVE = (UInt32)(2)
const CURLFTPSSL_CCC_LAST = (UInt32)(3)
# end enum curl_ftpccc

# begin enum curl_ftpauth
const curl_ftpauth = UInt32
const CURLFTPAUTH_DEFAULT = (UInt32)(0)
const CURLFTPAUTH_SSL = (UInt32)(1)
const CURLFTPAUTH_TLS = (UInt32)(2)
const CURLFTPAUTH_LAST = (UInt32)(3)
# end enum curl_ftpauth

# begin enum curl_ftpcreatedir
const curl_ftpcreatedir = UInt32
const CURLFTP_CREATE_DIR_NONE = (UInt32)(0)
const CURLFTP_CREATE_DIR = (UInt32)(1)
const CURLFTP_CREATE_DIR_RETRY = (UInt32)(2)
const CURLFTP_CREATE_DIR_LAST = (UInt32)(3)
# end enum curl_ftpcreatedir

# begin enum curl_ftpmethod
const curl_ftpmethod = UInt32
const CURLFTPMETHOD_DEFAULT = (UInt32)(0)
const CURLFTPMETHOD_MULTICWD = (UInt32)(1)
const CURLFTPMETHOD_NOCWD = (UInt32)(2)
const CURLFTPMETHOD_SINGLECWD = (UInt32)(3)
const CURLFTPMETHOD_LAST = (UInt32)(4)
# end enum curl_ftpmethod

const CURLHEADER_UNIFIED = 0
const CURLHEADER_SEPARATE = 1 << 0
const CURLPROTO_HTTP = 1 << 0
const CURLPROTO_HTTPS = 1 << 1
const CURLPROTO_FTP = 1 << 2
const CURLPROTO_FTPS = 1 << 3
const CURLPROTO_SCP = 1 << 4
const CURLPROTO_SFTP = 1 << 5
const CURLPROTO_TELNET = 1 << 6
const CURLPROTO_LDAP = 1 << 7
const CURLPROTO_LDAPS = 1 << 8
const CURLPROTO_DICT = 1 << 9
const CURLPROTO_FILE = 1 << 10
const CURLPROTO_TFTP = 1 << 11
const CURLPROTO_IMAP = 1 << 12
const CURLPROTO_IMAPS = 1 << 13
const CURLPROTO_POP3 = 1 << 14
const CURLPROTO_POP3S = 1 << 15
const CURLPROTO_SMTP = 1 << 16
const CURLPROTO_SMTPS = 1 << 17
const CURLPROTO_RTSP = 1 << 18
const CURLPROTO_RTMP = 1 << 19
const CURLPROTO_RTMPT = 1 << 20
const CURLPROTO_RTMPE = 1 << 21
const CURLPROTO_RTMPTE = 1 << 22
const CURLPROTO_RTMPS = 1 << 23
const CURLPROTO_RTMPTS = 1 << 24
const CURLPROTO_GOPHER = 1 << 25
const CURLPROTO_SMB = 1 << 26
const CURLPROTO_SMBS = 1 << 27
const CURLPROTO_ALL = ~0
const CURLOPTTYPE_LONG = 0
const CURLOPTTYPE_OBJECTPOINT = 10000
const CURLOPTTYPE_STRINGPOINT = 10000
const CURLOPTTYPE_FUNCTIONPOINT = 20000
const CURLOPTTYPE_OFF_T = 30000

# begin enum CURLoption
const CURLoption = UInt32
const CURLOPT_WRITEDATA = (UInt32)(10001)
const CURLOPT_URL = (UInt32)(10002)
const CURLOPT_PORT = (UInt32)(3)
const CURLOPT_PROXY = (UInt32)(10004)
const CURLOPT_USERPWD = (UInt32)(10005)
const CURLOPT_PROXYUSERPWD = (UInt32)(10006)
const CURLOPT_RANGE = (UInt32)(10007)
const CURLOPT_READDATA = (UInt32)(10009)
const CURLOPT_ERRORBUFFER = (UInt32)(10010)
const CURLOPT_WRITEFUNCTION = (UInt32)(20011)
const CURLOPT_READFUNCTION = (UInt32)(20012)
const CURLOPT_TIMEOUT = (UInt32)(13)
const CURLOPT_INFILESIZE = (UInt32)(14)
const CURLOPT_POSTFIELDS = (UInt32)(10015)
const CURLOPT_REFERER = (UInt32)(10016)
const CURLOPT_FTPPORT = (UInt32)(10017)
const CURLOPT_USERAGENT = (UInt32)(10018)
const CURLOPT_LOW_SPEED_LIMIT = (UInt32)(19)
const CURLOPT_LOW_SPEED_TIME = (UInt32)(20)
const CURLOPT_RESUME_FROM = (UInt32)(21)
const CURLOPT_COOKIE = (UInt32)(10022)
const CURLOPT_HTTPHEADER = (UInt32)(10023)
const CURLOPT_HTTPPOST = (UInt32)(10024)
const CURLOPT_SSLCERT = (UInt32)(10025)
const CURLOPT_KEYPASSWD = (UInt32)(10026)
const CURLOPT_CRLF = (UInt32)(27)
const CURLOPT_QUOTE = (UInt32)(10028)
const CURLOPT_HEADERDATA = (UInt32)(10029)
const CURLOPT_COOKIEFILE = (UInt32)(10031)
const CURLOPT_SSLVERSION = (UInt32)(32)
const CURLOPT_TIMECONDITION = (UInt32)(33)
const CURLOPT_TIMEVALUE = (UInt32)(34)
const CURLOPT_CUSTOMREQUEST = (UInt32)(10036)
const CURLOPT_STDERR = (UInt32)(10037)
const CURLOPT_POSTQUOTE = (UInt32)(10039)
const CURLOPT_OBSOLETE40 = (UInt32)(10040)
const CURLOPT_VERBOSE = (UInt32)(41)
const CURLOPT_HEADER = (UInt32)(42)
const CURLOPT_NOPROGRESS = (UInt32)(43)
const CURLOPT_NOBODY = (UInt32)(44)
const CURLOPT_FAILONERROR = (UInt32)(45)
const CURLOPT_UPLOAD = (UInt32)(46)
const CURLOPT_POST = (UInt32)(47)
const CURLOPT_DIRLISTONLY = (UInt32)(48)
const CURLOPT_APPEND = (UInt32)(50)
const CURLOPT_NETRC = (UInt32)(51)
const CURLOPT_FOLLOWLOCATION = (UInt32)(52)
const CURLOPT_TRANSFERTEXT = (UInt32)(53)
const CURLOPT_PUT = (UInt32)(54)
const CURLOPT_PROGRESSFUNCTION = (UInt32)(20056)
const CURLOPT_PROGRESSDATA = (UInt32)(10057)
const CURLOPT_AUTOREFERER = (UInt32)(58)
const CURLOPT_PROXYPORT = (UInt32)(59)
const CURLOPT_POSTFIELDSIZE = (UInt32)(60)
const CURLOPT_HTTPPROXYTUNNEL = (UInt32)(61)
const CURLOPT_INTERFACE = (UInt32)(10062)
const CURLOPT_KRBLEVEL = (UInt32)(10063)
const CURLOPT_SSL_VERIFYPEER = (UInt32)(64)
const CURLOPT_CAINFO = (UInt32)(10065)
const CURLOPT_MAXREDIRS = (UInt32)(68)
const CURLOPT_FILETIME = (UInt32)(69)
const CURLOPT_TELNETOPTIONS = (UInt32)(10070)
const CURLOPT_MAXCONNECTS = (UInt32)(71)
const CURLOPT_OBSOLETE72 = (UInt32)(72)
const CURLOPT_FRESH_CONNECT = (UInt32)(74)
const CURLOPT_FORBID_REUSE = (UInt32)(75)
const CURLOPT_RANDOM_FILE = (UInt32)(10076)
const CURLOPT_EGDSOCKET = (UInt32)(10077)
const CURLOPT_CONNECTTIMEOUT = (UInt32)(78)
const CURLOPT_HEADERFUNCTION = (UInt32)(20079)
const CURLOPT_HTTPGET = (UInt32)(80)
const CURLOPT_SSL_VERIFYHOST = (UInt32)(81)
const CURLOPT_COOKIEJAR = (UInt32)(10082)
const CURLOPT_SSL_CIPHER_LIST = (UInt32)(10083)
const CURLOPT_HTTP_VERSION = (UInt32)(84)
const CURLOPT_FTP_USE_EPSV = (UInt32)(85)
const CURLOPT_SSLCERTTYPE = (UInt32)(10086)
const CURLOPT_SSLKEY = (UInt32)(10087)
const CURLOPT_SSLKEYTYPE = (UInt32)(10088)
const CURLOPT_SSLENGINE = (UInt32)(10089)
const CURLOPT_SSLENGINE_DEFAULT = (UInt32)(90)
const CURLOPT_DNS_USE_GLOBAL_CACHE = (UInt32)(91)
const CURLOPT_DNS_CACHE_TIMEOUT = (UInt32)(92)
const CURLOPT_PREQUOTE = (UInt32)(10093)
const CURLOPT_DEBUGFUNCTION = (UInt32)(20094)
const CURLOPT_DEBUGDATA = (UInt32)(10095)
const CURLOPT_COOKIESESSION = (UInt32)(96)
const CURLOPT_CAPATH = (UInt32)(10097)
const CURLOPT_BUFFERSIZE = (UInt32)(98)
const CURLOPT_NOSIGNAL = (UInt32)(99)
const CURLOPT_SHARE = (UInt32)(10100)
const CURLOPT_PROXYTYPE = (UInt32)(101)
const CURLOPT_ACCEPT_ENCODING = (UInt32)(10102)
const CURLOPT_PRIVATE = (UInt32)(10103)
const CURLOPT_HTTP200ALIASES = (UInt32)(10104)
const CURLOPT_UNRESTRICTED_AUTH = (UInt32)(105)
const CURLOPT_FTP_USE_EPRT = (UInt32)(106)
const CURLOPT_HTTPAUTH = (UInt32)(107)
const CURLOPT_SSL_CTX_FUNCTION = (UInt32)(20108)
const CURLOPT_SSL_CTX_DATA = (UInt32)(10109)
const CURLOPT_FTP_CREATE_MISSING_DIRS = (UInt32)(110)
const CURLOPT_PROXYAUTH = (UInt32)(111)
const CURLOPT_FTP_RESPONSE_TIMEOUT = (UInt32)(112)
const CURLOPT_IPRESOLVE = (UInt32)(113)
const CURLOPT_MAXFILESIZE = (UInt32)(114)
const CURLOPT_INFILESIZE_LARGE = (UInt32)(30115)
const CURLOPT_RESUME_FROM_LARGE = (UInt32)(30116)
const CURLOPT_MAXFILESIZE_LARGE = (UInt32)(30117)
const CURLOPT_NETRC_FILE = (UInt32)(10118)
const CURLOPT_USE_SSL = (UInt32)(119)
const CURLOPT_POSTFIELDSIZE_LARGE = (UInt32)(30120)
const CURLOPT_TCP_NODELAY = (UInt32)(121)
const CURLOPT_FTPSSLAUTH = (UInt32)(129)
const CURLOPT_IOCTLFUNCTION = (UInt32)(20130)
const CURLOPT_IOCTLDATA = (UInt32)(10131)
const CURLOPT_FTP_ACCOUNT = (UInt32)(10134)
const CURLOPT_COOKIELIST = (UInt32)(10135)
const CURLOPT_IGNORE_CONTENT_LENGTH = (UInt32)(136)
const CURLOPT_FTP_SKIP_PASV_IP = (UInt32)(137)
const CURLOPT_FTP_FILEMETHOD = (UInt32)(138)
const CURLOPT_LOCALPORT = (UInt32)(139)
const CURLOPT_LOCALPORTRANGE = (UInt32)(140)
const CURLOPT_CONNECT_ONLY = (UInt32)(141)
const CURLOPT_CONV_FROM_NETWORK_FUNCTION = (UInt32)(20142)
const CURLOPT_CONV_TO_NETWORK_FUNCTION = (UInt32)(20143)
const CURLOPT_CONV_FROM_UTF8_FUNCTION = (UInt32)(20144)
const CURLOPT_MAX_SEND_SPEED_LARGE = (UInt32)(30145)
const CURLOPT_MAX_RECV_SPEED_LARGE = (UInt32)(30146)
const CURLOPT_FTP_ALTERNATIVE_TO_USER = (UInt32)(10147)
const CURLOPT_SOCKOPTFUNCTION = (UInt32)(20148)
const CURLOPT_SOCKOPTDATA = (UInt32)(10149)
const CURLOPT_SSL_SESSIONID_CACHE = (UInt32)(150)
const CURLOPT_SSH_AUTH_TYPES = (UInt32)(151)
const CURLOPT_SSH_PUBLIC_KEYFILE = (UInt32)(10152)
const CURLOPT_SSH_PRIVATE_KEYFILE = (UInt32)(10153)
const CURLOPT_FTP_SSL_CCC = (UInt32)(154)
const CURLOPT_TIMEOUT_MS = (UInt32)(155)
const CURLOPT_CONNECTTIMEOUT_MS = (UInt32)(156)
const CURLOPT_HTTP_TRANSFER_DECODING = (UInt32)(157)
const CURLOPT_HTTP_CONTENT_DECODING = (UInt32)(158)
const CURLOPT_NEW_FILE_PERMS = (UInt32)(159)
const CURLOPT_NEW_DIRECTORY_PERMS = (UInt32)(160)
const CURLOPT_POSTREDIR = (UInt32)(161)
const CURLOPT_SSH_HOST_PUBLIC_KEY_MD5 = (UInt32)(10162)
const CURLOPT_OPENSOCKETFUNCTION = (UInt32)(20163)
const CURLOPT_OPENSOCKETDATA = (UInt32)(10164)
const CURLOPT_COPYPOSTFIELDS = (UInt32)(10165)
const CURLOPT_PROXY_TRANSFER_MODE = (UInt32)(166)
const CURLOPT_SEEKFUNCTION = (UInt32)(20167)
const CURLOPT_SEEKDATA = (UInt32)(10168)
const CURLOPT_CRLFILE = (UInt32)(10169)
const CURLOPT_ISSUERCERT = (UInt32)(10170)
const CURLOPT_ADDRESS_SCOPE = (UInt32)(171)
const CURLOPT_CERTINFO = (UInt32)(172)
const CURLOPT_USERNAME = (UInt32)(10173)
const CURLOPT_PASSWORD = (UInt32)(10174)
const CURLOPT_PROXYUSERNAME = (UInt32)(10175)
const CURLOPT_PROXYPASSWORD = (UInt32)(10176)
const CURLOPT_NOPROXY = (UInt32)(10177)
const CURLOPT_TFTP_BLKSIZE = (UInt32)(178)
const CURLOPT_SOCKS5_GSSAPI_SERVICE = (UInt32)(10179)
const CURLOPT_SOCKS5_GSSAPI_NEC = (UInt32)(180)
const CURLOPT_PROTOCOLS = (UInt32)(181)
const CURLOPT_REDIR_PROTOCOLS = (UInt32)(182)
const CURLOPT_SSH_KNOWNHOSTS = (UInt32)(10183)
const CURLOPT_SSH_KEYFUNCTION = (UInt32)(20184)
const CURLOPT_SSH_KEYDATA = (UInt32)(10185)
const CURLOPT_MAIL_FROM = (UInt32)(10186)
const CURLOPT_MAIL_RCPT = (UInt32)(10187)
const CURLOPT_FTP_USE_PRET = (UInt32)(188)
const CURLOPT_RTSP_REQUEST = (UInt32)(189)
const CURLOPT_RTSP_SESSION_ID = (UInt32)(10190)
const CURLOPT_RTSP_STREAM_URI = (UInt32)(10191)
const CURLOPT_RTSP_TRANSPORT = (UInt32)(10192)
const CURLOPT_RTSP_CLIENT_CSEQ = (UInt32)(193)
const CURLOPT_RTSP_SERVER_CSEQ = (UInt32)(194)
const CURLOPT_INTERLEAVEDATA = (UInt32)(10195)
const CURLOPT_INTERLEAVEFUNCTION = (UInt32)(20196)
const CURLOPT_WILDCARDMATCH = (UInt32)(197)
const CURLOPT_CHUNK_BGN_FUNCTION = (UInt32)(20198)
const CURLOPT_CHUNK_END_FUNCTION = (UInt32)(20199)
const CURLOPT_FNMATCH_FUNCTION = (UInt32)(20200)
const CURLOPT_CHUNK_DATA = (UInt32)(10201)
const CURLOPT_FNMATCH_DATA = (UInt32)(10202)
const CURLOPT_RESOLVE = (UInt32)(10203)
const CURLOPT_TLSAUTH_USERNAME = (UInt32)(10204)
const CURLOPT_TLSAUTH_PASSWORD = (UInt32)(10205)
const CURLOPT_TLSAUTH_TYPE = (UInt32)(10206)
const CURLOPT_TRANSFER_ENCODING = (UInt32)(207)
const CURLOPT_CLOSESOCKETFUNCTION = (UInt32)(20208)
const CURLOPT_CLOSESOCKETDATA = (UInt32)(10209)
const CURLOPT_GSSAPI_DELEGATION = (UInt32)(210)
const CURLOPT_DNS_SERVERS = (UInt32)(10211)
const CURLOPT_ACCEPTTIMEOUT_MS = (UInt32)(212)
const CURLOPT_TCP_KEEPALIVE = (UInt32)(213)
const CURLOPT_TCP_KEEPIDLE = (UInt32)(214)
const CURLOPT_TCP_KEEPINTVL = (UInt32)(215)
const CURLOPT_SSL_OPTIONS = (UInt32)(216)
const CURLOPT_MAIL_AUTH = (UInt32)(10217)
const CURLOPT_SASL_IR = (UInt32)(218)
const CURLOPT_XFERINFOFUNCTION = (UInt32)(20219)
const CURLOPT_XOAUTH2_BEARER = (UInt32)(10220)
const CURLOPT_DNS_INTERFACE = (UInt32)(10221)
const CURLOPT_DNS_LOCAL_IP4 = (UInt32)(10222)
const CURLOPT_DNS_LOCAL_IP6 = (UInt32)(10223)
const CURLOPT_LOGIN_OPTIONS = (UInt32)(10224)
const CURLOPT_SSL_ENABLE_NPN = (UInt32)(225)
const CURLOPT_SSL_ENABLE_ALPN = (UInt32)(226)
const CURLOPT_EXPECT_100_TIMEOUT_MS = (UInt32)(227)
const CURLOPT_PROXYHEADER = (UInt32)(10228)
const CURLOPT_HEADEROPT = (UInt32)(229)
const CURLOPT_PINNEDPUBLICKEY = (UInt32)(10230)
const CURLOPT_UNIX_SOCKET_PATH = (UInt32)(10231)
const CURLOPT_SSL_VERIFYSTATUS = (UInt32)(232)
const CURLOPT_SSL_FALSESTART = (UInt32)(233)
const CURLOPT_PATH_AS_IS = (UInt32)(234)
const CURLOPT_PROXY_SERVICE_NAME = (UInt32)(10235)
const CURLOPT_SERVICE_NAME = (UInt32)(10236)
const CURLOPT_PIPEWAIT = (UInt32)(237)
const CURLOPT_DEFAULT_PROTOCOL = (UInt32)(10238)
const CURLOPT_STREAM_WEIGHT = (UInt32)(239)
const CURLOPT_STREAM_DEPENDS = (UInt32)(10240)
const CURLOPT_STREAM_DEPENDS_E = (UInt32)(10241)
const CURLOPT_TFTP_NO_OPTIONS = (UInt32)(242)
const CURLOPT_CONNECT_TO = (UInt32)(10243)
const CURLOPT_TCP_FASTOPEN = (UInt32)(244)
const CURLOPT_KEEP_SENDING_ON_ERROR = (UInt32)(245)
const CURLOPT_PROXY_CAINFO = (UInt32)(10246)
const CURLOPT_PROXY_CAPATH = (UInt32)(10247)
const CURLOPT_PROXY_SSL_VERIFYPEER = (UInt32)(248)
const CURLOPT_PROXY_SSL_VERIFYHOST = (UInt32)(249)
const CURLOPT_PROXY_SSLVERSION = (UInt32)(250)
const CURLOPT_PROXY_TLSAUTH_USERNAME = (UInt32)(10251)
const CURLOPT_PROXY_TLSAUTH_PASSWORD = (UInt32)(10252)
const CURLOPT_PROXY_TLSAUTH_TYPE = (UInt32)(10253)
const CURLOPT_PROXY_SSLCERT = (UInt32)(10254)
const CURLOPT_PROXY_SSLCERTTYPE = (UInt32)(10255)
const CURLOPT_PROXY_SSLKEY = (UInt32)(10256)
const CURLOPT_PROXY_SSLKEYTYPE = (UInt32)(10257)
const CURLOPT_PROXY_KEYPASSWD = (UInt32)(10258)
const CURLOPT_PROXY_SSL_CIPHER_LIST = (UInt32)(10259)
const CURLOPT_PROXY_CRLFILE = (UInt32)(10260)
const CURLOPT_PROXY_SSL_OPTIONS = (UInt32)(261)
const CURLOPT_PRE_PROXY = (UInt32)(10262)
const CURLOPT_PROXY_PINNEDPUBLICKEY = (UInt32)(10263)
const CURLOPT_ABSTRACT_UNIX_SOCKET = (UInt32)(10264)
const CURLOPT_SUPPRESS_CONNECT_HEADERS = (UInt32)(265)
const CURLOPT_REQUEST_TARGET = (UInt32)(10266)
const CURLOPT_SOCKS5_AUTH = (UInt32)(267)
const CURLOPT_SSH_COMPRESSION = (UInt32)(268)
const CURLOPT_MIMEPOST = (UInt32)(10269)
const CURLOPT_TIMEVALUE_LARGE = (UInt32)(30270)
const CURLOPT_HAPPY_EYEBALLS_TIMEOUT_MS = (UInt32)(271)
const CURLOPT_RESOLVER_START_FUNCTION = (UInt32)(20272)
const CURLOPT_RESOLVER_START_DATA = (UInt32)(10273)
const CURLOPT_HAPROXYPROTOCOL = (UInt32)(274)
const CURLOPT_DNS_SHUFFLE_ADDRESSES = (UInt32)(275)
const CURLOPT_TLS13_CIPHERS = (UInt32)(10276)
const CURLOPT_PROXY_TLS13_CIPHERS = (UInt32)(10277)
const CURLOPT_DISALLOW_USERNAME_IN_URL = (UInt32)(278)
const CURLOPT_MAXAGE_CONN = UInt32(288)
const CURLOPT_LASTENTRY = (UInt32)(10299)
# end enum CURLoption

const CURLOPT_XFERINFODATA = CURLOPT_PROGRESSDATA
const CURLOPT_SERVER_RESPONSE_TIMEOUT = CURLOPT_FTP_RESPONSE_TIMEOUT
const CURLOPT_POST301 = CURLOPT_POSTREDIR
const CURLOPT_SSLKEYPASSWD = CURLOPT_KEYPASSWD
const CURLOPT_FTPAPPEND = CURLOPT_APPEND
const CURLOPT_FTPLISTONLY = CURLOPT_DIRLISTONLY
const CURLOPT_FTP_SSL = CURLOPT_USE_SSL
const CURLOPT_SSLCERTPASSWD = CURLOPT_KEYPASSWD
const CURLOPT_KRB4LEVEL = CURLOPT_KRBLEVEL
const CURL_IPRESOLVE_WHATEVER = 0
const CURL_IPRESOLVE_V4 = 1
const CURL_IPRESOLVE_V6 = 2
const CURLOPT_RTSPHEADER = CURLOPT_HTTPHEADER

# begin enum ANONYMOUS
const CURL_HTTP_VERSION_NONE = (UInt32)(0)
const CURL_HTTP_VERSION_1_0 = (UInt32)(1)
const CURL_HTTP_VERSION_1_1 = (UInt32)(2)
const CURL_HTTP_VERSION_2_0 = (UInt32)(3)
const CURL_HTTP_VERSION_2TLS = (UInt32)(4)
const CURL_HTTP_VERSION_2_PRIOR_KNOWLEDGE = (UInt32)(5)
const CURL_HTTP_VERSION_LAST = (UInt32)(6)
# end enum ANONYMOUS

const CURL_HTTP_VERSION_2 = CURL_HTTP_VERSION_2_0

# begin enum ANONYMOUS
const CURL_RTSPREQ_NONE = (UInt32)(0)
const CURL_RTSPREQ_OPTIONS = (UInt32)(1)
const CURL_RTSPREQ_DESCRIBE = (UInt32)(2)
const CURL_RTSPREQ_ANNOUNCE = (UInt32)(3)
const CURL_RTSPREQ_SETUP = (UInt32)(4)
const CURL_RTSPREQ_PLAY = (UInt32)(5)
const CURL_RTSPREQ_PAUSE = (UInt32)(6)
const CURL_RTSPREQ_TEARDOWN = (UInt32)(7)
const CURL_RTSPREQ_GET_PARAMETER = (UInt32)(8)
const CURL_RTSPREQ_SET_PARAMETER = (UInt32)(9)
const CURL_RTSPREQ_RECORD = (UInt32)(10)
const CURL_RTSPREQ_RECEIVE = (UInt32)(11)
const CURL_RTSPREQ_LAST = (UInt32)(12)
# end enum ANONYMOUS

# begin enum CURL_NETRC_OPTION
const CURL_NETRC_OPTION = UInt32
const CURL_NETRC_IGNORED = (UInt32)(0)
const CURL_NETRC_OPTIONAL = (UInt32)(1)
const CURL_NETRC_REQUIRED = (UInt32)(2)
const CURL_NETRC_LAST = (UInt32)(3)
# end enum CURL_NETRC_OPTION

# begin enum ANONYMOUS
const CURL_SSLVERSION_DEFAULT = (UInt32)(0)
const CURL_SSLVERSION_TLSv1 = (UInt32)(1)
const CURL_SSLVERSION_SSLv2 = (UInt32)(2)
const CURL_SSLVERSION_SSLv3 = (UInt32)(3)
const CURL_SSLVERSION_TLSv1_0 = (UInt32)(4)
const CURL_SSLVERSION_TLSv1_1 = (UInt32)(5)
const CURL_SSLVERSION_TLSv1_2 = (UInt32)(6)
const CURL_SSLVERSION_TLSv1_3 = (UInt32)(7)
const CURL_SSLVERSION_LAST = (UInt32)(8)
# end enum ANONYMOUS

# begin enum ANONYMOUS
const CURL_SSLVERSION_MAX_NONE = (UInt32)(0)
const CURL_SSLVERSION_MAX_DEFAULT = (UInt32)(65536)
const CURL_SSLVERSION_MAX_TLSv1_0 = (UInt32)(262144)
const CURL_SSLVERSION_MAX_TLSv1_1 = (UInt32)(327680)
const CURL_SSLVERSION_MAX_TLSv1_2 = (UInt32)(393216)
const CURL_SSLVERSION_MAX_TLSv1_3 = (UInt32)(458752)
const CURL_SSLVERSION_MAX_LAST = (UInt32)(524288)
# end enum ANONYMOUS

# begin enum CURL_TLSAUTH
const CURL_TLSAUTH = UInt32
const CURL_TLSAUTH_NONE = (UInt32)(0)
const CURL_TLSAUTH_SRP = (UInt32)(1)
const CURL_TLSAUTH_LAST = (UInt32)(2)
# end enum CURL_TLSAUTH

const CURL_REDIR_GET_ALL = 0
const CURL_REDIR_POST_301 = 1
const CURL_REDIR_POST_302 = 2
const CURL_REDIR_POST_303 = 4
const CURL_REDIR_POST_ALL = (CURL_REDIR_POST_301 | CURL_REDIR_POST_302) | CURL_REDIR_POST_303

# begin enum curl_TimeCond
const curl_TimeCond = UInt32
const CURL_TIMECOND_NONE = (UInt32)(0)
const CURL_TIMECOND_IFMODSINCE = (UInt32)(1)
const CURL_TIMECOND_IFUNMODSINCE = (UInt32)(2)
const CURL_TIMECOND_LASTMOD = (UInt32)(3)
const CURL_TIMECOND_LAST = (UInt32)(4)
# end enum curl_TimeCond

struct curl_mime_s end

const curl_mime = Cvoid

struct curl_mimepart_s end

const curl_mimepart = Cvoid

# begin enum CURLformoption
const CURLformoption = UInt32
const CURLFORM_NOTHING = (UInt32)(0)
const CURLFORM_COPYNAME = (UInt32)(1)
const CURLFORM_PTRNAME = (UInt32)(2)
const CURLFORM_NAMELENGTH = (UInt32)(3)
const CURLFORM_COPYCONTENTS = (UInt32)(4)
const CURLFORM_PTRCONTENTS = (UInt32)(5)
const CURLFORM_CONTENTSLENGTH = (UInt32)(6)
const CURLFORM_FILECONTENT = (UInt32)(7)
const CURLFORM_ARRAY = (UInt32)(8)
const CURLFORM_OBSOLETE = (UInt32)(9)
const CURLFORM_FILE = (UInt32)(10)
const CURLFORM_BUFFER = (UInt32)(11)
const CURLFORM_BUFFERPTR = (UInt32)(12)
const CURLFORM_BUFFERLENGTH = (UInt32)(13)
const CURLFORM_CONTENTTYPE = (UInt32)(14)
const CURLFORM_CONTENTHEADER = (UInt32)(15)
const CURLFORM_FILENAME = (UInt32)(16)
const CURLFORM_END = (UInt32)(17)
const CURLFORM_OBSOLETE2 = (UInt32)(18)
const CURLFORM_STREAM = (UInt32)(19)
const CURLFORM_CONTENTLEN = (UInt32)(20)
const CURLFORM_LASTENTRY = (UInt32)(21)
# end enum CURLformoption

mutable struct curl_forms
    option::CURLformoption
    value::Ptr{UInt8}
end

# begin enum CURLFORMcode
const CURLFORMcode = UInt32
const CURL_FORMADD_OK = (UInt32)(0)
const CURL_FORMADD_MEMORY = (UInt32)(1)
const CURL_FORMADD_OPTION_TWICE = (UInt32)(2)
const CURL_FORMADD_NULL = (UInt32)(3)
const CURL_FORMADD_UNKNOWN_OPTION = (UInt32)(4)
const CURL_FORMADD_INCOMPLETE = (UInt32)(5)
const CURL_FORMADD_ILLEGAL_ARRAY = (UInt32)(6)
const CURL_FORMADD_DISABLED = (UInt32)(7)
const CURL_FORMADD_LAST = (UInt32)(8)
# end enum CURLFORMcode

const curl_formget_callback = Ptr{Cvoid}

mutable struct curl_slist
    data::Ptr{UInt8}
    next::Ptr{Cvoid}
end

const curl_ssl_backend = Cvoid

# begin enum CURLsslset
const CURLsslset = UInt32
const CURLSSLSET_OK = (UInt32)(0)
const CURLSSLSET_UNKNOWN_BACKEND = (UInt32)(1)
const CURLSSLSET_TOO_LATE = (UInt32)(2)
const CURLSSLSET_NO_BACKENDS = (UInt32)(3)
# end enum CURLsslset

mutable struct curl_certinfo
    num_of_certs::Cint
    certinfo::Ptr{Ptr{Cvoid}}
end

mutable struct curl_tlssessioninfo
    backend::curl_sslbackend
    internals::Ptr{Cvoid}
end

const CURLINFO_STRING = 0x00100000
const CURLINFO_LONG = 0x00200000
const CURLINFO_DOUBLE = 0x00300000
const CURLINFO_SLIST = 0x00400000
const CURLINFO_PTR = 0x00400000
const CURLINFO_SOCKET = 0x00500000
const CURLINFO_OFF_T = 0x00600000
const CURLINFO_MASK = 0x000fffff
const CURLINFO_TYPEMASK = 0x00f00000

# begin enum CURLINFO
const CURLINFO = UInt32
const CURLINFO_NONE = (UInt32)(0)
const CURLINFO_EFFECTIVE_URL = (UInt32)(1048577)
const CURLINFO_RESPONSE_CODE = (UInt32)(2097154)
const CURLINFO_TOTAL_TIME = (UInt32)(3145731)
const CURLINFO_NAMELOOKUP_TIME = (UInt32)(3145732)
const CURLINFO_CONNECT_TIME = (UInt32)(3145733)
const CURLINFO_PRETRANSFER_TIME = (UInt32)(3145734)
const CURLINFO_SIZE_UPLOAD = (UInt32)(3145735)
const CURLINFO_SIZE_UPLOAD_T = (UInt32)(6291463)
const CURLINFO_SIZE_DOWNLOAD = (UInt32)(3145736)
const CURLINFO_SIZE_DOWNLOAD_T = (UInt32)(6291464)
const CURLINFO_SPEED_DOWNLOAD = (UInt32)(3145737)
const CURLINFO_SPEED_DOWNLOAD_T = (UInt32)(6291465)
const CURLINFO_SPEED_UPLOAD = (UInt32)(3145738)
const CURLINFO_SPEED_UPLOAD_T = (UInt32)(6291466)
const CURLINFO_HEADER_SIZE = (UInt32)(2097163)
const CURLINFO_REQUEST_SIZE = (UInt32)(2097164)
const CURLINFO_SSL_VERIFYRESULT = (UInt32)(2097165)
const CURLINFO_FILETIME = (UInt32)(2097166)
const CURLINFO_FILETIME_T = (UInt32)(6291470)
const CURLINFO_CONTENT_LENGTH_DOWNLOAD = (UInt32)(3145743)
const CURLINFO_CONTENT_LENGTH_DOWNLOAD_T = (UInt32)(6291471)
const CURLINFO_CONTENT_LENGTH_UPLOAD = (UInt32)(3145744)
const CURLINFO_CONTENT_LENGTH_UPLOAD_T = (UInt32)(6291472)
const CURLINFO_STARTTRANSFER_TIME = (UInt32)(3145745)
const CURLINFO_CONTENT_TYPE = (UInt32)(1048594)
const CURLINFO_REDIRECT_TIME = (UInt32)(3145747)
const CURLINFO_REDIRECT_COUNT = (UInt32)(2097172)
const CURLINFO_PRIVATE = (UInt32)(1048597)
const CURLINFO_HTTP_CONNECTCODE = (UInt32)(2097174)
const CURLINFO_HTTPAUTH_AVAIL = (UInt32)(2097175)
const CURLINFO_PROXYAUTH_AVAIL = (UInt32)(2097176)
const CURLINFO_OS_ERRNO = (UInt32)(2097177)
const CURLINFO_NUM_CONNECTS = (UInt32)(2097178)
const CURLINFO_SSL_ENGINES = (UInt32)(4194331)
const CURLINFO_COOKIELIST = (UInt32)(4194332)
const CURLINFO_LASTSOCKET = (UInt32)(2097181)
const CURLINFO_FTP_ENTRY_PATH = (UInt32)(1048606)
const CURLINFO_REDIRECT_URL = (UInt32)(1048607)
const CURLINFO_PRIMARY_IP = (UInt32)(1048608)
const CURLINFO_APPCONNECT_TIME = (UInt32)(3145761)
const CURLINFO_CERTINFO = (UInt32)(4194338)
const CURLINFO_CONDITION_UNMET = (UInt32)(2097187)
const CURLINFO_RTSP_SESSION_ID = (UInt32)(1048612)
const CURLINFO_RTSP_CLIENT_CSEQ = (UInt32)(2097189)
const CURLINFO_RTSP_SERVER_CSEQ = (UInt32)(2097190)
const CURLINFO_RTSP_CSEQ_RECV = (UInt32)(2097191)
const CURLINFO_PRIMARY_PORT = (UInt32)(2097192)
const CURLINFO_LOCAL_IP = (UInt32)(1048617)
const CURLINFO_LOCAL_PORT = (UInt32)(2097194)
const CURLINFO_TLS_SESSION = (UInt32)(4194347)
const CURLINFO_ACTIVESOCKET = (UInt32)(5242924)
const CURLINFO_TLS_SSL_PTR = (UInt32)(4194349)
const CURLINFO_HTTP_VERSION = (UInt32)(2097198)
const CURLINFO_PROXY_SSL_VERIFYRESULT = (UInt32)(2097199)
const CURLINFO_PROTOCOL = (UInt32)(2097200)
const CURLINFO_SCHEME = (UInt32)(1048625)
const CURLINFO_TOTAL_TIME_T = (UInt32)(6291506)
const CURLINFO_NAMELOOKUP_TIME_T = (UInt32)(6291507)
const CURLINFO_CONNECT_TIME_T = (UInt32)(6291508)
const CURLINFO_PRETRANSFER_TIME_T = (UInt32)(6291509)
const CURLINFO_STARTTRANSFER_TIME_T = (UInt32)(6291510)
const CURLINFO_REDIRECT_TIME_T = (UInt32)(6291511)
const CURLINFO_APPCONNECT_TIME_T = (UInt32)(6291512)
const CURLINFO_LASTONE = (UInt32)(56)
# end enum CURLINFO

const CURLINFO_HTTP_CODE = CURLINFO_RESPONSE_CODE

# begin enum curl_closepolicy
const curl_closepolicy = UInt32
const CURLCLOSEPOLICY_NONE = (UInt32)(0)
const CURLCLOSEPOLICY_OLDEST = (UInt32)(1)
const CURLCLOSEPOLICY_LEAST_RECENTLY_USED = (UInt32)(2)
const CURLCLOSEPOLICY_LEAST_TRAFFIC = (UInt32)(3)
const CURLCLOSEPOLICY_SLOWEST = (UInt32)(4)
const CURLCLOSEPOLICY_CALLBACK = (UInt32)(5)
const CURLCLOSEPOLICY_LAST = (UInt32)(6)
# end enum curl_closepolicy

const CURL_GLOBAL_SSL = 1 << 0
const CURL_GLOBAL_WIN32 = 1 << 1
const CURL_GLOBAL_ALL = CURL_GLOBAL_SSL | CURL_GLOBAL_WIN32
const CURL_GLOBAL_NOTHING = 0
const CURL_GLOBAL_DEFAULT = CURL_GLOBAL_ALL
const CURL_GLOBAL_ACK_EINTR = 1 << 2

# begin enum curl_lock_data
const curl_lock_data = UInt32
const CURL_LOCK_DATA_NONE = (UInt32)(0)
const CURL_LOCK_DATA_SHARE = (UInt32)(1)
const CURL_LOCK_DATA_COOKIE = (UInt32)(2)
const CURL_LOCK_DATA_DNS = (UInt32)(3)
const CURL_LOCK_DATA_SSL_SESSION = (UInt32)(4)
const CURL_LOCK_DATA_CONNECT = (UInt32)(5)
const CURL_LOCK_DATA_PSL = (UInt32)(6)
const CURL_LOCK_DATA_LAST = (UInt32)(7)
# end enum curl_lock_data

# begin enum curl_lock_access
const curl_lock_access = UInt32
const CURL_LOCK_ACCESS_NONE = (UInt32)(0)
const CURL_LOCK_ACCESS_SHARED = (UInt32)(1)
const CURL_LOCK_ACCESS_SINGLE = (UInt32)(2)
const CURL_LOCK_ACCESS_LAST = (UInt32)(3)
# end enum curl_lock_access

const curl_lock_function = Ptr{Cvoid}
const curl_unlock_function = Ptr{Cvoid}

# begin enum CURLSHcode
const CURLSHcode = UInt32
const CURLSHE_OK = (UInt32)(0)
const CURLSHE_BAD_OPTION = (UInt32)(1)
const CURLSHE_IN_USE = (UInt32)(2)
const CURLSHE_INVALID = (UInt32)(3)
const CURLSHE_NOMEM = (UInt32)(4)
const CURLSHE_NOT_BUILT_IN = (UInt32)(5)
const CURLSHE_LAST = (UInt32)(6)
# end enum CURLSHcode

# begin enum CURLSHoption
const CURLSHoption = UInt32
const CURLSHOPT_NONE = (UInt32)(0)
const CURLSHOPT_SHARE = (UInt32)(1)
const CURLSHOPT_UNSHARE = (UInt32)(2)
const CURLSHOPT_LOCKFUNC = (UInt32)(3)
const CURLSHOPT_UNLOCKFUNC = (UInt32)(4)
const CURLSHOPT_USERDATA = (UInt32)(5)
const CURLSHOPT_LAST = (UInt32)(6)
# end enum CURLSHoption

# begin enum CURLversion
const CURLversion = UInt32
const CURLVERSION_FIRST = (UInt32)(0)
const CURLVERSION_SECOND = (UInt32)(1)
const CURLVERSION_THIRD = (UInt32)(2)
const CURLVERSION_FOURTH = (UInt32)(3)
const CURLVERSION_FIFTH = (UInt32)(4)
const CURLVERSION_LAST = (UInt32)(5)
# end enum CURLversion

const CURLVERSION_NOW = CURLVERSION_FIFTH

mutable struct curl_version_info_data
    age::CURLversion
    version::Ptr{UInt8}
    version_num::UInt32
    host::Ptr{UInt8}
    features::Int32
    ssl_version::Ptr{UInt8}
    ssl_version_num::Int32
    libz_version::Ptr{UInt8}
    protocols::Ptr{Ptr{UInt8}}
    ares::Ptr{UInt8}
    ares_num::Int32
    libidn::Ptr{UInt8}
    iconv_ver_num::Int32
    libssh_version::Ptr{UInt8}
    brotli_ver_num::UInt32
    brotli_version::Ptr{UInt8}
end

const CURL_VERSION_IPV6 = 1 << 0
const CURL_VERSION_KERBEROS4 = 1 << 1
const CURL_VERSION_SSL = 1 << 2
const CURL_VERSION_LIBZ = 1 << 3
const CURL_VERSION_NTLM = 1 << 4
const CURL_VERSION_GSSNEGOTIATE = 1 << 5
const CURL_VERSION_DEBUG = 1 << 6
const CURL_VERSION_ASYNCHDNS = 1 << 7
const CURL_VERSION_SPNEGO = 1 << 8
const CURL_VERSION_LARGEFILE = 1 << 9
const CURL_VERSION_IDN = 1 << 10
const CURL_VERSION_SSPI = 1 << 11
const CURL_VERSION_CONV = 1 << 12
const CURL_VERSION_CURLDEBUG = 1 << 13
const CURL_VERSION_TLSAUTH_SRP = 1 << 14
const CURL_VERSION_NTLM_WB = 1 << 15
const CURL_VERSION_HTTP2 = 1 << 16
const CURL_VERSION_GSSAPI = 1 << 17
const CURL_VERSION_KERBEROS5 = 1 << 18
const CURL_VERSION_UNIX_SOCKETS = 1 << 19
const CURL_VERSION_PSL = 1 << 20
const CURL_VERSION_HTTPS_PROXY = 1 << 21
const CURL_VERSION_MULTI_SSL = 1 << 22
const CURL_VERSION_BROTLI = 1 << 23
const CURLPAUSE_RECV = 1 << 0
const CURLPAUSE_RECV_CONT = 0
const CURLPAUSE_SEND = 1 << 2
const CURLPAUSE_SEND_CONT = 0
const CURLPAUSE_ALL = CURLPAUSE_RECV | CURLPAUSE_SEND
const CURLPAUSE_CONT = CURLPAUSE_RECV_CONT | CURLPAUSE_SEND_CONT

const CURLE_OBSOLETE16 = CURLE_HTTP2
const CURLE_OBSOLETE10 = CURLE_FTP_ACCEPT_FAILED
const CURLE_OBSOLETE12 = CURLE_FTP_ACCEPT_TIMEOUT

const CURLOPT_ENCODING = CURLOPT_ACCEPT_ENCODING
const CURLE_FTP_WEIRD_SERVER_REPLY = CURLE_WEIRD_SERVER_REPLY
const CURLE_UNKNOWN_TELNET_OPTION = CURLE_UNKNOWN_OPTION
const CURLE_SSL_PEER_CERTIFICATE = CURLE_PEER_FAILED_VERIFICATION
const CURLE_OBSOLETE = CURLE_OBSOLETE50
const CURLE_BAD_PASSWORD_ENTERED = CURLE_OBSOLETE46
const CURLE_BAD_CALLING_ORDER = CURLE_OBSOLETE44
const CURLE_FTP_USER_PASSWORD_INCORRECT = CURLE_OBSOLETE10
const CURLE_FTP_CANT_RECONNECT = CURLE_OBSOLETE16
const CURLE_FTP_COULDNT_GET_SIZE = CURLE_OBSOLETE32
const CURLE_FTP_COULDNT_SET_ASCII = CURLE_OBSOLETE29
const CURLE_FTP_WEIRD_USER_REPLY = CURLE_OBSOLETE12
const CURLE_FTP_WRITE_ERROR = CURLE_OBSOLETE20
const CURLE_LIBRARY_NOT_FOUND = CURLE_OBSOLETE40
const CURLE_MALFORMAT_USER = CURLE_OBSOLETE24
const CURLE_SHARE_IN_USE = CURLE_OBSOLETE57
const CURLE_URL_MALFORMAT_USER = CURLE_NOT_BUILT_IN
const CURLE_FTP_ACCESS_DENIED = CURLE_REMOTE_ACCESS_DENIED
const CURLE_FTP_COULDNT_SET_BINARY = CURLE_FTP_COULDNT_SET_TYPE
const CURLE_FTP_QUOTE_ERROR = CURLE_QUOTE_ERROR
const CURLE_TFTP_DISKFULL = CURLE_REMOTE_DISK_FULL
const CURLE_TFTP_EXISTS = CURLE_REMOTE_FILE_EXISTS
const CURLE_HTTP_RANGE_ERROR = CURLE_RANGE_ERROR
const CURLE_FTP_SSL_FAILED = CURLE_USE_SSL_FAILED
const CURLE_OPERATION_TIMEOUTED = CURLE_OPERATION_TIMEDOUT
const CURLE_HTTP_NOT_FOUND = CURLE_HTTP_RETURNED_ERROR
const CURLE_HTTP_PORT_FAILED = CURLE_INTERFACE_FAILED
const CURLE_FTP_COULDNT_STOR_FILE = CURLE_UPLOAD_FAILED
const CURLE_FTP_PARTIAL_FILE = CURLE_PARTIAL_FILE
const CURLE_FTP_BAD_DOWNLOAD_RESUME = CURLE_BAD_DOWNLOAD_RESUME
const CURLE_ALREADY_COMPLETE = 99999
const CURLOPT_FILE = CURLOPT_WRITEDATA
const CURLOPT_INFILE = CURLOPT_READDATA
const CURLOPT_WRITEHEADER = CURLOPT_HEADERDATA
const CURLOPT_WRITEINFO = CURLOPT_OBSOLETE40
const CURLOPT_CLOSEPOLICY = CURLOPT_OBSOLETE72

# multi.h

const CURLM = Cvoid

# begin enum CURLMcode
const CURLMcode = Cint
const CURLM_CALL_MULTI_PERFORM = (Int32)(-1)
const CURLM_OK = (Int32)(0)
const CURLM_BAD_HANDLE = (Int32)(1)
const CURLM_BAD_EASY_HANDLE = (Int32)(2)
const CURLM_OUT_OF_MEMORY = (Int32)(3)
const CURLM_INTERNAL_ERROR = (Int32)(4)
const CURLM_BAD_SOCKET = (Int32)(5)
const CURLM_UNKNOWN_OPTION = (Int32)(6)
const CURLM_ADDED_ALREADY = (Int32)(7)
const CURLM_RECURSIVE_API_CALL = (Int32)(8)
const CURLM_LAST = (Int32)(9)
# end enum CURLMcode

const CURLM_CALL_MULTI_SOCKET = CURLM_CALL_MULTI_PERFORM
const CURLPIPE_NOTHING = Clong(0)
const CURLPIPE_HTTP1 = Clong(1)
const CURLPIPE_MULTIPLEX = Clong(2)

# begin enum CURLMSG
const CURLMSG = UInt32
const CURLMSG_NONE = (UInt32)(0)
const CURLMSG_DONE = (UInt32)(1)
const CURLMSG_LAST = (UInt32)(2)
# end enum CURLMSG

mutable struct CURLMsg
    msg::CURLMSG
    easy_handle::Ptr{CURL}
    data::Cvoid
end

const CURL_WAIT_POLLIN = 0x0001
const CURL_WAIT_POLLPRI = 0x0002
const CURL_WAIT_POLLOUT = 0x0004

mutable struct curl_waitfd
    fd::curl_socket_t
    events::Int16
    revents::Int16
end

const CURL_POLL_NONE = 0
const CURL_POLL_IN = 1
const CURL_POLL_OUT = 2
const CURL_POLL_INOUT = 3
const CURL_POLL_REMOVE = 4
const CURL_SOCKET_TIMEOUT = CURL_SOCKET_BAD
const CURL_CSELECT_IN = 0x01
const CURL_CSELECT_OUT = 0x02
const CURL_CSELECT_ERR = 0x04

const curl_socket_callback = Ptr{Cvoid}
const curl_multi_timer_callback = Ptr{Cvoid}

# begin enum CURLMoption
const CURLMoption = UInt32
const CURLMOPT_SOCKETFUNCTION = (UInt32)(20001)
const CURLMOPT_SOCKETDATA = (UInt32)(10002)
const CURLMOPT_PIPELINING = (UInt32)(3)
const CURLMOPT_TIMERFUNCTION = (UInt32)(20004)
const CURLMOPT_TIMERDATA = (UInt32)(10005)
const CURLMOPT_MAXCONNECTS = (UInt32)(6)
const CURLMOPT_MAX_HOST_CONNECTIONS = (UInt32)(7)
const CURLMOPT_MAX_PIPELINE_LENGTH = (UInt32)(8)
const CURLMOPT_CONTENT_LENGTH_PENALTY_SIZE = (UInt32)(30009)
const CURLMOPT_CHUNK_LENGTH_PENALTY_SIZE = (UInt32)(30010)
const CURLMOPT_PIPELINING_SITE_BL = (UInt32)(10011)
const CURLMOPT_PIPELINING_SERVER_BL = (UInt32)(10012)
const CURLMOPT_MAX_TOTAL_CONNECTIONS = (UInt32)(13)
const CURLMOPT_PUSHFUNCTION = (UInt32)(20014)
const CURLMOPT_PUSHDATA = (UInt32)(10015)
const CURLMOPT_LASTENTRY = (UInt32)(10016)
# end enum CURLMoption

const CURL_PUSH_OK = 0
const CURL_PUSH_DENY = 1

struct curl_pushheaders end

const curl_push_callback = Ptr{Cvoid}
t   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LibCURL/src/lC_curl_h.jl{$      # Julia wrapper for header: /usr/local/opt/curl/include/curl/curl.h
# Automatically generated using Clang.jl wrap_c, version 0.0.0


function curl_strequal(s1, s2)
    ccall((:curl_strequal, libcurl), Cint, (Ptr{UInt8}, Ptr{UInt8}), s1, s2)
end

function curl_strnequal(s1, s2, n)
    ccall((:curl_strnequal, libcurl), Cint, (Ptr{UInt8}, Ptr{UInt8}, Csize_t), s1, s2, n)
end

function curl_mime_init(easy)
    ccall((:curl_mime_init, libcurl), Ptr{curl_mime}, (Ptr{CURL},), easy)
end

function curl_mime_free(mime)
    ccall((:curl_mime_free, libcurl), Cvoid, (Ptr{curl_mime},), mime)
end

function curl_mime_addpart(mime)
    ccall((:curl_mime_addpart, libcurl), Ptr{curl_mimepart}, (Ptr{curl_mime},), mime)
end

function curl_mime_name(part, name)
    ccall((:curl_mime_name, libcurl), CURLcode, (Ptr{curl_mimepart}, Ptr{UInt8}), part, name)
end

function curl_mime_filename(part, filename)
    ccall((:curl_mime_filename, libcurl), CURLcode, (Ptr{curl_mimepart}, Ptr{UInt8}), part, filename)
end

function curl_mime_type(part, mimetype)
    ccall((:curl_mime_type, libcurl), CURLcode, (Ptr{curl_mimepart}, Ptr{UInt8}), part, mimetype)
end

function curl_mime_encoder(part, encoding)
    ccall((:curl_mime_encoder, libcurl), CURLcode, (Ptr{curl_mimepart}, Ptr{UInt8}), part, encoding)
end

function curl_mime_data(part, data, datasize)
    ccall((:curl_mime_data, libcurl), CURLcode, (Ptr{curl_mimepart}, Ptr{UInt8}, Csize_t), part, data, datasize)
end

function curl_mime_filedata(part, filename)
    ccall((:curl_mime_filedata, libcurl), CURLcode, (Ptr{curl_mimepart}, Ptr{UInt8}), part, filename)
end

function curl_mime_data_cb(part, datasize, readfunc, seekfunc, freefunc, arg)
    ccall((:curl_mime_data_cb, libcurl), CURLcode, (Ptr{curl_mimepart}, curl_off_t, curl_read_callback, curl_seek_callback, curl_free_callback, Ptr{Cvoid}), part, datasize, readfunc, seekfunc, freefunc, arg)
end

function curl_mime_subparts(part, subparts)
    ccall((:curl_mime_subparts, libcurl), CURLcode, (Ptr{curl_mimepart}, Ptr{curl_mime}), part, subparts)
end

function curl_mime_headers(part, headers, take_ownership)
    ccall((:curl_mime_headers, libcurl), CURLcode, (Ptr{curl_mimepart}, Ptr{Cvoid}, Cint), part, headers, take_ownership)
end

function curl_formget(form, arg, append)
    ccall((:curl_formget, libcurl), Cint, (Ptr{Cvoid}, Ptr{Cvoid}, curl_formget_callback), form, arg, append)
end

function curl_formfree(form)
    ccall((:curl_formfree, libcurl), Cvoid, (Ptr{Cvoid},), form)
end

function curl_getenv(variable)
    ccall((:curl_getenv, libcurl), Ptr{UInt8}, (Ptr{UInt8},), variable)
end

function curl_version()
    ccall((:curl_version, libcurl), Ptr{UInt8}, ())
end

function curl_easy_escape(handle, string, length)
    ccall((:curl_easy_escape, libcurl), Ptr{UInt8}, (Ptr{CURL}, Ptr{UInt8}, Cint), handle, string, length)
end

function curl_escape(string, length)
    ccall((:curl_escape, libcurl), Ptr{UInt8}, (Ptr{UInt8}, Cint), string, length)
end

function curl_easy_unescape(handle, string, length, outlength)
    ccall((:curl_easy_unescape, libcurl), Ptr{UInt8}, (Ptr{CURL}, Ptr{UInt8}, Cint, Ptr{Cint}), handle, string, length, outlength)
end

function curl_unescape(string, length)
    ccall((:curl_unescape, libcurl), Ptr{UInt8}, (Ptr{UInt8}, Cint), string, length)
end

function curl_free(p)
    ccall((:curl_free, libcurl), Cvoid, (Ptr{Cvoid},), p)
end

function curl_global_init(flags)
    ccall((:curl_global_init, libcurl), CURLcode, (Clong,), flags)
end

function curl_global_init_mem(flags, m, f, r, s, c)
    ccall((:curl_global_init_mem, libcurl), CURLcode, (Clong, curl_malloc_callback, curl_free_callback, curl_realloc_callback, curl_strdup_callback, curl_calloc_callback), flags, m, f, r, s, c)
end

function curl_global_cleanup()
    ccall((:curl_global_cleanup, libcurl), Cvoid, ())
end

function curl_global_sslset(id, name, avail)
    ccall((:curl_global_sslset, libcurl), CURLsslset, (curl_sslbackend, Ptr{UInt8}, Ptr{Ptr{Ptr{curl_ssl_backend}}}), id, name, avail)
end

function curl_slist_append(arg1, arg2)
    ccall((:curl_slist_append, libcurl), Ptr{Cvoid}, (Ptr{Cvoid}, Ptr{UInt8}), arg1, arg2)
end

function curl_slist_free_all(arg1)
    ccall((:curl_slist_free_all, libcurl), Cvoid, (Ptr{Cvoid},), arg1)
end

function curl_getdate(p, unused)
    ccall((:curl_getdate, libcurl), time_t, (Ptr{UInt8}, Ptr{time_t}), p, unused)
end

function curl_share_init()
    ccall((:curl_share_init, libcurl), Ptr{CURLSH}, ())
end

function curl_share_setopt(handle, opt, param)
    ccall((:curl_share_setopt, libcurl), CURLSHcode, (Ptr{CURLSH}, CURLSHoption, Any...), handle, opt, param)
end

function curl_share_cleanup(arg1)
    ccall((:curl_share_cleanup, libcurl), CURLSHcode, (Ptr{CURLSH},), arg1)
end

function curl_version_info(arg1)
    ccall((:curl_version_info, libcurl), Ptr{curl_version_info_data}, (CURLversion,), arg1)
end

function curl_easy_strerror(arg1)
    ccall((:curl_easy_strerror, libcurl), Ptr{UInt8}, (CURLcode,), arg1)
end

function curl_share_strerror(arg1)
    ccall((:curl_share_strerror, libcurl), Ptr{UInt8}, (CURLSHcode,), arg1)
end

function curl_easy_pause(handle, bitmask)
    ccall((:curl_easy_pause, libcurl), CURLcode, (Ptr{CURL}, Cint), handle, bitmask)
end

function curl_easy_init()
    ccall((:curl_easy_init, libcurl), Ptr{CURL}, ())
end

function curl_easy_setopt(handle, opt, param)
    ccall((:curl_easy_setopt, libcurl), CURLcode, (Ptr{CURL}, CURLoption, Any...), handle, opt, param)
end

function curl_easy_perform(curl)
    ccall((:curl_easy_perform, libcurl), CURLcode, (Ptr{CURL},), curl)
end

function curl_easy_cleanup(curl)
    ccall((:curl_easy_cleanup, libcurl), Cvoid, (Ptr{CURL},), curl)
end

function curl_easy_getinfo(handle, info, arg)
    ccall((:curl_easy_getinfo, libcurl), CURLcode, (Ptr{CURL}, CURLINFO, Any...), handle, info, arg)
end

function curl_easy_duphandle(curl)
    ccall((:curl_easy_duphandle, libcurl), Ptr{CURL}, (Ptr{CURL},), curl)
end

function curl_easy_reset(curl)
    ccall((:curl_easy_reset, libcurl), Cvoid, (Ptr{CURL},), curl)
end

function curl_easy_recv(curl, buffer, buflen, n)
    ccall((:curl_easy_recv, libcurl), CURLcode, (Ptr{CURL}, Ptr{Cvoid}, Csize_t, Ptr{Csize_t}), curl, buffer, buflen, n)
end

function curl_easy_send(curl, buffer, buflen, n)
    ccall((:curl_easy_send, libcurl), CURLcode, (Ptr{CURL}, Ptr{Cvoid}, Csize_t, Ptr{Csize_t}), curl, buffer, buflen, n)
end

function curl_multi_init()
    ccall((:curl_multi_init, libcurl), Ptr{CURLM}, ())
end

function curl_multi_add_handle(multi_handle, curl_handle)
    ccall((:curl_multi_add_handle, libcurl), CURLMcode, (Ptr{CURLM}, Ptr{CURL}), multi_handle, curl_handle)
end

function curl_multi_remove_handle(multi_handle, curl_handle)
    ccall((:curl_multi_remove_handle, libcurl), CURLMcode, (Ptr{CURLM}, Ptr{CURL}), multi_handle, curl_handle)
end

function curl_multi_fdset(multi_handle, read_fd_set, write_fd_set, exc_fd_set, max_fd)
    ccall((:curl_multi_fdset, libcurl), CURLMcode, (Ptr{CURLM}, Ptr{fd_set}, Ptr{fd_set}, Ptr{fd_set}, Ptr{Cint}), multi_handle, read_fd_set, write_fd_set, exc_fd_set, max_fd)
end

function curl_multi_wait(multi_handle, extra_fds, extra_nfds, timeout_ms, ret)
    ccall((:curl_multi_wait, libcurl), CURLMcode, (Ptr{CURLM}, Ptr{Cvoid}, UInt32, Cint, Ptr{Cint}), multi_handle, extra_fds, extra_nfds, timeout_ms, ret)
end

function curl_multi_perform(multi_handle, running_handles)
    ccall((:curl_multi_perform, libcurl), CURLMcode, (Ptr{CURLM}, Ptr{Cint}), multi_handle, running_handles)
end

function curl_multi_cleanup(multi_handle)
    ccall((:curl_multi_cleanup, libcurl), CURLMcode, (Ptr{CURLM},), multi_handle)
end

function curl_multi_info_read(multi_handle, msgs_in_queue)
    ccall((:curl_multi_info_read, libcurl), Ptr{CURLMsg}, (Ptr{CURLM}, Ptr{Cint}), multi_handle, msgs_in_queue)
end

function curl_multi_strerror(arg1)
    ccall((:curl_multi_strerror, libcurl), Ptr{UInt8}, (CURLMcode,), arg1)
end

function curl_multi_socket(multi_handle, s, running_handles)
    ccall((:curl_multi_socket, libcurl), CURLMcode, (Ptr{CURLM}, curl_socket_t, Ptr{Cint}), multi_handle, s, running_handles)
end

function curl_multi_socket_action(multi_handle, s, ev_bitmask, running_handles)
    ccall((:curl_multi_socket_action, libcurl), CURLMcode, (Ptr{CURLM}, curl_socket_t, Cint, Ptr{Cint}), multi_handle, s, ev_bitmask, running_handles)
end

function curl_multi_socket_all(multi_handle, running_handles)
    ccall((:curl_multi_socket_all, libcurl), CURLMcode, (Ptr{CURLM}, Ptr{Cint}), multi_handle, running_handles)
end

function curl_multi_timeout(multi_handle, milliseconds)
    ccall((:curl_multi_timeout, libcurl), CURLMcode, (Ptr{CURLM}, Ptr{Clong}), multi_handle, milliseconds)
end

function curl_multi_setopt(multi_handle, opt, param)
    ccall((:curl_multi_setopt, libcurl), CURLMcode, (Ptr{CURLM}, CURLMoption, Any...), multi_handle, opt, param)
end

function curl_multi_assign(multi_handle, sockfd, sockp)
    ccall((:curl_multi_assign, libcurl), CURLMcode, (Ptr{CURLM}, curl_socket_t, Ptr{Cvoid}), multi_handle, sockfd, sockp)
end

function curl_pushheader_bynum(h, num)
    ccall((:curl_pushheader_bynum, libcurl), Ptr{UInt8}, (Ptr{Cvoid}, Csize_t), h, num)
end

function curl_pushheader_byname(h, name)
    ccall((:curl_pushheader_byname, libcurl), Ptr{UInt8}, (Ptr{Cvoid}, Ptr{UInt8}), h, name)
end
w   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LibCURL/src/lC_defines_h.jl3      #   Generating #define constants
const CURL_TYPEOF_CURL_OFF_T             = Clong
const CURL_FORMAT_CURL_OFF_T             = "ld"
const CURL_FORMAT_CURL_OFF_TU            = "lu"
const CURL_SUFFIX_CURL_OFF_T             = Clong
const CURL_SUFFIX_CURL_OFF_TU            = Culong
const CURL_TYPEOF_CURL_SOCKLEN_T         = socklen_t
const CURL_PULL_SYS_TYPES_H              = 1
const CURL_PULL_SYS_SOCKET_H             = 1
const CURL_SOCKET_BAD                    = -1
const CURLSSLBACKEND_LIBRESSL            = CURLSSLBACKEND_OPENSSL
const CURLSSLBACKEND_BORINGSSL           = CURLSSLBACKEND_OPENSSL
const CURLSSLBACKEND_CYASSL              = CURLSSLBACKEND_WOLFSSL
const CURL_HTTPPOST_FILENAME             = (1<<0)
const CURL_HTTPPOST_READFILE             = (1<<1)
const CURL_HTTPPOST_PTRNAME              = (1<<2)
const CURL_HTTPPOST_PTRCONTENTS          = (1<<3)
const CURL_HTTPPOST_BUFFER               = (1<<4)
const CURL_HTTPPOST_PTRBUFFER            = (1<<5)
const CURL_HTTPPOST_CALLBACK             = (1<<6)
const CURL_HTTPPOST_LARGE                = (1<<7)
const CURL_MAX_READ_SIZE                 = 524288
const CURL_MAX_WRITE_SIZE                = 16384
const CURL_MAX_HTTP_HEADER               = (100*1024)
const CURL_WRITEFUNC_PAUSE               = 0x10000001
const CURLFINFOFLAG_KNOWN_FILENAME       = (1<<0)
const CURLFINFOFLAG_KNOWN_FILETYPE       = (1<<1)
const CURLFINFOFLAG_KNOWN_TIME           = (1<<2)
const CURLFINFOFLAG_KNOWN_PERM           = (1<<3)
const CURLFINFOFLAG_KNOWN_UID            = (1<<4)
const CURLFINFOFLAG_KNOWN_GID            = (1<<5)
const CURLFINFOFLAG_KNOWN_SIZE           = (1<<6)
const CURLFINFOFLAG_KNOWN_HLINKCOUNT     = (1<<7)
const CURL_CHUNK_BGN_FUNC_OK             = 0
const CURL_CHUNK_BGN_FUNC_FAIL           = 1
const CURL_CHUNK_BGN_FUNC_SKIP           = 2
const CURL_CHUNK_END_FUNC_OK             = 0
const CURL_CHUNK_END_FUNC_FAIL           = 1
const CURL_FNMATCHFUNC_MATCH             = 0
const CURL_FNMATCHFUNC_NOMATCH           = 1
const CURL_FNMATCHFUNC_FAIL              = 2
const CURL_SEEKFUNC_OK                   = 0
const CURL_SEEKFUNC_FAIL                 = 1
const CURL_SEEKFUNC_CANTSEEK             = 2
const CURL_READFUNC_ABORT                = 0x10000000
const CURL_READFUNC_PAUSE                = 0x10000001
const CURL_SOCKOPT_OK                    = 0
const CURL_SOCKOPT_ERROR                 = 1
const CURL_SOCKOPT_ALREADY_CONNECTED     = 2
const CURLE_OBSOLETE16                   = CURLE_HTTP2
const CURLE_OBSOLETE10                   = CURLE_FTP_ACCEPT_FAILED
const CURLE_OBSOLETE12                   = CURLE_FTP_ACCEPT_TIMEOUT
const CURLOPT_ENCODING                   = CURLOPT_ACCEPT_ENCODING
const CURLE_FTP_WEIRD_SERVER_REPLY       = CURLE_WEIRD_SERVER_REPLY
const CURLE_UNKNOWN_TELNET_OPTION        = CURLE_UNKNOWN_OPTION
const CURLE_SSL_PEER_CERTIFICATE         = CURLE_PEER_FAILED_VERIFICATION
const CURLE_OBSOLETE                     = CURLE_OBSOLETE50
const CURLE_BAD_PASSWORD_ENTERED         = CURLE_OBSOLETE46
const CURLE_BAD_CALLING_ORDER            = CURLE_OBSOLETE44
const CURLE_FTP_USER_PASSWORD_INCORRECT  = CURLE_OBSOLETE10
const CURLE_FTP_CANT_RECONNECT           = CURLE_OBSOLETE16
const CURLE_FTP_COULDNT_GET_SIZE         = CURLE_OBSOLETE32
const CURLE_FTP_COULDNT_SET_ASCII        = CURLE_OBSOLETE29
const CURLE_FTP_WEIRD_USER_REPLY         = CURLE_OBSOLETE12
const CURLE_FTP_WRITE_ERROR              = CURLE_OBSOLETE20
const CURLE_LIBRARY_NOT_FOUND            = CURLE_OBSOLETE40
const CURLE_MALFORMAT_USER               = CURLE_OBSOLETE24
const CURLE_SHARE_IN_USE                 = CURLE_OBSOLETE57
const CURLE_URL_MALFORMAT_USER           = CURLE_NOT_BUILT_IN
const CURLE_FTP_ACCESS_DENIED            = CURLE_REMOTE_ACCESS_DENIED
const CURLE_FTP_COULDNT_SET_BINARY       = CURLE_FTP_COULDNT_SET_TYPE
const CURLE_FTP_QUOTE_ERROR              = CURLE_QUOTE_ERROR
const CURLE_TFTP_DISKFULL                = CURLE_REMOTE_DISK_FULL
const CURLE_TFTP_EXISTS                  = CURLE_REMOTE_FILE_EXISTS
const CURLE_HTTP_RANGE_ERROR             = CURLE_RANGE_ERROR
const CURLE_FTP_SSL_FAILED               = CURLE_USE_SSL_FAILED
const CURLE_OPERATION_TIMEOUTED          = CURLE_OPERATION_TIMEDOUT
const CURLE_HTTP_NOT_FOUND               = CURLE_HTTP_RETURNED_ERROR
const CURLE_HTTP_PORT_FAILED             = CURLE_INTERFACE_FAILED
const CURLE_FTP_COULDNT_STOR_FILE        = CURLE_UPLOAD_FAILED
const CURLE_FTP_PARTIAL_FILE             = CURLE_PARTIAL_FILE
const CURLE_FTP_BAD_DOWNLOAD_RESUME      = CURLE_BAD_DOWNLOAD_RESUME
const CURLE_ALREADY_COMPLETE             = 99999
const CURLOPT_FILE                       = CURLOPT_WRITEDATA
const CURLOPT_INFILE                     = CURLOPT_READDATA
const CURLOPT_WRITEHEADER                = CURLOPT_HEADERDATA
const CURLOPT_WRITEINFO                  = CURLOPT_OBSOLETE40
const CURLOPT_CLOSEPOLICY                = CURLOPT_OBSOLETE72
const CURLAUTH_NONE                      = (0)
const CURLAUTH_BASIC                     = ((1)<<0)
const CURLAUTH_DIGEST                    = ((1)<<1)
const CURLAUTH_NEGOTIATE                 = ((1)<<2)
const CURLAUTH_GSSNEGOTIATE              = CURLAUTH_NEGOTIATE
const CURLAUTH_GSSAPI                    = CURLAUTH_NEGOTIATE
const CURLAUTH_NTLM                      = ((1)<<3)
const CURLAUTH_DIGEST_IE                 = ((1)<<4)
const CURLAUTH_NTLM_WB                   = ((1)<<5)
const CURLAUTH_BEARER                    = ((1)<<6)
const CURLAUTH_ONLY                      = ((1)<<31)
const CURLAUTH_ANY                       = (~CURLAUTH_DIGEST_IE)
const CURLAUTH_ANYSAFE                   = (~(CURLAUTH_BASIC|CURLAUTH_DIGEST_IE))
const CURLSSH_AUTH_ANY                   = ~0
const CURLSSH_AUTH_NONE                  = 0
const CURLSSH_AUTH_PUBLICKEY             = (1<<0)
const CURLSSH_AUTH_PASSWORD              = (1<<1)
const CURLSSH_AUTH_HOST                  = (1<<2)
const CURLSSH_AUTH_KEYBOARD              = (1<<3)
const CURLSSH_AUTH_AGENT                 = (1<<4)
const CURLSSH_AUTH_GSSAPI                = (1<<5)
const CURLSSH_AUTH_DEFAULT               = CURLSSH_AUTH_ANY
const CURLGSSAPI_DELEGATION_NONE         = 0
const CURLGSSAPI_DELEGATION_POLICY_FLAG  = (1<<0)
const CURLGSSAPI_DELEGATION_FLAG         = (1<<1)
const CURL_ERROR_SIZE                    = 256
const CURLSSLOPT_ALLOW_BEAST             = (1<<0)
const CURLSSLOPT_NO_REVOKE               = (1<<1)
const CURL_HET_DEFAULT                   = Clong(200)
const CURLFTPSSL_NONE                    = CURLUSESSL_NONE
const CURLFTPSSL_TRY                     = CURLUSESSL_TRY
const CURLFTPSSL_CONTROL                 = CURLUSESSL_CONTROL
const CURLFTPSSL_ALL                     = CURLUSESSL_ALL
const CURLFTPSSL_LAST                    = CURLUSESSL_LAST
const CURLHEADER_UNIFIED                 = 0
const CURLHEADER_SEPARATE                = (1<<0)
const CURLPROTO_HTTP                     = (1<<0)
const CURLPROTO_HTTPS                    = (1<<1)
const CURLPROTO_FTP                      = (1<<2)
const CURLPROTO_FTPS                     = (1<<3)
const CURLPROTO_SCP                      = (1<<4)
const CURLPROTO_SFTP                     = (1<<5)
const CURLPROTO_TELNET                   = (1<<6)
const CURLPROTO_LDAP                     = (1<<7)
const CURLPROTO_LDAPS                    = (1<<8)
const CURLPROTO_DICT                     = (1<<9)
const CURLPROTO_FILE                     = (1<<10)
const CURLPROTO_TFTP                     = (1<<11)
const CURLPROTO_IMAP                     = (1<<12)
const CURLPROTO_IMAPS                    = (1<<13)
const CURLPROTO_POP3                     = (1<<14)
const CURLPROTO_POP3S                    = (1<<15)
const CURLPROTO_SMTP                     = (1<<16)
const CURLPROTO_SMTPS                    = (1<<17)
const CURLPROTO_RTSP                     = (1<<18)
const CURLPROTO_RTMP                     = (1<<19)
const CURLPROTO_RTMPT                    = (1<<20)
const CURLPROTO_RTMPE                    = (1<<21)
const CURLPROTO_RTMPTE                   = (1<<22)
const CURLPROTO_RTMPS                    = (1<<23)
const CURLPROTO_RTMPTS                   = (1<<24)
const CURLPROTO_GOPHER                   = (1<<25)
const CURLPROTO_SMB                      = (1<<26)
const CURLPROTO_SMBS                     = (1<<27)
const CURLPROTO_ALL                      = (~0)
const CURLOPTTYPE_LONG                   = 0
const CURLOPTTYPE_OBJECTPOINT            = 10000
const CURLOPTTYPE_STRINGPOINT            = 10000
const CURLOPTTYPE_FUNCTIONPOINT          = 20000
const CURLOPTTYPE_OFF_T                  = 30000
const CURLOPT_XFERINFODATA               = CURLOPT_PROGRESSDATA
const CURLOPT_SERVER_RESPONSE_TIMEOUT    = CURLOPT_FTP_RESPONSE_TIMEOUT
const CURLOPT_POST301                    = CURLOPT_POSTREDIR
const CURLOPT_SSLKEYPASSWD               = CURLOPT_KEYPASSWD
const CURLOPT_FTPAPPEND                  = CURLOPT_APPEND
const CURLOPT_FTPLISTONLY                = CURLOPT_DIRLISTONLY
const CURLOPT_FTP_SSL                    = CURLOPT_USE_SSL
const CURLOPT_SSLCERTPASSWD              = CURLOPT_KEYPASSWD
const CURLOPT_KRB4LEVEL                  = CURLOPT_KRBLEVEL
const CURL_IPRESOLVE_WHATEVER            = 0
const CURL_IPRESOLVE_V4                  = 1
const CURL_IPRESOLVE_V6                  = 2
const CURLOPT_RTSPHEADER                 = CURLOPT_HTTPHEADER
const CURL_HTTP_VERSION_2                = CURL_HTTP_VERSION_2_0
const CURL_REDIR_GET_ALL                 = 0
const CURL_REDIR_POST_301                = 1
const CURL_REDIR_POST_302                = 2
const CURL_REDIR_POST_303                = 4
const CURL_REDIR_POST_ALL                = (CURL_REDIR_POST_301|CURL_REDIR_POST_302|CURL_REDIR_POST_303)
const CURL_ZERO_TERMINATED               = reinterpret(Csize_t, -1)
const CURLINFO_STRING                    = 0x100000
const CURLINFO_LONG                      = 0x200000
const CURLINFO_DOUBLE                    = 0x300000
const CURLINFO_SLIST                     = 0x400000
const CURLINFO_PTR                       = 0x400000
const CURLINFO_SOCKET                    = 0x500000
const CURLINFO_OFF_T                     = 0x600000
const CURLINFO_MASK                      = 0x0fffff
const CURLINFO_TYPEMASK                  = 0xf00000
const CURLINFO_HTTP_CODE                 = CURLINFO_RESPONSE_CODE
const CURL_GLOBAL_SSL                    = (1<<0)
const CURL_GLOBAL_WIN32                  = (1<<1)
const CURL_GLOBAL_ALL                    = (CURL_GLOBAL_SSL|CURL_GLOBAL_WIN32)
const CURL_GLOBAL_NOTHING                = 0
const CURL_GLOBAL_DEFAULT                = CURL_GLOBAL_ALL
const CURL_GLOBAL_ACK_EINTR              = (1<<2)
const CURLVERSION_NOW                    = CURLVERSION_FIFTH
const CURL_VERSION_IPV6                  = (1<<0)
const CURL_VERSION_KERBEROS4             = (1<<1)
const CURL_VERSION_SSL                   = (1<<2)
const CURL_VERSION_LIBZ                  = (1<<3)
const CURL_VERSION_NTLM                  = (1<<4)
const CURL_VERSION_GSSNEGOTIATE          = (1<<5)
const CURL_VERSION_DEBUG                 = (1<<6)
const CURL_VERSION_ASYNCHDNS             = (1<<7)
const CURL_VERSION_SPNEGO                = (1<<8)
const CURL_VERSION_LARGEFILE             = (1<<9)
const CURL_VERSION_IDN                   = (1<<10)
const CURL_VERSION_SSPI                  = (1<<11)
const CURL_VERSION_CONV                  = (1<<12)
const CURL_VERSION_CURLDEBUG             = (1<<13)
const CURL_VERSION_TLSAUTH_SRP           = (1<<14)
const CURL_VERSION_NTLM_WB               = (1<<15)
const CURL_VERSION_HTTP2                 = (1<<16)
const CURL_VERSION_GSSAPI                = (1<<17)
const CURL_VERSION_KERBEROS5             = (1<<18)
const CURL_VERSION_UNIX_SOCKETS          = (1<<19)
const CURL_VERSION_PSL                   = (1<<20)
const CURL_VERSION_HTTPS_PROXY           = (1<<21)
const CURL_VERSION_MULTI_SSL             = (1<<22)
const CURL_VERSION_BROTLI                = (1<<23)
const CURLPAUSE_RECV                     = (1<<0)
const CURLPAUSE_RECV_CONT                = (0)
const CURLPAUSE_SEND                     = (1<<2)
const CURLPAUSE_SEND_CONT                = (0)
const CURLPAUSE_ALL                      = (CURLPAUSE_RECV|CURLPAUSE_SEND)
const CURLPAUSE_CONT                     = (CURLPAUSE_RECV_CONT|CURLPAUSE_SEND_CONT)
const CURLM_CALL_MULTI_SOCKET            = CURLM_CALL_MULTI_PERFORM
const CURLPIPE_NOTHING                   = Clong(0)
const CURLPIPE_HTTP1                     = Clong(1)
const CURLPIPE_MULTIPLEX                 = Clong(2)
const CURL_WAIT_POLLIN                   = 0x0001
const CURL_WAIT_POLLPRI                  = 0x0002
const CURL_WAIT_POLLOUT                  = 0x0004
const CURL_POLL_NONE                     = 0
const CURL_POLL_IN                       = 1
const CURL_POLL_OUT                      = 2
const CURL_POLL_INOUT                    = 3
const CURL_POLL_REMOVE                   = 4
const CURL_SOCKET_TIMEOUT                = CURL_SOCKET_BAD
const CURL_CSELECT_IN                    = 0x01
const CURL_CSELECT_OUT                   = 0x02
const CURL_CSELECT_ERR                   = 0x04
const CURL_PUSH_OK                       = 0
const CURL_PUSH_DENY                     = 1
s   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/LibCURL/src/Mime_ext.jlYP      module Mime_ext

export MimeExt

const MimeExt = Dict{String,String}(
    "ez" => "application/andrew-inset",
    "anx" => "application/annodex",
    "atom" => "application/atom+xml",
    "atomcat" => "application/atomcat+xml",
    "atomsrv" => "application/atomserv+xml",
    "lin" => "application/bbolin",
    "cu" => "application/cu-seeme",
    "davmount" => "application/davmount+xml",
    "dcm" => "application/dicom",
    "tsp" => "application/dsptype",
    "es" => "application/ecmascript",
    "spl" => "application/futuresplash",
    "hta" => "application/hta",
    "jar" => "application/java-archive",
    "ser" => "application/java-serialized-object",
    "class" => "application/java-vm",
    "js" => "application/javascript",
    "json" => "application/json",
    "m3g" => "application/m3g",
    "hqx" => "application/mac-binhex40",
    "cpt" => "application/mac-compactpro",
    "nb" => "application/mathematica",
    "nbp" => "application/mathematica",
    "mbox" => "application/mbox",
    "mdb" => "application/msaccess",
    "doc" => "application/msword",
    "dot" => "application/msword",
    "mxf" => "application/mxf",
    "bin" => "application/octet-stream",
    "oda" => "application/oda",
    "ogx" => "application/ogg",
    "one" => "application/onenote",
    "onetoc2" => "application/onenote",
    "onetmp" => "application/onenote",
    "onepkg" => "application/onenote",
    "pdf" => "application/pdf",
    "pgp" => "application/pgp-encrypted",
    "key" => "application/pgp-keys",
    "sig" => "application/pgp-signature",
    "prf" => "application/pics-rules",
    "ps" => "application/postscript",
    "ai" => "application/postscript",
    "eps" => "application/postscript",
    "epsi" => "application/postscript",
    "epsf" => "application/postscript",
    "eps2" => "application/postscript",
    "eps3" => "application/postscript",
    "rar" => "application/rar",
    "rdf" => "application/rdf+xml",
    "rtf" => "application/rtf",
    "stl" => "application/sla",
    "smi" => "application/smil",
    "smil" => "application/smil",
    "xhtml" => "application/xhtml+xml",
    "xht" => "application/xhtml+xml",
    "xml" => "application/xml",
    "xsl" => "application/xml",
    "xsd" => "application/xml",
    "xspf" => "application/xspf+xml",
    "zip" => "application/zip",
    "apk" => "application/vnd.android.package-archive",
    "cdy" => "application/vnd.cinderella",
    "kml" => "application/vnd.google-earth.kml+xml",
    "kmz" => "application/vnd.google-earth.kmz",
    "xul" => "application/vnd.mozilla.xul+xml",
    "xls" => "application/vnd.ms-excel",
    "xlb" => "application/vnd.ms-excel",
    "xlt" => "application/vnd.ms-excel",
    "xlam" => "application/vnd.ms-excel.addin.macroEnabled.12",
    "xlsb" => "application/vnd.ms-excel.sheet.binary.macroEnabled.12",
    "xlsm" => "application/vnd.ms-excel.sheet.macroEnabled.12",
    "xltm" => "application/vnd.ms-excel.template.macroEnabled.12",
    "eot" => "application/vnd.ms-fontobject",
    "thmx" => "application/vnd.ms-officetheme",
    "cat" => "application/vnd.ms-pki.seccat",
    "ppt" => "application/vnd.ms-powerpoint",
    "pps" => "application/vnd.ms-powerpoint",
    "ppam" => "application/vnd.ms-powerpoint.addin.macroEnabled.12",
    "pptm" => "application/vnd.ms-powerpoint.presentation.macroEnabled.12",
    "sldm" => "application/vnd.ms-powerpoint.slide.macroEnabled.12",
    "ppsm" => "application/vnd.ms-powerpoint.slideshow.macroEnabled.12",
    "potm" => "application/vnd.ms-powerpoint.template.macroEnabled.12",
    "docm" => "application/vnd.ms-word.document.macroEnabled.12",
    "dotm" => "application/vnd.ms-word.template.macroEnabled.12",
    "odc" => "application/vnd.oasis.opendocument.chart",
    "odb" => "application/vnd.oasis.opendocument.database",
    "odf" => "application/vnd.oasis.opendocument.formula",
    "odg" => "application/vnd.oasis.opendocument.graphics",
    "otg" => "application/vnd.oasis.opendocument.graphics-template",
    "odi" => "application/vnd.oasis.opendocument.image",
    "odp" => "application/vnd.oasis.opendocument.presentation",
    "otp" => "application/vnd.oasis.opendocument.presentation-template",
    "ods" => "application/vnd.oasis.opendocument.spreadsheet",
    "ots" => "application/vnd.oasis.opendocument.spreadsheet-template",
    "odt" => "application/vnd.oasis.opendocument.text",
    "odm" => "application/vnd.oasis.opendocument.text-master",
    "ott" => "application/vnd.oasis.opendocument.text-template",
    "oth" => "application/vnd.oasis.opendocument.text-web",
    "pptx" => "application/vnd.openxmlformats-officedocument.presentationml.presentation",
    "sldx" => "application/vnd.openxmlformats-officedocument.presentationml.slide",
    "ppsx" => "application/vnd.openxmlformats-officedocument.presentationml.slideshow",
    "potx" => "application/vnd.openxmlformats-officedocument.presentationml.template",
    "xlsx" => "application/vnd.openxmlformats-officedocument.spreadsheetml.sheet",
    "xlsx" => "application/vnd.openxmlformats-officedocument.spreadsheetml.sheet",
    "xltx" => "application/vnd.openxmlformats-officedocument.spreadsheetml.template",
    "xltx" => "application/vnd.openxmlformats-officedocument.spreadsheetml.template",
    "docx" => "application/vnd.openxmlformats-officedocument.wordprocessingml.document",
    "dotx" => "application/vnd.openxmlformats-officedocument.wordprocessingml.template",
    "cod" => "application/vnd.rim.cod",
    "mmf" => "application/vnd.smaf",
    "sdc" => "application/vnd.stardivision.calc",
    "sds" => "application/vnd.stardivision.chart",
    "sda" => "application/vnd.stardivision.draw",
    "sdd" => "application/vnd.stardivision.impress",
    "sdf" => "application/vnd.stardivision.math",
    "sdw" => "application/vnd.stardivision.writer",
    "sgl" => "application/vnd.stardivision.writer-global",
    "sxc" => "application/vnd.sun.xml.calc",
    "stc" => "application/vnd.sun.xml.calc.template",
    "sxd" => "application/vnd.sun.xml.draw",
    "std" => "application/vnd.sun.xml.draw.template",
    "sxi" => "application/vnd.sun.xml.impress",
    "sti" => "application/vnd.sun.xml.impress.template",
    "sxm" => "application/vnd.sun.xml.math",
    "sxw" => "application/vnd.sun.xml.writer",
    "sxg" => "application/vnd.sun.xml.writer.global",
    "stw" => "application/vnd.sun.xml.writer.template",
    "sis" => "application/vnd.symbian.install",
    "cap" => "application/vnd.tcpdump.pcap",
    "pcap" => "application/vnd.tcpdump.pcap",
    "vsd" => "application/vnd.visio",
    "wbxml" => "application/vnd.wap.wbxml",
    "wmlc" => "application/vnd.wap.wmlc",
    "wmlsc" => "application/vnd.wap.wmlscriptc",
    "wpd" => "application/vnd.wordperfect",
    "wp5" => "application/vnd.wordperfect5.1",
    "wk" => "application/x-123",
    "7z" => "application/x-7z-compressed",
    "abw" => "application/x-abiword",
    "dmg" => "application/x-apple-diskimage",
    "bcpio" => "application/x-bcpio",
    "torrent" => "application/x-bittorrent",
    "cab" => "application/x-cab",
    "cbr" => "application/x-cbr",
    "cbz" => "application/x-cbz",
    "cdf" => "application/x-cdf",
    "cda" => "application/x-cdf",
    "vcd" => "application/x-cdlink",
    "pgn" => "application/x-chess-pgn",
    "mph" => "application/x-comsol",
    "cpio" => "application/x-cpio",
    "csh" => "application/x-csh",
    "deb" => "application/x-debian-package",
    "udeb" => "application/x-debian-package",
    "dcr" => "application/x-director",
    "dir" => "application/x-director",
    "dxr" => "application/x-director",
    "dms" => "application/x-dms",
    "wad" => "application/x-doom",
    "dvi" => "application/x-dvi",
    "pfa" => "application/x-font",
    "pfb" => "application/x-font",
    "gsf" => "application/x-font",
    "pcf" => "application/x-font",
    "pcf.Z" => "application/x-font",
    "woff" => "application/x-font-woff",
    "mm" => "application/x-freemind",
    "spl" => "application/x-futuresplash",
    "gan" => "application/x-ganttproject",
    "gnumeric" => "application/x-gnumeric",
    "sgf" => "application/x-go-sgf",
    "gcf" => "application/x-graphing-calculator",
    "gtar" => "application/x-gtar",
    "tgz" => "application/x-gtar-compressed",
    "taz" => "application/x-gtar-compressed",
    "hdf" => "application/x-hdf",
    "hwp" => "application/x-hwp",
    "ica" => "application/x-ica",
    "info" => "application/x-info",
    "ins" => "application/x-internet-signup",
    "isp" => "application/x-internet-signup",
    "iii" => "application/x-iphone",
    "iso" => "application/x-iso9660-image",
    "jam" => "application/x-jam",
    "jnlp" => "application/x-java-jnlp-file",
    "jmz" => "application/x-jmol",
    "chrt" => "application/x-kchart",
    "kil" => "application/x-killustrator",
    "skp" => "application/x-koan",
    "skd" => "application/x-koan",
    "skt" => "application/x-koan",
    "skm" => "application/x-koan",
    "kpr" => "application/x-kpresenter",
    "kpt" => "application/x-kpresenter",
    "ksp" => "application/x-kspread",
    "kwd" => "application/x-kword",
    "kwt" => "application/x-kword",
    "latex" => "application/x-latex",
    "lha" => "application/x-lha",
    "lyx" => "application/x-lyx",
    "lzh" => "application/x-lzh",
    "lzx" => "application/x-lzx",
    "frm" => "application/x-maker",
    "maker" => "application/x-maker",
    "frame" => "application/x-maker",
    "fm" => "application/x-maker",
    "fb" => "application/x-maker",
    "book" => "application/x-maker",
    "fbdoc" => "application/x-maker",
    "md5" => "application/x-md5",
    "mif" => "application/x-mif",
    "m3u8" => "application/x-mpegURL",
    "wmd" => "application/x-ms-wmd",
    "wmz" => "application/x-ms-wmz",
    "com" => "application/x-msdos-program",
    "exe" => "application/x-msdos-program",
    "bat" => "application/x-msdos-program",
    "dll" => "application/x-msdos-program",
    "msi" => "application/x-msi",
    "nc" => "application/x-netcdf",
    "pac" => "application/x-ns-proxy-autoconfig",
    "dat" => "application/x-ns-proxy-autoconfig",
    "nwc" => "application/x-nwc",
    "o" => "application/x-object",
    "oza" => "application/x-oz-application",
    "p7r" => "application/x-pkcs7-certreqresp",
    "crl" => "application/x-pkcs7-crl",
    "pyc" => "application/x-python-code",
    "pyo" => "application/x-python-code",
    "qgs" => "application/x-qgis",
    "shp" => "application/x-qgis",
    "shx" => "application/x-qgis",
    "qtl" => "application/x-quicktimeplayer",
    "rdp" => "application/x-rdp",
    "rpm" => "application/x-redhat-package-manager",
    "rss" => "application/x-rss+xml",
    "rb" => "application/x-ruby",
    "sci" => "application/x-scilab",
    "sce" => "application/x-scilab",
    "xcos" => "application/x-scilab-xcos",
    "sh" => "application/x-sh",
    "sha1" => "application/x-sha1",
    "shar" => "application/x-shar",
    "swf" => "application/x-shockwave-flash",
    "swfl" => "application/x-shockwave-flash",
    "scr" => "application/x-silverlight",
    "sql" => "application/x-sql",
    "sit" => "application/x-stuffit",
    "sitx" => "application/x-stuffit",
    "sv4cpio" => "application/x-sv4cpio",
    "sv4crc" => "application/x-sv4crc",
    "tar" => "application/x-tar",
    "tcl" => "application/x-tcl",
    "gf" => "application/x-tex-gf",
    "pk" => "application/x-tex-pk",
    "texinfo" => "application/x-texinfo",
    "texi" => "application/x-texinfo",
    "~" => "application/x-trash",
    "%" => "application/x-trash",
    "bak" => "application/x-trash",
    "old" => "application/x-trash",
    "sik" => "application/x-trash",
    "t" => "application/x-troff",
    "tr" => "application/x-troff",
    "roff" => "application/x-troff",
    "man" => "application/x-troff-man",
    "me" => "application/x-troff-me",
    "ms" => "application/x-troff-ms",
    "ustar" => "application/x-ustar",
    "src" => "application/x-wais-source",
    "wz" => "application/x-wingz",
    "crt" => "application/x-x509-ca-cert",
    "xcf" => "application/x-xcf",
    "fig" => "application/x-xfig",
    "xpi" => "application/x-xpinstall",
    "amr" => "audio/amr",
    "awb" => "audio/amr-wb",
    "amr" => "audio/amr",
    "awb" => "audio/amr-wb",
    "axa" => "audio/annodex",
    "au" => "audio/basic",
    "snd" => "audio/basic",
    "csd" => "audio/csound",
    "orc" => "audio/csound",
    "sco" => "audio/csound",
    "flac" => "audio/flac",
    "mid" => "audio/midi",
    "midi" => "audio/midi",
    "kar" => "audio/midi",
    "mpga" => "audio/mpeg",
    "mpega" => "audio/mpeg",
    "mp2" => "audio/mpeg",
    "mp3" => "audio/mpeg",
    "m4a" => "audio/mpeg",
    "m3u" => "audio/mpegurl",
    "oga" => "audio/ogg",
    "ogg" => "audio/ogg",
    "spx" => "audio/ogg",
    "sid" => "audio/prs.sid",
    "aif" => "audio/x-aiff",
    "aiff" => "audio/x-aiff",
    "aifc" => "audio/x-aiff",
    "gsm" => "audio/x-gsm",
    "m3u" => "audio/x-mpegurl",
    "wma" => "audio/x-ms-wma",
    "wax" => "audio/x-ms-wax",
    "ra" => "audio/x-pn-realaudio",
    "rm" => "audio/x-pn-realaudio",
    "ram" => "audio/x-pn-realaudio",
    "ra" => "audio/x-realaudio",
    "pls" => "audio/x-scpls",
    "sd2" => "audio/x-sd2",
    "wav" => "audio/x-wav",
    "alc" => "chemical/x-alchemy",
    "cac" => "chemical/x-cache",
    "cache" => "chemical/x-cache",
    "csf" => "chemical/x-cache-csf",
    "cbin" => "chemical/x-cactvs-binary",
    "cascii" => "chemical/x-cactvs-binary",
    "ctab" => "chemical/x-cactvs-binary",
    "cdx" => "chemical/x-cdx",
    "cer" => "chemical/x-cerius",
    "c3d" => "chemical/x-chem3d",
    "chm" => "chemical/x-chemdraw",
    "cif" => "chemical/x-cif",
    "cmdf" => "chemical/x-cmdf",
    "cml" => "chemical/x-cml",
    "cpa" => "chemical/x-compass",
    "bsd" => "chemical/x-crossfire",
    "csml" => "chemical/x-csml",
    "csm" => "chemical/x-csml",
    "ctx" => "chemical/x-ctx",
    "cxf" => "chemical/x-cxf",
    "cef" => "chemical/x-cxf",
    "emb" => "chemical/x-embl-dl-nucleotide",
    "embl" => "chemical/x-embl-dl-nucleotide",
    "spc" => "chemical/x-galactic-spc",
    "inp" => "chemical/x-gamess-input",
    "gam" => "chemical/x-gamess-input",
    "gamin" => "chemical/x-gamess-input",
    "fch" => "chemical/x-gaussian-checkpoint",
    "fchk" => "chemical/x-gaussian-checkpoint",
    "cub" => "chemical/x-gaussian-cube",
    "gau" => "chemical/x-gaussian-input",
    "gjc" => "chemical/x-gaussian-input",
    "gjf" => "chemical/x-gaussian-input",
    "gal" => "chemical/x-gaussian-log",
    "gcg" => "chemical/x-gcg8-sequence",
    "gen" => "chemical/x-genbank",
    "hin" => "chemical/x-hin",
    "istr" => "chemical/x-isostar",
    "ist" => "chemical/x-isostar",
    "jdx" => "chemical/x-jcamp-dx",
    "dx" => "chemical/x-jcamp-dx",
    "kin" => "chemical/x-kinemage",
    "mcm" => "chemical/x-macmolecule",
    "mmd" => "chemical/x-macromodel-input",
    "mmod" => "chemical/x-macromodel-input",
    "mol" => "chemical/x-mdl-molfile",
    "rd" => "chemical/x-mdl-rdfile",
    "rxn" => "chemical/x-mdl-rxnfile",
    "sd" => "chemical/x-mdl-sdfile",
    "sdf" => "chemical/x-mdl-sdfile",
    "tgf" => "chemical/x-mdl-tgf",
    "mcif" => "chemical/x-mmcif",
    "mol2" => "chemical/x-mol2",
    "b" => "chemical/x-molconn-Z",
    "gpt" => "chemical/x-mopac-graph",
    "mop" => "chemical/x-mopac-input",
    "mopcrt" => "chemical/x-mopac-input",
    "mpc" => "chemical/x-mopac-input",
    "zmt" => "chemical/x-mopac-input",
    "moo" => "chemical/x-mopac-out",
    "mvb" => "chemical/x-mopac-vib",
    "asn" => "chemical/x-ncbi-asn1",
    "prt" => "chemical/x-ncbi-asn1-ascii",
    "ent" => "chemical/x-ncbi-asn1-ascii",
    "val" => "chemical/x-ncbi-asn1-binary",
    "aso" => "chemical/x-ncbi-asn1-binary",
    "asn" => "chemical/x-ncbi-asn1-spec",
    "pdb" => "chemical/x-pdb",
    "ent" => "chemical/x-pdb",
    "ros" => "chemical/x-rosdal",
    "sw" => "chemical/x-swissprot",
    "vms" => "chemical/x-vamas-iso14976",
    "vmd" => "chemical/x-vmd",
    "xtel" => "chemical/x-xtel",
    "xyz" => "chemical/x-xyz",
    "gif" => "image/gif",
    "ief" => "image/ief",
    "jpeg" => "image/jpeg",
    "jpg" => "image/jpeg",
    "jpe" => "image/jpeg",
    "pcx" => "image/pcx",
    "png" => "image/png",
    "svg" => "image/svg+xml",
    "svgz" => "image/svg+xml",
    "tiff" => "image/tiff",
    "tif" => "image/tiff",
    "djvu" => "image/vnd.djvu",
    "djv" => "image/vnd.djvu",
    "ico" => "image/vnd.microsoft.icon",
    "wbmp" => "image/vnd.wap.wbmp",
    "cr2" => "image/x-canon-cr2",
    "crw" => "image/x-canon-crw",
    "ras" => "image/x-cmu-raster",
    "cdr" => "image/x-coreldraw",
    "pat" => "image/x-coreldrawpattern",
    "cdt" => "image/x-coreldrawtemplate",
    "cpt" => "image/x-corelphotopaint",
    "erf" => "image/x-epson-erf",
    "art" => "image/x-jg",
    "jng" => "image/x-jng",
    "bmp" => "image/x-ms-bmp",
    "nef" => "image/x-nikon-nef",
    "orf" => "image/x-olympus-orf",
    "psd" => "image/x-photoshop",
    "pnm" => "image/x-portable-anymap",
    "pbm" => "image/x-portable-bitmap",
    "pgm" => "image/x-portable-graymap",
    "ppm" => "image/x-portable-pixmap",
    "rgb" => "image/x-rgb",
    "xbm" => "image/x-xbitmap",
    "xpm" => "image/x-xpixmap",
    "xwd" => "image/x-xwindowdump",
    "eml" => "message/rfc822",
    "igs" => "model/iges",
    "iges" => "model/iges",
    "msh" => "model/mesh",
    "mesh" => "model/mesh",
    "silo" => "model/mesh",
    "wrl" => "model/vrml",
    "vrml" => "model/vrml",
    "x3dv" => "model/x3d+vrml",
    "x3d" => "model/x3d+xml",
    "x3db" => "model/x3d+binary",
    "appcache" => "text/cache-manifest",
    "ics" => "text/calendar",
    "icz" => "text/calendar",
    "css" => "text/css",
    "csv" => "text/csv",
    "323" => "text/h323",
    "html" => "text/html",
    "htm" => "text/html",
    "shtml" => "text/html",
    "uls" => "text/iuls",
    "mml" => "text/mathml",
    "asc" => "text/plain",
    "txt" => "text/plain",
    "text" => "text/plain",
    "pot" => "text/plain",
    "brf" => "text/plain",
    "srt" => "text/plain",
    "rtx" => "text/richtext",
    "sct" => "text/scriptlet",
    "wsc" => "text/scriptlet",
    "tm" => "text/texmacs",
    "tsv" => "text/tab-separated-values",
    "jad" => "text/vnd.sun.j2me.app-descriptor",
    "wml" => "text/vnd.wap.wml",
    "wmls" => "text/vnd.wap.wmlscript",
    "bib" => "text/x-bibtex",
    "boo" => "text/x-boo",
    "h++" => "text/x-c++hdr",
    "hpp" => "text/x-c++hdr",
    "hxx" => "text/x-c++hdr",
    "hh" => "text/x-c++hdr",
    "c++" => "text/x-c++src",
    "cpp" => "text/x-c++src",
    "cxx" => "text/x-c++src",
    "cc" => "text/x-c++src",
    "h" => "text/x-chdr",
    "htc" => "text/x-component",
    "csh" => "text/x-csh",
    "c" => "text/x-csrc",
    "d" => "text/x-dsrc",
    "diff" => "text/x-diff",
    "patch" => "text/x-diff",
    "hs" => "text/x-haskell",
    "java" => "text/x-java",
    "ly" => "text/x-lilypond",
    "lhs" => "text/x-literate-haskell",
    "moc" => "text/x-moc",
    "p" => "text/x-pascal",
    "pas" => "text/x-pascal",
    "gcd" => "text/x-pcs-gcd",
    "pl" => "text/x-perl",
    "pm" => "text/x-perl",
    "py" => "text/x-python",
    "scala" => "text/x-scala",
    "etx" => "text/x-setext",
    "sfv" => "text/x-sfv",
    "sh" => "text/x-sh",
    "tcl" => "text/x-tcl",
    "tk" => "text/x-tcl",
    "tex" => "text/x-tex",
    "ltx" => "text/x-tex",
    "sty" => "text/x-tex",
    "cls" => "text/x-tex",
    "vcs" => "text/x-vcalendar",
    "vcf" => "text/x-vcard",
    "3gp" => "video/3gpp",
    "axv" => "video/annodex",
    "dl" => "video/dl",
    "dif" => "video/dv",
    "dv" => "video/dv",
    "fli" => "video/fli",
    "gl" => "video/gl",
    "mpeg" => "video/mpeg",
    "mpg" => "video/mpeg",
    "mpe" => "video/mpeg",
    "ts" => "video/MP2T",
    "mp4" => "video/mp4",
    "qt" => "video/quicktime",
    "mov" => "video/quicktime",
    "ogv" => "video/ogg",
    "webm" => "video/webm",
    "mxu" => "video/vnd.mpegurl",
    "flv" => "video/x-flv",
    "lsf" => "video/x-la-asf",
    "lsx" => "video/x-la-asf",
    "mng" => "video/x-mng",
    "asf" => "video/x-ms-asf",
    "asx" => "video/x-ms-asf",
    "wm" => "video/x-ms-wm",
    "wmv" => "video/x-ms-wmv",
    "wmx" => "video/x-ms-wmx",
    "wvx" => "video/x-ms-wvx",
    "avi" => "video/x-msvideo",
    "movie" => "video/x-sgi-movie",
    "mpv" => "video/x-matroska",
    "mkv" => "video/x-matroska",
    "ice" => "x-conference/x-cooltalk",
    "sisx" => "x-epoc/x-sisx-app",
    "vrm" => "x-world/x-vrml",
    "vrml" => "x-world/x-vrml",
    "wrl" => "x-world/x-vrml",
    "" => ""
)

end
v   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Downloads/src/Downloads.jl!J      """
The `Downloads` module exports a function [`download`](@ref), which provides cross-platform, multi-protocol,
in-process download functionality implemented with [libcurl](https://curl.haxx.se/libcurl/).   It is used
for the `Base.download` function in Julia 1.6 or later.

More generally, the module exports functions and types that provide lower-level control and diagnostic information
for file downloading:
- [`download`](@ref) — download a file from a URL, erroring if it can't be downloaded
- [`request`](@ref) — request a URL, returning a `Response` object indicating success
- [`Response`](@ref) — a type capturing the status and other metadata about a request
- [`RequestError`](@ref) — an error type thrown by `download` and `request` on error
- [`Downloader`](@ref) — an object encapsulating shared resources for downloading
"""
module Downloads

using Base.Experimental: @sync
using NetworkOptions
using ArgTools

include("Curl/Curl.jl")
using .Curl

export download, request, Downloader, Response, RequestError, default_downloader!

## public API types ##

"""
    Downloader(; [ grace::Real = 30 ])

`Downloader` objects are used to perform individual `download` operations.
Connections, name lookups and other resources are shared within a `Downloader`.
These connections and resources are cleaned up after a configurable grace period
(default: 30 seconds) since anything was downloaded with it, or when it is
garbage collected, whichever comes first. If the grace period is set to zero,
all resources will be cleaned up immediately as soon as there are no more
ongoing downloads in progress. If the grace period is set to `Inf` then
resources are not cleaned up until `Downloader` is garbage collected.
"""
mutable struct Downloader
    multi::Multi
    ca_roots::Union{String, Nothing}
    easy_hook::Union{Function, Nothing}

    Downloader(multi::Multi) = new(multi, get_ca_roots(), EASY_HOOK[])
end
Downloader(; grace::Real=30) = Downloader(Multi(grace_ms(grace)))

function grace_ms(grace::Real)
    grace < 0 && throw(ArgumentError("grace period cannot be negative: $grace"))
    grace <= typemax(UInt64) ÷ 1000 ? round(UInt64, 1000*grace) : typemax(UInt64)
end

function easy_hook(downloader::Downloader, easy::Easy, info::NamedTuple)
    downloader.easy_hook !== nothing && downloader.easy_hook(easy, info)
end

get_ca_roots() = Curl.SYSTEM_SSL ? ca_roots() : ca_roots_path()

function set_ca_roots(downloader::Downloader, easy::Easy)
    ca_roots = downloader.ca_roots
    ca_roots !== nothing && set_ca_roots_path(easy, ca_roots)
end

const DOWNLOAD_LOCK = ReentrantLock()
const DOWNLOADER = Ref{Union{Downloader, Nothing}}(nothing)

"""
`EASY_HOOK` is a modifable global hook to used as the default `easy_hook` on
new `Downloader` objects. This supplies a mechanism to set options for the
`Downloader` via `Curl.setopt`

It is expected to be function taking two arguments: an `Easy` struct and an
`info` NamedTuple with names `url`, `method` and `headers`.
"""
const EASY_HOOK = Ref{Union{Function, Nothing}}(nothing)

"""
    struct Response
        proto   :: String
        url     :: String
        status  :: Int
        message :: String
        headers :: Vector{Pair{String,String}}
    end

`Response` is a type capturing the properties of a successful response to a
request as an object. It has the following fields:

- `proto`: the protocol that was used to get the response
- `url`: the URL that was ultimately requested after following redirects
- `status`: the status code of the response, indicating success, failure, etc.
- `message`: a textual message describing the nature of the response
- `headers`: any headers that were returned with the response

The meaning and availability of some of these responses depends on the protocol
used for the request. For many protocols, including HTTP/S and S/FTP, a 2xx
status code indicates a successful response. For responses in protocols that do
not support headers, the headers vector will be empty. HTTP/2 does not include a
status message, only a status code, so the message will be empty.
"""
struct Response
    proto   :: Union{String, Nothing}
    url     :: String # redirected URL
    status  :: Int
    message :: String
    headers :: Vector{Pair{String,String}}
end

Curl.status_ok(response::Response) = status_ok(response.proto, response.status)

"""
    struct RequestError <: ErrorException
        url      :: String
        code     :: Int
        message  :: String
        response :: Response
    end

`RequestError` is a type capturing the properties of a failed response to a
request as an exception object:

- `url`: the original URL that was requested without any redirects
- `code`: the libcurl error code; `0` if a protocol-only error occurred
- `message`: the libcurl error message indicating what went wrong
- `response`: response object capturing what response info is available

The same `RequestError` type is thrown by `download` if the request was
successful but there was a protocol-level error indicated by a status code that
is not in the 2xx range, in which case `code` will be zero and the `message`
field will be the empty string. The `request` API only throws a `RequestError`
if the libcurl error `code` is non-zero, in which case the included `response`
object is likely to have a `status` of zero and an empty message. There are,
however, situations where a curl-level error is thrown due to a protocol error,
in which case both the inner and outer code and message may be of interest.
"""
struct RequestError <: Exception
    url      :: String # original URL
    code     :: Int
    message  :: String
    response :: Response
end

function Base.showerror(io::IO, err::RequestError)
    print(io, "RequestError: $(error_message(err)) while requesting $(err.url)")
end

function error_message(err::RequestError)
    errstr = err.message
    status = err.response.status
    message = err.response.message
    status_re = Regex(status == 0 ? "" : "\\b$status\\b")

    err.code == Curl.CURLE_OK &&
        return isempty(message) ? "Error status $status" :
            contains(message, status_re) ? message :
                "$message (status $status)"

    isempty(message) && !isempty(errstr) &&
        return status == 0 ? errstr : "$errstr (status $status)"

    isempty(message) && (message = "Status $status")
    isempty(errstr)  && (errstr = "curl error $(err.code)")

    !contains(message, status_re) && !contains(errstr, status_re) &&
        (errstr = "status $status; $errstr")

    return "$message ($errstr)"
end

## download API ##

"""
    download(url, [ output = tempname() ];
        [ method = "GET", ]
        [ headers = <none>, ]
        [ timeout = <none>, ]
        [ progress = <none>, ]
        [ verbose = false, ]
        [ debug = <none>, ]
        [ downloader = <default>, ]
    ) -> output

        url        :: AbstractString
        output     :: Union{AbstractString, AbstractCmd, IO}
        method     :: AbstractString
        headers    :: Union{AbstractVector, AbstractDict}
        timeout    :: Real
        progress   :: (total::Integer, now::Integer) --> Any
        verbose    :: Bool
        debug      :: (type, message) --> Any
        downloader :: Downloader

Download a file from the given url, saving it to `output` or if not specified, a
temporary path. The `output` can also be an `IO` handle, in which case the body
of the response is streamed to that handle and the handle is returned. If
`output` is a command, the command is run and output is sent to it on stdin.

If the `downloader` keyword argument is provided, it must be a `Downloader`
object. Resources and connections will be shared between downloads performed by
the same `Downloader` and cleaned up automatically when the object is garbage
collected or there have been no downloads performed with it for a grace period.
See `Downloader` for more info about configuration and usage.

If the `headers` keyword argument is provided, it must be a vector or dictionary
whose elements are all pairs of strings. These pairs are passed as headers when
downloading URLs with protocols that supports them, such as HTTP/S.

The `timeout` keyword argument specifies a timeout for the download to complete in
seconds, with a resolution of milliseconds. By default no timeout is set, but this
can also be explicitly requested by passing a timeout value of `Inf`. Separately,
if 20 seconds elapse without receiving any data, the download will timeout. See
extended help for how to disable this timeout.

If the `progress` keyword argument is provided, it must be a callback function
which will be called whenever there are updates about the size and status of the
ongoing download. The callback must take two integer arguments: `total` and
`now` which are the total size of the download in bytes, and the number of bytes
which have been downloaded so far. Note that `total` starts out as zero and
remains zero until the server gives an indication of the total size of the
download (e.g. with a `Content-Length` header), which may never happen. So a
well-behaved progress callback should handle a total size of zero gracefully.

If the `verbose` option is set to true, `libcurl`, which is used to implement
the download functionality will print debugging information to `stderr`. If the
`debug` option is set to a function accepting two `String` arguments, then the
verbose option is ignored and instead the data that would have been printed to
`stderr` is passed to the `debug` callback with `type` and `message` arguments.
The `type` argument indicates what kind of event has occurred, and is one of:
`TEXT`, `HEADER IN`, `HEADER OUT`, `DATA IN`, `DATA OUT`, `SSL DATA IN` or `SSL
DATA OUT`. The `message` argument is the description of the debug event.

## Extended Help

For further customization, use a [`Downloader`](@ref) and
[`easy_hook`s](https://github.com/JuliaLang/Downloads.jl#mutual-tls-using-downloads).
For example, to disable the 20 second timeout when no data is received, you may
use the following:

```jl
downloader = Downloads.Downloader()
downloader.easy_hook = (easy, info) -> Downloads.Curl.setopt(easy, Downloads.Curl.CURLOPT_LOW_SPEED_TIME, 0)

Downloads.download("https://httpbingo.julialang.org/delay/30"; downloader)
```
"""
function download(
    url        :: AbstractString,
    output     :: Union{ArgWrite, Nothing} = nothing;
    method     :: Union{AbstractString, Nothing} = nothing,
    headers    :: Union{AbstractVector, AbstractDict} = Pair{String,String}[],
    timeout    :: Real = Inf,
    progress   :: Union{Function, Nothing} = nothing,
    verbose    :: Bool = false,
    debug      :: Union{Function, Nothing} = nothing,
    downloader :: Union{Downloader, Nothing} = nothing,
) :: ArgWrite
    arg_write(output) do output
        response = request(
            url,
            output = output,
            method = method,
            headers = headers,
            timeout = timeout,
            progress = progress,
            verbose = verbose,
            debug = debug,
            downloader = downloader,
        )::Response
        status_ok(response) && return output
        throw(RequestError(url, Curl.CURLE_OK, "", response))
    end
end

## request API ##

"""
    request(url;
        [ input = <none>, ]
        [ output = <none>, ]
        [ method = input ? "PUT" : output ? "GET" : "HEAD", ]
        [ headers = <none>, ]
        [ timeout = <none>, ]
        [ progress = <none>, ]
        [ verbose = false, ]
        [ debug = <none>, ]
        [ throw = true, ]
        [ downloader = <default>, ]
    ) -> Union{Response, RequestError}

        url        :: AbstractString
        input      :: Union{AbstractString, AbstractCmd, IO}
        output     :: Union{AbstractString, AbstractCmd, IO}
        method     :: AbstractString
        headers    :: Union{AbstractVector, AbstractDict}
        timeout    :: Real
        progress   :: (dl_total, dl_now, ul_total, ul_now) --> Any
        verbose    :: Bool
        debug      :: (type, message) --> Any
        throw      :: Bool
        downloader :: Downloader

Make a request to the given url, returning a `Response` object capturing the
status, headers and other information about the response. The body of the
response is written to `output` if specified and discarded otherwise. For HTTP/S
requests, if an `input` stream is given, a `PUT` request is made; otherwise if
an `output` stream is given, a `GET` request is made; if neither is given a
`HEAD` request is made. For other protocols, appropriate default methods are
used based on what combination of input and output are requested. The following
options differ from the `download` function:

- `input` allows providing a request body; if provided default to `PUT` request
- `progress` is a callback taking four integers for upload and download progress
- `throw` controls whether to throw or return a `RequestError` on request error

Note that unlike `download` which throws an error if the requested URL could not
be downloaded (indicated by non-2xx status code), `request` returns a `Response`
object no matter what the status code of the response is. If there is an error
with getting a response at all, then a `RequestError` is thrown or returned.
"""
function request(
    url        :: AbstractString;
    input      :: Union{ArgRead, Nothing} = nothing,
    output     :: Union{ArgWrite, Nothing} = nothing,
    method     :: Union{AbstractString, Nothing} = nothing,
    headers    :: Union{AbstractVector, AbstractDict} = Pair{String,String}[],
    timeout    :: Real = Inf,
    progress   :: Union{Function, Nothing} = nothing,
    verbose    :: Bool = false,
    debug      :: Union{Function, Nothing} = nothing,
    throw      :: Bool = true,
    downloader :: Union{Downloader, Nothing} = nothing,
) :: Union{Response, RequestError}
    if downloader === nothing
        lock(DOWNLOAD_LOCK) do
            downloader = DOWNLOADER[]
            if downloader === nothing
                downloader = DOWNLOADER[] = Downloader()
            end
        end
    end
    local response
    have_input = input !== nothing
    have_output = output !== nothing
    input = something(input, devnull)
    output = something(output, devnull)
    input_size = arg_read_size(input)
    if input_size === nothing
        # take input_size from content-length header if one is supplied
        input_size = content_length(headers)
    end
    progress = p_func(progress, input, output)
    arg_read(input) do input
        arg_write(output) do output
            with_handle(Easy()) do easy
                # setup the request
                set_url(easy, url)
                set_timeout(easy, timeout)
                set_verbose(easy, verbose)
                set_debug(easy, debug)
                add_headers(easy, headers)

                # libcurl does not set the default header reliably so set it
                # explicitly unless user has specified it, xref
                # https://github.com/JuliaLang/Pkg.jl/pull/2357
                if !any(kv -> lowercase(kv[1]) == "user-agent", headers)
                    Curl.add_header(easy, "User-Agent", Curl.USER_AGENT)
                end

                if have_input
                    enable_upload(easy)
                    if input_size !== nothing
                        set_upload_size(easy, input_size)
                    end
                    if applicable(seek, input, 0)
                        set_seeker(easy) do offset
                            seek(input, Int(offset))
                        end
                    end
                else
                    set_body(easy, have_output && method != "HEAD")
                end
                method !== nothing && set_method(easy, method)
                progress !== nothing && enable_progress(easy)
                set_ca_roots(downloader, easy)
                info = (url = url, method = method, headers = headers)
                easy_hook(downloader, easy, info)

                # do the request
                add_handle(downloader.multi, easy)
                try # ensure handle is removed
                    @sync begin
                        @async for buf in easy.output
                            write(output, buf)
                        end
                        if progress !== nothing
                            @async for prog in easy.progress
                                progress(prog...)
                            end
                        end
                        if have_input
                            @async upload_data(easy, input)
                        end
                    end
                finally
                    remove_handle(downloader.multi, easy)
                end

                # return the response or throw an error
                response = Response(get_response_info(easy)...)
                easy.code == Curl.CURLE_OK && return response
                message = get_curl_errstr(easy)
                response = RequestError(url, easy.code, message, response)
                throw && Base.throw(response)
            end
        end
    end
    return response
end

## helper functions ##

function p_func(progress::Function, input::ArgRead, output::ArgWrite)
    hasmethod(progress, NTuple{4,Int}) && return progress
    hasmethod(progress, NTuple{2,Int}) ||
        throw(ArgumentError("invalid progress callback"))

    input === devnull && output !== devnull &&
        return (total, now, _, _) -> progress(total, now)
    input !== devnull && output === devnull &&
        return (_, _, total, now) -> progress(total, now)

    (dl_total, dl_now, ul_total, ul_now) ->
        progress(dl_total + ul_total, dl_now + ul_now)
end
p_func(progress::Nothing, input::ArgRead, output::ArgWrite) = nothing

arg_read_size(path::AbstractString) = filesize(path)
arg_read_size(io::Base.GenericIOBuffer) = bytesavailable(io)
arg_read_size(::Base.DevNull) = 0
arg_read_size(::Any) = nothing

function content_length(headers::Union{AbstractVector, AbstractDict})
    for (key, value) in headers
        if lowercase(key) == "content-length" && isa(value, AbstractString)
            return tryparse(Int, value)
        end
    end
    return nothing
end

"""
    default_downloader!(
        downloader = <none>
    )

        downloader :: Downloader

Set the default `Downloader`. If no argument is provided, resets the default downloader so that a fresh one is created the next time the default downloader is needed.
"""
function default_downloader!(
    downloader :: Union{Downloader, Nothing} = nothing
)
    lock(DOWNLOAD_LOCK) do
        DOWNLOADER[] = downloader
    end
end

# Precompile
let
    d = Downloader()
    download("file://" * @__FILE__; downloader=d)
    precompile(Tuple{typeof(Downloads.download), String, String})
    precompile(Tuple{typeof(Downloads.Curl.status_2xx_ok), Int64})
end

end # module
v   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Downloads/src/Curl/Curl.jl�      module Curl

export
    with_handle,
    Easy,
        set_url,
        set_method,
        set_verbose,
        set_debug,
        set_body,
        set_upload_size,
        set_seeker,
        set_ca_roots_path,
        set_timeout,
        add_headers,
        enable_upload,
        enable_progress,
        upload_data,
        get_protocol,
        get_effective_url,
        get_response_status,
        get_response_info,
        get_curl_errstr,
        status_ok,
    Multi,
        add_handle,
        remove_handle

using Base: @lock
using LibCURL
using LibCURL: curl_off_t, libcurl
# not exported: https://github.com/JuliaWeb/LibCURL.jl/issues/87

# constants that LibCURL should have but doesn't
const CURLE_PEER_FAILED_VERIFICATION = 60
const CURLSSLOPT_REVOKE_BEST_EFFORT = 1 << 3
const CURLOPT_PREREQFUNCTION = 20000 + 312
const CURLOPT_PREREQDATA = 10000 + 313

# these are incorrectly defined on Windows by LibCURL:
if Sys.iswindows()
    const curl_socket_t = Base.OS_HANDLE
    const CURL_SOCKET_TIMEOUT = Base.INVALID_OS_HANDLE
else
    const curl_socket_t = Cint
    const CURL_SOCKET_TIMEOUT = -1
end

# definitions affected by incorrect curl_socket_t (copied verbatim):
function curl_multi_socket_action(multi_handle, s, ev_bitmask, running_handles)
    ccall((:curl_multi_socket_action, libcurl), CURLMcode, (Ptr{CURLM}, curl_socket_t, Cint, Ptr{Cint}), multi_handle, s, ev_bitmask, running_handles)
end
function curl_multi_assign(multi_handle, sockfd, sockp)
    ccall((:curl_multi_assign, libcurl), CURLMcode, (Ptr{CURLM}, curl_socket_t, Ptr{Cvoid}), multi_handle, sockfd, sockp)
end

# additional curl_multi_socket_action method
function curl_multi_socket_action(multi_handle, s, ev_bitmask)
    curl_multi_socket_action(multi_handle, s, ev_bitmask, Ref{Cint}())
end

using FileWatching
using NetworkOptions
using Base: OS_HANDLE, preserve_handle, unpreserve_handle

include("utils.jl")

function __init__()
    @check curl_global_init(CURL_GLOBAL_ALL)
end

const CURL_VERSION_INFO = unsafe_load(curl_version_info(CURLVERSION_NOW))
if CURL_VERSION_INFO.ssl_version == Base.C_NULL
    const SSL_VERSION = ""
else
    const SSL_VERSION = unsafe_string(CURL_VERSION_INFO.ssl_version)::String
end
const SYSTEM_SSL =
    Sys.isapple() && startswith(SSL_VERSION, "SecureTransport") ||
    Sys.iswindows() && startswith(SSL_VERSION, "Schannel")

const CURL_VERSION_STR = unsafe_string(curl_version())
let m = match(r"^libcurl/(\d+\.\d+\.\d+)\b", CURL_VERSION_STR)
    m !== nothing || error("unexpected CURL_VERSION_STR value")
    curl = m.captures[1]
    julia = "$(VERSION.major).$(VERSION.minor)"
    global const CURL_VERSION = VersionNumber(curl)
    global const USER_AGENT = "curl/$curl julia/$julia"
end

include("Easy.jl")
include("Multi.jl")

function with_handle(f, handle::Union{Multi, Easy})
    try f(handle)
    finally
        Curl.done!(handle)
    end
end

"""
    setopt(easy::Easy, option::Integer, value)

Sets options on libcurl's "easy" interface. `option` corresponds to libcurl options on https://curl.se/libcurl/c/curl_easy_setopt.html
"""
setopt(easy::Easy, option::Integer, value) =
    @check curl_easy_setopt(easy.handle, option, value)

"""
    setopt(multi::Multi, option::Integer, value)

Sets options on libcurl's "multi" interface. `option` corresponds to libcurl options on https://curl.se/libcurl/c/curl_multi_setopt.html
"""
setopt(multi::Multi, option::Integer, value) =
    @check curl_multi_setopt(multi.handle, option, value)

end # module
w   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Downloads/src/Curl/utils.jlU
      if !@isdefined(contains)
    contains(haystack, needle) = occursin(needle, haystack)
    export contains
end

# basic C stuff

puts(s::Union{String,SubString{String}}) = ccall(:puts, Cint, (Ptr{Cchar},), s)

jl_malloc(n::Integer) = ccall(:jl_malloc, Ptr{Cvoid}, (Csize_t,), n)

# check if a call failed

macro check(ex::Expr)
    ex.head == :call ||
        error("@check: not a call: $ex")
    arg1 = ex.args[1] :: Symbol
    if arg1 == :ccall
        arg2 = ex.args[2]
        arg2 isa QuoteNode ||
            error("@check: ccallee must be a symbol")
        f = arg2.value :: Symbol
    else
        f = arg1
    end
    prefix = "$f: "
    if f in (:curl_easy_setopt, :curl_multi_setopt)
        unknown_option =
            f == :curl_easy_setopt  ? CURLE_UNKNOWN_OPTION :
            f == :curl_multi_setopt ? CURLM_UNKNOWN_OPTION : error()
        quote
            r = $(esc(ex))
            if r == $unknown_option
                @async @error $prefix * string(r) * """\n
                You may be using an old system libcurl library that doesn't understand options that Julia uses. You can try the following Julia code to see which libcurl library you are using:

                    using Libdl
                    filter!(contains("curl"), dllist())

                If this indicates that Julia is not using the libcurl library that is shipped with Julia, then that is likely to be the problem. This either means:

                  1. You are using an unofficial Julia build which is configured to use a system libcurl library that is not recent enough; you may be able to fix this by upgrading the system libcurl. You should complain to your distro maintainers for allowing Julia to use a too-old libcurl version and consider using official Julia binaries instead.

                  2. You are overriding the library load path by setting `LD_LIBRARY_PATH`, in which case you are in advanced usage territory. You can try upgrading the system libcurl, unsetting `LD_LIBRARY_PATH`, or otherwise arranging for Julia to load a recent libcurl library.

                If neither of these is the case and Julia is picking up a too old libcurl, please file an issue with the `Downloads.jl` package.

                """ maxlog=1_000
            elseif !iszero(r)
                @async @error $prefix * string(r) maxlog=1_000
            end
            r
        end
    else
        quote
            r = $(esc(ex))
            iszero(r) || @async @error $prefix * string(r) maxlog=1_000
            r
        end
    end
end

# curl string list structure

struct curl_slist_t
    data::Ptr{Cchar}
    next::Ptr{curl_slist_t}
end
v   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Downloads/src/Curl/Easy.jlkF      mutable struct Easy
    handle   :: Ptr{Cvoid}
    input    :: Union{Vector{UInt8},Nothing}
    ready    :: Threads.Event
    seeker   :: Union{Function,Nothing}
    output   :: Channel{Vector{UInt8}}
    progress :: Channel{NTuple{4,Int}}
    req_hdrs :: Ptr{curl_slist_t}
    res_hdrs :: Vector{String}
    code     :: CURLcode
    errbuf   :: Vector{UInt8}
    debug    :: Union{Function,Nothing}
    consem   :: Bool
end

const EMPTY_BYTE_VECTOR = UInt8[]

function Easy()
    easy = Easy(
        curl_easy_init(),
        EMPTY_BYTE_VECTOR,
        Threads.Event(),
        nothing,
        Channel{Vector{UInt8}}(Inf),
        Channel{NTuple{4,Int}}(Inf),
        C_NULL,
        String[],
        typemax(CURLcode),
        zeros(UInt8, CURL_ERROR_SIZE),
        nothing,
        false,
    )
    finalizer(done!, easy)
    add_callbacks(easy)
    set_defaults(easy)
    return easy
end

function done!(easy::Easy)
    connect_semaphore_release(easy)
    easy.handle == C_NULL && return
    curl_easy_cleanup(easy.handle)
    curl_slist_free_all(easy.req_hdrs)
    easy.handle = C_NULL
    return
end

# connect semaphore

# This semaphore limits the number of requests that can be in the connecting
# state at any given time, globally. Throttling this prevents libcurl from
# trying to start too many DNS resolver threads concurrently. It also helps
# ensure that not-yet-started requests get ßa chance to make some progress
# before adding more events from new requests to the system's workload.

const CONNECT_SEMAPHORE = Base.Semaphore(16) # empirically chosen (ie guessed)

function connect_semaphore_acquire(easy::Easy)
    @assert !easy.consem
    Base.acquire(CONNECT_SEMAPHORE)
    easy.consem = true
    return
end

function connect_semaphore_release(easy::Easy)
    easy.consem || return
    Base.release(CONNECT_SEMAPHORE)
    easy.consem = false
    return
end

# request options

function set_defaults(easy::Easy)
    # curl options
    setopt(easy, CURLOPT_NOSIGNAL, true)
    setopt(easy, CURLOPT_FOLLOWLOCATION, true)
    setopt(easy, CURLOPT_MAXREDIRS, 50)
    setopt(easy, CURLOPT_POSTREDIR, CURL_REDIR_POST_ALL)
    setopt(easy, CURLOPT_USERAGENT, USER_AGENT)
    setopt(easy, CURLOPT_NETRC, CURL_NETRC_OPTIONAL)
    setopt(easy, CURLOPT_COOKIEFILE, "")
    setopt(easy, CURLOPT_SSL_OPTIONS, CURLSSLOPT_REVOKE_BEST_EFFORT)

    # prevent downloads that hang forever:
    # - timeout no response on connect (more than 30s)
    # - if server transmits nothing for 20s, bail out
    setopt(easy, CURLOPT_CONNECTTIMEOUT, 30)
    setopt(easy, CURLOPT_LOW_SPEED_TIME, 20)
    setopt(easy, CURLOPT_LOW_SPEED_LIMIT, 1)

    # ssh-related options
    setopt(easy, CURLOPT_SSH_PRIVATE_KEYFILE, ssh_key_path())
    setopt(easy, CURLOPT_SSH_PUBLIC_KEYFILE, ssh_pub_key_path())
    key_pass = something(ssh_key_pass(), C_NULL)
    setopt(easy, CURLOPT_KEYPASSWD, key_pass)
end

function set_ca_roots_path(easy::Easy, path::AbstractString)
    Base.unsafe_convert(Cstring, path) # error checking
    opt = isdir(path) ? CURLOPT_CAPATH : CURLOPT_CAINFO
    setopt(easy, opt, path)
end

function set_url(easy::Easy, url::Union{String, SubString{String}})
    # TODO: ideally, Clang would generate Cstring signatures
    Base.unsafe_convert(Cstring, url) # error checking
    setopt(easy, CURLOPT_URL, url)
    set_ssl_verify(easy, verify_host(url, "ssl"))
    set_ssh_verify(easy, verify_host(url, "ssh"))
end
set_url(easy::Easy, url::AbstractString) = set_url(easy, String(url))

function set_ssl_verify(easy::Easy, verify::Bool)
    setopt(easy, CURLOPT_SSL_VERIFYPEER, verify)
end

function set_ssh_verify(easy::Easy, verify::Bool)
    if !verify
        setopt(easy, CURLOPT_SSH_KNOWNHOSTS, C_NULL)
    else
        file = ssh_known_hosts_file()
        setopt(easy, CURLOPT_SSH_KNOWNHOSTS, file)
    end
end

function set_method(easy::Easy, method::Union{String, SubString{String}})
    # TODO: ideally, Clang would generate Cstring signatures
    Base.unsafe_convert(Cstring, method) # error checking
    setopt(easy, CURLOPT_CUSTOMREQUEST, method)
end
set_method(easy::Easy, method::AbstractString) = set_method(easy, String(method))

function set_verbose(easy::Easy, verbose::Bool)
    setopt(easy, CURLOPT_VERBOSE, verbose)
end

function set_debug(easy::Easy, debug::Function)
    hasmethod(debug, Tuple{String,String}) ||
        throw(ArgumentError("debug callback must take (::String, ::String)"))
    easy.debug = debug
    add_debug_callback(easy)
    set_verbose(easy, true)
end

function set_debug(easy::Easy, debug::Nothing)
    easy.debug = nothing
    remove_debug_callback(easy)
end

function set_body(easy::Easy, body::Bool)
    setopt(easy, CURLOPT_NOBODY, !body)
end

function set_upload_size(easy::Easy, size::Integer)
    opt = Sys.WORD_SIZE ≥ 64 ? CURLOPT_INFILESIZE_LARGE : CURLOPT_INFILESIZE
    setopt(easy, opt, size)
end

function set_seeker(seeker::Function, easy::Easy)
    add_seek_callback(easy)
    easy.seeker = seeker
end

function set_timeout(easy::Easy, timeout::Real)
    timeout > 0 ||
        throw(ArgumentError("timeout must be positive, got $timeout"))
    if timeout ≤ typemax(Clong) ÷ 1000
        timeout_ms = round(Clong, timeout * 1000)
        setopt(easy, CURLOPT_TIMEOUT_MS, timeout_ms)
    else
        timeout = timeout ≤ typemax(Clong) ? round(Clong, timeout) : Clong(0)
        setopt(easy, CURLOPT_TIMEOUT, timeout)
    end
end

function add_header(easy::Easy, hdr::Union{String, SubString{String}})
    # TODO: ideally, Clang would generate Cstring signatures
    Base.unsafe_convert(Cstring, hdr) # error checking
    easy.req_hdrs = curl_slist_append(easy.req_hdrs, hdr)
    setopt(easy, CURLOPT_HTTPHEADER, easy.req_hdrs)
end

add_header(easy::Easy, hdr::AbstractString) = add_header(easy, string(hdr)::String)
add_header(easy::Easy, key::AbstractString, val::AbstractString) =
    add_header(easy, isempty(val) ? "$key;" : "$key: $val")
add_header(easy::Easy, key::AbstractString, val::Nothing) =
    add_header(easy, "$key:")
add_header(easy::Easy, pair::Pair) = add_header(easy, pair...)

function add_headers(easy::Easy, headers::Union{AbstractVector, AbstractDict})
    for hdr in headers
        hdr isa Pair{<:AbstractString, <:Union{AbstractString, Nothing}} ||
            throw(ArgumentError("invalid header: $(repr(hdr))"))
        add_header(easy, hdr)
    end
end

function enable_progress(easy::Easy, on::Bool=true)
    setopt(easy, CURLOPT_NOPROGRESS, !on)
end

function enable_upload(easy::Easy)
    add_upload_callback(easy::Easy)
    setopt(easy, CURLOPT_UPLOAD, true)
end

# response info

function get_protocol(easy::Easy)
    proto_ref = Ref{Clong}()
    r = @check curl_easy_getinfo(easy.handle, CURLINFO_PROTOCOL, proto_ref)
    r == CURLE_UNKNOWN_OPTION && error("The `libcurl` version you are using is too old and does not include the `CURLINFO_PROTOCOL` feature. Please upgrade or use a Julia build that uses its own `libcurl` library.")
    proto = proto_ref[]
    proto == CURLPROTO_DICT   && return "dict"
    proto == CURLPROTO_FILE   && return "file"
    proto == CURLPROTO_FTP    && return "ftp"
    proto == CURLPROTO_FTPS   && return "ftps"
    proto == CURLPROTO_GOPHER && return "gopher"
    proto == CURLPROTO_HTTP   && return "http"
    proto == CURLPROTO_HTTPS  && return "https"
    proto == CURLPROTO_IMAP   && return "imap"
    proto == CURLPROTO_IMAPS  && return "imaps"
    proto == CURLPROTO_LDAP   && return "ldap"
    proto == CURLPROTO_LDAPS  && return "ldaps"
    proto == CURLPROTO_POP3   && return "pop3"
    proto == CURLPROTO_POP3S  && return "pop3s"
    proto == CURLPROTO_RTMP   && return "rtmp"
    proto == CURLPROTO_RTMPE  && return "rtmpe"
    proto == CURLPROTO_RTMPS  && return "rtmps"
    proto == CURLPROTO_RTMPT  && return "rtmpt"
    proto == CURLPROTO_RTMPTE && return "rtmpte"
    proto == CURLPROTO_RTMPTS && return "rtmpts"
    proto == CURLPROTO_RTSP   && return "rtsp"
    proto == CURLPROTO_SCP    && return "scp"
    proto == CURLPROTO_SFTP   && return "sftp"
    proto == CURLPROTO_SMB    && return "smb"
    proto == CURLPROTO_SMBS   && return "smbs"
    proto == CURLPROTO_SMTP   && return "smtp"
    proto == CURLPROTO_SMTPS  && return "smtps"
    proto == CURLPROTO_TELNET && return "telnet"
    proto == CURLPROTO_TFTP   && return "tftp"
    return nothing
end

status_2xx_ok(status::Integer) = 200 ≤ status < 300
status_zero_ok(status::Integer) = status == 0

const PROTOCOL_STATUS = Dict{String,Function}(
    "dict"   => status_2xx_ok,
    "file"   => status_zero_ok,
    "ftp"    => status_2xx_ok,
    "ftps"   => status_2xx_ok,
    "http"   => status_2xx_ok,
    "https"  => status_2xx_ok,
    "ldap"   => status_zero_ok,
    "ldaps"  => status_zero_ok,
    "pop3"   => status_2xx_ok,
    "pop3s"  => status_2xx_ok,
    "rtsp"   => status_2xx_ok,
    "scp"    => status_zero_ok,
    "sftp"   => status_zero_ok,
    "smtp"   => status_2xx_ok,
    "smtps"  => status_2xx_ok,
)

function status_ok(proto::AbstractString, status::Integer)
    test = get(PROTOCOL_STATUS, proto, nothing)
    test !== nothing && return test(status)::Bool
    error("Downloads.jl doesn't know the correct request success criterion for $proto: you can use `request` and check the `status` field yourself or open an issue with Downloads with details an example URL that you are trying to download.")
end
status_ok(proto::Nothing, status::Integer) = false

function info_type(type::curl_infotype)
    type == 0 ? "TEXT" :
    type == 1 ? "HEADER IN" :
    type == 2 ? "HEADER OUT" :
    type == 3 ? "DATA IN" :
    type == 4 ? "DATA OUT" :
    type == 5 ? "SSL DATA IN" :
    type == 6 ? "SSL DATA OUT" :
                "UNKNOWN"
end

function get_effective_url(easy::Easy)
    url_ref = Ref{Ptr{Cchar}}()
    @check curl_easy_getinfo(easy.handle, CURLINFO_EFFECTIVE_URL, url_ref)
    return unsafe_string(url_ref[])
end

function get_response_status(easy::Easy)
    code_ref = Ref{Clong}()
    @check curl_easy_getinfo(easy.handle, CURLINFO_RESPONSE_CODE, code_ref)
    return Int(code_ref[])
end

function get_response_info(easy::Easy)
    proto = get_protocol(easy)
    url = get_effective_url(easy)
    status = get_response_status(easy)
    message = ""
    headers = Pair{String,String}[]
    if proto in ("http", "https")
        message = isempty(easy.res_hdrs) ? "" : easy.res_hdrs[1]
        for hdr in easy.res_hdrs
            if contains(hdr, r"^\s*$")
                # ignore
            elseif (m = match(r"^(HTTP/\d+(?:.\d+)?\s+\d+\b.*?)\s*$", hdr); m) !== nothing
                message = m.captures[1]::SubString{String}
                empty!(headers)
            elseif (m = match(r"^(\S[^:]*?)\s*:\s*(.*?)\s*$", hdr); m) !== nothing
                key = lowercase(m.captures[1]::SubString{String})
                val = m.captures[2]::SubString{String}
                push!(headers, key => val)
            else
                @warn "malformed HTTP header" url status header=hdr
            end
        end
    elseif proto in ("ftp", "ftps", "sftp")
        message = isempty(easy.res_hdrs) ? "" : easy.res_hdrs[end]
    else
        # TODO: parse headers of other protocols
    end
    message = chomp(message)
    endswith(message, '.') && (message = chop(message))
    return proto, url, status, message, headers
end

function get_curl_errstr(easy::Easy)
    easy.code == Curl.CURLE_OK && return ""
    errstr = easy.errbuf[1] == 0 ?
        unsafe_string(Curl.curl_easy_strerror(easy.code)) :
        GC.@preserve easy unsafe_string(pointer(easy.errbuf))
    return chomp(errstr)
end

# callbacks

function prereq_callback(
    easy_p           :: Ptr{Cvoid},
    conn_remote_ip   :: Ptr{Cchar},
    conn_local_ip    :: Ptr{Cchar},
    conn_remote_port :: Cint,
    conn_local_port  :: Cint,
)::Cint
    easy = unsafe_pointer_to_objref(easy_p)::Easy
    connect_semaphore_release(easy)
    return 0
end

function header_callback(
    data   :: Ptr{Cchar},
    size   :: Csize_t,
    count  :: Csize_t,
    easy_p :: Ptr{Cvoid},
)::Csize_t
    try
        easy = unsafe_pointer_to_objref(easy_p)::Easy
        n = size * count
        hdr = unsafe_string(data, n)
        push!(easy.res_hdrs, hdr)
        return n
    catch err
        @async @error("header_callback: unexpected error", err=err, maxlog=1_000)
        return typemax(Csize_t)
    end
end

# feed data to read_callback
function upload_data(easy::Easy, input::IO)
    while true
        data = eof(input) ? nothing : readavailable(input)
        easy.input === nothing && break
        easy.input = data
        curl_easy_pause(easy.handle, Curl.CURLPAUSE_CONT)
        wait(easy.ready)
        easy.input === nothing && break
        easy.ready = Threads.Event()
    end
end

function read_callback(
    data   :: Ptr{Cchar},
    size   :: Csize_t,
    count  :: Csize_t,
    easy_p :: Ptr{Cvoid},
)::Csize_t
    try
        easy = unsafe_pointer_to_objref(easy_p)::Easy
        buf = easy.input
        if buf === nothing
            notify(easy.ready)
            return 0 # done uploading
        end
        if isempty(buf)
            notify(easy.ready)
            return CURL_READFUNC_PAUSE # wait for more data
        end
        n = min(size * count, length(buf))
        ccall(:memcpy, Ptr{Cvoid}, (Ptr{Cvoid}, Ptr{Cvoid}, Csize_t), data, buf, n)
        deleteat!(buf, 1:n)
        return n
    catch err
        @async @error("read_callback: unexpected error", err=err, maxlog=1_000)
        return CURL_READFUNC_ABORT
    end
end

function seek_callback(
    easy_p :: Ptr{Cvoid},
    offset :: curl_off_t,
    origin :: Cint,
)::Cint
    try
        if origin != 0
            @async @error("seek_callback: unsupported seek origin", origin, maxlog=1_000)
            return CURL_SEEKFUNC_CANTSEEK
        end
        easy = unsafe_pointer_to_objref(easy_p)::Easy
        easy.seeker === nothing && return CURL_SEEKFUNC_CANTSEEK
        try easy.seeker(offset)
        catch err
            @async @error("seek_callback: seeker failed", err, maxlog=1_000)
            return CURL_SEEKFUNC_FAIL
        end
        return CURL_SEEKFUNC_OK
    catch err
        @async @error("seek_callback: unexpected error", err=err, maxlog=1_000)
        return CURL_SEEKFUNC_FAIL
    end
end

function write_callback(
    data   :: Ptr{Cchar},
    size   :: Csize_t,
    count  :: Csize_t,
    easy_p :: Ptr{Cvoid},
)::Csize_t
    try
        easy = unsafe_pointer_to_objref(easy_p)::Easy
        n = size * count
        buf = Array{UInt8}(undef, n)
        ccall(:memcpy, Ptr{Cvoid}, (Ptr{Cvoid}, Ptr{Cvoid}, Csize_t), buf, data, n)
        put!(easy.output, buf)
        return n
    catch err
        @async @error("write_callback: unexpected error", err=err, maxlog=1_000)
        return typemax(Csize_t)
    end
end

function progress_callback(
    easy_p   :: Ptr{Cvoid},
    dl_total :: curl_off_t,
    dl_now   :: curl_off_t,
    ul_total :: curl_off_t,
    ul_now   :: curl_off_t,
)::Cint
    try
        easy = unsafe_pointer_to_objref(easy_p)::Easy
        put!(easy.progress, (dl_total, dl_now, ul_total, ul_now))
        return 0
    catch err
        @async @error("progress_callback: unexpected error", err=err, maxlog=1_000)
        return -1
    end
end

function debug_callback(
    handle :: Ptr{Cvoid},
    type   :: curl_infotype,
    data   :: Ptr{Cchar},
    size   :: Csize_t,
    easy_p :: Ptr{Cvoid},
)::Cint
    try
        easy = unsafe_pointer_to_objref(easy_p)::Easy
        @assert easy.handle == handle
        easy.debug(info_type(type), unsafe_string(data, size))
        return 0
    catch err
        @async @error("debug_callback: unexpected error", err=err, maxlog=1_000)
        return -1
    end
end

function add_callbacks(easy::Easy)
    # pointer to easy object
    easy_p = pointer_from_objref(easy)
    setopt(easy, CURLOPT_PRIVATE, easy_p)

    # pointer to error buffer
    errbuf_p = pointer(easy.errbuf)
    setopt(easy, CURLOPT_ERRORBUFFER, errbuf_p)

    # set pre-request callback
    prereq_cb = @cfunction(prereq_callback,
        Cint, (Ptr{Cvoid}, Ptr{Cchar}, Ptr{Cchar}, Cint, Cint))
    setopt(easy, CURLOPT_PREREQFUNCTION, prereq_cb)
    setopt(easy, CURLOPT_PREREQDATA, easy_p)

    # set header callback
    header_cb = @cfunction(header_callback,
        Csize_t, (Ptr{Cchar}, Csize_t, Csize_t, Ptr{Cvoid}))
    setopt(easy, CURLOPT_HEADERFUNCTION, header_cb)
    setopt(easy, CURLOPT_HEADERDATA, easy_p)

    # set write callback
    write_cb = @cfunction(write_callback,
        Csize_t, (Ptr{Cchar}, Csize_t, Csize_t, Ptr{Cvoid}))
    setopt(easy, CURLOPT_WRITEFUNCTION, write_cb)
    setopt(easy, CURLOPT_WRITEDATA, easy_p)

    # set progress callback
    progress_cb = @cfunction(progress_callback,
        Cint, (Ptr{Cvoid}, curl_off_t, curl_off_t, curl_off_t, curl_off_t))
    setopt(easy, CURLOPT_XFERINFOFUNCTION, progress_cb)
    setopt(easy, CURLOPT_XFERINFODATA, easy_p)
end

function add_upload_callback(easy::Easy)
    # pointer to easy object
    easy_p = pointer_from_objref(easy)

    # set read callback
    read_cb = @cfunction(read_callback,
        Csize_t, (Ptr{Cchar}, Csize_t, Csize_t, Ptr{Cvoid}))
    setopt(easy, CURLOPT_READFUNCTION, read_cb)
    setopt(easy, CURLOPT_READDATA, easy_p)
end

function add_seek_callback(easy::Easy)
    # pointer to easy object
    easy_p = pointer_from_objref(easy)

    # set seek callback
    seek_cb = @cfunction(seek_callback,
        Cint, (Ptr{Cvoid}, curl_off_t, Cint))
    setopt(easy, CURLOPT_SEEKFUNCTION, seek_cb)
    setopt(easy, CURLOPT_SEEKDATA, easy_p)
end

function add_debug_callback(easy::Easy)
    # pointer to easy object
    easy_p = pointer_from_objref(easy)

    # set debug callback
    debug_cb = @cfunction(debug_callback,
        Cint, (Ptr{Cvoid}, curl_infotype, Ptr{Cchar}, Csize_t, Ptr{Cvoid}))
    setopt(easy, CURLOPT_DEBUGFUNCTION, debug_cb)
    setopt(easy, CURLOPT_DEBUGDATA, easy_p)
end

function remove_debug_callback(easy::Easy)
    setopt(easy, CURLOPT_DEBUGFUNCTION, C_NULL)
    setopt(easy, CURLOPT_DEBUGDATA, C_NULL)
end
w   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Downloads/src/Curl/Multi.jl�      mutable struct Multi
    lock   :: ReentrantLock
    handle :: Ptr{Cvoid}
    timer  :: Union{Nothing,Timer}
    easies :: Vector{Easy}
    grace  :: UInt64

    function Multi(grace::Integer = typemax(UInt64))
        multi = new(ReentrantLock(), C_NULL, nothing, Easy[], grace)
        finalizer(done!, multi)
        @lock MULTIS_LOCK push!(filter!(m -> m.value isa Multi, MULTIS), WeakRef(multi))
        return multi
    end
end

function init!(multi::Multi)
    multi.handle != C_NULL && return
    multi.handle = curl_multi_init()
    add_callbacks(multi)
    set_defaults(multi)
    nothing
end

function done!(multi::Multi)
    stoptimer!(multi)
    handle = multi.handle
    handle == C_NULL && return
    multi.handle = C_NULL
    curl_multi_cleanup(handle)
    nothing
end

function stoptimer!(multi::Multi)
    t = multi.timer
    if t !== nothing
        multi.timer = nothing
        close(t)
    end
    nothing
end

# adding & removing easy handles

function add_handle(multi::Multi, easy::Easy)
    connect_semaphore_acquire(easy)
    lock(multi.lock) do
        if isempty(multi.easies)
            preserve_handle(multi)
        end
        push!(multi.easies, easy)
        init!(multi)
        @check curl_multi_add_handle(multi.handle, easy.handle)
    end
end

const MULTIS_LOCK = Base.ReentrantLock()
const MULTIS = WeakRef[]
# Close any Multis and their timers at exit that haven't been finalized by then
Base.atexit() do
    while true
        w = @lock MULTIS_LOCK (isempty(MULTIS) ? nothing : pop!(MULTIS))
        w === nothing && break
        w = w.value
        w isa Multi && done!(w)
    end
end

function remove_handle(multi::Multi, easy::Easy)
    lock(multi.lock) do
        @check curl_multi_remove_handle(multi.handle, easy.handle)
        deleteat!(multi.easies, findlast(==(easy), multi.easies)::Int)
        isempty(multi.easies) || return
        stoptimer!(multi)
        if multi.grace <= 0
            done!(multi)
        elseif 0 < multi.grace < typemax(multi.grace)
            multi.timer = Timer(multi.grace/1000) do timer
                lock(multi.lock) do
                    multi.timer === timer || return
                    multi.timer = nothing
                    done!(multi)
                end
            end
        end
        unpreserve_handle(multi)
    end
    connect_semaphore_release(easy)
end

# multi-socket options

function set_defaults(multi::Multi)
    # currently no defaults
end

# multi-socket handle state updates

struct CURLMsg
   msg  :: CURLMSG
   easy :: Ptr{Cvoid}
   code :: CURLcode
end

function check_multi_info(multi::Multi)
    while true
        p = curl_multi_info_read(multi.handle, Ref{Cint}())
        p == C_NULL && return
        message = unsafe_load(convert(Ptr{CURLMsg}, p))
        if message.msg == CURLMSG_DONE
            easy_handle = message.easy
            easy_p_ref = Ref{Ptr{Cvoid}}()
            @check curl_easy_getinfo(easy_handle, CURLINFO_PRIVATE, easy_p_ref)
            easy = unsafe_pointer_to_objref(easy_p_ref[])::Easy
            @assert easy_handle == easy.handle
            easy.code = message.code
            close(easy.progress)
            close(easy.output)
            easy.input = nothing
            notify(easy.ready)
        else
            @async @error("curl_multi_info_read: unknown message", message, maxlog=1_000)
        end
    end
end

# curl callbacks

function do_multi(multi::Multi)
    @check curl_multi_socket_action(multi.handle, CURL_SOCKET_TIMEOUT, 0)
    check_multi_info(multi)
end

function timer_callback(
    multi_h    :: Ptr{Cvoid},
    timeout_ms :: Clong,
    multi_p    :: Ptr{Cvoid},
)::Cint
    try
        multi = unsafe_pointer_to_objref(multi_p)::Multi
        @assert multi_h == multi.handle
        stoptimer!(multi)
        if timeout_ms >= 0
            multi.timer = Timer(timeout_ms/1000) do timer
                lock(multi.lock) do
                    multi.timer === timer || return
                    multi.timer = nothing
                    do_multi(multi)
                end
            end
        elseif timeout_ms != -1
            @async @error("timer_callback: invalid timeout value", timeout_ms, maxlog=1_000)
            return -1
        end
        return 0
    catch err
        @async @error("timer_callback: unexpected error", err=err, maxlog=1_000)
        return -1
    end
end

function socket_callback(
    easy_h    :: Ptr{Cvoid},
    sock      :: curl_socket_t,
    action    :: Cint,
    multi_p   :: Ptr{Cvoid},
    watcher_p :: Ptr{Cvoid},
)::Cint
    try
        if action ∉ (CURL_POLL_IN, CURL_POLL_OUT, CURL_POLL_INOUT, CURL_POLL_REMOVE)
            @async @error("socket_callback: unexpected action", action, maxlog=1_000)
            return -1
        end
        multi = unsafe_pointer_to_objref(multi_p)::Multi
        if watcher_p != C_NULL
            old_watcher = unsafe_pointer_to_objref(watcher_p)::FDWatcher
            @check curl_multi_assign(multi.handle, sock, C_NULL)
            unpreserve_handle(old_watcher)
        end
        if action in (CURL_POLL_IN, CURL_POLL_OUT, CURL_POLL_INOUT)
            readable = action in (CURL_POLL_IN,  CURL_POLL_INOUT)
            writable = action in (CURL_POLL_OUT, CURL_POLL_INOUT)
            watcher = FDWatcher(OS_HANDLE(sock), readable, writable)
            preserve_handle(watcher)
            watcher_p = pointer_from_objref(watcher)
            @check curl_multi_assign(multi.handle, sock, watcher_p)
            task = @async while watcher.readable || watcher.writable # isopen(watcher)
                events = try
                    wait(watcher)
                catch err
                    err isa EOFError && return
                    err isa Base.IOError || rethrow()
                    FileWatching.FDEvent()
                end
                flags = CURL_CSELECT_IN  * isreadable(events) +
                        CURL_CSELECT_OUT * iswritable(events) +
                        CURL_CSELECT_ERR * (events.disconnect || events.timedout)
                lock(multi.lock) do
                    watcher.readable || watcher.writable || return # !isopen
                    @check curl_multi_socket_action(multi.handle, sock, flags)
                    check_multi_info(multi)
                end
            end
            @isdefined(errormonitor) && errormonitor(task)
        end
        @isdefined(old_watcher) && close(old_watcher)
        return 0
    catch err
        @async @error("socket_callback: unexpected error", err=err, maxlog=1_000)
        return -1
    end
end

function add_callbacks(multi::Multi)
    multi_p = pointer_from_objref(multi)

    # set timer callback
    timer_cb = @cfunction(timer_callback, Cint, (Ptr{Cvoid}, Clong, Ptr{Cvoid}))
    setopt(multi, CURLMOPT_TIMERFUNCTION, timer_cb)
    setopt(multi, CURLMOPT_TIMERDATA, multi_p)

    # set socket callback
    socket_cb = @cfunction(socket_callback,
        Cint, (Ptr{Cvoid}, curl_socket_t, Cint, Ptr{Cvoid}, Ptr{Cvoid}))
    setopt(multi, CURLMOPT_SOCKETFUNCTION, socket_cb)
    setopt(multi, CURLMOPT_SOCKETDATA, multi_p)
end
j   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Pkg/src/Pkg.jl{�      # This file is a part of Julia. License is MIT: https://julialang.org/license

module Pkg

if isdefined(Base, :Experimental) && isdefined(Base.Experimental, Symbol("@max_methods"))
    @eval Base.Experimental.@max_methods 1
end

import Random
import REPL
import TOML
using Dates

export @pkg_str
export PackageSpec
export PackageMode, PKGMODE_MANIFEST, PKGMODE_PROJECT
export UpgradeLevel, UPLEVEL_MAJOR, UPLEVEL_MINOR, UPLEVEL_PATCH
export PreserveLevel, PRESERVE_TIERED_INSTALLED, PRESERVE_TIERED, PRESERVE_ALL_INSTALLED, PRESERVE_ALL, PRESERVE_DIRECT, PRESERVE_SEMVER, PRESERVE_NONE
export Registry, RegistrySpec

depots() = Base.DEPOT_PATH
function depots1()
    d = depots()
    isempty(d) && Pkg.Types.pkgerror("no depots found in DEPOT_PATH")
    return d[1]
end

function pkg_server()
    server = get(ENV, "JULIA_PKG_SERVER", "https://pkg.julialang.org")
    isempty(server) && return nothing
    startswith(server, r"\w+://") || (server = "https://$server")
    return rstrip(server, '/')
end

logdir(depot = depots1()) = joinpath(depot, "logs")
devdir(depot = depots1()) = get(ENV, "JULIA_PKG_DEVDIR", joinpath(depot, "dev"))
envdir(depot = depots1()) = joinpath(depot, "environments")
const UPDATED_REGISTRY_THIS_SESSION = Ref(false)
const OFFLINE_MODE = Ref(false)
const RESPECT_SYSIMAGE_VERSIONS = Ref(true)
# For globally overriding in e.g. tests
const DEFAULT_IO = Ref{Union{IO,Nothing}}(nothing)
stderr_f() = something(DEFAULT_IO[], stderr)
stdout_f() = something(DEFAULT_IO[], stdout)
const PREV_ENV_PATH = Ref{String}("")

can_fancyprint(io::IO) = (io isa Base.TTY) && (get(ENV, "CI", nothing) != "true")
should_autoprecompile() = Base.JLOptions().use_compiled_modules == 1 && Base.get_bool_env("JULIA_PKG_PRECOMPILE_AUTO", true)

include("utils.jl")
include("MiniProgressBars.jl")
include("GitTools.jl")
include("PlatformEngines.jl")
include("Versions.jl")
include("Registry/Registry.jl")
include("Resolve/Resolve.jl")
include("Types.jl")
include("BinaryPlatforms_compat.jl")
include("Artifacts.jl")
include("Operations.jl")
include("API.jl")
include("REPLMode/REPLMode.jl")

import .REPLMode: @pkg_str
import .Types: UPLEVEL_MAJOR, UPLEVEL_MINOR, UPLEVEL_PATCH, UPLEVEL_FIXED
import .Types: PKGMODE_MANIFEST, PKGMODE_PROJECT
import .Types: PRESERVE_TIERED_INSTALLED, PRESERVE_TIERED, PRESERVE_ALL_INSTALLED, PRESERVE_ALL, PRESERVE_DIRECT, PRESERVE_SEMVER, PRESERVE_NONE

# Import artifacts API
using .Artifacts, .PlatformEngines


"""
    PackageMode

An enum with the instances

  * `PKGMODE_MANIFEST`
  * `PKGMODE_PROJECT`

Determines if operations should be made on a project or manifest level.
Used as an argument to [`Pkg.rm`](@ref), [`Pkg.update`](@ref) and [`Pkg.status`](@ref).
"""
const PackageMode = Types.PackageMode


"""
    UpgradeLevel

An enum with the instances

  * `UPLEVEL_FIXED`
  * `UPLEVEL_PATCH`
  * `UPLEVEL_MINOR`
  * `UPLEVEL_MAJOR`

Determines how much a package is allowed to be updated.
Used as an argument to  [`PackageSpec`](@ref) or as an argument to [`Pkg.update`](@ref).
"""
const UpgradeLevel = Types.UpgradeLevel

const PreserveLevel = Types.PreserveLevel

# Define new variables so tab comleting Pkg. works.
"""
    Pkg.add(pkg::Union{String, Vector{String}}; preserve=PRESERVE_TIERED)
    Pkg.add(pkg::Union{PackageSpec, Vector{PackageSpec}}; preserve=PRESERVE_TIERED)

Add a package to the current project. This package will be available by using the
`import` and `using` keywords in the Julia REPL, and if the current project is
a package, also inside that package.

## Resolution Tiers
`Pkg` resolves the set of packages in your environment using a tiered algorithm.
The `preserve` keyword argument allows you to key into a specific tier in the resolve algorithm.
The following table describes the argument values for `preserve` (in order of strictness):

| Value                       | Description                                                                        |
|:----------------------------|:-----------------------------------------------------------------------------------|
| `PRESERVE_ALL_INSTALLED`    | Like `PRESERVE_ALL` and only add those already installed                           |
| `PRESERVE_ALL`              | Preserve the state of all existing dependencies (including recursive dependencies) |
| `PRESERVE_DIRECT`           | Preserve the state of all existing direct dependencies                             |
| `PRESERVE_SEMVER`           | Preserve semver-compatible versions of direct dependencies                         |
| `PRESERVE_NONE`             | Do not attempt to preserve any version information                                 |
| `PRESERVE_TIERED_INSTALLED` | Like `PRESERVE_TIERED` except `PRESERVE_ALL_INSTALLED` is tried first              |
| `PRESERVE_TIERED`           | Use the tier that will preserve the most version information while                 |
|                             | allowing version resolution to succeed (this is the default)                       |

!!! note
    To change the default strategy to `PRESERVE_TIERED_INSTALLED` set the env var `JULIA_PKG_PRESERVE_TIERED_INSTALLED`
    to true.

After the installation of new packages the project will be precompiled. For more information see `pkg> ?precompile`.

With the `PRESERVE_ALL_INSTALLED` strategy the newly added packages will likely already be precompiled, but if not this
may be because either the combination of package versions resolved in this environment has not been resolved and
precompiled before, or the precompile cache has been deleted by the LRU cache storage
(see `JULIA_MAX_NUM_PRECOMPILE_FILES`).

!!! compat "Julia 1.9"
    The `PRESERVE_TIERED_INSTALLED` and `PRESERVE_ALL_INSTALLED` strategies requires at least Julia 1.9.

# Examples
```julia
Pkg.add("Example") # Add a package from registry
Pkg.add("Example"; preserve=Pkg.PRESERVE_ALL) # Add the `Example` package and strictly preserve existing dependencies
Pkg.add(name="Example", version="0.3") # Specify version; latest release in the 0.3 series
Pkg.add(name="Example", version="0.3.1") # Specify version; exact release
Pkg.add(url="https://github.com/JuliaLang/Example.jl", rev="master") # From url to remote gitrepo
Pkg.add(url="/remote/mycompany/juliapackages/OurPackage") # From path to local gitrepo
Pkg.add(url="https://github.com/Company/MonoRepo", subdir="juliapkgs/Package.jl)") # With subdir
```

After the installation of new packages the project will be precompiled. See more at [Environment Precompilation](@ref).

See also [`PackageSpec`](@ref), [`Pkg.develop`](@ref).
"""
const add = API.add

"""
    Pkg.precompile(; strict::Bool=false, timing::Bool=false)
    Pkg.precompile(pkg; strict::Bool=false, timing::Bool=false)
    Pkg.precompile(pkgs; strict::Bool=false, timing::Bool=false)

Precompile all or specific dependencies of the project in parallel.

Set `timing=true` to show the duration of the precompilation of each dependency.

!!! note
    Errors will only throw when precompiling the top-level dependencies, given that
    not all manifest dependencies may be loaded by the top-level dependencies on the given system.
    This can be overridden to make errors in all dependencies throw by setting the kwarg `strict` to `true`

!!! note
    This method is called automatically after any Pkg action that changes the manifest.
    Any packages that have previously errored during precompilation won't be retried in auto mode
    until they have changed. To disable automatic precompilation set `ENV["JULIA_PKG_PRECOMPILE_AUTO"]=0`.
    To manually control the number of tasks used set `ENV["JULIA_NUM_PRECOMPILE_TASKS"]`.

!!! compat "Julia 1.8"
    Specifying packages to precompile requires at least Julia 1.8.

!!! compat "Julia 1.9"
    Timing mode requires at least Julia 1.9.

# Examples
```julia
Pkg.precompile()
Pkg.precompile("Foo")
Pkg.precompile(["Foo", "Bar"])
```
"""
const precompile = API.precompile

"""
    Pkg.rm(pkg::Union{String, Vector{String}}; mode::PackageMode = PKGMODE_PROJECT)
    Pkg.rm(pkg::Union{PackageSpec, Vector{PackageSpec}}; mode::PackageMode = PKGMODE_PROJECT)

Remove a package from the current project. If `mode` is equal to
`PKGMODE_MANIFEST` also remove it from the manifest including all
recursive dependencies of `pkg`.

See also [`PackageSpec`](@ref), [`PackageMode`](@ref).
"""
const rm = API.rm

"""
    Pkg.why(pkg::Union{String, Vector{String}})
    Pkg.why(pkg::Union{PackageSpec, Vector{PackageSpec}})

Show the reason why this package is in the manifest.
The output is all the different ways to reach the package
through the dependency graph starting from the dependencies.

!!! compat "Julia 1.9"
    This function requires at least Julia 1.9.
"""
const why = API.why

"""
    Pkg.update(; level::UpgradeLevel=UPLEVEL_MAJOR, mode::PackageMode = PKGMODE_PROJECT, preserve::PreserveLevel)
    Pkg.update(pkg::Union{String, Vector{String}})
    Pkg.update(pkg::Union{PackageSpec, Vector{PackageSpec}})

If no positional argument is given, update all packages in the manifest if `mode` is `PKGMODE_MANIFEST` and packages in both manifest and project if `mode` is `PKGMODE_PROJECT`.
If no positional argument is given, `level` can be used to control by how much packages are allowed to be upgraded (major, minor, patch, fixed).

If packages are given as positional arguments, the `preserve` argument can be used to control what other packages are allowed to update:
- `PRESERVE_ALL` (default): Only allow `pkg` to update.
- `PRESERVE_DIRECT`: Only allow `pkg` and indirect dependencies that are not a direct dependency in the project to update.
- `PRESERVE_NONE`: Allow `pkg` and all its indirect dependencies to update.

After any package updates the project will be precompiled. See more at [Environment Precompilation](@ref).

See also [`PackageSpec`](@ref), [`PackageMode`](@ref), [`UpgradeLevel`](@ref).
"""
const update = API.up

"""
    Pkg.test(; kwargs...)
    Pkg.test(pkg::Union{String, Vector{String}; kwargs...)
    Pkg.test(pkgs::Union{PackageSpec, Vector{PackageSpec}}; kwargs...)

**Keyword arguments:**
  - `coverage::Bool=false`: enable or disable generation of coverage statistics.
  - `allow_reresolve::Bool=true`: allow Pkg to reresolve the package versions in the test environment
  - `julia_args::Union{Cmd, Vector{String}}`: options to be passed the test process.
  - `test_args::Union{Cmd, Vector{String}}`: test arguments (`ARGS`) available in the test process.

!!! compat "Julia 1.9"
    `allow_reresolve` requires at least Julia 1.9.

Run the tests for package `pkg`, or for the current project (which thus needs to be a package) if no
positional argument is given to `Pkg.test`. A package is tested by running its
`test/runtests.jl` file.

The tests are run by generating a temporary environment with only the `pkg` package
and its (recursive) dependencies in it. If a manifest file exists and the `allow_reresolve`
keyword argument is set to `false`, the versions in the manifest file are used.
Otherwise a feasible set of packages is resolved and installed.

During the tests, test-specific dependencies are active, which are
given in the project file as e.g.

```
[extras]
Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"

[targets]
test = ["Test"]
```

The tests are executed in a new process with `check-bounds=yes` and by default `startup-file=no`.
If using the startup file (`~/.julia/config/startup.jl`) is desired, start julia with `--startup-file=yes`.
Inlining of functions during testing can be disabled (for better coverage accuracy)
by starting julia with `--inline=no`. The tests can be run as if different command line arguments were
passed to julia by passing the arguments instead to the `julia_args` keyword argument, e.g.

```
Pkg.test("foo"; julia_args=["--inline"])
```

To pass some command line arguments to be used in the tests themselves, pass the arguments to the
`test_args` keyword argument. These could be used to control the code being tested, or to control the
tests in some way. For example, the tests could have optional additional tests:
```
if "--extended" in ARGS
    @test some_function()
end
```
which could be enabled by testing with
```
Pkg.test("foo"; test_args=["--extended"])
```
"""
const test = API.test

"""
    Pkg.gc(; collect_delay::Period=Day(7), io::IO=stderr)

Garbage-collect package and artifact installations by sweeping over all known
`Manifest.toml` and `Artifacts.toml` files, noting those that have been deleted, and then
finding artifacts and packages that are thereafter not used by any other projects,
marking them as "orphaned".  This method will only remove orphaned objects (package
versions, artifacts, and scratch spaces) that have been continually un-used for a period
of `collect_delay`; which defaults to seven days.
"""
const gc = API.gc


"""
    Pkg.build(; verbose = false, io::IO=stderr)
    Pkg.build(pkg::Union{String, Vector{String}}; verbose = false, io::IO=stderr)
    Pkg.build(pkgs::Union{PackageSpec, Vector{PackageSpec}}; verbose = false, io::IO=stderr)

Run the build script in `deps/build.jl` for `pkg` and all of its dependencies in
depth-first recursive order.
If no argument is given to `build`, the current project is built, which thus needs
to be a package.
This function is called automatically on any package that gets installed
for the first time.
`verbose = true` prints the build output to `stdout`/`stderr` instead of
redirecting to the `build.log` file.
"""
const build = API.build

"""
    Pkg.pin(pkg::Union{String, Vector{String}}; io::IO=stderr, all_pkgs::Bool=false)
    Pkg.pin(pkgs::Union{PackageSpec, Vector{PackageSpec}}; io::IO=stderr, all_pkgs::Bool=false)

Pin a package to the current version (or the one given in the `PackageSpec`) or to a certain
git revision. A pinned package is never automatically updated: if `pkg` is tracking a path,
or a repository, those remain tracked but will not update.
To get updates from the origin path or remote repository the package must first be freed.

!!! compat "Julia 1.7"
    The `all_pkgs` kwarg was introduced in julia 1.7.

# Examples
```julia
Pkg.pin("Example")
Pkg.pin(name="Example", version="0.3.1")
Pkg.pin(all_pkgs = true)
```
"""
const pin = API.pin

"""
    Pkg.free(pkg::Union{String, Vector{String}}; io::IO=stderr, all_pkgs::Bool=false)
    Pkg.free(pkgs::Union{PackageSpec, Vector{PackageSpec}}; io::IO=stderr, all_pkgs::Bool=false)

If `pkg` is pinned, remove the pin.
If `pkg` is tracking a path, e.g. after [`Pkg.develop`](@ref), go back to tracking registered versions.
To free all dependencies set `all_pkgs=true`.

!!! compat "Julia 1.7"
    The `all_pkgs` kwarg was introduced in julia 1.7.

# Examples
```julia
Pkg.free("Package")
Pkg.free(all_pkgs = true)
```


"""
const free = API.free


"""
    Pkg.develop(pkg::Union{String, Vector{String}}; io::IO=stderr, preserve=PRESERVE_TIERED, installed=false)
    Pkg.develop(pkgs::Union{PackageSpec, Vector{PackageSpec}}; io::IO=stderr, preserve=PRESERVE_TIERED, installed=false)

Make a package available for development by tracking it by path.
If `pkg` is given with only a name or by a URL, the package will be downloaded
to the location specified by the environment variable `JULIA_PKG_DEVDIR`, with
`joinpath(DEPOT_PATH[1],"dev")` being the default.

If `pkg` is given as a local path, the package at that path will be tracked.

The preserve strategies offered by `Pkg.add` are also available via the `preserve` kwarg.
See [`Pkg.add`](@ref) for more information.

# Examples
```julia
# By name
Pkg.develop("Example")

# By url
Pkg.develop(url="https://github.com/JuliaLang/Compat.jl")

# By path
Pkg.develop(path="MyJuliaPackages/Package.jl")
```

See also [`PackageSpec`](@ref), [`Pkg.add`](@ref).

"""
const develop = API.develop

"""
    Pkg.generate(pkgname::String)

Create a minimal project called `pkgname` in the current folder. For more featureful package creation, please see `PkgTemplates.jl`.
"""
const generate = API.generate

"""
    Pkg.dependencies()::Dict{UUID, PackageInfo}

This feature is considered experimental.

Query the dependency graph of the active project.
The result is a `Dict` that maps a package UUID to a `PackageInfo` struct representing the dependency (a package).

# `PackageInfo` fields

| Field                 | Description                                                                       |
|:------------------    |:----------------------------------------------------------------------------------|
| `name`                | The name of the package                                                           |
| `version`             | The version of the package (this is `Nothing` for stdlibs)                        |
| `tree_hash`           | A file hash of the package directory tree                                         |
| `is_direct_dep`       | The package is a direct dependency                                                |
| `is_pinned`           | Whether a package is pinned                                                       |
| `is_tracking_path`    | Whether a package is tracking a path                                              |
| `is_tracking_repo`    | Whether a package is tracking a repository                                        |
| `is_tracking_registry`| Whether a package is being tracked by registry i.e. not by path nor by repository |
| `git_revision`        | The git revision when tracking by repository                                      |
| `git_source`          | The git source when tracking by repository                                        |
| `source`              | The directory containing the source code for that package                         |
| `dependencies`        | The dependencies of that package as a vector of UUIDs                             |
"""
const dependencies = API.dependencies

"""
    Pkg.project()::ProjectInfo

This feature is considered experimental.

Request a `ProjectInfo` struct which contains information about the active project.

# `ProjectInfo` fields

| Field        | Description                                                                                 |
|:-------------|:--------------------------------------------------------------------------------------------|
| name         | The project's name                                                                          |
| uuid         | The project's UUID                                                                          |
| version      | The project's version                                                                       |
| ispackage    | Whether the project is a package (has a name and uuid)                                      |
| dependencies | The project's direct dependencies as a `Dict` which maps dependency name to dependency UUID |
| path         | The location of the project file which defines the active project                           |
"""
const project = API.project

"""
    Pkg.instantiate(; verbose = false, io::IO=stderr)

If a `Manifest.toml` file exists in the active project, download all
the packages declared in that manifest.
Otherwise, resolve a set of feasible packages from the `Project.toml` files
and install them.
`verbose = true` prints the build output to `stdout`/`stderr` instead of
redirecting to the `build.log` file.
If no `Project.toml` exist in the current active project, create one with all the
dependencies in the manifest and instantiate the resulting project.

After packages have been installed the project will be precompiled.
See more at [Environment Precompilation](@ref).
"""
const instantiate = API.instantiate

"""
    Pkg.resolve(; io::IO=stderr)

Update the current manifest with potential changes to the dependency graph
from packages that are tracking a path.
"""
const resolve = API.resolve

"""
    Pkg.status([pkgs...]; outdated::Bool=false, mode::PackageMode=PKGMODE_PROJECT, diff::Bool=false, compat::Bool=false, extensions::Bool=false, io::IO=stdout)


Print out the status of the project/manifest.

Packages marked with `⌃` have new versions that can be installed, e.g. via [`Pkg.up`](@ref).
Those marked with `⌅` have new versions available, but cannot be installed due to compatibility conflicts with other packages. To see why, set the
keyword argument `outdated=true`.

Setting `outdated=true` will only show packages that are not on the latest version,
their maximum version and why they are not on the latest version (either due to other
packages holding them back due to compatibility constraints, or due to compatibility in the project file).
As an example, a status output like:
```
pkg> Pkg.status(; outdated=true)
Status `Manifest.toml`
⌃ [a8cc5b0e] Crayons v2.0.0 [<v3.0.0], (<v4.0.4)
⌅ [b8a86587] NearestNeighbors v0.4.8 (<v0.4.9) [compat]
⌅ [2ab3a3ac] LogExpFunctions v0.2.5 (<v0.3.0): SpecialFunctions
```
means that the latest version of Crayons is 4.0.4 but the latest version compatible
with the `[compat]` section in the current project is 3.0.0.
The latest version of NearestNeighbors is 0.4.9 but due to compat constrains in the project
it is held back to 0.4.8.
The latest version of LogExpFunctions is 0.3.0 but SpecialFunctions
is holding it back to 0.2.5.

If `mode` is `PKGMODE_PROJECT`, print out status only about the packages
that are in the project (explicitly added). If `mode` is `PKGMODE_MANIFEST`,
print status also about those in the manifest (recursive dependencies). If there are
any packages listed as arguments, the output will be limited to those packages.

Setting `ext=true` will show dependencies with extensions and what extension dependencies
of those that are currently loaded.

Setting `diff=true` will, if the environment is in a git repository, limit
the output to the difference as compared to the last git commit.

See [`Pkg.project`](@ref) and [`Pkg.dependencies`](@ref) to get the project/manifest
status as a Julia object instead of printing it.

!!! compat "Julia 1.8"
    The `⌃` and `⌅` indicators were added in Julia 1.8.
    The `outdated` keyword argument requires at least Julia 1.8.

"""
const status = API.status

"""
    Pkg.compat()

Interactively edit the [compat] entries within the current Project.

    Pkg.compat(pkg::String, compat::String)

Set the [compat] string for the given package within the current Project.

See [Compatibility](@ref) for more information on the project [compat] section.
"""
const compat = API.compat

"""
    Pkg.activate([s::String]; shared::Bool=false, io::IO=stderr)
    Pkg.activate(; temp::Bool=false, shared::Bool=false, io::IO=stderr)

Activate the environment at `s`. The active environment is the environment
that is modified by executing package commands.
The logic for what path is activated is as follows:

  * If `shared` is `true`, the first existing environment named `s` from the depots
    in the depot stack will be activated. If no such environment exists,
    create and activate that environment in the first depot.
  * If `temp` is `true` this will create and activate a temporary environment which will
    be deleted when the julia process is exited.
  * If `s` is an existing path, then activate the environment at that path.
  * If `s` is a package in the current project and `s` is tracking a path, then
    activate the environment at the tracked path.
  * Otherwise, `s` is interpreted as a non-existing path, which is then activated.

If no argument is given to `activate`, then use the first project found in `LOAD_PATH`.

# Examples
```
Pkg.activate()
Pkg.activate("local/path")
Pkg.activate("MyDependency")
Pkg.activate(; temp=true)
```
"""
const activate = API.activate

"""
    Pkg.offline(b::Bool=true)

Enable (`b=true`) or disable (`b=false`) offline mode.

In offline mode Pkg tries to do as much as possible without connecting
to internet. For example, when adding a package Pkg only considers
versions that are already downloaded in version resolution.

To work in offline mode across Julia sessions you can
set the environment variable `JULIA_PKG_OFFLINE` to `"true"`.
"""
offline(b::Bool=true) = (OFFLINE_MODE[] = b; nothing)

"""
    Pkg.respect_sysimage_versions(b::Bool=true)

Enable (`b=true`) or disable (`b=false`) respecting versions that are in the
sysimage (enabled by default).

If this option is enabled, Pkg will only install packages that have been put into the sysimage
(e.g. via PackageCompiler) at the version of the package in the sysimage.
Also, trying to add a package at a URL or `develop` a package that is in the sysimage
will error.
"""
respect_sysimage_versions(b::Bool=true) = (RESPECT_SYSIMAGE_VERSIONS[] = b; nothing)

"""
    PackageSpec(name::String, [uuid::UUID, version::VersionNumber])
    PackageSpec(; name, url, path, subdir, rev, version, mode, level)

A `PackageSpec` is a representation of a package with various metadata.
This includes:

  * The `name` of the package.
  * The package's unique `uuid`.
  * A `version` (for example when adding a package). When upgrading, can also be an instance of
    the enum [`UpgradeLevel`](@ref). If the version is given as a `String` this means that unspecified versions
    are "free", for example `version="0.5"` allows any version `0.5.x` to be installed. If given as a `VersionNumber`,
    the exact version is used, for example `version=v"0.5.3"`.
  * A `url` and an optional git `rev`ision. `rev` can be a branch name or a git commit SHA1.
  * A local `path`. This is equivalent to using the `url` argument but can be more descriptive.
  * A `subdir` which can be used when adding a package that is not in the root of a repository.

Most functions in Pkg take a `Vector` of `PackageSpec` and do the operation on all the packages
in the vector.

Many functions that take a `PackageSpec` or a `Vector{PackageSpec}` can be called with a more concise notation with `NamedTuple`s.
For example, `Pkg.add` can be called either as the explicit or concise versions as:

| Explicit                                                            | Concise                                        |
|:--------------------------------------------------------------------|:-----------------------------------------------|
| `Pkg.add(PackageSpec(name="Package"))`                              | `Pkg.add(name = "Package")`                    |
| `Pkg.add(PackageSpec(url="www.myhost.com/MyPkg")))`                 | `Pkg.add(name = "Package")`                    |
|` Pkg.add([PackageSpec(name="Package"), PackageSpec(path="/MyPkg"])` | `Pkg.add([(;name="Package"), (;path="MyPkg")])`|

Below is a comparison between the REPL mode and the functional API:

| `REPL`               | `API`                                                 |
|:---------------------|:------------------------------------------------------|
| `Package`            | `PackageSpec("Package")`                              |
| `Package@0.2`        | `PackageSpec(name="Package", version="0.2")`          |
| -                    | `PackageSpec(name="Package", version=v"0.2.1")`       |
| `Package=a67d...`    | `PackageSpec(name="Package", uuid="a67d...")`         |
| `Package#master`     | `PackageSpec(name="Package", rev="master")`           |
| `local/path#feature` | `PackageSpec(path="local/path"; rev="feature")`       |
| `www.mypkg.com`      | `PackageSpec(url="www.mypkg.com")`                    |
| `--major Package`    | `PackageSpec(name="Package", version=UPLEVEL_MAJOR)` |

"""
const PackageSpec = Types.PackageSpec

"""
    setprotocol!(;
        domain::AbstractString = "github.com",
        protocol::Union{Nothing, AbstractString}=nothing
    )

Set the protocol used to access hosted packages when `add`ing a url or `develop`ing a package.
Defaults to delegating the choice to the package developer (`protocol === nothing`).
Other choices for `protocol` are `"https"` or `"git"`.

# Examples
```julia-repl
julia> Pkg.setprotocol!(domain = "github.com", protocol = "ssh")

julia> Pkg.setprotocol!(domain = "gitlab.mycompany.com")
```
"""
const setprotocol! = API.setprotocol!

"""
    undo()

Undoes the latest change to the active project. Only states in the current session are stored,
up to a maximum of $(API.max_undo_limit) states.

See also: [`redo`](@ref).
"""
const undo = API.undo

"""
    redo()

Redoes the changes from the latest [`undo`](@ref).
"""
const redo = API.redo

"""
    RegistrySpec(name::String)
    RegistrySpec(; name, url, path)

A `RegistrySpec` is a representation of a registry with various metadata, much like
[`PackageSpec`](@ref).

Most registry functions in Pkg take a `Vector` of `RegistrySpec` and do the operation
on all the registries in the vector.

# Examples

Below is a comparison between the REPL mode and the functional API::

| `REPL`               | `API`                                             |
|:---------------------|:--------------------------------------------------|
| `MyRegistry`         | `RegistrySpec("MyRegistry")`                      |
| `MyRegistry=a67d...` | `RegistrySpec(name="MyRegistry", uuid="a67d...")` |
| `local/path`         | `RegistrySpec(path="local/path")`                 |
| `www.myregistry.com` | `RegistrySpec(url="www.myregistry.com")`          |
"""
const RegistrySpec = Registry.RegistrySpec

"""
    upgrade_manifest()
    upgrade_manifest(manifest_path::String)

Upgrades the format of the current or specified manifest file from v1.0 to v2.0 without re-resolving.
"""
const upgrade_manifest = API.upgrade_manifest

"""
    is_manifest_current(ctx::Context = Context())

Returns whether the active manifest was resolved from the active project state.
For instance, if the project had compat entries changed, but the manifest wasn't re-resolved, this would return false.

If the manifest doesn't have the project hash recorded, `nothing` is returned.
"""
const is_manifest_current = API.is_manifest_current

function __init__()
    Pkg.UPDATED_REGISTRY_THIS_SESSION[] = false
    if isdefined(Base, :active_repl)
        REPLMode.repl_init(Base.active_repl)
    else
        atreplinit() do repl
            if isinteractive() && repl isa REPL.LineEditREPL
                isdefined(repl, :interface) || (repl.interface = REPL.setup_interface(repl))
                REPLMode.repl_init(repl)
            end
        end
    end
    push!(empty!(REPL.install_packages_hooks), REPLMode.try_prompt_pkg_add)
    Base.PKG_PRECOMPILE_HOOK[] = precompile # allows Base to use Pkg.precompile during loading
    OFFLINE_MODE[] = Base.get_bool_env("JULIA_PKG_OFFLINE", false)
    return nothing
end

################
# Deprecations #
################

function installed()
    @warn "Pkg.installed() is deprecated"
    deps = dependencies()
    installs = Dict{String, VersionNumber}()
    for (uuid, dep) in deps
        dep.is_direct_dep || continue
        dep.version === nothing && continue
        installs[dep.name] = dep.version::VersionNumber
    end
    return installs
end

function dir(pkg::String, paths::AbstractString...)
    @warn "`Pkg.dir(pkgname, paths...)` is deprecated; instead, do `import $pkg; joinpath(dirname(pathof($pkg)), \"..\", paths...)`." maxlog=1
    pkgid = Base.identify_package(pkg)
    pkgid === nothing && return nothing
    path = Base.locate_package(pkgid)
    path === nothing && return nothing
    return abspath(path, "..", "..", paths...)
end

###########
# AUTO GC #
###########

const DEPOT_ORPHANAGE_TIMESTAMPS = Dict{String,Float64}()
const _auto_gc_enabled = Ref{Bool}(true)
function _auto_gc(ctx::Types.Context; collect_delay::Period = Day(7))
    if !_auto_gc_enabled[]
        return
    end

    # If we don't know the last time this depot was GC'ed (because this is the
    # first time we've looked this session), or it looks like we might want to
    # collect; let's go ahead and hit the filesystem to find the mtime of the
    # `orphaned.toml` file, which should tell us how long since the last time
    # we GC'ed.
    orphanage_path = joinpath(logdir(depots1()), "orphaned.toml")
    delay_secs = Second(collect_delay).value
    curr_time = time()
    if curr_time - get(DEPOT_ORPHANAGE_TIMESTAMPS, depots1(), 0.0) >= delay_secs
        DEPOT_ORPHANAGE_TIMESTAMPS[depots1()] = mtime(orphanage_path)
    end

    if curr_time - DEPOT_ORPHANAGE_TIMESTAMPS[depots1()] > delay_secs
        printpkgstyle(ctx.io, :Info, "We haven't cleaned this depot up for a bit, running Pkg.gc()...", color = Base.info_color())
        try
            Pkg.gc(ctx; collect_delay)
            DEPOT_ORPHANAGE_TIMESTAMPS[depots1()] = curr_time
        catch ex
            @error("GC failed", exception=ex)
        end
    end
end


##################
# Precompilation #
##################

function _auto_precompile(ctx::Types.Context, pkgs::Vector{PackageSpec}=PackageSpec[]; warn_loaded = true, already_instantiated = false)
    if should_autoprecompile()
        Pkg.precompile(ctx, pkgs; internal_call=true, warn_loaded = warn_loaded, already_instantiated = already_instantiated)
    end
end

using LibGit2: LibGit2
using Tar: Tar
function _run_precompilation_script_setup()
    tmp = mktempdir()
    cd(tmp)
    empty!(DEPOT_PATH)
    pushfirst!(DEPOT_PATH, tmp)
    touch("Project.toml")
    Pkg.activate(".")
    Pkg.generate("TestPkg")
    uuid = TOML.parsefile(joinpath("TestPkg", "Project.toml"))["uuid"]
    mv("TestPkg", "TestPkg.jl")
    tree_hash = cd("TestPkg.jl") do
        sig = LibGit2.Signature("TEST", "TEST@TEST.COM", round(time()), 0)
        repo = LibGit2.init(".")
        LibGit2.add!(repo, "")
        commit = LibGit2.commit(repo, "initial commit"; author=sig, committer=sig)
        th = LibGit2.peel(LibGit2.GitTree, LibGit2.GitObject(repo, commit)) |> LibGit2.GitHash |> string
        close(repo)
        th
    end
    # Prevent cloning the General registry by adding a fake one
    mkpath("registries/Registry/T/TestPkg")
    write("registries/Registry/Registry.toml", """
        name = "Registry"
        uuid = "37c07fec-e54c-4851-934c-2e3885e4053e"
        repo = "https://github.com/JuliaRegistries/Registry.git"
        [packages]
        $uuid = { name = "TestPkg", path = "T/TestPkg" }
        """)
    write("registries/Registry/T/TestPkg/Compat.toml", """
          ["0"]
          julia = "1"
          """)
    write("registries/Registry/T/TestPkg/Deps.toml", """
          ["0"]
          Dates = "ade2ca70-3891-5945-98fb-dc099432e06a"
          """)
    write("registries/Registry/T/TestPkg/Versions.toml", """
          ["0.1.0"]
          git-tree-sha1 = "$tree_hash"
          """)
    write("registries/Registry/T/TestPkg/Package.toml", """
        name = "TestPkg"
        uuid = "$uuid"
        repo = "$(escape_string(tmp))/TestPkg.jl"
        """)
    Tar.create("registries/Registry", "registries/Registry.tar")
    cmd = `$(Pkg.PlatformEngines.exe7z()) a "registries/Registry.tar.gz" -tgzip "registries/Registry.tar"`
    run(pipeline(cmd, stdout = stdout_f(), stderr = stderr_f()))
    write("registries/Registry.toml", """
          git-tree-sha1 = "11b5fad51c4f98cfe0c145ceab0b8fb63fed6f81"
          uuid = "37c07fec-e54c-4851-934c-2e3885e4053e"
          path = "Registry.tar.gz"
    """)
    Base.rm("registries/Registry"; recursive=true)
    return tmp
end

function _run_precompilation_script_artifact()
    # Create simple artifact, bind it, then use it:
    foo_hash = Pkg.Artifacts.create_artifact(dir -> touch(joinpath(dir, "foo")))
    Artifacts.bind_artifact!("./Artifacts.toml", "foo", foo_hash)
    # Also create multiple platform-specific ones because that's a codepath we need precompiled
    Artifacts.bind_artifact!("./Artifacts.toml", "foo_plat", foo_hash; platform=Base.BinaryPlatforms.HostPlatform())
    # Because @artifact_str doesn't work at REPL-level, we JIT out a file that we can include()
    write("load_artifact.jl", """
          Pkg.Artifacts.artifact"foo"
          Pkg.Artifacts.artifact"foo_plat"
          """)
    foo_path = include("load_artifact.jl")
end

const CTRL_C = '\x03'
const precompile_script = """
    import Pkg
    _pwd = pwd()
    Pkg.UPDATED_REGISTRY_THIS_SESSION[] = true
    tmp = Pkg._run_precompilation_script_setup()
    $CTRL_C
    Pkg.add("TestPkg")
    Pkg.develop(Pkg.PackageSpec(path="TestPkg.jl"))
    Pkg.add(Pkg.PackageSpec(path="TestPkg.jl/"))
    Pkg.REPLMode.try_prompt_pkg_add(Symbol[:notapackage])
    Pkg.update(; update_registry=false)
    Pkg.precompile()
    ] add Te\t\t$CTRL_C
    ] st
    $CTRL_C
    Pkg._run_precompilation_script_artifact()
    rm(tmp; recursive=true)
    cd(_pwd)
    """

end # module
l   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Pkg/src/utils.jla      
function printpkgstyle(io::IO, cmd::Symbol, text::String, ignore_indent::Bool=false; color=:green)
    indent = textwidth(string(:Precompiling)) # "Precompiling" is the longest operation
    ignore_indent && (indent = 0)
    printstyled(io, lpad(string(cmd), indent), color=color, bold=true)
    println(io, " ", text)
end

function linewrap(str::String; io = stdout_f(), padding = 0, width = Base.displaysize(io)[2])
    text_chunks = split(str, ' ')
    lines = String[""]
    for chunk in text_chunks
        new_line_attempt = string(last(lines), chunk, " ")
        if length(strip(new_line_attempt)) > width - padding
            lines[end] = strip(last(lines))
            push!(lines, string(chunk, " "))
        else
            lines[end] = new_line_attempt
        end
    end
    return lines
end

const URL_regex = r"((file|git|ssh|http(s)?)|(git@[\w\-\.]+))(:(//)?)([\w\.@\:/\-~]+)(\.git)?(/)?"x
isurl(r::String) = occursin(URL_regex, r)

stdlib_dir() = normpath(joinpath(Sys.BINDIR::String, "..", "share", "julia", "stdlib", "v$(VERSION.major).$(VERSION.minor)"))
stdlib_path(stdlib::String) = joinpath(stdlib_dir(), stdlib)

function pathrepr(path::String)
    # print stdlib paths as @stdlib/Name
    if startswith(path, stdlib_dir())
        path = "@stdlib/" * basename(path)
    end
    return "`" * Base.contractuser(path) * "`"
end

function set_readonly(path)
    for (root, dirs, files) in walkdir(path)
        for file in files
            filepath = joinpath(root, file)
            # `chmod` on a link would change the permissions of the target.  If
            # the link points to a file within the same root, it will be
            # chmod'ed anyway, but we don't want to make directories read-only.
            # It's better not to mess with the other cases (links to files
            # outside of the root, links to non-file/non-directories, etc...)
            islink(filepath) && continue
            fmode = filemode(filepath)
            @static if Sys.iswindows()
                if Sys.isexecutable(filepath)
                    fmode |= 0o111
                end
            end
            try
                chmod(filepath, fmode & (typemax(fmode) ⊻ 0o222))
            catch
            end
        end
    end
    return nothing
end
set_readonly(::Nothing) = nothing

# try to call realpath on as much as possible
function safe_realpath(path)
    isempty(path) && return path
    if ispath(path)
        try
            return realpath(path)
        catch
            return path
        end
    end
    a, b = splitdir(path)
    return joinpath(safe_realpath(a), b)
end

# Windows sometimes throw on `isdir`...
function isdir_nothrow(path::String)
    try isdir(path)
    catch e
        false
    end
end

function isfile_nothrow(path::String)
    try isfile(path)
    catch e
        false
    end
end

function casesensitive_isdir(dir::String)
    dir = abspath(dir)
    lastdir = splitpath(dir)[end]
    isdir_nothrow(dir) && lastdir in readdir(joinpath(dir, ".."))
end

## ordering of UUIDs ##
if VERSION < v"1.2.0-DEV.269"  # Defined in Base as of #30947
    Base.isless(a::UUID, b::UUID) = a.value < b.value
end
w   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Pkg/src/MiniProgressBars.jl�
      module MiniProgressBars

export MiniProgressBar, start_progress, end_progress, show_progress, print_progress_bottom

using Printf

Base.@kwdef mutable struct MiniProgressBar
    max::Int = 1.0
    header::String = ""
    color::Symbol = :nothing
    width::Int = 40
    current::Int = 0.0
    prev::Int = 0.0
    has_shown::Bool = false
    time_shown::Float64 = 0.0
    percentage::Bool = true
    always_reprint::Bool = false
    indent::Int = 4
end

const PROGRESS_BAR_TIME_GRANULARITY = Ref(1 / 30.0) # 30 fps
const PROGRESS_BAR_PERCENTAGE_GRANULARITY = Ref(0.1)

function start_progress(io::IO, _::MiniProgressBar)
    ansi_disablecursor = "\e[?25l"
    print(io, ansi_disablecursor)
end

function show_progress(io::IO, p::MiniProgressBar; termwidth=nothing, carriagereturn=true)
    if p.max == 0
        perc = 0.0
        prev_perc = 0.0
    else
        perc = p.current / p.max * 100
        prev_perc = p.prev / p.max * 100
    end
    # Bail early if we are not updating the progress bar,
    # Saves printing to the terminal
    if !p.always_reprint && p.has_shown && !((perc - prev_perc) > PROGRESS_BAR_PERCENTAGE_GRANULARITY[])
        return
    end
    t = time()
    if p.has_shown && (t - p.time_shown) < PROGRESS_BAR_TIME_GRANULARITY[]
        return
    end
    p.time_shown = t
    p.prev = p.current
    p.has_shown = true

    progress_text = if p.percentage
        @sprintf "%2.1f %%" perc
    else
        string(p.current, "/",  p.max)
    end
    termwidth = @something termwidth displaysize(io)[2]
    max_progress_width = max(0, min(termwidth - textwidth(p.header) - textwidth(progress_text) - 10 , p.width))
    n_filled = ceil(Int, max_progress_width * perc / 100)
    n_left = max_progress_width - n_filled
    to_print = sprint(; context=io) do io
        print(io, " "^p.indent)
        printstyled(io, p.header, color=p.color, bold=true)
        print(io, " [")
        print(io, "="^n_filled, ">")
        print(io, " "^n_left, "]  ", )
        print(io, progress_text)
        carriagereturn && print(io, "\r")
    end
    # Print everything in one call
    print(io, to_print)
end

function end_progress(io, p::MiniProgressBar)
    ansi_enablecursor = "\e[?25h"
    ansi_clearline = "\e[2K"
    print(io, ansi_enablecursor * ansi_clearline)
end

# Useful when writing a progress bar in the bottom
# makes the bottom progress bar not flicker
# prog = MiniProgressBar(...)
# prog.end = n
# for progress in 1:n
#     print_progree_bottom(io)
#     println("stuff")
#     prog.current = progress
#     showproress(io, prog)
#  end
#
function print_progress_bottom(io::IO)
    ansi_clearline = "\e[2K"
    ansi_movecol1 = "\e[1G"
    ansi_moveup(n::Int) = string("\e[", n, "A")
    print(io, "\e[S" * ansi_moveup(1) * ansi_clearline * ansi_movecol1)
end

end
o   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Pkg/src/GitTools.jl�.      # This file is a part of Julia. License is MIT: https://julialang.org/license

module GitTools

using ..Pkg
using ..MiniProgressBars
import ..can_fancyprint, ..printpkgstyle, ..stdout_f
using SHA
import Base: SHA1
import LibGit2
using Printf

use_cli_git() = Base.get_bool_env("JULIA_PKG_USE_CLI_GIT", false)

function transfer_progress(progress::Ptr{LibGit2.TransferProgress}, p::Any)
    progress = unsafe_load(progress)
    @assert haskey(p, :transfer_progress)
    bar = p[:transfer_progress]
    @assert typeof(bar) == MiniProgressBar
    if progress.total_deltas != 0
        bar.header = "Resolving Deltas:"
        bar.max = progress.total_deltas
        bar.current = progress.indexed_deltas
    else
        bar.max = progress.total_objects
        bar.current = progress.received_objects
    end
    show_progress(stdout_f(), bar)
    return Cint(0)
end

const GIT_REGEX =
    r"^(?:(?<proto>git|ssh|https)://)?(?:[\w\.\+\-:]+@)?(?<hostname>.+?)(?(<proto>)/|:)(?<path>.+?)(?:\.git)?$"
const GIT_PROTOCOLS = Dict{String, Union{Nothing, String}}()
const GIT_USERS = Dict{String, Union{Nothing, String}}()

@deprecate setprotocol!(proto::Union{Nothing, AbstractString}) setprotocol!(protocol = proto) false

function setprotocol!(;
    domain::AbstractString="github.com",
    protocol::Union{Nothing, AbstractString}=nothing,
    user::Union{Nothing, AbstractString}=(protocol == "ssh" ? "git" : nothing)
)
    domain = lowercase(domain)
    GIT_PROTOCOLS[domain] = protocol
    GIT_USERS[domain] = user
end

function normalize_url(url::AbstractString)
    # LibGit2 is fussy about trailing slash. Make sure there is none.
    url = rstrip(url, '/')
    m = match(GIT_REGEX, url)
    m === nothing && return url

    host = m[:hostname]
    path = "$(m[:path]).git"

    proto = get(GIT_PROTOCOLS, lowercase(host), nothing)

    if proto === nothing
        url
    else
        user = get(GIT_USERS, lowercase(host), nothing)
        user = user === nothing ? "" : "$user@"

        "$proto://$user$host/$path"
    end
end

function ensure_clone(io::IO, target_path, url; kwargs...)
    if ispath(target_path)
        return LibGit2.GitRepo(target_path)
    else
        return GitTools.clone(io, url, target_path; kwargs...)
    end
end

function checkout_tree_to_path(repo::LibGit2.GitRepo, tree::LibGit2.GitObject, path::String)
    GC.@preserve path begin
        opts = LibGit2.CheckoutOptions(
            checkout_strategy = LibGit2.Consts.CHECKOUT_FORCE,
            target_directory = Base.unsafe_convert(Cstring, path)
        )
        LibGit2.checkout_tree(repo, tree, options=opts)
    end
end

function clone(io::IO, url, source_path; header=nothing, credentials=nothing, kwargs...)
    url = String(url)::String
    source_path = String(source_path)::String
    @assert !isdir(source_path) || isempty(readdir(source_path))
    url = normalize_url(url)
    printpkgstyle(io, :Cloning, header === nothing ? "git-repo `$url`" : header)
    bar = MiniProgressBar(header = "Fetching:", color = Base.info_color())
    fancyprint = can_fancyprint(io)
    callbacks = if fancyprint
        LibGit2.Callbacks(
            :transfer_progress => (
                @cfunction(transfer_progress, Cint, (Ptr{LibGit2.TransferProgress}, Any)),
                bar,
            )
        )
    else
        LibGit2.Callbacks()
    end
    fancyprint && start_progress(io, bar)
    if credentials === nothing
        credentials = LibGit2.CachedCredentials()
    end
    try
        if use_cli_git()
            cmd = `git clone --quiet $url $source_path`
            try
                run(pipeline(cmd; stdout=devnull))
            catch err
                Pkg.Types.pkgerror("The command $(cmd) failed, error: $err")
            end
            return LibGit2.GitRepo(source_path)
        else
            mkpath(source_path)
            return LibGit2.clone(url, source_path; callbacks=callbacks, credentials=credentials, kwargs...)
        end
    catch err
        rm(source_path; force=true, recursive=true)
        err isa LibGit2.GitError || err isa InterruptException || rethrow()
        if err isa InterruptException
            Pkg.Types.pkgerror("git clone of `$url` interrupted")
        elseif (err.class == LibGit2.Error.Net && err.code == LibGit2.Error.EINVALIDSPEC) ||
           (err.class == LibGit2.Error.Repository && err.code == LibGit2.Error.ENOTFOUND)
            Pkg.Types.pkgerror("git repository not found at `$(url)`")
        else
            Pkg.Types.pkgerror("failed to clone from $(url), error: $err")
        end
    finally
        Base.shred!(credentials)
        fancyprint && end_progress(io, bar)
    end
end

function fetch(io::IO, repo::LibGit2.GitRepo, remoteurl=nothing; header=nothing, credentials=nothing, refspecs=[""], kwargs...)
    if remoteurl === nothing
        remoteurl = LibGit2.with(LibGit2.get(LibGit2.GitRemote, repo, "origin")) do remote
            LibGit2.url(remote)
        end
    end
    fancyprint = can_fancyprint(io)
    remoteurl = normalize_url(remoteurl)
    printpkgstyle(io, :Updating, header === nothing ? "git-repo `$remoteurl`" : header)
    bar = MiniProgressBar(header = "Fetching:", color = Base.info_color())
    fancyprint = can_fancyprint(io)
    callbacks = if fancyprint
        LibGit2.Callbacks(
            :transfer_progress => (
                @cfunction(transfer_progress, Cint, (Ptr{LibGit2.TransferProgress}, Any)),
                bar,
            )
        )
    else
        LibGit2.Callbacks()
    end
    fancyprint && start_progress(io, bar)
    if credentials === nothing
        credentials = LibGit2.CachedCredentials()
    end
    try
        if use_cli_git()
            let remoteurl=remoteurl
                cd(LibGit2.path(repo)) do
                    cmd = `git fetch -q $remoteurl $(only(refspecs))`
                    try
                        run(pipeline(cmd; stdout=devnull))
                    catch err
                        Pkg.Types.pkgerror("The command $(cmd) failed, error: $err")
                    end
                end
            end
        else
            return LibGit2.fetch(repo; remoteurl=remoteurl, callbacks=callbacks, refspecs=refspecs, kwargs...)
        end
    catch err
        err isa LibGit2.GitError || rethrow()
        if (err.class == LibGit2.Error.Repository && err.code == LibGit2.Error.ERROR)
            Pkg.Types.pkgerror("Git repository not found at '$(remoteurl)'")
        else
            Pkg.Types.pkgerror("failed to fetch from $(remoteurl), error: $err")
        end
    finally
        Base.shred!(credentials)
        fancyprint && end_progress(io, bar)
    end
end


# This code gratefully adapted from https://github.com/simonbyrne/GitX.jl
@enum GitMode mode_dir=0o040000 mode_normal=0o100644 mode_executable=0o100755 mode_symlink=0o120000 mode_submodule=0o160000
Base.string(mode::GitMode) = string(UInt32(mode); base=8)
Base.print(io::IO, mode::GitMode) = print(io, string(mode))

function gitmode(path::AbstractString)
    # Windows doesn't deal with executable permissions in quite the same way,
    # `stat()` gives a different answer than we actually want, so we use
    # `isexecutable()` which uses `uv_fs_access()` internally.  On other
    # platforms however, we just want to check via `stat()`.
    function isexec(p)
        @static if Sys.iswindows()
            return Sys.isexecutable(p)
        end
        return !iszero(filemode(p) & 0o100)
    end
    if islink(path)
        return mode_symlink
    elseif isdir(path)
        return mode_dir
    elseif isexec(path)
        return mode_executable
    else
        return mode_normal
    end
end

"""
    blob_hash(HashType::Type, path::AbstractString)

Calculate the git blob hash of a given path.
"""
function blob_hash(::Type{HashType}, path::AbstractString) where HashType
    ctx = HashType()
    if islink(path)
        datalen = length(readlink(path))
    else
        datalen = filesize(path)
    end

    # First, the header
    SHA.update!(ctx, Vector{UInt8}("blob $(datalen)\0"))

    # Next, read data in in chunks of 4KB
    buff = Vector{UInt8}(undef, 4*1024)

    try
        if islink(path)
            update!(ctx, Vector{UInt8}(readlink(path)))
        else
            open(path, "r") do io
                while !eof(io)
                    num_read = readbytes!(io, buff)
                    update!(ctx, buff, num_read)
                end
            end
        end
    catch e
        if isa(e, InterruptException)
            rethrow(e)
        end
        @warn("Unable to open $(path) for hashing; git-tree-sha1 likely suspect")
    end

    # Finish it off and return the digest!
    return SHA.digest!(ctx)
end
blob_hash(path::AbstractString) = blob_hash(SHA1_CTX, path)

"""
    contains_files(root::AbstractString)

Helper function to determine whether a directory contains files; e.g. it is a
direct parent of a file or it contains some other directory that itself is a
direct parent of a file. This is used to exclude directories from tree hashing.
"""
function contains_files(path::AbstractString)
    st = lstat(path)
    ispath(st) || throw(ArgumentError("non-existent path: $(repr(path))"))
    isdir(st) || return true
    for p in readdir(path)
        contains_files(joinpath(path, p)) && return true
    end
    return false
end


"""
    tree_hash(HashType::Type, root::AbstractString)

Calculate the git tree hash of a given path.
"""
function tree_hash(::Type{HashType}, root::AbstractString; debug_out::Union{IO,Nothing} = nothing, indent::Int=0) where HashType
    entries = Tuple{String, Vector{UInt8}, GitMode}[]
    for f in sort(readdir(root; join=true); by = f -> gitmode(f) == mode_dir ? f*"/" : f)
        # Skip `.git` directories
        if basename(f) == ".git"
            continue
        end

        filepath = abspath(f)
        mode = gitmode(filepath)
        if mode == mode_dir
            # If this directory contains no files, then skip it
            contains_files(filepath) || continue

            # Otherwise, hash it up!
            child_stream = nothing
            if debug_out !== nothing
                child_stream = IOBuffer()
            end
            hash = tree_hash(HashType, filepath; debug_out=child_stream, indent=indent+1)
            if debug_out !== nothing
                indent_str = "| "^indent
                println(debug_out, "$(indent_str)+ [D] $(basename(filepath)) - $(bytes2hex(hash))")
                print(debug_out, String(take!(child_stream)))
                println(debug_out, indent_str)
            end
        else
            hash = blob_hash(HashType, filepath)
            if debug_out !== nothing
                indent_str = "| "^indent
                mode_str = mode == mode_normal ? "F" : "X"
                println(debug_out, "$(indent_str)[$(mode_str)] $(basename(filepath)) - $(bytes2hex(hash))")
            end
        end
        push!(entries, (basename(filepath), hash, mode))
    end

    content_size = 0
    for (n, h, m) in entries
        content_size += ndigits(UInt32(m); base=8) + 1 + sizeof(n) + 1 + sizeof(h)
    end

    # Return the hash of these entries
    ctx = HashType()
    SHA.update!(ctx, Vector{UInt8}("tree $(content_size)\0"))
    for (name, hash, mode) in entries
        SHA.update!(ctx, Vector{UInt8}("$(mode) $(name)\0"))
        SHA.update!(ctx, hash)
    end
    return SHA.digest!(ctx)
end
tree_hash(root::AbstractString; debug_out::Union{IO,Nothing} = nothing) = tree_hash(SHA.SHA1_CTX, root; debug_out)

function check_valid_HEAD(repo)
    try LibGit2.head(repo)
    catch err
        Pkg.Types.pkgerror("invalid git HEAD ($(err.msg))")
    end
end

function git_file_stream(repo::LibGit2.GitRepo, spec::String; fakeit::Bool=false)::IO
    blob = try LibGit2.GitBlob(repo, spec)
    catch err
        err isa LibGit2.GitError && err.code == LibGit2.Error.ENOTFOUND || rethrow()
        fakeit && return devnull
    end
    iob = IOBuffer(LibGit2.content(blob))
    close(blob)
    return iob
end

end # module
v   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Pkg/src/PlatformEngines.jl6^      # This file is a part of Julia. License is MIT: https://julialang.org/license

# Content in this file is extracted from BinaryProvider.jl, see LICENSE.method

module PlatformEngines

using SHA, Downloads, Tar
import ...Pkg: Pkg, TOML, pkg_server, depots1, can_fancyprint, stderr_f
using ..MiniProgressBars
using Base.BinaryPlatforms, p7zip_jll

export verify, unpack, package, download_verify_unpack

const EXE7Z_LOCK = ReentrantLock()
const EXE7Z = Ref{String}()

function exe7z()
    # If the JLL is available, use the wrapper function defined in there
    if p7zip_jll.is_available()
        return p7zip_jll.p7zip()
    end

    lock(EXE7Z_LOCK) do
        if !isassigned(EXE7Z)
            EXE7Z[] = find7z()
        end
        return Cmd([EXE7Z[]])
    end
end

function find7z()
    name = "7z"
    Sys.iswindows() && (name = "$name.exe")
    for dir in (joinpath("..", "libexec"), ".")
        path = normpath(Sys.BINDIR::String, dir, name)
        isfile(path) && return path
    end
    path = Sys.which(name)
    path !== nothing && return path
    error("7z binary not found")
end

is_secure_url(url::AbstractString) =
    occursin(r"^(https://|\w+://(127\.0\.0\.1|localhost)(:\d+)?($|/))"i, url)

function get_server_dir(
    url :: AbstractString,
    server :: Union{AbstractString, Nothing} = pkg_server(),
)
    server === nothing && return
    url == server || startswith(url, "$server/") || return
    m = match(r"^\w+://([^\\/]+)(?:$|/)", server)
    if m === nothing
        @warn "malformed Pkg server value" server
        return
    end
    isempty(Base.DEPOT_PATH) && return
    invalid_filename_chars = [':', '/', '<', '>', '"', '/', '\\', '|', '?', '*']
    dir = join(replace(c -> c in invalid_filename_chars ? '_' : c, collect(String(m[1]))))
    return joinpath(depots1(), "servers", dir)
end

const AUTH_ERROR_HANDLERS = Pair{Union{String, Regex},Any}[]

function handle_auth_error(url, err; verbose::Bool = false)
    handled, should_retry = false, false
    for (scheme, handler) in AUTH_ERROR_HANDLERS
        occursin(scheme, url) || continue
        handled, should_retry = handler(url, pkg_server(), err)
        handled && break
    end
    handled && should_retry && return get_auth_header(url; verbose = verbose)
    return nothing
end

"""
    register_auth_error_handler(urlscheme::Union{AbstractString, Regex}, f)

Registers `f` as the topmost handler for failures in package server authentication.

A handler is only invoked if `occursin(urlscheme, url)` is true (where `url` is the URL Pkg
is currently trying to download.)

`f` must be a function that takes three input arguments `(url, pkgserver, err)`, where `url` is the
URL currently being downloaded, `pkgserver = Pkg.pkg_server()` the current package server, and
`err` is one of `no-auth-file`, `insecure-connection`, `malformed-file`, `no-access-token`,
`no-refresh-key` or `insecure-refresh-url`.

The handler `f` needs to return a tuple of `Bool`s `(handled, should_retry)`. If `handled` is `false`,
the next handler in the stack will be called, otherwise handling terminates; `get_auth_header` is called again if `should_retry`
is `true`.

`register_auth_error_handler` returns a zero-arg function that can be called to deregister the handler.
"""
function register_auth_error_handler(urlscheme::Union{AbstractString, Regex}, @nospecialize(f))
    unique!(pushfirst!(AUTH_ERROR_HANDLERS, urlscheme => f))
    return () -> deregister_auth_error_handler(urlscheme, f)
end

"""
    deregister_auth_error_handler(urlscheme::Union{AbstractString, Regex}, f)

Removes `f` from the stack of authentication error handlers.
"""
function deregister_auth_error_handler(urlscheme::Union{String, Regex}, @nospecialize(f))
    filter!(handler -> !(handler.first == urlscheme && handler.second === f), AUTH_ERROR_HANDLERS)
    return nothing
end

function get_auth_header(url::AbstractString; verbose::Bool = false)
    server_dir = get_server_dir(url)
    server_dir === nothing && return
    auth_file = joinpath(server_dir, "auth.toml")
    isfile(auth_file) || return handle_auth_error(url, "no-auth-file"; verbose=verbose)
    # TODO: check for insecure auth file permissions
    if !is_secure_url(url)
        @warn "refusing to send auth info over insecure connection" url=url
        return handle_auth_error(url, "insecure-connection"; verbose=verbose)
    end
    # parse the auth file
    auth_info = try
        TOML.parsefile(auth_file)
    catch err
        @error "malformed auth file" file=auth_file err=err
        return handle_auth_error(url, "malformed-file"; verbose=verbose)
    end
    # check for an auth token
    if !haskey(auth_info, "access_token")
        @warn "auth file without access_token field" file=auth_file
        return handle_auth_error(url, "no-access-token"; verbose=verbose)
    end
    auth_token = auth_info["access_token"]::String
    auth_header = "Authorization" => "Bearer $auth_token"
    # handle token expiration and refresh
    expires_at = Inf
    if haskey(auth_info, "expires_at")
        expires_at = min(expires_at, Float64(auth_info["expires_at"])::Float64)
    end
    if haskey(auth_info, "expires_in")
        expires_at = min(expires_at, mtime(auth_file) + Float64(auth_info["expires_in"])::Float64)
    end
    # if token is good until ten minutes from now, use it
    time_now = time()
    if expires_at ≥ time_now + 10*60 # ten minutes
        return auth_header
    end
    if !haskey(auth_info, "refresh_url") || !haskey(auth_info, "refresh_token")
        if expires_at ≤ time_now
            @warn "expired auth without refresh keys" file=auth_file
        end
        # try it anyway since we can't refresh
        return something(handle_auth_error(url, "no-refresh-key"; verbose=verbose), auth_header)
    end
    refresh_url = auth_info["refresh_url"]::String
    if !is_secure_url(refresh_url)
        @warn "ignoring insecure auth refresh URL" url=refresh_url
        return something(handle_auth_error(url, "insecure-refresh-url"; verbose=verbose), auth_header)
    end
    verbose && @info "Refreshing expired auth token..." file=auth_file
    tmp = tempname()
    refresh_token = auth_info["refresh_token"]::String
    refresh_auth = "Authorization" => "Bearer $refresh_token"
    try download(refresh_url, tmp, auth_header=refresh_auth, verbose=verbose)
    catch err
        @warn "token refresh failure" file=auth_file url=refresh_url err=err
        rm(tmp, force=true)
        return handle_auth_error(url, "token-refresh-failed"; verbose=verbose)
    end
    auth_info = try TOML.parsefile(tmp)
    catch err
        @warn "discarding malformed auth file" url=refresh_url err=err
        rm(tmp, force=true)
        return something(handle_auth_error(url, "malformed-file"; verbose=verbose), auth_header)
    end
    if !haskey(auth_info, "access_token")
        if haskey(auth_info, "refresh_token")
            auth_info["refresh_token"] = "*"^64
        end
        @warn "discarding auth file without access token" auth=auth_info
        rm(tmp, force=true)
        return something(handle_auth_error(url, "no-access-token"; verbose=verbose), auth_header)
    end
    if haskey(auth_info, "expires_in")
        expires_in = auth_info["expires_in"]
        if expires_in isa Number
            expires_at = floor(time_now + Float64(expires_in)::Float64)
            # overwrite expires_at (avoids clock skew issues)
            auth_info["expires_at"] = expires_at
        end
    end
    let auth_info = auth_info
        open(tmp, write=true) do io
            TOML.print(io, auth_info, sorted=true)
        end
    end
    mv(tmp, auth_file, force=true)
    access_token = auth_info["access_token"]::String
    return "Authorization" => "Bearer $access_token"
end

# based on information in this post:
# https://github.community/t5/GitHub-Actions/Have-the-CI-environment-variable-set-by-default/m-p/32358/highlight/true#M1097
const CI_VARIABLES = [
    "APPVEYOR",
    "CI",
    "CI_SERVER",
    "CIRCLECI",
    "CONTINUOUS_INTEGRATION",
    "GITHUB_ACTIONS",
    "GITLAB_CI",
    "JULIA_CI",
    "JULIA_PKGEVAL",
    "JULIA_REGISTRYCI_AUTOMERGE",
    "TF_BUILD",
    "TRAVIS",
]

function get_metadata_headers(url::AbstractString)
    headers = Pair{String,String}[]
    server = pkg_server()
    server_dir = get_server_dir(url, server)
    server_dir === nothing && return headers
    push!(headers, "Julia-Pkg-Protocol" => "1.0")
    push!(headers, "Julia-Pkg-Server" => server)
    push!(headers, "Julia-Version" => string(VERSION))
    system = triplet(HostPlatform())
    push!(headers, "Julia-System" => system)
    ci_info = String[]
    for var in CI_VARIABLES
        val = get(ENV, var, nothing)
        state = val === nothing ? "n" :
            lowercase(val) in ("true", "t", "1", "yes", "y") ? "t" :
            lowercase(val) in ("false", "f", "0", "no", "n") ? "f" : "o"
        push!(ci_info, "$var=$state")
    end
    push!(headers, "Julia-CI-Variables" => join(ci_info, ';'))
    push!(headers, "Julia-Interactive" => string(isinteractive()))
    for (key, val) in ENV
        m = match(r"^JULIA_PKG_SERVER_([A-Z0-9_]+)$"i, key)
        m === nothing && continue
        val = strip(val)
        isempty(val) && continue
        words = split(m.captures[1], '_', keepempty=false)
        isempty(words) && continue
        hdr = "Julia-" * join(map(titlecase, words), '-')
        any(hdr == k for (k, v) in headers) && continue
        push!(headers, hdr => val)
    end
    return headers
end

function download(
    url::AbstractString,
    dest::AbstractString;
    verbose::Bool = false,
    headers::Vector{Pair{String,String}} = Pair{String,String}[],
    auth_header::Union{Pair{String,String}, Nothing} = nothing,
    io::IO=stderr_f()
)
    if auth_header === nothing
        auth_header = get_auth_header(url, verbose=verbose)
    end
    if auth_header !== nothing
        push!(headers, auth_header)
    end
    for header in get_metadata_headers(url)
        push!(headers, header)
    end

    do_fancy = verbose && can_fancyprint(io)
    progress = if do_fancy
        bar = MiniProgressBar(header="Downloading", color=Base.info_color())
        start_progress(io, bar)
        let bar=bar
            (total, now) -> begin
                bar.max = total
                bar.current = now
                show_progress(io, bar)
            end
        end
    else
        (total, now) -> nothing
    end
    try
        Downloads.download(url, dest; headers, progress)
    finally
        do_fancy && end_progress(io, bar)
    end
end

"""
    download_verify(
        url::AbstractString,
        hash::Union{AbstractString, Nothing},
        dest::AbstractString;
        verbose::Bool = false,
        force::Bool = false,
        quiet_download::Bool = false,
    )

Download file located at `url`, verify it matches the given `hash`, and throw
an error if anything goes wrong.  If `dest` already exists, just verify it. If
`force` is set to `true`, overwrite the given file if it exists but does not
match the given `hash`.

This method returns `true` if the file was downloaded successfully, `false`
if an existing file was removed due to the use of `force`, and throws an error
if `force` is not set and the already-existent file fails verification, or if
`force` is set, verification fails, and then verification fails again after
redownloading the file.

If `quiet_download` is set to `false`, this method will print to
stdout when downloading a new file.  If it is set to `true` (default, and `verbose` is
set to `false`) the downloading process will be completely silent.  If
`verbose` is set to `true`, messages about integrity verification will be
printed in addition to messages regarding downloading.
"""
function download_verify(
    url::AbstractString,
    hash::Union{AbstractString, Nothing},
    dest::AbstractString;
    verbose::Bool = false,
    force::Bool = false,
    quiet_download::Bool = false,
)
    # Whether the file existed in the first place
    file_existed = false

    if isfile(dest)
        file_existed = true
        if verbose
            @info("Destination file $(dest) already exists, verifying...")
        end

        # verify download, if it passes, return happy.  If it fails, (and
        # `force` is `true`, re-download!)
        if hash !== nothing && verify(dest, hash; verbose=verbose)
            return true
        elseif !force
            error("Verification failed, not overwriting $(dest)")
        end
    end

    # Make sure the containing folder exists
    mkpath(dirname(dest))

    # Download the file, optionally continuing
    f = retry(delays = fill(1.0, 3)) do
        try
            download(url, dest; verbose=verbose || !quiet_download)
        catch err
            @debug "download and verify failed" url dest err
            rethrow()
        end
    end
    f()
    if hash !== nothing && !verify(dest, hash; verbose=verbose)
        # If the file already existed, it's possible the initially downloaded chunk
        # was bad.  If verification fails after downloading, auto-delete the file
        # and start over from scratch.
        if file_existed
            if verbose
                @info("Continued download didn't work, restarting from scratch")
            end
            Base.rm(dest; force=true)

            # Download and verify from scratch
            download(url, dest; verbose=verbose || !quiet_download)
            if hash !== nothing && !verify(dest, hash; verbose=verbose)
                error("Verification failed. Download does not match expected hash")
            end
        else
            # If it didn't verify properly and we didn't resume, something is
            # very wrong and we must complain mightily.
            error("Verification failed. Download does not match expected hash")
        end
    end

    # If the file previously existed, this means we removed it (due to `force`)
    # and redownloaded, so return `false`.  If it didn't exist, then this means
    # that we successfully downloaded it, so return `true`.
    return !file_existed
end

# TODO: can probably delete this, only affects tests
function copy_symlinks()
    var = get(ENV, "BINARYPROVIDER_COPYDEREF", "")
    lowercase(var) in ("true", "t", "yes", "y", "1") ? true :
    lowercase(var) in ("false", "f", "no", "n", "0") ? false : nothing
end

function unpack(
    tarball_path::AbstractString,
    dest::AbstractString;
    verbose::Bool = false,
)
    Tar.extract(`$(exe7z()) x $tarball_path -so`, dest, copy_symlinks = copy_symlinks())
end

"""
    package(src_dir::AbstractString, tarball_path::AbstractString)

Compress `src_dir` into a tarball located at `tarball_path`.
"""
function package(src_dir::AbstractString, tarball_path::AbstractString; io=stderr_f())
    rm(tarball_path, force=true)
    cmd = `$(exe7z()) a -si -tgzip -mx9 $tarball_path`
    open(pipeline(cmd, stdout=devnull, stderr=io), write=true) do io
        Tar.create(src_dir, io)
    end
end

"""
    download_verify_unpack(
        url::AbstractString,
        hash::Union{AbstractString, Nothing},
        dest::AbstractString;
        tarball_path = nothing,
        ignore_existence::Bool = false,
        force::Bool = false,
        verbose::Bool = false,
        quiet_download::Bool = false,
        io::IO=stderr,
    )

Helper method to download tarball located at `url`, verify it matches the
given `hash`, then unpack it into folder `dest`.  In general, the method
`install()` should be used to download and install tarballs into a `Prefix`;
this method should only be used if the extra functionality of `install()` is
undesired.

If `tarball_path` is specified, the given `url` will be downloaded to
`tarball_path`, and it will not be removed after downloading and verification
is complete.  If it is not specified, the tarball will be downloaded to a
temporary location, and removed after verification is complete.

If `force` is specified, a verification failure will cause `tarball_path` to be
deleted (if it exists), the `dest` folder to be removed (if it exists) and the
tarball to be redownloaded and reverified.  If the verification check is failed
a second time, an exception is raised.  If `force` is not specified, a
verification failure will result in an immediate raised exception.

If `ignore_existence` is set, the tarball is unpacked even if the destination
directory already exists.

Returns `true` if a tarball was actually unpacked, `false` if nothing was
changed in the destination prefix.
"""
function download_verify_unpack(
    url::AbstractString,
    hash::Union{AbstractString, Nothing},
    dest::AbstractString;
    tarball_path = nothing,
    ignore_existence::Bool = false,
    force::Bool = false,
    verbose::Bool = false,
    quiet_download::Bool = false,
    io::IO=stderr_f(),
)
    # First, determine whether we should keep this tarball around
    remove_tarball = false
    if tarball_path === nothing
        remove_tarball = true

        function url_ext(url)
            url = basename(url)

            # Chop off urlparams
            qidx = findfirst(isequal('?'), url)
            if qidx !== nothing
                url = url[1:qidx]
            end

            # Try to detect extension
            dot_idx = findlast(isequal('.'), url)
            if dot_idx === nothing
                return nothing
            end

            return url[dot_idx+1:end]
        end

        # If extension of url contains a recognized extension, use it, otherwise use ".gz"
        ext = url_ext(url)
        if !(ext in ["tar", "gz", "tgz", "bz2", "xz"])
            ext = "gz"
        end

        # Work around windows limitations regarding tempname()
        tarball_path = "$(tempname())-download.$(ext)"
        tries = 0
        while isfile(tarball_path) && tries < 100
            tarball_path = "$(tempname())-download.$(ext)"
            tries += 1
        end
        if tries >= 100
            error("Unable to generate unused tempname! Clean up your temporary folder $(dirname(tempname())) and try again.")
        end
    end

    # Download the tarball; if it already existed and we needed to remove it
    # then we should remove the unpacked path as well
    should_delete = !download_verify(url, hash, tarball_path;
                                     force=force, verbose=verbose, quiet_download=quiet_download)
    if should_delete
        if verbose
            @info("Removing dest directory $(dest) as source tarball changed")
        end
        Base.rm(dest; recursive=true, force=true)
    end

    # If the destination path already exists, don't bother to unpack
    if !ignore_existence && isdir(dest)
        if verbose
            @info("Destination directory $(dest) already exists, returning")
        end

        # Signify that we didn't do any unpacking
        return false
    end

    try
        if verbose
            @info("Unpacking $(tarball_path) into $(dest)...")
        end
        open(`$(exe7z()) x $tarball_path -so`) do io
            Tar.extract(io, dest, copy_symlinks = copy_symlinks())
        end
    finally
        if remove_tarball
            Base.rm(tarball_path)
            # Remove cached tarball hash, if it exists.
            Base.rm(string(tarball_path, ".sha256"); force=true)
        end
    end

    # Signify that we did some unpacking!
    return true
end


"""
    verify(path::AbstractString, hash::AbstractString;
           verbose::Bool = false, report_cache_status::Bool = false)

Given a file `path` and a `hash`, calculate the SHA256 of the file and compare
it to `hash`.  This method caches verification results in a `"\$(path).sha256"`
file to accelerate reverification of files that have been previously verified.
If no `".sha256"` file exists, a full verification will be done and the file
will be created, with the calculated hash being stored within the `".sha256"`
file.  If a `".sha256"` file does exist, its contents are checked to ensure
that the hash contained within matches the given `hash` parameter, and its
modification time shows that the file located at `path` has not been modified
since the last verification.

If `report_cache_status` is set to `true`, then the return value will be a
`Symbol` giving a granular status report on the state of the hash cache, in
addition to the `true`/`false` signifying whether verification completed
successfully.
"""
function verify(path::AbstractString, hash::AbstractString; verbose::Bool = false,
                report_cache_status::Bool = false, hash_path::AbstractString="$(path).sha256")

    # Check hash string format
    if !occursin(r"^[0-9a-f]{64}$"i, hash)
        msg = "Hash value must be 64 hexadecimal characters (256 bits), "
        if !isascii(hash)
            msg *= "given hash value is non-ASCII"
        elseif occursin(r"^[0-9a-f]*$"i, hash)
            msg *= "given hash value has the wrong length ($(length(hash)))"
        else
            msg *= "given hash value contains non-hexadecimal characters"
        end
        msg *= ": $(repr(hash))"
        error(msg)
    end
    hash = lowercase(hash)

    # Check to see if the hash cache is consistent
    status = :hash_consistent

    # First, it must exist
    if isfile(hash_path)
        # Next, it must contain the same hash as what we're verifying against
        if read(hash_path, String) == hash
            # Next, it must be no older than the actual path
            if stat(hash_path).mtime >= stat(path).mtime
                # If all of that is true, then we're good!
                if verbose
                    @info("Hash cache is consistent, returning true")
                end
                status = :hash_cache_consistent

                # If we're reporting our status, then report it!
                if report_cache_status
                    return true, status
                else
                    return true
                end
            else
                if verbose
                    @info("File has been modified, hash cache invalidated")
                end
                status = :file_modified
            end
        else
            if verbose
                @info("Verification hash mismatch, hash cache invalidated")
            end
            status = :hash_cache_mismatch
        end
    else
        if verbose
            @info("No hash cache found")
        end
        status = :hash_cache_missing
    end

    calc_hash = open(path) do file
        bytes2hex(sha256(file))
    end
    @assert occursin(r"^[0-9a-f]{64}$", calc_hash)

    if verbose
        @info("Calculated hash $calc_hash for file $path")
    end

    if calc_hash != hash
        msg  = "Hash Mismatch!\n"
        msg *= "  Expected sha256:   $hash\n"
        msg *= "  Calculated sha256: $calc_hash"
        @error(msg)
        if report_cache_status
            return false, :hash_mismatch
        else
            return false
        end
    end

    # Try to save a hash cache if everything worked out fine
    try
        open(hash_path, "w") do file
            write(file, hash)
        end
    catch e
        if isa(e, InterruptException)
            rethrow(e)
        end

        if verbose
            @warn("Unable to create hash cache file $(hash_path)")
        end
    end

    if report_cache_status
        return true, status
    else
        return true
    end
end

# Verify the git-tree-sha1 hash of a compressed archive.
function verify_archive_tree_hash(tar_gz::AbstractString, expected_hash::Base.SHA1)
    # This can fail because unlike sha256 verification of the downloaded
    # tarball, tree hash verification requires that the file can i) be
    # decompressed and ii) is a proper archive.
    calc_hash = try
        Base.SHA1(open(Tar.tree_hash, `$(exe7z()) x $tar_gz -so`))
    catch err
        @warn "unable to decompress and read archive" exception=err
        return false
    end
    if calc_hash != expected_hash
        @warn "tarball content does not match expected git-tree-sha1"
        return false
    end
    return true
end

end # module PlatformEngines
v   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/p7zip_jll/src/p7zip_jll.jl#      # This file is a part of Julia. License is MIT: https://julialang.org/license

## dummy stub for https://github.com/JuliaBinaryWrappers/p7zip_jll.jl
baremodule p7zip_jll
using Base
Base.Experimental.@compiler_options compile=min optimize=0 infer=false

const PATH_list = String[]
const LIBPATH_list = String[]

export p7zip

# These get calculated in __init__()
const PATH = Ref("")
const LIBPATH = Ref("")
artifact_dir::String = ""
p7zip_path::String = ""
if Sys.iswindows()
    const p7zip_exe = "7z.exe"
else
    const p7zip_exe = "7z"
end

if Sys.iswindows()
    const LIBPATH_env = "PATH"
    const LIBPATH_default = ""
    const pathsep = ';'
elseif Sys.isapple()
    const LIBPATH_env = "DYLD_FALLBACK_LIBRARY_PATH"
    const LIBPATH_default = "~/lib:/usr/local/lib:/lib:/usr/lib"
    const pathsep = ':'
else
    const LIBPATH_env = "LD_LIBRARY_PATH"
    const LIBPATH_default = ""
    const pathsep = ':'
end

function adjust_ENV!(env::Dict{keytype(Base.EnvDict),valtype(Base.EnvDict)}, PATH::String, LIBPATH::String, adjust_PATH::Bool, adjust_LIBPATH::Bool)
    if adjust_LIBPATH
        LIBPATH_base = get(env, LIBPATH_env, expanduser(LIBPATH_default))
        if !isempty(LIBPATH_base)
            env[LIBPATH_env] = string(LIBPATH, pathsep, LIBPATH_base)
        else
            env[LIBPATH_env] = LIBPATH
        end
    end
    if adjust_PATH && (LIBPATH_env != "PATH" || !adjust_LIBPATH)
        if adjust_PATH
            if !isempty(get(env, "PATH", ""))
                env["PATH"] = string(PATH, pathsep, env["PATH"])
            else
                env["PATH"] = PATH
            end
        end
    end
    return env
end

function p7zip(f::Function; adjust_PATH::Bool = true, adjust_LIBPATH::Bool = true)
    env = adjust_ENV!(copy(ENV), PATH[], LIBPATH[], adjust_PATH, adjust_LIBPATH)
    withenv(env...) do
        return f(p7zip_path)
    end
end
function p7zip(; adjust_PATH::Bool = true, adjust_LIBPATH::Bool = true)
    env = adjust_ENV!(copy(ENV), PATH[], LIBPATH[], adjust_PATH, adjust_LIBPATH)
    return Cmd(Cmd([p7zip_path]); env)
end

function init_p7zip_path()
    # Prefer our own bundled p7zip, but if we don't have one, pick it up off of the PATH
    # If this is an in-tree build, `7z` will live in `bindir`.  Otherwise, it'll be in `private_libexecdir`
    for bundled_p7zip_path in (joinpath(Sys.BINDIR, Base.PRIVATE_LIBEXECDIR, p7zip_exe),
                               joinpath(Sys.BINDIR, p7zip_exe))
        if isfile(bundled_p7zip_path)
            global p7zip_path = abspath(bundled_p7zip_path)
            return
        end
    end
    global p7zip_path = something(Sys.which(p7zip_exe), p7zip_exe)
end

function __init__()
    global artifact_dir = dirname(Sys.BINDIR)
    init_p7zip_path()
    PATH[] = dirname(p7zip_path)
    push!(PATH_list, PATH[])
    append!(LIBPATH_list, [joinpath(Sys.BINDIR, Base.LIBDIR, "julia"), joinpath(Sys.BINDIR, Base.LIBDIR)])
    LIBPATH[] = join(LIBPATH_list, pathsep)
end

# JLLWrappers API compatibility shims.  Note that not all of these will really make sense.
# For instance, `find_artifact_dir()` won't actually be the artifact directory, because
# there isn't one.  It instead returns the overall Julia prefix.
is_available() = true
find_artifact_dir() = artifact_dir
dev_jll() = error("stdlib JLLs cannot be dev'ed")
best_wrapper = nothing

end  # module p7zip_jll
o   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Pkg/src/Versions.jl�4      # This file is a part of Julia. License is MIT: https://julialang.org/license

module Versions

export VersionBound, VersionRange, VersionSpec, semver_spec, isjoinable

################
# VersionBound #
################
struct VersionBound
    t::NTuple{3,UInt32}
    n::Int
    function VersionBound(tin::NTuple{n,Integer}) where n
        n <= 3 || throw(ArgumentError("VersionBound: you can only specify major, minor and patch versions"))
        n == 0 && return new((0,           0,      0), n)
        n == 1 && return new((tin[1],      0,      0), n)
        n == 2 && return new((tin[1], tin[2],      0), n)
        n == 3 && return new((tin[1], tin[2], tin[3]), n)
        error("invalid $n")
    end
end
VersionBound(t::Integer...) = VersionBound(t)
VersionBound(v::VersionNumber) = VersionBound(v.major, v.minor, v.patch)

Base.getindex(b::VersionBound, i::Int) = b.t[i]

function ≲(v::VersionNumber, b::VersionBound)
    b.n == 0 && return true
    b.n == 1 && return v.major <= b[1]
    b.n == 2 && return (v.major, v.minor) <= (b[1], b[2])
    return (v.major, v.minor, v.patch) <= (b[1], b[2], b[3])
end

function ≲(b::VersionBound, v::VersionNumber)
    b.n == 0 && return true
    b.n == 1 && return v.major >= b[1]
    b.n == 2 && return (v.major, v.minor) >= (b[1], b[2])
    return (v.major, v.minor, v.patch) >= (b[1], b[2], b[3])
end

function isless_ll(a::VersionBound, b::VersionBound)
    m, n = a.n, b.n
    for i = 1:min(m, n)
        a[i] < b[i] && return true
        a[i] > b[i] && return false
    end
    return m < n
end

stricterlower(a::VersionBound, b::VersionBound) = isless_ll(a, b) ? b : a

# Comparison between two upper bounds
function isless_uu(a::VersionBound, b::VersionBound)
    m, n = a.n, b.n
    for i = 1:min(m, n)
        a[i] < b[i] && return true
        a[i] > b[i] && return false
    end
    return m > n
end

stricterupper(a::VersionBound, b::VersionBound) = isless_uu(a, b) ? a : b

# `isjoinable` compares an upper bound of a range with the lower bound of the next range
# to determine if they can be joined, as in [1.5-2.8, 2.5-3] -> [1.5-3]. Used by `union!`.
# The equal-length-bounds case is special since e.g. `1.5` can be joined with `1.6`,
# `2.3.4` can be joined with `2.3.5` etc.

function isjoinable(up::VersionBound, lo::VersionBound)
    up.n == 0 && lo.n == 0 && return true
    if up.n == lo.n
        n = up.n
        for i = 1:(n - 1)
            up[i] > lo[i] && return true
            up[i] < lo[i] && return false
        end
        up[n] < lo[n] - 1 && return false
        return true
    else
        l = min(up.n, lo.n)
        for i = 1:l
            up[i] > lo[i] && return true
            up[i] < lo[i] && return false
        end
    end
    return true
end

Base.hash(r::VersionBound, h::UInt) = hash(r.t, hash(r.n, h))

# Hot code
function VersionBound(s::AbstractString)
    s = strip(s)
    s == "*" && return VersionBound()
    first(s) == 'v' && (s = SubString(s, 2))
    l = lastindex(s)

    p = findnext('.', s, 1)
    b = p === nothing ? l : (p-1)
    i = parse(Int64, SubString(s, 1, b))
    p === nothing && return VersionBound(i)

    a = p+1
    p = findnext('.', s, a)
    b = p === nothing ? l : (p-1)
    j = parse(Int64, SubString(s, a, b))
    p === nothing && return VersionBound(i, j)

    a = p+1
    p = findnext('.', s, a)
    b = p === nothing ? l : (p-1)
    k = parse(Int64, SubString(s, a, b))
    p === nothing && return VersionBound(i, j, k)

    error("invalid VersionBound string $(repr(s))")
end

################
# VersionRange #
################
struct VersionRange
    lower::VersionBound
    upper::VersionBound
    # NOTE: ranges are allowed to be empty; they are ignored by VersionSpec anyway
    function VersionRange(lo::VersionBound, hi::VersionBound)
        # lo.t == hi.t implies that digits past min(lo.n, hi.n) are zero
        # lo.n < hi.n example: 1.2-1.2.0 => 1.2.0
        # lo.n > hi.n example: 1.2.0-1.2 => 1.2
        lo.t == hi.t && (lo = hi)
        return new(lo, hi)
    end
end
VersionRange(b::VersionBound=VersionBound()) = VersionRange(b, b)
VersionRange(t::Integer...)                  = VersionRange(VersionBound(t...))
VersionRange(v::VersionNumber)               = VersionRange(VersionBound(v))
VersionRange(lo::VersionNumber, hi::VersionNumber) = VersionRange(VersionBound(lo), VersionBound(hi))

# The vast majority of VersionRanges are in practice equal to "1"
const VersionRange_1 = VersionRange(VersionBound("1"), VersionBound("1"))
function VersionRange(s::AbstractString)
    s == "1" && return VersionRange_1
    p = split(s, "-")
    if length(p) != 1 && length(p) != 2
        throw(ArgumentError("invalid version range: $(repr(s))"))
    end
    lower = VersionBound(p[1])
    upper = length(p) == 1 ? lower : VersionBound(p[2])
    return VersionRange(lower, upper)
end

function Base.isempty(r::VersionRange)
    for i = 1:min(r.lower.n, r.upper.n)
        r.lower[i] > r.upper[i] && return true
        r.lower[i] < r.upper[i] && return false
    end
    return false
end

function Base.print(io::IO, r::VersionRange)
    m, n = r.lower.n, r.upper.n
    if (m, n) == (0, 0)
        print(io, '*')
    elseif m == 0
        print(io, "0-")
        join(io, r.upper.t, '.')
    elseif n == 0
        join(io, r.lower.t, '.')
        print(io, "-*")
    else
        join(io, r.lower.t[1:m], '.')
        if r.lower != r.upper
            print(io, '-')
            join(io, r.upper.t[1:n], '.')
        end
    end
end
Base.show(io::IO, r::VersionRange) = print(io, "VersionRange(\"", r, "\")")

Base.in(v::VersionNumber, r::VersionRange) = r.lower ≲ v ≲ r.upper

Base.intersect(a::VersionRange, b::VersionRange) = VersionRange(stricterlower(a.lower, b.lower), stricterupper(a.upper, b.upper))

function Base.union!(ranges::Vector{<:VersionRange})
    l = length(ranges)
    l == 0 && return ranges

    sort!(ranges, lt=(a, b) -> (isless_ll(a.lower, b.lower) || (a.lower == b.lower && isless_uu(a.upper, b.upper))))

    k0 = 1
    ks = findfirst(!isempty, ranges)
    ks === nothing && return empty!(ranges)

    lo, up, k0 = ranges[ks].lower, ranges[ks].upper, 1
    for k = (ks + 1):l
        isempty(ranges[k]) && continue
        lo1, up1 = ranges[k].lower, ranges[k].upper
        if isjoinable(up, lo1)
            isless_uu(up, up1) && (up = up1)
            continue
        end
        vr = VersionRange(lo, up)
        @assert !isempty(vr)
        ranges[k0] = vr
        k0 += 1
        lo, up = lo1, up1
    end
    vr = VersionRange(lo, up)
    if !isempty(vr)
        ranges[k0] = vr
        k0 += 1
    end
    resize!(ranges, k0 - 1)
    return ranges
end

###############
# VersionSpec #
###############
struct VersionSpec
    ranges::Vector{VersionRange}
    VersionSpec(r::Vector{<:VersionRange}) = new(union!(r))
    VersionSpec(vs::VersionSpec) = vs
end

VersionSpec(r::VersionRange) = VersionSpec(VersionRange[r])
VersionSpec(v::VersionNumber) = VersionSpec(VersionRange(v))
const _all_versionsspec = VersionSpec(VersionRange())
VersionSpec() = _all_versionsspec
VersionSpec(s::AbstractString) = VersionSpec(VersionRange(s))
VersionSpec(v::AbstractVector) = VersionSpec(map(VersionRange, v))

# Hot code
function Base.in(v::VersionNumber, s::VersionSpec)
    for r in s.ranges
        v in r && return true
    end
    return false
end

Base.copy(vs::VersionSpec) = VersionSpec(vs)

const empty_versionspec = VersionSpec(VersionRange[])
const _empty_symbol = "∅"

Base.isempty(s::VersionSpec) = all(isempty, s.ranges)
@assert isempty(empty_versionspec)
# Hot code, measure performance before changing
function Base.intersect(A::VersionSpec, B::VersionSpec)
    (isempty(A) || isempty(B)) && return copy(empty_versionspec)
    ranges = Vector{VersionRange}(undef, length(A.ranges) * length(B.ranges))
    i = 1
    @inbounds for a in A.ranges, b in B.ranges
        ranges[i] = intersect(a, b)
        i += 1
    end
    VersionSpec(ranges)
end
Base.intersect(a::VersionNumber, B::VersionSpec) = a in B ? VersionSpec(a) : empty_versionspec
Base.intersect(A::VersionSpec, b::VersionNumber) = intersect(b, A)

function Base.union(A::VersionSpec, B::VersionSpec)
    A == B && return A
    Ar = copy(A.ranges)
    append!(Ar, B.ranges)
    union!(Ar)
    return VersionSpec(Ar)
end

Base.:(==)(A::VersionSpec, B::VersionSpec) = A.ranges == B.ranges
Base.hash(s::VersionSpec, h::UInt) = hash(s.ranges, h + (0x2fd2ca6efa023f44 % UInt))

function Base.print(io::IO, s::VersionSpec)
    isempty(s) && return print(io, _empty_symbol)
    length(s.ranges) == 1 && return print(io, s.ranges[1])
    print(io, '[')
    for i = 1:length(s.ranges)
        1 < i && print(io, ", ")
        print(io, s.ranges[i])
    end
    print(io, ']')
end
Base.show(io::IO, s::VersionSpec) = print(io, "VersionSpec(\"", s, "\")")


###################
# Semver notation #
###################

function semver_spec(s::String; throw = true)
    ranges = VersionRange[]
    for ver in strip.(split(strip(s), ','))
        range = nothing
        found_match = false
        for (ver_reg, f) in ver_regs
            if occursin(ver_reg, ver)
                range = f(match(ver_reg, ver))
                found_match = true
                break
            end
        end
        if !found_match
            if throw
                error("invalid version specifier: \"$s\"")
            else
                return nothing
            end
        end
        push!(ranges, range)
    end
    return VersionSpec(ranges)
end

function semver_interval(m::RegexMatch)
    @assert length(m.captures) == 4
    n_significant = count(x -> x !== nothing, m.captures) - 1
    typ, _major, _minor, _patch = m.captures
    major =                           parse(Int, _major)
    minor = (n_significant < 2) ? 0 : parse(Int, _minor)
    patch = (n_significant < 3) ? 0 : parse(Int, _patch)
    if n_significant == 3 && major == 0 && minor == 0 && patch == 0
        error("invalid version: \"0.0.0\"")
    end
    # Default type is :caret
    vertyp = (typ == "" || typ == "^") ? :caret : :tilde
    v0 = VersionBound((major, minor, patch))
    if vertyp === :caret
        if major != 0
            return VersionRange(v0, VersionBound((v0[1],)))
        elseif minor != 0
            return VersionRange(v0, VersionBound((v0[1], v0[2])))
        else
            if n_significant == 1
                return VersionRange(v0, VersionBound((0,)))
            elseif n_significant == 2
                return VersionRange(v0, VersionBound((0, 0,)))
            else
                return VersionRange(v0, VersionBound((0, 0, v0[3])))
            end
        end
    else
        if n_significant == 3 || n_significant == 2
            return VersionRange(v0, VersionBound((v0[1], v0[2],)))
        else
            return VersionRange(v0, VersionBound((v0[1],)))
        end
    end
end

const _inf = VersionBound("*")
function inequality_interval(m::RegexMatch)
    @assert length(m.captures) == 4
    typ, _major, _minor, _patch = m.captures
    n_significant = count(x -> x !== nothing, m.captures) - 1
    major =                           parse(Int, _major)
    minor = (n_significant < 2) ? 0 : parse(Int, _minor)
    patch = (n_significant < 3) ? 0 : parse(Int, _patch)
    if n_significant == 3 && major == 0 && minor == 0 && patch == 0
        error("invalid version: 0.0.0")
    end
    v = VersionBound(major, minor, patch)
    if occursin(r"^<\s*$", typ)
        nil = VersionBound(0, 0, 0)
        if v[3] == 0
            if v[2] == 0
                v1 = VersionBound(v[1]-1)
            else
                v1 = VersionBound(v[1], v[2]-1)
            end
        else
            v1 = VersionBound(v[1], v[2], v[3]-1)
        end
        return VersionRange(nil, v1)
    elseif occursin(r"^=\s*$", typ)
        return VersionRange(v)
    elseif occursin(r"^>=\s*$", typ) || occursin(r"^≥\s*$", typ)
           return VersionRange(v, _inf)
    else
        error("invalid prefix $typ")
    end
end

function hyphen_interval(m::RegexMatch)
    @assert length(m.captures) == 6
    _lower_major, _lower_minor, _lower_patch, _upper_major, _upper_minor, _upper_patch = m.captures
    if isnothing(_lower_minor)
        lower_bound = VersionBound(parse(Int, _lower_major))
    elseif isnothing(_lower_patch)
        lower_bound = VersionBound(parse(Int, _lower_major),
                                   parse(Int, _lower_minor))
    else
        lower_bound = VersionBound(parse(Int, _lower_major),
                                   parse(Int, _lower_minor),
                                   parse(Int, _lower_patch))
    end
    if isnothing(_upper_minor)
        upper_bound = VersionBound(parse(Int, _upper_major))
    elseif isnothing(_upper_patch)
        upper_bound = VersionBound(parse(Int, _upper_major),
                                   parse(Int, _upper_minor))
    else
        upper_bound = VersionBound(parse(Int, _upper_major),
                                   parse(Int, _upper_minor),
                                   parse(Int, _upper_patch))
    end
    return VersionRange(lower_bound, upper_bound)
end

const version = "v?([0-9]+?)(?:\\.([0-9]+?))?(?:\\.([0-9]+?))?"
const ver_regs =
Pair{Regex,Any}[
                Regex("^([~^]?)?$version\$") => semver_interval, # 0.5 ^0.4 ~0.3.2
                Regex("^((?:≥\\s*)|(?:>=\\s*)|(?:=\\s*)|(?:<\\s*)|(?:=\\s*))v?$version\$")  => inequality_interval,# < 0.2 >= 0.5,2
                Regex("^[\\s]*$version[\\s]*?\\s-\\s[\\s]*?$version[\\s]*\$") => hyphen_interval, # 0.7 - 1.3
]

end
x   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Pkg/src/Registry/Registry.jl�c      module Registry

import ..Pkg
using ..Pkg: depots1, printpkgstyle, stderr_f, isdir_nothrow, pathrepr, pkg_server,
             GitTools
using ..Pkg.PlatformEngines: download_verify_unpack, download, download_verify, exe7z, verify_archive_tree_hash
using UUIDs, LibGit2, TOML, Dates
import FileWatching

include("registry_instance.jl")

mutable struct RegistrySpec
    name::Union{String,Nothing}
    uuid::Union{UUID,Nothing}
    url::Union{String,Nothing}
    # the path field can be a local source when adding a registry
    # otherwise it is the path where the registry is installed
    path::Union{String,Nothing}
    linked::Union{Bool,Nothing}
end
RegistrySpec(name::String) = RegistrySpec(name = name)
RegistrySpec(;name::Union{String,Nothing}=nothing, uuid::Union{String,UUID,Nothing}=nothing,
url::Union{String,Nothing}=nothing, path::Union{String,Nothing}=nothing, linked::Union{Bool,Nothing}=nothing) =
    RegistrySpec(name, isa(uuid, String) ? UUID(uuid) : uuid, url, path, linked)

"""
    Pkg.Registry.add(registry::RegistrySpec)

Add new package registries.

The no-argument `Pkg.Registry.add()` will install the default registries.

# Examples
```julia
Pkg.Registry.add("General")
Pkg.Registry.add(RegistrySpec(uuid = "23338594-aafe-5451-b93e-139f81909106"))
Pkg.Registry.add(RegistrySpec(url = "https://github.com/JuliaRegistries/General.git"))
```
"""
add(reg::Union{String,RegistrySpec}; kwargs...) = add([reg]; kwargs...)
add(regs::Vector{String}; kwargs...) = add(RegistrySpec[RegistrySpec(name = name) for name in regs]; kwargs...)
add(; kwargs...) = add(RegistrySpec[]; kwargs...)
function add(regs::Vector{RegistrySpec}; io::IO=stderr_f(), depot=depots1())
    if isempty(regs)
        download_default_registries(io, only_if_empty = false; depot)
    else
        download_registries(io, regs, depot)
    end
end

const DEFAULT_REGISTRIES =
    RegistrySpec[RegistrySpec(name = "General",
                              uuid = UUID("23338594-aafe-5451-b93e-139f81909106"),
                              url = "https://github.com/JuliaRegistries/General.git")]

function pkg_server_registry_info()
    registry_info = Dict{UUID, Base.SHA1}()
    server = pkg_server()
    server === nothing && return nothing
    tmp_path = tempname()
    download_ok = false
    try
        f = retry(delays = fill(1.0, 3)) do
            download("$server/registries", tmp_path, verbose=false)
        end
        f()
        download_ok = true
    catch err
        @warn "could not download $server/registries" exception=err
    end
    download_ok || return nothing
    open(tmp_path) do io
        for line in eachline(io)
            if (m = match(r"^/registry/([^/]+)/([^/]+)$", line)) !== nothing
                uuid = UUID(m.captures[1]::SubString{String})
                hash = Base.SHA1(m.captures[2]::SubString{String})
                registry_info[uuid] = hash
            end
        end
    end
    Base.rm(tmp_path, force=true)
    return server, registry_info
end

function pkg_server_registry_urls()
    server_registry_info = pkg_server_registry_info()
    registry_urls = Dict{UUID, String}()
    server_registry_info === nothing && return registry_urls
    server, registry_info = server_registry_info
    for (uuid, hash) in registry_info
        registry_urls[uuid] = "$server/registry/$uuid/$hash"
    end
    return registry_urls
end

pkg_server_url_hash(url::String) = Base.SHA1(split(url, '/')[end])

function download_default_registries(io::IO; only_if_empty::Bool = true, depot=depots1())
    installed_registries = reachable_registries()
    # Only clone if there are no installed registries, unless called
    # with false keyword argument.
    if isempty(installed_registries) || !only_if_empty
        printpkgstyle(io, :Installing, "known registries into $(pathrepr(depot))")
        registries = copy(DEFAULT_REGISTRIES)
        for uuid in keys(pkg_server_registry_urls())
            if !(uuid in (reg.uuid for reg in registries))
                push!(registries, RegistrySpec(uuid = uuid))
            end
        end
        filter!(reg -> !(reg.uuid in installed_registries), registries)
        download_registries(io, registries, depot)
        return true
    end
    return false
end

# Hacky way to make e.g. `registry add General` work.
function populate_known_registries_with_urls!(registries::Vector{RegistrySpec})
    known_registries = DEFAULT_REGISTRIES # TODO: Some way to add stuff here?
    for reg in registries, known in known_registries
        if reg.uuid !== nothing
            if reg.uuid === known.uuid
                reg.url = known.url
                reg.path = known.path
                reg.linked = known.linked
            end
        elseif reg.name !== nothing
            if reg.name == known.name
                named_regs = filter(r -> r.name == reg.name, known_registries)
                if !all(r -> r.uuid == first(named_regs).uuid, named_regs)
                    Pkg.Types.pkgerror("multiple registries with name `$(reg.name)`, please specify with uuid.")
                end
                reg.uuid = known.uuid
                reg.url = known.url
                reg.path = known.path
                reg.linked = known.linked
            end
        end
    end
end

function registry_use_pkg_server()
    get(ENV, "JULIA_PKG_SERVER", nothing) !== ""
end

registry_read_from_tarball() =
    registry_use_pkg_server() && !Base.get_bool_env("JULIA_PKG_UNPACK_REGISTRY", false)

function check_registry_state(reg)
    reg_currently_uses_pkg_server = reg.tree_info !== nothing
    reg_should_use_pkg_server = registry_use_pkg_server()
    if reg_currently_uses_pkg_server && !reg_should_use_pkg_server
        msg = string(
            "Your registry may be outdated. We recommend that you run the ",
            "following command: ",
            "using Pkg; Pkg.Registry.rm(\"$(reg.name)\"); Pkg.Registry.add(\"$(reg.name)\")",
        )
        @warn(msg)
    end
    return nothing
end

function download_registries(io::IO, regs::Vector{RegistrySpec}, depot::String=depots1())
    populate_known_registries_with_urls!(regs)
    regdir = joinpath(depot, "registries")
    isdir(regdir) || mkpath(regdir)
    # only allow one julia process to download and install registries at a time
    FileWatching.mkpidlock(joinpath(regdir, ".pid"), stale_age = 10) do
    registry_urls = pkg_server_registry_urls()
    for reg in regs
        if reg.path !== nothing && reg.url !== nothing
            Pkg.Types.pkgerror("""
                ambiguous registry specification; both `url` and `path` are set:
                    url=\"$(reg.url)\"
                    path=\"$(reg.path)\"
                """
            )
        end
        url = get(registry_urls, reg.uuid, nothing)
        if url !== nothing && registry_read_from_tarball()
            tmp = tempname()
            try
                download_verify(url, nothing, tmp)
            catch err
                Pkg.Types.pkgerror("could not download $url \nException: $(sprint(showerror, err))")
            end
            _hash = pkg_server_url_hash(url)
            if !verify_archive_tree_hash(tmp, _hash)
                Pkg.Types.pkgerror("unable to verify download from $url")
            end
            if reg.name === nothing
                # Need to look up the registry name here
                reg_unc = uncompress_registry(tmp)
                reg.name = TOML.parse(reg_unc["Registry.toml"])["name"]::String
            end
            mv(tmp, joinpath(regdir, reg.name * ".tar.gz"); force=true)
            reg_info = Dict("uuid" => string(reg.uuid), "git-tree-sha1" => string(_hash), "path" => reg.name * ".tar.gz")
            open(joinpath(regdir, reg.name * ".toml"), "w") do io
                TOML.print(io, reg_info)
            end
        else
            mktempdir() do tmp
                if reg.path !== nothing && reg.linked == true # symlink to local source
                    registry = Registry.RegistryInstance(reg.path)
                    regpath = joinpath(regdir, registry.name)
                    printpkgstyle(io, :Symlinking, "registry from `$(Base.contractuser(reg.path))`")
                    isdir(dirname(regpath)) || mkpath(dirname(regpath))
                    symlink(reg.path, regpath)
                    isfile(joinpath(regpath, "Registry.toml")) || Pkg.Types.pkgerror("no `Registry.toml` file in linked registry.")
                    registry = Registry.RegistryInstance(regpath)
                    printpkgstyle(io, :Symlinked, "registry `$(Base.contractuser(registry.name))` to `$(Base.contractuser(regpath))`")
                    return
                elseif reg.url !== nothing && reg.linked == true
                    pkgerror("""
                    A symlinked registry was requested but `path` was not set and `url` was set to `$url`.
                    Set only `path` and `linked = true` to use registry symlinking.
                    """)
                elseif url !== nothing && registry_use_pkg_server()
                    # download from Pkg server
                    try
                        download_verify_unpack(url, nothing, tmp, ignore_existence = true, io = io)
                    catch err
                        Pkg.Types.pkgerror("could not download $url \nException: $(sprint(showerror, err))")
                    end
                    tree_info_file = joinpath(tmp, ".tree_info.toml")
                    hash = pkg_server_url_hash(url)
                    write(tree_info_file, "git-tree-sha1 = " * repr(string(hash)))
                elseif reg.path !== nothing # copy from local source
                    printpkgstyle(io, :Copying, "registry from `$(Base.contractuser(reg.path))`")
                    isfile(joinpath(reg.path, "Registry.toml")) || Pkg.Types.pkgerror("no `Registry.toml` file in source directory.")
                    registry = Registry.RegistryInstance(reg.path)
                    regpath = joinpath(regdir, registry.name)
                    cp(reg.path, regpath; force=true) # has to be cp given we're copying
                    printpkgstyle(io, :Copied, "registry `$(Base.contractuser(registry.name))` to `$(Base.contractuser(regpath))`")
                    return
                elseif reg.url !== nothing # clone from url
                    # retry to help spurious connection issues, particularly on CI
                    repo = retry(GitTools.clone, delays = fill(1.0, 5), check=(s,e)->isa(e, LibGit2.GitError))(io, reg.url, tmp; header = "registry from $(repr(reg.url))")
                    LibGit2.close(repo)
                else
                    Pkg.Types.pkgerror("no path or url specified for registry")
                end
                # verify that the clone looks like a registry
                if !isfile(joinpath(tmp, "Registry.toml"))
                    Pkg.Types.pkgerror("no `Registry.toml` file in cloned registry.")
                end
                registry = Registry.RegistryInstance(tmp)
                regpath = joinpath(regdir, registry.name)
                # copy to `depot`
                ispath(dirname(regpath)) || mkpath(dirname(regpath))
                if isfile(joinpath(regpath, "Registry.toml"))
                    existing_registry = Registry.RegistryInstance(regpath)
                    if registry.uuid == existing_registry.uuid
                        println(io,
                                "Registry `$(registry.name)` already exists in `$(Base.contractuser(regpath))`.")
                    else
                        throw(Pkg.Types.PkgError("registry `$(registry.name)=\"$(registry.uuid)\"` conflicts with " *
                            "existing registry `$(existing_registry.name)=\"$(existing_registry.uuid)\"`. " *
                            "To install it you can clone it manually into e.g. " *
                            "`$(Base.contractuser(joinpath(regdir, registry.name*"-2")))`."))
                    end
                elseif (url !== nothing && registry_use_pkg_server()) || reg.linked !== true
                    # if the dir doesn't exist, or exists but doesn't contain a Registry.toml
                    mv(tmp, regpath, force=true)
                    printpkgstyle(io, :Added, "registry `$(registry.name)` to `$(Base.contractuser(regpath))`")
                end
            end
        end
    end
    end # mkpidlock
    return nothing
end

"""
    Pkg.Registry.rm(registry::String)
    Pkg.Registry.rm(registry::RegistrySpec)

Remove registries.

# Examples
```julia
Pkg.Registry.rm("General")
Pkg.Registry.rm(RegistrySpec(uuid = "23338594-aafe-5451-b93e-139f81909106"))
```
"""
rm(reg::Union{String,RegistrySpec}; kwargs...) = rm([reg]; kwargs...)
rm(regs::Vector{String}; kwargs...) = rm([RegistrySpec(name = name) for name in regs]; kwargs...)
function rm(regs::Vector{RegistrySpec}; io::IO=stderr_f())
    for registry in find_installed_registries(io, regs; depots=first(Base.DEPOT_PATH))
        printpkgstyle(io, :Removing, "registry `$(registry.name)` from $(Base.contractuser(registry.path))")
        if isfile(registry.path)
            d = TOML.parsefile(registry.path)
            if haskey(d, "path")
               Base.rm(joinpath(dirname(registry.path), d["path"]); force=true)
            end
        end
        Base.rm(registry.path; force=true, recursive=true)
    end
    return nothing
end

# Search for the input registries among installed ones
function find_installed_registries(io::IO,
                                   needles::Union{Vector{Registry.RegistryInstance}, Vector{RegistrySpec}};
                                   depots=Base.DEPOT_PATH)
    haystack = reachable_registries(; depots)
    output = Registry.RegistryInstance[]
    for needle in needles
        if needle.name === nothing && needle.uuid === nothing
            Pkg.Types.pkgerror("no name or uuid specified for registry.")
        end
        found = false
        for candidate in haystack
            if needle.uuid !== nothing
                if needle.uuid == candidate.uuid
                    push!(output, candidate)
                    found = true
                end
            elseif needle.name !== nothing
                if needle.name == candidate.name
                    named_regs = filter(r -> r.name == needle.name, haystack)
                    if !all(r -> r.uuid == first(named_regs).uuid, named_regs)
                        Pkg.Types.pkgerror("multiple registries with name `$(needle.name)`, please specify with uuid.")
                    end
                    push!(output, candidate)
                    found = true
                end
            end
        end
        if !found
            println(io, "registry `$(needle.name === nothing ? needle.uuid :
                                         needle.uuid === nothing ? needle.name :
                                         "$(needle.name)=$(needle.uuid)")` not found.")
        end
    end
    return output
end

function get_registry_update_log()
    pkg_scratch_space = joinpath(DEPOT_PATH[1], "scratchspaces", "44cfe95a-1eb2-52ea-b672-e2afdf69b78f")
    pkg_reg_updated_file = joinpath(pkg_scratch_space, "registry_updates.toml")
    updated_registry_d = isfile(pkg_reg_updated_file) ? TOML.parsefile(pkg_reg_updated_file) : Dict{String, Any}()
    return updated_registry_d
end

function save_registry_update_log(d::Dict)
    pkg_scratch_space = joinpath(DEPOT_PATH[1], "scratchspaces", "44cfe95a-1eb2-52ea-b672-e2afdf69b78f")
    mkpath(pkg_scratch_space)
    pkg_reg_updated_file = joinpath(pkg_scratch_space, "registry_updates.toml")
    open(pkg_reg_updated_file, "w") do io
        TOML.print(io, d)
    end
end

"""
    Pkg.Registry.update()
    Pkg.Registry.update(registry::RegistrySpec)
    Pkg.Registry.update(registry::Vector{RegistrySpec})

Update registries. If no registries are given, update
all available registries.

# Examples
```julia
Pkg.Registry.update()
Pkg.Registry.update("General")
Pkg.Registry.update(RegistrySpec(uuid = "23338594-aafe-5451-b93e-139f81909106"))
```
"""
update(reg::Union{String,RegistrySpec}; kwargs...) = update([reg]; kwargs...)
update(regs::Vector{String}; kwargs...) = update([RegistrySpec(name = name) for name in regs]; kwargs...)
function update(regs::Vector{RegistrySpec} = RegistrySpec[]; io::IO=stderr_f(), force::Bool=true, depots = [depots1()], update_cooldown = Second(1))
    registry_update_log = get_registry_update_log()
    for depot in depots
        depot_regs = isempty(regs) ? reachable_registries(; depots=depot) : regs
        regdir = joinpath(depot, "registries")
        isdir(regdir) || mkpath(regdir)
        # only allow one julia process to update registries in this depot at a time
        FileWatching.mkpidlock(joinpath(regdir, ".pid"), stale_age = 10) do
        errors = Tuple{String, String}[]
        registry_urls = pkg_server_registry_urls()
        for reg in unique(r -> r.uuid, find_installed_registries(io, depot_regs; depots=[depot]); seen=Set{UUID}())
            prev_update = get(registry_update_log, string(reg.uuid), nothing)::Union{Nothing, DateTime}
            if prev_update !== nothing
                diff = now() - prev_update            
                if diff < update_cooldown
                    @debug "Skipping updating registry $(reg.name) since it is on cooldown: $(Dates.canonicalize(Millisecond(update_cooldown) - diff)) left"
                    continue
                end
            end
            let reg=reg, errors=errors
                regpath = pathrepr(reg.path)
                let regpath=regpath
                    if reg.tree_info !== nothing
                        printpkgstyle(io, :Updating, "registry at " * regpath)
                        old_hash = reg.tree_info
                        url = get(registry_urls, reg.uuid, nothing)
                        if url !== nothing
                            check_registry_state(reg)
                        end
                        if url !== nothing && (new_hash = pkg_server_url_hash(url)) != old_hash
                            # TODO: update faster by using a diff, if available
                            # TODO: DRY with the code in `download_default_registries`
                            let new_hash = new_hash, url = url
                                if registry_read_from_tarball()
                                    tmp = tempname()
                                    try
                                        download_verify(url, nothing, tmp)
                                    catch err
                                        push!(errors, (reg.path, "failed to download from $(url). Exception: $(sprint(showerror, err))"))
                                        @goto done_tarball_read
                                    end
                                    hash = pkg_server_url_hash(url)
                                    if !verify_archive_tree_hash(tmp, hash)
                                        push!(errors, (reg.path, "failed to verify download from $(url)"))
                                        @goto done_tarball_read
                                    end
                                    # If we have an uncompressed Pkg server registry, remove it and get the compressed version
                                    if isdir(reg.path)
                                        Base.rm(reg.path; recursive=true, force=true)
                                    end
                                    registry_path = dirname(reg.path)
                                    mv(tmp, joinpath(registry_path, reg.name * ".tar.gz"); force=true)
                                    reg_info = Dict("uuid" => string(reg.uuid), "git-tree-sha1" => string(hash), "path" => reg.name * ".tar.gz")
                                    open(joinpath(registry_path, reg.name * ".toml"), "w") do io
                                        TOML.print(io, reg_info)
                                    end
                                    registry_update_log[string(reg.uuid)] = now()
                                    @label done_tarball_read
                                else
                                    mktempdir() do tmp
                                        try
                                            download_verify_unpack(url, nothing, tmp, ignore_existence = true, io=io)
                                            registry_update_log[string(reg.uuid)] = now()
                                        catch err
                                            push!(errors, (reg.path, "failed to download and unpack from $(url). Exception: $(sprint(showerror, err))"))
                                            @goto done_tarball_unpack
                                        end
                                        tree_info_file = joinpath(tmp, ".tree_info.toml")
                                        write(tree_info_file, "git-tree-sha1 = " * repr(string(new_hash)))
                                        mv(tmp, reg.path, force=true)
                                        @label done_tarball_unpack
                                    end
                                end
                            end
                        end
                    elseif isdir(joinpath(reg.path, ".git"))
                        printpkgstyle(io, :Updating, "registry at " * regpath)
                        LibGit2.with(LibGit2.GitRepo(reg.path)) do repo
                            if LibGit2.isdirty(repo)
                                push!(errors, (regpath, "registry dirty"))
                                @goto done_git
                            end
                            if !LibGit2.isattached(repo)
                                push!(errors, (regpath, "registry detached"))
                                @goto done_git
                            end
                            if !("origin" in LibGit2.remotes(repo))
                                push!(errors, (regpath, "origin not in the list of remotes"))
                                @goto done_git
                            end
                            branch = LibGit2.headname(repo)
                            try
                                GitTools.fetch(io, repo; refspecs=["+refs/heads/$branch:refs/remotes/origin/$branch"])
                            catch e
                                e isa Pkg.Types.PkgError || rethrow()
                                push!(errors, (reg.path, "failed to fetch from repo: $(e.msg)"))
                                @goto done_git
                            end
                            attempts = 0
                            @label merge
                            ff_succeeded = try
                                LibGit2.merge!(repo; branch="refs/remotes/origin/$branch", fastforward=true)
                            catch e
                                attempts += 1
                                if e isa LibGit2.GitError && e.code == LibGit2.Error.ELOCKED && attempts <= 3
                                    @warn "Registry update attempt failed because repository is locked. Resetting and retrying." e
                                    LibGit2.reset!(repo, LibGit2.head_oid(repo), LibGit2.Consts.RESET_HARD)
                                    sleep(1)
                                    @goto merge
                                elseif e isa LibGit2.GitError && e.code == LibGit2.Error.ENOTFOUND
                                    push!(errors, (reg.path, "branch origin/$branch not found"))
                                    @goto done_git
                                else
                                    rethrow()
                                end

                            end

                            if !ff_succeeded
                                try LibGit2.rebase!(repo, "origin/$branch")
                                catch e
                                    e isa LibGit2.GitError || rethrow()
                                    push!(errors, (reg.path, "registry failed to rebase on origin/$branch"))
                                    @goto done_git
                                end
                            end
                            registry_update_log[string(reg.uuid)] = now()
                            @label done_git
                        end
                    end
                end
            end
        end
        if !isempty(errors)
            warn_str = "Some registries failed to update:"
            for (reg, err) in errors
                warn_str *= "\n    — $reg — $err"
            end
            @error warn_str
        end
        end # mkpidlock
    end
    save_registry_update_log(registry_update_log)
    return
end


"""
    Pkg.Registry.status()

Display information about available registries.

# Examples
```julia
Pkg.Registry.status()
```
"""
function status(io::IO=stderr_f())
    regs = reachable_registries()
    regs = unique(r -> r.uuid, regs; seen=Set{Union{UUID,Nothing}}())
    printpkgstyle(io, Symbol("Registry Status"), "")
    if isempty(regs)
        println(io, "  (no registries found)")
    else
        for reg in regs
            printstyled(io, " [$(string(reg.uuid)[1:8])]"; color = :light_black)
            print(io, " $(reg.name)")
            reg.repo === nothing || print(io, " ($(reg.repo))")
            println(io)
        end
    end
end

end # module
�   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Pkg/src/Registry/registry_instance.jlhA      using Base: UUID, SHA1
using TOML
using Tar
using ..Versions: VersionSpec, VersionRange

# The content of a registry is assumed to be constant during the
# lifetime of a `Registry`. Create a new `Registry` if you want to have
# a new view on the current registry.

function to_tar_path_format(file::AbstractString)
    @static if Sys.iswindows()
        file = replace(file, "\\" => "/")
    end
    return file
end

# See loading.jl
const TOML_CACHE = Base.TOMLCache(TOML.Parser(), Dict{String, Dict{String, Any}}())
const TOML_LOCK = ReentrantLock()
_parsefile(toml_file::AbstractString) = Base.parsed_toml(toml_file, TOML_CACHE, TOML_LOCK)
function parsefile(in_memory_registry::Union{Dict, Nothing}, folder::AbstractString, file::AbstractString)
    if in_memory_registry === nothing
        return _parsefile(joinpath(folder, file))
    else
        content = in_memory_registry[to_tar_path_format(file)]
        return TOML.Internals.parse(TOML.Parser(content; filepath=file))
    end
end

custom_isfile(in_memory_registry::Union{Dict, Nothing}, folder::AbstractString, file::AbstractString) =
    in_memory_registry === nothing ? isfile(joinpath(folder, file)) : haskey(in_memory_registry, to_tar_path_format(file))

# Info about each version of a package
mutable struct VersionInfo
    const git_tree_sha1::Base.SHA1
    const yanked::Bool
    uncompressed_compat::Dict{UUID, VersionSpec} # lazily initialized
    weak_uncompressed_compat::Dict{UUID, VersionSpec} # lazily initialized

    VersionInfo(git_tree_sha1::Base.SHA1, yanked::Bool) = new(git_tree_sha1, yanked)
end

# This is the information that exists in e.g. General/A/ACME
struct PkgInfo
    # Package.toml:
    repo::Union{String, Nothing}
    subdir::Union{String, Nothing}

    # Versions.toml:
    version_info::Dict{VersionNumber, VersionInfo}

    # Compat.toml
    compat::Dict{VersionRange, Dict{String, VersionSpec}}

    # Deps.toml
    deps::Dict{VersionRange, Dict{String, UUID}}

    # WeakCompat.toml
    weak_compat::Dict{VersionRange, Dict{String, VersionSpec}}

    # WeakDeps.toml
    weak_deps::Dict{VersionRange, Dict{String, UUID}}
end

isyanked(pkg::PkgInfo, v::VersionNumber) = pkg.version_info[v].yanked
treehash(pkg::PkgInfo, v::VersionNumber) = pkg.version_info[v].git_tree_sha1

function uncompress(compressed::Dict{VersionRange, Dict{String, T}}, vsorted::Vector{VersionNumber}) where {T}
    @assert issorted(vsorted)
    uncompressed = Dict{VersionNumber, Dict{String, T}}()
    for v in vsorted
        uncompressed[v] = Dict{String, T}()
    end
    for (vs, data) in compressed
        first = length(vsorted) + 1
        # We find the first and last version that are in the range
        # and since the versions are sorted, all versions in between are sorted
        for i in eachindex(vsorted)
            v = vsorted[i]
            v in vs && (first = i; break)
        end
        last = 0
        for i in reverse(eachindex(vsorted))
            v = vsorted[i]
            v in vs && (last = i; break)
        end
        for i in first:last
            v = vsorted[i]
            uv = uncompressed[v]
            for (key, value) in data
                if haskey(uv, key)
                    error("Overlapping ranges for $(key) for version $v in registry.")
                else
                    uv[key] = value
                end
            end
        end
    end
    return uncompressed
end

const JULIA_UUID = UUID("1222c4b2-2114-5bfd-aeef-88e4692bbb3e")
function initialize_uncompressed!(pkg::PkgInfo, versions = keys(pkg.version_info))
    # Only valid to call this with existing versions of the package
    # Remove all versions we have already uncompressed
    versions = filter!(v -> !isdefined(pkg.version_info[v], :uncompressed_compat), collect(versions))

    sort!(versions)

    uncompressed_compat      = uncompress(pkg.compat,      versions)
    uncompressed_deps        = uncompress(pkg.deps,        versions)

    for v in versions
        vinfo = pkg.version_info[v]
        compat = Dict{UUID, VersionSpec}()
        uncompressed_deps_v = uncompressed_deps[v]
        # Everything depends on Julia
        uncompressed_deps_v["julia"] = JULIA_UUID
        uncompressed_compat_v = uncompressed_compat[v]
        for (pkg, uuid) in uncompressed_deps_v
            vspec = get(uncompressed_compat_v, pkg, nothing)
            compat[uuid] = vspec === nothing ? VersionSpec() : vspec
        end
        @assert !isdefined(vinfo, :uncompressed_compat)
        vinfo.uncompressed_compat = compat
    end
    return pkg
end

function initialize_weak_uncompressed!(pkg::PkgInfo, versions = keys(pkg.version_info))
    # Only valid to call this with existing versions of the package
    # Remove all versions we have already uncompressed
    versions = filter!(v -> !isdefined(pkg.version_info[v], :weak_uncompressed_compat), collect(versions))

    sort!(versions)

    weak_uncompressed_compat = uncompress(pkg.weak_compat, versions)
    weak_uncompressed_deps   = uncompress(pkg.weak_deps,   versions)

    for v in versions
        vinfo = pkg.version_info[v]
        weak_compat = Dict{UUID, VersionSpec}()
        weak_uncompressed_deps_v = weak_uncompressed_deps[v]
        weak_uncompressed_compat_v = weak_uncompressed_compat[v]
        for (pkg, uuid) in weak_uncompressed_deps_v
            vspec = get(weak_uncompressed_compat_v, pkg, nothing)
            weak_compat[uuid] = vspec === nothing ? VersionSpec() : vspec
        end
        @assert !isdefined(vinfo, :weak_uncompressed_compat)
        vinfo.weak_uncompressed_compat = weak_compat
    end
    return pkg
end

function compat_info(pkg::PkgInfo)
    initialize_uncompressed!(pkg)
    return Dict(v => info.uncompressed_compat for (v, info) in pkg.version_info)
end

function weak_compat_info(pkg::PkgInfo)
    if isempty(pkg.weak_deps)
        return nothing
    end
    initialize_weak_uncompressed!(pkg)
    return Dict(v => info.weak_uncompressed_compat for (v, info) in pkg.version_info)
end

mutable struct PkgEntry
    # Registry.toml:
    const path::String
    const registry_path::String
    const name::String
    const uuid::UUID

    const in_memory_registry::Union{Dict{String, String}, Nothing}
    # Version.toml / (Compat.toml / Deps.toml):
    info::PkgInfo # lazily initialized

    PkgEntry(path, registry_path, name, uuid, in_memory_registry) = new(path, registry_path, name, uuid, in_memory_registry, #= undef =#)
end

registry_info(pkg::PkgEntry) = init_package_info!(pkg)

function init_package_info!(pkg::PkgEntry)
    # Already uncompressed the info for this package, return early
    isdefined(pkg, :info) && return pkg.info
    path = pkg.registry_path

    d_p = parsefile(pkg.in_memory_registry, pkg.registry_path, joinpath(pkg.path, "Package.toml"))
    name = d_p["name"]::String
    name != pkg.name && error("inconsistent name in Registry.toml ($(name)) and Package.toml ($(pkg.name)) for pkg at $(path)")
    repo = get(d_p, "repo", nothing)::Union{Nothing, String}
    subdir = get(d_p, "subdir", nothing)::Union{Nothing, String}

    # Versions.toml
    d_v = custom_isfile(pkg.in_memory_registry, pkg.registry_path, joinpath(pkg.path, "Versions.toml")) ?
        parsefile(pkg.in_memory_registry, pkg.registry_path, joinpath(pkg.path, "Versions.toml")) : Dict{String, Any}()
    version_info = Dict{VersionNumber, VersionInfo}(VersionNumber(k) =>
        VersionInfo(SHA1(v["git-tree-sha1"]::String), get(v, "yanked", false)::Bool) for (k, v) in d_v)

    # Compat.toml
    compat_data_toml = custom_isfile(pkg.in_memory_registry, pkg.registry_path, joinpath(pkg.path, "Compat.toml")) ?
        parsefile(pkg.in_memory_registry, pkg.registry_path, joinpath(pkg.path, "Compat.toml")) : Dict{String, Any}()
    compat = Dict{VersionRange, Dict{String, VersionSpec}}()
    for (v, data) in compat_data_toml
        data = data::Dict{String, Any}
        vr = VersionRange(v)
        d = Dict{String, VersionSpec}(dep => VersionSpec(vr_dep) for (dep, vr_dep::Union{String, Vector{String}}) in data)
        compat[vr] = d
    end

    # Deps.toml
    deps_data_toml = custom_isfile(pkg.in_memory_registry, pkg.registry_path, joinpath(pkg.path, "Deps.toml")) ?
        parsefile(pkg.in_memory_registry, pkg.registry_path, joinpath(pkg.path, "Deps.toml")) : Dict{String, Any}()
    deps = Dict{VersionRange, Dict{String, UUID}}()
    for (v, data) in deps_data_toml
        data = data::Dict{String, Any}
        vr = VersionRange(v)
        d = Dict{String, UUID}(dep => UUID(uuid) for (dep, uuid::String) in data)
        deps[vr] = d
    end
    # All packages depend on julia
    deps[VersionRange()] = Dict("julia" => JULIA_UUID)

    # WeakCompat.toml
    weak_compat_data_toml = custom_isfile(pkg.in_memory_registry, pkg.registry_path, joinpath(pkg.path, "WeakCompat.toml")) ?
        parsefile(pkg.in_memory_registry, pkg.registry_path, joinpath(pkg.path, "WeakCompat.toml")) : Dict{String, Any}()
    weak_compat = Dict{VersionRange, Dict{String, VersionSpec}}()
    for (v, data) in weak_compat_data_toml
        data = data::Dict{String, Any}
        vr = VersionRange(v)
        d = Dict{String, VersionSpec}(dep => VersionSpec(vr_dep) for (dep, vr_dep::Union{String, Vector{String}}) in data)
        weak_compat[vr] = d
    end

    # WeakDeps.toml
    weak_deps_data_toml = custom_isfile(pkg.in_memory_registry, pkg.registry_path, joinpath(pkg.path, "WeakDeps.toml")) ?
        parsefile(pkg.in_memory_registry, pkg.registry_path, joinpath(pkg.path, "WeakDeps.toml")) : Dict{String, Any}()
    weak_deps = Dict{VersionRange, Dict{String, UUID}}()
    for (v, data) in weak_deps_data_toml
        data = data::Dict{String, Any}
        vr = VersionRange(v)
        d = Dict{String, UUID}(dep => UUID(uuid) for (dep, uuid::String) in data)
        weak_deps[vr] = d
    end

    @assert !isdefined(pkg, :info)
    pkg.info = PkgInfo(repo, subdir, version_info, compat, deps, weak_compat, weak_deps)

    return pkg.info
end


function uncompress_registry(tar_gz::AbstractString)
    if !isfile(tar_gz)
        error("$(repr(tar_gz)): No such file")
    end
    data = Dict{String, String}()
    buf = Vector{UInt8}(undef, Tar.DEFAULT_BUFFER_SIZE)
    io = IOBuffer()
    open(`$(exe7z()) x $tar_gz -so`) do tar
        Tar.read_tarball(x->true, tar; buf=buf) do hdr, _
            if hdr.type == :file
                Tar.read_data(tar, io; size=hdr.size, buf=buf)
                data[hdr.path] = String(take!(io))
            end
        end
    end
    return data
end

struct RegistryInstance
    path::String
    name::String
    uuid::UUID
    repo::Union{String, Nothing}
    description::Union{String, Nothing}
    pkgs::Dict{UUID, PkgEntry}
    tree_info::Union{Base.SHA1, Nothing}
    in_memory_registry::Union{Nothing, Dict{String, String}}
    # various caches
    name_to_uuids::Dict{String, Vector{UUID}}
end

const REGISTRY_CACHE = Dict{String, Tuple{Base.SHA1, Bool, RegistryInstance}}()

function get_cached_registry(path, tree_info::Base.SHA1, compressed::Bool)
    if !ispath(path)
        delete!(REGISTRY_CACHE, path)
        return nothing
    end
    v = get(REGISTRY_CACHE, path, nothing)
    if v !== nothing
        cached_tree_info, cached_compressed, reg = v
        if cached_tree_info == tree_info && cached_compressed == compressed
            return reg
        end
    end
    # Prevent hogging up memory indefinitely
    length(REGISTRY_CACHE) > 20 && empty!(REGISTRY_CACHE)
    return nothing
end

function RegistryInstance(path::AbstractString)
    compressed_file = nothing
    if isfile(path)
        @assert splitext(path)[2] == ".toml"
        d_reg_info = parsefile(nothing, dirname(path), basename(path))
        compressed_file = d_reg_info["path"]::String
        tree_info = Base.SHA1(d_reg_info["git-tree-sha1"]::String)
    else
        tree_info_file = joinpath(path, ".tree_info.toml")
        tree_info = if isfile(tree_info_file)
            Base.SHA1(parsefile(nothing, path, ".tree_info.toml")["git-tree-sha1"]::String)
        else
            nothing
        end
    end
    # Reuse an existing cached registry if it exists for this content
    if tree_info !== nothing
        reg = get_cached_registry(path, tree_info, compressed_file !== nothing)
        if reg isa RegistryInstance
            return reg
        end
    end

    in_memory_registry = if compressed_file !== nothing
        uncompress_registry(joinpath(dirname(path), compressed_file))
    else
        nothing
    end

    d = parsefile(in_memory_registry, path, "Registry.toml")
    pkgs = Dict{UUID, PkgEntry}()
    for (uuid, info) in d["packages"]::Dict{String, Any}
        uuid = UUID(uuid::String)
        info::Dict{String, Any}
        name = info["name"]::String
        pkgpath = info["path"]::String
        pkg = PkgEntry(pkgpath, path, name, uuid, in_memory_registry)
        pkgs[uuid] = pkg
    end
    reg = RegistryInstance(
        path,
        d["name"]::String,
        UUID(d["uuid"]::String),
        get(d, "repo", nothing)::Union{String, Nothing},
        get(d, "description", nothing)::Union{String, Nothing},
        pkgs,
        tree_info,
        in_memory_registry,
        Dict{String, UUID}(),
    )
    if tree_info !== nothing
        REGISTRY_CACHE[path] = (tree_info, compressed_file !== nothing, reg)
    end
    return reg
end

function Base.show(io::IO, ::MIME"text/plain", r::RegistryInstance)
    println(io, "Registry: $(repr(r.name)) at $(repr(r.path)):")
    println(io, "  uuid: ", r.uuid)
    println(io, "  repo: ", r.repo)
    if r.tree_info !== nothing
        println(io, "  git-tree-sha1: ", r.tree_info)
    end
    println(io, "  packages: ", length(r.pkgs))
end

function uuids_from_name(r::RegistryInstance, name::String)
    create_name_uuid_mapping!(r)
    return get(Vector{UUID}, r.name_to_uuids, name)
end

function create_name_uuid_mapping!(r::RegistryInstance)
    isempty(r.name_to_uuids) || return
    for (uuid, pkg) in r.pkgs
        uuids = get!(Vector{UUID}, r.name_to_uuids, pkg.name)
        push!(uuids, pkg.uuid)
    end
    return
end

function verify_compressed_registry_toml(path::String)
    d = TOML.tryparsefile(path)
    if d isa TOML.ParserError
        @warn "Failed to parse registry TOML file at $(repr(path))" exception=d
        return false
    end
    for key in ("git-tree-sha1", "uuid", "path")
        if !haskey(d, key)
            @warn "Expected key $(repr(key)) to exist in registry TOML file at $(repr(path))"
            return false
        end
    end
    compressed_file = joinpath(dirname(path), d["path"]::String)
    if !isfile(compressed_file)
        @warn "Expected the compressed registry for $(repr(path)) to exist at $(repr(compressed_file))"
        return false
    end
    return true
end

function reachable_registries(; depots::Union{String, Vector{String}}=Base.DEPOT_PATH)
    # collect registries
    if depots isa String
        depots = [depots]
    end
    registries = RegistryInstance[]
    for d in depots
        isdir(d) || continue
        reg_dir = joinpath(d, "registries")
        isdir(reg_dir) || continue
        reg_paths = readdir(reg_dir; join=true)
        candidate_registries = String[]
        # All folders could be registries
        append!(candidate_registries, filter(isdir, reg_paths))
        if registry_read_from_tarball()
            compressed_registries = filter(endswith(".toml"), reg_paths)
            # if we are reading compressed registries, ignore compressed registries
            # with the same name
            compressed_registry_names = Set([splitext(basename(file))[1] for file in compressed_registries])
            filter!(x -> !(basename(x) in compressed_registry_names), candidate_registries)
            for compressed_registry in compressed_registries
                if verify_compressed_registry_toml(compressed_registry)
                    push!(candidate_registries, compressed_registry)
                end
            end
        end

        for candidate in candidate_registries
            # candidate can be either a folder or a TOML file
            if isfile(joinpath(candidate, "Registry.toml")) || isfile(candidate)
                push!(registries, RegistryInstance(candidate))
            end
        end
    end
    return registries
end

# Dict interface

function Base.haskey(r::RegistryInstance, uuid::UUID)
    return haskey(r.pkgs, uuid)
end

function Base.keys(r::RegistryInstance)
    return keys(r.pkgs)
end

Base.getindex(r::RegistryInstance, uuid::UUID) = r.pkgs[uuid]

Base.get(r::RegistryInstance, uuid::UUID, default) = get(r.pkgs, uuid, default)

Base.iterate(r::RegistryInstance) = iterate(r.pkgs)
Base.iterate(r::RegistryInstance, state) = iterate(r.pkgs, state)
v   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Pkg/src/Resolve/Resolve.jlYP      # This file is a part of Julia. License is MIT: https://julialang.org/license

module Resolve

using ..Versions
import ..stdout_f, ..stderr_f

using Printf
using Random
using UUIDs

export resolve, sanity_check, Graph, pkgID

####################
# Requires / Fixed #
####################
const Requires = Dict{UUID,VersionSpec}

struct Fixed
    version::VersionNumber
    requires::Requires
    weak::Set{UUID}
end
Fixed(v::VersionNumber, requires::Requires = Requires()) = Fixed(v, requires, Set{UUID}())

Base.:(==)(a::Fixed, b::Fixed) = a.version == b.version && a.requires == b.requires && a.weak == b.weak
Base.hash(f::Fixed, h::UInt) = hash((f.version, f.requires, f.weak), h + (0x68628b809fd417ca % UInt))

Base.show(io::IO, f::Fixed) = isempty(f.requires) ?
    print(io, "Fixed(", repr(f.version), ")") :
    isempty(f.weak) ?
    print(io, "Fixed(", repr(f.version), ",", f.requires, ")") :
    print(io, "Fixed(", repr(f.version), ",", f.requires, ", weak=", f.weak, ")")


struct ResolverError <: Exception
    msg::AbstractString
    ex::Union{Exception,Nothing}
end
ResolverError(msg::AbstractString) = ResolverError(msg, nothing)

function Base.showerror(io::IO, pkgerr::ResolverError)
    print(io, pkgerr.msg)
    if pkgerr.ex !== nothing
        pkgex = pkgerr.ex
        if isa(pkgex, CompositeException)
            for cex in pkgex
                print(io, "\n=> ")
                showerror(io, cex)
            end
        else
            print(io, "\n")
            showerror(io, pkgex)
        end
    end
end

const uuid_julia = UUID("1222c4b2-2114-5bfd-aeef-88e4692bbb3e")

include("versionweights.jl")
include("fieldvalues.jl")
include("graphtype.jl")
include("maxsum.jl")

"Resolve package dependencies."
function resolve(graph::Graph)
    sol = _resolve(graph::Graph, nothing, nothing)

    # return the solution as a Dict mapping UUID => VersionNumber
    return compute_output_dict(sol, graph)
end

function _resolve(graph::Graph, lower_bound::Union{Vector{Int},Nothing}, previous_sol::Union{Vector{Int},Nothing})
    np = graph.np
    spp = graph.spp
    gconstr = graph.gconstr

    if lower_bound ≢ nothing
        for p0 = 1:np
            v0 = lower_bound[p0]
            @assert v0 ≠ spp[p0]
            gconstr[p0][1:(v0-1)] .= false
        end
    end

    # attempt trivial solution first
    greedy_ok, sol = greedysolver(graph)

    greedy_ok && @goto solved

    log_event_global!(graph, "greedy solver failed")

    # trivial solution failed, use maxsum solver
    maxsum_ok, sol, staged = maxsum(graph)

    maxsum_ok && @goto solved

    log_event_global!(graph, "maxsum solver failed")

    @assert previous_sol ≡ nothing

    # the problem is unsat, force-trigger a failure
    # in order to produce a log - this will contain
    # information about the best that the solver could
    # achieve
    trigger_failure!(graph, sol, staged)

    @label solved

    # verify solution (debug code) and enforce its optimality
    @assert verify_solution(sol, graph)
    if greedy_ok
        log_event_global!(graph, "the solver found an optimal configuration")
        return sol
    else
        enforce_optimality!(sol, graph)
        if lower_bound ≢ nothing
            @assert all(sol .≥ lower_bound)
            @assert all((sol .≥ previous_sol) .| (previous_sol .== spp))
        end
        if sol ≠ previous_sol
            log_event_global!(graph, "the solver found a feasible configuration and will try to improve it")
            new_lower_bound = copy(sol)
            uninst_mask = sol .== spp
            new_lower_bound[uninst_mask] .= 1
            if lower_bound ≢ nothing
                lb_mask = uninst_mask .& (lower_bound .≠ spp)
                new_lower_bound[lb_mask] = lower_bound[lb_mask]
                @assert all(new_lower_bound .≥ lower_bound)
            end
            return _resolve(graph, new_lower_bound, sol)
        else
            log_event_global!(graph, "the solver found a feasible configuration and can't improve it")
            return sol
        end
    end
end

"""
Scan the graph for (explicit or implicit) contradictions. Returns a list of problematic
(package,version) combinations.
"""
function sanity_check(graph::Graph, sources::Set{UUID} = Set{UUID}(), verbose::Bool = true)
    req_inds = graph.req_inds
    fix_inds = graph.fix_inds

    id(p) = pkgID(p, graph)

    isempty(req_inds) || @warn("sanity check called on a graph with non-empty requirements")
    if !any(is_julia(graph, fp0) for fp0 in fix_inds)
        @warn("sanity check called on a graph without julia requirement, adding it")
        add_fixed!(graph, Dict(uuid_julia=>Fixed(VERSION)))
    end
    if length(fix_inds) ≠ 1
        @warn("sanity check called on a graph with extra fixed requirements (besides julia)")
    end

    isources = isempty(sources) ?
        Set{Int}(1:graph.np) :
        Set{Int}(graph.data.pdict[p] for p in sources)

    simplify_graph!(graph, isources)

    np = graph.np
    spp = graph.spp
    gadj = graph.gadj
    data = graph.data
    pkgs = data.pkgs
    pdict = data.pdict
    pvers = data.pvers
    eq_classes = data.eq_classes

    problematic = Tuple{String,VersionNumber}[]

    np == 0 && return problematic

    vers = [(pkgs[p0],pvers[p0][v0]) for p0 = 1:np for v0 = 1:(spp[p0]-1)]
    sort!(vers, by=pv->(-length(gadj[pdict[pv[1]]])))

    nv = length(vers)

    svdict = Dict{Tuple{UUID,VersionNumber},Int}(vers[i] => i for i = 1:nv)

    checked = falses(nv)

    last_str_len = 0

    for (i,(p,vn)) in enumerate(vers)
        if verbose
            frac_compl = i / nv
            print("\r", " "^last_str_len, "\r")
            progr_msg = @sprintf("%.3i/%.3i (%i%%) — problematic so far: %i", i, nv, round(Int, 100 * frac_compl), length(problematic))
            print(progr_msg)
            last_str_len = length(progr_msg)
        end

        length(gadj[pdict[p]]) == 0 && break
        checked[i] && continue

        push_snapshot!(graph)

        # enforce package version
        # TODO: use add_reqs! instead...
        p0 = graph.data.pdict[p]
        v0 = graph.data.vdict[p0][vn]
        fill!(graph.gconstr[p0], false)
        graph.gconstr[p0][v0] = true
        push!(graph.req_inds, p0)

        ok = false
        try
            simplify_graph_soft!(graph, Set{Int}([p0]), log_events = false)
        catch err
            isa(err, ResolverError) || rethrow()
            @goto done
        end

        ok, sol = greedysolver(graph)
        ok && @goto done
        ok, sol = maxsum(graph)

        @label done

        if !ok
            for vneq in eq_classes[p][vn]
                push!(problematic, (id(p), vneq))
            end
        else
            @assert verify_solution(sol, graph)
            sol_dict = compute_output_dict(sol, graph)
            for (sp,svn) in sol_dict
                j = svdict[sp,svn]
                checked[j] = true
            end
        end

        # state reset
        empty!(graph.req_inds)
        pop_snapshot!(graph)
    end
    if verbose
        print("\r", " "^last_str_len, "\r")
        println("found $(length(problematic)) problematic versions")
    end
    return sort!(problematic)
end

"""
Translate the solver output (a Vector{Int} of package states) into a Dict which
associates a VersionNumber to each installed package UUID.
"""
function compute_output_dict(sol::Vector{Int}, graph::Graph)
    np = graph.np
    spp = graph.spp
    fix_inds = graph.fix_inds
    pkgs = graph.data.pkgs
    pvers = graph.data.pvers
    pruned = graph.data.pruned

    want = Dict{UUID,VersionNumber}()
    for p0 = 1:np
        p0 ∈ fix_inds && continue
        p = pkgs[p0]
        s0 = sol[p0]
        s0 == spp[p0] && continue
        vn = pvers[p0][s0]
        want[p] = vn
    end
    for (p,vn) in pruned
        @assert !haskey(want, p)
        want[p] = vn
    end

    return want
end

"""
Preliminary solver attempt: tries to maximize each version; bails out as soon as
some non-trivial requirement is detected.
"""
function greedysolver(graph::Graph)
    spp = graph.spp
    gadj = graph.gadj
    gmsk = graph.gmsk
    np = graph.np

    push_snapshot!(graph)
    gconstr = graph.gconstr

    # initialize solution: all uninstalled
    sol = [spp[p0] for p0 = 1:np]

    # packages which are not allowed to be uninstalled
    # (NOTE: this is potentially a superset of graph.req_inds,
    #        since it may include implicit requirements)
    req_inds = Set{Int}(p0 for p0 = 1:np if !gconstr[p0][end])

    # set up required packages to their highest allowed versions
    for rp0 in req_inds
        # look for the highest version which satisfies the requirements
        rv0 = findlast(gconstr[rp0])
        @assert rv0 ≢ nothing && rv0 ≠ spp[rp0]
        sol[rp0] = rv0
        fill!(gconstr[rp0], false)
        gconstr[rp0][rv0] = true
    end

    # propagate the requirements
    try
        simplify_graph_soft!(graph, req_inds, log_events = false)
    catch err
        err isa ResolverError || rethrow()
        pop_snapshot!(graph)
        return (false, Int[])
    end

    # we start from required packages and explore the graph
    # following dependencies
    staged = req_inds
    seen = copy(staged)

    while !isempty(staged)
        staged_next = Set{Int}()
        for p0 in staged
            s0 = sol[p0]
            @assert s0 < spp[p0]

            # scan dependencies
            for (j1,p1) in enumerate(gadj[p0])
                msk = gmsk[p0][j1]
                # look for the highest version which satisfies the requirements
                v1 = findlast(msk[:,s0] .& gconstr[p1])
                v1 == spp[p1] && continue # p1 is not required by p0's current version
                # if we found a version, and the package was uninstalled
                # or the same version was already selected, we're ok;
                # otherwise we can't be sure what the optimal configuration is
                # and we bail out
                old_v1 = sol[p1]
                if v1 ≡ nothing || (old_v1 ≠ v1 && old_v1 ≠ spp[p1])
                    pop_snapshot!(graph)
                    return (false, Int[])
                elseif old_v1 == spp[p1]
                    sol[p1] = v1
                    push!(staged_next, p1)
                end
            end
        end
        union!(seen, staged_next)
        staged = staged_next
    end

    pop_snapshot!(graph)

    for p0 = 1:np
        log_event_greedysolved!(graph, p0, sol[p0])
    end

    return true, sol
end

"""
Verifies that the solver solution fulfills all hard constraints
(requirements and dependencies). This is intended as debug code.
"""
function verify_solution(sol::Vector{Int}, graph::Graph)
    np = graph.np
    spp = graph.spp
    gadj = graph.gadj
    gmsk = graph.gmsk
    gconstr = graph.gconstr

    @assert length(sol) == np
    @assert all(sol .> 0)

    # verify constraints and dependencies
    for p0 = 1:np
        s0 = sol[p0]
        gconstr[p0][s0] || (@warn("gconstr[$p0][$s0] fail"); return false)
        for (j1,p1) in enumerate(gadj[p0])
            msk = gmsk[p0][j1]
            s1 = sol[p1]
            msk[s1,s0] || (@warn("gmsk[$p0][$p1][$s1,$s0] fail"); return false)
        end
    end
    return true
end


"""
Uninstall unreachable packages:
start from the required ones and keep only the packages reachable from them along the graph.
"""
function _uninstall_unreachable!(sol::Vector{Int}, why::Vector{Union{Symbol,Int}}, graph::Graph)
    np = graph.np
    spp = graph.spp
    gadj = graph.gadj
    gmsk = graph.gmsk
    gconstr = graph.gconstr

    uninst = trues(np)
    staged = Set{Int}(p0 for p0 = 1:np if !gconstr[p0][end])
    seen = copy(staged) ∪ Set{Int}(p0 for p0 = 1:np if sol[p0] == spp[p0]) # we'll skip uninstalled packages

    while !isempty(staged)
        staged_next = Set{Int}()
        for p0 in staged
            s0 = sol[p0]
            @assert s0 ≠ spp[p0]
            uninst[p0] = false
            for (j1,p1) in enumerate(gadj[p0])
                p1 ∈ seen && continue            # we've already seen the package, or it is uninstalled
                gmsk[p0][j1][end,s0] && continue # the package is not required by p0 at version s0
                push!(staged_next, p1)
            end
        end
        union!(seen, staged_next)
        staged = staged_next
    end

    for p0 in findall(uninst)
        sol[p0] = spp[p0]
        why[p0] = :uninst
    end
end

"""
Push the given solution to a local optimum if needed: keeps increasing
the states of the given solution as long as no constraints are violated.
It might also install additional packages, if needed to bump the ones already
installed.
It also removes unnecessary parts of the solution which are unconnected
to the required packages.
"""
function enforce_optimality!(sol::Vector{Int}, graph::Graph)
    np = graph.np
    spp = graph.spp
    gadj = graph.gadj
    gmsk = graph.gmsk
    gconstr = graph.gconstr
    pkgs = graph.data.pkgs

    # keep a track for the log
    why = Union{Symbol,Int}[0 for p0 = 1:np]

    # Strategy:
    # There's a cycle in which first the unnecessary (unconnected) packages are removed,
    # then we make a pass over the whole packages trying to bump each of them.
    # We repeat the above two steps until no further action is allowed.
    # When attempting to bump a package, we may attempt to bump or install other packages
    # if needed. Except if the bump would uninstall a package, in which cases we don't
    # touch anything else: we do it only if it has no consequence at all. This strategy
    # favors installing packages as needed.
    # During the bumping pass, we keep an upper and lower bound for each package, which
    # progressively shrink. These are used when adjusting for the effect of an attempted bump.
    # The way it's written should ensure that no package is ever downgraded (unless it was
    # originally unneeded, and then got removed, and later reinstalled to a lower version as
    # a consequence of a bump of some other package).

    # move_up is used to keep track of which packages can move up
    # (they start installed and can be bumped) and which down (they start uninstalled and
    # can be installed)
    move_up = BitVector(undef, length(sol))
    # lower and upper bounds on the valid range of each package
    upperbound = similar(spp)
    lowerbound = similar(spp)
    # backup space for restoring the state if an attempted bump fails
    bk_sol = similar(sol)
    bk_lowerbound = similar(lowerbound)
    bk_upperbound = similar(upperbound)

    # auxiliary sets to perform breadth-first search on the graph
    staged = Set{Int}()
    staged_next = Set{Int}()

    old_sol = similar(sol)       # to detect if we made any changes
    allsols = Set{Vector{Int}}() # used to make 100% sure we avoid infinite loops

    while true
        copy!(old_sol, sol)
        push!(allsols, copy(sol))

        # step 1: uninstall unneeded packages
        _uninstall_unreachable!(sol, why, graph)

        # setp 2: try to bump each installed package in turn

        move_up .= sol .≠ spp
        copy!(upperbound, spp)
        let move_up = move_up
            lowerbound .= [move_up[p0] ? sol[p0] : 1 for p0 = 1:np]
        end

        for p0 = 1:np
            s0 = sol[p0]
            s0 == spp[p0] && (why[p0] = :uninst; continue) # the package is not installed
            move_up[p0] || continue # the package is only installed as a result of a previous bump, skip it

            @assert upperbound[p0] == spp[p0]

            # pick the next version that doesn't violate a constraint (if any)
            bump_range = collect(s0+1:spp[p0])
            bump = let gconstr = gconstr
                findfirst(v0->gconstr[p0][v0], bump_range)
            end

            # no such version was found, skip this package
            bump ≡ nothing && (why[p0] = :constr; continue)

            # assume that we will succeed in bumping the version (otherwise we
            # roll-back at the end)

            new_s0 = bump_range[bump]
            try_uninstall = new_s0 == spp[p0] # are we trying to uninstall a package?

            copy!(bk_sol, sol)
            copy!(bk_lowerbound, lowerbound)
            copy!(bk_upperbound, upperbound)
            sol[p0] = new_s0

            # if we're trying to uninstall, the bump is "soft": we don't update the
            # lower bound so that the package can be reinstalled later in the pass
            # if needed by another package
            try_uninstall || (lowerbound[p0] = new_s0) # note that we're in the move_up case

            empty!(staged)
            empty!(staged_next)
            push!(staged, p0)

            while !isempty(staged)
                for f0 in staged
                    for (j1,f1) in enumerate(gadj[f0])
                        s1 = sol[f1]
                        msk = gmsk[f0][j1]
                        if f1 == p0 || try_uninstall
                            # when uninstalling or looking at p0, no further changes are allowed
                            bump_range = [s1]
                        else
                            lb1 = lowerbound[f1]
                            ub1 = upperbound[f1]
                            @assert lb1 ≤ s1 ≤ ub1
                            if move_up[f1]
                                s1 > lb1 && @assert s1 == spp[f1]
                                # the arrangement of the range gives precedence to improving the
                                # current situation, but allows reinstalling a package if needed
                                bump_range = vcat(s1:ub1, s1-1:-1:lb1)
                            else
                                bump_range = collect(ub1:-1:lb1)
                            end
                        end
                        bump = let gconstr = gconstr
                            findfirst(v1->(gconstr[f1][v1] && msk[v1, sol[f0]]), bump_range)
                        end
                        if bump ≡ nothing
                            why[p0] = f1 # TODO: improve this? (ideally we might want the path from p0 to f1)
                            @goto abort
                        end
                        new_s1 = bump_range[bump]
                        sol[f1] = new_s1
                        new_s1 == s1 && continue
                        push!(staged_next, f1)
                        if move_up[f1]
                            lowerbound[f1] = new_s1
                        else
                            upperbound[f1] = new_s1
                        end
                    end
                end
                staged, staged_next = staged_next, staged
                empty!(staged_next)
            end

            # if we're here the bump was successful, there's nothing more to do
            continue

            ## abort the bumping: restore the solution
            @label abort

            copy!(sol, bk_sol)
            copy!(lowerbound, bk_lowerbound)
            copy!(upperbound, bk_upperbound)
        end
        sol ≠ old_sol || break
        # It might be possible in principle to contrive a situation in which
        # the solutions oscillate
        sol ∈ allsols && break
    end

    @assert verify_solution(sol, graph)

    for p0 = 1:np
        log_event_maxsumsolved!(graph, p0, sol[p0], why[p0])
    end
end

function apply_maxsum_trace!(graph::Graph, sol::Vector{Int})
    gconstr = graph.gconstr

    for (p0,s0) in enumerate(sol)
        s0 == 0 && continue
        gconstr0 = gconstr[p0]
        old_constr = copy(gconstr0)
        @assert old_constr[s0]
        fill!(gconstr0, false)
        gconstr0[s0] = true
        gconstr0 ≠ old_constr && log_event_maxsumtrace!(graph, p0, s0)
    end
end

function trigger_failure!(graph::Graph, sol::Vector{Int}, staged::Tuple{Int,Int})
    apply_maxsum_trace!(graph, sol)
    simplify_graph_soft!(graph, Set(findall(sol .> 0)), log_events = true) # this may throw an error...

    np = graph.np
    gconstr = graph.gconstr
    p0, v0 = staged

    @assert gconstr[p0][v0]
    fill!(gconstr[p0], false)
    gconstr[p0][v0] = true
    log_event_maxsumtrace!(graph, p0, v0)
    simplify_graph!(graph) # this may throw an error...
    outdict = resolve(graph) # ...otherwise, this MUST throw an error
    open(io->showlog(io, graph, view=:chronological), "logchrono.errresolve.txt", "w")
    error("this is not supposed to happen... $(Dict(pkgID(p, graph) => vn for (p,vn) in outdict))")
end

end # module
}   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Pkg/src/Resolve/versionweights.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

# The numeric type used to determine how the different
# versions of a package should be weighed
struct VersionWeight
    major::Int64
    minor::Int64
    patch::Int64
end
VersionWeight(major::Integer, minor::Integer) = VersionWeight(major, minor, 0)
VersionWeight(major::Integer) = VersionWeight(major, 0)
VersionWeight() = VersionWeight(0)
VersionWeight(vn::VersionNumber) = VersionWeight(vn.major, vn.minor, vn.patch)

Base.zero(::Type{VersionWeight}) = VersionWeight()

Base.typemin(::Type{VersionWeight}) = (x=typemin(Int64); VersionWeight(x, x, x))

Base.:(-)(a::VersionWeight, b::VersionWeight) =
    VersionWeight(a.major-b.major, a.minor-b.minor, a.patch-b.patch)

Base.:(+)(a::VersionWeight, b::VersionWeight) =
    VersionWeight(a.major+b.major, a.minor+b.minor, a.patch+b.patch)

Base.:(-)(a::VersionWeight) =
    VersionWeight(-a.major, -a.minor, -a.patch)

function Base.isless(a::VersionWeight, b::VersionWeight)
    (a.major, a.minor, a.patch) < (b.major, b.minor, b.patch)
end

Base.abs(a::VersionWeight) =
    VersionWeight(abs(a.major), abs(a.minor), abs(a.patch))

# This isn't nice, but it's for debugging only anyway
function Base.show(io::IO, a::VersionWeight)
    print(io, "(", a.major)
    a == VersionWeight(a.major) && @goto done
    print(io, ".", a.minor)
    a == VersionWeight(a.major, a.minor) && @goto done
    print(io, ".", a.patch)
    @label done
    print(io, ")")
end
z   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Pkg/src/Resolve/fieldvalues.jl�
      # This file is a part of Julia. License is MIT: https://julialang.org/license

# FieldValue is a hierarchical numeric type with 5 levels.
# When summing two FieldValues, the levels are summed independently.
# When comparing them, lower levels take precedence.
# The levels are used as such:
#  l0 : for hard constraints (dependencies and requirements)
#  l1 : for favoring higher versions of the explicitly required
#       packages
#  l2 : for favoring higher versions of all other packages
#  l3 : for favoring uninstallation of non-needed packages
#
struct FieldValue
    l0::Int64
    l1::VersionWeight
    l2::VersionWeight
    l3::Int64
    FieldValue(l0::Integer = 0,
               l1::VersionWeight = zero(VersionWeight),
               l2::VersionWeight = zero(VersionWeight),
               l3::Integer = 0) = new(l0, l1, l2, l3)
end

# This isn't nice, but it's for debugging only anyway
function Base.show(io::IO, a::FieldValue)
    print(io, a.l0)
    a == FieldValue(a.l0) && return
    print(io, ".", a.l1)
    a == FieldValue(a.l0, a.l1) && return
    print(io, ".", a.l2)
    a == FieldValue(a.l0, a.l1, a.l2) && return
    print(io, ".", a.l3)
    return
end

const Field = Vector{FieldValue}

Base.zero(::Type{FieldValue}) = FieldValue()

Base.typemin(::Type{FieldValue}) = (x=typemin(Int64); y=typemin(VersionWeight); FieldValue(x, y, y, x))

Base.:-(a::FieldValue, b::FieldValue) = FieldValue(a.l0-b.l0, a.l1-b.l1, a.l2-b.l2, a.l3-b.l3)
Base.:+(a::FieldValue, b::FieldValue) = FieldValue(a.l0+b.l0, a.l1+b.l1, a.l2+b.l2, a.l3+b.l3)

function Base.isless(a::FieldValue, b::FieldValue)
    a.l0 < b.l0 && return true
    a.l0 > b.l0 && return false
    return (a.l1, a.l2, a.l3) < (b.l1, b.l2, b.l3)
end

Base.abs(a::FieldValue) = FieldValue(abs(a.l0), abs(a.l1), abs(a.l2), abs(a.l3))

# if the maximum field has l0 < 0, it means that
# some hard constraint is being violated
validmax(a::FieldValue) = a.l0 >= 0

# like usual argmax, but favors the highest indices
# in case of a tie
function Base.argmax(f::Field)
    m = typemin(FieldValue)
    mi = 0
    for j = length(f):-1:1
        if f[j] > m
            m = f[j]
            mi = j
        end
    end
    @assert mi != 0
    return mi
end

# secondmax returns the (normalized) value of the second maximum in a
# field. It's used to determine the most polarized field.
function secondmax(f::Field, msk::BitVector = trues(length(f)))
    m = typemin(FieldValue)
    m2 = typemin(FieldValue)
    for i = 1:length(f)
        msk[i] || continue
        a = f[i]
        if a > m
            m2 = m
            m = a
        elseif a > m2
            m2 = a
        end
    end
    return m2 - m
end

# Support broadcasting like a scalar by default
Base.Broadcast.broadcastable(a::FieldValue) = Ref(a)
x   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Pkg/src/Resolve/graphtype.jl��      # This file is a part of Julia. License is MIT: https://julialang.org/license

# The ResolveLog is used to keep track of events that take place during the
# resolution process. We use one ResolveLogEntry per package, and record all events
# associated with that package. An event consists of two items: another
# entry representing another package's influence (or `nothing`) and
# a message for the log.
#
# Specialized functions called `log_event_[...]!` are used to store the
# various events. The events are also recorded in order in a shared
# ResolveJournal, which is used to provide a plain chronological view.
#
# The `showlog` functions are used for display, and called to create messages
# in case of resolution errors.

const UUID0 = UUID(UInt128(0))

const ResolveJournal = Vector{Tuple{UUID,String}}

mutable struct ResolveLogEntry
    journal::ResolveJournal # shared with all other entries
    pkg::UUID
    header::String
    events::Vector{Tuple{Any,String}} # here Any should ideally be Union{ResolveLogEntry,Nothing}
    ResolveLogEntry(journal::ResolveJournal, pkg::UUID, header::String = "") = new(journal, pkg, header, [])
end

function Base.push!(entry::ResolveLogEntry, reason::Tuple{Union{ResolveLogEntry,Nothing},String}, to_journal::Bool = true)
    push!(entry.events, reason)
    to_journal && entry.pkg ≠ uuid_julia && push!(entry.journal, (entry.pkg, reason[2]))
    return entry
end

mutable struct ResolveLog
    # init: used to keep track of all package entries which were created during
    #       initialization, since the `pool` can be pruned during the resolution
    #       process.
    init::ResolveLogEntry

    # globals: records global events not associated to any particular package
    globals::ResolveLogEntry

    # pool: records entries associated to each package
    pool::Dict{UUID,ResolveLogEntry}

    # journal: record all messages in order (shared between all entries)
    journal::ResolveJournal

    # exact: keeps track of whether the resolve process is still exact, or
    #        heuristics have been employed
    exact::Bool

    # verbose: print global events messages on screen
    verbose::Bool

    # UUID to names
    uuid_to_name::Dict{UUID,String}

    function ResolveLog(uuid_to_name::Dict{UUID,String}, verbose::Bool = false)
        journal = ResolveJournal()
        init = ResolveLogEntry(journal, UUID0, "")
        globals = ResolveLogEntry(journal, UUID0, "Global events:")
        return new(init, globals, Dict{UUID,ResolveLogEntry}(), journal, true, verbose, uuid_to_name)
    end
end

# Installation state: either a version, or uninstalled
const InstState = Union{VersionNumber,Nothing}


# GraphData is basically a part of Graph that collects data structures useful
# for interfacing the internal abstract representation of Graph with the
# input/output (e.g. converts between package UUIDs and node numbers, etc.)
mutable struct GraphData
    # packages list
    pkgs::Vector{UUID}

    # number of packages
    np::Int

    # states per package: one per version + uninstalled
    spp::Vector{Int}

    # package dict: associates an index to each package id
    pdict::Dict{UUID,Int}

    # package versions: for each package, keep the list of the
    #                   possible version numbers; this defines a
    #                   mapping from version numbers of a package
    #                   to indices
    pvers::Vector{Vector{VersionNumber}}

    # versions dict: associates a version index to each package
    #                version; such that
    #                  pvers[p0][vdict[p0][vn]] = vn
    vdict::Vector{Dict{VersionNumber,Int}}

    # UUID to names
    uuid_to_name::Dict{UUID,String}

    # pruned packages: during graph simplification, packages that
    #                  only have one allowed version are pruned.
    #                  This keeps track of them, so that they may
    #                  be returned in the solution (unless they
    #                  were explicitly fixed)
    pruned::Dict{UUID,VersionNumber}

    # equivalence classes: for each package and each of its possible
    #                      states, keep track of other equivalent states
    eq_classes::Dict{UUID,Dict{InstState,Set{InstState}}}

    # resolve log: keep track of the resolution process
    rlog::ResolveLog

    function GraphData(
            compat::Dict{UUID,Dict{VersionNumber,Dict{UUID,VersionSpec}}},
            uuid_to_name::Dict{UUID,String},
            verbose::Bool = false
        )
        # generate pkgs
        pkgs = sort!(collect(keys(compat)))
        np = length(pkgs)

        # generate pdict
        pdict = Dict{UUID,Int}(pkgs[p0] => p0 for p0 = 1:np)

        # generate spp and pvers
        pvers = [sort!(collect(keys(compat[pkgs[p0]]))) for p0 = 1:np]
        spp = length.(pvers) .+ 1

        # generate vdict
        vdict = [Dict{VersionNumber,Int}(vn => i for (i,vn) in enumerate(pvers[p0])) for p0 = 1:np]

        # nothing is pruned yet, of course
        pruned = Dict{UUID,VersionNumber}()

        # equivalence classes (at the beginning each state represents just itself)
        eq_vn(v0, p0) = (v0 == spp[p0] ? nothing : pvers[p0][v0])

        # Hot code, measure performance before changing
        eq_classes = Dict{UUID,Dict{InstState,Set{InstState}}}()
        for p0 = 1:np
            d = Dict{InstState, Set{InstState}}()
            for v0 = 1:spp[p0]
                let p0 = p0 # Due to https://github.com/JuliaLang/julia/issues/15276
                    d[eq_vn(v0,p0)] = Set([eq_vn(v0,p0)])
                end
            end
            eq_classes[pkgs[p0]] = d
        end

        # the resolution log is actually initialized below
        rlog = ResolveLog(uuid_to_name, verbose)

        data = new(pkgs, np, spp, pdict, pvers, vdict, uuid_to_name, pruned, eq_classes, rlog)

        init_log!(data)

        return data
    end

    function Base.copy(data::GraphData)
        pkgs = copy(data.pkgs)
        np = data.np
        spp = copy(data.spp)
        pdict = copy(data.pdict)
        pvers = [copy(data.pvers[p0]) for p0 = 1:np]
        vdict = [copy(data.vdict[p0]) for p0 = 1:np]
        pruned = copy(data.pruned)
        eq_classes = Dict(p => copy(eq) for (p,eq) in data.eq_classes)
        rlog = deepcopy(data.rlog)
        uuid_to_name = rlog.uuid_to_name

        return new(pkgs, np, spp, pdict, pvers, vdict, uuid_to_name, pruned, eq_classes, rlog)
    end
end

mutable struct Graph
    # data:
    #   stores all the structures required to map between
    #   parsed items (names, UUIDS, version numbers...) and
    #   the numeric representation used in the main Graph data
    #   structure.
    data::GraphData

    # adjacency matrix:
    #   for each package, has the list of neighbors
    #   indices
    gadj::Vector{Vector{Int}}

    # compatibility mask:
    #   for each package p0 has a list of bool masks.
    #   Each entry in the list gmsk[p0] is relative to the
    #   package p1 as read from gadj[p0].
    #   Each mask has dimension spp1 × spp0, where
    #   spp0 is the number of states of p0, and
    #   spp1 is the number of states of p1.
    gmsk::Vector{Vector{BitMatrix}}

    # constraints:
    #   a mask of allowed states for each package (e.g. to express
    #   requirements)
    gconstr::Vector{BitVector}

    # adjacency dict:
    #   allows one to retrieve the indices in gadj, so that
    #   gadj[p0][adjdict[p1][p0]] = p1
    #   ("At which index does package p1 appear in gadj[p0]?")
    adjdict::Vector{Dict{Int,Int}}

    # indices of the packages that were *explicitly* required
    #   used to favor their versions at resolution
    req_inds::Set{Int}

    # indices of the packages that were *explicitly* fixed
    #   used to avoid returning them in the solution
    fix_inds::Set{Int}

    ignored::BitVector

    # stack of constraints/ignored packages:
    #   allows to keep a sort of "versioning" of the constraints
    #   such that the solver can implement tentative solutions
    solve_stack::Vector{Tuple{Vector{BitVector},BitVector}}

    # states per package: same as in GraphData
    spp::Vector{Int}

    # number of packages (all Vectors above have this length)
    np::Int

    # some workspace vectors
    newmsg::Vector{FieldValue}
    diff::Vector{FieldValue}
    cavfld::Vector{FieldValue}

    function Graph(
            compat::Dict{UUID,Dict{VersionNumber,Dict{UUID,VersionSpec}}},
            compat_weak::Dict{UUID,Dict{VersionNumber,Set{UUID}}},
            uuid_to_name::Dict{UUID,String},
            reqs::Requires,
            fixed::Dict{UUID,Fixed},
            verbose::Bool = false,
            julia_version::Union{VersionNumber,Nothing} = VERSION
        )

        # Tell the resolver about julia itself
        uuid_to_name[uuid_julia] = "julia"
        if julia_version !== nothing
            fixed[uuid_julia] = Fixed(julia_version)
            compat[uuid_julia] = Dict(julia_version => Dict{VersionNumber,Dict{UUID,VersionSpec}}())
        else
            compat[uuid_julia] = Dict{VersionNumber,Dict{UUID,VersionSpec}}()
        end

        data = GraphData(compat, uuid_to_name, verbose)
        pkgs, np, spp, pdict, pvers, vdict, rlog = data.pkgs, data.np, data.spp, data.pdict, data.pvers, data.vdict, data.rlog
        extended_deps = let spp = spp # Due to https://github.com/JuliaLang/julia/issues/15276
            [Vector{Dict{Int,BitVector}}(undef, spp[p0]-1) for p0 = 1:np]
        end
        for p0 = 1:np, v0 = 1:(spp[p0]-1)
            vn = pvers[p0][v0]
            req = Dict{Int,VersionSpec}()
            uuid0 = pkgs[p0]
            vnmap = get(Dict{String,VersionSpec}, compat[uuid0], vn)
            for (uuid1, vs) in vnmap
                p1 = pdict[uuid1]
                p1 == p0 && error("Package $(pkgID(pkgs[p0], uuid_to_name)) version $vn has a dependency with itself")
                # check conflicts instead of intersecting?
                # (intersecting is used by fixed packages though...)
                req_p1 = get!(VersionSpec, req, p1)
                req[p1] = req_p1 ∩ vs
            end
            # Translate the requirements into bit masks
            # Hot code, measure performance before changing
            req_msk = Dict{Int,BitVector}()
            maybe_weak = haskey(compat_weak, uuid0) && haskey(compat_weak[uuid0], vn)
            for (p1, vs) in req
                pv = pvers[p1]
                req_msk_p1 = BitVector(undef, spp[p1])
                @inbounds for i in 1:spp[p1] - 1
                    req_msk_p1[i] = pv[i] ∈ vs
                end
                weak = maybe_weak && (pkgs[p1] ∈ compat_weak[uuid0][vn])
                req_msk_p1[end] = weak
                req_msk[p1] = req_msk_p1
            end
            extended_deps[p0][v0] = req_msk
        end

        gadj = [Int[] for p0 = 1:np]
        gmsk = [BitMatrix[] for p0 = 1:np]
        gconstr = let spp = spp # Due to https://github.com/JuliaLang/julia/issues/15276
            [trues(spp[p0]) for p0 = 1:np]
        end
        adjdict = [Dict{Int,Int}() for p0 = 1:np]

        for p0 = 1:np, v0 = 1:(spp[p0]-1), (p1,rmsk1) in extended_deps[p0][v0]
            @assert p0 ≠ p1
            j0 = get(adjdict[p1], p0, length(gadj[p0]) + 1)
            j1 = get(adjdict[p0], p1, length(gadj[p1]) + 1)

            @assert (j0 > length(gadj[p0]) && j1 > length(gadj[p1])) ||
                    (j0 ≤ length(gadj[p0]) && j1 ≤ length(gadj[p1]))

            if j0 > length(gadj[p0])
                push!(gadj[p0], p1)
                push!(gadj[p1], p0)
                j0 = length(gadj[p0])
                j1 = length(gadj[p1])

                adjdict[p1][p0] = j0
                adjdict[p0][p1] = j1

                bm = trues(spp[p1], spp[p0])
                bmt = trues(spp[p0], spp[p1])

                push!(gmsk[p0], bm)
                push!(gmsk[p1], bmt)
            else
                bm = gmsk[p0][j0]
                bmt = gmsk[p1][j1]
            end

            for v1 = 1:spp[p1]
                rmsk1[v1] && continue
                bm[v1, v0] = false
                bmt[v0, v1] = false
            end
        end

        req_inds = Set{Int}()
        fix_inds = Set{Int}()

        ignored = falses(np)
        solve_stack = Tuple{Vector{BitVector},BitVector}[]

        graph = new(data, gadj, gmsk, gconstr, adjdict, req_inds, fix_inds, ignored, solve_stack, spp, np,
                    FieldValue[], FieldValue[], FieldValue[])

        _add_fixed!(graph, fixed)
        _add_reqs!(graph, reqs, :explicit_requirement)

        @assert check_consistency(graph)
        check_constraints(graph)

        return graph
    end

    function Base.copy(graph::Graph)
        data = copy(graph.data)
        np = graph.np
        spp = data.spp
        gadj = [copy(graph.gadj[p0]) for p0 = 1:np]
        gmsk = [[copy(graph.gmsk[p0][j0]) for j0 = 1:length(gadj[p0])] for p0 = 1:np]
        gconstr = [copy(graph.gconstr[p0]) for p0 = 1:np]
        adjdict = [copy(graph.adjdict[p0]) for p0 = 1:np]
        req_inds = copy(graph.req_inds)
        fix_inds = copy(graph.fix_inds)
        ignored = copy(graph.ignored)
        solve_stack = [([copy(gc0) for gc0 in sav_gconstr],copy(sav_ignored)) for (sav_gconstr,sav_ignored) in graph.solve_stack]

        return new(data, gadj, gmsk, gconstr, adjdict, req_inds, fix_inds, ignored, solve_stack, spp, np)
    end
end


"""
Add explicit requirements to the graph.
"""
function add_reqs!(graph::Graph, reqs::Requires)
    _add_reqs!(graph, reqs, :explicit_requirement)
    check_constraints(graph)
    # TODO: add reqs to graph data?
    return graph
end

function _add_reqs!(graph::Graph, reqs::Requires, reason; weak_reqs::Set{UUID} = Set{UUID}())
    gconstr = graph.gconstr
    spp = graph.spp
    req_inds = graph.req_inds
    pdict = graph.data.pdict
    pvers = graph.data.pvers

    for (rp,rvs) in reqs
        haskey(pdict, rp) || error("unknown required package $(pkgID(rp, graph))")
        rp0 = pdict[rp]
        new_constr = trues(spp[rp0])
        for rv0 = 1:(spp[rp0]-1)
            rvn = pvers[rp0][rv0]
            rvn ∈ rvs || (new_constr[rv0] = false)
        end
        weak = rp ∈ weak_reqs
        new_constr[end] = weak
        old_constr = copy(gconstr[rp0])
        gconstr[rp0] .&= new_constr
        reason ≡ :explicit_requirement && push!(req_inds, rp0)
        old_constr ≠ gconstr[rp0] && log_event_req!(graph, rp, rvs, reason)
    end
    return graph
end

"Add fixed packages to the graph, and their requirements."
function add_fixed!(graph::Graph, fixed::Dict{UUID,Fixed})
    _add_fixed!(graph, fixed)
    check_constraints(graph)
    # TODO: add fixed to graph data?
    return graph
end

function _add_fixed!(graph::Graph, fixed::Dict{UUID,Fixed})
    gconstr = graph.gconstr
    spp = graph.spp
    fix_inds = graph.fix_inds
    pdict = graph.data.pdict
    vdict = graph.data.vdict

    for (fp,fx) in fixed
        haskey(pdict, fp) || error("unknown fixed package $(pkgID(fp, graph))")
        fp0 = pdict[fp]
        fv0 = vdict[fp0][fx.version]
        new_constr = falses(spp[fp0])
        new_constr[fv0] = true
        gconstr[fp0] .&= new_constr
        push!(fix_inds, fp0)
        bkitem = log_event_fixed!(graph, fp, fx)
        _add_reqs!(graph, fx.requires, (fp, bkitem); weak_reqs=fx.weak)
    end
    return graph
end

pkgID(p::UUID, rlog::ResolveLog) = pkgID(p, rlog.uuid_to_name)
pkgID(p::UUID, data::GraphData) = pkgID(p, data.uuid_to_name)
pkgID(p0::Int, data::GraphData) = pkgID(data.pkgs[p0], data)
pkgID(p, graph::Graph) = pkgID(p, graph.data)

## user-friendly representation of package IDs ##
function pkgID(p::UUID, uuid_to_name::Dict{UUID,String})
    name = get(uuid_to_name, p, "(unknown)")
    uuid_short = string(p)[1:8]
    return "$name [$uuid_short]"
end

function check_consistency(graph::Graph)
    np = graph.np
    spp = graph.spp
    gadj = graph.gadj
    gmsk = graph.gmsk
    gconstr = graph.gconstr
    adjdict = graph.adjdict
    req_inds = graph.req_inds
    fix_inds = graph.fix_inds
    ignored = graph.ignored
    solve_stack = graph.solve_stack
    data = graph.data
    pkgs = data.pkgs
    pdict = data.pdict
    pvers = data.pvers
    vdict = data.vdict
    pruned = data.pruned
    eq_classes = data.eq_classes
    rlog = data.rlog
    # TODO: check ignored and solve_stack

    @assert np ≥ 0
    for x in Any[spp, gadj, gmsk, gconstr, adjdict, ignored, rlog.pool, pkgs, pdict, pvers, vdict]
        @assert length(x)::Int == np
    end
    for p0 = 1:np
        @assert pdict[pkgs[p0]] == p0
        spp0 = spp[p0]
        @assert spp0 ≥ 1
        pvers0 = pvers[p0]
        vdict0 = vdict[p0]
        @assert length(pvers0) == spp0 - 1
        for v0 = 1:(spp0-1)
            @assert vdict0[pvers0[v0]] == v0
        end
        for (vn,v0) in vdict0
            @assert 1 ≤ v0 ≤ spp0-1
            @assert pvers0[v0] == vn
        end
        gconstr0 = gconstr[p0]
        @assert length(gconstr0) == spp0

        gadj0 = gadj[p0]
        gmsk0 = gmsk[p0]
        adjdict0 = adjdict[p0]
        @assert length(gmsk0) == length(gadj0)
        @assert length(adjdict0) == length(gadj0)
        for (j0,p1) in enumerate(gadj0)
            @assert p1 ≠ p0
            @assert adjdict[p1][p0] == j0
            spp1 = spp[p1]
            @assert size(gmsk0[j0]) == (spp1,spp0)
            j1 = adjdict0[p1]
            gmsk1 = gmsk[p1]
            # This assert is a bit too expensive
            # @assert gmsk1[j1] == permutedims(gmsk0[j0])
        end
    end
    for (p,p0) in pdict
        @assert 1 ≤ p0 ≤ np
        @assert pkgs[p0] == p
        @assert !haskey(pruned, p)
    end
    for p0 in req_inds
        @assert 1 ≤ p0 ≤ np
        @assert !gconstr[p0][end]
    end
    for p0 in fix_inds
        @assert 1 ≤ p0 ≤ np
        @assert !gconstr[p0][end]
        @assert count(gconstr[p0]) ≤ 1 # note: the 0 case should be handled by check_constraints
    end

    for (p,eq_cl) in eq_classes, (rvn,rvs) in eq_cl
        @assert rvn ∈ rvs
    end

    for (sav_gconstr,sav_ignored) in solve_stack
        @assert length(sav_ignored) == np
        @assert length(sav_gconstr) == np
        for p0 = 1:np
            @assert length(sav_gconstr[p0]) == spp[p0]
        end
    end

    return true
end

function push_snapshot!(graph::Graph)
    np = graph.np
    gconstr = graph.gconstr
    ignored = graph.ignored
    solve_stack = graph.solve_stack
    sav_gconstr = [copy(gc0) for gc0 in gconstr]
    sav_ignored = copy(ignored)
    push!(solve_stack, (gconstr, ignored))
    graph.gconstr = sav_gconstr
    graph.ignored = sav_ignored
    return graph
end

function pop_snapshot!(graph::Graph)
    np = graph.np
    solve_stack = graph.solve_stack
    @assert length(solve_stack) > 0
    sav_gconstr, sav_ignored = pop!(graph.solve_stack)
    graph.gconstr = sav_gconstr
    graph.ignored = sav_ignored
    return graph
end

function wipe_snapshots!(graph::Graph)
    np = graph.np
    solve_stack = graph.solve_stack
    if length(solve_stack) > 0
        graph.gconstr, graph.ignored = first(solve_stack)
        empty!(solve_stack)
    end
    return graph
end

# system colors excluding whites/greys/blacks and error-red
const CONFLICT_COLORS = [1:6; 10:14];
pkgID_color(pkgID) = CONFLICT_COLORS[mod1(hash(pkgID), end)]

logstr(pkgID) = logstr(pkgID, pkgID)
function logstr(pkgID, args...)
    # workout the string with the color codes, check stderr to decide if color is enabled
    return sprint(args; context=stderr::IO) do io, iargs
        printstyled(io, iargs...; color=pkgID_color(pkgID))
    end
end

"""
    range_compressed_versionspec(pool, subset=pool)

 - `pool`: all versions that exist (a superset of `subset`)
 - `subset`: the subset of those versions that we want to include in the spec.

Finds a minimal collection of ranges as a `VersionSpec`, that permits everything in the
`subset`, but does not permit anything else from the `pool`.
"""
function range_compressed_versionspec(pool, subset=pool)
    length(subset) == 1 && return VersionSpec(only(subset))
    # PREM-OPT: we keep re-sorting these, probably not required.
    sort!(pool)
    sort!(subset)
    @assert subset ⊆ pool

    contiguous_subsets = VersionRange[]

    range_start = first(subset)
    pool_ii = findfirst(isequal(range_start), pool) + 1  # skip-forward til we have started
    for s in @view subset[2:end]
        if s != pool[pool_ii]
            range_end = pool[pool_ii-1]  # previous element was last in this range
            push!(contiguous_subsets, VersionRange(range_start, range_end))
            range_start = s  # start a new range
            while (s != pool[pool_ii])  # advance til time to start
                pool_ii += 1
            end
        end
        pool_ii += 1
    end
    push!(contiguous_subsets, VersionRange(range_start, last(subset)))

    return VersionSpec(contiguous_subsets)
end

function init_log!(data::GraphData)
    np = data.np
    pkgs = data.pkgs
    pvers = data.pvers
    rlog = data.rlog
    for p0 = 1:np
        p = pkgs[p0]
        id = pkgID(p0, data)
        versions = pvers[p0]
        if isempty(versions)
            msg = "$(logstr(id)) has no known versions!" # This shouldn't happen?
        else
            vspec = range_compressed_versionspec(versions)
            vers = logstr(id, vspec)
            uuid = data.pkgs[p0]
            name = data.uuid_to_name[uuid]
            pkgid = Base.PkgId(uuid, name)
            msg = "possible versions are: $vers or uninstalled"
            if Base.in_sysimage(pkgid)
                msg *= " (package in sysimage!)"
            end
        end
        first_entry = get!(rlog.pool, p) do
            ResolveLogEntry(rlog.journal, p, "$(logstr(id)) log:")
        end

        if p ≠ uuid_julia
            push!(first_entry, (nothing, msg))
            push!(rlog.init, (first_entry, ""), false)
        end
    end
    return data
end

function log_event_fixed!(graph::Graph, fp::UUID, fx::Fixed)
    rlog = graph.data.rlog
    id = pkgID(fp, rlog)
    msg = "$(logstr(id)) is fixed to version $(logstr(id, fx.version))"
    entry = rlog.pool[fp]
    push!(entry, (nothing, msg))
    return entry
end

function _vs_string(p0::Int, vmask::BitVector, id::String, pvers::Vector{Vector{VersionNumber}})
    if any(vmask[1:(end-1)])
        vspec = range_compressed_versionspec(pvers[p0], pvers[p0][vmask[1:(end-1)]])
        vns = logstr(id, vspec)
        vmask[end] && (vns *= " or uninstalled")
    else
        @assert vmask[end]
        vns = "uninstalled"
    end
    return vns
end

function log_event_req!(graph::Graph, rp::UUID, rvs::VersionSpec, reason)
    rlog = graph.data.rlog
    gconstr = graph.gconstr
    pdict = graph.data.pdict
    pvers = graph.data.pvers
    id = pkgID(rp, rlog)
    msg = "restricted to versions $(logstr(id, rvs)) by "
    if reason isa Symbol
        @assert reason === :explicit_requirement
        other_entry = nothing
        msg *= "an explicit requirement"
    else
        other_p, other_entry = reason::Tuple{UUID,ResolveLogEntry}
        if other_p == uuid_julia
            msg *= "julia compatibility requirements"
            other_entry = nothing # don't propagate the log
        else
            msg *= logstr(pkgID(other_p, rlog))
        end
    end
    rp0 = pdict[rp]
    @assert !gconstr[rp0][end] || reason ≢ :explicit_requirement
    if any(gconstr[rp0])
        msg *= ", leaving only versions: $(_vs_string(rp0, gconstr[rp0], id, pvers))"
    else
        msg *= " — no versions left"
    end
    entry = rlog.pool[rp]
    push!(entry, (other_entry, msg))
    return entry
end

function log_event_global!(graph::Graph, msg::String)
    rlog = graph.data.rlog
    rlog.verbose && @info(msg)
    push!(rlog.globals, (nothing, msg))
end

function log_event_implicit_req!(graph::Graph, p1::Int, vmask::BitVector, p0::Int)
    rlog = graph.data.rlog
    gconstr = graph.gconstr
    pkgs = graph.data.pkgs
    pvers = graph.data.pvers

    p = pkgs[p1]
    id = pkgID(p, rlog)

    other_p, other_entry = pkgs[p0], rlog.pool[pkgs[p0]]
    other_id = pkgID(other_p, rlog)
    if any(vmask)
        if all(vmask[1:(end-1)])    # Check if all versions are allowed (except uninstalled)
            msg = ""
            other_entry = nothing   # Don't propagate the log if all versions allowed
        else
            msg = "restricted by "
            if other_p == uuid_julia
                msg *= "julia compatibility requirements "
                other_entry = nothing # don't propagate the log
            else
                msg *= "compatibility requirements with $(logstr(other_id)) "
            end
            msg *= "to versions: $(_vs_string(p1, vmask, id, pvers))"
            if vmask ≠ gconstr[p1]
                if any(gconstr[p1])
                    msg *= ", leaving only versions: $(_vs_string(p1, gconstr[p1], id, pvers))"
                else
                    msg *= " — no versions left"
                end
            end
        end
    else
        msg = "found to have no compatible versions left with "
        if other_p == uuid_julia
            msg *= "julia"
            other_entry = nothing # don't propagate the log
        else
            msg *= logstr(other_id)
        end
    end
    entry = rlog.pool[p]
    push!(entry, (other_entry, msg))
    return entry
end

function log_event_pruned!(graph::Graph, p0::Int, s0::Int)
    rlog = graph.data.rlog
    spp = graph.spp
    pkgs = graph.data.pkgs
    pvers = graph.data.pvers

    p = pkgs[p0]
    id = pkgID(p, rlog)
    if s0 == spp[p0]
        msg = "determined to be unneeded during graph pruning"
    else
        ver = logstr(id, pvers[p0][s0])
        msg = "fixed during graph pruning to its only remaining available version, $ver"
    end
    entry = rlog.pool[p]
    push!(entry, (nothing, msg))
    return entry
end

function log_event_greedysolved!(graph::Graph, p0::Int, s0::Int)
    rlog = graph.data.rlog
    spp = graph.spp
    pkgs = graph.data.pkgs
    pvers = graph.data.pvers

    p = pkgs[p0]
    id = pkgID(p, rlog)
    if s0 == spp[p0]
        msg = "determined to be unneeded by the solver"
    else
        ver = logstr(id, pvers[p0][s0])
        if s0 == spp[p0] - 1
            msg = "set by the solver to its maximum version: $ver"
        else
            msg = "set by the solver to the maximum version compatible with the constraints: $ver"
        end
    end
    entry = rlog.pool[p]
    push!(entry, (nothing, msg))
    return entry
end

function log_event_maxsumsolved!(graph::Graph, p0::Int, s0::Int, why::Symbol)
    rlog = graph.data.rlog
    spp = graph.spp
    pkgs = graph.data.pkgs
    pvers = graph.data.pvers

    p = pkgs[p0]
    id = pkgID(p, rlog)
    if s0 == spp[p0]
        @assert why === :uninst
        msg = "determined to be unneeded by the solver"
    else
        @assert why === :constr
        ver = logstr(id, pvers[p0][s0])
        if s0 == spp[p0] - 1
            msg = "set by the solver to its maximum version: $ver"
        else
            xver = logstr(id, pvers[p0][s0+1])
            msg = "set by the solver to version: $ver (version $xver would violate its constraints)"
        end
    end
    entry = rlog.pool[p]
    push!(entry, (nothing, msg))
    return entry
end

function log_event_maxsumsolved!(graph::Graph, p0::Int, s0::Int, p1::Int)
    rlog = graph.data.rlog
    spp = graph.spp
    pkgs = graph.data.pkgs
    pvers = graph.data.pvers

    p = pkgs[p0]
    id = pkgID(p, rlog)
    other_id = pkgID(pkgs[p1], rlog)
    @assert s0 ≠ spp[p0]
    ver = logstr(id, pvers[p0][s0])
    if s0 == spp[p0] - 1
        msg = "set by the solver to its maximum version: $ver (installation is required by $other_id)"
    else
        xver = logstr(id, pvers[p0][s0+1])
        msg = "set by the solver version: $ver (version $xver would violate a dependency relation with $other_id)"
    end
    other_entry = rlog.pool[pkgs[p1]]
    entry = rlog.pool[p]
    push!(entry, (other_entry, msg))
    return entry
end

function log_event_eq_classes!(graph::Graph, p0::Int)
    rlog = graph.data.rlog
    spp = graph.spp
    gconstr = graph.gconstr
    pkgs = graph.data.pkgs
    pvers = graph.data.pvers

    p = pkgs[p0]
    id = pkgID(p, rlog)
    msg = "versions reduced by equivalence to: "

    if any(gconstr[p0][1:(end-1)])
        vspec = range_compressed_versionspec(pvers[p0], pvers[p0][gconstr[p0][1:(end-1)]])
        msg *= logstr(id, vspec)
        gconstr[p0][end] && (msg *= " or uninstalled")
    elseif gconstr[p0][end]
        msg *= "uninstalled"
    else
        msg *= "no version"
    end

    entry = rlog.pool[p]
    push!(entry, (nothing, msg))
    return entry
end

function log_event_maxsumtrace!(graph::Graph, p0::Int, s0::Int)
    rlog = graph.data.rlog
    rlog.exact = false
    p = graph.data.pkgs[p0]
    id = pkgID(p, rlog)
    if s0 < graph.spp[p0]
        ver = logstr(id, graph.data.pvers[p0][s0])
        msg = "fixed by the MaxSum heuristic to version $ver"
    else
        msg = "determined to be unneeded by the MaxSum heuristic"
    end
    entry = rlog.pool[p]
    push!(entry, (nothing, msg))
    return entry
end

"Get the resolution log, detached"
get_resolve_log(graph::Graph) = deepcopy(graph.data.rlog)

const _logindent = " "

showlog(graph::Graph, args...; kw...) = showlog(stdout_f(), graph, args...; kw...)
showlog(io::IO, graph::Graph, args...; kw...) = showlog(io, graph.data.rlog, args...; kw...)
showlog(rlog::ResolveLog, args...; kw...) = showlog(stdout_f(), rlog, args...; kw...)

"""
Show the full resolution log. The `view` keyword controls how the events are displayed/grouped:

 * `:plain` for a shallow view, grouped by package, alphabetically (the default)
 * `:tree` for a tree view in which the log of a package is displayed as soon as it appears
           in the process (the top-level is still grouped by package, alphabetically)
 * `:chronological` for a flat view of all events in chronological order
"""
function showlog(io::IO, rlog::ResolveLog; view::Symbol = :plain)
    view ∈ [:plain, :tree, :chronological] || throw(ArgumentError("the view argument should be `:plain`, `:tree` or `:chronological`"))
    println(io, "Resolve log:")
    view === :chronological && return showlogjournal(io, rlog)
    seen = IdDict()
    recursive = (view === :tree)
    _show(io, rlog, rlog.globals, _logindent, seen, false)
    initentries = Union{ResolveLogEntry,Nothing}[event[1]::Union{ResolveLogEntry,Nothing} for event in rlog.init.events]
    for entry in sort!(initentries, by=(entry->pkgID(entry.pkg, rlog)))
        seen[entry] = true
        _show(io, rlog, entry, _logindent, seen, recursive)
    end
end

function showlogjournal(io::IO, rlog::ResolveLog)
    journal = rlog.journal
    id(p) = p == UUID0 ? "[global event]" : logstr(pkgID(p, rlog))
    padding = maximum(length(id(p)) for (p,_) in journal; init=0)
    for (p,msg) in journal
        println(io, ' ', rpad(id(p), padding), ": ", msg)
    end
end

"""
Show the resolution log for some package, and all the other packages that affected
it during resolution. The `view` option can be either `:plain` or `:tree` (works
the same as for `showlog(io, rlog)`); the default is `:tree`.
"""
function showlog(io::IO, rlog::ResolveLog, p::UUID; view::Symbol = :tree)
    view ∈ [:plain, :tree] || throw(ArgumentError("the view argument should be `:plain` or `:tree`"))
    entry = rlog.pool[p]
    if view === :tree
        _show(io, rlog, entry, _logindent, IdDict{Any,Any}(entry=>true), true)
    else
        entries = ResolveLogEntry[entry]
        function getentries(entry)
            for (other_entry,_) in entry.events
                (other_entry ≡ nothing || other_entry ∈ entries) && continue
                push!(entries, other_entry)
                getentries(other_entry)
            end
        end
        getentries(entry)
        for entry in entries
            _show(io, rlog, entry, _logindent, IdDict(), false)
        end
    end
end

# Show a recursive tree with requirements applied to a package, either directly or indirectly
function _show(io::IO, rlog::ResolveLog, entry::ResolveLogEntry, indent::String, seen::IdDict, recursive::Bool)
    toplevel = (indent == _logindent)
    firstglyph = toplevel ? "" : "└─"
    pre = toplevel ? "" : "  "
    println(io, indent, firstglyph, entry.header)
    l = length(entry.events)
    for (i,(otheritem,msg)) in enumerate(entry.events)
        if !isempty(msg)
            print(io, indent * pre, (i==l ? '└' : '├'), '─')
            println(io, msg)
            newindent = indent * pre * (i==l ? "  " : "│ ")
        else
            newindent = indent
        end
        otheritem ≡ nothing && continue
        recursive || continue
        if otheritem ∈ keys(seen)
            println(io, newindent, "└─", otheritem.header, " see above")
            continue
        end
        seen[otheritem] = true
        _show(io, rlog, otheritem, newindent, seen, recursive)
    end
end

is_julia(graph::Graph, p0::Int) = graph.data.pkgs[p0] == uuid_julia

"Check for contradictions in the constraints."
function check_constraints(graph::Graph)
    np = graph.np
    gconstr = graph.gconstr
    pkgs = graph.data.pkgs
    pvers = graph.data.pvers
    rlog = graph.data.rlog
    exact = graph.data.rlog.exact

    id(p0::Int) = pkgID(p0, graph)

    for p0 = 1:np
        any(gconstr[p0]) && continue
        if exact
            err_msg = "Unsatisfiable requirements detected for package $(logstr(id(p0))):\n"
        else
            err_msg = "Resolve failed to satisfy requirements for package $(logstr(id(p0))):\n"
        end
        err_msg *= sprint(showlog, rlog, pkgs[p0])
        throw(ResolverError(chomp(err_msg)))
    end
    return true
end

"""
Propagates current constraints, determining new implicit constraints.
Throws an error in case impossible requirements are detected, printing
a log trace.
"""
function propagate_constraints!(graph::Graph, sources::Set{Int} = Set{Int}(); log_events::Bool = true)
    np = graph.np
    spp = graph.spp
    gadj = graph.gadj
    gmsk = graph.gmsk
    gconstr = graph.gconstr
    adjdict = graph.adjdict
    ignored = graph.ignored
    pkgs = graph.data.pkgs
    pvers = graph.data.pvers
    rlog = graph.data.rlog
    exact = rlog.exact

    id(p0::Int) = pkgID(pkgs[p0], graph)

    log_events && log_event_global!(graph, "propagating constraints")

    # unless otherwise specified, start from packages which
    # are not allowed to be uninstalled
    staged = isempty(sources) ?
        Set{Int}(p0 for p0 = 1:np if !gconstr[p0][end]) :
        sources

    seen = copy(staged)

    while !isempty(staged)
        staged_next = Set{Int}()
        for p0 in staged
            gconstr0 = gconstr[p0]
            for (j1,p1) in enumerate(gadj[p0])
                # if p1 is ignored, the relation between it and all its neighbors
                # has already been propagated
                ignored[p1] && continue

                # we don't propagate to julia (purely to have better error messages)
                pkgs[p1] == uuid_julia && continue

                msk = gmsk[p0][j1]
                # consider the sub-mask with only allowed versions of p0
                sub_msk = msk[:,gconstr0]
                # if an entire row of the sub-mask is false, that version of p1
                # is effectively forbidden
                # (this is just like calling `any` row-wise)
                added_constr1 = any!(BitVector(undef, spp[p1]), sub_msk)
                # apply the new constraints, checking for contradictions
                # (keep the old ones for comparison)
                gconstr1 = gconstr[p1]
                old_gconstr1 = copy(gconstr1)
                gconstr1 .&= added_constr1
                # if the new constraints are more restrictive than the
                # previous ones, record it and propagate them next
                if gconstr1 ≠ old_gconstr1
                    push!(staged_next, p1)
                    log_events && log_event_implicit_req!(graph, p1, added_constr1, p0)
                elseif p1 ∉ seen
                    push!(staged_next, p1)
                end
                if !any(gconstr1)
                    if exact
                        err_msg = "Unsatisfiable requirements detected for package $(logstr(id(p1))):\n"
                    else
                        err_msg = "Resolve failed to satisfy requirements for package $(logstr(id(p1))):\n"
                    end
                    err_msg *= sprint(showlog, rlog, pkgs[p1])
                    throw(ResolverError(chomp(err_msg)))
                end
            end
        end
        union!(seen, staged_next)
        staged = staged_next
    end
    return graph
end

"""
Enforce the uninstalled state on all packages that are not reachable from the required ones
or from the packages in the `sources` argument.
"""
function disable_unreachable!(graph::Graph, sources::Set{Int} = Set{Int}())
    np = graph.np
    spp = graph.spp
    gadj = graph.gadj
    gmsk = graph.gmsk
    gconstr = graph.gconstr
    adjdict = graph.adjdict
    pkgs = graph.data.pkgs

    log_event_global!(graph, "disabling unreachable nodes")

    # 2nd argument are packages which are not allowed to be uninstalled
    staged = union(sources, Set{Int}(p0 for p0 = 1:np if !gconstr[p0][end]))
    seen = copy(staged)

    while !isempty(staged)
        staged_next = Set{Int}()
        for p0 in staged
            gconstr0idx = findall(gconstr[p0][1:(end-1)])
            for (j1,p1) in enumerate(gadj[p0])
                all(gmsk[p0][j1][end,gconstr0idx]) && continue # the package is not required by any of the allowed versions of p0
                p1 ∈ seen || push!(staged_next, p1)
            end
        end
        union!(seen, staged_next)
        staged = staged_next
    end

    # Force uninstalled state for all unseen packages
    for p0 = 1:np
        p0 ∈ seen && continue
        gconstr0 = gconstr[p0]
        @assert gconstr0[end]
        fill!(gconstr0, false)
        gconstr0[end] = true
    end

    return graph
end

function deep_clean!(graph::Graph)
    np = graph.np
    spp = graph.spp

    log_event_global!(graph, "cleaning graph")

    sumspp = sum(count(graph.gconstr[p0]) for p0 = 1:np)

    while true
        gconstr_msk = [trues(spp[p0]) for p0 = 1:np]

        str_len = 0

        for p0 = 1:np, v0 in findall(graph.gconstr[p0])
            print("\r" * " "^str_len * "\r")
            msg = "> $p0 / $np"
            print(msg)
            str_len = length(msg)
            push_snapshot!(graph)
            fill!(graph.gconstr[p0], false)
            graph.gconstr[p0][v0] = true
            try
                propagate_constraints!(graph, Set{Int}([p0]), log_events = false)
            catch err
                err isa ResolverError || rethrow()
                gconstr_msk[p0][v0] = false
            end
            pop_snapshot!(graph)
        end

        println()

        affected = Int[]
        for p0 = 1:np
            gconstr0 = graph.gconstr[p0]
            old_gconstr0 = copy(gconstr0)
            gconstr0 .&= gconstr_msk[p0]
            if old_gconstr0 ≠ gconstr0
                push!(affected, p0)
                #TODO : log event
            end
            if !any(gconstr0)
                # TODO : what should we do here??
                # throw(ResolverError("aaaaaaaaaaaaaahhhhhhhh")) # XXX
            end
        end
        println("> affected = $(length(affected))")
        isempty(affected) && break
    end

    sumspp_new = sum(count(graph.gconstr[p0]) for p0 = 1:np)

    log_event_global!(graph, "cleaned graph, stats (total n. of states): before = $(sumspp) after = $(sumspp_new) diff = $(sumspp-sumspp_new)")

    return graph
end

"""
Reduce the number of versions in the graph by putting all the versions of
a package that behave identically into equivalence classes, keeping only
the highest version of the class as representative.
"""
function compute_eq_classes!(graph::Graph)
    log_event_global!(graph, "computing version equivalence classes")

    np = graph.np
    sumspp = sum(graph.spp)
    for p0 = 1:np
        build_eq_classes1!(graph, p0)
    end

    log_event_global!(graph, "computed version equivalence classes, stats (total n. of states): before = $(sumspp) after = $(sum(graph.spp))")

    @assert check_consistency(graph)

    return graph
end

function build_eq_classes1!(graph::Graph, p0::Int)
    np = graph.np
    spp = graph.spp
    gadj = graph.gadj
    gmsk = graph.gmsk
    gconstr = graph.gconstr
    adjdict = graph.adjdict
    data = graph.data
    pkgs = data.pkgs
    pvers = data.pvers
    vdict = data.vdict
    eq_classes = data.eq_classes
    rlog = data.rlog

    # concatenate all the constraints; the columns of the
    # result encode the behavior of each version
    cmat = vcat(BitMatrix(permutedims(gconstr[p0])), gmsk[p0]...)
    cvecs = [cmat[:,v0] for v0 = 1:spp[p0]]

    # find unique behaviors
    repr_vecs = unique(cvecs)

    # number of equivalent classes
    neq = length(repr_vecs)

    neq == spp[p0] && return # nothing to do here

    # group versions into sets that behave identically
    eq_sets = [Set{Int}(v0 for v0 in 1:spp[p0] if cvecs[v0] == rvec) for rvec in repr_vecs]
    sort!(eq_sets, by=maximum)

    # each set is represented by its highest-valued member
    repr_vers = map(maximum, eq_sets)
    # the last representative must always be the uninstalled state
    @assert repr_vers[end] == spp[p0]

    # update equivalence classes
    eq_vn(v0) = (v0 == spp[p0] ? nothing : pvers[p0][v0])
    eq_classes0 = eq_classes[pkgs[p0]]
    for (v0,rvs) in zip(repr_vers, eq_sets)
        @assert v0 ∈ rvs
        vn0 = eq_vn(v0)
        for v1 in rvs
            v1 == v0 && continue
            vn1 = eq_vn(v1)
            @assert vn1 ≢ nothing
            union!(eq_classes0[vn0], eq_classes0[vn1])
            delete!(eq_classes0, vn1)
        end
    end

    # reduce the constraints and the interaction matrices
    spp[p0] = neq
    gconstr[p0] = gconstr[p0][repr_vers]
    for (j1,p1) in enumerate(gadj[p0])
        gmsk[p0][j1] = gmsk[p0][j1][:,repr_vers]

        j0 = adjdict[p0][p1]
        gmsk[p1][j0] = gmsk[p1][j0][repr_vers,:]
    end

    # reduce/rebuild version dictionaries
    pvers[p0] = pvers[p0][repr_vers[1:(end-1)]]
    vdict[p0] = Dict(vn => i for (i,vn) in enumerate(pvers[p0]))

    # put a record in the log
    log_event_eq_classes!(graph, p0)

    return
end

function compute_eq_classes_soft!(graph::Graph; log_events::Bool = true)
    log_events && log_event_global!(graph, "computing version equivalence classes")

    np = graph.np

    np == 0 && return graph

    ignored = graph.ignored
    gconstr = graph.gconstr
    sumspp = sum(count(gconstr[p0]) for p0 = 1:np)
    for p0 = 1:np
        ignored[p0] && continue
        build_eq_classes_soft1!(graph, p0)
    end
    sumspp_new = sum(count(gconstr[p0]) for p0 = 1:np)

    log_events && log_event_global!(graph, "computed version equivalence classes, stats (total n. of states): before = $(sumspp) after = $(sumspp_new) diff = $(sumspp_new-sumspp)")

    @assert check_consistency(graph)

    return graph
end

function build_eq_classes_soft1!(graph::Graph, p0::Int)
    np = graph.np
    spp = graph.spp
    gadj = graph.gadj
    gmsk = graph.gmsk
    gconstr = graph.gconstr
    ignored = graph.ignored

    # concatenate all the constraints; the columns of the
    # result encode the behavior of each version
    gadj0 = gadj[p0]
    gmsk0 = gmsk[p0]
    gconstr0 = gconstr[p0]
    eff_spp0 = count(gconstr0)
    cvecs = BitVector[vcat(BitVector(), (gmsk0[j1][gconstr[gadj0[j1]],v0] for j1 = 1:length(gadj0) if !ignored[gadj0[j1]])...) for v0 in findall(gconstr0)]

    @assert length(cvecs) == eff_spp0

    # find unique behaviors
    repr_vecs = unique(cvecs)

    # number of equivalent classes
    neq = length(repr_vecs)

    neq == eff_spp0 && return # nothing to do here

    # group versions into sets that behave identically
    # each set is represented by its highest-valued member
    repr_vers = sort!(Int[findlast(isequal(repr_vecs[w0]), cvecs) for w0 = 1:neq])
    @assert all(>(0), repr_vers)
    @assert repr_vers[end] == eff_spp0

    # convert the version numbers into the original numbering
    repr_vers = findall(gconstr0)[repr_vers]

    @assert all(gconstr0[repr_vers])

    # disable the other versions by introducing additional constraints
    fill!(gconstr0, false)
    gconstr0[repr_vers] .= true

    return
end

function update_ignored!(graph::Graph)
    np = graph.np
    gconstr = graph.gconstr
    ignored = graph.ignored

    for p0 = 1:np
        ignored[p0] = (count(gconstr[p0]) == 1)
    end

    return graph
end

"""
Prune away fixed and unnecessary packages, and the
disallowed versions for the remaining packages.
"""
function prune_graph!(graph::Graph)
    np = graph.np
    spp = graph.spp
    gadj = graph.gadj
    gmsk = graph.gmsk
    gconstr = graph.gconstr
    adjdict = graph.adjdict
    req_inds = graph.req_inds
    fix_inds = graph.fix_inds
    ignored = graph.ignored
    data = graph.data
    pkgs = data.pkgs
    pdict = data.pdict
    pvers = data.pvers
    vdict = data.vdict
    pruned = data.pruned
    rlog = data.rlog

    # We will remove all packages that only have one allowed state
    # (includes fixed packages and forbidden packages)
    pkg_mask = BitVector(count(gconstr[p0]) ≠ 1 for p0 = 1:np)
    new_np = count(pkg_mask)

    # a map that translates the new index ∈ 1:new_np into its
    # corresponding old index ∈ 1:np
    old_idx = findall(pkg_mask)
    # the reverse of the above
    new_idx = Dict{Int,Int}()
    for new_p0 = 1:new_np
        new_idx[old_idx[new_p0]] = new_p0
    end

    # Update requirement indices
    new_req_inds = Set{Int}()
    for p0 in req_inds
        pkg_mask[p0] || continue
        push!(new_req_inds, new_idx[p0])
    end

    # Fixed packages will all be pruned
    new_fix_inds = Set{Int}()
    for p0 in fix_inds
        @assert !pkg_mask[p0]
    end

    # Record which packages we are going to prune
    for p0 in findall(.~(pkg_mask))
        # Find the version
        s0 = findfirst(gconstr[p0])
        # We don't record fixed packages
        p0 ∈ fix_inds && (@assert s0 ≠ spp[p0]; continue)
        p0 ∈ req_inds && @assert s0 ≠ spp[p0]
        log_event_pruned!(graph, p0, s0)
        # We don't record as pruned packages that are not going to be installed
        s0 == spp[p0] && continue
        @assert !haskey(pruned, pkgs[p0])
        pruned[pkgs[p0]] = pvers[p0][s0]
    end

    # Update packages records
    new_pkgs = pkgs[pkg_mask]
    new_pdict = Dict(new_pkgs[new_p0]=>new_p0 for new_p0 = 1:new_np)
    new_ignored = ignored[pkg_mask]
    empty!(graph.solve_stack)

    # For each package (unless it's going to be pruned) we will remove all
    # versions that aren't allowed (but not the "uninstalled" state)
    function keep_vers(new_p0)
        p0 = old_idx[new_p0]
        return BitVector((v0 == spp[p0]) | gconstr[p0][v0] for v0 = 1:spp[p0])
    end
    vers_mask = [keep_vers(new_p0) for new_p0 = 1:new_np]

    # Update number of states per package
    new_spp = Int[count(vers_mask[new_p0]) for new_p0 = 1:new_np]

    # Update versions maps
    function compute_pvers(new_p0)
        p0 = old_idx[new_p0]
        pvers0 = pvers[p0]
        vmsk0 = vers_mask[new_p0]
        return pvers0[vmsk0[1:(end-1)]]
    end
    new_pvers = [compute_pvers(new_p0) for new_p0 = 1:new_np]

    # explicitly writing out the following loop since the generator equivalent caused type inference failure
    new_vdict = Vector{Dict{VersionNumber, Int}}(undef, length(new_pvers))
    for new_p0 in eachindex(new_vdict)
        new_vdict[new_p0] = Dict(vn => v0 for (v0,vn) in enumerate(new_pvers[new_p0]))
    end

    # The new constraints are all going to be `true`, except possibly
    # for the "uninstalled" state, which we copy over from the old
    function compute_gconstr(new_p0)
        p0 = old_idx[new_p0]
        new_gconstr0 = trues(new_spp[new_p0])
        new_gconstr0[end] = gconstr[p0][end]
        return new_gconstr0
    end
    new_gconstr = [compute_gconstr(new_p0) for new_p0 = 1:new_np]

    # Recreate the graph adjacency list, skipping some packages
    new_gadj = [Int[] for new_p0 = 1:new_np]
    new_adjdict = [Dict{Int,Int}() for new_p0 = 1:new_np]

    for new_p0 = 1:new_np, (j1,p1) in enumerate(gadj[old_idx[new_p0]])
        pkg_mask[p1] || continue
        new_p1 = new_idx[p1]

        new_j0 = get(new_adjdict[new_p1], new_p0, length(new_gadj[new_p0]) + 1)
        new_j1 = get(new_adjdict[new_p0], new_p1, length(new_gadj[new_p1]) + 1)

        @assert (new_j0 > length(new_gadj[new_p0]) && new_j1 > length(new_gadj[new_p1])) ||
                (new_j0 ≤ length(new_gadj[new_p0]) && new_j1 ≤ length(new_gadj[new_p1]))

        new_j0 > length(new_gadj[new_p0]) || continue
        push!(new_gadj[new_p0], new_p1)
        push!(new_gadj[new_p1], new_p0)
        @assert new_j0 == length(new_gadj[new_p0])
        @assert new_j1 == length(new_gadj[new_p1])

        new_adjdict[new_p1][new_p0] = new_j0
        new_adjdict[new_p0][new_p1] = new_j1
    end

    # Recompute compatibility masks on the new adjacency list, and filtering out some versions
    function compute_gmsk(new_p0, new_j0)
        p0 = old_idx[new_p0]
        new_p1 = new_gadj[new_p0][new_j0]
        p1 = old_idx[new_p1]
        j0 = adjdict[p1][p0]
        return gmsk[p0][j0][vers_mask[new_p1],vers_mask[new_p0]]
    end
    new_gmsk = [[compute_gmsk(new_p0, new_j0) for new_j0 = 1:length(new_gadj[new_p0])] for new_p0 = 1:new_np]

    # Reduce log pool (the other items are still reachable through rlog.init)
    rlog.pool = Dict(p=>rlog.pool[p] for p in new_pkgs)

    # Done

    log_event_global!(graph, "pruned graph — stats (n. of packages, mean connectivity): before = ($np,$(sum(spp)/length(spp))) after = ($new_np,$(sum(new_spp)/length(new_spp)))")

    # Replace old data with new
    data.pkgs = new_pkgs
    data.np = new_np
    data.spp = new_spp
    data.pdict = new_pdict
    data.pvers = new_pvers
    data.vdict = new_vdict
    # Notes:
    #   * uuid_to_name, eq_classes are unchanged
    #   * pruned and rlog were updated in-place

    # Replace old structures with new ones
    graph.gadj = new_gadj
    graph.gmsk = new_gmsk
    graph.gconstr = new_gconstr
    graph.adjdict = new_adjdict
    graph.req_inds = new_req_inds
    graph.fix_inds = new_fix_inds
    graph.ignored = new_ignored
    graph.spp = new_spp
    graph.np = new_np
    # Note: solve_stack was emptied in-place

    @assert check_consistency(graph)

    return graph
end

"""
Simplifies the graph by propagating constraints, disabling unreachable versions, pruning
and grouping versions into equivalence classes.
"""
function simplify_graph!(graph::Graph, sources::Set{Int} = Set{Int}(); clean_graph::Bool = false)
    propagate_constraints!(graph)
    disable_unreachable!(graph, sources)
    clean_graph && deep_clean!(graph)
    prune_graph!(graph)
    compute_eq_classes!(graph)
    return graph
end

function simplify_graph_soft!(graph::Graph, sources::Set{Int} = Set{Int}(); log_events = true)
    propagate_constraints!(graph, sources, log_events = log_events)
    update_ignored!(graph)
    compute_eq_classes_soft!(graph, log_events = log_events)
    update_ignored!(graph)
    return graph
end
u   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Pkg/src/Resolve/maxsum.jl/8      # This file is a part of Julia. License is MIT: https://julialang.org/license

# An exception type used internally to signal that an unsatisfiable
# constraint was detected
struct UnsatError <: Exception
    p0::Int
end

# Some parameters to drive the decimation process
mutable struct MaxSumParams
    dec_interval::Int # number of iterations between decimations
    dec_fraction::Float64 # fraction of nodes to decimate at every decimation
                          # step

    function MaxSumParams()
        accuracy = parse(Int, get(ENV, "JULIA_PKG_RESOLVE_ACCURACY",
                                  # Allow for `JULIA_PKGRESOLVE_ACCURACY` for backward
                                  # compatibility with Julia v1.7-
                                  get(ENV, "JULIA_PKGRESOLVE_ACCURACY", "1")))
        accuracy > 0 || error("JULIA_PKG_RESOLVE_ACCURACY must be > 0")
        dec_interval = accuracy * 5
        dec_fraction = 0.05 / accuracy
        return new(dec_interval, dec_fraction)
    end
end

# Messages has the cavity messages and the total fields, and
# gets updated iteratively (and occasionally decimated) until
# convergence
mutable struct Messages
    # cavity incoming messages: for each package p0,
    #                           for each neighbor p1 of p0,
    #                           msg[p0][p1] is a vector of length spp[p0]
    #                           messages are normalized (i.e. the max is always 0)
    msg::Vector{Vector{Field}}

    # overall fields: for each package p0,
    #                 fld[p0] is a vector of length spp[p0]
    #                 fields are not normalized
    fld::Vector{Field}

    # backup of the initial value of fld, to be used when resetting
    initial_fld::Vector{Field}

    function Messages(graph::Graph)
        np = graph.np
        spp = graph.spp
        gadj = graph.gadj
        gconstr = graph.gconstr
        req_inds = graph.req_inds
        ignored = graph.ignored
        pvers = graph.data.pvers
        pdict = graph.data.pdict

        ## generate wveights (v0 == spp[p0] is the "uninstalled" state)
        vweight = [[VersionWeight(v0 < spp[p0] ? pvers[p0][v0] : v"0") for v0 = 1:spp[p0]] for p0 = 1:np]

        # external fields: favor newest versions over older, and no-version over all;
        #                  explicit requirements use level l1 instead of l2
        fv(p0, v0) = p0 ∈ req_inds ?
            FieldValue(0, vweight[p0][v0],     zero(VersionWeight), (v0==spp[p0])) :
            FieldValue(0, zero(VersionWeight), vweight[p0][v0],     (v0==spp[p0]))
        fld = [[fv(p0, v0) for v0 = 1:spp[p0]] for p0 = 1:np]

        initial_fld = [copy(f0) for f0 in fld]

        # allocate cavity messages
        msg = [[Field(undef, spp[p0]) for j1 = 1:length(gadj[p0])] for p0 = 1:np]

        msgs = new(msg, fld, initial_fld)

        reset_messages!(msgs, graph)

        return msgs
    end
end

# enforce constraints and normalize fields;
# zero out all cavity messages
function reset_messages!(msgs::Messages, graph::Graph)
    msg = msgs.msg
    fld = msgs.fld
    initial_fld = msgs.initial_fld
    np = graph.np
    spp = graph.spp
    gconstr = graph.gconstr
    ignored = graph.ignored
    for p0 = 1:np
        ignored[p0] && continue
        map(m->fill!(m, zero(FieldValue)), msg[p0])
        copyto!(fld[p0], initial_fld[p0])
        gconstr0 = gconstr[p0]
        for v0 = 1:spp[p0]
            gconstr0[v0] || (fld[p0][v0] = FieldValue(-1))
        end
        fld[p0] .-= maximum(fld[p0])
    end
    return msgs
end

mutable struct SolutionTrace
    # the solution is built progressively by a decimation process
    solution::Vector{Int}
    num_nondecimated::Int

    best::Vector{Int}
    staged::Union{Tuple{Int,Int},Nothing}

    function SolutionTrace(graph::Graph)
        np = graph.np
        solution = zeros(Int, np)
        num_nondecimated = np

        best = zeros(Int, np)
        staged = nothing

        return new(solution, num_nondecimated, best, staged)
    end
end

function update_solution!(strace::SolutionTrace, graph::Graph)
    np = graph.np
    ignored = graph.ignored
    gconstr = graph.gconstr
    solution = strace.solution
    best = strace.best
    nnd = np
    fill!(solution, 0)
    for p0 in findall(ignored)
        s0 = findfirst(gconstr[p0])
        solution[p0] = s0
        nnd -= 1
    end
    strace.num_nondecimated = nnd
    if nnd ≤ sum(best .== 0)
        copyto!(best, solution)
        strace.staged = nothing
        return true
    else
        return false
    end
end

# This is the core of the max-sum solver:
# for a given node p0 (i.e. a package) updates all
# input cavity messages and fields of its neighbors
function update!(p0::Int, graph::Graph, msgs::Messages)
    gadj = graph.gadj
    gmsk = graph.gmsk
    adjdict = graph.adjdict
    ignored = graph.ignored
    spp = graph.spp
    np = graph.np
    cavfld = graph.cavfld
    newmsg = graph.newmsg
    diff = graph.diff

    msg = msgs.msg
    fld = msgs.fld

    maxdiff = zero(FieldValue)

    gadj0 = gadj[p0]
    msg0 = msg[p0]
    fld0 = fld[p0]
    spp0 = spp[p0]
    adjdict0 = adjdict[p0]

    # iterate over all neighbors of p0
    for j0 in 1:length(gadj0)
        p1 = gadj0[j0]
        ignored[p1] && continue
        j1 = adjdict0[p1]
        #@assert j0 == adjdict[p1][p0]
        bm1 = gmsk[p1][j1]
        spp1 = spp[p1]
        msg1 = msg[p1]

        # compute the output cavity field p0->p1
        resize!(cavfld, length(fld0))
        cavfld .= fld0 .- msg0[j0]

        # keep the old input cavity message p0->p1
        oldmsg = msg1[j1]

        # init the new message to minus infinity
        resize!(newmsg, spp1)
        fill!(newmsg, FieldValue(-1))

        # compute the new message by passing cavfld
        # through the constraint encoded in the bitmask
        # (equivalent to:
        #    newmsg = [maximum(cavfld[bm1[:,v1]]) for v1 = 1:spp1]
        # )
        # This is hot code for the resolver
        @inbounds for v1 = 1:spp1, v0 = 1:spp0
            bm1[v0, v1] || continue
            newmsg[v1] = max(newmsg[v1], cavfld[v0])
        end
        m = maximum(newmsg)
        validmax(m) || return Unsat(p0) # No state available without violating some
                                        # hard constraint

        # normalize the new message
        @inbounds for i in 1:length(newmsg)
            newmsg[i] -= m
        end

        resize!(diff, spp1)
        diff .= newmsg .- oldmsg
        maxdiff = max(maxdiff, maximum(abs, diff))

        # update the field of p1
        fld[p1] .+= diff

        # put the newly computed message in place
        copy!(msg1[j1], newmsg)
    end
    return maxdiff
end

# A simple shuffling machinery for the update order in iterate!()
# (wouldn't pass any random quality test but it's arguably enough)
mutable struct NodePerm
    p::Vector{Int}
    step::Int64
    NodePerm(np::Integer) = new(collect(1:np), 1)
end

function Random.shuffle!(perm::NodePerm)
    p = perm.p
    for j = length(p):-1:2
        k = perm.step % j + 1
        p[j], p[k] = p[k], p[j]
        perm.step += isodd(j) ? 1 : k
    end
    #@assert isperm(p)
end

Base.iterate(perm::NodePerm, state...) = iterate(perm.p, state...)

# Call update for all nodes (i.e. packages) in
# random order
function iterate!(graph::Graph, msgs::Messages, perm::NodePerm)
    maxdiff = zero(FieldValue)
    shuffle!(perm)
    for p0 in perm
        graph.ignored[p0] && continue
        maxdiff0 = update!(p0, graph, msgs)
        if maxdiff0 isa Unsat
            return maxdiff0
        end
        maxdiff = max(maxdiff, maxdiff0)
    end
    return maxdiff
end

function decimate1!(p0::Int, graph::Graph, strace::SolutionTrace, msgs::Messages)
    solution = strace.solution
    fld = msgs.fld
    adjdict = graph.adjdict
    gmsk = graph.gmsk
    gconstr = graph.gconstr

    @assert solution[p0] == 0
    @assert !graph.ignored[p0]
    fld0 = fld[p0]
    s0 = argmax(fld0)
    # only do the decimation if it is consistent with
    # the constraints...
    gconstr[p0][s0] || return 0
    # ...and with the previously decimated nodes
    for p1 in findall(solution .> 0)
        haskey(adjdict[p0], p1) || continue
        s1 = solution[p1]
        j1 = adjdict[p0][p1]
        gmsk[p1][j1][s0,s1] || return 0
    end
    solution[p0] = s0
    strace.num_nondecimated -= 1
    return s0
end

function decimate!(graph::Graph, strace::SolutionTrace, msgs::Messages, n::Integer)
    np = graph.np
    gconstr = graph.gconstr
    ignored = graph.ignored
    fld = msgs.fld

    @assert n ≥ 1
    dtrace = Tuple{Int,Int}[]
    dec = 0

    fldorder = sort(findall(.!(ignored)), by=p0->secondmax(fld[p0], gconstr[p0]))
    for p0 in fldorder
        s0 = decimate1!(p0, graph, strace, msgs)
        s0 == 0 && continue
        push!(dtrace, (p0,s0))
        dec += 1
        dec == n && break
    end

    return dtrace
end

function clean_forbidden!(graph::Graph, msgs::Messages)
    np = graph.np
    gconstr = graph.gconstr
    ignored = graph.ignored
    fld = msgs.fld
    affected = Tuple{Int,Int}[]

    for p0 = 1:np
        ignored[p0] && continue
        fld0 = fld[p0]
        gconstr0 = gconstr[p0]
        for v0 in findall(gconstr0)
            validmax(fld0[v0]) && continue
            push!(affected, (p0,v0))
        end
    end
    return affected
end

# Iterative solver: run iterate!() until convergence
# (occasionally calling decimate())
function maxsum(graph::Graph)
    params = MaxSumParams()

    perm = NodePerm(graph.np)
    strace = SolutionTrace(graph)
    msgs = Messages(graph)

    push_snapshot!(graph)
    # gconstr_sav = graph.gconstr
    # ignored_sav = graph.ignored
    ok = converge!(graph, msgs, strace, perm, params)
    # @assert graph.gconstr ≡ gconstr_sav
    # @assert graph.ignored ≡ ignored_sav
    pop_snapshot!(graph)
    if ok
        @assert strace.best == strace.solution
        @assert strace.num_nondecimated == 0
        @assert all(strace.solution .> 0)
        @assert strace.staged ≡ nothing
    else
        @assert strace.staged ≢ nothing
    end
    return ok, strace.best, strace.staged
end

function try_simplify_graph_soft!(graph, sources)
    try
        simplify_graph_soft!(graph, sources, log_events = false)
    catch err
        err isa ResolverError || rethrow()
        return false
    end
    return true
end

struct Unsat
    p0::Int
end

function converge!(graph::Graph, msgs::Messages, strace::SolutionTrace, perm::NodePerm, params::MaxSumParams)
    is_best_sofar = update_solution!(strace, graph)

    # this is the base of the recursion: the case when
    # the solver has succeeded in decimating everything
    strace.num_nondecimated == 0 && return true

    reset_messages!(msgs, graph)

    # perform some maxsum iterations, then decimate one node.
    # If failure happens during this process, we bail (return false)
    it = 0
    for it = 1:params.dec_interval
        maxdiff = iterate!(graph, msgs, perm)
        if maxdiff isa Unsat
            if is_best_sofar
                p0 = maxdiff.p0
                s0 = findlast(graph.gconstr[p0])
                strace.staged = (p0, s0)
            end
            return false
        end
        maxdiff == zero(FieldValue) && break
    end

    # if maxsum has found some forbidden states, remove
    # them and propagate the effect
    affected = clean_forbidden!(graph, msgs)

    isempty(affected) && @goto decimate

    sources = Set{Int}()
    for (p0,v0) in affected
        graph.gconstr[p0][v0] = false
        push!(sources, p0)
    end

    if !try_simplify_graph_soft!(graph, sources)
        # found an implicit contradiction
        is_best_sofar && (strace.staged = first(affected))
        return false
    end
    return converge!(graph, msgs, strace, perm, params)

    @label decimate

    ndec = max(1, round(Int, params.dec_fraction * strace.num_nondecimated))
    dtrace = decimate!(graph, strace, msgs, ndec)
    if isempty(dtrace)
        # decimation has failed, all candidate states are forbidden
        # (which shouldn't really happen, this is a failsafe)
        if is_best_sofar
            # pick the first decimation candidate
            smx(p1) = secondmax(msgs.fld[p1], graph.gconstr[p1])
            p0 = reduce((p1,p2)->(smx(p1)≤smx(p2) ? p1 : p2), findall(.!(graph.ignored)))
            s0 = argmax(fld[p0])
            strace.staged = dec_firstcandidate(graph, msgs)
        end
        return false
    end

    while true
        # decimation has succeeded, at least nominally.
        # We need to propagate its effects and check for contradictions

        lentr = length(dtrace)
        if lentr == 1 && is_best_sofar
            strace.staged = dtrace[1]
        end

        push_snapshot!(graph)
        # info("setting dtrace=$dtrace")
        for (p0,s0) in dtrace
            @assert !graph.ignored[p0]
            @assert graph.gconstr[p0][s0]
            fill!(graph.gconstr[p0], false)
            graph.gconstr[p0][s0] = true
            graph.ignored[p0] = true
        end

        # if decimation has produced an implicit contradiction, backtrack
        try_simplify_graph_soft!(graph, Set{Int}(first.(dtrace))) || @goto backtrack

        # otherwise, keep going...
        converge!(graph, msgs, strace, perm, params) && (pop_snapshot!(graph); return true)

        @label backtrack

        # warn("reverting dtrace=$dtrace")

        # if we're here, the last decimation step has been proven to lead
        # to an unsat situation at some point, we need to roll it back

        # revert the state of the constraints
        pop_snapshot!(graph)

        lentr == 1 && break
        # halve the dtrace
        deleteat!(dtrace, ((lentr÷2)+1):lentr)
    end

    @assert length(dtrace) == 1
    p0, s0 = dtrace[1]

    is_best_sofar && @assert strace.staged ≢ nothing

    # forbid the state used in the last attempt
    # (note that we're working on the "entry" snapshot here!)
    graph.gconstr[p0][s0] = false
    # check if we have finished all available possibilities
    any(graph.gconstr[p0]) || return false
    # if neither the s0 state nor its negation are valid, give up
    try_simplify_graph_soft!(graph, Set{Int}([p0])) || return false

    # keep going, with one possible state less...
    return converge!(graph, msgs, strace, perm, params)
end
l   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Pkg/src/Types.jl��      # This file is a part of Julia. License is MIT: https://julialang.org/license

module Types

using UUIDs
using Random
using Dates
import LibGit2
import REPL
import Base.string
using REPL.TerminalMenus

using TOML
import ..Pkg, ..Registry
import ..Pkg: GitTools, depots, depots1, logdir, set_readonly, safe_realpath, pkg_server, stdlib_dir, stdlib_path, isurl, stderr_f, RESPECT_SYSIMAGE_VERSIONS
import Base.BinaryPlatforms: Platform
using ..Pkg.Versions
import FileWatching

import Base: SHA1
using SHA

export UUID, SHA1, VersionRange, VersionSpec,
    PackageSpec, PackageEntry, EnvCache, Context, GitRepo, Context!, Manifest, Project, err_rep,
    PkgError, pkgerror, PkgPrecompileError,
    has_name, has_uuid, is_stdlib, is_or_was_stdlib, stdlib_version, is_unregistered_stdlib, stdlibs, write_env, write_env_usage, parse_toml,
    project_resolve!, project_deps_resolve!, manifest_resolve!, registry_resolve!, stdlib_resolve!, handle_repos_develop!, handle_repos_add!, ensure_resolved,
    registered_name,
    manifest_info,
    read_project, read_package, read_manifest,
    PackageMode, PKGMODE_MANIFEST, PKGMODE_PROJECT, PKGMODE_COMBINED,
    UpgradeLevel, UPLEVEL_FIXED, UPLEVEL_PATCH, UPLEVEL_MINOR, UPLEVEL_MAJOR,
    PreserveLevel, PRESERVE_ALL_INSTALLED, PRESERVE_ALL, PRESERVE_DIRECT, PRESERVE_SEMVER, PRESERVE_TIERED,
    PRESERVE_TIERED_INSTALLED, PRESERVE_NONE,
    projectfile_path, manifestfile_path

# Load in data about historical stdlibs
include("HistoricalStdlibs.jl")

deepcopy_toml(x) = x
function deepcopy_toml(@nospecialize(x::Vector))
    d = similar(x)
    for (i, v) in enumerate(x)
        d[i] = deepcopy_toml(v)
    end
    return d
end
function deepcopy_toml(x::Dict{String, Any})
    d = Dict{String, Any}()
    sizehint!(d, length(x))
    for (k, v) in x
        d[k] = deepcopy_toml(v)
    end
    return d
end

# See loading.jl
const TOML_CACHE = Base.TOMLCache(TOML.Parser(), Dict{String, Dict{String, Any}}())
const TOML_LOCK = ReentrantLock()
# Some functions mutate the returning Dict so return a copy of the cached value here
parse_toml(toml_file::AbstractString) =
    Base.invokelatest(deepcopy_toml, Base.parsed_toml(toml_file, TOML_CACHE, TOML_LOCK))::Dict{String, Any}

#################
# Pkg Error #
#################
struct PkgError <: Exception
    msg::String
end
pkgerror(msg::String...) = throw(PkgError(join(msg)))
Base.showerror(io::IO, err::PkgError) = print(io, err.msg)

#################
# Pkg Precompile Error #
#################
struct PkgPrecompileError <: Exception
    msg::String
end
Base.showerror(io::IO, err::PkgPrecompileError) = print(io, err.msg)
# This needs a show method to make `julia> err` show nicely
Base.show(io::IO, err::PkgPrecompileError) = print(io, "PkgPrecompileError: ", err.msg)


###############
# PackageSpec #
###############
@enum(UpgradeLevel, UPLEVEL_FIXED, UPLEVEL_PATCH, UPLEVEL_MINOR, UPLEVEL_MAJOR)
@enum(PreserveLevel, PRESERVE_ALL_INSTALLED, PRESERVE_ALL, PRESERVE_DIRECT, PRESERVE_SEMVER, PRESERVE_TIERED, PRESERVE_TIERED_INSTALLED, PRESERVE_NONE)
@enum(PackageMode, PKGMODE_PROJECT, PKGMODE_MANIFEST, PKGMODE_COMBINED)

const VersionTypes = Union{VersionNumber,VersionSpec,UpgradeLevel}

Base.@kwdef mutable struct GitRepo
    source::Union{Nothing,String} = nothing
    rev::Union{Nothing,String} = nothing
    subdir::Union{String, Nothing} = nothing
end

Base.:(==)(r1::GitRepo, r2::GitRepo) =
    r1.source == r2.source && r1.rev == r2.rev && r1.subdir == r2.subdir


mutable struct PackageSpec
    name::Union{Nothing,String}
    uuid::Union{Nothing,UUID}
    version::Union{Nothing,VersionTypes,String}
    tree_hash::Union{Nothing,SHA1}
    repo::GitRepo
    path::Union{Nothing,String}
    pinned::Bool
    # used for input only
    url::Union{Nothing, String}
    rev::Union{Nothing, String}
    subdir::Union{Nothing, String}

end
function PackageSpec(; name::Union{Nothing,AbstractString} = nothing,
                       uuid::Union{Nothing,UUID,AbstractString} = nothing,
                       version::Union{Nothing,VersionTypes,AbstractString} = VersionSpec(),
                       tree_hash::Union{Nothing,SHA1} = nothing,
                       repo::GitRepo = GitRepo(),
                       path::Union{Nothing,AbstractString} = nothing,
                       pinned::Bool = false,
                       url = nothing,
                       rev = nothing,
                       subdir = nothing)
    uuid = uuid === nothing ? nothing : UUID(uuid)
    return PackageSpec(name, uuid, version, tree_hash, repo, path, pinned, url, rev, subdir)
end
PackageSpec(name::AbstractString) = PackageSpec(;name=name)::PackageSpec
PackageSpec(name::AbstractString, uuid::UUID) = PackageSpec(;name=name, uuid=uuid)::PackageSpec
PackageSpec(name::AbstractString, version::VersionTypes) = PackageSpec(;name=name, version=version)::PackageSpec
PackageSpec(n::AbstractString, u::UUID, v::VersionTypes) = PackageSpec(;name=n, uuid=u, version=v)::PackageSpec

function Base.:(==)(a::PackageSpec, b::PackageSpec)
    return a.name == b.name && a.uuid == b.uuid && a.version == b.version &&
    a.tree_hash == b.tree_hash && a.repo == b.repo && a.path == b.path &&
    a.pinned == b.pinned
end

function err_rep(pkg::PackageSpec)
    x = pkg.name !== nothing && pkg.uuid !== nothing ? x = "$(pkg.name) [$(string(pkg.uuid)[1:8])]" :
        pkg.name !== nothing ? pkg.name :
        pkg.uuid !== nothing ? string(pkg.uuid)[1:8] :
        pkg.repo.source
    return "`$x`"
end

has_name(pkg::PackageSpec) = pkg.name !== nothing
has_uuid(pkg::PackageSpec) = pkg.uuid !== nothing
isresolved(pkg::PackageSpec) = pkg.uuid !== nothing && pkg.name !== nothing

function Base.show(io::IO, pkg::PackageSpec)
    vstr = repr(pkg.version)
    f = Pair{String, Any}[]

    pkg.name !== nothing && push!(f, "name" => pkg.name)
    pkg.uuid !== nothing && push!(f, "uuid" => pkg.uuid)
    pkg.tree_hash !== nothing && push!(f, "tree_hash" => pkg.tree_hash)
    pkg.path !== nothing && push!(f, "path" => pkg.path)
    pkg.url !== nothing && push!(f, "url" => pkg.url)
    pkg.rev !== nothing && push!(f, "rev" => pkg.rev)
    pkg.subdir !== nothing && push!(f, "subdir" => pkg.subdir)
    pkg.pinned && push!(f, "pinned" => pkg.pinned)
    push!(f, "version" => (vstr == "VersionSpec(\"*\")" ? "*" : vstr))
    if pkg.repo.source !== nothing
        push!(f, "repo/source" => string("\"", pkg.repo.source::String, "\""))
    end
    if pkg.repo.rev !== nothing
        push!(f, "repo/rev" => pkg.repo.rev)
    end
    if pkg.repo.subdir !== nothing
        push!(f, "repo/subdir" => pkg.repo.subdir)
    end
    print(io, "PackageSpec(\n")
    for (field, value) in f
        print(io, "  ", field, " = ", string(value)::String, "\n")
    end
    print(io, ")")
end

############
# EnvCache #
############

function projectfile_path(env_path::String; strict=false)
    for name in Base.project_names
        maybe_file = joinpath(env_path, name)
        isfile(maybe_file) && return maybe_file
    end
    return strict ? nothing : joinpath(env_path, "Project.toml")
end

function manifestfile_path(env_path::String; strict=false)
    man_names = @static Base.manifest_names isa Tuple ? Base.manifest_names : Base.manifest_names()
    for name in man_names
        maybe_file = joinpath(env_path, name)
        isfile(maybe_file) && return maybe_file
    end
    if strict
        return nothing
    else
        n_names = length(man_names)
        if n_names == 1
            return joinpath(env_path, only(man_name))
        else
            project = basename(projectfile_path(env_path)::String)
            idx = findfirst(x -> x == project, Base.project_names)
            @assert idx !== nothing
            idx = idx + (n_names - length(Base.project_names)) # ignore custom name if present
            return joinpath(env_path, man_names[idx])
        end
    end
end

function find_project_file(env::Union{Nothing,String}=nothing)
    project_file = nothing
    if env isa Nothing
        project_file = Base.active_project()
        project_file === nothing && pkgerror("no active project")
    elseif startswith(env, '@')
        project_file = Base.load_path_expand(env)
        project_file === nothing && pkgerror("package environment does not exist: $env")
    elseif env isa String
        if isdir(env)
            isempty(readdir(env)) || pkgerror("environment is a package directory: $env")
            project_file = joinpath(env, Base.project_names[end])
        else
            project_file = endswith(env, ".toml") ? abspath(env) :
                abspath(env, Base.project_names[end])
        end
    end
    @assert project_file isa String &&
        (isfile(project_file) || !ispath(project_file) ||
         isdir(project_file) && isempty(readdir(project_file)))
    return Pkg.safe_realpath(project_file)
end

Base.@kwdef mutable struct Compat
    val::VersionSpec
    str::String
end
Base.:(==)(t1::Compat, t2::Compat) = t1.val == t2.val
Base.hash(t::Compat, h::UInt) = hash(t.val, h)

Base.@kwdef mutable struct Project
    other::Dict{String,Any} = Dict{String,Any}()
    # Fields
    name::Union{String, Nothing} = nothing
    uuid::Union{UUID, Nothing} = nothing
    version::Union{VersionTypes, Nothing} = nothing
    manifest::Union{String, Nothing} = nothing
    # Sections
    deps::Dict{String,UUID} = Dict{String,UUID}()
    # deps that are also in weakdeps for backwards compat
    # we do not store them in deps because we want to ignore them
    # but for writing out the project file we need to remember them:
    _deps_weak::Dict{String,UUID} = Dict{String,UUID}()
    weakdeps::Dict{String,UUID} = Dict{String,UUID}()
    exts::Dict{String,Union{Vector{String}, String}} = Dict{String,String}()
    extras::Dict{String,UUID} = Dict{String,UUID}()
    targets::Dict{String,Vector{String}} = Dict{String,Vector{String}}()
    compat::Dict{String,Compat} = Dict{String,Compat}()
end
Base.:(==)(t1::Project, t2::Project) = all(x -> (getfield(t1, x) == getfield(t2, x))::Bool, fieldnames(Project))
Base.hash(t::Project, h::UInt) = foldr(hash, [getfield(t, x) for x in fieldnames(Project)], init=h)

# only hash the deps and compat fields as they are the only fields that affect a resolve
function project_resolve_hash(t::Project)
    iob = IOBuffer()
    foreach(((name, uuid),) -> println(iob, name, "=", uuid), sort!(collect(t.deps); by=first))
    foreach(((name, compat),) -> println(iob, name, "=", compat.val), sort!(collect(t.compat); by=first))
    return bytes2hex(sha1(seekstart(iob)))
end

Base.@kwdef mutable struct PackageEntry
    name::Union{String,Nothing} = nothing
    version::Union{VersionNumber,Nothing} = nothing
    path::Union{String,Nothing} = nothing
    pinned::Bool = false
    repo::GitRepo = GitRepo()
    tree_hash::Union{Nothing,SHA1} = nothing
    deps::Dict{String,UUID} = Dict{String,UUID}()
    weakdeps::Dict{String,UUID} = Dict{String,UUID}()
    exts::Dict{String,Union{Vector{String}, String}} = Dict{String,String}()
    uuid::Union{Nothing, UUID} = nothing
    other::Union{Dict,Nothing} = nothing
end
Base.:(==)(t1::PackageEntry, t2::PackageEntry) = t1.name == t2.name &&
    t1.version == t2.version &&
    t1.path == t2.path &&
    t1.pinned == t2.pinned &&
    t1.repo == t2.repo &&
    t1.tree_hash == t2.tree_hash &&
    t1.deps == t2.deps &&
    t1.weakdeps == t2.weakdeps &&
    t1.exts == t2.exts &&
    t1.uuid == t2.uuid
    # omits `other`
Base.hash(x::PackageEntry, h::UInt) = foldr(hash, [x.name, x.version, x.path, x.pinned, x.repo, x.tree_hash, x.deps, x.weakdeps, x.exts, x.uuid], init=h)  # omits `other`

Base.@kwdef mutable struct Manifest
    julia_version::Union{Nothing,VersionNumber} = nothing # only set to VERSION when resolving
    manifest_format::VersionNumber = v"2.0.0"
    deps::Dict{UUID,PackageEntry} = Dict{UUID,PackageEntry}()
    other::Dict{String,Any} = Dict{String,Any}()
end
Base.:(==)(t1::Manifest, t2::Manifest) = all(x -> (getfield(t1, x) == getfield(t2, x))::Bool, fieldnames(Manifest))
Base.hash(m::Manifest, h::UInt) = foldr(hash, [getfield(m, x) for x in fieldnames(Manifest)], init=h)
Base.getindex(m::Manifest, i_or_key) = getindex(m.deps, i_or_key)
Base.get(m::Manifest, key, default) = get(m.deps, key, default)
Base.setindex!(m::Manifest, i_or_key, value) = setindex!(m.deps, i_or_key, value)
Base.iterate(m::Manifest) = iterate(m.deps)
Base.iterate(m::Manifest, i::Int) = iterate(m.deps, i)
Base.length(m::Manifest) = length(m.deps)
Base.empty!(m::Manifest) = empty!(m.deps)
Base.values(m::Manifest) = values(m.deps)
Base.keys(m::Manifest) = keys(m.deps)
Base.haskey(m::Manifest, key) = haskey(m.deps, key)

function Base.show(io::IO, pkg::PackageEntry)
    f = []
    pkg.name        !== nothing && push!(f, "name"      => pkg.name)
    pkg.version     !== nothing && push!(f, "version"   => pkg.version)
    pkg.tree_hash   !== nothing && push!(f, "tree_hash" => pkg.tree_hash)
    pkg.path        !== nothing && push!(f, "dev/path"  => pkg.path)
    pkg.pinned                  && push!(f, "pinned"    => pkg.pinned)
    pkg.repo.source !== nothing && push!(f, "url/path"  => "`$(pkg.repo.source)`")
    pkg.repo.rev    !== nothing && push!(f, "rev"       => pkg.repo.rev)
    pkg.repo.subdir !== nothing && push!(f, "subdir"    => pkg.repo.subdir)
    print(io, "PackageEntry(\n")
    for (field, value) in f
        print(io, "  ", field, " = ", value, "\n")
    end
    print(io, ")")
end


mutable struct EnvCache
    # environment info:
    env::Union{Nothing,String}
    # paths for files:
    project_file::String
    manifest_file::String
    # name / uuid of the project
    pkg::Union{PackageSpec, Nothing}
    # cache of metadata:
    project::Project
    manifest::Manifest
    # What these where at creation of the EnvCache
    original_project::Project
    original_manifest::Manifest
end

function EnvCache(env::Union{Nothing,String}=nothing)
    project_file = find_project_file(env)
    project_dir = dirname(project_file)
    # read project file
    project = read_project(project_file)
    # initialize project package
    if project.name !== nothing && project.uuid !== nothing
        project_package = PackageSpec(
            name = project.name,
            uuid = project.uuid,
            version = something(project.version, VersionNumber("0.0")),
            path = project_dir,
        )
    else
        project_package = nothing
    end
    # determine manifest file
    dir = abspath(project_dir)
    manifest_file = project.manifest
    manifest_file = manifest_file !== nothing ?
        (isabspath(manifest_file) ? manifest_file : abspath(dir, manifest_file)) :
        manifestfile_path(dir)::String
    write_env_usage(manifest_file, "manifest_usage.toml")
    manifest = read_manifest(manifest_file)

    env′ = EnvCache(env,
        project_file,
        manifest_file,
        project_package,
        project,
        manifest,
        deepcopy(project),
        deepcopy(manifest),
        )

    return env′
end

include("project.jl")
include("manifest.jl")

function num_concurrent_downloads()
    val = get(ENV, "JULIA_PKG_CONCURRENT_DOWNLOADS", "8")
    num = tryparse(Int, val)
    isnothing(num) && error("Environment variable `JULIA_PKG_CONCURRENT_DOWNLOADS` expects an integer, instead found $(val)")
    if num < 1
        error("Number of concurrent downloads must be greater than 0")
    end
    return num
end
# ENV variables to set some of these defaults?
Base.@kwdef mutable struct Context
    env::EnvCache = EnvCache()
    io::IO = stderr_f()
    use_git_for_all_downloads::Bool = false
    use_only_tarballs_for_downloads::Bool = false
    num_concurrent_downloads::Int = num_concurrent_downloads()

    # Registris
    registries::Vector{Registry.RegistryInstance} = Registry.reachable_registries()

    # The Julia Version to resolve with respect to
    julia_version::Union{VersionNumber,Nothing} = VERSION
end

project_uuid(env::EnvCache) = env.pkg === nothing ? nothing : env.pkg.uuid
collides_with_project(env::EnvCache, pkg::PackageSpec) =
    is_project_name(env, pkg.name) || is_project_uuid(env, pkg.uuid)
is_project(env::EnvCache, pkg::PackageSpec) = is_project_uuid(env, pkg.uuid)
is_project_name(env::EnvCache, name::String) =
    env.pkg !== nothing && env.pkg.name == name
is_project_name(env::EnvCache, name::Nothing) = false
is_project_uuid(env::EnvCache, uuid::UUID) = project_uuid(env) == uuid

###########
# Context #
###########

const FORMER_STDLIBS = ["DelimitedFiles"]
const FORMER_STDLIBS_UUIDS = Set{UUID}()
const STDLIB = Ref{DictStdLibs}()
function load_stdlib()
    stdlib = DictStdLibs()
    for name in readdir(stdlib_dir())
        projfile = projectfile_path(stdlib_path(name); strict=true)
        nothing === projfile && continue
        project = parse_toml(projfile)
        uuid = get(project, "uuid", nothing)::Union{String, Nothing}
        v_str = get(project, "version", nothing)::Union{String, Nothing}
        version = isnothing(v_str) ? nothing : VersionNumber(v_str)
        nothing === uuid && continue
        if name in FORMER_STDLIBS
            push!(FORMER_STDLIBS_UUIDS, UUID(uuid))
            continue
        end
        stdlib[UUID(uuid)] = (name, version)
    end
    return stdlib
end

function stdlibs()
    if !isassigned(STDLIB)
        STDLIB[] = load_stdlib()
    end
    return STDLIB[]
end
is_stdlib(uuid::UUID) = uuid in keys(stdlibs())
# Includes former stdlibs
function is_or_was_stdlib(uuid::UUID, julia_version::Union{VersionNumber, Nothing})
    return is_stdlib(uuid, julia_version) || uuid in FORMER_STDLIBS_UUIDS
end


# Find the entry in `STDLIBS_BY_VERSION`
# that corresponds to the requested version, and use that.
# If we can't find one, defaults to `UNREGISTERED_STDLIBS`
function get_last_stdlibs(julia_version::VersionNumber; use_historical_for_current_version = false)
    if !use_historical_for_current_version && julia_version == VERSION
        return stdlibs()
    end
    last_stdlibs = UNREGISTERED_STDLIBS
    if isempty(STDLIBS_BY_VERSION)
        pkgerror("If you want to set `julia_version`, you must first populate the `STDLIBS_BY_VERSION` global constant")
    end
    for (version, stdlibs) in STDLIBS_BY_VERSION
        if VersionNumber(julia_version.major, julia_version.minor, julia_version.patch) < version
            break
        end
        last_stdlibs = stdlibs
    end
    return last_stdlibs
end
# If `julia_version` is set to `nothing`, that means (essentially) treat all registered
# stdlibs as normal packages so that we get the latest versions of everything, ignoring
# julia compat.  So we set the list of stdlibs to that of only the unregistered stdlibs.
get_last_stdlibs(::Nothing) = UNREGISTERED_STDLIBS

# Allow asking if something is an stdlib for a particular version of Julia
function is_stdlib(uuid::UUID, julia_version::Union{VersionNumber, Nothing})
    # Only use the cache if we are asking for stdlibs in a custom Julia version
    if julia_version == VERSION
        return is_stdlib(uuid)
    end

    last_stdlibs = get_last_stdlibs(julia_version)
    # Note that if the user asks for something like `julia_version = 0.7.0`, we'll
    # fall through with an empty `last_stdlibs`, which will always return `false`.
    return uuid in keys(last_stdlibs)
end

# Return the version of a stdlib with respect to a particular Julia version, or
# `nothing` if that stdlib is not versioned.  We only store version numbers for
# stdlibs that are external and thus could be installed from their repositories,
# e.g. things like `GMP_jll`, `Tar`, etc...
function stdlib_version(uuid::UUID, julia_version::Union{VersionNumber,Nothing})
    last_stdlibs = get_last_stdlibs(julia_version)
    if !(uuid in keys(last_stdlibs))
        return nothing
    end
    return last_stdlibs[uuid][2]
end

is_unregistered_stdlib(uuid::UUID) = haskey(UNREGISTERED_STDLIBS, uuid)

Context!(kw_context::Vector{Pair{Symbol,Any}})::Context =
    Context!(Context(); kw_context...)
function Context!(ctx::Context; kwargs...)
    for (k, v) in kwargs
        setfield!(ctx, k, v)
    end
    return ctx
end

function write_env_usage(source_file::AbstractString, usage_filepath::AbstractString)
    # Don't record ghost usage
    !isfile(source_file) && return

    # Ensure that log dir exists
    !ispath(logdir()) && mkpath(logdir())

    usage_file = joinpath(logdir(), usage_filepath)
    timestamp = now()

    ## Atomically write usage file using process id locking
    FileWatching.mkpidlock(usage_file * ".pid", stale_age = 3) do
        usage = if isfile(usage_file)
            TOML.parsefile(usage_file)
        else
            Dict{String, Any}()
        end

        # record new usage
        usage[source_file] = [Dict("time" => timestamp)]

        # keep only latest usage info
        for k in keys(usage)
            times = map(usage[k]) do d
                if haskey(d, "time")
                    Dates.DateTime(d["time"])
                else
                    # if there's no time entry because of a write failure be conservative and mark it as being used now
                    @debug "Usage file `$usage_filepath` has a missing `time` entry for `$k`. Marking as used `now()`"
                    Dates.now()
                end
            end
            usage[k] = [Dict("time" => maximum(times))]
        end

        open(usage_file, "w") do io
            TOML.print(io, usage, sorted=true)
        end
    end
    return
end

function read_package(path::String)
    project = read_project(path)
    if project.name === nothing
        pkgerror("expected a `name` entry in project file at `$(abspath(path))`")
    end
    if project.uuid === nothing
        pkgerror("expected a `uuid` entry in project file at `$(abspath(path))`")
    end
    name = project.name
    if !isfile(joinpath(dirname(path), "src", "$name.jl"))
        pkgerror("expected the file `src/$name.jl` to exist for package `$name` at `$(dirname(path))`")
    end
    return project
end

const refspecs = ["+refs/*:refs/remotes/cache/*"]

function relative_project_path(project_file::String, path::String)
    # compute path relative the project
    # realpath needed to expand symlinks before taking the relative path
    return relpath(Pkg.safe_realpath(abspath(path)),
                   Pkg.safe_realpath(dirname(project_file)))
end

function devpath(env::EnvCache, name::AbstractString, shared::Bool)
    @assert name != ""
    dev_dir = shared ? abspath(Pkg.devdir()) : joinpath(dirname(env.project_file), "dev")
    return joinpath(dev_dir, name)
end

function error_if_in_sysimage(pkg::PackageSpec)
    RESPECT_SYSIMAGE_VERSIONS[] || return false
    if pkg.uuid === nothing
        @error "Expected package $(pkg.name) to have a set UUID, please file a bug report."
        return false
    end
    pkgid = Base.PkgId(pkg.uuid, pkg.name)
    if Base.in_sysimage(pkgid)
        pkgerror("Tried to develop or add by URL package $(pkgid) which is already in the sysimage, use `Pkg.respect_sysimage_versions(false)` to disable this check.")
    end
end

function handle_repo_develop!(ctx::Context, pkg::PackageSpec, shared::Bool)
    # First, check if we can compute the path easily (which requires a given local path or name)
    is_local_path = pkg.repo.source !== nothing && !isurl(pkg.repo.source)
    if is_local_path || pkg.name !== nothing
        dev_path = is_local_path ? pkg.repo.source : devpath(ctx.env, pkg.name, shared)
        if pkg.repo.subdir !== nothing
            dev_path = joinpath(dev_path, pkg.repo.subdir)
        end
        # If given an explicit local path, that needs to exist
        if is_local_path && !isdir(dev_path)
            if isfile(dev_path)
                pkgerror("Dev path `$(dev_path)` is a file, but a directory is required.")
            else
                pkgerror("Dev path `$(dev_path)` does not exist.")
            end
        end
        if isdir(dev_path)
            resolve_projectfile!(ctx.env, pkg, dev_path)
            error_if_in_sysimage(pkg)
            if is_local_path
                pkg.path = isabspath(dev_path) ? dev_path : relative_project_path(ctx.env.manifest_file, dev_path)
            else
                pkg.path = shared ? dev_path : relative_project_path(ctx.env.manifest_file, dev_path)
            end
            return false
        end
    end
    # If we dev by name and it is in the Project + tracking a repo in the source we can get the repo from the Manifest
    if pkg.name !== nothing && pkg.uuid === nothing
        uuid = get(ctx.env.project.deps, pkg.name, nothing)
        if uuid !== nothing
            entry = manifest_info(ctx.env.manifest, uuid)
            if entry !== nothing
                pkg.repo.source = entry.repo.source
                pkg.repo.subdir = entry.repo.subdir
            end
        end
    end

    # Still haven't found the source, try get it from the registry
    if pkg.repo.source === nothing
        set_repo_source_from_registry!(ctx, pkg)
    end
    @assert pkg.repo.source !== nothing

    repo_path = tempname()
    cloned = false
    package_path = pkg.repo.subdir === nothing ? repo_path : joinpath(repo_path, pkg.repo.subdir)
    if !has_name(pkg)
        LibGit2.close(GitTools.ensure_clone(ctx.io, repo_path, pkg.repo.source))
        cloned = true
        resolve_projectfile!(ctx.env, pkg, package_path)
    end
    if pkg.repo.subdir !== nothing
        repo_name = split(pkg.repo.source, '/', keepempty=false)[end]
        # Make the develop path prettier.
        if endswith(repo_name, ".git")
            repo_name = chop(repo_name, tail=4)
        end
        if endswith(repo_name, ".jl")
            repo_name = chop(repo_name, tail=3)
        end
        dev_path = devpath(ctx.env, repo_name, shared)
    else
        dev_path = devpath(ctx.env, pkg.name, shared)
    end
    if isdir(dev_path)
        println(ctx.io, "Path `$(dev_path)` exists and looks like the correct repo. Using existing path.")
        new = false
    else
        mkpath(dirname(dev_path))
        if !cloned
            LibGit2.close(GitTools.ensure_clone(ctx.io, dev_path, pkg.repo.source))
        else
            mv(repo_path, dev_path)
        end
        new = true
    end
    if !has_uuid(pkg)
        resolve_projectfile!(ctx.env, pkg, dev_path)
    end
    error_if_in_sysimage(pkg)
    pkg.path = shared ? dev_path : relative_project_path(ctx.env.manifest_file, dev_path)
    if pkg.repo.subdir !== nothing
        pkg.path = joinpath(pkg.path, pkg.repo.subdir)
    end

    return new
end

function handle_repos_develop!(ctx::Context, pkgs::AbstractVector{PackageSpec}, shared::Bool)
    new_uuids = Set{UUID}()
    for pkg in pkgs
        new = handle_repo_develop!(ctx, pkg, shared)
        new && push!(new_uuids, pkg.uuid)
        @assert pkg.path !== nothing
        @assert has_uuid(pkg)
        pkg.repo = GitRepo() # clear repo field, no longer needed
    end
    return new_uuids
end

add_repo_cache_path(url::String) = joinpath(depots1(), "clones", string(hash(url)))

function set_repo_source_from_registry!(ctx, pkg)
    registry_resolve!(ctx.registries, pkg)
    # Didn't find the package in the registry, but maybe it exists in the updated registry
    if !isresolved(pkg)
        Pkg.Operations.update_registries(ctx; force=false)
        registry_resolve!(ctx.registries, pkg)
    end
    ensure_resolved(ctx, ctx.env.manifest, [pkg]; registry=true)
    # We might have been given a name / uuid combo that does not have an entry in the registry
    for reg in ctx.registries
        regpkg = get(reg, pkg.uuid, nothing)
        regpkg === nothing && continue
        info = Pkg.Registry.registry_info(regpkg)
        url = info.repo
        url === nothing && continue
        pkg.repo.source = url
        if info.subdir !== nothing
            pkg.repo.subdir = info.subdir
        end
        return
    end
    pkgerror("Repository for package with UUID `$(pkg.uuid)` could not be found in a registry.")
end


function handle_repo_add!(ctx::Context, pkg::PackageSpec)
    # The first goal is to populate pkg.repo.source if that wasn't given explicitly
    if pkg.repo.source === nothing
        @assert pkg.repo.rev !== nothing
        # First, we try resolving against the manifest and current registry to avoid updating registries if at all possible.
        # This also handles the case where we _only_ wish to switch the tracking branch for a package.
        manifest_resolve!(ctx.env.manifest, [pkg]; force=true)
        if isresolved(pkg)
            entry = manifest_info(ctx.env.manifest, pkg.uuid)
            if entry !== nothing
                pkg.repo.source = entry.repo.source
                pkg.repo.subdir = entry.repo.subdir
            end
        end
        if pkg.repo.source === nothing
            set_repo_source_from_registry!(ctx, pkg)
        end
    end
    @assert pkg.repo.source !== nothing

    # We now have the source of the package repo, check if it is a local path and if that exists
    repo_source = pkg.repo.source
    if !isurl(pkg.repo.source)
        if isdir(pkg.repo.source)
            if !isdir(joinpath(pkg.repo.source, ".git"))
                msg = "Did not find a git repository at `$(pkg.repo.source)`"
                if isfile(joinpath(pkg.repo.source, "Project.toml")) || isfile(joinpath(pkg.repo.source, "JuliaProject.toml"))
                    msg *= ", perhaps you meant `Pkg.develop`?"
                end
                pkgerror(msg)
            end
            LibGit2.with(GitTools.check_valid_HEAD, LibGit2.GitRepo(pkg.repo.source)) # check for valid git HEAD
            pkg.repo.source = isabspath(pkg.repo.source) ? safe_realpath(pkg.repo.source) : relative_project_path(ctx.env.manifest_file, pkg.repo.source)
            repo_source = normpath(joinpath(dirname(ctx.env.manifest_file), pkg.repo.source))
        else
            pkgerror("Path `$(pkg.repo.source)` does not exist.")
        end
    end

    let repo_source = repo_source
        # The type-assertions below are necessary presumably due to julia#36454
        LibGit2.with(GitTools.ensure_clone(ctx.io, add_repo_cache_path(repo_source::Union{Nothing,String}), repo_source::Union{Nothing,String}; isbare=true)) do repo
            repo_source_typed = repo_source::Union{Nothing,String}
            GitTools.check_valid_HEAD(repo)

            # If the user didn't specify rev, assume they want the default (master) branch if on a branch, otherwise the current commit
            if pkg.repo.rev === nothing
                pkg.repo.rev = LibGit2.isattached(repo) ? LibGit2.branch(repo) : string(LibGit2.GitHash(LibGit2.head(repo)))
            end

            obj_branch = get_object_or_branch(repo, pkg.repo.rev)
            fetched = false
            if obj_branch === nothing
                fetched = true
                GitTools.fetch(ctx.io, repo, repo_source_typed; refspecs=refspecs)
                obj_branch = get_object_or_branch(repo, pkg.repo.rev)
                if obj_branch === nothing
                    pkgerror("Did not find rev $(pkg.repo.rev) in repository")
                end
            end
            gitobject, isbranch = obj_branch

            # If we are tracking a branch and are not pinned we want to update the repo if we haven't done that yet
            innerentry = manifest_info(ctx.env.manifest, pkg.uuid)
            ispinned = innerentry !== nothing && innerentry.pinned
            if isbranch && !fetched && !ispinned
                GitTools.fetch(ctx.io, repo, repo_source_typed; refspecs=refspecs)
                gitobject, isbranch = get_object_or_branch(repo, pkg.repo.rev)
            end

            # Now we have the gitobject for our ref, time to find the tree hash for it
            tree_hash_object = LibGit2.peel(LibGit2.GitTree, gitobject)
            if pkg.repo.subdir !== nothing
                try
                    tree_hash_object = tree_hash_object[pkg.repo.subdir]
                catch e
                    e isa KeyError || rethrow()
                    pkgerror("Did not find subdirectory `$(pkg.repo.subdir)`")
                end
            end
            pkg.tree_hash = SHA1(string(LibGit2.GitHash(tree_hash_object)))

            # If we already resolved a uuid, we can bail early if this package is already installed at the current tree_hash
            if has_uuid(pkg)
                error_if_in_sysimage(pkg)
                version_path = Pkg.Operations.source_path(ctx.env.project_file, pkg, ctx.julia_version)
                isdir(version_path) && return false
            end

            temp_path = mktempdir()
            GitTools.checkout_tree_to_path(repo, tree_hash_object, temp_path)
            resolve_projectfile!(ctx.env, pkg, temp_path)
            error_if_in_sysimage(pkg)

            # Now that we are fully resolved (name, UUID, tree_hash, repo.source, repo.rev), we can finally
            # check to see if the package exists at its canonical path.
            version_path = Pkg.Operations.source_path(ctx.env.project_file, pkg, ctx.julia_version)
            isdir(version_path) && return false

            # Otherwise, move the temporary path into its correct place and set read only
            mkpath(version_path)
            mv(temp_path, version_path; force=true)
            set_readonly(version_path)
            return true
        end
    end
end

function handle_repos_add!(ctx::Context, pkgs::AbstractVector{PackageSpec})
    new_uuids = Set{UUID}()
    for pkg in pkgs
        handle_repo_add!(ctx, pkg) && push!(new_uuids, pkg.uuid)
        @assert pkg.name !== nothing && pkg.uuid !== nothing && pkg.tree_hash !== nothing
    end
    return new_uuids
end

function resolve_projectfile!(env::EnvCache, pkg, project_path)
    project_file = projectfile_path(project_path; strict=true)
    project_file === nothing && pkgerror(string("could not find project file (Project.toml or JuliaProject.toml) in package at `",
                    something(pkg.repo.source, pkg.path, project_path), "` maybe `subdir` needs to be specified"))
    project_data = read_package(project_file)
    if pkg.uuid === nothing || pkg.uuid == project_data.uuid
        pkg.uuid = project_data.uuid
    else
        pkgerror("UUID `$(project_data.uuid)` given by project file `$project_file` does not match given UUID `$(pkg.uuid)`")
    end
    if pkg.name === nothing || pkg.name == project_data.name
        pkg.name = project_data.name
    else
        pkgerror("name `$(project_data.name)` given by project file `$project_file` does not match given name `$(pkg.name)`")
    end
end

get_object_or_branch(repo, rev::SHA1) =
    get_object_or_branch(repo, string(rev))

# Returns nothing if rev could not be found in repo
function get_object_or_branch(repo, rev)
    try
        gitobject = LibGit2.GitObject(repo, "remotes/cache/heads/" * rev)
        return gitobject, true
    catch err
        err isa LibGit2.GitError && err.code == LibGit2.Error.ENOTFOUND || rethrow()
    end
    try
        gitobject = LibGit2.GitObject(repo, "remotes/origin/" * rev)
        return gitobject, true
    catch err
        err isa LibGit2.GitError && err.code == LibGit2.Error.ENOTFOUND || rethrow()
    end
    try
        gitobject = LibGit2.GitObject(repo, rev)
        return gitobject, false
    catch err
        err isa LibGit2.GitError && err.code == LibGit2.Error.ENOTFOUND || rethrow()
    end
    return nothing
end

########################################
# Resolving packages from name or uuid #
########################################

function project_resolve!(env::EnvCache, pkgs::AbstractVector{PackageSpec})
    for pkg in pkgs
        if has_uuid(pkg) && !has_name(pkg) && Types.is_project_uuid(env, pkg.uuid)
            pkg.name = env.pkg.name
        end
        if has_name(pkg) && !has_uuid(pkg) && Types.is_project_name(env, pkg.name)
            pkg.uuid = env.pkg.uuid
        end
    end
end

# Disambiguate name/uuid package specifications using project info.
function project_deps_resolve!(env::EnvCache, pkgs::AbstractVector{PackageSpec})
    uuids = env.project.deps
    names = Dict(uuid => name for (name, uuid) in uuids)
    for pkg in pkgs
        if has_name(pkg) && !has_uuid(pkg) && pkg.name in keys(uuids)
            pkg.uuid = uuids[pkg.name]
        end
        if has_uuid(pkg) && !has_name(pkg) && pkg.uuid in keys(names)
            pkg.name = names[pkg.uuid]
        end
    end
end

# Disambiguate name/uuid package specifications using manifest info.
function manifest_resolve!(manifest::Manifest, pkgs::AbstractVector{PackageSpec}; force=false)
    uuids = Dict{String,Vector{UUID}}()
    names = Dict{UUID,String}()
    for (uuid, entry) in manifest
        push!(get!(uuids, entry.name, UUID[]), uuid)
        names[uuid] = entry.name # can be duplicate but doesn't matter
    end
    for pkg in pkgs
        if has_name(pkg) && !has_uuid(pkg) && pkg.name in keys(uuids)
            length(uuids[pkg.name]) == 1 && (pkg.uuid = uuids[pkg.name][1])
        end
        if has_uuid(pkg) && !has_name(pkg) && pkg.uuid in keys(names)
            pkg.name = names[pkg.uuid]
        end
    end
end

# Disambiguate name/uuid package specifications using registry info.
registry_resolve!(registries::Vector{Registry.RegistryInstance}, pkg::PackageSpec) = registry_resolve!(registries, [pkg])
function registry_resolve!(registries::Vector{Registry.RegistryInstance}, pkgs::AbstractVector{PackageSpec})
    # if there are no half-specified packages, return early
    any(pkg -> has_name(pkg) ⊻ has_uuid(pkg), pkgs) || return
    for pkg in pkgs
        @assert has_name(pkg) || has_uuid(pkg)
        if has_name(pkg) && !has_uuid(pkg)
            pkg.uuid = registered_uuid(registries, pkg.name)
        end
        if has_uuid(pkg) && !has_name(pkg)
            pkg.name = registered_name(registries, pkg.uuid)
        end
    end
    return pkgs
end

function stdlib_resolve!(pkgs::AbstractVector{PackageSpec})
    for pkg in pkgs
        @assert has_name(pkg) || has_uuid(pkg)
        if has_name(pkg) && !has_uuid(pkg)
            for (uuid, (name, version)) in stdlibs()
                name == pkg.name && (pkg.uuid = uuid)
            end
        end
        if !has_name(pkg) && has_uuid(pkg)
            name, version = get(stdlibs(), pkg.uuid, (nothing, nothing))
            nothing !== name && (pkg.name = name)
        end
    end
end

# Ensure that all packages are fully resolved
function ensure_resolved(ctx::Context, manifest::Manifest,
        pkgs::AbstractVector{PackageSpec};
        registry::Bool=false,)::Nothing
    unresolved_uuids = Dict{String,Vector{UUID}}()
    for pkg in pkgs
        has_uuid(pkg) && continue
        !has_name(pkg) && pkgerror("Package $pkg has neither name nor uuid")
        uuids = [uuid for (uuid, entry) in manifest if entry.name == pkg.name]
        sort!(uuids, by=uuid -> uuid.value)
        unresolved_uuids[pkg.name] = uuids
    end
    unresolved_names = UUID[]
    for pkg in pkgs
        has_name(pkg) && continue
        push!(unresolved_names, pkg.uuid)
    end
    isempty(unresolved_uuids) && isempty(unresolved_names) && return
    msg = sprint(context = ctx.io) do io
        if !isempty(unresolved_uuids)
            print(io, "The following package names could not be resolved:")
            for (name, uuids) in sort!(collect(unresolved_uuids), by=lowercase ∘ first)
                print(io, "\n * $name (")
                if length(uuids) == 0
                    what = ["project", "manifest"]
                    registry && push!(what, "registry")
                    print(io, "not found in ")
                    join(io, what, ", ", " or ")
                    print(io, ")")
                    all_names = available_names(ctx; manifest, include_registries = registry)
                    all_names_ranked, any_score_gt_zero = fuzzysort(name, all_names)
                    if any_score_gt_zero
                        println(io)
                        prefix = "   Suggestions:"
                        printstyled(io, prefix, color = Base.info_color())
                        REPL.printmatches(io, name, all_names_ranked; cols = REPL._displaysize(ctx.io)[2] - length(prefix))
                    end
                else
                    join(io, uuids, ", ", " or ")
                    print(io, " in manifest but not in project)")
                end
            end
        end
        if !isempty(unresolved_names)
            println(io, "The following package uuids could not be resolved:")
            for uuid in unresolved_names
                println(io, " * $uuid")
            end
        end
    end
    pkgerror(msg)
end

# copied from REPL to efficiently expose if any score is >0
function fuzzysort(search::String, candidates::Vector{String})
    scores = map(cand -> (REPL.fuzzyscore(search, cand), -Float64(REPL.levenshtein(search, cand))), candidates)
    candidates[sortperm(scores)] |> reverse, any(s -> s[1] > 0, scores)
end

function available_names(ctx::Context = Context(); manifest::Manifest = ctx.env.manifest, include_registries::Bool = true)
    all_names = String[]
    for (_, pkgentry) in manifest
        push!(all_names, pkgentry.name)
    end
    if include_registries
        for reg in ctx.registries
            for (_, pkgentry) in reg.pkgs
                push!(all_names, pkgentry.name)
            end
        end
    end
    return unique(all_names)
end

function registered_uuids(registries::Vector{Registry.RegistryInstance}, name::String)
    uuids = Set{UUID}()
    for reg in registries
        union!(uuids, Registry.uuids_from_name(reg, name))
    end
    return uuids
end
# Determine a single UUID for a given name, prompting if needed
function registered_uuid(registries::Vector{Registry.RegistryInstance}, name::String)::Union{Nothing,UUID}
    uuids = registered_uuids(registries, name)
    length(uuids) == 0 && return nothing
    length(uuids) == 1 && return first(uuids)
    repo_infos = Tuple{String, String, UUID}[]
    for uuid in uuids
        for reg in registries
            pkg = get(reg, uuid, nothing)
            pkg === nothing && continue
            info = Pkg.Registry.registry_info(pkg)
            repo = info.repo
            repo === nothing && continue
            push!(repo_infos, (reg.name, repo, uuid))
        end
    end
    unique!(repo_infos)
    if isinteractive()
        # prompt for which UUID was intended:
        menu = RadioMenu(String["Registry: $(value[1]) - Repo: $(value[2]) - UUID: $(value[3])" for value in repo_infos])
        choice = request("There are multiple registered `$name` packages, choose one:", menu)
        choice == -1 && return nothing
        return repo_infos[choice][3]
    else
        pkgerror("there are multiple registered `$name` packages, explicitly set the uuid")
    end
end

# Determine current name for a given package UUID

function registered_name(registries::Vector{Registry.RegistryInstance}, uuid::UUID)::Union{Nothing,String}
    name = nothing
    for reg in registries
        regpkg = get(reg, uuid, nothing)
        regpkg === nothing && continue
        name′ = regpkg.name
        if name !== nothing
            name′ == name || pkgerror("package `$uuid` has multiple registered name values: $name, $name′")
        end
        name = name′
    end
    return name
end

# Find package by UUID in the manifest file
manifest_info(::Manifest, uuid::Nothing) = nothing
function manifest_info(manifest::Manifest, uuid::UUID)::Union{PackageEntry,Nothing}
    return get(manifest, uuid, nothing)
end
function write_env(env::EnvCache; update_undo=true,
                   skip_writing_project::Bool=false)
    if (env.project != env.original_project) && (!skip_writing_project)
        write_project(env)
    end
    if env.manifest != env.original_manifest
        write_manifest(env)
    end
    update_undo && Pkg.API.add_snapshot_to_undo(env)
end


end # module
x   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Pkg/src/HistoricalStdlibs.jl      using Base: UUID

const DictStdLibs = Dict{UUID,Tuple{String,Union{VersionNumber,Nothing}}}

# Julia standard libraries with duplicate entries removed so as to store only the
# first release in a set of releases that all contain the same set of stdlibs.
#
# This needs to be populated via HistoricalStdlibVersions.jl by consumers
# (e.g. BinaryBuilder) that want to use the "resolve things as if it were a
# different Julia version than what is currently running" feature.
const STDLIBS_BY_VERSION = Pair{VersionNumber, DictStdLibs}[]

# This is a list of stdlibs that must _always_ be treated as stdlibs,
# because they cannot be resolved in the registry; they have only ever existed within
# the Julia stdlib source tree, and because of that, trying to resolve them will fail.
const UNREGISTERED_STDLIBS = DictStdLibs(
    UUID("2a0f44e3-6c83-55bd-87e4-b1978d98bd5f") => ("Base64", nothing),
    UUID("8bf52ea8-c179-5cab-976a-9e18b702a9bc") => ("CRC32c", nothing),
    UUID("ade2ca70-3891-5945-98fb-dc099432e06a") => ("Dates", nothing),
    UUID("8ba89e20-285c-5b6f-9357-94700520ee1b") => ("Distributed", nothing),
    UUID("7b1f6079-737a-58dc-b8bc-7a2ca5c1b5ee") => ("FileWatching", nothing),
    UUID("9fa8497b-333b-5362-9e8d-4d0656e87820") => ("Future", nothing),
    UUID("b77e0a4c-d291-57a0-90e8-8db25a27a240") => ("InteractiveUtils", nothing),
    UUID("76f85450-5226-5b5a-8eaa-529ad045b433") => ("LibGit2", nothing),
    UUID("8f399da3-3557-5675-b5ff-fb832c97cbdb") => ("Libdl", nothing),
    UUID("37e2e46d-f89d-539d-b4ee-838fcccc9c8e") => ("LinearAlgebra", nothing),
    UUID("56ddb016-857b-54e1-b83d-db4d58db5568") => ("Logging", nothing),
    UUID("d6f4376e-aef5-505a-96c1-9c027394607a") => ("Markdown", nothing),
    UUID("a63ad114-7e13-5084-954f-fe012c677804") => ("Mmap", nothing),
    UUID("44cfe95a-1eb2-52ea-b672-e2afdf69b78f") => ("Pkg", nothing),
    UUID("de0858da-6303-5e67-8744-51eddeeeb8d7") => ("Printf", nothing),
    UUID("9abbd945-dff8-562f-b5e8-e1ebf5ef1b79") => ("Profile", nothing),
    UUID("3fa0cd96-eef1-5676-8a61-b3b8758bbffb") => ("REPL", nothing),
    UUID("9a3f8284-a2c9-5f02-9a11-845980a1fd5c") => ("Random", nothing),
    UUID("9e88b42a-f829-5b0c-bbe9-9e923198166b") => ("Serialization", nothing),
    UUID("1a1011a3-84de-559e-8e89-a11a2f7dc383") => ("SharedArrays", nothing),
    UUID("6462fe0b-24de-5631-8697-dd941f90decc") => ("Sockets", nothing),
    UUID("2f01184e-e22b-5df5-ae63-d93ebab69eaf") => ("SparseArrays", nothing),
    UUID("10745b16-79ce-11e8-11f9-7d13ad32a3b2") => ("Statistics", nothing),
    UUID("4607b0f0-06f3-5cda-b6b1-a6196a1729e9") => ("SuiteSparse", nothing),
    UUID("8dfed614-e22c-5e08-85e1-65c5234f0b40") => ("Test", nothing),
    UUID("cf7118a7-6976-5b1a-9a39-7adc72f591a4") => ("UUIDs", nothing),
    UUID("4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5") => ("Unicode", nothing),
)
n   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Pkg/src/project.jl�      #########
# UTILS #
#########
listed_deps(project::Project) =
    append!(collect(keys(project.deps)), collect(keys(project.extras)), collect(keys(project.weakdeps)))

###########
# READING #
###########
read_project_uuid(::Nothing) = nothing
function read_project_uuid(uuid::String)
    try uuid = UUID(uuid)
    catch err
        err isa ArgumentError || rethrow()
        pkgerror("Could not parse project UUID as a UUID")
    end
    return uuid
end
read_project_uuid(uuid) = pkgerror("Expected project UUID to be a string")

read_project_version(::Nothing) = nothing
function read_project_version(version::String)
    try version = VersionNumber(version)
    catch err
        err isa ArgumentError || rethrow()
        pkgerror("Could not parse project version as a version")
    end
end
read_project_version(version) = pkgerror("Expected project version to be a string")

read_project_deps(::Nothing, section::String) = Dict{String,UUID}()
function read_project_deps(raw::Dict{String,Any}, section_name::String)
    deps = Dict{String,UUID}()
    for (name, uuid) in raw
        try
            uuid = UUID(uuid)
        catch err
            err isa ArgumentError || rethrow()
            pkgerror("Malformed value for `$name` in `$(section_name)` section.")
        end
        deps[name] = uuid
    end
    return deps
end
function read_project_deps(raw, section_name::String)
    pkgerror("Expected `$(section_name)` section to be a key-value list")
end

read_project_targets(::Nothing, project::Project) = Dict{String,Any}()
function read_project_targets(raw::Dict{String,Any}, project::Project)
    for (target, deps) in raw
        deps isa Vector{String} || pkgerror("""
            Expected value for target `$target` to be a list of dependency names.
        """)
    end
    return raw
end
read_project_targets(raw, project::Project) =
    pkgerror("Expected `targets` section to be a key-value list")

read_project_compat(::Nothing, project::Project) = Dict{String,Compat}()
function read_project_compat(raw::Dict{String,Any}, project::Project)
    compat = Dict{String,Compat}()
    for (name, version) in raw
        version = version::String
        try
            compat[name] = Compat(semver_spec(version), version)
        catch err
            pkgerror("Could not parse compatibility version for dependency `$name`")
        end
    end
    return compat
end
read_project_compat(raw, project::Project) =
    pkgerror("Expected `compat` section to be a key-value list")

function validate(project::Project; file=nothing)
    # deps
    location_string = file === nothing ? "" : " at $(repr(file))."
    dep_uuids = collect(values(project.deps))
    if length(dep_uuids) != length(unique(dep_uuids))
        pkgerror("Two different dependencies can not have the same uuid" * location_string)
    end
    weak_dep_uuids = collect(values(project.weakdeps))
    if length(weak_dep_uuids) != length(unique(weak_dep_uuids))
        pkgerror("Two different weak dependencies can not have the same uuid" * location_string)
    end
    # extras
    extra_uuids = collect(values(project.extras))
    if length(extra_uuids) != length(unique(extra_uuids))
        pkgerror("Two different `extra` dependencies can not have the same uuid" * location_string)
    end
    # TODO decide what to do in when `add`ing a dep that is already in `extras`
    #   also, reintroduce test files for this
    #=
    dep_names = keys(project.deps)
    for (name, uuid) in project.extras
        name in dep_names && pkgerror("name `$name` is listed in both `deps` and `extras`")
        uuid in dep_uuids && pkgerror("uuid `$uuid` is listed in both `deps` and `extras`")
    end
    =#
    # targets
    listed = listed_deps(project)
    for (target, deps) in project.targets, dep in deps
        if length(deps) != length(unique(deps))
            pkgerror("A dependency was named twice in target `$target`")
        end
        dep in listed || pkgerror("""
            Dependency `$dep` in target `$target` not listed in `deps`, `weakdeps` or `extras` section
            """ * location_string)
    end
    # compat
    for (name, version) in project.compat
        name == "julia" && continue
        name in listed ||
            pkgerror("Compat `$name` not listed in `deps`, `weakdeps` or `extras` section" * location_string)
    end
end

function Project(raw::Dict; file=nothing)
    project = Project()
    project.other    = raw
    project.name     = get(raw, "name", nothing)::Union{String, Nothing}
    project.manifest = get(raw, "manifest", nothing)::Union{String, Nothing}
    project.uuid     = read_project_uuid(get(raw, "uuid", nothing))
    project.version  = read_project_version(get(raw, "version", nothing))
    project.deps     = read_project_deps(get(raw, "deps", nothing), "deps")
    project.weakdeps = read_project_deps(get(raw, "weakdeps", nothing), "weakdeps")
    project.exts     = get(Dict{String, String}, raw, "extensions")
    project.extras   = read_project_deps(get(raw, "extras", nothing), "extras")
    project.compat   = read_project_compat(get(raw, "compat", nothing), project)
    project.targets  = read_project_targets(get(raw, "targets", nothing), project)

    # Handle deps in both [deps] and [weakdeps]
    project._deps_weak = Dict(intersect(project.deps, project.weakdeps))
    filter!(p->!haskey(project._deps_weak, p.first), project.deps)
    validate(project; file)
    return project
end

function read_project(f_or_io::Union{String, IO})
    raw = try
        if f_or_io isa IO
            TOML.parse(read(f_or_io, String))
        else
            isfile(f_or_io) ? parse_toml(f_or_io) : return Project()
        end
    catch e
        if e isa TOML.ParserError
            pkgerror("Could not parse project: ", sprint(showerror, e))
        end
        rethrow()
    end
    return Project(raw; file= f_or_io isa IO ? nothing : f_or_io)
end


###########
# WRITING #
###########
function destructure(project::Project)::Dict
    raw = deepcopy(project.other)

    # sanity check for consistency between compat value and string representation
    for (name, compat) in project.compat
        if compat.val != semver_spec(compat.str)
            pkgerror("inconsistency between compat values and string representation")
        end
    end

    # if a field is set to its default value, don't include it in the write
    function entry!(key::String, src)
        should_delete(x::Dict) = isempty(x)
        should_delete(x)       = x === nothing
        should_delete(src) ? delete!(raw, key) : (raw[key] = src)
    end

    entry!("name",     project.name)
    entry!("uuid",     project.uuid)
    entry!("version",  project.version)
    entry!("manifest", project.manifest)
    entry!("deps",     merge(project.deps, project._deps_weak))
    entry!("weakdeps", project.weakdeps)
    entry!("extras",   project.extras)
    entry!("compat",   Dict(name => x.str for (name, x) in project.compat))
    entry!("targets",  project.targets)
    return raw
end

const _project_key_order = ["name", "uuid", "keywords", "license", "desc", "deps", "weakdeps", "extensions", "compat"]
project_key_order(key::String) =
    something(findfirst(x -> x == key, _project_key_order), length(_project_key_order) + 1)

function write_project(env::EnvCache)
    mkpath(dirname(env.project_file))
    write_project(env.project, env.project_file)
end
write_project(project::Project, project_file::AbstractString) =
    write_project(destructure(project), project_file)
function write_project(io::IO, project::Dict)
    TOML.print(io, project, sorted=true, by=key -> (project_key_order(key), key)) do x
        x isa UUID || x isa VersionNumber || pkgerror("unhandled type `$(typeof(x))`")
        return string(x)
    end
    return nothing
end
function write_project(project::Dict, project_file::AbstractString)
    str = sprint(write_project, project)
    write(project_file, str)
end
o   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Pkg/src/manifest.jl�7      ###########
# READING #
###########
function read_field(name::String, default, info, map)
    x = get(info, name, default)
    if default === nothing
        x === nothing && return nothing
    else
        x == default && return default
    end
    x isa String || pkgerror("Expected field `$name` to be a String.")
    return map(x)
end

function read_pinned(pinned)
    pinned === nothing && return false
    pinned isa Bool && return pinned
    pkgerror("Expected field `pinned` to be a Boolean.")
end

function safe_SHA1(sha::String)
    try sha = SHA1(sha)
    catch err
        err isa ArgumentError || rethrow()
        pkgerror("Could not parse `git-tree-sha1` field as a SHA.")
    end
    return sha
end

function safe_uuid(uuid::String)::UUID
    try uuid = UUID(uuid)
    catch err
        err isa ArgumentError || rethrow()
        pkgerror("Could not parse `uuid` field as a UUID.")
    end
    return uuid
end

function safe_bool(bool::String)
    try bool = parse(Bool, bool)
    catch err
        err isa ArgumentError || rethrow()
        pkgerror("Could not parse `pinned` field as a Bool.")
    end
    return bool
end

# note: returns raw version *not* parsed version
function safe_version(version::String)::VersionNumber
    try version = VersionNumber(version)
    catch err
        err isa ArgumentError || rethrow()
        pkgerror("Could not parse `version` as a `VersionNumber`.")
    end
    return version
end

# turn /-paths into \-paths on Windows
function safe_path(path::String)
    if Sys.iswindows() && !isabspath(path)
        path = joinpath(split(path, "/")...)
    end
    return path
end

read_deps(::Nothing) = Dict{String, UUID}()
read_deps(deps) = pkgerror("Expected `deps` field to be either a list or a table.")
function read_deps(deps::AbstractVector)
    ret = String[]
    for dep in deps
        dep isa String || pkgerror("Expected `dep` entry to be a String.")
        push!(ret, dep)
    end
    return ret
end
function read_deps(raw::Dict{String, Any})::Dict{String,UUID}
    deps = Dict{String,UUID}()
    for (name, uuid) in raw
        deps[name] = safe_uuid(uuid)
    end
    return deps
end

struct Stage1
    uuid::UUID
    entry::PackageEntry
    deps::Union{Vector{String}, Dict{String,UUID}}
    weakdeps::Union{Vector{String}, Dict{String,UUID}}
end

normalize_deps(name, uuid, deps, manifest; isext=false) = deps
function normalize_deps(name, uuid, deps::Vector{String}, manifest::Dict{String,Vector{Stage1}}; isext=false)
    if length(deps) != length(unique(deps))
        pkgerror("Duplicate entry in `$name=$uuid`'s `deps` field.")
    end
    final = Dict{String,UUID}()
    for dep in deps
        infos = get(manifest, dep, nothing)
        if !isext
            if infos === nothing
                pkgerror("`$name=$uuid` depends on `$dep`, ",
                        "but no such entry exists in the manifest.")
            end
        end
        # should have used dict format instead of vector format
        if isnothing(infos) || length(infos) != 1
            pkgerror("Invalid manifest format. ",
                    "`$name=$uuid`'s dependency on `$dep` is ambiguous.")
        end
        final[dep] = infos[1].uuid
    end
    return final
end

function validate_manifest(julia_version::Union{Nothing,VersionNumber}, manifest_format::VersionNumber, stage1::Dict{String,Vector{Stage1}}, other::Dict{String, Any})
    # expand vector format deps
    for (name, infos) in stage1, info in infos
        info.entry.deps = normalize_deps(name, info.uuid, info.deps, stage1)
    end
    for (name, infos) in stage1, info in infos
        info.entry.weakdeps = normalize_deps(name, info.uuid, info.weakdeps, stage1; isext=true)
    end
    # invariant: all dependencies are now normalized to Dict{String,UUID}
    deps = Dict{UUID, PackageEntry}()
    for (name, infos) in stage1, info in infos
        deps[info.uuid] = info.entry
    end
    # now just verify the graph structure
    for (entry_uuid, entry) in deps
        for (deptype, isext) in [(entry.deps, false), (entry.weakdeps, true)]
            for (name, uuid) in deptype
                dep_entry = get(deps, uuid, nothing)
                if !isext
                    if dep_entry === nothing
                        pkgerror("`$(entry.name)=$(entry_uuid)` depends on `$name=$uuid`, ",
                                "but no such entry exists in the manifest.")
                    end
                    if dep_entry.name != name
                        pkgerror("`$(entry.name)=$(entry_uuid)` depends on `$name=$uuid`, ",
                                "but entry with UUID `$uuid` has name `$(dep_entry.name)`.")
                    end
                end
            end
        end
    end
    return Manifest(; julia_version, manifest_format, deps, other)
end

function Manifest(raw::Dict{String, Any}, f_or_io::Union{String, IO})::Manifest
    julia_version = haskey(raw, "julia_version") ? VersionNumber(raw["julia_version"]::String) : nothing
    manifest_format = VersionNumber(raw["manifest_format"]::String)
    if !in(manifest_format.major, 1:2)
        if f_or_io isa IO
            @warn "Unknown Manifest.toml format version detected in streamed manifest. Unexpected behavior may occur" manifest_format
        else
            @warn "Unknown Manifest.toml format version detected in file `$(f_or_io)`. Unexpected behavior may occur" manifest_format maxlog = 1 _id = Symbol(f_or_io)
        end
    end
    stage1 = Dict{String,Vector{Stage1}}()
    if haskey(raw, "deps") # deps field doesn't exist if there are no deps
        deps_raw = raw["deps"]::Dict{String, Any}
        for (name::String, infos) in deps_raw
            infos = infos::Vector{Any}
            for info in infos
                info = info::Dict{String, Any}
                entry = PackageEntry()
                entry.name = name
                uuid = nothing
                deps = nothing
                weakdeps = nothing
                try
                    entry.pinned      = read_pinned(get(info, "pinned", nothing))
                    uuid              = read_field("uuid",          nothing, info, safe_uuid)::UUID
                    entry.version     = read_field("version",       nothing, info, safe_version)
                    entry.path        = read_field("path",          nothing, info, safe_path)
                    entry.repo.source = read_field("repo-url",      nothing, info, identity)
                    entry.repo.rev    = read_field("repo-rev",      nothing, info, identity)
                    entry.repo.subdir = read_field("repo-subdir",   nothing, info, identity)
                    entry.tree_hash   = read_field("git-tree-sha1", nothing, info, safe_SHA1)
                    entry.uuid        = uuid
                    deps = read_deps(get(info::Dict, "deps", nothing)::Union{Nothing, Dict{String, Any}, Vector{String}})
                    weakdeps = read_deps(get(info::Dict, "weakdeps", nothing)::Union{Nothing, Dict{String, Any}, Vector{String}})
                    entry.exts = get(Dict{String, String}, info, "extensions")
                catch
                    # TODO: Should probably not unconditionally log something
                    # @debug "Could not parse manifest entry for `$name`" f_or_io
                    rethrow()
                end
                entry.other = info
                stage1[name] = push!(get(stage1, name, Stage1[]), Stage1(uuid, entry, deps, weakdeps))
            end
        end
        # by this point, all the fields of the `PackageEntry`s have been type casted
        # but we have *not* verified the _graph_ structure of the manifest
    end
    other = Dict{String, Any}()
    for (k, v) in raw
        if k in ("julia_version", "deps", "manifest_format")
            continue
        end
        other[k] = v
    end
    return validate_manifest(julia_version, manifest_format, stage1, other)
end

function read_manifest(f_or_io::Union{String, IO})
    raw = try
        if f_or_io isa IO
            TOML.parse(read(f_or_io, String))
        else
            isfile(f_or_io) ? parse_toml(f_or_io) : return Manifest()
        end
    catch e
        if e isa TOML.ParserError
            pkgerror("Could not parse manifest: ", sprint(showerror, e))
        end
        rethrow()
    end
    if Base.is_v1_format_manifest(raw)
        raw = convert_v1_format_manifest(raw)
    end
    return Manifest(raw, f_or_io)
end

function convert_v1_format_manifest(old_raw_manifest::Dict)
    new_raw_manifest = Dict{String, Any}(
            "deps" => old_raw_manifest,
            "manifest_format" => "1.0.0" # must be a string here to match raw dict
            # don't set julia_version as it is unknown in old manifests
        )
    return new_raw_manifest
end

###########
# WRITING #
###########
function destructure(manifest::Manifest)::Dict
    function entry!(entry, key, value; default=nothing)
        if value == default
            delete!(entry, key)
        else
            entry[key] = value
        end
    end

    unique_name = Dict{String,Bool}()
    for (uuid, entry) in manifest
        unique_name[entry.name] = !haskey(unique_name, entry.name)
    end

    # maintain the format of the manifest when writing
    if manifest.manifest_format.major == 1
        raw = Dict{String,Vector{Dict{String,Any}}}()
    elseif manifest.manifest_format.major == 2
        raw = Dict{String,Any}()
        if !isnothing(manifest.julia_version) # don't write julia_version if nothing
            raw["julia_version"] = manifest.julia_version
        end
        raw["manifest_format"] = string(manifest.manifest_format.major, ".", manifest.manifest_format.minor)
        raw["deps"] = Dict{String,Vector{Dict{String,Any}}}()
        for (k, v) in manifest.other
            raw[k] = v
        end
    end

    for (uuid, entry) in manifest
        new_entry = something(entry.other, Dict{String,Any}())
        new_entry["uuid"] = string(uuid)
        entry!(new_entry, "version", entry.version)
        entry!(new_entry, "git-tree-sha1", entry.tree_hash)
        entry!(new_entry, "pinned", entry.pinned; default=false)
        path = entry.path
        if path !== nothing && Sys.iswindows() && !isabspath(path)
            path = join(splitpath(path), "/")
        end
        entry!(new_entry, "path", path)
        repo_source = entry.repo.source
        if repo_source !== nothing && Sys.iswindows() && !isabspath(repo_source) && !isurl(repo_source)
            repo_source = join(splitpath(repo_source), "/")
        end
        entry!(new_entry, "repo-url", repo_source)
        entry!(new_entry, "repo-rev", entry.repo.rev)
        entry!(new_entry, "repo-subdir", entry.repo.subdir)
        for (deptype, depname) in [(entry.deps, "deps"), (entry.weakdeps, "weakdeps")]
            if isempty(deptype)
                delete!(new_entry, depname)
            else
                if all(dep -> haskey(unique_name, first(dep)), deptype) && all(dep -> unique_name[first(dep)], deptype)
                    new_entry[depname] = sort(collect(keys(deptype)))
                else
                    new_entry[depname] = Dict{String,String}()
                    for (name, uuid) in deptype
                        new_entry[depname][name] = string(uuid)
                    end
                end
            end
        end

        # TODO: Write this inline
        if !isempty(entry.exts)
            entry!(new_entry, "extensions", entry.exts)
        end
        if manifest.manifest_format.major == 1
            push!(get!(raw, entry.name, Dict{String,Any}[]), new_entry)
        elseif manifest.manifest_format.major == 2
            push!(get!(raw["deps"], entry.name, Dict{String,Any}[]), new_entry)
        end
    end
    return raw
end

function write_manifest(env::EnvCache)
    mkpath(dirname(env.manifest_file))
    write_manifest(env.manifest, env.manifest_file)
end
function write_manifest(manifest::Manifest, manifest_file::AbstractString)
    if manifest.manifest_format.major == 1
        @warn """The active manifest file at `$(manifest_file)` has an old format that is being maintained.
            To update to the new format, which is supported by Julia versions ≥ 1.6.2, run `import Pkg; Pkg.upgrade_manifest()` which will upgrade the format without re-resolving.
            To then record the julia version re-resolve with `Pkg.resolve()` and if there are resolve conflicts consider `Pkg.update()`.""" maxlog = 1 _id = Symbol(manifest_file)
    end
    return write_manifest(destructure(manifest), manifest_file)
end
function write_manifest(io::IO, manifest::Manifest)
    return write_manifest(io, destructure(manifest))
end
function write_manifest(io::IO, raw_manifest::Dict)
    print(io, "# This file is machine-generated - editing it directly is not advised\n\n")
    TOML.print(io, raw_manifest, sorted=true) do x
        (typeof(x) in [String, Nothing, UUID, SHA1, VersionNumber]) && return string(x)
        error("unhandled type `$(typeof(x))`")
    end
    return nothing
end
function write_manifest(raw_manifest::Dict, manifest_file::AbstractString)
    str = sprint(write_manifest, raw_manifest)
    write(manifest_file, str)
end

############
# METADATA #
############

function check_warn_manifest_julia_version_compat(manifest::Manifest, manifest_file::String)
    isempty(manifest.deps) && return
    if manifest.manifest_format < v"2"
        @warn """The active manifest file is an older format with no julia version entry. Dependencies may have \
        been resolved with a different julia version.""" maxlog = 1 _file = manifest_file _line = 0 _module = nothing
        return
    end
    v = manifest.julia_version
    if v === nothing
        @warn """The active manifest file is missing a julia version entry. Dependencies may have \
        been resolved with a different julia version.""" maxlog = 1 _file = manifest_file _line = 0 _module = nothing
        return
    end
    if Base.thisminor(v) != Base.thisminor(VERSION)
        @warn """The active manifest file has dependencies that were resolved with a different julia \
        version ($(manifest.julia_version)). Unexpected behavior may occur.""" maxlog = 1 _file = manifest_file _line = 0 _module = nothing
    end
end
}   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Pkg/src/BinaryPlatforms_compat.jl]      module BinaryPlatforms

using Base.BinaryPlatforms
export platform_key_abi, platform_dlext, valid_dl_path, arch, libc,
       libgfortran_version, libstdcxx_version, cxxstring_abi, parse_dl_name_version,
       detect_libgfortran_version, detect_libstdcxx_version, detect_cxxstring_abi,
       call_abi, wordsize, triplet, select_platform, platforms_match,
       CompilerABI, Platform, UnknownPlatform, Linux, MacOS, Windows, FreeBSD

import Base.BinaryPlatforms: libgfortran_version, libstdcxx_version, platform_name,
                             wordsize, platform_dlext, tags, arch, libc, call_abi,
                             cxxstring_abi

struct UnknownPlatform <: AbstractPlatform
    UnknownPlatform(args...; kwargs...) = new()
end
tags(::UnknownPlatform) = Dict{String,String}("os"=>"unknown")


struct CompilerABI
    libgfortran_version::Union{Nothing,VersionNumber}
    libstdcxx_version::Union{Nothing,VersionNumber}
    cxxstring_abi::Union{Nothing,Symbol}

    function CompilerABI(;libgfortran_version::Union{Nothing, VersionNumber} = nothing,
                         libstdcxx_version::Union{Nothing, VersionNumber} = nothing,
                         cxxstring_abi::Union{Nothing, Symbol} = nothing)
        return new(libgfortran_version, libstdcxx_version, cxxstring_abi)
    end
end

# Easy replacement constructor
function CompilerABI(cabi::CompilerABI; libgfortran_version=nothing,
                                        libstdcxx_version=nothing,
                                        cxxstring_abi=nothing)
    return CompilerABI(;
        libgfortran_version=something(libgfortran_version, Some(cabi.libgfortran_version)),
        libstdcxx_version=something(libstdcxx_version, Some(cabi.libstdcxx_version)),
        cxxstring_abi=something(cxxstring_abi, Some(cabi.cxxstring_abi)),
    )
end

libgfortran_version(cabi::CompilerABI) = cabi.libgfortran_version
libstdcxx_version(cabi::CompilerABI) = cabi.libstdcxx_version
cxxstring_abi(cabi::CompilerABI) = cabi.cxxstring_abi

for T in (:Linux, :Windows, :MacOS, :FreeBSD)
    @eval begin
        struct $(T) <: AbstractPlatform
            p::Platform
            function $(T)(arch::Symbol; compiler_abi=nothing, kwargs...)
                if compiler_abi !== nothing
                    kwargs = (; kwargs...,
                        :libgfortran_version => libgfortran_version(compiler_abi),
                        :libstdcxx_version => libstdcxx_version(compiler_abi),
                        :cxxstring_abi => cxxstring_abi(compiler_abi)
                    )
                end
                return new(Platform(string(arch), $(string(T)); kwargs..., validate_strict=true))
            end
        end
    end
end

const PlatformUnion = Union{Linux,MacOS,Windows,FreeBSD}

# First, methods we need to coerce to Symbol for backwards-compatibility
for f in (:arch, :libc, :call_abi, :cxxstring_abi)
    @eval begin
        function $(f)(p::PlatformUnion)
            str = $(f)(p.p)
            if str === nothing
                return nothing
            end
            return Symbol(str)
        end
    end
end

# Next, things we don't need to coerce
for f in (:libgfortran_version, :libstdcxx_version, :platform_name, :wordsize, :platform_dlext, :tags, :triplet)
    @eval begin
        $(f)(p::PlatformUnion) = $(f)(p.p)
    end
end

# Finally, add equality testing between these wrapper types and other AbstractPlatforms
@eval begin
    Base.:(==)(a::PlatformUnion, b::AbstractPlatform) = b == a.p
end

# Add one-off functions
MacOS(; kwargs...) = MacOS(:x86_64; kwargs...)
FreeBSD(; kwargs...) = FreeBSD(:x86_64; kwargs...)

function triplet(p::AbstractPlatform)
    # We are going to sub off to `Base.BinaryPlatforms.triplet()` here,
    # with the important exception that we override `os_version` to better
    # mimic the old behavior of `triplet()`
    if Sys.isfreebsd(p)
        p = deepcopy(p)
        p["os_version"] = "11.1.0"
    elseif Sys.isapple(p)
        p = deepcopy(p)
        p["os_version"] = "14.0.0"
    end
    return Base.BinaryPlatforms.triplet(p)
end

"""
    platform_key_abi(machine::AbstractString)

Returns the platform key for the current platform, or any other though the
the use of the `machine` parameter.

This method is deprecated, import `Base.BinaryPlatforms` and use either `HostPlatform()`
to get the current host platform, or `parse(Base.BinaryPlatforms.Platform, triplet)`
to parse the triplet for some other platform instead.
"""
platform_key_abi() = HostPlatform()
platform_key_abi(triplet::AbstractString) = parse(Platform, triplet)

"""
    valid_dl_path(path::AbstractString, platform::Platform)

Return `true` if the given `path` ends in a valid dynamic library filename.
E.g. returns `true` for a path like `"usr/lib/libfoo.so.3.5"`, but returns
`false` for a path like `"libbar.so.f.a"`.

This method is deprecated and will be removed in Julia 2.0.
"""
function valid_dl_path(path::AbstractString, platform::AbstractPlatform)
    try
        parse_dl_name_version(path, string(os(platform))::String)
        return true
    catch e
        if isa(e, ArgumentError)
            return false
        end
        rethrow(e)
    end
end

end # module BinaryPlatforms
p   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Pkg/src/Artifacts.jl;a      module Artifacts

using Artifacts, Base.BinaryPlatforms, SHA
using ..MiniProgressBars, ..PlatformEngines
using Tar: can_symlink

import ..set_readonly, ..GitTools, ..TOML, ..pkg_server, ..can_fancyprint,
       ..stderr_f, ..printpkgstyle

import Base: get, SHA1
import Artifacts: artifact_names, ARTIFACTS_DIR_OVERRIDE, ARTIFACT_OVERRIDES, artifact_paths,
                  artifacts_dirs, pack_platform!, unpack_platform, load_artifacts_toml,
                  query_override, with_artifacts_directory, load_overrides
import ..Types: write_env_usage, parse_toml


export create_artifact, artifact_exists, artifact_path, remove_artifact, verify_artifact,
       artifact_meta, artifact_hash, bind_artifact!, unbind_artifact!, download_artifact,
       find_artifacts_toml, ensure_artifact_installed, @artifact_str, archive_artifact,
       select_downloadable_artifacts

"""
    create_artifact(f::Function)

Creates a new artifact by running `f(artifact_path)`, hashing the result, and moving it
to the artifact store (`~/.julia/artifacts` on a typical installation).  Returns the
identifying tree hash of this artifact.
"""
function create_artifact(f::Function)
    # Ensure the `artifacts` directory exists in our default depot
    artifacts_dir = first(artifacts_dirs())
    mkpath(artifacts_dir)

    # Temporary directory where we'll do our creation business
    temp_dir = mktempdir(artifacts_dir)

    try
        # allow the user to do their work inside the temporary directory
        f(temp_dir)

        # Calculate the tree hash for this temporary directory
        artifact_hash = SHA1(GitTools.tree_hash(temp_dir))

        # If we created a dupe, just let the temp directory get destroyed. It's got the
        # same contents as whatever already exists after all, so it doesn't matter.  Only
        # move its contents if it actually contains new contents.  Note that we explicitly
        # set `honor_overrides=false` here, as we wouldn't want to drop things into the
        # system directory by accidentally creating something with the same content-hash
        # as something that was foolishly overridden.  This should be virtually impossible
        # unless the user has been very unwise, but let's be cautious.
        new_path = artifact_path(artifact_hash; honor_overrides=false)
        _mv_temp_artifact_dir(temp_dir, new_path)

        # Give the people what they want
        return artifact_hash
    finally
        # Always attempt to cleanup
        rm(temp_dir; recursive=true, force=true)
    end
end

"""
    _mv_temp_artifact_dir(temp_dir::String, new_path::String)::Nothing
Either rename the directory at `temp_dir` to `new_path` and set it to read-only
or if `new_path` artifact already exists try to do nothing.
"""
function _mv_temp_artifact_dir(temp_dir::String, new_path::String)::Nothing
    if !isdir(new_path)
        # This next step is like
        # `mv(temp_dir, new_path)`.
        # However, `mv` defaults to `cp` if `rename` returns an error.
        # `cp` is not atomic, so avoid the potential of calling it.
        err = ccall(:jl_fs_rename, Int32, (Cstring, Cstring), temp_dir, new_path)
        # Ignore rename error, but ensure `new_path` exists.
        if !isdir(new_path)
            error("$(repr(new_path)) could not be made")
        end
        chmod(new_path, filemode(dirname(new_path)))
        set_readonly(new_path)
    end
    nothing
end

"""
    remove_artifact(hash::SHA1; honor_overrides::Bool=false)

Removes the given artifact (identified by its SHA1 git tree hash) from disk.  Note that
if an artifact is installed in multiple depots, it will be removed from all of them.  If
an overridden artifact is requested for removal, it will be silently ignored; this method
will never attempt to remove an overridden artifact.

In general, we recommend that you use `Pkg.gc()` to manage artifact installations and do
not use `remove_artifact()` directly, as it can be difficult to know if an artifact is
being used by another package.
"""
function remove_artifact(hash::SHA1)
    if query_override(hash) !== nothing
        # We never remove overridden artifacts.
        return
    end

    # Get all possible paths (rooted in all depots)
    possible_paths = artifacts_dirs(bytes2hex(hash.bytes))
    for path in possible_paths
        if isdir(path)
            rm(path; recursive=true, force=true)
        end
    end
end

"""
    verify_artifact(hash::SHA1; honor_overrides::Bool=false)

Verifies that the given artifact (identified by its SHA1 git tree hash) is installed on-
disk, and retains its integrity.  If the given artifact is overridden, skips the
verification unless `honor_overrides` is set to `true`.
"""
function verify_artifact(hash::SHA1; honor_overrides::Bool=false)
    # Silently skip overridden artifacts unless we really ask for it
    if !honor_overrides
        if query_override(hash) !== nothing
            return true
        end
    end

    # If it doesn't even exist, then skip out
    if !artifact_exists(hash)
        return false
    end

    # Otherwise actually run the verification
    return all(hash.bytes .== GitTools.tree_hash(artifact_path(hash)))
end

"""
    archive_artifact(hash::SHA1, tarball_path::String; honor_overrides::Bool=false)

Archive an artifact into a tarball stored at `tarball_path`, returns the SHA256 of the
resultant tarball as a hexadecimal string. Throws an error if the artifact does not
exist.  If the artifact is overridden, throws an error unless `honor_overrides` is set.
"""
function archive_artifact(hash::SHA1, tarball_path::String; honor_overrides::Bool=false)
    if !honor_overrides
        if query_override(hash) !== nothing
            error("Will not archive an overridden artifact unless `honor_overrides` is set!")
        end
    end

    if !artifact_exists(hash)
        error("Unable to archive artifact $(bytes2hex(hash.bytes)): does not exist!")
    end

    # Package it up
    package(artifact_path(hash), tarball_path)

    # Calculate its sha256 and return that
    return open(tarball_path, "r") do io
        return bytes2hex(sha256(io))
    end
end

"""
    bind_artifact!(artifacts_toml::String, name::String, hash::SHA1;
                   platform::Union{AbstractPlatform,Nothing} = nothing,
                   download_info::Union{Vector{Tuple},Nothing} = nothing,
                   lazy::Bool = false,
                   force::Bool = false)

Writes a mapping of `name` -> `hash` within the given `(Julia)Artifacts.toml` file. If
`platform` is not `nothing`, this artifact is marked as platform-specific, and will be
a multi-mapping.  It is valid to bind multiple artifacts with the same name, but
different `platform`s and `hash`'es within the same `artifacts_toml`.  If `force` is set
to `true`, this will overwrite a pre-existant mapping, otherwise an error is raised.

`download_info` is an optional vector that contains tuples of URLs and a hash.  These
URLs will be listed as possible locations where this artifact can be obtained.  If `lazy`
is set to `true`, even if download information is available, this artifact will not be
downloaded until it is accessed via the `artifact"name"` syntax, or
`ensure_artifact_installed()` is called upon it.
"""
function bind_artifact!(artifacts_toml::String, name::String, hash::SHA1;
                        platform::Union{AbstractPlatform,Nothing} = nothing,
                        download_info::Union{Vector{<:Tuple},Nothing} = nothing,
                        lazy::Bool = false,
                        force::Bool = false)
    # First, check to see if this artifact is already bound:
    if isfile(artifacts_toml)
        artifact_dict = parse_toml(artifacts_toml)

        if !force && haskey(artifact_dict, name)
            meta = artifact_dict[name]
            if !isa(meta, Vector)
                error("Mapping for '$name' within $(artifacts_toml) already exists!")
            elseif any(isequal(platform), unpack_platform(x, name, artifacts_toml) for x in meta)
                error("Mapping for '$name'/$(triplet(platform)) within $(artifacts_toml) already exists!")
            end
        end
    else
        artifact_dict = Dict{String, Any}()
    end

    # Otherwise, the new piece of data we're going to write out is this dict:
    meta = Dict{String,Any}(
        "git-tree-sha1" => bytes2hex(hash.bytes),
    )

    # If we're set to be lazy, then lazy we shall be
    if lazy
        meta["lazy"] = true
    end

    # Integrate download info, if it is given.  We represent the download info as a
    # vector of dicts, each with its own `url` and `sha256`, since different tarballs can
    # expand to the same tree hash.
    if download_info !== nothing
        meta["download"] = [
            Dict("url" => dl[1],
                 "sha256" => dl[2],
            ) for dl in download_info
        ]
    end

    if platform === nothing
        artifact_dict[name] = meta
    else
        # Add platform-specific keys to our `meta` dict
        pack_platform!(meta, platform)

        # Insert this entry into the list of artifacts
        if !haskey(artifact_dict, name)
            artifact_dict[name] = [meta]
        else
            # Delete any entries that contain identical platforms
            artifact_dict[name] = filter(
                x -> unpack_platform(x, name, artifacts_toml) != platform,
                artifact_dict[name]
            )
            push!(artifact_dict[name], meta)
        end
    end

    # Spit it out onto disk
    let artifact_dict = artifact_dict
        parent_dir = dirname(artifacts_toml)
        temp_artifacts_toml = isempty(parent_dir) ? tempname(pwd()) : tempname(parent_dir)
        open(temp_artifacts_toml, "w") do io
            TOML.print(io, artifact_dict, sorted=true)
        end
        mv(temp_artifacts_toml, artifacts_toml; force=true)
    end

    # Mark that we have used this Artifact.toml
    write_env_usage(artifacts_toml, "artifact_usage.toml")
    return
end


"""
    unbind_artifact!(artifacts_toml::String, name::String; platform = nothing)

Unbind the given `name` from an `(Julia)Artifacts.toml` file.
Silently fails if no such binding exists within the file.
"""
function unbind_artifact!(artifacts_toml::String, name::String;
                         platform::Union{AbstractPlatform,Nothing} = nothing)
    artifact_dict = parse_toml(artifacts_toml)
    if !haskey(artifact_dict, name)
        return
    end

    if platform === nothing
        delete!(artifact_dict, name)
    else
        artifact_dict[name] = filter(
            x -> unpack_platform(x, name, artifacts_toml) != platform,
            artifact_dict[name]
        )
    end

    open(artifacts_toml, "w") do io
        TOML.print(io, artifact_dict, sorted=true)
    end
    return
end

"""
    download_artifact(tree_hash::SHA1, tarball_url::String, tarball_hash::String;
                      verbose::Bool = false, io::IO=stderr)

Download/install an artifact into the artifact store.  Returns `true` on success,
returns an error object on failure.

!!! compat "Julia 1.8"
    As of Julia 1.8 this function returns the error object rather than `false` when
    failure occurs
"""
function download_artifact(
    tree_hash::SHA1,
    tarball_url::String,
    tarball_hash::Union{String, Nothing} = nothing;
    verbose::Bool = false,
    quiet_download::Bool = false,
    io::IO=stderr_f(),
)
    if artifact_exists(tree_hash)
        return true
    end

    # Ensure the `artifacts` directory exists in our default depot
    artifacts_dir = first(artifacts_dirs())
    mkpath(artifacts_dir)
    # expected artifact path
    dst = joinpath(artifacts_dir, bytes2hex(tree_hash.bytes))

    # We download by using a temporary directory.  We do this because the download may
    # be corrupted or even malicious; we don't want to clobber someone else's artifact
    # by trusting the tree hash that has been given to us; we will instead download it
    # to a temporary directory, calculate the true tree hash, then move it to the proper
    # location only after knowing what it is, and if something goes wrong in the process,
    # everything should be cleaned up.

    # Temporary directory where we'll do our creation business
    temp_dir = mktempdir(artifacts_dir)

    try
        download_verify_unpack(tarball_url, tarball_hash, temp_dir, ignore_existence=true, verbose=verbose,
                quiet_download=quiet_download, io=io)
        calc_hash = SHA1(GitTools.tree_hash(temp_dir))

        # Did we get what we expected?  If not, freak out.
        if calc_hash.bytes != tree_hash.bytes
            msg = """
            Tree Hash Mismatch!
              Expected git-tree-sha1:   $(bytes2hex(tree_hash.bytes))
              Calculated git-tree-sha1: $(bytes2hex(calc_hash.bytes))
            """
            # Since tree hash calculation is rather fragile and file system dependent,
            # we allow setting JULIA_PKG_IGNORE_HASHES=1 to ignore the error and move
            # the artifact to the expected location and return true
            ignore_hash_env_set = get(ENV, "JULIA_PKG_IGNORE_HASHES", "") != ""
            if ignore_hash_env_set
                ignore_hash = Base.get_bool_env("JULIA_PKG_IGNORE_HASHES", false)
                ignore_hash === nothing && @error(
                    "Invalid ENV[\"JULIA_PKG_IGNORE_HASHES\"] value",
                    ENV["JULIA_PKG_IGNORE_HASHES"],
                )
                ignore_hash = something(ignore_hash, false)
            else
                # default: false except Windows users who can't symlink
                ignore_hash = Sys.iswindows() &&
                    !mktempdir(can_symlink, artifacts_dir)
            end
            if ignore_hash
                desc = ignore_hash_env_set ?
                    "Environment variable \$JULIA_PKG_IGNORE_HASHES is true" :
                    "System is Windows and user cannot create symlinks"
                msg *= "\n$desc: \
                    ignoring hash mismatch and moving \
                    artifact to the expected location"
                @error(msg)
            else
                error(msg)
            end
        end
        # Move it to the location we expected
        _mv_temp_artifact_dir(temp_dir, dst)
    catch err
        @debug "download_artifact error" tree_hash tarball_url tarball_hash err
        if isa(err, InterruptException)
            rethrow(err)
        end
        # If something went wrong during download, return the error
        return err
    finally
        # Always attempt to cleanup
        rm(temp_dir; recursive=true, force=true)
    end
    return true
end

"""
    ensure_artifact_installed(name::String, artifacts_toml::String;
                              platform::AbstractPlatform = HostPlatform(),
                              pkg_uuid::Union{Base.UUID,Nothing}=nothing,
                              verbose::Bool = false,
                              quiet_download::Bool = false,
                              io::IO=stderr)

Ensures an artifact is installed, downloading it via the download information stored in
`artifacts_toml` if necessary.  Throws an error if unable to install.
"""
function ensure_artifact_installed(name::String, artifacts_toml::String;
                                   platform::AbstractPlatform = HostPlatform(),
                                   pkg_uuid::Union{Base.UUID,Nothing}=nothing,
                                   verbose::Bool = false,
                                   quiet_download::Bool = false,
                                   io::IO=stderr_f())
    meta = artifact_meta(name, artifacts_toml; pkg_uuid=pkg_uuid, platform=platform)
    if meta === nothing
        error("Cannot locate artifact '$(name)' in '$(artifacts_toml)'")
    end

    return ensure_artifact_installed(name, meta, artifacts_toml; platform=platform,
                                     verbose=verbose, quiet_download=quiet_download, io=io)
end

function ensure_artifact_installed(name::String, meta::Dict, artifacts_toml::String;
                                   platform::AbstractPlatform = HostPlatform(),
                                   verbose::Bool = false,
                                   quiet_download::Bool = false,
                                   io::IO=stderr_f())
    hash = SHA1(meta["git-tree-sha1"])

    if !artifact_exists(hash)
        errors = Any[]
        # first try downloading from Pkg server
        # TODO: only do this if Pkg server knows about this package
        if (server = pkg_server()) !== nothing
            url = "$server/artifact/$hash"
            download_success = let url=url
                @debug "Downloading artifact from Pkg server" name artifacts_toml platform url
                with_show_download_info(io, name, quiet_download) do
                    download_artifact(hash, url; verbose=verbose, quiet_download=quiet_download, io=io)
                end
            end
            # download_success is either `true` or an error object
            if download_success === true
                return artifact_path(hash)
            else
                @debug "Failed to download artifact from Pkg server" download_success
                push!(errors, (url, download_success))
            end
        end

        # If this artifact does not exist on-disk already, ensure it has download
        # information, then download it!
        if !haskey(meta, "download")
            error("Cannot automatically install '$(name)'; no download section in '$(artifacts_toml)'")
        end

        # Attempt to download from all sources
        for entry in meta["download"]
            url = entry["url"]
            tarball_hash = entry["sha256"]
            download_success = let url=url
                @debug "Downloading artifact" name artifacts_toml platform url
                with_show_download_info(io, name, quiet_download) do
                    download_artifact(hash, url, tarball_hash; verbose=verbose, quiet_download=quiet_download, io=io)
                end
            end
            # download_success is either `true` or an error object
            if download_success === true
                return artifact_path(hash)
            else
                @debug "Failed to download artifact" download_success
                push!(errors, (url, download_success))
            end
        end
        errmsg = """
        Unable to automatically download/install artifact '$(name)' from sources listed in '$(artifacts_toml)'.
        Sources attempted:
        """
        for (url, err) in errors
            errmsg *= "- $(url)\n"
            errmsg *= "    Error: $(sprint(showerror, err))\n"
        end
        error(errmsg)
    else
        return artifact_path(hash)
    end
end

function with_show_download_info(f, io, name, quiet_download)
    fancyprint = can_fancyprint(io)
    if !quiet_download
        fancyprint && print_progress_bottom(io)
        printpkgstyle(io, :Downloading, "artifact: $name")
    end
    success = false
    try
        result = f()
        success = result === true
        return result
    finally
        if !quiet_download
            fancyprint && print(io, "\033[1A") # move cursor up one line
            fancyprint && print(io, "\033[2K") # clear line
            if success 
                fancyprint && printpkgstyle(io, :Downloaded, "artifact: $name")
            else
                printpkgstyle(io, :Failure, "artifact: $name", color = :red)
            end
        end
    end
end

"""
    ensure_all_artifacts_installed(artifacts_toml::String;
                                   platform = HostPlatform(),
                                   pkg_uuid = nothing,
                                   include_lazy = false,
                                   verbose = false,
                                   quiet_download = false,
                                   io::IO=stderr)

Installs all non-lazy artifacts from a given `(Julia)Artifacts.toml` file. `package_uuid` must
be provided to properly support overrides from `Overrides.toml` entries in depots.

If `include_lazy` is set to `true`, then lazy packages will be installed as well.

This function is deprecated and should be replaced with the following snippet:

    artifacts = select_downloadable_artifacts(artifacts_toml; platform, include_lazy)
    for name in keys(artifacts)
        ensure_artifact_installed(name, artifacts[name], artifacts_toml; platform=platform)
    end

!!! warning
    This function is deprecated in Julia 1.6 and will be removed in a future version.
    Use `select_downloadable_artifacts()` and `ensure_artifact_installed()` instead.
"""
function ensure_all_artifacts_installed(artifacts_toml::String;
                                        platform::AbstractPlatform = HostPlatform(),
                                        pkg_uuid::Union{Nothing,Base.UUID} = nothing,
                                        include_lazy::Bool = false,
                                        verbose::Bool = false,
                                        quiet_download::Bool = false,
                                        io::IO=stderr_f())
    # This function should not be called anymore; use `select_downloadable_artifacts()` directly.
    Base.depwarn("`ensure_all_artifacts_installed()` is deprecated; iterate over `select_downloadable_artifacts()` output with `ensure_artifact_installed()`.", :ensure_all_artifacts_installed)
    # Collect all artifacts we're supposed to install
    artifacts = select_downloadable_artifacts(artifacts_toml; platform, include_lazy, pkg_uuid)
    for name in keys(artifacts)
        # Otherwise, let's try and install it!
        ensure_artifact_installed(name, artifacts[name], artifacts_toml; platform=platform,
                                  verbose=verbose, quiet_download=quiet_download, io=io)
    end
end

"""
    extract_all_hashes(artifacts_toml::String;
                       platform = HostPlatform(),
                       pkg_uuid = nothing,
                       include_lazy = false)

Extract all hashes from a given `(Julia)Artifacts.toml` file. `package_uuid` must
be provided to properly support overrides from `Overrides.toml` entries in depots.

If `include_lazy` is set to `true`, then lazy packages will be installed as well.
"""
function extract_all_hashes(artifacts_toml::String;
                            platform::AbstractPlatform = HostPlatform(),
                            pkg_uuid::Union{Nothing,Base.UUID} = nothing,
                            include_lazy::Bool = false)
    hashes = Base.SHA1[]
    if !isfile(artifacts_toml)
        return hashes
    end

    artifact_dict = load_artifacts_toml(artifacts_toml; pkg_uuid=pkg_uuid)

    for name in keys(artifact_dict)
        # Get the metadata about this name for the requested platform
        meta = artifact_meta(name, artifact_dict, artifacts_toml; platform=platform)

        # If there are no instances of this name for the desired platform, skip it
        meta === nothing && continue

        # If it's a lazy one and we aren't including lazy ones, skip
        if get(meta, "lazy", false) && !include_lazy
            continue
        end

        # Otherwise, add it to the list!
        push!(hashes, Base.SHA1(meta["git-tree-sha1"]))
    end

    return hashes
end

# Support `AbstractString`s, but avoid compilers needing to track backedges for callers
# of these functions in case a user defines a new type that is `<: AbstractString`
archive_artifact(hash::SHA1, tarball_path::AbstractString; kwargs...) =
    archive_artifact(hash, string(tarball_path)::String; kwargs...)
bind_artifact!(artifacts_toml::AbstractString, name::AbstractString, hash::SHA1; kwargs...) =
    bind_artifact!(string(artifacts_toml)::String, string(name)::String, hash; kwargs...)
unbind_artifact!(artifacts_toml::AbstractString, name::AbstractString) =
    unbind_artifact!(string(artifacts_toml)::String, string(name)::String)
download_artifact(tree_hash::SHA1, tarball_url::AbstractString, args...; kwargs...) =
    download_artifact(tree_hash, string(tarball_url)::String, args...; kwargs...)
ensure_artifact_installed(name::AbstractString, artifacts_toml::AbstractString; kwargs...) =
    ensure_artifact_installed(string(name)::String, string(artifacts_toml)::String; kwargs...)
ensure_artifact_installed(name::AbstractString, meta::Dict, artifacts_toml::AbstractString; kwargs...) =
    ensure_artifact_installed(string(name)::String, meta, string(artifacts_toml)::String; kwargs...)
ensure_all_artifacts_installed(artifacts_toml::AbstractString; kwargs...) =
    ensure_all_artifacts_installed(string(artifacts_toml)::String; kwargs...)
extract_all_hashes(artifacts_toml::AbstractString; kwargs...) =
    extract_all_hashes(string(artifacts_toml)::String; kwargs...)

end # module Artifacts
q   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Pkg/src/Operations.jl�     # This file is a part of Julia. License is MIT: https://julialang.org/license

module Operations

using UUIDs
using Random: randstring
import LibGit2, Dates, TOML

import REPL
using REPL.TerminalMenus
using ..Types, ..Resolve, ..PlatformEngines, ..GitTools, ..MiniProgressBars
import ..depots, ..depots1, ..devdir, ..set_readonly, ..Types.PackageEntry
import ..Artifacts: ensure_artifact_installed, artifact_names, extract_all_hashes,
                    artifact_exists, select_downloadable_artifacts
using Base.BinaryPlatforms
import ...Pkg
import ...Pkg: pkg_server, Registry, pathrepr, can_fancyprint, printpkgstyle, stderr_f, OFFLINE_MODE
import ...Pkg: UPDATED_REGISTRY_THIS_SESSION, RESPECT_SYSIMAGE_VERSIONS, should_autoprecompile

#########
# Utils #
#########

function default_preserve()
    if Base.get_bool_env("JULIA_PKG_PRESERVE_TIERED_INSTALLED", false)
        PRESERVE_TIERED_INSTALLED
    else
        PRESERVE_TIERED
    end
end

function find_installed(name::String, uuid::UUID, sha1::SHA1)
    slug_default = Base.version_slug(uuid, sha1)
    # 4 used to be the default so look there first
    for slug in (slug_default, Base.version_slug(uuid, sha1, 4))
        for depot in depots()
            path = abspath(depot, "packages", name, slug)
            ispath(path) && return path
        end
    end
    return abspath(depots1(), "packages", name, slug_default)
end

# more accurate name is `should_be_tracking_registered_version`
# the only way to know for sure is to key into the registries
tracking_registered_version(pkg::Union{PackageSpec, PackageEntry}, julia_version=VERSION) =
    !is_stdlib(pkg.uuid, julia_version) && pkg.path === nothing && pkg.repo.source === nothing

function source_path(manifest_file::String, pkg::Union{PackageSpec, PackageEntry}, julia_version = VERSION)
    pkg.tree_hash   !== nothing ? find_installed(pkg.name, pkg.uuid, pkg.tree_hash) :
    pkg.path        !== nothing ? joinpath(dirname(manifest_file), pkg.path) :
    is_or_was_stdlib(pkg.uuid, julia_version) ? Types.stdlib_path(pkg.name) :
    nothing
end

#TODO rename
function load_version(version, fixed, preserve::PreserveLevel)
    if version === nothing
        return VersionSpec() # some stdlibs dont have a version
    elseif fixed
        return version # dont change state if a package is fixed
    elseif preserve == PRESERVE_ALL || preserve == PRESERVE_ALL_INSTALLED || preserve == PRESERVE_DIRECT
        return something(version, VersionSpec())
    elseif preserve == PRESERVE_SEMVER && version != VersionSpec()
        return Types.semver_spec("$(version.major).$(version.minor).$(version.patch)")
    elseif preserve == PRESERVE_NONE
        return VersionSpec()
    end
end

function load_direct_deps(env::EnvCache, pkgs::Vector{PackageSpec}=PackageSpec[];
                          preserve::PreserveLevel=PRESERVE_DIRECT)
    pkgs = copy(pkgs)
    for (name::String, uuid::UUID) in env.project.deps
        findfirst(pkg -> pkg.uuid == uuid, pkgs) === nothing || continue # do not duplicate packages
        entry = manifest_info(env.manifest, uuid)
        push!(pkgs, entry === nothing ?
              PackageSpec(;uuid=uuid, name=name) :
              PackageSpec(;
                uuid      = uuid,
                name      = name,
                path      = entry.path,
                repo      = entry.repo,
                pinned    = entry.pinned,
                tree_hash = entry.tree_hash, # TODO should tree_hash be changed too?
                version   = load_version(entry.version, isfixed(entry), preserve),
              ))
    end
    return pkgs
end

function load_manifest_deps(manifest::Manifest, pkgs::Vector{PackageSpec}=PackageSpec[];
                            preserve::PreserveLevel=PRESERVE_ALL)
    pkgs = copy(pkgs)
    for (uuid, entry) in manifest
        findfirst(pkg -> pkg.uuid == uuid, pkgs) === nothing || continue # do not duplicate packages
        push!(pkgs, PackageSpec(
            uuid      = uuid,
            name      = entry.name,
            path      = entry.path,
            pinned    = entry.pinned,
            repo      = entry.repo,
            tree_hash = entry.tree_hash, # TODO should tree_hash be changed too?
            version   = load_version(entry.version, isfixed(entry), preserve),
        ))
    end
    return pkgs
end

function load_all_deps(env::EnvCache, pkgs::Vector{PackageSpec}=PackageSpec[];
                       preserve::PreserveLevel=PRESERVE_ALL)
    pkgs = load_manifest_deps(env.manifest, pkgs; preserve=preserve)
    return load_direct_deps(env, pkgs; preserve=preserve)
end

function is_instantiated(env::EnvCache; platform = HostPlatform())::Bool
    # Load everything
    pkgs = load_all_deps(env)
    # If the top-level project is a package, ensure it is instantiated as well
    if env.pkg !== nothing
        # Top-level project may already be in the manifest (cyclic deps)
        # so only add it if it isn't there
        idx = findfirst(x -> x.uuid == env.pkg.uuid, pkgs)
        if idx === nothing
            push!(pkgs, Types.PackageSpec(name=env.pkg.name, uuid=env.pkg.uuid, version=env.pkg.version, path=dirname(env.project_file)))
        end
    else
        # Make sure artifacts for project exist even if it is not a package
        check_artifacts_downloaded(dirname(env.project_file); platform) || return false
    end
    # Make sure all paths/artifacts exist
    return all(pkg -> is_package_downloaded(env.manifest_file, pkg; platform), pkgs)
end

function update_manifest!(env::EnvCache, pkgs::Vector{PackageSpec}, deps_map, julia_version)
    manifest = env.manifest
    empty!(manifest)
    # if we're updating env.pkg that refers to another manifest, we want to change
    # pkg.path, if present, to be relative to the manifest instead of an abspath
    if env.project.manifest !== nothing && env.pkg.path !== nothing
        env.pkg.path = Types.relative_project_path(env.manifest_file,
                        project_rel_path(env, source_path(env.manifest_file, env.pkg)))
    end
    if env.pkg !== nothing
        pkgs = push!(copy(pkgs), env.pkg::PackageSpec)
    end
    for pkg in pkgs
        entry = PackageEntry(;name = pkg.name, version = pkg.version, pinned = pkg.pinned,
                             tree_hash = pkg.tree_hash, path = pkg.path, repo = pkg.repo, uuid=pkg.uuid)
        if is_stdlib(pkg.uuid, julia_version)
            # Only set stdlib versions for versioned (external) stdlibs
            entry.version = stdlib_version(pkg.uuid, julia_version)
        end
        if Types.is_project(env, pkg)
            entry.deps = env.project.deps
        else
            entry.deps = deps_map[pkg.uuid]
        end
        env.manifest[pkg.uuid] = entry
    end
    prune_manifest(env)
    record_project_hash(env)
end

# This has to be done after the packages have been downloaded
# since we need access to the Project file to read the information
# about extensions
function fixup_ext!(env, pkgs)
    for pkg in pkgs
        v = joinpath(source_path(env.manifest_file, pkg), "Project.toml")
        if haskey(env.manifest, pkg.uuid)
            entry = env.manifest[pkg.uuid]
            if isfile(v)
                p = Types.read_project(v)
                entry.weakdeps = p.weakdeps
                entry.exts = p.exts
                for (name, _) in p.weakdeps
                    if !haskey(p.deps, name)
                        delete!(entry.deps, name)
                    end
                end
            end
        end
    end
    prune_manifest(env)
end

####################
# Registry Loading #
####################

function load_tree_hash!(registries::Vector{Registry.RegistryInstance}, pkg::PackageSpec, julia_version)
    tracking_registered_version(pkg, julia_version) || return pkg
    hash = nothing
    for reg in registries
        reg_pkg = get(reg, pkg.uuid, nothing)
        reg_pkg === nothing && continue
        pkg_info = Registry.registry_info(reg_pkg)
        version_info = get(pkg_info.version_info, pkg.version, nothing)
        version_info === nothing && continue
        hash′ = version_info.git_tree_sha1
        if hash !== nothing
            hash == hash′ || pkgerror("hash mismatch in registries for $(pkg.name) at version $(pkg.version)")
        end
        hash = hash′
    end
    pkg.tree_hash = hash
    return pkg
end

#######################################
# Dependency gathering and resolution #
#######################################
get_compat(proj::Project, name::String) = haskey(proj.compat, name) ? proj.compat[name].val : Types.VersionSpec()
get_compat_str(proj::Project, name::String) = haskey(proj.compat, name) ? proj.compat[name].str : nothing
function set_compat(proj::Project, name::String, compat::String)
    semverspec = Types.semver_spec(compat, throw = false)
    isnothing(semverspec) && return false
    proj.compat[name] = Types.Compat(semverspec, compat)
    return true
end
function set_compat(proj::Project, name::String, ::Nothing)
    delete!(proj.compat, name)
    return true
end

function reset_all_compat!(proj::Project)
    for name in keys(proj.compat)
        compat = proj.compat[name]
        if compat.val != Types.semver_spec(compat.str)
            proj.compat[name] = Types.Compat(Types.semver_spec(compat.str), compat.str)
        end
    end
    return nothing
end

function collect_project(pkg::PackageSpec, path::String)
    deps = PackageSpec[]
    weakdeps = Set{UUID}()
    project_file = projectfile_path(path; strict=true)
    if project_file === nothing
        pkgerror("could not find project file for package $(err_rep(pkg)) at `$path`")
    end
    project = read_package(project_file)
    #=
    # TODO, this should either error or be quiet
    julia_compat = get_compat(project, "julia")
    if julia_compat !== nothing && !(VERSION in julia_compat)
        println(io, "julia version requirement for package $(err_rep(pkg)) not satisfied")
    end
    =#
    for (name, uuid) in project.deps
        vspec = get_compat(project, name)
        push!(deps, PackageSpec(name, uuid, vspec))
    end
    for (name, uuid) in project.weakdeps
        vspec = get_compat(project, name)
        push!(deps, PackageSpec(name, uuid, vspec))
        push!(weakdeps, uuid)
    end
    if project.version !== nothing
        pkg.version = project.version
    else
        # @warn("project file for $(pkg.name) is missing a `version` entry")
        pkg.version = VersionNumber(0)
    end
    return deps, weakdeps
end

is_tracking_path(pkg) = pkg.path !== nothing
is_tracking_repo(pkg) = pkg.repo.source !== nothing
is_tracking_registry(pkg) = !is_tracking_path(pkg) && !is_tracking_repo(pkg)
isfixed(pkg) = !is_tracking_registry(pkg) || pkg.pinned

function collect_developed!(env::EnvCache, pkg::PackageSpec, developed::Vector{PackageSpec})
    source = project_rel_path(env, source_path(env.manifest_file, pkg))
    source_env = EnvCache(projectfile_path(source))
    pkgs = load_all_deps(source_env)
    for pkg in filter(is_tracking_path, pkgs)
        if any(x -> x.uuid == pkg.uuid, developed)
            continue
        end
        # normalize path
        pkg.path = Types.relative_project_path(env.manifest_file,
                   project_rel_path(source_env,
                   source_path(source_env.manifest_file, pkg)))
        push!(developed, pkg)
        collect_developed!(env, pkg, developed)
    end
end

function collect_developed(env::EnvCache, pkgs::Vector{PackageSpec})
    developed = PackageSpec[]
    for pkg in filter(is_tracking_path, pkgs)
        collect_developed!(env, pkg, developed)
    end
    return developed
end

function collect_fixed!(env::EnvCache, pkgs::Vector{PackageSpec}, names::Dict{UUID, String})
    deps_map = Dict{UUID,Vector{PackageSpec}}()
    weak_map = Dict{UUID,Set{UUID}}()
    if env.pkg !== nothing
        pkg = env.pkg
        deps, weakdeps = collect_project(pkg, dirname(env.project_file))
        deps_map[pkg.uuid] = deps
        weak_map[pkg.uuid] = weakdeps
        names[pkg.uuid] = pkg.name
    end
    for pkg in pkgs
        path = project_rel_path(env, source_path(env.manifest_file, pkg))
        if !isdir(path)
            pkgerror("expected package $(err_rep(pkg)) to exist at path `$path`")
        end
        deps, weakdeps = collect_project(pkg, path)
        deps_map[pkg.uuid] = deps
        weak_map[pkg.uuid] = weakdeps
    end

    fixed = Dict{UUID,Resolve.Fixed}()
    # Collect the dependencies for the fixed packages
    for (uuid, deps) in deps_map
        q = Dict{UUID, VersionSpec}()
        for dep in deps
            names[dep.uuid] = dep.name
            q[dep.uuid] = dep.version
        end
        if Types.is_project_uuid(env, uuid)
            fix_pkg = env.pkg
        else
            idx = findfirst(pkg -> pkg.uuid == uuid, pkgs)
            fix_pkg = pkgs[idx]
        end
        fixed[uuid] = Resolve.Fixed(fix_pkg.version, q, weak_map[uuid])
    end
    return fixed
end

# drops build detail in version but keeps the main prerelease context
# i.e. dropbuild(v"2.0.1-rc1.21321") == v"2.0.1-rc1"
dropbuild(v::VersionNumber) = VersionNumber(v.major, v.minor, v.patch, isempty(v.prerelease) ? () : (v.prerelease[1],))

# Resolve a set of versions given package version specs
# looks at uuid, version, repo/path,
# sets version to a VersionNumber
# adds any other packages which may be in the dependency graph
# all versioned packages should have a `tree_hash`
function resolve_versions!(env::EnvCache, registries::Vector{Registry.RegistryInstance}, pkgs::Vector{PackageSpec}, julia_version,
                           installed_only::Bool)
    installed_only = installed_only || OFFLINE_MODE[]
    # compatibility
    if julia_version !== nothing
        # only set the manifest julia_version if ctx.julia_version is not nothing
        env.manifest.julia_version = dropbuild(VERSION)
        v = intersect(julia_version, get_compat(env.project, "julia"))
        if isempty(v)
            @warn "julia version requirement for project not satisfied" _module=nothing _file=nothing
        end
    end

    jll_fix = Dict{UUID, VersionNumber}()
    for pkg in pkgs
        if !is_stdlib(pkg.uuid) && endswith(pkg.name, "_jll") && pkg.version isa VersionNumber
            jll_fix[pkg.uuid] = pkg.version
        end
    end

    names = Dict{UUID, String}(uuid => name for (uuid, (name, version)) in stdlibs())
    # recursive search for packages which are tracking a path
    developed = collect_developed(env, pkgs)
    # But we only want to use information for those packages that we don't know about
    for pkg in developed
        if !any(x -> x.uuid == pkg.uuid, pkgs)
            push!(pkgs, pkg)
        end
    end
    # this also sets pkg.version for fixed packages
    fixed = collect_fixed!(env, filter(!is_tracking_registry, pkgs), names)
    # non fixed packages are `add`ed by version: their version is either restricted or free
    # fixed packages are `dev`ed or `add`ed by repo
    # at this point, fixed packages have a version and `deps`

    @assert length(Set(pkg.uuid::UUID for pkg in pkgs)) == length(pkgs)

    # check compat
    for pkg in pkgs
        compat = get_compat(env.project, pkg.name)
        v = intersect(pkg.version, compat)
        if isempty(v)
            throw(Resolve.ResolverError(
                "empty intersection between $(pkg.name)@$(pkg.version) and project compatibility $(compat)"))
        end
        # Work around not clobbering 0.x.y+ for checked out old type of packages
        if !(pkg.version isa VersionNumber)
            pkg.version = v
        end
    end

    for pkg in pkgs
        names[pkg.uuid] = pkg.name
    end

    # Unless using the unbounded or historical resolver, always allow stdlibs to update. Helps if the previous resolve
    # happened on a different julia version / commit and the stdlib version in the manifest is not the current stdlib version
    unbind_stdlibs = julia_version === VERSION
    reqs = Resolve.Requires(pkg.uuid => is_stdlib(pkg.uuid) && unbind_stdlibs ? VersionSpec("*") : VersionSpec(pkg.version) for pkg in pkgs)
    graph, compat_map = deps_graph(env, registries, names, reqs, fixed, julia_version, installed_only)
    Resolve.simplify_graph!(graph)
    vers = Resolve.resolve(graph)

    # Fixup jlls that got their build numbers stripped
    vers_fix = copy(vers)
    for (uuid, vers) in vers
        old_v = get(jll_fix, uuid, nothing)
        # We only fixup a JLL if the old major/minor/patch matches the new major/minor/patch
        if old_v !== nothing && Base.thispatch(old_v) == Base.thispatch(vers_fix[uuid])
            vers_fix[uuid] = old_v
        end
    end
    vers = vers_fix

    # update vector of package versions
    for (uuid, ver) in vers
        idx = findfirst(p -> p.uuid == uuid, pkgs)
        if idx !== nothing
            pkg = pkgs[idx]
            # Fixed packages are not returned by resolve (they already have their version set)
            pkg.version = vers[pkg.uuid]
        else
            name = is_stdlib(uuid) ? first(stdlibs()[uuid]) : registered_name(registries, uuid)
            push!(pkgs, PackageSpec(;name=name, uuid=uuid, version=ver))
        end
    end
    final_deps_map = Dict{UUID, Dict{String, UUID}}()
    for pkg in pkgs
        load_tree_hash!(registries, pkg, julia_version)
        deps = begin
            if pkg.uuid in keys(fixed)
                deps_fixed = Dict{String, UUID}()
                for dep in keys(fixed[pkg.uuid].requires)
                    deps_fixed[names[dep]] = dep
                end
                deps_fixed
            else
                d = Dict{String, UUID}()
                for (uuid, _) in compat_map[pkg.uuid][pkg.version]
                    d[names[uuid]]  = uuid
                end
                d
            end
        end
        # julia is an implicit dependency
        filter!(d -> d.first != "julia", deps)
        final_deps_map[pkg.uuid] = deps
    end
    return final_deps_map
end

get_or_make!(d::Dict{K,V}, k::K) where {K,V} = get!(d, k) do; V() end

const JULIA_UUID = UUID("1222c4b2-2114-5bfd-aeef-88e4692bbb3e")
const PKGORIGIN_HAVE_VERSION = :version in fieldnames(Base.PkgOrigin)
function deps_graph(env::EnvCache, registries::Vector{Registry.RegistryInstance}, uuid_to_name::Dict{UUID,String},
                    reqs::Resolve.Requires, fixed::Dict{UUID,Resolve.Fixed}, julia_version,
                    installed_only::Bool)
    uuids = Set{UUID}()
    union!(uuids, keys(reqs))
    union!(uuids, keys(fixed))
    for fixed_uuids in map(fx->keys(fx.requires), values(fixed))
        union!(uuids, fixed_uuids)
    end

    stdlibs_for_julia_version = Types.get_last_stdlibs(julia_version)
    seen = Set{UUID}()

    # pkg -> version -> (dependency => compat):
    all_compat = Dict{UUID,Dict{VersionNumber,Dict{UUID,VersionSpec}}}()
    weak_compat = Dict{UUID,Dict{VersionNumber,Set{UUID}}}()

    for (fp, fx) in fixed
        all_compat[fp]   = Dict(fx.version => Dict{UUID,VersionSpec}())
    end

    while true
        unseen = setdiff(uuids, seen)
        isempty(unseen) && break
        for uuid in unseen
            push!(seen, uuid)
            uuid in keys(fixed) && continue
            all_compat_u = get_or_make!(all_compat, uuid)
            weak_compat_u = get_or_make!(weak_compat, uuid)

            uuid_is_stdlib = false
            stdlib_name = ""
            stdlib_version = nothing
            if haskey(stdlibs_for_julia_version, uuid)
                uuid_is_stdlib = true
                stdlib_name, stdlib_version = stdlibs_for_julia_version[uuid]
            end

            # If we're requesting resolution of a package that is an
            # unregistered stdlib we must special-case it here.  This is further
            # complicated by the fact that we can ask this question relative to
            # a Julia version.
            if (julia_version != VERSION && is_unregistered_stdlib(uuid)) || uuid_is_stdlib
                path = Types.stdlib_path(stdlibs_for_julia_version[uuid][1])
                proj_file = projectfile_path(path; strict=true)
                @assert proj_file !== nothing
                proj = read_package(proj_file)

                v = something(proj.version, VERSION)

                # TODO look at compat section for stdlibs?
                all_compat_u_vr = get_or_make!(all_compat_u, v)
                for (_, other_uuid) in proj.deps
                    push!(uuids, other_uuid)
                    all_compat_u_vr[other_uuid] = VersionSpec()
                end

                if !isempty(proj.weakdeps)
                    weak_all_compat_u_vr = get_or_make!(weak_compat_u, v)
                    for (_, other_uuid) in proj.weakdeps
                        push!(uuids, other_uuid)
                        all_compat_u_vr[other_uuid] = VersionSpec()
                        push!(weak_all_compat_u_vr, other_uuid)
                    end
                end
            else
                for reg in registries
                    pkg = get(reg, uuid, nothing)
                    pkg === nothing && continue
                    info = Registry.registry_info(pkg)

                    function add_compat!(d, cinfo)
                        for (v, compat_info) in cinfo
                            # Filter yanked and if we are in offline mode also downloaded packages
                            # TODO, pull this into a function
                            Registry.isyanked(info, v) && continue
                            if installed_only
                                pkg_spec = PackageSpec(name=pkg.name, uuid=pkg.uuid, version=v, tree_hash=Registry.treehash(info, v))
                                is_package_downloaded(env.manifest_file, pkg_spec) || continue
                            end

                            # Skip package version that are not the same as external packages in sysimage
                            if PKGORIGIN_HAVE_VERSION && RESPECT_SYSIMAGE_VERSIONS[] && julia_version == VERSION
                                pkgid = Base.PkgId(uuid, pkg.name)
                                if Base.in_sysimage(pkgid)
                                    pkgorigin = get(Base.pkgorigins, pkgid, nothing)
                                    if pkgorigin !== nothing && pkgorigin.version !== nothing
                                        if v != pkgorigin.version
                                            continue
                                        end
                                    end
                                end
                            end
                            dv = get_or_make!(d, v)
                            merge!(dv, compat_info)
                            union!(uuids, keys(compat_info))
                        end
                    end
                    add_compat!(all_compat_u, Registry.compat_info(info))
                    weak_compat_info = Registry.weak_compat_info(info)
                    if weak_compat_info !== nothing
                        add_compat!(all_compat_u, weak_compat_info)
                        # Version to Set
                        for (v, compat_info) in  weak_compat_info
                            weak_compat_u[v] = keys(compat_info)
                        end
                    end
                end
            end
        end
    end

    for uuid in uuids
        uuid == JULIA_UUID && continue
        if !haskey(uuid_to_name, uuid)
            name = registered_name(registries, uuid)
            name === nothing && pkgerror("cannot find name corresponding to UUID $(uuid) in a registry")
            uuid_to_name[uuid] = name
            entry = manifest_info(env.manifest, uuid)
            entry ≡ nothing && continue
            uuid_to_name[uuid] = entry.name
        end
    end

    return Resolve.Graph(all_compat, weak_compat, uuid_to_name, reqs, fixed, false, julia_version),
           all_compat
end

########################
# Package installation #
########################

function get_archive_url_for_version(url::String, ref)
    if (m = match(r"https://github.com/(.*?)/(.*?).git", url)) !== nothing
        return "https://api.github.com/repos/$(m.captures[1])/$(m.captures[2])/tarball/$(ref)"
    end
    return nothing
end

# Returns if archive successfully installed
function install_archive(
    urls::Vector{Pair{String,Bool}},
    hash::SHA1,
    version_path::String;
    io::IO=stderr_f()
)::Bool
    tmp_objects = String[]
    url_success = false
    for (url, top) in urls
        path = tempname() * randstring(6)
        push!(tmp_objects, path) # for cleanup
        url_success = true
        try
            PlatformEngines.download(url, path; verbose=false, io=io)
        catch e
            e isa InterruptException && rethrow()
            url_success = false
        end
        url_success || continue
        dir = joinpath(tempdir(), randstring(12))
        push!(tmp_objects, dir) # for cleanup
        # Might fail to extract an archive (https://github.com/JuliaPackaging/PkgServer.jl/issues/126)
        try
            unpack(path, dir; verbose=false)
        catch e
            e isa InterruptException && rethrow()
            @warn "failed to extract archive downloaded from $(url)"
            url_success = false
        end
        url_success || continue
        if top
            unpacked = dir
        else
            dirs = readdir(dir)
            # 7z on Win might create this spurious file
            filter!(x -> x != "pax_global_header", dirs)
            @assert length(dirs) == 1
            unpacked = joinpath(dir, dirs[1])
        end
        # Assert that the tarball unpacked to the tree sha we wanted
        # TODO: Enable on Windows when tree_hash handles
        # executable bits correctly, see JuliaLang/julia #33212.
        if !Sys.iswindows()
            if SHA1(GitTools.tree_hash(unpacked)) != hash
                @warn "tarball content does not match git-tree-sha1"
                url_success = false
            end
            url_success || continue
        end
        # Move content to version path
        !isdir(version_path) && mkpath(version_path)
        mv(unpacked, version_path; force=true)
        break # successful install
    end
    # Clean up and exit
    foreach(x -> Base.rm(x; force=true, recursive=true), tmp_objects)
    return url_success
end

const refspecs = ["+refs/*:refs/remotes/cache/*"]
function install_git(
    io::IO,
    uuid::UUID,
    name::String,
    hash::SHA1,
    urls::Set{String},
    version_path::String
)::Nothing
    repo = nothing
    tree = nothing
    # TODO: Consolidate this with some of the repo handling in Types.jl
    try
        clones_dir = joinpath(depots1(), "clones")
        ispath(clones_dir) || mkpath(clones_dir)
        repo_path = joinpath(clones_dir, string(uuid))
        repo = GitTools.ensure_clone(io, repo_path, first(urls); isbare=true,
                                     header = "[$uuid] $name from $(first(urls))")
        git_hash = LibGit2.GitHash(hash.bytes)
        for url in urls
            try LibGit2.with(LibGit2.GitObject, repo, git_hash) do g
                end
                break # object was found, we can stop
            catch err
                err isa LibGit2.GitError && err.code == LibGit2.Error.ENOTFOUND || rethrow()
            end
            GitTools.fetch(io, repo, url, refspecs=refspecs)
        end
        tree = try
            LibGit2.GitObject(repo, git_hash)
        catch err
            err isa LibGit2.GitError && err.code == LibGit2.Error.ENOTFOUND || rethrow()
            error("$name: git object $(string(hash)) could not be found")
        end
        tree isa LibGit2.GitTree ||
            error("$name: git object $(string(hash)) should be a tree, not $(typeof(tree))")
        mkpath(version_path)
        GitTools.checkout_tree_to_path(repo, tree, version_path)
        return
    finally
        repo !== nothing && LibGit2.close(repo)
        tree !== nothing && LibGit2.close(tree)
    end
end

function collect_artifacts(pkg_root::String; platform::AbstractPlatform=HostPlatform())
    # Check to see if this package has an (Julia)Artifacts.toml
    artifacts_tomls = Tuple{String,Base.TOML.TOMLDict}[]
    for f in artifact_names
        artifacts_toml = joinpath(pkg_root, f)
        if isfile(artifacts_toml)
            selector_path = joinpath(pkg_root, ".pkg", "select_artifacts.jl")

            # If there is a dynamic artifact selector, run that in an appropriate sandbox to select artifacts
            if isfile(selector_path)
                # Despite the fact that we inherit the project, since the in-memory manifest
                # has not been updated yet, if we try to load any dependencies, it may fail.
                # Therefore, this project inheritance is really only for Preferences, not dependencies.
                select_cmd = Cmd(`$(gen_build_code(selector_path; inherit_project=true)) -t1 --startup-file=no $(triplet(platform))`)
                meta_toml = String(read(select_cmd))
                res = TOML.tryparse(meta_toml)
                if res isa TOML.ParserError
                    errstr = sprint(showerror, res; context=stderr)
                    pkgerror("failed to parse TOML output from running $(repr(selector_path)), got: \n$errstr")
                else
                    push!(artifacts_tomls, (artifacts_toml, TOML.parse(meta_toml)))
                end
            else
                # Otherwise, use the standard selector from `Artifacts`
                artifacts = select_downloadable_artifacts(artifacts_toml; platform)
                push!(artifacts_tomls, (artifacts_toml, artifacts))
            end
            break
        end
    end
    return artifacts_tomls
end

function download_artifacts(env::EnvCache;
                            platform::AbstractPlatform=HostPlatform(),
                            julia_version = VERSION,
                            verbose::Bool=false,
                            io::IO=stderr_f())
    pkg_roots = String[]
    for (uuid, pkg) in env.manifest
        pkg = manifest_info(env.manifest, uuid)
        pkg_root = source_path(env.manifest_file, pkg, julia_version)
        pkg_root === nothing || push!(pkg_roots, pkg_root)
    end
    push!(pkg_roots, dirname(env.project_file))
    for pkg_root in pkg_roots
        for (artifacts_toml, artifacts) in collect_artifacts(pkg_root; platform)
            # For each Artifacts.toml, install each artifact we've collected from it
            for name in keys(artifacts)
                ensure_artifact_installed(name, artifacts[name], artifacts_toml;
                                            verbose, quiet_download=!(io isa Base.TTY), io=io)
            end
            write_env_usage(artifacts_toml, "artifact_usage.toml")
        end
    end
end

function check_artifacts_downloaded(pkg_root::String; platform::AbstractPlatform=HostPlatform())
    for (artifacts_toml, artifacts) in collect_artifacts(pkg_root; platform)
        for name in keys(artifacts)
            if !artifact_exists(Base.SHA1(artifacts[name]["git-tree-sha1"]))
                return false
            end
            break
        end
    end
    return true
end


function find_urls(registries::Vector{Registry.RegistryInstance}, uuid::UUID)
    urls = Set{String}()
    for reg in registries
        reg_pkg = get(reg, uuid, nothing)
        reg_pkg === nothing && continue
        info = Registry.registry_info(reg_pkg)
        repo = info.repo
        repo === nothing && continue
        push!(urls, repo)
    end
    return urls
end


function download_source(ctx::Context; readonly=true)
    pkgs_to_install = NamedTuple{(:pkg, :urls, :path), Tuple{PackageEntry, Set{String}, String}}[]
    for pkg in values(ctx.env.manifest)
        tracking_registered_version(pkg, ctx.julia_version) || continue
        path = source_path(ctx.env.manifest_file, pkg, ctx.julia_version)
        path === nothing && continue
        ispath(path) && continue
        urls = find_urls(ctx.registries, pkg.uuid)
        push!(pkgs_to_install, (;pkg, urls, path))
    end

    length(pkgs_to_install) == 0 && return Set{UUID}()

    ########################################
    # Install from archives asynchronously #
    ########################################

    missed_packages = eltype(pkgs_to_install)[]
    widths = [textwidth(pkg.name) for (pkg, _) in pkgs_to_install]
    max_name = maximum(widths; init=0)

    # Check what registries the current pkg server tracks
    server_registry_info = Registry.pkg_server_registry_info()

    @sync begin
        jobs = Channel{eltype(pkgs_to_install)}(ctx.num_concurrent_downloads)
        results = Channel(ctx.num_concurrent_downloads)

        @async begin
            for pkg in pkgs_to_install
                put!(jobs, pkg)
            end
        end

        for i in 1:ctx.num_concurrent_downloads
            @async begin
                for (pkg, urls, path) in jobs
                    if ctx.use_git_for_all_downloads
                        put!(results, (pkg, false, (urls, path)))
                        continue
                    end
                    try
                        archive_urls = Pair{String,Bool}[]
                        # Check if the current package is available in one of the registries being tracked by the pkg server
                        # In that case, download from the package server
                        if server_registry_info !== nothing
                            server, registry_info = server_registry_info
                            for reg in ctx.registries
                                if reg.uuid in keys(registry_info)
                                    if haskey(reg, pkg.uuid)
                                        url = "$server/package/$(pkg.uuid)/$(pkg.tree_hash)"
                                        push!(archive_urls, url => true)
                                        break
                                    end
                                end
                            end
                        end
                        for repo_url in urls
                            url = get_archive_url_for_version(repo_url, pkg.tree_hash)
                            url !== nothing && push!(archive_urls, url => false)
                        end
                        success = install_archive(archive_urls, pkg.tree_hash, path, io=ctx.io)
                        if success && readonly
                            set_readonly(path) # In add mode, files should be read-only
                        end
                        if ctx.use_only_tarballs_for_downloads && !success
                            pkgerror("failed to get tarball from $(urls)")
                        end
                        put!(results, (pkg, success, (urls, path)))
                    catch err
                        put!(results, (pkg, err, catch_backtrace()))
                    end
                end
            end
        end

        bar = MiniProgressBar(; indent=2, header = "Progress", color = Base.info_color(),
                                  percentage=false, always_reprint=true)
        bar.max = length(pkgs_to_install)
        fancyprint = can_fancyprint(ctx.io)
        try
            for i in 1:length(pkgs_to_install)
                pkg::PackageEntry, exc_or_success, bt_or_pathurls = take!(results)
                exc_or_success isa Exception && pkgerror("Error when installing package $(pkg.name):\n",
                                                        sprint(Base.showerror, exc_or_success, bt_or_pathurls))
                success, (urls, path) = exc_or_success, bt_or_pathurls
                success || push!(missed_packages, (; pkg, urls, path))
                bar.current = i
                str = sprint(; context=ctx.io) do io
                    if success
                        fancyprint && print_progress_bottom(io)
                        vstr = if pkg.version !== nothing
                            "v$(pkg.version)"
                        else
                            short_treehash = string(pkg.tree_hash)[1:16]
                            "[$short_treehash]"
                        end
                        printpkgstyle(io, :Installed, string(rpad(pkg.name * " ", max_name + 2, "─"), " ", vstr))
                        fancyprint && show_progress(io, bar)
                    end
                end
                print(ctx.io, str)
            end
        finally
            fancyprint && end_progress(ctx.io, bar)
            close(jobs)
        end
    end

    ##################################################
    # Use LibGit2 to download any remaining packages #
    ##################################################
    for (pkg, urls, path) in missed_packages
        uuid = pkg.uuid
        install_git(ctx.io, pkg.uuid, pkg.name, pkg.tree_hash, urls, path)
        readonly && set_readonly(path)
        vstr = if pkg.version !== nothing
            "v$(pkg.version)"
        else
            short_treehash = string(pkg.tree_hash)[1:16]
            "[$short_treehash]"
        end
        printpkgstyle(ctx.io, :Installed, string(rpad(pkg.name * " ", max_name + 2, "─"), " ", vstr))
    end

    return Set{UUID}(entry.pkg.uuid for entry in pkgs_to_install)
end

################################
# Manifest update and pruning #
################################
project_rel_path(env::EnvCache, path::String) = normpath(joinpath(dirname(env.manifest_file), path))

function prune_manifest(env::EnvCache)
    # if project uses another manifest, only prune project entry in manifest
    if dirname(env.project_file) != dirname(env.manifest_file)
        proj_entry = env.manifest[env.project.uuid]
        proj_entry.deps = env.project.deps
    else
        keep = collect(values(env.project.deps))
        env.manifest = prune_manifest(env.manifest, keep)
    end
    return env.manifest
end

function prune_manifest(manifest::Manifest, keep::Vector{UUID})
    while !isempty(keep)
        clean = true
        for (uuid, entry) in manifest
            uuid in keep || continue
            for dep in values(entry.deps)
                dep in keep && continue
                push!(keep, dep)
                clean = false
            end
        end
        clean && break
    end
    manifest.deps = Dict(uuid => entry for (uuid, entry) in manifest if uuid in keep)
    return manifest
end

function record_project_hash(env::EnvCache)
    env.manifest.other["project_hash"] = Types.project_resolve_hash(env.project)
end

#########
# Build #
#########
get_deps(env::EnvCache, new_uuids::Set{UUID}) = _get_deps!(Set{UUID}(), env, new_uuids)
function _get_deps!(collected_uuids::Set{UUID}, env::EnvCache, new_uuids)
    for uuid in new_uuids
        is_stdlib(uuid) && continue
        uuid in collected_uuids && continue
        push!(collected_uuids, uuid)
        children_uuids = if Types.is_project_uuid(env, uuid)
            Set(values(env.project.deps))
        else
            info = manifest_info(env.manifest, uuid)
            if info === nothing
                pkgerror("could not find manifest entry for package with uuid $(uuid)")
            end
            Set(values(info.deps))
        end
        _get_deps!(collected_uuids, env, children_uuids)
    end
    return collected_uuids
end

# TODO: This function should be replaceable with `is_instantiated` but
# see https://github.com/JuliaLang/Pkg.jl/issues/2470
function any_package_not_installed(manifest::Manifest)
    for (uuid, entry) in manifest
        if Base.locate_package(Base.PkgId(uuid, entry.name)) === nothing
            return true
        end
    end
    return false
end

function build(ctx::Context, uuids::Set{UUID}, verbose::Bool)
    if any_package_not_installed(ctx.env.manifest) || !isfile(ctx.env.manifest_file)
        Pkg.instantiate(ctx, allow_build = false, allow_autoprecomp = false)
    end
    all_uuids = get_deps(ctx.env, uuids)
    build_versions(ctx, all_uuids; verbose)
end

function dependency_order_uuids(env::EnvCache, uuids::Vector{UUID})::Dict{UUID,Int}
    order = Dict{UUID,Int}()
    seen = UUID[]
    k::Int = 0
    function visit(uuid::UUID)
        uuid in seen &&
            return @warn("Dependency graph not a DAG, linearizing anyway")
        haskey(order, uuid) && return
        push!(seen, uuid)
        if Types.is_project_uuid(env, uuid)
            deps = values(env.project.deps)
        else
            entry = manifest_info(env.manifest, uuid)
            deps = values(entry.deps)
        end
        foreach(visit, deps)
        pop!(seen)
        order[uuid] = k += 1
    end
    visit(uuid::String) = visit(UUID(uuid))
    foreach(visit, uuids)
    return order
end

function gen_build_code(build_file::String; inherit_project::Bool = false)
    code = """
        $(Base.load_path_setup_code(false))
        cd($(repr(dirname(build_file))))
        include($(repr(build_file)))
        """
    # This will make it so that running Pkg.build runs the build in a session with --startup=no
    # *unless* the parent julia session is started with --startup=yes explicitly.
    startup_flag = Base.JLOptions().startupfile == 1 ? "yes" : "no"
    return ```
        $(Base.julia_cmd()) -O0 --color=no --history-file=no
        --startup-file=$startup_flag
        $(inherit_project ? `--project=$(Base.active_project())` : ``)
        --eval $code
        ```
end

with_load_path(f::Function, new_load_path::String) = with_load_path(f, [new_load_path])
function with_load_path(f::Function, new_load_path::Vector{String})
    old_load_path = copy(Base.LOAD_PATH)
    copy!(Base.LOAD_PATH, new_load_path)
    try
        f()
    finally
        copy!(LOAD_PATH, old_load_path)
    end
end

const PkgUUID = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
pkg_scratchpath() = joinpath(depots1(), "scratchspaces", PkgUUID)

builddir(source_path::String) = joinpath(source_path, "deps")
buildfile(source_path::String) = joinpath(builddir(source_path), "build.jl")
function build_versions(ctx::Context, uuids::Set{UUID}; verbose=false)
    # collect builds for UUIDs with `deps/build.jl` files
    builds = Tuple{UUID,String,String,VersionNumber}[]
    for uuid in uuids
        is_stdlib(uuid) && continue
        if Types.is_project_uuid(ctx.env, uuid)
            path = dirname(ctx.env.project_file)
            name = ctx.env.pkg.name
            version = ctx.env.pkg.version
        else
            entry = manifest_info(ctx.env.manifest, uuid)
            if entry === nothing
                error("could not find entry with uuid $uuid in manifest $(ctx.env.manifest_file)")
            end
            name = entry.name
            path = source_path(ctx.env.manifest_file, entry)
            if path === nothing
                pkgerror("Failed to find path for package $name")
            end
            version = something(entry.version, v"0.0")
        end
        ispath(path) || error("Build path for $name does not exist: $path")
        ispath(buildfile(path)) && push!(builds, (uuid, name, path, version))
    end
    # toposort builds by dependencies
    order = dependency_order_uuids(ctx.env, map(first, builds))
    sort!(builds, by = build -> order[first(build)])
    max_name = maximum(build->textwidth(build[2]), builds; init=0)

    bar = MiniProgressBar(; indent=2, header = "Progress", color = Base.info_color(),
                              percentage=false, always_reprint=true)
    bar.max = length(builds)
    fancyprint = can_fancyprint(ctx.io)
    fancyprint && start_progress(ctx.io, bar)

    # build each package versions in a child process
    try
    for (n, (uuid, name, source_path, version)) in enumerate(builds)
        pkg = PackageSpec(;uuid=uuid, name=name, version=version)
        build_file = buildfile(source_path)
        # compatibility shim
        local build_project_override, build_project_preferences
        if isfile(projectfile_path(builddir(source_path)))
            build_project_override = nothing
            with_load_path([builddir(source_path), Base.LOAD_PATH...]) do
                build_project_preferences = Base.get_preferences()
            end
        else
            build_project_override = gen_target_project(ctx, pkg, source_path, "build")
            with_load_path([something(projectfile_path(source_path)), Base.LOAD_PATH...]) do
                build_project_preferences = Base.get_preferences()
            end
        end

        # Put log output in Pkg's scratchspace if the package is content addressed
        # by tree sha and in the build directory if it is tracked by path etc.
        entry = manifest_info(ctx.env.manifest, uuid)
        if entry !== nothing && entry.tree_hash !== nothing
            key = string(entry.tree_hash)
            scratch = joinpath(pkg_scratchpath(), key)
            mkpath(scratch)
            log_file = joinpath(scratch, "build.log")
            # Associate the logfile with the package being built
            dict = Dict{String,Any}(scratch => [
                Dict{String,Any}("time" => Dates.now(), "parent_projects" => [projectfile_path(source_path)])
            ])
            open(joinpath(depots1(), "logs", "scratch_usage.toml"), "a") do io
                TOML.print(io, dict)
            end
        else
            log_file = splitext(build_file)[1] * ".log"
        end

        fancyprint && print_progress_bottom(ctx.io)

        printpkgstyle(ctx.io, :Building,
                      rpad(name * " ", max_name + 1, "─") * "→ " * pathrepr(log_file))
        bar.current = n-1

        fancyprint && show_progress(ctx.io, bar)

        let log_file=log_file
            sandbox(ctx, pkg, source_path, builddir(source_path), build_project_override; preferences=build_project_preferences) do
                flush(ctx.io)
                ok = open(log_file, "w") do log
                    std = verbose ? ctx.io : log
                    success(pipeline(gen_build_code(buildfile(source_path)),
                                    stdout=std, stderr=std))
                end
                ok && return
                n_lines = isinteractive() ? 100 : 5000
                # TODO: Extract last n  lines more efficiently
                log_lines = readlines(log_file)
                log_show = join(log_lines[max(1, length(log_lines) - n_lines):end], '\n')
                full_log_at, last_lines =
                if length(log_lines) > n_lines
                    "\n\nFull log at $log_file",
                    ", showing the last $n_lines of log"
                else
                    "", ""
                end
                pkgerror("Error building `$(pkg.name)`$last_lines: \n$log_show$full_log_at")
            end
        end
    end
    finally
        fancyprint && end_progress(ctx.io, bar)
    end
    return
end

##############
# Operations #
##############
function rm(ctx::Context, pkgs::Vector{PackageSpec}; mode::PackageMode)
    drop = UUID[]
    # find manifest-mode drops
    if mode == PKGMODE_MANIFEST
        for pkg in pkgs
            info = manifest_info(ctx.env.manifest, pkg.uuid)
            if info !== nothing
                pkg.uuid in drop || push!(drop, pkg.uuid)
            else
                str = has_name(pkg) ? pkg.name : string(pkg.uuid)
                @warn("`$str` not in manifest, ignoring")
            end
        end
    end
    # drop reverse dependencies
    while !isempty(drop)
        clean = true
        for (uuid, entry) in ctx.env.manifest
            deps = values(entry.deps)
            isempty(drop ∩ deps) && continue
            uuid ∉ drop || continue
            push!(drop, uuid)
            clean = false
        end
        clean && break
    end
    # find project-mode drops
    if mode == PKGMODE_PROJECT
        for pkg in pkgs
            found = false
            for (name::String, uuid::UUID) in ctx.env.project.deps
                pkg.name == name || pkg.uuid == uuid || continue
                pkg.name == name ||
                    error("project file name mismatch for `$uuid`: $(pkg.name) ≠ $name")
                pkg.uuid == uuid ||
                    error("project file UUID mismatch for `$name`: $(pkg.uuid) ≠ $uuid")
                uuid in drop || push!(drop, uuid)
                found = true
                break
            end
            found && continue
            str = has_name(pkg) ? pkg.name : string(pkg.uuid)
            @warn("`$str` not in project, ignoring")
        end
    end
    # delete drops from project
    n = length(ctx.env.project.deps)
    filter!(ctx.env.project.deps) do (_, uuid)
        uuid ∉ drop
    end
    if length(ctx.env.project.deps) == n
        println(ctx.io, "No changes")
        return
    end
    # only declare `compat` for remaining direct or `extra` dependencies
    # `julia` is always an implicit direct dependency
    filter!(ctx.env.project.compat) do (name, _)
        name == "julia" || name in keys(ctx.env.project.deps) || name in keys(ctx.env.project.extras) || name in keys(ctx.env.project.weakdeps)
    end
    deps_names = union(keys(ctx.env.project.deps), keys(ctx.env.project.extras))
    filter!(ctx.env.project.targets) do (target, deps)
        !isempty(filter!(in(deps_names), deps))
    end
    # only keep reachable manifest entries
    prune_manifest(ctx.env)
    record_project_hash(ctx.env)
    # update project & manifest
    write_env(ctx.env)
    show_update(ctx.env, ctx.registries; io=ctx.io)
end

update_package_add(ctx::Context, pkg::PackageSpec, ::Nothing, is_dep::Bool) = pkg
function update_package_add(ctx::Context, pkg::PackageSpec, entry::PackageEntry, is_dep::Bool)
    if entry.pinned
        if pkg.version == VersionSpec()
            println(ctx.io, "`$(pkg.name)` is pinned at `v$(entry.version)`: maintaining pinned version")
        end
        return PackageSpec(; uuid=pkg.uuid, name=pkg.name, pinned=true,
                           version=entry.version, tree_hash=entry.tree_hash,
                           path=entry.path, repo=entry.repo)
    end
    if entry.path !== nothing || entry.repo.source !== nothing || pkg.repo.source !== nothing
        return pkg # overwrite everything, nothing to copy over
    end
    if is_stdlib(pkg.uuid)
        return pkg # stdlibs are not versioned like other packages
    elseif is_dep && ((isa(pkg.version, VersionNumber) && entry.version == pkg.version) ||
                      (!isa(pkg.version, VersionNumber) && entry.version ∈ pkg.version))
        # leave the package as is at the installed version
        return PackageSpec(; uuid=pkg.uuid, name=pkg.name, version=entry.version,
                           tree_hash=entry.tree_hash)
    end
    # adding a new version not compatible with the old version, so we just overwrite
    return pkg
end

# Update registries AND read them back in.
function update_registries(ctx::Context; force::Bool=true, kwargs...)
    OFFLINE_MODE[] && return
    !force && UPDATED_REGISTRY_THIS_SESSION[] && return
    Registry.update(; io=ctx.io, kwargs...)
    copy!(ctx.registries, Registry.reachable_registries())
    UPDATED_REGISTRY_THIS_SESSION[] = true
end

function is_all_registered(registries::Vector{Registry.RegistryInstance}, pkgs::Vector{PackageSpec})
    pkgs = filter(tracking_registered_version, pkgs)
    for pkg in pkgs
        if !any(r->haskey(r, pkg.uuid), registries)
            return pkg
        end
    end
    return true
end

function check_registered(registries::Vector{Registry.RegistryInstance}, pkgs::Vector{PackageSpec})
    pkg = is_all_registered(registries, pkgs)
    if pkg isa PackageSpec
        pkgerror("expected package $(err_rep(pkg)) to be registered")
    end
    return nothing
end

# Check if the package can be added without colliding/overwriting things
function assert_can_add(ctx::Context, pkgs::Vector{PackageSpec})
    for pkg in pkgs
        @assert pkg.name !== nothing && pkg.uuid !== nothing
        # package with the same name exist in the project: assert that they have the same uuid
        existing_uuid = get(ctx.env.project.deps, pkg.name, pkg.uuid)
        existing_uuid == pkg.uuid ||
            pkgerror("""Refusing to add package $(err_rep(pkg)).
                     Package `$(pkg.name)=$(existing_uuid)` with the same name already exists as a direct dependency.
                     To remove the existing package, use `import Pkg; Pkg.rm("$(pkg.name)")`.
                     """)
        # package with the same uuid exist in the project: assert they have the same name
        name = findfirst(==(pkg.uuid), ctx.env.project.deps)
        name === nothing || name == pkg.name ||
            pkgerror("""Refusing to add package $(err_rep(pkg)).
                     Package `$name=$(pkg.uuid)` with the same UUID already exists as a direct dependency.
                     To remove the existing package, use `import Pkg; Pkg.rm("$name")`.
                     """)
        # package with the same uuid exist in the manifest: assert they have the same name
        entry = get(ctx.env.manifest, pkg.uuid, nothing)
        entry === nothing || entry.name == pkg.name ||
            pkgerror("""Refusing to add package $(err_rep(pkg)).
                     Package `$(entry.name)=$(pkg.uuid)` with the same UUID already exists in the manifest.
                     To remove the existing package, use `import Pkg; Pkg.rm(Pkg.PackageSpec(uuid="$(pkg.uuid)"); mode=Pkg.PKGMODE_MANIFEST)`.
                     """)
    end
end

function tiered_resolve(env::EnvCache, registries::Vector{Registry.RegistryInstance}, pkgs::Vector{PackageSpec}, julia_version,
                        try_all_installed::Bool)
    if try_all_installed
        try # do not modify existing subgraph and only add installed versions of the new packages
            @debug "tiered_resolve: trying PRESERVE_ALL_INSTALLED"
            return targeted_resolve(env, registries, pkgs, PRESERVE_ALL_INSTALLED, julia_version)
        catch err
            err isa Resolve.ResolverError || rethrow()
        end
    end
    try # do not modify existing subgraph
        @debug "tiered_resolve: trying PRESERVE_ALL"
        return targeted_resolve(env, registries, pkgs, PRESERVE_ALL, julia_version)
    catch err
        err isa Resolve.ResolverError || rethrow()
    end
    try # do not modify existing direct deps
        @debug "tiered_resolve: trying PRESERVE_DIRECT"
        return targeted_resolve(env, registries, pkgs, PRESERVE_DIRECT, julia_version)
    catch err
        err isa Resolve.ResolverError || rethrow()
    end
    try
        @debug "tiered_resolve: trying PRESERVE_SEMVER"
        return targeted_resolve(env, registries, pkgs, PRESERVE_SEMVER, julia_version)
    catch err
        err isa Resolve.ResolverError || rethrow()
    end
    @debug "tiered_resolve: trying PRESERVE_NONE"
    return targeted_resolve(env, registries, pkgs, PRESERVE_NONE, julia_version)
end

function targeted_resolve(env::EnvCache, registries::Vector{Registry.RegistryInstance}, pkgs::Vector{PackageSpec}, preserve::PreserveLevel, julia_version)
    if preserve == PRESERVE_ALL || preserve == PRESERVE_ALL_INSTALLED
        pkgs = load_all_deps(env, pkgs; preserve)
    else
        pkgs = load_direct_deps(env, pkgs; preserve)
    end
    check_registered(registries, pkgs)

    deps_map = resolve_versions!(env, registries, pkgs, julia_version, preserve == PRESERVE_ALL_INSTALLED)
    return pkgs, deps_map
end

function _resolve(io::IO, env::EnvCache, registries::Vector{Registry.RegistryInstance},
                    pkgs::Vector{PackageSpec}, preserve::PreserveLevel, julia_version)
    printpkgstyle(io, :Resolving, "package versions...")
    if preserve == PRESERVE_TIERED_INSTALLED
        tiered_resolve(env, registries, pkgs, julia_version, true)
    elseif preserve == PRESERVE_TIERED
        tiered_resolve(env, registries, pkgs, julia_version, false)
    else
        targeted_resolve(env, registries, pkgs, preserve, julia_version)
    end
end

function add(ctx::Context, pkgs::Vector{PackageSpec}, new_git=Set{UUID}();
             preserve::PreserveLevel=default_preserve(), platform::AbstractPlatform=HostPlatform())
    assert_can_add(ctx, pkgs)
    # load manifest data
    for (i, pkg) in pairs(pkgs)
        entry = manifest_info(ctx.env.manifest, pkg.uuid)
        is_dep = any(uuid -> uuid == pkg.uuid, [uuid for (name, uuid) in ctx.env.project.deps])
        pkgs[i] = update_package_add(ctx, pkg, entry, is_dep)
    end
    foreach(pkg -> ctx.env.project.deps[pkg.name] = pkg.uuid, pkgs) # update set of deps
    # resolve
    pkgs, deps_map = _resolve(ctx.io, ctx.env, ctx.registries, pkgs, preserve, ctx.julia_version)
    update_manifest!(ctx.env, pkgs, deps_map, ctx.julia_version)
    new_apply = download_source(ctx)
    fixup_ext!(ctx.env, pkgs)

    # After downloading resolutionary packages, search for (Julia)Artifacts.toml files
    # and ensure they are all downloaded and unpacked as well:
    download_artifacts(ctx.env, platform=platform, julia_version=ctx.julia_version, io=ctx.io)

    write_env(ctx.env) # write env before building
    show_update(ctx.env, ctx.registries; io=ctx.io)
    build_versions(ctx, union(new_apply, new_git))
end

# Input: name, uuid, and path
function develop(ctx::Context, pkgs::Vector{PackageSpec}, new_git::Set{UUID};
                 preserve::PreserveLevel=default_preserve(), platform::AbstractPlatform=HostPlatform())
    assert_can_add(ctx, pkgs)
    # no need to look at manifest.. dev will just nuke whatever is there before
    for pkg in pkgs
        ctx.env.project.deps[pkg.name] = pkg.uuid
    end
    # resolve & apply package versions
    pkgs, deps_map = _resolve(ctx.io, ctx.env, ctx.registries, pkgs, preserve, ctx.julia_version)
    update_manifest!(ctx.env, pkgs, deps_map, ctx.julia_version)
    new_apply = download_source(ctx)
    fixup_ext!(ctx.env, pkgs)
    download_artifacts(ctx.env; platform=platform, julia_version=ctx.julia_version, io=ctx.io)
    write_env(ctx.env) # write env before building
    show_update(ctx.env, ctx.registries; io=ctx.io)
    build_versions(ctx, union(new_apply, new_git))
end

# load version constraint
# if version isa VersionNumber -> set tree_hash too
up_load_versions!(ctx::Context, pkg::PackageSpec, ::Nothing, level::UpgradeLevel) = false
function up_load_versions!(ctx::Context, pkg::PackageSpec, entry::PackageEntry, level::UpgradeLevel)
    entry.version !== nothing || return false # no version to set
    if entry.pinned || level == UPLEVEL_FIXED
        pkg.version = entry.version
        pkg.tree_hash = entry.tree_hash
    elseif entry.repo.source !== nothing # repo packages have a version but are treated special
        pkg.repo = entry.repo
        if level == UPLEVEL_MAJOR
            # Updating a repo package is equivalent to adding it
            new = Types.handle_repo_add!(ctx, pkg)
            pkg.version = entry.version
            if pkg.tree_hash != entry.tree_hash
                # TODO parse find_installed and set new version
            end
            return new
        else
            pkg.version = entry.version
            pkg.tree_hash = entry.tree_hash
        end
    else
        ver = entry.version
        r = level == UPLEVEL_PATCH ? VersionRange(ver.major, ver.minor) :
            level == UPLEVEL_MINOR ? VersionRange(ver.major) :
            level == UPLEVEL_MAJOR ? VersionRange() :
                error("unexpected upgrade level: $level")
        pkg.version = VersionSpec(r)
    end
    return false
end

up_load_manifest_info!(pkg::PackageSpec, ::Nothing) = nothing
function up_load_manifest_info!(pkg::PackageSpec, entry::PackageEntry)
    pkg.name = entry.name # TODO check name is same
    pkg.repo = entry.repo # TODO check that repo is same
    pkg.path = entry.path
    pkg.pinned = entry.pinned
    # `pkg.version` and `pkg.tree_hash` is set by `up_load_versions!`
end


function load_manifest_deps_up(env::EnvCache, pkgs::Vector{PackageSpec}=PackageSpec[];
                            preserve::PreserveLevel=PRESERVE_ALL)
    manifest = env.manifest
    project = env.project
    explicit_upgraded = Set(pkg.uuid for pkg in pkgs)

    recursive_indirect_dependencies_of_explicitly_upgraded = Set{UUID}()
    frontier = copy(explicit_upgraded)
    new_frontier = Set{UUID}()
    while !(isempty(frontier))
        for uuid in frontier
            entry = get(env.manifest, uuid, nothing)
            entry === nothing && continue
            uuid_deps = values(entry.deps)
            for uuid_dep in uuid_deps
                if !(uuid_dep in recursive_indirect_dependencies_of_explicitly_upgraded) #
                    push!(recursive_indirect_dependencies_of_explicitly_upgraded, uuid_dep)
                    push!(new_frontier, uuid_dep)
                end
            end
        end
        copy!(frontier, new_frontier)
        empty!(new_frontier)
    end

    pkgs = copy(pkgs)
    for (uuid, entry) in manifest
        findfirst(pkg -> pkg.uuid == uuid, pkgs) === nothing || continue # do not duplicate packages
        uuid in explicit_upgraded && continue # Allow explicit upgraded packages to upgrade.
        if preserve == PRESERVE_NONE && uuid in recursive_indirect_dependencies_of_explicitly_upgraded
            continue
        elseif preserve == PRESERVE_DIRECT && uuid in recursive_indirect_dependencies_of_explicitly_upgraded && !(uuid in values(project.deps))
            continue
        end

        # The rest of the packages get fixed
        push!(pkgs, PackageSpec(
            uuid      = uuid,
            name      = entry.name,
            path      = entry.path,
            pinned    = entry.pinned,
            repo      = entry.repo,
            tree_hash = entry.tree_hash, # TODO should tree_hash be changed too?
            version   = something(entry.version, VersionSpec())
        ))
    end
    return pkgs
end

function targeted_resolve_up(env::EnvCache, registries::Vector{Registry.RegistryInstance}, pkgs::Vector{PackageSpec}, preserve::PreserveLevel, julia_version)
    pkgs = load_manifest_deps_up(env, pkgs; preserve=preserve)
    check_registered(registries, pkgs)
    deps_map = resolve_versions!(env, registries, pkgs, julia_version, preserve == PRESERVE_ALL_INSTALLED)
    return pkgs, deps_map
end

function up(ctx::Context, pkgs::Vector{PackageSpec}, level::UpgradeLevel;
            skip_writing_project::Bool=false, preserve::Union{Nothing,PreserveLevel}=nothing)
    new_git = Set{UUID}()
    # TODO check all pkg.version == VersionSpec()
    # set version constraints according to `level`
    for pkg in pkgs
        new = up_load_versions!(ctx, pkg, manifest_info(ctx.env.manifest, pkg.uuid), level)
        new && push!(new_git, pkg.uuid) #TODO put download + push! in utility function
    end
    # load rest of manifest data (except for version info)
    for pkg in pkgs
        up_load_manifest_info!(pkg, manifest_info(ctx.env.manifest, pkg.uuid))
    end
    if preserve !== nothing
        pkgs, deps_map = targeted_resolve_up(ctx.env, ctx.registries, pkgs, preserve, ctx.julia_version)
    else
        pkgs = load_direct_deps(ctx.env, pkgs; preserve = (level == UPLEVEL_FIXED ? PRESERVE_NONE : PRESERVE_DIRECT))
        check_registered(ctx.registries, pkgs)
        deps_map = resolve_versions!(ctx.env, ctx.registries, pkgs, ctx.julia_version, false)
    end
    update_manifest!(ctx.env, pkgs, deps_map, ctx.julia_version)
    new_apply = download_source(ctx)
    fixup_ext!(ctx.env, pkgs)
    download_artifacts(ctx.env, julia_version=ctx.julia_version, io=ctx.io)
    write_env(ctx.env; skip_writing_project) # write env before building
    show_update(ctx.env, ctx.registries; io=ctx.io, hidden_upgrades_info = true)
    build_versions(ctx, union(new_apply, new_git))
end

function update_package_pin!(registries::Vector{Registry.RegistryInstance}, pkg::PackageSpec, entry::Union{Nothing, PackageEntry})
    if entry === nothing
        pkgerror("package $(err_rep(pkg)) not found in the manifest, run `Pkg.resolve()` and retry.")
    end

    #if entry.pinned && pkg.version == VersionSpec()
    #    println(ctx.io, "package $(err_rep(pkg)) already pinned")
    #end
    # update pinned package
    pkg.pinned = true
    if is_stdlib(pkg.uuid)
        return nothing # nothing left to do
    elseif pkg.version == VersionSpec()
        pkg.version = entry.version # pin at current version
        pkg.repo = entry.repo
        pkg.tree_hash = entry.tree_hash
        pkg.path = entry.path
    else # given explicit registered version
        if entry.repo.source !== nothing || entry.path !== nothing
            # A pin in this case includes an implicit `free` to switch to tracking registered versions
            # First, make sure the package is registered so we have something to free to
            if is_all_registered(registries, [pkg]) !== true
                pkgerror("unable to pin unregistered package $(err_rep(pkg)) to an arbitrary version")
            end
        end
    end
end

is_fully_pinned(ctx::Context) = !isempty(ctx.env.manifest.deps) && all(kv -> last(kv).pinned, ctx.env.manifest.deps)

function pin(ctx::Context, pkgs::Vector{PackageSpec})
    foreach(pkg -> update_package_pin!(ctx.registries, pkg, manifest_info(ctx.env.manifest, pkg.uuid)), pkgs)
    pkgs = load_direct_deps(ctx.env, pkgs)

    # TODO: change pin to not take a version and just have it pin on the current version. Then there is no need to resolve after a pin
    pkgs, deps_map = _resolve(ctx.io, ctx.env, ctx.registries, pkgs, PRESERVE_TIERED, ctx.julia_version)

    update_manifest!(ctx.env, pkgs, deps_map, ctx.julia_version)
    new = download_source(ctx)
    fixup_ext!(ctx.env, pkgs)
    download_artifacts(ctx.env; julia_version=ctx.julia_version, io=ctx.io)
    write_env(ctx.env) # write env before building
    show_update(ctx.env, ctx.registries; io=ctx.io)
    build_versions(ctx, new)
end

function update_package_free!(registries::Vector{Registry.RegistryInstance}, pkg::PackageSpec, entry::PackageEntry, err_if_free::Bool)
    if entry.pinned
        pkg.pinned = false
        is_stdlib(pkg.uuid) && return # nothing left to do
        pkg.version = entry.version
        pkg.repo = entry.repo
        pkg.tree_hash = entry.tree_hash
        return
    end
    if entry.path !== nothing || entry.repo.source !== nothing
        # make sure the package is registered so we have something to free to
        if is_all_registered(registries, [pkg]) !== true
            pkgerror("unable to free unregistered package $(err_rep(pkg))")
        end
        return # -> name, uuid
    end
    if err_if_free
        pkgerror("expected package $(err_rep(pkg)) to be pinned, tracking a path,",
             " or tracking a repository")
    end
    return
end

# TODO: this is two technically different operations with the same name
# split into two subfunctions ...
function free(ctx::Context, pkgs::Vector{PackageSpec}; err_if_free=true)
    foreach(pkg -> update_package_free!(ctx.registries, pkg, manifest_info(ctx.env.manifest, pkg.uuid), err_if_free), pkgs)

    if any(pkg -> pkg.version == VersionSpec(), pkgs)
        pkgs = load_direct_deps(ctx.env, pkgs)
        check_registered(ctx.registries, pkgs)

        # TODO: change free to not take a version and just have it pin on the current version. Then there is no need to resolve after a pin
        pkgs, deps_map = _resolve(ctx.io, ctx.env, ctx.registries, pkgs, PRESERVE_TIERED, ctx.julia_version)

        update_manifest!(ctx.env, pkgs, deps_map, ctx.julia_version)
        new = download_source(ctx)
        fixup_ext!(ctx.env, pkgs)
        download_artifacts(ctx.env, io=ctx.io)
        write_env(ctx.env) # write env before building
        show_update(ctx.env, ctx.registries; io=ctx.io)
        build_versions(ctx, new)
    else
        foreach(pkg -> manifest_info(ctx.env.manifest, pkg.uuid).pinned = false, pkgs)
        write_env(ctx.env)
        show_update(ctx.env, ctx.registries; io=ctx.io)
    end
end

function gen_test_code(source_path::String; coverage, julia_args::Cmd, test_args::Cmd)
    test_file = testfile(source_path)
    code = """
        $(Base.load_path_setup_code(false))
        cd($(repr(dirname(test_file))))
        append!(empty!(ARGS), $(repr(test_args.exec)))
        include($(repr(test_file)))
        """
    return gen_subprocess_cmd(code, source_path; coverage, julia_args)
end

function gen_test_precompile_code(source_path::String; coverage, julia_args::Cmd, test_args::Cmd)
    # Note that we cannot load the dev-ed Pkg here during Pkg testing
    # so the `Pkg.precompile` that is run here is the one in the sysimage
    code = """
        Pkg = Base.require(Base.PkgId(Base.UUID("44cfe95a-1eb2-52ea-b672-e2afdf69b78f"), "Pkg"))
        $(Base.load_path_setup_code(false))
        append!(empty!(ARGS), $(repr(test_args.exec)))
        Pkg.precompile(warn_loaded = false)
        """
    return gen_subprocess_cmd(code, source_path; coverage, julia_args)
end

function get_threads_spec()
    if Threads.nthreads(:interactive) > 0
        "$(Threads.nthreads(:default)),$(Threads.nthreads(:interactive))"
    else
        "$(Threads.nthreads(:default))"
    end
end

function gen_subprocess_cmd(code::String, source_path::String; coverage, julia_args)
    coverage_arg = if coverage isa Bool
        coverage ? string("@", source_path) : "none"
    elseif coverage isa AbstractString
        coverage
    else
        throw(ArgumentError("coverage should be a boolean or a string."))
    end
    return ```
        $(Base.julia_cmd())
        --code-coverage=$(coverage_arg)
        --color=$(Base.have_color === nothing ? "auto" : Base.have_color ? "yes" : "no")
        --compiled-modules=$(Bool(Base.JLOptions().use_compiled_modules) ? "yes" : "no")
        --check-bounds=yes
        --warn-overwrite=yes
        --depwarn=$(Base.JLOptions().depwarn == 2 ? "error" : "yes")
        --inline=$(Bool(Base.JLOptions().can_inline) ? "yes" : "no")
        --startup-file=$(Base.JLOptions().startupfile == 1 ? "yes" : "no")
        --track-allocation=$(("none", "user", "all")[Base.JLOptions().malloc_log + 1])
        --threads=$(get_threads_spec())
        $(julia_args)
        --eval $(code)
    ```
end

function with_temp_env(fn::Function, temp_env::String)
    load_path = copy(LOAD_PATH)
    active_project = Base.ACTIVE_PROJECT[]
    try
        push!(empty!(LOAD_PATH), "@", temp_env)
        Base.ACTIVE_PROJECT[] = nothing
        fn()
    finally
        append!(empty!(LOAD_PATH), load_path)
        Base.ACTIVE_PROJECT[] = active_project
    end
end

# pick out a set of subgraphs and preserve their versions
function sandbox_preserve(env::EnvCache, target::PackageSpec, test_project::String)
    env = deepcopy(env)
    # include root in manifest (in case any dependencies point back to it)
    if env.pkg !== nothing
        env.manifest[env.pkg.uuid] = PackageEntry(;name=env.pkg.name, path=dirname(env.project_file),
                                                  deps=env.project.deps)
    end
    # if the source manifest is an old format, upgrade the manifest_format so
    # that warnings aren't thrown for the temp sandbox manifest
    if env.manifest.manifest_format < v"2.0"
        env.manifest.manifest_format = v"2.0"
    end
    # preserve important nodes
    keep = [target.uuid]
    append!(keep, collect(values(read_project(test_project).deps)))
    record_project_hash(env)
    # prune and return
    return prune_manifest(env.manifest, keep)
end

function abspath!(env::EnvCache, manifest::Manifest)
    for (uuid, entry) in manifest
        if entry.path !== nothing
            entry.path = project_rel_path(env, entry.path)
        end
    end
    return manifest
end

# ctx + pkg used to compute parent dep graph
function sandbox(fn::Function, ctx::Context, target::PackageSpec, target_path::String,
                 sandbox_path::String, sandbox_project_override;
                 preferences::Union{Nothing,Dict{String,Any}} = nothing,
                 force_latest_compatible_version::Bool=false,
                 allow_earlier_backwards_compatible_versions::Bool=true,
                 allow_reresolve::Bool=true)
    active_manifest = manifestfile_path(dirname(ctx.env.manifest_file))
    sandbox_project = projectfile_path(sandbox_path)

    mktempdir() do tmp
        tmp_project  = projectfile_path(tmp)
        tmp_manifest = manifestfile_path(tmp)
        tmp_preferences = joinpath(tmp, first(Base.preferences_names))

        # Copy env info over to temp env
        if sandbox_project_override !== nothing
            Types.write_project(sandbox_project_override, tmp_project)
        elseif isfile(sandbox_project)
            cp(sandbox_project, tmp_project)
            chmod(tmp_project, 0o600)
        end
        # create merged manifest
        # - copy over active subgraph
        # - abspath! to maintain location of all deved nodes
        working_manifest = abspath!(ctx.env, sandbox_preserve(ctx.env, target, tmp_project))
        # - copy over fixed subgraphs from test subgraph
        # really only need to copy over "special" nodes
        sandbox_env = Types.EnvCache(projectfile_path(sandbox_path))
        sandbox_manifest = abspath!(sandbox_env, sandbox_env.manifest)
        for (name, uuid) in sandbox_env.project.deps
            entry = get(sandbox_manifest, uuid, nothing)
            if entry !== nothing && isfixed(entry)
                subgraph = prune_manifest(sandbox_manifest, [uuid])
                for (uuid, entry) in subgraph
                    if haskey(working_manifest, uuid)
                        pkgerror("can not merge projects")
                    end
                    working_manifest[uuid] = entry
                end
            end
        end

        Types.write_manifest(working_manifest, tmp_manifest)
        # Copy over preferences
        if preferences !== nothing
            open(tmp_preferences, "w") do io
                TOML.print(io, preferences::Dict{String, Any})
            end
        end

        # sandbox
        with_temp_env(tmp) do
            temp_ctx = Context()
            temp_ctx.env.project.deps[target.name] = target.uuid

            if force_latest_compatible_version
                apply_force_latest_compatible_version!(
                    temp_ctx;
                    target_name = target.name,
                    allow_earlier_backwards_compatible_versions,
                )
            end

            try
                Pkg.resolve(temp_ctx; io=devnull, skip_writing_project=true)
                @debug "Using _parent_ dep graph"
            catch err# TODO
                err isa Resolve.ResolverError || rethrow()
                allow_reresolve || rethrow()
                @debug err
                @warn "Could not use exact versions of packages in manifest, re-resolving"
                temp_ctx.env.manifest.deps = Dict(uuid => entry for (uuid, entry) in temp_ctx.env.manifest.deps if isfixed(entry))
                Pkg.resolve(temp_ctx; io=devnull, skip_writing_project=true)
                @debug "Using _clean_ dep graph"
            end

            reset_all_compat!(temp_ctx.env.project)
            write_env(temp_ctx.env, update_undo = false)

            # Run sandboxed code
            path_sep = Sys.iswindows() ? ';' : ':'
            withenv(fn, "JULIA_LOAD_PATH" => "@$(path_sep)$(tmp)", "JULIA_PROJECT" => nothing)
        end
    end
end


# Mostly here to give PkgEval some more coverage for packages
# that still use test/REQUIRE. Ignores version bounds
function parse_REQUIRE(require_path::String)
    packages = String[]
    for entry in eachline(require_path)
        if startswith(entry, '#') || isempty(entry)
            continue
        end
        # For lines like @osx Foo, ignore @osx
        words = split(entry)
        if startswith(words[1], '@')
            popfirst!(words)
        end
        push!(packages, popfirst!(words))
    end
    return packages
end

# "targets" based test deps -> "test/Project.toml" based deps
function gen_target_project(ctx::Context, pkg::PackageSpec, source_path::String, target::String)
    env = ctx.env
    registries = ctx.registries
    test_project = Types.Project()
    if projectfile_path(source_path; strict=true) === nothing
        # no project file, assuming this is an old REQUIRE package
        test_project.deps = copy(env.manifest[pkg.uuid].deps)
        if target == "test"
            test_REQUIRE_path = joinpath(source_path, "test", "REQUIRE")
            if isfile(test_REQUIRE_path)
                @warn "using test/REQUIRE files is deprecated and current support is lacking in some areas"
                test_pkgs = parse_REQUIRE(test_REQUIRE_path)
                package_specs = [PackageSpec(name=pkg) for pkg in test_pkgs]
                registry_resolve!(registries, package_specs)
                stdlib_resolve!(package_specs)
                ensure_resolved(ctx, env.manifest, package_specs, registry=true)
                for spec in package_specs
                    test_project.deps[spec.name] = spec.uuid
                end
            end
        end
        return test_project
    end
    # collect relevant info from source
    source_env = EnvCache(projectfile_path(source_path))
    # collect regular dependencies
    test_project.deps = source_env.project.deps
    # collect test dependencies
    for name in get(source_env.project.targets, target, String[])
        uuid = nothing
        for list in [source_env.project.extras, source_env.project.weakdeps]
            uuid = get(list, name, nothing)
            uuid === nothing || break
        end
        if uuid === nothing
            pkgerror("`$name` declared as a `$target` dependency, but no such entry in `extras` or `weakdeps`")
        end
        test_project.deps[name] = uuid
    end
    # collect compat entries
    for (name, uuid) in test_project.deps
        compat = get_compat_str(source_env.project, name)
        compat === nothing && continue
        set_compat(test_project, name, compat)
    end
    return test_project
end

testdir(source_path::String) = joinpath(source_path, "test")
testfile(source_path::String) = joinpath(testdir(source_path), "runtests.jl")
function test(ctx::Context, pkgs::Vector{PackageSpec};
              coverage=false, julia_args::Cmd=``, test_args::Cmd=``,
              test_fn=nothing,
              force_latest_compatible_version::Bool=false,
              allow_earlier_backwards_compatible_versions::Bool=true,
              allow_reresolve::Bool=true)
    Pkg.instantiate(ctx; allow_autoprecomp = false) # do precomp later within sandbox

    # load manifest data
    for pkg in pkgs
        is_stdlib(pkg.uuid) && continue
        if Types.is_project_uuid(ctx.env, pkg.uuid)
            pkg.path = dirname(ctx.env.project_file)
            pkg.version = ctx.env.pkg.version
        else
            entry = manifest_info(ctx.env.manifest, pkg.uuid)
            pkg.version = entry.version
            pkg.tree_hash = entry.tree_hash
            pkg.repo = entry.repo
            pkg.path = entry.path
            pkg.pinned = entry.pinned
        end
    end

    # See if we can find the test files for all packages
    missing_runtests = String[]
    source_paths     = String[] # source_path is the package root (not /src)
    for pkg in pkgs
        sourcepath = project_rel_path(ctx.env, source_path(ctx.env.manifest_file, pkg, ctx.julia_version)) # TODO
        !isfile(testfile(sourcepath)) && push!(missing_runtests, pkg.name)
        push!(source_paths, sourcepath)
    end
    if !isempty(missing_runtests)
        pkgerror(length(missing_runtests) == 1 ? "Package " : "Packages ",
                join(missing_runtests, ", "),
                " did not provide a `test/runtests.jl` file")
    end

    # sandbox
    pkgs_errored = Tuple{String, Base.Process}[]
    for (pkg, source_path) in zip(pkgs, source_paths)
        # compatibility shim between "targets" and "test/Project.toml"
        local test_project_preferences, test_project_override
        if isfile(projectfile_path(testdir(source_path)))
            test_project_override = nothing
            with_load_path([testdir(source_path), Base.LOAD_PATH...]) do
                test_project_preferences = Base.get_preferences()
            end
        else
            test_project_override = gen_target_project(ctx, pkg, source_path, "test")
            with_load_path([something(projectfile_path(source_path)), Base.LOAD_PATH...]) do
                test_project_preferences = Base.get_preferences()
            end
        end
        # now we sandbox
        printpkgstyle(ctx.io, :Testing, pkg.name)
        sandbox(ctx, pkg, source_path, testdir(source_path), test_project_override; preferences=test_project_preferences, force_latest_compatible_version, allow_earlier_backwards_compatible_versions, allow_reresolve) do
            test_fn !== nothing && test_fn()
            sandbox_ctx = Context(;io=ctx.io)
            status(sandbox_ctx.env, sandbox_ctx.registries; mode=PKGMODE_COMBINED, io=sandbox_ctx.io, ignore_indent = false, show_usagetips = false)

            if should_autoprecompile()
                # Precompile in a child process with the test julia args to ensure native caches match test setup
                cmd = gen_test_precompile_code(source_path; coverage, julia_args, test_args)
                p, interrupted = subprocess_handler(cmd, ctx, sandbox_ctx, "Precompilation of test environment interrupted. Exiting the test precompilation process")
                if !success(p)
                    if interrupted
                        return
                    else
                        printpkgstyle(ctx.io, :Testing, "Precompilation of test environment failed. Continuing to tests", color = Base.warn_color())
                    end
                end
            end

            printpkgstyle(ctx.io, :Testing, "Running tests...")
            flush(ctx.io)
            cmd = gen_test_code(source_path; coverage, julia_args, test_args)
            p, interrupted = subprocess_handler(cmd, ctx, sandbox_ctx, "Tests interrupted. Exiting the test process")
            if success(p)
                printpkgstyle(ctx.io, :Testing, pkg.name * " tests passed ")
            elseif !interrupted
                push!(pkgs_errored, (pkg.name, p))
            end
        end
    end

    # TODO: Should be included in Base
    function signal_name(signal::Integer)
        if signal == Base.SIGHUP
            "HUP"
        elseif signal == Base.SIGINT
            "INT"
        elseif signal == Base.SIGQUIT
            "QUIT"
        elseif signal == Base.SIGKILL
            "KILL"
        elseif signal == Base.SIGPIPE
            "PIPE"
        elseif signal == Base.SIGTERM
            "TERM"
        else
            string(signal)
        end
    end

    # report errors
    if !isempty(pkgs_errored)
        function reason(p)
            if Base.process_signaled(p)
                " (received signal: " * signal_name(p.termsignal) * ")"
            elseif Base.process_exited(p) && p.exitcode != 1
                " (exit code: " * string(p.exitcode) * ")"
            else
                ""
            end
        end

        if length(pkgs_errored) == 1
            pkg_name, p = first(pkgs_errored)
            pkgerror("Package $pkg_name errored during testing$(reason(p))")
        else
            failures = ["• $pkg_name$(reason(p))" for (pkg_name, p) in pkgs_errored]
            pkgerror("Packages errored during testing:\n", join(failures, "\n"))
        end
    end
end

# Handles the interrupting of a subprocess gracefully to avoid orphaning
function subprocess_handler(cmd::Cmd, ctx, sandbox_ctx, error_msg::String)
    @debug "Running command" cmd
    p = run(pipeline(ignorestatus(cmd), stdout = sandbox_ctx.io, stderr = stderr_f()), wait = false)
    interrupted = false
    try
        wait(p)
    catch e
        if e isa InterruptException
            interrupted = true
            print("\n")
            printpkgstyle(ctx.io, :Testing, "$error_msg\n", color = Base.error_color())
            # Give some time for the child interrupt handler to print a stacktrace and exit,
            # then kill the process if still running
            if timedwait(() -> !process_running(p), 4) == :timed_out
                kill(p, Base.SIGKILL)
            end
        else
            rethrow()
        end
    end
    return p, interrupted
end

# Display

function stat_rep(x::PackageSpec; name=true)
    name = name ? "$(x.name)" : ""
    version = x.version == VersionSpec() ? "" : "v$(x.version)"
    rev = ""
    if x.repo.rev !== nothing
        rev = occursin(r"\b([a-f0-9]{40})\b", x.repo.rev) ? x.repo.rev[1:7] : x.repo.rev
    end
    subdir_str = x.repo.subdir === nothing ? "" : ":$(x.repo.subdir)"
    repo = Operations.is_tracking_repo(x) ? "`$(x.repo.source)$(subdir_str)#$(rev)`" : ""
    path = Operations.is_tracking_path(x) ? "$(pathrepr(x.path))" : ""
    pinned = x.pinned ? "⚲" : ""
    return join(filter(!isempty, [name,version,repo,path,pinned]), " ")
end

print_single(io::IO, pkg::PackageSpec) = print(io, stat_rep(pkg))

is_instantiated(::Nothing) = false
is_instantiated(x::PackageSpec) = x.version != VersionSpec() || is_stdlib(x.uuid)
# Compare an old and new node of the dependency graph and print a single line to summarize the change
function print_diff(io::IO, old::Union{Nothing,PackageSpec}, new::Union{Nothing,PackageSpec})
    if !is_instantiated(old) && is_instantiated(new)
        printstyled(io, "+ $(stat_rep(new))"; color=:light_green)
    elseif !is_instantiated(new)
        printstyled(io, "- $(stat_rep(old))"; color=:light_red)
    elseif is_tracking_registry(old) && is_tracking_registry(new) &&
           new.version isa VersionNumber && old.version isa VersionNumber && new.version != old.version
        if new.version > old.version
            printstyled(io, "↑ $(stat_rep(old)) ⇒ $(stat_rep(new; name=false))"; color=:light_yellow)
        else
            printstyled(io, "↓ $(stat_rep(old)) ⇒ $(stat_rep(new; name=false))"; color=:light_magenta)
        end
    else
        printstyled(io, "~ $(stat_rep(old)) ⇒ $(stat_rep(new; name=false))"; color=:light_yellow)
    end
end

function status_compat_info(pkg::PackageSpec, env::EnvCache, regs::Vector{Registry.RegistryInstance})
    pkg.version isa VersionNumber || return nothing # Can happen when there is no manifest
    manifest, project = env.manifest, env.project
    packages_holding_back = String[]
    max_version, max_version_in_compat = v"0", v"0"
    for reg in regs
        reg_pkg = get(reg, pkg.uuid, nothing)
        reg_pkg === nothing && continue
        info = Registry.registry_info(reg_pkg)
        reg_compat_info = Registry.compat_info(info)
        versions = keys(reg_compat_info)
        versions = filter(v -> !Registry.isyanked(info, v), versions)
        max_version_reg = maximum(versions; init=v"0")
        max_version = max(max_version, max_version_reg)
        compat_spec = get_compat(env.project, pkg.name)
        versions_in_compat = filter(in(compat_spec), keys(reg_compat_info))
        max_version_in_compat = max(max_version_in_compat, maximum(versions_in_compat; init=v"0"))
    end
    max_version == v"0" && return nothing
    pkg.version >= max_version && return nothing

    pkgid = Base.PkgId(pkg.uuid, pkg.name)
    if PKGORIGIN_HAVE_VERSION && RESPECT_SYSIMAGE_VERSIONS[] && Base.in_sysimage(pkgid)
        pkgorigin = get(Base.pkgorigins, pkgid, nothing)
        if pkgorigin !== nothing && pkg.version !== nothing && pkg.version == pkgorigin.version
            return ["sysimage"], max_version, max_version_in_compat
        end
    end

    # Check compat of project
    if pkg.version == max_version_in_compat && max_version_in_compat != max_version
        return ["compat"], max_version, max_version_in_compat
    end

    manifest_info = get(manifest, pkg.uuid, nothing)
    manifest_info === nothing && return nothing

    # Check compat of dependencies
    for (uuid, dep_pkg) in manifest
        is_stdlib(uuid) && continue
        if !(pkg.uuid in values(dep_pkg.deps))
            continue
        end
        dep_info = get(manifest, uuid, nothing)
        dep_info === nothing && continue
        for reg in regs
            reg_pkg = get(reg, uuid, nothing)
            reg_pkg === nothing && continue
            info = Registry.registry_info(reg_pkg)
            reg_compat_info = Registry.compat_info(info)
            compat_info_v = get(reg_compat_info, dep_info.version, nothing)
            compat_info_v === nothing && continue
            compat_info_v_uuid = get(compat_info_v, pkg.uuid, nothing)
            compat_info_v_uuid === nothing && continue
            if !(max_version in compat_info_v_uuid)
                push!(packages_holding_back, dep_pkg.name)
            end
        end
    end

    # Check compat with Julia itself
    julia_compatible_versions = Set{VersionNumber}()
    for reg in regs
        reg_pkg = get(reg, pkg.uuid, nothing)
        reg_pkg === nothing && continue
        info = Registry.registry_info(reg_pkg)
        reg_compat_info = Registry.compat_info(info)
        compat_info_v = get(reg_compat_info, pkg.version, nothing)
        versions = keys(reg_compat_info)
        for v in versions
            compat_info_v = get(reg_compat_info, v, nothing)
            compat_info_v === nothing && continue
            compat_info_v_uuid = compat_info_v[JULIA_UUID]
            if VERSION in compat_info_v_uuid
                push!(julia_compatible_versions, v)
            end
        end
    end
    if !(max_version in julia_compatible_versions)
        push!(packages_holding_back, "julia")
    end

    return sort!(unique!(packages_holding_back)), max_version, max_version_in_compat
end

function diff_array(old_env::Union{EnvCache,Nothing}, new_env::EnvCache; manifest=true)
    function index_pkgs(pkgs, uuid)
        idx = findfirst(pkg -> pkg.uuid == uuid, pkgs)
        return idx === nothing ? nothing : pkgs[idx]
    end
    # load deps
    new = manifest ? load_manifest_deps(new_env.manifest) : load_direct_deps(new_env)
    T, S = Union{UUID,Nothing}, Union{PackageSpec,Nothing}
    if old_env === nothing
        return Tuple{T,S,S}[(pkg.uuid, nothing, pkg)::Tuple{T,S,S} for pkg in new]
    end
    old = manifest ? load_manifest_deps(old_env.manifest) : load_direct_deps(old_env)
    # merge old and new into single array
    all_uuids = union(T[pkg.uuid for pkg in old], T[pkg.uuid for pkg in new])
    return Tuple{T,S,S}[(uuid, index_pkgs(old, uuid), index_pkgs(new, uuid))::Tuple{T,S,S} for uuid in all_uuids]
end

function is_package_downloaded(manifest_file::String, pkg::PackageSpec; platform=HostPlatform())
    sourcepath = source_path(manifest_file, pkg)
    identifier = pkg.name !== nothing ? pkg.name : pkg.uuid
    (sourcepath === nothing) && pkgerror("Could not locate the source code for the $(identifier) package. Are you trying to use a manifest generated by a different version of Julia?")
    isdir(sourcepath) || return false
    check_artifacts_downloaded(sourcepath; platform) || return false
    return true
end

function status_ext_info(pkg::PackageSpec, env::EnvCache)
    manifest = env.manifest
    manifest_info = get(manifest, pkg.uuid, nothing)
    manifest_info === nothing && return nothing
    weakdepses = manifest_info.weakdeps
    exts = manifest_info.exts
    if !isempty(weakdepses) && !isempty(exts)
        v = ExtInfo[]
        for (ext, extdeps) in exts
            extdeps isa String && (extdeps = String[extdeps])
            ext_loaded = (Base.get_extension(Base.PkgId(pkg.uuid, pkg.name), Symbol(ext)) !== nothing)
            # Check if deps are loaded
            extdeps_info= Tuple{String, Bool}[]
            for extdep in extdeps
                uuid = weakdepses[extdep]
                loaded = haskey(Base.loaded_modules, Base.PkgId(uuid, extdep))
                push!(extdeps_info, (extdep, loaded))
            end
            push!(v, ExtInfo((ext, ext_loaded), extdeps_info))
        end
        return v
    end
    return nothing
end

struct ExtInfo
    ext::Tuple{String, Bool} # name, loaded
    weakdeps::Vector{Tuple{String, Bool}} # name, loaded
end
struct PackageStatusData
    uuid::UUID
    old::Union{Nothing, PackageSpec}
    new::Union{Nothing, PackageSpec}
    downloaded::Bool
    upgradable::Bool
    heldback::Bool
    compat_data::Union{Nothing, Tuple{Vector{String}, VersionNumber, VersionNumber}}
    changed::Bool
    extinfo::Union{Nothing, Vector{ExtInfo}}
end

function print_status(env::EnvCache, old_env::Union{Nothing,EnvCache}, registries::Vector{Registry.RegistryInstance}, header::Symbol,
                      uuids::Vector, names::Vector; manifest=true, diff=false, ignore_indent::Bool, outdated::Bool, extensions::Bool, io::IO,
                      mode::PackageMode, hidden_upgrades_info::Bool, show_usagetips::Bool=true)
    not_installed_indicator = sprint((io, args) -> printstyled(io, args...; color=Base.error_color()), "→", context=io)
    upgradable_indicator = sprint((io, args) -> printstyled(io, args...; color=:green), "⌃", context=io)
    heldback_indicator = sprint((io, args) -> printstyled(io, args...; color=Base.warn_color()), "⌅", context=io)
    filter = !isempty(uuids) || !isempty(names)
    # setup
    xs = diff_array(old_env, env; manifest=manifest)
    # filter and return early if possible
    if isempty(xs) && !diff
        printpkgstyle(io, header, "$(pathrepr(manifest ? env.manifest_file : env.project_file)) (empty " *
                      (manifest ? "manifest" : "project") * ")", ignore_indent)
        return nothing
    end
    no_changes = all(p-> p[2] == p[3], xs)
    if no_changes
        printpkgstyle(io, Symbol("No Changes"), "to $(pathrepr(manifest ? env.manifest_file : env.project_file))", ignore_indent)
    else
        xs = !filter ? xs : eltype(xs)[(id, old, new) for (id, old, new) in xs if (id in uuids || something(new, old).name in names)]
        if isempty(xs)
            printpkgstyle(io, Symbol("No Matches"),
                        "in $(diff ? "diff for " : "")$(pathrepr(manifest ? env.manifest_file : env.project_file))", ignore_indent)
            return nothing
        end
        # main print
        printpkgstyle(io, header, pathrepr(manifest ? env.manifest_file : env.project_file), ignore_indent)
        # Sort stdlibs and _jlls towards the end in status output
        xs = sort!(xs, by = (x -> (is_stdlib(x[1]), endswith(something(x[3], x[2]).name, "_jll"), something(x[3], x[2]).name, x[1])))
    end

    all_packages_downloaded = true
    no_packages_upgradable = true
    no_visible_packages_heldback = true
    no_packages_heldback = true
    lpadding = 2

    package_statuses = PackageStatusData[]
    for (uuid, old, new) in xs
        if Types.is_project_uuid(env, uuid)
            continue
        end
        latest_version = true
        # Outdated info
        cinfo = nothing
        ext_info = nothing
        if !isnothing(new) && !is_stdlib(new.uuid)
            cinfo = status_compat_info(new, env, registries)
            if cinfo !== nothing
                latest_version = false
            end
        end
        # if we are running with outdated, only show packages that are upper bounded
        if outdated && latest_version
            continue
        end

        if !isnothing(new) && !is_stdlib(new.uuid)
            ext_info = status_ext_info(new, env)
        end

        if extensions && ext_info === nothing
            continue
        end


        # TODO: Show extension deps for project as well?

        pkg_downloaded = !is_instantiated(new) || is_package_downloaded(env.manifest_file, new)

        new_ver_avail = !latest_version && !Operations.is_tracking_repo(new) && !Operations.is_tracking_path(new)
        pkg_upgradable = new_ver_avail && isempty(cinfo[1])
        pkg_heldback = new_ver_avail && !isempty(cinfo[1])

        if !pkg_downloaded && (pkg_upgradable || pkg_heldback)
            # allow space in the gutter for two icons on a single line
            lpadding = 3
        end
        changed = old != new
        all_packages_downloaded &= (!changed || pkg_downloaded)
        no_packages_upgradable &= (!changed || !pkg_upgradable)
        no_visible_packages_heldback &= (!changed || !pkg_heldback)
        no_packages_heldback &= !pkg_heldback

        push!(package_statuses, PackageStatusData(uuid, old, new, pkg_downloaded, pkg_upgradable, pkg_heldback, cinfo, changed, ext_info))
    end

    for pkg in package_statuses
        diff && !pkg.changed && continue # in diff mode don't print packages that didn't change

        pad = 0
        print_padding(x) = (print(io, x); pad += 1)

        if !pkg.downloaded
            print_padding(not_installed_indicator)
        elseif lpadding > 2
            print_padding(" ")
        end
        if pkg.upgradable
            print_padding(upgradable_indicator)
        elseif pkg.heldback
            print_padding(heldback_indicator)
        end

        # Fill the remaining padding with spaces
        while pad < lpadding
            print_padding(" ")
        end

        printstyled(io, "[", string(pkg.uuid)[1:8], "] "; color = :light_black)

        diff ? print_diff(io, pkg.old, pkg.new) : print_single(io, pkg.new)

        if outdated && !diff && pkg.compat_data !== nothing
            packages_holding_back, max_version, max_version_compat = pkg.compat_data
            if pkg.new.version !== max_version_compat && max_version_compat != max_version
                printstyled(io, " [<v", max_version_compat, "]", color=:light_magenta)
                printstyled(io, ",")
            end
            printstyled(io, " (<v", max_version, ")"; color=Base.warn_color())
            if packages_holding_back == ["compat"]
                printstyled(io, " [compat]"; color=:light_magenta)
            elseif packages_holding_back == ["sysimage"]
                printstyled(io, " [sysimage]"; color=:light_magenta)
            else
                pkg_str = isempty(packages_holding_back) ? "" : string(": ", join(packages_holding_back, ", "))
                printstyled(io, pkg_str; color=Base.warn_color())
            end
        end

        if extensions && !diff && pkg.extinfo !== nothing
            println(io)
            for (i, ext) in enumerate(pkg.extinfo)
                sym = i == length(pkg.extinfo) ? '└' : '├'
                function print_ext_entry(io, (name, installed))
                    color = installed ? :light_green : :light_black
                    printstyled(io, name, ;color)
                end
                print(io, "              ", sym, "─ ")
                print_ext_entry(io, ext.ext)

                print(io, " [")
                join(io,sprint.(print_ext_entry, ext.weakdeps; context=io), ", ")
                print(io, "]")
                if i != length(pkg.extinfo)
                    println(io)
                end
            end
        end

        println(io)
    end

    if !no_changes && !all_packages_downloaded
        printpkgstyle(io, :Info, "Packages marked with $not_installed_indicator are not downloaded, use `instantiate` to download", color=Base.info_color(), ignore_indent)
    end
    if !outdated && (mode != PKGMODE_COMBINED || (manifest == true))
        tipend = manifest ? " -m" : ""
        tip = show_usagetips ? " To see why use `status --outdated$tipend`" : ""
        if !no_packages_upgradable && no_visible_packages_heldback
            printpkgstyle(io, :Info, "Packages marked with $upgradable_indicator have new versions available and may be upgradable.", color=Base.info_color(), ignore_indent)
        end
        if !no_visible_packages_heldback && no_packages_upgradable
            printpkgstyle(io, :Info, "Packages marked with $heldback_indicator have new versions available but compatibility constraints restrict them from upgrading.$tip", color=Base.info_color(), ignore_indent)
        end
        if !no_visible_packages_heldback && !no_packages_upgradable
            printpkgstyle(io, :Info, "Packages marked with $upgradable_indicator and $heldback_indicator have new versions available. Those with $upgradable_indicator may be upgradable, but those with $heldback_indicator are restricted by compatibility constraints from upgrading.$tip", color=Base.info_color(), ignore_indent)
        end
        if !manifest && hidden_upgrades_info && no_visible_packages_heldback && !no_packages_heldback
            # only warn if showing project and outdated indirect deps are hidden
            printpkgstyle(io, :Info, "Some packages have new versions but compatibility constraints restrict them from upgrading.$tip", color=Base.info_color(), ignore_indent)
        end
    end

    return nothing
end

function git_head_env(env, project_dir)
    new_env = EnvCache()
    try
        LibGit2.with(LibGit2.GitRepo(project_dir)) do repo
            git_path = LibGit2.path(repo)
            project_path = relpath(env.project_file, git_path)
            manifest_path = relpath(env.manifest_file, git_path)
            new_env.project = read_project(GitTools.git_file_stream(repo, "HEAD:$project_path", fakeit=true))
            new_env.manifest = read_manifest(GitTools.git_file_stream(repo, "HEAD:$manifest_path", fakeit=true))
            return new_env
        end
    catch err
        err isa PkgError || rethrow(err)
        return nothing
    end
end

function show_update(env::EnvCache, registries::Vector{Registry.RegistryInstance}; io::IO, hidden_upgrades_info = false)
    old_env = EnvCache()
    old_env.project = env.original_project
    old_env.manifest = env.original_manifest
    status(env, registries; header=:Updating, mode=PKGMODE_COMBINED, env_diff=old_env, ignore_indent=false, io=io, hidden_upgrades_info)
    return nothing
end

function status(env::EnvCache, registries::Vector{Registry.RegistryInstance}, pkgs::Vector{PackageSpec}=PackageSpec[];
                header=nothing, mode::PackageMode=PKGMODE_PROJECT, git_diff::Bool=false, env_diff=nothing, ignore_indent=true,
                io::IO, outdated::Bool=false, extensions::Bool=false, hidden_upgrades_info::Bool=false, show_usagetips::Bool=true)
    io == Base.devnull && return
    # if a package, print header
    if header === nothing && env.pkg !== nothing
       printpkgstyle(io, :Project, string(env.pkg.name, " v", env.pkg.version), true; color=Base.info_color())
    end
    # load old env
    old_env = nothing
    if git_diff
        project_dir = dirname(env.project_file)
        if !ispath(joinpath(project_dir, ".git"))
            @warn "diff option only available for environments in git repositories, ignoring."
        else
            old_env = git_head_env(env, project_dir)
            if old_env === nothing
                @warn "could not read project from HEAD, displaying absolute status instead."
            end
        end
    elseif env_diff !== nothing
        old_env = env_diff
    end
    # display
    filter_uuids = [pkg.uuid::UUID for pkg in pkgs if pkg.uuid !== nothing]
    filter_names = [pkg.name::String for pkg in pkgs if pkg.name !== nothing]
    diff = old_env !== nothing
    header = something(header, diff ? :Diff : :Status)
    if mode == PKGMODE_PROJECT || mode == PKGMODE_COMBINED
        print_status(env, old_env, registries, header, filter_uuids, filter_names; manifest=false, diff, ignore_indent, io, outdated, extensions, mode, hidden_upgrades_info, show_usagetips)
    end
    if mode == PKGMODE_MANIFEST || mode == PKGMODE_COMBINED
        print_status(env, old_env, registries, header, filter_uuids, filter_names; diff, ignore_indent, io, outdated, extensions, mode, hidden_upgrades_info, show_usagetips)
    end
    if is_manifest_current(env) === false
        tip = show_usagetips ? " It is recommended to `Pkg.resolve()` or consider `Pkg.update()` if necessary." : ""
        printpkgstyle(io, :Warning, "The project dependencies or compat requirements have changed since the manifest was last resolved.$tip",
            ignore_indent; color=Base.warn_color())
    end
end

function is_manifest_current(env::EnvCache)
    if haskey(env.manifest.other, "project_hash")
        recorded_hash = env.manifest.other["project_hash"]
        current_hash = Types.project_resolve_hash(env.project)
        return recorded_hash == current_hash
    else
        # Manifest doesn't have a hash of the source Project recorded
        return nothing
    end
end

function compat_line(io, pkg, uuid, compat_str, longest_dep_len; indent = "  ")
    iob = IOBuffer()
    ioc = IOContext(iob, :color => get(io, :color, false)::Bool)
    if isnothing(uuid)
        print(ioc, "$indent           ")
    else
        printstyled(ioc, "$indent[", string(uuid)[1:8], "] "; color = :light_black)
    end
    print(ioc, rpad(pkg, longest_dep_len))
    if isnothing(compat_str)
        printstyled(ioc, " none"; color = :light_black)
    else
        print(ioc, " ", compat_str)
    end
    return String(take!(iob))
end

function print_compat(ctx::Context, pkgs_in::Vector{PackageSpec} = PackageSpec[]; io = nothing)
    io = something(io, ctx.io)
    printpkgstyle(io, :Compat, pathrepr(ctx.env.project_file))
    names = [pkg.name for pkg in pkgs_in]
    pkgs = isempty(pkgs_in) ? ctx.env.project.deps : filter(pkg -> in(first(pkg), names), ctx.env.project.deps)
    add_julia = isempty(pkgs_in) || any(p->p.name == "julia", pkgs_in)
    longest_dep_len = isempty(pkgs) ? length("julia") : max(reduce(max, map(length, collect(keys(pkgs)))), length("julia"))
    if add_julia
        println(io, compat_line(io, "julia", nothing, get_compat_str(ctx.env.project, "julia"), longest_dep_len))
    end
    for (dep, uuid) in pkgs
        println(io, compat_line(io, dep, uuid, get_compat_str(ctx.env.project, dep), longest_dep_len))
    end
end
print_compat(pkg::String; kwargs...) = print_compat(Context(), pkg; kwargs...)
print_compat(; kwargs...) = print_compat(Context(); kwargs...)

function apply_force_latest_compatible_version!(ctx::Types.Context;
                                                target_name = nothing,
                                                allow_earlier_backwards_compatible_versions::Bool = true)
    deps_from_env = load_direct_deps(ctx.env)
    deps = [(; name = x.name, uuid = x.uuid) for x in deps_from_env]
    for dep in deps
        if !is_stdlib(dep.uuid)
            apply_force_latest_compatible_version!(
                ctx,
                dep;
                target_name,
                allow_earlier_backwards_compatible_versions,
            )
        end
    end
    return nothing
end

function apply_force_latest_compatible_version!(ctx::Types.Context,
                                                dep::NamedTuple{(:name, :uuid), Tuple{String, Base.UUID}};
                                                target_name = nothing,
                                                allow_earlier_backwards_compatible_versions::Bool = true)
    name, uuid = dep
    has_compat = haskey(ctx.env.project.compat, name)
    if !has_compat
        if name != target_name
            @warn(
                "Dependency does not have a [compat] entry",
                name, uuid, target_name,
            )
        end
        return nothing
    end
    old_compat_spec = ctx.env.project.compat[name].val
    latest_compatible_version = get_latest_compatible_version(
        ctx,
        uuid,
        old_compat_spec,
    )
    earliest_backwards_compatible_version = get_earliest_backwards_compatible_version(latest_compatible_version)
    if allow_earlier_backwards_compatible_versions
        version_for_intersect = only_major_minor_patch(earliest_backwards_compatible_version)
    else
        version_for_intersect = only_major_minor_patch(latest_compatible_version)
    end
    compat_for_intersect = Pkg.Types.semver_spec("≥ $(version_for_intersect)")
    new_compat_spec = Base.intersect(old_compat_spec, compat_for_intersect)
    ctx.env.project.compat[name].val = new_compat_spec
    return nothing
end

function only_major_minor_patch(ver::Base.VersionNumber)
    return Base.VersionNumber(ver.major, ver.minor, ver.patch)
end

function get_earliest_backwards_compatible_version(ver::Base.VersionNumber)
    (ver.major > 0) && return Base.VersionNumber(ver.major, 0, 0)
    (ver.minor > 0) && return Base.VersionNumber(0, ver.minor, 0)
    return Base.VersionNumber(0, 0, ver.patch)
end

function get_latest_compatible_version(ctx::Types.Context,
                                       uuid::Base.UUID,
                                       compat_spec::VersionSpec)
    all_registered_versions = get_all_registered_versions(ctx, uuid)
    compatible_versions = filter(in(compat_spec), all_registered_versions)
    latest_compatible_version = maximum(compatible_versions)
    return latest_compatible_version
end

function get_all_registered_versions(ctx::Types.Context,
                                     uuid::Base.UUID)
    versions = Set{VersionNumber}()
    for reg in ctx.registries
        pkg = get(reg, uuid, nothing)
        if pkg !== nothing
            info = Registry.registry_info(pkg)
            union!(versions, keys(info.version_info))
        end
    end
    return versions
end

end # module
j   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Pkg/src/API.jlax     # This file is a part of Julia. License is MIT: https://julialang.org/license

module API

using UUIDs
using Printf
import Random
using Dates
import LibGit2
import Logging
using Serialization
using REPL.TerminalMenus
import FileWatching

import Base: StaleCacheKey

import ..depots, ..depots1, ..logdir, ..devdir, ..printpkgstyle
import ..Operations, ..GitTools, ..Pkg, ..Registry
import ..can_fancyprint, ..pathrepr, ..isurl, ..PREV_ENV_PATH
using ..Types, ..TOML
using ..Types: VersionTypes
using Base.BinaryPlatforms
import ..stderr_f, ..stdout_f
using ..Artifacts: artifact_paths
using ..MiniProgressBars
import ..Resolve: ResolverError

include("generate.jl")

Base.@kwdef struct PackageInfo
    name::String
    version::Union{Nothing,VersionNumber}
    tree_hash::Union{Nothing,String}
    is_direct_dep::Bool
    is_pinned::Bool
    is_tracking_path::Bool
    is_tracking_repo::Bool
    is_tracking_registry::Bool
    git_revision::Union{Nothing,String}
    git_source::Union{Nothing,String}
    source::String
    dependencies::Dict{String,UUID}
end

function Base.:(==)(a::PackageInfo, b::PackageInfo)
    return a.name == b.name && a.version == b.version && a.tree_hash == b.tree_hash &&
        a.is_direct_dep == b.is_direct_dep &&
        a.is_pinned == b.is_pinned && a.is_tracking_path == b.is_tracking_path &&
        a.is_tracking_repo == b.is_tracking_repo &&
        a.is_tracking_registry == b.is_tracking_registry &&
        a.git_revision == b.git_revision && a.git_source == b.git_source &&
        a.source == b.source && a.dependencies == b.dependencies
end

function package_info(env::EnvCache, pkg::PackageSpec)::PackageInfo
    entry = manifest_info(env.manifest, pkg.uuid)
    if entry === nothing
        pkgerror("expected package $(err_rep(pkg)) to exist in the manifest",
                 " (use `resolve` to populate the manifest)")
    end
    package_info(env, pkg, entry)
end

function package_info(env::EnvCache, pkg::PackageSpec, entry::PackageEntry)::PackageInfo
    git_source = pkg.repo.source === nothing ? nothing :
        isurl(pkg.repo.source::String) ? pkg.repo.source::String :
        Operations.project_rel_path(env, pkg.repo.source::String)
    info = PackageInfo(
        name                 = pkg.name,
        version              = pkg.version != VersionSpec() ? pkg.version : nothing,
        tree_hash            = pkg.tree_hash === nothing ? nothing : string(pkg.tree_hash), # TODO or should it just be a SHA?
        is_direct_dep        = pkg.uuid in values(env.project.deps),
        is_pinned            = pkg.pinned,
        is_tracking_path     = pkg.path !== nothing,
        is_tracking_repo     = pkg.repo.rev !== nothing || pkg.repo.source !== nothing,
        is_tracking_registry = Operations.is_tracking_registry(pkg),
        git_revision         = pkg.repo.rev,
        git_source           = git_source,
        source               = Operations.project_rel_path(env, Operations.source_path(env.manifest_file, pkg)),
        dependencies         = copy(entry.deps), #TODO is copy needed?
    )
    return info
end

dependencies() = dependencies(EnvCache())
function dependencies(env::EnvCache)
    pkgs = Operations.load_all_deps(env)
    return Dict(pkg.uuid::UUID => package_info(env, pkg) for pkg in pkgs)
end
function dependencies(fn::Function, uuid::UUID)
    dep = get(dependencies(), uuid, nothing)
    if dep === nothing
        pkgerror("dependency with UUID `$uuid` does not exist")
    end
    fn(dep)
end


Base.@kwdef struct ProjectInfo
    name::Union{Nothing,String}
    uuid::Union{Nothing,UUID}
    version::Union{Nothing,VersionNumber}
    ispackage::Bool
    dependencies::Dict{String,UUID}
    path::String
end

project() = project(EnvCache())
function project(env::EnvCache)::ProjectInfo
    pkg = env.pkg
    return ProjectInfo(
        name         = pkg === nothing ? nothing : pkg.name,
        uuid         = pkg === nothing ? nothing : pkg.uuid,
        version      = pkg === nothing ? nothing : pkg.version::VersionNumber,
        ispackage    = pkg !== nothing,
        dependencies = env.project.deps,
        path         = env.project_file
    )
end

function check_package_name(x::AbstractString, mode::Union{Nothing,String,Symbol}=nothing)
    if !Base.isidentifier(x)
        message = sprint() do iostr
            print(iostr, "`$x` is not a valid package name")
            if endswith(lowercase(x), ".jl")
                print(iostr, ". Perhaps you meant `$(chop(x; tail=3))`")
            end
            if mode !== nothing && any(occursin.(['\\','/'], x)) # maybe a url or a path
                print(iostr, "\nThe argument appears to be a URL or path, perhaps you meant ",
                    "`Pkg.$mode(url=\"...\")` or `Pkg.$mode(path=\"...\")`.")
            end
        end
        pkgerror(message)
    end
    return
end
check_package_name(::Nothing, ::Any) = nothing

function require_not_empty(pkgs, f::Symbol)
    isempty(pkgs) && pkgerror("$f requires at least one package")
end

# Provide some convenience calls
for f in (:develop, :add, :rm, :up, :pin, :free, :test, :build, :status, :why, :precompile)
    @eval begin
        $f(pkg::Union{AbstractString, PackageSpec}; kwargs...) = $f([pkg]; kwargs...)
        $f(pkgs::Vector{<:AbstractString}; kwargs...)          = $f([PackageSpec(pkg) for pkg in pkgs]; kwargs...)
        function $f(pkgs::Vector{PackageSpec}; io::IO=$(f === :status ? :stdout_f : :stderr_f)(), kwargs...)
            $(f != :precompile) && Registry.download_default_registries(io)
            ctx = Context()
            # Save initial environment for undo/redo functionality
            if $(f != :precompile) && !saved_initial_snapshot[]
                add_snapshot_to_undo(ctx.env)
                saved_initial_snapshot[] = true
            end
            kwargs = merge((;kwargs...), (:io => io,))
            pkgs = deepcopy(pkgs) # don't mutate input
            foreach(handle_package_input!, pkgs)
            ret = $f(ctx, pkgs; kwargs...)
            $(f in (:add, :up, :pin, :free, :build)) && Pkg._auto_precompile(ctx)
            $(f in (:up, :pin, :free, :rm)) && Pkg._auto_gc(ctx)
            return ret
        end
        $f(ctx::Context; kwargs...) = $f(ctx, PackageSpec[]; kwargs...)
        function $f(; name::Union{Nothing,AbstractString}=nothing, uuid::Union{Nothing,String,UUID}=nothing,
                      version::Union{VersionNumber, String, VersionSpec, Nothing}=nothing,
                      url=nothing, rev=nothing, path=nothing, mode=PKGMODE_PROJECT, subdir=nothing, kwargs...)
            pkg = PackageSpec(; name, uuid, version, url, rev, path, subdir)
            if $f === status || $f === rm || $f === up
                kwargs = merge((;kwargs...), (:mode => mode,))
            end
            # Handle $f() case
            if all(isnothing, [name,uuid,version,url,rev,path,subdir])
                $f(PackageSpec[]; kwargs...)
            else
                $f(pkg; kwargs...)
            end
        end
        function $f(pkgs::Vector{<:NamedTuple}; kwargs...)
            $f([PackageSpec(;pkg...) for pkg in pkgs]; kwargs...)
        end
    end
end

function develop(ctx::Context, pkgs::Vector{PackageSpec}; shared::Bool=true,
                 preserve::PreserveLevel=Operations.default_preserve(), platform::AbstractPlatform=HostPlatform(), kwargs...)
    require_not_empty(pkgs, :develop)
    Context!(ctx; kwargs...)

    for pkg in pkgs
        check_package_name(pkg.name, "develop")
        if pkg.name == "julia" # if julia is passed as a package the solver gets tricked
            pkgerror("`julia` is not a valid package name")
        end
        if pkg.name === nothing && pkg.uuid === nothing && pkg.repo.source === nothing
            pkgerror("name, UUID, URL, or filesystem path specification required when calling `develop`")
        end
        if pkg.repo.rev !== nothing
            pkgerror("rev argument not supported by `develop`; consider using `add` instead")
        end
        if pkg.version != VersionSpec()
            pkgerror("version specification invalid when calling `develop`:",
                     " `$(pkg.version)` specified for package $(err_rep(pkg))")
        end
        # not strictly necessary to check these fields early, but it is more efficient
        if pkg.name !== nothing && (length(findall(x -> x.name == pkg.name, pkgs)) > 1)
            pkgerror("it is invalid to specify multiple packages with the same name: $(err_rep(pkg))")
        end
        if pkg.uuid !== nothing && (length(findall(x -> x.uuid == pkg.uuid, pkgs)) > 1)
            pkgerror("it is invalid to specify multiple packages with the same UUID: $(err_rep(pkg))")
        end
    end

    new_git = handle_repos_develop!(ctx, pkgs, shared)

    for pkg in pkgs
        if Types.collides_with_project(ctx.env, pkg)
            pkgerror("package $(err_rep(pkg)) has the same name or UUID as the active project")
        end
        if length(findall(x -> x.uuid == pkg.uuid, pkgs)) > 1
            pkgerror("it is invalid to specify multiple packages with the same UUID: $(err_rep(pkg))")
        end
    end

    Operations.develop(ctx, pkgs, new_git; preserve=preserve, platform=platform)
    return
end

function add(ctx::Context, pkgs::Vector{PackageSpec}; preserve::PreserveLevel=Operations.default_preserve(),
             platform::AbstractPlatform=HostPlatform(), kwargs...)
    require_not_empty(pkgs, :add)
    Context!(ctx; kwargs...)

    for pkg in pkgs
        check_package_name(pkg.name, "add")
        if pkg.name == "julia" # if julia is passed as a package the solver gets tricked
            pkgerror("`julia` is not a valid package name")
        end
        if pkg.name === nothing && pkg.uuid === nothing && pkg.repo.source === nothing
            pkgerror("name, UUID, URL, or filesystem path specification required when calling `add`")
        end
        if pkg.repo.source !== nothing || pkg.repo.rev !== nothing
            if pkg.version != VersionSpec()
                pkgerror("version specification invalid when tracking a repository:",
                         " `$(pkg.version)` specified for package $(err_rep(pkg))")
            end
        end
        # not strictly necessary to check these fields early, but it is more efficient
        if pkg.name !== nothing && (length(findall(x -> x.name == pkg.name, pkgs)) > 1)
            pkgerror("it is invalid to specify multiple packages with the same name: $(err_rep(pkg))")
        end
        if pkg.uuid !== nothing && (length(findall(x -> x.uuid == pkg.uuid, pkgs)) > 1)
            pkgerror("it is invalid to specify multiple packages with the same UUID: $(err_rep(pkg))")
        end
    end

    repo_pkgs = [pkg for pkg in pkgs if (pkg.repo.source !== nothing || pkg.repo.rev !== nothing)]
    new_git = handle_repos_add!(ctx, repo_pkgs)
    # repo + unpinned -> name, uuid, repo.rev, repo.source, tree_hash
    # repo + pinned -> name, uuid, tree_hash

    Operations.update_registries(ctx; force=false, update_cooldown=Day(1))

    project_deps_resolve!(ctx.env, pkgs)
    registry_resolve!(ctx.registries, pkgs)
    stdlib_resolve!(pkgs)
    ensure_resolved(ctx, ctx.env.manifest, pkgs, registry=true)

    for pkg in pkgs
        if Types.collides_with_project(ctx.env, pkg)
            pkgerror("package $(err_rep(pkg)) has same name or UUID as the active project")
        end
        if length(findall(x -> x.uuid == pkg.uuid, pkgs)) > 1
            pkgerror("it is invalid to specify multiple packages with the same UUID: $(err_rep(pkg))")
        end
    end

    Operations.add(ctx, pkgs, new_git; preserve, platform)
    return
end

function rm(ctx::Context, pkgs::Vector{PackageSpec}; mode=PKGMODE_PROJECT, all_pkgs::Bool=false, kwargs...)
    Context!(ctx; kwargs...)
    if all_pkgs
        !isempty(pkgs) && pkgerror("cannot specify packages when operating on all packages")
        append_all_pkgs!(pkgs, ctx, mode)
    else
        require_not_empty(pkgs, :rm)
    end

    for pkg in pkgs
        if pkg.name === nothing && pkg.uuid === nothing
            pkgerror("name or UUID specification required when calling `rm`")
        end
        if !(pkg.version == VersionSpec() && pkg.pinned == false &&
             pkg.tree_hash === nothing && pkg.repo.source === nothing &&
             pkg.repo.rev === nothing && pkg.path === nothing)
            pkgerror("packages may only be specified by name or UUID when calling `rm`")
        end
    end

    mode == PKGMODE_PROJECT && project_deps_resolve!(ctx.env, pkgs)
    mode == PKGMODE_MANIFEST && manifest_resolve!(ctx.env.manifest, pkgs)
    ensure_resolved(ctx, ctx.env.manifest, pkgs)

    Operations.rm(ctx, pkgs; mode)

    return
end


function append_all_pkgs!(pkgs, ctx, mode)
    if mode == PKGMODE_PROJECT || mode == PKGMODE_COMBINED
        for (name::String, uuid::UUID) in ctx.env.project.deps
            push!(pkgs, PackageSpec(name=name, uuid=uuid))
        end
    end
    if mode == PKGMODE_MANIFEST || mode == PKGMODE_COMBINED
        for (uuid, entry) in ctx.env.manifest
            push!(pkgs, PackageSpec(name=entry.name, uuid=uuid))
        end
    end
    return
end

function up(ctx::Context, pkgs::Vector{PackageSpec};
            level::UpgradeLevel=UPLEVEL_MAJOR, mode::PackageMode=PKGMODE_PROJECT,
            preserve::Union{Nothing,PreserveLevel}= isempty(pkgs) ? nothing : PRESERVE_ALL,
            update_registry::Bool=true,
            skip_writing_project::Bool=false,
            kwargs...)
    Context!(ctx; kwargs...)
    if Operations.is_fully_pinned(ctx)
        printpkgstyle(ctx.io, :Update, "All dependencies are pinned - nothing to update.", color = Base.info_color())
        return
    end
    if update_registry
        Registry.download_default_registries(ctx.io)
        Operations.update_registries(ctx; force=true)
    end
    Operations.prune_manifest(ctx.env)
    if isempty(pkgs)
        append_all_pkgs!(pkgs, ctx, mode)
    else
        mode == PKGMODE_PROJECT && project_deps_resolve!(ctx.env, pkgs)
        mode == PKGMODE_MANIFEST && manifest_resolve!(ctx.env.manifest, pkgs)
        project_deps_resolve!(ctx.env, pkgs)
        manifest_resolve!(ctx.env.manifest, pkgs)
        ensure_resolved(ctx, ctx.env.manifest, pkgs)
    end
    Operations.up(ctx, pkgs, level; skip_writing_project, preserve)
    return
end

resolve(; io::IO=stderr_f(), kwargs...) = resolve(Context(;io); kwargs...)
function resolve(ctx::Context; skip_writing_project::Bool=false, kwargs...)
    up(ctx; level=UPLEVEL_FIXED, mode=PKGMODE_MANIFEST, update_registry=false, skip_writing_project, kwargs...)
    return nothing
end

function pin(ctx::Context, pkgs::Vector{PackageSpec}; all_pkgs::Bool=false, kwargs...)
    Context!(ctx; kwargs...)
    if all_pkgs
        !isempty(pkgs) && pkgerror("cannot specify packages when operating on all packages")
        append_all_pkgs!(pkgs, ctx, PKGMODE_MANIFEST)
    else
        require_not_empty(pkgs, :pin)
    end

    for pkg in pkgs
        if pkg.name === nothing && pkg.uuid === nothing
            pkgerror("name or UUID specification required when calling `pin`")
        end
        if pkg.repo.source !== nothing
            pkgerror("repository specification invalid when calling `pin`:",
                     " `$(pkg.repo.source)` specified for package $(err_rep(pkg))")
        end
        if pkg.repo.rev !== nothing
            pkgerror("git revision specification invalid when calling `pin`:",
                     " `$(pkg.repo.rev)` specified for package $(err_rep(pkg))")
        end
        version = pkg.version
        if version isa VersionSpec
            if version.ranges[1].lower != version.ranges[1].upper # TODO test this
                pkgerror("pinning a package requires a single version, not a versionrange")
            end
        end
    end

    project_deps_resolve!(ctx.env, pkgs)
    ensure_resolved(ctx, ctx.env.manifest, pkgs)
    Operations.pin(ctx, pkgs)
    return
end

function free(ctx::Context, pkgs::Vector{PackageSpec}; all_pkgs::Bool=false, kwargs...)
    Context!(ctx; kwargs...)
    if all_pkgs
        !isempty(pkgs) && pkgerror("cannot specify packages when operating on all packages")
        append_all_pkgs!(pkgs, ctx, PKGMODE_MANIFEST)
    else
        require_not_empty(pkgs, :free)
    end

    for pkg in pkgs
        if pkg.name === nothing && pkg.uuid === nothing
            pkgerror("name or UUID specification required when calling `free`")
        end
        if !(pkg.version == VersionSpec() && pkg.pinned == false &&
             pkg.tree_hash === nothing && pkg.repo.source === nothing &&
             pkg.repo.rev === nothing && pkg.path === nothing)
            pkgerror("packages may only be specified by name or UUID when calling `free`")
        end
    end

    manifest_resolve!(ctx.env.manifest, pkgs)
    ensure_resolved(ctx, ctx.env.manifest, pkgs)

    Operations.free(ctx, pkgs; err_if_free = !all_pkgs)
    return
end

function test(ctx::Context, pkgs::Vector{PackageSpec};
              coverage=false, test_fn=nothing,
              julia_args::Union{Cmd, AbstractVector{<:AbstractString}}=``,
              test_args::Union{Cmd, AbstractVector{<:AbstractString}}=``,
              force_latest_compatible_version::Bool=false,
              allow_earlier_backwards_compatible_versions::Bool=true,
              allow_reresolve::Bool=true,
              kwargs...)
    julia_args = Cmd(julia_args)
    test_args = Cmd(test_args)
    Context!(ctx; kwargs...)

    if isempty(pkgs)
        ctx.env.pkg === nothing && pkgerror("trying to test unnamed project") #TODO Allow this?
        push!(pkgs, ctx.env.pkg)
    else
        project_resolve!(ctx.env, pkgs)
        project_deps_resolve!(ctx.env, pkgs)
        manifest_resolve!(ctx.env.manifest, pkgs)
        ensure_resolved(ctx, ctx.env.manifest, pkgs)
    end
    Operations.test(
        ctx,
        pkgs;
        coverage,
        test_fn,
        julia_args,
        test_args,
        force_latest_compatible_version,
        allow_earlier_backwards_compatible_versions,
        allow_reresolve,
    )
    return
end

is_manifest_current(ctx::Context = Context()) = Operations.is_manifest_current(ctx.env)

const UsageDict = Dict{String,DateTime}
const UsageByDepotDict = Dict{String,UsageDict}

"""
    gc(ctx::Context=Context(); collect_delay::Period=Day(7), verbose=false, kwargs...)

Garbage-collect package and artifact installations by sweeping over all known
`Manifest.toml` and `Artifacts.toml` files, noting those that have been deleted, and then
finding artifacts and packages that are thereafter not used by any other projects,
marking them as "orphaned".  This method will only remove orphaned objects (package
versions, artifacts, and scratch spaces) that have been continually un-used for a period
of `collect_delay`; which defaults to seven days.

Garbage collection is only applied to the "user depot", e.g. the first entry in the
depot path. If you want to run `gc` on all depots set `force=true` (this might require
admin privileges depending on the setup).

Use verbose mode (`verbose=true`) for detailed output.
"""
function gc(ctx::Context=Context(); collect_delay::Period=Day(7), verbose=false, force=false, kwargs...)
    Context!(ctx; kwargs...)
    env = ctx.env

    # Only look at user-depot unless force=true
    gc_depots = force ? depots() : [depots1()]

    # First, we load in our `manifest_usage.toml` files which will tell us when our
    # "index files" (`Manifest.toml`, `Artifacts.toml`) were last used.  We will combine
    # this knowledge across depots, condensing it all down to a single entry per extant
    # index file, to manage index file growth with would otherwise continue unbounded. We
    # keep the lists of index files separated by depot so that we can write back condensed
    # versions that are only ever subsets of what we read out of them in the first place.

    # Collect last known usage dates of manifest and artifacts toml files, split by depot
    manifest_usage_by_depot = UsageByDepotDict()
    artifact_usage_by_depot = UsageByDepotDict()

    # Collect both last known usage dates, as well as parent projects for each scratch space
    scratch_usage_by_depot = UsageByDepotDict()
    scratch_parents_by_depot = Dict{String, Dict{String, Set{String}}}()

    # Load manifest files from all depots
    for depot in gc_depots
        # When a manifest/artifact.toml is installed/used, we log it within the
        # `manifest_usage.toml` files within `write_env_usage()` and `bind_artifact!()`
        function reduce_usage!(f::Function, usage_filepath)
            if !isfile(usage_filepath)
                return
            end

            for (filename, infos) in parse_toml(usage_filepath)
                f.(Ref(filename), infos)
            end
        end

        # Extract usage data from this depot, (taking only the latest state for each
        # tracked manifest/artifact.toml), then merge the usage values from each file
        # into the overall list across depots to create a single, coherent view across
        # all depots.
        usage = UsageDict()
        let usage=usage
            reduce_usage!(joinpath(logdir(depot), "manifest_usage.toml")) do filename, info
                # For Manifest usage, store only the last DateTime for each filename found
                usage[filename] = max(get(usage, filename, DateTime(0)), DateTime(info["time"])::DateTime)
            end
        end
        manifest_usage_by_depot[depot] = usage

        usage = UsageDict()
        let usage=usage
            reduce_usage!(joinpath(logdir(depot), "artifact_usage.toml")) do filename, info
                # For Artifact usage, store only the last DateTime for each filename found
                usage[filename] = max(get(usage, filename, DateTime(0)), DateTime(info["time"])::DateTime)
            end
        end
        artifact_usage_by_depot[depot] = usage

        # track last-used
        usage = UsageDict()
        parents = Dict{String, Set{String}}()
        let usage=usage
            reduce_usage!(joinpath(logdir(depot), "scratch_usage.toml")) do filename, info
                # For Artifact usage, store only the last DateTime for each filename found
                usage[filename] = max(get(usage, filename, DateTime(0)), DateTime(info["time"])::DateTime)
                if !haskey(parents, filename)
                    parents[filename] = Set{String}()
                end
                for parent in info["parent_projects"]
                    push!(parents[filename], parent)
                end
            end
        end
        scratch_usage_by_depot[depot] = usage
        scratch_parents_by_depot[depot] = parents
    end

    # Next, figure out which files are still existent
    all_manifest_tomls = unique(f for (_, files) in manifest_usage_by_depot for f in keys(files))
    all_artifact_tomls = unique(f for (_, files) in artifact_usage_by_depot for f in keys(files))
    all_scratch_dirs = unique(f for (_, dirs) in scratch_usage_by_depot for f in keys(dirs))
    all_scratch_parents = Set{String}()
    for (depot, parents) in scratch_parents_by_depot
        for parent in values(parents)
            union!(all_scratch_parents, parent)
        end
    end

    all_manifest_tomls = Set(filter(Pkg.isfile_nothrow, all_manifest_tomls))
    all_artifact_tomls = Set(filter(Pkg.isfile_nothrow, all_artifact_tomls))
    all_scratch_dirs = Set(filter(Pkg.isdir_nothrow, all_scratch_dirs))
    all_scratch_parents = Set(filter(Pkg.isfile_nothrow, all_scratch_parents))

    # Immediately write these back as condensed toml files
    function write_condensed_toml(f::Function, usage_by_depot, fname)
        for (depot, usage) in usage_by_depot
            # Run through user-provided filter/condenser
            usage = f(depot, usage)

            # Write out the TOML file for this depot
            usage_path = joinpath(logdir(depot), fname)
            if !(isempty(usage)::Bool) || isfile(usage_path)
                let usage=usage
                    open(usage_path, "w") do io
                        TOML.print(io, usage, sorted=true)
                    end
                end
            end
        end
    end

    # Write condensed Manifest usage
    let all_manifest_tomls=all_manifest_tomls
        write_condensed_toml(manifest_usage_by_depot, "manifest_usage.toml") do depot, usage
            # Keep only manifest usage markers that are still existent
            let usage=usage
                filter!(((k,v),) -> k in all_manifest_tomls, usage)

                # Expand it back into a dict-of-dicts
                return Dict(k => [Dict("time" => v)] for (k, v) in usage)
            end
        end
    end

    # Write condensed Artifact usage
    let all_artifact_tomls=all_artifact_tomls
        write_condensed_toml(artifact_usage_by_depot, "artifact_usage.toml") do depot, usage
            let usage = usage
                filter!(((k,v),) -> k in all_artifact_tomls, usage)
                return Dict(k => [Dict("time" => v)] for (k, v) in usage)
            end
        end
    end

    # Write condensed scratch space usage
    let all_scratch_parents=all_scratch_parents, all_scratch_dirs=all_scratch_dirs
        write_condensed_toml(scratch_usage_by_depot, "scratch_usage.toml") do depot, usage
            # Keep only scratch directories that still exist
            filter!(((k,v),) -> k in all_scratch_dirs, usage)

            # Expand it back into a dict-of-dicts
            expanded_usage = Dict{String,Vector{Dict}}()
            for (k, v) in usage
                # Drop scratch spaces whose parents are all non-existent
                parents = scratch_parents_by_depot[depot][k]
                filter!(p -> p in all_scratch_parents, parents)
                if isempty(parents)
                    continue
                end

                expanded_usage[k] = [Dict(
                    "time" => v,
                    "parent_projects" => collect(parents),
                )]
            end
            return expanded_usage
        end
    end

    function process_manifest_pkgs(path)
        # Read the manifest in
        manifest = try
            read_manifest(path)
        catch e
            @warn "Reading manifest file at $path failed with error" exception = e
            return nothing
        end

        # Collect the locations of every package referred to in this manifest
        pkg_dir(uuid, entry) = Operations.find_installed(entry.name, uuid, entry.tree_hash)
        return [pkg_dir(u, e) for (u, e) in manifest if e.tree_hash !== nothing]
    end

    # TODO: Merge with function above to not read manifest twice?
    function process_manifest_repos(path)
        # Read the manifest in
        manifest = try
            read_manifest(path)
        catch e
            # Do not warn here, assume that `process_manifest_pkgs` has already warned
            return nothing
        end

        # Collect the locations of every repo referred to in this manifest
        return [Types.add_repo_cache_path(e.repo.source) for (u, e) in manifest if e.repo.source !== nothing]
    end

    function process_artifacts_toml(path, pkgs_to_delete)
        # Not only do we need to check if this file doesn't exist, we also need to check
        # to see if it this artifact is contained within a package that is going to go
        # away.  This places an implicit ordering between marking packages and marking
        # artifacts; the package marking must be done first so that we can ensure that
        # all artifacts that are solely bound within such packages also get reaped.
        if any(startswith(path, package_dir) for package_dir in pkgs_to_delete)
            return nothing
        end

        artifact_dict = try
            parse_toml(path)
        catch e
            @warn "Reading artifacts file at $path failed with error" exception = e
            return nothing
        end

        artifact_path_list = String[]
        for name in keys(artifact_dict)
            getpaths(meta) = artifact_paths(SHA1(hex2bytes(meta["git-tree-sha1"])))
            if isa(artifact_dict[name], Vector)
                for platform_meta in artifact_dict[name]
                    append!(artifact_path_list, getpaths(platform_meta))
                end
            else
                append!(artifact_path_list, getpaths(artifact_dict[name]))
            end
        end
        return artifact_path_list
    end

    function process_scratchspace(path, pkgs_to_delete)
        # Find all parents of this path
        parents = String[]

        # It is slightly awkward that we need to reach out to our `*_by_depot`
        # datastructures here; that's because unlike Artifacts and Manifests we're not
        # parsing a TOML file to find paths within it here, we're actually doing the
        # inverse, finding files that point to this directory.
        for (depot, parent_map) in scratch_parents_by_depot
            if haskey(parent_map, path)
                append!(parents, parent_map[path])
            end
        end

        # Look to see if all parents are packages that will be removed, if so, filter
        # this scratchspace out by returning `nothing`
        if all(any(startswith(p, dir) for dir in pkgs_to_delete) for p in parents)
            return nothing
        end
        return [path]
    end

    # Mark packages/artifacts as active or not by calling the appropriate user function
    function mark(process_func::Function, index_files, ctx::Context; do_print=true, verbose=false, file_str=nothing)
        marked_paths = String[]
        active_index_files = Set{String}()
        for index_file in index_files
            # Check to see if it's still alive
            paths = process_func(index_file)
            if paths !== nothing
                # Mark found paths, and record the index_file for printing
                push!(active_index_files, index_file)
                append!(marked_paths, paths)
            end
        end

        if do_print
            @assert file_str !== nothing
            n = length(active_index_files)
            printpkgstyle(ctx.io, :Active, "$(file_str): $(n) found")
            if verbose
                foreach(active_index_files) do f
                    println(ctx.io, "        $(pathrepr(f))")
                end
            end
        end
        # Return the list of marked paths
        return Set(marked_paths)
    end

    gc_time = now()
    function merge_orphanages!(new_orphanage, paths, deletion_list, old_orphanage = UsageDict())
        for path in paths
            free_time = something(
                get(old_orphanage, path, nothing),
                gc_time,
            )

            # No matter what, store the free time in the new orphanage. This allows
            # something terrible to go wrong while trying to delete the artifact/
            # package and it will still try to be deleted next time.  The only time
            # something is removed from an orphanage is when it didn't exist before
            # we even started the `gc` run.
            new_orphanage[path] = free_time

            # If this path was orphaned long enough ago, add it to the deletion list.
            # Otherwise, we continue to propagate its orphaning date but don't delete
            # it.  It will get cleaned up at some future `gc`, or it will be used
            # again during a future `gc` in which case it will not persist within the
            # orphanage list.
            if gc_time - free_time >= collect_delay
                push!(deletion_list, path)
            end
        end
    end


    # Scan manifests, parse them, read in all UUIDs listed and mark those as active
    # printpkgstyle(ctx.io, :Active, "manifests:")
    packages_to_keep = mark(process_manifest_pkgs, all_manifest_tomls, ctx,
        verbose=verbose, file_str="manifest files")

    # Do an initial scan of our depots to get a preliminary `packages_to_delete`.
    packages_to_delete = String[]
    for depot in gc_depots
        depot_orphaned_packages = String[]
        packagedir = abspath(depot, "packages")
        if isdir(packagedir)
            for name in readdir(packagedir)
                !isdir(joinpath(packagedir, name)) && continue

                for slug in readdir(joinpath(packagedir, name))
                    pkg_dir = joinpath(packagedir, name, slug)
                    !isdir(pkg_dir) && continue

                    if !(pkg_dir in packages_to_keep)
                        push!(depot_orphaned_packages, pkg_dir)
                    end
                end
            end
        end
        merge_orphanages!(UsageDict(), depot_orphaned_packages, packages_to_delete)
    end


    # Next, do the same for artifacts.  Note that we MUST do this after calculating
    # `packages_to_delete`, as `process_artifacts_toml()` uses it internally to discount
    # `Artifacts.toml` files that will be deleted by the future culling operation.
    # printpkgstyle(ctx.io, :Active, "artifacts:")
    artifacts_to_keep = let packages_to_delete=packages_to_delete
        mark(x -> process_artifacts_toml(x, packages_to_delete),
             all_artifact_tomls, ctx; verbose=verbose, file_str="artifact files")
    end
    repos_to_keep = mark(process_manifest_repos, all_manifest_tomls, ctx; do_print=false)
    # printpkgstyle(ctx.io, :Active, "scratchspaces:")
    spaces_to_keep = let packages_to_delete=packages_to_delete
        mark(x -> process_scratchspace(x, packages_to_delete),
             all_scratch_dirs, ctx; verbose=verbose, file_str="scratchspaces")
    end

    # Collect all orphaned paths (packages, artifacts and repos that are not reachable).  These
    # are implicitly defined in that we walk all packages/artifacts installed, then if
    # they were not marked in the above steps, we reap them.
    packages_to_delete = String[]
    artifacts_to_delete = String[]
    repos_to_delete = String[]
    spaces_to_delete = String[]

    for depot in gc_depots
        # We track orphaned objects on a per-depot basis, writing out our `orphaned.toml`
        # tracking file immediately, only pushing onto the overall `*_to_delete` lists if
        # the package has been orphaned for at least a period of `collect_delay`
        depot_orphaned_packages = String[]
        depot_orphaned_artifacts = String[]
        depot_orphaned_repos = String[]
        depot_orphaned_scratchspaces = String[]

        packagedir = abspath(depot, "packages")
        if isdir(packagedir)
            for name in readdir(packagedir)
                !isdir(joinpath(packagedir, name)) && continue

                for slug in readdir(joinpath(packagedir, name))
                    pkg_dir = joinpath(packagedir, name, slug)
                    !isdir(pkg_dir) && continue

                    if !(pkg_dir in packages_to_keep)
                        push!(depot_orphaned_packages, pkg_dir)
                    end
                end
            end
        end

        reposdir = abspath(depot, "clones")
        if isdir(reposdir)
            for repo in readdir(reposdir)
                repo_dir = joinpath(reposdir, repo)
                !isdir(repo_dir) && continue
                if !(repo_dir in repos_to_keep)
                    push!(depot_orphaned_repos, repo_dir)
                end
            end
        end

        artifactsdir = abspath(depot, "artifacts")
        if isdir(artifactsdir)
            for hash in readdir(artifactsdir)
                artifact_path = joinpath(artifactsdir, hash)
                !isdir(artifact_path) && continue

                if !(artifact_path in artifacts_to_keep)
                    push!(depot_orphaned_artifacts, artifact_path)
                end
            end
        end

        scratchdir = abspath(depot, "scratchspaces")
        if isdir(scratchdir)
            for uuid in readdir(scratchdir)
                uuid_dir = joinpath(scratchdir, uuid)
                !isdir(uuid_dir) && continue
                for space in readdir(uuid_dir)
                    space_dir_or_file = joinpath(uuid_dir, space)
                    if isdir(space_dir_or_file)
                        if !(space_dir_or_file in spaces_to_keep)
                            push!(depot_orphaned_scratchspaces, space_dir_or_file)
                        end
                    elseif uuid == Operations.PkgUUID && isfile(space_dir_or_file)
                        # special cleanup for the precompile cache files that Pkg saves
                        if any(prefix->startswith(basename(space_dir_or_file), prefix), ("suspend_cache_", "pending_cache_"))
                            if mtime(space_dir_or_file) < (time() - (24*60*60))
                                push!(depot_orphaned_scratchspaces, space_dir_or_file)
                            end
                        end
                    end
                end
            end
        end

        # Read in this depot's `orphaned.toml` file:
        orphanage_file = joinpath(logdir(depot), "orphaned.toml")
        new_orphanage = UsageDict()
        old_orphanage = try
            TOML.parse(String(read(orphanage_file)))
        catch
            UsageDict()
        end

        # Update the package and artifact lists of things to delete, and
        # create the `new_orphanage` list for this depot.
        merge_orphanages!(new_orphanage, depot_orphaned_packages, packages_to_delete, old_orphanage)
        merge_orphanages!(new_orphanage, depot_orphaned_artifacts, artifacts_to_delete, old_orphanage)
        merge_orphanages!(new_orphanage, depot_orphaned_repos, repos_to_delete, old_orphanage)
        merge_orphanages!(new_orphanage, depot_orphaned_scratchspaces, spaces_to_delete, old_orphanage)

        # Write out the `new_orphanage` for this depot
        mkpath(dirname(orphanage_file))
        open(orphanage_file, "w") do io
            TOML.print(io, new_orphanage, sorted=true)
        end
    end

    # Next, we calculate the space savings we're about to gain!
    pretty_byte_str = (size) -> begin
        bytes, mb = Base.prettyprint_getunits(size, length(Base._mem_units), Int64(1024))
        return @sprintf("%.3f %s", bytes, Base._mem_units[mb])
    end

    function recursive_dir_size(path)
        size = 0
        try
            for (root, dirs, files) in walkdir(path)
                for file in files
                    path = joinpath(root, file)
                    try
                        size += lstat(path).size
                    catch ex
                        @error("Failed to calculate size of $path", exception=ex)
                    end
                end
            end
        catch ex
            @error("Failed to calculate size of $path", exception=ex)
        end
        return size
    end

    # Delete paths for unreachable package versions and artifacts, and computing size saved
    function delete_path(path)
        path_size = if isfile(path)
            try
                lstat(path).size
            catch ex
                @error("Failed to calculate size of $path", exception=ex)
                0
            end
        else
            recursive_dir_size(path)
        end
        try
            Base.Filesystem.prepare_for_deletion(path)
            Base.rm(path; recursive=true, force=true)
        catch e
            @warn("Failed to delete $path", exception=e)
            return 0
        end
        if verbose
            printpkgstyle(ctx.io, :Deleted, pathrepr(path) * " (" *
                pretty_byte_str(path_size) * ")")
        end
        return path_size
    end

    package_space_freed = 0
    repo_space_freed = 0
    artifact_space_freed = 0
    scratch_space_freed = 0
    for path in packages_to_delete
        package_space_freed += delete_path(path)
    end
    for path in repos_to_delete
        repo_space_freed += delete_path(path)
    end
    for path in artifacts_to_delete
        artifact_space_freed += delete_path(path)
    end
    for path in spaces_to_delete
        scratch_space_freed += delete_path(path)
    end

    # Prune package paths that are now empty
    for depot in gc_depots
        packagedir = abspath(depot, "packages")
        !isdir(packagedir) && continue

        for name in readdir(packagedir)
            name_path = joinpath(packagedir, name)
            !isdir(name_path) && continue
            !isempty(readdir(name_path)) && continue

            Base.rm(name_path)
        end
    end

    # Prune scratch space UUID folders that are now empty
    for depot in gc_depots
        scratch_dir = abspath(depot, "scratchspaces")
        !isdir(scratch_dir) && continue

        for uuid in readdir(scratch_dir)
            uuid_dir = joinpath(scratch_dir, uuid)
            !isdir(uuid_dir) && continue
            if isempty(readdir(uuid_dir))
                Base.rm(uuid_dir)
            end
        end
    end

    ndel_pkg = length(packages_to_delete)
    ndel_repo = length(repos_to_delete)
    ndel_art = length(artifacts_to_delete)
    ndel_space = length(spaces_to_delete)

    function print_deleted(ndel, freed, name)
        if ndel <= 0
            return
        end

        s = ndel == 1 ? "" : "s"
        bytes_saved_string = pretty_byte_str(freed)
        printpkgstyle(ctx.io, :Deleted, "$(ndel) $(name)$(s) ($bytes_saved_string)")
    end
    print_deleted(ndel_pkg, package_space_freed, "package installation")
    print_deleted(ndel_repo, repo_space_freed, "repo")
    print_deleted(ndel_art, artifact_space_freed, "artifact installation")
    print_deleted(ndel_space, scratch_space_freed, "scratchspace")

    if ndel_pkg == 0 && ndel_art == 0 && ndel_repo == 0 && ndel_space == 0
        printpkgstyle(ctx.io, :Deleted, "no artifacts, repos, packages or scratchspaces")
    end

    return
end

function build(ctx::Context, pkgs::Vector{PackageSpec}; verbose=false, kwargs...)
    Context!(ctx; kwargs...)

    if isempty(pkgs)
        if ctx.env.pkg !== nothing
            push!(pkgs, ctx.env.pkg)
        else
            for (uuid, entry) in ctx.env.manifest
                push!(pkgs, PackageSpec(entry.name, uuid))
            end
        end
    end
    project_resolve!(ctx.env, pkgs)
    manifest_resolve!(ctx.env.manifest, pkgs)
    ensure_resolved(ctx, ctx.env.manifest, pkgs)
    Operations.build(ctx, Set{UUID}(pkg.uuid for pkg in pkgs), verbose)
end

function get_or_make_pkgspec(pkgspecs::Vector{PackageSpec}, ctx::Context, uuid)
    i = findfirst(ps -> ps.uuid == uuid, pkgspecs)
    if !isnothing(i)
        return pkgspecs[i]
    elseif !isnothing(ctx.env.pkg) && uuid == ctx.env.pkg.uuid
        # uuid is of the active Project
        return ctx.env.pkg
    elseif haskey(ctx.env.manifest, uuid)
        pkgent = ctx.env.manifest[uuid]
        # If we have an unusual situation such as an un-versioned package (like an stdlib that
        # is being overridden) its `version` may be `nothing`.
        pkgver = something(pkgent.version, VersionSpec())
        return PackageSpec(uuid = uuid, name = pkgent.name, version = pkgver, tree_hash = pkgent.tree_hash)
    else
        # this branch should never be hit, so if it is throw a regular error with a stacktrace
        error("UUID $uuid not found. It does not match the Project uuid nor any dependency")
    end
end

function precompile(ctx::Context, pkgs::Vector{PackageSpec}; internal_call::Bool=false,
                    strict::Bool=false, warn_loaded = true, already_instantiated = false, timing::Bool = false,
                    _from_loading::Bool=false, kwargs...)
    Context!(ctx; kwargs...)
    already_instantiated || instantiate(ctx; allow_autoprecomp=false, kwargs...)
    time_start = time_ns()

    # Windows sometimes hits a ReadOnlyMemoryError, so we halve the default number of tasks. Issue #2323
    # TODO: Investigate why this happens in windows and restore the full task limit
    default_num_tasks = Sys.iswindows() ? div(Sys.CPU_THREADS::Int, 2) + 1 : Sys.CPU_THREADS::Int + 1
    default_num_tasks = min(default_num_tasks, 16) # limit for better stability on shared resource systems

    num_tasks = parse(Int, get(ENV, "JULIA_NUM_PRECOMPILE_TASKS", string(default_num_tasks)))
    parallel_limiter = Base.Semaphore(num_tasks)
    io = ctx.io
    fancyprint = can_fancyprint(io) && !timing

    hascolor = get(io, :color, false)::Bool
    color_string(cstr::String, col::Union{Int64, Symbol}) = _color_string(cstr, col, hascolor)

    recall_precompile_state() # recall suspended and force-queued packages
    !internal_call && precomp_unsuspend!() # when manually called, unsuspend all packages that were suspended due to precomp errors

    direct_deps = [
        Base.PkgId(uuid, name)
        for (name, uuid) in ctx.env.project.deps if !Base.in_sysimage(Base.PkgId(uuid, name))
    ]
    stale_cache = Dict{StaleCacheKey, Bool}()
    exts = Dict{Base.PkgId, String}() # ext -> parent
    # make a flat map of each dep and its direct deps
    depsmap = Dict{Base.PkgId, Vector{Base.PkgId}}()
    pkg_specs = PackageSpec[]
    pkg_exts_map = Dict{Base.PkgId, Vector{Base.PkgId}}()
    for dep in ctx.env.manifest
        pkg = Base.PkgId(first(dep), last(dep).name)
        Base.in_sysimage(pkg) && continue
        deps = [Base.PkgId(last(x), first(x)) for x in last(dep).deps]
        depsmap[pkg] = filter!(!Base.in_sysimage, deps)
        # add any extensions
        weakdeps = last(dep).weakdeps
        pkg_exts = Dict{Base.PkgId, Vector{Base.PkgId}}()
        prev_ext = nothing
        for (ext_name, extdep_names) in last(dep).exts
            ext_deps = Base.PkgId[]
            push!(ext_deps, pkg) # depends on parent package
            all_extdeps_available = true
            extdep_names = extdep_names isa String ? String[extdep_names] : extdep_names
            for extdep_name in extdep_names
                extdep_uuid = weakdeps[extdep_name]
                if extdep_uuid in keys(ctx.env.manifest.deps) || Base.in_sysimage(Base.PkgId(extdep_uuid, extdep_name))
                    push!(ext_deps, Base.PkgId(extdep_uuid, extdep_name))
                else
                    all_extdeps_available = false
                    break
                end
            end
            all_extdeps_available || continue
            if prev_ext isa Base.PkgId
                # also make the exts depend on eachother sequentially to avoid race
                push!(ext_deps, prev_ext)
            end
            ext_uuid = Base.uuid5(pkg.uuid, ext_name)
            ext = Base.PkgId(ext_uuid, ext_name)
            prev_ext = ext
            push!(pkg_specs, PackageSpec(uuid = ext_uuid, name = ext_name)) # create this here as the name cannot be looked up easily later via the uuid
            filter!(!Base.in_sysimage, ext_deps)
            depsmap[ext] = ext_deps
            exts[ext] = pkg.name
            pkg_exts[ext] = ext_deps
        end
        if !isempty(pkg_exts)
            pkg_exts_map[pkg] = collect(keys(pkg_exts))
        end
    end
    # this loop must be run after the full depsmap has been populated
    for (pkg, pkg_exts) in pkg_exts_map
        # find any packages that depend on the extension(s)'s deps and replace those deps in their deps list with the extension(s),
        # basically injecting the extension into the precompile order in the graph, to avoid race to precompile extensions
        for (_pkg, deps) in depsmap # for each manifest dep
            if !in(_pkg, keys(exts)) && pkg in deps # if not an extension and depends on pkg
                append!(deps, pkg_exts) # add the package extensions to deps
                filter!(!isequal(pkg), deps) # remove the pkg from deps
            end
        end
    end

    # if the active environment is a package, add that
    ctx_env_pkg = ctx.env.pkg
    if ctx_env_pkg !== nothing && isfile(joinpath(dirname(ctx.env.project_file), "src", "$(ctx_env_pkg.name).jl"))
        project_pkgid = Base.PkgId(ctx_env_pkg.uuid, ctx_env_pkg.name)
        depsmap[project_pkgid] = [
            Base.PkgId(last(x), first(x))
            for x in ctx.env.project.deps if !Base.in_sysimage(Base.PkgId(last(x), first(x)))
        ]
        push!(direct_deps, Base.PkgId(ctx_env_pkg.uuid, ctx_env_pkg.name))
    else
        project_pkgid = nothing
    end

    # return early if no deps
    if isempty(depsmap)
        if isempty(pkgs)
            return
        elseif _from_loading
            # if called from loading precompilation it may be a package from another environment stack so
            # don't error and allow serial precompilation to try
            # TODO: actually handle packages from other envs in the stack
            return
        else
            pkgerror("No direct dependencies outside of the sysimage found matching $(repr([p.name for p in pkgs]))")
        end
    end

    # initialize signalling
    started = Dict{Base.PkgId,Bool}()
    was_processed = Dict{Base.PkgId,Base.Event}()
    was_recompiled = Dict{Base.PkgId,Bool}()
    for pkgid in keys(depsmap)
        started[pkgid] = false
        was_processed[pkgid] = Base.Event()
        was_recompiled[pkgid] = false
        push!(pkg_specs, get_or_make_pkgspec(pkg_specs, ctx, pkgid.uuid))
    end

    # remove packages that are suspended because they errored before
    # note that when `Pkg.precompile` is manually called, all suspended packages are unsuspended
    precomp_prune_suspended!(pkg_specs)

    # find and guard against circular deps
    circular_deps = Base.PkgId[]
    # Three states
    # !haskey -> never visited
    # true -> cannot be compiled due to a cycle (or not yet determined)
    # false -> not depending on a cycle
    could_be_cycle = Dict{Base.PkgId, Bool}()
    function scan_pkg!(pkg, dmap)
        did_visit_dep = true
        inpath = get!(could_be_cycle, pkg) do
            did_visit_dep = false
            return true
        end
        if did_visit_dep ? inpath : scan_deps!(pkg, dmap)
            # Found a cycle. Delete this and all parents
            return true
        end
        return false
    end
    function scan_deps!(pkg, dmap)
        for dep in dmap[pkg]
            scan_pkg!(dep, dmap) && return true
        end
        could_be_cycle[pkg] = false
        return false
    end
    for pkg in keys(depsmap)
        if scan_pkg!(pkg, depsmap)
            push!(circular_deps, pkg)
            notify(was_processed[pkg])
        end
    end
    if !isempty(circular_deps)
        @warn """Circular dependency detected. Precompilation will be skipped for:\n  $(join(string.(circular_deps), "\n  "))"""
    end

    # if a list of packages is given, restrict to dependencies of given packages
    if !isempty(pkgs)
        pkgs_names = [p.name for p in pkgs]
        function collect_all_deps(depsmap, dep, alldeps=Set{Base.PkgId}())
            for _dep in depsmap[dep]
                if !(_dep in alldeps)
                    push!(alldeps, _dep)
                    collect_all_deps(depsmap, _dep, alldeps)
                end
            end
            return alldeps
        end
        keep = Set{Base.PkgId}()
        for dep in depsmap
            dep_pkgid = first(dep)
            if dep_pkgid.name in pkgs_names
                push!(keep, dep_pkgid)
                collect_all_deps(depsmap, dep_pkgid, keep)
            end
        end
        for ext in keys(exts)
            if issubset(collect_all_deps(depsmap, ext), keep) # if all extension deps are kept
                push!(keep, ext)
            end
        end
        filter!(d->in(first(d), keep), depsmap)
        if isempty(depsmap)
            if _from_loading
                # if called from loading precompilation it may be a package from another environment stack so
                # don't error and allow serial precompilation to try
                # TODO: actually handle packages from other envs in the stack
                return
            else
                pkgerror("No direct dependencies outside of the sysimage found matching $(repr(pkgs_names))")
            end
        end
        target = join(pkgs_names, ", ")
    else
        target = "project..."
    end

    pkg_queue = Base.PkgId[]
    failed_deps = Dict{Base.PkgId, String}()
    skipped_deps = Base.PkgId[]
    precomperr_deps = Base.PkgId[] # packages that may succeed after a restart (i.e. loaded packages with no cache file)

    print_lock = ctx.io isa Base.LibuvStream ? ctx.io.lock::ReentrantLock : ReentrantLock()
    first_started = Base.Event()
    printloop_should_exit::Bool = !fancyprint # exit print loop immediately if not fancy printing
    interrupted_or_done = Base.Event()

    ansi_moveup(n::Int) = string("\e[", n, "A")
    ansi_movecol1 = "\e[1G"
    ansi_cleartoend = "\e[0J"
    ansi_cleartoendofline = "\e[0K"
    ansi_enablecursor = "\e[?25h"
    ansi_disablecursor = "\e[?25l"
    n_done::Int = 0
    n_already_precomp::Int = 0
    n_loaded::Int = 0
    interrupted = false

    function handle_interrupt(err, in_printloop = false)
        notify(interrupted_or_done)
        in_printloop || wait(t_print) # wait to let the print loop cease first
        if err isa InterruptException
            lock(print_lock) do
                println(io, " Interrupted: Exiting precompilation...")
            end
            interrupted = true
            return true
        else
            return false
        end
    end

    std_outputs = Dict{Base.PkgId,String}()
    taskwaiting = Set{Base.PkgId}()
    pkgspidlocked = Dict{Base.PkgId,String}()
    pkg_liveprinted = nothing

    function monitor_std(pkg, pipe; single_requested_pkg=false)
        try
            liveprinting = false
            while !eof(pipe)
                str = readline(pipe, keep=true)
                if single_requested_pkg && (liveprinting || !isempty(str))
                    lock(print_lock) do
                        if !liveprinting
                            printpkgstyle(io, :Info, "Given $(pkg.name) was explicitly requested, output will be shown live $ansi_cleartoendofline",
                                color = Base.info_color())
                            liveprinting = true
                            pkg_liveprinted = pkg
                        end
                        print(io, ansi_cleartoendofline, str)
                    end
                end
                std_outputs[pkg] = string(get(std_outputs, pkg, ""), str)
                if !in(pkg, taskwaiting) && occursin("waiting for IO to finish", str)
                    !fancyprint && lock(print_lock) do
                        println(io, pkg.name, color_string(" Waiting for background task / IO / timer.", Base.warn_color()))
                    end
                    push!(taskwaiting, pkg)
                end
                if !fancyprint && in(pkg, taskwaiting)
                    lock(print_lock) do
                        print(io, str)
                    end
                end
            end
        catch err
            err isa InterruptException || rethrow()
        end
    end

    ## fancy print loop
    t_print = @async begin
        try
            wait(first_started)
            (isempty(pkg_queue) || interrupted_or_done.set) && return
            fancyprint && lock(print_lock) do
                printpkgstyle(io, :Precompiling, target)
                print(io, ansi_disablecursor)
            end
            t = Timer(0; interval=1/10)
            anim_chars = ["◐","◓","◑","◒"]
            i = 1
            last_length = 0
            bar = MiniProgressBar(; indent=2, header = "Progress", color = Base.info_color(), percentage=false, always_reprint=true)
            n_total = length(depsmap)
            bar.max = n_total - n_already_precomp
            final_loop = false
            n_print_rows = 0
            while !printloop_should_exit
                lock(print_lock) do
                    term_size = Base.displaysize(ctx.io)::Tuple{Int,Int}
                    num_deps_show = term_size[1] - 3
                    pkg_queue_show = if !interrupted_or_done.set && length(pkg_queue) > num_deps_show
                        last(pkg_queue, num_deps_show)
                    else
                        pkg_queue
                    end
                    str_ = sprint() do iostr
                        if i > 1
                            print(iostr, ansi_cleartoend)
                        end
                        bar.current = n_done - n_already_precomp
                        bar.max = n_total - n_already_precomp
                        # when sizing to the terminal width subtract a little to give some tolerance to resizing the
                        # window between print cycles
                        termwidth = displaysize(io)[2] - 4
                        if !final_loop
                            str = sprint(io -> show_progress(io, bar; termwidth, carriagereturn=false); context=io)
                            print(iostr, Base._truncate_at_width_or_chars(true, str, termwidth), "\n")
                        end
                        for dep in pkg_queue_show
                            loaded = warn_loaded && haskey(Base.loaded_modules, dep)
                            _name = haskey(exts, dep) ? string(exts[dep], " → ", dep.name) : dep.name
                            name = dep in direct_deps ? _name : string(color_string(_name, :light_black))
                            line = if dep in precomperr_deps
                                string(color_string("  ? ", Base.warn_color()), name)
                            elseif haskey(failed_deps, dep)
                                string(color_string("  ✗ ", Base.error_color()), name)
                            elseif was_recompiled[dep]
                                !loaded && interrupted_or_done.set && continue
                                loaded || @async begin # keep successful deps visible for short period
                                    sleep(1);
                                    filter!(!isequal(dep), pkg_queue)
                                end
                                string(color_string("  ✓ ", loaded ? Base.warn_color() : :green), name)
                            elseif started[dep]
                                # Offset each spinner animation using the first character in the package name as the seed.
                                # If not offset, on larger terminal fonts it looks odd that they all sync-up
                                anim_char = anim_chars[(i + Int(dep.name[1])) % length(anim_chars) + 1]
                                anim_char_colored = dep in direct_deps ? anim_char : color_string(anim_char, :light_black)
                                waiting = if haskey(pkgspidlocked, dep)
                                    who_has_lock = pkgspidlocked[dep]
                                    color_string(" Being precompiled by $(who_has_lock)", Base.info_color())
                                elseif dep in taskwaiting
                                    color_string(" Waiting for background task / IO / timer. Interrupt to inspect", Base.warn_color())
                                else
                                    ""
                                end
                                string("  ", anim_char_colored, " ", name, waiting)
                            else
                                string("    ", name)
                            end
                            println(iostr, Base._truncate_at_width_or_chars(true, line, termwidth))
                        end
                    end
                    last_length = length(pkg_queue_show)
                    n_print_rows = count("\n", str_)
                    print(io, str_)
                    printloop_should_exit = interrupted_or_done.set && final_loop
                    final_loop = interrupted_or_done.set # ensures one more loop to tidy last task after finish
                    i += 1
                    printloop_should_exit || print(io, ansi_moveup(n_print_rows), ansi_movecol1)
                end
                wait(t)
            end
        catch err
            handle_interrupt(err, true) || rethrow()
        finally
            fancyprint && print(io, ansi_enablecursor)
        end
    end
    tasks = Task[]
    if !_from_loading
        Base.LOADING_CACHE[] = Base.LoadingCache()
    end
    ## precompilation loop
    for (pkg, deps) in depsmap
        cachepaths = Base.find_all_in_cache_path(pkg)
        sourcepath = Base.locate_package(pkg)
        if sourcepath === nothing
            failed_deps[pkg] = "Error: Missing source file for $(pkg)"
            notify(was_processed[pkg])
            continue
        end
        # Heuristic for when precompilation is disabled
        if occursin(r"\b__precompile__\(\s*false\s*\)", read(sourcepath, String))
            notify(was_processed[pkg])
            continue
        end

        single_requested_pkg = if length(pkgs) == 1
            only(pkgs).name == pkg.name
        elseif project_pkgid isa Base.PkgId
            pkg == project_pkgid # if a package project is being precompiled, consider the package requested
        else
            false
        end

        task = @async begin
            try
                loaded = haskey(Base.loaded_modules, pkg)
                for dep in deps # wait for deps to finish
                    wait(was_processed[dep])
                end

                pkgspec = get_or_make_pkgspec(pkg_specs, ctx, pkg.uuid)
                suspended = precomp_suspended(pkgspec)
                queued = precomp_queued(pkgspec)

                circular = pkg in circular_deps
                is_stale = true
                if !circular && (queued || (!suspended && (is_stale = !Base.isprecompiled(pkg; ignore_loaded=true, stale_cache, cachepaths, sourcepath))))
                    Base.acquire(parallel_limiter)
                    is_direct_dep = pkg in direct_deps

                    # std monitoring
                    std_pipe = Base.link_pipe!(Pipe(); reader_supports_async=true, writer_supports_async=true)
                    t_monitor = @async monitor_std(pkg, std_pipe; single_requested_pkg)

                    _name = haskey(exts, pkg) ? string(exts[pkg], " → ", pkg.name) : pkg.name
                    name = is_direct_dep ? _name : string(color_string(_name, :light_black))
                    !fancyprint && lock(print_lock) do
                        isempty(pkg_queue) && printpkgstyle(io, :Precompiling, target)
                    end
                    push!(pkg_queue, pkg)
                    started[pkg] = true
                    fancyprint && notify(first_started)
                    if interrupted_or_done.set
                        notify(was_processed[pkg])
                        Base.release(parallel_limiter)
                        return
                    end
                    try
                        # allows processes to wait if another process is precompiling a given package to
                        # a functionally identical package cache (except for preferences, which may differ)
                        t = @elapsed ret = maybe_cachefile_lock(io, print_lock, fancyprint, pkg, pkgspidlocked, hascolor) do
                            Logging.with_logger(Logging.NullLogger()) do
                                # The false here means we ignore loaded modules, so precompile for a fresh session
                                Base.compilecache(pkg, sourcepath, std_pipe, std_pipe, false)
                            end
                        end
                        t_str = timing ? string(lpad(round(t * 1e3, digits = 1), 9), " ms") : ""
                        if ret isa Base.PrecompilableError
                            push!(precomperr_deps, pkg)
                            precomp_queue!(get_or_make_pkgspec(pkg_specs, ctx, pkg.uuid))
                            !fancyprint && lock(print_lock) do
                                println(io, t_str, color_string("  ? ", Base.warn_color()), name)
                            end
                        else
                            queued && precomp_dequeue!(get_or_make_pkgspec(pkg_specs, ctx, pkg.uuid))
                            !fancyprint && lock(print_lock) do
                                println(io, t_str, color_string("  ✓ ", loaded ? Base.warn_color() : :green), name)
                            end
                            was_recompiled[pkg] = true
                        end
                        loaded && (n_loaded += 1)
                    catch err
                        close(std_pipe.in) # close pipe to end the std output monitor
                        wait(t_monitor)
                        if err isa ErrorException || (err isa ArgumentError && startswith(err.msg, "Invalid header in cache file"))
                            failed_deps[pkg] = (strict || is_direct_dep) ? string(sprint(showerror, err), "\n", strip(get(std_outputs, pkg, ""))) : ""
                            delete!(std_outputs, pkg) # so it's not shown as warnings, given error report
                            !fancyprint && lock(print_lock) do
                                println(io, timing ? " "^9 : "", color_string("  ✗ ", Base.error_color()), name)
                            end
                            queued && precomp_dequeue!(get_or_make_pkgspec(pkg_specs, ctx, pkg.uuid))
                            precomp_suspend!(get_or_make_pkgspec(pkg_specs, ctx, pkg.uuid))
                        else
                            rethrow()
                        end
                    finally
                        isopen(std_pipe.in) && close(std_pipe.in) # close pipe to end the std output monitor
                        wait(t_monitor)
                        Base.release(parallel_limiter)
                    end
                else
                    is_stale || (n_already_precomp += 1)
                    suspended && push!(skipped_deps, pkg)
                end
                n_done += 1
                notify(was_processed[pkg])
            catch err_outer
                handle_interrupt(err_outer) || rethrow()
                notify(was_processed[pkg])
            finally
                filter!(!istaskdone, tasks)
                length(tasks) == 1 && notify(interrupted_or_done)
            end
        end
        push!(tasks, task)
    end
    isempty(tasks) && notify(interrupted_or_done)
    try
        wait(interrupted_or_done)
    catch err
        handle_interrupt(err) || rethrow()
    finally
        Base.LOADING_CACHE[] = nothing
    end
    notify(first_started) # in cases of no-op or !fancyprint
    save_precompile_state() # save lists to scratch space
    fancyprint && wait(t_print)
    quick_exit = !all(istaskdone, tasks) || interrupted # if some not finished internal error is likely
    seconds_elapsed = round(Int, (time_ns() - time_start) / 1e9)
    ndeps = count(values(was_recompiled))
    if ndeps > 0 || !isempty(failed_deps) || (quick_exit && !isempty(std_outputs))
        str = sprint() do iostr
            if !quick_exit
                plural = ndeps == 1 ? "y" : "ies"
                print(iostr, "  $(ndeps) dependenc$(plural) successfully precompiled in $(seconds_elapsed) seconds")
                if n_already_precomp > 0 || !isempty(circular_deps) || !isempty(skipped_deps)
                    n_already_precomp > 0 && (print(iostr, ". $n_already_precomp already precompiled"))
                    !isempty(circular_deps) && (print(iostr, ". $(length(circular_deps)) skipped due to circular dependency"))
                    !isempty(skipped_deps) && (print(iostr, ". $(length(skipped_deps)) skipped during auto due to previous errors"))
                    print(iostr, ".")
                end
                if n_loaded > 0
                    plural1 = n_loaded == 1 ? "y" : "ies"
                    plural2 = n_loaded == 1 ? "a different version is" : "different versions are"
                    plural3 = n_loaded == 1 ? "" : "s"
                    print(iostr, "\n  ",
                        color_string(string(n_loaded), Base.warn_color()),
                        " dependenc$(plural1) precompiled but $(plural2) currently loaded. Restart julia to access the new version$(plural3)"
                    )
                end
                if !isempty(precomperr_deps)
                    pluralpc = length(precomperr_deps) == 1 ? "y" : "ies"
                    print(iostr, "\n  ",
                        color_string(string(length(precomperr_deps)), Base.warn_color()),
                        " dependenc$(pluralpc) failed but may be precompilable after restarting julia"
                    )
                end
            end
            # show any stderr output, even if Pkg.precompile has been interrupted (quick_exit=true), given user may be
            # interrupting a hanging precompile job with stderr output. julia#48371
            filter!(kv -> !isempty(strip(last(kv))), std_outputs) # remove empty output
            if !isempty(std_outputs)
                plural1 = length(std_outputs) == 1 ? "y" : "ies"
                plural2 = length(std_outputs) == 1 ? "" : "s"
                print(iostr, "\n  ", color_string("$(length(std_outputs))", Base.warn_color()), " dependenc$(plural1) had output during precompilation:")
                for (pkgid, err) in std_outputs
                    err = if pkgid == pkg_liveprinted
                        "[Output was shown above]"
                    else
                        join(split(strip(err), "\n"), color_string("\n│  ", Base.warn_color()))
                    end
                    name = haskey(exts, pkgid) ? string(exts[pkgid], " → ", pkgid.name) : pkgid.name
                    print(iostr, color_string("\n┌ ", Base.warn_color()), name, color_string("\n│  ", Base.warn_color()), err, color_string("\n└  ", Base.warn_color()))
                end
            end
        end
        let str=str
            lock(print_lock) do
                println(io, str)
            end
        end
        quick_exit && return
        err_str = ""
        n_direct_errs = 0
        for (dep, err) in failed_deps
            if strict || (dep in direct_deps)
                err_str = string(err_str, "\n$dep\n\n$err", (n_direct_errs > 0 ? "\n" : ""))
                n_direct_errs += 1
            end
        end
        if err_str != ""
            pluralde = n_direct_errs == 1 ? "y" : "ies"
            direct = strict ? "" : "direct "
            err_msg = "The following $n_direct_errs $(direct)dependenc$(pluralde) failed to precompile:\n$(err_str[1:end-1])"
            if internal_call # aka. auto-precompilation
                if isinteractive() && !get(ENV, "CI", false)
                    plural1 = length(failed_deps) == 1 ? "y" : "ies"
                    println(io, "  ", color_string("$(length(failed_deps))", Base.error_color()), " dependenc$(plural1) errored.")
                    println(io, "  For a report of the errors see `julia> err`. To retry use `pkg> precompile`")
                    setglobal!(Base.MainInclude, :err, PkgPrecompileError(err_msg))
                else
                    # auto-precompilation shouldn't throw but if the user can't easily access the
                    # error messages, just show them
                    print(io, "\n", err_msg)
                end
            else
                println(io)
                pkgerror(err_msg)
            end
        end
    end
    nothing
end

function _color_string(cstr::String, col::Union{Int64, Symbol}, hascolor)
    if hascolor
        enable_ansi  = get(Base.text_colors, col, Base.text_colors[:default])
        disable_ansi = get(Base.disable_text_style, col, Base.text_colors[:default])
        return string(enable_ansi, cstr, disable_ansi)
    else
        return cstr
    end
end

function maybe_cachefile_lock(f, io::IO, print_lock::ReentrantLock, fancyprint::Bool, pkg::Base.PkgId, pkgspidlocked::Dict{Base.PkgId,String}, hascolor)
    stale_age = Base.compilecache_pidlock_stale_age
    pidfile = Base.compilecache_pidfile_path(pkg)
    cachefile = FileWatching.trymkpidlock(f, pidfile; stale_age)
    if cachefile === false
        pid, hostname, age = FileWatching.Pidfile.parse_pidfile(pidfile)
        pkgspidlocked[pkg] = if isempty(hostname) || hostname == gethostname()
            if pid == getpid()
                "an async task in this process (pidfile: $pidfile)"
            else
                "another process (pid: $pid, pidfile: $pidfile)"
            end
        else
            "another machine (hostname: $hostname, pid: $pid, pidfile: $pidfile)"
        end
        !fancyprint && lock(print_lock) do
            println(io, "    ", pkg.name, _color_string(" Being precompiled by $(pkgspidlocked[pkg])", Base.info_color(), hascolor))
        end
        # wait until the lock is available
        FileWatching.mkpidlock(pidfile; stale_age) do
            # double-check in case the other process crashed or the lock expired
            if Base.isprecompiled(pkg; ignore_loaded=true) # don't use caches for this as the env state will have changed
                return nothing # returning nothing indicates a process waited for another
            else
                delete!(pkgspidlocked, pkg)
                return f() # precompile
            end
        end
    end
    return cachefile
end

const pkgs_precompile_suspended = PackageSpec[] # packages that shouldn't be retried during autoprecomp
const pkgs_precompile_pending = PackageSpec[] # packages that need to be retried after restart
function save_precompile_state()
    path = Operations.pkg_scratchpath()
    for (prefix, store) in (("suspend_cache_", pkgs_precompile_suspended), ("pending_cache_", pkgs_precompile_pending))
        fpath = joinpath(path, string(prefix, hash(string(Base.active_project(), Base.VERSION))))
        if isempty(store)
            Base.rm(fpath, force=true)
        else
            mkpath(path); Base.rm(fpath, force=true)
            open(fpath, "w") do io
                serialize(io, store)
            end
        end
    end
    return nothing
end
function recall_precompile_state()
    for (prefix, store) in (("suspend_cache_", pkgs_precompile_suspended), ("pending_cache_", pkgs_precompile_pending))
        fpath = joinpath(Operations.pkg_scratchpath(), string(prefix, hash(string(Base.active_project(), Base.VERSION))))
        if isfile(fpath)
            open(fpath) do io
                try
                    pkgspecs = deserialize(io)::Vector{PackageSpec}
                    append!(empty!(store), pkgspecs)
                catch
                    empty!(store)
                end
            end
            Base.rm(fpath, force=true)
        else
            empty!(store)
        end
    end
    return nothing
end
function precomp_suspend!(pkg::PackageSpec)
    precomp_suspended(pkg) || push!(pkgs_precompile_suspended, pkg)
    return
end
precomp_unsuspend!() = empty!(pkgs_precompile_suspended)
precomp_suspended(pkg::PackageSpec) = pkg in pkgs_precompile_suspended
function precomp_prune_suspended!(pkgs::Vector{PackageSpec})
    filter!(in(pkgs), pkgs_precompile_suspended)
    unique!(pkgs_precompile_suspended)
    return
end

function precomp_queue!(pkg::PackageSpec)
    precomp_suspended(pkg) || push!(pkgs_precompile_pending, pkg)
    return
end
precomp_dequeue!(pkg::PackageSpec) = filter!(!isequal(pkg), pkgs_precompile_pending)
precomp_queued(pkg::PackageSpec) = pkg in pkgs_precompile_pending

function tree_hash(repo::LibGit2.GitRepo, tree_hash::String)
    try
        return LibGit2.GitObject(repo, tree_hash)
    catch err
        err isa LibGit2.GitError && err.code == LibGit2.Error.ENOTFOUND || rethrow()
    end
    return nothing
end

instantiate(; kwargs...) = instantiate(Context(); kwargs...)
function instantiate(ctx::Context; manifest::Union{Bool, Nothing}=nothing,
                     update_registry::Bool=true, verbose::Bool=false,
                     platform::AbstractPlatform=HostPlatform(), allow_build::Bool=true, allow_autoprecomp::Bool=true, kwargs...)
    Context!(ctx; kwargs...)
    if Registry.download_default_registries(ctx.io)
        copy!(ctx.registries, Registry.reachable_registries())
    end
    if !isfile(ctx.env.project_file) && isfile(ctx.env.manifest_file)
        _manifest = Pkg.Types.read_manifest(ctx.env.manifest_file)
        Types.check_warn_manifest_julia_version_compat(_manifest, ctx.env.manifest_file)
        deps = Dict{String,String}()
        for (uuid, pkg) in _manifest
            if pkg.name in keys(deps)
                # TODO, query what package to put in Project when in interactive mode?
                pkgerror("cannot instantiate a manifest without project file when the manifest has multiple packages with the same name ($(pkg.name))")
            end
            deps[pkg.name] = string(uuid)
        end
        Types.write_project(Dict("deps" => deps), ctx.env.project_file)
        return instantiate(Context(); manifest=manifest, update_registry=update_registry, allow_autoprecomp=allow_autoprecomp, verbose=verbose, platform=platform, kwargs...)
    end
    if (!isfile(ctx.env.manifest_file) && manifest === nothing) || manifest == false
        # given no manifest exists, only allow invoking a registry update if there are project deps
        allow_registry_update = isfile(ctx.env.project_file) && !isempty(ctx.env.project.deps)
        up(ctx; update_registry = update_registry && allow_registry_update)
        allow_autoprecomp && Pkg._auto_precompile(ctx, already_instantiated = true)
        return
    end
    if !isfile(ctx.env.manifest_file) && manifest == true
        pkgerror("expected manifest file at `$(ctx.env.manifest_file)` but it does not exist")
    end
    Types.check_warn_manifest_julia_version_compat(ctx.env.manifest, ctx.env.manifest_file)

    if Operations.is_manifest_current(ctx.env) === false
        @warn """The project dependencies or compat requirements have changed since the manifest was last resolved.
        It is recommended to `Pkg.resolve()` or consider `Pkg.update()` if necessary."""
    end

    Operations.prune_manifest(ctx.env)
    for (name, uuid) in ctx.env.project.deps
        get(ctx.env.manifest, uuid, nothing) === nothing || continue
        pkgerror("`$name` is a direct dependency, but does not appear in the manifest.",
                 " If you intend `$name` to be a direct dependency, run `Pkg.resolve()` to populate the manifest.",
                 " Otherwise, remove `$name` with `Pkg.rm(\"$name\")`.",
                 " Finally, run `Pkg.instantiate()` again.")
    end
    # check if all source code and artifacts are downloaded to exit early
    if Operations.is_instantiated(ctx.env; platform)
        allow_autoprecomp && Pkg._auto_precompile(ctx, already_instantiated = true)
        return
    end

    pkgs = Operations.load_all_deps(ctx.env)
    try
        # First try without updating the registry
        Operations.check_registered(ctx.registries, pkgs)
    catch e
        if !(e isa PkgError) || update_registry == false
            rethrow(e)
        end
        Operations.update_registries(ctx; force=false)
        Operations.check_registered(ctx.registries, pkgs)
    end
    new_git = UUID[]
    # Handling packages tracking repos
    for pkg in pkgs
        repo_source = pkg.repo.source
        repo_source !== nothing || continue
        sourcepath = Operations.source_path(ctx.env.manifest_file, pkg, ctx.julia_version)
        isdir(sourcepath) && continue
        ## Download repo at tree hash
        # determine canonical form of repo source
        if !isurl(repo_source)
            repo_source = normpath(joinpath(dirname(ctx.env.project_file), repo_source))
        end
        if !isurl(repo_source) && !isdir(repo_source)
            pkgerror("Did not find path `$(repo_source)` for $(err_rep(pkg))")
        end
        repo_path = Types.add_repo_cache_path(repo_source)
        let repo_source=repo_source
            LibGit2.with(GitTools.ensure_clone(ctx.io, repo_path, repo_source; isbare=true)) do repo
                # We only update the clone if the tree hash can't be found
                tree_hash_object = tree_hash(repo, string(pkg.tree_hash))
                if tree_hash_object === nothing
                    GitTools.fetch(ctx.io, repo, repo_source; refspecs=Types.refspecs)
                    tree_hash_object = tree_hash(repo, string(pkg.tree_hash))
                end
                if tree_hash_object === nothing
                    pkgerror("Did not find tree_hash $(pkg.tree_hash) for $(err_rep(pkg))")
                end
                mkpath(sourcepath)
                GitTools.checkout_tree_to_path(repo, tree_hash_object, sourcepath)
                push!(new_git, pkg.uuid)
            end
        end
    end

    # Install all packages
    new_apply = Operations.download_source(ctx)
    # Install all artifacts
    Operations.download_artifacts(ctx.env; platform, verbose, io=ctx.io)
    # Run build scripts
    allow_build && Operations.build_versions(ctx, union(new_apply, new_git); verbose=verbose)

    allow_autoprecomp && Pkg._auto_precompile(ctx, already_instantiated = true)
end


@deprecate status(mode::PackageMode) status(mode=mode)

function status(ctx::Context, pkgs::Vector{PackageSpec}; diff::Bool=false, mode=PKGMODE_PROJECT, outdated::Bool=false, compat::Bool=false, extensions::Bool=false, io::IO=stdout_f())
    if compat
        diff && pkgerror("Compat status has no `diff` mode")
        outdated && pkgerror("Compat status has no `outdated` mode")
        extensions && pkgerror("Compat status has no `extensions` mode")
        Operations.print_compat(ctx, pkgs; io)
    else
        Operations.status(ctx.env, ctx.registries, pkgs; mode, git_diff=diff, io, outdated, extensions)
    end
    return nothing
end


function activate(;temp=false, shared=false, prev=false, io::IO=stderr_f())
    shared && pkgerror("Must give a name for a shared environment")
    temp && return activate(mktempdir(); io=io)
    if prev
        if isempty(PREV_ENV_PATH[])
            pkgerror("No previously active environment found")
        else
            return activate(PREV_ENV_PATH[]; io=io)
        end
    end
    if !isnothing(Base.active_project())
        PREV_ENV_PATH[] = Base.active_project()
    end
    Base.ACTIVE_PROJECT[] = nothing
    p = Base.active_project()
    p === nothing || printpkgstyle(io, :Activating, "project at $(pathrepr(dirname(p)))")
    add_snapshot_to_undo()
    return nothing
end
function _activate_dep(dep_name::AbstractString)
    Base.active_project() === nothing && return
    ctx = nothing
    try
        ctx = Context()
    catch err
        err isa PkgError || rethrow()
        return
    end
    uuid = get(ctx.env.project.deps, dep_name, nothing)
    if uuid !== nothing
        entry = manifest_info(ctx.env.manifest, uuid)
        if entry.path !== nothing
            return joinpath(dirname(ctx.env.manifest_file), entry.path::String)
        end
    end
end
function activate(path::AbstractString; shared::Bool=false, temp::Bool=false, io::IO=stderr_f())
    temp && pkgerror("Can not give `path` argument when creating a temporary environment")
    if !shared
        # `pkg> activate path`/`Pkg.activate(path)` does the following
        # 1. if path exists, activate that
        # 2. if path exists in deps, and the dep is deved, activate that path (`devpath` above)
        # 3. activate the non-existing directory (e.g. as in `pkg> activate .` for initing a new env)
        if Pkg.isdir_nothrow(path)
            fullpath = abspath(path)
        else
            fullpath = _activate_dep(path)
            if fullpath === nothing
                fullpath = abspath(path)
            end
        end
    else
        # initialize `fullpath` in case of empty `Pkg.depots()`
        fullpath = ""
        # loop over all depots to check if the shared environment already exists
        for depot in Pkg.depots()
            fullpath = joinpath(Pkg.envdir(depot), path)
            isdir(fullpath) && break
        end
        # this disallows names such as "Foo/bar", ".", "..", etc
        if basename(abspath(fullpath)) != path
            pkgerror("not a valid name for a shared environment: $(path)")
        end
        # unless the shared environment already exists, place it in the first depots
        if !isdir(fullpath)
            fullpath = joinpath(Pkg.envdir(Pkg.depots1()), path)
        end
    end
    if !isnothing(Base.active_project())
        PREV_ENV_PATH[] = Base.active_project()
    end
    Base.ACTIVE_PROJECT[] = Base.load_path_expand(fullpath)
    p = Base.active_project()
    if p !== nothing
        n = ispath(p) ? "" : "new "
        printpkgstyle(io, :Activating, "$(n)project at $(pathrepr(dirname(p)))")
    end
    add_snapshot_to_undo()
    return nothing
end
function activate(f::Function, new_project::AbstractString)
    old = Base.ACTIVE_PROJECT[]
    Base.ACTIVE_PROJECT[] = new_project
    try
        f()
    finally
        Base.ACTIVE_PROJECT[] = old
    end
end

function compat(ctx::Context; io = nothing)
    io = something(io, ctx.io)
    can_fancyprint(io) || pkgerror("Pkg.compat cannot be run interactively in this terminal")
    printpkgstyle(io, :Compat, pathrepr(ctx.env.project_file))
    longest_dep_len = max(5, length.(collect(keys(ctx.env.project.deps)))...)
    opt_strs = String[]
    opt_pkgs = String[]
    compat_str = Operations.get_compat_str(ctx.env.project, "julia")
    push!(opt_strs, Operations.compat_line(io, "julia", nothing, compat_str, longest_dep_len, indent = ""))
    push!(opt_pkgs, "julia")
    for (dep, uuid) in sort(collect(ctx.env.project.deps); by = x->x.first)
        compat_str = Operations.get_compat_str(ctx.env.project, dep)
        push!(opt_strs, Operations.compat_line(io, dep, uuid, compat_str, longest_dep_len, indent = ""))
        push!(opt_pkgs, dep)
    end
    menu = TerminalMenus.RadioMenu(opt_strs, pagesize=length(opt_strs))
    choice = try
        TerminalMenus.request("  Select an entry to edit:", menu)
    catch err
        if err isa InterruptException # if ^C is entered
            println(io)
            return false
        end
        rethrow()
    end
    choice == -1 && return false
    dep = opt_pkgs[choice]
    current_compat_str = something(Operations.get_compat_str(ctx.env.project, dep), "")
    resp = try
        prompt = "  Edit compat entry for $(dep):"
        print(io, prompt)
        buffer = current_compat_str
        cursor = length(buffer)
        start_pos = length(prompt) + 2
        move_start = "\e[$(start_pos)G"
        clear_to_end = "\e[0J"
        ccall(:jl_tty_set_mode, Int32, (Ptr{Cvoid},Int32), stdin.handle, true)
        while true
            print(io, move_start, clear_to_end, buffer, "\e[$(start_pos + cursor)G")
            inp = TerminalMenus._readkey(stdin)
            if inp == '\r' # Carriage return
                println(io)
                break
            elseif inp == '\x03' # cltr-C
                println(io)
                return
            elseif inp == TerminalMenus.ARROW_RIGHT
                cursor = min(length(buffer), cursor + 1)
            elseif inp == TerminalMenus.ARROW_LEFT
                cursor = max(0, cursor - 1)
            elseif inp == TerminalMenus.HOME_KEY
                cursor = (0)
            elseif inp == TerminalMenus.END_KEY
                cursor = length(buffer)
            elseif inp == TerminalMenus.DEL_KEY
                if cursor == 0
                    buffer = buffer[2:end]
                elseif cursor < length(buffer)
                    buffer = buffer[1:cursor] * buffer[(cursor + 2):end]
                end
            elseif inp isa TerminalMenus.Key
                # ignore all other escaped (multi-byte) keys
            elseif inp == '\x7f' # backspace
                if cursor == 1
                    buffer = buffer[2:end]
                elseif cursor == length(buffer)
                    buffer = buffer[1:end - 1]
                elseif cursor > 0
                    buffer = buffer[1:(cursor-1)] * buffer[(cursor + 1):end]
                else
                    continue
                end
                cursor -= 1
            else
                if cursor == 0
                    buffer = inp * buffer
                elseif cursor == length(buffer)
                    buffer = buffer * inp
                else
                    buffer = buffer[1:cursor] * inp * buffer[(cursor + 1):end]
                end
                cursor += 1
            end
        end
        buffer
    finally
        ccall(:jl_tty_set_mode, Int32, (Ptr{Cvoid},Int32), stdin.handle, false)
    end
    new_entry = strip(resp)
    compat(ctx, dep, string(new_entry))
    return
end
function compat(ctx::Context, pkg::String, compat_str::Union{Nothing,String}; io = nothing, kwargs...)
    io = something(io, ctx.io)
    pkg = pkg == "Julia" ? "julia" : pkg
    isnothing(compat_str) || (compat_str = string(strip(compat_str, '"')))
    if haskey(ctx.env.project.deps, pkg) || pkg == "julia"
        success = Operations.set_compat(ctx.env.project, pkg, isnothing(compat_str) ? nothing : isempty(compat_str) ? nothing : compat_str)
        success === false && pkgerror("invalid compat version specifier \"$(compat_str)\"")
        write_env(ctx.env)
        if isnothing(compat_str) || isempty(compat_str)
            printpkgstyle(io, :Compat, "entry removed for $(pkg)")
        else
            printpkgstyle(io, :Compat, "entry set:\n  $(pkg) = $(repr(compat_str))")
        end
        printpkgstyle(io, :Resolve, "checking for compliance with the new compat rules...")
        try
            resolve(ctx)
        catch e
            if e isa ResolverError
                printpkgstyle(io, :Error, string(e.msg), color = Base.warn_color())
                printpkgstyle(io, :Suggestion, "Call `update` to attempt to meet the compatibility requirements.", color = Base.info_color())
            else
                rethrow()
            end
        end
        return
    else
        pkgerror("No package named $pkg in current Project")
    end
end
compat(pkg::String; kwargs...) = compat(pkg, nothing; kwargs...)
compat(pkg::String, compat_str::Union{Nothing,String}; kwargs...) = compat(Context(), pkg, compat_str; kwargs...)
compat(;kwargs...) = compat(Context(); kwargs...)

#######
# why #
#######

function why(ctx::Context, pkgs::Vector{PackageSpec}; io::IO, kwargs...)
    require_not_empty(pkgs, :why)

    manifest_resolve!(ctx.env.manifest, pkgs)
    project_deps_resolve!(ctx.env, pkgs)
    ensure_resolved(ctx, ctx.env.manifest, pkgs)

    # Store all packages that has a dependency on us (all dependees)
    incoming = Dict{UUID, Set{UUID}}()
    for (uuid, dep_pkgs) in ctx.env.manifest
        for (dep, dep_uuid) in dep_pkgs.deps
            haskey(incoming, dep_uuid) || (incoming[dep_uuid] = Set{UUID}())
            push!(incoming[dep_uuid], uuid)
        end
    end

    function find_paths!(final_paths, current, path = UUID[])
        push!(path, current)
        current in values(ctx.env.project.deps) && push!(final_paths, path) # record once we've traversed to a project dep
        haskey(incoming, current) || return # but only return if we've reached a leaf that nothing depends on
        for p in incoming[current]
            if p in path
                # detected dependency cycle and none of the dependencies in the cycle
                # are in the project could happen when manually modifying
                # the project and running this function function before a
                # resolve
                continue
            end
            find_paths!(final_paths, p, copy(path))
        end
    end

    first = true
    for pkg in pkgs
        !first && println(io)
        first = false
        final_paths = Set{Vector{UUID}}()
        find_paths!(final_paths, pkg.uuid)
        foreach(reverse!, final_paths)
        final_paths_names = map(x -> [ctx.env.manifest[uuid].name for uuid in x], collect(final_paths))
        sort!(final_paths_names, by = x -> (x, length(x)))
        delimiter = sprint((io, args) -> printstyled(io, args...; color=:light_green), "→", context=io)
        for path in final_paths_names
            println(io, "  ", join(path, " $delimiter "))
        end
    end
end


########
# Undo #
########

struct UndoSnapshot
    date::DateTime
    project::Types.Project
    manifest::Types.Manifest
end
mutable struct UndoState
    idx::Int
    entries::Vector{UndoSnapshot}
end
UndoState() = UndoState(0, UndoSnapshot[])
const undo_entries = Dict{String, UndoState}()
const max_undo_limit = 50
const saved_initial_snapshot = Ref(false)

function add_snapshot_to_undo(env=nothing)
    # only attempt to take a snapshot if there is
    # an active project to be found
    if env === nothing
        if Base.active_project() === nothing
            return
        else
            env = EnvCache()
        end
    end
    state = get!(undo_entries, env.project_file) do
        UndoState()
    end
    # Is the current state the same as the previous one, do nothing
    if !isempty(state.entries) && env.project == env.original_project && env.manifest.deps == env.original_manifest.deps
        return
    end
    snapshot = UndoSnapshot(now(), env.project, env.manifest)
    deleteat!(state.entries, 1:(state.idx-1))
    pushfirst!(state.entries, snapshot)
    state.idx = 1

    resize!(state.entries, min(length(state.entries), max_undo_limit))
end

undo(ctx = Context()) = redo_undo(ctx, :undo,  1)
redo(ctx = Context()) = redo_undo(ctx, :redo, -1)
function redo_undo(ctx, mode::Symbol, direction::Int)
    @assert direction == 1 || direction == -1
    state = get(undo_entries, ctx.env.project_file, nothing)
    state === nothing && pkgerror("no undo state for current project")
    state.idx == (mode === :redo ? 1 : length(state.entries)) && pkgerror("$mode: no more states left")

    state.idx += direction
    snapshot = state.entries[state.idx]
    ctx.env.manifest, ctx.env.project = snapshot.manifest, snapshot.project
    write_env(ctx.env; update_undo=false)
    Operations.show_update(ctx.env, ctx.registries; io=ctx.io)
end


function setprotocol!(;
    domain::AbstractString="github.com",
    protocol::Union{Nothing, AbstractString}=nothing
)
    GitTools.setprotocol!(domain=domain, protocol=protocol)
    return nothing
end

@deprecate setprotocol!(proto::Union{Nothing, AbstractString}) setprotocol!(protocol = proto) false

function handle_package_input!(pkg::PackageSpec)
    if pkg.path !== nothing && pkg.url !== nothing
        pkgerror("`path` and `url` are conflicting specifications")
    end
    pkg.repo = Types.GitRepo(rev = pkg.rev, source = pkg.url !== nothing ? pkg.url : pkg.path,
                         subdir = pkg.subdir)
    pkg.path = nothing
    pkg.tree_hash = nothing
    if pkg.version === nothing
        pkg.version = VersionSpec()
    end
    if !(pkg.version isa VersionNumber)
        pkg.version = VersionSpec(pkg.version)
    end
    pkg.uuid = pkg.uuid isa String ? UUID(pkg.uuid) : pkg.uuid
end

function upgrade_manifest(man_path::String)
    dir = mktempdir()
    cp(man_path, joinpath(dir, "Manifest.toml"))
    Pkg.activate(dir) do
        Pkg.upgrade_manifest()
    end
    mv(joinpath(dir, "Manifest.toml"), man_path, force = true)
end
function upgrade_manifest(ctx::Context = Context())
    before_format = ctx.env.manifest.manifest_format
    if before_format == v"2.0"
        pkgerror("Format of manifest file at `$(ctx.env.manifest_file)` already up to date: manifest_format == $(before_format)")
    elseif before_format != v"1.0"
        pkgerror("Format of manifest file at `$(ctx.env.manifest_file)` version is unrecognized: manifest_format == $(before_format)")
    end
    ctx.env.manifest.manifest_format = v"2.0"
    Types.write_manifest(ctx.env)
    printpkgstyle(ctx.io, :Updated, "Format of manifest file at `$(ctx.env.manifest_file)` updated from v$(before_format.major).$(before_format.minor) to v2.0")
    return nothing
end

end # module
o   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Pkg/src/generate.jl�      # This file is a part of Julia. License is MIT: https://julialang.org/license

function generate(path::String; io::IO=stderr_f())
    base = basename(path)
    pkg = endswith(lowercase(base), ".jl") ? chop(base, tail=3) : base
    Base.isidentifier(pkg) || pkgerror("$(repr(pkg)) is not a valid package name")
    isdir(path) && pkgerror("$(abspath(path)) already exists")
    printpkgstyle(io, :Generating, " project $pkg:")
    uuid = project(io, pkg, path)
    entrypoint(io, pkg, path)
    return Dict(pkg => uuid)
end

function genfile(f::Function, io::IO, dir::AbstractString, file::AbstractString)
    path = joinpath(dir, file)
    println(io, "    $(Base.contractuser(path))")
    mkpath(dirname(path))
    open(f, path, "w")
    return
end

function project(io::IO, pkg::AbstractString, dir::AbstractString)
    mkpath(dir)

    name = email = nothing
    gitname = LibGit2.getconfig("user.name", "")
    isempty(gitname) || (name = gitname)
    gitmail = LibGit2.getconfig("user.email", "")
    isempty(gitmail) || (email = gitmail)

    if name === nothing
        for env in ["GIT_AUTHOR_NAME", "GIT_COMMITTER_NAME", "USER", "USERNAME", "NAME"]
            name = get(ENV, env, nothing)
            name !== nothing && break
        end
    end

    name === nothing && (name = "Unknown")

    if email === nothing
        for env in ["GIT_AUTHOR_EMAIL", "GIT_COMMITTER_EMAIL", "EMAIL"];
            email = get(ENV, env, nothing)
            email !== nothing && break
        end
    end

    authors = ["$name " * (email === nothing ? "" : "<$email>")]

    uuid = UUIDs.uuid4()
    genfile(io, dir, "Project.toml") do file_io
        toml = Dict{String,Any}("authors" => authors,
                                "name" => pkg,
                                "uuid" => string(uuid),
                                "version" => "0.1.0",
                                )
        TOML.print(file_io, toml, sorted=true, by=key -> (Types.project_key_order(key), key))
    end
    return uuid
end

function entrypoint(io::IO, pkg::AbstractString, dir)
    genfile(io, joinpath(dir, "src"), "$pkg.jl") do file_io
        print(file_io,
           """
            module $pkg

            greet() = print("Hello World!")

            end # module $pkg
            """
        )
    end
end
x   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Pkg/src/REPLMode/REPLMode.jl�i      # This file is a part of Julia. License is MIT: https://julialang.org/license

module REPLMode

using Markdown, UUIDs, Dates

import REPL
import REPL: LineEdit, REPLCompletions
import REPL: TerminalMenus

import ..casesensitive_isdir, ..OFFLINE_MODE, ..linewrap, ..pathrepr
using ..Types, ..Operations, ..API, ..Registry, ..Resolve
import ..stdout_f, ..stderr_f

const TEST_MODE = Ref{Bool}(false)
const PRINTED_REPL_WARNING = Ref{Bool}(false)

#########################
# Specification Structs #
#########################

#---------#
# Options #
#---------#
const OptionDeclaration = Vector{Pair{Symbol,Any}}
struct OptionSpec
    name::String
    short_name::Union{Nothing,String}
    api::Pair{Symbol, Any}
    takes_arg::Bool
end

# TODO assert names matching lex regex
# assert now so that you don't fail at user time
# see function `REPLMode.api_options`
function OptionSpec(;name::String,
                    short_name::Union{Nothing,String}=nothing,
                    takes_arg::Bool=false,
                    api::Pair{Symbol,<:Any})::OptionSpec
    takes_arg && @assert hasmethod(api.second, Tuple{String})
    return OptionSpec(name, short_name, api, takes_arg)
end

function OptionSpecs(decs::Vector{OptionDeclaration})
    specs = Dict{String, OptionSpec}()
    for x in decs
        opt_spec = OptionSpec(;x...)
        @assert !haskey(specs, opt_spec.name) # don't overwrite
        specs[opt_spec.name] = opt_spec
        if opt_spec.short_name !== nothing
            @assert !haskey(specs, opt_spec.short_name::String) # don't overwrite
            specs[opt_spec.short_name::String] = opt_spec
        end
    end
    return specs
end

#-----------#
# Arguments #
#-----------#
struct ArgSpec
    count::Pair
    parser::Function
end

#----------#
# Commands #
#----------#
const CommandDeclaration = Vector{Pair{Symbol,Any}}
struct CommandSpec
    canonical_name::String
    short_name::Union{Nothing,String}
    api::Function
    should_splat::Bool
    argument_spec::ArgSpec
    option_specs::Dict{String,OptionSpec}
    completions::Union{Nothing,Function}
    description::String
    help::Union{Nothing,Markdown.MD}
end

default_parser(xs, options) = unwrap(xs)
function CommandSpec(;name::Union{Nothing,String}           = nothing,
                     short_name::Union{Nothing,String}      = nothing,
                     api::Union{Nothing,Function}           = nothing,
                     should_splat::Bool                     = true,
                     option_spec::Vector{OptionDeclaration} = OptionDeclaration[],
                     help::Union{Nothing,Markdown.MD}       = nothing,
                     description::Union{Nothing,String}     = nothing,
                     completions::Union{Nothing,Function}   = nothing,
                     arg_count::Pair                        = (0=>0),
                     arg_parser::Function                   = default_parser,
                     )::CommandSpec
    name === nothing        && error("Supply a canonical name")
    description === nothing && error("Supply a description")
    api === nothing         && error("Supply API dispatch function for `$(name)`")
    # TODO assert isapplicable completions dict, string
    return CommandSpec(name, short_name, api, should_splat, ArgSpec(arg_count, arg_parser),
                       OptionSpecs(option_spec), completions, description, help)
end

function CommandSpecs(declarations::Vector{CommandDeclaration})
    specs = Dict{String,CommandSpec}()
    for dec in declarations
        spec = CommandSpec(;dec...)
        @assert !haskey(specs, spec.canonical_name) "duplicate spec entry"
        specs[spec.canonical_name] = spec
        if spec.short_name !== nothing
            @assert !haskey(specs, spec.short_name::String) "duplicate spec entry"
            specs[spec.short_name::String] = spec
        end
    end
    return specs
end

function CompoundSpecs(compound_declarations)
    compound_specs = Dict{String,Dict{String,CommandSpec}}()
    for (name, command_declarations) in compound_declarations
        specs = CommandSpecs(command_declarations)
        @assert !haskey(compound_specs, name) "duplicate super spec entry"
        compound_specs[name] = specs
    end
    return compound_specs
end

###########
# Parsing #
###########

# QString: helper struct for retaining quote information
struct QString
    raw::String
    isquoted::Bool
end
unwrap(xs::Vector{QString}) = map(x -> x.raw, xs)

#---------#
# Options #
#---------#
struct Option
    val::String
    argument::Union{Nothing,String}
    Option(val::AbstractString) = new(val, nothing)
    Option(val::AbstractString, arg::Union{Nothing,String}) = new(val, arg)
end
Base.show(io::IO, opt::Option) = print(io, "--$(opt.val)", opt.argument === nothing ? "" : "=$(opt.argument)")
wrap_option(option::String)  = length(option) == 1 ? "-$option" : "--$option"
is_opt(word::AbstractString) = first(word) == '-' && word != "-"

function parse_option(word::AbstractString)::Option
    m = match(r"^(?: -([a-z]) | --((?:[a-z]{1,}-?)*)(?:\s*=\s*(\S*))? )$"ix, word)
    m === nothing && pkgerror("malformed option: ", repr(word))
    option_name = m.captures[1] !== nothing ? something(m.captures[1]) : something(m.captures[2])
    option_arg  = m.captures[3] === nothing ? nothing : String(something(m.captures[3]))
    return Option(option_name, option_arg)
end

#-----------#
# Statement #
#-----------#
# Statement: text-based representation of a command
Base.@kwdef mutable struct Statement
    super::Union{Nothing,String}                  = nothing
    spec::Union{Nothing,CommandSpec}              = nothing
    options::Union{Vector{Option},Vector{String}} = String[]
    arguments::Vector{QString}                    = QString[]
end

function lex(cmd::String)::Vector{QString}
    replace_comma = (nothing!=match(r"^(add|rm|remove|status|precompile)+\s", cmd))
    in_doublequote = false
    in_singlequote = false
    qstrings = QString[]
    token_in_progress = Char[]

    push_token!(is_quoted) = begin
        push!(qstrings, QString(String(token_in_progress), is_quoted))
        empty!(token_in_progress)
    end

    for c in cmd
        if c == '"'
            if in_singlequote # raw char
                push!(token_in_progress, c)
            else # delimiter
                in_doublequote ? push_token!(true) : push_token!(false)
                in_doublequote = !in_doublequote
            end
        elseif c == '\''
            if in_doublequote # raw char
                push!(token_in_progress, c)
            else # delimiter
                in_singlequote ? push_token!(true) : push_token!(false)
                in_singlequote = !in_singlequote
            end
        elseif c == ' '
            if in_doublequote || in_singlequote # raw char
                push!(token_in_progress, c)
            else # delimiter
                push_token!(false)
            end
        elseif c == ';'
            if in_doublequote || in_singlequote # raw char
                push!(token_in_progress, c)
            else # special delimiter
                push_token!(false)
                push!(qstrings, QString(";", false))
            end
        elseif c == ','
            if in_doublequote || in_singlequote || !replace_comma # raw char
                # don't replace ',' in quotes
                push!(token_in_progress, c)
            else
                push_token!(false)
                push!(qstrings, QString("", false))
            end
        else
            push!(token_in_progress, c)
        end
    end
    (in_doublequote || in_singlequote) ? pkgerror("unterminated quote") : push_token!(false)
    # to avoid complexity in the main loop, empty tokens are allowed above and
    # filtered out before returning
    return filter(x->!isempty(x.raw), qstrings)
end

function tokenize(cmd::String)
    cmd = replace(replace(cmd, "\r\n" => "; "), "\n" => "; ") # for multiline commands
    qstrings = lex(cmd)
    statements = foldl(qstrings; init=[QString[]]) do collection, next
        (next.raw == ";" && !next.isquoted) ?
            push!(collection, QString[]) :
            push!(collection[end], next)
        return collection
    end
    return statements
end

function core_parse(words::Vector{QString}; only_cmd=false)
    statement = Statement()
    word::Union{Nothing,QString} = nothing
    function next_word!()
        isempty(words) && return false
        word = popfirst!(words)
        return true
    end

    # begin parsing
    next_word!() || return statement, ((word === nothing) ? nothing : word.raw)
    # handle `?` alias for help
    # It is special in that it requires no space between command and args
    if word.raw[1]=='?' && !word.isquoted
        length(word.raw) > 1 && pushfirst!(words, QString(word.raw[2:end],false))
        word = QString("?", false)
    end
    # determine command
    super = get(SPECS, word.raw, nothing)
    if super !== nothing # explicit
        statement.super = word.raw
        next_word!() || return statement, word.raw
        command = get(super, word.raw, nothing)
        command !== nothing || return statement, word.raw
    else # try implicit package
        super = SPECS["package"]
        command = get(super, word.raw, nothing)
        command !== nothing || return statement, word.raw
    end
    statement.spec = command

    only_cmd && return statement, word.raw # hack to hook in `help` command

    next_word!() || return statement, word.raw

    # full option parsing is delayed so that the completions parser can use the raw string
    while is_opt(word.raw)
        push!(statement.options, word.raw)
        next_word!() || return statement, word.raw
    end

    pushfirst!(words, word)
    statement.arguments = words
    return statement, words[end].raw
end

parse(input::String) =
    map(Base.Iterators.filter(!isempty, tokenize(input))) do words
        statement, input_word = core_parse(words)
        statement.spec === nothing && pkgerror("`$input_word` is not a recognized command. Type ? for help with available commands")
        statement.options = map(parse_option, statement.options)
        statement
    end

#------------#
# APIOptions #
#------------#

# Do NOT introduce a constructor for APIOptions
# as long as it's an alias for Dict
const APIOptions = Dict{Symbol, Any}
function api_options(options::Vector{Option},
                     specs::Dict{String, OptionSpec})
    api_opts = APIOptions()
    enforce_option(options, specs)
    for option in options
        spec = specs[option.val]
        api_opts[spec.api.first] = spec.takes_arg ?
            spec.api.second(option.argument) :
            spec.api.second
    end
    return api_opts
end

Context!(ctx::APIOptions)::Context = Types.Context!(collect(ctx))

#---------#
# Command #
#---------#
Base.@kwdef struct Command
    spec::Union{Nothing,CommandSpec} = nothing
    options::APIOptions              = APIOptions()
    arguments::Vector                = []
end

function enforce_option(option::Option, specs::Dict{String,OptionSpec})
    spec = get(specs, option.val, nothing)
    spec !== nothing || pkgerror("option '$(option.val)' is not a valid option")
    if spec.takes_arg
        option.argument !== nothing ||
            pkgerror("option '$(option.val)' expects an argument, but no argument given")
    else # option is a switch
        option.argument === nothing ||
            pkgerror("option '$(option.val)' does not take an argument, but '$(option.argument)' given")
    end
end

"""
checks:
- options are understood by the given command
- options do not conflict (e.g. `rm --project --manifest`)
- options which take an argument are given arguments
- options which do not take arguments are not given arguments
"""
function enforce_option(options::Vector{Option}, specs::Dict{String,OptionSpec})
    unique_keys = Symbol[]
    get_key(opt::Option) = specs[opt.val].api.first

    # per option checking
    foreach(x->enforce_option(x,specs), options)
    # checking for compatible options
    for opt in options
        key = get_key(opt)
        if key in unique_keys
            conflicting = filter(opt->get_key(opt) == key, options)
            pkgerror("Conflicting options: $conflicting")
        else
            push!(unique_keys, key)
        end
    end
end

"""
Final parsing (and checking) step.
This step is distinct from `parse` in that it relies on the command specifications.
"""
function Command(statement::Statement)::Command
    # options
    options = api_options(statement.options, statement.spec.option_specs)
    # arguments
    arg_spec = statement.spec.argument_spec
    arguments = arg_spec.parser(statement.arguments, options)
    if !((arg_spec.count.first <= length(arguments) <= arg_spec.count.second)::Bool)
        pkgerror("Wrong number of arguments")
    end
    return Command(statement.spec, options, arguments)
end

#############
# Execution #
#############
function do_cmd(repl::REPL.AbstractREPL, input::String; do_rethrow=false)
    if !isinteractive() && !TEST_MODE[] && !PRINTED_REPL_WARNING[]
        @warn "The Pkg REPL mode is intended for interactive use only, and should not be used from scripts. It is recommended to use the functional API instead."
        PRINTED_REPL_WARNING[] = true
    end
    try
        statements = parse(input)
        commands   = map(Command, statements)
        xs = []
        for command in commands
            push!(xs, do_cmd!(command, repl))
        end
        return TEST_MODE[] ? xs : nothing
    catch err
        do_rethrow && rethrow()
        if err isa PkgError || err isa Resolve.ResolverError
            Base.display_error(repl.t.err_stream, ErrorException(sprint(showerror, err)), Ptr{Nothing}[])
        else
            Base.display_error(repl.t.err_stream, err, Base.catch_backtrace())
        end
    end
end

function do_cmd!(command::Command, repl)
    # REPL specific commands
    command.spec === SPECS["package"]["help"] && return Base.invokelatest(do_help!, command, repl)
    # API commands
    if command.spec.should_splat
        TEST_MODE[] && return command.spec.api, command.arguments..., command.options
        command.spec.api(command.arguments...; collect(command.options)...) # TODO is invokelatest still needed?
    else
        TEST_MODE[] && return command.spec.api, command.arguments, command.options
        command.spec.api(command.arguments; collect(command.options)...)
    end
end

function parse_command(words::Vector{QString})
    statement, word = core_parse(words; only_cmd=true)
    if statement.super === nothing && statement.spec === nothing
        pkgerror("invalid input: `$word` is not a command")
    end
    return statement.spec === nothing ?  statement.super : statement.spec
end

function do_help!(command::Command, repl::REPL.AbstractREPL)
    disp = REPL.REPLDisplay(repl)
    if isempty(command.arguments)
        Base.display(disp, help)
        return
    end
    help_md = md""

    cmd = parse_command(command.arguments)
    if cmd isa String
        # gather all helps for super spec `cmd`
        all_specs = sort!(unique(values(SPECS[cmd]));
                          by=(spec->spec.canonical_name))
        for spec in all_specs
            isempty(help_md.content) || push!(help_md.content, md"---")
            push!(help_md.content, spec.help)
        end
    elseif cmd isa CommandSpec
        push!(help_md.content, cmd.help)
    end
    !isempty(command.arguments) && @warn "More than one command specified, only rendering help for first"
    Base.display(disp, help_md)
end

######################
# REPL mode creation #
######################

# Provide a string macro pkg"cmd" that can be used in the same way
# as the REPLMode `pkg> cmd`. Useful for testing and in environments
# where we do not have a REPL, e.g. IJulia.
struct MiniREPL <: REPL.AbstractREPL
    display::TextDisplay
    t::REPL.Terminals.TTYTerminal
end
function MiniREPL()
    MiniREPL(TextDisplay(stdout_f()), REPL.Terminals.TTYTerminal(get(ENV, "TERM", Sys.iswindows() ? "" : "dumb"), stdin, stdout_f(), stderr_f()))
end
REPL.REPLDisplay(repl::MiniREPL) = repl.display

const minirepl = Ref{MiniREPL}()

__init__() = minirepl[] = MiniREPL()

macro pkg_str(str::String)
    :($(do_cmd)(minirepl[], $str; do_rethrow=true))
end

pkgstr(str::String) = do_cmd(minirepl[], str; do_rethrow=true)

struct PkgCompletionProvider <: LineEdit.CompletionProvider end

function LineEdit.complete_line(c::PkgCompletionProvider, s)
    partial = REPL.beforecursor(s.input_buffer)
    full = LineEdit.input_string(s)
    ret, range, should_complete = completions(full, lastindex(partial))
    return ret, partial[range], should_complete
end

prev_project_file = nothing
prev_project_timestamp = nothing
prev_prefix = ""

function projname(project_file::String)
    project = try
        Types.read_project(project_file)
    catch
        nothing
    end
    if project === nothing || project.name === nothing
        name = basename(dirname(project_file))
    else
        name = project.name::String
    end
    for depot in Base.DEPOT_PATH
        envdir = joinpath(depot, "environments")
        if startswith(abspath(project_file), abspath(envdir))
            return "@" * name
        end
    end
    return name
end

function promptf()
    global prev_project_timestamp, prev_prefix, prev_project_file
    project_file = try
        Types.find_project_file()
    catch
        nothing
    end
    prefix = ""
    if project_file !== nothing
        if prev_project_file == project_file && prev_project_timestamp == mtime(project_file)
            prefix = prev_prefix
        else
            project_name = projname(project_file)
            if project_name !== nothing
                if textwidth(project_name) > 30
                    project_name = first(project_name, 27) * "..."
                end
                prefix = "($(project_name)) "
                prev_prefix = prefix
                prev_project_timestamp = mtime(project_file)
                prev_project_file = project_file
            end
        end
    end
    if OFFLINE_MODE[]
        prefix = "$(prefix)[offline] "
    end
    return "$(prefix)pkg> "
end

# Set up the repl Pkg REPLMode
function create_mode(repl::REPL.AbstractREPL, main::LineEdit.Prompt)
    pkg_mode = LineEdit.Prompt(promptf;
        prompt_prefix = repl.options.hascolor ? Base.text_colors[:blue] : "",
        prompt_suffix = "",
        complete = PkgCompletionProvider(),
        sticky = true)

    pkg_mode.repl = repl
    hp = main.hist
    hp.mode_mapping[:pkg] = pkg_mode
    pkg_mode.hist = hp

    search_prompt, skeymap = LineEdit.setup_search_keymap(hp)
    prefix_prompt, prefix_keymap = LineEdit.setup_prefix_keymap(hp, pkg_mode)

    pkg_mode.on_done = (s, buf, ok) -> begin
        ok || return REPL.transition(s, :abort)
        input = String(take!(buf))
        REPL.reset(repl)
        do_cmd(repl, input)
        REPL.prepare_next(repl)
        REPL.reset_state(s)
        s.current_mode.sticky || REPL.transition(s, main)
    end

    mk = REPL.mode_keymap(main)

    shell_mode = nothing
    for mode in Base.active_repl.interface.modes
        if mode isa LineEdit.Prompt
            mode.prompt == "shell> " && (shell_mode = mode)
        end
    end

    repl_keymap = Dict()
    if shell_mode !== nothing
        let shell_mode=shell_mode
            repl_keymap[';'] = function (s,o...)
                if isempty(s) || position(LineEdit.buffer(s)) == 0
                    buf = copy(LineEdit.buffer(s))
                    LineEdit.transition(s, shell_mode) do
                        LineEdit.state(s, shell_mode).input_buffer = buf
                    end
                else
                    LineEdit.edit_insert(s, ';')
                end
            end
        end
    end

    b = Dict{Any,Any}[
        skeymap, repl_keymap, mk, prefix_keymap, LineEdit.history_keymap,
        LineEdit.default_keymap, LineEdit.escape_defaults
    ]
    pkg_mode.keymap_dict = LineEdit.keymap(b)
    return pkg_mode
end

function repl_init(repl::REPL.AbstractREPL)
    main_mode = repl.interface.modes[1]
    pkg_mode = create_mode(repl, main_mode)
    push!(repl.interface.modes, pkg_mode)
    keymap = Dict{Any,Any}(
        ']' => function (s,args...)
            if isempty(s) || position(LineEdit.buffer(s)) == 0
                buf = copy(LineEdit.buffer(s))
                LineEdit.transition(s, pkg_mode) do
                    LineEdit.state(s, pkg_mode).input_buffer = buf
                end
            else
                LineEdit.edit_insert(s, ']')
            end
        end
    )
    main_mode.keymap_dict = LineEdit.keymap_merge(main_mode.keymap_dict, keymap)
    return
end

########
# SPEC #
########
include("completions.jl")
include("argument_parsers.jl")
include("command_declarations.jl")
const SPECS = CompoundSpecs(compound_declarations)

########
# HELP #
########
function canonical_names()
    # add "package" commands
    xs = [(spec.canonical_name => spec) for spec in unique(values(SPECS["package"]))]
    sort!(xs, by=first)
    # add other super commands, e.g. "registry"
    for (super, specs) in SPECS
        super != "package" || continue # skip "package"
        temp = [(join([super, spec.canonical_name], " ") => spec) for spec in unique(values(specs))]
        append!(xs, sort!(temp, by=first))
    end
    return xs
end

function gen_help()
    help = md"""
**Welcome to the Pkg REPL-mode**. To return to the `julia>` prompt, either press
backspace when the input line is empty or press Ctrl+C.

Full documentation available at https://pkgdocs.julialang.org/

**Synopsis**

    pkg> cmd [opts] [args]

Multiple commands can be given on the same line by interleaving a `;` between the commands.
Some commands have an alias, indicated below.

**Commands**
"""
    for (command, spec) in canonical_names()
        short_name = spec.short_name === nothing ? "" : ", `" * spec.short_name::String * '`'
        push!(help.content, Markdown.parse("`$command`$short_name: $(spec.description)"))
    end
    return help
end

const help = gen_help()
const REG_WARNED = Ref{Bool}(false)

function try_prompt_pkg_add(pkgs::Vector{Symbol})
    ctx = try
        Context()
    catch
        # Context() will error if there isn't an active project.
        # If we can't even do that, exit early.
        return false
    end
    if isempty(ctx.registries)
        if !REG_WARNED[]
            printstyled(ctx.io, " │ "; color=:green)
            printstyled(ctx.io, "Attempted to find missing packages in package registries but no registries are installed.\n")
            printstyled(ctx.io, " └ "; color=:green)
            printstyled(ctx.io, "Use package mode to install a registry. `pkg> registry add` will install the default registries.\n\n")
            REG_WARNED[] = true
        end
        return false
    end
    available_uuids = [Types.registered_uuids(ctx.registries, String(pkg)) for pkg in pkgs] # vector of vectors
    filter!(u -> all(!isequal(Operations.JULIA_UUID), u), available_uuids) # "julia" is in General but not installable
    isempty(available_uuids) && return false
    available_pkgs = pkgs[isempty.(available_uuids) .== false]
    isempty(available_pkgs) && return false
    resp = try
        plural1 = length(pkgs) == 1 ? "" : "s"
        plural2 = length(available_pkgs) == 1 ? "a package" : "packages"
        plural3 = length(available_pkgs) == 1 ? "is" : "are"
        plural4 = length(available_pkgs) == 1 ? "" : "s"
        missing_pkg_list = length(pkgs) == 1 ? String(pkgs[1]) : "[$(join(pkgs, ", "))]"
        available_pkg_list = length(available_pkgs) == 1 ? String(available_pkgs[1]) : "[$(join(available_pkgs, ", "))]"
        msg1 = "Package$(plural1) $(missing_pkg_list) not found, but $(plural2) named $(available_pkg_list) $(plural3) available from a registry."
        for line in linewrap(msg1, io = ctx.io, padding = length(" │ "))
            printstyled(ctx.io, " │ "; color=:green)
            println(ctx.io, line)
        end
        printstyled(ctx.io, " │ "; color=:green)
        println(ctx.io, "Install package$(plural4)?")
        msg2 = string("add ", join(available_pkgs, ' '))
        for (i, line) in pairs(linewrap(msg2; io = ctx.io, padding = length(string(" |   ", REPLMode.promptf()))))
            printstyled(ctx.io, " │   "; color=:green)
            if i == 1
                printstyled(ctx.io, REPLMode.promptf(); color=:blue)
            else
                print(ctx.io, " "^length(REPLMode.promptf()))
            end
            println(ctx.io, line)
        end
        printstyled(ctx.io, " └ "; color=:green)
        Base.prompt(stdin, ctx.io, "(y/n/o)", default = "y")
    catch err
        if err isa InterruptException # if ^C is entered
            println(ctx.io)
            return false
        end
        rethrow()
    end
    if isnothing(resp) # if ^D is entered
        println(ctx.io)
        return false
    end
    resp = strip(resp)
    lower_resp = lowercase(resp)
    if lower_resp in ["y", "yes"]
        API.add(string.(available_pkgs))
    elseif lower_resp in ["o"]
        editable_envs = filter(v -> v != "@stdlib", LOAD_PATH)
        option_list = String[]
        keybindings = Char[]
        shown_envs = String[]
        # We use digits 1-9 as keybindings in the env selection menu
        # That's why we can display at most 9 items in the menu
        for i in 1:min(length(editable_envs), 9)
            env = editable_envs[i]
            expanded_env = Base.load_path_expand(env)

            isnothing(expanded_env) && continue

            n = length(option_list) + 1
            push!(option_list, "$(n): $(pathrepr(expanded_env)) ($(env))")
            push!(keybindings, only("$n"))
            push!(shown_envs, expanded_env)
        end
        menu = TerminalMenus.RadioMenu(option_list, keybindings=keybindings, pagesize=length(option_list))
        default = something(
            # select the first non-default env by default, if possible
            findfirst(!=(Base.active_project()), shown_envs),
            1
        )
        print(ctx.io, "\e[1A\e[1G\e[0J") # go up one line, to the start, and clear it
        printstyled(ctx.io, " └ "; color=:green)
        choice = try
            TerminalMenus.request("Select environment:", menu, cursor=default)
        catch err
            if err isa InterruptException # if ^C is entered
                println(ctx.io)
                return false
            end
            rethrow()
        end
        choice == -1 && return false
        API.activate(shown_envs[choice]) do
            API.add(string.(available_pkgs))
        end
    elseif (lower_resp in ["n"])
        return false
    else
        println(ctx.io, "Selection not recognized")
        return false
    end
    if length(available_pkgs) < length(pkgs)
        return false # declare that some pkgs couldn't be installed
    else
        return true
    end
end

end #module
{   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Pkg/src/REPLMode/completions.jl�!      ########################
# Completion Functions #
########################
function _shared_envs()
    possible = String[]
    for depot in Base.DEPOT_PATH
        envdir = joinpath(depot, "environments")
        isdir(envdir) || continue
        append!(possible, readdir(envdir))
    end
    return possible
end

function complete_activate(options, partial, i1, i2)
    shared = get(options, :shared, false)
    if shared
        return _shared_envs()
    elseif !isempty(partial) && first(partial) == '@'
        return "@" .* _shared_envs()
    else
        return complete_local_dir(partial, i1, i2)
    end
end

function complete_local_dir(s, i1, i2)
    expanded_user = false
    oldi2 = i2
    if !isempty(s) && s[1] == '~'
        expanded_user = true
        s = expanduser(s)
        i2 += textwidth(homedir()) - 1
    end
    return complete_expanded_local_dir(s, i1, i2, expanded_user, oldi2)  # easiest way to avoid #15276 from boxing `s`
end

function complete_expanded_local_dir(s, i1, i2, expanded_user, oldi2)
    cmp = REPL.REPLCompletions.complete_path(s, i2, shell_escape=true)
    cmp2 = cmp[2]
    completions = [REPL.REPLCompletions.completion_text(p) for p in cmp[1]]
    completions = filter!(x -> isdir(s[1:prevind(s, first(cmp2)-i1+1)]*x), completions)
    if expanded_user
        if length(completions) == 1 && endswith(joinpath(homedir(), ""), first(completions))
            completions = [joinpath(s, "")]
        else
            completions = [joinpath(dirname(s), x) for x in completions]
        end
        return completions, i1:oldi2, true
    end

    return completions, cmp[2], !isempty(completions)
end


const JULIA_UUID = UUID("1222c4b2-2114-5bfd-aeef-88e4692bbb3e")
function complete_remote_package(partial)
    isempty(partial) && return String[]
    cmp = Set{String}()
    for reg in Registry.reachable_registries()
        for (uuid, regpkg) in reg
            name = regpkg.name
            name in cmp && continue
            if startswith(regpkg.name, partial)
                pkg = Registry.registry_info(regpkg)
                compat_info = Registry.compat_info(pkg)
                # Filter versions
                for (v, uncompressed_compat) in compat_info
                    Registry.isyanked(pkg, v) && continue
                    # TODO: Filter based on offline mode
                    is_julia_compat = nothing
                    for (pkg_uuid, vspec) in uncompressed_compat
                        if pkg_uuid == JULIA_UUID
                            found_julia_compat = true
                            is_julia_compat = VERSION in vspec
                            is_julia_compat && continue
                        end
                    end
                    # Found a compatible version or compat on julia at all => compatible
                    if is_julia_compat === nothing || is_julia_compat
                        push!(cmp, name)
                        break
                    end
                end
            end
        end
    end
    return sort!(collect(cmp))
end

function complete_help(options, partial)
    names = String[]
    for cmds in values(SPECS)
         append!(names, [spec.canonical_name for spec in values(cmds)])
    end
    return sort!(unique!(append!(names, collect(keys(SPECS)))))
end

function complete_installed_packages(options, partial)
    env = try EnvCache()
    catch err
        err isa PkgError || rethrow()
        return String[]
    end
    mode = get(options, :mode, PKGMODE_PROJECT)
    return mode == PKGMODE_PROJECT ?
        collect(keys(env.project.deps)) :
        unique!([entry.name for (uuid, entry) in env.manifest])
end

function complete_all_installed_packages(options, partial)
    env = try EnvCache()
    catch err
        err isa PkgError || rethrow()
        return String[]
    end
    return unique!([entry.name for (uuid, entry) in env.manifest])
end

function complete_installed_packages_and_compat(options, partial)
    env = try EnvCache()
    catch err
        err isa PkgError || rethrow()
        return String[]
    end
    return map(vcat(collect(keys(env.project.deps)), "julia")) do d
        compat_str = Operations.get_compat_str(env.project, d)
        isnothing(compat_str) ? d : string(d, " ", compat_str)
    end
end

function complete_add_dev(options, partial, i1, i2)
    comps, idx, _ = complete_local_dir(partial, i1, i2)
    if occursin(Base.Filesystem.path_separator_re, partial)
        return comps, idx, !isempty(comps)
    end
    comps = vcat(comps, sort(complete_remote_package(partial)))
    if !isempty(partial)
        append!(comps, filter!(startswith(partial), first.(values(Types.stdlibs()))))
    end
    return comps, idx, !isempty(comps)
end

########################
# COMPLETION INTERFACE #
########################
function default_commands()
    names = collect(keys(SPECS))
    append!(names, map(x -> getproperty(x, :canonical_name), values(SPECS["package"])))
    return sort(unique(names))
end

function complete_command(statement::Statement, final::Bool, on_sub::Bool)
    if statement.super !== nothing
        if (!on_sub && final) || (on_sub && !final)
            # last thing determined was the super -> complete canonical names of subcommands
            specs = SPECS[statement.super]
            names = map(x -> getproperty(x, :canonical_name), values(specs))
            return sort(unique(names))
        end
    end
    # complete default names
    return default_commands()
end

complete_opt(opt_specs) =
    unique(sort(map(wrap_option,
                    map(x -> getproperty(x, :name),
                        collect(values(opt_specs))))))

function complete_argument(spec::CommandSpec, options::Vector{String},
                           partial::AbstractString, offset::Int,
                           index::Int)
    spec.completions === nothing && return String[]
    # finish parsing opts
    local opts
    try
        opts = api_options(map(parse_option, options), spec.option_specs)
    catch e
        e isa PkgError && return String[]
        rethrow()
    end
    return applicable(spec.completions, opts, partial, offset, index) ?
        spec.completions(opts, partial, offset, index) :
        spec.completions(opts, partial)
end

function _completions(input, final, offset, index)
    statement, word_count, partial = nothing, nothing, nothing
    try
        words = tokenize(input)[end]
        word_count = length(words)
        statement, partial = core_parse(words)
        if final
            partial = "" # last token is finalized -> no partial
        end
    catch
        return String[], 0:-1, false
    end
    # number of tokens which specify the command
    command_size = count([statement.super !== nothing, true])
    command_is_focused() = !((word_count == command_size && final) || word_count > command_size)

    if statement.spec === nothing # spec not determined -> complete command
        !command_is_focused() && return String[], 0:-1, false
        x = complete_command(statement, final, word_count == 2)
    else
        command_is_focused() && return String[], 0:-1, false

        if final # complete arg by default
            x = complete_argument(statement.spec, statement.options, partial, offset, index)
        else # complete arg or opt depending on last token
            x = is_opt(partial) ?
                complete_opt(statement.spec.option_specs) :
                complete_argument(statement.spec, statement.options, partial, offset, index)
        end
    end

    # In the case where the completion function wants to deal with indices, it will return a fully
    # computed completion tuple, just return it
    # Else, the completions function will just deal with strings and will return a Vector{String}
    if isa(x, Tuple)
        return x
    else
        possible = filter(possible -> startswith(possible, partial), x)
        return possible, offset:index, !isempty(possible)
    end
end

function completions(full, index)::Tuple{Vector{String},UnitRange{Int},Bool}
    pre = full[1:index]
    isempty(pre) && return default_commands(), 0:-1, false # empty input -> complete commands
    offset_adjust = 0
    if length(pre) >= 2 && pre[1] == '?' && pre[2] != ' '
        # supports completion on things like `pkg> ?act` with no space
        pre = string(pre[1], " ", pre[2:end])
        offset_adjust = -1
    end
    last = split(pre, ' ', keepempty=true)[end]
    offset = isempty(last) ? index+1+offset_adjust : last.offset+1+offset_adjust
    final  = isempty(last) # is the cursor still attached to the final token?
    return _completions(pre, final, offset, index)
end
�   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Pkg/src/REPLMode/argument_parsers.jl�       import ..isdir_nothrow, ..Registry.RegistrySpec, ..isurl

struct PackageIdentifier
    val::String
end

struct VersionToken
    version::String
end

struct Rev
    rev::String
end

struct Subdir
    dir::String
end

const PackageToken = Union{PackageIdentifier,
                           VersionToken,
                           Rev,
                           Subdir}

packagetoken(word::String)::PackageToken =
    first(word) == '@' ? VersionToken(word[2:end]) :
    first(word) == '#' ? Rev(word[2:end]) :
    first(word) == ':' ? Subdir(word[2:end]) :
    PackageIdentifier(word)

###############
# PackageSpec #
###############
"""
Parser for PackageSpec objects.
"""
function parse_package(args::Vector{QString}, options; add_or_dev=false)::Vector{PackageSpec}
    words′ = package_lex(args)
    words = String[]
    for word in words′
        if (m = match(r"https://github.com/(.*?)/(.*?)/(?:tree|commit)/(.*?)$", word)) !== nothing
            push!(words, "https://github.com/$(m.captures[1])/$(m.captures[2])")
            push!(words, "#$(m.captures[3])")
        else
            push!(words, word)
        end
    end
    args = PackageToken[packagetoken(pkgword) for pkgword in words]

    return parse_package_args(args; add_or_dev=add_or_dev)
end

    # Match a git repository URL. This includes uses of `@` and `:` but
    # requires that it has `.git` at the end.
let url = raw"((git|ssh|http(s)?)|(git@[\w\-\.]+))(:(//)?)([\w\.@\:/\-~]+)(\.git$)(/)?",

    # Match a `NAME=UUID` package specifier.
    name_uuid = raw"[^@\#\s:]+\s*=\s*[^@\#\s:]+",

    # Match a `#BRANCH` branch or tag specifier.
    branch = raw"\#\s*[^@\#\s]*",

    # Match an `@VERSION` version specifier.
    version = raw"@\s*[^@\#\s]*",

    # Match a `:SUBDIR` subdir specifier.
    subdir = raw":[^@\#\s]+",

    # Match any other way to specify a package. This includes package
    # names, local paths, and URLs that don't match the `url` part. In
    # order not to clash with the branch, version, and subdir
    # specifiers, these cannot include `@` or `#`, and `:` is only
    # allowed if followed by `/` or `\`. For URLs matching this part
    # of the regex, that means that `@` (e.g. user names) and `:`
    # (e.g. port) cannot be used but it doesn't have to end with
    # `.git`.
    other = raw"([^@\#\s:] | :(/|\\))+"

    # Combine all of the above.
    global const package_id_re = Regex(
        "$url | $name_uuid | $branch | $version | $subdir | $other", "x")
end

function package_lex(qwords::Vector{QString})::Vector{String}
    words = String[]
    for qword in qwords
        qword.isquoted ?
            push!(words, qword.raw) :
            append!(words, map(m->m.match, eachmatch(package_id_re, qword.raw)))
    end
    return words
end

function parse_package_args(args::Vector{PackageToken}; add_or_dev=false)::Vector{PackageSpec}
    # check for and apply PackageSpec modifier (e.g. `#foo` or `@v1.0.2`)
    function apply_modifier!(pkg::PackageSpec, args::Vector{PackageToken})
        (isempty(args) || args[1] isa PackageIdentifier) && return
        modifier = popfirst!(args)
        if modifier isa Subdir
            pkg.subdir = modifier.dir
            (isempty(args) || args[1] isa PackageIdentifier) && return
            modifier = popfirst!(args)
        end

        if modifier isa VersionToken
            pkg.version = modifier.version
        elseif modifier isa Rev
            pkg.rev = modifier.rev
        else
            pkgerror("Package name/uuid must precede subdir specifier `$args`.")
        end
    end

    pkgs = PackageSpec[]
    while !isempty(args)
        arg = popfirst!(args)
        if arg isa PackageIdentifier
            pkg = parse_package_identifier(arg; add_or_develop=add_or_dev)
            apply_modifier!(pkg, args)
            push!(pkgs, pkg)
        # Modifiers without a corresponding package identifier -- this is a user error
        else
            arg isa VersionToken ?
                pkgerror("Package name/uuid must precede version specifier `@$arg`.") :
            arg isa Rev ?
                pkgerror("Package name/uuid must precede revision specifier `#$(arg.rev)`.") :
                pkgerror("Package name/uuid must precede subdir specifier `[$arg]`.")
        end
    end
    return pkgs
end

let uuid = raw"(?i)[0-9a-z]{8}-[0-9a-z]{4}-[0-9a-z]{4}-[0-9a-z]{4}-[0-9a-z]{12}(?-i)",
    name = raw"(\w+)(?:\.jl)?"
    global const name_re = Regex("^$name\$")
    global const uuid_re = Regex("^$uuid\$")
    global const name_uuid_re = Regex("^$name\\s*=\\s*($uuid)\$")
end
# packages can be identified through: uuid, name, or name+uuid
# additionally valid for add/develop are: local path, url
function parse_package_identifier(pkg_id::PackageIdentifier; add_or_develop=false)::PackageSpec
    word = pkg_id.val
    if add_or_develop
        if isurl(word)
            return PackageSpec(; url=word)
        elseif any(occursin.(['\\','/'], word)) || word == "." || word == ".."
            if casesensitive_isdir(expanduser(word))
                return PackageSpec(; path=normpath(expanduser(word)))
            else
                pkgerror("`$word` appears to be a local path, but directory does not exist")
            end
        end
        if occursin(name_re, word) && casesensitive_isdir(expanduser(word))
            @info "Use `./$word` to add or develop the local directory at `$(Base.contractuser(abspath(word)))`."
        end
    end
    if occursin(uuid_re, word)
        return PackageSpec(;uuid=UUID(word))
    elseif occursin(name_re, word)
        m = match(name_re, word)
        return PackageSpec(String(something(m.captures[1])))
    elseif occursin(name_uuid_re, word)
        m = match(name_uuid_re, word)
        return PackageSpec(String(something(m.captures[1])), UUID(something(m.captures[2])))
    else
        pkgerror("Unable to parse `$word` as a package.")
    end
end

################
# RegistrySpec #
################
function parse_registry(raw_args::Vector{QString}, options; add=false)
    regs = RegistrySpec[]
    foreach(x -> push!(regs, parse_registry(x; add=add)), unwrap(raw_args))
    return regs
end

# Registries can be identified through: uuid, name, or name+uuid
# when updating/removing. When adding we can accept a local path or url.
function parse_registry(word::AbstractString; add=false)::RegistrySpec
    word = expanduser(word)
    registry = RegistrySpec()
    if add && isdir_nothrow(word) # TODO: Should be casesensitive_isdir
        if isdir(joinpath(word, ".git")) # add path as url and clone it from there
            registry.url = abspath(word)
        else # put the path
            registry.path = abspath(word)
        end
    elseif occursin(uuid_re, word)
        registry.uuid = UUID(word)
    elseif occursin(name_re, word)
        m = match(name_re, word)
        registry.name = String(something(m.captures[1]))
    elseif occursin(name_uuid_re, word)
        m = match(name_uuid_re, word)
        registry.name = String(something(m.captures[1]))
        registry.uuid = UUID(something(m.captures[2]))
    elseif add
        # Guess it is a url then
        registry.url = String(word)
    else
        pkgerror("`$word` cannot be parsed as a registry")
    end
    return registry
end

#
# # Other
#
function parse_activate(args::Vector{QString}, options)
    isempty(args) && return [] # nothing to do
    if length(args) == 1
        x = first(args)
        if x.isquoted
            return [x.raw]
        end
        x = x.raw
        if x == "-"
            options[:prev] = true
            return []
        elseif first(x) == '@'
            options[:shared] = true
            return [x[2:end]]
        else
            return [expanduser(x)]
        end
    end
    return args # this is currently invalid input for "activate"
end

#
# # Option Maps
#
function do_preserve(x::String)
    x == "installed"        && return Types.PRESERVE_ALL_INSTALLED
    x == "all"              && return Types.PRESERVE_ALL
    x == "direct"           && return Types.PRESERVE_DIRECT
    x == "semver"           && return Types.PRESERVE_SEMVER
    x == "none"             && return Types.PRESERVE_NONE
    x == "tiered_installed" && return Types.PRESERVE_TIERED_INSTALLED
    x == "tiered"           && return Types.PRESERVE_TIERED
    pkgerror("`$x` is not a valid argument for `--preserve`.")
end
�   /cache/build/builder-amdci4-2/julialang/julia-release-1-dot-10/usr/share/julia/stdlib/v1.10/Pkg/src/REPLMode/command_declarations.jlwV      const PSA = Pair{Symbol,Any}

compound_declarations = [
"package" => CommandDeclaration[
PSA[:name => "test",
    :api => API.test,
    :should_splat => false,
    :arg_count => 0 => Inf,
    :arg_parser => parse_package,
    :option_spec => [
        PSA[:name => "coverage", :api => :coverage => true],
    ],
    :completions => complete_installed_packages,
    :description => "run tests for packages",
    :help => md"""
    test [--coverage] pkg[=uuid] ...

Run the tests for package `pkg`. This is done by running the file `test/runtests.jl`
in the package directory. The option `--coverage` can be used to run the tests with
coverage enabled. The `startup.jl` file is disabled during testing unless
julia is started with `--startup-file=yes`.
""",
],
PSA[:name => "help",
    :short_name => "?",
    :api => identity, # dummy API function
    :arg_count => 0 => Inf,
    :arg_parser => ((x,y) -> x),
    :completions => complete_help,
    :description => "show this message",
    :help => md"""
    [?|help]

List available commands along with short descriptions.

    [?|help] cmd

If `cmd` is a partial command, display help for all subcommands.
If `cmd` is a full command, display help for `cmd`.
""",
],
PSA[:name => "instantiate",
    :api => API.instantiate,
    :option_spec => [
        PSA[:name => "project", :short_name => "p", :api => :manifest => false],
        PSA[:name => "manifest", :short_name => "m", :api => :manifest => true],
        PSA[:name => "verbose", :short_name => "v", :api => :verbose => true],
    ],
    :description => "downloads all the dependencies for the project",
    :help => md"""
    instantiate [-v|--verbose]
    instantiate [-v|--verbose] [-m|--manifest]
    instantiate [-v|--verbose] [-p|--project]

Download all the dependencies for the current project at the version given by the project's manifest.
If no manifest exists or the `--project` option is given, resolve and download the dependencies compatible with the project.

After packages have been installed the project will be precompiled. For more information see `pkg> ?precompile`.
""",
],
PSA[:name => "remove",
    :short_name => "rm",
    :api => API.rm,
    :should_splat => false,
    :arg_count => 0 => Inf,
    :arg_parser => parse_package,
    :option_spec => [
        PSA[:name => "project", :short_name => "p", :api => :mode => PKGMODE_PROJECT],
        PSA[:name => "manifest", :short_name => "m", :api => :mode => PKGMODE_MANIFEST],
        PSA[:name => "all", :api => :all_pkgs => true],
    ],
    :completions => complete_installed_packages,
    :description => "remove packages from project or manifest",
    :help => md"""
    [rm|remove] [-p|--project] pkg[=uuid] ...
    [rm|remove] [-p|--project] [--all]

Remove package `pkg` from the project file. Since the name `pkg` can only
refer to one package in a project this is unambiguous, but you can specify
a `uuid` anyway, and the command is ignored, with a warning, if package name
and UUID do not match. When a package is removed from the project file, it
may still remain in the manifest if it is required by some other package in
the project. Project mode operation is the default, so passing `-p` or
`--project` is optional unless it is preceded by the `-m` or `--manifest`
options at some earlier point. All packages can be removed by passing `--all`.

    [rm|remove] [-m|--manifest] pkg[=uuid] ...
    [rm|remove] [-m|--manifest] [--all]

Remove package `pkg` from the manifest file. If the name `pkg` refers to
multiple packages in the manifest, `uuid` disambiguates it. Removing a package
from the manifest forces the removal of all packages that depend on it, as well
as any no-longer-necessary manifest packages due to project package removals.
All packages can be removed by passing `--all`.
""",
],
PSA[:name => "add",
    :api => API.add,
    :should_splat => false,
    :arg_count => 1 => Inf,
    :arg_parser => ((x,y) -> parse_package(x,y; add_or_dev=true)),
    :option_spec => [
        PSA[:name => "preserve", :takes_arg => true, :api => :preserve => do_preserve],
    ],
    :completions => complete_add_dev,
    :description => "add packages to project",
    :help => md"""
    add [--preserve=<opt>] pkg[=uuid] [@version] [#rev] ...

Add package `pkg` to the current project file. If `pkg` could refer to
multiple different packages, specifying `uuid` allows you to disambiguate.
`@version` optionally allows specifying which versions of packages to add. Version specifications
are of the form `@1`, `@1.2` or `@1.2.3`, allowing any version with a prefix
that matches, or ranges thereof, such as `@1.2-3.4.5`. A git revision can be
specified by `#branch` or `#commit`.

If a local path is used as an argument to `add`, the path needs to be a git repository.
The project will then track that git repository just like it would track a remote repository online.
If the package is not located at the top of the git repository, a subdirectory can be specified with
`path:subdir/path`.

`Pkg` resolves the set of packages in your environment using a tiered approach.
The `--preserve` command line option allows you to key into a specific tier in the resolve algorithm.
The following table describes the command line arguments to `--preserve` (in order of strictness).

| Argument           | Description                                                                        |
|:-------------------|:-----------------------------------------------------------------------------------|
| `installed`        | Like `all` except also only add versions that are already installed                |
| `all`              | Preserve the state of all existing dependencies (including recursive dependencies) |
| `direct`           | Preserve the state of all existing direct dependencies                             |
| `semver`           | Preserve semver-compatible versions of direct dependencies                         |
| `none`             | Do not attempt to preserve any version information                                 |
| `tiered_installed` | Like `tiered` except first try to add only installed versions                      |
| **`tiered`**       | Use the tier that will preserve the most version information while                 |
|                    | allowing version resolution to succeed (this is the default)                       |

Note: To make the default strategy `tiered_installed` set the env var `JULIA_PKG_PRESERVE_TIERED_INSTALLED` to
true.

After the installation of new packages the project will be precompiled. For more information see `pkg> ?precompile`.

With the `installed` strategy the newly added packages will likely already be precompiled, but if not this may be
because either the combination of package versions resolved in this environment has not been resolved and
precompiled before, or the precompile cache has been deleted by the LRU cache storage
(see `JULIA_MAX_NUM_PRECOMPILE_FILES`).

**Examples**
```
pkg> add Example
pkg> add --preserve=all Example
pkg> add Example@0.5
pkg> add Example#master
pkg> add Example#c37b675
pkg> add https://github.com/JuliaLang/Example.jl#master
pkg> add git@github.com:JuliaLang/Example.jl.git
pkg> add "git@github.com:JuliaLang/Example.jl.git"#master
pkg> add https://github.com/Company/MonoRepo:juliapkgs/Package.jl
pkg> add Example=7876af07-990d-54b4-ab0e-23690620f79a
```
""",
],
PSA[:name => "develop",
    :short_name => "dev",
    :api => API.develop,
    :should_splat => false,
    :arg_count => 1 => Inf,
    :arg_parser => ((x,y) -> parse_package(x,y; add_or_dev=true)),
    :option_spec => [
        PSA[:name => "strict", :api => :strict => true],
        PSA[:name => "local", :api => :shared => false],
        PSA[:name => "shared", :api => :shared => true],
        PSA[:name => "preserve", :takes_arg => true, :api => :preserve => do_preserve],
    ],
    :completions => complete_add_dev,
    :description => "clone the full package repo locally for development",
    :help => md"""
    [dev|develop] [--preserve=<opt>] [--shared|--local] pkg[=uuid] ...
    [dev|develop] [--preserve=<opt>] path

Make a package available for development. If `pkg` is an existing local path, that path will be recorded in
the manifest and used. Otherwise, a full git clone of `pkg` is made. The location of the clone is
controlled by the `--shared` (default) and `--local` arguments. The `--shared` location defaults to
`~/.julia/dev`, but can be controlled with the `JULIA_PKG_DEVDIR` environment variable.

When `--local` is given, the clone is placed in a `dev` folder in the current project. This
is not supported for paths, only registered packages.

This operation is undone by `free`.

The preserve strategies offered by `add` are also available via the `preserve` argument.
See `add` for more information.

**Examples**
```jl
pkg> develop Example
pkg> develop https://github.com/JuliaLang/Example.jl
pkg> develop ~/mypackages/Example
pkg> develop --local Example
```
""",
],
PSA[:name => "free",
    :api => API.free,
    :should_splat => false,
    :arg_count => 0 => Inf,
    :option_spec => [
        PSA[:name => "all", :api => :all_pkgs => true],
    ],
    :arg_parser => parse_package,
    :completions => complete_installed_packages,
    :description => "undoes a `pin`, `develop`, or stops tracking a repo",
    :help => md"""
    free pkg[=uuid] ...
    free [--all]

Free pinned packages, which allows it to be upgraded or downgraded again. If the package is checked out (see `help develop`) then this command
makes the package no longer being checked out. Specifying `--all` will free all dependencies (direct and indirect).
""",
],
PSA[:name => "why",
    :api => API.why,
    :should_splat => false,
    :arg_count => 1 => 1,
    :arg_parser => parse_package,
    :completions => complete_all_installed_packages,
    :description => "shows why a package is in the manifest",
    :help => md"""
    why pkg[=uuid] ...

Show the reason why packages are in the manifest, printed as a path through the
dependency graph starting at the direct dependencies.

!!! compat "Julia 1.9"
    The `why` function is added in Julia 1.9
""",
],
PSA[:name => "pin",
    :api => API.pin,
    :should_splat => false,
    :arg_count => 0 => Inf,
    :option_spec => [
        PSA[:name => "all", :api => :all_pkgs => true],
    ],
    :arg_parser => parse_package,
    :completions => complete_installed_packages,
    :description => "pins the version of packages",
    :help => md"""
    pin pkg[=uuid] ...
    pin [--all]

Pin packages to given versions, or the current version if no version is specified. A pinned package has its version fixed and will not be upgraded or downgraded.
A pinned package has the symbol `⚲` next to its version in the status list.. Specifying `--all` will pin all dependencies (direct and indirect).

**Examples**
```
pkg> pin Example
pkg> pin Example@0.5.0
pkg> pin Example=7876af07-990d-54b4-ab0e-23690620f79a@0.5.0
pkg> pin --all
```
""",
],
PSA[:name => "build",
    :api => API.build,
    :should_splat => false,
    :arg_count => 0 => Inf,
    :arg_parser => parse_package,
    :option_spec => [
        PSA[:name => "verbose", :short_name => "v", :api => :verbose => true],
    ],
    :completions => complete_installed_packages,
    :description => "run the build script for packages",
    :help => md"""
    build [-v|--verbose] pkg[=uuid] ...

Run the build script in `deps/build.jl` for `pkg` and all of its dependencies in depth-first recursive order.
If no packages are given, run the build scripts for all packages in the manifest.
The `-v`/`--verbose` option redirects build output to `stdout`/`stderr` instead of the `build.log` file.
The `startup.jl` file is disabled during building unless julia is started with `--startup-file=yes`.
""",
],
PSA[:name => "resolve",
    :api => API.resolve,
    :description => "resolves to update the manifest from changes in dependencies of developed packages",
    :help => md"""
    resolve

Resolve the project i.e. run package resolution and update the Manifest. This is useful in case the dependencies of developed
packages have changed causing the current Manifest to be out of sync.
""",
],
PSA[:name => "activate",
    :api => API.activate,
    :arg_count => 0 => 1,
    :arg_parser => parse_activate,
    :option_spec => [
        PSA[:name => "shared", :api => :shared => true],
        PSA[:name => "temp", :api => :temp => true],
    ],
    :completions => complete_activate,
    :description => "set the primary environment the package manager manipulates",
    :help => md"""
    activate
    activate [--shared] path
    activate --temp

Activate the environment at the given `path`, or use the first project found in `LOAD_PATH` if no `path` is specified.
The active environment is the environment that is modified by executing package commands.
When the option `--shared` is given, `path` will be assumed to be a directory name and searched for in the
`environments` folders of the depots in the depot stack. In case no such environment exists in any of the depots,
it will be placed in the first depot of the stack.
Use the `--temp` option to create temporary environments which are removed when the julia
process is exited.
""" ,
],
PSA[:name => "update",
    :short_name => "up",
    :api => API.up,
    :should_splat => false,
    :arg_count => 0 => Inf,
    :arg_parser => parse_package,
    :option_spec => [
        PSA[:name => "project",  :short_name => "p", :api => :mode => PKGMODE_PROJECT],
        PSA[:name => "manifest", :short_name => "m", :api => :mode => PKGMODE_MANIFEST],
        PSA[:name => "major", :api => :level => UPLEVEL_MAJOR],
        PSA[:name => "minor", :api => :level => UPLEVEL_MINOR],
        PSA[:name => "patch", :api => :level => UPLEVEL_PATCH],
        PSA[:name => "fixed", :api => :level => UPLEVEL_FIXED],
        PSA[:name => "preserve", :takes_arg => true, :api => :preserve => do_preserve],
    ],
    :completions => complete_installed_packages,
    :description => "update packages in manifest",
    :help => md"""
    [up|update] [-p|--project]  [opts] pkg[=uuid] [@version] ...
    [up|update] [-m|--manifest] [opts] pkg[=uuid] [@version] ...

    opts: --major | --minor | --patch | --fixed
          --preserve=<all/direct/none>

Update `pkg` within the constraints of the indicated version
specifications. These specifications are of the form `@1`, `@1.2` or `@1.2.3`, allowing
any version with a prefix that matches, or ranges thereof, such as `@1.2-3.4.5`.
In `--project` mode, package specifications only match project packages, while
in `--manifest` mode they match any manifest package. Bound level options force
the following packages to be upgraded only within the current major, minor,
patch version; if the `--fixed` upgrade level is given, then the following
packages will not be upgraded at all.

After any package updates the project will be precompiled. For more information see `pkg> ?precompile`.
""",
],
PSA[:name => "generate",
    :api => API.generate,
    :arg_count => 1 => 1,
    :arg_parser => ((x,y) -> map(expanduser, unwrap(x))),
    :description => "generate files for a new project",
    :help => md"""
    generate pkgname

Create a minimal project called `pkgname` in the current folder. For more featureful package creation, please see `PkgTemplates.jl`.
""",
],
PSA[:name => "precompile",
    :api => API.precompile,
    :arg_count => 0 => Inf,
    :completions => complete_installed_packages,
    :description => "precompile all the project dependencies",
    :help => md"""
    precompile
    precompile pkgs...

Precompile all or specified dependencies of the project in parallel.
The `startup.jl` file is disabled during precompilation unless julia is started with `--startup-file=yes`.

Errors will only throw when precompiling the top-level dependencies, given that
not all manifest dependencies may be loaded by the top-level dependencies on the given system.

This method is called automatically after any Pkg action that changes the manifest.
Any packages that have previously errored during precompilation won't be retried in auto mode
until they have changed. To disable automatic precompilation set the environment variable `JULIA_PKG_PRECOMPILE_AUTO=0`.
To manually control the number of tasks used set the environment variable `JULIA_NUM_PRECOMPILE_TASKS`.
""",
],
PSA[:name => "status",
    :short_name => "st",
    :api => API.status,
    :should_splat => false,
    :arg_count => 0 => Inf,
    :arg_parser => parse_package,
    :option_spec => [
        PSA[:name => "project",  :short_name => "p", :api => :mode => PKGMODE_PROJECT],
        PSA[:name => "manifest", :short_name => "m", :api => :mode => PKGMODE_MANIFEST],
        PSA[:name => "diff", :short_name => "d", :api => :diff => true],
        PSA[:name => "outdated", :short_name => "o", :api => :outdated => true],
        PSA[:name => "compat", :short_name => "c", :api => :compat => true],
        PSA[:name => "extensions", :short_name => "e", :api => :extensions => true],
    ],
    :completions => complete_installed_packages,
    :description => "summarize contents of and changes to environment",
    :help => md"""
    [st|status] [-d|--diff] [-o|--outdated] [pkgs...]
    [st|status] [-d|--diff] [-o|--outdated] [-p|--project] [pkgs...]
    [st|status] [-d|--diff] [-o|--outdated] [-m|--manifest] [pkgs...]
    [st|status] [-d|--diff] [-e|--extensions] [-p|--project] [pkgs...]
    [st|status] [-d|--diff] [-e|--extensions] [-m|--manifest] [pkgs...]
    [st|status] [-c|--compat] [pkgs...]

Show the status of the current environment. Packages marked with `⌃` have new
versions that may be installed, e.g. via `pkg> up`. Those marked with `⌅` have
new versions available, but cannot be installed due to compatibility
constraints. To see why use `pkg> status --outdated` which shows any packages
that are not at their latest version and if any packages are holding them back.

Use `pkg> status --extensions` to show dependencies with extensions and what extension dependencies
of those that are currently loaded.

In `--project` mode (default), the status of the project file is summarized. In `--manifest`
mode the output also includes the recursive dependencies of added packages given in the manifest.
If there are any packages listed as arguments the output will be limited to those packages.
The `--diff` option will, if the environment is in a git repository, limit
the output to the difference as compared to the last git commit.
The `--compat` option alone shows project compat entries.

!!! compat "Julia 1.8"
    The `⌃` and `⌅` indicators were added in Julia 1.8
    The `--outdated` and `--compat` options require at least Julia 1.8.
""",
],
PSA[:name => "compat",
    :api => API.compat,
    :arg_count => 0 => 2,
    :completions => complete_installed_packages_and_compat,
    :description => "edit compat entries in the current Project and re-resolve",
    :help => md"""
    compat [pkg] [compat_string]

Edit project [compat] entries directly, or via an interactive menu by not specifying any arguments.
When directly editing use tab to complete the package name and any existing compat entry.
Specifying a package with a blank compat entry will remove the entry.
After changing compat entries a `resolve` will be attempted to check whether the current
environment is compliant with the new compat rules.
""",
],
PSA[:name => "gc",
    :api => API.gc,
    :option_spec => [
        PSA[:name => "all", :api => :collect_delay => Hour(0)],
        PSA[:name => "verbose", :short_name => "v", :api => :verbose => true],
    ],
    :description => "garbage collect packages not used for a significant time",
    :help => md"""
    gc [-v|--verbose] [--all]

Free disk space by garbage collecting packages not used for a significant time.
The `--all` option will garbage collect all packages which can not be immediately
reached from any existing project.
Use verbose mode for detailed output.
""",
],
PSA[:name => "undo",
    :api => API.undo,
    :description => "undo the latest change to the active project",
    :help => md"""
    undo

Undoes the latest change to the active project.
""",
],
PSA[:name => "redo",
    :api => API.redo,
    :description => "redo the latest change to the active project",
    :help => md"""
    redo

Redoes the changes from the latest [`undo`](@ref).
""",
],
], #package
"registry" => CommandDeclaration[
PSA[:name => "add",
    :api => Registry.add,
    :should_splat => false,
    :arg_count => 0 => Inf,
    :arg_parser => ((x,y) -> parse_registry(x,y; add = true)),
    :description => "add package registries",
    :help => md"""
    registry add reg...

Add package registries `reg...` to the user depot. Without arguments
it adds known registries, i.e. the General registry and registries
served by the configured package server.

**Examples**
```
pkg> registry add General
pkg> registry add https://www.my-custom-registry.com
pkg> registry add
```
""",
],
PSA[:name => "remove",
    :short_name => "rm",
    :api => Registry.rm,
    :should_splat => false,
    :arg_count => 1 => Inf,
    :arg_parser => parse_registry,
    :description => "remove package registries",
    :help => md"""
    registry [rm|remove] reg...

Remove package registries `reg...`.

**Examples**
```
pkg> registry [rm|remove] General
```
""",
],
PSA[:name => "update",
    :short_name => "up",
    :api => Registry.update,
    :should_splat => false,
    :arg_count => 0 => Inf,
    :arg_parser => parse_registry,
    :description => "update package registries",
    :help => md"""
    registry [up|update]
    registry [up|update] reg...

Update package registries `reg...`. If no registries are specified
all registries will be updated.

**Examples**
```
pkg> registry up
pkg> registry up General
```
""",
],
PSA[:name => "status",
    :short_name => "st",
    :api => Registry.status,
    :description => "information about installed registries",
    :help => md"""
    registry [st|status]

Display information about installed registries.

**Examples**
```
pkg> registry status
```
""",
]
], #registry
] #command_declarations
    